How to Choose a Good Topic for the IB Math AA Internal Assessment

The right topic decides half the grade. Here are the criteria and the mistakes I see year after year in the classroom.

The Math AA Internal Assessment is 20% of the final grade. That's not nothing. And unlike the papers, it isn't decided in one May morning — it's built over months. The vast majority of IA problems appear before the first formula is written, when the student picks the wrong topic. This article is meant to help avoid that.

What the IB actually assesses

The IA is marked against five criteria. The official names and maximum marks are:

• Criterion A · Presentation (4 pts). Coherence, structural clarity, conciseness.
• Criterion B · Mathematical communication (4 pts). Correct notation, explicit definitions, terminology.
• Criterion C · Personal engagement (3 pts). The topic matters to the student; there's a personal voice.
• Criterion D · Reflection (3 pts). Critical analysis, not description.
• Criterion E · Use of mathematics (6 pts at SL, 6 pts at HL). The core of the grade.

Out of twenty possible points, six depend on E and another four on B. That means 50% of the IA depends on mathematical level and correctness. So before thinking about any other criterion, the key question is: is the mathematics I'm going to use actually at my SL or HL level?

"An IA using Year 10-level mathematics, written flawlessly, won't score above 8 out of 20. Formal correctness doesn't make up for a lack of level."

The initial mistake: thinking about the topic first

Students usually start with the topic ("I'll do something about football," "I like music") and then look for mathematics to plug in. In my experience, this leads to a decorative IA: mathematics taped onto a topic that was already decided.

The reverse order works far better:

1. Start from a mathematical technique you enjoyed in the course (optimisation, integrals, conditional probability, vectors, series, differential equations at HL).
2. Find a real-world context where that technique solves something concrete.
3. Formulate a bounded research question.

This way, the mathematics is secured from minute one, and the topic works as a vehicle rather than an excuse.

How to phrase the research question

A good research question is concrete, bounded and mathematically solvable. Compare these two versions of the same idea:

The first version could lead anywhere. The second demands parametrising the parabola, differentiating with respect to the angle, optimising and discussing the model's error. That's real mathematics.

The five-minute test

Before committing to a topic, try writing in five minutes:

• The research question in one sentence.
• The three or four mathematical tools you'll use.
• What kind of conclusion you expect (numerical, comparative, a model).

If you can't do this, the topic isn't ready yet.

Three mistakes I see every year

1. Topic too simple

"Calculate the area of a football pitch using integrals." The pitch is a rectangle. There are no real integrals here, just a trivial calculation in disguise. It usually scores 2-3 on criterion E.

2. Topic too ambitious

"Apply neural networks to predict the stock market." Unless the student has prior training, the mathematics involved (gradient descent, backpropagation, high-dimensional linear algebra) sits outside the SL and even the HL curriculum. The IB does not reward going beyond your level — it penalises mathematics that clearly isn't understood.

3. Decorative mathematics

The personal topic takes over the whole piece and mathematics only appears as decoration: a linear regression run on a calculator with no justification, a probability calculated from memory. The IA is a mathematical piece of work, not an essay with a numerical appendix.

Examples of strong questions for SL and HL

For SL (enough mathematics using the course's standard toolkit):

• "Exponential modelling of coffee cooling: fitting constants and error against experimental data."
• "Probability of winning a national lottery draw: combinatorial analysis versus intuitive perception."
• "Optimising the cylindrical packaging of a soft drink: do commercial cans match the theoretical optimum?"

For HL (requiring extra tools such as series, differential equations or complex numbers):

• "SIR model of a virus spreading through a school: analysing a system of differential equations with real data."
• "Convergence of the Fourier series for an audio signal: approximation and error as a function of the number of terms."
• "Applying complex numbers to AC circuit analysis: calculating impedance and phase shift."

Recommended structure for the 12-20 pages

1. Introduction and personal engagement (1-2 pp). Why this topic, what led you to it.
2. Research question and framing (1 p).
3. Mathematical framework (2-3 pp). Definitions, formulas, assumptions.
4. Development (5-8 pp). Calculation, modelling, justification.
5. Analysis and validation (2-3 pp). Comparison with data, error, domain of validity.
6. Reflection and conclusion (1-2 pp). Limitations, what you'd do differently, extensions.
7. Bibliography.

When to ask for help

The IB requires the student's own originality, but the supervisor has a legitimate role: approving the topic, reading a draft and giving general feedback. At the academy, we work on IAs from the moment a student brings their first ideas through to the final draft. We don't write it for them — we help them see whether the mathematics they're using reaches the required level and whether the question is defensible. You can check out our dedicated IB programme or read the AA vs AI comparison if you're still choosing a route.