{ "schema_version": 3, "updated": "2026-09-01", "count": 1037, "topics": [ { "no": 1, "source_index": 159, "id": "topic-159-nash-equilibria-in-extended-rock-paper-scissors-games", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Nash-Gleichgewichte im Stein-Schere-Papier mit Erweiterungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Nash-Gleichgewichte im Stein-Schere-Papier mit Erweiterungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "Nash equilibria in extended rock-paper-scissors games", "methods": [ "Functions & modelling" ], "description": "Turn “Nash equilibria in extended rock-paper-scissors games” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 2, "source_index": 374, "id": "topic-374-modelling-delay-propagation-along-a-bus-route", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 6, 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Modellierung der Verspätungsfortpflanzung entlang einer Buslinie", "methods": [ "Funktionen & Modellierung", "Graphentheorie" ], "description": "Formuliere zu „Modellierung der Verspätungsfortpflanzung entlang einer Buslinie“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Modelling delay propagation along a bus route", "methods": [ "Functions & modelling", "Graph theory" ], "description": "Turn “Modelling delay propagation along a bus route” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "graph_theory" ] }, { "no": 3, "source_index": 167, "id": "topic-167-modelling-blood-glucose-levels-after-meals-with-the-bergman-minimal-mo", "category_key": "biomathematics-medicine", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13, 19 ], "safety_code": 3, "source_course_label": "AA HL / AI HL", "de": { "category": "Biomathematik & Medizin", "title": "Modellierung des Blutzuckerspiegels nach Mahlzeiten (Bergman-Minimalmodell)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung" ], "description": "Formuliere zu „Modellierung des Blutzuckerspiegels nach Mahlzeiten (Bergman-Minimalmodell)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Modelling blood-glucose levels after meals with the Bergman minimal model", "methods": [ "Functions & modelling", "Differential calculus" ], "description": "Turn “Modelling blood-glucose levels after meals with the Bergman minimal model” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus" ] }, { "no": 4, "source_index": 386, "id": "topic-386-route-optimisation-for-school-deliveries-with-capacity-constraints", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 6, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Routenoptimierung für schulische Lieferungen mit Kapazitätsgrenzen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Routenoptimierung für schulische Lieferungen mit Kapazitätsgrenzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Route optimisation for school deliveries with capacity constraints", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Geometry", "Optimisation" ], "description": "Turn “Route optimisation for school deliveries with capacity constraints” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "geometry", "optimization" ] }, { "no": 5, "source_index": 177, "id": "topic-177-calculating-a-family-s-ecological-footprint-using-geometric-means", "category_key": "environmental-mathematics-sustainability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Berechnung des ökologischen Fußabdrucks einer Familie über geometrische Mittel", "methods": [ "Stochastik", "Geometrie" ], "description": "Entwickle aus „Berechnung des ökologischen Fußabdrucks einer Familie über geometrische Mittel“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Calculating a family's ecological footprint using geometric means", "methods": [ "Statistics & probability", "Geometry" ], "description": "Turn “Calculating a family's ecological footprint using geometric means” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry" ] }, { "no": 6, "source_index": 398, "id": "topic-398-centrality-measures-in-an-anonymised-school-collaboration-network", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 7, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Zentralitätsmaße in einem anonymisierten schulischen Kooperationsnetzwerk", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Zentralitätsmaße in einem anonymisierten schulischen Kooperationsnetzwerk“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Centrality measures in an anonymised school collaboration network", "methods": [ "Graph theory" ], "description": "Turn “Centrality measures in an anonymised school collaboration network” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 7, "source_index": 187, "id": "topic-187-calculating-the-optimal-approach-speed-in-long-jump", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Berechnung der optimalen Anlaufgeschwindigkeit beim Weitsprung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Anlaufgeschwindigkeit beim Weitsprung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Calculating the optimal approach speed in long jump", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating the optimal approach speed in long jump” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 8, "source_index": 410, "id": "topic-410-shannon-entropy-across-different-written-languages", "category_key": "information-coding-theory", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 8, 9, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Shannon-Entropie verschiedener geschriebener Sprachen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Shannon-Entropie verschiedener geschriebener Sprachen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Shannon entropy across different written languages", "methods": [ "Geometry" ], "description": "Turn “Shannon entropy across different written languages” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 9, "source_index": 197, "id": "topic-197-benford-s-law-in-financial-data-and-election-results", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 9 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Untersuchung von Benfords Gesetz in Finanzdaten und Wahlergebnissen", "methods": [ "Simulation & Algorithmen" ], "description": "Formuliere zu „Untersuchung von Benfords Gesetz in Finanzdaten und Wahlergebnissen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Benford's law in financial data and election results", "methods": [ "Simulation & algorithms" ], "description": "Turn “Benford's law in financial data and election results” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "simulation" ] }, { "no": 10, "source_index": 422, "id": "topic-422-optimising-pid-control-for-a-line-following-robot", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 11, 12 ], "measurement_codes": [ 5, 7, 13, 20 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "PID-Regelung eines Linienfolger-Roboters optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Folgen & Reihen", "Optimierung" ], "description": "Formuliere zu „PID-Regelung eines Linienfolger-Roboters optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Optimising PID control for a line-following robot", "methods": [ "Functions & modelling", "Differential calculus", "Sequences & series", "Optimisation" ], "description": "Turn “Optimising PID control for a line-following robot” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "sequences_series", "optimization" ] }, { "no": 11, "source_index": 207, "id": "topic-207-the-logistic-map-and-the-transition-to-chaos", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Untersuchung der logistischen Abbildung und des Übergangs zum Chaos", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der logistischen Abbildung und des Übergangs zum Chaos“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "The logistic map and the transition to chaos", "methods": [ "Functions & modelling" ], "description": "Turn “The logistic map and the transition to chaos” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 12, "source_index": 434, "id": "topic-434-choosing-thresholds-for-edge-detection-on-personal-photographs", "category_key": "image-processing-computer-graphics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Schwellwertwahl bei der Kantenerkennung auf eigenen Fotos", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Schwellwertwahl bei der Kantenerkennung auf eigenen Fotos“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Choosing thresholds for edge detection on personal photographs", "methods": [ "Graph theory" ], "description": "Turn “Choosing thresholds for edge detection on personal photographs” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 13, "source_index": 214, "id": "topic-214-calculating-optimal-room-acoustics-for-a-music-studio", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 9, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Berechnung der optimalen Raumakustik für ein Musikstudio", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Raumakustik für ein Musikstudio“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Calculating optimal room acoustics for a music studio", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ], "description": "Turn “Calculating optimal room acoustics for a music studio” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ] }, { "no": 14, "source_index": 444, "id": "topic-444-heaps-law-and-vocabulary-growth-in-long-texts", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 8, 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Heapsches Gesetz und das Wachstum des Wortschatzes in langen Texten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Heapsches Gesetz und das Wachstum des Wortschatzes in langen Texten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Heaps’ law and vocabulary growth in long texts", "methods": [ "Functions & modelling" ], "description": "Turn “Heaps’ law and vocabulary growth in long texts” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 15, "source_index": 223, "id": "topic-223-proportions-in-the-human-face-and-claims-about-the-golden-ratio", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 1, 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Untersuchung der Proportionen im menschlichen Gesicht (Goldener Schnitt)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Proportionen im menschlichen Gesicht (Goldener Schnitt)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Proportions in the human face and claims about the golden ratio", "methods": [ "Geometry" ], "description": "Turn “Proportions in the human face and claims about the golden ratio” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 16, "source_index": 454, "id": "topic-454-estimating-forgetting-curves-from-personal-flashcard-logs", "category_key": "education-learning-analytics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Vergessenskurven aus eigenen Karteikartenprotokollen schätzen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Vergessenskurven aus eigenen Karteikartenprotokollen schätzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "Estimating forgetting curves from personal flashcard logs", "methods": [ "Functions & modelling" ], "description": "Turn “Estimating forgetting curves from personal flashcard logs” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 17, "source_index": 232, "id": "topic-232-calculating-satellite-orbits-with-kepler-s-laws", "category_key": "astronomy-spaceflight", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13, 17 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Berechnung der Umlaufbahnen von Satelliten (Keplersche Gesetze)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Berechnung der Umlaufbahnen von Satelliten (Keplersche Gesetze)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Calculating satellite orbits with Kepler's laws", "methods": [ "Functions & modelling" ], "description": "Turn “Calculating satellite orbits with Kepler's laws” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 18, "source_index": 464, "id": "topic-464-estimating-price-elasticity-from-public-retail-data", "category_key": "economic-models-markets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Preiselastizität aus öffentlichen Einzelhandelsdaten schätzen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Preiselastizität aus öffentlichen Einzelhandelsdaten schätzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Estimating price elasticity from public retail data", "methods": [ "Functions & modelling" ], "description": "Turn “Estimating price elasticity from public retail data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 19, "source_index": 240, "id": "topic-240-reaction-time-distributions-within-a-class", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 6, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Untersuchung der Reaktionszeit und ihrer Verteilung in der Klasse", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Reaktionszeit und ihrer Verteilung in der Klasse“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Psychology & cognition", "title": "Reaction-time distributions within a class", "methods": [ "Statistics & probability" ], "description": "Turn “Reaction-time distributions within a class” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 20, "source_index": 474, "id": "topic-474-comparing-exponential-smoothing-and-autoregressive-models-for-electricity-dema", "category_key": "time-series-forecasting", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Exponentielle Glättung und autoregressive Modelle für Stromnachfrage vergleichen", "methods": [ "Funktionen & Modellierung", "Folgen & Reihen", "Zeitreihenanalyse", "Algebra" ], "description": "Entwickle aus „Exponentielle Glättung und autoregressive Modelle für Stromnachfrage vergleichen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Comparing exponential smoothing and autoregressive models for electricity demand", "methods": [ "Functions & modelling", "Sequences & series", "Time-series analysis", "Algebra" ], "description": "Turn “Comparing exponential smoothing and autoregressive models for electricity demand” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "sequences_series", "time_series", "algebra" ] }, { "no": 21, "source_index": 248, "id": "topic-248-calculating-expected-loss-for-different-insurance-types", "category_key": "probability-risk", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 5 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Berechnung des erwarteten Schadens bei verschiedenen Versicherungstypen", "methods": [ "Stochastik", "Finanzmathematik" ], "description": "Entwickle aus „Berechnung des erwarteten Schadens bei verschiedenen Versicherungstypen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Calculating expected loss for different insurance types", "methods": [ "Statistics & probability", "Financial mathematics" ], "description": "Turn “Calculating expected loss for different insurance types” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "financial_math" ] }, { "no": 22, "source_index": 484, "id": "topic-484-distortion-in-different-map-projections-as-a-function-of-latitude", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Verzerrungen verschiedener Kartenprojektionen in Abhängigkeit vom Breitengrad", "methods": [ "Algebra" ], "description": "Formuliere zu „Verzerrungen verschiedener Kartenprojektionen in Abhängigkeit vom Breitengrad“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Distortion in different map projections as a function of latitude", "methods": [ "Algebra" ], "description": "Turn “Distortion in different map projections as a function of latitude” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 23, "source_index": 256, "id": "topic-256-calculating-the-best-value-pizza-size-by-area-and-price", "category_key": "culinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 9 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Berechnung der optimalen Pizzagröße (Fläche vs. Preis)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Pizzagröße (Fläche vs. Preis)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "Calculating the best-value pizza size by area and price", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Calculating the best-value pizza size by area and price” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 24, "source_index": 494, "id": "topic-494-minimising-truss-weight-under-load-constraints", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 11 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Gewicht eines Fachwerks unter Lastgrenzen minimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Gewicht eines Fachwerks unter Lastgrenzen minimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Minimising truss weight under load constraints", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Minimising truss weight under load constraints” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 25, "source_index": 264, "id": "topic-264-newton-s-law-of-cooling-for-coffee-in-ceramic-glass-metal-and-paper-cu", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Newtonsches Abkühlgesetz: Kaffee in verschiedenen Behältern (Keramik, Glas, Metall, Pappbecher)", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ], "description": "Formuliere zu „Newtonsches Abkühlgesetz: Kaffee in verschiedenen Behältern (Keramik, Glas, Metall, Pappbecher)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Newton's law of cooling for coffee in ceramic, glass, metal and paper cups", "methods": [ "Functions & modelling", "Differential equations" ], "description": "Turn “Newton's law of cooling for coffee in ceramic, glass, metal and paper cups” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations" ] }, { "no": 26, "source_index": 504, "id": "topic-504-an-age-structured-vaccination-model-with-different-contact-matrices", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Altersstrukturiertes Impfmodell mit verschiedenen Kontaktmatrizen", "methods": [ "Funktionen & Modellierung", "Matrizen" ], "description": "Formuliere zu „Altersstrukturiertes Impfmodell mit verschiedenen Kontaktmatrizen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "An age-structured vaccination model with different contact matrices", "methods": [ "Functions & modelling", "Matrices" ], "description": "Turn “An age-structured vaccination model with different contact matrices” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "matrices" ] }, { "no": 27, "source_index": 284, "id": "topic-284-evaporation-rates-of-water-ethanol-acetone-and-salt-water-under-contro", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 6, 16 ], "safety_code": 2, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Verdunstungsrate von Wasser, Ethanol, Aceton und Salzwasser unter gleichen Bedingungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Verdunstungsrate von Wasser, Ethanol, Aceton und Salzwasser unter gleichen Bedingungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Evaporation rates of water, ethanol, acetone and salt water under controlled conditions", "methods": [ "Functions & modelling" ], "description": "Turn “Evaporation rates of water, ethanol, acetone and salt water under controlled conditions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 28, "source_index": 514, "id": "topic-514-an-expected-goals-model-using-shot-location-and-angle", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 7, 9, 11 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Expected-Goals-Modell aus Schussposition und Winkel", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ], "description": "Formuliere zu „Expected-Goals-Modell aus Schussposition und Winkel“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "An expected-goals model using shot location and angle", "methods": [ "Functions & modelling", "Trigonometry" ], "description": "Turn “An expected-goals model using shot location and angle” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry" ] }, { "no": 29, "source_index": 304, "id": "topic-304-discharge-curves-of-aa-batteries-from-different-brands-under-a-constan", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Entladungskurve AA-Batterien verschiedener Marken unter konstanter Last (z. B. LED)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Entladungskurve AA-Batterien verschiedener Marken unter konstanter Last (z. B. LED)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Discharge curves of AA batteries from different brands under a constant load", "methods": [ "Functions & modelling" ], "description": "Turn “Discharge curves of AA batteries from different brands under a constant load” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 30, "source_index": 524, "id": "topic-524-monopoly-landing-probabilities-using-a-transition-matrix", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Landewahrscheinlichkeiten bei Monopoly mit einer Übergangsmatrix", "methods": [ "Stochastik", "Matrizen" ], "description": "Entwickle aus „Landewahrscheinlichkeiten bei Monopoly mit einer Übergangsmatrix“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Recreational games & mathematics", "title": "Monopoly landing probabilities using a transition matrix", "methods": [ "Statistics & probability", "Matrices" ], "description": "Turn “Monopoly landing probabilities using a transition matrix” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "matrices" ] }, { "no": 31, "source_index": 324, "id": "topic-324-density-of-water-and-ethanol-at-temperatures-from-10-c-to-60-c", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 1, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Dichte von Wasser und Ethanol bei verschiedenen Temperaturen (10°C – 60°C)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Dichte von Wasser und Ethanol bei verschiedenen Temperaturen (10°C – 60°C)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Density of water and ethanol at temperatures from 10°C to 60°C", "methods": [ "Functions & modelling" ], "description": "Turn “Density of water and ethanol at temperatures from 10°C to 60°C” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 32, "source_index": 534, "id": "topic-534-derangements-in-secret-santa-without-self-assignment", "category_key": "combinatorics-discrete-probability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Derangements beim Wichteln ohne Selbstzuordnung", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Derangements beim Wichteln ohne Selbstzuordnung“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Derangements in Secret Santa without self-assignment", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “Derangements in Secret Santa without self-assignment” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 33, "source_index": 344, "id": "topic-344-optimising-coffee-brewing-extraction-rate-versus-temperature-profile", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 2, 3, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Optimaler Kaffee: Extraktionsrate vs. Temperaturverlauf beim Brühen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimaler Kaffee: Extraktionsrate vs. Temperaturverlauf beim Brühen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Optimising coffee brewing: extraction rate versus temperature profile", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising coffee brewing: extraction rate versus temperature profile” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 34, "source_index": 544, "id": "topic-544-sea-level-trends-with-measurement-uncertainty-and-confidence-intervals", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Meeresspiegeltrend mit Messunsicherheit und Konfidenzintervallen", "methods": [ "Stochastik", "Zeitreihenanalyse" ], "description": "Entwickle aus „Meeresspiegeltrend mit Messunsicherheit und Konfidenzintervallen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "Sea-level trends with measurement uncertainty and confidence intervals", "methods": [ "Statistics & probability", "Time-series analysis" ], "description": "Turn “Sea-level trends with measurement uncertainty and confidence intervals” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "time_series" ] }, { "no": 35, "source_index": 354, "id": "topic-354-particulate-filter-residue-mass-across-different-locations", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Feinstaubfilter: Masse Rückstand auf selbstgebautem Filter vs. Umgebung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Feinstaubfilter: Masse Rückstand auf selbstgebautem Filter vs. Umgebung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Particulate-filter residue mass across different locations", "methods": [ "Functions & modelling" ], "description": "Turn “Particulate-filter residue mass across different locations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 36, "source_index": 364, "id": "topic-364-surface-heat-loss-from-the-human-head-with-and-without-a-hat-after-exe", "category_key": "physiology", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 12 ], "measurement_codes": [ 4, 3, 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Physiologie", "title": "Wärmeverlust des menschlichen Kopfes: IR-Temperatur mit und ohne Mütze nach Sport", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wärmeverlust des menschlichen Kopfes: IR-Temperatur mit und ohne Mütze nach Sport“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Physiology", "title": "Surface heat loss from the human head with and without a hat after exercise", "methods": [ "Geometry" ], "description": "Turn “Surface heat loss from the human head with and without a hat after exercise” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 37, "source_index": 369, "id": "topic-369-water-absorption-of-brick-wood-concrete-and-plaster-over-time", "category_key": "materials", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 6, 18 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Materialien", "title": "Wasseraufnahme verschiedener Baumaterialien (Ziegel, Holz, Beton, Gips) über Zeit", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Wasseraufnahme verschiedener Baumaterialien (Ziegel, Holz, Beton, Gips) über Zeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Materials", "title": "Water absorption of brick, wood, concrete and plaster over time", "methods": [ "Time-series analysis" ], "description": "Turn “Water absorption of brick, wood, concrete and plaster over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 38, "source_index": 1, "id": "topic-001-the-golden-ratio-in-architectural-proportions-across-different-culture", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 1, 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Der Goldene Schnitt in architektonischen Proportionen verschiedener Kulturen", "methods": [ "Zahlentheorie", "Geometrie", "Algebra" ], "description": "Formuliere zu „Der Goldene Schnitt in architektonischen Proportionen verschiedener Kulturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "The golden ratio in architectural proportions across different cultures", "methods": [ "Number theory", "Geometry", "Algebra" ], "description": "Turn “The golden ratio in architectural proportions across different cultures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "geometry", "algebra" ] }, { "no": 39, "source_index": 21, "id": "topic-021-optimising-container-dimensions-under-cost-and-surface-area-constraint", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 1, 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Optimierung von Behälterdimensionen unter Kosten-/Flächenbedingungen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Optimierung von Behälterdimensionen unter Kosten-/Flächenbedingungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Optimising container dimensions under cost and surface-area constraints", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Optimising container dimensions under cost and surface-area constraints” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 40, "source_index": 42, "id": "topic-042-chi-squared-tests-study-habits-screen-time-and-sleep", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Chi-Quadrat-Tests: Studiengewohnheiten, Bildschirmzeit, Schlaf", "methods": [ "Stochastik" ], "description": "Entwickle aus „Chi-Quadrat-Tests: Studiengewohnheiten, Bildschirmzeit, Schlaf“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Chi-squared tests: study habits, screen time and sleep", "methods": [ "Statistics & probability" ], "description": "Turn “Chi-squared tests: study habits, screen time and sleep” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 41, "source_index": 63, "id": "topic-063-an-sir-model-for-the-spread-of-disease", "category_key": "mathematical-modelling", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL / AI HL", "de": { "category": "Mathematische Modellierung", "title": "SIR-Modell für Krankheitsausbreitung", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ], "description": "Formuliere zu „SIR-Modell für Krankheitsausbreitung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "An SIR model for the spread of disease", "methods": [ "Functions & modelling", "Differential equations" ], "description": "Turn “An SIR model for the spread of disease” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations" ] }, { "no": 42, "source_index": 83, "id": "topic-083-tessellations-which-regular-polygons-tile-the-plane", "category_key": "geometry-topology", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Tessellationen: Welche regulären Polygone pflastern die Ebene?", "methods": [ "Geometrie" ], "description": "Formuliere zu „Tessellationen: Welche regulären Polygone pflastern die Ebene?“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Tessellations: which regular polygons tile the plane?", "methods": [ "Geometry" ], "description": "Turn “Tessellations: which regular polygons tile the plane?” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 43, "source_index": 102, "id": "topic-102-compound-interest-versus-simple-interest-over-different-periods", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Zinseszins vs. einfacher Zins über verschiedene Perioden", "methods": [ "Finanzmathematik" ], "description": "Formuliere zu „Zinseszins vs. einfacher Zins über verschiedene Perioden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Compound interest versus simple interest over different periods", "methods": [ "Financial mathematics" ], "description": "Turn “Compound interest versus simple interest over different periods” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "financial_math" ] }, { "no": 44, "source_index": 119, "id": "topic-119-mathematical-induction-for-sums-and-divisibility-identities", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Vollständige Induktion: Summen- und Teilbarkeitsidentitäten", "methods": [ "Beweisführung" ], "description": "Die Idee „Vollständige Induktion: Summen- und Teilbarkeitsidentitäten“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Mathematical induction for sums and divisibility identities", "methods": [ "Proof" ], "description": "Develop “Mathematical induction for sums and divisibility identities” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 45, "source_index": 134, "id": "topic-134-graph-colouring-problems", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Untersuchung von Graphenfärbungsproblemen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Graphenfärbungsproblemen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Graph-colouring problems", "methods": [ "Geometry" ], "description": "Turn “Graph-colouring problems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 46, "source_index": 144, "id": "topic-144-the-mathematics-of-recipes-ratios-and-scaling", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Mathematik der Kochrezepte: Verhältnisse und Skalierung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematik der Kochrezepte: Verhältnisse und Skalierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "The mathematics of recipes: ratios and scaling", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of recipes: ratios and scaling” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 47, "source_index": 160, "id": "topic-160-optimal-blackjack-hand-strategy-using-probability", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 8 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Optimale Blattstrategie im Blackjack durch Wahrscheinlichkeitsrechnung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ], "description": "Entwickle aus „Optimale Blattstrategie im Blackjack durch Wahrscheinlichkeitsrechnung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Game theory & decision-making", "title": "Optimal blackjack hand strategy using probability", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ], "description": "Turn “Optimal blackjack hand strategy using probability” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ] }, { "no": 48, "source_index": 375, "id": "topic-375-optimal-bike-sharing-station-locations-using-weighted-voronoi-diagrams", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Optimale Standorte für Fahrradverleihstationen mit gewichteten Voronoi-Diagrammen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Optimale Standorte für Fahrradverleihstationen mit gewichteten Voronoi-Diagrammen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Optimal bike-sharing station locations using weighted Voronoi diagrams", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Geometry", "Optimisation" ], "description": "Turn “Optimal bike-sharing station locations using weighted Voronoi diagrams” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "geometry", "optimization" ] }, { "no": 49, "source_index": 168, "id": "topic-168-modelling-medication-concentration-and-dosage-over-time-with-pharmacok", "category_key": "biomathematics-medicine", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 9, 11 ], "measurement_codes": [ 6, 13 ], "safety_code": 3, "source_course_label": "AA HL", "de": { "category": "Biomathematik & Medizin", "title": "Berechnung der optimalen Medikamentendosis über Zeit (Pharmakokinetik)", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Differentialrechnung", "Zeitreihenanalyse", "Optimierung" ], "description": "Entwickle aus „Berechnung der optimalen Medikamentendosis über Zeit (Pharmakokinetik)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Biomathematics & medicine", "title": "Modelling medication concentration and dosage over time with pharmacokinetics", "methods": [ "Functions & modelling", "Differential equations", "Differential calculus", "Time-series analysis", "Optimisation" ], "description": "Turn “Modelling medication concentration and dosage over time with pharmacokinetics” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_equations", "differential_calculus", "time_series", "optimization" ] }, { "no": 50, "source_index": 387, "id": "topic-387-reorder-points-and-safety-stock-under-variable-demand", "category_key": "operations-research-logistics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Bestellpunkt und Sicherheitsbestand bei schwankender Nachfrage", "methods": [ "Geometrie" ], "description": "Formuliere zu „Bestellpunkt und Sicherheitsbestand bei schwankender Nachfrage“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Reorder points and safety stock under variable demand", "methods": [ "Geometry" ], "description": "Turn “Reorder points and safety stock under variable demand” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 51, "source_index": 178, "id": "topic-178-optimising-waste-separation-with-probability-models", "category_key": "environmental-mathematics-sustainability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Optimierung der Mülltrennung durch Wahrscheinlichkeitsmodelle", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ], "description": "Entwickle aus „Optimierung der Mülltrennung durch Wahrscheinlichkeitsmodelle“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Optimising waste separation with probability models", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ], "description": "Turn “Optimising waste separation with probability models” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ] }, { "no": 52, "source_index": 399, "id": "topic-399-community-detection-in-a-network-of-music-artists", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 8, 9, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Community Detection in einem Netzwerk von Musikinterpreten", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Community Detection in einem Netzwerk von Musikinterpreten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Community detection in a network of music artists", "methods": [ "Graph theory" ], "description": "Turn “Community detection in a network of music artists” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 53, "source_index": 188, "id": "topic-188-mathematical-analysis-of-rotation-in-figure-skating-using-angular-mome", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 7, 15 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Mathematische Analyse der Drehung beim Eiskunstlauf (Drehimpuls)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematische Analyse der Drehung beim Eiskunstlauf (Drehimpuls)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Mathematical analysis of rotation in figure skating using angular momentum", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical analysis of rotation in figure skating using angular momentum” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 54, "source_index": 411, "id": "topic-411-arithmetic-coding-compared-with-huffman-coding", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Arithmetische Codierung im Vergleich zur Huffman-Codierung", "methods": [ "Geometrie" ], "description": "Formuliere zu „Arithmetische Codierung im Vergleich zur Huffman-Codierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Arithmetic coding compared with Huffman coding", "methods": [ "Geometry" ], "description": "Turn “Arithmetic coding compared with Huffman coding” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 55, "source_index": 198, "id": "topic-198-a-basic-fourier-based-classification-of-music-genres", "category_key": "data-science-introductory-algorithms", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 8 ], "measurement_codes": [ 9, 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Einfache Klassifikation von Musikgenres durch Fourier-Analyse (Grundlagen)", "methods": [ "Stochastik", "Fourier-Analyse", "Simulation & Algorithmen" ], "description": "Entwickle aus „Einfache Klassifikation von Musikgenres durch Fourier-Analyse (Grundlagen)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Data science & introductory algorithms", "title": "A basic Fourier-based classification of music genres", "methods": [ "Statistics & probability", "Fourier analysis", "Simulation & algorithms" ], "description": "Turn “A basic Fourier-based classification of music genres” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "fourier_analysis", "simulation" ] }, { "no": 56, "source_index": 423, "id": "topic-423-using-a-kalman-filter-to-smooth-a-noisy-distance-sensor", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 11, 12 ], "measurement_codes": [ 13, 20, 21 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Kalman-Filter zur Glättung eines verrauschten Abstandssensors", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Kalman-Filter zur Glättung eines verrauschten Abstandssensors“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Using a Kalman filter to smooth a noisy distance sensor", "methods": [ "Functions & modelling" ], "description": "Turn “Using a Kalman filter to smooth a noisy distance sensor” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 57, "source_index": 208, "id": "topic-208-modelling-the-double-pendulum-and-its-unpredictability", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Modellierung des Doppelpendels und seiner Unvorhersagbarkeit", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Regression", "Zahlentheorie" ], "description": "Entwickle aus „Modellierung des Doppelpendels und seiner Unvorhersagbarkeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Chaos & dynamical systems", "title": "Modelling the double pendulum and its unpredictability", "methods": [ "Functions & modelling", "Differential equations", "Regression", "Number theory" ], "description": "Turn “Modelling the double pendulum and its unpredictability” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_equations", "regression", "number_theory" ] }, { "no": 58, "source_index": 435, "id": "topic-435-perspective-correction-of-a-photograph-using-a-homography", "category_key": "image-processing-computer-graphics", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Perspektivkorrektur eines Fotos mit einer Homographie", "methods": [ "Geometrie" ], "description": "Formuliere zu „Perspektivkorrektur eines Fotos mit einer Homographie“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Perspective correction of a photograph using a homography", "methods": [ "Geometry" ], "description": "Turn “Perspective correction of a photograph using a homography” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 59, "source_index": 215, "id": "topic-215-overtone-series-in-different-musical-instruments", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Untersuchung der Obertonreihen verschiedener Musikinstrumente", "methods": [ "Trigonometrie", "Folgen & Reihen", "Fourier-Analyse" ], "description": "Formuliere zu „Untersuchung der Obertonreihen verschiedener Musikinstrumente“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Overtone series in different musical instruments", "methods": [ "Trigonometry", "Sequences & series", "Fourier analysis" ], "description": "Turn “Overtone series in different musical instruments” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "sequences_series", "fourier_analysis" ] }, { "no": 60, "source_index": 445, "id": "topic-445-modelling-letter-sequences-with-markov-chains", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Buchstabenfolgen mit Markov-Ketten modellieren", "methods": [ "Funktionen & Modellierung", "Stochastik", "Matrizen", "Folgen & Reihen" ], "description": "Entwickle aus „Buchstabenfolgen mit Markov-Ketten modellieren“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Language & text mathematics", "title": "Modelling letter sequences with Markov chains", "methods": [ "Functions & modelling", "Statistics & probability", "Matrices", "Sequences & series" ], "description": "Turn “Modelling letter sequences with Markov chains” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "matrices", "sequences_series" ] }, { "no": 61, "source_index": 224, "id": "topic-224-calculating-perspective-in-painting-using-one-point-perspective", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Berechnung von Perspektiven in der Malerei (Zentralperspektive)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung von Perspektiven in der Malerei (Zentralperspektive)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Calculating perspective in painting using one-point perspective", "methods": [ "Geometry" ], "description": "Turn “Calculating perspective in painting using one-point perspective” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 62, "source_index": 455, "id": "topic-455-simplified-item-response-theory-for-estimating-item-difficulty", "category_key": "education-learning-analytics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 4, 7, 10, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Vereinfachte Item-Response-Theorie zur Schätzung von Aufgaben­schwierigkeit", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Vereinfachte Item-Response-Theorie zur Schätzung von Aufgaben­schwierigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "Simplified item response theory for estimating item difficulty", "methods": [ "Functions & modelling" ], "description": "Turn “Simplified item response theory for estimating item difficulty” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 63, "source_index": 233, "id": "topic-233-modelling-tidal-forces-and-their-mathematical-periodicity", "category_key": "astronomy-spaceflight", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Modellierung der Gezeitenkräfte und ihrer mathematischen Periodizität", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Zeitreihenanalyse" ], "description": "Entwickle aus „Modellierung der Gezeitenkräfte und ihrer mathematischen Periodizität“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Astronomy & spaceflight", "title": "Modelling tidal forces and their mathematical periodicity", "methods": [ "Functions & modelling", "Trigonometry", "Time-series analysis" ], "description": "Turn “Modelling tidal forces and their mathematical periodicity” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "trigonometry", "time_series" ] }, { "no": 64, "source_index": 465, "id": "topic-465-lorenz-curves-and-decomposition-of-the-gini-coefficient", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Lorenzkurven und Zerlegung des Gini-Koeffizienten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Lorenzkurven und Zerlegung des Gini-Koeffizienten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Lorenz curves and decomposition of the Gini coefficient", "methods": [ "Functions & modelling" ], "description": "Turn “Lorenz curves and decomposition of the Gini coefficient” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 65, "source_index": 241, "id": "topic-241-modelling-the-ebbinghaus-forgetting-curve-with-exponential-decay", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Modellierung der Vergessenskurve nach Ebbinghaus durch exponentiellen Zerfall", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Modellierung der Vergessenskurve nach Ebbinghaus durch exponentiellen Zerfall“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Psychology & cognition", "title": "Modelling the Ebbinghaus forgetting curve with exponential decay", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling the Ebbinghaus forgetting curve with exponential decay” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 66, "source_index": 475, "id": "topic-475-seasonal-decomposition-of-bicycle-rental-data", "category_key": "time-series-forecasting", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Saisonale Zerlegung von Fahrradverleihdaten", "methods": [ "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Saisonale Zerlegung von Fahrradverleihdaten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Seasonal decomposition of bicycle-rental data", "methods": [ "Sequences & series", "Time-series analysis" ], "description": "Turn “Seasonal decomposition of bicycle-rental data” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "time_series" ] }, { "no": 67, "source_index": 249, "id": "topic-249-modelling-smoking-risk-with-life-expectancy-data", "category_key": "probability-risk", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 12 ], "measurement_codes": [ 0 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Untersuchung des Risikos von Raucherverhalten durch Lebenserwartungsmodelle", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Untersuchung des Risikos von Raucherverhalten durch Lebenserwartungsmodelle“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Modelling smoking risk with life-expectancy data", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “Modelling smoking risk with life-expectancy data” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 68, "source_index": 485, "id": "topic-485-comparing-great-circle-and-rhumb-line-routes-for-long-journeys", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 10 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Großkreisroute und Loxodrome bei langen Reisen vergleichen", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Großkreisroute und Loxodrome bei langen Reisen vergleichen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Comparing great-circle and rhumb-line routes for long journeys", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “Comparing great-circle and rhumb-line routes for long journeys” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 69, "source_index": 257, "id": "topic-257-modelling-coffee-brewing-through-extraction-rates-and-temperature", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 3, 13, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Modellierung des Kaffeekochens: Extraktionsraten und Temperaturen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung des Kaffeekochens: Extraktionsraten und Temperaturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "Modelling coffee brewing through extraction rates and temperature", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling coffee brewing through extraction rates and temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 70, "source_index": 495, "id": "topic-495-optimising-a-beam-cross-section-under-bending", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 10, 11 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Querschnitt eines Balkens unter Biegebeanspruchung optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Querschnitt eines Balkens unter Biegebeanspruchung optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Optimising a beam cross-section under bending", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising a beam cross-section under bending” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 71, "source_index": 265, "id": "topic-265-insulating-performance-of-cup-materials-time-taken-to-approach-room-te", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 3, 4, 1, 6 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Isolationswirkung von Bechermaterialien: Zeit bis zur Raumtemperatur", "methods": [ "Geometrie" ], "description": "Formuliere zu „Isolationswirkung von Bechermaterialien: Zeit bis zur Raumtemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Insulating performance of cup materials: time taken to approach room temperature", "methods": [ "Geometry" ], "description": "Turn “Insulating performance of cup materials: time taken to approach room temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 72, "source_index": 505, "id": "topic-505-estimating-the-effective-reproduction-number-from-a-public-case-series", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Effektive Reproduktionszahl aus einer öffentlichen Fallzeitreihe schätzen", "methods": [ "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Effektive Reproduktionszahl aus einer öffentlichen Fallzeitreihe schätzen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Epidemiology & public health", "title": "Estimating the effective reproduction number from a public case series", "methods": [ "Sequences & series", "Time-series analysis" ], "description": "Turn “Estimating the effective reproduction number from a public case series” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "time_series" ] }, { "no": 73, "source_index": 285, "id": "topic-285-determining-the-density-of-different-woods-from-mass-and-volume", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 1, 13, 14 ], "safety_code": 3, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Dichte-Bestimmung verschiedener Holzsorten durch Masse und Volumenmessung", "methods": [ "Geometrie" ], "description": "Formuliere zu „Dichte-Bestimmung verschiedener Holzsorten durch Masse und Volumenmessung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Determining the density of different woods from mass and volume", "methods": [ "Geometry" ], "description": "Turn “Determining the density of different woods from mass and volume” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 74, "source_index": 515, "id": "topic-515-entropy-of-serve-placement-in-tennis", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Entropie der Aufschlagplatzierung im Tennis", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Entropie der Aufschlagplatzierung im Tennis“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Entropy of serve placement in tennis", "methods": [ "Functions & modelling" ], "description": "Turn “Entropy of serve placement in tennis” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 75, "source_index": 305, "id": "topic-305-solar-cell-power-at-different-light-angles-and-distances", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 5, 1, 10, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Leistung einer Solarzelle bei verschiedenen Lichtwinkeln (0° – 90°) und Abständen", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Leistung einer Solarzelle bei verschiedenen Lichtwinkeln (0° – 90°) und Abständen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Solar-cell power at different light angles and distances", "methods": [ "Trigonometry" ], "description": "Turn “Solar-cell power at different light angles and distances” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 76, "source_index": 525, "id": "topic-525-optimal-nim-strategy-using-binary-representation", "category_key": "recreational-games-mathematics", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Optimale Nim-Strategie mit Binärdarstellung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimale Nim-Strategie mit Binärdarstellung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "Optimal Nim strategy using binary representation", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimal Nim strategy using binary representation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 77, "source_index": 325, "id": "topic-325-electrolysis-of-water-electrode-mass-change-versus-applied-voltage", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 5, 16, 21 ], "safety_code": 2, "source_course_label": "AA HL", "de": { "category": "Kombinierte Experimente", "title": "Elektrolyse von Wasser: Masseänderung an Elektroden vs. angelegte Spannung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Elektrolyse von Wasser: Masseänderung an Elektroden vs. angelegte Spannung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Electrolysis of water: electrode mass change versus applied voltage", "methods": [ "Functions & modelling" ], "description": "Turn “Electrolysis of water: electrode mass change versus applied voltage” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 78, "source_index": 535, "id": "topic-535-the-coupon-collector-problem-for-trading-cards", "category_key": "combinatorics-discrete-probability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 7, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Coupon-Collector-Problem bei Sammelkarten", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Coupon-Collector-Problem bei Sammelkarten“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "The coupon collector problem for trading cards", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “The coupon collector problem for trading cards” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 79, "source_index": 345, "id": "topic-345-which-teapot-material-retains-heat-longest-cast-iron-glass-or-porcelai", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 3, 4, 1, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Teekannen-Test: Welches Material (Gusseisen, Glas, Porzellan) hält Temperatur am längsten?", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Teekannen-Test: Welches Material (Gusseisen, Glas, Porzellan) hält Temperatur am längsten?“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Which teapot material retains heat longest: cast iron, glass or porcelain?", "methods": [ "Functions & modelling" ], "description": "Turn “Which teapot material retains heat longest: cast iron, glass or porcelain?” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 80, "source_index": 545, "id": "topic-545-decomposing-tides-with-harmonic-analysis", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Gezeiten mit harmonischer Analyse zerlegen", "methods": [ "Fourier-Analyse" ], "description": "Formuliere zu „Gezeiten mit harmonischer Analyse zerlegen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "Decomposing tides with harmonic analysis", "methods": [ "Fourier analysis" ], "description": "Turn “Decomposing tides with harmonic analysis” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "fourier_analysis" ] }, { "no": 81, "source_index": 355, "id": "topic-355-rainwater-precipitation-amount-temperature-and-electrical-conductivity", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 2, 3, 5, 1 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Regenwasser: Masse Niederschlag, Temperatur und elektrische Leitfähigkeit", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Regenwasser: Masse Niederschlag, Temperatur und elektrische Leitfähigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Rainwater: precipitation amount, temperature and electrical conductivity", "methods": [ "Functions & modelling" ], "description": "Turn “Rainwater: precipitation amount, temperature and electrical conductivity” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 82, "source_index": 365, "id": "topic-365-skin-surface-temperature-recovery-after-a-safe-cold-water-exposure", "category_key": "physiology", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 4, 1, 3, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Physiologie", "title": "Hauttemperatur verschiedener Körperregionen nach Kaltwasseranwendung (IR-Mapping)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Hauttemperatur verschiedener Körperregionen nach Kaltwasseranwendung (IR-Mapping)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Physiology", "title": "Skin-surface temperature recovery after a safe cold-water exposure", "methods": [ "Geometry" ], "description": "Turn “Skin-surface temperature recovery after a safe cold-water exposure” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 83, "source_index": 370, "id": "topic-370-heat-distribution-around-skateboard-or-longboard-axles-after-riding", "category_key": "materials", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 4, 3, 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Materialien", "title": "Wärmeverteilung auf einem Skateboard/Longboard nach Fahrt (Reibung an Achsen)", "methods": [ "Stochastik" ], "description": "Entwickle aus „Wärmeverteilung auf einem Skateboard/Longboard nach Fahrt (Reibung an Achsen)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Materials", "title": "Heat distribution around skateboard or longboard axles after riding", "methods": [ "Statistics & probability" ], "description": "Turn “Heat distribution around skateboard or longboard axles after riding” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 84, "source_index": 2, "id": "topic-002-modelling-population-growth-logistic-versus-exponential-models", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 13 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Modellierung von Populationswachstum: Logistisch vs. Exponentiell", "methods": [ "Funktionen & Modellierung", "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Modellierung von Populationswachstum: Logistisch vs. Exponentiell“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Modelling population growth: logistic versus exponential models", "methods": [ "Functions & modelling", "Number theory", "Algebra" ], "description": "Turn “Modelling population growth: logistic versus exponential models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "number_theory", "algebra" ] }, { "no": 85, "source_index": 22, "id": "topic-022-newton-s-law-of-cooling-modelling-with-differential-equations", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 3, 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Newtons Abkühlungsgesetz: Modellierung mit Differentialgleichungen", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Algebra" ], "description": "Formuliere zu „Newtons Abkühlungsgesetz: Modellierung mit Differentialgleichungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Newton's law of cooling: modelling with differential equations", "methods": [ "Functions & modelling", "Differential equations", "Algebra" ], "description": "Turn “Newton's law of cooling: modelling with differential equations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations", "algebra" ] }, { "no": 86, "source_index": 43, "id": "topic-043-the-birthday-paradox-simulation-versus-theoretical-probability", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 5 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Geburtstagsparadoxon: Simulation vs. theoretische Wahrscheinlichkeit", "methods": [ "Stochastik", "Simulation & Algorithmen" ], "description": "Entwickle aus „Geburtstagsparadoxon: Simulation vs. theoretische Wahrscheinlichkeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "The birthday paradox: simulation versus theoretical probability", "methods": [ "Statistics & probability", "Simulation & algorithms" ], "description": "Turn “The birthday paradox: simulation versus theoretical probability” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "simulation" ] }, { "no": 87, "source_index": 64, "id": "topic-064-predator-prey-dynamics-the-lotka-volterra-equations", "category_key": "mathematical-modelling", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Mathematische Modellierung", "title": "Räuber-Beute-Dynamik: Lotka-Volterra-Gleichungen", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Algebra" ], "description": "Formuliere zu „Räuber-Beute-Dynamik: Lotka-Volterra-Gleichungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Predator-prey dynamics: the Lotka-Volterra equations", "methods": [ "Functions & modelling", "Differential equations", "Algebra" ], "description": "Turn “Predator-prey dynamics: the Lotka-Volterra equations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations", "algebra" ] }, { "no": 88, "source_index": 84, "id": "topic-084-the-seven-bridges-of-k-nigsberg-and-graph-theory", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Geometrie & Topologie", "title": "Königsberger Brückenproblem und Graphentheorie", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Königsberger Brückenproblem und Graphentheorie“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "The Seven Bridges of Königsberg and graph theory", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “The Seven Bridges of Königsberg and graph theory” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 89, "source_index": 103, "id": "topic-103-mortgage-repayment-how-much-can-an-extra-payment-save", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 5 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Hypothekenrückzahlung: Wie viel spart eine Extrazahlung?", "methods": [ "Finanzmathematik" ], "description": "Formuliere zu „Hypothekenrückzahlung: Wie viel spart eine Extrazahlung?“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Mortgage repayment: how much can an extra payment save?", "methods": [ "Financial mathematics" ], "description": "Turn “Mortgage repayment: how much can an extra payment save?” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "financial_math" ] }, { "no": 90, "source_index": 120, "id": "topic-120-boolean-algebra-and-logic-gates-de-morgan-s-laws", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Boolesche Algebra und Logikgatter: De Morgansche Gesetze", "methods": [ "Beweisführung", "Algebra" ], "description": "Formuliere zu „Boolesche Algebra und Logikgatter: De Morgansche Gesetze“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "Boolean algebra and logic gates: De Morgan's laws", "methods": [ "Proof", "Algebra" ], "description": "Turn “Boolean algebra and logic gates: De Morgan's laws” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "proof", "algebra" ] }, { "no": 91, "source_index": 135, "id": "topic-135-analysing-sorting-algorithms-running-time-and-comparisons", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Analyse von Sortieralgorithmen (Laufzeit, Vergleiche)", "methods": [ "Geometrie", "Simulation & Algorithmen" ], "description": "Formuliere zu „Analyse von Sortieralgorithmen (Laufzeit, Vergleiche)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Analysing sorting algorithms: running time and comparisons", "methods": [ "Geometry", "Simulation & algorithms" ], "description": "Turn “Analysing sorting algorithms: running time and comparisons” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "simulation" ] }, { "no": 92, "source_index": 145, "id": "topic-145-optimising-how-to-pack-a-suitcase-or-backpack", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Optimierung des Packens eines Koffers/Rucksacks", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimierung des Packens eines Koffers/Rucksacks“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Optimising how to pack a suitcase or backpack", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising how to pack a suitcase or backpack” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 93, "source_index": 161, "id": "topic-161-the-mathematics-of-auction-systems-english-versus-dutch-auctions", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7, 8 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Die Mathematik von Auktionssystemen (englisch vs. holändisch)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Die Mathematik von Auktionssystemen (englisch vs. holändisch)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "The mathematics of auction systems: English versus Dutch auctions", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of auction systems: English versus Dutch auctions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 94, "source_index": 376, "id": "topic-376-shortest-route-versus-fastest-route-under-time-dependent-traffic", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Kürzeste Route versus schnellste Route bei zeitabhängigem Verkehr", "methods": [ "Graphentheorie", "Optimierung" ], "description": "Formuliere zu „Kürzeste Route versus schnellste Route bei zeitabhängigem Verkehr“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Shortest route versus fastest route under time-dependent traffic", "methods": [ "Graph theory", "Optimisation" ], "description": "Turn “Shortest route versus fastest route under time-dependent traffic” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "optimization" ] }, { "no": 95, "source_index": 169, "id": "topic-169-heart-rate-variability-analysed-with-statistical-methods", "category_key": "biomathematics-medicine", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 8, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Untersuchung der Herzratenvariabilität mit statistischen Methoden", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Herzratenvariabilität mit statistischen Methoden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Heart-rate variability analysed with statistical methods", "methods": [ "Functions & modelling" ], "description": "Turn “Heart-rate variability analysed with statistical methods” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 96, "source_index": 388, "id": "topic-388-staff-scheduling-with-integer-linear-optimisation", "category_key": "operations-research-logistics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Dienstplanung mit ganzzahliger linearer Optimierung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Dienstplanung mit ganzzahliger linearer Optimierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Staff scheduling with integer linear optimisation", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Staff scheduling with integer linear optimisation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 97, "source_index": 179, "id": "topic-179-modelling-seasonal-water-levels-in-local-lakes", "category_key": "environmental-mathematics-sustainability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Modellierung des Wasserspiegels in lokalen Seen über die Jahreszeiten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung des Wasserspiegels in lokalen Seen über die Jahreszeiten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Modelling seasonal water levels in local lakes", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling seasonal water levels in local lakes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 98, "source_index": 400, "id": "topic-400-epidemic-thresholds-in-networks-with-different-degree-distributions", "category_key": "networks-social-systems", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Epidemische Schwellenwerte in Netzwerken mit unterschiedlicher Gradverteilung", "methods": [ "Stochastik", "Graphentheorie", "Trigonometrie" ], "description": "Entwickle aus „Epidemische Schwellenwerte in Netzwerken mit unterschiedlicher Gradverteilung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Networks & social systems", "title": "Epidemic thresholds in networks with different degree distributions", "methods": [ "Statistics & probability", "Graph theory", "Trigonometry" ], "description": "Turn “Epidemic thresholds in networks with different degree distributions” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "graph_theory", "trigonometry" ] }, { "no": 99, "source_index": 189, "id": "topic-189-modelling-force-distribution-while-climbing-on-different-wall-angles", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 13, 15 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Modellierung der Kraftverteilung beim Klettern an verschiedenen Wänden", "methods": [ "Funktionen & Modellierung", "Stochastik", "Vektorrechnung", "Trigonometrie" ], "description": "Entwickle aus „Modellierung der Kraftverteilung beim Klettern an verschiedenen Wänden“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Sports biomechanics & movement", "title": "Modelling force distribution while climbing on different wall angles", "methods": [ "Functions & modelling", "Statistics & probability", "Vector mathematics", "Trigonometry" ], "description": "Turn “Modelling force distribution while climbing on different wall angles” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "vectors", "trigonometry" ] }, { "no": 100, "source_index": 412, "id": "topic-412-error-correction-with-hamming-codes-under-simulated-channel-noise", "category_key": "information-coding-theory", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Fehlerkorrektur mit Hamming-Codes bei simuliertem Kanalrauschen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Fehlerkorrektur mit Hamming-Codes bei simuliertem Kanalrauschen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Error correction with Hamming codes under simulated channel noise", "methods": [ "Geometry" ], "description": "Turn “Error correction with Hamming codes under simulated channel noise” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 101, "source_index": 199, "id": "topic-199-analysing-sentiment-trends-on-social-media-over-time", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Analyse von Sentiment-Trends in sozialen Medien über Zeit", "methods": [ "Simulation & Algorithmen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Analyse von Sentiment-Trends in sozialen Medien über Zeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Data science & introductory algorithms", "title": "Analysing sentiment trends on social media over time", "methods": [ "Simulation & algorithms", "Time-series analysis" ], "description": "Turn “Analysing sentiment trends on social media over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "simulation", "time_series" ] }, { "no": 102, "source_index": 424, "id": "topic-424-inverse-kinematics-of-a-two-link-robot-arm", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 11 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 1, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Inverse Kinematik eines zweigliedrigen Roboterarms", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Inverse Kinematik eines zweigliedrigen Roboterarms“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Inverse kinematics of a two-link robot arm", "methods": [ "Functions & modelling" ], "description": "Turn “Inverse kinematics of a two-link robot arm” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 103, "source_index": 209, "id": "topic-209-sensitivity-to-initial-conditions-and-the-butterfly-effect", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Analyse der Sensitivität gegenüber Anfangsbedingungen (Schmetterlingseffekt)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Analyse der Sensitivität gegenüber Anfangsbedingungen (Schmetterlingseffekt)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "Sensitivity to initial conditions and the butterfly effect", "methods": [ "Functions & modelling" ], "description": "Turn “Sensitivity to initial conditions and the butterfly effect” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 104, "source_index": 436, "id": "topic-436-comparing-median-and-gaussian-filters-under-different-image-noise", "category_key": "image-processing-computer-graphics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Median- und Gaußfilter bei verschiedenem Bildrauschen vergleichen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Median- und Gaußfilter bei verschiedenem Bildrauschen vergleichen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Image processing & computer graphics", "title": "Comparing median and Gaussian filters under different image noise", "methods": [ "Statistics & probability" ], "description": "Turn “Comparing median and Gaussian filters under different image noise” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 105, "source_index": 216, "id": "topic-216-modelling-dissonance-with-interval-frequency-ratios", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 9, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Modellierung der Dissonanz durch Intervall-Frequenzverhältnisse", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ], "description": "Formuliere zu „Modellierung der Dissonanz durch Intervall-Frequenzverhältnisse“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Modelling dissonance with interval-frequency ratios", "methods": [ "Functions & modelling", "Trigonometry" ], "description": "Turn “Modelling dissonance with interval-frequency ratios” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry" ] }, { "no": 106, "source_index": 446, "id": "topic-446-comparing-readability-formulas-and-sentence-length-distributions", "category_key": "language-text-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 8, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Lesbarkeitsformeln und Verteilungen von Satzlängen vergleichen", "methods": [ "Stochastik", "Geometrie", "Beweisführung" ], "description": "Die Idee „Lesbarkeitsformeln und Verteilungen von Satzlängen vergleichen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Language & text mathematics", "title": "Comparing readability formulas and sentence-length distributions", "methods": [ "Statistics & probability", "Geometry", "Proof" ], "description": "Develop “Comparing readability formulas and sentence-length distributions” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "geometry", "proof" ] }, { "no": 107, "source_index": 225, "id": "topic-225-mathematical-analysis-of-escher-tessellations-and-symmetry-groups", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 8 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Mathematische Analyse von Eschers Tessellationen und Symmetriegruppen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Mathematische Analyse von Eschers Tessellationen und Symmetriegruppen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Mathematical analysis of Escher tessellations and symmetry groups", "methods": [ "Geometry" ], "description": "Turn “Mathematical analysis of Escher tessellations and symmetry groups” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 108, "source_index": 456, "id": "topic-456-modelling-learning-curves-in-typing-or-mental-arithmetic-practice", "category_key": "education-learning-analytics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 11, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Lernkurven beim Tippen oder Kopfrechnen modellieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Lernkurven beim Tippen oder Kopfrechnen modellieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "Modelling learning curves in typing or mental arithmetic practice", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling learning curves in typing or mental arithmetic practice” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 109, "source_index": 234, "id": "topic-234-light-curves-of-variable-stars", "category_key": "astronomy-spaceflight", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 10, 17 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Untersuchung der Helligkeitskurven von Variablen Sternen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Helligkeitskurven von Variablen Sternen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Light curves of variable stars", "methods": [ "Functions & modelling" ], "description": "Turn “Light curves of variable stars” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 110, "source_index": 466, "id": "topic-466-stability-of-the-cobweb-model-under-delayed-supply-response", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Stabilität des Cobweb-Modells bei verzögerter Angebotsreaktion", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Stabilität des Cobweb-Modells bei verzögerter Angebotsreaktion“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Stability of the cobweb model under delayed supply response", "methods": [ "Functions & modelling" ], "description": "Turn “Stability of the cobweb model under delayed supply response” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 111, "source_index": 242, "id": "topic-242-analysing-mathematical-patterns-in-sleep-and-rem-cycles", "category_key": "psychology-cognition", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 6 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Analyse der mathematischen Muster in Träumen (REM-Zyklen)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Analyse der mathematischen Muster in Träumen (REM-Zyklen)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Psychology & cognition", "title": "Analysing mathematical patterns in sleep and REM cycles", "methods": [ "Functions & modelling" ], "description": "Turn “Analysing mathematical patterns in sleep and REM cycles” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 112, "source_index": 476, "id": "topic-476-sensitivity-of-different-forecast-error-metrics", "category_key": "time-series-forecasting", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Empfindlichkeit verschiedener Prognosefehlermaße", "methods": [ "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Empfindlichkeit verschiedener Prognosefehlermaße“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Sensitivity of different forecast-error metrics", "methods": [ "Sequences & series", "Time-series analysis" ], "description": "Turn “Sensitivity of different forecast-error metrics” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "time_series" ] }, { "no": 113, "source_index": 250, "id": "topic-250-modelling-the-failure-probability-of-technical-devices", "category_key": "probability-risk", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Modellierung der Ausfallwahrscheinlichkeit technischer Geräte (Zuverlässigkeit)", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Modellierung der Ausfallwahrscheinlichkeit technischer Geräte (Zuverlässigkeit)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Modelling the failure probability of technical devices", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “Modelling the failure probability of technical devices” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 114, "source_index": 486, "id": "topic-486-gps-error-in-dense-urban-areas-and-open-spaces", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 12 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "GPS-Fehler in dichter Bebauung und auf freiem Feld", "methods": [ "Geometrie" ], "description": "Formuliere zu „GPS-Fehler in dichter Bebauung und auf freiem Feld“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "GPS error in dense urban areas and open spaces", "methods": [ "Geometry" ], "description": "Turn “GPS error in dense urban areas and open spaces” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 115, "source_index": 258, "id": "topic-258-the-geometry-of-pasta-shapes-and-their-cooking-times", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 6 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Untersuchung der geometrischen Formen von Nudeln und deren Kochzeit", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der geometrischen Formen von Nudeln und deren Kochzeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "The geometry of pasta shapes and their cooking times", "methods": [ "Geometry" ], "description": "Turn “The geometry of pasta shapes and their cooking times” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 116, "source_index": 496, "id": "topic-496-modelling-heat-sink-fin-shape-for-heat-transfer", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 11, 12 ], "measurement_codes": [ 3, 4, 13, 20, 21 ], "safety_code": 2, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Kühlrippenform für Wärmeabgabe modellieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Kühlrippenform für Wärmeabgabe modellieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Modelling heat-sink fin shape for heat transfer", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Modelling heat-sink fin shape for heat transfer” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 117, "source_index": 266, "id": "topic-266-heating-surfaces-of-different-colours-in-sunlight-black-white-red-and-", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 4, 1 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Erwärmung von Oberflächen verschiedener Farben im Sonnenlicht (schwarz, weiß, rot, silber)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Erwärmung von Oberflächen verschiedener Farben im Sonnenlicht (schwarz, weiß, rot, silber)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Heating surfaces of different colours in sunlight: black, white, red and silver", "methods": [ "Geometry" ], "description": "Turn “Heating surfaces of different colours in sunlight: black, white, red and silver” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 118, "source_index": 506, "id": "topic-506-optimal-pool-size-in-pooled-diagnostic-testing", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Optimale Poolgröße bei gepoolten diagnostischen Tests", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimale Poolgröße bei gepoolten diagnostischen Tests“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Optimal pool size in pooled diagnostic testing", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimal pool size in pooled diagnostic testing” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 119, "source_index": 286, "id": "topic-286-water-content-of-fruits-and-vegetables-measured-by-oven-drying", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Wassergehalt verschiedener Früchte und Gemüse durch Trocknung im Backofen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wassergehalt verschiedener Früchte und Gemüse durch Trocknung im Backofen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Water content of fruits and vegetables measured by oven drying", "methods": [ "Functions & modelling" ], "description": "Turn “Water content of fruits and vegetables measured by oven drying” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 120, "source_index": 516, "id": "topic-516-passing-network-centrality-and-match-outcome", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 7, 9, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Passnetzwerk-Zentralität und Spielergebnis", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Passnetzwerk-Zentralität und Spielergebnis“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Passing-network centrality and match outcome", "methods": [ "Graph theory" ], "description": "Turn “Passing-network centrality and match outcome” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 121, "source_index": 306, "id": "topic-306-internal-resistance-of-alkaline-nimh-and-lithium-batteries", "category_key": "electricity", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 5, 13 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Elektrizität", "title": "Innenwiderstand verschiedener Batterietypen (Alkaline, NiMH, Lithium)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Innenwiderstand verschiedener Batterietypen (Alkaline, NiMH, Lithium)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Internal resistance of alkaline, NiMH and lithium batteries", "methods": [ "Functions & modelling" ], "description": "Turn “Internal resistance of alkaline, NiMH and lithium batteries” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 122, "source_index": 526, "id": "topic-526-clue-density-and-uniqueness-in-sudoku-puzzles", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Hinweisdichte und Eindeutigkeit bei Sudoku-Rätseln", "methods": [ "Kombinatorik" ], "description": "Die Idee „Hinweisdichte und Eindeutigkeit bei Sudoku-Rätseln“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Recreational games & mathematics", "title": "Clue density and uniqueness in Sudoku puzzles", "methods": [ "Combinatorics" ], "description": "Develop “Clue density and uniqueness in Sudoku puzzles” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "combinatorics" ] }, { "no": 123, "source_index": 326, "id": "topic-326-specific-heat-capacity-of-different-liquids-under-equal-energy-input", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Spezifische Wärmekapazität verschiedener Flüssigkeiten (gleiche Energiezufuhr, ΔT messen)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Spezifische Wärmekapazität verschiedener Flüssigkeiten (gleiche Energiezufuhr, ΔT messen)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Specific heat capacity of different liquids under equal energy input", "methods": [ "Functions & modelling" ], "description": "Turn “Specific heat capacity of different liquids under equal energy input” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 124, "source_index": 536, "id": "topic-536-occupancy-problems-in-random-seating-arrangements", "category_key": "combinatorics-discrete-probability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 7, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Belegungsprobleme bei zufälligen Sitzordnungen", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Belegungsprobleme bei zufälligen Sitzordnungen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Occupancy problems in random seating arrangements", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “Occupancy problems in random seating arrangements” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 125, "source_index": 346, "id": "topic-346-ice-cream-melting-rate-mass-loss-and-surface-temperature-across-differ", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 4, 1, 3 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Eiscreme-Schmelzrate: Masseverlust und Oberflächentemperatur verschiedener Sorten/Fettgehalte", "methods": [ "Geometrie" ], "description": "Formuliere zu „Eiscreme-Schmelzrate: Masseverlust und Oberflächentemperatur verschiedener Sorten/Fettgehalte“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Ice-cream melting rate: mass loss and surface temperature across different formulations", "methods": [ "Geometry" ], "description": "Turn “Ice-cream melting rate: mass loss and surface temperature across different formulations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 126, "source_index": 546, "id": "topic-546-investigating-urban-heat-islands-with-spatial-regression", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 9, 11, 12 ], "measurement_codes": [ 3, 4, 8, 12, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Städtische Wärmeinseln mit räumlicher Regression untersuchen", "methods": [ "Funktionen & Modellierung", "Regression" ], "description": "Entwickle aus „Städtische Wärmeinseln mit räumlicher Regression untersuchen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "Investigating urban heat islands with spatial regression", "methods": [ "Functions & modelling", "Regression" ], "description": "Turn “Investigating urban heat islands with spatial regression” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression" ] }, { "no": 127, "source_index": 356, "id": "topic-356-compost-mass-loss-and-core-temperature-over-four-weeks", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 2, 3, 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Kompost: Masseverlust und Kerntemperatur über 4 Wochen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Kompost: Masseverlust und Kerntemperatur über 4 Wochen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Compost: mass loss and core temperature over four weeks", "methods": [ "Functions & modelling" ], "description": "Turn “Compost: mass loss and core temperature over four weeks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 128, "source_index": 366, "id": "topic-366-sweat-related-body-mass-change-during-exercise-under-different-ambient", "category_key": "physiology", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 2, 3, 13, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Physiologie", "title": "Masse Schweißverlust während 30 Minuten Sport bei verschiedenen Temperaturen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Masse Schweißverlust während 30 Minuten Sport bei verschiedenen Temperaturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Physiology", "title": "Sweat-related body-mass change during exercise under different ambient conditions", "methods": [ "Functions & modelling" ], "description": "Turn “Sweat-related body-mass change during exercise under different ambient conditions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 129, "source_index": 371, "id": "topic-371-moisture-absorption-by-three-dimensional-printing-filaments", "category_key": "materials", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 6, 13, 18 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Materialien", "title": "Masseänderung von 3D-Druck-Filamenten beim Absorieren von Feuchtigkeit", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Masseänderung von 3D-Druck-Filamenten beim Absorieren von Feuchtigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Materials", "title": "Moisture absorption by three-dimensional printing filaments", "methods": [ "Functions & modelling" ], "description": "Turn “Moisture absorption by three-dimensional printing filaments” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 130, "source_index": 3, "id": "topic-003-rsa-encryption-and-prime-number-theory", "category_key": "algebra-number-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Algebra & Zahlentheorie", "title": "RSA-Verschlüsselung und Primzahltheorie", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Die Idee „RSA-Verschlüsselung und Primzahltheorie“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "RSA encryption and prime number theory", "methods": [ "Number theory", "Algebra" ], "description": "Develop “RSA encryption and prime number theory” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 131, "source_index": 23, "id": "topic-023-calculating-work-done-by-a-variable-force-in-sport", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Berechnung der Arbeit einer variablen Kraft im Sport", "methods": [ "Funktionen & Modellierung", "Integralrechnung" ], "description": "Formuliere zu „Berechnung der Arbeit einer variablen Kraft im Sport“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Calculating work done by a variable force in sport", "methods": [ "Functions & modelling", "Integral calculus" ], "description": "Turn “Calculating work done by a variable force in sport” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "integral_calculus" ] }, { "no": 132, "source_index": 44, "id": "topic-044-regression-carbon-dioxide-emissions-and-global-temperatures", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 9 ], "measurement_codes": [ 3, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Regression: CO2-Emissionen und globale Temperaturen", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression" ], "description": "Entwickle aus „Regression: CO2-Emissionen und globale Temperaturen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Regression: carbon dioxide emissions and global temperatures", "methods": [ "Functions & modelling", "Statistics & probability", "Regression" ], "description": "Turn “Regression: carbon dioxide emissions and global temperatures” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "regression" ] }, { "no": 133, "source_index": 65, "id": "topic-065-the-trajectory-of-a-basketball-or-tennis-shot", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Flugbahn eines Basketball-/Tenniswurfs", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Flugbahn eines Basketball-/Tenniswurfs“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "The trajectory of a basketball or tennis shot", "methods": [ "Functions & modelling" ], "description": "Turn “The trajectory of a basketball or tennis shot” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 134, "source_index": 85, "id": "topic-085-fractal-geometry-and-the-coastline-paradox", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Geometrie & Topologie", "title": "Fraktale Geometrie und Küstenlinienparadoxon", "methods": [ "Geometrie" ], "description": "Formuliere zu „Fraktale Geometrie und Küstenlinienparadoxon“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Fractal geometry and the coastline paradox", "methods": [ "Geometry" ], "description": "Turn “Fractal geometry and the coastline paradox” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 135, "source_index": 104, "id": "topic-104-the-true-cost-of-minimum-credit-card-payments", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 4, "courses": [ "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL", "de": { "category": "Finanzmathematik", "title": "Wahre Kosten von Mindestzahlungen bei