IB DP Maths AA · Exam special · AA and AI · SL & HL · from the 2024–25 subject reports · ~8 min read
IB Maths IA Guide: How to Score Highly on the Exploration (AA & AI)
A practical guide to the IB Maths exploration for AA and AI, SL and HL: what each criterion rewards, how to choose a topic with enough mathematics, a structure that works and the mistakes moderators flagged in the 2024–25 reports.
How the IA is markedCriterion A–EChoosing a topicTopic ideasStructureNotation & technologyAI use & citingCommon mistakes
RSby Riyaz Sir
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mentorriyaz.in
No tag = SL and HLHL ONLY HL students onlyFORMULA BOOKLET given in the examM1A1 how marks are awardedhighlight = comes up again and againHANDY worth memorisingTest yourself at the end
In 30 seconds
- The exploration is 20% of your final grade at both SL and HL, in AA and AI. It is marked out of 20 by your teacher and then moderated by the IB.
- Moderators said the same things in almost every 2024–25 report: reflection is the weakest criterion, personal engagement is often over-rewarded, and "complex" mathematics that the student doesn't understand scores lower than appropriate mathematics explained well.
- A typical length is 12 to 20 pages, double-spaced. Concise and focused beats long.
By the end you can
- Understand exactly what each of the five criteria rewards.
- Choose a topic that gives you enough mathematics to reach the top bands.
- Avoid the mistakes moderators see most often.
1How the exploration is marked
| Criterion | What it rewards | Marks |
|---|---|---|
| A · Presentation | Organised, coherent and concise: a clear aim, a logical flow, a conclusion | 4 |
| B · Mathematical communication | Correct notation, symbols and terms; labelled graphs and tables; defined variables | 4 |
| C · Personal engagement | Your own thinking driving the work: your questions, choices and insights | 3 |
| D · Reflection | Critical comments on your methods and results, throughout, not only at the end | 3 |
| E · Use of mathematics | Relevant mathematics at the level of your course, correct and understood | 6 |
- Criterion E is assessed at the level of your course. The HL descriptor expects more sophistication and rigour than the SL one.
- Total: 20 marks. In November 2024 and May 2025 a 7 needed 17/20 at HL and 18/20 at SL; see the AA grade boundaries.
Exam tipFirst assessment 2029: the new Maths guides keep the exploration at 20 marks but reorganise the assessment into four criteria. If you start the course for 2029 or later, check the new criteria with your teacher; the advice on this page about depth, reflection and communication still applies.
2What moderators said, criterion by criterion
A · Presentation
- State one clear aim early, and keep the whole exploration focused on it. Explorations with a broad or vague aim lost the "coherent" mark.
- Cut repetition. Many explorations were too long because they repeated method steps or background.
- Proofread the layout: graphs or tables split across pages and headings stranded at the bottom of a page were flagged as careless.
B · Mathematical communication
- No calculator notation. Write x², 3 × 10⁴ and √x with an equation editor, not x^2, 3E4 or sqrt(x).
- Define every variable where it first appears, with its units.
- Graphs: readable text, labelled axes with units, and a title or caption. Faint screenshots from software lost marks.
- Approximations: use ≈ whenever you round, and keep a consistent accuracy (state it).
- Tables: large tables go in an appendix; a table in the text fits on one page.
C · Personal engagement
- Saying why you like the topic is not engagement. Moderators gave most explorations 1 or 2 out of 3 because the "personal" part was only the introduction.
- What does count: asking your own questions, collecting or creating your own data, trying an approach that didn't work and explaining why, extending the problem, making decisions and justifying them.
- Show it throughout, in your own voice ("I decided to…", "this surprised me because…").
D · Reflection
- The weakest criterion in nearly every report. Most students summarised results in the conclusion and called it reflection.
- Critical reflection asks: Is the result reasonable? What are the limitations of the method or model? What assumptions did I make, and how much do they matter? What would happen if I changed a parameter? How could the method be extended?
- Put a short reflective comment after each major step, not only at the end.
E · Use of mathematics
- Appropriate, not complex. Using mathematics you don't fully understand (often physics-style differential equations or matrices beyond the course) led to procedural work with little insight and lower marks.
- Explain why you chose each technique. Understanding is shown by the choice, not only by carrying it out.
- SL content can score at HL, but work that never goes beyond SL level usually can't reach the top band at HL.
- Statistics explorations often stopped at R² or a single test. Justify the model, check its conditions and interpret the result in context.
3Choosing a topic
- Start from a question, not a topic. "How many shuffles randomise a deck of cards?" is a question; "card shuffling" is a topic.
- Check the mathematics before you commit. Write down 3–4 techniques you will use. If they're all from the first year of the course, the topic is probably too thin.
- Personal but mathematical. Data you collect yourself can help Criterion C, but the mathematics must be the focus.
Topic ideas with real depth
| Question | Mathematics | Course |
|---|---|---|
| What is the best angle to shoot a basketball from the free-throw line? | Projectile models, optimisation, derivatives | AA |
| How does a spirograph pattern depend on its gear sizes? | Parametric equations, LCM, periodicity | AA HL |
| Can I model the shape of a hanging chain, and is it a parabola? | Curve fitting, catenary vs quadratic, least squares | AA/AI |
| How long until a rumour reaches everyone in my school? | Logistic model, differential equations, fitting data | AI HL |
| Where should a new metro station go to serve the most people? | Voronoi diagrams, distances, optimisation | AI |
| Do penalty-shootout results depend on kicking first? | χ² test, binomial model, conditions | AI |
| What is the volume of a vase or wine glass? | Volumes of revolution, curve fitting, error analysis | AA/AI HL |
| How fast does a cup of chai cool, and is Newton's law accurate? | Exponential models, linearising, residuals | AA/AI |
Common mistakeTopics moderators see too often: linear regression of two sports statistics, a TSP and Voronoi "template" exploration, the golden ratio described from websites. They can work, but only with your own data, questions and analysis.
4A structure that works
- Introduction: your aim (one sentence), why it matters to you, and a short plan.
- Development: sections in a logical order; each one says what you're doing and why, shows the mathematics, and ends with a short reflection.
- Conclusion: answer the aim directly, then limitations and possible extensions.
- Bibliography and appendices: sources cited properly; large tables and code in the appendix.
5Technology and AI tools
- Software is welcome: GeoGebra, Desmos, spreadsheets and Python can all help, but the exploration must not read like a computer-science project. Explain the mathematics behind what the software does.
- Generative AI must be used within the IB's academic integrity rules and cited. Moderators noted explorations that lost the student's own voice; work you can't explain doesn't help Criterion E.
- Screenshots add little unless you explain what they show.
6Final checklist
- One clear aim, answered in the conclusion.
- Every variable defined; no calculator notation; ≈ used for rounded values.
- Reflection after each major step, plus limitations at the end.
- Each technique justified ("I used… because…").
- Graphs readable, labelled, and not split across pages.
- Sources and any AI use cited.
Linking questionFor the mathematics behind many of these ideas see Integration and kinematics, Differential equations and Maclaurin series and Chi-squared and t-tests.
Test yourself — cover the answers first
Quick check
- How many marks is the Maths exploration out of?
- Which criterion is weakest in most explorations?
- Is saying why you chose a topic enough for personal engagement?
- Should you use the most advanced mathematics you can find?
- Where should a large data table go?
Show answers
- 20
- D, reflection
- no; it must show in your own thinking throughout
- no; use appropriate mathematics you understand and can explain
- in an appendix
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