Focus the object
Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
1037 topic ideas – page 40 of 42.
Topics 976 to 1000 with explanations, methods, course and equipment guidance.
Mathematics and applications
Compare 1037 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 |
|---|---|---|---|---|---|---|
| 976 | Raspberry Pi & human–computer interactionTime of day, test duration, and change in reaction speed Investigate how “Time of day, test duration, and change in reaction speed” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1471112 | 131419 | 3 |
| 977 | Temperature modelling & vehicle safetyInterior temperature of an empty parked car as a function of outside temperature and time Investigate how “Interior temperature of an empty parked car as a function of outside temperature and time” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1671112 | 34101213 | 1 |
| 978 | Temperature modelling & vehicle safetyDashboard and seat colour as determinants of surface temperature in an empty car Investigate how “Dashboard and seat colour as determinants of surface temperature in an empty car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1671112 | 34101213 | 1 |
| 979 | Temperature modelling & vehicle safetyEffectiveness of different sunshades in reducing the heating of an empty vehicle Investigate how “Effectiveness of different sunshades in reducing the heating of an empty vehicle” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1671112 | 34101213 | 1 |
| 980 | Temperature modelling & vehicle safetyWindow gap and air exchange: effect on the heating of an empty parked car Investigate how “Window gap and air exchange: effect on the heating of an empty parked car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1671112 | 34101213 | 1 |
| 981 | Temperature modelling & vehicle safetyPrediction model and warning threshold for dangerous interior temperatures in a car Investigate how “Prediction model and warning threshold for dangerous interior temperatures in a car” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 1671112 | 34101213 | 1 |
| 982 | Football economics & sports statisticsPlayer salaries at a football club and league points achieved Investigate how “Player salaries at a football club and league points achieved” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 983 | Football economics & sports statisticsTransfer spending and final league position Investigate how “Transfer spending and final league position” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 984 | Football economics & sports statisticsSquad market value and probability of advancing in a tournament Investigate how “Squad market value and probability of advancing in a tournament” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 985 | Football economics & sports statisticsAttendance and sporting success of a club over a season Investigate how “Attendance and sporting success of a club over a season” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 986 | Football economics & sports statisticsTicket price, stadium occupancy, and home-match revenue Investigate how “Ticket price, stadium occupancy, and home-match revenue” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 987 | Football economics & sports statisticsPossession and win probability across different leagues Investigate how “Possession and win probability across different leagues” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 988 | Football economics & sports statisticsExpected goals and actual goals: model performance over a season Investigate how “Expected goals and actual goals: model performance over a season” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 989 | Football economics & sports statisticsManager changes and change in average points per match Investigate how “Manager changes and change in average points per match” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 990 | Football economics & sports statisticsTravel distance and the strength of home advantage Investigate how “Travel distance and the strength of home advantage” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 991 | Football economics & sports statisticsInvestment in youth development and later market value of the first-team squad Investigate how “Investment in youth development and later market value of the first-team squad” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 3891112 | 13 | 0 |
| 992 | Business mathematicsNumber of employees and revenue across industries Investigate how “Number of employees and revenue across industries” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 993 | Business mathematicsNumber of employees and company profit Investigate how “Number of employees and company profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 994 | Business mathematicsRevenue per employee as a function of company size Investigate how “Revenue per employee as a function of company size” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 995 | Business mathematicsWorkforce growth and subsequent revenue development Investigate how “Workforce growth and subsequent revenue development” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 996 | Business mathematicsEmployee turnover and operating profit margin Investigate how “Employee turnover and operating profit margin” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 997 | Innovation & patent statisticsNumber of patent applications and company profit Investigate how “Number of patent applications and company profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 998 | Innovation & patent statisticsCitation-weighted patents and a company's market value Investigate how “Citation-weighted patents and a company's market value” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 999 | Innovation & patent statisticsResearch and development expenditure, patent count, and revenue growth Investigate how “Research and development expenditure, patent count, and revenue growth” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 0 |
| 1000 | Innovation & patent statisticsTime lag between a patent application and a measurable change in profit Investigate how “Time lag between a patent application and a measurable change in profit” can be described and compared quantitatively using self-collected measurements or suitable open data. Statistics and probability help test relationships, variation, and uncertainty; differential and integral calculus can extend trend models with rates of change or cumulative effects. |
3 | 9 | 91112 | 13 | 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 1037 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.