Cambridge A Level Maths (9709)
9709 Paper 1 (Pure Mathematics 1): Topics, Format and How to Prepare
Cambridge 9709 Paper 1 (Pure Mathematics 1) is a 1 hour 50 minute paper worth 75 marks, with 10 to 12 questions on eight topics: quadratics, functions, coordinate geometry, circular measure, trigonometry, series, differentiation and integration. It is compulsory for both AS and A Level, worth 60% of the AS and 30% of the A Level.
Part of the guide Cambridge A Level Maths 9709: Papers, Routes, Grading and How to Prepare
Key takeaways
- 1 hour 50 minutes, 75 marks, 10 to 12 structured questions, all compulsory.
- Compulsory for AS and A Level: 60% of the AS, 30% of the A Level.
- Eight topics: quadratics, functions, coordinate geometry, circular measure, trigonometry, series, differentiation, integration.
- Every other 9709 paper assumes Paper 1, so it is the paper to secure first.
- In June 2026 an A on Paper 1 needed 59 to 61 out of 75 depending on the variant.
Paper 1 is the one 9709 paper every student sits, whether you are doing AS or the full A Level. Cambridge calls it the foundation for all the other components, which is why it is worth getting secure before anything else.
What is the format of 9709 Paper 1?
| Detail | Paper 1: Pure Mathematics 1 |
|---|---|
| Time | 1 hour 50 minutes |
| Marks | 75 |
| Questions | 10 to 12 structured questions, all compulsory |
| Weighting | 60% of AS Level, 30% of A Level |
| Calculator | Scientific calculator allowed |
| Formula list | MF19 provided |
| Variants | 9709/11, 9709/12, 9709/13 (plus 9709/15 in some series) |
Questions often have parts (a), (b), (c) and sometimes sketches. They get longer towards the end of the paper.
What topics are in Paper 1?
1.1 Quadratics. Completing the square and using it to find the vertex; the discriminant and the number of real roots (including “repeated root”); solving quadratic equations and inequalities; simultaneous equations where one is linear and one quadratic; equations that are quadratic in a function of x, such as x⁴ − 5x² + 4 = 0 or tan²x = 1 + tan x.
1.2 Functions. Domain, range, one-one functions, inverse and composite functions; the graphical link between a function and its inverse; transformations of graphs (translations, stretches, reflections).
1.3 Coordinate geometry. Equations of straight lines in any form; parallel and perpendicular lines; the equation of a circle; intersections of lines, circles and curves.
1.4 Circular measure. Radians, arc length s = rθ and sector area A = ½r²θ.
1.5 Trigonometry. Graphs of sine, cosine and tangent; exact values for 30°, 45° and 60°; inverse trig notation and principal values; the identities tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; solving trig equations in a given interval.
1.6 Series. Binomial expansion of (a + b)ⁿ for positive integer n; arithmetic and geometric progressions; sum to infinity and the condition for it to exist.
1.7 Differentiation. Gradients, the derivative of xⁿ for rational n, the chain rule, tangents and normals, rates of change, stationary points and their nature.
1.8 Integration. Integration as the reverse of differentiation, finding a curve from its gradient, definite integrals (including simple improper ones), area under a curve and volumes of revolution.
Prior knowledge from IGCSE or O Level is assumed, including surd manipulation and the shapes of y = kxⁿ graphs.
What mark do you need?
In June 2026, the component thresholds for Paper 1 were:
| Component | A | B | C |
|---|---|---|---|
| 11 | 59 | 48 | 37 |
| 12 | 61 | 51 | 37 |
| 13 | 61 | 52 | 39 |
All out of 75. Remember the A* is decided on your total across all papers, so on Paper 1 you want as close to full marks as you can get: around 68 or more if you are aiming for an A* overall (see the A* plan).
How should you prepare for Paper 1?
- Quadratics and functions first. They appear inside almost every other topic, from trig equations to stationary points.
- Drill exact values and the two trig identities until they need no thought.
- Learn the formulas MF19 does not give you: the circle equation, gradient and distance formulas, the chain rule and the volume of revolution (full list here).
- Practise by topic, then do full papers in 1 hour 50 minutes. Aim for about 1.5 minutes per mark.
- Show the method every time. The June 2024 examiner report for Paper 11 stresses that quadratic and trig equations need visible working (factorisation, formula with substitution, or completing the square), not answers copied from a calculator.
Watch the lessons
The lectures below work through Paper 1 differentiation past paper questions and the basics of integration. Use them alongside the topic order above.
Back to the Cambridge A Level Maths 9709 guide.
Frequently asked questions
- How long is 9709 Paper 1?
- 1 hour 50 minutes for 75 marks. That is about 1.5 minutes per mark, so a 6-mark question deserves about 9 minutes.
- Is a calculator allowed in 9709 Paper 1?
- Yes, a scientific calculator is allowed, but no marks are given for unsupported calculator answers. Quadratic and trigonometric equations need visible working.
- Is Paper 1 the same as P1?
- Yes. P1 is the older name for Paper 1: Pure Mathematics 1. Component codes like 9709/11, 9709/12 and 9709/13 are its variants.
- What mark do I need for an A in Paper 1?
- In June 2026 the A threshold for Paper 1 was 59 out of 75 for variant 1 and 61 for variants 2 and 3. There is no A* on a single paper; A* is decided on the A Level total.
Sources
Checked against these official documents on 26 Oct 2026. Boards update them, so check the latest version before your exam.
