GCSE Maths (AQA) chapter 4: Geometry and measures MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

77 exam-style questions on Geometry and measures, 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.

77 questions · 8 topics · 10 per test

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What chapter 4 covers

Ten Geometry and measures questions with answers

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

1. OA = a and OB = b. M is the midpoint of AB. Which expression is the vector OM?

  1. A
    ½(b − a)
  2. B
    a + ½b
  3. C
    ½(a + b)
  4. D
    b − a
Show answer

Answer: C. OM = OA + ½AB = a + ½(b − a) = ½a + ½b = ½(a + b). ½(b − a) is only AM.

2. Two similar solids have surface areas 45 cm2 and 80 cm2. The smaller has volume 54 cm3. What is the volume of the larger?

  1. A
    96 cm3
  2. B
    128 cm3
  3. C
    72 cm3
  4. D
    170.7 cm3
Show answer

Answer: B. Area factor 80/45 = 16/9, so the length factor is 4/3 and the volume factor is 64/27. 54 × 64/27 = 128 cm3. Multiplying by the area factor gives 96 cm3.

3. Calculator. A triangle has sides 8 cm and 10 cm and area 30 cm2. The angle between these sides is acute. Find the angle, to 1 decimal place.

  1. A
    22.0°
  2. B
    48.6°
  3. C
    41.4°
  4. D
    36.9°
Show answer

Answer: B. 30 = ½ × 8 × 10 × sin C, so sin C = 30 ÷ 40 = 0.75 and C = 48.6°. Forgetting the ½ gives sin C = 0.375 and 22.0°.

4. a is the column vector (3, −2) and b is the column vector (−1, 4), with the top entry written first. What is 2a − b?

  1. A
    (5, 0)
  2. B
    (7, −8)
  3. C
    (4, −6)
  4. D
    (7, 0)
Show answer

Answer: B. 2a = (6, −4), and 2a − b = (6 − (−1), −4 − 4) = (7, −8). (5, 0) is 2a + b.

5. ka + 3b is parallel to 2a + 6b. What is k?

  1. A
    6
  2. B
    2
  3. C
    3
  4. D
    1
Show answer

Answer: D. 2a + 6b = 2(a + 3b), so ka + 3b must be a multiple of a + 3b with the b-part 3b, giving k = 1.

6. Calculator. In triangle ABC, AB = 9 cm, AC = 7 cm and angle BAC = 50°. What is BC, to 3 significant figures?

  1. A
    9.46 cm
  2. B
    7.00 cm
  3. C
    14.5 cm
  4. D
    49.0 cm
Show answer

Answer: B. Cosine rule: BC2 = 72 + 92 − 2 × 7 × 9 × cos 50° = 130 − 81.0 = 49.0, so BC = 7.00 cm. Forgetting the 2 gives 9.46; 49.0 forgets the square root.

7. ABCD is a parallelogram with AB = p and AD = q. Which expression is the vector BD?

  1. A
    p − q
  2. B
    q − p
  3. C
    p + q
  4. D
    −p − q
Show answer

Answer: B. BD = BA + AD = −p + q = q − p. p + q is the other diagonal, AC.

8. A chord of length 16 cm is in a circle of radius 10 cm. How far is the chord from the centre?

  1. A
    12.8 cm
  2. B
    2 cm
  3. C
    6 cm
  4. D
    8 cm
Show answer

Answer: C. The perpendicular from the centre bisects the chord, making a right-angled triangle with sides 8 cm and d and hypotenuse 10 cm: d = √(100 − 64) = 6 cm. Adding the squares gives 12.8 cm.

9. Triangle ABC is similar to triangle DEF. AB = 6 cm, DE = 15 cm and BC = 8 cm. BC and EF are corresponding sides. What is EF?

  1. A
    17 cm
  2. B
    20 cm
  3. C
    3.2 cm
  4. D
    24 cm
Show answer

Answer: B. Scale factor = 15 ÷ 6 = 2.5, so EF = 8 × 2.5 = 20 cm. Adding 9 cm to every side (17 cm) is not an enlargement.

10. In triangle PQR, PQ = 7 cm, QR = 9 cm and angle PQR = 50°. In triangle XYZ, XY = 7 cm, YZ = 9 cm and angle XYZ = 50°. Which condition shows the triangles are congruent?

  1. A
    SAS
  2. B
    SSS
  3. C
    ASA
  4. D
    RHS
Show answer

Answer: A. Two sides and the angle between them (the included angle) are equal: SAS. We do not know the third sides, so it is not SSS.

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Ways to practise this chapter

Geometry and measures: questions students ask

How many Geometry and measures MCQs are there?

77, each with the answer and a short explanation, across 8 topics: G1–G4, G15 Angles, polygons and bearings, G7–G8 Transformations, G9–G10 Circle theorems, G14, G16–G18 Area, volume and surface area, G5–G6, G19 Congruence and similarity, G20–G21 Pythagoras and trigonometry, G22–G23 Sine rule, cosine rule and area of a triangle, G24–G25 Vectors. Every chapter test draws ten of them, so you can take it many times.

Is the GCSE Maths (AQA) chapter 4 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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