IB Maths IA Ideas — Exploration Topics (AA & AI)

If you want the full breakdown of criteria, structure and how the exploration is marked, read the companion IB Maths IA guide first — this article is deliberately about choosing the topic, not writing it up.

The word "exploration" matters: this is not a homework sheet or a copied derivation — it is you investigating a question and reasoning your way through it. For how each criterion is scored and the structure examiners expect, see the full IA guide.

• Personal engagement — a real reason you chose this. A dataset you collected, a game you play, a decision you had to make. Fabricated enthusiasm reads as fabricated.
• Focus — one clear question, not a survey. "How steep can a wheelchair ramp be before it fails building regulations, and what does that mean for my school entrance?" beats "the maths of ramps."
• Right-level maths — challenging for your course but yours to control. AA leans to calculus, algebra and proof; AI leans to statistics, modelling and real data.
• Your own analysis — you do the working, interpret the graphs, question the results. Anything you could paste from Wikipedia earns nothing.

• AA wants analytical depth: differentiation and integration, sequences and series, functions, trigonometric identities, a bit of proof. An AA exploration is often "derive, model, optimise, justify."
• AI wants real-world modelling and data: regression, correlation, hypothesis testing, chi-squared, exponential models, interpreting messy figures. An AI exploration is often "collect, model, test, interpret."

Take football: an AA angle optimises the launch angle of a free kick using projectile calculus; an AI angle uses a season of shot data to test whether shot distance predicts goals via regression. Same passion, different maths. If you're still deciding between the courses themselves, Maths AA vs AI — which to choose compares them properly.

Calculus & optimisation — best for AA

• Optimising the dimensions of a real container (a drinks can, a takeaway box, packaging you use at your part-time job) to minimise material for a fixed volume — classic optimisation with genuine data.
• Modelling the curve of a building's roof, a bridge, or an arch you can photograph, then finding its area or gradient with functions and integration.
• The mathematics of a rollercoaster loop — modelling the track with piecewise functions and checking where the ride "feels" heaviest using derivatives.

Statistics & data — best for AI

• Analysing a personal dataset: your Spotify listening, sleep vs. productivity, your own past exam scores, or a sports team's season — with correlation, regression, or a hypothesis test.
• Testing whether a dice, a coin, or a game mechanic is fair using observed vs. expected frequencies and chi-squared.
• Comparing two groups you care about (revision method A vs. B, two players, two products) with a difference-of-means test.

Modelling — AA or AI

• Modelling the cooling of a hot drink with Newton's law of cooling and your own thermometer readings (AA if you solve the differential equation; AI if you fit an exponential to data).
• Modelling the spread of something — a rumour, a trend, a queue — with a suitable growth function.
• Population or resource models (a local species, followers on an account, product sales) using exponential or logistic functions.

Geometry & trigonometry — AA or AI

• The maths of music and sound waves: modelling notes with sine functions, exploring why certain intervals sound consonant (AA-friendly).
• Tessellations and tiling in art, Islamic geometry, or a floor you like — angles, symmetry, and area.
• The geometry of a sport shot — the optimal angle for a basketball free throw, a snooker cannon, or a penalty.

Probability & games — AA or AI

• The probability behind a card or board game you play — expected value of a move, the odds of a hand, whether a strategy is actually better.
• The maths of a casino game (roulette, blackjack basics) and why the house edge is what it is.
• Expected value of a decision you face — insurance, a loot box, a betting-style choice — with a clear recommendation at the end.

Number & algebra — best for AA

• Cryptography and modular arithmetic: how a simple cipher or the RSA idea works, implemented on a small example you compute yourself.
• The mathematics behind a barcode, ISBN, or IBAN check digit — modular arithmetic that catches errors.
• The golden ratio or Fibonacci in something you've noticed — plants, spirals, design — with your own measurements.

1. Name the interest in one line ("I coach junior swimmers").
2. Find the maths hiding in it ("times drop with training — how fast, and does it plateau?").
3. Write it as one answerable question ("Can I model my squad's 50m times over a season, and predict the plateau?").
4. Check you can get data or set up the maths yourself — if not, narrow further.

If your question can't be answered in ~15 pages, it's still too big. One tight question you fully explore beats three you skim.

• Too broad — "the maths of the universe" has nowhere to go. Narrow until it's almost too small.
• Copied maths — reproducing a famous derivation you don't understand. Moderators recognise it instantly and it scores nothing for engagement or use of maths.
• No personal engagement — a topic picked because it "sounds mathsy." Your voice has to be in it.
• No actual maths to do — a fascinating subject where you end up describing rather than calculating. If you can't picture the equations and graphs, it isn't an IA yet.
• Wrong level — trivial GCSE-level arithmetic, or postgraduate theory you can only quote. Aim for challenging-but-yours.

• Talk to your teacher early. They've seen dozens of IAs and will flag "too broad" or "no maths" before you waste weeks.
• Do a one-page trial run. If you can't produce a page of real working, the topic won't stretch to a full exploration.
• Sanity-check the level against your syllabus. The Maths AA SL course and Maths AI SL course lessons show exactly which techniques count as course-level for each route.
• Cut ruthlessly. Most first drafts have two IAs fighting inside them — keep the one you care about most.

What is a good Maths IA topic?

One that links a real interest of yours to mathematics at your course level, framed as a single focused question you can answer yourself. "Good" is less about the subject and more about the fit: enough maths to explore, genuine engagement, and analysis that's clearly your own.

What's the difference between an AA and AI exploration?

AA explorations lean on calculus, algebra and proof — deriving, optimising and justifying. AI explorations lean on statistics, modelling and real data — collecting, fitting, testing and interpreting. The same interest usually suggests a different question for each course.

How many pages should the exploration be?

Roughly 12–20 pages, depending on the current guide. Quality and focus matter far more than length — a tight 13-page exploration beats a padded 20-page one.

Can I use a dataset from the internet?

Yes, but personal or self-collected data almost always scores better on engagement, and you must interpret it yourself. Cite the source, and make sure the analysis is genuinely yours.

How do I know if my maths is the right level?

Compare the techniques against your syllabus lessons. If you're only using material from below IB level, push harder; if you can only quote a result without following the working, simplify.