IB Maths: Applications and Interpretation chapter 3: Geometry and trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

36 exam-style questions on Geometry and trigonometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

36 questions · 4 topics · 10 per test

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What chapter 3 covers

Ten Geometry and trigonometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. Find the equation of the perpendicular bisector of (−1, 4) and (5, 2).

  1. A
    y = −3x + 9
  2. B
    y = 3x + 3
  3. C
    y = 3x − 3
  4. D
    y = −x/3 + 11/3
Show answer

Answer: C. Midpoint (2, 3); gradient of the segment = −2 ÷ 6 = −1/3, so the bisector has gradient 3: y − 3 = 3(x − 2), y = 3x − 3. The last option is the line through the two points.

2. A triangular garden has sides 6 m, 8 m and 11 m. Find its area.

  1. A
    24.0 m2
  2. B
    46.8 m2
  3. C
    33.0 m2
  4. D
    23.4 m2
Show answer

Answer: D. Find an angle first: cos C = (36 + 64 − 121) ÷ 96, so C = 102.6°. Area = ½ × 6 × 8 × sin 102.6° = 23.4 m2. 24.0 m2 wrongly assumes a right angle.

3. A ship sails 30 km on a bearing of 060° and then 40 km on a bearing of 150°. How far is it from its starting point?

  1. A
    70 km
  2. B
    36.1 km
  3. C
    50 km
  4. D
    60.8 km
Show answer

Answer: C. The change of direction is 150° − 60° = 90°, so the path makes a right angle: √(302 + 402) = 50 km. 70 km just adds the legs.

4. Two sides of a triangle are 7 cm and 9 cm and the angle between them is 50°. Find the third side.

  1. A
    14.5 cm
  2. B
    7.00 cm
  3. C
    11.4 cm
  4. D
    2.90 cm
Show answer

Answer: B. c2 = 49 + 81 − 126 cos 50° = 49.0, so c = 7.00 cm. 2.90 cm comes from a GDC in radian mode; 14.5 cm adds the last term.

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

  1. A
    070°
  2. B
    290°
  3. C
    250°
  4. D
    110°
Show answer

Answer: C. The back bearing differs by 180°: 070° + 180° = 250°.

6. Find the volume of a right cone with base radius 4 cm and height 9 cm.

  1. A
    151 cm3
  2. B
    452 cm3
  3. C
    37.7 cm3
  4. D
    113 cm3
Show answer

Answer: A. V = (1/3)πr2h = (1/3)π × 16 × 9 = 48π = 151 cm3. 452 cm3 forgets the 1/3 (it is the cylinder).

7. Find the equation of the perpendicular bisector of A(2, 1) and B(6, 5).

  1. A
    y = x − 1
  2. B
    y = −x + 7
  3. C
    y = −x + 3
  4. D
    y = x + 7
Show answer

Answer: B. Midpoint (4, 3), gradient AB = 1, so the bisector has gradient −1: y − 3 = −(x − 4), y = −x + 7. y = x − 1 is the line AB itself.

8. From a point 40 m from the base of a tower on level ground, the angle of elevation of the top is 28°. Find the height of the tower.

  1. A
    18.8 m
  2. B
    35.3 m
  3. C
    75.2 m
  4. D
    21.3 m
Show answer

Answer: D. tan 28° = h ÷ 40, so h = 40 tan 28° = 21.3 m. 75.2 m divides by tan instead of multiplying.

9. A 6 m ladder leans against a vertical wall with its foot 1.8 m from the wall on level ground. Find the angle between the ladder and the ground.

  1. A
    72.5°
  2. B
    17.5°
  3. C
    16.7°
  4. D
    73.3°
Show answer

Answer: A. cos θ = 1.8 ÷ 6 = 0.3, so θ = 72.5°. 17.5° is the angle between the ladder and the wall.

10. In a right-angled triangle the side opposite angle θ is 5 cm and the side adjacent to θ is 8 cm. Find θ.

  1. A
    58.0°
  2. B
    38.7°
  3. C
    51.3°
  4. D
    32.0°
Show answer

Answer: D. tan θ = 5 ÷ 8, so θ = 32.0°. 38.7° uses sin, which needs the hypotenuse, not the adjacent side.

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Ways to practise this chapter

Geometry and trigonometry: questions students ask

How many Geometry and trigonometry MCQs are there?

36, each with the answer and a short explanation, across 4 topics: SL3.1 Three-dimensional geometry: distance, solids and angles, SL3.2 Right-angled and non-right-angled trigonometry, SL3.3, SL3.4 Applications of trigonometry: elevation, bearings, arcs and sectors, SL3.5, SL3.6 Perpendicular bisectors and Voronoi diagrams. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Applications and Interpretation chapter 3 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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