IB Maths IA | 50 Topic Ideas and How the Exploration Criteria Are Marked

The IB Mathematics internal assessment is a mathematical exploration written by the student. A useful topic is not simply interesting; it must generate enough Mathematics for the student to formulate a question, make assumptions, calculate or reason, interpret results and reflect on limitations.

This guide provides topic prompts, not ready-made investigations. Students should create their own research question, obtain or generate their own data where appropriate, make their own modelling decisions and write their own analysis. A tutor can teach the Mathematics and critique reasoning; the assessed exploration must remain the student’s work.

Current IA criteria through the November 2028 course

• A: Presentation
• B: Mathematical communication
• C: Personal engagement
• D: Reflection
• E: Use of mathematics

The exploration is worth 20% of the current course grade and is internally assessed then externally moderated.

New IA criteria for first assessment May 2029

Criterion	Marks	Main idea
A: Problem specification	4	Context and desired outcomes
B: Abstraction	6	Assumptions, tools, techniques and mathematical form
C: Computation	4	Calculations and mathematical communication
D: Interpretation	6	Results, evaluation and refinement

50 IA starting ideas

1. Model the cooling of a hot drink under different containers.
2. Compare queue waiting-time models at two service points.
3. Investigate optimal launch angle when air-resistance assumptions are changed.
4. Model smartphone battery discharge with exponential or piecewise functions.
5. Investigate the relationship between stride length and running speed.
6. Model daylight hours across latitude using trigonometric functions.
7. Compare different interpolation methods for missing environmental data.
8. Investigate compound-interest outcomes under different contribution schedules.
9. Model mortgage repayment sensitivity to interest-rate changes.
10. Compare flat-rate and effective-rate borrowing mathematically.
11. Optimise packaging dimensions under fixed-volume constraints.
12. Investigate surface-area-to-volume ratios in biological structures.
13. Model sound intensity or decibel change with logarithms.
14. Study musical tuning systems through frequency ratios.
15. Analyse rhythm patterns with modular arithmetic.
16. Investigate symmetry groups in a tiling or design.
17. Model traffic flow through a simple network.
18. Use graph theory to compare route efficiency on a local transport map.
19. Investigate shortest-path algorithms on a small real network.
20. Model spread of information using a simple recurrence or differential equation.
21. Investigate logistic versus exponential population models.
22. Compare numerical methods for solving a nonlinear equation.
23. Investigate error in trapezium versus Simpson-style numerical integration.
24. Model a bouncing ball using geometric sequences.
25. Investigate projectile data collected from video frames.
26. Analyse the geometry of camera perspective.
27. Model shadow length through trigonometry.
28. Investigate correlation between two measurable sports variables.
29. Compare linear and nonlinear regression on a real data set.
30. Investigate whether a normal model fits a chosen measurement.
31. Compare binomial and normal approximations for repeated trials.
32. Investigate sampling variability using repeated random samples.
33. Simulate the central limit effect with different parent distributions.
34. Investigate false-positive rates and conditional probability in screening.
35. Model reliability of a simple system using probability.
36. Analyse expected value in a non-gambling decision problem.
37. Investigate fair division methods.
38. Compare voting/apportionment methods mathematically without advocating a political choice.
39. Investigate geometric constructions in architecture.
40. Model a spiral found in a designed or natural object.
41. Investigate fractal dimension in a simple image or coastline-like boundary.
42. Analyse recurrence in a savings or inventory system.
43. Investigate Markov-chain behaviour in a small state-transition model.
44. Model disease spread with a simplified compartment model while clearly stating limitations.
45. Investigate dose decay or half-life mathematically using public non-personal data.
46. Analyse an image-compression idea with matrices.
47. Investigate transformations used in computer graphics.
48. Model a simple portfolio’s expected return and variance using public historical data.
49. Compare numerical optimisation methods on a simple objective function.
50. Create and analyse a personally meaningful mathematical model whose assumptions can be tested and refined.

A five-test topic filter

1. Can you state a precise mathematical question?
2. Is the Mathematics appropriate to your course level?
3. Can you make genuine modelling or analytical decisions?
4. Can you evaluate assumptions and limitations?
5. Can you obtain enough evidence without copying another student’s exploration?

Avoid these weak IA patterns

• A textbook derivation with no personal mathematical decisions.
• A huge data set with only basic descriptive statistics.
• A topic so advanced that the student cannot explain the Mathematics independently.
• A copied online “high-scoring IA” structure.
• A beautiful graph with no mathematical interpretation.

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Official sources checked 26 September 2026: current IB Mathematics guides/examiner instructions and the new 2029 AA/AI subject briefs.

World Mathematics route: return to the World Mathematics Atlas for the wider map across examinations, curricula, competitions, mathematical objects and university routes.