A Level Maths · Pure · Year 12 and 13
Trigonometry runs through both years: triangles and equations in degrees in Year 12, then radians, reciprocal functions, compound angles and the R sin(x ± α) form in Year 13. It is also where proof-style 'show that' identity questions live.
AS content is usually taught in Year 12. The full A Level adds the Year 13 content.
Solve the equation $\sqrt{2}\cos x - 1 = 0$ for $0 \le x \le 2\pi$. Give your answers exactly in radians.
Then practise: skills to practise · open trigonometry practice questions.
Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.
| Board | Specification reference | Examined in |
|---|---|---|
| AQA 7357 | AQA section E | Paper 1, and Section A of Papers 2 and 3 |
| Edexcel 9MA0 | Edexcel topic Pure 5 | Paper 1 and Paper 2 |
| OCR A H240 | OCR reference 1.05 | Paper 1, and the pure sections of Papers 2 and 3 |
Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.
A sector of a circle has radius $r\text{ cm}$ and a central angle of $\theta$ radians. The area of the sector is exactly $5$ times the length of its arc. Find the exact value of $r$.
Mark scheme: in the 48-hour free trial.
Given that $\sin x = \frac{3}{5}$ and $x$ is an acute angle ($0 < x < \frac{\pi}{2}$), find the exact values of $\cos x$ and $\tan x$.
Mark scheme: in the 48-hour free trial.
A chord subtends an angle of $1.6$ radians at the centre of a circle of radius $9$ cm. Calculate the area of the minor segment bounded by this chord, to 1 decimal place.
Mark scheme: in the 48-hour free trial.
Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.
These skills sit in the Pure II unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.
Trigonometry can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.
| Board | Recent papers that can test it |
|---|---|
| Edexcel 9MA0 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 |
| AQA 7357 | Paper 1: June 2023, June 2022, November 2021 Paper 2: June 2023, June 2022, November 2021 Paper 3: June 2023, June 2022, November 2021 |
| OCR H240 | Paper 1: June 2024, June 2023, June 2022 Paper 2: June 2024, June 2023, June 2022 Paper 3: June 2024, June 2023, June 2022 |
Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →
Yes. Trigonometry is part of the A Level Maths content that every board examines: AQA section E, Edexcel Pure 5, OCR 1.05. It is assessed in AQA Paper 1, and Section A of Papers 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.
Both. The AS content, usually taught in Year 12, is: Sine rule, cosine rule and the area of a triangle, ½ab sin C; Graphs of sine, cosine and tangent, and exact values; The identities tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; Solving trigonometric equations in a given interval. The full A Level adds: Radian measure, arc length and sector area; small-angle approximations; sec, cosec and cot; arcsin, arccos and arctan; Compound-angle and double-angle formulae; Writing a cos θ + b sin θ as R cos(θ ± α) or R sin(θ ± α); Proving identities and solving harder equations.
Use degrees when the question gives angles in degrees, and radians whenever calculus, arc length or sector area is involved, or the interval is given in terms of π. Check the mode before every trigonometry question.
Free, no sign-up. Then try every topic for 48 hours, no card needed.
Take the free diagnostic
A Level Math Revision