IB Maths IA Topic Ideas That Actually Score Well

Almost every guide to IB maths IA topic ideas is a list of two hundred titles with no explanation of why any of them would score well. That is the opposite of what the assessment rewards. The IA is marked against five criteria, only one of which is about mathematics, and a well-chosen ordinary topic beats an ambitious one every single time.

This guide explains what the criteria actually reward, gives topics that are shaped to score, and names the specific mistakes that cost marks in Criterion C and E — the two where most students quietly lose four or five marks before they have written a word.

What the IA is marked on

The exploration is 20 marks, worth 20 per cent of the final grade in both Analysis and Approaches and Applications and Interpretation, at both HL and SL. The five criteria are:

• A — Presentation (4 marks). Is it organised, coherent and readable? Does it have a clear aim stated early and followed through?
• B — Mathematical communication (4 marks). Correct notation, defined variables, sensible use of graphs and tables. Not the same as writing style.
• C — Personal engagement (3 marks). Evidence of independent thinking, not enthusiasm in the introduction.
• D — Reflection (3 marks). Meaningful, ongoing, and critical — not a paragraph at the end saying what you learned.
• E — Use of mathematics (6 marks). The largest single band. Must be commensurate with the level of the course.

Read that list again and notice what it does not say. It does not reward difficulty for its own sake. A correct, well-explored piece of mathematics at the right level scores far better than an advanced technique used incorrectly or without understanding.

The mistake that decides most IA grades

The single most common failure is choosing a topic that is genuinely interesting but leaves nothing to explore. A student writes about the mathematics of a rollercoaster, describes a curve, calculates a gradient, and stops. Criterion E rewards mathematics that is developed, and there is nothing to develop.

The fix is a structural test you can apply before committing. A topic works if you can answer yes to all three:

• Is there a question, not just a subject? "Modelling the spread of a rumour in my year group" is a question. "The mathematics of epidemics" is a subject.
• Can you do something with the result? Compare two models, test a prediction against data, vary a parameter and explain what changes.
• Is the mathematics at your course level? HL Analysis needs calculus, series or complex work. SL Applications needs statistics and modelling done properly, not calculus done badly.

Topic ideas that are shaped to score

These are grouped by course, because the same title can be excellent in one and hopeless in another. Unlike most lists of IB maths IA topic ideas, each one below already contains the thing to explore.

Analysis and Approaches HL

• Modelling a damped oscillation from a video of a real pendulum, and testing whether the exponential decay constant matches theory
• Comparing Newton-Raphson and the bisection method on a function where one fails, and explaining why
• Deriving the volume of an irregular object by rotating a fitted polynomial, then checking against water displacement
• Using Taylor series to approximate a function, and quantifying how the error grows with distance from the centre
• Optimising the shape of a container under a real material constraint, then testing the result against actual packaging

Analysis and Approaches SL

• Fitting a trigonometric model to daylight-hours data for two cities at different latitudes and explaining the difference in amplitude
• Modelling the cooling of a drink and testing whether Newton's law of cooling holds for your data
• Comparing linear and exponential models for a quantity that grows, and justifying which fits better using residuals
• Using calculus to find the optimal angle for a ramp, then measuring whether reality agrees

Applications and Interpretation HL

• Building a Markov chain for a repeated game and finding its steady state, then simulating to check
• Using a chi-squared test on data you collected yourself, with an honest discussion of sampling bias
• Modelling a queue with exponential arrivals and testing the prediction against timings you record
• Graph-theoretic analysis of a real transport network, including a shortest-path algorithm applied by hand

Applications and Interpretation SL

• Testing whether two variables in a dataset you gathered are genuinely correlated, and what that does and does not imply
• Using regression to predict something checkable, then reporting how wrong the prediction turned out to be
• Modelling depreciation of a real asset with two different models and comparing them against the actual figures

Criterion C: what personal engagement actually means

Students lose marks here more than anywhere else because they interpret engagement as enthusiasm. Writing "I have always loved football" earns nothing. Engagement is evidenced by what you did, not what you felt.

What scores: collecting your own data rather than downloading a set. Adapting a standard method because your situation did not fit it. Testing something the textbook does not test. Making a choice and justifying it with a reason specific to your investigation.

What does not score: an emotional introduction, a personal anecdote unconnected to the mathematics, or a topic chosen because it sounds impressive.

Criterion D: reflection has to be ongoing

Three marks are available and most students collect one, because they treat reflection as a concluding paragraph. The criterion asks for reflection that is meaningful and ongoing — appearing wherever a decision is made.

In practice that means writing a sentence at each junction explaining why you went one way: why you discarded a model, why you kept an outlier, what a residual pattern told you, what the limitation of your data means for the conclusion. A limitations section that names real limitations, and says what they change, is worth more than a page of summary.

A four-week schedule

Week 1 — choose and test. Pick three candidate topics and apply the three-part test above to each. Discard any that fail. Write a one-paragraph aim for the survivor. Show it to your teacher before going further; a topic problem found now costs an hour, found later it costs the grade.

Week 2 — gather and explore. Collect your data or set up your model. Do the core mathematics. Write down every decision as you make it — this is the raw material for Criterion D, and reconstructing it afterwards never reads as genuine.

Week 3 — develop. This is where Criterion E marks live. Extend the work: a second method, a comparison, a sensitivity check, a validation against reality. A first draft that stops at the first result will land in the middle band.

Week 4 — write and cut. Aim for 12 to 20 pages. Fix notation systematically, label every graph, define every variable at first use. Then read only for Criteria A and B — they are four marks each and are the cheapest marks in the whole assessment to secure.

Where students building an IA usually need help

Two points cause the most trouble: choosing a topic that will still be alive in week three, and pushing the mathematics far enough for the top band of Criterion E without overreaching into something you cannot justify. Both are judgement calls, and both are much easier with someone who has marked these before.

Our IB Maths AA HL guide covers the syllabus and paper structure the IA sits alongside, and our course pages list the IB tracks we teach. Students who are also sitting olympiad papers often use our timed practice papers to keep the pure-mathematics side sharp while the IA is running.

The short version

Choose a question rather than a subject, at your course's mathematical level, that leaves something to develop. Record your decisions as you make them, because that is what Criteria C and D are actually asking for. Then spend the last week on presentation and notation, where eight of the twenty marks sit and almost nobody looks twice.