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 24 of 36.
Topics 576 to 600 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 |
|---|---|---|---|---|---|---|
| 576 | Ice, freezing, and strengthIce thickness and maximum load Produce ice beams of equal width but different thicknesses. Test whether breaking load increases linearly, quadratically, or cubically with thickness. |
3 | 9 | 11112 | 231520 | 1 |
| 577 | Ice, freezing, and strengthFreeze–thaw cycles and strength loss Expose ice samples to different numbers of controlled freeze–thaw cycles. Model strength loss as a linear or exponential process. |
3 | 9 | 11112 | 320 | 0 |
| 578 | Ice, freezing, and strengthCrack length and breaking load Create standardized small notches of different lengths in equal-sized ice beams. Investigate how initial crack length affects breaking load. |
3 | 9 | 11112 | 1231520 | 1 |
| 579 | CO₂, indoor air, plants, and respirationNumber of occupants and CO₂ increase Measure the slope of CO₂ concentration with different numbers of occupants in the same room. Estimate an average emission rate per person. |
3 | 9 | 1461112 | 131416 | 3 |
| 580 | CO₂, indoor air, plants, and respirationCO₂ decay curve and air-exchange rate Record the concentration after occupants leave a room. Fit an exponential model and estimate the air-exchange rate. |
3 | 9 | 1461112 | 131620 | 0 |
| 581 | CO₂, indoor air, plants, and respirationWindow opening and ventilation effectiveness Vary the window angle or open area. Compare the time constants of the resulting CO₂ decay curves. |
3 | 9 | 161112 | 1612 | 0 |
| 582 | CO₂, indoor air, plants, and respirationSingle-sided and cross ventilation Compare one open window with two opposite openings. Determine air-exchange rate and time required to reach a defined CO₂ level. |
3 | 9 | 161112 | 612 | 0 |
| 583 | CO₂, indoor air, plants, and respirationFan position and CO₂ distribution Place a fan in different positions and measure at several room locations. Evaluate both decay rate and spatial variation. |
3 | 6 | 161112 | 6 | 1 |
| 584 | CO₂, indoor air, plants, and respirationSensor height and measured concentration Measure CO₂ near floor, table, and head height and at different distances from occupants. Create a spatial interpolation model. |
3 | 9 | 1461112 | 113161820 | 3 |
| 585 | CO₂, indoor air, plants, and respirationSpeaking and CO₂ increase Compare equal periods of quiet sitting and normal speaking with the same number of occupants and ventilation conditions. |
3 | 9 | 1461112 | 614 | 3 |
| 586 | CO₂, indoor air, plants, and respirationLight activity and CO₂ production Compare sitting with standardized light movement in a well-ventilated room. Estimate the relative change in CO₂ emission rate. |
3 | 9 | 1361112 | 710 | 0 |
| 587 | CO₂, indoor air, plants, and respirationRoom volume and CO₂ rise rate Conduct comparable measurements in rooms of different sizes. Test whether the rise rate is approximately inversely proportional to room volume. |
3 | 9 | 1361112 | 312 | 0 |
| 588 | CO₂, indoor air, plants, and respirationPredicting occupancy from CO₂ data Use concentration, rate of change, temperature, and time to estimate occupancy. Compare linear regression, classification, and time-series models. |
3 | 9 | 13461011 | 3613141620 | 3 |
| 589 | CO₂, indoor air, plants, and respirationLight intensity and net CO₂ uptake Place a plant with constant leaf area in a transparent measurement chamber and vary light intensity. Fit a saturation model. |
3 | 9 | 161112 | 1020 | 0 |
| 590 | CO₂, indoor air, plants, and respirationLight colour and net CO₂ exchange Compare different light colours at approximately equal measured intensity. Analyse the CO₂ rate of change rather than only the final value. |
3 | 9 | 1361112 | 10 | 0 |
| 591 | CO₂, indoor air, plants, and respirationLeaf area and CO₂ uptake Determine leaf area photographically and compare it with the CO₂ decrease rate under constant lighting. |
3 | 9 | 1261112 | 71011 | 0 |
| 592 | CO₂, indoor air, plants, and respirationSoil moisture and net CO₂ exchange Investigate the same plant species at different soil-moisture levels. Search for an optimum rather than automatically assuming a linear relationship. |
3 | 9 | 1681112 | 1318 | 0 |
| 593 | CO₂, indoor air, plants, and respirationTemperature and plant CO₂ exchange Measure the net CO₂ exchange of the same plant at several moderate temperatures under identical lighting. Compare exponential and optimum-curve models. |
3 | 9 | 161112 | 31020 | 0 |
| 594 | CO₂, indoor air, plants, and respirationPlant day–night cycle Record CO₂, temperature, humidity, and light for at least 24 hours. Develop a piecewise or periodic time-series model. |
3 | 6 | 1361112 | 3610121318 | 0 |
| 595 | CO₂, indoor air, plants, and respirationYeast fermentation and CO₂ production Separately vary temperature, sugar concentration, or sugar type. Measure the CO₂ rise rate and determine the time of maximum production. |
3 | 9 | 1681112 | 3616 | 0 |
| 596 | CO₂, indoor air, plants, and respirationSoil respiration and CO₂ Compare equal quantities of soil at different temperatures or moisture levels. Model CO₂ release using multiple regression. |
3 | 6 | 161112 | 3131820 | 0 |
| 597 | Batteries and energyBattery runtime and ambient temperature Operate the same defined load using identical cells at several moderate temperatures. Compare discharge time and delivered energy. |
3 | 9 | 131112 | 2356 | 2 |
| 598 | Batteries and energyVoltage drop and temperature Measure open-circuit voltage and voltage under a constant load. Estimate apparent internal resistance at different temperatures. |
3 | 9 | 131112 | 235 | 2 |
| 599 | Batteries and energyScreen brightness and smartphone battery life Play the same local video file at several brightness levels. Model percentage battery loss per hour. |
3 | 9 | 12681112 | 5671120 | 2 |
| 600 | Batteries and energySignal quality and battery drain Perform the same data transfer at different measured signal strengths. Analyse battery drain, transfer time, and data rate together. |
3 | 9 | 11112 | 561217 | 2 |
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.