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O Level & A Level Mathematics (Cambridge)

O Level Mathematics — Geometry, Mensuration and Trigonometry, Set 1

Take the O Level Mathematics — Geometry, Mensuration and Trigonometry, Set 1: 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 size of each interior angle of a regular octagon?

    • A. 45°
    • B. 135° ✓
    • C. 120°
    • D. 1080°

    Answer: B. 135°

    Explanation: Each exterior angle is 360° ÷ 8 = 45°, so each interior angle is 180° − 45° = 135°.

  2. Q2. Each exterior angle of a regular polygon is 24°. How many sides does it have?

    • A. 24
    • B. 9
    • C. 12
    • D. 15 ✓

    Answer: D. 15

    Explanation: 360° ÷ 24° = 15 sides.

  3. Q3. In the figure, two parallel lines are cut by a transversal. Find x.

    Two parallel lines cut by a transversal. At the lower intersection the angle between the transversal and the parallel line, on the right and above the line, is 65 degrees. At the upper intersection the angle on the right and below the line is marked x.
    • A. 25°
    • B. 130°
    • C. 115° ✓
    • D. 65°

    Answer: C. 115°

    Explanation: The 65° angle and x are co-interior (same side of the transversal, between the parallel lines), so x = 180° − 65° = 115°.

  4. Q4. What is the angle in a semicircle?

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

    Answer: B. 90°

    Explanation: An angle subtended by a diameter at the circumference is always 90°.

  5. Q5. An angle at the circumference is 35°. What is the angle at the centre subtended by the same arc?

    • A. 35°
    • B. 17.5°
    • C. 70° ✓
    • D. 145°

    Answer: C. 70°

    Explanation: The angle at the centre is twice the angle at the circumference.

The other 15 questions

Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.

  1. Q6. One angle of a cyclic quadrilateral is 110°. What is the opposite angle?

    • A. 90°
    • B. 110°
    • C. 250°
    • D. 70°

  2. Q7. A 10 m ladder leans against a wall with its foot 6 m from the wall. How high up the wall does it reach?

    • A. 11.7 m
    • B. 8 m
    • C. 16 m
    • D. 4 m

  3. Q8. In the figure, the hypotenuse is 12 cm and the angle is 35°. Find x, correct to 3 significant figures.

    Right-angled triangle with hypotenuse 12 cm, an angle of 35 degrees at the bottom left, and the vertical side opposite that angle marked x.
    • A. 6.88 cm
    • B. 8.40 cm
    • C. 9.83 cm
    • D. 14.6 cm

  4. Q9. A right-angled triangle has opposite side 5 cm and adjacent side 12 cm. Find the angle, to 1 decimal place.

    • A. 22.6°
    • B. 24.6°
    • C. 65.4°
    • D. 67.4°

  5. Q10. In triangle ABC, A = 30°, a = 8 cm and B = 45°. Find b, to 3 significant figures.

    • A. 12.0 cm
    • B. 9.80 cm
    • C. 5.66 cm
    • D. 11.3 cm

  6. Q11. In triangle ABC, b = 5 cm, c = 7 cm and A = 60°. Find a, to 3 significant figures.

    • A. 8.54 cm
    • B. 12.0 cm
    • C. 6.24 cm
    • D. 4.36 cm

  7. Q12. Find the area of a triangle with sides 6 cm and 8 cm and an included angle of 30°.

    • A. 24 cm²
    • B. 12 cm²
    • C. 48 cm²
    • D. 20.8 cm²

  8. Q13. The figure shows a sector of radius 7 cm and angle 72°. Taking π = 22/7, find the arc length.

    Sector of a circle with radius 7 cm and angle 72 degrees.
    • A. 8.8 cm
    • B. 30.8 cm
    • C. 17.6 cm
    • D. 4.4 cm

  9. Q14. Using the same sector (radius 7 cm, angle 72°, π = 22/7), find its area.

    Sector of a circle with radius 7 cm and angle 72 degrees.
    • A. 154 cm²
    • B. 30.8 cm²
    • C. 8.8 cm²
    • D. 61.6 cm²

  10. Q15. Taking π = 22/7, find the volume of a cylinder with radius 7 cm and height 10 cm.

    • A. 220 cm³
    • B. 4400 cm³
    • C. 1540 cm³
    • D. 440 cm³

  11. Q16. Find the volume of a cone with radius 3 cm and height 4 cm, in terms of π.

    • A. 12π cm³
    • B. 4π cm³
    • C. 15π cm³
    • D. 36π cm³

  12. Q17. Two similar solids have lengths in the ratio 2 : 3. What is the ratio of their volumes?

    • A. 6 : 9
    • B. 2 : 3
    • C. 4 : 9
    • D. 8 : 27

  13. Q18. The bearing of B from A is 070°. What is the bearing of A from B?

    • A. 070°
    • B. 290°
    • C. 110°
    • D. 250°

  14. Q19. What is the magnitude of the vector (3, 4)?

    • A. 5
    • B. 7
    • C. 25
    • D. 12

  15. Q20. The point (2, 5) is reflected in the x-axis. What are its new coordinates?

    • A. (5, 2)
    • B. (−2, −5)
    • C. (2, −5)
    • D. (−2, 5)