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 30 of 36.
Topics 726 to 750 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 |
|---|---|---|---|---|---|---|
| 726 | Oscillations, coupling, and chaosMass and spring period with spring-mass correction Measure period for different loads and estimate effective spring mass. |
3 | 9 | 161112 | 26 | 0 |
| 727 | Oscillations, coupling, and chaosSpring nonlinearity Investigate a spring or elastic band over a wider safe extension range. |
3 | 9 | 11112 | 215 | 0 |
| 728 | Oscillations, coupling, and chaosWire geometry and torsion pendulum Vary the length or radius of a torsion wire. |
3 | 2 | 11112 | 113 | 0 |
| 729 | Oscillations, coupling, and chaosPlatform mass and metronome synchronization Place metronomes on movable platforms of different mass. |
3 | 2 | 11112 | 2611 | 0 |
| 730 | Oscillations, coupling, and chaosInitial difference and chaotic divergence of a double pendulum Release two nearly identical double pendulums with small initial differences. |
3 | 2 | 1681112 | 11117 | 1 |
| 731 | Friction, rolling, and granular materialsMoment of inertia and ramp acceleration Roll different bodies down the same incline. |
3 | 9 | 11112 | 13 | 0 |
| 732 | Friction, rolling, and granular materialsWheel radius and rolling resistance Pull equally loaded wheels of different radii over the same surface. |
3 | 9 | 131112 | 1251520 | 0 |
| 733 | Friction, rolling, and granular materialsTyre pressure and rolling resistance Measure coast-down distance at different permitted tyre pressures. |
3 | 9 | 131112 | 15820 | 0 |
| 734 | Friction, rolling, and granular materialsNormal force and coefficient of friction Pull the same object with different added masses. |
3 | 2 | 1101112 | 21315 | 0 |
| 735 | Friction, rolling, and granular materialsApparent contact area and friction Pull the same block on different faces. |
3 | 9 | 11112 | 1315 | 0 |
| 736 | Friction, rolling, and granular materialsMeasured roughness and friction Create reproducible roughness levels and define an image-based roughness index. |
3 | 6 | 1231112 | 713 | 0 |
| 737 | Friction, rolling, and granular materialsLubricant viscosity and bearing coast-down time Compare suitable safe lubricants in a small bearing. |
3 | 9 | 131112 | 1361220 | 0 |
| 738 | Friction, rolling, and granular materialsParticle shape and angle of repose Compare spherical, angular, and elongated grains of similar size. |
3 | 6 | 181112 | 11112 | 0 |
| 739 | Friction, rolling, and granular materialsOutlet diameter and granular discharge Discharge sand or rice through openings of different sizes. |
3 | 9 | 181112 | 1320 | 0 |
| 740 | Friction, rolling, and granular materialsSpin rate and precession of a top Measure spin and precession rates of a top over time. |
3 | 6 | 11112 | 36121320 | 0 |
| 741 | Flight, aerodynamic drag, and propellersPaper-helicopter blade length Vary rotor-blade length while keeping total mass constant. |
3 | 9 | 131112 | 12561020 | 1 |
| 742 | Flight, aerodynamic drag, and propellersFold angle of a paper rotor Vary the pitch angle of paper rotor blades. |
3 | 9 | 131112 | 151020 | 1 |
| 743 | Flight, aerodynamic drag, and propellersWing aspect ratio and glide ratio Build paper aircraft with equal wing area but different spans. |
3 | 6 | 121112 | 15101320 | 1 |
| 744 | Flight, aerodynamic drag, and propellersCentre-of-mass position and flight stability Move a small mass along the same paper aircraft. |
3 | 2 | 1101112 | 2571020 | 1 |
| 745 | Flight, aerodynamic drag, and propellersLaunch angle and range with air resistance Use a safe soft projectile and record its trajectory. |
3 | 2 | 11112 | 157101320 | 1 |
| 746 | Flight, aerodynamic drag, and propellersSpin and lateral flight deflection Launch light balls with controlled spin and analyse lateral deflection. |
3 | 9 | 181112 | 57101320 | 1 |
| 747 | Flight, aerodynamic drag, and propellersParachute area and terminal velocity Drop equal-mass model parachutes of different areas. |
3 | 9 | 121112 | 257101220 | 1 |
| 748 | Flight, aerodynamic drag, and propellersVent diameter and parachute stability Vary the central vent diameter in equal-sized parachutes. |
3 | 9 | 131112 | 15610 | 1 |
| 749 | Flight, aerodynamic drag, and propellersPropeller pitch and thrust Test small low-voltage propellers with different blade angles. |
3 | 9 | 131112 | 1351020 | 1 |
| 750 | Flight, aerodynamic drag, and propellersNumber of blades and propeller efficiency Compare similar propellers with different blade counts. |
3 | 6 | 11112 | 3510 | 1 |
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.