Kreditkarten", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Finanzmathematik", "Optimierung" ], "description": "Formuliere zu „Wahre Kosten von Mindestzahlungen bei Kreditkarten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "The true cost of minimum credit-card payments", "methods": [ "Functions & modelling", "Differential calculus", "Financial mathematics", "Optimisation" ], "description": "Turn “The true cost of minimum credit-card payments” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "financial_math", "optimization" ] }, { "no": 136, "source_index": 121, "id": "topic-121-cantor-s-infinities-countability-and-the-diagonal-argument", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Cantors Unendlichkeiten: Abzählbarkeit, Diagonalargument", "methods": [ "Beweisführung" ], "description": "Die Idee „Cantors Unendlichkeiten: Abzählbarkeit, Diagonalargument“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Cantor's infinities: countability and the diagonal argument", "methods": [ "Proof" ], "description": "Develop “Cantor's infinities: countability and the diagonal argument” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 137, "source_index": 136, "id": "topic-136-huffman-coding-and-data-compression", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Untersuchung von Huffman-Codierung und Datenkompression", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Huffman-Codierung und Datenkompression“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Huffman coding and data compression", "methods": [ "Geometry" ], "description": "Turn “Huffman coding and data compression” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 138, "source_index": 146, "id": "topic-146-room-acoustics-and-reverberation-time", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Untersuchung der Akustik eines Raumes (Nachhallzeit)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Akustik eines Raumes (Nachhallzeit)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Room acoustics and reverberation time", "methods": [ "Functions & modelling" ], "description": "Turn “Room acoustics and reverberation time” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 139, "source_index": 162, "id": "topic-162-the-prisoner-s-dilemma-in-repeated-games", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Untersuchung des Gefangenendilemmas in wiederholten Spielen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung des Gefangenendilemmas in wiederholten Spielen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "The prisoner's dilemma in repeated games", "methods": [ "Functions & modelling" ], "description": "Turn “The prisoner's dilemma in repeated games” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 140, "source_index": 377, "id": "topic-377-a-queueing-model-for-airport-security-lanes", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Warteschlangenmodell für Sicherheitskontrollen an einem Flughafen", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Warteschlangenmodell für Sicherheitskontrollen an einem Flughafen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Transport & mobility mathematics", "title": "A queueing model for airport security lanes", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “A queueing model for airport security lanes” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 141, "source_index": 170, "id": "topic-170-modelling-tumour-growth-gompertz-versus-exponential-models", "category_key": "biomathematics-medicine", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AA HL / AI HL", "de": { "category": "Biomathematik & Medizin", "title": "Modellierung der Tumorwachstumsrate (Gompertz-Modell vs. exponentiell)", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Modellierung der Tumorwachstumsrate (Gompertz-Modell vs. exponentiell)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Modelling tumour growth: Gompertz versus exponential models", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling tumour growth: Gompertz versus exponential models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 142, "source_index": 389, "id": "topic-389-efficient-parcel-packing-with-the-bin-packing-problem", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 5, 7, 11 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Paketgrößen mit dem Bin-Packing-Problem effizient zusammenstellen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Paketgrößen mit dem Bin-Packing-Problem effizient zusammenstellen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Efficient parcel packing with the bin-packing problem", "methods": [ "Geometry" ], "description": "Turn “Efficient parcel packing with the bin-packing problem” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 143, "source_index": 180, "id": "topic-180-statistical-analysis-of-the-effectiveness-of-recycling-programmes", "category_key": "environmental-mathematics-sustainability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Statistische Analyse der Effektivität von Recyclingprogrammen", "methods": [ "Simulation & Algorithmen" ], "description": "Formuliere zu „Statistische Analyse der Effektivität von Recyclingprogrammen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Statistical analysis of the effectiveness of recycling programmes", "methods": [ "Simulation & algorithms" ], "description": "Turn “Statistical analysis of the effectiveness of recycling programmes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "simulation" ] }, { "no": 144, "source_index": 401, "id": "topic-401-power-grid-robustness-under-targeted-node-removal", "category_key": "networks-social-systems", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Robustheit eines Stromnetzes bei gezieltem Entfernen von Knoten", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Robustheit eines Stromnetzes bei gezieltem Entfernen von Knoten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Power-grid robustness under targeted node removal", "methods": [ "Graph theory" ], "description": "Turn “Power-grid robustness under targeted node removal” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 145, "source_index": 190, "id": "topic-190-optimising-swimming-technique-through-drag-models", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 6, 13 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Berechnung des optimalen Schwimmstils durch Strömungswiderstand", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung des optimalen Schwimmstils durch Strömungswiderstand“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Optimising swimming technique through drag models", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising swimming technique through drag models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 146, "source_index": 413, "id": "topic-413-reedsolomon-codes-and-the-damage-tolerance-of-qr-codes", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 11 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Reed-Solomon-Codes und die Beschädigungstoleranz von QR-Codes", "methods": [ "Geometrie" ], "description": "Formuliere zu „Reed-Solomon-Codes und die Beschädigungstoleranz von QR-Codes“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Reed–Solomon codes and the damage tolerance of QR codes", "methods": [ "Geometry" ], "description": "Turn “Reed–Solomon codes and the damage tolerance of QR codes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 147, "source_index": 200, "id": "topic-200-testing-the-predictive-accuracy-of-weather-apps-with-regression", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Untersuchung der Vorhersagegüte von Wetter-Apps durch Regression", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Zahlentheorie", "Simulation & Algorithmen" ], "description": "Entwickle aus „Untersuchung der Vorhersagegüte von Wetter-Apps durch Regression“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Data science & introductory algorithms", "title": "Testing the predictive accuracy of weather apps with regression", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Number theory", "Simulation & algorithms" ], "description": "Turn “Testing the predictive accuracy of weather apps with regression” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "regression", "number_theory", "simulation" ] }, { "no": 148, "source_index": 425, "id": "topic-425-a-and-dijkstra-algorithms-for-path-planning-on-grid-maps", "category_key": "robotics-control-sensing", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "A*- und Dijkstra-Algorithmus bei der Pfadplanung auf Gitternetzen", "methods": [ "Graphentheorie", "Simulation & Algorithmen" ], "description": "Formuliere zu „A*- und Dijkstra-Algorithmus bei der Pfadplanung auf Gitternetzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "A* and Dijkstra algorithms for path planning on grid maps", "methods": [ "Graph theory", "Simulation & algorithms" ], "description": "Turn “A* and Dijkstra algorithms for path planning on grid maps” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "simulation" ] }, { "no": 149, "source_index": 210, "id": "topic-210-julia-sets-and-their-dependence-on-parameters", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Untersuchung der Julia-Mengen und ihrer Parameterabhängigkeit", "methods": [ "Komplexe Zahlen" ], "description": "Formuliere zu „Untersuchung der Julia-Mengen und ihrer Parameterabhängigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "Julia sets and their dependence on parameters", "methods": [ "Complex numbers" ], "description": "Turn “Julia sets and their dependence on parameters” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "complex_numbers" ] }, { "no": 150, "source_index": 437, "id": "topic-437-fractal-dimension-of-natural-image-textures", "category_key": "image-processing-computer-graphics", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 6, 7, 10 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Fraktale Dimension natürlicher Bildtexturen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Fraktale Dimension natürlicher Bildtexturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Fractal dimension of natural image textures", "methods": [ "Geometry" ], "description": "Turn “Fractal dimension of natural image textures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 151, "source_index": 217, "id": "topic-217-mathematical-analysis-of-rhythm-patterns-across-music-genres", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Mathematische Analyse von Rhythmusmustern in verschiedenen Musikgenres", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Mathematische Analyse von Rhythmusmustern in verschiedenen Musikgenres“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Mathematical analysis of rhythm patterns across music genres", "methods": [ "Trigonometry" ], "description": "Turn “Mathematical analysis of rhythm patterns across music genres” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 152, "source_index": 447, "id": "topic-447-stylometry-using-function-word-frequencies", "category_key": "language-text-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Stilometrie mit Funktionswort-Häufigkeiten", "methods": [ "Algebra" ], "description": "Formuliere zu „Stilometrie mit Funktionswort-Häufigkeiten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Stylometry using function-word frequencies", "methods": [ "Algebra" ], "description": "Turn “Stylometry using function-word frequencies” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 153, "source_index": 226, "id": "topic-226-curves-in-typeface-design-b-zier-curves", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Untersuchung der Kurven in der Schriftgestaltung (Bézier-Kurven)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Kurven in der Schriftgestaltung (Bézier-Kurven)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Curves in typeface design: Bézier curves", "methods": [ "Geometry" ], "description": "Turn “Curves in typeface design: Bézier curves” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 154, "source_index": 457, "id": "topic-457-the-relationship-between-response-time-and-answer-accuracy", "category_key": "education-learning-analytics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 12 ], "measurement_codes": [ 6, 13, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Zusammenhang zwischen Bearbeitungszeit und Antwortgenauigkeit", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Zusammenhang zwischen Bearbeitungszeit und Antwortgenauigkeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Education & learning analytics", "title": "The relationship between response time and answer accuracy", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “The relationship between response time and answer accuracy” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 155, "source_index": 235, "id": "topic-235-calculating-stellar-distances-by-parallax", "category_key": "astronomy-spaceflight", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 1, 13, 17 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Berechnung der Entfernung zu Sternen durch Parallaxenmessung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Berechnung der Entfernung zu Sternen durch Parallaxenmessung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Calculating stellar distances by parallax", "methods": [ "Functions & modelling" ], "description": "Turn “Calculating stellar distances by parallax” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 156, "source_index": 467, "id": "topic-467-simulating-cournot-and-bertrand-duopoly-models", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Cournot- und Bertrand-Duopolmodelle simulieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Cournot- und Bertrand-Duopolmodelle simulieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Simulating Cournot and Bertrand duopoly models", "methods": [ "Functions & modelling" ], "description": "Turn “Simulating Cournot and Bertrand duopoly models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 157, "source_index": 243, "id": "topic-243-optimising-break-intervals-in-study-sessions-with-a-pomodoro-model", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Berechnung der optimalen Pausenverteilung beim Lernen (Pomodoro-Modell)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ], "description": "Entwickle aus „Berechnung der optimalen Pausenverteilung beim Lernen (Pomodoro-Modell)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Psychology & cognition", "title": "Optimising break intervals in study sessions with a Pomodoro model", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ], "description": "Turn “Optimising break intervals in study sessions with a Pomodoro model” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ] }, { "no": 158, "source_index": 477, "id": "topic-477-detecting-structural-breaks-in-long-term-temperature-series", "category_key": "time-series-forecasting", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Strukturbrüche in langfristigen Temperaturreihen erkennen", "methods": [ "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Strukturbrüche in langfristigen Temperaturreihen erkennen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Detecting structural breaks in long-term temperature series", "methods": [ "Sequences & series", "Time-series analysis" ], "description": "Turn “Detecting structural breaks in long-term temperature series” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "time_series" ] }, { "no": 159, "source_index": 251, "id": "topic-251-calculating-optimal-diversification-in-an-investment-portfolio", "category_key": "probability-risk", "assessment_code": 3, "course_code": 5, "courses": [ "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Berechnung der optimalen Diversifikation eines Aktienportfolios", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Finanzmathematik", "Optimierung" ], "description": "Entwickle aus „Berechnung der optimalen Diversifikation eines Aktienportfolios“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Calculating optimal diversification in an investment portfolio", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Financial mathematics", "Optimisation" ], "description": "Turn “Calculating optimal diversification in an investment portfolio” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "financial_math", "optimization" ] }, { "no": 160, "source_index": 487, "id": "topic-487-position-finding-by-bearings-and-triangulation", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Ortsbestimmung durch Peilung und Triangulation", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Ortsbestimmung durch Peilung und Triangulation“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Position finding by bearings and triangulation", "methods": [ "Functions & modelling" ], "description": "Turn “Position finding by bearings and triangulation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 161, "source_index": 259, "id": "topic-259-calculating-optimal-lasagne-layering-with-heat-conduction-models", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 3, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Berechnung der optimalen Schichtung von Lasagne (Wärmeleitung)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Schichtung von Lasagne (Wärmeleitung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "Calculating optimal lasagne layering with heat-conduction models", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating optimal lasagne layering with heat-conduction models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 162, "source_index": 497, "id": "topic-497-wind-turbine-blade-pitch-and-theoretical-power", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 9, 11 ], "measurement_codes": [ 12, 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Blattwinkel einer Windturbine und theoretische Leistung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ], "description": "Formuliere zu „Blattwinkel einer Windturbine und theoretische Leistung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Wind-turbine blade pitch and theoretical power", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ], "description": "Turn “Wind-turbine blade pitch and theoretical power” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ] }, { "no": 163, "source_index": 267, "id": "topic-267-heat-distribution-across-a-laptop-under-cpu-load", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 4, 3, 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmeverteilung auf einem Laptop unter CPU-Last (Tastatur, Unterseite, Lüfterauslass)", "methods": [ "Stochastik" ], "description": "Entwickle aus „Wärmeverteilung auf einem Laptop unter CPU-Last (Tastatur, Unterseite, Lüfterauslass)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Thermodynamics", "title": "Heat distribution across a laptop under CPU load", "methods": [ "Statistics & probability" ], "description": "Turn “Heat distribution across a laptop under CPU load” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 164, "source_index": 507, "id": "topic-507-survival-analysis-of-waiting-times-using-public-health-data", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Überlebensanalyse von Wartezeiten mit öffentlichen Gesundheitsdaten", "methods": [ "Stochastik" ], "description": "Entwickle aus „Überlebensanalyse von Wartezeiten mit öffentlichen Gesundheitsdaten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Epidemiology & public health", "title": "Survival analysis of waiting times using public health data", "methods": [ "Statistics & probability" ], "description": "Turn “Survival analysis of waiting times using public health data” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 165, "source_index": 287, "id": "topic-287-carbon-dioxide-loss-from-fizzy-drinks-over-48-hours-under-different-st", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 6 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "CO₂-Verlust kohlensäurehaltiger Getränke über 48 Stunden (offen vs. verschlossen vs. Kühlschrank)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „CO₂-Verlust kohlensäurehaltiger Getränke über 48 Stunden (offen vs. verschlossen vs. Kühlschrank)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Carbon dioxide loss from fizzy drinks over 48 hours under different storage conditions", "methods": [ "Functions & modelling" ], "description": "Turn “Carbon dioxide loss from fizzy drinks over 48 hours under different storage conditions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 166, "source_index": 517, "id": "topic-517-predictive-accuracy-of-different-elo-rating-variants", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Vorhersagegüte verschiedener Elo-Rating-Varianten", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Zahlentheorie" ], "description": "Die Idee „Vorhersagegüte verschiedener Elo-Rating-Varianten“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Sports analytics & tactics", "title": "Predictive accuracy of different Elo-rating variants", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Number theory" ], "description": "Develop “Predictive accuracy of different Elo-rating variants” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "functions_modeling", "stochastics", "regression", "number_theory" ] }, { "no": 167, "source_index": 307, "id": "topic-307-voltage-drop-along-copper-cables-of-different-lengths-and-cross-sectio", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Spannungsabfall über Kupferkabel verschiedener Länge (10 – 200 cm) und Querschnitte", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Spannungsabfall über Kupferkabel verschiedener Länge (10 – 200 cm) und Querschnitte“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Voltage drop along copper cables of different lengths and cross-sections", "methods": [ "Functions & modelling" ], "description": "Turn “Voltage drop along copper cables of different lengths and cross-sections” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 168, "source_index": 527, "id": "topic-527-the-group-structure-of-the-rubiks-cube", "category_key": "recreational-games-mathematics", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 8, 10 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Gruppenstruktur des Rubik-Würfels", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Gruppenstruktur des Rubik-Würfels“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "The group structure of the Rubik’s Cube", "methods": [ "Functions & modelling" ], "description": "Turn “The group structure of the Rubik’s Cube” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 169, "source_index": 327, "id": "topic-327-solar-cell-voltage-loss-as-temperature-increases", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 4, 5, 1, 3 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "de": { "category": "Kombinierte Experimente", "title": "Solarzellen: Spannungsabfall bei zunehmender Temperatur (Erwärmung durch Lampe)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Solarzellen: Spannungsabfall bei zunehmender Temperatur (Erwärmung durch Lampe)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Solar-cell voltage loss as temperature increases", "methods": [ "Functions & modelling" ], "description": "Turn “Solar-cell voltage loss as temperature increases” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 170, "source_index": 537, "id": "topic-537-the-connectivity-threshold-in-random-graphs", "category_key": "combinatorics-discrete-probability", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Schwellenwert für Zusammenhang in Zufallsgraphen", "methods": [ "Funktionen & Modellierung", "Stochastik", "Trigonometrie", "Kombinatorik" ], "description": "Die Idee „Schwellenwert für Zusammenhang in Zufallsgraphen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "The connectivity threshold in random graphs", "methods": [ "Functions & modelling", "Statistics & probability", "Trigonometry", "Combinatorics" ], "description": "Develop “The connectivity threshold in random graphs” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "functions_modeling", "stochastics", "trigonometry", "combinatorics" ] }, { "no": 171, "source_index": 347, "id": "topic-347-bread-baking-water-loss-and-core-temperature-over-time", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2, 3 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Brotbacken: Masseänderung (Wasserverlust) und Kerntemperatur während des Backens", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Brotbacken: Masseänderung (Wasserverlust) und Kerntemperatur während des Backens“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Kitchen & everyday life", "title": "Bread baking: water loss and core temperature over time", "methods": [ "Time-series analysis" ], "description": "Turn “Bread baking: water loss and core temperature over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 172, "source_index": 547, "id": "topic-547-comparing-drought-indices-using-moving-windows", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Dürreindizes mit gleitenden Zeitfenstern vergleichen", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Dürreindizes mit gleitenden Zeitfenstern vergleichen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "Comparing drought indices using moving windows", "methods": [ "Time-series analysis" ], "description": "Turn “Comparing drought indices using moving windows” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 173, "source_index": 357, "id": "topic-357-solar-cooker-water-temperature-and-evaporation-mass-at-different-angle", "category_key": "environment", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 2, 3, 1, 10 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Umwelt", "title": "Solar-Kocher: Wassertemperatur und Masse Verdunstung bei verschiedenen Winkeln", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Solar-Kocher: Wassertemperatur und Masse Verdunstung bei verschiedenen Winkeln“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Solar cooker: water temperature and evaporation mass at different angles", "methods": [ "Trigonometry" ], "description": "Turn “Solar cooker: water temperature and evaporation mass at different angles” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 174, "source_index": 367, "id": "topic-367-hand-surface-temperature-before-and-after-a-low-risk-cognitive-task", "category_key": "physiology", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 4, 3, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Physiologie", "title": "Wärmebild von Händen vor und nach Stressaufgabe (Mathe-Rätsel, Präsentation)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wärmebild von Händen vor und nach Stressaufgabe (Mathe-Rätsel, Präsentation)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Physiology", "title": "Hand-surface temperature before and after a low-risk cognitive task", "methods": [ "Geometry" ], "description": "Turn “Hand-surface temperature before and after a low-risk cognitive task” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 175, "source_index": 372, "id": "topic-372-thermal-response-of-granite-wood-and-stainless-steel-worktops", "category_key": "materials", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 3, 4, 1 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Materialien", "title": "Temperaturleitfähigkeit verschiedener Küchenarbeitsplatten (Granit, Holz, Edelstahl)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Temperaturleitfähigkeit verschiedener Küchenarbeitsplatten (Granit, Holz, Edelstahl)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Materials", "title": "Thermal response of granite, wood and stainless-steel worktops", "methods": [ "Functions & modelling" ], "description": "Turn “Thermal response of granite, wood and stainless-steel worktops” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 176, "source_index": 4, "id": "topic-004-pascal-s-triangle-patterns-binomial-coefficients-and-combinatorics", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Pascals Dreieck: Muster, Binomialkoeffizienten, Kombinatorik", "methods": [ "Zahlentheorie", "Trigonometrie", "Geometrie", "Kombinatorik", "Algebra" ], "description": "Formuliere zu „Pascals Dreieck: Muster, Binomialkoeffizienten, Kombinatorik“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Pascal's triangle: patterns, binomial coefficients and combinatorics", "methods": [ "Number theory", "Trigonometry", "Geometry", "Combinatorics", "Algebra" ], "description": "Turn “Pascal's triangle: patterns, binomial coefficients and combinatorics” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "trigonometry", "geometry", "combinatorics", "algebra" ] }, { "no": 177, "source_index": 24, "id": "topic-024-convergence-of-series-the-harmonic-series-basel-problem-and-geometric-", "category_key": "analysis-calculus", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Konvergenz von Reihen: Harmonische Reihe, Basel-Problem, geometrische Reihe", "methods": [ "Geometrie", "Folgen & Reihen" ], "description": "Formuliere zu „Konvergenz von Reihen: Harmonische Reihe, Basel-Problem, geometrische Reihe“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Convergence of series: the harmonic series, Basel problem and geometric series", "methods": [ "Geometry", "Sequences & series" ], "description": "Turn “Convergence of series: the harmonic series, Basel problem and geometric series” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "sequences_series" ] }, { "no": 178, "source_index": 45, "id": "topic-045-the-monty-hall-problem-simulation-versus-theory", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 7, "courses": [ "aa", "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Monty-Hall-Problem: Simulationsmodell vs. Theorie", "methods": [ "Funktionen & Modellierung", "Stochastik", "Simulation & Algorithmen" ], "description": "Entwickle aus „Monty-Hall-Problem: Simulationsmodell vs. Theorie“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "The Monty Hall problem: simulation versus theory", "methods": [ "Functions & modelling", "Statistics & probability", "Simulation & algorithms" ], "description": "Turn “The Monty Hall problem: simulation versus theory” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "simulation" ] }, { "no": 179, "source_index": 66, "id": "topic-066-logistic-growth-in-social-media-followers-and-viral-trends", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Logistisches Wachstum: Social-Media-Follower, virale Trends", "methods": [ "Funktionen & Modellierung", "Zeitreihenanalyse" ], "description": "Entwickle aus „Logistisches Wachstum: Social-Media-Follower, virale Trends“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Mathematical modelling", "title": "Logistic growth in social-media followers and viral trends", "methods": [ "Functions & modelling", "Time-series analysis" ], "description": "Turn “Logistic growth in social-media followers and viral trends” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "time_series" ] }, { "no": 180, "source_index": 86, "id": "topic-086-platonic-solids-euler-s-formula-and-why-there-are-exactly-five", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 2 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Platonische Körper: Eulersche Formel und warum es genau fünf gibt", "methods": [ "Geometrie" ], "description": "Formuliere zu „Platonische Körper: Eulersche Formel und warum es genau fünf gibt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Platonic solids: Euler's formula and why there are exactly five", "methods": [ "Geometry" ], "description": "Turn “Platonic solids: Euler's formula and why there are exactly five” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 181, "source_index": 105, "id": "topic-105-saving-strategies-lump-sum-investment-versus-regular-deposits", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 4, "courses": [ "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL", "de": { "category": "Finanzmathematik", "title": "Sparstrategien: Einmalanlage vs. regelmäßige Einzahlungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Sparstrategien: Einmalanlage vs. regelmäßige Einzahlungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Saving strategies: lump-sum investment versus regular deposits", "methods": [ "Functions & modelling" ], "description": "Turn “Saving strategies: lump-sum investment versus regular deposits” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 182, "source_index": 122, "id": "topic-122-arrow-s-impossibility-theorem-and-voting-systems", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Arrow’s Unmöglichkeitstheorem und Wahlsysteme", "methods": [ "Beweisführung" ], "description": "Die Idee „Arrow’s Unmöglichkeitstheorem und Wahlsysteme“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Arrow's impossibility theorem and voting systems", "methods": [ "Proof" ], "description": "Develop “Arrow's impossibility theorem and voting systems” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 183, "source_index": 137, "id": "topic-137-modelling-networks-with-adjacency-matrices", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Modellierung von Netzwerken mit Adjazenzmatrizen", "methods": [ "Funktionen & Modellierung", "Graphentheorie", "Matrizen", "Geometrie" ], "description": "Formuliere zu „Modellierung von Netzwerken mit Adjazenzmatrizen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Modelling networks with adjacency matrices", "methods": [ "Functions & modelling", "Graph theory", "Matrices", "Geometry" ], "description": "Turn “Modelling networks with adjacency matrices” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "graph_theory", "matrices", "geometry" ] }, { "no": 184, "source_index": 147, "id": "topic-147-modelling-an-optimal-running-pace", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Modellierung der optimalen Laufgeschwindigkeit", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Modellierung der optimalen Laufgeschwindigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Modelling an optimal running pace", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Modelling an optimal running pace” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 185, "source_index": 163, "id": "topic-163-optimal-positioning-in-penalty-kicks-using-mixed-strategies", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Optimale Positionierung im Elfmeterschießen durch Mixed Strategies", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimale Positionierung im Elfmeterschießen durch Mixed Strategies“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "Optimal positioning in penalty kicks using mixed strategies", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimal positioning in penalty kicks using mixed strategies” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 186, "source_index": 378, "id": "topic-378-reliability-of-train-headways-using-coefficients-of-variation-and-outliers", "category_key": "transport-mobility-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 9, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Zuverlässigkeit von Zugfolgezeiten mit Variationskoeffizient und Ausreißern", "methods": [ "Folgen & Reihen" ], "description": "Formuliere zu „Zuverlässigkeit von Zugfolgezeiten mit Variationskoeffizient und Ausreißern“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Reliability of train headways using coefficients of variation and outliers", "methods": [ "Sequences & series" ], "description": "Turn “Reliability of train headways using coefficients of variation and outliers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "sequences_series" ] }, { "no": 187, "source_index": 171, "id": "topic-171-mathematical-analysis-of-mosquito-population-spread", "category_key": "biomathematics-medicine", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 12 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Mathematische Analyse der Ausbreitung von Mückenpopulationen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematische Analyse der Ausbreitung von Mückenpopulationen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Mathematical analysis of mosquito-population spread", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical analysis of mosquito-population spread” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 188, "source_index": 390, "id": "topic-390-location-optimisation-for-public-defibrillators-under-response-time-constraint", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 11, 12 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Standortoptimierung öffentlicher Defibrillatoren unter Zeitgrenzen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Standortoptimierung öffentlicher Defibrillatoren unter Zeitgrenzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Location optimisation for public defibrillators under response-time constraints", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Location optimisation for public defibrillators under response-time constraints” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 189, "source_index": 181, "id": "topic-181-calculating-optimal-home-insulation-using-heat-conduction", "category_key": "environmental-mathematics-sustainability", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 3, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Berechnung der optimalen Dämmung für ein Haus (Wärmeleitung)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Dämmung für ein Haus (Wärmeleitung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Calculating optimal home insulation using heat conduction", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating optimal home insulation using heat conduction” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 190, "source_index": 402, "id": "topic-402-small-world-properties-of-a-regional-transport-network", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Small-World-Eigenschaften eines regionalen Verkehrsnetzes", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Small-World-Eigenschaften eines regionalen Verkehrsnetzes“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Small-world properties of a regional transport network", "methods": [ "Graph theory" ], "description": "Turn “Small-world properties of a regional transport network” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 191, "source_index": 191, "id": "topic-191-optimising-launch-angles-in-archery", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 1 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Untersuchung der Winkeloptimierung beim Bogenschießen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Untersuchung der Winkeloptimierung beim Bogenschießen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Optimising launch angles in archery", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ], "description": "Turn “Optimising launch angles in archery” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ] }, { "no": 192, "source_index": 414, "id": "topic-414-mutual-information-between-weather-variables-and-forecast-accuracy", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Gegenseitige Information zwischen Wettervariablen und Prognosegüte", "methods": [ "Stochastik", "Geometrie", "Zeitreihenanalyse" ], "description": "Entwickle aus „Gegenseitige Information zwischen Wettervariablen und Prognosegüte“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Information & coding theory", "title": "Mutual information between weather variables and forecast accuracy", "methods": [ "Statistics & probability", "Geometry", "Time-series analysis" ], "description": "Turn “Mutual information between weather variables and forecast accuracy” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry", "time_series" ] }, { "no": 193, "source_index": 201, "id": "topic-201-calculating-text-similarity-with-introductory-vector-models", "category_key": "data-science-introductory-algorithms", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Berechnung von Ähnlichkeiten zwischen Texten mit Vektormodellen (Einführung)", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Simulation & Algorithmen" ], "description": "Formuliere zu „Berechnung von Ähnlichkeiten zwischen Texten mit Vektormodellen (Einführung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Calculating text similarity with introductory vector models", "methods": [ "Functions & modelling", "Vector mathematics", "Simulation & algorithms" ], "description": "Turn “Calculating text similarity with introductory vector models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "vectors", "simulation" ] }, { "no": 194, "source_index": 426, "id": "topic-426-sensor-fusion-for-accelerometer-and-gyroscope-data", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 11, 12 ], "measurement_codes": [ 7, 13, 20 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Sensorfusion von Beschleunigungssensor und Gyroskop", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Sensorfusion von Beschleunigungssensor und Gyroskop“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Sensor fusion for accelerometer and gyroscope data", "methods": [ "Functions & modelling" ], "description": "Turn “Sensor fusion for accelerometer and gyroscope data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 195, "source_index": 211, "id": "topic-211-calculating-lyapunov-exponents-for-simple-functions", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Berechnung von Ljapunov-Exponenten für einfache Funktionen", "methods": [ "Algebra" ], "description": "Formuliere zu „Berechnung von Ljapunov-Exponenten für einfache Funktionen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "Calculating Lyapunov exponents for simple functions", "methods": [ "Algebra" ], "description": "Turn “Calculating Lyapunov exponents for simple functions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 196, "source_index": 438, "id": "topic-438-colour-segmentation-using-k-means-clustering", "category_key": "image-processing-computer-graphics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 11 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Farbsegmentierung mit k-Means-Clustering", "methods": [ "Stochastik" ], "description": "Entwickle aus „Farbsegmentierung mit k-Means-Clustering“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Image processing & computer graphics", "title": "Colour segmentation using k-means clustering", "methods": [ "Statistics & probability" ], "description": "Turn “Colour segmentation using k-means clustering” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 197, "source_index": 218, "id": "topic-218-calculating-string-lengths-for-alternative-tuning-systems", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9, 13, 14 ], "safety_code": 3, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Berechnung der Saitenlänge für alternative Stimmungen", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Berechnung der Saitenlänge für alternative Stimmungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Calculating string lengths for alternative tuning systems", "methods": [ "Trigonometry" ], "description": "Turn “Calculating string lengths for alternative tuning systems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 198, "source_index": 448, "id": "topic-448-uncertainty-in-sentiment-scores-from-different-lexicons", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Unsicherheit von Sentimentwerten bei verschiedenen Wörterbüchern", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Unsicherheit von Sentimentwerten bei verschiedenen Wörterbüchern“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Uncertainty in sentiment scores from different lexicons", "methods": [ "Functions & modelling" ], "description": "Turn “Uncertainty in sentiment scores from different lexicons” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 199, "source_index": 227, "id": "topic-227-calculating-optimal-stage-lighting-through-angle-analysis", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 1, 10, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Berechnung der optimalen Bühnenbeleuchtung durch Winkelanalyse", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Bühnenbeleuchtung durch Winkelanalyse“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Calculating optimal stage lighting through angle analysis", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ], "description": "Turn “Calculating optimal stage lighting through angle analysis” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ] }, { "no": 200, "source_index": 458, "id": "topic-458-optimising-test-item-order-under-fatigue", "category_key": "education-learning-analytics", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 4, 7, 11, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Optimale Reihenfolge von Testaufgaben unter Ermüdung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Folgen & Reihen", "Optimierung" ], "description": "Formuliere zu „Optimale Reihenfolge von Testaufgaben unter Ermüdung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "Optimising test-item order under fatigue", "methods": [ "Functions & modelling", "Differential calculus", "Sequences & series", "Optimisation" ], "description": "Turn “Optimising test-item order under fatigue” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "sequences_series", "optimization" ] }, { "no": 201, "source_index": 236, "id": "topic-236-modelling-a-rocket-trajectory-with-air-resistance", "category_key": "astronomy-spaceflight", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Modellierung der Raketenbahn unter Berücksichtigung von Luftwiderstand", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung der Raketenbahn unter Berücksichtigung von Luftwiderstand“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Modelling a rocket trajectory with air resistance", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling a rocket trajectory with air resistance” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 202, "source_index": 468, "id": "topic-468-how-basket-weights-affect-a-consumer-price-index", "category_key": "economic-models-markets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Einfluss unterschiedlicher Warenkorbgewichte auf einen Preisindex", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Einfluss unterschiedlicher Warenkorbgewichte auf einen Preisindex“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "How basket weights affect a consumer price index", "methods": [ "Functions & modelling" ], "description": "Turn “How basket weights affect a consumer price index” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 203, "source_index": 244, "id": "topic-244-the-stroop-effect-analysed-with-statistical-hypothesis-tests", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 0 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Untersuchung des Stroop-Effekts durch statistische Hypothesentests", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung des Stroop-Effekts durch statistische Hypothesentests“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Psychology & cognition", "title": "The Stroop effect analysed with statistical hypothesis tests", "methods": [ "Functions & modelling" ], "description": "Turn “The Stroop effect analysed with statistical hypothesis tests” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 204, "source_index": 478, "id": "topic-478-cross-correlation-between-search-trends-and-sales", "category_key": "time-series-forecasting", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Kreuzkorrelation zwischen Suchtrends und Verkaufszahlen", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Kreuzkorrelation zwischen Suchtrends und Verkaufszahlen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Cross-correlation between search trends and sales", "methods": [ "Functions & modelling", "Regression", "Geometry", "Sequences & series", "Time-series analysis" ], "description": "Turn “Cross-correlation between search trends and sales” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "geometry", "sequences_series", "time_series" ] }, { "no": 205, "source_index": 252, "id": "topic-252-perceived-risk-versus-measured-risk-air-travel-and-driving", "category_key": "probability-risk", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 12 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Analyse der Risikowahrnehmung vs. realem Risiko (Flugzeug vs. Auto)", "methods": [ "Stochastik" ], "description": "Entwickle aus „Analyse der Risikowahrnehmung vs. realem Risiko (Flugzeug vs. Auto)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Perceived risk versus measured risk: air travel and driving", "methods": [ "Statistics & probability" ], "description": "Turn “Perceived risk versus measured risk: air travel and driving” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 206, "source_index": 488, "id": "topic-488-interpolating-local-temperatures-with-inverse-distance-weighting", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11 ], "measurement_codes": [ 3, 8, 12, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Lokale Temperaturwerte mit inverser Distanzgewichtung interpolieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Lokale Temperaturwerte mit inverser Distanzgewichtung interpolieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Interpolating local temperatures with inverse-distance weighting", "methods": [ "Functions & modelling" ], "description": "Turn “Interpolating local temperatures with inverse-distance weighting” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 207, "source_index": 260, "id": "topic-260-analysing-bubble-distributions-in-bread-and-sparkling-drinks-with-a-po", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 5 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Analyse der Bläschenverteilung in Brot und Champagner (Poisson)", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Analyse der Bläschenverteilung in Brot und Champagner (Poisson)“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Culinary mathematics", "title": "Analysing bubble distributions in bread and sparkling drinks with a Poisson model", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “Analysing bubble distributions in bread and sparkling drinks with a Poisson model” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 208, "source_index": 498, "id": "topic-498-optimising-bottle-shape-for-material-use-and-stability", "category_key": "engineering-design-optimisation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 5, 11, 12 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Flaschenform zwischen Materialbedarf und Kippsicherheit optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Flaschenform zwischen Materialbedarf und Kippsicherheit optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Optimising bottle shape for material use and stability", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Optimising bottle shape for material use and stability” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 209, "source_index": 268, "id": "topic-268-temperature-gradients-in-a-classroom-from-floor-to-desk-height-and-cei", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 3, 4, 1, 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Temperaturgradienten in einem Klassenzimmer: Boden – Tischhöhe – Decke über einen Tag", "methods": [ "Funktionen & Modellierung", "Differentialrechnung" ], "description": "Formuliere zu „Temperaturgradienten in einem Klassenzimmer: Boden – Tischhöhe – Decke über einen Tag“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Temperature gradients in a classroom from floor to desk height and ceiling over a day", "methods": [ "Functions & modelling", "Differential calculus" ], "description": "Turn “Temperature gradients in a classroom from floor to desk height and ceiling over a day” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus" ] }, { "no": 210, "source_index": 508, "id": "topic-508-covering-a-contact-tracing-network-with-a-minimum-number-of-tests", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Abdeckung eines Kontaktverfolgungsnetzes mit minimalen Tests", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Optimierung" ], "description": "Formuliere zu „Abdeckung eines Kontaktverfolgungsnetzes mit minimalen Tests“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Covering a contact-tracing network with a minimum number of tests", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Optimisation" ], "description": "Turn “Covering a contact-tracing network with a minimum number of tests” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "optimization" ] }, { "no": 211, "source_index": 288, "id": "topic-288-absorption-rates-of-toilet-paper-kitchen-roll-and-newspaper", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2, 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Absorptionsrate verschiedener Papiersorten (Toilettenpapier, Küchenrolle, Zeitung)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Absorptionsrate verschiedener Papiersorten (Toilettenpapier, Küchenrolle, Zeitung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Absorption rates of toilet paper, kitchen roll and newspaper", "methods": [ "Functions & modelling" ], "description": "Turn “Absorption rates of toilet paper, kitchen roll and newspaper” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 212, "source_index": 518, "id": "topic-518-optimal-substitution-timing-using-a-hazard-model", "category_key": "sports-analytics-tactics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Optimaler Zeitpunkt für Auswechslungen mit einem Hazard-Modell", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimaler Zeitpunkt für Auswechslungen mit einem Hazard-Modell“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Optimal substitution timing using a hazard model", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimal substitution timing using a hazard model” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 213, "source_index": 308, "id": "topic-308-charging-and-discharging-capacitors-of-different-capacitances", "category_key": "electricity", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Elektrizität", "title": "Lade- und Entladekurve von Kondensatoren verschiedener Kapazität (100µF – 1000µF)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Lade- und Entladekurve von Kondensatoren verschiedener Kapazität (100µF – 1000µF)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Charging and discharging capacitors of different capacitances", "methods": [ "Functions & modelling" ], "description": "Turn “Charging and discharging capacitors of different capacitances” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 214, "source_index": 528, "id": "topic-528-wordle-strategies-using-entropy-and-information-gain", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Wordle-Strategien mit Entropie und Informationsgewinn", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wordle-Strategien mit Entropie und Informationsgewinn“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "Wordle strategies using entropy and information gain", "methods": [ "Geometry" ], "description": "Turn “Wordle strategies using entropy and information gain” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 215, "source_index": 328, "id": "topic-328-evaporation-mass-loss-versus-surface-temperature-in-wind-sun-and-shade", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 4, 1, 3 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Verdunstung: Masseverlust vs. Oberflächentemperatur (Wind, Sonne, Schatten)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Verdunstung: Masseverlust vs. Oberflächentemperatur (Wind, Sonne, Schatten)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Evaporation: mass loss versus surface temperature in wind, sun and shade", "methods": [ "Geometry" ], "description": "Turn “Evaporation: mass loss versus surface temperature in wind, sun and shade” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 216, "source_index": 538, "id": "topic-538-catalan-numbers-in-parenthesisations-and-lattice-paths", "category_key": "combinatorics-discrete-probability", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Catalan-Zahlen bei Klammerungen und Gitterpfaden", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Catalan-Zahlen bei Klammerungen und Gitterpfaden“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Catalan numbers in parenthesisations and lattice paths", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “Catalan numbers in parenthesisations and lattice paths” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 217, "source_index": 348, "id": "topic-348-yoghurt-fermentation-temperature-profile-and-mass-change", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2, 3, 16 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Joghurt-Gärung: Masse konstant? Temperaturverlauf im Joghurtbereiter", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Joghurt-Gärung: Masse konstant? Temperaturverlauf im Joghurtbereiter“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Yoghurt fermentation: temperature profile and mass change", "methods": [ "Functions & modelling" ], "description": "Turn “Yoghurt fermentation: temperature profile and mass change” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 218, "source_index": 548, "id": "topic-548-river-rating-curves-from-water-level-and-discharge", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 8, 12, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Abflusskurven eines Flusses aus Wasserstand und Durchfluss", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Abflusskurven eines Flusses aus Wasserstand und Durchfluss“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "River rating curves from water level and discharge", "methods": [ "Functions & modelling" ], "description": "Turn “River rating curves from water level and discharge” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 219, "source_index": 358, "id": "topic-358-heat-loss-from-buildings-using-facade-surface-temperature-measurements", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 2, 6 ], "measurement_codes": [ 4, 1, 3 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Wärmeverlust von Häusern: IR-Oberflächentemperatur verschiedener Fassadenmaterialien", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wärmeverlust von Häusern: IR-Oberflächentemperatur verschiedener Fassadenmaterialien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Heat loss from buildings using facade surface-temperature measurements", "methods": [ "Geometry" ], "description": "Turn “Heat loss from buildings using facade surface-temperature measurements” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 220, "source_index": 368, "id": "topic-368-reaction-time-and-naturally-observed-body-temperature-variation", "category_key": "physiology", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 3, 13, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Physiologie", "title": "Körpertemperatur und Leistungsfähigkeit: Reaktionstest bei verschiedenen Kerntemperaturen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Körpertemperatur und Leistungsfähigkeit: Reaktionstest bei verschiedenen Kerntemperaturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Physiology", "title": "Reaction time and naturally observed body-temperature variation", "methods": [ "Functions & modelling" ], "description": "Turn “Reaction time and naturally observed body-temperature variation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 221, "source_index": 373, "id": "topic-373-electrical-conductivity-of-pencil-lines-with-grades-from-2h-to-6b", "category_key": "materials", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 5, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Materialien", "title": "Elektrische Leitfähigkeit von Bleistiftstrichen verschiedener Härtegrade (2H – 6B)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Elektrische Leitfähigkeit von Bleistiftstrichen verschiedener Härtegrade (2H – 6B)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Materials", "title": "Electrical conductivity of pencil lines with grades from 2H to 6B", "methods": [ "Functions & modelling" ], "description": "Turn “Electrical conductivity of pencil lines with grades from 2H to 6B” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 222, "source_index": 5, "id": "topic-005-fibonacci-numbers-and-the-limiting-ratio-of-consecutive-terms", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Fibonacci-Zahlen und der Grenzwert aufeinanderfolgender Terme", "methods": [ "Zahlentheorie", "Folgen & Reihen", "Algebra" ], "description": "Formuliere zu „Fibonacci-Zahlen und der Grenzwert aufeinanderfolgender Terme“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Fibonacci numbers and the limiting ratio of consecutive terms", "methods": [ "Number theory", "Sequences & series", "Algebra" ], "description": "Turn “Fibonacci numbers and the limiting ratio of consecutive terms” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "sequences_series", "algebra" ] }, { "no": 223, "source_index": 25, "id": "topic-025-the-mathematics-of-rainbow-formation-snell-s-law-refraction-and-optimi", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Mathematik der Regenbogenbildung: Snellius, Brechung, Optimierung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Mathematik der Regenbogenbildung: Snellius, Brechung, Optimierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "The mathematics of rainbow formation: Snell's law, refraction and optimisation", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “The mathematics of rainbow formation: Snell's law, refraction and optimisation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 224, "source_index": 46, "id": "topic-046-statistical-bias-in-media-reporting", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 9, 12 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Statistische Verzerrung in Medienberichterstattung", "methods": [ "Stochastik" ], "description": "Entwickle aus „Statistische Verzerrung in Medienberichterstattung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Statistical bias in media reporting", "methods": [ "Statistics & probability" ], "description": "Turn “Statistical bias in media reporting” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 225, "source_index": 67, "id": "topic-067-traffic-flow-at-roundabouts-or-traffic-lights", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 0 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Mathematische Modellierung", "title": "Verkehrsfluss an Kreisverkehren oder Ampeln", "methods": [ "Funktionen & Modellierung", "Geometrie" ], "description": "Formuliere zu „Verkehrsfluss an Kreisverkehren oder Ampeln“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Traffic flow at roundabouts or traffic lights", "methods": [ "Functions & modelling", "Geometry" ], "description": "Turn “Traffic flow at roundabouts or traffic lights” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "geometry" ] }, { "no": 226, "source_index": 87, "id": "topic-087-using-vectors-to-model-three-dimensional-reflections-in-a-kaleidoscope", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 4 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Geometrie & Topologie", "title": "Vektoren zur Modellierung 3D-Spiegelungen im Kaleidoskop", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Geometrie" ], "description": "Formuliere zu „Vektoren zur Modellierung 3D-Spiegelungen im Kaleidoskop“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Using vectors to model three-dimensional reflections in a kaleidoscope", "methods": [ "Functions & modelling", "Vector mathematics", "Geometry" ], "description": "Turn “Using vectors to model three-dimensional reflections in a kaleidoscope” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "vectors", "geometry" ] }, { "no": 227, "source_index": 106, "id": "topic-106-an-introduction-to-the-black-scholes-model-for-option-pricing", "category_key": "financial-mathematics", "assessment_code": 2, "course_code": 5, "courses": [ "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI HL", "de": { "category": "Finanzmathematik", "title": "Black-Scholes-Modell für Optionspreise (einführend)", "methods": [ "Funktionen & Modellierung", "Finanzmathematik" ], "description": "Formuliere zu „Black-Scholes-Modell für Optionspreise (einführend)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "An introduction to the Black-Scholes model for option pricing", "methods": [ "Functions & modelling", "Financial mathematics" ], "description": "Turn “An introduction to the Black-Scholes model for option pricing” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "financial_math" ] }, { "no": 228, "source_index": 123, "id": "topic-123-truth-tables-and-their-minimisation", "category_key": "logic-set-theory-proof", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 7 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung von Wahrheitstabellen und deren Minimierung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Beweisführung" ], "description": "Formuliere zu „Untersuchung von Wahrheitstabellen und deren Minimierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "Truth tables and their minimisation", "methods": [ "Functions & modelling", "Differential calculus", "Proof" ], "description": "Turn “Truth tables and their minimisation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "proof" ] }, { "no": 229, "source_index": 138, "id": "topic-138-heuristics-for-the-travelling-salesperson-problem", "category_key": "discrete-mathematics-computer-science", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 8 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Untersuchung der Traveling-Salesman-Problem-Heuristiken", "methods": [ "Geometrie", "Simulation & Algorithmen" ], "description": "Formuliere zu „Untersuchung der Traveling-Salesman-Problem-Heuristiken“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Heuristics for the travelling salesperson problem", "methods": [ "Geometry", "Simulation & algorithms" ], "description": "Turn “Heuristics for the travelling salesperson problem” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "simulation" ] }, { "no": 230, "source_index": 148, "id": "topic-148-analysing-the-efficiency-of-water-pumps", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Analyse der Effizienz von Wasserpumpen", "methods": [ "Optimierung" ], "description": "Formuliere zu „Analyse der Effizienz von Wasserpumpen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Analysing the efficiency of water pumps", "methods": [ "Optimisation" ], "description": "Turn “Analysing the efficiency of water pumps” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "optimization" ] }, { "no": 231, "source_index": 164, "id": "topic-164-the-mathematics-behind-bidding-strategies-in-the-price-is-right", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7, 8 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Die Mathematik hinter „Price is Right“-Bietstrategien", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Die Mathematik hinter „Price is Right“-Bietstrategien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "The mathematics behind bidding strategies in The Price Is Right", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics behind bidding strategies in The Price Is Right” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 232, "source_index": 379, "id": "topic-379-propagation-of-traffic-waves-in-stop-and-go-congestion", "category_key": "transport-mobility-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Ausbreitung von Verkehrswellen im Stop-and-go-Verkehr", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Ausbreitung von Verkehrswellen im Stop-and-go-Verkehr“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Propagation of traffic waves in stop-and-go congestion", "methods": [ "Trigonometry" ], "description": "Turn “Propagation of traffic waves in stop-and-go congestion” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 233, "source_index": 172, "id": "topic-172-bmi-and-its-statistical-validity-across-different-populations", "category_key": "biomathematics-medicine", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Berechnung des BMI und dessen statistische Aussagekraft in verschiedenen Populationen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Berechnung des BMI und dessen statistische Aussagekraft in verschiedenen Populationen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "BMI and its statistical validity across different populations", "methods": [ "Functions & modelling" ], "description": "Turn “BMI and its statistical validity across different populations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 234, "source_index": 391, "id": "topic-391-investigating-project-completion-times-with-pert-and-monte-carlo-simulation", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Projektlaufzeiten mit PERT und Monte-Carlo-Simulation untersuchen", "methods": [ "Geometrie", "Simulation & Algorithmen" ], "description": "Formuliere zu „Projektlaufzeiten mit PERT und Monte-Carlo-Simulation untersuchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Investigating project completion times with PERT and Monte Carlo simulation", "methods": [ "Geometry", "Simulation & algorithms" ], "description": "Turn “Investigating project completion times with PERT and Monte Carlo simulation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "simulation" ] }, { "no": 235, "source_index": 182, "id": "topic-182-correlation-between-air-quality-and-asthma-incidence", "category_key": "environmental-mathematics-sustainability", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6, 9, 10 ], "measurement_codes": [ 12 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Untersuchung der Korrelation zwischen Luftqualität und Asthmafällen", "methods": [ "Funktionen & Modellierung", "Regression" ], "description": "Entwickle aus „Untersuchung der Korrelation zwischen Luftqualität und Asthmafällen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Correlation between air quality and asthma incidence", "methods": [ "Functions & modelling", "Regression" ], "description": "Turn “Correlation between air quality and asthma incidence” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression" ] }, { "no": 236, "source_index": 403, "id": "topic-403-applying-pagerank-to-a-scientific-citation-network", "category_key": "networks-social-systems", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "PageRank auf einem wissenschaftlichen Zitationsnetzwerk", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „PageRank auf einem wissenschaftlichen Zitationsnetzwerk“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Applying PageRank to a scientific citation network", "methods": [ "Graph theory" ], "description": "Turn “Applying PageRank to a scientific citation network” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 237, "source_index": 192, "id": "topic-192-mathematical-analysis-of-the-magnus-effect-in-a-football-free-kick", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Mathematische Analyse des Magnus-Effekts beim Fußball-Freistoß", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematische Analyse des Magnus-Effekts beim Fußball-Freistoß“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Mathematical analysis of the Magnus effect in a football free kick", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical analysis of the Magnus effect in a football free kick” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 238, "source_index": 415, "id": "topic-415-image-complexity-and-achievable-compression-ratio", "category_key": "information-coding-theory", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 11 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Bildkomplexität und erreichbare Kompressionsrate", "methods": [ "Geometrie" ], "description": "Formuliere zu „Bildkomplexität und erreichbare Kompressionsrate“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Image complexity and achievable compression ratio", "methods": [ "Geometry" ], "description": "Turn “Image complexity and achievable compression ratio” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 239, "source_index": 202, "id": "topic-202-modelling-netflix-style-recommendations-with-simple-distance-measures", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 8 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Modellierung von Netflix-Empfehlungen durch einfache Distanzmaße", "methods": [ "Funktionen & Modellierung", "Simulation & Algorithmen" ], "description": "Formuliere zu „Modellierung von Netflix-Empfehlungen durch einfache Distanzmaße“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Modelling Netflix-style recommendations with simple distance measures", "methods": [ "Functions & modelling", "Simulation & algorithms" ], "description": "Turn “Modelling Netflix-style recommendations with simple distance measures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "simulation" ] }, { "no": 240, "source_index": 427, "id": "topic-427-position-estimation-by-trilateration-with-ultrasonic-sensors", "category_key": "robotics-control-sensing", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 7, 11 ], "measurement_codes": [ 1, 13, 20, 21 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Ortsbestimmung durch Trilateration mit Ultraschallsensoren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Ortsbestimmung durch Trilateration mit Ultraschallsensoren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Position estimation by trilateration with ultrasonic sensors", "methods": [ "Functions & modelling" ], "description": "Turn “Position estimation by trilateration with ultrasonic sensors” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 241, "source_index": 212, "id": "topic-212-modelling-population-fluctuations-with-discrete-dynamical-systems", "category_key": "chaos-dynamical-systems", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Modellierung von Populationsschwankungen mit diskreten dynamischen Systemen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung von Populationsschwankungen mit diskreten dynamischen Systemen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "Modelling population fluctuations with discrete dynamical systems", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling population fluctuations with discrete dynamical systems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 242, "source_index": 439, "id": "topic-439-investigating-facial-landmark-symmetry-with-anonymised-images", "category_key": "image-processing-computer-graphics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Symmetrie von Gesichtslandmarken mit anonymisierten Bildern untersuchen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Symmetrie von Gesichtslandmarken mit anonymisierten Bildern untersuchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Investigating facial-landmark symmetry with anonymised images", "methods": [ "Functions & modelling" ], "description": "Turn “Investigating facial-landmark symmetry with anonymised images” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 243, "source_index": 219, "id": "topic-219-sound-propagation-through-different-materials", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Untersuchung der Ausbreitung von Schall in verschiedenen Materialien", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Untersuchung der Ausbreitung von Schall in verschiedenen Materialien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Sound propagation through different materials", "methods": [ "Trigonometry" ], "description": "Turn “Sound propagation through different materials” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 244, "source_index": 449, "id": "topic-449-levenshtein-distances-between-regional-spelling-variants", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Levenshtein-Distanzen zwischen regionalen Schreibvarianten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Levenshtein-Distanzen zwischen regionalen Schreibvarianten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Levenshtein distances between regional spelling variants", "methods": [ "Functions & modelling" ], "description": "Turn “Levenshtein distances between regional spelling variants” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 245, "source_index": 228, "id": "topic-228-modelling-wave-patterns-in-textile-design", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Modellierung von Wellenmustern in der Textilgestaltung", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ], "description": "Formuliere zu „Modellierung von Wellenmustern in der Textilgestaltung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Modelling wave patterns in textile design", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ], "description": "Turn “Modelling wave patterns in textile design” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ] }, { "no": 246, "source_index": 459, "id": "topic-459-a-mathematical-comparison-of-grade-normalisation-methods", "category_key": "education-learning-analytics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Methoden zur Notennormalisierung mathematisch vergleichen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Methoden zur Notennormalisierung mathematisch vergleichen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "A mathematical comparison of grade-normalisation methods", "methods": [ "Functions & modelling" ], "description": "Turn “A mathematical comparison of grade-normalisation methods” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 247, "source_index": 237, "id": "topic-237-mathematical-patterns-in-planetary-resonances", "category_key": "astronomy-spaceflight", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Analyse der mathematischen Muster in Planetenresonanzen", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Analyse der mathematischen Muster in Planetenresonanzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Mathematical patterns in planetary resonances", "methods": [ "Trigonometry" ], "description": "Turn “Mathematical patterns in planetary resonances” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 248, "source_index": 469, "id": "topic-469-optimal-bidding-in-a-first-price-auction-under-risk-aversion", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Optimales Gebot in einer Erstpreisauktion bei Risikoaversion", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimales Gebot in einer Erstpreisauktion bei Risikoaversion“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Optimal bidding in a first-price auction under risk aversion", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimal bidding in a first-price auction under risk aversion” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 249, "source_index": 245, "id": "topic-245-modelling-decision-fatigue-with-probability-models", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 5, "courses": [ "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, HL", "de": { "category": "Psychologie & Kognition", "title": "Modellierung der Entscheidungsmüdigkeit durch Wahrscheinlichkeitsmodelle", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Modellierung der Entscheidungsmüdigkeit durch Wahrscheinlichkeitsmodelle“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Psychology & cognition", "title": "Modelling decision fatigue with probability models", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “Modelling decision fatigue with probability models” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 250, "source_index": 479, "id": "topic-479-autocorrelation-of-heart-rate-during-interval-training", "category_key": "time-series-forecasting", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 8, 13, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Autokorrelation der Herzfrequenz beim Intervalltraining", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Autokorrelation der Herzfrequenz beim Intervalltraining“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Autocorrelation of heart rate during interval training", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Sequences & series", "Time-series analysis" ], "description": "Turn “Autocorrelation of heart rate during interval training” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "trigonometry", "sequences_series", "time_series" ] }, { "no": 251, "source_index": 253, "id": "topic-253-the-probability-of-natural-disasters-at-a-particular-location", "category_key": "probability-risk", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Untersuchung der Wahrscheinlichkeit von Naturkatastrophen an einem Ort", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Wahrscheinlichkeit von Naturkatastrophen an einem Ort“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "The probability of natural disasters at a particular location", "methods": [ "Statistics & probability" ], "description": "Turn “The probability of natural disasters at a particular location” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 252, "source_index": 489, "id": "topic-489-investigating-voronoi-service-areas-for-fire-stations", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 11, 12 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Voronoi-Versorgungsgebiete von Feuerwachen untersuchen", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Voronoi-Versorgungsgebiete von Feuerwachen untersuchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Investigating Voronoi service areas for fire stations", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “Investigating Voronoi service areas for fire stations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 253, "source_index": 261, "id": "topic-261-modelling-fermentation-in-bread-and-yoghurt-with-exponential-growth", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Modellierung des Gärvorgangs bei Brot und Joghurt (exponentielles Wachstum)", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Modellierung des Gärvorgangs bei Brot und Joghurt (exponentielles Wachstum)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "Modelling fermentation in bread and yoghurt with exponential growth", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling fermentation in bread and yoghurt with exponential growth” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 254, "source_index": 499, "id": "topic-499-optimising-the-placement-of-acoustic-panels-in-a-room", "category_key": "engineering-design-optimisation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 11 ], "measurement_codes": [ 1, 9, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Positionierung von Akustikpaneelen in einem Raum optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Positionierung von Akustikpaneelen in einem Raum optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Optimising the placement of acoustic panels in a room", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising the placement of acoustic panels in a room” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 255, "source_index": 269, "id": "topic-269-cooling-curves-of-aluminium-copper-and-iron-from-the-same-starting-tem", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Abkühlkurven verschiedener Metalle (Aluminium, Kupfer, Eisen) von gleicher Starttemperatur", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ], "description": "Formuliere zu „Abkühlkurven verschiedener Metalle (Aluminium, Kupfer, Eisen) von gleicher Starttemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Cooling curves of aluminium, copper and iron from the same starting temperature", "methods": [ "Functions & modelling", "Differential equations" ], "description": "Turn “Cooling curves of aluminium, copper and iron from the same starting temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations" ] }, { "no": 256, "source_index": 509, "id": "topic-509-a-queueing-model-for-hospital-beds", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Warteschlangenmodell für Krankenhausbetten", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Warteschlangenmodell für Krankenhausbetten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Epidemiology & public health", "title": "A queueing model for hospital beds", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “A queueing model for hospital beds” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 257, "source_index": 289, "id": "topic-289-osmosis-mass-change-of-potato-slices-in-salt-solutions-from-0-to-20", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2, 13, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Osmose: Masseänderung von Kartoffelscheiben in Salzlösungen (0% – 20%)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Osmose: Masseänderung von Kartoffelscheiben in Salzlösungen (0% – 20%)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Osmosis: mass change of potato slices in salt solutions from 0% to 20%", "methods": [ "Functions & modelling" ], "description": "Turn “Osmosis: mass change of potato slices in salt solutions from 0% to 20%” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 258, "source_index": 519, "id": "topic-519-residual-errors-in-a-mathematical-model-of-baseball-pitches", "category_key": "sports-analytics-tactics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 7, 11, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Restfehler eines mathematischen Modells für Baseballwürfe", "methods": [ "Funktionen & Modellierung", "Regression" ], "description": "Entwickle aus „Restfehler eines mathematischen Modells für Baseballwürfe“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Sports analytics & tactics", "title": "Residual errors in a mathematical model of baseball pitches", "methods": [ "Functions & modelling", "Regression" ], "description": "Turn “Residual errors in a mathematical model of baseball pitches” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression" ] }, { "no": 259, "source_index": 309, "id": "topic-309-electrical-conductivity-of-water-juice-cola-and-salt-water", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 11, 13, 16 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Elektrische Leitfähigkeit verschiedener Getränke (Wasser, Saft, Cola, Salzwasser)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Elektrische Leitfähigkeit verschiedener Getränke (Wasser, Saft, Cola, Salzwasser)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Electrical conductivity of water, juice, cola and salt water", "methods": [ "Functions & modelling" ], "description": "Turn “Electrical conductivity of water, juice, cola and salt water” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 260, "source_index": 529, "id": "topic-529-the-combinatorial-structure-of-the-card-game-set", "category_key": "recreational-games-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 8, 10 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Kombinatorische Struktur des Kartenspiels SET", "methods": [ "Kombinatorik" ], "description": "Die Idee „Kombinatorische Struktur des Kartenspiels SET“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Recreational games & mathematics", "title": "The combinatorial structure of the card game SET", "methods": [ "Combinatorics" ], "description": "Develop “The combinatorial structure of the card game SET” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "combinatorics" ] }, { "no": 261, "source_index": 329, "id": "topic-329-freezing-point-depression-dissolved-salt-or-sugar-mass-versus-minimum-", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 13, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Gefrierpunktserniedrigung: Masse Salz/Zucker vs. erreichte Minimaltemperatur", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Gefrierpunktserniedrigung: Masse Salz/Zucker vs. erreichte Minimaltemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Freezing-point depression: dissolved salt or sugar mass versus minimum temperature", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Freezing-point depression: dissolved salt or sugar mass versus minimum temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 262, "source_index": 539, "id": "topic-539-computational-investigation-of-small-ramsey-numbers", "category_key": "combinatorics-discrete-probability", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Kleine Ramsey-Zahlen computergestützt untersuchen", "methods": [ "Stochastik", "Kombinatorik", "Simulation & Algorithmen" ], "description": "Die Idee „Kleine Ramsey-Zahlen computergestützt untersuchen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Computational investigation of small Ramsey numbers", "methods": [ "Statistics & probability", "Combinatorics", "Simulation & algorithms" ], "description": "Develop “Computational investigation of small Ramsey numbers” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics", "simulation" ] }, { "no": 263, "source_index": 349, "id": "topic-349-water-and-mass-loss-from-cheese-or-cured-food-during-refrigerated-stor", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Wurst/Käse: Wasserverlust und Gewichtsverlust im Kühlschrank über eine Woche", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wurst/Käse: Wasserverlust und Gewichtsverlust im Kühlschrank über eine Woche“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Water and mass loss from cheese or cured food during refrigerated storage", "methods": [ "Functions & modelling" ], "description": "Turn “Water and mass loss from cheese or cured food during refrigerated storage” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 264, "source_index": 549, "id": "topic-549-the-gutenbergrichter-law-for-earthquake-frequencies", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Gutenberg-Richter-Gesetz für Erdbebenhäufigkeiten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Gutenberg-Richter-Gesetz für Erdbebenhäufigkeiten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "The Gutenberg–Richter law for earthquake frequencies", "methods": [ "Functions & modelling" ], "description": "Turn “The Gutenberg–Richter law for earthquake frequencies” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 265, "source_index": 359, "id": "topic-359-algal-growth-biomass-and-aquarium-water-temperature-over-time", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 6, 13 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Algenwachstum: Biomasse (Masse) und Wassertemperatur im Aquarium über Zeit", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Algenwachstum: Biomasse (Masse) und Wassertemperatur im Aquarium über Zeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Environment", "title": "Algal growth: biomass and aquarium-water temperature over time", "methods": [ "Time-series analysis" ], "description": "Turn “Algal growth: biomass and aquarium-water temperature over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 266, "source_index": 6, "id": "topic-006-number-systems-and-modular-arithmetic-in-computer-science", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Zahlensysteme und modulare Arithmetik in der Informatik", "methods": [ "Zahlentheorie", "Geometrie", "Algebra" ], "description": "Die Idee „Zahlensysteme und modulare Arithmetik in der Informatik“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "Number systems and modular arithmetic in computer science", "methods": [ "Number theory", "Geometry", "Algebra" ], "description": "Develop “Number systems and modular arithmetic in computer science” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "geometry", "algebra" ] }, { "no": 267, "source_index": 26, "id": "topic-026-modelling-roller-coaster-curves-with-cubic-and-quintic-functions", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Achterbahnkurven modellieren mit kubischen/quintischen Funktionen", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Achterbahnkurven modellieren mit kubischen/quintischen Funktionen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Modelling roller-coaster curves with cubic and quintic functions", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling roller-coaster curves with cubic and quintic functions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 268, "source_index": 47, "id": "topic-047-correlation-between-study-time-and-predicted-ib-grades", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 4, "courses": [ "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Korrelation: Lernstunden und vorhergesagte IB-Noten", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression" ], "description": "Entwickle aus „Korrelation: Lernstunden und vorhergesagte IB-Noten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Correlation between study time and predicted IB grades", "methods": [ "Functions & modelling", "Statistics & probability", "Regression" ], "description": "Turn “Correlation between study time and predicted IB grades” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "regression" ] }, { "no": 269, "source_index": 68, "id": "topic-068-the-mathematics-of-music-frequency-ratios-and-overtones", "category_key": "mathematical-modelling", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Mathematik der Musik: Frequenzverhältnisse, Obertöne", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Fourier-Analyse" ], "description": "Formuliere zu „Mathematik der Musik: Frequenzverhältnisse, Obertöne“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "The mathematics of music: frequency ratios and overtones", "methods": [ "Functions & modelling", "Trigonometry", "Fourier analysis" ], "description": "Turn “The mathematics of music: frequency ratios and overtones” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry", "fourier_analysis" ] }, { "no": 270, "source_index": 88, "id": "topic-088-non-euclidean-geometry-angle-sums-on-a-sphere-and-a-hyperbolic-surface", "category_key": "geometry-topology", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Geometrie & Topologie", "title": "Nicht-euklidische Geometrie: Winkelsumme auf Kugel/Hyperboloid", "methods": [ "Trigonometrie", "Geometrie" ], "description": "Formuliere zu „Nicht-euklidische Geometrie: Winkelsumme auf Kugel/Hyperboloid“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Non-Euclidean geometry: angle sums on a sphere and a hyperbolic surface", "methods": [ "Trigonometry", "Geometry" ], "description": "Turn “Non-Euclidean geometry: angle sums on a sphere and a hyperbolic surface” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "geometry" ] }, { "no": 271, "source_index": 107, "id": "topic-107-returns-across-different-types-of-investment", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 9 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Untersuchung der Rendite verschiedener Anlageformen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Rendite verschiedener Anlageformen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Returns across different types of investment", "methods": [ "Geometry" ], "description": "Turn “Returns across different types of investment” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 272, "source_index": 124, "id": "topic-124-different-proofs-that-there-are-infinitely-many-primes", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Beweis der Unendlichkeit der Primzahlen (verschiedene Beweise)", "methods": [ "Zahlentheorie", "Beweisführung" ], "description": "Die Idee „Beweis der Unendlichkeit der Primzahlen (verschiedene Beweise)“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Different proofs that there are infinitely many primes", "methods": [ "Number theory", "Proof" ], "description": "Develop “Different proofs that there are infinitely many primes” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "proof" ] }, { "no": 273, "source_index": 139, "id": "topic-139-hash-functions-and-collisions", "category_key": "discrete-mathematics-computer-science", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Analyse von Hash-Funktionen und Kollisionen", "methods": [ "Geometrie", "Algebra" ], "description": "Formuliere zu „Analyse von Hash-Funktionen und Kollisionen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Hash functions and collisions", "methods": [ "Geometry", "Algebra" ], "description": "Turn “Hash functions and collisions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "algebra" ] }, { "no": 274, "source_index": 149, "id": "topic-149-the-mathematics-of-photography-exposure-and-aperture", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 8 ], "measurement_codes": [ 7, 10 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Untersuchung der Mathematik hinter Fotografie (Belichtung, Blende)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Mathematik hinter Fotografie (Belichtung, Blende)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "The mathematics of photography: exposure and aperture", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of photography: exposure and aperture” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 275, "source_index": 165, "id": "topic-165-zero-sum-games-in-classic-board-games", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Untersuchung von Zero-Sum-Games in klassischen Brettspielen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung von Zero-Sum-Games in klassischen Brettspielen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "Zero-sum games in classic board games", "methods": [ "Functions & modelling" ], "description": "Turn “Zero-sum games in classic board games” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 276, "source_index": 380, "id": "topic-380-optimising-signal-phases-at-a-four-way-intersection", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11 ], "measurement_codes": [ 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Optimierung der Ampelphasen an einer vierarmigen Kreuzung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimierung der Ampelphasen an einer vierarmigen Kreuzung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Optimising signal phases at a four-way intersection", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising signal phases at a four-way intersection” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 277, "source_index": 173, "id": "topic-173-correlation-between-sleep-duration-and-cognitive-performance", "category_key": "biomathematics-medicine", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Untersuchung der Korrelation zwischen Schlafdauer und kognitiver Leistung", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ], "description": "Entwickle aus „Untersuchung der Korrelation zwischen Schlafdauer und kognitiver Leistung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Biomathematics & medicine", "title": "Correlation between sleep duration and cognitive performance", "methods": [ "Functions & modelling", "Regression", "Geometry" ], "description": "Turn “Correlation between sleep duration and cognitive performance” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "geometry" ] }, { "no": 278, "source_index": 392, "id": "topic-392-multi-objective-optimisation-of-delivery-time-and-carbon-emissions", "category_key": "operations-research-logistics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Mehrzieloptimierung von Lieferzeit und CO₂-Ausstoß", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Mehrzieloptimierung von Lieferzeit und CO₂-Ausstoß“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Multi-objective optimisation of delivery time and carbon emissions", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Multi-objective optimisation of delivery time and carbon emissions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 279, "source_index": 183, "id": "topic-183-modelling-plastic-degradation-in-oceans-with-exponential-decay", "category_key": "environmental-mathematics-sustainability", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Modellierung des Plastikabbaus in Ozeanen durch exponentielle Zerfallsmodelle", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Modellierung des Plastikabbaus in Ozeanen durch exponentielle Zerfallsmodelle“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Modelling plastic degradation in oceans with exponential decay", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling plastic degradation in oceans with exponential decay” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 280, "source_index": 404, "id": "topic-404-assortativity-in-passing-networks-from-team-sports", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 7, 9 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Assortativität in Passnetzwerken von Mannschaftssportarten", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Assortativität in Passnetzwerken von Mannschaftssportarten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Assortativity in passing networks from team sports", "methods": [ "Graph theory" ], "description": "Turn “Assortativity in passing networks from team sports” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 281, "source_index": 193, "id": "topic-193-modelling-an-optimal-stride-pattern-for-the-100-metre-sprint", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Modellierung der optimalen Schrittfolge beim 100-Meter-Lauf", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Folgen & Reihen", "Optimierung" ], "description": "Formuliere zu „Modellierung der optimalen Schrittfolge beim 100-Meter-Lauf“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Modelling an optimal stride pattern for the 100-metre sprint", "methods": [ "Functions & modelling", "Differential calculus", "Sequences & series", "Optimisation" ], "description": "Turn “Modelling an optimal stride pattern for the 100-metre sprint” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "sequences_series", "optimization" ] }, { "no": 282, "source_index": 416, "id": "topic-416-collision-probabilities-for-simple-checksums", "category_key": "information-coding-theory", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Kollisionswahrscheinlichkeit einfacher Prüfsummen", "methods": [ "Stochastik", "Geometrie" ], "description": "Entwickle aus „Kollisionswahrscheinlichkeit einfacher Prüfsummen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Information & coding theory", "title": "Collision probabilities for simple checksums", "methods": [ "Statistics & probability", "Geometry" ], "description": "Turn “Collision probabilities for simple checksums” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry" ] }, { "no": 283, "source_index": 203, "id": "topic-203-cluster-formation-in-friendship-networks", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Untersuchung der Clusterbildung in Freundschaftsnetzwerken", "methods": [ "Graphentheorie", "Geometrie", "Simulation & Algorithmen" ], "description": "Formuliere zu „Untersuchung der Clusterbildung in Freundschaftsnetzwerken“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Cluster formation in friendship networks", "methods": [ "Graph theory", "Geometry", "Simulation & algorithms" ], "description": "Turn “Cluster formation in friendship networks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry", "simulation" ] }, { "no": 284, "source_index": 428, "id": "topic-428-stability-of-a-simplified-self-balancing-robot-model", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 11 ], "measurement_codes": [ 13, 20 ], "safety_code": 1, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Stabilität eines vereinfachten Modells für einen selbstbalancierenden Roboter", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Stabilität eines vereinfachten Modells für einen selbstbalancierenden Roboter“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Stability of a simplified self-balancing robot model", "methods": [ "Functions & modelling" ], "description": "Turn “Stability of a simplified self-balancing robot model” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 285, "source_index": 213, "id": "topic-213-arnold-tongues-in-the-circle-map", "category_key": "chaos-dynamical-systems", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 8, 10 ], "measurement_codes": [ 9, 14 ], "safety_code": 3, "source_course_label": "AA HL", "de": { "category": "Chaos & Dynamische Systeme", "title": "Untersuchung der Arnold-Zungen in der Kreisabbildung", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Arnold-Zungen in der Kreisabbildung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Chaos & dynamical systems", "title": "Arnold tongues in the circle map", "methods": [ "Geometry" ], "description": "Turn “Arnold tongues in the circle map” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 286, "source_index": 440, "id": "topic-440-the-discrete-cosine-transform-in-jpeg-compression", "category_key": "image-processing-computer-graphics", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Diskrete Kosinustransformation bei der JPEG-Kompression", "methods": [ "Trigonometrie", "Geometrie" ], "description": "Formuliere zu „Diskrete Kosinustransformation bei der JPEG-Kompression“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "The discrete cosine transform in JPEG compression", "methods": [ "Trigonometry", "Geometry" ], "description": "Turn “The discrete cosine transform in JPEG compression” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "geometry" ] }, { "no": 287, "source_index": 220, "id": "topic-220-modelling-vibrato-frequency-and-its-perception", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 9, 13, 14 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Modellierung der Vibrato-Frequenz und ihrer Wahrnehmung", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ], "description": "Formuliere zu „Modellierung der Vibrato-Frequenz und ihrer Wahrnehmung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Modelling vibrato frequency and its perception", "methods": [ "Functions & modelling", "Trigonometry" ], "description": "Turn “Modelling vibrato frequency and its perception” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry" ] }, { "no": 288, "source_index": 450, "id": "topic-450-n-gram-entropy-in-texts-by-different-authors", "category_key": "language-text-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 8, 9, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "N-Gramm-Entropie in Texten verschiedener Autorinnen und Autoren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „N-Gramm-Entropie in Texten verschiedener Autorinnen und Autoren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "N-gram entropy in texts by different authors", "methods": [ "Functions & modelling" ], "description": "Turn “N-gram entropy in texts by different authors” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 289, "source_index": 229, "id": "topic-229-analysing-proportions-in-fashion-clothing-sizes-and-golden-ratio-claim", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 9 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Analyse der Proportionen in der Modewelt (Kleidergrößen, Golden Ratio)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Analyse der Proportionen in der Modewelt (Kleidergrößen, Golden Ratio)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Analysing proportions in fashion: clothing sizes and golden-ratio claims", "methods": [ "Geometry" ], "description": "Turn “Analysing proportions in fashion: clothing sizes and golden-ratio claims” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 290, "source_index": 460, "id": "topic-460-bootstrap-confidence-intervals-for-small-learning-groups", "category_key": "education-learning-analytics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 7, 12 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Bootstrap-Konfidenzintervalle für kleine Lerngruppen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Bootstrap-Konfidenzintervalle für kleine Lerngruppen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Education & learning analytics", "title": "Bootstrap confidence intervals for small learning groups", "methods": [ "Statistics & probability" ], "description": "Turn “Bootstrap confidence intervals for small learning groups” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 291, "source_index": 238, "id": "topic-238-calculating-optimal-launch-windows-with-hohmann-transfers", "category_key": "astronomy-spaceflight", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Berechnung der optimalen Startfenster für Raumfahrtmissionen (Hohmann-Transfer)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Startfenster für Raumfahrtmissionen (Hohmann-Transfer)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Astronomy & spaceflight", "title": "Calculating optimal launch windows with Hohmann transfers", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating optimal launch windows with Hohmann transfers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 292, "source_index": 470, "id": "topic-470-investigating-volatility-clustering-in-exchange-rate-data", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Volatilitätscluster in Wechselkursdaten untersuchen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Volatilitätscluster in Wechselkursdaten untersuchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Investigating volatility clustering in exchange-rate data", "methods": [ "Functions & modelling" ], "description": "Turn “Investigating volatility clustering in exchange-rate data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 293, "source_index": 246, "id": "topic-246-correlation-between-music-genre-and-mathematical-performance", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 8 ], "measurement_codes": [ 9, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Analyse der Korrelation zwischen Musikgenre und mathematischer Leistung", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ], "description": "Entwickle aus „Analyse der Korrelation zwischen Musikgenre und mathematischer Leistung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Psychology & cognition", "title": "Correlation between music genre and mathematical performance", "methods": [ "Functions & modelling", "Regression", "Geometry" ], "description": "Turn “Correlation between music genre and mathematical performance” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "geometry" ] }, { "no": 294, "source_index": 480, "id": "topic-480-bootstrap-prediction-intervals-for-short-time-series", "category_key": "time-series-forecasting", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Bootstrap-Prognoseintervalle für kurze Zeitreihen", "methods": [ "Funktionen & Modellierung", "Regression", "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Bootstrap-Prognoseintervalle für kurze Zeitreihen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Bootstrap prediction intervals for short time series", "methods": [ "Functions & modelling", "Regression", "Sequences & series", "Time-series analysis" ], "description": "Turn “Bootstrap prediction intervals for short time series” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "sequences_series", "time_series" ] }, { "no": 295, "source_index": 254, "id": "topic-254-modelling-cafeteria-queues-with-a-poisson-process", "category_key": "probability-risk", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Modellierung der Warteschlangen an der Cafeteria durch Poisson-Verteilung", "methods": [ "Funktionen & Modellierung", "Stochastik" ], "description": "Entwickle aus „Modellierung der Warteschlangen an der Cafeteria durch Poisson-Verteilung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Modelling cafeteria queues with a Poisson process", "methods": [ "Functions & modelling", "Statistics & probability" ], "description": "Turn “Modelling cafeteria queues with a Poisson process” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics" ] }, { "no": 296, "source_index": 490, "id": "topic-490-spatial-autocorrelation-of-house-prices-using-morans-i", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Räumliche Autokorrelation von Immobilienpreisen mit Moran’s I", "methods": [ "Funktionen & Modellierung", "Regression" ], "description": "Entwickle aus „Räumliche Autokorrelation von Immobilienpreisen mit Moran’s I“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Spatial autocorrelation of house prices using Moran’s I", "methods": [ "Functions & modelling", "Regression" ], "description": "Turn “Spatial autocorrelation of house prices using Moran’s I” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression" ] }, { "no": 297, "source_index": 262, "id": "topic-262-calculating-an-optimal-chocolate-melting-temperature", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 3, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Berechnung der optimalen Schokoladen-Schmelztemperatur", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Schokoladen-Schmelztemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "Calculating an optimal chocolate-melting temperature", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating an optimal chocolate-melting temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 298, "source_index": 500, "id": "topic-500-a-daily-angle-schedule-for-a-single-axis-solar-tracker", "category_key": "engineering-design-optimisation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 7, 11 ], "measurement_codes": [ 5, 10, 13, 20 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Tagesplan für den Winkel eines einachsigen Solartrackers", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Zeitreihenanalyse", "Optimierung" ], "description": "Entwickle aus „Tagesplan für den Winkel eines einachsigen Solartrackers“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Engineering design & optimisation", "title": "A daily angle schedule for a single-axis solar tracker", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Time-series analysis", "Optimisation" ], "description": "Turn “A daily angle schedule for a single-axis solar tracker” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "time_series", "optimization" ] }, { "no": 299, "source_index": 270, "id": "topic-270-heat-storage-in-sand-clay-and-humus-under-equal-energy-input", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 3, 4, 1 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmespeicherung von Bodenproben (Sand, Lehm, Humus) bei gleicher Energiezufuhr", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmespeicherung von Bodenproben (Sand, Lehm, Humus) bei gleicher Energiezufuhr“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Heat storage in sand, clay and humus under equal energy input", "methods": [ "Functions & modelling" ], "description": "Turn “Heat storage in sand, clay and humus under equal energy input” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 300, "source_index": 510, "id": "topic-510-modelling-seasonal-influenza-with-harmonic-functions", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Saisonale Influenza mit harmonischen Funktionen modellieren", "methods": [ "Funktionen & Modellierung", "Algebra" ], "description": "Formuliere zu „Saisonale Influenza mit harmonischen Funktionen modellieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Modelling seasonal influenza with harmonic functions", "methods": [ "Functions & modelling", "Algebra" ], "description": "Turn “Modelling seasonal influenza with harmonic functions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "algebra" ] }, { "no": 301, "source_index": 290, "id": "topic-290-corrosion-of-iron-nails-in-water-salt-water-cola-and-vinegar", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 2, 6, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Korrosion von Eisennägeln in verschiedenen Medien (Wasser, Salzwasser, Cola, Essig)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Korrosion von Eisennägeln in verschiedenen Medien (Wasser, Salzwasser, Cola, Essig)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Corrosion of iron nails in water, salt water, cola and vinegar", "methods": [ "Functions & modelling" ], "description": "Turn “Corrosion of iron nails in water, salt water, cola and vinegar” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 302, "source_index": 520, "id": "topic-520-cycling-power-as-a-function-of-gradient-and-speed", "category_key": "sports-analytics-tactics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11 ], "measurement_codes": [ 8, 13, 19 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Radsportleistung in Abhängigkeit von Steigung und Geschwindigkeit", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Algebra" ], "description": "Formuliere zu „Radsportleistung in Abhängigkeit von Steigung und Geschwindigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Cycling power as a function of gradient and speed", "methods": [ "Functions & modelling", "Differential calculus", "Algebra" ], "description": "Turn “Cycling power as a function of gradient and speed” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "algebra" ] }, { "no": 303, "source_index": 310, "id": "topic-310-voltage-from-homemade-galvanic-cells-using-lemons-potatoes-cola-and-ap", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 5 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Spannung selbstgebauter galvanischer Zellen: Zitrone, Kartoffel, Cola, Apfel", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Spannung selbstgebauter galvanischer Zellen: Zitrone, Kartoffel, Cola, Apfel“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Voltage from homemade galvanic cells using lemons, potatoes, cola and apples", "methods": [ "Functions & modelling" ], "description": "Turn “Voltage from homemade galvanic cells using lemons, potatoes, cola and apples” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 304, "source_index": 530, "id": "topic-530-probability-inference-in-minesweeper", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Wahrscheinlichkeitsinferenz bei Minesweeper", "methods": [ "Stochastik" ], "description": "Entwickle aus „Wahrscheinlichkeitsinferenz bei Minesweeper“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Recreational games & mathematics", "title": "Probability inference in Minesweeper", "methods": [ "Statistics & probability" ], "description": "Turn “Probability inference in Minesweeper” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 305, "source_index": 330, "id": "topic-330-conductivity-versus-salt-concentration-in-aqueous-solutions", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 5, 11, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Leitfähigkeit vs. Salzkonzentration: Masse NaCl aufgelöst, Spannung gemessen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Leitfähigkeit vs. Salzkonzentration: Masse NaCl aufgelöst, Spannung gemessen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Conductivity versus salt concentration in aqueous solutions", "methods": [ "Functions & modelling" ], "description": "Turn “Conductivity versus salt concentration in aqueous solutions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 306, "source_index": 540, "id": "topic-540-constructing-and-counting-latin-squares", "category_key": "combinatorics-discrete-probability", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Lateinische Quadrate konstruieren und zählen", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Lateinische Quadrate konstruieren und zählen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Constructing and counting Latin squares", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “Constructing and counting Latin squares” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 307, "source_index": 350, "id": "topic-350-packaging-fruit-mass-loss-under-cling-film-vacuum-storage-and-wax-wrap", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 12 ], "measurement_codes": [ 2, 6 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Verpackungstest: Masseverlust von Obst in Frischhaltefolie vs. Vakuum vs. Wachstuch", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Verpackungstest: Masseverlust von Obst in Frischhaltefolie vs. Vakuum vs. Wachstuch“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Packaging fruit: mass loss under cling film, vacuum storage and wax wrap", "methods": [ "Functions & modelling" ], "description": "Turn “Packaging fruit: mass loss under cling film, vacuum storage and wax wrap” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 308, "source_index": 550, "id": "topic-550-wave-energy-from-a-simplified-ocean-wave-spectrum", "category_key": "climate-earth-ocean-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Klima, Erde & Ozeane", "title": "Wellenenergie aus einem vereinfachten Ozeanwellen-Spektrum", "methods": [ "Trigonometrie", "Fourier-Analyse" ], "description": "Formuliere zu „Wellenenergie aus einem vereinfachten Ozeanwellen-Spektrum“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Climate, Earth & ocean mathematics", "title": "Wave energy from a simplified ocean-wave spectrum", "methods": [ "Trigonometry", "Fourier analysis" ], "description": "Turn “Wave energy from a simplified ocean-wave spectrum” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "fourier_analysis" ] }, { "no": 309, "source_index": 360, "id": "topic-360-paving-stones-versus-grass-daytime-surface-temperature-and-night-time-", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 3, 4, 1, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Pflastersteine vs. Rasen: Oberflächentemperatur am Tag (IR) und Abkühlung nachts (Kontakt)", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie" ], "description": "Formuliere zu „Pflastersteine vs. Rasen: Oberflächentemperatur am Tag (IR) und Abkühlung nachts (Kontakt)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Paving stones versus grass: daytime surface temperature and night-time cooling", "methods": [ "Functions & modelling", "Differential equations", "Geometry" ], "description": "Turn “Paving stones versus grass: daytime surface temperature and night-time cooling” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations", "geometry" ] }, { "no": 310, "source_index": 7, "id": "topic-007-magic-squares-algebraic-construction-methods", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Magische Quadrate: Algebraische Konstruktionsmethoden", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Magische Quadrate: Algebraische Konstruktionsmethoden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Magic squares: algebraic construction methods", "methods": [ "Number theory", "Algebra" ], "description": "Turn “Magic squares: algebraic construction methods” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 311, "source_index": 27, "id": "topic-027-riemann-sums-and-numerical-integration", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Riemann-Summen und numerische Integration", "methods": [ "Funktionen & Modellierung", "Integralrechnung", "Numerische Verfahren" ], "description": "Formuliere zu „Riemann-Summen und numerische Integration“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Riemann sums and numerical integration", "methods": [ "Functions & modelling", "Integral calculus", "Numerical methods" ], "description": "Turn “Riemann sums and numerical integration” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "integral_calculus", "numerical_methods" ] }, { "no": 312, "source_index": 48, "id": "topic-048-the-normal-distribution-in-sports-performance-data", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Normalverteilung bei sportlichen Leistungsdaten", "methods": [ "Stochastik", "Geometrie" ], "description": "Entwickle aus „Normalverteilung bei sportlichen Leistungsdaten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "The normal distribution in sports performance data", "methods": [ "Statistics & probability", "Geometry" ], "description": "Turn “The normal distribution in sports performance data” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry" ] }, { "no": 313, "source_index": 69, "id": "topic-069-modelling-the-spread-of-rumours-in-a-school-community", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Mathematische Modellierung", "title": "Verbreitung von Gerüchten in der Schulgemeinschaft", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Verbreitung von Gerüchten in der Schulgemeinschaft“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling the spread of rumours in a school community", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling the spread of rumours in a school community” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 314, "source_index": 89, "id": "topic-089-the-golden-spiral-in-selected-natural-forms", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 6 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung der Goldenen Spirale in der Natur", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Goldenen Spirale in der Natur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "The golden spiral in selected natural forms", "methods": [ "Geometry" ], "description": "Turn “The golden spiral in selected natural forms” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 315, "source_index": 108, "id": "topic-108-calculating-the-effective-annual-percentage-rate-on-consumer-loans", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 4, "courses": [ "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 5 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL", "de": { "category": "Finanzmathematik", "title": "Berechnung des effektiven Jahreszinses bei Konsumkrediten", "methods": [ "Finanzmathematik" ], "description": "Formuliere zu „Berechnung des effektiven Jahreszinses bei Konsumkrediten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Calculating the effective annual percentage rate on consumer loans", "methods": [ "Financial mathematics" ], "description": "Turn “Calculating the effective annual percentage rate on consumer loans” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "financial_math" ] }, { "no": 316, "source_index": 125, "id": "topic-125-paradoxes-in-set-theory", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung von Paradoxa in der Mengenlehre", "methods": [ "Beweisführung" ], "description": "Die Idee „Untersuchung von Paradoxa in der Mengenlehre“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Paradoxes in set theory", "methods": [ "Proof" ], "description": "Develop “Paradoxes in set theory” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 317, "source_index": 140, "id": "topic-140-binary-trees-and-their-properties", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Untersuchung von Binärbäumen und deren Eigenschaften", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Binärbäumen und deren Eigenschaften“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Binary trees and their properties", "methods": [ "Geometry" ], "description": "Turn “Binary trees and their properties” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 318, "source_index": 150, "id": "topic-150-modelling-optimal-lighting-in-a-room", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 10, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Modellierung der optimalen Beleuchtung in einem Raum", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Modellierung der optimalen Beleuchtung in einem Raum“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Modelling optimal lighting in a room", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Modelling optimal lighting in a room” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 319, "source_index": 166, "id": "topic-166-modelling-negotiation-strategies-with-cooperative-game-theory", "category_key": "game-theory-decision-making", "assessment_code": 3, "course_code": 5, "courses": [ "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, HL", "de": { "category": "Spieltheorie & Entscheidungsfindung", "title": "Modellierung von Verhandlungsstrategien mit kooperativer Spieltheorie", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung von Verhandlungsstrategien mit kooperativer Spieltheorie“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Game theory & decision-making", "title": "Modelling negotiation strategies with cooperative game theory", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling negotiation strategies with cooperative game theory” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 320, "source_index": 381, "id": "topic-381-a-capacity-model-for-pedestrian-flow-in-school-corridors", "category_key": "transport-mobility-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 11, 12 ], "measurement_codes": [ 6, 7, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Kapazitätsmodell für Fußgängerströme in Schulkorridoren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Kapazitätsmodell für Fußgängerströme in Schulkorridoren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "A capacity model for pedestrian flow in school corridors", "methods": [ "Functions & modelling" ], "description": "Turn “A capacity model for pedestrian flow in school corridors” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 321, "source_index": 174, "id": "topic-174-modelling-the-spread-of-antibiotic-resistance-in-bacterial-populations", "category_key": "biomathematics-medicine", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AA HL", "de": { "category": "Biomathematik & Medizin", "title": "Modellierung der Ausbreitung von Antibiotikaresistenzen in Bakterienpopulationen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung der Ausbreitung von Antibiotikaresistenzen in Bakterienpopulationen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Modelling the spread of antibiotic resistance in bacterial populations", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling the spread of antibiotic resistance in bacterial populations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 322, "source_index": 393, "id": "topic-393-maximum-flow-for-distributing-meals-in-a-school-canteen", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Maximaler Fluss für die Verteilung von Mahlzeiten in einer Schulkantine", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Geometrie", "Optimierung" ], "description": "Entwickle aus „Maximaler Fluss für die Verteilung von Mahlzeiten in einer Schulkantine“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Operations research & logistics", "title": "Maximum flow for distributing meals in a school canteen", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Geometry", "Optimisation" ], "description": "Turn “Maximum flow for distributing meals in a school canteen” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "geometry", "optimization" ] }, { "no": 323, "source_index": 184, "id": "topic-184-optimising-solar-panel-orientation-for-maximum-energy-yield", "category_key": "environmental-mathematics-sustainability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 10 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Optimierung der Solarpanel-Ausrichtung für maximale Energiegewinnung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimierung der Solarpanel-Ausrichtung für maximale Energiegewinnung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Optimising solar-panel orientation for maximum energy yield", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising solar-panel orientation for maximum energy yield” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 324, "source_index": 405, "id": "topic-405-the-size-of-information-cascades-in-social-networks", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Größe von Informationskaskaden in sozialen Netzwerken", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Größe von Informationskaskaden in sozialen Netzwerken“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "The size of information cascades in social networks", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “The size of information cascades in social networks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 325, "source_index": 194, "id": "topic-194-calculating-stability-in-different-yoga-poses-using-centre-of-mass", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 3 ], "measurement_codes": [ 1, 7, 13, 15 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Berechnung der Stabilität bei verschiedenen Yoga-Posen (Schwerpunkt)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Berechnung der Stabilität bei verschiedenen Yoga-Posen (Schwerpunkt)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Calculating stability in different yoga poses using centre of mass", "methods": [ "Functions & modelling" ], "description": "Turn “Calculating stability in different yoga poses using centre of mass” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 326, "source_index": 417, "id": "topic-417-lempelziv-complexity-of-public-dna-sequences", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Lempel-Ziv-Komplexität öffentlich verfügbarer DNA-Sequenzen", "methods": [ "Geometrie", "Folgen & Reihen" ], "description": "Formuliere zu „Lempel-Ziv-Komplexität öffentlich verfügbarer DNA-Sequenzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Lempel–Ziv complexity of public DNA sequences", "methods": [ "Geometry", "Sequences & series" ], "description": "Turn “Lempel–Ziv complexity of public DNA sequences” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "sequences_series" ] }, { "no": 327, "source_index": 204, "id": "topic-204-time-series-analysis-forecasting-share-prices-with-moving-averages", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Analyse von Zeitreihen: Vorhersage von Aktienkursen mit gleitenden Durchschnitten", "methods": [ "Funktionen & Modellierung", "Regression", "Zahlentheorie", "Folgen & Reihen", "Finanzmathematik", "Simulation & Algorithmen" ], "description": "Entwickle aus „Analyse von Zeitreihen: Vorhersage von Aktienkursen mit gleitenden Durchschnitten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Data science & introductory algorithms", "title": "Time-series analysis: forecasting share prices with moving averages", "methods": [ "Functions & modelling", "Regression", "Number theory", "Sequences & series", "Financial mathematics", "Simulation & algorithms" ], "description": "Turn “Time-series analysis: forecasting share prices with moving averages” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression", "number_theory", "sequences_series", "financial_math", "simulation" ] }, { "no": 328, "source_index": 429, "id": "topic-429-modelling-pwm-duty-cycle-and-motor-speed", "category_key": "robotics-control-sensing", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 7, 11 ], "measurement_codes": [ 5, 6, 13, 20 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "PWM-Tastgrad und Motordrehzahl mathematisch modellieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „PWM-Tastgrad und Motordrehzahl mathematisch modellieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Modelling PWM duty cycle and motor speed", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling PWM duty cycle and motor speed” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 329, "source_index": 441, "id": "topic-441-aliasing-and-sampling-frequency-in-digital-patterns", "category_key": "image-processing-computer-graphics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 10 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Aliasing und Abtastfrequenz bei digitalen Mustern", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Aliasing und Abtastfrequenz bei digitalen Mustern“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Aliasing and sampling frequency in digital patterns", "methods": [ "Trigonometry" ], "description": "Turn “Aliasing and sampling frequency in digital patterns” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 330, "source_index": 221, "id": "topic-221-analysing-the-mathematical-structure-of-canons-and-fugues", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Analyse der mathematischen Struktur von Kanons und Fugen", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Analyse der mathematischen Struktur von Kanons und Fugen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Analysing the mathematical structure of canons and fugues", "methods": [ "Trigonometry" ], "description": "Turn “Analysing the mathematical structure of canons and fugues” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 331, "source_index": 451, "id": "topic-451-building-topic-clusters-with-cosine-similarity", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Themencluster mit Kosinusähnlichkeit bilden", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Themencluster mit Kosinusähnlichkeit bilden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Building topic clusters with cosine similarity", "methods": [ "Trigonometry" ], "description": "Turn “Building topic clusters with cosine similarity” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 332, "source_index": 230, "id": "topic-230-the-mathematics-of-three-dimensional-printing-structures-and-infill-pa", "category_key": "art-design-architecture", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kunst, Design & Architektur", "title": "Untersuchung der Mathematik von 3D-Druck-Strukturen (Infill-Patterns)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Mathematik von 3D-Druck-Strukturen (Infill-Patterns)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "The mathematics of three-dimensional printing structures and infill patterns", "methods": [ "Geometry" ], "description": "Turn “The mathematics of three-dimensional printing structures and infill patterns” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 333, "source_index": 461, "id": "topic-461-modelling-mastery-development-with-a-markov-chain", "category_key": "education-learning-analytics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 4, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Kompetenzentwicklung als Markov-Modell", "methods": [ "Funktionen & Modellierung", "Stochastik", "Matrizen" ], "description": "Entwickle aus „Kompetenzentwicklung als Markov-Modell“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Education & learning analytics", "title": "Modelling mastery development with a Markov chain", "methods": [ "Functions & modelling", "Statistics & probability", "Matrices" ], "description": "Turn “Modelling mastery development with a Markov chain” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "matrices" ] }, { "no": 334, "source_index": 239, "id": "topic-239-the-distribution-of-asteroids-in-the-solar-system", "category_key": "astronomy-spaceflight", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 17 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Astronomie & Raumfahrt", "title": "Untersuchung der Verteilung von Asteroiden im Sonnensystem", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Verteilung von Asteroiden im Sonnensystem“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Astronomy & spaceflight", "title": "The distribution of asteroids in the Solar System", "methods": [ "Statistics & probability" ], "description": "Turn “The distribution of asteroids in the Solar System” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 335, "source_index": 471, "id": "topic-471-limitations-of-simple-laffer-curve-models", "category_key": "economic-models-markets", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Grenzen einfacher Laffer-Kurven-Modelle", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Grenzen einfacher Laffer-Kurven-Modelle“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Limitations of simple Laffer-curve models", "methods": [ "Functions & modelling" ], "description": "Turn “Limitations of simple Laffer-curve models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 336, "source_index": 247, "id": "topic-247-calculating-an-optimal-group-size-for-effective-learning", "category_key": "psychology-cognition", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Psychologie & Kognition", "title": "Berechnung der optimalen Gruppengröße für effektives Lernen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Gruppengröße für effektives Lernen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Psychology & cognition", "title": "Calculating an optimal group size for effective learning", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating an optimal group size for effective learning” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 337, "source_index": 481, "id": "topic-481-fourier-analysis-of-daily-traffic-patterns", "category_key": "time-series-forecasting", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Fourier-Analyse täglicher Verkehrsmuster", "methods": [ "Folgen & Reihen", "Fourier-Analyse", "Zeitreihenanalyse" ], "description": "Entwickle aus „Fourier-Analyse täglicher Verkehrsmuster“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Fourier analysis of daily traffic patterns", "methods": [ "Sequences & series", "Fourier analysis", "Time-series analysis" ], "description": "Turn “Fourier analysis of daily traffic patterns” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "fourier_analysis", "time_series" ] }, { "no": 338, "source_index": 255, "id": "topic-255-calculating-the-risk-of-base-rate-errors-in-everyday-decisions", "category_key": "probability-risk", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 13, 19 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Wahrscheinlichkeit & Risiko", "title": "Berechnung des Risikos von Häufigkeitsirrtümern im Alltag", "methods": [ "Stochastik" ], "description": "Entwickle aus „Berechnung des Risikos von Häufigkeitsirrtümern im Alltag“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Probability & risk", "title": "Calculating the risk of base-rate errors in everyday decisions", "methods": [ "Statistics & probability" ], "description": "Turn “Calculating the risk of base-rate errors in everyday decisions” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 339, "source_index": 491, "id": "topic-491-fractal-dimension-of-local-road-networks", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 7, 9, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Fraktale Dimension lokaler Straßennetze", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Fraktale Dimension lokaler Straßennetze“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Fractal dimension of local road networks", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “Fractal dimension of local road networks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 340, "source_index": 263, "id": "topic-263-the-mathematics-of-laminated-dough-folds", "category_key": "culinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kulinarische Mathematik", "title": "Untersuchung der Mathematik von Teig-Faltungen (Laminierte Strukturen)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Mathematik von Teig-Faltungen (Laminierte Strukturen)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Culinary mathematics", "title": "The mathematics of laminated dough folds", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of laminated dough folds” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 341, "source_index": 501, "id": "topic-501-modelling-thrust-and-power-consumption-of-small-drone-propellers", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 7, 11, 12 ], "measurement_codes": [ 5, 6, 13, 15, 20 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Schub und Leistungsaufnahme kleiner Drohnenpropeller modellieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Schub und Leistungsaufnahme kleiner Drohnenpropeller modellieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Modelling thrust and power consumption of small drone propellers", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Modelling thrust and power consumption of small drone propellers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 342, "source_index": 271, "id": "topic-271-melting-rate-of-ice-shapes-volume-surface-area-and-form", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 1 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Kühlgeschwindigkeit von Eiswürfeln: Volumen, Oberfläche und Form (Würfel vs. Kugel vs. Scheibe)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Kühlgeschwindigkeit von Eiswürfeln: Volumen, Oberfläche und Form (Würfel vs. Kugel vs. Scheibe)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Melting rate of ice shapes: volume, surface area and form", "methods": [ "Geometry" ], "description": "Turn “Melting rate of ice shapes: volume, surface area and form” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 343, "source_index": 511, "id": "topic-511-comparing-diagnostic-test-thresholds-using-roc-curves", "category_key": "epidemiology-public-health", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Schwellenwerte diagnostischer Tests mit ROC-Kurven vergleichen", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Schwellenwerte diagnostischer Tests mit ROC-Kurven vergleichen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Comparing diagnostic-test thresholds using ROC curves", "methods": [ "Trigonometry" ], "description": "Turn “Comparing diagnostic-test thresholds using ROC curves” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 344, "source_index": 291, "id": "topic-291-fermentation-carbon-dioxide-loss-from-yeast-sugar-solutions-of-differe", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Gärvorgang: CO₂-Verlust bei Hefe-Zucker-Lösungen verschiedener Konzentration", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Gärvorgang: CO₂-Verlust bei Hefe-Zucker-Lösungen verschiedener Konzentration“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Fermentation: carbon dioxide loss from yeast-sugar solutions of different concentrations", "methods": [ "Functions & modelling" ], "description": "Turn “Fermentation: carbon dioxide loss from yeast-sugar solutions of different concentrations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 345, "source_index": 521, "id": "topic-521-optimising-pacing-strategies-using-swimming-split-times", "category_key": "sports-analytics-tactics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Pacing-Strategien anhand von Schwimm-Splitzeiten optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Pacing-Strategien anhand von Schwimm-Splitzeiten optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Optimising pacing strategies using swimming split times", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising pacing strategies using swimming split times” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 346, "source_index": 311, "id": "topic-311-photovoltaic-power-loss-under-partial-shading-in-series-and-parallel-c", "category_key": "electricity", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 5, 7, 10, 13 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "de": { "category": "Elektrizität", "title": "Photovoltaik: Leistungsabfall bei Teilschattierung (Serien- vs. Parallelschaltung)", "methods": [ "Folgen & Reihen" ], "description": "Formuliere zu „Photovoltaik: Leistungsabfall bei Teilschattierung (Serien- vs. Parallelschaltung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Photovoltaic power loss under partial shading in series and parallel circuits", "methods": [ "Sequences & series" ], "description": "Turn “Photovoltaic power loss under partial shading in series and parallel circuits” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "sequences_series" ] }, { "no": 347, "source_index": 531, "id": "topic-531-mathematically-balancing-a-self-designed-dice-game", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 8, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Ein selbst entwickeltes Würfelspiel mathematisch ausbalancieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Ein selbst entwickeltes Würfelspiel mathematisch ausbalancieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "Mathematically balancing a self-designed dice game", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematically balancing a self-designed dice game” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 348, "source_index": 331, "id": "topic-331-heat-capacity-of-coins-made-from-different-alloys", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 3, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Wärmekapazität von Münzen verschiedener Legierungen (Masse, ΔT in Wasserbad)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmekapazität von Münzen verschiedener Legierungen (Masse, ΔT in Wasserbad)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Heat capacity of coins made from different alloys", "methods": [ "Functions & modelling" ], "description": "Turn “Heat capacity of coins made from different alloys” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 349, "source_index": 541, "id": "topic-541-the-inclusionexclusion-principle-in-password-policies", "category_key": "combinatorics-discrete-probability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Inklusions-Exklusions-Prinzip bei Passwortregeln", "methods": [ "Stochastik", "Kombinatorik" ], "description": "Die Idee „Inklusions-Exklusions-Prinzip bei Passwortregeln“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "The inclusion–exclusion principle in password policies", "methods": [ "Statistics & probability", "Combinatorics" ], "description": "Develop “The inclusion–exclusion principle in password policies” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics" ] }, { "no": 350, "source_index": 351, "id": "topic-351-surface-temperature-patterns-after-different-forms-of-exercise", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 12 ], "measurement_codes": [ 3, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Körpertemperatur nach verschiedenen Sportarten (Laufen vs. Schwimmen vs. Yoga)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Körpertemperatur nach verschiedenen Sportarten (Laufen vs. Schwimmen vs. Yoga)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Surface-temperature patterns after different forms of exercise", "methods": [ "Geometry" ], "description": "Turn “Surface-temperature patterns after different forms of exercise” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 351, "source_index": 361, "id": "topic-361-household-waste-separation-mass-of-different-fractions-per-week", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 2 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Mülltrennung: Masse verschiedener Fraktionen pro Haushalt pro Woche", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mülltrennung: Masse verschiedener Fraktionen pro Haushalt pro Woche“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Household waste separation: mass of different fractions per week", "methods": [ "Functions & modelling" ], "description": "Turn “Household waste separation: mass of different fractions per week” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 352, "source_index": 8, "id": "topic-008-the-collatz-conjecture-convergence-behaviour-for-different-starting-va", "category_key": "algebra-number-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Collatz-Vermutung: Konvergenzverhalten für Startwerte", "methods": [ "Zahlentheorie", "Beweisführung", "Algebra" ], "description": "Die Idee „Collatz-Vermutung: Konvergenzverhalten für Startwerte“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "The Collatz conjecture: convergence behaviour for different starting values", "methods": [ "Number theory", "Proof", "Algebra" ], "description": "Develop “The Collatz conjecture: convergence behaviour for different starting values” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "proof", "algebra" ] }, { "no": 353, "source_index": 28, "id": "topic-028-parameter-changes-in-the-logistic-function", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Analysis & Calculus", "title": "Parameteränderungen in der logistischen Funktion", "methods": [ "Algebra" ], "description": "Formuliere zu „Parameteränderungen in der logistischen Funktion“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Parameter changes in the logistic function", "methods": [ "Algebra" ], "description": "Turn “Parameter changes in the logistic function” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 354, "source_index": 49, "id": "topic-049-bayes-theorem-and-the-reliability-of-medical-tests", "category_key": "statistics-probability", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10, 12 ], "measurement_codes": [ 0 ], "safety_code": 3, "source_course_label": "AA HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Bayes-Theorem: Zuverlässigkeit medizinischer Tests", "methods": [ "Stochastik", "Beweisführung" ], "description": "Die Idee „Bayes-Theorem: Zuverlässigkeit medizinischer Tests“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Statistics & probability", "title": "Bayes' theorem and the reliability of medical tests", "methods": [ "Statistics & probability", "Proof" ], "description": "Develop “Bayes' theorem and the reliability of medical tests” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "proof" ] }, { "no": 355, "source_index": 70, "id": "topic-070-modelling-the-spread-of-wildfires", "category_key": "mathematical-modelling", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 7, 9 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung der Ausbreitung von Waldbränden", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung der Ausbreitung von Waldbränden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling the spread of wildfires", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling the spread of wildfires” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 356, "source_index": 90, "id": "topic-090-calculating-sightlines-in-a-theatre-or-concert-hall", "category_key": "geometry-topology", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 2, 6, 8 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Berechnung von Sichtlinien in einem Theater/Konzertsaal", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung von Sichtlinien in einem Theater/Konzertsaal“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Calculating sightlines in a theatre or concert hall", "methods": [ "Geometry" ], "description": "Turn “Calculating sightlines in a theatre or concert hall” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 357, "source_index": 109, "id": "topic-109-modelling-the-effect-of-inflation-on-purchasing-power", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Modellierung von Inflationsauswirkungen auf Kaufkraft", "methods": [ "Funktionen & Modellierung", "Finanzmathematik" ], "description": "Formuliere zu „Modellierung von Inflationsauswirkungen auf Kaufkraft“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Modelling the effect of inflation on purchasing power", "methods": [ "Functions & modelling", "Financial mathematics" ], "description": "Turn “Modelling the effect of inflation on purchasing power” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "financial_math" ] }, { "no": 358, "source_index": 126, "id": "topic-126-modelling-logic-puzzles-with-propositional-logic", "category_key": "logic-set-theory-proof", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Modellierung logischer Rätsel mit Aussagenlogik", "methods": [ "Funktionen & Modellierung", "Beweisführung" ], "description": "Formuliere zu „Modellierung logischer Rätsel mit Aussagenlogik“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "Modelling logic puzzles with propositional logic", "methods": [ "Functions & modelling", "Proof" ], "description": "Turn “Modelling logic puzzles with propositional logic” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "proof" ] }, { "no": 359, "source_index": 141, "id": "topic-141-modelling-game-strategies-with-game-trees", "category_key": "discrete-mathematics-computer-science", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Modellierung von Spielstrategien mit Spielbäumen", "methods": [ "Funktionen & Modellierung", "Geometrie" ], "description": "Formuliere zu „Modellierung von Spielstrategien mit Spielbäumen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Modelling game strategies with game trees", "methods": [ "Functions & modelling", "Geometry" ], "description": "Turn “Modelling game strategies with game trees” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "geometry" ] }, { "no": 360, "source_index": 151, "id": "topic-151-the-mathematics-of-perfume-evaporation-and-diffusion", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Untersuchung der Mathematik von Parfüms (Verdunstung, Diffusion)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Mathematik von Parfüms (Verdunstung, Diffusion)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "The mathematics of perfume: evaporation and diffusion", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of perfume: evaporation and diffusion” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 361, "source_index": 382, "id": "topic-382-ride-sharing-as-a-weighted-bipartite-matching-problem", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 5, 6, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Fahrgemeinschaften als gewichtetes bipartites Zuordnungsproblem", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Fahrgemeinschaften als gewichtetes bipartites Zuordnungsproblem“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "Ride sharing as a weighted bipartite matching problem", "methods": [ "Functions & modelling" ], "description": "Turn “Ride sharing as a weighted bipartite matching problem” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 362, "source_index": 175, "id": "topic-175-the-geometry-and-optimisation-of-leaf-vein-networks", "category_key": "biomathematics-medicine", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Analyse der Geometrie von Blattadern und deren Optimierung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Analyse der Geometrie von Blattadern und deren Optimierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "The geometry and optimisation of leaf-vein networks", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Geometry", "Optimisation" ], "description": "Turn “The geometry and optimisation of leaf-vein networks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "geometry", "optimization" ] }, { "no": 363, "source_index": 394, "id": "topic-394-minimising-waste-in-a-cutting-stock-problem-for-sheet-material", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 11 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Verschnittminimierung beim Zuschneiden von Plattenmaterial", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie" ], "description": "Formuliere zu „Verschnittminimierung beim Zuschneiden von Plattenmaterial“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Minimising waste in a cutting-stock problem for sheet material", "methods": [ "Functions & modelling", "Differential calculus", "Geometry" ], "description": "Turn “Minimising waste in a cutting-stock problem for sheet material” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry" ] }, { "no": 364, "source_index": 185, "id": "topic-185-mathematical-analysis-of-wind-energy-potential-at-a-location", "category_key": "environmental-mathematics-sustainability", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 12 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Mathematische Analyse von Windenergiepotenzial an einem Standort", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematische Analyse von Windenergiepotenzial an einem Standort“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Mathematical analysis of wind-energy potential at a location", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical analysis of wind-energy potential at a location” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 365, "source_index": 406, "id": "topic-406-a-minimum-spanning-tree-for-a-campus-cable-network", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 6, 7, 11 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Minimaler Spannbaum für ein Campus-Kabelnetz", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Optimierung" ], "description": "Formuliere zu „Minimaler Spannbaum für ein Campus-Kabelnetz“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "A minimum spanning tree for a campus cable network", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Optimisation" ], "description": "Turn “A minimum spanning tree for a campus cable network” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "optimization" ] }, { "no": 366, "source_index": 195, "id": "topic-195-mathematical-patterns-in-dance-choreography", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 8 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Untersuchung der mathematischen Muster in Choreografien (Tanz)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der mathematischen Muster in Choreografien (Tanz)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Mathematical patterns in dance choreography", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical patterns in dance choreography” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 367, "source_index": 418, "id": "topic-418-channel-capacity-of-a-binary-symmetric-channel", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Kanalkapazität eines binär-symmetrischen Übertragungskanals", "methods": [ "Geometrie" ], "description": "Formuliere zu „Kanalkapazität eines binär-symmetrischen Übertragungskanals“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Channel capacity of a binary symmetric channel", "methods": [ "Geometry" ], "description": "Turn “Channel capacity of a binary symmetric channel” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 368, "source_index": 205, "id": "topic-205-introductory-image-compression-with-singular-value-decomposition", "category_key": "data-science-introductory-algorithms", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Einfache Bildkompression durch Singulärwertzerlegung (Konzept)", "methods": [ "Matrizen", "Simulation & Algorithmen" ], "description": "Formuliere zu „Einfache Bildkompression durch Singulärwertzerlegung (Konzept)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Introductory image compression with singular value decomposition", "methods": [ "Matrices", "Simulation & algorithms" ], "description": "Turn “Introductory image compression with singular value decomposition” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "matrices", "simulation" ] }, { "no": 369, "source_index": 430, "id": "topic-430-optimising-bezier-curves-for-smooth-robot-turns", "category_key": "robotics-control-sensing", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 11 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Bézier-Kurven für weiche Roboterkurven optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Bézier-Kurven für weiche Roboterkurven optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Optimising Bézier curves for smooth robot turns", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising Bézier curves for smooth robot turns” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 370, "source_index": 442, "id": "topic-442-3d-projection-matrices-and-camera-field-of-view", "category_key": "image-processing-computer-graphics", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "3D-Projektionsmatrizen und das Sichtfeld einer Kamera", "methods": [ "Matrizen" ], "description": "Formuliere zu „3D-Projektionsmatrizen und das Sichtfeld einer Kamera“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "3D projection matrices and camera field of view", "methods": [ "Matrices" ], "description": "Turn “3D projection matrices and camera field of view” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "matrices" ] }, { "no": 371, "source_index": 222, "id": "topic-222-calculating-the-resonant-frequencies-of-glasses-in-a-glass-harmonica", "category_key": "music-acoustics-waves", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 9, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Musik, Akustik & Wellen", "title": "Berechnung der Resonanzfrequenzen von Gläsern (Glasarmonika)", "methods": [ "Trigonometrie" ], "description": "Formuliere zu „Berechnung der Resonanzfrequenzen von Gläsern (Glasarmonika)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Music, acoustics & waves", "title": "Calculating the resonant frequencies of glasses in a glass harmonica", "methods": [ "Trigonometry" ], "description": "Turn “Calculating the resonant frequencies of glasses in a glass harmonica” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry" ] }, { "no": 372, "source_index": 452, "id": "topic-452-analysing-character-networks-in-a-novel", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 8, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Figurennetzwerke in einem Roman analysieren", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Figurennetzwerke in einem Roman analysieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Language & text mathematics", "title": "Analysing character networks in a novel", "methods": [ "Graph theory" ], "description": "Turn “Analysing character networks in a novel” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 373, "source_index": 231, "id": "topic-231-calculating-tension-in-tent-structures-based-on-hyperbolic-paraboloids", "category_key": "art-design-architecture", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Kunst, Design & Architektur", "title": "Berechnung der Spannung in Zeltkonstruktionen (Hyperbolische Paraboloide)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung der Spannung in Zeltkonstruktionen (Hyperbolische Paraboloide)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Art, design & architecture", "title": "Calculating tension in tent structures based on hyperbolic paraboloids", "methods": [ "Geometry" ], "description": "Turn “Calculating tension in tent structures based on hyperbolic paraboloids” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 374, "source_index": 462, "id": "topic-462-attendance-and-performance-while-accounting-for-possible-confounders", "category_key": "education-learning-analytics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Anwesenheit und Leistung unter Berücksichtigung möglicher Störvariablen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Anwesenheit und Leistung unter Berücksichtigung möglicher Störvariablen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Education & learning analytics", "title": "Attendance and performance while accounting for possible confounders", "methods": [ "Geometry" ], "description": "Turn “Attendance and performance while accounting for possible confounders” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 375, "source_index": 472, "id": "topic-472-network-effects-and-adoption-curves-for-digital-platforms", "category_key": "economic-models-markets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Netzwerkeffekte und Adoptionskurven digitaler Plattformen", "methods": [ "Funktionen & Modellierung", "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Netzwerkeffekte und Adoptionskurven digitaler Plattformen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Network effects and adoption curves for digital platforms", "methods": [ "Functions & modelling", "Graph theory", "Geometry" ], "description": "Turn “Network effects and adoption curves for digital platforms” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "graph_theory", "geometry" ] }, { "no": 376, "source_index": 482, "id": "topic-482-comparing-random-walk-and-mean-reversion-models-for-exchange-rates", "category_key": "time-series-forecasting", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Random-Walk- und Mean-Reversion-Modelle für Wechselkurse vergleichen", "methods": [ "Funktionen & Modellierung", "Stochastik", "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Random-Walk- und Mean-Reversion-Modelle für Wechselkurse vergleichen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "Comparing random-walk and mean-reversion models for exchange rates", "methods": [ "Functions & modelling", "Statistics & probability", "Sequences & series", "Time-series analysis" ], "description": "Turn “Comparing random-walk and mean-reversion models for exchange rates” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "sequences_series", "time_series" ] }, { "no": 377, "source_index": 492, "id": "topic-492-approximating-watersheds-from-a-digital-elevation-model", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Wasserscheiden aus einem digitalen Höhenmodell approximieren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wasserscheiden aus einem digitalen Höhenmodell approximieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Approximating watersheds from a digital elevation model", "methods": [ "Functions & modelling" ], "description": "Turn “Approximating watersheds from a digital elevation model” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 378, "source_index": 502, "id": "topic-502-comparing-catenary-parabolic-and-circular-arc-bridge-models", "category_key": "engineering-design-optimisation", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 6, 10, 12 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Kettenlinie, Parabel und Kreisbogen als Brückenmodelle vergleichen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Kettenlinie, Parabel und Kreisbogen als Brückenmodelle vergleichen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Comparing catenary, parabolic and circular-arc bridge models", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “Comparing catenary, parabolic and circular-arc bridge models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 379, "source_index": 272, "id": "topic-272-thermal-conductivity-of-metal-rods-measured-by-the-time-taken-for-wax-", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 3, 6, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmeleitfähigkeit von Metallstäben: Zeit bis Wachs an der entfernten Seite schmilzt", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmeleitfähigkeit von Metallstäben: Zeit bis Wachs an der entfernten Seite schmilzt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Thermal conductivity of metal rods measured by the time taken for wax to melt", "methods": [ "Functions & modelling" ], "description": "Turn “Thermal conductivity of metal rods measured by the time taken for wax to melt” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 380, "source_index": 512, "id": "topic-512-herd-immunity-under-heterogeneous-contact-rates", "category_key": "epidemiology-public-health", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Herdenimmunität bei heterogenen Kontaktraten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Herdenimmunität bei heterogenen Kontaktraten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Herd immunity under heterogeneous contact rates", "methods": [ "Functions & modelling" ], "description": "Turn “Herd immunity under heterogeneous contact rates” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 381, "source_index": 292, "id": "topic-292-sublimation-of-dry-ice-mass-loss-over-time-at-constant-conditions", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 6, 21 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Sublimation von Trockeneis: Masseverlust bei konstanter Temperatur über Zeit", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Sublimation von Trockeneis: Masseverlust bei konstanter Temperatur über Zeit“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Material properties", "title": "Sublimation of dry ice: mass loss over time at constant conditions", "methods": [ "Time-series analysis" ], "description": "Turn “Sublimation of dry ice: mass loss over time at constant conditions” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 382, "source_index": 522, "id": "topic-522-analysing-volleyball-rotations-as-markov-transitions", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 11 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Volleyballrotationen als Markov-Übergänge analysieren", "methods": [ "Stochastik" ], "description": "Entwickle aus „Volleyballrotationen als Markov-Übergänge analysieren“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Sports analytics & tactics", "title": "Analysing volleyball rotations as Markov transitions", "methods": [ "Statistics & probability" ], "description": "Turn “Analysing volleyball rotations as Markov transitions” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 383, "source_index": 312, "id": "topic-312-thermoelectric-voltage-as-a-function-of-temperature-difference-using-a", "category_key": "electricity", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 5, 13 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Elektrizität", "title": "Thermoelektrischer Effekt: Spannung als Funktion der Temperaturdifferenz (Peltier-Element)", "methods": [ "Algebra" ], "description": "Formuliere zu „Thermoelektrischer Effekt: Spannung als Funktion der Temperaturdifferenz (Peltier-Element)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Thermoelectric voltage as a function of temperature difference using a Peltier element", "methods": [ "Algebra" ], "description": "Turn “Thermoelectric voltage as a function of temperature difference using a Peltier element” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 384, "source_index": 532, "id": "topic-532-designing-escape-room-routes-as-a-directed-graph", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 8, 11 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Escape-Room-Routen als gerichteten Graphen entwerfen", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Escape-Room-Routen als gerichteten Graphen entwerfen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "Designing escape-room routes as a directed graph", "methods": [ "Graph theory" ], "description": "Turn “Designing escape-room routes as a directed graph” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 385, "source_index": 332, "id": "topic-332-thermocouple-voltage-as-a-function-of-hot-to-cold-water-bath-temperatu", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 3, 5, 13, 16 ], "safety_code": 1, "source_course_label": "AA HL", "de": { "category": "Kombinierte Experimente", "title": "Thermoelement: Spannung als Funktion der Temperaturdifferenz (heißes vs. kaltes Wasserbad)", "methods": [ "Algebra" ], "description": "Formuliere zu „Thermoelement: Spannung als Funktion der Temperaturdifferenz (heißes vs. kaltes Wasserbad)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Thermocouple voltage as a function of hot-to-cold water-bath temperature difference", "methods": [ "Algebra" ], "description": "Turn “Thermocouple voltage as a function of hot-to-cold water-bath temperature difference” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "algebra" ] }, { "no": 386, "source_index": 542, "id": "topic-542-testing-the-poisson-approximation-for-rare-events", "category_key": "combinatorics-discrete-probability", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Poisson-Approximation für seltene Ereignisse prüfen", "methods": [ "Stochastik", "Kombinatorik", "Numerische Verfahren" ], "description": "Die Idee „Poisson-Approximation für seltene Ereignisse prüfen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Testing the Poisson approximation for rare events", "methods": [ "Statistics & probability", "Combinatorics", "Numerical methods" ], "description": "Develop “Testing the Poisson approximation for rare events” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "combinatorics", "numerical_methods" ] }, { "no": 387, "source_index": 352, "id": "topic-352-hand-surface-temperature-recovery-after-a-safe-cold-water-exposure", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 4, 1, 3, 6 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Küche & Alltag", "title": "Wärmebild einer Hand nach Eisbad: Wiedererwärmung über Zeit mit IR-Thermometer", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wärmebild einer Hand nach Eisbad: Wiedererwärmung über Zeit mit IR-Thermometer“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Hand surface-temperature recovery after a safe cold-water exposure", "methods": [ "Geometry" ], "description": "Turn “Hand surface-temperature recovery after a safe cold-water exposure” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 388, "source_index": 362, "id": "topic-362-water-mass-loss-from-plastic-and-glass-containers-over-time", "category_key": "environment", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Umwelt", "title": "Plastikflaschen vs. Glas: Wasserverdunstung/Masseverlust durch das Material hindurch", "methods": [ "Zeitreihenanalyse" ], "description": "Entwickle aus „Plastikflaschen vs. Glas: Wasserverdunstung/Masseverlust durch das Material hindurch“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Environment", "title": "Water mass loss from plastic and glass containers over time", "methods": [ "Time-series analysis" ], "description": "Turn “Water mass loss from plastic and glass containers over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "time_series" ] }, { "no": 389, "source_index": 9, "id": "topic-009-perfect-numbers-and-their-rarity", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung perfekter Zahlen und ihre Seltenheit", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Die Idee „Untersuchung perfekter Zahlen und ihre Seltenheit“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "Perfect numbers and their rarity", "methods": [ "Number theory", "Algebra" ], "description": "Develop “Perfect numbers and their rarity” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 390, "source_index": 29, "id": "topic-029-optimising-the-flight-path-of-a-paper-aeroplane", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 1, 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Optimierung der Flugbahn eines Papierfliegers", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimierung der Flugbahn eines Papierfliegers“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Optimising the flight path of a paper aeroplane", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising the flight path of a paper aeroplane” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 391, "source_index": 50, "id": "topic-050-grade-distributions-across-different-school-subjects", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Verteilung von Noten in verschiedenen Fächern", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Verteilung von Noten in verschiedenen Fächern“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Grade distributions across different school subjects", "methods": [ "Statistics & probability" ], "description": "Turn “Grade distributions across different school subjects” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 392, "source_index": 71, "id": "topic-071-optimising-seating-arrangements-in-a-classroom", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Optimierung der Sitzplatzverteilung in einem Klassenzimmer", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ], "description": "Entwickle aus „Optimierung der Sitzplatzverteilung in einem Klassenzimmer“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Mathematical modelling", "title": "Optimising seating arrangements in a classroom", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ], "description": "Turn “Optimising seating arrangements in a classroom” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ] }, { "no": 393, "source_index": 91, "id": "topic-091-symmetry-in-islamic-art", "category_key": "geometry-topology", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 8 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung von Symmetrien in islamischer Kunst", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Symmetrien in islamischer Kunst“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Symmetry in Islamic art", "methods": [ "Geometry" ], "description": "Turn “Symmetry in Islamic art” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 394, "source_index": 110, "id": "topic-110-insurance-models-and-premium-calculations", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 5 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Untersuchung von Versicherungsmodellen und Prämienberechnung", "methods": [ "Funktionen & Modellierung", "Finanzmathematik" ], "description": "Formuliere zu „Untersuchung von Versicherungsmodellen und Prämienberechnung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Insurance models and premium calculations", "methods": [ "Functions & modelling", "Financial mathematics" ], "description": "Turn “Insurance models and premium calculations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "financial_math" ] }, { "no": 395, "source_index": 127, "id": "topic-127-an-introduction-to-g-del-s-incompleteness-theorems", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung der Gödelschen Unvollständigkeitssätze (einführend)", "methods": [ "Beweisführung" ], "description": "Formuliere zu „Untersuchung der Gödelschen Unvollständigkeitssätze (einführend)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "An introduction to Gödel's incompleteness theorems", "methods": [ "Proof" ], "description": "Turn “An introduction to Gödel's incompleteness theorems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "proof" ] }, { "no": 396, "source_index": 142, "id": "topic-142-error-detecting-codes-and-hamming-distance", "category_key": "discrete-mathematics-computer-science", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Untersuchung von Fehlererkennenden Codes (Hamming-Distanz)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Fehlererkennenden Codes (Hamming-Distanz)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Error-detecting codes and Hamming distance", "methods": [ "Geometry" ], "description": "Turn “Error-detecting codes and Hamming distance” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 397, "source_index": 152, "id": "topic-152-analysing-the-stability-of-towers-built-from-blocks", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 15, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Analyse der Stabilität von Türmen aus Bauklötzen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Analyse der Stabilität von Türmen aus Bauklötzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Analysing the stability of towers built from blocks", "methods": [ "Functions & modelling" ], "description": "Turn “Analysing the stability of towers built from blocks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 398, "source_index": 383, "id": "topic-383-an-accessibility-index-for-public-transport-stops-using-weighted-distances", "category_key": "transport-mobility-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Erreichbarkeitsindex von Haltestellen mit gewichteten Entfernungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Erreichbarkeitsindex von Haltestellen mit gewichteten Entfernungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "An accessibility index for public-transport stops using weighted distances", "methods": [ "Functions & modelling" ], "description": "Turn “An accessibility index for public-transport stops using weighted distances” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 399, "source_index": 176, "id": "topic-176-mathematical-modelling-of-visual-acuity-and-corrective-lens-power", "category_key": "biomathematics-medicine", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13, 19 ], "safety_code": 3, "source_course_label": "AA, SL/HL", "de": { "category": "Biomathematik & Medizin", "title": "Mathematische Modellierung der Sehschärfe und Brillenstärkeberechnung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Mathematische Modellierung der Sehschärfe und Brillenstärkeberechnung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Biomathematics & medicine", "title": "Mathematical modelling of visual acuity and corrective-lens power", "methods": [ "Functions & modelling" ], "description": "Turn “Mathematical modelling of visual acuity and corrective-lens power” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 400, "source_index": 395, "id": "topic-395-conflict-minimising-exam-timetabling-with-graph-colouring", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Konfliktarme Prüfungsplanung mit Graphenfärbung", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie" ], "description": "Formuliere zu „Konfliktarme Prüfungsplanung mit Graphenfärbung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Conflict-minimising exam timetabling with graph colouring", "methods": [ "Functions & modelling", "Differential calculus", "Geometry" ], "description": "Turn “Conflict-minimising exam timetabling with graph colouring” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry" ] }, { "no": 401, "source_index": 186, "id": "topic-186-calculating-carbon-dioxide-emissions-per-kilometre-for-different-forms", "category_key": "environmental-mathematics-sustainability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Umweltmathematik & Nachhaltigkeit", "title": "Berechnung des CO₂-Ausstoßes verschiedener Verkehrsmittel pro km", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung des CO₂-Ausstoßes verschiedener Verkehrsmittel pro km“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environmental mathematics & sustainability", "title": "Calculating carbon dioxide emissions per kilometre for different forms of transport", "methods": [ "Geometry" ], "description": "Turn “Calculating carbon dioxide emissions per kilometre for different forms of transport” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 402, "source_index": 407, "id": "topic-407-network-motifs-in-a-public-food-web-dataset", "category_key": "networks-social-systems", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Netzwerkmotive in einem öffentlichen Nahrungsnetz", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Netzwerkmotive in einem öffentlichen Nahrungsnetz“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Network motifs in a public food-web dataset", "methods": [ "Graph theory" ], "description": "Turn “Network motifs in a public food-web dataset” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 403, "source_index": 196, "id": "topic-196-analysing-the-optimal-riding-position-on-a-road-bicycle", "category_key": "sports-biomechanics-movement", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Sportbiomechanik & Bewegung", "title": "Analyse der optimalen Sitzposition auf einem Rennrad", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Analyse der optimalen Sitzposition auf einem Rennrad“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports biomechanics & movement", "title": "Analysing the optimal riding position on a road bicycle", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Analysing the optimal riding position on a road bicycle” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 404, "source_index": 419, "id": "topic-419-password-entropy-and-common-human-choice-patterns", "category_key": "information-coding-theory", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 7, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Passwortentropie und typische menschliche Auswahlmuster", "methods": [ "Geometrie" ], "description": "Formuliere zu „Passwortentropie und typische menschliche Auswahlmuster“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Password entropy and common human choice patterns", "methods": [ "Geometry" ], "description": "Turn “Password entropy and common human choice patterns” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 405, "source_index": 206, "id": "topic-206-password-strength-patterns-through-combinatorics", "category_key": "data-science-introductory-algorithms", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Datenwissenschaft & Einfache Algorithmen", "title": "Untersuchung der Muster in Passwortstärke durch Kombinatorik", "methods": [ "Kombinatorik", "Simulation & Algorithmen" ], "description": "Formuliere zu „Untersuchung der Muster in Passwortstärke durch Kombinatorik“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Data science & introductory algorithms", "title": "Password-strength patterns through combinatorics", "methods": [ "Combinatorics", "Simulation & algorithms" ], "description": "Turn “Password-strength patterns through combinatorics” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "combinatorics", "simulation" ] }, { "no": 406, "source_index": 431, "id": "topic-431-error-propagation-at-the-endpoint-of-a-robot-arm", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 12 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 1, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Fehlerfortpflanzung am Endpunkt eines Roboterarms", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Fehlerfortpflanzung am Endpunkt eines Roboterarms“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Error