IB Maths: Analysis and Approaches chapter 3: Geometry and trigonometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

51 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.

51 questions · 5 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. A solid is made of a right cone of radius 3 cm and height 4 cm on top of a hemisphere of radius 3 cm, with flat faces joined. Find its volume, in terms of π.

  1. A
    48π cm3
  2. B
    54π cm3
  3. C
    18π cm3
  4. D
    30π cm3
Show answer

Answer: D. Cone = (1/3)π(9)(4) = 12π and hemisphere = (2/3)π(27) = 18π, total 30π cm3. Using a full sphere gives 48π.

2. A sector has radius 10 cm and angle 0.8 radians. Find its perimeter.

  1. A
    8 cm
  2. B
    18 cm
  3. C
    28 cm
  4. D
    40 cm
Show answer

Answer: C. Arc = 10 × 0.8 = 8 cm, and the perimeter also includes two radii: 8 + 10 + 10 = 28 cm.

3. A right-angled triangle has shorter sides 5 cm and 12 cm. Find its smallest angle.

  1. A
    67.4°
  2. B
    24.6°
  3. C
    65.4°
  4. D
    22.6°
Show answer

Answer: D. The smallest angle is opposite the 5 cm side: tan θ = 5/12, θ = 22.6°. sin−1(5/12) is wrong because 12 is not the hypotenuse (13 is).

4. Find the exact value of cos(5π/4).

  1. A
    √2/2
  2. B
    −1/2
  3. C
    −√3/2
  4. D
    −√2/2
Show answer

Answer: D. 5π/4 is in the third quadrant, where cosine is negative, with reference angle π/4: cos(5π/4) = −√2/2.

5. For which interval of θ is sin θ > 0 and cos θ < 0?

  1. A
    π/2 < θ < π
  2. B
    0 < θ < π/2
  3. C
    π < θ < 3π/2
  4. D
    3π/2 < θ < 2π
Show answer

Answer: A. On the unit circle, cos θ is the x-coordinate and sin θ the y-coordinate. Positive y and negative x means the second quadrant, π/2 < θ < π.

6. Find the midpoint of (2, −4, 6) and (8, 0, −2).

  1. A
    (3, 2, −4)
  2. B
    (5, −2, 2)
  3. C
    (10, −4, 4)
  4. D
    (5, −2, 4)
Show answer

Answer: B. Average each coordinate: ((2 + 8)/2, (−4 + 0)/2, (6 − 2)/2) = (5, −2, 2).

7. Describe the transformation that maps y = sin x onto y = sin(x − π/4).

  1. A
    translation of π/4 to the right
  2. B
    translation of π/4 to the left
  3. C
    translation of π/4 up
  4. D
    horizontal stretch with scale factor π/4
Show answer

Answer: A. f(x − c) moves the graph c units to the right, so this is a translation of π/4 to the right.

8. Find the area of a triangle with sides 6 cm and 9 cm and an included angle of 30°.

  1. A
    13.5 cm2
  2. B
    27.0 cm2
  3. C
    23.4 cm2
  4. D
    46.8 cm2
Show answer

Answer: A. Area = ½ab sin C = ½ × 6 × 9 × sin 30° = 27 × 0.5 = 13.5 cm2. Forgetting the ½ gives 27.

9. A rider’s height on a big wheel is h = 22 − 20cos(πt/15) metres, t seconds after boarding. Find the first time the rider is 32 m high.

  1. A
    5 s
  2. B
    10 s
  3. C
    15 s
  4. D
    20 s
Show answer

Answer: B. 32 = 22 − 20cos(πt/15) gives cos(πt/15) = −½, so πt/15 = 2π/3 and t = 10 s. Using cos = +½ gives 5 s.

10. Write down the exact value of sin(π/3).

  1. A
    √3/2
  2. B
    1/2
  3. C
    √2/2
  4. D
    √3
Show answer

Answer: A. π/3 = 60° and sin 60° = √3/2. 1/2 is cos(π/3).

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Ways to practise this chapter

Geometry and trigonometry: questions students ask

How many Geometry and trigonometry MCQs are there?

51, each with the answer and a short explanation, across 5 topics: SL3.1 Three-dimensional geometry, SL3.2, SL3.3 Trigonometry of triangles and its applications, SL3.4, SL3.5 Radians, the unit circle and exact values, SL3.6, SL3.8 Trigonometric identities and equations, SL3.7 Circular functions and their graphs. Every chapter test draws ten of them, so you can take it many times.

Is the IB Maths: Analysis and Approaches 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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