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IB Mathematics · Complete topic list
900 topic ideas – page 31 of 36.
Topics 751 to 775 with explanations, methods, course and equipment guidance.
Mathematics and applications
Compare 900 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 |
|---|---|---|---|---|---|---|
| 751 | Structures, beams, and material geometrySpan length and beam deflection Load the same beam at different support separations. |
3 | 6 | 11112 | 121320 | 0 |
| 752 | Structures, beams, and material geometryCross-section orientation and stiffness Load a rectangular beam in different orientations. |
3 | 9 | 131112 | 21520 | 0 |
| 753 | Structures, beams, and material geometryHollow-section wall thickness and buckling load Build equal-sized hollow columns with different wall thicknesses. |
3 | 9 | 1281112 | 21620 | 0 |
| 754 | Structures, beams, and material geometryLoad position and beam deflection Move the same load between beam supports. |
3 | 9 | 11112 | 2320 | 0 |
| 755 | Structures, beams, and material geometryTruss angle and load capacity Build trusses with equal member counts but different angles. |
3 | 9 | 1231112 | 121520 | 0 |
| 756 | Structures, beams, and material geometryArch rise and load capacity Compare model arches with different rise-to-span ratios. |
3 | 9 | 131112 | 121520 | 0 |
| 757 | Structures, beams, and material geometryCorrugation wavelength and bending stiffness Fold paper into corrugations of different width and height. |
3 | 9 | 11112 | 121520 | 0 |
| 758 | Structures, beams, and material geometryHoneycomb cell size Build equal-sized honeycombs with different cell sizes. |
3 | 9 | 1231112 | 1320 | 0 |
| 759 | Structures, beams, and material geometryFibre orientation in a laminate Laminate paper or fabric layers at different orientations. |
3 | 9 | 11112 | 1131520 | 0 |
| 760 | Structures, beams, and material geometry3D-print infill and stiffness Print identical specimens with different infill percentages or patterns. |
3 | 6 | 121112 | 213151720 | 0 |
| 761 | Electrical circuits and sensorsWire length and electrical resistance Measure resistance of the same wire material at several lengths. |
3 | 9 | 161112 | 1520 | 1 |
| 762 | Electrical circuits and sensorsWire diameter and resistance Compare equal-length wires of different diameters. |
3 | 6 | 11112 | 151320 | 1 |
| 763 | Electrical circuits and sensorsTemperature and conductor resistance Measure conductor resistance over a moderate temperature range. |
3 | 6 | 131112 | 3513 | 1 |
| 764 | Electrical circuits and sensorsLED colour and current–voltage characteristic Record current–voltage curves of different LED colours. |
3 | 9 | 131112 | 5 | 1 |
| 765 | Electrical circuits and sensorsResistance and RC charging time Keep capacitance constant and vary resistance. |
3 | 9 | 11112 | 56 | 1 |
| 766 | Electrical circuits and sensorsCapacitance and RC discharge time Keep resistance constant and vary capacitance. |
3 | 9 | 131112 | 56 | 1 |
| 767 | Electrical circuits and sensorsCapacitor type and leakage current Compare long-term voltage loss in different suitable capacitors. |
3 | 9 | 11112 | 5620 | 1 |
| 768 | Electrical circuits and sensorsIlluminance and LDR resistance Measure an LDR at different illuminance levels. |
3 | 6 | 121112 | 5710131720 | 1 |
| 769 | Electrical circuits and sensorsThermistor resistance and temperature Create a thermistor calibration curve. |
3 | 6 | 1381112 | 351320 | 1 |
| 770 | Electrical circuits and sensorsCapacitance and RLC resonance frequency Vary capacitance while keeping the inductor constant. |
3 | 2 | 11112 | 3561320 | 1 |
| 771 | Light, optics, and image formationDistance and illuminance Measure illuminance from a small light source at many distances. |
3 | 6 | 131112 | 127101317 | 0 |
| 772 | Light, optics, and image formationPolarizer angle and light intensity Rotate two polarizing filters relative to one another. |
3 | 9 | 11112 | 17101120 | 0 |
| 773 | Light, optics, and image formationSugar concentration and refractive index Measure refraction angles for solutions of different concentrations. |
3 | 6 | 11112 | 17101316 | 0 |
| 774 | Light, optics, and image formationPrism geometry and minimum deviation Investigate prisms at different incidence angles. |
3 | 9 | 131112 | 171021 | 0 |
| 775 | Light, optics, and image formationObject distance and image distance Measure image distance for many object positions. |
3 | 6 | 131112 | 171013 | 0 |
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 900 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.