propagation at the endpoint of a robot arm", "methods": [ "Functions & modelling" ], "description": "Turn “Error propagation at the endpoint of a robot arm” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 407, "source_index": 443, "id": "topic-443-estimating-optical-flow-in-short-video-sequences", "category_key": "image-processing-computer-graphics", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 11, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildverarbeitung & Computergrafik", "title": "Optischen Fluss in kurzen Videoaufnahmen schätzen", "methods": [ "Folgen & Reihen" ], "description": "Formuliere zu „Optischen Fluss in kurzen Videoaufnahmen schätzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Image processing & computer graphics", "title": "Estimating optical flow in short video sequences", "methods": [ "Sequences & series" ], "description": "Turn “Estimating optical flow in short video sequences” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "sequences_series" ] }, { "no": 408, "source_index": 453, "id": "topic-453-investigating-periodic-structures-in-poetic-metre", "category_key": "language-text-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 8, 10, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sprach- & Textmathematik", "title": "Periodische Strukturen in Gedichtmetren untersuchen", "methods": [ "Trigonometrie", "Zeitreihenanalyse" ], "description": "Entwickle aus „Periodische Strukturen in Gedichtmetren untersuchen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Language & text mathematics", "title": "Investigating periodic structures in poetic metre", "methods": [ "Trigonometry", "Time-series analysis" ], "description": "Turn “Investigating periodic structures in poetic metre” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "trigonometry", "time_series" ] }, { "no": 409, "source_index": 463, "id": "topic-463-reliability-of-peer-assessment-using-inter-rater-correlation", "category_key": "education-learning-analytics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 4, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Bildungsdaten & Lernanalyse", "title": "Zuverlässigkeit von Peer-Bewertungen mit Interrater-Korrelation", "methods": [ "Funktionen & Modellierung", "Regression" ], "description": "Entwickle aus „Zuverlässigkeit von Peer-Bewertungen mit Interrater-Korrelation“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Education & learning analytics", "title": "Reliability of peer assessment using inter-rater correlation", "methods": [ "Functions & modelling", "Regression" ], "description": "Turn “Reliability of peer assessment using inter-rater correlation” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "regression" ] }, { "no": 410, "source_index": 473, "id": "topic-473-association-rules-in-anonymised-market-basket-data", "category_key": "economic-models-markets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Wirtschaftsmodelle & Märkte", "title": "Assoziationsregeln in anonymisierten Warenkorbdaten", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Assoziationsregeln in anonymisierten Warenkorbdaten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Economic models & markets", "title": "Association rules in anonymised market-basket data", "methods": [ "Functions & modelling" ], "description": "Turn “Association rules in anonymised market-basket data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 411, "source_index": 483, "id": "topic-483-how-different-imputation-methods-affect-time-series-trends", "category_key": "time-series-forecasting", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Zeitreihen & Prognosen", "title": "Einfluss verschiedener Imputationsmethoden auf Zeitreihentrends", "methods": [ "Folgen & Reihen", "Zeitreihenanalyse" ], "description": "Entwickle aus „Einfluss verschiedener Imputationsmethoden auf Zeitreihentrends“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Time series & forecasting", "title": "How different imputation methods affect time-series trends", "methods": [ "Sequences & series", "Time-series analysis" ], "description": "Turn “How different imputation methods affect time-series trends” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "sequences_series", "time_series" ] }, { "no": 412, "source_index": 493, "id": "topic-493-choosing-an-optimal-map-scale-for-a-hiking-route", "category_key": "geospatial-cartographic-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 6, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Geodaten & Kartografie", "title": "Optimaler Kartenmaßstab für die Darstellung einer Wanderroute", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Optimierung" ], "description": "Formuliere zu „Optimaler Kartenmaßstab für die Darstellung einer Wanderroute“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geospatial & cartographic mathematics", "title": "Choosing an optimal map scale for a hiking route", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Optimisation" ], "description": "Turn “Choosing an optimal map scale for a hiking route” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "optimization" ] }, { "no": 413, "source_index": 503, "id": "topic-503-optimising-pallet-stacking-for-mixed-package-sizes", "category_key": "engineering-design-optimisation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 5, 7, 11 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Optimierung & Ingenieurdesign", "title": "Palettenstapelung für gemischte Verpackungsgrößen optimieren", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Palettenstapelung für gemischte Verpackungsgrößen optimieren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Engineering design & optimisation", "title": "Optimising pallet stacking for mixed package sizes", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising pallet stacking for mixed package sizes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 414, "source_index": 273, "id": "topic-273-temperature-change-while-baking-a-muffin-core-versus-surface-temperatu", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 3 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Temperaturverlauf beim Backen eines Muffins: Kerntemperatur vs. Außentemperatur", "methods": [ "Geometrie" ], "description": "Formuliere zu „Temperaturverlauf beim Backen eines Muffins: Kerntemperatur vs. Außentemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Temperature change while baking a muffin: core versus surface temperature", "methods": [ "Geometry" ], "description": "Turn “Temperature change while baking a muffin: core versus surface temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 415, "source_index": 513, "id": "topic-513-lag-between-wastewater-signals-and-reported-cases", "category_key": "epidemiology-public-health", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Epidemiologie & öffentliche Gesundheit", "title": "Zeitverzug zwischen Abwassersignal und gemeldeten Fällen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Zeitverzug zwischen Abwassersignal und gemeldeten Fällen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Epidemiology & public health", "title": "Lag between wastewater signals and reported cases", "methods": [ "Functions & modelling" ], "description": "Turn “Lag between wastewater signals and reported cases” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 416, "source_index": 293, "id": "topic-293-hygroscopicity-of-salts-and-sugars-mass-gain-from-moisture-in-air", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 6, 13, 18 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Hygroskopizität verschiedener Salze und Zuckerarten: Massezunahme an Luft", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Hygroskopizität verschiedener Salze und Zuckerarten: Massezunahme an Luft“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Hygroscopicity of salts and sugars: mass gain from moisture in air", "methods": [ "Functions & modelling" ], "description": "Turn “Hygroscopicity of salts and sugars: mass gain from moisture in air” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 417, "source_index": 523, "id": "topic-523-basketball-shot-selection-using-expected-points", "category_key": "sports-analytics-tactics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 11, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Sportanalyse & Taktik", "title": "Wurfauswahl im Basketball mit erwartetem Punktwert", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wurfauswahl im Basketball mit erwartetem Punktwert“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Sports analytics & tactics", "title": "Basketball shot selection using expected points", "methods": [ "Functions & modelling" ], "description": "Turn “Basketball shot selection using expected points” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 418, "source_index": 313, "id": "topic-313-temperature-dependent-resistance-of-an-incandescent-lamp", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 5 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Temperaturabhängiger Widerstand einer Glühlampe", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Temperaturabhängiger Widerstand einer Glühlampe“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Temperature-dependent resistance of an incandescent lamp", "methods": [ "Functions & modelling" ], "description": "Turn “Temperature-dependent resistance of an incandescent lamp” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 419, "source_index": 533, "id": "topic-533-investigating-first-player-advantage-in-a-board-game", "category_key": "recreational-games-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 8, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Spiele & Freizeitmathematik", "title": "Vorteil der Startposition in einem Brettspiel untersuchen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Vorteil der Startposition in einem Brettspiel untersuchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Recreational games & mathematics", "title": "Investigating first-player advantage in a board game", "methods": [ "Functions & modelling" ], "description": "Turn “Investigating first-player advantage in a board game” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 420, "source_index": 333, "id": "topic-333-calorimetry-determining-the-specific-heat-capacity-of-a-metal", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 3, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Kalorimetrie: Spezifische Wärmekapazität von Metall (Masse Metall, Masse Wasser, ΔT)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Kalorimetrie: Spezifische Wärmekapazität von Metall (Masse Metall, Masse Wasser, ΔT)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Calorimetry: determining the specific heat capacity of a metal", "methods": [ "Functions & modelling" ], "description": "Turn “Calorimetry: determining the specific heat capacity of a metal” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 421, "source_index": 543, "id": "topic-543-load-distribution-in-the-balls-into-bins-model", "category_key": "combinatorics-discrete-probability", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Kombinatorik & diskrete Wahrscheinlichkeit", "title": "Lastverteilung beim Balls-in-Bins-Modell", "methods": [ "Funktionen & Modellierung", "Stochastik", "Kombinatorik" ], "description": "Die Idee „Lastverteilung beim Balls-in-Bins-Modell“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Combinatorics & discrete probability", "title": "Load distribution in the balls-into-bins model", "methods": [ "Functions & modelling", "Statistics & probability", "Combinatorics" ], "description": "Develop “Load distribution in the balls-into-bins model” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "functions_modeling", "stochastics", "combinatorics" ] }, { "no": 422, "source_index": 353, "id": "topic-353-temperature-change-in-a-vacuum-flask-over-24-hours", "category_key": "kitchen-everyday-life", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 6, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Küche & Alltag", "title": "Temperaturverlauf in einer Thermoskanne über 24 Stunden", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Temperaturverlauf in einer Thermoskanne über 24 Stunden“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Kitchen & everyday life", "title": "Temperature change in a vacuum flask over 24 hours", "methods": [ "Functions & modelling" ], "description": "Turn “Temperature change in a vacuum flask over 24 hours” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 423, "source_index": 363, "id": "topic-363-water-samples-dissolved-solid-mass-and-electrical-conductivity", "category_key": "environment", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 2, 5, 13 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Umwelt", "title": "Wasserverschmutzung: Masse gelöster Feststoffe und elektrische Leitfähigkeit (Spannung)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wasserverschmutzung: Masse gelöster Feststoffe und elektrische Leitfähigkeit (Spannung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Environment", "title": "Water samples: dissolved-solid mass and electrical conductivity", "methods": [ "Functions & modelling" ], "description": "Turn “Water samples: dissolved-solid mass and electrical conductivity” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 424, "source_index": 10, "id": "topic-010-the-relationship-between-continued-fractions-and-irrational-numbers", "category_key": "algebra-number-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Die Beziehung zwischen Kettenbrüchen und irrationalen Zahlen", "methods": [ "Funktionen & Modellierung", "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Die Beziehung zwischen Kettenbrüchen und irrationalen Zahlen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "The relationship between continued fractions and irrational numbers", "methods": [ "Functions & modelling", "Number theory", "Algebra" ], "description": "Turn “The relationship between continued fractions and irrational numbers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "number_theory", "algebra" ] }, { "no": 425, "source_index": 30, "id": "topic-030-speed-and-acceleration-while-cycling", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 8 ], "safety_code": 3, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Untersuchung der Geschwindigkeit und Beschleunigung beim Fahrradfahren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Geschwindigkeit und Beschleunigung beim Fahrradfahren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Speed and acceleration while cycling", "methods": [ "Functions & modelling" ], "description": "Turn “Speed and acceleration while cycling” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 426, "source_index": 51, "id": "topic-051-comparing-mean-median-and-mode-in-salary-data", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 9, 12 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Vergleich von Mittelwert, Median und Modus in Gehaltsdaten", "methods": [ "Stochastik" ], "description": "Entwickle aus „Vergleich von Mittelwert, Median und Modus in Gehaltsdaten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Comparing mean, median and mode in salary data", "methods": [ "Statistics & probability" ], "description": "Turn “Comparing mean, median and mode in salary data” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 427, "source_index": 72, "id": "topic-072-modelling-water-supply-in-a-city", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung der Wasserversorgung in einer Stadt", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung der Wasserversorgung in einer Stadt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling water supply in a city", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling water supply in a city” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 428, "source_index": 92, "id": "topic-092-modelling-shadows-cast-by-sundials", "category_key": "geometry-topology", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 3 ], "measurement_codes": [ 7, 10, 13, 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Modellierung von Schattenwurf bei Sonnenuhren", "methods": [ "Funktionen & Modellierung", "Geometrie" ], "description": "Formuliere zu „Modellierung von Schattenwurf bei Sonnenuhren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Modelling shadows cast by sundials", "methods": [ "Functions & modelling", "Geometry" ], "description": "Turn “Modelling shadows cast by sundials” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "geometry" ] }, { "no": 429, "source_index": 111, "id": "topic-111-comparing-vehicle-leasing-with-purchasing", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 12 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Vergleich von Leasing vs. Kauf bei Fahrzeugen", "methods": [ "Finanzmathematik" ], "description": "Formuliere zu „Vergleich von Leasing vs. Kauf bei Fahrzeugen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Comparing vehicle leasing with purchasing", "methods": [ "Financial mathematics" ], "description": "Turn “Comparing vehicle leasing with purchasing” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "financial_math" ] }, { "no": 430, "source_index": 128, "id": "topic-128-proof-methods-direct-proof-contraposition-and-contradiction", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Beweisverfahren: Direkter Beweis, Kontraposition, Widerspruch", "methods": [ "Beweisführung" ], "description": "Die Idee „Beweisverfahren: Direkter Beweis, Kontraposition, Widerspruch“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Proof methods: direct proof, contraposition and contradiction", "methods": [ "Proof" ], "description": "Develop “Proof methods: direct proof, contraposition and contradiction” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 431, "source_index": 143, "id": "topic-143-recurrence-relations-and-the-tower-of-hanoi", "category_key": "discrete-mathematics-computer-science", "assessment_code": 2, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Diskrete Mathematik & Informatik", "title": "Analyse von Rekursionsgleichungen (Türme von Hanoi)", "methods": [ "Geometrie", "Folgen & Reihen", "Algebra" ], "description": "Formuliere zu „Analyse von Rekursionsgleichungen (Türme von Hanoi)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Discrete mathematics & computer science", "title": "Recurrence relations and the Tower of Hanoi", "methods": [ "Geometry", "Sequences & series", "Algebra" ], "description": "Turn “Recurrence relations and the Tower of Hanoi” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "sequences_series", "algebra" ] }, { "no": 432, "source_index": 153, "id": "topic-153-modelling-an-optimal-racket-length-in-sport", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Modellierung der optimalen Schlägerlänge im Sport", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Modellierung der optimalen Schlägerlänge im Sport“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Modelling an optimal racket length in sport", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Modelling an optimal racket length in sport” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 433, "source_index": 384, "id": "topic-384-e-bike-energy-consumption-as-a-function-of-gradient-and-speed", "category_key": "transport-mobility-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11 ], "measurement_codes": [ 5, 8, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Energieverbrauch eines E-Bikes in Abhängigkeit von Steigung und Geschwindigkeit", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Algebra" ], "description": "Formuliere zu „Energieverbrauch eines E-Bikes in Abhängigkeit von Steigung und Geschwindigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Transport & mobility mathematics", "title": "E-bike energy consumption as a function of gradient and speed", "methods": [ "Functions & modelling", "Differential calculus", "Algebra" ], "description": "Turn “E-bike energy consumption as a function of gradient and speed” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "algebra" ] }, { "no": 434, "source_index": 396, "id": "topic-396-budget-selection-as-a-knapsack-problem-using-dynamic-programming", "category_key": "operations-research-logistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 5, 7, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Budgetauswahl als Rucksackproblem mit dynamischer Programmierung", "methods": [ "Geometrie", "Simulation & Algorithmen" ], "description": "Formuliere zu „Budgetauswahl als Rucksackproblem mit dynamischer Programmierung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Operations research & logistics", "title": "Budget selection as a knapsack problem using dynamic programming", "methods": [ "Geometry", "Simulation & algorithms" ], "description": "Turn “Budget selection as a knapsack problem using dynamic programming” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "simulation" ] }, { "no": 435, "source_index": 408, "id": "topic-408-simplified-influence-maximisation-under-a-limited-campaign-budget", "category_key": "networks-social-systems", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Vereinfachte Einflussmaximierung bei begrenztem Werbebudget", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie" ], "description": "Formuliere zu „Vereinfachte Einflussmaximierung bei begrenztem Werbebudget“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Networks & social systems", "title": "Simplified influence maximisation under a limited campaign budget", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory" ], "description": "Turn “Simplified influence maximisation under a limited campaign budget” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory" ] }, { "no": 436, "source_index": 420, "id": "topic-420-secret-sharing-using-polynomial-interpolation", "category_key": "information-coding-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 7, 10, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Secret Sharing mit polynomialer Interpolation", "methods": [ "Geometrie", "Numerische Verfahren", "Algebra" ], "description": "Formuliere zu „Secret Sharing mit polynomialer Interpolation“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Secret sharing using polynomial interpolation", "methods": [ "Geometry", "Numerical methods", "Algebra" ], "description": "Turn “Secret sharing using polynomial interpolation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "numerical_methods", "algebra" ] }, { "no": 437, "source_index": 432, "id": "topic-432-discrete-feedback-control-for-room-temperature", "category_key": "robotics-control-sensing", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11, 12 ], "measurement_codes": [ 3, 13 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Diskrete Rückkopplung zur Regelung einer Raumtemperatur", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Diskrete Rückkopplung zur Regelung einer Raumtemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Discrete feedback control for room temperature", "methods": [ "Functions & modelling" ], "description": "Turn “Discrete feedback control for room temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 438, "source_index": 274, "id": "topic-274-heating-of-asphalt-grass-and-water-in-midday-sun", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 3, 4, 1 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Erwärmung von Asphalt, Rasen und Wasser in der Mittagssonne", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Erwärmung von Asphalt, Rasen und Wasser in der Mittagssonne“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Heating of asphalt, grass and water in midday sun", "methods": [ "Functions & modelling" ], "description": "Turn “Heating of asphalt, grass and water in midday sun” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 439, "source_index": 294, "id": "topic-294-burning-rates-of-candles-with-different-diameters-and-wax-types", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 9 ], "measurement_codes": [ 2, 1, 6, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Brennrate von Kerzen verschiedener Durchmesser und Wachssorten", "methods": [ "Geometrie" ], "description": "Formuliere zu „Brennrate von Kerzen verschiedener Durchmesser und Wachssorten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Burning rates of candles with different diameters and wax types", "methods": [ "Geometry" ], "description": "Turn “Burning rates of candles with different diameters and wax types” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 440, "source_index": 314, "id": "topic-314-voltage-and-capacity-change-of-a-lithium-ion-battery-over-repeated-cha", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Spannungsverlauf eines Li-Ion-Akkus über 50 Lade-/Entladezyklen (Alterung)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Spannungsverlauf eines Li-Ion-Akkus über 50 Lade-/Entladezyklen (Alterung)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Voltage and capacity change of a lithium-ion battery over repeated charge cycles", "methods": [ "Functions & modelling" ], "description": "Turn “Voltage and capacity change of a lithium-ion battery over repeated charge cycles” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 441, "source_index": 334, "id": "topic-334-electroplating-cathode-mass-gain-versus-voltage-and-time", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 5, 13, 21 ], "safety_code": 2, "source_course_label": "AA HL", "de": { "category": "Kombinierte Experimente", "title": "Elektroplattierung: Massezunahme der Kathode vs. angelegte Spannung und Zeit", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Elektroplattierung: Massezunahme der Kathode vs. angelegte Spannung und Zeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Electroplating: cathode mass gain versus voltage and time", "methods": [ "Functions & modelling" ], "description": "Turn “Electroplating: cathode mass gain versus voltage and time” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 442, "source_index": 11, "id": "topic-011-euler-s-totient-function-and-its-properties", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung der Eulerschen Phi-Funktion und ihrer Eigenschaften", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Untersuchung der Eulerschen Phi-Funktion und ihrer Eigenschaften“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Euler's totient function and its properties", "methods": [ "Number theory", "Algebra" ], "description": "Turn “Euler's totient function and its properties” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 443, "source_index": 31, "id": "topic-031-modelling-breathing-with-sinusoidal-functions", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Modellierung der Atmung mit Sinusfunktionen", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Algebra" ], "description": "Formuliere zu „Modellierung der Atmung mit Sinusfunktionen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Modelling breathing with sinusoidal functions", "methods": [ "Functions & modelling", "Trigonometry", "Algebra" ], "description": "Turn “Modelling breathing with sinusoidal functions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry", "algebra" ] }, { "no": 444, "source_index": 52, "id": "topic-052-waiting-times-in-the-school-cafeteria", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Wartezeiten an der Schulkantine", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Wartezeiten an der Schulkantine“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Waiting times in the school cafeteria", "methods": [ "Statistics & probability" ], "description": "Turn “Waiting times in the school cafeteria” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 445, "source_index": 73, "id": "topic-073-the-propagation-of-sound-waves-in-rooms", "category_key": "mathematical-modelling", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Mathematische Modellierung", "title": "Untersuchung der Ausbreitung von Schallwellen in Räumen", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ], "description": "Formuliere zu „Untersuchung der Ausbreitung von Schallwellen in Räumen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "The propagation of sound waves in rooms", "methods": [ "Functions & modelling", "Trigonometry" ], "description": "Turn “The propagation of sound waves in rooms” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "trigonometry" ] }, { "no": 446, "source_index": 93, "id": "topic-093-sphere-packing-density-in-three-dimensions", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 20 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung der Packungsdichte von Kugeln in 3D", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung der Packungsdichte von Kugeln in 3D“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Sphere-packing density in three dimensions", "methods": [ "Geometry" ], "description": "Turn “Sphere-packing density in three dimensions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 447, "source_index": 112, "id": "topic-112-calculating-the-break-even-point-for-a-small-business", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Berechnung des Break-Even-Punkts für ein eigenes Geschäft", "methods": [ "Trigonometrie", "Finanzmathematik" ], "description": "Formuliere zu „Berechnung des Break-Even-Punkts für ein eigenes Geschäft“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Calculating the break-even point for a small business", "methods": [ "Trigonometry", "Financial mathematics" ], "description": "Turn “Calculating the break-even point for a small business” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "financial_math" ] }, { "no": 448, "source_index": 129, "id": "topic-129-equivalence-relations-and-partitions", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung von Äquivalenzrelationen und Partitionen", "methods": [ "Beweisführung" ], "description": "Die Idee „Untersuchung von Äquivalenzrelationen und Partitionen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Equivalence relations and partitions", "methods": [ "Proof" ], "description": "Develop “Equivalence relations and partitions” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 449, "source_index": 154, "id": "topic-154-the-mathematics-of-origami-folds", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 8 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Untersuchung der Mathematik von Origami-Faltungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Mathematik von Origami-Faltungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "The mathematics of origami folds", "methods": [ "Functions & modelling" ], "description": "Turn “The mathematics of origami folds” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 450, "source_index": 385, "id": "topic-385-predicting-parking-occupancy-with-a-markov-chain", "category_key": "transport-mobility-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Verkehrs- & Mobilitätsmathematik", "title": "Vorhersage der Parkplatzbelegung mit einer Markov-Kette", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Zahlentheorie", "Matrizen" ], "description": "Entwickle aus „Vorhersage der Parkplatzbelegung mit einer Markov-Kette“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Transport & mobility mathematics", "title": "Predicting parking occupancy with a Markov chain", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Number theory", "Matrices" ], "description": "Turn “Predicting parking occupancy with a Markov chain” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "regression", "number_theory", "matrices" ] }, { "no": 451, "source_index": 397, "id": "topic-397-checkout-capacity-planning-with-queueing-theory", "category_key": "operations-research-logistics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 11, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Operations Research & Logistik", "title": "Kapazitätsplanung für Kassen mit Warteschlangentheorie", "methods": [ "Stochastik", "Geometrie" ], "description": "Entwickle aus „Kapazitätsplanung für Kassen mit Warteschlangentheorie“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Operations research & logistics", "title": "Checkout capacity planning with queueing theory", "methods": [ "Statistics & probability", "Geometry" ], "description": "Turn “Checkout capacity planning with queueing theory” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry" ] }, { "no": 452, "source_index": 409, "id": "topic-409-anonymising-a-friendship-network-and-measuring-changes-in-degree-distribution", "category_key": "networks-social-systems", "assessment_code": 3, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 4, 7, 12 ], "measurement_codes": [ 13, 14 ], "safety_code": 3, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Netzwerke & soziale Systeme", "title": "Anonymisierung eines Freundschaftsnetzwerks und Veränderung der Gradverteilung", "methods": [ "Stochastik", "Graphentheorie" ], "description": "Entwickle aus „Anonymisierung eines Freundschaftsnetzwerks und Veränderung der Gradverteilung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Networks & social systems", "title": "Anonymising a friendship network and measuring changes in degree distribution", "methods": [ "Statistics & probability", "Graph theory" ], "description": "Turn “Anonymising a friendship network and measuring changes in degree distribution” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "graph_theory" ] }, { "no": 453, "source_index": 421, "id": "topic-421-comparing-run-length-encoding-for-pixel-art-and-photographs", "category_key": "information-coding-theory", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 2, 7, 8, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Informations- & Kodierungstheorie", "title": "Run-Length-Encoding bei Pixelkunst und Fotos vergleichen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Run-Length-Encoding bei Pixelkunst und Fotos vergleichen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Information & coding theory", "title": "Comparing run-length encoding for pixel art and photographs", "methods": [ "Geometry" ], "description": "Turn “Comparing run-length encoding for pixel art and photographs” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 454, "source_index": 433, "id": "topic-433-simplified-slam-geometry-using-known-landmarks", "category_key": "robotics-control-sensing", "assessment_code": 2, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 2, 7, 10, 11 ], "measurement_codes": [ 7, 8, 13, 20 ], "safety_code": 1, "source_course_label": "AA & AI, HL", "editorial_source": "PreLearning expansion 2026-08-31", "de": { "category": "Robotik, Regelung & Sensorik", "title": "Vereinfachte SLAM-Geometrie mit bekannten Landmarken", "methods": [ "Geometrie" ], "description": "Formuliere zu „Vereinfachte SLAM-Geometrie mit bekannten Landmarken“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Robotics, control & sensing", "title": "Simplified SLAM geometry using known landmarks", "methods": [ "Geometry" ], "description": "Turn “Simplified SLAM geometry using known landmarks” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 455, "source_index": 275, "id": "topic-275-heat-loss-through-single-double-and-triple-glazing-in-winter", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 4, 1, 3 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmeverlust verschiedener Fenstertypen (Einfach, Doppel, Dreifachglas) im Winter", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmeverlust verschiedener Fenstertypen (Einfach, Doppel, Dreifachglas) im Winter“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Heat loss through single, double and triple glazing in winter", "methods": [ "Functions & modelling" ], "description": "Turn “Heat loss through single, double and triple glazing in winter” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 456, "source_index": 295, "id": "topic-295-water-loss-from-cut-flowers-in-different-solutions", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 6, 16 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Wasserverlust von Schnittblumen in verschiedenen Lösungen (Wasser, Sprite, Aspirin, Zucker)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wasserverlust von Schnittblumen in verschiedenen Lösungen (Wasser, Sprite, Aspirin, Zucker)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Water loss from cut flowers in different solutions", "methods": [ "Functions & modelling" ], "description": "Turn “Water loss from cut flowers in different solutions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 457, "source_index": 315, "id": "topic-315-power-output-of-a-small-wind-turbine-at-simulated-wind-speeds", "category_key": "electricity", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 12 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Elektrizität", "title": "Leistung eines kleinen Windrads bei simulierten Windgeschwindigkeiten (Ventilator)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Leistung eines kleinen Windrads bei simulierten Windgeschwindigkeiten (Ventilator)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Power output of a small wind turbine at simulated wind speeds", "methods": [ "Functions & modelling" ], "description": "Turn “Power output of a small wind turbine at simulated wind speeds” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 458, "source_index": 335, "id": "topic-335-corrosion-and-conductivity-metal-mass-loss-versus-electrical-response-", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 5, 13, 16 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Korrosion + Leitfähigkeit: Masseverlust von Metall vs. Spannung in der Lösung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Korrosion + Leitfähigkeit: Masseverlust von Metall vs. Spannung in der Lösung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Corrosion and conductivity: metal mass loss versus electrical response of the solution", "methods": [ "Functions & modelling" ], "description": "Turn “Corrosion and conductivity: metal mass loss versus electrical response of the solution” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 459, "source_index": 12, "id": "topic-012-diophantine-equations-and-their-solvability", "category_key": "algebra-number-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Diophantische Gleichungen und deren Lösbarkeit", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Die Idee „Diophantische Gleichungen und deren Lösbarkeit“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "Diophantine equations and their solvability", "methods": [ "Number theory", "Algebra" ], "description": "Develop “Diophantine equations and their solvability” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 460, "source_index": 32, "id": "topic-032-calculating-the-volume-of-irregular-objects-by-integration", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Berechnung des Volumens unregelmäßiger Objekte durch Integration", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung des Volumens unregelmäßiger Objekte durch Integration“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Calculating the volume of irregular objects by integration", "methods": [ "Geometry" ], "description": "Turn “Calculating the volume of irregular objects by integration” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 461, "source_index": 53, "id": "topic-053-analysing-success-rates-in-basketball-or-throwing-tasks", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Analyse der Trefferquote beim Basketball/Werfen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Analyse der Trefferquote beim Basketball/Werfen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Analysing success rates in basketball or throwing tasks", "methods": [ "Statistics & probability" ], "description": "Turn “Analysing success rates in basketball or throwing tasks” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 462, "source_index": 74, "id": "topic-074-modelling-the-growth-of-bacterial-cultures", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13, 21 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung des Wachstums von Bakterienkulturen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung des Wachstums von Bakterienkulturen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling the growth of bacterial cultures", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling the growth of bacterial cultures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 463, "source_index": 94, "id": "topic-094-reflection-geometry-in-architecture", "category_key": "geometry-topology", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 2, 6, 8 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Geometrie von Spiegelungen in der Architektur", "methods": [ "Geometrie" ], "description": "Formuliere zu „Geometrie von Spiegelungen in der Architektur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Reflection geometry in architecture", "methods": [ "Geometry" ], "description": "Turn “Reflection geometry in architecture” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 464, "source_index": 113, "id": "topic-113-lottery-probabilities-and-expected-value", "category_key": "financial-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Untersuchung von Lottogewinn-Wahrscheinlichkeiten und erwartetem Wert", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung von Lottogewinn-Wahrscheinlichkeiten und erwartetem Wert“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Financial mathematics", "title": "Lottery probabilities and expected value", "methods": [ "Statistics & probability" ], "description": "Turn “Lottery probabilities and expected value” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 465, "source_index": 130, "id": "topic-130-modelling-circuits-with-karnaugh-veitch-maps", "category_key": "logic-set-theory-proof", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Modellierung von Schaltkreisen mit Karnaugh-Veitch-Diagrammen", "methods": [ "Funktionen & Modellierung", "Geometrie", "Beweisführung" ], "description": "Formuliere zu „Modellierung von Schaltkreisen mit Karnaugh-Veitch-Diagrammen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "Modelling circuits with Karnaugh-Veitch maps", "methods": [ "Functions & modelling", "Geometry", "Proof" ], "description": "Turn “Modelling circuits with Karnaugh-Veitch maps” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "geometry", "proof" ] }, { "no": 466, "source_index": 155, "id": "topic-155-comparing-the-efficiency-of-stairs-and-lifts", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Analyse der Effizienz von Treppe vs. Aufzug", "methods": [ "Optimierung" ], "description": "Formuliere zu „Analyse der Effizienz von Treppe vs. Aufzug“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Comparing the efficiency of stairs and lifts", "methods": [ "Optimisation" ], "description": "Turn “Comparing the efficiency of stairs and lifts” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "optimization" ] }, { "no": 467, "source_index": 276, "id": "topic-276-surface-temperature-recovery-after-ten-minutes-of-exercise", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 12 ], "measurement_codes": [ 3, 19 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Körpertemperatur-Recovery nach 10 Minuten Sport: Abkühlkurve verschiedener Personen", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie" ], "description": "Formuliere zu „Körpertemperatur-Recovery nach 10 Minuten Sport: Abkühlkurve verschiedener Personen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Surface-temperature recovery after ten minutes of exercise", "methods": [ "Functions & modelling", "Differential equations", "Geometry" ], "description": "Turn “Surface-temperature recovery after ten minutes of exercise” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations", "geometry" ] }, { "no": 468, "source_index": 296, "id": "topic-296-mass-change-caused-by-adsorption-onto-activated-carbon", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Masseänderung durch Adsorption an Aktivkohle in verschiedenen Lösungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Masseänderung durch Adsorption an Aktivkohle in verschiedenen Lösungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Mass change caused by adsorption onto activated carbon", "methods": [ "Functions & modelling" ], "description": "Turn “Mass change caused by adsorption onto activated carbon” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 469, "source_index": 316, "id": "topic-316-electrical-conductivity-of-soil-samples-at-different-moisture-levels", "category_key": "electricity", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 2, 5, 13, 18 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Elektrizität", "title": "Elektrische Leitfähigkeit von Bodenproben bei verschiedener Feuchtigkeit", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Elektrische Leitfähigkeit von Bodenproben bei verschiedener Feuchtigkeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Electrical conductivity of soil samples at different moisture levels", "methods": [ "Functions & modelling" ], "description": "Turn “Electrical conductivity of soil samples at different moisture levels” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 470, "source_index": 336, "id": "topic-336-heat-storage-capacity-of-equal-masses-of-stone-metal-and-wood", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Wärmespeicherfähigkeit: gleiche Masse verschiedener Materialien, Temperaturverlauf", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmespeicherfähigkeit: gleiche Masse verschiedener Materialien, Temperaturverlauf“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Heat-storage capacity of equal masses of stone, metal and wood", "methods": [ "Functions & modelling" ], "description": "Turn “Heat-storage capacity of equal masses of stone, metal and wood” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 471, "source_index": 13, "id": "topic-013-properties-of-mersenne-primes", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung der Eigenschaften von Mersenne-Primzahlen", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Die Idee „Untersuchung der Eigenschaften von Mersenne-Primzahlen“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "Properties of Mersenne primes", "methods": [ "Number theory", "Algebra" ], "description": "Develop “Properties of Mersenne primes” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 472, "source_index": 33, "id": "topic-033-limits-and-l-h-pital-s-rule", "category_key": "analysis-calculus", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Untersuchung von Grenzwerten mit der L'Hôpitalschen Regel", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung von Grenzwerten mit der L'Hôpitalschen Regel“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Limits and L'Hôpital's rule", "methods": [ "Functions & modelling" ], "description": "Turn “Limits and L'Hôpital's rule” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 473, "source_index": 54, "id": "topic-054-testing-the-randomness-of-music-shuffle-functions", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 8 ], "measurement_codes": [ 9 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Zufälligkeit von Musik-Shuffle-Funktionen", "methods": [ "Stochastik", "Algebra" ], "description": "Entwickle aus „Untersuchung der Zufälligkeit von Musik-Shuffle-Funktionen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Testing the randomness of music shuffle functions", "methods": [ "Statistics & probability", "Algebra" ], "description": "Turn “Testing the randomness of music shuffle functions” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "algebra" ] }, { "no": 474, "source_index": 75, "id": "topic-075-optimising-routes-to-school-or-work", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 4, 11 ], "measurement_codes": [ 8, 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Optimierung der Routenplanung für die Schule/Arbeit", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Optimierung" ], "description": "Formuliere zu „Optimierung der Routenplanung für die Schule/Arbeit“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Optimising routes to school or work", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Optimisation" ], "description": "Turn “Optimising routes to school or work” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "optimization" ] }, { "no": 475, "source_index": 95, "id": "topic-095-curves-of-constant-width-and-the-reuleaux-triangle", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung von Kurven konstanter Breite (Reuleaux-Dreieck)", "methods": [ "Trigonometrie", "Geometrie" ], "description": "Formuliere zu „Untersuchung von Kurven konstanter Breite (Reuleaux-Dreieck)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Curves of constant width and the Reuleaux triangle", "methods": [ "Trigonometry", "Geometry" ], "description": "Turn “Curves of constant width and the Reuleaux triangle” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "trigonometry", "geometry" ] }, { "no": 476, "source_index": 114, "id": "topic-114-modelling-exchange-rate-fluctuations", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Modellierung von Wechselkurs-Schwankungen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung von Wechselkurs-Schwankungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Modelling exchange-rate fluctuations", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling exchange-rate fluctuations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 477, "source_index": 131, "id": "topic-131-properties-of-relations-reflexivity-symmetry-and-transitivity", "category_key": "logic-set-theory-proof", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung der Eigenschaften von Relationen (reflexiv, symmetrisch, transitiv)", "methods": [ "Beweisführung" ], "description": "Formuliere zu „Untersuchung der Eigenschaften von Relationen (reflexiv, symmetrisch, transitiv)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Logic, set theory & proof", "title": "Properties of relations: reflexivity, symmetry and transitivity", "methods": [ "Proof" ], "description": "Turn “Properties of relations: reflexivity, symmetry and transitivity” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "proof" ] }, { "no": 478, "source_index": 156, "id": "topic-156-modelling-the-amount-of-coffee-needed-to-maximise-caffeine-extraction", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Modellierung der optimalen Kaffeemenge für maximalen Koffeingehalt", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Modellierung der optimalen Kaffeemenge für maximalen Koffeingehalt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Modelling the amount of coffee needed to maximise caffeine extraction", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Modelling the amount of coffee needed to maximise caffeine extraction” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 479, "source_index": 277, "id": "topic-277-temperature-changes-in-chemical-hot-and-cold-packs", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 3, 4, 1, 13 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Temperaturänderung bei chemischen Warm- und Kaltpacks", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Temperaturänderung bei chemischen Warm- und Kaltpacks“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Temperature changes in chemical hot and cold packs", "methods": [ "Functions & modelling" ], "description": "Turn “Temperature changes in chemical hot and cold packs” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 480, "source_index": 297, "id": "topic-297-filtration-efficiency-measured-by-suspended-solid-mass-in-different-wa", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 2 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Filtrationseffizienz: Schwebstoffmasse in Teichwasser, Leitungswasser, Regenwasser", "methods": [ "Optimierung" ], "description": "Formuliere zu „Filtrationseffizienz: Schwebstoffmasse in Teichwasser, Leitungswasser, Regenwasser“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Filtration efficiency measured by suspended-solid mass in different water samples", "methods": [ "Optimisation" ], "description": "Turn “Filtration efficiency measured by suspended-solid mass in different water samples” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "optimization" ] }, { "no": 481, "source_index": 317, "id": "topic-317-voltage-distribution-in-series-and-parallel-circuits-with-identical-la", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10, 12 ], "measurement_codes": [ 5 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Spannungsabfall in Reihen- vs. Parallelschaltung identischer Lampen", "methods": [ "Stochastik", "Folgen & Reihen" ], "description": "Entwickle aus „Spannungsabfall in Reihen- vs. Parallelschaltung identischer Lampen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Electricity", "title": "Voltage distribution in series and parallel circuits with identical lamps", "methods": [ "Statistics & probability", "Sequences & series" ], "description": "Turn “Voltage distribution in series and parallel circuits with identical lamps” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "sequences_series" ] }, { "no": 482, "source_index": 337, "id": "topic-337-battery-discharge-across-different-temperatures-using-safe-manufacture", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 3, 5 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Batterieentladung bei verschiedenen Temperaturen: Spannung und Masse (Gasbildung?)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Batterieentladung bei verschiedenen Temperaturen: Spannung und Masse (Gasbildung?)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Battery discharge across different temperatures using safe manufacturer-approved conditions", "methods": [ "Functions & modelling" ], "description": "Turn “Battery discharge across different temperatures using safe manufacturer-approved conditions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 483, "source_index": 14, "id": "topic-014-the-mathematics-of-isbn-and-iban-check-digits", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 7, "courses": [ "aa", "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL", "de": { "category": "Algebra & Zahlentheorie", "title": "Die Mathematik der ISBN- und IBAN-Prüfziffern", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Die Mathematik der ISBN- und IBAN-Prüfziffern“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "The mathematics of ISBN and IBAN check digits", "methods": [ "Number theory", "Algebra" ], "description": "Turn “The mathematics of ISBN and IBAN check digits” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 484, "source_index": 34, "id": "topic-034-areas-between-curves-and-their-meaning-in-economics", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Flächen zwischen Kurven und ihre Bedeutung in der Ökonomie", "methods": [ "Stochastik", "Geometrie" ], "description": "Entwickle aus „Flächen zwischen Kurven und ihre Bedeutung in der Ökonomie“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Analysis & calculus", "title": "Areas between curves and their meaning in economics", "methods": [ "Statistics & probability", "Geometry" ], "description": "Turn “Areas between curves and their meaning in economics” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "geometry" ] }, { "no": 485, "source_index": 55, "id": "topic-055-comparing-probabilities-in-different-games-of-chance", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Vergleich von Wahrscheinlichkeiten bei verschiedenen Glücksspielen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Vergleich von Wahrscheinlichkeiten bei verschiedenen Glücksspielen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Comparing probabilities in different games of chance", "methods": [ "Statistics & probability" ], "description": "Turn “Comparing probabilities in different games of chance” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 486, "source_index": 76, "id": "topic-076-modelling-climate-change-with-simple-climate-models", "category_key": "mathematical-modelling", "assessment_code": 3, "course_code": 5, "courses": [ "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung des Klimawandels mit einfachen Klimamodellen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung des Klimawandels mit einfachen Klimamodellen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling climate change with simple climate models", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling climate change with simple climate models” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 487, "source_index": 96, "id": "topic-096-calculating-areas-with-pick-s-theorem", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 10 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Berechnung von Flächen mittels Pick’s Theorem", "methods": [ "Geometrie", "Beweisführung" ], "description": "Formuliere zu „Berechnung von Flächen mittels Pick’s Theorem“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Calculating areas with Pick's theorem", "methods": [ "Geometry", "Proof" ], "description": "Turn “Calculating areas with Pick's theorem” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry", "proof" ] }, { "no": 488, "source_index": 115, "id": "topic-115-calculating-economic-order-quantity-with-the-eoq-model", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Berechnung der optimalen Bestellmenge (EOQ-Modell)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Berechnung der optimalen Bestellmenge (EOQ-Modell)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Calculating economic order quantity with the EOQ model", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Calculating economic order quantity with the EOQ model” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 489, "source_index": 132, "id": "topic-132-a-proof-of-the-fundamental-theorem-of-arithmetic", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Beweis des Fundamentalsatzes der Arithmetik", "methods": [ "Beweisführung" ], "description": "Die Idee „Beweis des Fundamentalsatzes der Arithmetik“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "A proof of the fundamental theorem of arithmetic", "methods": [ "Proof" ], "description": "Develop “A proof of the fundamental theorem of arithmetic” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "proof" ] }, { "no": 490, "source_index": 157, "id": "topic-157-the-mathematics-of-soap-bubbles-and-minimal-surfaces", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Untersuchung der Mathematik von Seifenblasen (Minimalflächen)", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ], "description": "Formuliere zu „Untersuchung der Mathematik von Seifenblasen (Minimalflächen)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "The mathematics of soap bubbles and minimal surfaces", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ], "description": "Turn “The mathematics of soap bubbles and minimal surfaces” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ] }, { "no": 491, "source_index": 278, "id": "topic-278-thermal-radiation-from-matte-black-and-shiny-metal-surfaces-at-the-sam", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 4, 1, 3 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmestrahlung verschiedener Oberflächen gleicher Temperatur (schwarz Matt vs. Metall glänzend)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Wärmestrahlung verschiedener Oberflächen gleicher Temperatur (schwarz Matt vs. Metall glänzend)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Thermal radiation from matte black and shiny metal surfaces at the same temperature", "methods": [ "Geometry" ], "description": "Turn “Thermal radiation from matte black and shiny metal surfaces at the same temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 492, "source_index": 298, "id": "topic-298-comparing-fat-content-in-crisps-by-supervised-solvent-extraction", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 16, 21 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Fettgehalt verschiedener Kartoffelchips durch Petrol-Ether-Extraktion (Masse vor/nach)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Fettgehalt verschiedener Kartoffelchips durch Petrol-Ether-Extraktion (Masse vor/nach)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Comparing fat content in crisps by supervised solvent extraction", "methods": [ "Functions & modelling" ], "description": "Turn “Comparing fat content in crisps by supervised solvent extraction” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 493, "source_index": 318, "id": "topic-318-surface-resistance-of-wood-metal-plastic-and-water", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 1 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Oberflächenwiderstand verschiedener Materialien (Holz, Metall, Kunststoff, Wasser, Haut)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Oberflächenwiderstand verschiedener Materialien (Holz, Metall, Kunststoff, Wasser, Haut)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Surface resistance of wood, metal, plastic and water", "methods": [ "Geometry" ], "description": "Turn “Surface resistance of wood, metal, plastic and water” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 494, "source_index": 338, "id": "topic-338-drying-curves-of-wet-clay-or-paper-mass-loss-and-surface-temperature", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 4, 1, 3 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Trocknungskurven: Masseverlust und Oberflächentemperatur von nassem Ton/Papier", "methods": [ "Geometrie" ], "description": "Formuliere zu „Trocknungskurven: Masseverlust und Oberflächentemperatur von nassem Ton/Papier“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Drying curves of wet clay or paper: mass loss and surface temperature", "methods": [ "Geometry" ], "description": "Turn “Drying curves of wet clay or paper: mass loss and surface temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 495, "source_index": 15, "id": "topic-015-number-sequences-and-their-explicit-formulae", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung von Zahlenfolgen und deren explizite Formeln", "methods": [ "Zahlentheorie", "Geometrie", "Folgen & Reihen", "Algebra" ], "description": "Formuliere zu „Untersuchung von Zahlenfolgen und deren explizite Formeln“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Number sequences and their explicit formulae", "methods": [ "Number theory", "Geometry", "Sequences & series", "Algebra" ], "description": "Turn “Number sequences and their explicit formulae” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "geometry", "sequences_series", "algebra" ] }, { "no": 496, "source_index": 35, "id": "topic-035-modelling-oscillations-with-damped-harmonic-oscillators", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Modellierung von Schwingungen mit gedämpften harmonischen Oszillatoren", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ], "description": "Formuliere zu „Modellierung von Schwingungen mit gedämpften harmonischen Oszillatoren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Modelling oscillations with damped harmonic oscillators", "methods": [ "Functions & modelling", "Differential equations" ], "description": "Turn “Modelling oscillations with damped harmonic oscillators” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations" ] }, { "no": 497, "source_index": 56, "id": "topic-056-correlation-between-weather-and-mood", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 10 ], "measurement_codes": [ 12, 14 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Korrelation zwischen Wetter und Stimmung", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression" ], "description": "Entwickle aus „Untersuchung der Korrelation zwischen Wetter und Stimmung“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Correlation between weather and mood", "methods": [ "Functions & modelling", "Statistics & probability", "Regression" ], "description": "Turn “Correlation between weather and mood” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "functions_modeling", "stochastics", "regression" ] }, { "no": 498, "source_index": 77, "id": "topic-077-the-propagation-of-light-through-different-media", "category_key": "mathematical-modelling", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 10 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Untersuchung der Ausbreitung von Licht in verschiedenen Medien", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Ausbreitung von Licht in verschiedenen Medien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "The propagation of light through different media", "methods": [ "Functions & modelling" ], "description": "Turn “The propagation of light through different media” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 499, "source_index": 97, "id": "topic-097-voronoi-diagrams-in-natural-structures", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung von Voronoi-Diagrammen in der Natur", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Untersuchung von Voronoi-Diagrammen in der Natur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Voronoi diagrams in natural structures", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “Voronoi diagrams in natural structures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 500, "source_index": 116, "id": "topic-116-depreciation-methods-in-accounting", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Untersuchung von Abschreibungsmethoden in der Buchhaltung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung von Abschreibungsmethoden in der Buchhaltung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Depreciation methods in accounting", "methods": [ "Functions & modelling" ], "description": "Turn “Depreciation methods in accounting” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 501, "source_index": 133, "id": "topic-133-axiom-systems-through-the-example-of-geometry", "category_key": "logic-set-theory-proof", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Logik, Mengenlehre & Beweise", "title": "Untersuchung von Axiomensystemen am Beispiel der Geometrie", "methods": [ "Geometrie", "Beweisführung" ], "description": "Die Idee „Untersuchung von Axiomensystemen am Beispiel der Geometrie“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Logic, set theory & proof", "title": "Axiom systems through the example of geometry", "methods": [ "Geometry", "Proof" ], "description": "Develop “Axiom systems through the example of geometry” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "geometry", "proof" ] }, { "no": 502, "source_index": 158, "id": "topic-158-analysing-the-distribution-of-stars-in-the-night-sky", "category_key": "applied-interdisciplinary-mathematics", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 17 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Angewandte Mathematik & Interdisziplinär", "title": "Analyse der Verteilung von Sternen am Nachthimmel", "methods": [ "Stochastik" ], "description": "Entwickle aus „Analyse der Verteilung von Sternen am Nachthimmel“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Applied & interdisciplinary mathematics", "title": "Analysing the distribution of stars in the night sky", "methods": [ "Statistics & probability" ], "description": "Turn “Analysing the distribution of stars in the night sky” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 503, "source_index": 279, "id": "topic-279-temperature-change-inside-a-compost-heap-over-fourteen-days", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 3, 6 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Temperaturverlauf in einem Komposthaufen über 14 Tage", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Temperaturverlauf in einem Komposthaufen über 14 Tage“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Temperature change inside a compost heap over fourteen days", "methods": [ "Functions & modelling" ], "description": "Turn “Temperature change inside a compost heap over fourteen days” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 504, "source_index": 299, "id": "topic-299-salt-content-of-water-samples-measured-by-evaporation-and-residue-mass", "category_key": "material-properties", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 2, 11, 13, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Salzgehalt verschiedener Wasserproben durch vollständige Verdunstung (Rückstandsmasse)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Salzgehalt verschiedener Wasserproben durch vollständige Verdunstung (Rückstandsmasse)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Salt content of water samples measured by evaporation and residue mass", "methods": [ "Functions & modelling" ], "description": "Turn “Salt content of water samples measured by evaporation and residue mass” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 505, "source_index": 319, "id": "topic-319-power-output-of-a-bicycle-dynamo-at-different-rotational-speeds", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3, 11 ], "measurement_codes": [ 5, 8, 9, 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Leistung eines Fahrraddynamos bei verschiedenen Drehzahlen (Geschwindigkeiten)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Leistung eines Fahrraddynamos bei verschiedenen Drehzahlen (Geschwindigkeiten)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Power output of a bicycle dynamo at different rotational speeds", "methods": [ "Functions & modelling" ], "description": "Turn “Power output of a bicycle dynamo at different rotational speeds” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 506, "source_index": 339, "id": "topic-339-baking-soda-and-vinegar-carbon-dioxide-mass-loss-and-temperature-chang", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 2, 3, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Chemische Reaktion: Masse CO₂-Verlust und Temperaturanstieg (Backpulver + Essig)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Chemische Reaktion: Masse CO₂-Verlust und Temperaturanstieg (Backpulver + Essig)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Baking soda and vinegar: carbon dioxide mass loss and temperature change", "methods": [ "Functions & modelling" ], "description": "Turn “Baking soda and vinegar: carbon dioxide mass loss and temperature change” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 507, "source_index": 16, "id": "topic-016-the-mathematics-behind-sudoku-solving-strategies", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 7, "courses": [ "aa", "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 7, 8 ], "measurement_codes": [ 13, 16 ], "safety_code": 0, "source_course_label": "AA & AI, SL", "de": { "category": "Algebra & Zahlentheorie", "title": "Die Mathematik hinter Sudoku-Lösungsstrategien", "methods": [ "Zahlentheorie", "Kombinatorik", "Algebra" ], "description": "Formuliere zu „Die Mathematik hinter Sudoku-Lösungsstrategien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "The mathematics behind Sudoku-solving strategies", "methods": [ "Number theory", "Combinatorics", "Algebra" ], "description": "Turn “The mathematics behind Sudoku-solving strategies” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "combinatorics", "algebra" ] }, { "no": 508, "source_index": 36, "id": "topic-036-optimising-a-vehicle-s-fuel-consumption", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Analysis & Calculus", "title": "Optimierung des Treibstoffverbrauchs eines Fahrzeugs", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ], "description": "Formuliere zu „Optimierung des Treibstoffverbrauchs eines Fahrzeugs“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Optimising a vehicle's fuel consumption", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ], "description": "Turn “Optimising a vehicle's fuel consumption” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ] }, { "no": 509, "source_index": 57, "id": "topic-057-statistical-analysis-of-election-results-and-forecasts", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 9 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Statistische Analyse von Wahlergebnissen und Prognosen", "methods": [ "Stochastik", "Zeitreihenanalyse" ], "description": "Entwickle aus „Statistische Analyse von Wahlergebnissen und Prognosen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Statistical analysis of election results and forecasts", "methods": [ "Statistics & probability", "Time-series analysis" ], "description": "Turn “Statistical analysis of election results and forecasts” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics", "time_series" ] }, { "no": 510, "source_index": 78, "id": "topic-078-modelling-population-change-in-a-city", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6, 9, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung der Bevölkerungsentwicklung einer Stadt", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung der Bevölkerungsentwicklung einer Stadt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling population change in a city", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling population change in a city” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 511, "source_index": 98, "id": "topic-098-geometric-constructions-of-ellipses-and-parabolas", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Geometrische Konstruktion von Ellipsen und Parabeln", "methods": [ "Geometrie" ], "description": "Formuliere zu „Geometrische Konstruktion von Ellipsen und Parabeln“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Geometric constructions of ellipses and parabolas", "methods": [ "Geometry" ], "description": "Turn “Geometric constructions of ellipses and parabolas” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 512, "source_index": 117, "id": "topic-117-comparing-fixed-term-and-instant-access-savings-rates-over-ten-years", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 9 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Vergleich von Festgeld- und Tagesgeldzinsen über 10 Jahre", "methods": [ "Finanzmathematik" ], "description": "Formuliere zu „Vergleich von Festgeld- und Tagesgeldzinsen über 10 Jahre“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Comparing fixed-term and instant-access savings rates over ten years", "methods": [ "Financial mathematics" ], "description": "Turn “Comparing fixed-term and instant-access savings rates over ten years” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "financial_math" ] }, { "no": 513, "source_index": 280, "id": "topic-280-cooling-molten-wax-or-chocolate-phase-transition-and-solidification", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 3, 4, 13 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Thermodynamik", "title": "Abkühlung von geschmolzenem Wachs/Schokolade: Phasenübergang und Erstarrung", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ], "description": "Formuliere zu „Abkühlung von geschmolzenem Wachs/Schokolade: Phasenübergang und Erstarrung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Cooling molten wax or chocolate: phase transition and solidification", "methods": [ "Functions & modelling", "Differential equations" ], "description": "Turn “Cooling molten wax or chocolate: phase transition and solidification” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_equations" ] }, { "no": 514, "source_index": 300, "id": "topic-300-biomass-growth-of-cress-or-sprouts-over-fourteen-days", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 2, 6 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Biomasse-Wachstum von Kresse oder Sprossen über 14 Tage", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Biomasse-Wachstum von Kresse oder Sprossen über 14 Tage“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Biomass growth of cress or sprouts over fourteen days", "methods": [ "Functions & modelling" ], "description": "Turn “Biomass growth of cress or sprouts over fourteen days” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 515, "source_index": 320, "id": "topic-320-bioelectric-voltages-in-selected-fruits-vegetables-and-plant-tissues", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 6 ], "measurement_codes": [ 5 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Bioelektrische Spannungen verschiedener Pflanzen (Kartoffel, Zitrone, Blattstiel)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Bioelektrische Spannungen verschiedener Pflanzen (Kartoffel, Zitrone, Blattstiel)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Bioelectric voltages in selected fruits, vegetables and plant tissues", "methods": [ "Functions & modelling" ], "description": "Turn “Bioelectric voltages in selected fruits, vegetables and plant tissues” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 516, "source_index": 340, "id": "topic-340-resistance-change-as-a-resistor-heats-during-current-flow", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 4, 5, 1, 3 ], "safety_code": 1, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Widerstand von Widerständen bei Erwärmung durch Stromfluss (Spannung + IR)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Widerstand von Widerständen bei Erwärmung durch Stromfluss (Spannung + IR)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Resistance change as a resistor heats during current flow", "methods": [ "Functions & modelling" ], "description": "Turn “Resistance change as a resistor heats during current flow” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 517, "source_index": 17, "id": "topic-017-palindromic-numbers-in-different-bases", "category_key": "algebra-number-theory", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 7 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung von Palindromzahlen in verschiedenen Basen", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Untersuchung von Palindromzahlen in verschiedenen Basen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Palindromic numbers in different bases", "methods": [ "Number theory", "Algebra" ], "description": "Turn “Palindromic numbers in different bases” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 518, "source_index": 37, "id": "topic-037-curvature-in-bridges-and-arches", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Untersuchung der Krümmung von Brücken und Bögen", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie" ], "description": "Formuliere zu „Untersuchung der Krümmung von Brücken und Bögen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Curvature in bridges and arches", "methods": [ "Functions & modelling", "Differential calculus", "Geometry" ], "description": "Turn “Curvature in bridges and arches” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "differential_calculus", "geometry" ] }, { "no": 519, "source_index": 58, "id": "topic-058-battery-life-across-different-brands", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 12 ], "measurement_codes": [ 5 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Lebensdauer von Batterien verschiedener Marken", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Lebensdauer von Batterien verschiedener Marken“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Battery life across different brands", "methods": [ "Statistics & probability" ], "description": "Turn “Battery life across different brands” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 520, "source_index": 79, "id": "topic-079-the-trajectory-of-a-frisbee-or-boomerang", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 3 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Untersuchung der Flugbahn von Frisbees oder Bumerangs", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Flugbahn von Frisbees oder Bumerangs“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "The trajectory of a frisbee or boomerang", "methods": [ "Functions & modelling" ], "description": "Turn “The trajectory of a frisbee or boomerang” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 521, "source_index": 99, "id": "topic-099-properties-of-torus-knots", "category_key": "geometry-topology", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung der Eigenschaften von Torusknoten", "methods": [ "Graphentheorie", "Geometrie" ], "description": "Formuliere zu „Untersuchung der Eigenschaften von Torusknoten“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Properties of torus knots", "methods": [ "Graph theory", "Geometry" ], "description": "Turn “Properties of torus knots” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory", "geometry" ] }, { "no": 522, "source_index": 118, "id": "topic-118-modelling-retirement-savings-under-different-scenarios", "category_key": "financial-mathematics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Finanzmathematik", "title": "Modellierung der Altersvorsorge mit verschiedenen Szenarien", "methods": [ "Funktionen & Modellierung", "Finanzmathematik" ], "description": "Formuliere zu „Modellierung der Altersvorsorge mit verschiedenen Szenarien“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Financial mathematics", "title": "Modelling retirement savings under different scenarios", "methods": [ "Functions & modelling", "Financial mathematics" ], "description": "Turn “Modelling retirement savings under different scenarios” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "financial_math" ] }, { "no": 523, "source_index": 281, "id": "topic-281-surface-heating-of-smartphone-batteries-during-gaming-streaming-and-st", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 4, 1, 5 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Erwärmung von Smartphone-Akkus bei Gaming, Streaming und Standby", "methods": [ "Geometrie" ], "description": "Formuliere zu „Erwärmung von Smartphone-Akkus bei Gaming, Streaming und Standby“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Surface heating of smartphone batteries during gaming, streaming and standby", "methods": [ "Geometry" ], "description": "Turn “Surface heating of smartphone batteries during gaming, streaming and standby” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 524, "source_index": 301, "id": "topic-301-density-and-air-fraction-in-different-chocolate-bars-measured-by-water", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 12 ], "measurement_codes": [ 2 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Dichte und Luftanteil verschiedener Schokoladenmarken durch Wasserverdrängung", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Dichte und Luftanteil verschiedener Schokoladenmarken durch Wasserverdrängung“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Density and air fraction in different chocolate bars measured by water displacement", "methods": [ "Functions & modelling" ], "description": "Turn “Density and air fraction in different chocolate bars measured by water displacement” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 525, "source_index": 321, "id": "topic-321-piezoelectric-voltage-under-different-applied-forces", "category_key": "electricity", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 5, 15 ], "safety_code": 2, "source_course_label": "AA, SL/HL", "de": { "category": "Elektrizität", "title": "Piezoelektrischer Effekt: Spannung bei Druck auf verschiedene Materialien (Quarz, Keramik)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Piezoelektrischer Effekt: Spannung bei Druck auf verschiedene Materialien (Quarz, Keramik)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Piezoelectric voltage under different applied forces", "methods": [ "Functions & modelling" ], "description": "Turn “Piezoelectric voltage under different applied forces” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 526, "source_index": 341, "id": "topic-341-plant-growth-biomass-versus-leaf-surface-temperature", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 2, 4, 3 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Pflanzenwachstum: Biomasse (Masse) vs. Blatttemperatur (Stressindikator)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Pflanzenwachstum: Biomasse (Masse) vs. Blatttemperatur (Stressindikator)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Plant growth: biomass versus leaf-surface temperature", "methods": [ "Geometry" ], "description": "Turn “Plant growth: biomass versus leaf-surface temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 527, "source_index": 18, "id": "topic-018-the-distribution-and-density-of-prime-numbers", "category_key": "algebra-number-theory", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Die Verteilung der Primzahlen und die Primzahldichte", "methods": [ "Stochastik", "Zahlentheorie", "Algebra" ], "description": "Die Idee „Die Verteilung der Primzahlen und die Primzahldichte“ lässt sich durch eigene Beispiele, Herleitungen oder eine kleine computergestützte Exploration präzisieren. Formuliere eine klare Vermutung, prüfe sie systematisch und vergleiche alternative Beweis- oder Modellansätze." }, "en": { "category": "Algebra & number theory", "title": "The distribution and density of prime numbers", "methods": [ "Statistics & probability", "Number theory", "Algebra" ], "description": "Develop “The distribution and density of prime numbers” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches." }, "method_keys": [ "stochastics", "number_theory", "algebra" ] }, { "no": 528, "source_index": 38, "id": "topic-038-calculating-the-centroid-of-irregular-regions", "category_key": "analysis-calculus", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Berechnung des Schwerpunkts unregelmäßiger Flächen", "methods": [ "Funktionen & Modellierung", "Integralrechnung", "Geometrie" ], "description": "Formuliere zu „Berechnung des Schwerpunkts unregelmäßiger Flächen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Calculating the centroid of irregular regions", "methods": [ "Functions & modelling", "Integral calculus", "Geometry" ], "description": "Turn “Calculating the centroid of irregular regions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "integral_calculus", "geometry" ] }, { "no": 529, "source_index": 59, "id": "topic-059-waiting-times-on-public-transport", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 6, 8 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Analyse der Wartezeiten bei öffentlichen Verkehrsmitteln", "methods": [ "Stochastik" ], "description": "Entwickle aus „Analyse der Wartezeiten bei öffentlichen Verkehrsmitteln“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Waiting times on public transport", "methods": [ "Statistics & probability" ], "description": "Turn “Waiting times on public transport” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 530, "source_index": 80, "id": "topic-080-modelling-household-water-consumption", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung des Wasserverbrauchs im Haushalt", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung des Wasserverbrauchs im Haushalt“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling household water consumption", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling household water consumption” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 531, "source_index": 100, "id": "topic-100-great-circle-distances-on-earth", "category_key": "geometry-topology", "assessment_code": 3, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Geometrie & Topologie", "title": "Berechnung von Entfernungen auf der Erdkugel (Großkreise)", "methods": [ "Geometrie" ], "description": "Formuliere zu „Berechnung von Entfernungen auf der Erdkugel (Großkreise)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Great-circle distances on Earth", "methods": [ "Geometry" ], "description": "Turn “Great-circle distances on Earth” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 532, "source_index": 282, "id": "topic-282-heat-output-of-led-halogen-and-incandescent-lamps-at-comparable-bright", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 4, 1, 3, 10 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Wärmeabgabe verschiedener Lampen-Technologien bei gleicher Helligkeit (LED, Halogen, Glühbirne)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Wärmeabgabe verschiedener Lampen-Technologien bei gleicher Helligkeit (LED, Halogen, Glühbirne)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "Heat output of LED, halogen and incandescent lamps at comparable brightness", "methods": [ "Functions & modelling" ], "description": "Turn “Heat output of LED, halogen and incandescent lamps at comparable brightness” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 533, "source_index": 302, "id": "topic-302-sugar-solubility-in-water-from-20-c-to-80-c", "category_key": "material-properties", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 3, 13, 16 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Sättigungsmenge von Zucker in Wasser bei Temperaturen von 20°C bis 80°C", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Sättigungsmenge von Zucker in Wasser bei Temperaturen von 20°C bis 80°C“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Sugar solubility in water from 20°C to 80°C", "methods": [ "Functions & modelling" ], "description": "Turn “Sugar solubility in water from 20°C to 80°C” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 534, "source_index": 322, "id": "topic-322-thermocouple-voltage-for-different-metal-pairs-and-junction-temperatur", "category_key": "electricity", "assessment_code": 1, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6 ], "measurement_codes": [ 3, 5, 13 ], "safety_code": 2, "source_course_label": "AA HL", "de": { "category": "Elektrizität", "title": "Thermoelement: Spannung bei Erwärmung einer Lötstelle mit verschiedenen Metallpaaren", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Thermoelement: Spannung bei Erwärmung einer Lötstelle mit verschiedenen Metallpaaren“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Thermocouple voltage for different metal pairs and junction temperatures", "methods": [ "Functions & modelling" ], "description": "Turn “Thermocouple voltage for different metal pairs and junction temperatures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 535, "source_index": 342, "id": "topic-342-comparing-coffee-cups-using-mass-surface-temperature-and-core-temperat", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5, 11 ], "measurement_codes": [ 2, 3, 4, 1 ], "safety_code": 0, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Kaffeetassen-Vergleich: Masse, Wärmeverlust (Oberfläche IR) und Kerntemperatur", "methods": [ "Geometrie" ], "description": "Formuliere zu „Kaffeetassen-Vergleich: Masse, Wärmeverlust (Oberfläche IR) und Kerntemperatur“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Combined experiments", "title": "Comparing coffee cups using mass, surface temperature and core temperature", "methods": [ "Geometry" ], "description": "Turn “Comparing coffee cups using mass, surface temperature and core temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 536, "source_index": 19, "id": "topic-019-repeating-patterns-in-decimal-expansions", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 10 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Algebra & Zahlentheorie", "title": "Untersuchung von Wiederholungsmustern in Dezimalbrüchen", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Untersuchung von Wiederholungsmustern in Dezimalbrüchen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "Repeating patterns in decimal expansions", "methods": [ "Number theory", "Algebra" ], "description": "Turn “Repeating patterns in decimal expansions” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 537, "source_index": 39, "id": "topic-039-taylor-series-and-their-convergence", "category_key": "analysis-calculus", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 10, 12 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Analysis & Calculus", "title": "Untersuchung von Taylor-Reihen und ihrer Konvergenz", "methods": [ "Folgen & Reihen" ], "description": "Formuliere zu „Untersuchung von Taylor-Reihen und ihrer Konvergenz“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Taylor series and their convergence", "methods": [ "Sequences & series" ], "description": "Turn “Taylor series and their convergence” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "sequences_series" ] }, { "no": 538, "source_index": 60, "id": "topic-060-the-normal-distribution-of-student-heights-in-a-class", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 4, "courses": [ "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1, 4 ], "measurement_codes": [ 14 ], "safety_code": 3, "source_course_label": "AI, SL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Normalverteilung bei Körpergrößen in der Klasse", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Normalverteilung bei Körpergrößen in der Klasse“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "The normal distribution of student heights in a class", "methods": [ "Statistics & probability" ], "description": "Turn “The normal distribution of student heights in a class” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 539, "source_index": 81, "id": "topic-081-light-propagation-in-optical-fibres", "category_key": "mathematical-modelling", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 10, 13 ], "safety_code": 0, "source_course_label": "AA HL", "de": { "category": "Mathematische Modellierung", "title": "Untersuchung der Ausbreitung von Licht in einer Faseroptik", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Untersuchung der Ausbreitung von Licht in einer Faseroptik“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Light propagation in optical fibres", "methods": [ "Functions & modelling" ], "description": "Turn “Light propagation in optical fibres” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 540, "source_index": 101, "id": "topic-101-penrose-tilings", "category_key": "geometry-topology", "assessment_code": 2, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 11 ], "measurement_codes": [ 20 ], "safety_code": 0, "source_course_label": "AA, HL", "de": { "category": "Geometrie & Topologie", "title": "Untersuchung von Penrose-Parkettierungen", "methods": [ "Geometrie" ], "description": "Formuliere zu „Untersuchung von Penrose-Parkettierungen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Geometry & topology", "title": "Penrose tilings", "methods": [ "Geometry" ], "description": "Turn “Penrose tilings” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "geometry" ] }, { "no": 541, "source_index": 283, "id": "topic-283-a-temperature-map-of-a-hotplate-centre-to-edge-variation", "category_key": "thermodynamics", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 5 ], "measurement_codes": [ 4, 3 ], "safety_code": 1, "source_course_label": "AI, SL/HL", "de": { "category": "Thermodynamik", "title": "Temperaturkarte einer Kochplatte im Betrieb: Unterschiede Mitte vs. Rand", "methods": [ "Graphentheorie" ], "description": "Formuliere zu „Temperaturkarte einer Kochplatte im Betrieb: Unterschiede Mitte vs. Rand“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Thermodynamics", "title": "A temperature map of a hotplate: centre-to-edge variation", "methods": [ "Graph theory" ], "description": "Turn “A temperature map of a hotplate: centre-to-edge variation” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "graph_theory" ] }, { "no": 542, "source_index": 303, "id": "topic-303-drying-rates-of-cotton-polyester-wool-and-microfibre-textiles", "category_key": "material-properties", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 12 ], "measurement_codes": [ 2, 6 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Stoffeigenschaften", "title": "Trocknungsgeschwindigkeit verschiedener Textilien (Baumwolle, Polyester, Wolle, Mikrofaser)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Trocknungsgeschwindigkeit verschiedener Textilien (Baumwolle, Polyester, Wolle, Mikrofaser)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Material properties", "title": "Drying rates of cotton, polyester, wool and microfibre textiles", "methods": [ "Functions & modelling" ], "description": "Turn “Drying rates of cotton, polyester, wool and microfibre textiles” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 543, "source_index": 323, "id": "topic-323-battery-discharge-at-different-ambient-temperatures", "category_key": "electricity", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 3, 5 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Elektrizität", "title": "Entladung eines Akkus bei verschiedenen Umgebungstemperaturen (0°C, 20°C, 40°C)", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Entladung eines Akkus bei verschiedenen Umgebungstemperaturen (0°C, 20°C, 40°C)“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Electricity", "title": "Battery discharge at different ambient temperatures", "methods": [ "Functions & modelling" ], "description": "Turn “Battery discharge at different ambient temperatures” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 544, "source_index": 343, "id": "topic-343-ice-formation-frost-mass-gain-and-surface-temperature-over-time", "category_key": "combined-experiments", "assessment_code": 1, "course_code": 3, "courses": [ "aa" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 2, 4, 1, 3 ], "safety_code": 0, "source_course_label": "AA, SL/HL", "de": { "category": "Kombinierte Experimente", "title": "Eisbildung: Massezunahme durch Frost und Oberflächentemperatur der Eisschicht", "methods": [ "Geometrie", "Zeitreihenanalyse" ], "description": "Entwickle aus „Eisbildung: Massezunahme durch Frost und Oberflächentemperatur der Eisschicht“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Combined experiments", "title": "Ice formation: frost mass gain and surface temperature over time", "methods": [ "Geometry", "Time-series analysis" ], "description": "Turn “Ice formation: frost mass gain and surface temperature over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "geometry", "time_series" ] }, { "no": 545, "source_index": 20, "id": "topic-020-the-mathematics-of-barcodes-and-qr-codes", "category_key": "algebra-number-theory", "assessment_code": 1, "course_code": 7, "courses": [ "aa", "ai" ], "levels": [ "sl" ], "personal_engagement_codes": [ 1 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, SL", "de": { "category": "Algebra & Zahlentheorie", "title": "Die Mathematik der Barcodes und QR-Codes", "methods": [ "Zahlentheorie", "Algebra" ], "description": "Formuliere zu „Die Mathematik der Barcodes und QR-Codes“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Algebra & number theory", "title": "The mathematics of barcodes and QR codes", "methods": [ "Number theory", "Algebra" ], "description": "Turn “The mathematics of barcodes and QR codes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "number_theory", "algebra" ] }, { "no": 546, "source_index": 40, "id": "topic-040-modelling-plant-growth-rates", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 6, 11 ], "measurement_codes": [ 13 ], "safety_code": 1, "source_course_label": "AA & AI, SL/HL", "de": { "category": "Analysis & Calculus", "title": "Modellierung von Wachstumsraten von Pflanzen", "methods": [ "Funktionen & Modellierung" ], "description": "Formuliere zu „Modellierung von Wachstumsraten von Pflanzen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Analysis & calculus", "title": "Modelling plant growth rates", "methods": [ "Functions & modelling" ], "description": "Turn “Modelling plant growth rates” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling" ] }, { "no": 547, "source_index": 61, "id": "topic-061-comparing-box-plots-across-different-school-grading-systems", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 4, 12 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Vergleich von Box-Plots bei verschiedenen Schulnotensystemen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Vergleich von Box-Plots bei verschiedenen Schulnotensystemen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "Comparing box plots across different school grading systems", "methods": [ "Statistics & probability" ], "description": "Turn “Comparing box plots across different school grading systems” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 548, "source_index": 82, "id": "topic-082-modelling-the-efficiency-of-solar-energy-systems", "category_key": "mathematical-modelling", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 1, 11 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AI, SL/HL", "de": { "category": "Mathematische Modellierung", "title": "Modellierung der Effizienz von Solarmodellen", "methods": [ "Funktionen & Modellierung", "Optimierung" ], "description": "Formuliere zu „Modellierung der Effizienz von Solarmodellen“ eine messbare oder mathematisch klar definierte Forschungsfrage. Entwickle ein geeignetes Modell, prüfe es an eigenen Daten, Konstruktionen oder Beispielen und reflektiere Annahmen, Fehlerquellen und mögliche Verbesserungen." }, "en": { "category": "Mathematical modelling", "title": "Modelling the efficiency of solar-energy systems", "methods": [ "Functions & modelling", "Optimisation" ], "description": "Turn “Modelling the efficiency of solar-energy systems” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements." }, "method_keys": [ "functions_modeling", "optimization" ] }, { "no": 549, "source_index": 41, "id": "topic-041-analysing-speed-distributions-in-traffic-flow", "category_key": "analysis-calculus", "assessment_code": 1, "course_code": 8, "courses": [ "aa", "ai" ], "levels": [ "hl" ], "personal_engagement_codes": [ 6 ], "measurement_codes": [ 0 ], "safety_code": 0, "source_course_label": "AA & AI, HL", "de": { "category": "Analysis & Calculus", "title": "Analyse der Geschwindigkeitsverteilung bei Verkehrsströmen", "methods": [ "Stochastik" ], "description": "Entwickle aus „Analyse der Geschwindigkeitsverteilung bei Verkehrsströmen“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Analysis & calculus", "title": "Analysing speed distributions in traffic flow", "methods": [ "Statistics & probability" ], "description": "Turn “Analysing speed distributions in traffic flow” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 550, "source_index": 62, "id": "topic-062-the-probability-of-twin-births", "category_key": "statistics-probability", "assessment_code": 1, "course_code": 6, "courses": [ "ai" ], "levels": [ "hl", "sl" ], "personal_engagement_codes": [ 9 ], "measurement_codes": [ 13 ], "safety_code": 3, "source_course_label": "AI, SL/HL", "de": { "category": "Statistik & Wahrscheinlichkeit", "title": "Untersuchung der Wahrscheinlichkeit von Zwillingsgeburten", "methods": [ "Stochastik" ], "description": "Entwickle aus „Untersuchung der Wahrscheinlichkeit von Zwillingsgeburten“ eine klar eingegrenzte Forschungsfrage und wähle einen nachvollziehbaren Datensatz oder eine eigene Messreihe. Vergleiche passende Modelle, untersuche Residuen und bewerte Unsicherheiten, Ausreißer sowie Grenzen der Aussage." }, "en": { "category": "Statistics & probability", "title": "The probability of twin births", "methods": [ "Statistics & probability" ], "description": "Turn “The probability of twin births” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations." }, "method_keys": [ "stochastics" ] }, { "no": 551, "source_index": 1001, "id": "topic-551-water-temperature-and-flow-velocity", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 1, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Wassertemperatur und Fließgeschwindigkeit", "description": "Miss den Volumenstrom durch ein dünnes Rohr bei konstantem Druckgefälle und verschiedenen Temperaturen. Vergleiche lineare, polynomiale und viskositätsbasierte Modelle.