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IB Mathematics · Complete topic list
1037 topic ideas – page 37 of 42.
Topics 901 to 925 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 |
|---|---|---|---|---|---|---|
| 901 | Baking & food modelsButter proportion and its effect on baking time, height, and surface of muffins Investigate how “Butter proportion and its effect on baking time, height, and surface of muffins” 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 | 236713 | 1 |
| 902 | Baking & food modelsSugar proportion and its effect on browning, diameter, and crispness of cookies Investigate how “Sugar proportion and its effect on browning, diameter, and crispness of cookies” 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 | 236713 | 1 |
| 903 | Baking & food modelsFlour type and its effect on cake volume and pore structure Investigate how “Flour type and its effect on cake volume and pore structure” 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 | 236713 | 1 |
| 904 | Baking & food modelsNumber of eggs and its effect on the height, elasticity, and mass loss of a sponge cake Investigate how “Number of eggs and its effect on the height, elasticity, and mass loss of a sponge cake” 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 | 236713 | 1 |
| 905 | Baking & food modelsWater-to-milk ratio and its effect on baking time and moisture loss in bread Investigate how “Water-to-milk ratio and its effect on baking time and moisture loss in bread” 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 | 236713 | 1 |
| 906 | Baking & food modelsAmount of baking powder and its effect on batter volume, pore size, and final height Investigate how “Amount of baking powder and its effect on batter volume, pore size, and final height” 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 | 236713 | 1 |
| 907 | Baking & food modelsButter, margarine, or oil: comparing the spread and surface of baked goods Investigate how “Butter, margarine, or oil: comparing the spread and surface of baked goods” 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 | 236713 | 1 |
| 908 | Baking & food modelsOptimising an ingredient ratio for maximum baking volume with minimum mass loss Investigate how “Optimising an ingredient ratio for maximum baking volume with minimum mass loss” 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 | 236713 | 1 |
| 909 | Baking & food modelsOven temperature and its effect on core temperature, baking time, and final height Investigate how “Oven temperature and its effect on core temperature, baking time, and final height” 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 | 2346713 | 1 |
| 910 | Baking & food modelsOven temperature and browning: colour analysis of the surface during baking Investigate how “Oven temperature and browning: colour analysis of the surface during baking” 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 | 2346713 | 1 |
| 911 | Baking & food modelsConstant or stepwise oven temperature: comparing volume and moisture loss Investigate how “Constant or stepwise oven temperature: comparing volume and moisture loss” 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 | 2346713 | 1 |
| 912 | Baking & food modelsPosition in the oven and its effect on temperature distribution and baking outcome Investigate how “Position in the oven and its effect on temperature distribution and baking outcome” 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 | 2346713 | 1 |
| 913 | Baking & food modelsPreheating time and its effect on baking time, energy demand, and product size Investigate how “Preheating time and its effect on baking time, energy demand, and product size” 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 | 2346713 | 1 |
| 914 | Baking & food modelsFan oven or conventional heat: comparing baking time, surface, and energy use Investigate how “Fan oven or conventional heat: comparing baking time, surface, and energy use” 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 | 2346713 | 1 |
| 915 | Ice & heat transferSurface-area-to-volume ratio and melting time of ice cubes Investigate how “Surface-area-to-volume ratio and melting time of ice cubes” 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 | 12346713 | 0 |
| 916 | Ice & heat transferAmbient temperature and the changing melting rate of an ice cube Investigate how “Ambient temperature and the changing melting rate of an ice cube” 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 | 12346713 | 0 |
| 917 | Ice & heat transferSalt concentration and its effect on the melting point and melting time of ice Investigate how “Salt concentration and its effect on the melting point and melting time of ice” 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 | 12346713 | 0 |
| 918 | Ice & heat transferSpread of food colouring as a coloured ice cube melts Investigate how “Spread of food colouring as a coloured ice cube melts” 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 | 12346713 | 0 |
| 919 | Ice & heat transferCube, sphere, or cylinder: comparing shapes with equal ice mass Investigate how “Cube, sphere, or cylinder: comparing shapes with equal ice mass” 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 | 12346713 | 0 |
| 920 | Ice & heat transferAir movement and its effect on ice-melting time Investigate how “Air movement and its effect on ice-melting time” 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 | 12346713 | 0 |
| 921 | Ice & heat transferSupport material and its effect on heat flow and melting time Investigate how “Support material and its effect on heat flow and melting time” 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 | 12346713 | 0 |
| 922 | Ice & heat transferInitial ice temperature and its effect on total thawing time Investigate how “Initial ice temperature and its effect on total thawing time” 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 | 12346713 | 0 |
| 923 | Vehicle mathematicsPower-to-weight ratio and 0–100 km/h acceleration in a vehicle comparison Investigate which conditions produce the best result for “Power-to-weight ratio and 0–100 km/h acceleration in a vehicle 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 |
| 924 | Vehicle mathematicsDrag coefficient C_d and acceleration at higher speeds Investigate which conditions produce the best result for “Drag coefficient C_d and acceleration at higher speeds” 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 |
| 925 | Vehicle mathematicsRelationship between drag coefficient, frontal area, and fuel consumption Investigate which conditions produce the best result for “Relationship between drag coefficient, frontal area, and fuel 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 |
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.