Hi A Level students
These are comprehensive revision notes for Cambridge International AS & A Level Mathematics 9709, free and open to anyone. Every component is covered — the two pure papers, Mechanics, and both Probability & Statistics papers.
9709 is unusual: you do not sit all six papers. You sit a combination, and which one depends on your school and your level. If you are not certain which papers you are entered for, read Start here before anything else — revising a paper you will never sit is the most expensive mistake available in this subject.
Please take note that although succinct notes are essential towards your revision, they should not be the only materials you cover — working through past paper questions is just as important. Mathematics rewards the pen moving more than the eye scanning.
Happy revising. — Mr. Suta
🧭Start here
Which papers you sit, the four valid combinations, what the calculator rules are, and how to use the list of formulae. Five minutes here saves a term of revising the wrong component.
📚The components
Six papers exist; you sit two for AS Level or four for A Level. Use the rail on the left, or the cards below, to open any topic.
Pure Mathematics 1 — Paper 1
The foundation, and the only paper every 9709 candidate sits, at both AS and A Level. Quadratics, functions, coordinate geometry, radians, trigonometry, series, and a first course in differentiation and integration.
Pure Mathematics 2 & 3 — Papers 2 and 3
Paper 2 is the AS-only pure paper; Paper 3 is the A Level one. Paper 2 is largely a subset of Paper 3, so the six shared topics are written once below and the three Paper 3 additions — vectors, differential equations and complex numbers — are marked P3. The subset is not exact: a handful of techniques inside the shared topics belong to one paper only, and those carry a P3 or a P2 badge on the page itself.
Mechanics — Paper 4
Applied mathematics for forces and motion. Taken by AS candidates on the Mechanics route, and by A Level candidates on the Mechanics + Statistics combination.
Probability & Statistics 1 — Paper 5
The statistics paper that appears in both A Level combinations, so almost every A Level candidate sits it. Data representation, counting, probability, discrete random variables and the normal distribution.
Probability & Statistics 2 — Paper 6
The second statistics paper, sat by A Level candidates on the Statistics route. Poisson, combinations of random variables, continuous random variables, sampling and hypothesis testing.
🧩How to use these pages
Every topic page follows the same shape: what you need to be able to do, then the mathematics broken into the syllabus sub-topics, a worked example, six practice questions with full solutions, and a clearly separated list of other people’s resources.
Material that appears on one pure paper but not the other is badged wherever it occurs, so you can read straight past what you will not sit. P3 means Paper 3 only — vectors, differential equations, complex numbers, partial fractions, the binomial expansion for rational \(n\), \( \tan^{-1} \) and its integral, and the harder integration techniques. P2 means Paper 2 only, which in this syllabus is the trapezium rule and nothing else.
Worked examples end by naming the specific mistake that costs marks on that topic. Those paragraphs are the most useful part of the page and the easiest to skip.
🎓Official Cambridge resources
These are the documents that actually govern the course. Your school has access to all of them through the Cambridge School Support Hub, so ask me if you cannot reach one.
- The 9709 syllabus document — check you have the version for your examination years. The paper combinations and the assessment details are set out at the front, and the examinable content is listed sub-topic by sub-topic.
- List of formulae (MF19) — you are given this in every paper. Work with it open from day one so you know what is printed and what is not.
- Examiner reports — the single most under-used resource. Examiners describe, in plain language, exactly what candidates got wrong last session.
- Specimen papers and mark schemes — written for the current syllabus.
📜A note on past papers
Past papers are the most valuable revision you can do in this subject, and your school can give you properly licensed ones. Ask me and I will get you past questions by topic.
Two warnings when you use them. First, check the syllabus year: 9709 was restructured, and older papers include components that no longer exist and omit content that is now examinable. Second, mark your own work against the mark scheme rather than the answer alone — the method marks are where the grade is won, and you cannot see those by checking the final number.