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Water temperature and flow velocity", "description": "Measure the flow rate through a narrow tube at constant pressure head and different temperatures. Compare linear, polynomial, and viscosity-based models.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 552, "source_index": 1002, "id": "topic-552-streambed-roughness-and-velocity", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 2, 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 2, "method_keys": [ "functions_modeling" ], "de": { "category": "Wasser und Strömung", "title": "Rauheit des Flussbetts und Geschwindigkeit", "description": "Verwende glatte Folie, Sandpapier, Sand und Kies als austauschbare Untergründe. Untersuche, wie ein selbst definierter Rauheitsindex mit Geschwindigkeit und Abfluss zusammenhängt.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Water and flow", "title": "Streambed roughness and velocity", "description": "Use smooth plastic, sandpaper, sand, and gravel as interchangeable beds. Investigate how a defined roughness index relates to velocity and discharge.", "methods": [ "Functions & modelling" ] } }, { "no": 553, "source_index": 1003, "id": "topic-553-channel-slope-and-discharge", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 3, "method_keys": [ "functions_modeling", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Gefälle und Abflussmenge", "description": "Verändere das Gefälle eines Versuchsgerinnes bei ansonsten gleichen Bedingungen. Prüfe, ob ein Potenzmodell den Zusammenhang zwischen Gefälle und Abfluss gut beschreibt.", "methods": [ "Funktionen & Modellierung", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Channel slope and discharge", "description": "Vary the slope of a model channel while keeping other conditions constant. Test whether a power model describes the relationship between slope and discharge.", "methods": [ "Functions & modelling", "Algebra" ] } }, { "no": 554, "source_index": 1004, "id": "topic-554-bend-radius-and-velocity-distribution", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 8, 11 ], "measurement_codes": [ 1, 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 4, "method_keys": [ "stochastics", "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Kurvenradius und Geschwindigkeitsverteilung", "description": "Baue Gerinne mit unterschiedlichen Kurvenradien und filme schwimmende Markierungspartikel. Vergleiche die Geschwindigkeit an Innen- und Außenseite der Kurve.", "methods": [ "Stochastik", "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Bend radius and velocity distribution", "description": "Build channels with different bend radii and film floating tracer particles. Compare velocities along the inner and outer sides of each bend.", "methods": [ "Statistics & probability", "Geometry" ] } }, { "no": 555, "source_index": 1005, "id": "topic-555-channel-sinuosity-and-travel-time", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 5, "method_keys": [ "functions_modeling", "stochastics", "geometry", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Mäandergrad und Durchlaufzeit", "description": "Vergleiche gerade und mäanderförmige Gerinne mit derselben Höhendifferenz. Modelliere die Durchlaufzeit in Abhängigkeit von Weglänge und Anzahl der Kurven.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Geometrie", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Channel sinuosity and travel time", "description": "Compare straight and meandering channels with the same elevation drop. Model travel time as a function of path length and number of bends.", "methods": [ "Functions & modelling", "Statistics & probability", "Geometry", "Algebra" ] } }, { "no": 556, "source_index": 1006, "id": "topic-556-cross-sectional-shape-and-discharge", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 6, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Querschnittsform und Abfluss", "description": "Vergleiche rechteckige, dreieckige und halbkreisförmige Gerinne mit ähnlicher Querschnittsfläche. Beziehe den benetzten Umfang und den hydraulischen Radius ein.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Cross-sectional shape and discharge", "description": "Compare rectangular, triangular, and semicircular channels with similar cross-sectional areas. Include wetted perimeter and hydraulic radius in the model.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 557, "source_index": 1007, "id": "topic-557-water-depth-and-wave-speed", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11, 12 ], "measurement_codes": [ 1, 5, 7, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 7, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Wassertiefe und Wellengeschwindigkeit", "description": "Erzeuge kleine Wellen in einer langen flachen Wanne und bestimme ihre Geschwindigkeit per Videoanalyse. Vergleiche ein lineares mit einem Wurzelmodell.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Water depth and wave speed", "description": "Generate small waves in a long shallow tray and determine their speed using video analysis. Compare a linear model with a square-root model.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 558, "source_index": 1008, "id": "topic-558-obstacle-density-and-flow-loss", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 5, 6, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 8, "method_keys": [ "functions_modeling" ], "de": { "category": "Wasser und Strömung", "title": "Hindernisdichte und Strömungsverlust", "description": "Platziere unterschiedlich viele gleich große Steine oder Stäbe im Gerinne. Miss Durchlaufzeit, Wasserstand vor den Hindernissen und Abflussmenge.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Water and flow", "title": "Obstacle density and flow loss", "description": "Place different numbers of equal-sized stones or rods in the channel. Measure travel time, upstream water level, and discharge.", "methods": [ "Functions & modelling" ] } }, { "no": 559, "source_index": 1009, "id": "topic-559-artificial-aquatic-plants-and-flow", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 1, 5, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 9, "method_keys": [ "functions_modeling" ], "de": { "category": "Wasser und Strömung", "title": "Künstliche Wasserpflanzen und Strömung", "description": "Simuliere Wasserpflanzen durch flexible Streifen oder Halme. Untersuche getrennt den Einfluss von Pflanzendichte, Höhe oder Flexibilität.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Water and flow", "title": "Artificial aquatic plants and flow", "description": "Simulate aquatic plants using flexible strips or stems. Separately investigate the effects of plant density, height, or flexibility.", "methods": [ "Functions & modelling" ] } }, { "no": 560, "source_index": 1010, "id": "topic-560-grain-size-and-onset-of-sediment-transport", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 12, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 10, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Korngröße und Beginn des Sedimenttransports", "description": "Erhöhe schrittweise die Strömung, bis Sand- oder Kieskörner verschiedener Größe bewegt werden. Modelliere die kritische Geschwindigkeit als Funktion des Korndurchmessers.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Grain size and onset of sediment transport", "description": "Gradually increase the flow until sand or gravel grains of different sizes begin to move. Model critical velocity as a function of grain diameter.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 561, "source_index": 1011, "id": "topic-561-particle-size-and-settling-velocity", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 10, 11, 12 ], "measurement_codes": [ 5, 11, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 11, "method_keys": [ "functions_modeling", "number_theory", "geometry", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Partikelgröße und Sinkgeschwindigkeit", "description": "Lass kugelförmige Partikel oder sortierte Sandkörner durch eine Wassersäule sinken. Vergleiche lineare, quadratische und andere Potenzmodelle.", "methods": [ "Funktionen & Modellierung", "Zahlentheorie", "Geometrie", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Particle size and settling velocity", "description": "Allow spherical particles or sorted sand grains to settle through a water column. Compare linear, quadratic, and other power models.", "methods": [ "Functions & modelling", "Number theory", "Geometry", "Algebra" ] } }, { "no": 562, "source_index": 1012, "id": "topic-562-temperature-and-dye-dispersion", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 5, 6, 7, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 12, "method_keys": [ "stochastics", "geometry", "time_series" ], "de": { "category": "Wasser und Strömung", "title": "Temperatur und Ausbreitung eines Farbstoffs", "description": "Gib einen gleich großen Farbtropfen in ruhendes Wasser unterschiedlicher Temperatur. Bestimme mit Bildanalyse die farbige Fläche oder Farbvarianz über der Zeit.", "methods": [ "Stochastik", "Geometrie", "Zeitreihenanalyse" ] }, "en": { "category": "Water and flow", "title": "Temperature and dye dispersion", "description": "Place an equal-sized dye drop into still water at different temperatures. Use image analysis to measure coloured area or colour variance over time.", "methods": [ "Statistics & probability", "Geometry", "Time-series analysis" ] } }, { "no": 563, "source_index": 1013, "id": "topic-563-solution-concentration-and-flow-rate", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 5, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 13, "method_keys": [ "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Konzentration einer Lösung und Volumenstrom", "description": "Vergleiche Wasser mit verschiedenen Zucker- oder Glycerinanteilen in einem dünnen Rohr. Untersuche, wie die Konzentration den Volumenstrom verändert.", "methods": [ "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Solution concentration and flow rate", "description": "Compare water containing different proportions of sugar or glycerol in a narrow tube. Investigate how concentration changes the flow rate.", "methods": [ "Geometry" ] } }, { "no": 564, "source_index": 1014, "id": "topic-564-water-head-and-jet-range", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 14, "method_keys": [ "functions_modeling" ], "de": { "category": "Wasser und Strömung", "title": "Wasserhöhe und Reichweite eines Wasserstrahls", "description": "Lass Wasser aus einer seitlichen Öffnung eines Behälters austreten. Variiere die Wasserhöhe über der Öffnung und modelliere die horizontale Reichweite.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Water and flow", "title": "Water head and jet range", "description": "Allow water to leave through a side opening in a container. Vary the water height above the opening and model the horizontal range.", "methods": [ "Functions & modelling" ] } }, { "no": 565, "source_index": 1015, "id": "topic-565-outlet-area-and-drainage-time", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 6, 10, 11, 12 ], "measurement_codes": [ 5, 6, 12, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 15, "method_keys": [ "functions_modeling", "differential_equations", "geometry", "proof", "time_series", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Öffnungsfläche und Entleerungszeit", "description": "Entleere identische Behälter durch Öffnungen verschiedener Größe. Erfasse zusätzlich den Wasserstand über der Zeit und entwickle ein Differentialgleichungsmodell.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie", "Beweisführung", "Zeitreihenanalyse", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Outlet area and drainage time", "description": "Drain identical containers through openings of different sizes. Also record water level over time and develop a differential-equation model.", "methods": [ "Functions & modelling", "Differential equations", "Geometry", "Proof", "Time-series analysis", "Algebra" ] } }, { "no": 566, "source_index": 1016, "id": "topic-566-height-difference-and-siphon-performance", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 6, 11, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 16, "method_keys": [ "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Höhendifferenz und Siphonleistung", "description": "Verändere die Höhendifferenz zwischen zwei Wasserbehältern bei gleichem Schlauch. Miss Volumenstrom und Entleerungszeit.", "methods": [ "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Height difference and siphon performance", "description": "Vary the height difference between two water containers while using the same tube. Measure flow rate and drainage time.", "methods": [ "Geometry" ] } }, { "no": 567, "source_index": 1017, "id": "topic-567-soil-composition-and-infiltration", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 5, 6, 16, 18 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 17, "method_keys": [ "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Bodenzusammensetzung und Infiltration", "description": "Vergleiche definierte Mischungen aus Sand, Gartenerde und Ton. Erfasse die eingedrungene Wassermenge als Funktion der Zeit.", "methods": [ "Algebra" ] }, "en": { "category": "Water and flow", "title": "Soil composition and infiltration", "description": "Compare defined mixtures of sand, soil, and clay. Record cumulative water infiltration as a function of time.", "methods": [ "Algebra" ] } }, { "no": 568, "source_index": 1018, "id": "topic-568-filter-grain-size-and-filtration-performance", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 6, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 18, "method_keys": [ "geometry" ], "de": { "category": "Wasser und Strömung", "title": "Filterkorngröße und Filterleistung", "description": "Untersuche, wie Korngröße und Schichtdicke eines Sandfilters die Durchflusszeit und Trübung beeinflussen.", "methods": [ "Geometrie" ] }, "en": { "category": "Water and flow", "title": "Filter grain size and filtration performance", "description": "Investigate how the grain size and layer depth of a sand filter affect flow time and turbidity.", "methods": [ "Geometry" ] } }, { "no": 569, "source_index": 1019, "id": "topic-569-decay-of-a-water-vortex", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 19, "method_keys": [ "functions_modeling", "trigonometry", "algebra" ], "de": { "category": "Wasser und Strömung", "title": "Abklingen eines Wasserwirbels", "description": "Erzeuge einen möglichst reproduzierbaren Wirbel und filme die Winkelgeschwindigkeit eines Markierungspunkts. Prüfe exponentielle und Potenz-Abklingmodelle.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Algebra" ] }, "en": { "category": "Water and flow", "title": "Decay of a water vortex", "description": "Create a reproducible vortex and film the angular velocity of a marker. Test exponential and power-decay models.", "methods": [ "Functions & modelling", "Trigonometry", "Algebra" ] } }, { "no": 570, "source_index": 1020, "id": "topic-570-water-wheel-blade-angle", "category_key": "water-and-flow", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 15, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 20, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Wasser und Strömung", "title": "Schaufelwinkel eines Wasserrads", "description": "Baue Wasserräder mit verschiedenen Schaufelwinkeln. Miss Drehzahl, Drehmoment oder elektrische Leistung und bestimme einen optimalen Winkel.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Water and flow", "title": "Water-wheel blade angle", "description": "Build water wheels with different blade angles. Measure rotational speed, torque, or electrical output and determine an optimal angle.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 571, "source_index": 1021, "id": "topic-571-air-bubble-fraction-and-flexural-strength", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 2, 3, 7, 11, 15 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 21, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Lufteinschlussanteil und Biegefestigkeit", "description": "Fotografiere gleich große Eisproben vor dem Belastungstest und bestimme den sichtbaren Blasenflächenanteil. Vergleiche ihn mit der maximalen Bruchlast.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Air-bubble fraction and flexural strength", "description": "Photograph equal-sized ice samples before loading and calculate the visible bubble-area fraction. Compare it with maximum breaking load.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 572, "source_index": 1022, "id": "topic-572-bubble-size-and-fracture-strength", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 1, 3, 7, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 22, "method_keys": [ "functions_modeling", "stochastics", "regression", "number_theory", "geometry" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Blasengröße und Bruchfestigkeit", "description": "Bestimme mittleren Blasendurchmesser, Streuung und Blasenzahl durch Bildanalyse. Verwende eine multiple Regression zur Vorhersage der Festigkeit.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Zahlentheorie", "Geometrie" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Bubble size and fracture strength", "description": "Determine mean bubble diameter, variation, and bubble count using image analysis. Use multiple regression to predict strength.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Number theory", "Geometry" ] } }, { "no": 573, "source_index": 1023, "id": "topic-573-freezing-rate-and-trapped-air", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 3, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 23, "method_keys": [ "functions_modeling" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Gefriergeschwindigkeit und Lufteinschlüsse", "description": "Lass identische Wassermengen unterschiedlich schnell gefrieren, beispielsweise mit verschiedenen Isolationsschichten. Miss Blasenanteil, Transparenz und Festigkeit.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Freezing rate and trapped air", "description": "Freeze identical amounts of water at different rates, for example using different insulation layers. Measure bubble content, transparency, and strength.", "methods": [ "Functions & modelling" ] } }, { "no": 574, "source_index": 1024, "id": "topic-574-ice-temperature-and-breaking-stress", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 3, 5, 15, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 24, "method_keys": [ "geometry" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Eistemperatur und Bruchspannung", "description": "Teste standardisierte Eisstäbe bei mehreren Temperaturen unter 0 °C. Berechne aus Bruchlast und Probengeometrie eine vergleichbare Bruchspannung.", "methods": [ "Geometrie" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Ice temperature and breaking stress", "description": "Test standardized ice beams at several temperatures below 0 °C. Calculate a comparable breaking stress from failure load and sample geometry.", "methods": [ "Geometry" ] } }, { "no": 575, "source_index": 1025, "id": "topic-575-salinity-and-ice-strength", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 11, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 25, "method_keys": [ "functions_modeling" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Salzgehalt und Festigkeit", "description": "Stelle Eisproben mit unterschiedlichen, genau gemessenen Salzkonzentrationen her. Untersuche Festigkeit, Dichte und Bruchverhalten.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Salinity and ice strength", "description": "Produce ice samples with different accurately measured salt concentrations. Investigate strength, density, and fracture behaviour.", "methods": [ "Functions & modelling" ] } }, { "no": 576, "source_index": 1026, "id": "topic-576-ice-thickness-and-maximum-load", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 3, 15, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 26, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Eisdicke und maximale Belastung", "description": "Fertige gleich breite Eisstäbe verschiedener Dicke an. Prüfe, ob die Bruchlast linear, quadratisch oder kubisch mit der Dicke zunimmt.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Ice thickness and maximum load", "description": "Produce ice beams of equal width but different thicknesses. Test whether breaking load increases linearly, quadratically, or cubically with thickness.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 577, "source_index": 1027, "id": "topic-577-freezethaw-cycles-and-strength-loss", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 27, "method_keys": [ "functions_modeling", "algebra" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Gefrier-Tau-Zyklen und Festigkeitsverlust", "description": "Unterziehe Eisproben unterschiedlich vielen kontrollierten Gefrier-Tau-Zyklen. Modelliere den Festigkeitsverlust als linearen oder exponentiellen Prozess.", "methods": [ "Funktionen & Modellierung", "Algebra" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Freeze–thaw cycles and strength loss", "description": "Expose ice samples to different numbers of controlled freeze–thaw cycles. Model strength loss as a linear or exponential process.", "methods": [ "Functions & modelling", "Algebra" ] } }, { "no": 578, "source_index": 1028, "id": "topic-578-crack-length-and-breaking-load", "category_key": "ice-freezing-and-strength", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 2, 3, 15, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 28, "method_keys": [ "functions_modeling" ], "de": { "category": "Eis, Gefrieren und Festigkeit", "title": "Risslänge und Bruchlast", "description": "Erzeuge standardisierte kleine Kerben unterschiedlicher Länge in gleich großen Eisstäben. Untersuche, wie die anfängliche Risslänge die Bruchlast beeinflusst.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Ice, freezing, and strength", "title": "Crack length and breaking load", "description": "Create standardized small notches of different lengths in equal-sized ice beams. Investigate how initial crack length affects breaking load.", "methods": [ "Functions & modelling" ] } }, { "no": 579, "source_index": 1029, "id": "topic-579-number-of-occupants-and-co2-increase", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 6, 11, 12 ], "measurement_codes": [ 13, 14, 16 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 29, "method_keys": [ "functions_modeling" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Personenzahl und CO₂-Anstieg", "description": "Miss die Steigung der CO₂-Konzentration bei unterschiedlich vielen Personen im gleichen Raum. Schätze daraus eine mittlere Emissionsrate pro Person.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Number of occupants and CO₂ increase", "description": "Measure the slope of CO₂ concentration with different numbers of occupants in the same room. Estimate an average emission rate per person.", "methods": [ "Functions & modelling" ] } }, { "no": 580, "source_index": 1030, "id": "topic-580-co2-decay-curve-and-air-exchange-rate", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 6, 11, 12 ], "measurement_codes": [ 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 30, "method_keys": [ "functions_modeling", "algebra" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "CO₂-Abklingkurve und Luftwechselrate", "description": "Erfasse die Konzentration nach dem Verlassen eines belegten Raums. Passe ein Exponentialmodell an und bestimme daraus die Luftwechselrate.", "methods": [ "Funktionen & Modellierung", "Algebra" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "CO₂ decay curve and air-exchange rate", "description": "Record the concentration after occupants leave a room. Fit an exponential model and estimate the air-exchange rate.", "methods": [ "Functions & modelling", "Algebra" ] } }, { "no": 581, "source_index": 1031, "id": "topic-581-window-opening-and-ventilation-effectiveness", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 31, "method_keys": [ "trigonometry", "geometry" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Fensteröffnung und Lüftungswirkung", "description": "Variiere Öffnungswinkel oder offene Fensterfläche. Vergleiche die Zeitkonstante der jeweiligen CO₂-Abklingkurven.", "methods": [ "Trigonometrie", "Geometrie" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Window opening and ventilation effectiveness", "description": "Vary the window angle or open area. Compare the time constants of the resulting CO₂ decay curves.", "methods": [ "Trigonometry", "Geometry" ] } }, { "no": 582, "source_index": 1032, "id": "topic-582-single-sided-and-cross-ventilation", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 6, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 32, "method_keys": [ "functions_modeling" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Einseitige Lüftung und Querlüftung", "description": "Vergleiche ein geöffnetes Fenster mit zwei gegenüberliegenden Öffnungen. Bestimme Luftwechselrate und Zeit bis zu einem festgelegten CO₂-Wert.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Single-sided and cross ventilation", "description": "Compare one open window with two opposite openings. Determine air-exchange rate and time required to reach a defined CO₂ level.", "methods": [ "Functions & modelling" ] } }, { "no": 583, "source_index": 1033, "id": "topic-583-fan-position-and-co2-distribution", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 6 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 33, "method_keys": [ "stochastics" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Ventilatorposition und CO₂-Verteilung", "description": "Platziere einen Ventilator an verschiedenen Stellen und miss gleichzeitig oder nacheinander an mehreren Raumpunkten. Bewerte Abklingrate und räumliche Streuung.", "methods": [ "Stochastik" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Fan position and CO₂ distribution", "description": "Place a fan in different positions and measure at several room locations. Evaluate both decay rate and spatial variation.", "methods": [ "Statistics & probability" ] } }, { "no": 584, "source_index": 1034, "id": "topic-584-sensor-height-and-measured-concentration", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 6, 11, 12 ], "measurement_codes": [ 1, 13, 16, 18, 20 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 34, "method_keys": [ "functions_modeling", "numerical_methods" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Sensorhöhe und Messwert", "description": "Miss CO₂ in Boden-, Tisch- und Kopfhöhe sowie in verschiedenen Abständen zu Personen. Erstelle ein räumliches Interpolationsmodell.", "methods": [ "Funktionen & Modellierung", "Numerische Verfahren" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Sensor height and measured concentration", "description": "Measure CO₂ near floor, table, and head height and at different distances from occupants. Create a spatial interpolation model.", "methods": [ "Functions & modelling", "Numerical methods" ] } }, { "no": 585, "source_index": 1035, "id": "topic-585-speaking-and-co2-increase", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 6, 11, 12 ], "measurement_codes": [ 6, 14 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 35, "method_keys": [ "functions_modeling" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Sprechen und CO₂-Anstieg", "description": "Vergleiche identische Zeitabschnitte mit ruhigem Sitzen und normalem Sprechen bei gleicher Personenzahl und Lüftung.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Speaking and CO₂ increase", "description": "Compare equal periods of quiet sitting and normal speaking with the same number of occupants and ventilation conditions.", "methods": [ "Functions & modelling" ] } }, { "no": 586, "source_index": 1036, "id": "topic-586-light-activity-and-co2-production", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 7, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 36, "method_keys": [ "functions_modeling" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Leichte Aktivität und CO₂-Produktion", "description": "Vergleiche Sitzen mit einer standardisierten leichten Bewegung in einem gut gelüfteten Raum. Schätze die relative Änderung der CO₂-Emissionsrate.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Light activity and CO₂ production", "description": "Compare sitting with standardized light movement in a well-ventilated room. Estimate the relative change in CO₂ emission rate.", "methods": [ "Functions & modelling" ] } }, { "no": 587, "source_index": 1037, "id": "topic-587-room-volume-and-co2-rise-rate", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 3, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 37, "method_keys": [ "geometry" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Raumvolumen und Geschwindigkeit des CO₂-Anstiegs", "description": "Führe vergleichbare Messungen in unterschiedlich großen Räumen durch. Prüfe, ob die Anstiegsrate näherungsweise umgekehrt proportional zum Raumvolumen ist.", "methods": [ "Geometrie" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Room volume and CO₂ rise rate", "description": "Conduct comparable measurements in rooms of different sizes. Test whether the rise rate is approximately inversely proportional to room volume.", "methods": [ "Geometry" ] } }, { "no": 588, "source_index": 1038, "id": "topic-588-predicting-occupancy-from-co2-data", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 4, 6, 10, 11 ], "measurement_codes": [ 3, 6, 13, 14, 16, 20 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 38, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "regression", "number_theory", "sequences_series" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Personenzahl aus CO₂-Daten vorhersagen", "description": "Nutze Konzentration, Änderungsrate, Temperatur und Uhrzeit zur Schätzung der Personenzahl. Vergleiche lineare Regression, Klassifikation und Zeitreihenmodelle.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Regression", "Zahlentheorie", "Folgen & Reihen" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Predicting occupancy from CO₂ data", "description": "Use concentration, rate of change, temperature, and time to estimate occupancy. Compare linear regression, classification, and time-series models.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Regression", "Number theory", "Sequences & series" ] } }, { "no": 589, "source_index": 1039, "id": "topic-589-light-intensity-and-net-co2-uptake", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 10, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 39, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Lichtintensität und Netto-CO₂-Aufnahme", "description": "Platziere eine Pflanze mit gleicher Blattfläche in einer transparenten Messkammer und variiere die Lichtintensität. Passe ein Sättigungsmodell an.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Light intensity and net CO₂ uptake", "description": "Place a plant with constant leaf area in a transparent measurement chamber and vary light intensity. Fit a saturation model.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 590, "source_index": 1040, "id": "topic-590-light-colour-and-net-co2-exchange", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 40, "method_keys": [ "functions_modeling", "differential_calculus" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Lichtfarbe und Netto-CO₂-Austausch", "description": "Vergleiche verschiedene Lichtfarben bei möglichst gleicher gemessener Lichtintensität. Untersuche die CO₂-Änderungsrate statt nur den Endwert.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Light colour and net CO₂ exchange", "description": "Compare different light colours at approximately equal measured intensity. Analyse the CO₂ rate of change rather than only the final value.", "methods": [ "Functions & modelling", "Differential calculus" ] } }, { "no": 591, "source_index": 1041, "id": "topic-591-leaf-area-and-co2-uptake", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11, 12 ], "measurement_codes": [ 7, 10, 11 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 41, "method_keys": [ "geometry" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Blattfläche und CO₂-Aufnahme", "description": "Bestimme die Blattfläche fotografisch und vergleiche sie mit der CO₂-Abnahmerate unter konstantem Licht.", "methods": [ "Geometrie" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Leaf area and CO₂ uptake", "description": "Determine leaf area photographically and compare it with the CO₂ decrease rate under constant lighting.", "methods": [ "Geometry" ] } }, { "no": 592, "source_index": 1042, "id": "topic-592-soil-moisture-and-net-co2-exchange", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 13, 18 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 42, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Bodenfeuchtigkeit und Netto-CO₂-Austausch", "description": "Untersuche dieselbe Pflanzenart bei unterschiedlichen Bodenfeuchten. Suche nach einem Optimum statt automatisch einen linearen Zusammenhang anzunehmen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Soil moisture and net CO₂ exchange", "description": "Investigate the same plant species at different soil-moisture levels. Search for an optimum rather than automatically assuming a linear relationship.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 593, "source_index": 1043, "id": "topic-593-temperature-and-plant-co2-exchange", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 10, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 43, "method_keys": [ "functions_modeling", "differential_calculus", "algebra", "optimization" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Temperatur und pflanzlicher CO₂-Austausch", "description": "Miss den Netto-CO₂-Austausch derselben Pflanze bei mehreren moderaten Temperaturen und gleicher Beleuchtung. Vergleiche exponentielle und optimale Kurvenmodelle.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Algebra", "Optimierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Temperature and plant CO₂ exchange", "description": "Measure the net CO₂ exchange of the same plant at several moderate temperatures under identical lighting. Compare exponential and optimum-curve models.", "methods": [ "Functions & modelling", "Differential calculus", "Algebra", "Optimisation" ] } }, { "no": 594, "source_index": 1044, "id": "topic-594-plant-daynight-cycle", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 3, 6, 10, 12, 13, 18 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 44, "method_keys": [ "functions_modeling", "trigonometry", "sequences_series", "time_series" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Tages- und Nachtverlauf einer Pflanze", "description": "Zeichne CO₂, Temperatur, Feuchtigkeit und Licht über mindestens 24 Stunden auf. Entwickle ein stückweises oder periodisches Zeitreihenmodell.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Folgen & Reihen", "Zeitreihenanalyse" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Plant day–night cycle", "description": "Record CO₂, temperature, humidity, and light for at least 24 hours. Develop a piecewise or periodic time-series model.", "methods": [ "Functions & modelling", "Trigonometry", "Sequences & series", "Time-series analysis" ] } }, { "no": 595, "source_index": 1045, "id": "topic-595-yeast-fermentation-and-co2-production", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 3, 6, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 45, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Hefefermentation und CO₂-Produktion", "description": "Variiere einzeln Temperatur, Zuckerkonzentration oder Zuckerart. Messe die CO₂-Anstiegsrate und bestimme den Zeitpunkt der maximalen Produktion.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Yeast fermentation and CO₂ production", "description": "Separately vary temperature, sugar concentration, or sugar type. Measure the CO₂ rise rate and determine the time of maximum production.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 596, "source_index": 1046, "id": "topic-596-soil-respiration-and-co2", "category_key": "co2-indoor-air-plants-and-respiration", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 13, 18, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 46, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "CO₂, Raumluft, Pflanzen und Atmung", "title": "Bodenatmung und CO₂", "description": "Vergleiche gleiche Bodenmengen bei unterschiedlichen Temperaturen oder Feuchtigkeiten. Modelliere die CO₂-Freisetzung mit einer multiplen Regression.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "CO₂, indoor air, plants, and respiration", "title": "Soil respiration and CO₂", "description": "Compare equal quantities of soil at different temperatures or moisture levels. Model CO₂ release using multiple regression.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 597, "source_index": 1047, "id": "topic-597-battery-runtime-and-ambient-temperature", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 3, 5, 6 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 47, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Akkulaufzeit und Umgebungstemperatur", "description": "Betreibe dieselbe definierte Last mit identischen Zellen bei mehreren moderaten Temperaturen. Vergleiche Entladezeit und abgegebene Energie.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Battery runtime and ambient temperature", "description": "Operate the same defined load using identical cells at several moderate temperatures. Compare discharge time and delivered energy.", "methods": [ "Functions & modelling" ] } }, { "no": 598, "source_index": 1048, "id": "topic-598-voltage-drop-and-temperature", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 3, 5 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 48, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Spannungseinbruch und Temperatur", "description": "Miss Leerlaufspannung und Spannung unter einer konstanten Last. Schätze daraus den scheinbaren Innenwiderstand bei verschiedenen Temperaturen.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Voltage drop and temperature", "description": "Measure open-circuit voltage and voltage under a constant load. Estimate apparent internal resistance at different temperatures.", "methods": [ "Functions & modelling" ] } }, { "no": 599, "source_index": 1049, "id": "topic-599-screen-brightness-and-smartphone-battery-life", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 8, 11, 12 ], "measurement_codes": [ 5, 6, 7, 11, 20 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 49, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Displayhelligkeit und Smartphone-Akkudauer", "description": "Spiele dieselbe lokale Videodatei bei mehreren Helligkeitsstufen ab. Modelliere den prozentualen Akkuverlust pro Stunde.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Screen brightness and smartphone battery life", "description": "Play the same local video file at several brightness levels. Model percentage battery loss per hour.", "methods": [ "Functions & modelling" ] } }, { "no": 600, "source_index": 1050, "id": "topic-600-signal-quality-and-battery-drain", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 6, 12, 17 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 50, "method_keys": [ "geometry" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Empfangsqualität und Akkuverbrauch", "description": "Führe dieselbe Datenübertragung bei verschiedenen gemessenen Signalstärken durch. Untersuche Akkuverbrauch, Übertragungszeit und Datenrate gemeinsam.", "methods": [ "Geometrie" ] }, "en": { "category": "Batteries and energy", "title": "Signal quality and battery drain", "description": "Perform the same data transfer at different measured signal strengths. Analyse battery drain, transfer time, and data rate together.", "methods": [ "Geometry" ] } }, { "no": 601, "source_index": 1051, "id": "topic-601-wi-fi-versus-mobile-data", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 3, 5 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 51, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "WLAN gegenüber Mobilfunk", "description": "Übertrage dieselbe Datenmenge oder streame denselben Inhalt über WLAN und Mobilfunk. Verwende gepaarte Messungen bei demselben Gerät.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Wi-Fi versus mobile data", "description": "Transfer the same amount of data or stream the same content over Wi-Fi and mobile data. Use paired measurements on the same device.", "methods": [ "Functions & modelling" ] } }, { "no": 602, "source_index": 1052, "id": "topic-602-refresh-rate-and-energy-consumption", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 7 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 52, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Bildwiederholrate und Energieverbrauch", "description": "Vergleiche den Akkuverlust bei unterschiedlichen Bildwiederholraten unter identischer Darstellung und Helligkeit.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Refresh rate and energy consumption", "description": "Compare battery loss at different screen refresh rates while keeping displayed content and brightness constant.", "methods": [ "Functions & modelling" ] } }, { "no": 603, "source_index": 1053, "id": "topic-603-local-ai-computation-and-battery-load", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 2, 3, 5, 6, 20 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 53, "method_keys": [ "functions_modeling" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Lokale KI-Berechnung und Akkubelastung", "description": "Führe eine feste Anzahl lokaler KI-Inferenzen mit Modellen verschiedener Größe aus. Vergleiche Energie pro Berechnung, Laufzeit und Gerätetemperatur.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Batteries and energy", "title": "Local AI computation and battery load", "description": "Run a fixed number of local AI inferences using models of different sizes. Compare energy per inference, runtime, and device temperature.", "methods": [ "Functions & modelling" ] } }, { "no": 604, "source_index": 1054, "id": "topic-604-power-bank-efficiency", "category_key": "batteries-and-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 5 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 54, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Akkus, Batterien und Energie", "title": "Wirkungsgrad einer Powerbank", "description": "Miss Eingangs- und Ausgangsenergie bei verschiedenen Lastströmen. Bestimme, bei welcher Last der Wirkungsgrad maximal ist.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Batteries and energy", "title": "Power-bank efficiency", "description": "Measure input and output energy at different load currents. Determine the load at which efficiency is greatest.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 605, "source_index": 1055, "id": "topic-605-speed-of-sound-in-air-and-temperature", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 6, 9, 11, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 55, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Schall und Akustik", "title": "Schallgeschwindigkeit in Luft und Temperatur", "description": "Bestimme die Laufzeit zwischen zwei Mikrofonen oder über ein Echo bei mehreren Temperaturen. Vergleiche lineare und wurzelförmige Modelle.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Sound and acoustics", "title": "Speed of sound in air and temperature", "description": "Determine travel time between two microphones or by echo at several temperatures. Compare linear and square-root-type models.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 606, "source_index": 1056, "id": "topic-606-speed-of-sound-in-water-and-temperature", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6, 10, 11, 12 ], "measurement_codes": [ 1, 3, 9, 12, 16 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 56, "method_keys": [ "proof" ], "de": { "category": "Schall und Akustik", "title": "Schallgeschwindigkeit in Wasser und Temperatur", "description": "Nutze wasserdichte Sender und Empfänger in einem Behälter konstanter Länge. Das Thema eignet sich wegen der anspruchsvolleren Messung besonders für ein EE.", "methods": [ "Beweisführung" ] }, "en": { "category": "Sound and acoustics", "title": "Speed of sound in water and temperature", "description": "Use waterproof transmitters and receivers in a container of constant length. Because of the more demanding measurement, this topic is especially suitable for an EE.", "methods": [ "Proof" ] } }, { "no": 607, "source_index": 1057, "id": "topic-607-salinity-and-sound-speed", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 6, 9, 11, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 57, "method_keys": [ "functions_modeling" ], "de": { "category": "Schall und Akustik", "title": "Salzgehalt und Schallgeschwindigkeit", "description": "Miss die Laufzeit eines akustischen oder Ultraschallsignals durch Lösungen unterschiedlicher Salzkonzentration bei konstanter Temperatur.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Sound and acoustics", "title": "Salinity and sound speed", "description": "Measure the travel time of an acoustic or ultrasonic signal through solutions with different salt concentrations at constant temperature.", "methods": [ "Functions & modelling" ] } }, { "no": 608, "source_index": 1058, "id": "topic-608-humidity-and-speed-of-sound", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 6, 9, 12, 18 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 58, "method_keys": [ "functions_modeling" ], "de": { "category": "Schall und Akustik", "title": "Luftfeuchtigkeit und Schallgeschwindigkeit", "description": "Variiere die Luftfeuchtigkeit in einem kontrollierten, nicht luftdicht belegten Versuchsraum und kontrolliere gleichzeitig die Temperatur.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Sound and acoustics", "title": "Humidity and speed of sound", "description": "Vary humidity in a controlled experimental space without human exposure in a sealed environment, while simultaneously controlling temperature.", "methods": [ "Functions & modelling" ] } }, { "no": 609, "source_index": 1059, "id": "topic-609-tube-length-and-resonance-frequency", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 6, 9, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 59, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Schall und Akustik", "title": "Rohrlänge und Resonanzfrequenz", "description": "Miss die Resonanzfrequenzen offener und einseitig geschlossener Rohre verschiedener Länge. Untersuche den Zusammenhang zwischen Frequenz und Kehrwert der Länge.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Sound and acoustics", "title": "Tube length and resonance frequency", "description": "Measure resonant frequencies of open and one-end-closed tubes of different lengths. Investigate the relationship between frequency and inverse tube length.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 610, "source_index": 1060, "id": "topic-610-water-level-in-a-bottle-and-pitch", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 6, 9, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 60, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Schall und Akustik", "title": "Wasserstand in einer Flasche und Tonhöhe", "description": "Verändere das Luft- beziehungsweise Wasservolumen in identischen Flaschen. Vergleiche unterschiedliche geometrische Modelle für die Frequenz.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Sound and acoustics", "title": "Water level in a bottle and pitch", "description": "Vary the air or water volume in identical bottles. Compare different geometric models for the resulting frequency.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 611, "source_index": 1061, "id": "topic-611-material-and-sound-attenuation", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 9, 11, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 61, "method_keys": [ "functions_modeling", "trigonometry", "algebra" ], "de": { "category": "Schall und Akustik", "title": "Material und Schalldämpfung", "description": "Platziere Materialien verschiedener Art und Dicke zwischen Lautsprecher und Mikrofon. Modelliere die Dämpfung in Dezibel in Abhängigkeit von Dicke und Frequenz.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Algebra" ] }, "en": { "category": "Sound and acoustics", "title": "Material and sound attenuation", "description": "Place materials of different types and thicknesses between a speaker and microphone. Model attenuation in decibels as a function of thickness and frequency.", "methods": [ "Functions & modelling", "Trigonometry", "Algebra" ] } }, { "no": 612, "source_index": 1062, "id": "topic-612-furnishing-and-reverberation-time", "category_key": "sound-and-acoustics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 6, 9, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 62, "method_keys": [ "functions_modeling" ], "de": { "category": "Schall und Akustik", "title": "Möblierung und Nachhallzeit", "description": "Miss die Nachhallzeit eines Raums bei unterschiedlichen Mengen absorbierender Materialien. Vergleiche Messungen mit einem raumakustischen Modell.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Sound and acoustics", "title": "Furnishing and reverberation time", "description": "Measure room reverberation time with different amounts of absorbing material. Compare measurements with an acoustic room model.", "methods": [ "Functions & modelling" ] } }, { "no": 613, "source_index": 1063, "id": "topic-613-magnetic-field-strength-and-distance", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 1, 5, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 63, "method_keys": [ "functions_modeling", "vectors", "proof", "algebra" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Magnetfeldstärke und Abstand", "description": "Miss die Magnetfeldstärke entlang einer festen Achse bei zunehmendem Abstand. Bestimme den Exponenten eines Potenzmodells.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Beweisführung", "Algebra" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Magnetic field strength and distance", "description": "Measure magnetic-field strength along a fixed axis at increasing distances. Determine the exponent of a power model.", "methods": [ "Functions & modelling", "Vector mathematics", "Proof", "Algebra" ] } }, { "no": 614, "source_index": 1064, "id": "topic-614-magnetic-field-component-and-angle", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 1, 5, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 64, "method_keys": [ "functions_modeling", "vectors", "trigonometry", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Magnetfeldkomponente und Winkel", "description": "Drehe den Sensor in festen Winkelschritten relativ zum Magneten. Prüfe, ob die gemessene Feldkomponente einem trigonometrischen Modell folgt.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Trigonometrie", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Magnetic-field component and angle", "description": "Rotate the sensor in fixed angular steps relative to the magnet. Test whether the measured field component follows a trigonometric model.", "methods": [ "Functions & modelling", "Vector mathematics", "Trigonometry", "Proof" ] } }, { "no": 615, "source_index": 1065, "id": "topic-615-number-and-spacing-of-magnets", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6, 10, 11, 12 ], "measurement_codes": [ 1, 5, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 65, "method_keys": [ "vectors", "geometry", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Anzahl und Abstand mehrerer Magnete", "description": "Vergleiche gestapelte Magnete sowie Magnete mit unterschiedlichen Zwischenräumen. Untersuche Feldstärke und räumliche Gleichmäßigkeit.", "methods": [ "Vektorrechnung", "Geometrie", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Number and spacing of magnets", "description": "Compare stacked magnets and magnets separated by different gaps. Investigate field strength and spatial uniformity.", "methods": [ "Vector mathematics", "Geometry", "Proof" ] } }, { "no": 616, "source_index": 1066, "id": "topic-616-material-between-magnet-and-sensor", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8, 10, 11, 12 ], "measurement_codes": [ 2, 5 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 66, "method_keys": [ "vectors", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Material zwischen Magnet und Sensor", "description": "Platziere gleich dicke Schichten aus Kunststoff, Aluminium, Stahl oder anderen Materialien zwischen Magnet und Sensor. Untersuche Feldänderung und Feldumlenkung.", "methods": [ "Vektorrechnung", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Material between magnet and sensor", "description": "Place equal-thickness layers of plastic, aluminium, steel, or other materials between magnet and sensor. Investigate changes and redirection of the field.", "methods": [ "Vector mathematics", "Proof" ] } }, { "no": 617, "source_index": 1067, "id": "topic-617-current-and-magnetic-field-of-a-coil", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 5, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 67, "method_keys": [ "vectors", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Stromstärke und Magnetfeld einer Spule", "description": "Verändere den Strom durch eine feste Spule innerhalb sicherer Grenzwerte. Miss das Magnetfeld im Zentrum und an mehreren Außenpunkten.", "methods": [ "Vektorrechnung", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Current and magnetic field of a coil", "description": "Vary the current through a fixed coil within safe limits. Measure the magnetic field at the centre and at several external points.", "methods": [ "Vector mathematics", "Proof" ] } }, { "no": 618, "source_index": 1068, "id": "topic-618-number-of-turns-and-magnetic-field", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 10, 11, 12 ], "measurement_codes": [ 1, 5, 12, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 68, "method_keys": [ "functions_modeling", "vectors", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Windungszahl und Magnetfeld", "description": "Baue Spulen gleicher Länge mit verschiedenen Windungszahlen. Halte den Strom konstant und untersuche den Zusammenhang mit der Feldstärke.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Number of turns and magnetic field", "description": "Build coils of equal length with different numbers of turns. Keep current constant and investigate the relationship with field strength.", "methods": [ "Functions & modelling", "Vector mathematics", "Proof" ] } }, { "no": 619, "source_index": 1069, "id": "topic-619-magnet-speed-and-induced-voltage", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 5, 6, 12 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 69, "method_keys": [ "functions_modeling", "differential_calculus", "vectors", "geometry", "proof" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Magnetgeschwindigkeit und Induktionsspannung", "description": "Bewege denselben Magneten mit unterschiedlichen Geschwindigkeiten durch eine Spule. Vergleiche maximale Spannung und gesamte Spannungs-Zeit-Fläche.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Vektorrechnung", "Geometrie", "Beweisführung" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Magnet speed and induced voltage", "description": "Move the same magnet through a coil at different speeds. Compare peak voltage and total voltage–time area.", "methods": [ "Functions & modelling", "Differential calculus", "Vector mathematics", "Geometry", "Proof" ] } }, { "no": 620, "source_index": 1070, "id": "topic-620-eddy-current-braking-and-magnet-distance", "category_key": "magnetic-fields-and-electromagnetic-induction", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 1, 5, 6, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 70, "method_keys": [ "functions_modeling", "differential_equations", "vectors", "proof", "algebra" ], "de": { "category": "Magnetfelder und elektromagnetische Induktion", "title": "Wirbelstrombremse und Magnetabstand", "description": "Lass einen Magneten an einer Aluminium- oder Kupferplatte vorbeipendeln. Modelliere die Abklingzeit der Schwingung in Abhängigkeit vom Abstand.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Vektorrechnung", "Beweisführung", "Algebra" ] }, "en": { "category": "Magnetic fields and electromagnetic induction", "title": "Eddy-current braking and magnet distance", "description": "Allow a magnet to swing past an aluminium or copper plate. Model oscillation decay time as a function of separation distance.", "methods": [ "Functions & modelling", "Differential equations", "Vector mathematics", "Proof", "Algebra" ] } }, { "no": 621, "source_index": 1071, "id": "topic-621-wi-fi-signal-strength-and-distance", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 13, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 71, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "WLAN-Signalstärke und Entfernung", "description": "Miss die Signalstärke entlang einer geraden Strecke bei freier Sicht. Passe ein logarithmisches Entfernungsmodell an und untersuche die Residuen.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Wi-Fi signal strength and distance", "description": "Measure signal strength along a straight line with clear line of sight. Fit a logarithmic distance model and examine residuals.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 622, "source_index": 1072, "id": "topic-622-wall-material-and-signal-attenuation", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 10, 11, 12 ], "measurement_codes": [ 2 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 72, "method_keys": [ "geometry", "proof" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Wandmaterial und Signaldämpfung", "description": "Vergleiche Holz, Glas, Gipskarton, Ziegel und Beton bei ähnlicher Geometrie. Berechne den zusätzlichen Verlust gegenüber freier Sicht.", "methods": [ "Geometrie", "Beweisführung" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Wall material and signal attenuation", "description": "Compare wood, glass, plasterboard, brick, and concrete under similar geometry. Calculate additional loss relative to a clear line of sight.", "methods": [ "Geometry", "Proof" ] } }, { "no": 623, "source_index": 1073, "id": "topic-623-material-thickness-and-signal-attenuation", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 73, "method_keys": [ "functions_modeling" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Materialdicke und Signaldämpfung", "description": "Staple mehrere identische Platten oder Materiallagen. Prüfe, ob der Verlust in Dezibel näherungsweise linear mit der Dicke wächst.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Material thickness and signal attenuation", "description": "Stack several identical panels or layers. Test whether loss in decibels increases approximately linearly with thickness.", "methods": [ "Functions & modelling" ] } }, { "no": 624, "source_index": 1074, "id": "topic-624-wet-and-dry-material", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 18 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 74, "method_keys": [ "functions_modeling" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Feuchtes und trockenes Material", "description": "Vergleiche kontrolliert befeuchtete und trockene Proben desselben Materials. Erfasse Masse, Feuchtegrad und Signalverlust.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Wet and dry material", "description": "Compare controlled wet and dry samples of the same material. Record mass, moisture level, and signal loss.", "methods": [ "Functions & modelling" ] } }, { "no": 625, "source_index": 1075, "id": "topic-625-device-orientation-and-hand-position", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 3, 11, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 75, "method_keys": [ "stochastics", "trigonometry" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Geräteausrichtung und Handposition", "description": "Drehe das Smartphone in festen Winkeln oder ändere eine standardisierte Handposition. Analysiere Mittelwert und Streuung der Signalstärke.", "methods": [ "Stochastik", "Trigonometrie" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Device orientation and hand position", "description": "Rotate the smartphone through fixed angles or change a standardized hand position. Analyse the mean and variation of signal strength.", "methods": [ "Statistics & probability", "Trigonometry" ] } }, { "no": 626, "source_index": 1076, "id": "topic-626-line-of-sight-corners-and-walls", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 76, "method_keys": [ "functions_modeling" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Sichtverbindung, Ecken und Wände", "description": "Vergleiche direkte Sicht, eine Gebäudeecke und mehrere Zwischenwände bei ähnlicher Entfernung. Entwickle ein additives Dämpfungsmodell.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Line of sight, corners, and walls", "description": "Compare direct line of sight, one building corner, and several intervening walls at similar distances. Develop an additive attenuation model.", "methods": [ "Functions & modelling" ] } }, { "no": 627, "source_index": 1077, "id": "topic-627-2-4-ghz-versus-5-ghz", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 6 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 77, "method_keys": [ "trigonometry" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "2,4 GHz gegenüber 5 GHz", "description": "Miss beide Frequenzbänder an denselben Positionen und hinter denselben Materialien. Vergleiche Reichweite, Dämpfung und Datenrate.", "methods": [ "Trigonometrie" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "2.4 GHz versus 5 GHz", "description": "Measure both frequency bands at the same positions and behind the same materials. Compare range, attenuation, and data rate.", "methods": [ "Trigonometry" ] } }, { "no": 628, "source_index": 1078, "id": "topic-628-signal-strength-throughput-and-packet-loss", "category_key": "mobile-reception-wi-fi-and-radio-attenuation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 6, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 78, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Handyempfang, WLAN und Funkdämpfung", "title": "Signalstärke, Datenrate und Paketverlust", "description": "Erfasse an vielen Positionen gleichzeitig RSSI, Übertragungsrate, Latenz und Paketverlust. Suche nach Schwellenwerten oder stückweisen Zusammenhängen.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Mobile reception, Wi-Fi, and radio attenuation", "title": "Signal strength, throughput, and packet loss", "description": "At many positions, record RSSI, throughput, latency, and packet loss. Search for thresholds or piecewise relationships.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 629, "source_index": 1079, "id": "topic-629-scramble-length-and-minimum-solution-distance", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 11, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 79, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "geometry", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Scramble-Länge und minimale Lösungsdistanz", "description": "Erzeuge 2×2×2-Scrambles unterschiedlicher Länge und bestimme mit vollständiger Suche die optimale Lösung. Untersuche den Sättigungseffekt.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Geometrie", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Scramble length and minimum solution distance", "description": "Generate 2×2×2 scrambles of different lengths and determine the optimal solution using exhaustive search. Investigate the saturation effect.", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Geometry", "Optimisation" ] } }, { "no": 630, "source_index": 1080, "id": "topic-630-distribution-of-optimal-solution-distances", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 11, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 80, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Verteilung optimaler Lösungsdistanzen", "description": "Analysiere alle oder eine große Stichprobe von 2×2×2-Zuständen. Bestimme Häufigkeitsverteilung, Erwartungswert und Varianz der minimalen Zugzahl.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Distribution of optimal solution distances", "description": "Analyse all or a large sample of 2×2×2 states. Determine the distribution, mean, and variance of minimum solution length.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Optimisation" ] } }, { "no": 631, "source_index": 1081, "id": "topic-631-practice-time-and-solving-speed", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 4, 8, 11, 12 ], "measurement_codes": [ 3, 6, 11, 12, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 81, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "algebra", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Übungszeit und Lösungsgeschwindigkeit", "description": "Miss die Lösungszeit einer Person über viele standardisierte Übungseinheiten. Vergleiche exponentielle, logarithmische und Potenz-Lernkurven.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Algebra", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Practice time and solving speed", "description": "Measure one person’s solving time over many standardized practice sessions. Compare exponential, logarithmic, and power learning curves.", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Algebra", "Optimisation" ] } }, { "no": 632, "source_index": 1082, "id": "topic-632-comparing-solving-methods", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 6, 11, 12, 13, 16 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 82, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Vergleich verschiedener Lösungsverfahren", "description": "Vergleiche Anfänger-, CFOP- und computergestützte Verfahren hinsichtlich Zugzahl, Zeit und Variabilität. Erstelle eine Pareto-Analyse aus Geschwindigkeit und Effizienz.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Comparing solving methods", "description": "Compare beginner, CFOP, and computer-assisted methods in terms of move count, time, and variation. Create a Pareto analysis of speed and efficiency.", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Optimisation" ] } }, { "no": 633, "source_index": 1083, "id": "topic-633-heuristic-quality-and-computational-effort", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 8, 11, 12 ], "measurement_codes": [ 6, 11, 13, 16, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 83, "method_keys": [ "functions_modeling", "differential_calculus", "graph_theory", "geometry", "simulation", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Qualität einer Heuristik und Rechenaufwand", "description": "Verändere bei A\\*- oder IDA\\*-Suche die Stärke der Heuristik. Miss untersuchte Zustände, Speicherbedarf, Laufzeit und Lösungsqualität.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Graphentheorie", "Geometrie", "Simulation & Algorithmen", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Heuristic quality and computational effort", "description": "Vary heuristic strength in A\\* or IDA\\* search. Measure explored states, memory use, runtime, and solution quality.", "methods": [ "Functions & modelling", "Differential calculus", "Graph theory", "Geometry", "Simulation & algorithms", "Optimisation" ] } }, { "no": 634, "source_index": 1084, "id": "topic-634-half-turn-and-quarter-turn-metrics", "category_key": "rubiks-cube-graph-theory-and-optimization", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 11, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 84, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "optimization" ], "de": { "category": "Rubik’s Cube, Graphentheorie und Optimierung", "title": "Half-Turn Metric und Quarter-Turn Metric", "description": "Löse dieselben Zustände mit beiden Zugdefinitionen. Untersuche Verteilung und Verhältnis der jeweils minimalen Lösungsdistanzen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Optimierung" ] }, "en": { "category": "Rubik’s Cube, graph theory, and optimization", "title": "Half-turn and quarter-turn metrics", "description": "Solve the same states using both move definitions. Investigate the distribution and ratio of the resulting minimum solution distances.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Optimisation" ] } }, { "no": 635, "source_index": 1085, "id": "topic-635-prompt-specificity-and-answer-quality", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 85, "method_keys": [ "geometry" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Promptgenauigkeit und Antwortqualität", "description": "Formuliere dieselbe Aufgabe mit unterschiedlich vielen präzisen Bedingungen. Miss Korrektheit, Vollständigkeit und Zahl nicht erfüllter Anforderungen.", "methods": [ "Geometrie" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Prompt specificity and answer quality", "description": "Present the same task with different levels of precise detail. Measure correctness, completeness, and number of unmet requirements.", "methods": [ "Geometry" ] } }, { "no": 636, "source_index": 1086, "id": "topic-636-zero-shot-versus-few-shot-prompting", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 3, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 86, "method_keys": [ "functions_modeling", "stochastics" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Zero-shot gegenüber Few-shot", "description": "Gib dem Modell null, ein, drei oder fünf gelöste Beispiele. Untersuche, wie die Anzahl der Beispiele die Trefferquote verändert.", "methods": [ "Funktionen & Modellierung", "Stochastik" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Zero-shot versus few-shot prompting", "description": "Give the model zero, one, three, or five solved examples. Investigate how the number of examples changes accuracy.", "methods": [ "Functions & modelling", "Statistics & probability" ] } }, { "no": 637, "source_index": 1087, "id": "topic-637-german-and-english-prompts", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 10, 11, 12 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 87, "method_keys": [ "proof" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Deutsche und englische Prompts", "description": "Übersetze einen festen Aufgabensatz möglichst bedeutungsgleich. Vergleiche Korrektheit, Antwortlänge und Konsistenz zwischen den Sprachen.", "methods": [ "Beweisführung" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "German and English prompts", "description": "Translate a fixed set of tasks as equivalently as possible. Compare correctness, response length, and consistency between languages.", "methods": [ "Proof" ] } }, { "no": 638, "source_index": 1088, "id": "topic-638-irrelevant-information-in-prompts", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 88, "method_keys": [ "geometry" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Irrelevante Informationen im Prompt", "description": "Ergänze Aufgaben schrittweise um bedeutungslose oder ablenkende Informationen. Messe, ab welcher Menge die Leistung erkennbar abnimmt.", "methods": [ "Geometrie" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Irrelevant information in prompts", "description": "Gradually add irrelevant or distracting information to tasks. Measure at what amount performance begins to decline.", "methods": [ "Geometry" ] } }, { "no": 639, "source_index": 1089, "id": "topic-639-typographical-and-linguistic-noise", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8, 10, 11, 12 ], "measurement_codes": [ 11, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 89, "method_keys": [ "functions_modeling", "stochastics", "proof", "algebra" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Tippfehler und sprachliche Störungen", "description": "Füge kontrolliert Buchstabendreher, fehlende Leerzeichen oder Satzzeichenfehler ein. Modelliere die Genauigkeit in Abhängigkeit vom Störungsgrad.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Beweisführung", "Algebra" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Typographical and linguistic noise", "description": "Introduce controlled letter swaps, missing spaces, or punctuation errors. Model accuracy as a function of noise level.", "methods": [ "Functions & modelling", "Statistics & probability", "Proof", "Algebra" ] } }, { "no": 640, "source_index": 1090, "id": "topic-640-repeatability-of-identical-ai-queries", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 90, "method_keys": [ "numerical_methods" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Wiederholbarkeit identischer KI-Anfragen", "description": "Stelle dieselbe Frage vielfach in unabhängigen Durchläufen. Bestimme Übereinstimmungsrate, Antwortentropie und Streuung numerischer Ergebnisse.", "methods": [ "Numerische Verfahren" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Repeatability of identical AI queries", "description": "Ask the same question in many independent runs. Determine agreement rate, response entropy, and variation in numerical results.", "methods": [ "Numerical methods" ] } }, { "no": 641, "source_index": 1091, "id": "topic-641-free-response-versus-fixed-output-format", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 91, "method_keys": [ "geometry" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Freie Antwort gegenüber festem Ausgabeformat", "description": "Fordere einmal freien Text und einmal eine feste Tabelle oder ein JSON-ähnliches Schema. Vergleiche Formatfehler und inhaltliche Fehler getrennt.", "methods": [ "Geometrie" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Free response versus fixed output format", "description": "Request free text in one condition and a fixed table or JSON-like schema in another. Compare formatting and content errors separately.", "methods": [ "Geometry" ] } }, { "no": 642, "source_index": 1092, "id": "topic-642-source-requirements-and-verifiable-claims", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 92, "method_keys": [ "functions_modeling" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Quellenanforderung und überprüfbare Aussagen", "description": "Vergleiche Antworten ohne Quellenanforderung mit Antworten, für die überprüfbare Belege verlangt werden. Kontrolliere jede Quellenangabe tatsächlich.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Source requirements and verifiable claims", "description": "Compare responses without a source requirement with responses requiring verifiable evidence. Independently check every cited source.", "methods": [ "Functions & modelling" ] } }, { "no": 643, "source_index": 1093, "id": "topic-643-position-bias-in-multiple-choice-questions", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 93, "method_keys": [ "sequences_series" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Positionsverzerrung bei Multiple Choice", "description": "Vertausche bei identischen Fragen systematisch die Reihenfolge der Antwortoptionen. Prüfe, ob bestimmte Positionen überproportional gewählt werden.", "methods": [ "Folgen & Reihen" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Position bias in multiple-choice questions", "description": "Systematically change the order of answer options for identical questions. Test whether particular positions are selected disproportionately.", "methods": [ "Sequences & series" ] } }, { "no": 644, "source_index": 1094, "id": "topic-644-robustness-to-small-numerical-changes", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 10, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 94, "method_keys": [ "numerical_methods" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Robustheit gegenüber kleinen Zahlenänderungen", "description": "Verändere Zahlenwerte einer Mathematikaufgabe geringfügig, ohne die Struktur zu ändern. Untersuche sprunghafte Fehler und lokale Antwortstabilität.", "methods": [ "Numerische Verfahren" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Robustness to small numerical changes", "description": "Slightly change numerical values in a mathematics problem without changing its structure. Investigate sudden errors and local answer stability.", "methods": [ "Numerical methods" ] } }, { "no": 645, "source_index": 1095, "id": "topic-645-image-brightness-and-classification-accuracy", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 8, 11, 12 ], "measurement_codes": [ 7 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 95, "method_keys": [ "stochastics" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Bildhelligkeit und Klassifikationsgenauigkeit", "description": "Erstelle abgestufte Versionen derselben Bilder mit unterschiedlicher Helligkeit und unterschiedlichem Kontrast. Bestimme Genauigkeit und Konfidenz.", "methods": [ "Stochastik" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Image brightness and classification accuracy", "description": "Create graded versions of the same images with different brightness and contrast. Determine accuracy and confidence.", "methods": [ "Statistics & probability" ] } }, { "no": 646, "source_index": 1096, "id": "topic-646-rotation-and-partial-occlusion", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 3, 7, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 96, "method_keys": [ "functions_modeling", "trigonometry", "geometry", "algebra" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Rotation und teilweise Verdeckung", "description": "Drehe Bilder in festen Winkeln oder verdecke einen kontrollierten Flächenanteil. Modelliere die Erkennungsrate als Funktion von Winkel oder Verdeckungsgrad.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie", "Algebra" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Rotation and partial occlusion", "description": "Rotate images through fixed angles or cover a controlled proportion of each image. Model recognition rate as a function of angle or occlusion.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry", "Algebra" ] } }, { "no": 647, "source_index": 1097, "id": "topic-647-training-set-size-and-model-accuracy", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 4, 8, 10, 11, 12 ], "measurement_codes": [ 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 97, "method_keys": [ "functions_modeling", "stochastics", "proof" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Trainingsdatensatzgröße und Modellgenauigkeit", "description": "Trainiere dasselbe kleine Klassifikationsmodell mit zunehmenden Datenmengen. Erstelle Lernkurven für Trainings- und Testfehler.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Beweisführung" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Training-set size and model accuracy", "description": "Train the same small classification model using increasing amounts of data. Create learning curves for training and test error.", "methods": [ "Functions & modelling", "Statistics & probability", "Proof" ] } }, { "no": 648, "source_index": 1098, "id": "topic-648-class-imbalance-and-evaluation-metrics", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 4, 8, 10, 11, 12 ], "measurement_codes": [ 3, 12, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 98, "method_keys": [ "stochastics", "matrices", "proof" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Ungleich verteilte Klassen und Bewertungsmetriken", "description": "Verändere den Anteil der Klassen im Trainingsdatensatz. Vergleiche Accuracy, Precision, Recall, F1-Wert und Konfusionsmatrizen.", "methods": [ "Stochastik", "Matrizen", "Beweisführung" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Class imbalance and evaluation metrics", "description": "Change the class proportions in the training dataset. Compare accuracy, precision, recall, F1 score, and confusion matrices.", "methods": [ "Statistics & probability", "Matrices", "Proof" ] } }, { "no": 649, "source_index": 1099, "id": "topic-649-model-size-accuracy-and-speed", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 6, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 99, "method_keys": [ "functions_modeling", "stochastics", "optimization" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Modellgröße, Genauigkeit und Geschwindigkeit", "description": "Vergleiche Modelle oder Komprimierungsstufen bei derselben Aufgabe. Erstelle eine Pareto-Grenze aus Genauigkeit, Laufzeit, Speicherbedarf und Energieverbrauch.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Optimierung" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Model size, accuracy, and speed", "description": "Compare models or compression levels on the same task. Create a Pareto frontier using accuracy, runtime, memory use, and energy consumption.", "methods": [ "Functions & modelling", "Statistics & probability", "Optimisation" ] } }, { "no": 650, "source_index": 1100, "id": "topic-650-classical-regression-versus-ai-models", "category_key": "experiments-with-artificial-intelligence", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 6, 7, 8, 11 ], "measurement_codes": [ 3, 5, 9, 13, 16, 20 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 100, "method_keys": [ "functions_modeling", "regression", "simulation", "algebra" ], "de": { "category": "Experimente mit künstlicher Intelligenz", "title": "Klassische Regression gegenüber KI-Modellen", "description": "Nutze eigene Wasser-, CO₂-, Akku- oder Schalldaten. Vergleiche lineare beziehungsweise polynomiale Regression mit einem Machine-Learning-Modell anhand unbekannter Testdaten.", "methods": [ "Funktionen & Modellierung", "Regression", "Simulation & Algorithmen", "Algebra" ] }, "en": { "category": "Experiments with artificial intelligence", "title": "Classical regression versus AI models", "description": "Use your own water, CO₂, battery, or sound data. Compare linear or polynomial regression with a machine-learning model using unseen test data.", "methods": [ "Functions & modelling", "Regression", "Simulation & algorithms", "Algebra" ] } }, { "no": 651, "source_index": 1101, "id": "topic-651-nozzle-shape-and-discharge-coefficient", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 3, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 101, "method_keys": [ "functions_modeling", "regression", "graph_theory", "geometry" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Düsenform und Ausflusskoeffizient", "description": "Vergleiche scharfkantige, abgerundete und konische Düsen bei gleicher Öffnungsfläche und gleichem Wasserstand.", "methods": [ "Funktionen & Modellierung", "Regression", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Nozzle shape and discharge coefficient", "description": "Compare sharp-edged, rounded, and conical nozzles at equal outlet area and water head.", "methods": [ "Functions & modelling", "Regression", "Graph theory", "Geometry" ] } }, { "no": 652, "source_index": 1102, "id": "topic-652-pipe-diameter-and-volume-flow-rate", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 102, "method_keys": [ "functions_modeling", "regression", "geometry", "algebra" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Rohrdurchmesser und Volumenstrom", "description": "Verändere den Innendurchmesser eines Rohres bei konstanter Länge und Höhendifferenz.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Algebra" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Pipe diameter and volume flow rate", "description": "Vary the internal pipe diameter while keeping length and pressure head constant.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Algebra" ] } }, { "no": 653, "source_index": 1103, "id": "topic-653-pipe-length-and-pressure-loss", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 103, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Rohrlänge und Druckverlust", "description": "Verwende Rohre gleichen Durchmessers, aber unterschiedlicher Länge, und miss Volumenstrom oder Druckverlust.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Pipe length and pressure loss", "description": "Use pipes of equal diameter but different lengths and measure flow rate or pressure loss.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 654, "source_index": 1104, "id": "topic-654-number-of-pipe-bends-and-flow-loss", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 104, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Anzahl der Rohrbögen und Strömungsverlust", "description": "Untersuche Rohre mit null bis mehreren Bögen unterschiedlicher Winkel.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Number of pipe bends and flow loss", "description": "Investigate pipes containing zero to several bends of different angles.