Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
900 topic ideas – page 17 of 36.
Topics 401 to 425 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 |
|---|---|---|---|---|---|---|
| 401 | Environmental mathematics & sustainabilityCalculating carbon dioxide emissions per kilometre for different forms of transport Turn “Calculating carbon dioxide emissions per kilometre for different forms of transport” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 6 | 16 | 813 | 0 |
| 402 | Networks & social systemsNetwork motifs in a public food-web dataset Turn “Network motifs in a public food-web dataset” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 7912 | 13 | 0 |
| 403 | Sports biomechanics & movementAnalysing the optimal riding position on a road bicycle Turn “Analysing the optimal riding position on a road bicycle” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1311 | 0 | 0 |
| 404 | Information & coding theoryPassword entropy and common human choice patterns Turn “Password entropy and common human choice patterns” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 5712 | 13 | 0 |
| 405 | Data science & introductory algorithmsPassword-strength patterns through combinatorics Turn “Password-strength patterns through combinatorics” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1 | 0 | 0 |
| 406 | Robotics, control & sensingError propagation at the endpoint of a robot arm Turn “Error propagation at the endpoint of a robot arm” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 271012 | 11320 | 1 |
| 407 | Image processing & computer graphicsEstimating optical flow in short video sequences Turn “Estimating optical flow in short video sequences” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 271112 | 713 | 0 |
| 408 | Language & text mathematicsInvestigating periodic structures in poetic metre Turn “Investigating periodic structures in poetic metre” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 9 | 81012 | 13 | 0 |
| 409 | Education & learning analyticsReliability of peer assessment using inter-rater correlation Turn “Reliability of peer assessment using inter-rater correlation” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
1 | 6 | 412 | 1314 | 3 |
| 410 | Economic models & marketsAssociation rules in anonymised market-basket data Turn “Association rules in anonymised market-basket data” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 6 | 57912 | 13 | 3 |
| 411 | Time series & forecastingHow different imputation methods affect time-series trends Turn “How different imputation methods affect time-series trends” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 6 | 7912 | 13 | 0 |
| 412 | Geospatial & cartographic mathematicsChoosing an optimal map scale for a hiking route Turn “Choosing an optimal map scale for a hiking route” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 2611 | 813 | 0 |
| 413 | Engineering design & optimisationOptimising pallet stacking for mixed package sizes Turn “Optimising pallet stacking for mixed package sizes” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 25711 | 11320 | 0 |
| 414 | ThermodynamicsTemperature change while baking a muffin: core versus surface temperature Turn “Temperature change while baking a muffin: core versus surface temperature” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 1511 | 3 | 1 |
| 415 | Epidemiology & public healthLag between wastewater signals and reported cases Turn “Lag between wastewater signals and reported cases” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 6 | 91112 | 13 | 0 |
| 416 | Material propertiesHygroscopicity of salts and sugars: mass gain from moisture in air Turn “Hygroscopicity of salts and sugars: mass gain from moisture in air” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 112 | 261318 | 0 |
| 417 | Sports analytics & tacticsBasketball shot selection using expected points Turn “Basketball shot selection using expected points” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 1371112 | 713 | 0 |
| 418 | ElectricityTemperature-dependent resistance of an incandescent lamp Turn “Temperature-dependent resistance of an incandescent lamp” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 1 | 35 | 1 |
| 419 | Recreational games & mathematicsInvestigating first-player advantage in a board game Turn “Investigating first-player advantage in a board game” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 17812 | 13 | 0 |
| 420 | Combined experimentsCalorimetry: determining the specific heat capacity of a metal Turn “Calorimetry: determining the specific heat capacity of a metal” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 112 | 2316 | 0 |
| 421 | Combinatorics & discrete probabilityLoad distribution in the balls-into-bins model Develop “Load distribution in the balls-into-bins model” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
2 | 8 | 71011 | 13 | 0 |
| 422 | Kitchen & everyday lifeTemperature change in a vacuum flask over 24 hours Turn “Temperature change in a vacuum flask over 24 hours” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 1 | 3613 | 0 |
| 423 | EnvironmentWater samples: dissolved-solid mass and electrical conductivity Turn “Water samples: dissolved-solid mass and electrical conductivity” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 6 | 16 | 2513 | 1 |
| 424 | Algebra & number theoryThe relationship between continued fractions and irrational numbers Turn “The relationship between continued fractions and irrational numbers” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 1 | 0 | 0 |
| 425 | Analysis & calculusSpeed and acceleration while cycling Turn “Speed and acceleration while cycling” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 13 | 8 | 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.