O Level Mathematics: Trigonometry Practice Questions (Cambridge 4024)

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs — Cambridge International holds copyright in its own papers. Use these alongside the official past papers available from your board.

Most questions practise a skill tested in the June 2025 papers. Questions marked (no calculator) are Paper 1 style; the rest allow a calculator, as in Paper 2. After each answer there is a tip and the real question to try next.

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Questions

1. (no calculator) A right-angled triangle has a hypotenuse of 10 cm. One of its angles is 30°. Find the length of the side opposite the 30° angle. [2]

2. (no calculator) The two shorter sides of a right-angled triangle are 8 cm and 15 cm. Find the hypotenuse. [2]

3. A triangular field ABC has AB = 120 m, BC = 95 m and angle ABC = 104°. (a) Find AC. (b) Fencing is sold in rolls of 25 m. How many rolls are needed to fence the whole perimeter? [4]

4. In triangle ABC, angle A = 40°, angle B = 75° and BC = 12 cm. Find AC. [3]

5. Find the area of a triangle with sides 8 cm and 11 cm and an included angle of 35°. [2]

6. The bearing of B from A is 060°. Find the bearing of A from B. [1]

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Answers

1. opposite = 10 × sin 30° [1] = 10 × ½ = 5 cm [1].

Tip: learn the exact values of sin, cos and tan of 30°, 45° and 60° for the non-calculator paper.

2. √(8² + 15²) = √289 [1] = 17 cm [1].

Tip: add the squares of the shorter sides when finding the hypotenuse.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 14.

3. (a) AC² = 120² + 95² − 2 × 120 × 95 × cos 104° [1] = 28 941, so AC = 170.1 m [1]. (b) Perimeter = 120 + 95 + 170.1 = 385.1 m [1]. 385.1 ÷ 25 = 15.4, so 16 rolls [1].

Tip: round up when you need enough of something to cover a length.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 22.

4. AC / sin 75° = 12 / sin 40° [1]. AC = 12 × sin 75° ÷ sin 40° [1] = 18.0 cm [1].

Tip: pair each side with the angle opposite it.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 22.

5. ½ × 8 × 11 × sin 35° [1] = 25.2 cm² [1].

Tip: the angle must be the one between the two sides you use.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 22.

6. 060° + 180° = 240° [1].

Tip: a back bearing differs by 180°, and bearings are always three figures.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 6.

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Where marks are usually lost

• Rounding down when a whole number of items must cover a length.
• Using the cosine rule with the wrong angle.
• Writing a bearing with fewer than three figures.