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 655, "source_index": 1105, "id": "topic-655-inlet-shape-and-flow-rate", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 105, "method_keys": [ "functions_modeling", "stochastics", "graph_theory", "geometry" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Einlassform und Volumenstrom", "description": "Vergleiche scharfkantige, trichterförmige und abgerundete Rohreinlässe.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Inlet shape and flow rate", "description": "Compare sharp-edged, funnel-shaped, and rounded pipe inlets.", "methods": [ "Functions & modelling", "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 656, "source_index": 1106, "id": "topic-656-uniformity-of-a-perforated-pipe", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 106, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "geometry", "optimization" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Gleichmäßigkeit eines perforierten Rohres", "description": "Verändere Lochdurchmesser oder Lochabstände entlang eines Rohres und miss den Ausfluss jedes Lochs.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Geometrie", "Optimierung" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Uniformity of a perforated pipe", "description": "Vary hole diameter or spacing along a pipe and measure discharge from each hole.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Geometry", "Optimisation" ] } }, { "no": 657, "source_index": 1107, "id": "topic-657-opening-angle-of-a-triangular-weir", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 107, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Öffnungswinkel eines Dreieckswehrs", "description": "Lass Wasser durch V-förmige Wehre verschiedener Winkel fließen.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Opening angle of a triangular weir", "description": "Pass water through V-shaped weirs with different opening angles.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 658, "source_index": 1108, "id": "topic-658-width-of-a-rectangular-weir", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 108, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Breite eines Rechteckswehrs", "description": "Variiere die Breite eines rechteckigen Überlaufs und miss Abfluss und Wasserhöhe.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Width of a rectangular weir", "description": "Vary the width of a rectangular weir and measure discharge and water depth.", "methods": [ "Functions & modelling" ] } }, { "no": 659, "source_index": 1109, "id": "topic-659-venturi-constriction-and-pressure-difference", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 109, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Venturi-Verengung und Druckdifferenz", "description": "Baue Rohre mit verschiedenen Verengungsverhältnissen und miss den Druck vor und in der Engstelle.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Venturi constriction and pressure difference", "description": "Build tubes with different constriction ratios and measure pressure before and inside the throat.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 660, "source_index": 1110, "id": "topic-660-pump-head-and-pump-performance", "category_key": "further-water-flow-and-hydraulic-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 110, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Weitere Wasserströmungs- und Hydraulikexperimente", "title": "Förderhöhe und Pumpenleistung", "description": "Miss den Volumenstrom einer kleinen Wasserpumpe bei verschiedenen Förderhöhen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Further water-flow and hydraulic experiments", "title": "Pump head and pump performance", "description": "Measure the flow rate of a small water pump at different delivery heights.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 661, "source_index": 1111, "id": "topic-661-salt-concentration-and-immersion-depth", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 11, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 111, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Salzkonzentration und Eintauchtiefe", "description": "Lass denselben Schwimmkörper in Lösungen verschiedener Dichte schwimmen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Salt concentration and immersion depth", "description": "Float the same object in solutions of different densities.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 662, "source_index": 1112, "id": "topic-662-hull-shape-and-maximum-payload", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 2, 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 112, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Rumpfform und maximale Zuladung", "description": "Baue Boote aus gleich großen Folien- oder Papierstücken mit verschiedenen Querschnitten.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Hull shape and maximum payload", "description": "Build boats from equal-sized sheets using different cross-sections.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 663, "source_index": 1113, "id": "topic-663-centre-of-mass-height-and-stability", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 1, 2, 5, 15, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 113, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Schwerpunktshöhe und Kippstabilität", "description": "Verändere die Höhe eines Gewichts in einem Modellboot und miss den Krängungswinkel.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Centre-of-mass height and stability", "description": "Change the height of a weight in a model boat and measure the heel angle.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 664, "source_index": 1114, "id": "topic-664-draft-and-oscillation-period-of-a-floating-body", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 2, 5, 6, 15, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 114, "method_keys": [ "functions_modeling" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Eintauchtiefe und Schwingungsdauer eines Schwimmkörpers", "description": "Drücke einen Schwimmkörper wiederholt leicht nach unten und filme seine vertikale Schwingung.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Draft and oscillation period of a floating body", "description": "Displace a floating body vertically and record its oscillation.", "methods": [ "Functions & modelling" ] } }, { "no": 665, "source_index": 1115, "id": "topic-665-towing-speed-and-hydrodynamic-drag", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 115, "method_keys": [ "functions_modeling" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Zuggeschwindigkeit und Wasserwiderstand", "description": "Ziehe denselben Körper mit verschiedenen konstanten Geschwindigkeiten durch Wasser.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Towing speed and hydrodynamic drag", "description": "Tow the same body through water at different constant speeds.", "methods": [ "Functions & modelling" ] } }, { "no": 666, "source_index": 1116, "id": "topic-666-object-shape-and-drag-coefficient", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 5, 11, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 116, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Körperform und Widerstandskoeffizient", "description": "Vergleiche Kugel, Würfel, Zylinder und stromlinienförmige Körper gleicher Stirnfläche.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Object shape and drag coefficient", "description": "Compare spherical, cubic, cylindrical, and streamlined objects with equal frontal area.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 667, "source_index": 1117, "id": "topic-667-air-volume-in-a-cartesian-diver", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 117, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Luftvolumen eines kartesischen Tauchers", "description": "Verändere das eingeschlossene Luftvolumen und bestimme den Druck, bei dem der Taucher schwebt oder sinkt.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Air volume in a Cartesian diver", "description": "Vary the trapped air volume and determine the pressure at neutral buoyancy.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 668, "source_index": 1118, "id": "topic-668-ballast-position-and-trim-angle", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 1, 2, 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 118, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Ballastposition und Trimmlage", "description": "Verschiebe ein Gewicht längs eines Modellboots und miss den Neigungswinkel.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Ballast position and trim angle", "description": "Move a weight along a model boat and measure its trim angle.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 669, "source_index": 1119, "id": "topic-669-bubble-diameter-and-rise-velocity", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 10, 11, 12 ], "measurement_codes": [ 1, 3, 5, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 119, "method_keys": [ "functions_modeling", "number_theory", "geometry", "algebra" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Blasendurchmesser und Aufstiegsgeschwindigkeit", "description": "Erzeuge Luftblasen unterschiedlicher Größe und filme ihren Aufstieg in einer Wassersäule.", "methods": [ "Funktionen & Modellierung", "Zahlentheorie", "Geometrie", "Algebra" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Bubble diameter and rise velocity", "description": "Generate bubbles of different sizes and record their rise through water.", "methods": [ "Functions & modelling", "Number theory", "Geometry", "Algebra" ] } }, { "no": 670, "source_index": 1120, "id": "topic-670-hydrometer-stem-diameter-and-sensitivity", "category_key": "buoyancy-floating-bodies-and-water-resistance", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 1, 5, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 120, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Auftrieb, Schwimmkörper und Wasserwiderstand", "title": "Stieldurchmesser eines Hydrometers und Empfindlichkeit", "description": "Baue Hydrometer mit unterschiedlich dicken Stielen und vergleiche die Höhenänderung bei kleinen Dichteunterschieden.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Buoyancy, floating bodies, and water resistance", "title": "Hydrometer stem diameter and sensitivity", "description": "Build hydrometers with different stem diameters and compare their sensitivity.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 671, "source_index": 1121, "id": "topic-671-capillary-radius-and-rise-height", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 121, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Kapillarradius und Steighöhe", "description": "Miss die Wasserhöhe in Kapillaren verschiedener Radien.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Capillary radius and rise height", "description": "Measure water rise in capillaries of different radii.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 672, "source_index": 1122, "id": "topic-672-surfactant-concentration-and-contact-angle", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 5, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 122, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Tensidkonzentration und Kontaktwinkel", "description": "Gib unterschiedliche Mengen Spülmittel in Wasser und miss den Kontaktwinkel auf derselben Oberfläche.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Surfactant concentration and contact angle", "description": "Add different concentrations of detergent and measure contact angle on the same surface.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 673, "source_index": 1123, "id": "topic-673-surface-coating-and-contact-angle-hysteresis", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 2, 5, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 123, "method_keys": [ "trigonometry", "geometry" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Oberflächenbeschichtung und Kontaktwinkelhysterese", "description": "Vergleiche unbehandeltes Glas, Wachs, Kunststoff und andere Beschichtungen.", "methods": [ "Trigonometrie", "Geometrie" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Surface coating and contact-angle hysteresis", "description": "Compare untreated glass, wax, plastic, and other coatings.", "methods": [ "Trigonometry", "Geometry" ] } }, { "no": 674, "source_index": 1124, "id": "topic-674-nozzle-diameter-and-droplet-mass", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 2, 5, 15, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 124, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Düsendurchmesser und Tropfenmasse", "description": "Bestimme die Masse eines Tropfens unmittelbar vor dem Ablösen von Düsen verschiedener Größe.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Nozzle diameter and droplet mass", "description": "Determine droplet mass at detachment from nozzles of different diameters.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 675, "source_index": 1125, "id": "topic-675-drop-height-and-spreading-factor", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6, 10, 11, 12 ], "measurement_codes": [ 1, 5, 7, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 125, "method_keys": [ "functions_modeling", "regression", "geometry", "proof" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Fallhöhe und Ausbreitung eines Wassertropfens", "description": "Lass gleich große Tropfen aus verschiedenen Höhen auf dieselbe Fläche fallen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Beweisführung" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Drop height and spreading factor", "description": "Drop equal-sized droplets from different heights onto the same surface.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Proof" ] } }, { "no": 676, "source_index": 1126, "id": "topic-676-initial-radius-and-evaporation-time", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 6, 7, 11, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 126, "method_keys": [ "functions_modeling", "differential_equations", "geometry", "sequences_series", "time_series", "algebra" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Anfangsradius und Verdunstungszeit", "description": "Fotografiere Tropfen verschiedener Ausgangsgröße während der Verdunstung.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie", "Folgen & Reihen", "Zeitreihenanalyse", "Algebra" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Initial radius and evaporation time", "description": "Photograph droplets of different initial sizes during evaporation.", "methods": [ "Functions & modelling", "Differential equations", "Geometry", "Sequences & series", "Time-series analysis", "Algebra" ] } }, { "no": 677, "source_index": 1127, "id": "topic-677-air-speed-and-droplet-evaporation", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 12, 16, 18, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 127, "method_keys": [ "functions_modeling", "stochastics", "geometry", "algebra" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Luftgeschwindigkeit und Tropfenverdunstung", "description": "Setze identische Tropfen verschiedenen kontrollierten Luftströmungen aus.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Geometrie", "Algebra" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Air speed and droplet evaporation", "description": "Expose identical droplets to different controlled air speeds.", "methods": [ "Functions & modelling", "Statistics & probability", "Geometry", "Algebra" ] } }, { "no": 678, "source_index": 1128, "id": "topic-678-wetted-perimeter-and-surface-load-capacity", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 2, 5, 10, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 128, "method_keys": [ "functions_modeling", "differential_calculus", "geometry" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Benetzter Umfang und Tragfähigkeit der Wasseroberfläche", "description": "Lege leichte Draht- oder Folienformen verschiedener Umfänge vorsichtig auf Wasser.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Wetted perimeter and surface load capacity", "description": "Place lightweight wire or foil shapes with different perimeters on water.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry" ] } }, { "no": 679, "source_index": 1129, "id": "topic-679-frame-geometry-and-minimum-soap-film-area", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 5, 7, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 129, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "numerical_methods", "optimization" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Rahmengeometrie und minimale Seifenfilmfläche", "description": "Erzeuge Seifenfilme zwischen Drahtformen verschiedener Geometrie.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Numerische Verfahren", "Optimierung" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Frame geometry and minimum soap-film area", "description": "Create soap films between wire frames of different geometries.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Numerical methods", "Optimisation" ] } }, { "no": 680, "source_index": 1130, "id": "topic-680-glycerol-fraction-and-soap-bubble-lifetime", "category_key": "surface-tension-capillarity-and-droplets", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 130, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "geometry", "optimization" ], "de": { "category": "Oberflächenspannung, Kapillarität und Tropfen", "title": "Glycerinanteil und Lebensdauer einer Seifenblase", "description": "Variiere den Glycerinanteil einer Seifenlösung und miss die Lebensdauer vieler Blasen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Geometrie", "Optimierung" ] }, "en": { "category": "Surface tension, capillarity, and droplets", "title": "Glycerol fraction and soap-bubble lifetime", "description": "Vary glycerol concentration and measure the lifetime of many bubbles.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Geometry", "Optimisation" ] } }, { "no": 681, "source_index": 1131, "id": "topic-681-frequency-and-wavelength-of-water-waves", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 11, 12, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 131, "method_keys": [ "functions_modeling", "regression", "trigonometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Frequenz und Wellenlänge von Wasserwellen", "description": "Erzeuge Wellen verschiedener Frequenz bei konstanter Wassertiefe.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Frequency and wavelength of water waves", "description": "Generate waves of different frequencies at constant water depth.", "methods": [ "Functions & modelling", "Regression", "Trigonometry" ] } }, { "no": 682, "source_index": 1132, "id": "topic-682-gap-width-and-diffraction-angle", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 132, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Spaltbreite und Beugungswinkel", "description": "Lass Wasserwellen durch Spalte verschiedener Breite laufen.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Gap width and diffraction angle", "description": "Pass water waves through gaps of different widths.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 683, "source_index": 1133, "id": "topic-683-source-separation-and-interference-pattern", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 133, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Quellenabstand und Interferenzmuster", "description": "Erzeuge zwei gleichfrequente Wellenquellen mit variablem Abstand.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Source separation and interference pattern", "description": "Generate two equal-frequency wave sources with variable separation.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 684, "source_index": 1134, "id": "topic-684-fluid-viscosity-and-wave-damping", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 134, "method_keys": [ "trigonometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Flüssigkeitsviskosität und Wellendämpfung", "description": "Vergleiche die Abnahme der Wellenamplitude in Wasser-Glycerin-Mischungen.", "methods": [ "Trigonometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Fluid viscosity and wave damping", "description": "Compare wave-amplitude decay in water–glycerol mixtures.", "methods": [ "Trigonometry" ] } }, { "no": 685, "source_index": 1135, "id": "topic-685-container-length-and-sloshing-resonance", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 6, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 135, "method_keys": [ "functions_modeling", "trigonometry", "fourier_analysis" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Behälterlänge und Schwappresonanz", "description": "Bestimme die Resonanzfrequenz von Wasser in Behältern verschiedener Länge.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Fourier-Analyse" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Container length and sloshing resonance", "description": "Determine the sloshing resonance frequency in containers of different lengths.", "methods": [ "Functions & modelling", "Trigonometry", "Fourier analysis" ] } }, { "no": 686, "source_index": 1136, "id": "topic-686-fill-level-and-sloshing-modes", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 3, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 136, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Füllstand und Schwappmoden", "description": "Verändere den Füllstand eines Behälters und identifiziere mehrere Resonanzfrequenzen.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Fill level and sloshing modes", "description": "Vary fill level and identify several resonance frequencies.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 687, "source_index": 1137, "id": "topic-687-initial-water-height-and-dam-break-front", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 6, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 137, "method_keys": [ "functions_modeling", "trigonometry", "algebra" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Anfangswasserhöhe und Dammbruchfront", "description": "Öffne eine kleine Trennwand in einem Modellkanal und filme die Ausbreitungsfront.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Algebra" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Initial water height and dam-break front", "description": "Release water behind a small barrier and film the advancing front.", "methods": [ "Functions & modelling", "Trigonometry", "Algebra" ] } }, { "no": 688, "source_index": 1138, "id": "topic-688-discharge-and-hydraulic-jump", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 138, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Abfluss und hydraulischer Sprung", "description": "Erzeuge in einem flachen Kanal einen hydraulischen Sprung und miss seine Position und Höhenverhältnisse.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Discharge and hydraulic jump", "description": "Create a hydraulic jump and measure its position and depth ratio.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 689, "source_index": 1139, "id": "topic-689-shore-slope-and-wave-run-up", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 1, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 139, "method_keys": [ "functions_modeling", "differential_calculus", "regression", "trigonometry", "optimization" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Uferneigung und Wellenauflauf", "description": "Baue Modellstrände verschiedener Neigung und miss die maximale Auflaufhöhe.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Regression", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Shore slope and wave run-up", "description": "Build model beaches with different slopes and measure maximum wave run-up.", "methods": [ "Functions & modelling", "Differential calculus", "Regression", "Trigonometry", "Optimisation" ] } }, { "no": 690, "source_index": 1140, "id": "topic-690-breakwater-porosity-and-wave-transmission", "category_key": "water-waves-resonance-and-hydraulic-transitions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 140, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Wasserwellen, Resonanz und hydraulische Übergänge", "title": "Porosität eines Wellenbrechers und Wellenübertragung", "description": "Vergleiche Modellwellenbrecher mit verschiedenen Lückenanteilen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Water waves, resonance, and hydraulic transitions", "title": "Breakwater porosity and wave transmission", "description": "Compare model breakwaters with different gap fractions.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 691, "source_index": 1141, "id": "topic-691-sugar-concentration-and-freezing-point", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 141, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Zuckerkonzentration und Gefrierpunkt", "description": "Miss den Gefrierbeginn von Lösungen verschiedener Zuckerkonzentration.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Sugar concentration and freezing point", "description": "Measure the onset of freezing for solutions with different sugar concentrations.", "methods": [ "Functions & modelling" ] } }, { "no": 692, "source_index": 1142, "id": "topic-692-solute-type-and-freezing-point-depression", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 3, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 142, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Stoffart und Gefrierpunktserniedrigung", "description": "Vergleiche sichere gelöste Stoffe bei gleicher Teilchenkonzentration.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Solute type and freezing-point depression", "description": "Compare safe dissolved substances at equal particle concentration.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 693, "source_index": 1143, "id": "topic-693-surface-roughness-and-supercooling", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 143, "method_keys": [ "stochastics", "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Oberflächenrauheit und Unterkühlung", "description": "Kühle gleiche Wasserproben in Gefäßen mit unterschiedlich rauer Innenfläche.", "methods": [ "Stochastik", "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Surface roughness and supercooling", "description": "Cool equal water samples in containers with different internal roughness.", "methods": [ "Statistics & probability", "Geometry" ] } }, { "no": 694, "source_index": 1144, "id": "topic-694-insulation-thickness-and-freezing-time", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 5, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 144, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Isolationsdicke und Gefrierzeit", "description": "Ummantle identische kleine Wasserbehälter mit verschiedenen Isolationsdicken.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Insulation thickness and freezing time", "description": "Wrap identical small water containers with different insulation thicknesses.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 695, "source_index": 1145, "id": "topic-695-container-shape-and-freezing-time", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 6, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 145, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Behälterform und Gefrierzeit", "description": "Vergleiche Behälter mit gleichem Volumen, aber unterschiedlichem Oberfläche-Volumen-Verhältnis.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Container shape and freezing time", "description": "Compare equal-volume containers with different surface-area-to-volume ratios.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 696, "source_index": 1146, "id": "topic-696-surface-colour-and-ice-melting", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 146, "method_keys": [ "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Oberflächenfarbe und Eisschmelze", "description": "Bedecke Eisproben mit gleich großen dunklen und hellen Flächen und bestrahle sie kontrolliert.", "methods": [ "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Surface colour and ice melting", "description": "Cover ice samples with equal dark and light surfaces under controlled illumination.", "methods": [ "Geometry" ] } }, { "no": 697, "source_index": 1147, "id": "topic-697-fragment-size-and-melting-time", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 3, 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 147, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Fragmentgröße und Schmelzdauer", "description": "Zerteile gleiche Eismassen in unterschiedlich viele annähernd gleich große Stücke.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Fragment size and melting time", "description": "Divide equal ice masses into different numbers of similar fragments.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 698, "source_index": 1148, "id": "topic-698-salt-pattern-and-melt-channel-formation", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 3, 7, 11, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 148, "method_keys": [ "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Salzmuster und Ausbildung von Schmelzkanälen", "description": "Streue gleiche Salzmengen in Linien-, Punkt- oder Gittermustern auf Eis.", "methods": [ "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Salt pattern and melt-channel formation", "description": "Apply equal salt quantities in line, point, or grid patterns.", "methods": [ "Geometry" ] } }, { "no": 699, "source_index": 1149, "id": "topic-699-snow-compaction-and-thermal-insulation", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 13, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 149, "method_keys": [ "functions_modeling", "differential_calculus", "regression" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Verdichtungsgrad von Schnee und Wärmedämmung", "description": "Vergleiche lockeren und unterschiedlich stark verdichteten Schnee oder fein zerstoßenes Eis.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Regression" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Snow compaction and thermal insulation", "description": "Compare loose and differently compacted snow or crushed ice.", "methods": [ "Functions & modelling", "Differential calculus", "Regression" ] } }, { "no": 700, "source_index": 1150, "id": "topic-700-snow-grain-size-and-melting-rate", "category_key": "further-ice-snow-and-freezing-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 11, 12 ], "measurement_codes": [ 3, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 150, "method_keys": [ "geometry" ], "de": { "category": "Weitere Eis-, Schnee- und Gefrierexperimente", "title": "Korngröße und Schmelzgeschwindigkeit von Schnee", "description": "Siebe Schnee oder zerstoßenes Eis in verschiedene Größenklassen.", "methods": [ "Geometrie" ] }, "en": { "category": "Further ice, snow, and freezing experiments", "title": "Snow grain size and melting rate", "description": "Separate snow or crushed ice into different grain-size classes.", "methods": [ "Geometry" ] } }, { "no": 701, "source_index": 1151, "id": "topic-701-door-opening-frequency-and-co2-decay", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 6, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 151, "method_keys": [ "functions_modeling", "trigonometry", "sequences_series", "time_series" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Türöffnungsfrequenz und CO₂-Abbau", "description": "Öffne eine Tür in standardisierten Intervallen, ohne den Raum absichtlich mit CO₂ anzureichern.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Folgen & Reihen", "Zeitreihenanalyse" ] }, "en": { "category": "Further CO₂ experiments", "title": "Door-opening frequency and CO₂ decay", "description": "Open a door at standardized intervals without artificially enriching the room with CO₂.", "methods": [ "Functions & modelling", "Trigonometry", "Sequences & series", "Time-series analysis" ] } }, { "no": 702, "source_index": 1152, "id": "topic-702-ventilation-setting-and-steady-state-co2-level", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 2, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 152, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Lüftungsstufe und stationärer CO₂-Wert", "description": "Vergleiche verschiedene Stufen einer vorhandenen mechanischen Lüftung bei ähnlicher Raumnutzung.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Further CO₂ experiments", "title": "Ventilation setting and steady-state CO₂ level", "description": "Compare different settings of an existing mechanical ventilation system.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 703, "source_index": 1153, "id": "topic-703-break-schedule-and-peak-co2-concentration", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 6, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 153, "method_keys": [ "functions_modeling", "differential_equations", "differential_calculus", "trigonometry", "geometry", "algebra" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Pausenrhythmus und maximale CO₂-Konzentration", "description": "Vergleiche Unterrichtsperioden mit unterschiedlich angeordneten Lüftungspausen.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Differentialrechnung", "Trigonometrie", "Geometrie", "Algebra" ] }, "en": { "category": "Further CO₂ experiments", "title": "Break schedule and peak CO₂ concentration", "description": "Compare occupied periods with differently timed ventilation breaks.", "methods": [ "Functions & modelling", "Differential equations", "Differential calculus", "Trigonometry", "Geometry", "Algebra" ] } }, { "no": 704, "source_index": 1154, "id": "topic-704-lag-between-occupancy-and-co2-response", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 6, 13, 14, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 154, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Verzögerung zwischen Belegung und CO₂-Signal", "description": "Erfasse genaue Eintritts- und Austrittszeiten und untersuche die zeitliche Verzögerung des Sensorsignals.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Further CO₂ experiments", "title": "Lag between occupancy and CO₂ response", "description": "Record occupancy changes and analyse the delayed CO₂ response.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 705, "source_index": 1155, "id": "topic-705-co2-sensor-response-time", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 6, 16, 19 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 155, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Reaktionszeit eines CO₂-Sensors", "description": "Bewege einen Sensor zwischen zwei natürlich vorkommenden Konzentrationsbereichen, etwa Außenluft und belegtem Raum.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further CO₂ experiments", "title": "CO₂ sensor response time", "description": "Move a sensor between two naturally occurring concentration ranges.", "methods": [ "Functions & modelling" ] } }, { "no": 706, "source_index": 1156, "id": "topic-706-agreement-between-multiple-co2-sensors", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 156, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Übereinstimmung mehrerer CO₂-Sensoren", "description": "Platziere mehrere Sensoren über längere Zeit direkt nebeneinander.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Further CO₂ experiments", "title": "Agreement between multiple CO₂ sensors", "description": "Place several sensors side by side for an extended period.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 707, "source_index": 1157, "id": "topic-707-distance-from-ventilation-opening-and-co2-gradient", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 3, 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 157, "method_keys": [ "functions_modeling", "differential_calculus", "regression", "numerical_methods" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Abstand zur Lüftungsöffnung und CO₂-Gradient", "description": "Miss gleichzeitig oder wiederholt entlang einer Linie zwischen Raummitte und Fenster beziehungsweise Luftauslass.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Regression", "Numerische Verfahren" ] }, "en": { "category": "Further CO₂ experiments", "title": "Distance from ventilation opening and CO₂ gradient", "description": "Measure along a line between the room centre and an opening or air outlet.", "methods": [ "Functions & modelling", "Differential calculus", "Regression", "Numerical methods" ] } }, { "no": 708, "source_index": 1158, "id": "topic-708-plant-species-and-normalized-net-co2-exchange", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 2, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 158, "method_keys": [ "stochastics", "geometry", "sequences_series" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Pflanzenart und normierter Netto-CO₂-Austausch", "description": "Vergleiche mehrere Pflanzenarten bei gleicher Beleuchtung und normiere auf Blattfläche oder Blattmasse.", "methods": [ "Stochastik", "Geometrie", "Folgen & Reihen" ] }, "en": { "category": "Further CO₂ experiments", "title": "Plant species and normalized net CO₂ exchange", "description": "Compare plant species under identical lighting and normalize by leaf area or mass.", "methods": [ "Statistics & probability", "Geometry", "Sequences & series" ] } }, { "no": 709, "source_index": 1159, "id": "topic-709-germination-stage-and-co2-release", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 3, 6, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 159, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Keimungsstadium und CO₂-Freisetzung", "description": "Miss gleiche Samenmassen vor, während und nach der Keimung in kleinen Messkammern.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further CO₂ experiments", "title": "Germination stage and CO₂ release", "description": "Measure equal seed masses before, during, and after germination.", "methods": [ "Functions & modelling" ] } }, { "no": 710, "source_index": 1160, "id": "topic-710-temperature-and-co2-degassing-from-a-beverage", "category_key": "further-co2-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 6, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 160, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere CO₂-Experimente", "title": "Temperatur und CO₂-Entgasung eines Getränks", "description": "Vergleiche gleiche Mengen eines kohlensäurehaltigen Getränks bei verschiedenen Temperaturen in einer kleinen unbesetzten Messkammer.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further CO₂ experiments", "title": "Temperature and CO₂ degassing from a beverage", "description": "Compare equal beverage samples at different temperatures.", "methods": [ "Functions & modelling" ] } }, { "no": 711, "source_index": 1161, "id": "topic-711-container-material-and-cooling-constant", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 2, 3, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 161, "method_keys": [ "functions_modeling", "differential_equations", "stochastics", "regression", "geometry" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Behältermaterial und Abkühlkonstante", "description": "Vergleiche Metall-, Glas-, Keramik- und Kunststoffgefäße gleicher Geometrie.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Stochastik", "Regression", "Geometrie" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Container material and cooling constant", "description": "Compare metal, glass, ceramic, and plastic containers of similar geometry.", "methods": [ "Functions & modelling", "Differential equations", "Statistics & probability", "Regression", "Geometry" ] } }, { "no": 712, "source_index": 1162, "id": "topic-712-surface-area-to-volume-ratio-and-cooling", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 162, "method_keys": [ "functions_modeling", "differential_equations", "regression", "geometry" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Oberfläche-Volumen-Verhältnis und Abkühlung", "description": "Verwende Behälter unterschiedlicher Form mit gleicher Flüssigkeitsmenge.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Regression", "Geometrie" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Surface-area-to-volume ratio and cooling", "description": "Use differently shaped containers holding equal liquid volumes.", "methods": [ "Functions & modelling", "Differential equations", "Regression", "Geometry" ] } }, { "no": 713, "source_index": 1163, "id": "topic-713-lid-opening-and-heat-loss", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 163, "method_keys": [ "functions_modeling", "differential_equations", "geometry", "algebra" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Deckelöffnung und Wärmeverlust", "description": "Verändere die offene Fläche eines Deckels bei sonst identischem Gefäß.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie", "Algebra" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Lid opening and heat loss", "description": "Vary the open area of a lid on an otherwise identical container.", "methods": [ "Functions & modelling", "Differential equations", "Geometry", "Algebra" ] } }, { "no": 714, "source_index": 1164, "id": "topic-714-stirring-speed-and-heat-transfer", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 12, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 164, "method_keys": [ "functions_modeling" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Rührgeschwindigkeit und Wärmeübergang", "description": "Rühre eine warme Flüssigkeit mit mehreren kontrollierten Geschwindigkeiten.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Stirring speed and heat transfer", "description": "Stir a warm liquid at several controlled speeds.", "methods": [ "Functions & modelling" ] } }, { "no": 715, "source_index": 1165, "id": "topic-715-air-speed-and-convective-cooling", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 12, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 165, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Luftgeschwindigkeit und konvektive Kühlung", "description": "Richte einen Ventilator mit verschiedenen Stufen auf denselben warmen Körper.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Air speed and convective cooling", "description": "Direct different fan speeds at the same warm object.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 716, "source_index": 1166, "id": "topic-716-surface-emissivity-and-radiative-cooling", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 4, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 166, "method_keys": [ "functions_modeling", "differential_equations", "geometry" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Oberflächenemissivität und Strahlungskühlung", "description": "Vergleiche identische Behälter mit matten, glänzenden, dunklen und hellen Außenflächen.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Surface emissivity and radiative cooling", "description": "Compare identical containers with different surface finishes.", "methods": [ "Functions & modelling", "Differential equations", "Geometry" ] } }, { "no": 717, "source_index": 1167, "id": "topic-717-number-of-insulation-layers", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 10, 11, 12 ], "measurement_codes": [ 3, 5 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 167, "method_keys": [ "functions_modeling", "differential_calculus", "proof", "optimization" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Anzahl der Isolationsschichten", "description": "Ummantle ein Gefäß mit null bis mehreren identischen Schichten.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Beweisführung", "Optimierung" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Number of insulation layers", "description": "Wrap a container in zero to several identical insulation layers.", "methods": [ "Functions & modelling", "Differential calculus", "Proof", "Optimisation" ] } }, { "no": 718, "source_index": 1168, "id": "topic-718-wet-surface-and-evaporative-cooling", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 3, 13, 18 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 168, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Feuchte Oberfläche und Verdunstungskühlung", "description": "Variiere die Größe eines feuchten Tuchs um denselben Behälter.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Wet surface and evaporative cooling", "description": "Vary the area of a wet cloth surrounding the same container.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 719, "source_index": 1169, "id": "topic-719-mass-of-a-phase-change-material", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 3, 6, 11 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 169, "method_keys": [ "algebra" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Masse eines Phasenwechselmaterials", "description": "Verwende unterschiedliche Mengen Eis oder eines geeigneten Kühlpacks und miss die Dauer eines Temperaturplateaus.", "methods": [ "Algebra" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Mass of a phase-change material", "description": "Use different masses of ice or a suitable cold pack.", "methods": [ "Algebra" ] } }, { "no": 720, "source_index": 1170, "id": "topic-720-temperature-profile-along-a-metal-rod", "category_key": "heat-transfer-and-temperature-profiles", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 3, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 170, "method_keys": [ "functions_modeling", "differential_equations", "algebra" ], "de": { "category": "Wärmeübertragung und Temperaturverläufe", "title": "Temperaturprofil entlang eines Metallstabs", "description": "Erwärme ein Ende eines Metallstabs moderat und miss die Temperatur an mehreren Positionen.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Algebra" ] }, "en": { "category": "Heat transfer and temperature profiles", "title": "Temperature profile along a metal rod", "description": "Moderately heat one end of a metal rod and measure temperature at several positions.", "methods": [ "Functions & modelling", "Differential equations", "Algebra" ] } }, { "no": 721, "source_index": 1171, "id": "topic-721-pendulum-length-and-corrected-period", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 2, 6, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 171, "method_keys": [ "functions_modeling", "differential_equations", "regression" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Pendellänge und Periodendauer mit Korrektur", "description": "Miss viele Perioden für realistische Pendellängen und bestimme daraus gg.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Regression" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Pendulum length and corrected period", "description": "Measure many periods for several pendulum lengths and estimate gg.", "methods": [ "Functions & modelling", "Differential equations", "Regression" ] } }, { "no": 722, "source_index": 1172, "id": "topic-722-release-angle-and-pendulum-period", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 6, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 172, "method_keys": [ "functions_modeling", "differential_equations", "integral_calculus", "trigonometry", "sequences_series", "numerical_methods" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Auslenkungswinkel und Pendelperiode", "description": "Untersuche kleine bis größere Anfangswinkel, statt nur die Kleinwinkelnäherung zu bestätigen.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Integralrechnung", "Trigonometrie", "Folgen & Reihen", "Numerische Verfahren" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Release angle and pendulum period", "description": "Investigate small and larger release angles.", "methods": [ "Functions & modelling", "Differential equations", "Integral calculus", "Trigonometry", "Sequences & series", "Numerical methods" ] } }, { "no": 723, "source_index": 1173, "id": "topic-723-pendulum-bob-shape-and-air-damping", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 173, "method_keys": [ "functions_modeling", "differential_equations", "geometry" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Pendelkörperform und Luftdämpfung", "description": "Vergleiche Körper gleicher Masse, aber unterschiedlicher Stirnfläche.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Pendulum-bob shape and air damping", "description": "Compare equal-mass bobs with different frontal areas.", "methods": [ "Functions & modelling", "Differential equations", "Geometry" ] } }, { "no": 724, "source_index": 1174, "id": "topic-724-fluid-viscosity-and-pendulum-damping", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 174, "method_keys": [ "functions_modeling", "differential_equations", "algebra" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Flüssigkeitsviskosität und Pendeldämpfung", "description": "Lass einen kleinen Körper teilweise oder vollständig in Flüssigkeiten verschiedener Viskosität schwingen.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Algebra" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Fluid viscosity and pendulum damping", "description": "Oscillate a body in liquids of different viscosities.", "methods": [ "Functions & modelling", "Differential equations", "Algebra" ] } }, { "no": 725, "source_index": 1175, "id": "topic-725-coupling-strength-and-energy-transfer-between-pendulums", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 6, 15, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 175, "method_keys": [ "functions_modeling", "differential_equations", "algebra" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Kopplungsstärke und Energieübertragung zweier Pendel", "description": "Verbinde zwei Pendel durch Federn unterschiedlicher Stärke.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Algebra" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Coupling strength and energy transfer between pendulums", "description": "Couple two pendulums using springs of different stiffness.", "methods": [ "Functions & modelling", "Differential equations", "Algebra" ] } }, { "no": 726, "source_index": 1176, "id": "topic-726-mass-and-spring-period-with-spring-mass-correction", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 2, 6 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 176, "method_keys": [ "functions_modeling" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Masse und Federperiode mit Federmassenkorrektur", "description": "Miss die Periodendauer für verschiedene Massen und bestimme die effektive Federmasse.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Mass and spring period with spring-mass correction", "description": "Measure period for different loads and estimate effective spring mass.", "methods": [ "Functions & modelling" ] } }, { "no": 727, "source_index": 1177, "id": "topic-727-spring-nonlinearity", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 15 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 177, "method_keys": [ "algebra" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Nichtlinearität einer Feder", "description": "Untersuche eine Feder oder ein elastisches Band über einen größeren, aber sicheren Dehnungsbereich.", "methods": [ "Algebra" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Spring nonlinearity", "description": "Investigate a spring or elastic band over a wider safe extension range.", "methods": [ "Algebra" ] } }, { "no": 728, "source_index": 1178, "id": "topic-728-wire-geometry-and-torsion-pendulum", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 178, "method_keys": [ "functions_modeling", "differential_equations", "regression", "geometry", "algebra" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Drahtgeometrie und Torsionspendel", "description": "Variiere Länge oder Radius eines Torsionsdrahts.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Regression", "Geometrie", "Algebra" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Wire geometry and torsion pendulum", "description": "Vary the length or radius of a torsion wire.", "methods": [ "Functions & modelling", "Differential equations", "Regression", "Geometry", "Algebra" ] } }, { "no": 729, "source_index": 1179, "id": "topic-729-platform-mass-and-metronome-synchronization", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 6, 11 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 179, "method_keys": [ "functions_modeling", "differential_equations", "geometry" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Plattformmasse und Synchronisation von Metronomen", "description": "Stelle mehrere Metronome auf bewegliche Plattformen unterschiedlicher Masse.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Geometrie" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Platform mass and metronome synchronization", "description": "Place metronomes on movable platforms of different mass.", "methods": [ "Functions & modelling", "Differential equations", "Geometry" ] } }, { "no": 730, "source_index": 1180, "id": "topic-730-initial-difference-and-chaotic-divergence-of-a-double-pendulum", "category_key": "oscillations-coupling-and-chaos", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 1, 11, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 180, "method_keys": [ "functions_modeling", "differential_equations" ], "de": { "category": "Schwingungen, Kopplung und Chaos", "title": "Anfangsabweichung und chaotische Divergenz eines Doppelpendels", "description": "Starte zwei nahezu identische Doppelpendel mit kleinen Anfangsunterschieden.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen" ] }, "en": { "category": "Oscillations, coupling, and chaos", "title": "Initial difference and chaotic divergence of a double pendulum", "description": "Release two nearly identical double pendulums with small initial differences.", "methods": [ "Functions & modelling", "Differential equations" ] } }, { "no": 731, "source_index": 1181, "id": "topic-731-moment-of-inertia-and-ramp-acceleration", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 181, "method_keys": [ "geometry" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Trägheitsmoment und Beschleunigung auf einer Rampe", "description": "Lass Vollzylinder, Hohlzylinder, Kugeln und Ringe dieselbe Rampe hinabrollen.", "methods": [ "Geometrie" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Moment of inertia and ramp acceleration", "description": "Roll different bodies down the same incline.", "methods": [ "Geometry" ] } }, { "no": 732, "source_index": 1182, "id": "topic-732-wheel-radius-and-rolling-resistance", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 2, 5, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 182, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Radradius und Rollwiderstand", "description": "Ziehe gleich belastete Räder verschiedener Radien über dieselbe Oberfläche.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Wheel radius and rolling resistance", "description": "Pull equally loaded wheels of different radii over the same surface.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 733, "source_index": 1183, "id": "topic-733-tyre-pressure-and-rolling-resistance", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 5, 8, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 183, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Reifendruck und Rollwiderstand", "description": "Miss die Ausrollstrecke eines Fahrradrads oder Modellreifens bei unterschiedlichen zulässigen Drücken.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Tyre pressure and rolling resistance", "description": "Measure coast-down distance at different permitted tyre pressures.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ] } }, { "no": 734, "source_index": 1184, "id": "topic-734-normal-force-and-coefficient-of-friction", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 2, 13, 15 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 184, "method_keys": [ "functions_modeling", "regression", "geometry", "proof" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Normalkraft und Reibungskoeffizient", "description": "Ziehe denselben Körper mit verschiedenen Zusatzmassen über dieselbe Fläche.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Beweisführung" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Normal force and coefficient of friction", "description": "Pull the same object with different added masses.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Proof" ] } }, { "no": 735, "source_index": 1185, "id": "topic-735-apparent-contact-area-and-friction", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 13, 15 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 185, "method_keys": [ "geometry" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Scheinbare Kontaktfläche und Reibung", "description": "Ziehe denselben Quader auf verschiedenen Seiten über die gleiche Oberfläche.", "methods": [ "Geometrie" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Apparent contact area and friction", "description": "Pull the same block on different faces.", "methods": [ "Geometry" ] } }, { "no": 736, "source_index": 1186, "id": "topic-736-measured-roughness-and-friction", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 186, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Gemessene Rauheit und Reibung", "description": "Erzeuge mehrere reproduzierbare Rauheitsstufen und bestimme einen fotografischen Rauheitsindex.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Measured roughness and friction", "description": "Create reproducible roughness levels and define an image-based roughness index.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 737, "source_index": 1187, "id": "topic-737-lubricant-viscosity-and-bearing-coast-down-time", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 6, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 187, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Schmiermittelviskosität und Lagerauslaufzeit", "description": "Vergleiche geeignete, ungefährliche Schmiermittel in einem kleinen Lager.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Lubricant viscosity and bearing coast-down time", "description": "Compare suitable safe lubricants in a small bearing.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 738, "source_index": 1188, "id": "topic-738-particle-shape-and-angle-of-repose", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 11, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 188, "method_keys": [ "stochastics", "trigonometry", "geometry" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Teilchenform und Schüttwinkel", "description": "Vergleiche kugelförmige, kantige und längliche Körner ähnlicher Größe.", "methods": [ "Stochastik", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Particle shape and angle of repose", "description": "Compare spherical, angular, and elongated grains of similar size.", "methods": [ "Statistics & probability", "Trigonometry", "Geometry" ] } }, { "no": 739, "source_index": 1189, "id": "topic-739-outlet-diameter-and-granular-discharge", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 3, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 189, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Öffnungsdurchmesser und Granulatausfluss", "description": "Lass Sand oder Reis durch Öffnungen verschiedener Größe fließen.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Outlet diameter and granular discharge", "description": "Discharge sand or rice through openings of different sizes.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 740, "source_index": 1190, "id": "topic-740-spin-rate-and-precession-of-a-top", "category_key": "friction-rolling-and-granular-materials", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 6, 12, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 190, "method_keys": [ "functions_modeling", "geometry", "sequences_series", "time_series" ], "de": { "category": "Reibung, Rollen und Granulate", "title": "Kreiseldrehzahl und Präzession", "description": "Miss Drehzahl und Präzessionsgeschwindigkeit eines Kreisels über die Zeit.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Folgen & Reihen", "Zeitreihenanalyse" ] }, "en": { "category": "Friction, rolling, and granular materials", "title": "Spin rate and precession of a top", "description": "Measure spin and precession rates of a top over time.", "methods": [ "Functions & modelling", "Geometry", "Sequences & series", "Time-series analysis" ] } }, { "no": 741, "source_index": 1191, "id": "topic-741-paper-helicopter-blade-length", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 2, 5, 6, 10, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 191, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Rotorblattlänge eines Papierhubschraubers", "description": "Variiere die Rotorblattlänge bei gleicher Gesamtmasse.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Paper-helicopter blade length", "description": "Vary rotor-blade length while keeping total mass constant.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 742, "source_index": 1192, "id": "topic-742-fold-angle-of-a-paper-rotor", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 5, 10, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 192, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Faltwinkel eines Papierrotors", "description": "Verändere den Anstellwinkel der Rotorblätter.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Fold angle of a paper rotor", "description": "Vary the pitch angle of paper rotor blades.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 743, "source_index": 1193, "id": "topic-743-wing-aspect-ratio-and-glide-ratio", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 10, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 193, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Flügelstreckung und Gleitverhältnis", "description": "Baue Papierflugzeuge mit gleicher Flügelfläche, aber unterschiedlicher Spannweite.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Wing aspect ratio and glide ratio", "description": "Build paper aircraft with equal wing area but different spans.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 744, "source_index": 1194, "id": "topic-744-centre-of-mass-position-and-flight-stability", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 2, 5, 7, 10, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 194, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "proof", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Schwerpunktlage und Flugstabilität", "description": "Verschiebe eine kleine Zusatzmasse entlang desselben Papierflugzeugs.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Beweisführung", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Centre-of-mass position and flight stability", "description": "Move a small mass along the same paper aircraft.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Proof", "Optimisation" ] } }, { "no": 745, "source_index": 1195, "id": "topic-745-launch-angle-and-range-with-air-resistance", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 5, 7, 10, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 195, "method_keys": [ "functions_modeling", "differential_equations", "differential_calculus", "trigonometry", "numerical_methods", "algebra" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Abwurfwinkel und Reichweite mit Luftwiderstand", "description": "Verwende einen sicheren Ball oder eine weiche Wurfvorrichtung und filme die Bahn.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Differentialrechnung", "Trigonometrie", "Numerische Verfahren", "Algebra" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Launch angle and range with air resistance", "description": "Use a safe soft projectile and record its trajectory.", "methods": [ "Functions & modelling", "Differential equations", "Differential calculus", "Trigonometry", "Numerical methods", "Algebra" ] } }, { "no": 746, "source_index": 1196, "id": "topic-746-spin-and-lateral-flight-deflection", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 5, 7, 10, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 196, "method_keys": [ "functions_modeling", "differential_calculus", "regression" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Drall und seitliche Flugbahn", "description": "Versetze leichte Bälle mit reproduzierbarem Drall und analysiere ihre seitliche Abweichung.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Regression" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Spin and lateral flight deflection", "description": "Launch light balls with controlled spin and analyse lateral deflection.", "methods": [ "Functions & modelling", "Differential calculus", "Regression" ] } }, { "no": 747, "source_index": 1197, "id": "topic-747-parachute-area-and-terminal-velocity", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 2, 5, 7, 10, 12, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 197, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Fallschirmfläche und Endgeschwindigkeit", "description": "Lass gleich schwere Modellfallschirme verschiedener Fläche fallen.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Parachute area and terminal velocity", "description": "Drop equal-mass model parachutes of different areas.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 748, "source_index": 1198, "id": "topic-748-vent-diameter-and-parachute-stability", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 5, 6, 10 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 198, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Zentralöffnung und Fallschirmstabilität", "description": "Variiere die Größe einer Öffnung in gleich großen Fallschirmen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Vent diameter and parachute stability", "description": "Vary the central vent diameter in equal-sized parachutes.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 749, "source_index": 1199, "id": "topic-749-propeller-pitch-and-thrust", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 5, 10, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 199, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Propellersteigung und Schub", "description": "Teste kleine Niederspannungspropeller mit verschiedenen Blattwinkeln.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Propeller pitch and thrust", "description": "Test small low-voltage propellers with different blade angles.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 750, "source_index": 1200, "id": "topic-750-number-of-blades-and-propeller-efficiency", "category_key": "flight-aerodynamic-drag-and-propellers", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 10 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 200, "method_keys": [ "stochastics", "optimization" ], "de": { "category": "Flug, Luftwiderstand und Propeller", "title": "Blattzahl und Propellerwirkungsgrad", "description": "Vergleiche Propeller ähnlicher Größe mit unterschiedlicher Blattzahl.", "methods": [ "Stochastik", "Optimierung" ] }, "en": { "category": "Flight, aerodynamic drag, and propellers", "title": "Number of blades and propeller efficiency", "description": "Compare similar propellers with different blade counts.", "methods": [ "Statistics & probability", "Optimisation" ] } }, { "no": 751, "source_index": 1201, "id": "topic-751-span-length-and-beam-deflection", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 2, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 201, "method_keys": [ "functions_modeling", "regression", "geometry", "algebra" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Spannweite und Balkendurchbiegung", "description": "Belaste denselben Balken bei verschiedenen Auflageabständen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Algebra" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Span length and beam deflection", "description": "Load the same beam at different support separations.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Algebra" ] } }, { "no": 752, "source_index": 1202, "id": "topic-752-cross-section-orientation-and-stiffness", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 202, "method_keys": [ "geometry" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Querschnittsorientierung und Steifigkeit", "description": "Belaste einen rechteckigen Balken einmal flach und einmal hochkant.", "methods": [ "Geometrie" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Cross-section orientation and stiffness", "description": "Load a rectangular beam in different orientations.", "methods": [ "Geometry" ] } }, { "no": 753, "source_index": 1203, "id": "topic-753-hollow-section-wall-thickness-and-buckling-load", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 11, 12 ], "measurement_codes": [ 2, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 203, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Wanddicke eines Hohlprofils und Knicklast", "description": "Baue Papier- oder Kunststoffrohre gleicher Außenmaße mit unterschiedlicher Wanddicke.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Hollow-section wall thickness and buckling load", "description": "Build equal-sized hollow columns with different wall thicknesses.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 754, "source_index": 1204, "id": "topic-754-load-position-and-beam-deflection", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 3, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 204, "method_keys": [ "geometry", "algebra" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Lastposition und Balkendurchbiegung", "description": "Verschiebe dieselbe Last zwischen den Auflagern.", "methods": [ "Geometrie", "Algebra" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Load position and beam deflection", "description": "Move the same load between beam supports.", "methods": [ "Geometry", "Algebra" ] } }, { "no": 755, "source_index": 1205, "id": "topic-755-truss-angle-and-load-capacity", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 1, 2, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 205, "method_keys": [ "functions_modeling", "differential_calculus", "vectors", "trigonometry", "geometry", "optimization" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Dreieckswinkel und Tragfähigkeit eines Fachwerks", "description": "Baue Fachwerke mit gleicher Stabzahl, aber unterschiedlichen Dreieckswinkeln.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Vektorrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Truss angle and load capacity", "description": "Build trusses with equal member counts but different angles.", "methods": [ "Functions & modelling", "Differential calculus", "Vector mathematics", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 756, "source_index": 1206, "id": "topic-756-arch-rise-and-load-capacity", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 2, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 206, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Stichhöhe eines Bogens und Belastbarkeit", "description": "Vergleiche Modellbögen mit verschiedenen Verhältnissen von Höhe zu Spannweite.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Arch rise and load capacity", "description": "Compare model arches with different rise-to-span ratios.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 757, "source_index": 1207, "id": "topic-757-corrugation-wavelength-and-bending-stiffness", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 2, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 207, "method_keys": [ "trigonometry", "geometry" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Wellenlänge einer Wellpappe und Biegesteifigkeit", "description": "Falte Papier in regelmäßige Wellen unterschiedlicher Breite und Höhe.", "methods": [ "Trigonometrie", "Geometrie" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Corrugation wavelength and bending stiffness", "description": "Fold paper into corrugations of different width and height.", "methods": [ "Trigonometry", "Geometry" ] } }, { "no": 758, "source_index": 1208, "id": "topic-758-honeycomb-cell-size", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 208, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Zellgröße einer Wabenstruktur", "description": "Baue Waben gleicher Außenabmessung mit unterschiedlich großen Zellen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Honeycomb cell size", "description": "Build equal-sized honeycombs with different cell sizes.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 759, "source_index": 1209, "id": "topic-759-fibre-orientation-in-a-laminate", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 13, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 209, "method_keys": [ "functions_modeling", "matrices", "trigonometry", "geometry" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "Faserrichtung eines Laminats", "description": "Klebe Papier- oder Gewebelagen in verschiedenen Winkelanordnungen.", "methods": [ "Funktionen & Modellierung", "Matrizen", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "Fibre orientation in a laminate", "description": "Laminate paper or fabric layers at different orientations.", "methods": [ "Functions & modelling", "Matrices", "Trigonometry", "Geometry" ] } }, { "no": 760, "source_index": 1210, "id": "topic-760-3d-print-infill-and-stiffness", "category_key": "structures-beams-and-material-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 2, 13, 15, 17, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 210, "method_keys": [ "functions_modeling", "regression", "geometry", "optimization" ], "de": { "category": "Tragwerke, Balken und Materialgeometrie", "title": "3D-Druck-Füllgrad und Steifigkeit", "description": "Drucke identische Proben mit verschiedenen Füllgraden oder Füllmustern.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Optimierung" ] }, "en": { "category": "Structures, beams, and material geometry", "title": "3D-print infill and stiffness", "description": "Print identical specimens with different infill percentages or patterns.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Optimisation" ] } }, { "no": 761, "source_index": 1211, "id": "topic-761-wire-length-and-electrical-resistance", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 5, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 211, "method_keys": [ "functions_modeling" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Drahtlänge und elektrischer Widerstand", "description": "Miss den Widerstand desselben Drahtmaterials bei mehreren Längen.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Wire length and electrical resistance", "description": "Measure resistance of the same wire material at several lengths.", "methods": [ "Functions & modelling" ] } }, { "no": 762, "source_index": 1212, "id": "topic-762-wire-diameter-and-resistance", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 212, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Drahtdurchmesser und Widerstand", "description": "Vergleiche Drähte gleichen Materials und gleicher Länge mit unterschiedlichen Durchmessern.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Wire diameter and resistance", "description": "Compare equal-length wires of different diameters.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 763, "source_index": 1213, "id": "topic-763-temperature-and-conductor-resistance", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 5, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 213, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Temperatur und Widerstand eines Leiters", "description": "Miss den Widerstand eines geeigneten Leiters in einem moderaten Temperaturbereich.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Temperature and conductor resistance", "description": "Measure conductor resistance over a moderate temperature range.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 764, "source_index": 1214, "id": "topic-764-led-colour-and-currentvoltage-characteristic", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 5 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 214, "method_keys": [ "functions_modeling" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "LED-Farbe und Strom-Spannungs-Kennlinie", "description": "Erfasse Kennlinien verschiedenfarbiger LEDs mit Vorwiderstand und Kleinspannung.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Electrical circuits and sensors", "title": "LED colour and current–voltage characteristic", "description": "Record current–voltage curves of different LED colours.", "methods": [ "Functions & modelling" ] } }, { "no": 765, "source_index": 1215, "id": "topic-765-resistance-and-rc-charging-time", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 6 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 215, "method_keys": [ "algebra" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Widerstand und RC-Ladezeit", "description": "Halte die Kapazität konstant und variiere den Widerstand.", "methods": [ "Algebra" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Resistance and RC charging time", "description": "Keep capacitance constant and vary resistance.", "methods": [ "Algebra" ] } }, { "no": 766, "source_index": 1216, "id": "topic-766-capacitance-and-rc-discharge-time", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 5, 6 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 216, "method_keys": [ "algebra" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Kapazität und RC-Entladezeit", "description": "Halte den Widerstand konstant und verwende verschiedene Kondensatoren.", "methods": [ "Algebra" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Capacitance and RC discharge time", "description": "Keep resistance constant and vary capacitance.", "methods": [ "Algebra" ] } }, { "no": 767, "source_index": 1217, "id": "topic-767-capacitor-type-and-leakage-current", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 6, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 217, "method_keys": [ "functions_modeling", "algebra" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Kondensatortyp und Leckstrom", "description": "Vergleiche den langfristigen Spannungsverlust verschiedener geeigneter Kondensatoren.", "methods": [ "Funktionen & Modellierung", "Algebra" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Capacitor type and leakage current", "description": "Compare long-term voltage loss in different suitable capacitors.", "methods": [ "Functions & modelling", "Algebra" ] } }, { "no": 768, "source_index": 1218, "id": "topic-768-illuminance-and-ldr-resistance", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 5, 7, 10, 13, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 218, "method_keys": [ "functions_modeling", "regression", "algebra" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Beleuchtungsstärke und LDR-Widerstand", "description": "Miss den Widerstand eines Fotowiderstands bei verschiedenen Lichtstärken.", "methods": [ "Funktionen & Modellierung", "Regression", "Algebra" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Illuminance and LDR resistance", "description": "Measure an LDR at different illuminance levels.", "methods": [ "Functions & modelling", "Regression", "Algebra" ] } }, { "no": 769, "source_index": 1219, "id": "topic-769-thermistor-resistance-and-temperature", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 219, "method_keys": [ "functions_modeling", "regression", "numerical_methods", "algebra" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Thermistorwiderstand und Temperatur", "description": "Erstelle eine eigene Thermistorkalibrierung.", "methods": [ "Funktionen & Modellierung", "Regression", "Numerische Verfahren", "Algebra" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Thermistor resistance and temperature", "description": "Create a thermistor calibration curve.", "methods": [ "Functions & modelling", "Regression", "Numerical methods", "Algebra" ] } }, { "no": 770, "source_index": 1220, "id": "topic-770-capacitance-and-rlc-resonance-frequency", "category_key": "electrical-circuits-and-sensors", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 6, 13, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 220, "method_keys": [ "functions_modeling", "trigonometry", "geometry", "fourier_analysis" ], "de": { "category": "Elektrische Schaltungen und Sensoren", "title": "Kapazität und Resonanzfrequenz eines RLC-Kreises", "description": "Verändere die Kapazität bei gleicher Spule.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie", "Fourier-Analyse" ] }, "en": { "category": "Electrical circuits and sensors", "title": "Capacitance and RLC resonance frequency", "description": "Vary capacitance while keeping the inductor constant.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry", "Fourier analysis" ] } }, { "no": 771, "source_index": 1221, "id": "topic-771-distance-and-illuminance", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 2, 7, 10, 13, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 221, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Abstand und Beleuchtungsstärke", "description": "Miss die Beleuchtungsstärke einer kleinen Lichtquelle bei vielen Abständen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Light, optics, and image formation", "title": "Distance and illuminance", "description": "Measure illuminance from a small light source at many distances.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 772, "source_index": 1222, "id": "topic-772-polarizer-angle-and-light-intensity", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 7, 10, 11, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 222, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Polarisationswinkel und Lichtintensität", "description": "Drehe zwei Polarisationsfilter relativ zueinander.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Light, optics, and image formation", "title": "Polarizer angle and light intensity", "description": "Rotate two polarizing filters relative to one another.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 773, "source_index": 1223, "id": "topic-773-sugar-concentration-and-refractive-index", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 7, 10, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 223, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry", "algebra" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Zuckerkonzentration und Brechungsindex", "description": "Miss den Brechungswinkel von Lösungen verschiedener Konzentration.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie", "Algebra" ] }, "en": { "category": "Light, optics, and image formation", "title": "Sugar concentration and refractive index", "description": "Measure refraction angles for solutions of different concentrations.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry", "Algebra" ] } }, { "no": 774, "source_index": 1224, "id": "topic-774-prism-geometry-and-minimum-deviation", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 7, 10, 21 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 224, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Prismengeometrie und Minimalablenkung", "description": "Vergleiche Prismen verschiedener Winkel oder untersuche ein Prisma bei verschiedenen Einfallswinkeln.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Light, optics, and image formation", "title": "Prism geometry and minimum deviation", "description": "Investigate prisms at different incidence angles.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 775, "source_index": 1225, "id": "topic-775-object-distance-and-image-distance", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 7, 10, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 225, "method_keys": [ "functions_modeling", "regression", "geometry", "algebra" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Gegenstandsweite und Bildweite einer Linse", "description": "Miss Bildweiten für viele Gegenstandspositionen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Algebra" ] }, "en": { "category": "Light, optics, and image formation", "title": "Object distance and image distance", "description": "Measure image distance for many object positions.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Algebra" ] } }, { "no": 776, "source_index": 1226, "id": "topic-776-aperture-and-depth-of-field", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 7, 10, 11, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 226, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Blendenöffnung und Schärfentiefe", "description": "Fotografiere ein schräges Maßband mit verschiedenen Blendenöffnungen.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Light, optics, and image formation", "title": "Aperture and depth of field", "description": "Photograph an angled scale using different apertures.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 777, "source_index": 1227, "id": "topic-777-slit-width-and-diffraction-pattern", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 11, 12 ], "measurement_codes": [ 7, 10, 20, 21 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 227, "method_keys": [ "functions_modeling", "differential_calculus", "geometry" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Spaltbreite und Beugungsmuster", "description": "Beleuchte Einzelspalte verschiedener Breite mit einem geeigneten Schul-Laser.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie" ] }, "en": { "category": "Light, optics, and image formation", "title": "Slit width and diffraction pattern", "description": "Illuminate single slits of different widths using suitable school equipment.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry" ] } }, { "no": 778, "source_index": 1228, "id": "topic-778-grating-spacing-and-diffraction-angle", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 7, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 228, "method_keys": [ "trigonometry", "geometry", "algebra" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Gitterabstand und Beugungswinkel", "description": "Vergleiche Beugungsgitter mit unterschiedlichen Linienzahlen.", "methods": [ "Trigonometrie", "Geometrie", "Algebra" ] }, "en": { "category": "Light, optics, and image formation", "title": "Grating spacing and diffraction angle", "description": "Compare diffraction gratings with different line densities.", "methods": [ "Trigonometry", "Geometry", "Algebra" ] } }, { "no": 779, "source_index": 1229, "id": "topic-779-dye-concentration-and-light-transmission", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 7, 10, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 229, "method_keys": [ "functions_modeling", "regression", "geometry", "algebra" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Farbstoffkonzentration und Lichtdurchlässigkeit", "description": "Miss die Transmission sicherer Farblösungen verschiedener Konzentration.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie", "Algebra" ] }, "en": { "category": "Light, optics, and image formation", "title": "Dye concentration and light transmission", "description": "Measure transmission through safe dye solutions.", "methods": [ "Functions & modelling", "Regression", "Geometry", "Algebra" ] } }, { "no": 780, "source_index": 1230, "id": "topic-780-optical-fibre-bend-radius-and-light-loss", "category_key": "light-optics-and-image-formation", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 2, 3, 7, 10, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 230, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Licht, Optik und Bildentstehung", "title": "Biegeradius einer optischen Faser und Lichtverlust", "description": "Biege eine Kunststoff-Lichtleitfaser mit definierten Radien.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Light, optics, and image formation", "title": "Optical-fibre bend radius and light loss", "description": "Bend a plastic optical fibre to defined radii.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 781, "source_index": 1231, "id": "topic-781-solar-panel-tilt-angle", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 5, 10, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 231, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Neigungswinkel eines Solarmoduls", "description": "Miss die Leistung eines kleinen Solarmoduls bei kontrollierter Lichtquelle und verschiedenen Neigungen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Solar and renewable energy", "title": "Solar-panel tilt angle", "description": "Measure a small panel at different tilt angles.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 782, "source_index": 1232, "id": "topic-782-azimuth-angle-and-solar-output", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 3, 5, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 232, "method_keys": [ "trigonometry", "geometry" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Azimutwinkel und Solarleistung", "description": "Drehe das Modul horizontal relativ zur Lichtquelle.", "methods": [ "Trigonometrie", "Geometrie" ] }, "en": { "category": "Solar and renewable energy", "title": "Azimuth angle and solar output", "description": "Rotate the panel horizontally relative to the light source.", "methods": [ "Trigonometry", "Geometry" ] } }, { "no": 783, "source_index": 1233, "id": "topic-783-panel-temperature-and-electrical-power", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 10, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 233, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Modultemperatur und elektrische Leistung", "description": "Miss Spannung und Leistung eines kleinen Moduls über einen moderaten Temperaturbereich.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Solar and renewable energy", "title": "Panel temperature and electrical power", "description": "Measure panel voltage and output over a moderate temperature range.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 784, "source_index": 1234, "id": "topic-784-shaded-fraction-and-solar-output", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 10 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 234, "method_keys": [ "geometry" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Verschattungsanteil und Solarleistung", "description": "Bedecke definierte Flächenanteile eines kleinen Moduls.", "methods": [ "Geometrie" ] }, "en": { "category": "Solar and renewable energy", "title": "Shaded fraction and solar output", "description": "Cover defined fractions of a small solar panel.", "methods": [ "Geometry" ] } }, { "no": 785, "source_index": 1235, "id": "topic-785-shading-position-and-output", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 10, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 235, "method_keys": [ "functions_modeling", "stochastics", "graph_theory", "geometry" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Verschattungsposition und Leistung", "description": "Bedecke bei gleichem Flächenanteil unterschiedliche Zellbereiche.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Solar and renewable energy", "title": "Shading position and output", "description": "Shade different cell regions while keeping shaded area constant.", "methods": [ "Functions & modelling", "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 786, "source_index": 1236, "id": "topic-786-dust-coverage-and-solar-yield", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 10, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 236, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Staubbedeckung und Solarertrag", "description": "Verteile sichere, reproduzierbare Mengen eines feinen Materials auf einer Schutzfolie über dem Modul.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Solar and renewable energy", "title": "Dust coverage and solar yield", "description": "Apply reproducible dust coverage to a protective film above the panel.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 787, "source_index": 1237, "id": "topic-787-reflector-geometry-and-focal-concentration", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 5, 10, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 237, "method_keys": [ "stochastics", "geometry" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Reflektorgeometrie und Brennpunktkonzentration", "description": "Vergleiche parabolische, kreisförmige und segmentierte kleine Reflektoren bei begrenzter Leistung.", "methods": [ "Stochastik", "Geometrie" ] }, "en": { "category": "Solar and renewable energy", "title": "Reflector geometry and focal concentration", "description": "Compare small reflector geometries under low-power illumination.", "methods": [ "Statistics & probability", "Geometry" ] } }, { "no": 788, "source_index": 1238, "id": "topic-788-reflector-angle-in-a-model-solar-cooker", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 5, 10, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 238, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Reflektorwinkel eines Solarkochermodells", "description": "Verändere den Winkel mehrerer Reflektorflächen um einen kleinen Behälter.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Solar and renewable energy", "title": "Reflector angle in a model solar cooker", "description": "Vary reflector angles around a small model container.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 789, "source_index": 1239, "id": "topic-789-temperature-difference-and-thermoelectric-voltage", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 3, 5, 10, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 239, "method_keys": [ "functions_modeling", "stochastics", "regression" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Temperaturdifferenz und Thermoelementspannung", "description": "Miss die Spannung eines kleinen Thermoelements oder Thermogenerators bei verschiedenen Temperaturdifferenzen.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression" ] }, "en": { "category": "Solar and renewable energy", "title": "Temperature difference and thermoelectric voltage", "description": "Measure voltage at different temperature differences.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression" ] } }, { "no": 790, "source_index": 1240, "id": "topic-790-blade-pitch-of-a-small-wind-turbine", "category_key": "solar-and-renewable-energy", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 5, 10, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 240, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Solarenergie und erneuerbare Energien", "title": "Blattwinkel einer Kleinwindturbine", "description": "Teste sichere Modellrotoren bei mehreren Blattwinkeln und gleicher Luftströmung.