# 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.

- Page: https://mathvsarham.com/articles/9709-paper-1-pure-mathematics-1/
- Author: Arham (https://mathvsarham.com/about/)
- Category: Cambridge A Level Maths (9709)
- Part of: Cambridge A Level Maths 9709: Papers, Routes, Grading and How to Prepare (https://mathvsarham.com/articles/cambridge-a-level-maths-9709/)
- Published: 2026-10-26
- Last checked: 2026-10-26

## 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](https://mathvsarham.com/articles/how-to-get-an-a-star-in-a-level-maths/)).

## How should you prepare for Paper 1?

1. **Quadratics and functions first.** They appear inside almost every other topic, from trig equations to stationary points.
2. **Drill exact values and the two trig identities** until they need no thought.
3. **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](https://mathvsarham.com/articles/mf19-formula-list/)).
4. **Practise by topic, then do full papers in 1 hour 50 minutes.** Aim for about 1.5 minutes per mark.
5. **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](https://mathvsarham.com/articles/cambridge-a-level-maths-9709/).

## 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

- [Cambridge 9709 syllabus for 2026 and 2027: Pure Mathematics 1 content](https://www.cambridgeinternational.org/Images/697427-2026-2027-syllabus.pdf)
- [Cambridge 9709 grade thresholds, June 2026](https://www.cambridgeinternational.org/Images/761530-mathematics-9709-june-2026-grade-threshold-table.pdf)
- [Cambridge 9709 examiner report, June 2024](https://www.cambridgeinternational.org/Images/567737-june-2024-examiner-report.pdf)

## Related lectures

- [Solving Past Papers | Differentiation | Class 28 | AS Level P1 9709](https://mathvsarham.com/lectures/fhS3CrFYlFs/)
- [Introduction to Integration: Rules & Curve Equations | Class 29 | AS Level P1 9709](https://mathvsarham.com/lectures/t6I2Sne25_s/)

## Past papers

- [9709 Mathematics](https://mathvsarham.com/past-papers/)