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Define the object, dataset, time period, variable or mathematical structure as precisely as possible.
IB Mathematics · Complete topic list
900 topic ideas – page 32 of 36.
Topics 776 to 800 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 |
|---|---|---|---|---|---|---|
| 776 | Light, optics, and image formationAperture and depth of field Photograph an angled scale using different apertures. |
3 | 6 | 121112 | 1710111320 | 0 |
| 777 | Light, optics, and image formationSlit width and diffraction pattern Illuminate single slits of different widths using suitable school equipment. |
3 | 9 | 141112 | 7102021 | 2 |
| 778 | Light, optics, and image formationGrating spacing and diffraction angle Compare diffraction gratings with different line densities. |
3 | 9 | 161112 | 1710 | 0 |
| 779 | Light, optics, and image formationDye concentration and light transmission Measure transmission through safe dye solutions. |
3 | 6 | 131112 | 710131620 | 0 |
| 780 | Light, optics, and image formationOptical-fibre bend radius and light loss Bend a plastic optical fibre to defined radii. |
3 | 9 | 181112 | 12371020 | 0 |
| 781 | Solar and renewable energySolar-panel tilt angle Measure a small panel at different tilt angles. |
3 | 9 | 131112 | 1351020 | 0 |
| 782 | Solar and renewable energyAzimuth angle and solar output Rotate the panel horizontally relative to the light source. |
3 | 9 | 11112 | 13510 | 0 |
| 783 | Solar and renewable energyPanel temperature and electrical power Measure panel voltage and output over a moderate temperature range. |
3 | 6 | 11112 | 351013 | 1 |
| 784 | Solar and renewable energyShaded fraction and solar output Cover defined fractions of a small solar panel. |
3 | 9 | 11112 | 3510 | 0 |
| 785 | Solar and renewable energyShading position and output Shade different cell regions while keeping shaded area constant. |
3 | 6 | 11112 | 35101320 | 0 |
| 786 | Solar and renewable energyDust coverage and solar yield Apply reproducible dust coverage to a protective film above the panel. |
3 | 6 | 11112 | 51013 | 0 |
| 787 | Solar and renewable energyReflector geometry and focal concentration Compare small reflector geometries under low-power illumination. |
3 | 6 | 11112 | 351016 | 0 |
| 788 | Solar and renewable energyReflector angle in a model solar cooker Vary reflector angles around a small model container. |
3 | 9 | 131112 | 1351020 | 1 |
| 789 | Solar and renewable energyTemperature difference and thermoelectric voltage Measure voltage at different temperature differences. |
3 | 6 | 131112 | 351013 | 1 |
| 790 | Solar and renewable energyBlade pitch of a small wind turbine Test model rotors at different blade pitches. |
3 | 9 | 131112 | 135101220 | 0 |
| 791 | Reaction rates, diffusion, and solutionsTemperature and effervescent-tablet dissolution Measure the full mass or volume trajectory rather than only total time. |
3 | 9 | 1381112 | 23671216 | 0 |
| 792 | Reaction rates, diffusion, and solutionsTablet surface area and reaction rate Compare whole, divided, and crushed tablets of equal mass. |
3 | 9 | 131112 | 2121620 | 1 |
| 793 | Reaction rates, diffusion, and solutionsInitial concentration and reaction order Use a safe school reaction measurable by colour or conductivity. |
3 | 9 | 141112 | 111216 | 1 |
| 794 | Reaction rates, diffusion, and solutionsCatalyst amount and oxygen production Use dilute peroxide with a suitable catalase source under school supervision. |
3 | 9 | 13461112 | 12162021 | 2 |
| 795 | Reaction rates, diffusion, and solutionsConcentration and titration-curve shape Record the complete pH curve of a safe acid–base titration. |
3 | 9 | 131112 | 11121621 | 2 |
| 796 | Reaction rates, diffusion, and solutionsTemperature and diffusion coefficient in agar Measure dye-front radius in agar at different temperatures. |
3 | 9 | 11112 | 131216 | 0 |
| 797 | Reaction rates, diffusion, and solutionsSupersaturation and crystal growth Photograph safe crystals at different initial concentrations. |
3 | 9 | 12101112 | 1711121620 | 1 |
| 798 | Reaction rates, diffusion, and solutionsTemperature and solubility Determine maximum solubility at several temperatures. |
3 | 9 | 11112 | 3121620 | 0 |
| 799 | Reaction rates, diffusion, and solutionsSalt concentration and conductivity Create a calibration series extending into the nonlinear range. |
3 | 6 | 11112 | 1112131620 | 0 |
| 800 | Reaction rates, diffusion, and solutionsIllumination time and dye degradation Expose safe dye solutions to standardized light. |
3 | 6 | 131112 | 610121316 | 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.