A-Level Mathematics is the gateway qualification for almost every STEM degree. It is examined as a linear two-year course — everything is assessed at the end, so the students who do best are the ones who build understanding steadily rather than cramming. This is my complete guide to preparing for it well.
Exam structure at a glance
The three major UK boards (Edexcel 9MA0, AQA 7357, OCR H240) share the same content and a similar shape:
| Papers | 3 papers, each 2 hours, 100 marks |
| Split | ~2/3 Pure Mathematics, ~1/3 Applied (Statistics + Mechanics) |
| Calculator | Allowed in all papers |
| Grading | A*–E, assessed entirely at the end of Year 13 |
Always confirm the current specification for your exact board — content is stable, but paper weightings and the large data set change.
The complete topic checklist
Pure Mathematics (the core)
- Proof (deduction, exhaustion, contradiction, counterexample)
- Algebra & functions (indices, surds, quadratics, simultaneous equations, inequalities, polynomials, partial fractions, modulus, transformations)
- Coordinate geometry (straight lines, circles, parametric equations)
- Sequences & series (arithmetic, geometric, binomial expansion, recurrence)
- Trigonometry (radians, identities, addition & double-angle formulae, R-form, solving equations)
- Exponentials & logarithms (laws, and , modelling)
- Differentiation (chain/product/quotient, implicit, parametric, applications)
- Integration (standard integrals, substitution, by parts, partial fractions, areas, differential equations)
- Numerical methods (iteration, Newton–Raphson, trapezium rule)
- Vectors (2D and 3D)
Statistics
- Sampling methods
- Data presentation & interpretation (incl. the large data set)
- Probability (conditional probability, Venn/tree diagrams)
- Statistical distributions (binomial, normal)
- Hypothesis testing (binomial, normal mean, correlation)
Mechanics
- Kinematics (constant acceleration, motion graphs, calculus with variable acceleration)
- Forces & Newton's laws (resolving, connected particles, friction)
- Moments
- Projectiles
A realistic two-year plan
- Year 12, term 1–2: Pure foundations — algebra, functions, coordinate geometry, trig. Don't move on until the algebra is automatic; it underpins everything.
- Year 12, term 3: Differentiation + integration basics, plus Statistics fundamentals.
- Year 13, term 1: The harder Pure (parametric, implicit, integration techniques, vectors) and Mechanics.
- Year 13, term 2: Synthesis — mixed-topic questions, timed past papers, an error log.
- Year 13, term 3: Full past papers, mark-scheme discipline, targeted revision of your weakest topics.
The mistakes that cost the most marks
- Skipping method lines. Mark schemes reward method. A correct answer with no working can score zero on "show that" questions.
- Weak algebra. Most lost marks in calculus and trig are actually algebra slips. Drill the fundamentals.
- Misreading the question. Exact vs decimal, radians vs degrees, "hence" meaning "use the previous part."
- Practising recognition, not reasoning. If you can only do a question after seeing its type, you haven't learned it yet.
How IvyfordMath helps
Every A-Level Maths question on IvyfordMath is hand-curated with a worked solution on every miss, so a mistake becomes the most useful thing in your session. Our reasoning practice trains the "why does this step follow?" skill that separates a B from an A*.
— Mike Vuu, Oxford Mathematics graduate and founder of IvyfordMath.