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 28 of 36.
Topics 676 to 700 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 |
|---|---|---|---|---|---|---|
| 676 | Surface tension, capillarity, and dropletsInitial radius and evaporation time Photograph droplets of different initial sizes during evaporation. |
3 | 2 | 121112 | 15671113 | 1 |
| 677 | Surface tension, capillarity, and dropletsAir speed and droplet evaporation Expose identical droplets to different controlled air speeds. |
3 | 6 | 11112 | 512161820 | 0 |
| 678 | Surface tension, capillarity, and dropletsWetted perimeter and surface load capacity Place lightweight wire or foil shapes with different perimeters on water. |
3 | 9 | 161112 | 25101620 | 1 |
| 679 | Surface tension, capillarity, and dropletsFrame geometry and minimum soap-film area Create soap films between wire frames of different geometries. |
3 | 9 | 1231112 | 571316 | 0 |
| 680 | Surface tension, capillarity, and dropletsGlycerol fraction and soap-bubble lifetime Vary glycerol concentration and measure the lifetime of many bubbles. |
3 | 9 | 11112 | 561620 | 0 |
| 681 | Water waves, resonance, and hydraulic transitionsFrequency and wavelength of water waves Generate waves of different frequencies at constant water depth. |
3 | 6 | 161112 | 1611121316 | 0 |
| 682 | Water waves, resonance, and hydraulic transitionsGap width and diffraction angle Pass water waves through gaps of different widths. |
3 | 9 | 1361112 | 11620 | 0 |
| 683 | Water waves, resonance, and hydraulic transitionsSource separation and interference pattern Generate two equal-frequency wave sources with variable separation. |
3 | 9 | 1361112 | 161620 | 0 |
| 684 | Water waves, resonance, and hydraulic transitionsFluid viscosity and wave damping Compare wave-amplitude decay in water–glycerol mixtures. |
3 | 9 | 161112 | 1316 | 0 |
| 685 | Water waves, resonance, and hydraulic transitionsContainer length and sloshing resonance Determine the sloshing resonance frequency in containers of different lengths. |
3 | 2 | 161112 | 136131620 | 0 |
| 686 | Water waves, resonance, and hydraulic transitionsFill level and sloshing modes Vary fill level and identify several resonance frequencies. |
3 | 9 | 1361112 | 361620 | 0 |
| 687 | Water waves, resonance, and hydraulic transitionsInitial water height and dam-break front Release water behind a small barrier and film the advancing front. |
3 | 9 | 1361112 | 161620 | 1 |
| 688 | Water waves, resonance, and hydraulic transitionsDischarge and hydraulic jump Create a hydraulic jump and measure its position and depth ratio. |
3 | 9 | 1361112 | 11620 | 0 |
| 689 | Water waves, resonance, and hydraulic transitionsShore slope and wave run-up Build model beaches with different slopes and measure maximum wave run-up. |
3 | 9 | 12361112 | 1131620 | 0 |
| 690 | Water waves, resonance, and hydraulic transitionsBreakwater porosity and wave transmission Compare model breakwaters with different gap fractions. |
3 | 9 | 1361112 | 131620 | 0 |
| 691 | Further ice, snow, and freezing experimentsSugar concentration and freezing point Measure the onset of freezing for solutions with different sugar concentrations. |
3 | 9 | 11112 | 31620 | 0 |
| 692 | Further ice, snow, and freezing experimentsSolute type and freezing-point depression Compare safe dissolved substances at equal particle concentration. |
3 | 6 | 1381112 | 3131620 | 0 |
| 693 | Further ice, snow, and freezing experimentsSurface roughness and supercooling Cool equal water samples in containers with different internal roughness. |
3 | 6 | 161112 | 316 | 0 |
| 694 | Further ice, snow, and freezing experimentsInsulation thickness and freezing time Wrap identical small water containers with different insulation thicknesses. |
3 | 9 | 161112 | 3561620 | 0 |
| 695 | Further ice, snow, and freezing experimentsContainer shape and freezing time Compare equal-volume containers with different surface-area-to-volume ratios. |
3 | 6 | 131112 | 361320 | 0 |
| 696 | Further ice, snow, and freezing experimentsSurface colour and ice melting Cover ice samples with equal dark and light surfaces under controlled illumination. |
3 | 9 | 11112 | 310 | 0 |
| 697 | Further ice, snow, and freezing experimentsFragment size and melting time Divide equal ice masses into different numbers of similar fragments. |
3 | 6 | 11112 | 23613 | 0 |
| 698 | Further ice, snow, and freezing experimentsSalt pattern and melt-channel formation Apply equal salt quantities in line, point, or grid patterns. |
3 | 9 | 11112 | 1371117 | 0 |
| 699 | Further ice, snow, and freezing experimentsSnow compaction and thermal insulation Compare loose and differently compacted snow or crushed ice. |
3 | 9 | 11112 | 35131720 | 1 |
| 700 | Further ice, snow, and freezing experimentsSnow grain size and melting rate Separate snow or crushed ice into different grain-size classes. |
3 | 9 | 141112 | 312 | 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.