Edexcel International GCSE Maths Similar Shapes Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Geometry and Trigonometry

Similar Shapes: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every similar shapes question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 8 questions worth 30 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

14 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q3

ABCD and EFGH are similar quadrilaterals. In ABCD: AB = 9.6 cm and CD = 4 cm. In EFGH: EF = 6 cm and FG = 5.7 cm. Angles A and E are right angles, and the angles at B and F, and at D and H, are equal.

ABCD9.6 cm4 cmEFGH6 cm5.7 cm

(a) Work out the length of GH. (2)

(b) Work out the length of BC. (2)

Show solution
  1. Matching sides: AB ↔ EF, BC ↔ FG, CD ↔ GH.
  2. Scale factor from the small shape to the large shape = AB ÷ EF = 9.6 ÷ 6 = 1.6

Part (a)

  1. GH matches CD in the large shape. Going from large to small, divide by 1.6: 4 ÷ 1.6

Answer: 2.5 cm

Part (b)

  1. BC matches FG. Going from small to large, multiply by 1.6: 5.7 × 1.6

Answer: 9.12 cm

24 marksHigherJanuary 2022 · Paper 1H (4MA1/1H) · Q17

A and B are two similar vases. Vase A has height 10 cm. Vase B has height 15 cm. The difference between the volume of vase A and the volume of vase B is 1197 cm3. Calculate the volume of vase A.

Show solution
  1. Length scale factor = 15 ÷ 10 = 1.5, so volume scale factor = 1.53 = 3.375
  2. Volume of B = 3.375 × volume of A. Let A’s volume be V: 3.375V − V = 1197
  3. 2.375V = 1197

Answer: V = 504 cm3

34 marksHigherJanuary 2022 · Paper 1HR (4MA1/1HR) · Q18

The three solids A, B and C are similar such that the surface area of A : the surface area of B = 4 : 9 and the volume of B : the volume of C = 125 : 343. Work out the ratio the height of A : the height of C. Give your ratio in its simplest form.

Show solution
  1. Area ratio 4 : 9 gives a length ratio of √4 : √9 = 2 : 3 (A : B)
  2. Volume ratio 125 : 343 gives a length ratio of ∛125 : ∛343 = 5 : 7 (B : C)
  3. Make B the same in both: A : B = 2 : 3 = 10 : 15 and B : C = 5 : 7 = 15 : 21
  4. So A : B : C = 10 : 15 : 21

Answer: 10 : 21

44 marksHigherJune 2024 · Paper 1HR (4MA1/1HR) · Q18

The diagram shows two similar vases, A and B. The height of vase A is 30 cm. The height of vase B is 12 cm. Given that surface area of vase A − surface area of vase B = 178.5 cm2, find the surface area of vase A.

30 cm12 cmAB
Show solution
  1. Length scale factor from B to A = 30 ÷ 12 = 2.5
  2. Areas scale by the square of the length scale factor: area scale factor = 2.52 = 6.25
  3. So surface area of A = 6.25 × surface area of B. Let B’s surface area be S.
  4. 6.25S − S = 178.5, so 5.25S = 178.5 and S = 34 cm2
  5. Surface area of A = 6.25 × 34

Answer: 212.5 cm2

53 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q20

R and S are two similar solid shapes. Shape R has surface area 108 cm2 and volume 135 cm3. Shape S has surface area 300 cm2. Work out the volume of shape S.

Show solution
  1. Area scale factor = 300 ÷ 108 = 25⁄9
  2. Length scale factor = √(25⁄9) = 5⁄3
  3. Volume scale factor = (5⁄3)3 = 125⁄27
  4. Volume of S = 135 × 125⁄27

Answer: 625 cm3

63 marksHigherJanuary 2021 · Paper 1H (4MA1/1H) · Q20

A and B are two similar solids. A has a volume of 1836 cm3. B has a volume of 4352 cm3. B has a total surface area of 1120 cm2. Work out the total surface area of A.

Show solution
  1. Volume scale factor from A to B = 4352 ÷ 1836 = 64⁄27
  2. Length scale factor = ∛(64⁄27) = 4⁄3, so area scale factor = (4⁄3)2 = 16⁄9
  3. Going from B back to A, divide by 16⁄9: 1120 × 9⁄16

Answer: 630 cm2

74 marksHigherJune 2022 · Paper 1HR (4MA1/1HR) · Q20

The diagram shows two similar metal statues, A and B. The volume of statue B is 20% less than the volume of statue A. The surface area of statue B is k% less than the surface area of statue A. Work out the value of k. Give your answer correct to 3 significant figures.

Show solution
  1. Volume of B = 0.8 × volume of A, so the volume scale factor from A to B is 0.8.
  2. Length scale factor = ∛0.8 = 0.9283…
  3. Area scale factor = (∛0.8)2 = 0.82⁄3 = 0.8617…
  4. So B’s surface area is 86.17…% of A’s, which is 100 − 86.17… = 13.82…% less.

Answer: k = 13.8

84 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q26

R, S and T are three similar vases. The volume of vase S is 72.8% more than the volume of vase R. The height of vase R is h cm. The height of vase T is 6h cm. The surface area of vase S is A cm2. The surface area of vase T is kA cm2. Work out the value of k.

Show solution
  1. Volume of S = 1.728 × volume of R, so the volume scale factor from R to S is 1.728.
  2. Length scale factor = cube root of the volume scale factor: ∛1.728 = 1.2. So the height of S = 1.2h.
  3. Length scale factor from S to T = 6h ÷ 1.2h = 5
  4. Area scale factor = square of the length scale factor = 52 = 25

Answer: k = 25

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