Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
1037 topic ideas – page 41 of 42.
Topics 1001 to 1025 with explanations, methods, course and equipment guidance.
Mathematics and applications
Compare 1037 ideas clearly.
The list mixes calculus, statistics, modelling, geometry, number theory, computer science, sport, environmental topics and other areas. Each entry includes a short explanation and visible methods such as differential calculus, integral calculus, statistics or regression.
Planning guidance, not official topic approvalThe IA, EE, AA, Math AI, SL and HL classifications are editorial guidance. The current subject guide, assessment session, mathematical depth, focus and school approval remain decisive.
1
Select an idea. Titles and areas are starting points, not finished research questions.
2
Check A and C. These codes give an initial indication of assessment type, course and level.
3
Read P, M and S. They show possible independent direction, tools, and safety or data-protection needs.
| No. | Topic idea | A | C | P | M | S |
|---|---|---|---|---|---|---|
| 1001 | Innovation & patent statisticsTechnological diversity of a patent portfolio and profitability 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. |
3 | 9 | 91112 | 13 | 0 |
| 1002 | Financial markets & mediaNumber of daily company announcements and stock return 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. |
3 | 9 | 791112 | 13 | 0 |
| 1003 | Financial markets & mediaNews sentiment and short-term price change 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. |
3 | 9 | 791112 | 13 | 0 |
| 1004 | Financial markets & mediaPublication time of a news item and subsequent price volatility 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. |
3 | 9 | 791112 | 13 | 0 |
| 1005 | Financial markets & mediaAI-related company announcements and abnormal stock returns 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. |
3 | 9 | 791112 | 13 | 0 |
| 1006 | Financial markets & mediaMedia attention and trading volume of a stock 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. |
3 | 9 | 791112 | 13 | 0 |
| 1007 | Financial markets & mediaCorrection of false information and duration of the subsequent price recovery 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. |
3 | 9 | 791112 | 13 | 0 |
| 1008 | Artificial intelligence & data analysisAccuracy of AI answers as a function of the difficulty of mathematical questions 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. |
3 | 9 | 791112 | 13 | 0 |
| 1009 | Artificial intelligence & data analysisRAG versus no RAG: effect of external sources on the accuracy of AI answers 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. |
3 | 9 | 791112 | 13 | 0 |
| 1010 | Artificial intelligence & data analysisPrompt length and accuracy of an AI answer 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. |
3 | 9 | 791112 | 13 | 0 |
| 1011 | Artificial intelligence & data analysisLanguage-model temperature and variation in repeated answers 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. |
3 | 9 | 791112 | 13 | 0 |
| 1012 | Artificial intelligence & data analysisHallucination rate of an AI across different knowledge domains 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. |
3 | 9 | 791112 | 13 | 0 |
| 1013 | Artificial intelligence & data analysisModel size, usage cost, and answer quality in comparison 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. |
3 | 9 | 791112 | 13 | 0 |
| 1014 | Artificial intelligence & data analysisConsistency of an AI when the same question is asked repeatedly 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. |
3 | 9 | 791112 | 13 | 0 |
| 1015 | Artificial intelligence & data analysisConfusion matrix of an AI image classifier under changing lighting conditions 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. |
3 | 9 | 791112 | 13 | 0 |
| 1016 | Artificial intelligence & data analysisAI forecast versus a simple baseline model: comparing error metrics 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. |
3 | 9 | 791112 | 13 | 0 |
| 1017 | Artificial intelligence & data analysisMeasuring possible bias in AI answers using controlled prompt variants 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. |
3 | 9 | 791112 | 13 | 0 |
| 1018 | Artificial intelligence & data analysisAI response latency as a function of input and output length 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. |
3 | 9 | 791112 | 13 | 0 |
| 1019 | Artificial intelligence & data analysisSynthetic versus real training data: effect on classification performance 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. |
3 | 9 | 791112 | 13 | 0 |
| 1020 | Learning research with AILearning gain between pre-test and post-test with AI-supported tutoring 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. |
3 | 9 | 1471112 | 131419 | 3 |
| 1021 | Learning research with AIAI-supported review intervals compared with a fixed study plan 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. |
3 | 9 | 1471112 | 131419 | 3 |
| 1022 | Learning research with AINumber and depth of AI hints as determinants of independently solved tasks 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. |
3 | 9 | 1471112 | 131419 | 3 |
| 1023 | Learning research with AITask-completion time and learning success with AI support compared with a textbook 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. |
3 | 9 | 1471112 | 131419 | 3 |
| 1024 | Learning research with AIKnowledge retention after seven days with and without AI feedback 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. |
3 | 9 | 1471112 | 131419 | 3 |
| 1025 | Learning research with AIAdaptive task difficulty using Raspberry Pi, touchscreen, and AI evaluation 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. |
3 | 9 | 1471112 | 131419 | 3 |
No topic ideas match this combination.
Code legend
What A, C, P, M and S mean.
The table stays narrow on a phone by replacing long descriptions with numeric codes. Entries may contain several P and M codes.
