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IB Mathematics · Complete topic list
900 topic ideas – page 34 of 36.
Topics 826 to 850 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 |
|---|---|---|---|---|---|---|
| 826 | Safe human-participant investigationsPractice trials and typing speed Repeatedly type the same neutral short text. |
3 | 9 | 181112 | 312 | 0 |
| 827 | Safe human-participant investigationsStance width and postural sway Record body sway at different safe stance widths. |
3 | 2 | 1381112 | 1613 | 0 |
| 828 | Safe human-participant investigationsWrist angle and grip force Measure grip force at several comfortable wrist angles. |
3 | 9 | 1381112 | 11520 | 0 |
| 829 | Safe human-participant investigationsWalking speed and step length Record normal walking at several comfortable speeds. |
3 | 9 | 1381112 | 131220 | 0 |
| 830 | Safe human-participant investigationsMetronome tempo and gait synchronization Compare prescribed metronome tempos with actual step timing. |
3 | 9 | 181112 | 611 | 0 |
| 831 | Sport and motion analysisBasketball release and entry angles Record shots from the same distance and determine release and entry angles. |
3 | 9 | 131112 | 17 | 1 |
| 832 | Sport and motion analysisFootball launch angle and range Record controlled ball launches at different angles. |
3 | 9 | 1381112 | 157131720 | 1 |
| 833 | Sport and motion analysisBall temperature and rebound height Condition balls within safe moderate temperature ranges. |
3 | 9 | 131112 | 137 | 1 |
| 834 | Sport and motion analysisBall pressure and coefficient of restitution Use a ball within its permitted pressure range. |
3 | 6 | 131112 | 1713 | 1 |
| 835 | Sport and motion analysisSpin and table-tennis rebound angle Generate reproducible topspin or backspin. |
3 | 6 | 12381112 | 171213 | 1 |
| 836 | Sport and motion analysisGear ratio and cycling cadence Use different gear ratios at constant safe speed. |
3 | 9 | 131112 | 67812 | 1 |
| 837 | Sport and motion analysisTake-off angle and standing-jump distance Analyse safe normal standing jumps using video. |
3 | 9 | 1231112 | 1720 | 1 |
| 838 | Sport and motion analysisRope length and maximum skipping frequency Vary skipping-rope length within a comfortable range. |
3 | 9 | 131112 | 136720 | 1 |
| 839 | Sport and motion analysisStroke rate and rowing-ergometer power Use short moderate intervals with the same participant. |
3 | 9 | 13481112 | 367 | 1 |
| 840 | Sport and motion analysisThrowing distance and dart dispersion Use a safe soft-dart setup at several distances. |
3 | 6 | 1381112 | 1720 | 1 |
| 841 | Further magnetic-field experimentsThree-dimensional field map of a bar magnet Measure the field on a regular spatial grid. |
3 | 9 | 1681112 | 1320 | 0 |
| 842 | Further magnetic-field experimentsAxial and equatorial magnetic field Measure at equal distances along axial and equatorial directions. |
3 | 9 | 11112 | 117 | 0 |
| 843 | Further magnetic-field experimentsMagnet temperature and field strength Test a permanent magnet over a moderate safe temperature range. |
3 | 2 | 11112 | 317 | 1 |
| 844 | Further magnetic-field experimentsCore material and solenoid field Compare air core with suitable ferromagnetic cores. |
3 | 9 | 11112 | 51720 | 0 |
| 845 | Further magnetic-field experimentsAir gap in a magnetic circuit Vary the gap between two magnetic-core sections. |
3 | 9 | 11112 | 13520 | 0 |
| 846 | Further magnetic-field experimentsHysteresis loop of a soft magnetic material Record magnetization while increasing and decreasing current. |
3 | 9 | 131112 | 513 | 0 |
| 847 | Further magnetic-field experimentsShield geometry and magnetic-field attenuation Compare different shielding geometries. |
3 | 6 | 11112 | 13 | 0 |
| 848 | Further magnetic-field experimentsCoil spacing and Helmholtz-field uniformity Vary separation between two equal coils. |
3 | 9 | 131112 | 1 | 0 |
| 849 | Further magnetic-field experimentsCoil radius and magnetic-field strength Build equal-turn coils with different radii. |
3 | 9 | 1231112 | 15121720 | 0 |
| 850 | Further magnetic-field experimentsSeparation and magnetic attraction force Measure attraction force between two magnets using a scale. |
3 | 9 | 11112 | 115 | 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.