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Solar and renewable energy", "title": "Blade pitch of a small wind turbine", "description": "Test model rotors at different blade pitches.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 791, "source_index": 1241, "id": "topic-791-temperature-and-effervescent-tablet-dissolution", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 2, 3, 6, 7, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 241, "method_keys": [ "geometry", "algebra" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Temperatur und Auflösungszeit einer Brausetablette", "description": "Miss nicht nur die Gesamtzeit, sondern den Massen- oder Volumenverlauf.", "methods": [ "Geometrie", "Algebra" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Temperature and effervescent-tablet dissolution", "description": "Measure the full mass or volume trajectory rather than only total time.", "methods": [ "Geometry", "Algebra" ] } }, { "no": 792, "source_index": 1242, "id": "topic-792-tablet-surface-area-and-reaction-rate", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 12, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 242, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Oberfläche und Reaktionsgeschwindigkeit einer Tablette", "description": "Vergleiche ganze, halbierte und reproduzierbar zerkleinerte Tabletten gleicher Masse.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Tablet surface area and reaction rate", "description": "Compare whole, divided, and crushed tablets of equal mass.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 793, "source_index": 1243, "id": "topic-793-initial-concentration-and-reaction-order", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 11, 12 ], "measurement_codes": [ 11, 12, 16 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 243, "method_keys": [ "functions_modeling" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Ausgangskonzentration und Reaktionsordnung", "description": "Verwende eine ungefährliche, farblich oder leitfähig messbare Schulreaktion.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Initial concentration and reaction order", "description": "Use a safe school reaction measurable by colour or conductivity.", "methods": [ "Functions & modelling" ] } }, { "no": 794, "source_index": 1244, "id": "topic-794-catalyst-amount-and-oxygen-production", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 4, 6, 11, 12 ], "measurement_codes": [ 12, 16, 20, 21 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 244, "method_keys": [ "functions_modeling", "differential_calculus" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Katalysatormenge und Sauerstoffproduktion", "description": "Zersetze verdünnte Wasserstoffperoxidlösung mit einer geeigneten biologischen Katalasequelle unter Schulaufsicht.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Catalyst amount and oxygen production", "description": "Use dilute peroxide with a suitable catalase source under school supervision.", "methods": [ "Functions & modelling", "Differential calculus" ] } }, { "no": 795, "source_index": 1245, "id": "topic-795-concentration-and-titration-curve-shape", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 11, 12, 16, 21 ], "safety_code": 2, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 245, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "algebra" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Konzentration und Form einer Titrationskurve", "description": "Erfasse den gesamten pH-Verlauf einer sicheren Säure-Base-Titration.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Algebra" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Concentration and titration-curve shape", "description": "Record the complete pH curve of a safe acid–base titration.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Algebra" ] } }, { "no": 796, "source_index": 1246, "id": "topic-796-temperature-and-diffusion-coefficient-in-agar", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 3, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 246, "method_keys": [ "geometry" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Temperatur und Diffusionskoeffizient in Agar", "description": "Miss den Radius einer Farbfront in Agar bei mehreren Temperaturen.", "methods": [ "Geometrie" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Temperature and diffusion coefficient in agar", "description": "Measure dye-front radius in agar at different temperatures.", "methods": [ "Geometry" ] } }, { "no": 797, "source_index": 1247, "id": "topic-797-supersaturation-and-crystal-growth", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 10, 11, 12 ], "measurement_codes": [ 1, 7, 11, 12, 16, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 247, "method_keys": [ "functions_modeling", "number_theory", "geometry", "algebra" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Übersättigung und Kristallwachstum", "description": "Fotografiere sichere Kristalle bei verschiedenen Anfangskonzentrationen.", "methods": [ "Funktionen & Modellierung", "Zahlentheorie", "Geometrie", "Algebra" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Supersaturation and crystal growth", "description": "Photograph safe crystals at different initial concentrations.", "methods": [ "Functions & modelling", "Number theory", "Geometry", "Algebra" ] } }, { "no": 798, "source_index": 1248, "id": "topic-798-temperature-and-solubility", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 248, "method_keys": [ "functions_modeling", "differential_calculus", "algebra", "optimization" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Temperatur und Löslichkeit", "description": "Bestimme die maximale lösliche Menge eines sicheren Stoffes bei mehreren Temperaturen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Algebra", "Optimierung" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Temperature and solubility", "description": "Determine maximum solubility at several temperatures.", "methods": [ "Functions & modelling", "Differential calculus", "Algebra", "Optimisation" ] } }, { "no": 799, "source_index": 1249, "id": "topic-799-salt-concentration-and-conductivity", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 11, 12, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 249, "method_keys": [ "functions_modeling", "regression", "sequences_series" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Salzkonzentration und Leitfähigkeit", "description": "Erstelle eine Kalibrierreihe bis in den nichtlinearen Bereich.", "methods": [ "Funktionen & Modellierung", "Regression", "Folgen & Reihen" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Salt concentration and conductivity", "description": "Create a calibration series extending into the nonlinear range.", "methods": [ "Functions & modelling", "Regression", "Sequences & series" ] } }, { "no": 800, "source_index": 1250, "id": "topic-800-illumination-time-and-dye-degradation", "category_key": "reaction-rates-diffusion-and-solutions", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 6, 10, 12, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 250, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Reaktionsgeschwindigkeit, Diffusion und Lösungen", "title": "Beleuchtungsdauer und Farbstoffabbau", "description": "Setze sichere Farblösungen standardisiertem Licht aus und analysiere die Farbintensität.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Reaction rates, diffusion, and solutions", "title": "Illumination time and dye degradation", "description": "Expose safe dye solutions to standardized light.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 801, "source_index": 1251, "id": "topic-801-salinity-and-germination-probability", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 11, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 251, "method_keys": [ "functions_modeling", "stochastics", "regression", "trigonometry", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Salzgehalt und Keimwahrscheinlichkeit", "description": "Lass gleiche Samenanzahlen bei verschiedenen Salzkonzentrationen keimen.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Salinity and germination probability", "description": "Germinate equal seed samples at different salinities.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 802, "source_index": 1252, "id": "topic-802-temperature-and-germination-time-distribution", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 6, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 252, "method_keys": [ "functions_modeling", "stochastics", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Temperatur und Verteilung der Keimzeiten", "description": "Erfasse für jeden einzelnen Samen die Zeit bis zur Keimung.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Temperature and germination-time distribution", "description": "Record the germination time of every individual seed.", "methods": [ "Functions & modelling", "Statistics & probability", "Geometry" ] } }, { "no": 803, "source_index": 1253, "id": "topic-803-light-direction-and-phototropism", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11, 12 ], "measurement_codes": [ 1, 6, 7, 10, 11, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 253, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "algebra" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Lichtrichtung und Phototropismus", "description": "Verändere den Einfallswinkel einer Lichtquelle und filme die Krümmung junger Pflanzen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Algebra" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Light direction and phototropism", "description": "Vary light direction and record plant curvature.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Algebra" ] } }, { "no": 804, "source_index": 1254, "id": "topic-804-photoperiod-and-plant-growth", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 11, 12 ], "measurement_codes": [ 1, 6, 7, 10, 11, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 254, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "time_series", "optimization" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Tageslänge und Pflanzenwachstum", "description": "Vergleiche mehrere Beleuchtungsdauern bei gleicher täglichen oder kontrollierter Gesamtlichtmenge.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Zeitreihenanalyse", "Optimierung" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Photoperiod and plant growth", "description": "Compare different photoperiods under controlled total light exposure.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Time-series analysis", "Optimisation" ] } }, { "no": 805, "source_index": 1255, "id": "topic-805-air-speed-and-transpiration", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 2, 3, 6, 12, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 255, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Luftgeschwindigkeit und Transpiration", "description": "Miss den Massenverlust gleichartiger Pflanzen bei verschiedenen Ventilatorstufen.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Air speed and transpiration", "description": "Measure plant mass loss at different air speeds.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 806, "source_index": 1256, "id": "topic-806-humidity-and-transpiration-rate", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 10, 12, 18, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 256, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Luftfeuchtigkeit und Transpirationsrate", "description": "Vergleiche kontrollierte Feuchtigkeitsbereiche bei gleicher Beleuchtung.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Humidity and transpiration rate", "description": "Compare controlled humidity ranges under identical lighting.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 807, "source_index": 1257, "id": "topic-807-leaf-position-and-stomatal-density", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 257, "method_keys": [ "functions_modeling", "stochastics", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Blattposition und Spaltöffnungsdichte", "description": "Erstelle mikroskopische Blattabdrücke aus verschiedenen Bereichen derselben Pflanze.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Leaf position and stomatal density", "description": "Create leaf impressions from different positions on the same plant.", "methods": [ "Functions & modelling", "Statistics & probability", "Geometry" ] } }, { "no": 808, "source_index": 1258, "id": "topic-808-tilt-angle-and-root-curvature", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 258, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Neigungswinkel und Wurzelkrümmung", "description": "Drehe Keimlinge um verschiedene Winkel und filme ihre gravitropische Reaktion.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Tilt angle and root curvature", "description": "Rotate seedlings by different angles and record root curvature.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry" ] } }, { "no": 809, "source_index": 1259, "id": "topic-809-planting-density-and-biomass", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 2, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 259, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Pflanzdichte und Biomasse", "description": "Variiere die Anzahl gleicher Pflanzen pro Fläche.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Planting density and biomass", "description": "Vary the number of equal plants per unit area.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 810, "source_index": 1260, "id": "topic-810-leaf-area-perimeter-and-fractal-structure", "category_key": "plant-growth-and-plant-geometry", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 6, 8, 11 ], "measurement_codes": [ 7, 11 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 260, "method_keys": [ "geometry" ], "de": { "category": "Pflanzenwachstum und Pflanzengeometrie", "title": "Blattfläche, Umfang und fraktale Struktur", "description": "Fotografiere Blätter verschiedener Arten oder Entwicklungsstadien.", "methods": [ "Geometrie" ] }, "en": { "category": "Plant growth and plant geometry", "title": "Leaf area, perimeter, and fractal structure", "description": "Photograph leaves from different species or growth stages.", "methods": [ "Geometry" ] } }, { "no": 811, "source_index": 1261, "id": "topic-811-cooking-time-and-pasta-water-absorption", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 261, "method_keys": [ "functions_modeling" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Kochzeit und Wasseraufnahme von Nudeln", "description": "Wiege identische Nudeln in kurzen Zeitabständen während des Kochens.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Food and cooking processes", "title": "Cooking time and pasta water absorption", "description": "Weigh identical pasta samples at regular cooking intervals.", "methods": [ "Functions & modelling" ] } }, { "no": 812, "source_index": 1262, "id": "topic-812-temperature-and-rice-water-absorption", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 6, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 262, "method_keys": [ "functions_modeling" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Temperatur und Wasseraufnahme von Reis", "description": "Vergleiche identische Reismengen bei mehreren konstanten Temperaturen.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Food and cooking processes", "title": "Temperature and rice water absorption", "description": "Compare equal rice samples at several constant temperatures.", "methods": [ "Functions & modelling" ] } }, { "no": 813, "source_index": 1263, "id": "topic-813-salt-concentration-and-potato-osmosis", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 2, 11, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 263, "method_keys": [ "functions_modeling", "stochastics", "regression", "numerical_methods", "algebra" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Salzkonzentration und Osmose in Kartoffeln", "description": "Miss die Massenänderung gleich großer Kartoffelstücke in Salzlösungen.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Numerische Verfahren", "Algebra" ] }, "en": { "category": "Food and cooking processes", "title": "Salt concentration and potato osmosis", "description": "Measure mass change of equal potato pieces in saline solutions.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Numerical methods", "Algebra" ] } }, { "no": 814, "source_index": 1264, "id": "topic-814-acid-concentration-and-apple-browning", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 6, 13, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 264, "method_keys": [ "functions_modeling", "geometry", "sequences_series", "time_series" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Säurekonzentration und Bräunung von Äpfeln", "description": "Behandle gleiche Apfelstücke mit unterschiedlichen Zitronensäurekonzentrationen.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Folgen & Reihen", "Zeitreihenanalyse" ] }, "en": { "category": "Food and cooking processes", "title": "Acid concentration and apple browning", "description": "Treat equal apple pieces with different citric-acid concentrations.", "methods": [ "Functions & modelling", "Geometry", "Sequences & series", "Time-series analysis" ] } }, { "no": 815, "source_index": 1265, "id": "topic-815-gelatin-concentration-and-gel-stiffness", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 2, 6, 15, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 265, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "algebra", "optimization" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Gelatinekonzentration und Gelsteifigkeit", "description": "Miss Eindringtiefe, Schwingungsfrequenz oder Belastungsdurchbiegung von Gelen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Algebra", "Optimierung" ] }, "en": { "category": "Food and cooking processes", "title": "Gelatin concentration and gel stiffness", "description": "Measure indentation, oscillation, or deflection of gels.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Algebra", "Optimisation" ] } }, { "no": 816, "source_index": 1266, "id": "topic-816-brew-time-and-coffee-extraction", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 2, 6, 11, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 266, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Brühzeit und Kaffeeextraktion", "description": "Miss bei konstantem Mahlgrad Farbe, Leitfähigkeit oder Gesamtmasse gelöster Stoffe.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Food and cooking processes", "title": "Brew time and coffee extraction", "description": "Measure colour, conductivity, or dissolved solids at constant grind size.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 817, "source_index": 1267, "id": "topic-817-grind-size-and-coffee-bed-flow-time", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 2, 6, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 267, "method_keys": [ "functions_modeling" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Mahlgrad und Durchlaufzeit eines Kaffeebetts", "description": "Verwende standardisierte Mahlgrößen und gleiche Kaffeemasse.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Food and cooking processes", "title": "Grind size and coffee-bed flow time", "description": "Use standardized grind sizes and equal coffee mass.", "methods": [ "Functions & modelling" ] } }, { "no": 818, "source_index": 1268, "id": "topic-818-dough-temperature-and-cookie-spread", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 3, 6, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 268, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "optimization" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Teigtemperatur und Ausbreitung eines Kekses", "description": "Backe identische Portionen mit unterschiedlichen Ausgangstemperaturen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Optimierung" ] }, "en": { "category": "Food and cooking processes", "title": "Dough temperature and cookie spread", "description": "Bake identical portions at different initial temperatures.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Optimisation" ] } }, { "no": 819, "source_index": 1269, "id": "topic-819-kernel-mass-and-popcorn-expansion", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 10, 11, 12 ], "measurement_codes": [ 2, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 269, "method_keys": [ "functions_modeling", "regression", "number_theory", "geometry" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Kornmasse und Popcornvolumen", "description": "Wiege einzelne Maiskörner und bestimme nach dem Poppen ihr Volumen.", "methods": [ "Funktionen & Modellierung", "Regression", "Zahlentheorie", "Geometrie" ] }, "en": { "category": "Food and cooking processes", "title": "Kernel mass and popcorn expansion", "description": "Weigh individual kernels and estimate popped volume.", "methods": [ "Functions & modelling", "Regression", "Number theory", "Geometry" ] } }, { "no": 820, "source_index": 1270, "id": "topic-820-temperature-and-egg-white-coagulation", "category_key": "food-and-cooking-processes", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 3, 6, 7 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 270, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry" ], "de": { "category": "Lebensmittel und Kochprozesse", "title": "Temperatur und Gerinnungszeit von Eiweiß", "description": "Erwärme kleine Proben kontrolliert und bestimme die Trübungsänderung fotografisch.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie" ] }, "en": { "category": "Food and cooking processes", "title": "Temperature and egg-white coagulation", "description": "Heat small samples under controlled conditions and measure opacity.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry" ] } }, { "no": 821, "source_index": 1271, "id": "topic-821-heart-rate-recovery-over-time", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 2, 6, 10, 13, 19 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 271, "method_keys": [ "trigonometry", "time_series" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Zeitverlauf der Herzfrequenzerholung", "description": "Miss nach einer standardisierten leichten Belastung die Herzfrequenz in kurzen Abständen.", "methods": [ "Trigonometrie", "Zeitreihenanalyse" ] }, "en": { "category": "Safe human-participant investigations", "title": "Heart-rate recovery over time", "description": "Measure heart rate after standardized light exercise.", "methods": [ "Trigonometry", "Time-series analysis" ] } }, { "no": 822, "source_index": 1272, "id": "topic-822-step-cadence-and-heart-rate", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 19, 20 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 272, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Schrittfrequenz und Herzfrequenz", "description": "Führe kurze, moderate Step-Übungen mit verschiedenen Metronomfrequenzen durch.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Safe human-participant investigations", "title": "Step cadence and heart rate", "description": "Perform short moderate step exercises at different cadences.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 823, "source_index": 1273, "id": "topic-823-breathing-rate-recovery-after-light-exercise", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 2, 6, 10, 19 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 273, "method_keys": [ "trigonometry" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Atemfrequenzerholung nach leichter Belastung", "description": "Erfasse Atemzüge pro Minute nach einer standardisierten kurzen Aktivität.", "methods": [ "Trigonometrie" ] }, "en": { "category": "Safe human-participant investigations", "title": "Breathing-rate recovery after light exercise", "description": "Record breathing rate after standardized light activity.", "methods": [ "Trigonometry" ] } }, { "no": 824, "source_index": 1274, "id": "topic-824-warning-interval-and-reaction-time", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 19, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 274, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Vorwarnzeit und Reaktionszeit", "description": "Variiere die Zeit zwischen Warnsignal und eigentlichem Reiz.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ] }, "en": { "category": "Safe human-participant investigations", "title": "Warning interval and reaction time", "description": "Vary the interval between a warning signal and the target stimulus.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ] } }, { "no": 825, "source_index": 1275, "id": "topic-825-target-size-distance-and-selection-time", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 8, 11, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 3, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 275, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Zielgröße, Entfernung und Auswahlzeit", "description": "Lass Personen Bildschirmziele unterschiedlicher Größe und Entfernung anklicken.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Safe human-participant investigations", "title": "Target size, distance, and selection time", "description": "Ask participants to select screen targets of different sizes and distances.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 826, "source_index": 1276, "id": "topic-826-practice-trials-and-typing-speed", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 3, 12 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 276, "method_keys": [ "optimization" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Übungsdurchgänge und Tippgeschwindigkeit", "description": "Lass denselben kurzen, neutralen Text wiederholt abschreiben.", "methods": [ "Optimierung" ] }, "en": { "category": "Safe human-participant investigations", "title": "Practice trials and typing speed", "description": "Repeatedly type the same neutral short text.", "methods": [ "Optimisation" ] } }, { "no": 827, "source_index": 1277, "id": "topic-827-stance-width-and-postural-sway", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 277, "method_keys": [ "trigonometry", "fourier_analysis" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Standbreite und Körperschwankung", "description": "Filme eine Markierung am Oberkörper bei verschiedenen sicheren Standbreiten.", "methods": [ "Trigonometrie", "Fourier-Analyse" ] }, "en": { "category": "Safe human-participant investigations", "title": "Stance width and postural sway", "description": "Record body sway at different safe stance widths.", "methods": [ "Trigonometry", "Fourier analysis" ] } }, { "no": 828, "source_index": 1278, "id": "topic-828-wrist-angle-and-grip-force", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 15, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 278, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Handgelenkswinkel und Griffkraft", "description": "Miss mit einem geeigneten Dynamometer bei mehreren komfortablen Handgelenkswinkeln.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Safe human-participant investigations", "title": "Wrist angle and grip force", "description": "Measure grip force at several comfortable wrist angles.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 829, "source_index": 1279, "id": "topic-829-walking-speed-and-step-length", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 3, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 279, "method_keys": [ "functions_modeling" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Gehgeschwindigkeit und Schrittlänge", "description": "Filme normales Gehen bei mehreren selbst gewählten sicheren Geschwindigkeiten.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Safe human-participant investigations", "title": "Walking speed and step length", "description": "Record normal walking at several comfortable speeds.", "methods": [ "Functions & modelling" ] } }, { "no": 830, "source_index": 1280, "id": "topic-830-metronome-tempo-and-gait-synchronization", "category_key": "safe-human-participant-investigations", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 11 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 280, "method_keys": [ "functions_modeling" ], "de": { "category": "Sichere Untersuchungen mit Menschen", "title": "Metronomtempo und Gang-Synchronisation", "description": "Vergleiche vorgegebene Tempi mit tatsächlich gemessenen Schrittzeitpunkten.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Safe human-participant investigations", "title": "Metronome tempo and gait synchronization", "description": "Compare prescribed metronome tempos with actual step timing.", "methods": [ "Functions & modelling" ] } }, { "no": 831, "source_index": 1281, "id": "topic-831-basketball-release-and-entry-angles", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 7 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 281, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "trigonometry", "optimization" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Abwurfwinkel und Eintrittswinkel beim Basketball", "description": "Filme Würfe aus derselben Entfernung und bestimme Abwurf- und Korbeintrittswinkel.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Sport and motion analysis", "title": "Basketball release and entry angles", "description": "Record shots from the same distance and determine release and entry angles.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Trigonometry", "Optimisation" ] } }, { "no": 832, "source_index": 1282, "id": "topic-832-football-launch-angle-and-range", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 5, 7, 13, 17, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 282, "method_keys": [ "functions_modeling", "differential_calculus", "regression", "trigonometry", "optimization" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Abschusswinkel und Reichweite eines Fußballs", "description": "Filme kontrollierte Schüsse oder sichere Ballstarts bei verschiedenen Winkeln.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Regression", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Sport and motion analysis", "title": "Football launch angle and range", "description": "Record controlled ball launches at different angles.", "methods": [ "Functions & modelling", "Differential calculus", "Regression", "Trigonometry", "Optimisation" ] } }, { "no": 833, "source_index": 1283, "id": "topic-833-ball-temperature-and-rebound-height", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 7 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 283, "method_keys": [ "algebra" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Balltemperatur und Rücksprunghöhe", "description": "Konditioniere Tennis- oder Gummibälle in zulässigen moderaten Temperaturbereichen.", "methods": [ "Algebra" ] }, "en": { "category": "Sport and motion analysis", "title": "Ball temperature and rebound height", "description": "Condition balls within safe moderate temperature ranges.", "methods": [ "Algebra" ] } }, { "no": 834, "source_index": 1284, "id": "topic-834-ball-pressure-and-coefficient-of-restitution", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 284, "method_keys": [ "functions_modeling", "regression", "sequences_series" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Ballinnendruck und Rückprallkoeffizient", "description": "Verwende einen Ball innerhalb seines zugelassenen Druckbereichs.", "methods": [ "Funktionen & Modellierung", "Regression", "Folgen & Reihen" ] }, "en": { "category": "Sport and motion analysis", "title": "Ball pressure and coefficient of restitution", "description": "Use a ball within its permitted pressure range.", "methods": [ "Functions & modelling", "Regression", "Sequences & series" ] } }, { "no": 835, "source_index": 1285, "id": "topic-835-spin-and-table-tennis-rebound-angle", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 8, 11, 12 ], "measurement_codes": [ 1, 7, 12, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 285, "method_keys": [ "functions_modeling", "regression", "trigonometry", "geometry" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Drall und Rückprallwinkel eines Tischtennisballs", "description": "Erzeuge möglichst reproduzierbaren Vorwärts- oder Rückwärtsdrall.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Sport and motion analysis", "title": "Spin and table-tennis rebound angle", "description": "Generate reproducible topspin or backspin.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Geometry" ] } }, { "no": 836, "source_index": 1286, "id": "topic-836-gear-ratio-and-cycling-cadence", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 6, 7, 8, 12 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 286, "method_keys": [ "trigonometry" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Übersetzungsverhältnis und Trittfrequenz", "description": "Fahre bei sicherer konstanter Geschwindigkeit mit verschiedenen Fahrradgängen oder nutze einen Trainingsständer.", "methods": [ "Trigonometrie" ] }, "en": { "category": "Sport and motion analysis", "title": "Gear ratio and cycling cadence", "description": "Use different gear ratios at constant safe speed.", "methods": [ "Trigonometry" ] } }, { "no": 837, "source_index": 1287, "id": "topic-837-take-off-angle-and-standing-jump-distance", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 1, 7, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 287, "method_keys": [ "functions_modeling", "trigonometry" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Absprungwinkel und Weite beim Standweitsprung", "description": "Analysiere nur sichere, normale Sprünge per Video.", "methods": [ "Funktionen & Modellierung", "Trigonometrie" ] }, "en": { "category": "Sport and motion analysis", "title": "Take-off angle and standing-jump distance", "description": "Analyse safe normal standing jumps using video.", "methods": [ "Functions & modelling", "Trigonometry" ] } }, { "no": 838, "source_index": 1288, "id": "topic-838-rope-length-and-maximum-skipping-frequency", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1, 3, 6, 7, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 288, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Seillänge und maximale Sprungfrequenz", "description": "Verändere die Seillänge in einem komfortablen Bereich.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Sport and motion analysis", "title": "Rope length and maximum skipping frequency", "description": "Vary skipping-rope length within a comfortable range.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 839, "source_index": 1289, "id": "topic-839-stroke-rate-and-rowing-ergometer-power", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 4, 8, 11, 12 ], "measurement_codes": [ 3, 6, 7 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 289, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "optimization" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Schlagfrequenz und Leistung am Ruderergometer", "description": "Nutze kurze, moderate Intervalle und dieselbe Person.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Sport and motion analysis", "title": "Stroke rate and rowing-ergometer power", "description": "Use short moderate intervals with the same participant.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Optimisation" ] } }, { "no": 840, "source_index": 1290, "id": "topic-840-throwing-distance-and-dart-dispersion", "category_key": "sport-and-motion-analysis", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 7, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 290, "method_keys": [ "functions_modeling", "stochastics", "geometry" ], "de": { "category": "Sport und Bewegungsanalyse", "title": "Wurfentfernung und Streuung beim Dart", "description": "Verwende ein sicheres Softdart-System und mehrere Entfernungen.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Geometrie" ] }, "en": { "category": "Sport and motion analysis", "title": "Throwing distance and dart dispersion", "description": "Use a safe soft-dart setup at several distances.", "methods": [ "Functions & modelling", "Statistics & probability", "Geometry" ] } }, { "no": 841, "source_index": 1291, "id": "topic-841-three-dimensional-field-map-of-a-bar-magnet", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 8, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 291, "method_keys": [ "functions_modeling", "vectors", "numerical_methods" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Dreidimensionale Feldkarte eines Stabmagneten", "description": "Miss das Feld auf einem regelmäßigen räumlichen Gitter.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Numerische Verfahren" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Three-dimensional field map of a bar magnet", "description": "Measure the field on a regular spatial grid.", "methods": [ "Functions & modelling", "Vector mathematics", "Numerical methods" ] } }, { "no": 842, "source_index": 1292, "id": "topic-842-axial-and-equatorial-magnetic-field", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 292, "method_keys": [ "vectors" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Axiales und äquatoriales Magnetfeld", "description": "Miss bei gleichen Abständen entlang der Längsachse und seitlich des Magneten.", "methods": [ "Vektorrechnung" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Axial and equatorial magnetic field", "description": "Measure at equal distances along axial and equatorial directions.", "methods": [ "Vector mathematics" ] } }, { "no": 843, "source_index": 1293, "id": "topic-843-magnet-temperature-and-field-strength", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 3, 17 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 293, "method_keys": [ "functions_modeling", "differential_equations", "vectors" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Magnettemperatur und Feldstärke", "description": "Untersuche einen Permanentmagneten nur in einem moderaten, sicheren Temperaturbereich.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Vektorrechnung" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Magnet temperature and field strength", "description": "Test a permanent magnet over a moderate safe temperature range.", "methods": [ "Functions & modelling", "Differential equations", "Vector mathematics" ] } }, { "no": 844, "source_index": 1294, "id": "topic-844-core-material-and-solenoid-field", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 5, 17, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 294, "method_keys": [ "functions_modeling", "vectors" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Kernmaterial und Magnetfeld einer Spule", "description": "Vergleiche Luftkern und verschiedene geeignete ferromagnetische Kerne.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Core material and solenoid field", "description": "Compare air core with suitable ferromagnetic cores.", "methods": [ "Functions & modelling", "Vector mathematics" ] } }, { "no": 845, "source_index": 1295, "id": "topic-845-air-gap-in-a-magnetic-circuit", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 3, 5, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 295, "method_keys": [ "functions_modeling", "vectors", "geometry" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Luftspalt und magnetischer Kreis", "description": "Verändere den Abstand zwischen zwei Kernteilen einer Spule.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Geometrie" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Air gap in a magnetic circuit", "description": "Vary the gap between two magnetic-core sections.", "methods": [ "Functions & modelling", "Vector mathematics", "Geometry" ] } }, { "no": 846, "source_index": 1296, "id": "topic-846-hysteresis-loop-of-a-soft-magnetic-material", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 5, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 296, "method_keys": [ "vectors", "geometry", "numerical_methods" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Hystereseschleife eines weichen Magnetmaterials", "description": "Erfasse mit Kleinspannung und geeigneter Messschaltung Magnetisierung beim Auf- und Abfahren des Stroms.", "methods": [ "Vektorrechnung", "Geometrie", "Numerische Verfahren" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Hysteresis loop of a soft magnetic material", "description": "Record magnetization while increasing and decreasing current.", "methods": [ "Vector mathematics", "Geometry", "Numerical methods" ] } }, { "no": 847, "source_index": 1297, "id": "topic-847-shield-geometry-and-magnetic-field-attenuation", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 297, "method_keys": [ "functions_modeling", "regression", "vectors", "geometry" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Abschirmgeometrie und Magnetfelddämpfung", "description": "Vergleiche offene Platten, U-Formen, Zylinder und geschlossene Geometrien aus demselben geeigneten Material.", "methods": [ "Funktionen & Modellierung", "Regression", "Vektorrechnung", "Geometrie" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Shield geometry and magnetic-field attenuation", "description": "Compare different shielding geometries.", "methods": [ "Functions & modelling", "Regression", "Vector mathematics", "Geometry" ] } }, { "no": 848, "source_index": 1298, "id": "topic-848-coil-spacing-and-helmholtz-field-uniformity", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 11, 12 ], "measurement_codes": [ 1 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 298, "method_keys": [ "functions_modeling", "differential_calculus", "vectors", "geometry", "algebra", "optimization" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Spulenabstand und Feldgleichmäßigkeit eines Helmholtz-Aufbaus", "description": "Verändere den Abstand zweier gleicher Spulen und miss das Feld entlang der Mittelachse.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Vektorrechnung", "Geometrie", "Algebra", "Optimierung" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Coil spacing and Helmholtz-field uniformity", "description": "Vary separation between two equal coils.", "methods": [ "Functions & modelling", "Differential calculus", "Vector mathematics", "Geometry", "Algebra", "Optimisation" ] } }, { "no": 849, "source_index": 1299, "id": "topic-849-coil-radius-and-magnetic-field-strength", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 11, 12 ], "measurement_codes": [ 1, 5, 12, 17, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 299, "method_keys": [ "functions_modeling", "vectors", "geometry" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Spulenradius und Feldstärke", "description": "Baue Spulen gleicher Windungszahl mit verschiedenen Radien und gleichem Strom.", "methods": [ "Funktionen & Modellierung", "Vektorrechnung", "Geometrie" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Coil radius and magnetic-field strength", "description": "Build equal-turn coils with different radii.", "methods": [ "Functions & modelling", "Vector mathematics", "Geometry" ] } }, { "no": 850, "source_index": 1300, "id": "topic-850-separation-and-magnetic-attraction-force", "category_key": "further-magnetic-field-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 11, 12 ], "measurement_codes": [ 1, 15 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 300, "method_keys": [ "vectors" ], "de": { "category": "Weitere Magnetfeldexperimente", "title": "Abstand und magnetische Anziehungskraft", "description": "Miss die Kraft zwischen zwei Magneten mit einer Waage bei sicheren Abständen.", "methods": [ "Vektorrechnung" ] }, "en": { "category": "Further magnetic-field experiments", "title": "Separation and magnetic attraction force", "description": "Measure attraction force between two magnets using a scale.", "methods": [ "Vector mathematics" ] } }, { "no": 851, "source_index": 1301, "id": "topic-851-string-length-and-fundamental-frequency", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 6, 9, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 301, "method_keys": [ "functions_modeling", "trigonometry", "fourier_analysis" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Saitenlänge und Grundfrequenz", "description": "Verändere die schwingende Länge derselben gespannten Saite.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Fourier-Analyse" ] }, "en": { "category": "Further sound and music experiments", "title": "String length and fundamental frequency", "description": "Vary the vibrating length of the same stretched string.", "methods": [ "Functions & modelling", "Trigonometry", "Fourier analysis" ] } }, { "no": 852, "source_index": 1302, "id": "topic-852-string-tension-and-frequency", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 2, 5, 6, 9, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 302, "method_keys": [ "functions_modeling", "regression", "trigonometry" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Saitenspannung und Frequenz", "description": "Verändere die Spannung durch bekannte Massen.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie" ] }, "en": { "category": "Further sound and music experiments", "title": "String tension and frequency", "description": "Vary string tension using known masses.", "methods": [ "Functions & modelling", "Regression", "Trigonometry" ] } }, { "no": 853, "source_index": 1303, "id": "topic-853-linear-density-and-string-frequency", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 2, 5, 6, 9, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 303, "method_keys": [ "functions_modeling", "trigonometry", "algebra" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Lineare Massendichte und Saitenfrequenz", "description": "Vergleiche Saiten unterschiedlicher Masse pro Länge bei gleicher Spannung.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Algebra" ] }, "en": { "category": "Further sound and music experiments", "title": "Linear density and string frequency", "description": "Compare strings with different mass per unit length.", "methods": [ "Functions & modelling", "Trigonometry", "Algebra" ] } }, { "no": 854, "source_index": 1304, "id": "topic-854-membrane-tension-and-drum-frequency", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 5, 6, 9, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 304, "method_keys": [ "functions_modeling", "regression", "trigonometry", "fourier_analysis" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Membranspannung und Trommelfrequenz", "description": "Spanne dieselbe Membran in mehreren reproduzierbaren Stufen.", "methods": [ "Funktionen & Modellierung", "Regression", "Trigonometrie", "Fourier-Analyse" ] }, "en": { "category": "Further sound and music experiments", "title": "Membrane tension and drum frequency", "description": "Stretch the same membrane to several reproducible tension levels.", "methods": [ "Functions & modelling", "Regression", "Trigonometry", "Fourier analysis" ] } }, { "no": 855, "source_index": 1305, "id": "topic-855-frequency-and-chladni-patterns", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 9, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 305, "method_keys": [ "graph_theory", "trigonometry", "geometry" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Frequenz und Chladni-Figuren", "description": "Erzeuge auf einer kleinen Platte bei verschiedenen Frequenzen Knotenlinien.", "methods": [ "Graphentheorie", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Further sound and music experiments", "title": "Frequency and Chladni patterns", "description": "Generate nodal patterns on a small plate at different frequencies.", "methods": [ "Graph theory", "Trigonometry", "Geometry" ] } }, { "no": 856, "source_index": 1306, "id": "topic-856-frequency-difference-and-beat-frequency", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 6, 9, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 306, "method_keys": [ "trigonometry", "fourier_analysis" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Frequenzdifferenz und Schwebungsfrequenz", "description": "Spiele zwei nahe Frequenzen gleichzeitig ab und analysiere die Amplitudenhüllkurve.", "methods": [ "Trigonometrie", "Fourier-Analyse" ] }, "en": { "category": "Further sound and music experiments", "title": "Frequency difference and beat frequency", "description": "Play two nearby frequencies simultaneously.", "methods": [ "Trigonometry", "Fourier analysis" ] } }, { "no": 857, "source_index": 1307, "id": "topic-857-source-speed-and-doppler-shift", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 9, 12, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 307, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Quellengeschwindigkeit und Dopplerverschiebung", "description": "Bewege eine sichere kleine Tonquelle mit bekannter Geschwindigkeit.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Further sound and music experiments", "title": "Source speed and Doppler shift", "description": "Move a safe small sound source at known speeds.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 858, "source_index": 1308, "id": "topic-858-neck-geometry-and-helmholtz-resonance", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 9, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 308, "method_keys": [ "functions_modeling", "trigonometry", "geometry" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Halsgeometrie und Helmholtz-Resonanz", "description": "Variiere Halslänge oder Öffnungsfläche eines Flaschenresonators bei konstantem Volumen.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Further sound and music experiments", "title": "Neck geometry and Helmholtz resonance", "description": "Vary neck length or opening area at constant cavity volume.", "methods": [ "Functions & modelling", "Trigonometry", "Geometry" ] } }, { "no": 859, "source_index": 1309, "id": "topic-859-distance-and-sound-intensity", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 1, 3, 9 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 309, "method_keys": [ "geometry" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Entfernung und Schallintensität", "description": "Miss bei konstanter Lautsprecherleistung und möglichst reflexionsarmer Umgebung.", "methods": [ "Geometrie" ] }, "en": { "category": "Further sound and music experiments", "title": "Distance and sound intensity", "description": "Measure at constant speaker output in a low-reflection environment.", "methods": [ "Geometry" ] } }, { "no": 860, "source_index": 1310, "id": "topic-860-room-dimensions-and-acoustic-modes", "category_key": "further-sound-and-music-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 1, 6, 9 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 310, "method_keys": [ "functions_modeling", "differential_calculus", "trigonometry", "geometry", "optimization" ], "de": { "category": "Weitere Schall- und Musikexperimente", "title": "Raumabmessungen und Eigenfrequenzen", "description": "Miss dominante tiefe Frequenzen in einem rechteckigen Raum.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Trigonometrie", "Geometrie", "Optimierung" ] }, "en": { "category": "Further sound and music experiments", "title": "Room dimensions and acoustic modes", "description": "Measure dominant low-frequency modes in a rectangular room.", "methods": [ "Functions & modelling", "Differential calculus", "Trigonometry", "Geometry", "Optimisation" ] } }, { "no": 861, "source_index": 1311, "id": "topic-861-surface-material-and-heating", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 10, 11, 12, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 311, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Oberflächenmaterial und Aufheizung", "description": "Vergleiche Asphalt-, Stein-, Holz-, Gras- oder Modelloberflächen unter gleicher Bestrahlung.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Surface material and heating", "description": "Compare different surfaces under equal illumination.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 862, "source_index": 1312, "id": "topic-862-soil-depth-and-temperature-profile", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 3, 6, 11, 12, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 312, "method_keys": [ "functions_modeling", "trigonometry", "time_series" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Bodentiefe und Temperaturverlauf", "description": "Miss über einen Tag oder unter einer Lampe in mehreren Tiefen.", "methods": [ "Funktionen & Modellierung", "Trigonometrie", "Zeitreihenanalyse" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Soil depth and temperature profile", "description": "Measure at several soil depths over time.", "methods": [ "Functions & modelling", "Trigonometry", "Time-series analysis" ] } }, { "no": 863, "source_index": 1313, "id": "topic-863-shade-fraction-and-microtemperature", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 3, 6, 12, 13, 17, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 313, "method_keys": [ "functions_modeling", "regression", "geometry" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Beschattungsgrad und Mikrotemperatur", "description": "Erzeuge unterschiedlich stark beschattete Modellflächen oder vergleiche geeignete reale Standorte.", "methods": [ "Funktionen & Modellierung", "Regression", "Geometrie" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Shade fraction and microtemperature", "description": "Compare differently shaded model or real locations.", "methods": [ "Functions & modelling", "Regression", "Geometry" ] } }, { "no": 864, "source_index": 1314, "id": "topic-864-wind-speed-and-evaporation-rate", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 2, 3, 12, 16, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 314, "method_keys": [ "functions_modeling", "geometry", "algebra" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Windgeschwindigkeit und Verdunstungsrate", "description": "Miss den Massenverlust gleicher flacher Wasserschalen bei mehreren Luftgeschwindigkeiten.", "methods": [ "Funktionen & Modellierung", "Geometrie", "Algebra" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Wind speed and evaporation rate", "description": "Measure mass loss from equal water trays at different air speeds.", "methods": [ "Functions & modelling", "Geometry", "Algebra" ] } }, { "no": 865, "source_index": 1315, "id": "topic-865-exposed-water-area-and-evaporation", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 6, 12, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 315, "method_keys": [ "geometry" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Freie Wasseroberfläche und Verdunstung", "description": "Verwende Gefäße mit gleicher Wassermenge, aber unterschiedlichen Öffnungsflächen.", "methods": [ "Geometrie" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Exposed water area and evaporation", "description": "Use equal water volumes with different exposed areas.", "methods": [ "Geometry" ] } }, { "no": 866, "source_index": 1316, "id": "topic-866-roof-colour-and-model-building-temperature", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 2, 6, 11, 12 ], "measurement_codes": [ 3, 12, 20 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 316, "method_keys": [ "functions_modeling", "differential_equations", "differential_calculus" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Dachfarbe und Modellgebäudetemperatur", "description": "Baue identische kleine Häuser mit unterschiedlich reflektierenden Dächern.", "methods": [ "Funktionen & Modellierung", "Differentialgleichungen", "Differentialrechnung" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Roof colour and model-building temperature", "description": "Build identical model houses with different roof reflectivity.", "methods": [ "Functions & modelling", "Differential equations", "Differential calculus" ] } }, { "no": 867, "source_index": 1317, "id": "topic-867-green-roof-substrate-depth", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 11, 12 ], "measurement_codes": [ 1, 2, 12, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 317, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Substrattiefe eines Gründachmodells", "description": "Vergleiche Modellboxen mit verschiedenen Erd- oder Substratschichten.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Green-roof substrate depth", "description": "Compare model roofs with different substrate depths.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 868, "source_index": 1318, "id": "topic-868-leaf-litter-depth-and-soil-moisture", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 6, 12, 18, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 318, "method_keys": [ "functions_modeling" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Laubschichtdicke und Bodenfeuchte", "description": "Bedecke gleiche Bodenproben mit unterschiedlich dicken Laubschichten.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Leaf-litter depth and soil moisture", "description": "Cover equal soil samples with different litter depths.", "methods": [ "Functions & modelling" ] } }, { "no": 869, "source_index": 1319, "id": "topic-869-rain-angle-and-collection-accuracy", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 11, 12 ], "measurement_codes": [ 1, 12 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 319, "method_keys": [ "stochastics", "trigonometry", "geometry" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Neigung des Niederschlags und Auffanggenauigkeit", "description": "Simuliere schrägen Regen und vergleiche verschiedene Regenmesserformen.", "methods": [ "Stochastik", "Trigonometrie", "Geometrie" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Rain angle and collection accuracy", "description": "Simulate angled rainfall and compare rain-gauge geometries.", "methods": [ "Statistics & probability", "Trigonometry", "Geometry" ] } }, { "no": 870, "source_index": 1320, "id": "topic-870-turbidity-and-light-penetration-in-water", "category_key": "environment-weather-and-microclimate", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 8, 11, 12 ], "measurement_codes": [ 10, 12, 13, 16 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 320, "method_keys": [ "functions_modeling", "regression" ], "de": { "category": "Umwelt, Wetter und Mikroklima", "title": "Trübung und Lichtdurchdringung von Wasser", "description": "Erzeuge reproduzierbare Konzentrationen ungefährlicher Schwebstoffe.", "methods": [ "Funktionen & Modellierung", "Regression" ] }, "en": { "category": "Environment, weather, and microclimate", "title": "Turbidity and light penetration in water", "description": "Create reproducible concentrations of safe suspended particles.", "methods": [ "Functions & modelling", "Regression" ] } }, { "no": 871, "source_index": 1321, "id": "topic-871-sampling-temperature-and-response-behaviour", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 10, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 321, "method_keys": [ "proof", "optimization" ], "de": { "category": "Weitere KI-Experimente", "title": "Sampling-Temperatur und Antwortverhalten", "description": "Teste denselben festen Aufgabensatz bei verschiedenen verfügbaren Sampling-Einstellungen.", "methods": [ "Beweisführung", "Optimierung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Sampling temperature and response behaviour", "description": "Test the same fixed task set at different sampling settings.", "methods": [ "Proof", "Optimisation" ] } }, { "no": 872, "source_index": 1322, "id": "topic-872-context-length-and-information-use", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 322, "method_keys": [ "functions_modeling", "geometry" ], "de": { "category": "Weitere KI-Experimente", "title": "Kontextlänge und Informationsnutzung", "description": "Platziere dieselbe relevante Information in Texten unterschiedlicher Länge.", "methods": [ "Funktionen & Modellierung", "Geometrie" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Context length and information use", "description": "Place the same relevant information in contexts of different lengths.", "methods": [ "Functions & modelling", "Geometry" ] } }, { "no": 873, "source_index": 1323, "id": "topic-873-chunk-size-in-a-retrieval-augmented-system", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 3 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 323, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "optimization" ], "de": { "category": "Weitere KI-Experimente", "title": "Abschnittsgröße in einem RAG-System", "description": "Zerlege dieselben Dokumente in unterschiedlich große, sich teilweise überlappende Abschnitte.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Optimierung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Chunk size in a retrieval-augmented system", "description": "Split the same documents into differently sized overlapping chunks.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Optimisation" ] } }, { "no": 874, "source_index": 1324, "id": "topic-874-number-of-retrieved-passages-and-answer-quality", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 324, "method_keys": [ "functions_modeling", "differential_calculus", "optimization" ], "de": { "category": "Weitere KI-Experimente", "title": "Zahl abgerufener Textabschnitte und Antwortqualität", "description": "Verändere kk, während Fragen, Dokumente und Modell konstant bleiben.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Optimierung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Number of retrieved passages and answer quality", "description": "Vary the number of retrieved passages while keeping all else constant.", "methods": [ "Functions & modelling", "Differential calculus", "Optimisation" ] } }, { "no": 875, "source_index": 1325, "id": "topic-875-label-noise-and-model-performance", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 3, 12, 13, 20, 21 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 325, "method_keys": [ "functions_modeling", "stochastics", "matrices", "geometry" ], "de": { "category": "Weitere KI-Experimente", "title": "Falsch beschriftete Trainingsdaten und Modellleistung", "description": "Ersetze kontrolliert einen Anteil korrekter Labels durch zufällige falsche Labels.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Matrizen", "Geometrie" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Label noise and model performance", "description": "Replace a controlled fraction of labels with incorrect labels.", "methods": [ "Functions & modelling", "Statistics & probability", "Matrices", "Geometry" ] } }, { "no": 876, "source_index": 1326, "id": "topic-876-data-augmentation-method-and-robustness", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 326, "method_keys": [ "functions_modeling" ], "de": { "category": "Weitere KI-Experimente", "title": "Art der Datenaugmentation und Robustheit", "description": "Vergleiche Zuschneiden, Spiegeln, Farbrauschen und Kombinationen bei demselben kleinen Modell.", "methods": [ "Funktionen & Modellierung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Data-augmentation method and robustness", "description": "Compare augmentation methods using the same model.", "methods": [ "Functions & modelling" ] } }, { "no": 877, "source_index": 1327, "id": "topic-877-feature-scaling-and-training-convergence", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 8, 11, 12 ], "measurement_codes": [ 12, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 327, "method_keys": [ "simulation" ], "de": { "category": "Weitere KI-Experimente", "title": "Merkmalskalierung und Trainingskonvergenz", "description": "Trainiere denselben Algorithmus mit unskalierten, standardisierten und normalisierten Merkmalen.", "methods": [ "Simulation & Algorithmen" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Feature scaling and training convergence", "description": "Train the same algorithm using different feature scaling methods.", "methods": [ "Simulation & algorithms" ] } }, { "no": 878, "source_index": 1328, "id": "topic-878-decision-threshold-and-error-cost", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 8, 11, 12 ], "measurement_codes": [ 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 328, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "trigonometry", "optimization" ], "de": { "category": "Weitere KI-Experimente", "title": "Entscheidungsschwelle und Fehlerkosten", "description": "Verändere die Klassifikationsschwelle eines festen Modells.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Trigonometrie", "Optimierung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Decision threshold and error cost", "description": "Vary the decision threshold of a fixed classifier.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Trigonometry", "Optimisation" ] } }, { "no": 879, "source_index": 1329, "id": "topic-879-ensemble-size-and-prediction-variance", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 10, 11, 12 ], "measurement_codes": [ 12, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 329, "method_keys": [ "functions_modeling", "stochastics", "regression", "number_theory" ], "de": { "category": "Weitere KI-Experimente", "title": "Ensemblegröße und Vorhersagevarianz", "description": "Kombiniere zunehmend viele unabhängig trainierte kleine Modelle.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Zahlentheorie" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Ensemble size and prediction variance", "description": "Combine increasing numbers of independently trained small models.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Number theory" ] } }, { "no": 880, "source_index": 1330, "id": "topic-880-human-ai-and-humanai-collaboration", "category_key": "further-artificial-intelligence-experiments", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 8, 10, 11, 12 ], "measurement_codes": [ 13, 20, 21 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 330, "method_keys": [ "functions_modeling", "proof" ], "de": { "category": "Weitere KI-Experimente", "title": "Mensch, KI und Mensch-KI-Kombination", "description": "Lass denselben überprüfbaren Aufgabensatz unter drei klar getrennten Bedingungen bearbeiten.", "methods": [ "Funktionen & Modellierung", "Beweisführung" ] }, "en": { "category": "Further artificial-intelligence experiments", "title": "Human, AI, and human–AI collaboration", "description": "Solve the same verified tasks under three conditions.", "methods": [ "Functions & modelling", "Proof" ] } }, { "no": 881, "source_index": 1331, "id": "topic-881-input-size-and-sorting-runtime", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 11, 12 ], "measurement_codes": [ 6, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 331, "method_keys": [ "functions_modeling", "simulation" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Eingabegröße und Laufzeit von Sortieralgorithmen", "description": "Vergleiche mehrere Algorithmen auf identischer Hardware und mit vielen Wiederholungen.", "methods": [ "Funktionen & Modellierung", "Simulation & Algorithmen" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Input size and sorting runtime", "description": "Compare algorithms on identical hardware with repeated trials.", "methods": [ "Functions & modelling", "Simulation & algorithms" ] } }, { "no": 882, "source_index": 1332, "id": "topic-882-obstacle-density-and-a-versus-dijkstra-efficiency", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 8, 11, 12 ], "measurement_codes": [ 1, 6, 11, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 332, "method_keys": [ "graph_theory", "simulation", "optimization" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Hindernisdichte und Effizienz von A\\* gegenüber Dijkstra", "description": "Erzeuge Gitterkarten mit kontrolliertem Hindernisanteil.", "methods": [ "Graphentheorie", "Simulation & Algorithmen", "Optimierung" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Obstacle density and A\\* versus Dijkstra efficiency", "description": "Generate grid maps with controlled obstacle density.", "methods": [ "Graph theory", "Simulation & algorithms", "Optimisation" ] } }, { "no": 883, "source_index": 1333, "id": "topic-883-interpolation-method-and-spatial-prediction-error", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 7, 8, 10 ], "measurement_codes": [ 3, 10, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 333, "method_keys": [ "functions_modeling", "regression", "number_theory", "vectors", "simulation", "numerical_methods" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Interpolationsmethode und räumlicher Vorhersagefehler", "description": "Entferne gezielt Messpunkte aus einer Temperatur-, Magnetfeld- oder Lichtkarte.", "methods": [ "Funktionen & Modellierung", "Regression", "Zahlentheorie", "Vektorrechnung", "Simulation & Algorithmen", "Numerische Verfahren" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Interpolation method and spatial prediction error", "description": "Remove selected points from a measured spatial field.", "methods": [ "Functions & modelling", "Regression", "Number theory", "Vector mathematics", "Simulation & algorithms", "Numerical methods" ] } }, { "no": 884, "source_index": 1334, "id": "topic-884-step-size-and-numerical-integration-error", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11, 12 ], "measurement_codes": [ 3, 12, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 334, "method_keys": [ "simulation", "numerical_methods" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Schrittweite und Fehler numerischer Integration", "description": "Integriere experimentelle Geschwindigkeits-, Leistungs- oder CO₂-Raten mit verschiedenen Verfahren.", "methods": [ "Simulation & Algorithmen", "Numerische Verfahren" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Step size and numerical-integration error", "description": "Integrate experimental rate data using different methods.", "methods": [ "Simulation & algorithms", "Numerical methods" ] } }, { "no": 885, "source_index": 1335, "id": "topic-885-sampling-rate-and-frequency-estimation", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 2, "courses": [ "aa" ], "levels": [ "hl" ], "personal_engagement_codes": [ 1, 7, 11, 12 ], "measurement_codes": [ 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 335, "method_keys": [ "trigonometry", "fourier_analysis", "simulation", "time_series" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Abtastrate und Frequenzbestimmung", "description": "Zeichne dasselbe periodische Signal mit verschiedenen Abtastraten auf.", "methods": [ "Trigonometrie", "Fourier-Analyse", "Simulation & Algorithmen", "Zeitreihenanalyse" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Sampling rate and frequency estimation", "description": "Record the same periodic signal at different sampling rates.", "methods": [ "Trigonometry", "Fourier analysis", "Simulation & algorithms", "Time-series analysis" ] } }, { "no": 886, "source_index": 1336, "id": "topic-886-repeated-calculations-and-rounding-error", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 7, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 336, "method_keys": [ "stochastics", "simulation" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Rechenoperationen und Rundungsfehler", "description": "Vergleiche mathematisch äquivalente Rechenwege mit begrenzter Gleitkommapräzision.", "methods": [ "Stochastik", "Simulation & Algorithmen" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Repeated calculations and rounding error", "description": "Compare mathematically equivalent calculations at limited precision.", "methods": [ "Statistics & probability", "Simulation & algorithms" ] } }, { "no": 887, "source_index": 1337, "id": "topic-887-occlusion-and-qr-code-recognition", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 337, "method_keys": [ "functions_modeling", "stochastics", "regression", "geometry", "simulation" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Verdeckungsanteil und QR-Code-Erkennung", "description": "Bedecke definierte Flächenanteile von QR-Codes verschiedener Fehlerkorrekturstufen.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Geometrie", "Simulation & Algorithmen" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Occlusion and QR-code recognition", "description": "Cover defined portions of QR codes at different correction levels.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Geometry", "Simulation & algorithms" ] } }, { "no": 888, "source_index": 1338, "id": "topic-888-image-compression-and-information-loss", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 11, 12 ], "measurement_codes": [ 7, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 338, "method_keys": [ "functions_modeling", "differential_calculus", "geometry", "simulation", "optimization" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Bildkompression und Informationsverlust", "description": "Speichere dieselben Bilder mit verschiedenen Qualitätsstufen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Geometrie", "Simulation & Algorithmen", "Optimierung" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Image compression and information loss", "description": "Save identical images at different compression levels.", "methods": [ "Functions & modelling", "Differential calculus", "Geometry", "Simulation & algorithms", "Optimisation" ] } }, { "no": 889, "source_index": 1339, "id": "topic-889-pseudorandom-generator-and-statistical-uniformity", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 8, 11, 12 ], "measurement_codes": [ 1, 13, 17 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 339, "method_keys": [ "functions_modeling", "stochastics", "regression", "geometry", "simulation" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Pseudozufallszahlengenerator und statistische Gleichmäßigkeit", "description": "Vergleiche mehrere Generatoren oder unterschiedliche Startwerte.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Regression", "Geometrie", "Simulation & Algorithmen" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Pseudorandom generator and statistical uniformity", "description": "Compare several generators or seed values.", "methods": [ "Functions & modelling", "Statistics & probability", "Regression", "Geometry", "Simulation & algorithms" ] } }, { "no": 890, "source_index": 1340, "id": "topic-890-bit-error-pattern-and-detection-probability", "category_key": "algorithms-digital-measurement-and-data-quality", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11, 12 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 340, "method_keys": [ "stochastics", "combinatorics", "simulation" ], "de": { "category": "Algorithmen, digitale Messungen und Datenqualität", "title": "Bitfehlermuster und Erkennungswahrscheinlichkeit", "description": "Simuliere Einzel-, Mehrfach- und Burstfehler für Prüfsummen oder einfache Fehlerkorrekturcodes.", "methods": [ "Stochastik", "Kombinatorik", "Simulation & Algorithmen" ] }, "en": { "category": "Algorithms, digital measurement, and data quality", "title": "Bit-error pattern and detection probability", "description": "Simulate different bit-error patterns.", "methods": [ "Statistics & probability", "Combinatorics", "Simulation & algorithms" ] } }, { "no": 891, "source_index": 1341, "id": "topic-891-optimal-cylinder-proportions", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 3, 8, 11, 12 ], "measurement_codes": [ 1, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 341, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "geometry", "optimization" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Optimale Zylinderproportionen", "description": "Baue Zylinder gleichen Volumens mit verschiedenen Radius-Höhen-Verhältnissen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Geometrie", "Optimierung" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Optimal cylinder proportions", "description": "Build equal-volume cylinders with different radius-to-height ratios.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Geometry", "Optimisation" ] } }, { "no": 892, "source_index": 1342, "id": "topic-892-corner-cut-and-maximum-box-volume", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 8, 11, 12 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 342, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "geometry", "algebra" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Eckenausschnitt und maximales Schachtelvolumen", "description": "Schneide aus gleich großen Kartonblättern Quadrate verschiedener Seitenlänge aus.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Geometrie", "Algebra" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Corner cut and maximum box volume", "description": "Cut different corner squares from equal sheets.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Geometry", "Algebra" ] } }, { "no": 893, "source_index": 1343, "id": "topic-893-circle-packing-and-area-efficiency", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 7, 8, 11, 12 ], "measurement_codes": [ 1, 3, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 343, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "geometry", "simulation" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Kreispackung und Flächeneffizienz", "description": "Vergleiche regelmäßige, versetzte und algorithmisch gefundene Anordnungen.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Geometrie", "Simulation & Algorithmen" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Circle packing and area efficiency", "description": "Compare regular, staggered, and algorithmically generated arrangements.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Geometry", "Simulation & algorithms" ] } }, { "no": 894, "source_index": 1344, "id": "topic-894-folding-pattern-and-paper-compression-strength", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 2, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 344, "method_keys": [ "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Faltmuster und Druckfestigkeit von Papier", "description": "Vergleiche Akkordeon-, Miura-, Dreiecks- und eigene Faltungen bei gleicher Papierfläche.", "methods": [ "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Folding pattern and paper compression strength", "description": "Compare different folding patterns using equal paper area.", "methods": [ "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 895, "source_index": 1345, "id": "topic-895-geometric-irregularity-and-die-fairness", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 3, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 345, "method_keys": [ "functions_modeling", "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Geometrische Unregelmäßigkeit und Würfelfairness", "description": "Verändere bei selbst gefertigten ungefährlichen Würfeln kontrolliert eine geometrische Eigenschaft.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Geometric irregularity and die fairness", "description": "Introduce controlled geometric asymmetry into model dice.", "methods": [ "Functions & modelling", "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 896, "source_index": 1346, "id": "topic-896-number-of-shuffles-and-card-disorder", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 346, "method_keys": [ "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Anzahl der Mischvorgänge und Kartenunordnung", "description": "Vergleiche verschiedene Mischmethoden anhand nummerierter Karten.", "methods": [ "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Number of shuffles and card disorder", "description": "Compare shuffle methods using numbered cards.", "methods": [ "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 897, "source_index": 1347, "id": "topic-897-dimension-and-random-walk-return-time", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 6, 13 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 347, "method_keys": [ "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Dimension und Rückkehrzeit eines Random Walk", "description": "Simuliere oder realisiere Zufallswege auf einer Linie, einem Gitter und gegebenenfalls in drei Dimensionen.", "methods": [ "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Dimension and random-walk return time", "description": "Study random walks in different dimensions.", "methods": [ "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 898, "source_index": 1348, "id": "topic-898-single-versus-multiple-queues", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 3, 6, 13, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 348, "method_keys": [ "functions_modeling", "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Eine gemeinsame oder mehrere getrennte Warteschlangen", "description": "Simuliere Bedienzeiten mit Karten, Würfeln oder Software.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Single versus multiple queues", "description": "Simulate service times using cards, dice, or software.", "methods": [ "Functions & modelling", "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 899, "source_index": 1349, "id": "topic-899-traffic-light-cycle-and-average-delay", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 3, 6, 7, 8, 11 ], "measurement_codes": [ 1, 10, 13 ], "safety_code": 1, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 349, "method_keys": [ "functions_modeling", "differential_calculus", "stochastics", "graph_theory", "geometry", "simulation" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Ampelzyklus und durchschnittliche Verzögerung", "description": "Simuliere eine Kreuzung mit gemessenen oder künstlich erzeugten Ankunftsraten.", "methods": [ "Funktionen & Modellierung", "Differentialrechnung", "Stochastik", "Graphentheorie", "Geometrie", "Simulation & Algorithmen" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Traffic-light cycle and average delay", "description": "Simulate an intersection using measured or synthetic arrival rates.", "methods": [ "Functions & modelling", "Differential calculus", "Statistics & probability", "Graph theory", "Geometry", "Simulation & algorithms" ] } }, { "no": 900, "source_index": 1350, "id": "topic-900-node-failure-and-network-robustness", "category_key": "geometry-probability-queues-and-networks", "assessment_code": 3, "course_code": 6, "courses": [ "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 8, 11, 12 ], "measurement_codes": [ 1, 13, 17, 20 ], "safety_code": 0, "source_course_label": "Editorial guidance", "editorial_source": "User-supplied bilingual expansion 2026-08-31", "source_topic_number": 350, "method_keys": [ "functions_modeling", "stochastics", "graph_theory", "geometry" ], "de": { "category": "Geometrie, Wahrscheinlichkeit, Warteschlangen und Netzwerke", "title": "Knotenausfall und Stabilität eines Netzwerks", "description": "Entferne systematisch zufällige oder besonders stark vernetzte Knoten aus einem Modellnetzwerk.", "methods": [ "Funktionen & Modellierung", "Stochastik", "Graphentheorie", "Geometrie" ] }, "en": { "category": "Geometry, probability, queues, and networks", "title": "Node failure and network robustness", "description": "Remove random or highly connected nodes from a model network.", "methods": [ "Functions & modelling", "Statistics & probability", "Graph theory", "Geometry" ] } }, { "no": 901, "source_index": 2374, "id": "topic-source510-374-butter-proportion-and-its-effect-on-baking-time-height-and-surface-of-muffins", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 374, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Butteranteil und sein Einfluss auf Backzeit, Höhe und Oberfläche von Muffins", "description": "Untersucht wird, wie sich „Butteranteil und sein Einfluss auf Backzeit, Höhe und Oberfläche von Muffins“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Butter proportion and its effect on baking time, height, and surface of muffins", "description": "Investigate how “Butter proportion and its effect on baking time, height, and surface of muffins” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 902, "source_index": 2375, "id": "topic-source510-375-sugar-proportion-and-its-effect-on-browning-diameter-and-crispness-of-cookies", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 375, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Zuckeranteil und sein Einfluss auf Bräunung, Durchmesser und Knusprigkeit von Keksen", "description": "Untersucht wird, wie sich „Zuckeranteil und sein Einfluss auf Bräunung, Durchmesser und Knusprigkeit von Keksen“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Sugar proportion and its effect on browning, diameter, and crispness of cookies", "description": "Investigate how “Sugar proportion and its effect on browning, diameter, and crispness of cookies” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 903, "source_index": 2376, "id": "topic-source510-376-flour-type-and-its-effect-on-cake-volume-and-pore-structure", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 376, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Mehlsorte und ihr Einfluss auf Volumen und Porenstruktur eines Kuchens", "description": "Untersucht wird, wie sich „Mehlsorte und ihr Einfluss auf Volumen und Porenstruktur eines Kuchens“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Flour type and its effect on cake volume and pore structure", "description": "Investigate how “Flour type and its effect on cake volume and pore structure” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 904, "source_index": 2377, "id": "topic-source510-377-number-of-eggs-and-its-effect-on-the-height-elasticity-and-mass-loss-of-a-sponge-cake", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 377, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Anzahl der Eier und ihr Einfluss auf Höhe, Elastizität und Masseverlust eines Biskuits", "description": "Untersucht wird, wie sich „Anzahl der Eier und ihr Einfluss auf Höhe, Elastizität und Masseverlust eines Biskuits“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Number of eggs and its effect on the height, elasticity, and mass loss of a sponge cake", "description": "Investigate how “Number of eggs and its effect on the height, elasticity, and mass loss of a sponge cake” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 905, "source_index": 2378, "id": "topic-source510-378-water-to-milk-ratio-and-its-effect-on-baking-time-and-moisture-loss-in-bread", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 378, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Verhältnis von Wasser zu Milch und sein Einfluss auf Backzeit und Feuchtigkeitsverlust bei Brot", "description": "Untersucht wird, wie sich „Verhältnis von Wasser zu Milch und sein Einfluss auf Backzeit und Feuchtigkeitsverlust bei Brot“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Water-to-milk ratio and its effect on baking time and moisture loss in bread", "description": "Investigate how “Water-to-milk ratio and its effect on baking time and moisture loss in bread” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 906, "source_index": 2379, "id": "topic-source510-379-amount-of-baking-powder-and-its-effect-on-batter-volume-pore-size-and-final-height", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 379, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Backpulvermenge und ihr Einfluss auf Teigvolumen, Porengröße und Endhöhe", "description": "Untersucht wird, wie sich „Backpulvermenge und ihr Einfluss auf Teigvolumen, Porengröße und Endhöhe“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Amount of baking powder and its effect on batter volume, pore size, and final height", "description": "Investigate how “Amount of baking powder and its effect on batter volume, pore size, and final height” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 907, "source_index": 2380, "id": "topic-source510-380-butter-margarine-or-oil-comparing-the-spread-and-surface-of-baked-goods", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 380, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Butter, Margarine oder Öl: Vergleich der Ausbreitung und Oberfläche von Gebäck", "description": "Untersucht wird, wie sich „Butter, Margarine oder Öl: Vergleich der Ausbreitung und Oberfläche von Gebäck“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Butter, margarine, or oil: comparing the spread and surface of baked goods", "description": "Investigate how “Butter, margarine, or oil: comparing the spread and surface of baked goods” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 908, "source_index": 2381, "id": "topic-source510-381-optimising-an-ingredient-ratio-for-maximum-baking-volume-with-minimum-mass-loss", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 381, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Optimierung eines Zutatenverhältnisses für maximales Backvolumen bei minimalem Masseverlust", "description": "Untersucht wird, wie sich „Optimierung eines Zutatenverhältnisses für maximales Backvolumen bei minimalem Masseverlust“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Optimising an ingredient ratio for maximum baking volume with minimum mass loss", "description": "Investigate how “Optimising an ingredient ratio for maximum baking volume with minimum mass loss” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 909, "source_index": 2382, "id": "topic-source510-382-oven-temperature-and-its-effect-on-core-temperature-baking-time-and-final-height", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 382, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Ofentemperatur und ihr Einfluss auf Kerntemperatur, Backzeit und Endhöhe", "description": "Untersucht wird, wie sich „Ofentemperatur und ihr Einfluss auf Kerntemperatur, Backzeit und Endhöhe“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Oven temperature and its effect on core temperature, baking time, and final height", "description": "Investigate how “Oven temperature and its effect on core temperature, baking time, and final height” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 910, "source_index": 2383, "id": "topic-source510-383-oven-temperature-and-browning-colour-analysis-of-the-surface-during-baking", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 383, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Ofentemperatur und Bräunung: Farbanalyse der Oberfläche während des Backens", "description": "Untersucht wird, wie sich „Ofentemperatur und Bräunung: Farbanalyse der Oberfläche während des Backens“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Oven temperature and browning: colour analysis of the surface during baking", "description": "Investigate how “Oven temperature and browning: colour analysis of the surface during baking” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 911, "source_index": 2384, "id": "topic-source510-384-constant-or-stepwise-oven-temperature-comparing-volume-and-moisture-loss", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 384, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Konstante oder stufenweise Ofentemperatur: Vergleich von Volumen und Feuchtigkeitsverlust", "description": "Untersucht wird, wie sich „Konstante oder stufenweise Ofentemperatur: Vergleich von Volumen und Feuchtigkeitsverlust“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Constant or stepwise oven temperature: comparing volume and moisture loss", "description": "Investigate how “Constant or stepwise oven temperature: comparing volume and moisture loss” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 912, "source_index": 2385, "id": "topic-source510-385-position-in-the-oven-and-its-effect-on-temperature-distribution-and-baking-outcome", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 385, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Position im Backofen und ihr Einfluss auf Temperaturverteilung und Backergebnis", "description": "Untersucht wird, wie sich „Position im Backofen und ihr Einfluss auf Temperaturverteilung und Backergebnis“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Position in the oven and its effect on temperature distribution and baking outcome", "description": "Investigate how “Position in the oven and its effect on temperature distribution and baking outcome” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 913, "source_index": 2386, "id": "topic-source510-386-preheating-time-and-its-effect-on-baking-time-energy-demand-and-product-size", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 386, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Vorheizdauer und ihr Einfluss auf Backzeit, Energiebedarf und Produktgröße", "description": "Untersucht wird, wie sich „Vorheizdauer und ihr Einfluss auf Backzeit, Energiebedarf und Produktgröße“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Preheating time and its effect on baking time, energy demand, and product size", "description": "Investigate how “Preheating time and its effect on baking time, energy demand, and product size” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 914, "source_index": 2387, "id": "topic-source510-387-fan-oven-or-conventional-heat-comparing-baking-time-surface-and-energy-use", "category_key": "baking-food-models", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 2, 3, 4, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 387, "de": { "category": "Backen & Lebensmittelmodelle", "title": "Umluft oder Ober-/Unterhitze: Vergleich von Backdauer, Oberfläche und Energieverbrauch", "description": "Untersucht wird, wie sich „Umluft oder Ober-/Unterhitze: Vergleich von Backdauer, Oberfläche und Energieverbrauch“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Baking & food models", "title": "Fan oven or conventional heat: comparing baking time, surface, and energy use", "description": "Investigate how “Fan oven or conventional heat: comparing baking time, surface, and energy use” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 915, "source_index": 2388, "id": "topic-source510-388-surface-area-to-volume-ratio-and-melting-time-of-ice-cubes", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 388, "de": { "category": "Eis & Wärmeübertragung", "title": "Oberfläche-Volumen-Verhältnis und Schmelzdauer von Eiswürfeln", "description": "Untersucht wird, wie sich „Oberfläche-Volumen-Verhältnis und Schmelzdauer von Eiswürfeln“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Surface-area-to-volume ratio and melting time of ice cubes", "description": "Investigate how “Surface-area-to-volume ratio and melting time of ice cubes” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 916, "source_index": 2389, "id": "topic-source510-389-ambient-temperature-and-the-changing-melting-rate-of-an-ice-cube", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 389, "de": { "category": "Eis & Wärmeübertragung", "title": "Umgebungstemperatur und Verlauf der Schmelzgeschwindigkeit eines Eiswürfels", "description": "Untersucht wird, wie sich „Umgebungstemperatur und Verlauf der Schmelzgeschwindigkeit eines Eiswürfels“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Ambient temperature and the changing melting rate of an ice cube", "description": "Investigate how “Ambient temperature and the changing melting rate of an ice cube” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 917, "source_index": 2390, "id": "topic-source510-390-salt-concentration-and-its-effect-on-the-melting-point-and-melting-time-of-ice", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 390, "de": { "category": "Eis & Wärmeübertragung", "title": "Salzkonzentration und ihr Einfluss auf Schmelzpunkt und Schmelzdauer von Eis", "description": "Untersucht wird, wie sich „Salzkonzentration und ihr Einfluss auf Schmelzpunkt und Schmelzdauer von Eis“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Salt concentration and its effect on the melting point and melting time of ice", "description": "Investigate how “Salt concentration and its effect on the melting point and melting time of ice” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 918, "source_index": 2391, "id": "topic-source510-391-spread-of-food-colouring-as-a-coloured-ice-cube-melts", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 391, "de": { "category": "Eis & Wärmeübertragung", "title": "Ausbreitung von Lebensmittelfarbe beim Schmelzen eines gefärbten Eiswürfels", "description": "Untersucht wird, wie sich „Ausbreitung von Lebensmittelfarbe beim Schmelzen eines gefärbten Eiswürfels“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Spread of food colouring as a coloured ice cube melts", "description": "Investigate how “Spread of food colouring as a coloured ice cube melts” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 919, "source_index": 2392, "id": "topic-source510-392-cube-sphere-or-cylinder-comparing-shapes-with-equal-ice-mass", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 392, "de": { "category": "Eis & Wärmeübertragung", "title": "Würfel, Kugel oder Zylinder: Formvergleich bei gleicher Eismasse", "description": "Untersucht wird, wie sich „Würfel, Kugel oder Zylinder: Formvergleich bei gleicher Eismasse“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Cube, sphere, or cylinder: comparing shapes with equal ice mass", "description": "Investigate how “Cube, sphere, or cylinder: comparing shapes with equal ice mass” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 920, "source_index": 2393, "id": "topic-source510-393-air-movement-and-its-effect-on-ice-melting-time", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 393, "de": { "category": "Eis & Wärmeübertragung", "title": "Luftbewegung und ihr Einfluss auf die Schmelzdauer von Eis", "description": "Untersucht wird, wie sich „Luftbewegung und ihr Einfluss auf die Schmelzdauer von Eis“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Air movement and its effect on ice-melting time", "description": "Investigate how “Air movement and its effect on ice-melting time” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 921, "source_index": 2394, "id": "topic-source510-394-support-material-and-its-effect-on-heat-flow-and-melting-time", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 394, "de": { "category": "Eis & Wärmeübertragung", "title": "Material des Untergrunds und sein Einfluss auf Wärmefluss und Schmelzdauer", "description": "Untersucht wird, wie sich „Material des Untergrunds und sein Einfluss auf Wärmefluss und Schmelzdauer“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Support material and its effect on heat flow and melting time", "description": "Investigate how “Support material and its effect on heat flow and melting time” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 922, "source_index": 2395, "id": "topic-source510-395-initial-ice-temperature-and-its-effect-on-total-thawing-time", "category_key": "ice-heat-transfer", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 2, 3, 4, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 395, "de": { "category": "Eis & Wärmeübertragung", "title": "Anfangstemperatur des Eises und ihr Einfluss auf die gesamte Auftauzeit", "description": "Untersucht wird, wie sich „Anfangstemperatur des Eises und ihr Einfluss auf die gesamte Auftauzeit“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Ice & heat transfer", "title": "Initial ice temperature and its effect on total thawing time", "description": "Investigate how “Initial ice temperature and its effect on total thawing time” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 923, "source_index": 2396, "id": "topic-source510-396-power-to-weight-ratio-and-0-100-km-h-acceleration-in-a-vehicle-comparison", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 396, "de": { "category": "Fahrzeugmathematik", "title": "Leistungsgewicht und Beschleunigung von 0 auf 100 km/h im Fahrzeugvergleich", "description": "Untersucht wird, welche Bedingungen bei „Leistungsgewicht und Beschleunigung von 0 auf 100 km/h im Fahrzeugvergleich“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Power-to-weight ratio and 0–100 km/h acceleration in a vehicle comparison", "description": "Investigate which conditions produce the best result for “Power-to-weight ratio and 0–100 km/h acceleration in a vehicle comparison” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 924, "source_index": 2397, "id": "topic-source510-397-drag-coefficient-c-d-and-acceleration-at-higher-speeds", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 397, "de": { "category": "Fahrzeugmathematik", "title": "Luftwiderstandsbeiwert cW und Beschleunigung bei höheren Geschwindigkeiten", "description": "Untersucht wird, welche Bedingungen bei „Luftwiderstandsbeiwert cW und Beschleunigung bei höheren Geschwindigkeiten“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Drag coefficient C_d and acceleration at higher speeds", "description": "Investigate which conditions produce the best result for “Drag coefficient C_d and acceleration at higher speeds” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 925, "source_index": 2398, "id": "topic-source510-398-relationship-between-drag-coefficient-frontal-area-and-fuel-consumption", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 398, "de": { "category": "Fahrzeugmathematik", "title": "Zusammenhang zwischen cW-Wert, Stirnfläche und Kraftstoffverbrauch", "description": "Untersucht wird, welche Bedingungen bei „Zusammenhang zwischen cW-Wert, Stirnfläche und Kraftstoffverbrauch“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Relationship between drag coefficient, frontal area, and fuel consumption", "description": "Investigate which conditions produce the best result for “Relationship between drag coefficient, frontal area, and fuel consumption” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 926, "source_index": 2399, "id": "topic-source510-399-torque-curve-and-theoretical-acceleration-in-different-gears", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 399, "de": { "category": "Fahrzeugmathematik", "title": "Drehmomentkurve und theoretische Beschleunigung in verschiedenen Gängen", "description": "Untersucht wird, welche Bedingungen bei „Drehmomentkurve und theoretische Beschleunigung in verschiedenen Gängen“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Torque curve and theoretical acceleration in different gears", "description": "Investigate which conditions produce the best result for “Torque curve and theoretical acceleration in different gears” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 927, "source_index": 2400, "id": "topic-source510-400-vehicle-mass-and-its-effect-on-acceleration-and-braking-distance-models", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 400, "de": { "category": "Fahrzeugmathematik", "title": "Fahrzeugmasse und ihr Einfluss auf Beschleunigungs- und Bremswegmodelle", "description": "Untersucht wird, welche Bedingungen bei „Fahrzeugmasse und ihr Einfluss auf Beschleunigungs- und Bremswegmodelle“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Vehicle mass and its effect on acceleration and braking-distance models", "description": "Investigate which conditions produce the best result for “Vehicle mass and its effect on acceleration and braking-distance models” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 928, "source_index": 2401, "id": "topic-source510-401-stated-fuel-consumption-engine-power-and-measured-acceleration-in-a-model-comparison", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 401, "de": { "category": "Fahrzeugmathematik", "title": "Angegebener Verbrauch, Motorleistung und gemessene Beschleunigung im Modellvergleich", "description": "Untersucht wird, welche Bedingungen bei „Angegebener Verbrauch, Motorleistung und gemessene Beschleunigung im Modellvergleich“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Stated fuel consumption, engine power, and measured acceleration in a model comparison", "description": "Investigate which conditions produce the best result for “Stated fuel consumption, engine power, and measured acceleration in a model comparison” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 929, "source_index": 2402, "id": "topic-source510-402-optimal-cruising-speed-from-aerodynamic-drag-rolling-resistance-and-energy-consumption", "category_key": "vehicle-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 402, "de": { "category": "Fahrzeugmathematik", "title": "Optimale Reisegeschwindigkeit aus Luftwiderstand, Rollwiderstand und Energieverbrauch", "description": "Untersucht wird, welche Bedingungen bei „Optimale Reisegeschwindigkeit aus Luftwiderstand, Rollwiderstand und Energieverbrauch“ zu einem bestmöglichen Ergebnis führen und wie empfindlich dieses Optimum auf veränderte Annahmen reagiert. Differentialrechnung und Integralrechnung unterstützen Optimierung und Gesamtbilanz; Statistik und Stochastik zeigen, ob das Ergebnis trotz Streuung und unsicherer Daten stabil bleibt.