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Course Overview
IB Math Analysis & Approaches (AA) HL is one of the most rigorous mathematics courses in the IB Diploma Programme. It is designed for students who will pursue mathematics, physics, engineering, or economics at university, and it requires genuine mathematical fluency — not just procedural skill.
AA HL is taught over two years (Years 1 and 2 of IB) and examined in May or November. The final grade (1–7) comes from external exams (80%) and an internal assessment — the Math IA (20%).
May 2026 exam dates: IB Mathematics exams take place in May 2026. Paper 1 and 2 are typically in the first two weeks of May; Paper 3 follows in the same period. Check your IB school's timetable for exact dates.
Topic Breakdown
| Topic | Hours (SL) | Hours (HL) | Exam Weight |
|---|
| 1. Number & Algebra | 19 | 39 | ~16% |
| 2. Functions | 21 | 32 | ~17% |
| 3. Geometry & Trigonometry | 25 | 51 | ~21% |
| 4. Statistics & Probability | 27 | 33 | ~17% |
| 5. Calculus | 28 | 55 | ~29% |
Calculus is the single most heavily examined topic area. It appears on every exam paper and dominates Paper 3. Prioritise this above all others.
HL-Only Topics
HL students learn additional content beyond the SL syllabus. These HL-only topics are regularly tested in Paper 3 and challenging Paper 2 questions:
- Proof by mathematical induction — series summation, divisibility, matrix powers
- Complex numbers — de Moivre's theorem, nth roots of complex numbers, Euler's form
- Advanced calculus — integration by parts, substitution, differential equations (separable + integrating factor), L'Hôpital's rule, Maclaurin series
- Vectors (3D) — vector equations of lines and planes, angles between planes, intersections
- Statistics — Poisson distribution, continuous probability distributions, unbiased estimators
- Advanced functions — odd/even functions, reciprocal functions, composite function analysis
Exam Structure & Paper Strategy
| Paper | Duration | Calculator? | Marks | Weight |
|---|
| Paper 1 | 2h | No | 110 | 30% |
| Paper 2 | 2h | Yes (GDC) | 110 | 30% |
| Paper 3 | 1h | Yes (GDC) | 55 | 20% |
| Internal Assessment (IA) | — | — | 20 | 20% |
Paper 1 (No Calculator)
- Work on algebraic fluency — trigonometric identities, exact values, derivative/integral by hand.
- Leave sufficient time for longer questions (typically 8–12 marks each in Section B).
- If you cannot get an exact answer, write a setup equation — method marks are awarded even without a final answer.
Paper 2 (Calculator)
- Use your GDC (TI-84 or equivalent) for numerical integration, solving equations graphically, and regression.
- Store intersection values before using them in further calculations.
- Section B questions often span 3–4 parts — read the full question before starting.
Paper 3: The Problem-Solving Paper
Paper 3 is unique to HL and is the most challenging paper. It consists of two extended response questions (typically 30 marks each) that test your ability to explore unfamiliar contexts and apply mathematical techniques in creative ways.
Paper 3 insight: Unlike Papers 1 and 2, Paper 3 often introduces mathematics you have not explicitly studied. The question guides you through a novel exploration, building up a result step by step. Your job is not to recall memorised techniques, but to reason from the given information. Partial credit is generous — every step you complete correctly earns marks, even if you cannot complete the question.
Internal Assessment
The Math IA is a 12–20 page exploration worth 20% of your final grade. It should demonstrate mathematical understanding, personal engagement, and reflection.
- Choose a topic you genuinely find interesting. Assessors can tell the difference between genuine curiosity and a generic exploration.
- Aim for the right level of complexity. The IA should be challenging enough to allow you to demonstrate HL mathematics, but not so complex that you cannot show genuine understanding.
- Avoid overused topics. The Golden Ratio, Fibonacci sequences, and basic modelling topics are seen by assessors hundreds of times and rarely score well.
- Include personal reflection. The "reflection" criterion (Criterion E) requires you to discuss the limitations of your approach and what you would explore further.
How to Score 7
Grade 7 boundary (approximate): Typically 75–82% across all three papers. The exact boundary varies by year.
- Master the core topics first. Calculus, functions, and vectors appear across all three papers. Students who master these have the foundation for a 7.
- Don't neglect HL-only topics. Complex numbers and proof by induction appear reliably in Paper 3.
- Practise with IB past papers. The IB question style is specific — IB marking criteria reward clear notation, defined variables, and contextual answers.
- Get a strong IA. A 17–18/20 IA can carry you if exam performance is slightly below 7-boundary.
IB Math AA HL Tutoring
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