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IB Mathematics · Complete topic list
1037 topic ideas – page 38 of 42.
Topics 926 to 950 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 |
|---|---|---|---|---|---|---|
| 926 | Vehicle mathematicsTorque curve and theoretical acceleration in different gears Investigate which conditions produce the best result for “Torque curve and theoretical acceleration in different gears” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data. |
3 | 9 | 91112 | 13 | 0 |
| 927 | Vehicle mathematicsVehicle mass and its effect on acceleration and braking-distance models Investigate which conditions produce the best result for “Vehicle mass and its effect on acceleration and braking-distance models” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data. |
3 | 9 | 91112 | 13 | 0 |
| 928 | Vehicle mathematicsStated fuel consumption, engine power, and measured acceleration in a model comparison Investigate which conditions produce the best result for “Stated fuel consumption, engine power, and measured acceleration in a model comparison” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data. |
3 | 9 | 91112 | 13 | 0 |
| 929 | Vehicle mathematicsOptimal cruising speed from aerodynamic drag, rolling resistance, and energy consumption Investigate which conditions produce the best result for “Optimal cruising speed from aerodynamic drag, rolling resistance, and energy consumption” and how sensitive that optimum is to changed assumptions. Differential and integral calculus support optimisation and overall balances; statistics and probability show whether the result remains stable despite variation and uncertain data. |
3 | 9 | 91112 | 13 | 0 |
| 930 | Electric & magnetic fieldsMagnet shape and the spatial distribution of measured magnetic-field strength Investigate how “Magnet shape and the spatial distribution of measured magnetic-field strength” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 931 | Electric & magnetic fieldsDistance law for the field strength of a bar magnet Investigate how “Distance law for the field strength of a bar magnet” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 932 | Electric & magnetic fieldsNumber of coil turns and current as determinants of a solenoid's magnetic field Investigate how “Number of coil turns and current as determinants of a solenoid's magnetic field” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 933 | Electric & magnetic fieldsShielding effect of different materials on a magnetic field Investigate how “Shielding effect of different materials on a magnetic field” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 934 | Electric & magnetic fieldsSafety distance and field strength below or beside high-voltage power lines Investigate how “Safety distance and field strength below or beside high-voltage power lines” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 935 | Electric & magnetic fieldsElectromagnetic field strength of household appliances as a function of distance Investigate how “Electromagnetic field strength of household appliances as a function of distance” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 936 | Electric & magnetic fieldsSuperposition of the magnetic fields of two magnets in different arrangements Investigate how “Superposition of the magnetic fields of two magnets in different arrangements” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 121112 | 151320 | 1 |
| 937 | Experimental physicsDetermining gravitational acceleration with a simple pendulum at different lengths Investigate how “Determining gravitational acceleration with a simple pendulum at different lengths” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 16713 | 1 |
| 938 | Experimental physicsDetermining gravitational acceleration through video analysis of free fall Investigate how “Determining gravitational acceleration through video analysis of free fall” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 16713 | 1 |
| 939 | Experimental physicsIndirect measurement of gravitational acceleration on an inclined plane Investigate how “Indirect measurement of gravitational acceleration on an inclined plane” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 16713 | 1 |
| 940 | Experimental physicsA smartphone accelerometer in a lift as a model of apparent weight Investigate how “A smartphone accelerometer in a lift as a model of apparent weight” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 16713 | 1 |
| 941 | Experimental physicsStability of repeated gravitational-acceleration measurements across time of day and experimental setup Investigate how “Stability of repeated gravitational-acceleration measurements across time of day and experimental setup” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 16713 | 1 |
| 942 | Solar energy & thermal effectsSolar-cell voltage as an indirect measure of solar activity and irradiance over a day Investigate how “Solar-cell voltage as an indirect measure of solar activity and irradiance over a day” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 943 | Solar energy & thermal effectsSolar-cell current as a function of angle of incidence and solar elevation Investigate how “Solar-cell current as a function of angle of incidence and solar elevation” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 944 | Solar energy & thermal effectsModule temperature and its effect on voltage, current, and electrical power Investigate how “Module temperature and its effect on voltage, current, and electrical power” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 945 | Solar energy & thermal effectsCloud cover and short-interval fluctuations in solar power Investigate how “Cloud cover and short-interval fluctuations in solar power” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 946 | Solar energy & thermal effectsHeat absorption by light and dark surfaces as an indirect measure of solar effects Investigate how “Heat absorption by light and dark surfaces as an indirect measure of solar effects” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 947 | Solar energy & thermal effectsDaily solar-energy yield as the integral of a measured power curve Investigate how “Daily solar-energy yield as the integral of a measured power curve” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 3451013 | 1 |
| 948 | Thermal expansionLinear expansion of a metal rod as a function of temperature Investigate how “Linear expansion of a metal rod as a function of temperature” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 1351320 | 1 |
| 949 | Thermal expansionComparing the thermal-expansion coefficients of aluminium, steel, and copper Investigate how “Comparing the thermal-expansion coefficients of aluminium, steel, and copper” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 1351320 | 1 |
| 950 | Thermal expansionCurrent, heating, and change in length of a metal wire Investigate how “Current, heating, and change in length of a metal wire” changes over time or in response to a varied quantity and which model best describes the pattern. Differential calculus can determine rates of change and integral calculus can capture cumulative effects; statistics and probability help assess measurement error, variation, and model fit. |
3 | 9 | 1711 | 1351320 | 1 |
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.