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Vehicle mathematics", "title": "Optimal cruising speed from aerodynamic drag, rolling resistance, and energy consumption", "description": "Investigate which conditions produce the best result for “Optimal cruising speed from aerodynamic drag, rolling resistance, and energy consumption” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 930, "source_index": 2403, "id": "topic-source510-403-magnet-shape-and-the-spatial-distribution-of-measured-magnetic-field-strength", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 403, "de": { "category": "Elektrische & magnetische Felder", "title": "Magnetform und räumliche Verteilung der gemessenen Magnetfeldstärke", "description": "Untersucht wird, wie sich „Magnetform und räumliche Verteilung der gemessenen Magnetfeldstärke“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Magnet shape and the spatial distribution of measured magnetic-field strength", "description": "Investigate how “Magnet shape and the spatial distribution of measured magnetic-field strength” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 931, "source_index": 2404, "id": "topic-source510-404-distance-law-for-the-field-strength-of-a-bar-magnet", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 404, "de": { "category": "Elektrische & magnetische Felder", "title": "Abstandsgesetz der Feldstärke eines Stabmagneten", "description": "Untersucht wird, wie sich „Abstandsgesetz der Feldstärke eines Stabmagneten“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Distance law for the field strength of a bar magnet", "description": "Investigate how “Distance law for the field strength of a bar magnet” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 932, "source_index": 2405, "id": "topic-source510-405-number-of-coil-turns-and-current-as-determinants-of-a-solenoid-s-magnetic-field", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 405, "de": { "category": "Elektrische & magnetische Felder", "title": "Windungszahl und Stromstärke als Einflussgrößen des Magnetfelds einer Spule", "description": "Untersucht wird, wie sich „Windungszahl und Stromstärke als Einflussgrößen des Magnetfelds einer Spule“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Number of coil turns and current as determinants of a solenoid's magnetic field", "description": "Investigate how “Number of coil turns and current as determinants of a solenoid's magnetic field” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 933, "source_index": 2406, "id": "topic-source510-406-shielding-effect-of-different-materials-on-a-magnetic-field", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 406, "de": { "category": "Elektrische & magnetische Felder", "title": "Abschirmwirkung verschiedener Materialien auf ein Magnetfeld", "description": "Untersucht wird, wie sich „Abschirmwirkung verschiedener Materialien auf ein Magnetfeld“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Shielding effect of different materials on a magnetic field", "description": "Investigate how “Shielding effect of different materials on a magnetic field” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 934, "source_index": 2407, "id": "topic-source510-407-safety-distance-and-field-strength-below-or-beside-high-voltage-power-lines", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 407, "de": { "category": "Elektrische & magnetische Felder", "title": "Sicherheitsabstand und Feldstärke unter beziehungsweise neben Hochspannungsleitungen", "description": "Untersucht wird, wie sich „Sicherheitsabstand und Feldstärke unter beziehungsweise neben Hochspannungsleitungen“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Safety distance and field strength below or beside high-voltage power lines", "description": "Investigate how “Safety distance and field strength below or beside high-voltage power lines” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 935, "source_index": 2408, "id": "topic-source510-408-electromagnetic-field-strength-of-household-appliances-as-a-function-of-distance", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 408, "de": { "category": "Elektrische & magnetische Felder", "title": "Elektromagnetische Feldstärke von Haushaltsgeräten in Abhängigkeit vom Abstand", "description": "Untersucht wird, wie sich „Elektromagnetische Feldstärke von Haushaltsgeräten in Abhängigkeit vom Abstand“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Electromagnetic field strength of household appliances as a function of distance", "description": "Investigate how “Electromagnetic field strength of household appliances as a function of distance” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 936, "source_index": 2409, "id": "topic-source510-409-superposition-of-the-magnetic-fields-of-two-magnets-in-different-arrangements", "category_key": "electric-magnetic-fields", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 11, 12 ], "measurement_codes": [ 1, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 409, "de": { "category": "Elektrische & magnetische Felder", "title": "Überlagerung der Magnetfelder zweier Magnete in verschiedener Anordnung", "description": "Untersucht wird, wie sich „Überlagerung der Magnetfelder zweier Magnete in verschiedener Anordnung“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Electric & magnetic fields", "title": "Superposition of the magnetic fields of two magnets in different arrangements", "description": "Investigate how “Superposition of the magnetic fields of two magnets in different arrangements” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 937, "source_index": 2410, "id": "topic-source510-410-determining-gravitational-acceleration-with-a-simple-pendulum-at-different-lengths", "category_key": "experimental-physics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 410, "de": { "category": "Experimentelle Physik", "title": "Bestimmung der Erdbeschleunigung mit einem Fadenpendel bei verschiedenen Längen", "description": "Untersucht wird, wie sich „Bestimmung der Erdbeschleunigung mit einem Fadenpendel bei verschiedenen Längen“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Experimental physics", "title": "Determining gravitational acceleration with a simple pendulum at different lengths", "description": "Investigate how “Determining gravitational acceleration with a simple pendulum at different lengths” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 938, "source_index": 2411, "id": "topic-source510-411-determining-gravitational-acceleration-through-video-analysis-of-free-fall", "category_key": "experimental-physics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 411, "de": { "category": "Experimentelle Physik", "title": "Bestimmung der Erdbeschleunigung durch Videoanalyse eines freien Falls", "description": "Untersucht wird, wie sich „Bestimmung der Erdbeschleunigung durch Videoanalyse eines freien Falls“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Experimental physics", "title": "Determining gravitational acceleration through video analysis of free fall", "description": "Investigate how “Determining gravitational acceleration through video analysis of free fall” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 939, "source_index": 2412, "id": "topic-source510-412-indirect-measurement-of-gravitational-acceleration-on-an-inclined-plane", "category_key": "experimental-physics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 412, "de": { "category": "Experimentelle Physik", "title": "Indirekte Messung der Erdbeschleunigung auf einer schiefen Ebene", "description": "Untersucht wird, wie sich „Indirekte Messung der Erdbeschleunigung auf einer schiefen Ebene“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Experimental physics", "title": "Indirect measurement of gravitational acceleration on an inclined plane", "description": "Investigate how “Indirect measurement of gravitational acceleration on an inclined plane” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 940, "source_index": 2413, "id": "topic-source510-413-a-smartphone-accelerometer-in-a-lift-as-a-model-of-apparent-weight", "category_key": "experimental-physics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 413, "de": { "category": "Experimentelle Physik", "title": "Smartphone-Beschleunigungssensor im Aufzug als Modell für scheinbares Gewicht", "description": "Untersucht wird, wie sich „Smartphone-Beschleunigungssensor im Aufzug als Modell für scheinbares Gewicht“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Experimental physics", "title": "A smartphone accelerometer in a lift as a model of apparent weight", "description": "Investigate how “A smartphone accelerometer in a lift as a model of apparent weight” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 941, "source_index": 2414, "id": "topic-source510-414-stability-of-repeated-gravitational-acceleration-measurements-across-time-of-day-and-exper", "category_key": "experimental-physics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 414, "de": { "category": "Experimentelle Physik", "title": "Stabilität wiederholter Messungen der Erdbeschleunigung über Tageszeit und Versuchsanordnung", "description": "Untersucht wird, wie sich „Stabilität wiederholter Messungen der Erdbeschleunigung über Tageszeit und Versuchsanordnung“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Experimental physics", "title": "Stability of repeated gravitational-acceleration measurements across time of day and experimental setup", "description": "Investigate how “Stability of repeated gravitational-acceleration measurements across time of day and experimental setup” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 942, "source_index": 2415, "id": "topic-source510-415-solar-cell-voltage-as-an-indirect-measure-of-solar-activity-and-irradiance-over-a-day", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 415, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Solarzellenspannung als indirektes Maß für Sonnenaktivität und Einstrahlung im Tagesverlauf", "description": "Untersucht wird, wie sich „Solarzellenspannung als indirektes Maß für Sonnenaktivität und Einstrahlung im Tagesverlauf“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Solar-cell voltage as an indirect measure of solar activity and irradiance over a day", "description": "Investigate how “Solar-cell voltage as an indirect measure of solar activity and irradiance over a day” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 943, "source_index": 2416, "id": "topic-source510-416-solar-cell-current-as-a-function-of-angle-of-incidence-and-solar-elevation", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 416, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Stromstärke einer Solarzelle in Abhängigkeit von Einfallswinkel und Sonnenstand", "description": "Untersucht wird, wie sich „Stromstärke einer Solarzelle in Abhängigkeit von Einfallswinkel und Sonnenstand“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Solar-cell current as a function of angle of incidence and solar elevation", "description": "Investigate how “Solar-cell current as a function of angle of incidence and solar elevation” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 944, "source_index": 2417, "id": "topic-source510-417-module-temperature-and-its-effect-on-voltage-current-and-electrical-power", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 417, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Modultemperatur und ihr Einfluss auf Spannung, Stromstärke und elektrische Leistung", "description": "Untersucht wird, wie sich „Modultemperatur und ihr Einfluss auf Spannung, Stromstärke und elektrische Leistung“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Module temperature and its effect on voltage, current, and electrical power", "description": "Investigate how “Module temperature and its effect on voltage, current, and electrical power” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 945, "source_index": 2418, "id": "topic-source510-418-cloud-cover-and-short-interval-fluctuations-in-solar-power", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 418, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Bewölkungsgrad und Schwankung der Solarleistung in kurzen Zeitintervallen", "description": "Untersucht wird, wie sich „Bewölkungsgrad und Schwankung der Solarleistung in kurzen Zeitintervallen“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Cloud cover and short-interval fluctuations in solar power", "description": "Investigate how “Cloud cover and short-interval fluctuations in solar power” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 946, "source_index": 2419, "id": "topic-source510-419-heat-absorption-by-light-and-dark-surfaces-as-an-indirect-measure-of-solar-effects", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 419, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Wärmeaufnahme heller und dunkler Oberflächen als indirekte Messung der Sonnenwirkung", "description": "Untersucht wird, wie sich „Wärmeaufnahme heller und dunkler Oberflächen als indirekte Messung der Sonnenwirkung“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Heat absorption by light and dark surfaces as an indirect measure of solar effects", "description": "Investigate how “Heat absorption by light and dark surfaces as an indirect measure of solar effects” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 947, "source_index": 2420, "id": "topic-source510-420-daily-solar-energy-yield-as-the-integral-of-a-measured-power-curve", "category_key": "solar-energy-thermal-effects", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 3, 4, 5, 10, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 420, "de": { "category": "Solarenergie & Wärmewirkung", "title": "Täglicher Solarenergieertrag als Integral einer gemessenen Leistungskurve", "description": "Untersucht wird, wie sich „Täglicher Solarenergieertrag als Integral einer gemessenen Leistungskurve“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Solar energy & thermal effects", "title": "Daily solar-energy yield as the integral of a measured power curve", "description": "Investigate how “Daily solar-energy yield as the integral of a measured power curve” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 948, "source_index": 2421, "id": "topic-source510-421-linear-expansion-of-a-metal-rod-as-a-function-of-temperature", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 421, "de": { "category": "Thermische Ausdehnung", "title": "Längenausdehnung eines Metallstabs in Abhängigkeit von der Temperatur", "description": "Untersucht wird, wie sich „Längenausdehnung eines Metallstabs in Abhängigkeit von der Temperatur“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Linear expansion of a metal rod as a function of temperature", "description": "Investigate how “Linear expansion of a metal rod as a function of temperature” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 949, "source_index": 2422, "id": "topic-source510-422-comparing-the-thermal-expansion-coefficients-of-aluminium-steel-and-copper", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 422, "de": { "category": "Thermische Ausdehnung", "title": "Vergleich der Wärmeausdehnungskoeffizienten von Aluminium, Stahl und Kupfer", "description": "Untersucht wird, wie sich „Vergleich der Wärmeausdehnungskoeffizienten von Aluminium, Stahl und Kupfer“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Comparing the thermal-expansion coefficients of aluminium, steel, and copper", "description": "Investigate how “Comparing the thermal-expansion coefficients of aluminium, steel, and copper” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 950, "source_index": 2423, "id": "topic-source510-423-current-heating-and-change-in-length-of-a-metal-wire", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 423, "de": { "category": "Thermische Ausdehnung", "title": "Stromstärke, Erwärmung und Längenänderung eines Metalldrahts", "description": "Untersucht wird, wie sich „Stromstärke, Erwärmung und Längenänderung eines Metalldrahts“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Current, heating, and change in length of a metal wire", "description": "Investigate how “Current, heating, and change in length of a metal wire” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 951, "source_index": 2424, "id": "topic-source510-424-expansion-during-heating-and-contraction-during-cooling-investigating-hysteresis", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 424, "de": { "category": "Thermische Ausdehnung", "title": "Ausdehnung beim Erwärmen und Kontraktion beim Abkühlen: Untersuchung einer Hysterese", "description": "Untersucht wird, wie sich „Ausdehnung beim Erwärmen und Kontraktion beim Abkühlen: Untersuchung einer Hysterese“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Expansion during heating and contraction during cooling: investigating hysteresis", "description": "Investigate how “Expansion during heating and contraction during cooling: investigating hysteresis” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 952, "source_index": 2425, "id": "topic-source510-425-curvature-of-a-bimetallic-strip-as-a-function-of-temperature", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 425, "de": { "category": "Thermische Ausdehnung", "title": "Krümmung eines Bimetallstreifens in Abhängigkeit von der Temperatur", "description": "Untersucht wird, wie sich „Krümmung eines Bimetallstreifens in Abhängigkeit von der Temperatur“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Curvature of a bimetallic strip as a function of temperature", "description": "Investigate how “Curvature of a bimetallic strip as a function of temperature” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 953, "source_index": 2426, "id": "topic-source510-426-model-of-a-bridge-expansion-joint-for-seasonal-temperature-changes", "category_key": "thermal-expansion", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 11 ], "measurement_codes": [ 1, 3, 5, 13, 20 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 426, "de": { "category": "Thermische Ausdehnung", "title": "Modell einer Brücken-Dehnungsfuge für saisonale Temperaturänderungen", "description": "Untersucht wird, wie sich „Modell einer Brücken-Dehnungsfuge für saisonale Temperaturänderungen“ über die Zeit oder in Abhängigkeit von einer veränderten Größe entwickelt und welches Modell den Verlauf am besten beschreibt. Differentialrechnung kann Änderungsraten bestimmen und Integralrechnung Gesamtwirkungen erfassen; Statistik und Stochastik helfen, Messfehler, Streuung und Modellgüte zu beurteilen.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Thermal expansion", "title": "Model of a bridge expansion joint for seasonal temperature changes", "description": "Investigate how “Model of a bridge expansion joint for seasonal temperature changes” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 954, "source_index": 2427, "id": "topic-source510-427-buffon-s-needle-experiment-effect-of-needle-length-and-line-spacing-on-the-approximation-o", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 427, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Buffons Nadelversuch: Einfluss von Nadellänge und Linienabstand auf die Näherung von π", "description": "Im Mittelpunkt steht, wie sich „Buffons Nadelversuch: Einfluss von Nadellänge und Linienabstand auf die Näherung von π“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Buffon's needle experiment: effect of needle length and line spacing on the approximation of π", "description": "The focus is on describing “Buffon's needle experiment: effect of needle length and line spacing on the approximation of π” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 955, "source_index": 2428, "id": "topic-source510-428-monte-carlo-approximation-of-pi-using-random-points-in-a-square", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 428, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Monte-Carlo-Näherung von π durch zufällige Punkte im Quadrat", "description": "Im Mittelpunkt steht, wie sich „Monte-Carlo-Näherung von π durch zufällige Punkte im Quadrat“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Monte Carlo approximation of π using random points in a square", "description": "The focus is on describing “Monte Carlo approximation of π using random points in a square” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 956, "source_index": 2429, "id": "topic-source510-429-circumference-and-diameter-of-real-objects-experimental-verification-of-pi-with-error-anal", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 429, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Umfang und Durchmesser realer Gegenstände: experimenteller Nachweis von π mit Fehleranalyse", "description": "Im Mittelpunkt steht, wie sich „Umfang und Durchmesser realer Gegenstände: experimenteller Nachweis von π mit Fehleranalyse“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Circumference and diameter of real objects: experimental verification of π with error analysis", "description": "The focus is on describing “Circumference and diameter of real objects: experimental verification of π with error analysis” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 957, "source_index": 2430, "id": "topic-source510-430-determining-pi-from-pendulum-periods-with-known-pendulum-length-and-gravitational-accelera", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 430, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Bestimmung von π über Pendelperioden bei bekannter Pendellänge und Erdbeschleunigung", "description": "Im Mittelpunkt steht, wie sich „Bestimmung von π über Pendelperioden bei bekannter Pendellänge und Erdbeschleunigung“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Determining π from pendulum periods with known pendulum length and gravitational acceleration", "description": "The focus is on describing “Determining π from pendulum periods with known pendulum length and gravitational acceleration” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 958, "source_index": 2431, "id": "topic-source510-431-wheel-rotations-and-distance-travelled-as-an-experimental-approximation-of-pi", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 12 ], "measurement_codes": [ 1, 6, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 431, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Radumdrehungen und Wegstrecke als experimentelle Näherung von π", "description": "Im Mittelpunkt steht, wie sich „Radumdrehungen und Wegstrecke als experimentelle Näherung von π“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Wheel rotations and distance travelled as an experimental approximation of π", "description": "The focus is on describing “Wheel rotations and distance travelled as an experimental approximation of π” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 959, "source_index": 2432, "id": "topic-source510-432-compound-interest-with-ever-shorter-compounding-intervals-as-an-approximation-to-e", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 11 ], "measurement_codes": [ 3, 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 432, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Zinseszins mit immer kürzeren Verzinsungsintervallen als Annäherung an die Zahl e", "description": "Im Mittelpunkt stehen die mathematischen Strukturen und Begründungen hinter „Zinseszins mit immer kürzeren Verzinsungsintervallen als Annäherung an die Zahl e“, die anhand eigener Beispiele, Herleitungen oder Simulationen nachvollziehbar gemacht werden. Je nach Eingrenzung können Differentialrechnung oder Integralrechnung die analytische Struktur zeigen; Statistik und Stochastik sind sinnvoll, wenn zusätzlich Simulationen oder Datensätze ausgewertet werden.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Compound interest with ever shorter compounding intervals as an approximation to e", "description": "The investigation centres on the mathematical structures and reasoning behind “Compound interest with ever shorter compounding intervals as an approximation to e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 960, "source_index": 2433, "id": "topic-source510-433-numerical-investigation-of-the-sequence-1-1-n-n-as-evidence-for-e", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 11 ], "measurement_codes": [ 3, 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 433, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Numerische Untersuchung der Folge (1 + 1/n)^n als Nachweis der Zahl e", "description": "Im Mittelpunkt stehen die mathematischen Strukturen und Begründungen hinter „Numerische Untersuchung der Folge (1 + 1/n)^n als Nachweis der Zahl e“, die anhand eigener Beispiele, Herleitungen oder Simulationen nachvollziehbar gemacht werden. Je nach Eingrenzung können Differentialrechnung oder Integralrechnung die analytische Struktur zeigen; Statistik und Stochastik sind sinnvoll, wenn zusätzlich Simulationen oder Datensätze ausgewertet werden.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Numerical investigation of the sequence (1 + 1/n)^n as evidence for e", "description": "The investigation centres on the mathematical structures and reasoning behind “Numerical investigation of the sequence (1 + 1/n)^n as evidence for e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 961, "source_index": 2434, "id": "topic-source510-434-estimating-e-by-fitting-exponential-growth-and-cooling-models", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 11 ], "measurement_codes": [ 3, 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 434, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Schätzung der Zahl e durch Anpassung exponentieller Wachstums- und Abkühlungsmodelle", "description": "Im Mittelpunkt stehen die mathematischen Strukturen und Begründungen hinter „Schätzung der Zahl e durch Anpassung exponentieller Wachstums- und Abkühlungsmodelle“, die anhand eigener Beispiele, Herleitungen oder Simulationen nachvollziehbar gemacht werden. Je nach Eingrenzung können Differentialrechnung oder Integralrechnung die analytische Struktur zeigen; Statistik und Stochastik sind sinnvoll, wenn zusätzlich Simulationen oder Datensätze ausgewertet werden.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Estimating e by fitting exponential growth and cooling models", "description": "The investigation centres on the mathematical structures and reasoning behind “Estimating e by fitting exponential growth and cooling models”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 962, "source_index": 2435, "id": "topic-source510-435-products-of-uniformly-distributed-random-numbers-and-the-expected-number-of-factors-before", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 11 ], "measurement_codes": [ 3, 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 435, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Zufallsprodukte gleichverteilter Zahlen und die erwartete Anzahl bis zum Unterschreiten eines Grenzwerts", "description": "Im Mittelpunkt stehen die mathematischen Strukturen und Begründungen hinter „Zufallsprodukte gleichverteilter Zahlen und die erwartete Anzahl bis zum Unterschreiten eines Grenzwerts“, die anhand eigener Beispiele, Herleitungen oder Simulationen nachvollziehbar gemacht werden. Je nach Eingrenzung können Differentialrechnung oder Integralrechnung die analytische Struktur zeigen; Statistik und Stochastik sind sinnvoll, wenn zusätzlich Simulationen oder Datensätze ausgewertet werden.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Products of uniformly distributed random numbers and the expected number of factors before falling below a threshold", "description": "The investigation centres on the mathematical structures and reasoning behind “Products of uniformly distributed random numbers and the expected number of factors before falling below a threshold”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 963, "source_index": 2436, "id": "topic-source510-436-capacitor-discharge-and-the-time-constant-as-an-experimental-route-to-e", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 7, 10, 11 ], "measurement_codes": [ 3, 5, 6, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 436, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Kondensatorentladung und die Zeitkonstante als experimenteller Zugang zur Zahl e", "description": "Im Mittelpunkt stehen die mathematischen Strukturen und Begründungen hinter „Kondensatorentladung und die Zeitkonstante als experimenteller Zugang zur Zahl e“, die anhand eigener Beispiele, Herleitungen oder Simulationen nachvollziehbar gemacht werden. Je nach Eingrenzung können Differentialrechnung oder Integralrechnung die analytische Struktur zeigen; Statistik und Stochastik sind sinnvoll, wenn zusätzlich Simulationen oder Datensätze ausgewertet werden.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Capacitor discharge and the time constant as an experimental route to e", "description": "The investigation centres on the mathematical structures and reasoning behind “Capacitor discharge and the time constant as an experimental route to e”, demonstrated through original examples, derivations, or simulations. Depending on the focus, differential or integral calculus can reveal the analytical structure; statistics and probability are useful when simulations or data sets are also evaluated.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 964, "source_index": 2437, "id": "topic-source510-437-leaf-arrangements-in-a-plant-and-their-closeness-to-the-golden-angle", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 437, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Blattstellungen einer Pflanze und ihre Nähe zum Goldenen Winkel", "description": "Im Mittelpunkt steht, wie sich „Blattstellungen einer Pflanze und ihre Nähe zum Goldenen Winkel“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Leaf arrangements in a plant and their closeness to the golden angle", "description": "The focus is on describing “Leaf arrangements in a plant and their closeness to the golden angle” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 965, "source_index": 2438, "id": "topic-source510-438-proportions-of-everyday-products-compared-with-the-golden-ratio", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 438, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Proportionen von Alltagsprodukten im Vergleich zum Goldenen Schnitt", "description": "Im Mittelpunkt steht, wie sich „Proportionen von Alltagsprodukten im Vergleich zum Goldenen Schnitt“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Proportions of everyday products compared with the golden ratio", "description": "The focus is on describing “Proportions of everyday products compared with the golden ratio” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 966, "source_index": 2439, "id": "topic-source510-439-image-composition-and-the-golden-ratio-in-self-taken-photographs", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 439, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Bildkomposition und Goldener Schnitt in selbst aufgenommenen Fotografien", "description": "Im Mittelpunkt steht, wie sich „Bildkomposition und Goldener Schnitt in selbst aufgenommenen Fotografien“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Image composition and the golden ratio in self-taken photographs", "description": "The focus is on describing “Image composition and the golden ratio in self-taken photographs” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 967, "source_index": 2440, "id": "topic-source510-440-proportions-of-the-hand-and-finger-segments-compared-with-the-golden-ratio", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 440, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Proportionen von Hand und Fingergliedern im Vergleich zum Goldenen Schnitt", "description": "Im Mittelpunkt steht, wie sich „Proportionen von Hand und Fingergliedern im Vergleich zum Goldenen Schnitt“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Proportions of the hand and finger segments compared with the golden ratio", "description": "The focus is on describing “Proportions of the hand and finger segments compared with the golden ratio” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 968, "source_index": 2441, "id": "topic-source510-441-convergence-of-successive-fibonacci-ratios-to-the-golden-ratio", "category_key": "mathematical-constants-experiments", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 2, 8, 10 ], "measurement_codes": [ 1, 7, 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 441, "de": { "category": "Mathematische Konstanten & Experimente", "title": "Konvergenz aufeinanderfolgender Fibonacci-Quotienten zum Goldenen Schnitt", "description": "Im Mittelpunkt steht, wie sich „Konvergenz aufeinanderfolgender Fibonacci-Quotienten zum Goldenen Schnitt“ durch geometrische Größen, Proportionen und ein überprüfbares Modell beschreiben lässt. Geometrie und Trigonometrie bilden den Kern; Differentialrechnung und Integralrechnung können Krümmung, Flächen oder Volumen untersuchen, während Statistik und Stochastik Messabweichungen bewerten.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Mathematical constants & experiments", "title": "Convergence of successive Fibonacci ratios to the golden ratio", "description": "The focus is on describing “Convergence of successive Fibonacci ratios to the golden ratio” through geometric quantities, proportions, and a testable model. Geometry and trigonometry form the core; differential and integral calculus can investigate curvature, areas, or volumes, while statistics and probability evaluate measurement variation.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 969, "source_index": 2442, "id": "topic-source510-442-reaction-time-to-different-colours-using-a-raspberry-pi-and-touchscreen", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 442, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Reaktionszeit auf verschiedene Farben mit Raspberry Pi und Touchscreen", "description": "Untersucht wird, wie sich „Reaktionszeit auf verschiedene Farben mit Raspberry Pi und Touchscreen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Reaction time to different colours using a Raspberry Pi and touchscreen", "description": "Investigate how “Reaction time to different colours using a Raspberry Pi and touchscreen” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 970, "source_index": 2443, "id": "topic-source510-443-auditory-or-visual-stimuli-comparing-reaction-time-with-a-raspberry-pi", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 443, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Akustische oder visuelle Reize: Vergleich der Reaktionszeit mit Raspberry Pi", "description": "Untersucht wird, wie sich „Akustische oder visuelle Reize: Vergleich der Reaktionszeit mit Raspberry Pi“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Auditory or visual stimuli: comparing reaction time with a Raspberry Pi", "description": "Investigate how “Auditory or visual stimuli: comparing reaction time with a Raspberry Pi” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 971, "source_index": 2444, "id": "topic-source510-444-learning-curve-in-repeated-touchscreen-tasks", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 444, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Lernkurve bei wiederholten Touchscreen-Aufgaben", "description": "Untersucht wird, wie sich „Lernkurve bei wiederholten Touchscreen-Aufgaben“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Learning curve in repeated touchscreen tasks", "description": "Investigate how “Learning curve in repeated touchscreen tasks” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 972, "source_index": 2445, "id": "topic-source510-445-display-time-and-number-of-recalled-characters-in-a-digital-short-term-memory-test", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 445, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Anzeigezeit und erinnerte Zeichenmenge in einem digitalen Kurzzeitgedächtnis-Test", "description": "Untersucht wird, wie sich „Anzeigezeit und erinnerte Zeichenmenge in einem digitalen Kurzzeitgedächtnis-Test“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Display time and number of recalled characters in a digital short-term memory test", "description": "Investigate how “Display time and number of recalled characters in a digital short-term memory test” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 973, "source_index": 2446, "id": "topic-source510-446-fitts-s-law-target-size-distance-and-tapping-time-on-a-touchscreen", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 446, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Fitts' Gesetz: Zielgröße, Abstand und Antippzeit auf dem Touchscreen", "description": "Untersucht wird, wie sich „Fitts' Gesetz: Zielgröße, Abstand und Antippzeit auf dem Touchscreen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Fitts's law: target size, distance, and tapping time on a touchscreen", "description": "Investigate how “Fitts's law: target size, distance, and tapping time on a touchscreen” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 974, "source_index": 2447, "id": "topic-source510-447-virtual-keyboard-size-and-the-relationship-between-typing-speed-and-error-rate", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 447, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Virtuelle Tastengröße und Zusammenhang zwischen Tippgeschwindigkeit und Fehlerquote", "description": "Untersucht wird, wie sich „Virtuelle Tastengröße und Zusammenhang zwischen Tippgeschwindigkeit und Fehlerquote“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Virtual keyboard size and the relationship between typing speed and error rate", "description": "Investigate how “Virtual keyboard size and the relationship between typing speed and error rate” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 975, "source_index": 2448, "id": "topic-source510-448-adaptive-quiz-response-time-difficulty-and-accuracy-on-a-raspberry-pi", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 448, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Adaptives Quiz: Antwortzeit, Schwierigkeit und Trefferquote auf einem Raspberry Pi", "description": "Untersucht wird, wie sich „Adaptives Quiz: Antwortzeit, Schwierigkeit und Trefferquote auf einem Raspberry Pi“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Adaptive quiz: response time, difficulty, and accuracy on a Raspberry Pi", "description": "Investigate how “Adaptive quiz: response time, difficulty, and accuracy on a Raspberry Pi” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 976, "source_index": 2449, "id": "topic-source510-449-time-of-day-test-duration-and-change-in-reaction-speed", "category_key": "raspberry-pi-human-computer-interaction", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 449, "de": { "category": "Raspberry Pi & Mensch-Computer-Interaktion", "title": "Tageszeit, Versuchsdauer und Veränderung der Reaktionsgeschwindigkeit", "description": "Untersucht wird, wie sich „Tageszeit, Versuchsdauer und Veränderung der Reaktionsgeschwindigkeit“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Raspberry Pi & human–computer interaction", "title": "Time of day, test duration, and change in reaction speed", "description": "Investigate how “Time of day, test duration, and change in reaction speed” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 977, "source_index": 2450, "id": "topic-source510-450-interior-temperature-of-an-empty-parked-car-as-a-function-of-outside-temperature-and-time", "category_key": "temperature-modelling-vehicle-safety", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11, 12 ], "measurement_codes": [ 3, 4, 10, 12, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 450, "de": { "category": "Temperaturmodellierung & Fahrzeugsicherheit", "title": "Innenraumtemperatur eines leeren geparkten Autos in Abhängigkeit von Außentemperatur und Zeit", "description": "Untersucht wird, wie sich „Innenraumtemperatur eines leeren geparkten Autos in Abhängigkeit von Außentemperatur und Zeit“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Temperature modelling & vehicle safety", "title": "Interior temperature of an empty parked car as a function of outside temperature and time", "description": "Investigate how “Interior temperature of an empty parked car as a function of outside temperature and time” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 978, "source_index": 2451, "id": "topic-source510-451-dashboard-and-seat-colour-as-determinants-of-surface-temperature-in-an-empty-car", "category_key": "temperature-modelling-vehicle-safety", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11, 12 ], "measurement_codes": [ 3, 4, 10, 12, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 451, "de": { "category": "Temperaturmodellierung & Fahrzeugsicherheit", "title": "Farbe von Armaturenbrett und Sitzfläche als Einfluss auf Oberflächentemperaturen im leeren Auto", "description": "Untersucht wird, wie sich „Farbe von Armaturenbrett und Sitzfläche als Einfluss auf Oberflächentemperaturen im leeren Auto“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Temperature modelling & vehicle safety", "title": "Dashboard and seat colour as determinants of surface temperature in an empty car", "description": "Investigate how “Dashboard and seat colour as determinants of surface temperature in an empty car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 979, "source_index": 2452, "id": "topic-source510-452-effectiveness-of-different-sunshades-in-reducing-the-heating-of-an-empty-vehicle", "category_key": "temperature-modelling-vehicle-safety", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11, 12 ], "measurement_codes": [ 3, 4, 10, 12, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 452, "de": { "category": "Temperaturmodellierung & Fahrzeugsicherheit", "title": "Wirksamkeit verschiedener Sonnenschutzblenden gegen die Erwärmung eines leeren Fahrzeugs", "description": "Untersucht wird, wie sich „Wirksamkeit verschiedener Sonnenschutzblenden gegen die Erwärmung eines leeren Fahrzeugs“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Temperature modelling & vehicle safety", "title": "Effectiveness of different sunshades in reducing the heating of an empty vehicle", "description": "Investigate how “Effectiveness of different sunshades in reducing the heating of an empty vehicle” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 980, "source_index": 2453, "id": "topic-source510-453-window-gap-and-air-exchange-effect-on-the-heating-of-an-empty-parked-car", "category_key": "temperature-modelling-vehicle-safety", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11, 12 ], "measurement_codes": [ 3, 4, 10, 12, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 453, "de": { "category": "Temperaturmodellierung & Fahrzeugsicherheit", "title": "Fensterspalt und Luftaustausch: Einfluss auf die Erwärmung eines leeren geparkten Autos", "description": "Untersucht wird, wie sich „Fensterspalt und Luftaustausch: Einfluss auf die Erwärmung eines leeren geparkten Autos“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Temperature modelling & vehicle safety", "title": "Window gap and air exchange: effect on the heating of an empty parked car", "description": "Investigate how “Window gap and air exchange: effect on the heating of an empty parked car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 981, "source_index": 2454, "id": "topic-source510-454-prediction-model-and-warning-threshold-for-dangerous-interior-temperatures-in-a-car", "category_key": "temperature-modelling-vehicle-safety", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 6, 7, 11, 12 ], "measurement_codes": [ 3, 4, 10, 12, 13 ], "safety_code": 1, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 454, "de": { "category": "Temperaturmodellierung & Fahrzeugsicherheit", "title": "Vorhersagemodell und Warnschwelle für gefährliche Innenraumtemperaturen im Auto", "description": "Untersucht wird, wie sich „Vorhersagemodell und Warnschwelle für gefährliche Innenraumtemperaturen im Auto“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Temperature modelling & vehicle safety", "title": "Prediction model and warning threshold for dangerous interior temperatures in a car", "description": "Investigate how “Prediction model and warning threshold for dangerous interior temperatures in a car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 982, "source_index": 2455, "id": "topic-source510-455-player-salaries-at-a-football-club-and-league-points-achieved", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 455, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Spielergehälter eines Fußballvereins und erreichte Ligapunkte", "description": "Untersucht wird, wie sich „Spielergehälter eines Fußballvereins und erreichte Ligapunkte“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Player salaries at a football club and league points achieved", "description": "Investigate how “Player salaries at a football club and league points achieved” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 983, "source_index": 2456, "id": "topic-source510-456-transfer-spending-and-final-league-position", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 456, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Transferausgaben und Tabellenplatz am Ende einer Saison", "description": "Untersucht wird, wie sich „Transferausgaben und Tabellenplatz am Ende einer Saison“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Transfer spending and final league position", "description": "Investigate how “Transfer spending and final league position” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 984, "source_index": 2457, "id": "topic-source510-457-squad-market-value-and-probability-of-advancing-in-a-tournament", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 457, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Kader-Marktwert und Wahrscheinlichkeit des Weiterkommens in einem Turnier", "description": "Untersucht wird, wie sich „Kader-Marktwert und Wahrscheinlichkeit des Weiterkommens in einem Turnier“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Squad market value and probability of advancing in a tournament", "description": "Investigate how “Squad market value and probability of advancing in a tournament” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 985, "source_index": 2458, "id": "topic-source510-458-attendance-and-sporting-success-of-a-club-over-a-season", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 458, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Zuschauerzahl und sportlicher Erfolg eines Vereins im Saisonverlauf", "description": "Untersucht wird, wie sich „Zuschauerzahl und sportlicher Erfolg eines Vereins im Saisonverlauf“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Attendance and sporting success of a club over a season", "description": "Investigate how “Attendance and sporting success of a club over a season” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 986, "source_index": 2459, "id": "topic-source510-459-ticket-price-stadium-occupancy-and-home-match-revenue", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 459, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Ticketpreis, Stadionauslastung und Heimspielerlös", "description": "Untersucht wird, wie sich „Ticketpreis, Stadionauslastung und Heimspielerlös“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Ticket price, stadium occupancy, and home-match revenue", "description": "Investigate how “Ticket price, stadium occupancy, and home-match revenue” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 987, "source_index": 2460, "id": "topic-source510-460-possession-and-win-probability-across-different-leagues", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 460, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Ballbesitz und Gewinnwahrscheinlichkeit in verschiedenen Ligen", "description": "Untersucht wird, wie sich „Ballbesitz und Gewinnwahrscheinlichkeit in verschiedenen Ligen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Possession and win probability across different leagues", "description": "Investigate how “Possession and win probability across different leagues” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 988, "source_index": 2461, "id": "topic-source510-461-expected-goals-and-actual-goals-model-performance-over-a-season", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 461, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Expected Goals und tatsächliche Tore: Modellgüte über eine Saison", "description": "Untersucht wird, wie sich „Expected Goals und tatsächliche Tore: Modellgüte über eine Saison“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Expected goals and actual goals: model performance over a season", "description": "Investigate how “Expected goals and actual goals: model performance over a season” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 989, "source_index": 2462, "id": "topic-source510-462-manager-changes-and-change-in-average-points-per-match", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 462, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Trainerwechsel und Veränderung der durchschnittlichen Punkte pro Spiel", "description": "Untersucht wird, wie sich „Trainerwechsel und Veränderung der durchschnittlichen Punkte pro Spiel“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Manager changes and change in average points per match", "description": "Investigate how “Manager changes and change in average points per match” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 990, "source_index": 2463, "id": "topic-source510-463-travel-distance-and-the-strength-of-home-advantage", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 463, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Reiseentfernung und Stärke des Heimvorteils", "description": "Untersucht wird, wie sich „Reiseentfernung und Stärke des Heimvorteils“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Travel distance and the strength of home advantage", "description": "Investigate how “Travel distance and the strength of home advantage” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 991, "source_index": 2464, "id": "topic-source510-464-investment-in-youth-development-and-later-market-value-of-the-first-team-squad", "category_key": "football-economics-sports-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 3, 8, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 464, "de": { "category": "Fußballökonomie & Sportstatistik", "title": "Investitionen in Nachwuchsarbeit und späterer Marktwert des Profikaders", "description": "Untersucht wird, wie sich „Investitionen in Nachwuchsarbeit und späterer Marktwert des Profikaders“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Football economics & sports statistics", "title": "Investment in youth development and later market value of the first-team squad", "description": "Investigate how “Investment in youth development and later market value of the first-team squad” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 992, "source_index": 2465, "id": "topic-source510-465-number-of-employees-and-revenue-across-industries", "category_key": "business-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 465, "de": { "category": "Unternehmensmathematik", "title": "Anzahl der Beschäftigten und Umsatz im Branchenvergleich", "description": "Untersucht wird, wie sich „Anzahl der Beschäftigten und Umsatz im Branchenvergleich“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Business mathematics", "title": "Number of employees and revenue across industries", "description": "Investigate how “Number of employees and revenue across industries” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 993, "source_index": 2466, "id": "topic-source510-466-number-of-employees-and-company-profit", "category_key": "business-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 466, "de": { "category": "Unternehmensmathematik", "title": "Anzahl der Beschäftigten und Unternehmensgewinn", "description": "Untersucht wird, wie sich „Anzahl der Beschäftigten und Unternehmensgewinn“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Business mathematics", "title": "Number of employees and company profit", "description": "Investigate how “Number of employees and company profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 994, "source_index": 2467, "id": "topic-source510-467-revenue-per-employee-as-a-function-of-company-size", "category_key": "business-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 467, "de": { "category": "Unternehmensmathematik", "title": "Umsatz pro Beschäftigtem in Abhängigkeit von der Unternehmensgröße", "description": "Untersucht wird, wie sich „Umsatz pro Beschäftigtem in Abhängigkeit von der Unternehmensgröße“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Business mathematics", "title": "Revenue per employee as a function of company size", "description": "Investigate how “Revenue per employee as a function of company size” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 995, "source_index": 2468, "id": "topic-source510-468-workforce-growth-and-subsequent-revenue-development", "category_key": "business-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 468, "de": { "category": "Unternehmensmathematik", "title": "Personalwachstum und nachfolgende Umsatzentwicklung", "description": "Untersucht wird, wie sich „Personalwachstum und nachfolgende Umsatzentwicklung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Business mathematics", "title": "Workforce growth and subsequent revenue development", "description": "Investigate how “Workforce growth and subsequent revenue development” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 996, "source_index": 2469, "id": "topic-source510-469-employee-turnover-and-operating-profit-margin", "category_key": "business-mathematics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 469, "de": { "category": "Unternehmensmathematik", "title": "Mitarbeiterfluktuation und operative Gewinnmarge", "description": "Untersucht wird, wie sich „Mitarbeiterfluktuation und operative Gewinnmarge“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Business mathematics", "title": "Employee turnover and operating profit margin", "description": "Investigate how “Employee turnover and operating profit margin” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 997, "source_index": 2470, "id": "topic-source510-470-number-of-patent-applications-and-company-profit", "category_key": "innovation-patent-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 470, "de": { "category": "Innovations- & Patentstatistik", "title": "Anzahl der Patentanmeldungen und Unternehmensgewinn", "description": "Untersucht wird, wie sich „Anzahl der Patentanmeldungen und Unternehmensgewinn“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Innovation & patent statistics", "title": "Number of patent applications and company profit", "description": "Investigate how “Number of patent applications and company profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 998, "source_index": 2471, "id": "topic-source510-471-citation-weighted-patents-and-a-company-s-market-value", "category_key": "innovation-patent-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 471, "de": { "category": "Innovations- & Patentstatistik", "title": "Zitationsgewichtete Patente und Börsenwert eines Unternehmens", "description": "Untersucht wird, wie sich „Zitationsgewichtete Patente und Börsenwert eines Unternehmens“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Innovation & patent statistics", "title": "Citation-weighted patents and a company's market value", "description": "Investigate how “Citation-weighted patents and a company's market value” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 999, "source_index": 2472, "id": "topic-source510-472-research-and-development-expenditure-patent-count-and-revenue-growth", "category_key": "innovation-patent-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 472, "de": { "category": "Innovations- & Patentstatistik", "title": "Forschungs- und Entwicklungsausgaben, Patentzahl und Umsatzwachstum", "description": "Untersucht wird, wie sich „Forschungs- und Entwicklungsausgaben, Patentzahl und Umsatzwachstum“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Innovation & patent statistics", "title": "Research and development expenditure, patent count, and revenue growth", "description": "Investigate how “Research and development expenditure, patent count, and revenue growth” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1000, "source_index": 2473, "id": "topic-source510-473-time-lag-between-a-patent-application-and-a-measurable-change-in-profit", "category_key": "innovation-patent-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 473, "de": { "category": "Innovations- & Patentstatistik", "title": "Zeitverzögerung zwischen Patentanmeldung und messbarer Gewinnveränderung", "description": "Untersucht wird, wie sich „Zeitverzögerung zwischen Patentanmeldung und messbarer Gewinnveränderung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Innovation & patent statistics", "title": "Time lag between a patent application and a measurable change in profit", "description": "Investigate how “Time lag between a patent application and a measurable change in profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1001, "source_index": 2474, "id": "topic-source510-474-technological-diversity-of-a-patent-portfolio-and-profitability", "category_key": "innovation-patent-statistics", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 474, "de": { "category": "Innovations- & Patentstatistik", "title": "Technologische Vielfalt eines Patentportfolios und Profitabilität", "description": "Untersucht wird, wie sich „Technologische Vielfalt eines Patentportfolios und Profitabilität“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Innovation & patent statistics", "title": "Technological diversity of a patent portfolio and profitability", "description": "Investigate how “Technological diversity of a patent portfolio and profitability” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1002, "source_index": 2475, "id": "topic-source510-475-number-of-daily-company-announcements-and-stock-return", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 475, "de": { "category": "Finanzmärkte & Medien", "title": "Anzahl täglicher Unternehmensmeldungen und Aktienrendite", "description": "Untersucht wird, wie sich „Anzahl täglicher Unternehmensmeldungen und Aktienrendite“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "Number of daily company announcements and stock return", "description": "Investigate how “Number of daily company announcements and stock return” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1003, "source_index": 2476, "id": "topic-source510-476-news-sentiment-and-short-term-price-change", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 476, "de": { "category": "Finanzmärkte & Medien", "title": "Nachrichtenstimmung und kurzfristige Kursveränderung", "description": "Untersucht wird, wie sich „Nachrichtenstimmung und kurzfristige Kursveränderung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "News sentiment and short-term price change", "description": "Investigate how “News sentiment and short-term price change” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1004, "source_index": 2477, "id": "topic-source510-477-publication-time-of-a-news-item-and-subsequent-price-volatility", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 477, "de": { "category": "Finanzmärkte & Medien", "title": "Veröffentlichungszeit einer Nachricht und anschließende Kursvolatilität", "description": "Untersucht wird, wie sich „Veröffentlichungszeit einer Nachricht und anschließende Kursvolatilität“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "Publication time of a news item and subsequent price volatility", "description": "Investigate how “Publication time of a news item and subsequent price volatility” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1005, "source_index": 2478, "id": "topic-source510-478-ai-related-company-announcements-and-abnormal-stock-returns", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 478, "de": { "category": "Finanzmärkte & Medien", "title": "KI-bezogene Unternehmensmeldungen und abnormale Aktienrenditen", "description": "Untersucht wird, wie sich „KI-bezogene Unternehmensmeldungen und abnormale Aktienrenditen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "AI-related company announcements and abnormal stock returns", "description": "Investigate how “AI-related company announcements and abnormal stock returns” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1006, "source_index": 2479, "id": "topic-source510-479-media-attention-and-trading-volume-of-a-stock", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 479, "de": { "category": "Finanzmärkte & Medien", "title": "Medienaufmerksamkeit und Handelsvolumen einer Aktie", "description": "Untersucht wird, wie sich „Medienaufmerksamkeit und Handelsvolumen einer Aktie“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "Media attention and trading volume of a stock", "description": "Investigate how “Media attention and trading volume of a stock” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1007, "source_index": 2480, "id": "topic-source510-480-correction-of-false-information-and-duration-of-the-subsequent-price-recovery", "category_key": "financial-markets-media", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 480, "de": { "category": "Finanzmärkte & Medien", "title": "Korrektur einer Falschmeldung und Dauer der anschließenden Kurserholung", "description": "Untersucht wird, wie sich „Korrektur einer Falschmeldung und Dauer der anschließenden Kurserholung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Financial markets & media", "title": "Correction of false information and duration of the subsequent price recovery", "description": "Investigate how “Correction of false information and duration of the subsequent price recovery” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1008, "source_index": 2481, "id": "topic-source510-481-accuracy-of-ai-answers-as-a-function-of-the-difficulty-of-mathematical-questions", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 481, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Richtigkeit von KI-Antworten in Abhängigkeit vom Schwierigkeitsgrad mathematischer Fragen", "description": "Untersucht wird, wie sich „Richtigkeit von KI-Antworten in Abhängigkeit vom Schwierigkeitsgrad mathematischer Fragen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Accuracy of AI answers as a function of the difficulty of mathematical questions", "description": "Investigate how “Accuracy of AI answers as a function of the difficulty of mathematical questions” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1009, "source_index": 2482, "id": "topic-source510-482-rag-versus-no-rag-effect-of-external-sources-on-the-accuracy-of-ai-answers", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 482, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "RAG oder kein RAG: Einfluss externer Quellen auf die Richtigkeit von KI-Antworten", "description": "Untersucht wird, wie sich „RAG oder kein RAG: Einfluss externer Quellen auf die Richtigkeit von KI-Antworten“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "RAG versus no RAG: effect of external sources on the accuracy of AI answers", "description": "Investigate how “RAG versus no RAG: effect of external sources on the accuracy of AI answers” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1010, "source_index": 2483, "id": "topic-source510-483-prompt-length-and-accuracy-of-an-ai-answer", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 483, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Promptlänge und Richtigkeit einer KI-Antwort", "description": "Untersucht wird, wie sich „Promptlänge und Richtigkeit einer KI-Antwort“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Prompt length and accuracy of an AI answer", "description": "Investigate how “Prompt length and accuracy of an AI answer” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1011, "source_index": 2484, "id": "topic-source510-484-language-model-temperature-and-variation-in-repeated-answers", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 484, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Temperatureinstellung eines Sprachmodells und Streuung wiederholter Antworten", "description": "Untersucht wird, wie sich „Temperatureinstellung eines Sprachmodells und Streuung wiederholter Antworten“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Language-model temperature and variation in repeated answers", "description": "Investigate how “Language-model temperature and variation in repeated answers” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1012, "source_index": 2485, "id": "topic-source510-485-hallucination-rate-of-an-ai-across-different-knowledge-domains", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 485, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Halluzinationsrate einer KI in verschiedenen Wissensgebieten", "description": "Untersucht wird, wie sich „Halluzinationsrate einer KI in verschiedenen Wissensgebieten“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Hallucination rate of an AI across different knowledge domains", "description": "Investigate how “Hallucination rate of an AI across different knowledge domains” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1013, "source_index": 2486, "id": "topic-source510-486-model-size-usage-cost-and-answer-quality-in-comparison", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 486, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Modellgröße, Nutzungskosten und Antwortqualität im Vergleich", "description": "Untersucht wird, wie sich „Modellgröße, Nutzungskosten und Antwortqualität im Vergleich“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Model size, usage cost, and answer quality in comparison", "description": "Investigate how “Model size, usage cost, and answer quality in comparison” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1014, "source_index": 2487, "id": "topic-source510-487-consistency-of-an-ai-when-the-same-question-is-asked-repeatedly", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 487, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Konsistenz einer KI bei mehrfach identisch gestellten Fragen", "description": "Untersucht wird, wie sich „Konsistenz einer KI bei mehrfach identisch gestellten Fragen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Consistency of an AI when the same question is asked repeatedly", "description": "Investigate how “Consistency of an AI when the same question is asked repeatedly” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1015, "source_index": 2488, "id": "topic-source510-488-confusion-matrix-of-an-ai-image-classifier-under-changing-lighting-conditions", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 488, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Konfusionsmatrix eines KI-Bildklassifikators bei veränderten Lichtbedingungen", "description": "Untersucht wird, wie sich „Konfusionsmatrix eines KI-Bildklassifikators bei veränderten Lichtbedingungen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Confusion matrix of an AI image classifier under changing lighting conditions", "description": "Investigate how “Confusion matrix of an AI image classifier under changing lighting conditions” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1016, "source_index": 2489, "id": "topic-source510-489-ai-forecast-versus-a-simple-baseline-model-comparing-error-metrics", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 489, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "KI-Prognose gegen einfaches Basismodell: Vergleich von Fehlermaßen", "description": "Untersucht wird, wie sich „KI-Prognose gegen einfaches Basismodell: Vergleich von Fehlermaßen“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "AI forecast versus a simple baseline model: comparing error metrics", "description": "Investigate how “AI forecast versus a simple baseline model: comparing error metrics” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1017, "source_index": 2490, "id": "topic-source510-490-measuring-possible-bias-in-ai-answers-using-controlled-prompt-variants", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 490, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Messung möglicher Verzerrungen in KI-Antworten mit kontrollierten Promptvarianten", "description": "Untersucht wird, wie sich „Messung möglicher Verzerrungen in KI-Antworten mit kontrollierten Promptvarianten“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Measuring possible bias in AI answers using controlled prompt variants", "description": "Investigate how “Measuring possible bias in AI answers using controlled prompt variants” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1018, "source_index": 2491, "id": "topic-source510-491-ai-response-latency-as-a-function-of-input-and-output-length", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 491, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Antwortlatenz einer KI in Abhängigkeit von Eingabe- und Ausgabelänge", "description": "Untersucht wird, wie sich „Antwortlatenz einer KI in Abhängigkeit von Eingabe- und Ausgabelänge“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "AI response latency as a function of input and output length", "description": "Investigate how “AI response latency as a function of input and output length” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1019, "source_index": 2492, "id": "topic-source510-492-synthetic-versus-real-training-data-effect-on-classification-performance", "category_key": "artificial-intelligence-data-analysis", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 7, 9, 11, 12 ], "measurement_codes": [ 13 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 492, "de": { "category": "Künstliche Intelligenz & Datenanalyse", "title": "Synthetische oder reale Trainingsdaten: Einfluss auf die Klassifikationsgüte", "description": "Untersucht wird, wie sich „Synthetische oder reale Trainingsdaten: Einfluss auf die Klassifikationsgüte“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Artificial intelligence & data analysis", "title": "Synthetic versus real training data: effect on classification performance", "description": "Investigate how “Synthetic versus real training data: effect on classification performance” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1020, "source_index": 2493, "id": "topic-source510-493-learning-gain-between-pre-test-and-post-test-with-ai-supported-tutoring", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 493, "de": { "category": "Lernforschung mit KI", "title": "Lernzuwachs zwischen Vor- und Nachtest mit KI-gestützter Nachhilfe", "description": "Untersucht wird, wie sich „Lernzuwachs zwischen Vor- und Nachtest mit KI-gestützter Nachhilfe“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "Learning gain between pre-test and post-test with AI-supported tutoring", "description": "Investigate how “Learning gain between pre-test and post-test with AI-supported tutoring” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1021, "source_index": 2494, "id": "topic-source510-494-ai-supported-review-intervals-compared-with-a-fixed-study-plan", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 494, "de": { "category": "Lernforschung mit KI", "title": "KI-gestützte Wiederholungsintervalle im Vergleich zu einem festen Lernplan", "description": "Untersucht wird, wie sich „KI-gestützte Wiederholungsintervalle im Vergleich zu einem festen Lernplan“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "AI-supported review intervals compared with a fixed study plan", "description": "Investigate how “AI-supported review intervals compared with a fixed study plan” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1022, "source_index": 2495, "id": "topic-source510-495-number-and-depth-of-ai-hints-as-determinants-of-independently-solved-tasks", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 495, "de": { "category": "Lernforschung mit KI", "title": "Anzahl und Tiefe von KI-Hinweisen als Einfluss auf selbstständig gelöste Aufgaben", "description": "Untersucht wird, wie sich „Anzahl und Tiefe von KI-Hinweisen als Einfluss auf selbstständig gelöste Aufgaben“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "Number and depth of AI hints as determinants of independently solved tasks", "description": "Investigate how “Number and depth of AI hints as determinants of independently solved tasks” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1023, "source_index": 2496, "id": "topic-source510-496-task-completion-time-and-learning-success-with-ai-support-compared-with-a-textbook", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 496, "de": { "category": "Lernforschung mit KI", "title": "Bearbeitungszeit und Lernerfolg mit KI-Unterstützung im Vergleich zum Lehrbuch", "description": "Untersucht wird, wie sich „Bearbeitungszeit und Lernerfolg mit KI-Unterstützung im Vergleich zum Lehrbuch“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "Task-completion time and learning success with AI support compared with a textbook", "description": "Investigate how “Task-completion time and learning success with AI support compared with a textbook” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1024, "source_index": 2497, "id": "topic-source510-497-knowledge-retention-after-seven-days-with-and-without-ai-feedback", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 497, "de": { "category": "Lernforschung mit KI", "title": "Wissensbehalt nach sieben Tagen mit und ohne KI-Feedback", "description": "Untersucht wird, wie sich „Wissensbehalt nach sieben Tagen mit und ohne KI-Feedback“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "Knowledge retention after seven days with and without AI feedback", "description": "Investigate how “Knowledge retention after seven days with and without AI feedback” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1025, "source_index": 2498, "id": "topic-source510-498-adaptive-task-difficulty-using-raspberry-pi-touchscreen-and-ai-evaluation", "category_key": "learning-research-with-ai", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 4, 7, 11, 12 ], "measurement_codes": [ 13, 14, 19 ], "safety_code": 3, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 498, "de": { "category": "Lernforschung mit KI", "title": "Adaptive Aufgabenschwierigkeit mit Raspberry Pi, Touchscreen und KI-Auswertung", "description": "Untersucht wird, wie sich „Adaptive Aufgabenschwierigkeit mit Raspberry Pi, Touchscreen und KI-Auswertung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Learning research with AI", "title": "Adaptive task difficulty using Raspberry Pi, touchscreen, and AI evaluation", "description": "Investigate how “Adaptive task difficulty using Raspberry Pi, touchscreen, and AI evaluation” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1026, "source_index": 2499, "id": "topic-source510-499-effect-of-screen-brightness-on-the-battery-life-of-a-smartphone", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 499, "de": { "category": "Smartphone-Daten & Technik", "title": "Bildschirmhelligkeit und Akkulaufzeit eines Smartphones", "description": "Untersucht wird, wie sich „Bildschirmhelligkeit und Akkulaufzeit eines Smartphones“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Effect of screen brightness on the battery life of a smartphone", "description": "Investigate how “Effect of screen brightness on the battery life of a smartphone” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1027, "source_index": 2500, "id": "topic-source510-500-wi-fi-4g-or-5g-effect-of-network-type-on-battery-life", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 500, "de": { "category": "Smartphone-Daten & Technik", "title": "WLAN, 4G oder 5G: Einfluss der Netzart auf die Akkulaufzeit", "description": "Untersucht wird, wie sich „WLAN, 4G oder 5G: Einfluss der Netzart auf die Akkulaufzeit“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Wi-Fi, 4G, or 5G: effect of network type on battery life", "description": "Investigate how “Wi-Fi, 4G, or 5G: effect of network type on battery life” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1028, "source_index": 2501, "id": "topic-source510-501-charging-power-and-the-smartphone-charging-time-curve-from-0-to-100-per-cent", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 501, "de": { "category": "Smartphone-Daten & Technik", "title": "Ladeleistung und Verlauf der Smartphone-Ladezeit von 0 bis 100 Prozent", "description": "Untersucht wird, wie sich „Ladeleistung und Verlauf der Smartphone-Ladezeit von 0 bis 100 Prozent“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Charging power and the smartphone charging-time curve from 0 to 100 per cent", "description": "Investigate how “Charging power and the smartphone charging-time curve from 0 to 100 per cent” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1029, "source_index": 2502, "id": "topic-source510-502-charge-cycles-and-measurable-decline-in-battery-capacity", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 502, "de": { "category": "Smartphone-Daten & Technik", "title": "Ladezyklen und messbare Abnahme der Akkukapazität", "description": "Untersucht wird, wie sich „Ladezyklen und messbare Abnahme der Akkukapazität“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Charge cycles and measurable decline in battery capacity", "description": "Investigate how “Charge cycles and measurable decline in battery capacity” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1030, "source_index": 2503, "id": "topic-source510-503-smartphone-price-and-actual-useful-life-of-different-models", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 503, "de": { "category": "Smartphone-Daten & Technik", "title": "Smartphone-Preis und tatsächliche Nutzungsdauer verschiedener Modelle", "description": "Untersucht wird, wie sich „Smartphone-Preis und tatsächliche Nutzungsdauer verschiedener Modelle“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Smartphone price and actual useful life of different models", "description": "Investigate how “Smartphone price and actual useful life of different models” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1031, "source_index": 2504, "id": "topic-source510-504-smartphone-sales-as-a-function-of-price-and-feature-set", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 504, "de": { "category": "Smartphone-Daten & Technik", "title": "Verkaufszahlen von Smartphones in Abhängigkeit von Preis und Funktionsumfang", "description": "Untersucht wird, wie sich „Verkaufszahlen von Smartphones in Abhängigkeit von Preis und Funktionsumfang“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Smartphone sales as a function of price and feature set", "description": "Investigate how “Smartphone sales as a function of price and feature set” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1032, "source_index": 2505, "id": "topic-source510-505-daily-smartphone-use-and-sleep-duration-in-an-anonymised-survey", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 505, "de": { "category": "Smartphone-Daten & Technik", "title": "Tägliche Handynutzungsdauer und Schlafdauer in einer anonymisierten Erhebung", "description": "Untersucht wird, wie sich „Tägliche Handynutzungsdauer und Schlafdauer in einer anonymisierten Erhebung“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Daily smartphone use and sleep duration in an anonymised survey", "description": "Investigate how “Daily smartphone use and sleep duration in an anonymised survey” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1033, "source_index": 2506, "id": "topic-source510-506-distribution-of-usage-time-across-app-categories", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 506, "de": { "category": "Smartphone-Daten & Technik", "title": "Verteilung der Nutzungszeit auf App-Kategorien", "description": "Untersucht wird, wie sich „Verteilung der Nutzungszeit auf App-Kategorien“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Distribution of usage time across app categories", "description": "Investigate how “Distribution of usage time across app categories” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1034, "source_index": 2507, "id": "topic-source510-507-screen-time-processor-load-and-battery-temperature", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 507, "de": { "category": "Smartphone-Daten & Technik", "title": "Bildschirmzeit, Prozessorlast und Akkutemperatur", "description": "Untersucht wird, wie sich „Bildschirmzeit, Prozessorlast und Akkutemperatur“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Screen time, processor load, and battery temperature", "description": "Investigate how “Screen time, processor load, and battery temperature” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1035, "source_index": 2508, "id": "topic-source510-508-smartphone-gps-accuracy-in-urban-areas-woodland-and-open-terrain", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 508, "de": { "category": "Smartphone-Daten & Technik", "title": "GPS-Genauigkeit des Smartphones in Stadt, Wald und freiem Gelände", "description": "Untersucht wird, wie sich „GPS-Genauigkeit des Smartphones in Stadt, Wald und freiem Gelände“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Smartphone GPS accuracy in urban areas, woodland, and open terrain", "description": "Investigate how “Smartphone GPS accuracy in urban areas, woodland, and open terrain” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1036, "source_index": 2509, "id": "topic-source510-509-camera-resolution-file-size-and-smartphone-processing-time", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 509, "de": { "category": "Smartphone-Daten & Technik", "title": "Kameraauflösung, Dateigröße und Verarbeitungszeit eines Smartphones", "description": "Untersucht wird, wie sich „Kameraauflösung, Dateigröße und Verarbeitungszeit eines Smartphones“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Camera resolution, file size, and smartphone processing time", "description": "Investigate how “Camera resolution, file size, and smartphone processing time” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] }, { "no": 1037, "source_index": 2510, "id": "topic-source510-510-device-age-and-launch-time-of-selected-apps", "category_key": "smartphone-data-technology", "assessment_code": 3, "course_code": 9, "courses": [ "aa", "ai" ], "levels": [ "sl", "hl" ], "personal_engagement_codes": [ 1, 5, 7, 11, 12 ], "measurement_codes": [ 5, 6, 7, 8, 13, 14 ], "safety_code": 0, "source_course_label": "AA or AI, SL/HL", "editorial_source": "User-supplied 510-topic catalogue, entries 374–510", "source_topic_number": 510, "de": { "category": "Smartphone-Daten & Technik", "title": "Gerätealter und Startzeit ausgewählter Apps", "description": "Untersucht wird, wie sich „Gerätealter und Startzeit ausgewählter Apps“ mit selbst erhobenen Messreihen oder geeigneten offenen Daten quantitativ beschreiben und vergleichen lässt. Statistik und Stochastik helfen, Zusammenhänge, Streuung und Unsicherheit zu prüfen; Differentialrechnung und Integralrechnung können Trendmodelle um Änderungsraten oder kumulierte Effekte erweitern.", "methods": [ "Differentialrechnung", "Integralrechnung", "Statistik", "Stochastik" ] }, "en": { "category": "Smartphone data & technology", "title": "Device age and launch time of selected apps", "description": "Investigate how “Device age and launch time of selected apps” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects.", "methods": [ "Differential calculus", "Integral calculus", "Statistics", "Probability" ] }, "method_keys": [ "differential_calculus", "integral_calculus", "statistics", "stochastics" ] } ] }