IA & EE guides
The IB Maths IA (exploration), step by step
The Maths IA is a written exploration of a piece of mathematics you choose. It is worth 20% of your final grade in both Analysis and Approaches and Applications and Interpretation, at SL and HL. This guide covers what is marked, how to choose a topic that can score well, and how to structure it.
- 20% of your grade
- 12 to 20 pages
- 20 marks
- AA and AI, SL and HL
More in this guide
40 topic ideas
40 original ideas with starting questions, by area.
Criteria explained
The five criteria in plain words, with slips and a checklist for each.
Annotated outlines
Four original outlines showing where each criterion is earned.
The five criteria, in plain words
Our summaries of what each criterion rewards. These apply to students on the current courses (exams up to November 2028). New maths courses from 2029 will use different criteria.
| Criterion | Marks | What it rewards, in plain words |
|---|---|---|
| A. Presentation | 4 | A clear aim, a logical order and a conclusion, so a reader can follow it without help. |
| B. Mathematical communication | 4 | Correct notation, defined variables, labelled graphs and tables, and maths written the way mathematicians write it. |
| C. Personal engagement | 3 | Evidence that you made the choices: your own question, your own data or examples, your own way through the problem. |
| D. Reflection | 3 | Thinking about your results as you go: what they mean, what limits them, what you would change. |
| E. Use of mathematics | 6 | Maths at the right level for your course, used correctly and understood. At HL this means HL-level maths; the criterion carries the most marks. |
Choosing a topic that can score well
- Start with a question, not a topic"Which shape of paper cup holds the most for the least card?" leads somewhere. "Calculus" does not.
- Check the maths reaches your levelCriterion E carries 6 of the 20 marks. If the maths ends at a formula from Year 10, the topic is too thin.
- Make it yoursData you collect, a situation from your life, or a variation nobody gave you. That is what criterion C rewards.
- Keep it finishable12 to 20 pages goes quickly. One good question answered well beats three questions started.
Ideas to start from
Starting points only. Each one needs your own question and your own data.
- Modelling cooling: how fast a drink cools in different cups, fitted with an exponential model (AA and AI).
- Best-fit packaging: the cylinder or cone that uses the least material for a fixed volume (calculus, AA).
- Queues and waiting times: modelling a real queue you can observe with a probability distribution (AI).
- Sports data: testing whether a player's form is streaky or random with a statistical test (AI).
- Shapes in design: using parametric curves or complex numbers to describe a logo or a building outline (AA HL).
- Population or growth: comparing logistic and exponential models against published data (AA and AI).
A sample outline
- Introduction and aimWhat you are investigating, why it interests you, and what you will do.
- Background mathsOnly the maths you need, explained in your own words.
- ExplorationThe main work: data, models, calculations and graphs, with reflection as you go.
- Conclusion and evaluationThe answer to your aim, its limits, and what you would extend.
Common mistakes that cost marks
- Maths below the level of the course, which caps criterion E.
- Copying a textbook derivation instead of applying the idea to your own problem.
- Calculator output pasted in without explanation or units.
- Reflection only at the end, when criterion D rewards it throughout.
- Variables not defined and graphs without labels (criterion B).
Our promise
We teach. We never write it for you.
This guide explains how the work is assessed and how to plan it. We never write, edit or rewrite any part of a student's IA or EE, and nor should anyone else: the IB treats work produced or heavily edited by someone else (a person or an AI tool) as not your own. If you use an AI tool for ideas or checking, say so and cite it, as your school will ask.
Learn the maths properly
The Photon Guidebooks
Every topic you might use in an IA, taught from the basics, with worked examples and practice.
Maths AA HL · AA SL · AI HL · AI SL
Draft Coach feedback on IA drafts is coming in 2027.
Written by Ejaz Ahmad, IB teacher since 2015. Checked against the IB's published guide, October 2026. Photon Resources is independent of the IB.