AAssessment type
- 1
- Internal Assessment (IA)
- 2
- Mathematics Extended Essay (EE)
- 3
- Potentially suitable for an IA or EE, depending on focus and mathematical depth
CCourse and level
- 1
- Mathematics AA SL
- 2
- Mathematics AA HL
- 3
- Mathematics AA at SL or HL
- 4
- Mathematics AI SL
- 5
- Mathematics AI HL
- 6
- Mathematics AI at SL or HL
- 7
- Mathematics AA or AI at SL
- 8
- Mathematics AA or AI at HL
- 9
- Mathematics AA or AI at SL or HL
PWays to demonstrate independent direction and personal engagement
- 1
- Own data, measurements, observations or experiment
- 2
- Own photographs, drawings, constructions or models
- 3
- Own sport, video, GPS or tracker context
- 4
- Own school or class survey or observation
- 5
- Own everyday, household, consumer or financial data
- 6
- Local context: environment, buildings, traffic, climate or nature
- 7
- Own programming, simulation or algorithm
- 8
- Personal interest: music, art, games, design or another hobby
- 9
- Public data selected, prepared and analysed independently
- 10
- Own conjecture, proof idea, generalisation or theoretical comparison
- 11
- Own modelling decision, construction, optimisation or adaptation
- 12
- Critical comparison of assumptions, errors, limitations or ethical issues
MMeasuring instruments, tools or data access
- 0
- No specialist physical instrument; a calculator, CAS, spreadsheet or open data may be sufficient
- 1
- Ruler, tape measure, calliper or protractor
- 2
- Balance or precision scale
- 3
- Contact thermometer or temperature data logger
- 4
- Infrared thermometer or thermal camera
- 5
- Multimeter or another electrical measuring instrument
- 6
- Stopwatch or timer
- 7
- Camera or smartphone for photographic and video analysis
- 8
- GPS device or fitness tracker
- 9
- Microphone, sound-level meter or audio-analysis software
- 10
- Light meter, light sensor or solar sensor
- 11
- Conductivity, pH or salinity meter
- 12
- Weather instruments, such as an anemometer or rain gauge
- 13
- Computer, spreadsheet, CAS, GeoGebra, Desmos or Python
- 14
- Survey form, data sheet or observation record
- 15
- Force sensor or spring balance
- 16
- Laboratory glassware, measuring cylinder or pipette
- 17
- Telescope, binoculars or a suitable camera
- 18
- Humidity or material-moisture sensor
- 19
- Non-invasive physiology sensor, such as heart-rate or reaction-time measurement
- 20
- Physical model, 3D printer or material samples
- 21
- Specialist school laboratory equipment
SSafety and data protection
- 0
- Likely to be low risk within normal school practice
- 1
- Supervision recommended, for example for heat, electricity, sport or traffic observation
- 2
- Carry out only in a school laboratory or with qualified supervision
- 3
- Sensitive personal or health data: consent, anonymisation and preferably secondary data; no medical self-intervention
From heading to investigation
A topic becomes workable only through independent decisions.
The table is designed to speed up the first step. The actual research question emerges through focus, mathematical choice and critical checking.
Select the mathematics
Decide which models, proofs, statistical procedures or optimisation steps can genuinely answer the question.
Plan independent direction
Use your own data, comparisons, modelling choices, extensions or proof ideas rather than reproducing a standard procedure.
Reflect on limitations
Examine assumptions, sources of error, data quality, model limitations, safety and possible improvements.
Personal engagement and independent direction
A personal connection is more than one sentence in the introduction.
The P codes indicate possible ways to shape an investigation independently. Independent thinking becomes visible through justified decisions, appropriate data selection, personal model variants, meaningful comparisons and critical reflection. A code does not guarantee a particular mark.
Review the IA requirementsFrequently asked questions
Use the topic list correctly.
Are the titles finished research questions?
No. They name a possible direction. A question for assessed work must be focused more narrowly, matched to the course and level, and connected to a clear mathematical method.
What does A = 3 mean?
The broad direction could be developed as an IA or Mathematics EE, depending on focus and depth. An EE will normally require a substantially deeper mathematical argument and an appropriate research scope.
Is C an official IB classification?
No. C is editorial guidance for Mathematics AA or Math AI and SL or HL. Final suitability depends on the specific research question and the current requirements.
Do I need to own the listed instruments?
No. M indicates typical or possible tools. Many topics can use open data, a spreadsheet, CAS, GeoGebra, Desmos or Python. Adapt the topic to resources that are genuinely available.
How should topics involving health or personal data be handled?
Prefer anonymised or publicly available secondary data. Original data collection needs consent, data protection, school approval and a low-risk method. Diagnosis, medication changes and invasive self-experimentation do not belong in a Mathematics project.
The complete list is also machine-readable.
The same 1037 entries are available as plain text and bilingual JSON for search, accessibility and AI systems.
Authoritative foundations
Check the current curriculum version before starting.
The catalogue complements the PreLearning explanations. Current official IB documents and the school's instructions remain authoritative.