O Level Mathematics: Geometry 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. Find the size of one interior angle of a regular decagon (10 sides). [2]

2. Each exterior angle of a regular polygon is 24°. (a) How many sides does it have? (b) Find the sum of its interior angles. [3]

3. Triangle ABC is isosceles with AB = AC. Angle BAC = 48°. Find angle ABC. [1]

4. PQRS is a cyclic quadrilateral. Angle PQR = 104°. Find angle PSR, giving a reason. [2]

5. A straight line touches a circle at P. A chord PS makes an angle of 37° with the tangent. Q is a point on the circle in the other segment. Find angle PQS, giving a reason. [2]

6. Two tangents are drawn from a point T to a circle with centre O. They touch the circle at A and B. Angle ATB = 40°. Find angle AOB. [2]

7. Two solids are mathematically similar. Their surface areas are 50 cm² and 200 cm². The smaller solid has a volume of 30 cm³. Find the volume of the larger solid. [3]

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Answers

1. Exterior angle = 360° ÷ 10 = 36° [1]. Interior angle = 180° − 36° = 144° [1].

Tip: find the exterior angle first; it is always 360° divided by the number of sides.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 8.

2. (a) 360 ÷ 24 = 15 sides [1]. (b) (15 − 2) × 180° [1] = 2340° [1].

Tip: the sum of interior angles of an n-sided polygon is (n − 2) × 180°.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 8.

3. (180° − 48°) ÷ 2 = 66° [1].

Tip: the two equal angles are the ones opposite the equal sides.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 12, Question 4.

4. 180° − 104° = 76° [1], because opposite angles of a cyclic quadrilateral add up to 180° [1].

Tip: give the geometric reason in words; it often carries its own mark.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 14.

5. Angle PQS = 37° [1], by the alternate segment theorem: the angle between a tangent and a chord equals the angle in the alternate segment [1].

Tip: name the theorem; “angles are equal” on its own does not earn the reason mark.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 14.

6. The angles OAT and OBT are 90°, because a tangent is perpendicular to the radius [1]. Angle AOB = 360° − 90° − 90° − 40° = 140° [1].

Tip: look for the two right angles where the radii meet the tangents.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 14.

7. Area ratio 1 : 4, so length ratio 1 : 2 [1]. Volume ratio 1 : 8 [1]. Larger volume = 30 × 8 = 240 cm³ [1].

Tip: go from the area ratio back to the length ratio before you cube it.

Try the real question next: Cambridge O Level Mathematics 4024, June 2025, Paper 22, Question 21.

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Where marks are usually lost

• Missing the geometric reason for an angle.
• Using the interior angle where the exterior angle is needed.
• Using the area scale factor as the volume scale factor.