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IB Mathematics · Complete topic list
900 topic ideas – page 35 of 36.
Topics 851 to 875 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 |
|---|---|---|---|---|---|---|
| 851 | Further sound and music experimentsString length and fundamental frequency Vary the vibrating length of the same stretched string. |
3 | 2 | 1381112 | 1691320 | 0 |
| 852 | Further sound and music experimentsString tension and frequency Vary string tension using known masses. |
3 | 6 | 181112 | 25691320 | 0 |
| 853 | Further sound and music experimentsLinear density and string frequency Compare strings with different mass per unit length. |
3 | 9 | 181112 | 1256920 | 0 |
| 854 | Further sound and music experimentsMembrane tension and drum frequency Stretch the same membrane to several reproducible tension levels. |
3 | 2 | 181112 | 56913 | 0 |
| 855 | Further sound and music experimentsFrequency and Chladni patterns Generate nodal patterns on a small plate at different frequencies. |
3 | 9 | 181112 | 6913 | 0 |
| 856 | Further sound and music experimentsFrequency difference and beat frequency Play two nearby frequencies simultaneously. |
3 | 2 | 181112 | 6913 | 0 |
| 857 | Further sound and music experimentsSource speed and Doppler shift Move a safe small sound source at known speeds. |
3 | 6 | 181112 | 9121320 | 0 |
| 858 | Further sound and music experimentsNeck geometry and Helmholtz resonance Vary neck length or opening area at constant cavity volume. |
3 | 9 | 181112 | 1920 | 0 |
| 859 | Further sound and music experimentsDistance and sound intensity Measure at constant speaker output in a low-reflection environment. |
3 | 9 | 13681112 | 139 | 0 |
| 860 | Further sound and music experimentsRoom dimensions and acoustic modes Measure dominant low-frequency modes in a rectangular room. |
3 | 9 | 13681112 | 169 | 0 |
| 861 | Environment, weather, and microclimateSurface material and heating Compare different surfaces under equal illumination. |
3 | 9 | 161112 | 310111220 | 1 |
| 862 | Environment, weather, and microclimateSoil depth and temperature profile Measure at several soil depths over time. |
3 | 6 | 1361112 | 136111213 | 0 |
| 863 | Environment, weather, and microclimateShade fraction and microtemperature Compare differently shaded model or real locations. |
3 | 6 | 161112 | 3612131720 | 0 |
| 864 | Environment, weather, and microclimateWind speed and evaporation rate Measure mass loss from equal water trays at different air speeds. |
3 | 9 | 161112 | 23121620 | 0 |
| 865 | Environment, weather, and microclimateExposed water area and evaporation Use equal water volumes with different exposed areas. |
3 | 9 | 161112 | 61216 | 0 |
| 866 | Environment, weather, and microclimateRoof colour and model-building temperature Build identical model houses with different roof reflectivity. |
3 | 2 | 1261112 | 31220 | 1 |
| 867 | Environment, weather, and microclimateGreen-roof substrate depth Compare model roofs with different substrate depths. |
3 | 9 | 1361112 | 121220 | 0 |
| 868 | Environment, weather, and microclimateLeaf-litter depth and soil moisture Cover equal soil samples with different litter depths. |
3 | 9 | 161112 | 16121820 | 0 |
| 869 | Environment, weather, and microclimateRain angle and collection accuracy Simulate angled rainfall and compare rain-gauge geometries. |
3 | 6 | 161112 | 112 | 1 |
| 870 | Environment, weather, and microclimateTurbidity and light penetration in water Create reproducible concentrations of safe suspended particles. |
3 | 6 | 13681112 | 10121316 | 0 |
| 871 | Further artificial-intelligence experimentsSampling temperature and response behaviour Test the same fixed task set at different sampling settings. |
3 | 2 | 18101112 | 3 | 0 |
| 872 | Further artificial-intelligence experimentsContext length and information use Place the same relevant information in contexts of different lengths. |
3 | 9 | 181112 | 120 | 0 |
| 873 | Further artificial-intelligence experimentsChunk size in a retrieval-augmented system Split the same documents into differently sized overlapping chunks. |
3 | 9 | 1381112 | 3 | 0 |
| 874 | Further artificial-intelligence experimentsNumber of retrieved passages and answer quality Vary the number of retrieved passages while keeping all else constant. |
3 | 9 | 181112 | 1320 | 0 |
| 875 | Further artificial-intelligence experimentsLabel noise and model performance Replace a controlled fraction of labels with incorrect labels. |
3 | 6 | 181112 | 312132021 | 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.