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 13 of 36.
Topics 301 to 325 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 |
|---|---|---|---|---|---|---|
| 301 | Material propertiesCorrosion of iron nails in water, salt water, cola and vinegar Turn “Corrosion of iron nails in water, salt water, cola and vinegar” 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 | 111 | 2613 | 1 |
| 302 | Sports analytics & tacticsCycling power as a function of gradient and speed Turn “Cycling power as a function of gradient and speed” 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 | 13611 | 81319 | 1 |
| 303 | ElectricityVoltage from homemade galvanic cells using lemons, potatoes, cola and apples Turn “Voltage from homemade galvanic cells using lemons, potatoes, cola and apples” 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 | 15 | 5 | 2 |
| 304 | Recreational games & mathematicsProbability inference in Minesweeper Turn “Probability inference in Minesweeper” 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 | 781011 | 13 | 0 |
| 305 | Combined experimentsConductivity versus salt concentration in aqueous solutions Turn “Conductivity versus salt concentration in aqueous solutions” 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 | 1 | 251113 | 1 |
| 306 | Combinatorics & discrete probabilityConstructing and counting Latin squares Develop “Constructing and counting Latin squares” 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 | 2710 | 1320 | 0 |
| 307 | Kitchen & everyday lifePackaging fruit: mass loss under cling film, vacuum storage and wax wrap Turn “Packaging fruit: mass loss under cling film, vacuum storage and wax wrap” 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 | 1512 | 26 | 1 |
| 308 | Climate, Earth & ocean mathematicsWave energy from a simplified ocean-wave spectrum Turn “Wave energy from a simplified ocean-wave spectrum” 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 | 91011 | 13 | 0 |
| 309 | EnvironmentPaving stones versus grass: daytime surface temperature and night-time cooling Turn “Paving stones versus grass: daytime surface temperature and night-time cooling” 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 | 6 | 34113 | 0 |
| 310 | Algebra & number theoryMagic squares: algebraic construction methods Turn “Magic squares: algebraic construction methods” 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 | 1211 | 20 | 0 |
| 311 | Analysis & calculusRiemann sums and numerical integration Turn “Riemann sums and numerical integration” 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 | 2 | 12 | 13 | 0 |
| 312 | Statistics & probabilityThe normal distribution in sports performance data Turn “The normal distribution in sports performance data” 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 | 13 | 0 | 0 |
| 313 | Mathematical modellingModelling the spread of rumours in a school community Turn “Modelling the spread of rumours in a school community” 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 | 8 | 1 | 0 | 0 |
| 314 | Geometry & topologyThe golden spiral in selected natural forms Turn “The golden spiral in selected natural forms” 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 | 126 | 7 | 0 |
| 315 | Financial mathematicsCalculating the effective annual percentage rate on consumer loans Turn “Calculating the effective annual percentage rate on consumer loans” 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 | 4 | 5 | 13 | 0 |
| 316 | Logic, set theory & proofParadoxes in set theory Develop “Paradoxes in set theory” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
2 | 2 | 10 | 0 | 0 |
| 317 | Discrete mathematics & computer scienceBinary trees and their properties Turn “Binary trees and their properties” 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 | 1211 | 20 | 0 |
| 318 | Applied & interdisciplinary mathematicsModelling optimal lighting in a room Turn “Modelling optimal lighting in a room” 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 | 111 | 1013 | 0 |
| 319 | Game theory & decision-makingModelling negotiation strategies with cooperative game theory Turn “Modelling negotiation strategies with cooperative game theory” 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 | 5 | 1811 | 13 | 0 |
| 320 | Transport & mobility mathematicsA capacity model for pedestrian flow in school corridors Turn “A capacity model for pedestrian flow in school corridors” 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 | 141112 | 6714 | 3 |
| 321 | Biomathematics & medicineModelling the spread of antibiotic resistance in bacterial populations Turn “Modelling the spread of antibiotic resistance in bacterial populations” 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 | 1711 | 13 | 3 |
| 322 | Operations research & logisticsMaximum flow for distributing meals in a school canteen Turn “Maximum flow for distributing meals in a school canteen” 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 | 4711 | 13 | 0 |
| 323 | Environmental mathematics & sustainabilityOptimising solar-panel orientation for maximum energy yield Turn “Optimising solar-panel orientation for maximum energy yield” 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 | 1611 | 10 | 0 |
| 324 | Networks & social systemsThe size of information cascades in social networks Turn “The size of information cascades in social networks” 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 |
| 325 | Sports biomechanics & movementCalculating stability in different yoga poses using centre of mass Turn “Calculating stability in different yoga poses using centre of mass” 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 | 123 | 171315 | 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 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.