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O Level & A Level Mathematics (Cambridge)

O Level Mathematics — Geometry, Mensuration and Trigonometry, Set 2

Take the O Level Mathematics — Geometry, Mensuration and Trigonometry, Set 2: 20 multiple-choice questions (30 minutes) with instant scoring and a full…

What this test covers

Sample questions with answers

The first 5 questions of this test, with the correct answer and explanation.

  1. Q1. What is the sum of the interior angles of a pentagon?

    • A. 720°
    • B. 360°
    • C. 900°
    • D. 540° ✓

    Answer: D. 540°

    Explanation: (5 − 2) × 180° = 540°.

  2. Q2. Each interior angle of a regular polygon is 150°. How many sides does it have?

    • A. 10
    • B. 6
    • C. 12 ✓
    • D. 15

    Answer: C. 12

    Explanation: Each exterior angle is 30°, and 360° ÷ 30° = 12.

  3. Q3. The angles of a triangle are in the ratio 1 : 2 : 6. What is the largest angle?

    • A. 120° ✓
    • B. 60°
    • C. 100°
    • D. 90°

    Answer: A. 120°

    Explanation: One part = 180° ÷ 9 = 20°, so the largest is 6 × 20° = 120°.

  4. Q4. What is the angle between a tangent and the radius at the point of contact?

    • A. 45°
    • B. 180°
    • C. 60°
    • D. 90° ✓

    Answer: D. 90°

    Explanation: A tangent is perpendicular to the radius at the point of contact.

  5. Q5. One angle in a segment of a circle is 48°. What is another angle in the same segment, standing on the same chord?

    • A. 24°
    • B. 96°
    • C. 132°
    • D. 48° ✓

    Answer: D. 48°

    Explanation: Angles in the same segment are equal.

The other 15 questions

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  1. Q6. The angle between a tangent and a chord is 62°. What is the angle in the alternate segment?

    • A. 124°
    • B. 118°
    • C. 62°
    • D. 28°

  2. Q7. What is the length of the diagonal of a 9 cm by 12 cm rectangle?

    • A. 21 cm
    • B. 225 cm
    • C. 10.4 cm
    • D. 15 cm

  3. Q8. An isosceles triangle has sides 10 cm, 10 cm and 12 cm. What is its area?

    • A. 30 cm²
    • B. 48 cm²
    • C. 96 cm²
    • D. 60 cm²

  4. Q9. In a right-angled triangle, the side adjacent to a 40° angle is 8 cm. Find the hypotenuse, to 3 significant figures.

    • A. 10.4 cm
    • B. 6.13 cm
    • C. 9.53 cm
    • D. 12.4 cm

  5. Q10. A 30 m tower is 50 m from an observer on level ground. Find the angle of elevation of the top, to 1 decimal place.

    • A. 31.0°
    • B. 59.0°
    • C. 36.9°
    • D. 30.0°

  6. Q11. In triangle ABC, a = 10 cm, A = 50° and b = 8 cm. Find angle B, to 1 decimal place.

    • A. 52.2°
    • B. 37.8°
    • C. 73.2°
    • D. 40.0°

  7. Q12. A triangle has sides 7 cm, 8 cm and 9 cm. Find its largest angle, to 1 decimal place.

    • A. 48.2°
    • B. 90.0°
    • C. 73.4°
    • D. 58.4°

  8. Q13. Taking π = 22/7, find the circumference of a circle of radius 14 cm.

    • A. 616 cm
    • B. 44 cm
    • C. 176 cm
    • D. 88 cm

  9. Q14. Taking π = 22/7, find the area of a circle of diameter 14 cm.

    • A. 308 cm²
    • B. 154 cm²
    • C. 616 cm²
    • D. 44 cm²

  10. Q15. Find the surface area of a sphere of radius 3 cm, in terms of π.

    • A. 9π cm²
    • B. 108π cm²
    • C. 36π cm²
    • D. 12π cm²

  11. Q16. A prism has a cross-sectional area of 12 cm² and a length of 15 cm. What is its volume?

    • A. 360 cm³
    • B. 180 cm³
    • C. 27 cm³
    • D. 90 cm³

  12. Q17. A trapezium has parallel sides of 6 cm and 10 cm and a height of 5 cm. What is its area?

    • A. 30 cm²
    • B. 40 cm²
    • C. 80 cm²
    • D. 300 cm²

  13. Q18. A shape with area 5 cm² is enlarged by scale factor 3. What is the area of the image?

    • A. 15 cm²
    • B. 8 cm²
    • C. 45 cm²
    • D. 135 cm²

  14. Q19. a = (2, −1) and b = (3, 4). Find 2a + b.

    • A. (7, 2)
    • B. (4, 2)
    • C. (7, 6)
    • D. (5, 3)

  15. Q20. The point (3, 1) is rotated 90° clockwise about the origin. What are its new coordinates?

    • A. (1, −3)
    • B. (−1, 3)
    • C. (1, 3)
    • D. (−3, −1)