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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 5 of 36.
Topics 101 to 125 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 |
|---|---|---|---|---|---|---|
| 101 | Data science & introductory algorithmsAnalysing sentiment trends on social media over time Turn “Analysing sentiment trends on social media over time” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 6 | 1 | 6 | 0 |
| 102 | Robotics, control & sensingInverse kinematics of a two-link robot arm Turn “Inverse kinematics of a two-link robot arm” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 271011 | 11320 | 1 |
| 103 | Chaos & dynamical systemsSensitivity to initial conditions and the butterfly effect Turn “Sensitivity to initial conditions and the butterfly effect” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 2 | 17 | 13 | 0 |
| 104 | Image processing & computer graphicsComparing median and Gaussian filters under different image noise Turn “Comparing median and Gaussian filters under different image noise” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 9 | 2712 | 713 | 0 |
| 105 | Music, acoustics & wavesModelling dissonance with interval-frequency ratios Turn “Modelling dissonance with interval-frequency ratios” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 1811 | 913 | 0 |
| 106 | Language & text mathematicsComparing readability formulas and sentence-length distributions Develop “Comparing readability formulas and sentence-length distributions” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
1 | 6 | 8912 | 13 | 0 |
| 107 | Art, design & architectureMathematical analysis of Escher tessellations and symmetry groups Turn “Mathematical analysis of Escher tessellations and symmetry groups” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 148 | 0 | 0 |
| 108 | Education & learning analyticsModelling learning curves in typing or mental arithmetic practice Turn “Modelling learning curves in typing or mental arithmetic practice” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 141112 | 613 | 3 |
| 109 | Astronomy & spaceflightLight curves of variable stars Turn “Light curves of variable stars” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 6 | 1 | 1017 | 0 |
| 110 | Economic models & marketsStability of the cobweb model under delayed supply response Turn “Stability of the cobweb model under delayed supply response” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 71011 | 13 | 0 |
| 111 | Psychology & cognitionAnalysing mathematical patterns in sleep and REM cycles Turn “Analysing mathematical patterns in sleep and REM cycles” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 6 | 1 | 6 | 3 |
| 112 | Time series & forecastingSensitivity of different forecast-error metrics Turn “Sensitivity of different forecast-error metrics” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 9 | 71012 | 13 | 0 |
| 113 | Probability & riskModelling the failure probability of technical devices Turn “Modelling the failure probability of technical devices” into a focused research question and select a transparent dataset or your own measurements. Compare suitable models, examine residuals, and evaluate uncertainty, outliers, and limitations. |
3 | 6 | 11112 | 13 | 0 |
| 114 | Geospatial & cartographic mathematicsGPS error in dense urban areas and open spaces Turn “GPS error in dense urban areas and open spaces” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 1612 | 813 | 0 |
| 115 | Culinary mathematicsThe geometry of pasta shapes and their cooking times Turn “The geometry of pasta shapes and their cooking times” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 3 | 15 | 6 | 0 |
| 116 | Engineering design & optimisationModelling heat-sink fin shape for heat transfer Turn “Modelling heat-sink fin shape for heat transfer” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 271112 | 34132021 | 2 |
| 117 | ThermodynamicsHeating surfaces of different colours in sunlight: black, white, red and silver Turn “Heating surfaces of different colours in sunlight: black, white, red and silver” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 9 | 1 | 341 | 0 |
| 118 | Epidemiology & public healthOptimal pool size in pooled diagnostic testing Turn “Optimal pool size in pooled diagnostic testing” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
2 | 8 | 791011 | 13 | 0 |
| 119 | Material propertiesWater content of fruits and vegetables measured by oven drying Turn “Water content of fruits and vegetables measured by oven drying” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 6 | 15 | 2 | 1 |
| 120 | Sports analytics & tacticsPassing-network centrality and match outcome Turn “Passing-network centrality and match outcome” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
3 | 9 | 37912 | 713 | 0 |
| 121 | ElectricityInternal resistance of alkaline, NiMH and lithium batteries Turn “Internal resistance of alkaline, NiMH and lithium batteries” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 2 | 112 | 513 | 1 |
| 122 | Recreational games & mathematicsClue density and uniqueness in Sudoku puzzles Develop “Clue density and uniqueness in Sudoku puzzles” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
3 | 9 | 781011 | 13 | 0 |
| 123 | Combined experimentsSpecific heat capacity of different liquids under equal energy input Turn “Specific heat capacity of different liquids under equal energy input” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 3 | 1 | 23 | 0 |
| 124 | Combinatorics & discrete probabilityOccupancy problems in random seating arrangements Develop “Occupancy problems in random seating arrangements” through original examples, derivations, or a small computational exploration. State a precise conjecture, test it systematically, and compare alternative proof or modelling approaches. |
3 | 9 | 4710 | 13 | 0 |
| 125 | Kitchen & everyday lifeIce-cream melting rate: mass loss and surface temperature across different formulations Turn “Ice-cream melting rate: mass loss and surface temperature across different formulations” into a measurable or mathematically precise research question. Develop an appropriate model, test it with your own data, constructions, or examples, and evaluate assumptions, errors, and possible improvements. |
1 | 6 | 112 | 2413 | 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.