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.
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AS content is usually taught in Year 12. The full A Level adds the Year 13 content. Sitting AS exams or mocks? See the AS Level Maths checklist.
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 | Papers 1, 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, one with its full mark scheme open. 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 7-day 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 $\tan x$.
M1 for using the Pythagorean identity $\cos^2 x = 1 - \sin^2 x$ or drawing a right-angled triangle.
A1 for finding $\cos x = \frac{4}{5}$ (taking the positive root for an acute angle).
M1 for using the ratio identity $\tan x = \frac{\sin x}{\cos x}$.
A1 for finding $\tan x = \frac{3/5}{4/5} = \frac{3}{4}$.
Every question here has a full worked solution. See them all →
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 7-day 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.
Full question sets with mark schemes: small angle approximations and radians questions (18)
Revision notes: Trigonometry: rules, graphs, identities and equations · Radians, arcs, sectors and small angles · Reciprocal and inverse trigonometric functions · Compound and double angles, and the R form · Trigonometric proofs, equations and modelling
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 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 |
| AQA 7357 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
| OCR H240 | Paper 1: June 2025, June 2024, June 2023 Paper 2: June 2025, June 2024, June 2023 Paper 3: June 2025, June 2024, June 2023 |
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 Papers 1, 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.
Stretch yourself: original geometry problems at Senior level (ages 16 to 18), with hints and full solutions: Problem S20 · Problem S76 · Problem S19 · Problem S75. All 22 →
Formulas in this topic: Arc length · Area of a sector · Cosine rule · Double angle formulas · Sine rule · Trig identities. All formulas A–Z
Applying for maths, computer science or economics? TMUA practice on this topic: Trig graphs, identities and equations · Radians, arcs and sectors. TMUA preparation: notes, questions and mock papers → Taking STEP? STEP-style problems: Trigonometry.
Thinking about an EPQ? Maths EPQ ideas that use this topic: The parallel postulate and new geometries · When the small-angle approximation fails · Why instruments sound different · all 93 ideas
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