October 21, 2026
IB Math IA Topic Ideas
Short answer: the best IA topic is a question you can state in one sentence, answer with mathematics from your own course, and care about enough to write 12 to 20 pages on. The exploration is 20% of your grade at SL and HL in both AA and AI, marked out of 20 on five criteria, and the IB's guides say plainly that “it is the quality of the mathematical writing that is important, not the length”.
What the five criteria reward
| Criterion | Marks | What scores |
|---|---|---|
| A: Presentation | 4 | Coherent, well organized, concise |
| B: Mathematical communication | 4 | Correct notation, defined terms, graphs and tables that carry meaning |
| C: Personal engagement | 3 | Your own question, data or decisions, not a textbook walk-through |
| D: Reflection | 3 | Checking results, limitations, what you would change |
| E: Use of mathematics | 6 | Mathematics at the level of your course, used correctly and with understanding |
Criterion E is the biggest, and the guides set its bar at your course: the mathematics “should be commensurate with the level of the course”, and going beyond the syllabus is neither expected nor penalized. A topic that needs mathematics you cannot explain scores worse than a simpler one you own.
Topic ideas by syllabus area
Starting points, not titles. Each one still needs your own data, measurements or decision to become a question.
- Calculus: How fast does a drink cool? Measure it, fit an exponential model, and test Newton's law of cooling against your data.
- Calculus: Is a real drink can the cheapest shape? Minimise surface area for its volume and compare with the can on your desk.
- Calculus: Find the volume of a vase or bottle by fitting a curve to its profile and revolving it.
- Statistics: Does the home team really win more? Test a season of scores against what chance predicts.
- Statistics: Sleep and test marks in your year group: a survey, a regression line, and an honest look at what it cannot show.
- Probability: How likely is a losing streak in a game you play? Model it, then simulate it.
- Functions: Model a bouncing ball: a geometric sequence for the heights and a quadratic for each arc.
- Functions: Fit a logistic curve to a growth you can measure: a plant, a video's views, a school's enrolment.
- Geometry and trigonometry: Which cinema seat has the best view of the screen? Angles, trig and a maximum.
- Geometry and trigonometry: At what tilt should a solar panel sit in your city? Periodic functions for the sun's path.
- Sequences and series: Two ways to repay the same loan: compare the schedules with geometric series.
- Sequences and series: Does the golden ratio appear in a design you can measure? Fibonacci ratios, and at AA, a proof of the limit.
From topic to question
- Narrow it until the aim fits in one sentence with a measurable answer: not “the maths of music” but “which tuning makes a major third closest to a 5:4 ratio?”
- Pick the mathematics before the data. Name the syllabus sections you will use and check they can actually answer the question.
- Collect something yourself: a measurement, a survey, a decision between two options. That is where personal engagement comes from.
- Outline the sections against the criteria: aim, method, mathematics, results, reflection, bibliography.
- Reflect as you go. Every result gets a sentence on what it means and what limits it, not a paragraph bolted on at the end.
What weak explorations share
A history of a topic with no question. Mathematics copied from a source and not explained. Software doing the work with no sign the student understands the output. Thirty pages. A topic so broad the aim never gets answered. Each one loses marks on a specific criterion above, which is why the outline step matters.
Starting the DP in 2027 or later?
The IB's new briefs, first assessed in 2029, keep the exploration at 20% and 30 hours but regroup the criteria into problem specification (4), abstraction (6), computation (4) and interpretation (6). Same shape as the steps above: a specified question, a mathematical model, correct work, and an interpreted answer.
IB Math IA FAQ
How long should a math IA be?+
The guides say approximately 12 to 20 pages, double spaced, including diagrams and graphs but not the bibliography, and that the quality of the mathematical writing matters, not the length.
Can my teacher help with my IA?+
Yes. The guides say teachers and students must discuss the exploration, that students must not be penalized for seeking guidance, and that the teacher reads and advises on one draft.
Do I need mathematics beyond the syllabus to score well?+
No. The guides say the mathematics should be commensurate with the level of the course, and that work outside the syllabus is not expected and not penalized.
What happens if I do not submit one?+
You receive no grade for the course. The guides state it in bold, and the exploration is 20% at both SL and HL.
Sources, read October 20, 2026: Mathematics: analysis and approaches guide; Mathematics: applications and interpretation guide; Subject brief: analysis and approaches, first assessment 2029; Subject brief: applications and interpretation, first assessment 2029.
Keep the exam side moving too
The IA is 20%; the papers are 80%. Martian Lab's Grade 12 IB Math course has practice tests for calculus, statistics and probability, every question with a worked solution. The first test in each unit is free.
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