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Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
900 topic ideas – page 29 of 36.
Topics 701 to 725 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 |
|---|---|---|---|---|---|---|
| 701 | Further CO₂ experimentsDoor-opening frequency and CO₂ decay Open a door at standardized intervals without artificially enriching the room with CO₂. |
3 | 6 | 1681112 | 61320 | 0 |
| 702 | Further CO₂ experimentsVentilation setting and steady-state CO₂ level Compare different settings of an existing mechanical ventilation system. |
3 | 6 | 161112 | 21320 | 0 |
| 703 | Further CO₂ experimentsBreak schedule and peak CO₂ concentration Compare occupied periods with differently timed ventilation breaks. |
3 | 2 | 131112 | 3616 | 0 |
| 704 | Further CO₂ experimentsLag between occupancy and CO₂ response Record occupancy changes and analyse the delayed CO₂ response. |
3 | 6 | 131112 | 6131420 | 0 |
| 705 | Further CO₂ experimentsCO₂ sensor response time Move a sensor between two naturally occurring concentration ranges. |
3 | 9 | 1361112 | 61619 | 0 |
| 706 | Further CO₂ experimentsAgreement between multiple CO₂ sensors Place several sensors side by side for an extended period. |
3 | 6 | 11112 | 1613 | 0 |
| 707 | Further CO₂ experimentsDistance from ventilation opening and CO₂ gradient Measure along a line between the room centre and an opening or air outlet. |
3 | 9 | 161112 | 13613 | 0 |
| 708 | Further CO₂ experimentsPlant species and normalized net CO₂ exchange Compare plant species under identical lighting and normalize by leaf area or mass. |
3 | 6 | 1681112 | 210 | 0 |
| 709 | Further CO₂ experimentsGermination stage and CO₂ release Measure equal seed masses before, during, and after germination. |
3 | 9 | 11112 | 23620 | 0 |
| 710 | Further CO₂ experimentsTemperature and CO₂ degassing from a beverage Compare equal beverage samples at different temperatures. |
3 | 9 | 11112 | 3620 | 1 |
| 711 | Heat transfer and temperature profilesContainer material and cooling constant Compare metal, glass, ceramic, and plastic containers of similar geometry. |
3 | 2 | 1381112 | 231320 | 1 |
| 712 | Heat transfer and temperature profilesSurface-area-to-volume ratio and cooling Use differently shaped containers holding equal liquid volumes. |
3 | 2 | 131112 | 313 | 1 |
| 713 | Heat transfer and temperature profilesLid opening and heat loss Vary the open area of a lid on an otherwise identical container. |
3 | 2 | 131112 | 320 | 1 |
| 714 | Heat transfer and temperature profilesStirring speed and heat transfer Stir a warm liquid at several controlled speeds. |
3 | 9 | 131112 | 31220 | 1 |
| 715 | Heat transfer and temperature profilesAir speed and convective cooling Direct different fan speeds at the same warm object. |
3 | 6 | 131112 | 3121320 | 1 |
| 716 | Heat transfer and temperature profilesSurface emissivity and radiative cooling Compare identical containers with different surface finishes. |
3 | 2 | 131112 | 3420 | 1 |
| 717 | Heat transfer and temperature profilesNumber of insulation layers Wrap a container in zero to several identical insulation layers. |
3 | 2 | 13101112 | 35 | 1 |
| 718 | Heat transfer and temperature profilesWet surface and evaporative cooling Vary the area of a wet cloth surrounding the same container. |
3 | 6 | 131112 | 231318 | 1 |
| 719 | Heat transfer and temperature profilesMass of a phase-change material Use different masses of ice or a suitable cold pack. |
3 | 9 | 131112 | 23611 | 1 |
| 720 | Heat transfer and temperature profilesTemperature profile along a metal rod Moderately heat one end of a metal rod and measure temperature at several positions. |
3 | 2 | 1361112 | 320 | 1 |
| 721 | Oscillations, coupling, and chaosPendulum length and corrected period Measure many periods for several pendulum lengths and estimate gg. |
3 | 2 | 11112 | 1261320 | 0 |
| 722 | Oscillations, coupling, and chaosRelease angle and pendulum period Investigate small and larger release angles. |
3 | 2 | 131112 | 161320 | 1 |
| 723 | Oscillations, coupling, and chaosPendulum-bob shape and air damping Compare equal-mass bobs with different frontal areas. |
3 | 2 | 11112 | 2 | 0 |
| 724 | Oscillations, coupling, and chaosFluid viscosity and pendulum damping Oscillate a body in liquids of different viscosities. |
3 | 2 | 11112 | 3 | 0 |
| 725 | Oscillations, coupling, and chaosCoupling strength and energy transfer between pendulums Couple two pendulums using springs of different stiffness. |
3 | 2 | 11112 | 61517 | 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.