Overview
The best IB Maths AA Exploration topic is narrow, personal, and analytically rich — a question you can develop with the calculus, trigonometry, and algebra that make Analysis & Approaches what it is. This post gives example topics by area and shows how to turn a vague interest into a focused Exploration. For the full write-up on criteria and structure, see the [IB Maths AA IA guide](/blog/ib-maths-aa-ia-guide).
What makes a strong AA topic
This section covers What makes a strong AA topic — what IB examiners reward most often in past papers and coursework.
- Narrow — "modelling my free-throw arc with a quadratic and optimising release angle" beats "an investigation into projectiles".
- Personal — a genuine hook earns personal engagement marks generic topics never will.
- Analytical — AA rewards calculus, proof, trigonometry, sequences and series, complex numbers. The mathematics should stretch slightly beyond what you were simply taught.
- Yours to develop — you derive or extend something, rather than just applying a formula once.
Example Exploration topics by area
For the IB Diploma Programme, treat these as starting points — identical online topics are an authenticity risk.
Calculus and optimisation
- Optimising the shape of a can (or tent, or ramp) to minimise material for a fixed volume — a clean optimisation with real derivatives.
- Modelling the volume of a real object as a solid of revolution and comparing your integral to a measured value.
- Rates of change in a real process (cooling coffee, draining tank) modelled with a differential equation.
Trigonometry and geometry
- Modelling tides or daylight hours with a sinusoidal function fitted to real data, then predicting.
- The mathematics of a spiral (shells, galaxies, staircases) using polar or parametric curves.
Sequences, series and proof
- Where a real recurrence appears (loan repayments, drug dosage) analysed as a geometric or recursive sequence.
- Exploring a proof or identity you find elegant — building it carefully and testing its limits.
Modelling and probability
- A fair-game or strategy analysis (a dice game, a sport scenario) using expected value.
- Fitting and comparing models for something you measured, judging which fits best and why.
How to turn an interest into a topic
For the IB Diploma Programme, start from something you care about, then narrow in three moves: pick the mathematical tool the situation naturally needs (a derivative, a periodic function, a sequence); define one clear question you can actually answer; and plan the extension — what you will derive, optimise, or compare so the work is yours. Now you have an Exploration, not a summary.
Planning your Exploration on MarkScheme
Draft early and self-mark against the official criteria before your supervisor deadline. Strengthen the underlying methods with the free [Maths AA HL](/ib/courses/maths-aa-hl) and [SL](/ib/courses/maths-aa-sl) lessons, review [Maths AA past papers](/ib/past-papers/maths-aa-hl) for technique, and [get an answer marked](/mark) to keep exam skills sharp alongside the IA.
Frequently asked questions
This section covers Frequently asked questions — what IB examiners reward most often in past papers and coursework.
How complex should the maths be?
"Commensurate with the course" — roughly your syllabus level, applied correctly, reaching slightly beyond. Wheeling in university results you cannot justify does not help.
Can I use a topic I found online?
As inspiration only. Change the context, data, or extension so the Exploration is genuinely yours — mirroring an online example loses personal-engagement marks and risks integrity issues.
AA or AI topic?
AA suits analytical, calculus- and proof-led questions. If your idea is really about collecting data and modelling it statistically, it fits Maths AI better.