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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 33 of 36.
Topics 801 to 825 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 |
|---|---|---|---|---|---|---|
| 801 | Plant growth and plant geometrySalinity and germination probability Germinate equal seed samples at different salinities. |
3 | 6 | 161112 | 111316 | 0 |
| 802 | Plant growth and plant geometryTemperature and germination-time distribution Record the germination time of every individual seed. |
3 | 6 | 161112 | 3620 | 0 |
| 803 | Plant growth and plant geometryLight direction and phototropism Vary light direction and record plant curvature. |
3 | 9 | 1261112 | 167101120 | 0 |
| 804 | Plant growth and plant geometryPhotoperiod and plant growth Compare different photoperiods under controlled total light exposure. |
3 | 9 | 12361112 | 167101113 | 0 |
| 805 | Plant growth and plant geometryAir speed and transpiration Measure plant mass loss at different air speeds. |
3 | 6 | 1681112 | 2361213 | 0 |
| 806 | Plant growth and plant geometryHumidity and transpiration rate Compare controlled humidity ranges under identical lighting. |
3 | 9 | 161112 | 10121820 | 0 |
| 807 | Plant growth and plant geometryLeaf position and stomatal density Create leaf impressions from different positions on the same plant. |
3 | 6 | 161112 | 1320 | 0 |
| 808 | Plant growth and plant geometryTilt angle and root curvature Rotate seedlings by different angles and record root curvature. |
3 | 9 | 161112 | 1612 | 0 |
| 809 | Plant growth and plant geometryPlanting density and biomass Vary the number of equal plants per unit area. |
3 | 9 | 161112 | 220 | 0 |
| 810 | Plant growth and plant geometryLeaf area, perimeter, and fractal structure Photograph leaves from different species or growth stages. |
3 | 9 | 1236811 | 711 | 1 |
| 811 | Food and cooking processesCooking time and pasta water absorption Weigh identical pasta samples at regular cooking intervals. |
3 | 9 | 161112 | 161620 | 0 |
| 812 | Food and cooking processesTemperature and rice water absorption Compare equal rice samples at several constant temperatures. |
3 | 9 | 161112 | 361620 | 0 |
| 813 | Food and cooking processesSalt concentration and potato osmosis Measure mass change of equal potato pieces in saline solutions. |
3 | 6 | 1381112 | 2111316 | 0 |
| 814 | Food and cooking processesAcid concentration and apple browning Treat equal apple pieces with different citric-acid concentrations. |
3 | 6 | 11112 | 6131620 | 0 |
| 815 | Food and cooking processesGelatin concentration and gel stiffness Measure indentation, oscillation, or deflection of gels. |
3 | 9 | 131112 | 126151620 | 0 |
| 816 | Food and cooking processesBrew time and coffee extraction Measure colour, conductivity, or dissolved solids at constant grind size. |
3 | 9 | 11112 | 261120 | 0 |
| 817 | Food and cooking processesGrind size and coffee-bed flow time Use standardized grind sizes and equal coffee mass. |
3 | 9 | 131112 | 2620 | 0 |
| 818 | Food and cooking processesDough temperature and cookie spread Bake identical portions at different initial temperatures. |
3 | 9 | 11112 | 13620 | 0 |
| 819 | Food and cooking processesKernel mass and popcorn expansion Weigh individual kernels and estimate popped volume. |
3 | 6 | 1101112 | 213 | 0 |
| 820 | Food and cooking processesTemperature and egg-white coagulation Heat small samples under controlled conditions and measure opacity. |
3 | 9 | 1231112 | 367 | 1 |
| 821 | Safe human-participant investigationsHeart-rate recovery over time Measure heart rate after standardized light exercise. |
3 | 6 | 1381112 | 126101319 | 3 |
| 822 | Safe human-participant investigationsStep cadence and heart rate Perform short moderate step exercises at different cadences. |
3 | 9 | 181112 | 61920 | 3 |
| 823 | Safe human-participant investigationsBreathing-rate recovery after light exercise Record breathing rate after standardized light activity. |
3 | 9 | 181112 | 261019 | 0 |
| 824 | Safe human-participant investigationsWarning interval and reaction time Vary the interval between a warning signal and the target stimulus. |
3 | 9 | 181112 | 61920 | 0 |
| 825 | Safe human-participant investigationsTarget size, distance, and selection time Ask participants to select screen targets of different sizes and distances. |
3 | 6 | 1481112 | 16713 | 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 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.