Cambridge AS and A Level Maths (9709), explained
Cambridge 9709 is one of the most widely taken A Level Maths courses in the world, including at many international schools in India. Its six papers can be combined in several ways, which confuses many students. This guide sets out the papers, the routes and every topic.
On this page
The six papers
- Paper 1: Pure Mathematics 1: 1 hour 50 minutes, 75 marks. Compulsory for AS and A Level: 60% of AS or 30% of A Level.
- Paper 2: Pure Mathematics 2: 1 hour 15 minutes, 50 marks. AS Level only: 40% of AS.
- Paper 3: Pure Mathematics 3: 1 hour 50 minutes, 75 marks. A Level only: 30% of A Level.
- Paper 4: Mechanics: 1 hour 15 minutes, 50 marks. 40% of AS or 20% of A Level.
- Paper 5: Probability & Statistics 1: 1 hour 15 minutes, 50 marks. 40% of AS or 20% of A Level.
- Paper 6: Probability & Statistics 2: 1 hour 15 minutes, 50 marks. A Level only: 20% of A Level.
The routes
You take two papers for AS Level and four for A Level.
- AS Level: Paper 1 with Paper 2 (pure only, which cannot lead on to the A Level), Paper 1 with Paper 4 (pure and mechanics), or Paper 1 with Paper 5 (pure and statistics).
- A Level: Papers 1, 3, 4 and 5 (pure, mechanics and statistics), or Papers 1, 3, 5 and 6 (pure and statistics).
- Staged or all at once: you can take AS in one year and complete the A Level later, carrying your AS result forward, or sit all four papers in one series.
AS Level is graded a to e; the full A Level is graded A* to E.
The topics, paper by paper
- Pure Mathematics 1: quadratics, functions, coordinate geometry, circular measure, trigonometry, series, differentiation and integration.
- Pure Mathematics 2: algebra, logarithmic and exponential functions, trigonometry, differentiation, integration, and numerical solution of equations.
- Pure Mathematics 3: the Pure 2 topics in more depth, plus vectors, differential equations and complex numbers.
- Mechanics: forces and equilibrium, kinematics of motion in a straight line, momentum, Newton's laws of motion, and energy, work and power.
- Probability & Statistics 1: representation of data, permutations and combinations, probability, discrete random variables and the normal distribution.
- Probability & Statistics 2: the Poisson distribution, linear combinations of random variables, continuous random variables, sampling and estimation, and hypothesis tests.
Pure 2 and Pure 3 share topic headings. Pure 3 goes further in each and adds three new areas, which is why Pure 2 is not available as part of the full A Level.
A Pure 1 question
Find the coordinates of the stationary point of y = x² − 6x + 11 and state whether it is a minimum or maximum.
- dy/dx = 2x − 6 = 0 gives x = 3; y = 9 − 18 + 11 = 2.
- d²y/dx² = 2 > 0, so (3, 2) is a minimum.
A Probability & Statistics 1 question
X ~ N(50, 4²). Find P(X < 56).
- Standardise: z = (56 − 50) / 4 = 1.5.
- From tables, Φ(1.5) = 0.9332, so P(X < 56) = 0.933.
A Mechanics question
A 4 kg box is pulled along a smooth floor by a horizontal force of 10 N. Find its acceleration and its speed after 3 s from rest.
- F = ma: a = 10 / 4 = 2.5 m s−2.
- v = u + at = 0 + 2.5 × 3 = 7.5 m s−1.
Command words to know
9709 questions use command words with precise meanings. Misreading them costs marks.
- Show that: the answer is given, so every step of the working must be shown clearly.
- Hence: use the result you have just found; another method may score nothing.
- Hence or otherwise: the previous result is the expected route, but other correct methods earn the marks.
- Find the exact value: no decimals; leave surds, fractions, π or logarithms in the answer.
- Sketch: show the shape and key features, such as intercepts and turning points, without plotting points.
Exam conditions
- A calculator is allowed in every paper.
- You get Cambridge's list of formulae and statistical tables for 9709. It does not include everything, so learn standard results.
- Answers are expected to three significant figures unless the question says otherwise, and angles in degrees to one decimal place. Check each question's instruction.
How to plan
- Confirm your route with your school before you start revising applied papers.
- Make Pure 1 secure first: it is in every route and underpins Pure 3.
- Practise papers by variant: papers such as 12 and 13 are variants of Paper 1 for different time zones, so all are good practice.
- Read the examiner reports to see the common errors in each paper.
Common mistakes
- Revising Pure 2 when you are on the full A Level route, which uses Pure 3.
- Losing accuracy marks by rounding to fewer than three significant figures.
- Ignoring the statistical tables and formula list until the exam.
- Treating Mechanics as physics: answers must follow mathematical modelling conventions.
Practice questions
Try each one before opening the answer.
Q1. Which papers make up an A Level with Mechanics?
Show answer
Q2. Find the sum of the first 15 terms of the arithmetic progression 4, 7, 10, …
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Q3. A Poisson variable has mean 3. Find P(X = 0).
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Frequently asked questions
Is 9709 the same as the UK A Level Maths?
No. 9709 is Cambridge International's own syllabus with six papers and several routes, unlike the three-paper UK A Levels. The pure content is similar.
Can I take Paper 2 for the full A Level?
No. Paper 2 is offered only as part of AS Level. The full A Level uses Paper 3.
Where do I find 9709 past papers?
Cambridge publishes recent papers on its website; our 9709 past papers page links to every one with mark schemes.
Key takeaways
- Six papers: Pure 1 to 3, Mechanics, and Probability & Statistics 1 and 2.
- AS: Paper 1 plus 2, 4 or 5.
- A Level: 1, 3, 4, 5 or 1, 3, 5, 6.
- Calculator and formula list in every paper.
- Pure 1 underpins everything.