Paper 3 is the third external examination for IB Math AA HL and AI HL students. It is unique in the IB because it presents students with an extended, multi-part mathematical problem that requires investigation and reasoning — not just recall and procedure.
| Feature | Details |
|---|---|
| Duration | 1 hour |
| Questions | 2 extended response questions (~28 marks each) |
| Total marks | 55 marks |
| Weight in final grade | 20% |
| Calculator | Yes (GDC required) |
| Syllabus tested | Can draw from any part of the syllabus, often focuses on HL-only content |
While Paper 3 can cover any syllabus content, certain themes recur across years:
| Theme | Frequency | Typical Techniques Involved |
|---|---|---|
| Complex numbers (de Moivre's, roots of unity) | Very common | Induction, geometric series, Euler's formula |
| Integration and differential equations | Very common | Integrating factor, separable variables, substitution |
| Proof and mathematical induction | Common | Strong induction, divisibility, matrix induction |
| Series and convergence | Common | Maclaurin series, convergence tests, sums |
| Calculus explorations (new functions) | Common | L'Hôpital's rule, advanced differentiation, limits |
| Statistics (distributions, estimators) | Occasional | Unbiased estimators, combined distributions |
| Number theory or combinatorics | Occasional | Pigeonhole principle, modular arithmetic |
The Paper 3 question structure is intentionally scaffolded. Each question has 5–8 sub-parts (a, b, c...) that build progressively toward a deeper result. Here is the reliable approach:
Before answering anything, read both questions completely. Identify which question you are more likely to make progress on. Most students find that they can attempt both questions, but one will be more accessible.
The early parts of Paper 3 questions are generally accessible — they introduce the mathematical context and establish the tools you will need. These parts often carry 4–6 marks each and should be answered with full working.
The phrase "use your result from part (b)" appears frequently. Carry your result forward even if you are not certain it is correct. If you made an error in part (b), you can still score "follow-through" marks in part (c) if your method in (c) is correct.
If you cannot complete a sub-part, write down what you know and what you are trying to find. State a relevant theorem or definition. Partial marks are awarded for relevant working, even without a complete solution.
Paper 3 marking is generous with partial credit. The mark scheme awards marks for:
One hour for ~55 marks means approximately 65 seconds per mark. The practical breakdown:
Paper 3 rewards a specific kind of mathematical reasoning that can be developed with practice. Our IB HL tutors work through Paper 3 problems with you in real time, teaching the problem-solving approach as well as the content.
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