Edexcel International GCSE Maths Direct and Inverse Proportion Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Equations, Formulae and Identities

Direct and Inverse Proportion: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every direct and inverse proportion question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 7 questions worth 28 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.

13 marksHigherJune 2020 · Paper 1H (4MA1/1H) · Q14

F is inversely proportional to the square of v. Given that F = 6.5 when v = 4, find a formula for F in terms of v.

Show solution
  1. “Inversely proportional to the square of v” means F = k⁄v2
  2. Substitute F = 6.5 and v = 4: 6.5 = k⁄16
  3. Multiply both sides by 16: k = 104

Answer: F = 104⁄v2

23 marksHigherJanuary 2022 · Paper 1H (4MA1/1H) · Q15

A is inversely proportional to C2. A = 40 when C = 1.5. Calculate the value of C when A = 1000.

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  1. A = k⁄C2: 40 = k⁄2.25, so k = 90
  2. 1000 = 90⁄C2, so C2 = 0.09

Answer: C = 0.3

33 marksHigherJanuary 2023 · Paper 1H (4MA1/1H) · Q17

y is inversely proportional to √x. y = c4 when x = c2 where c is a positive constant. Find a formula for y in terms of x and c. Give your answer in its simplest form.

Show solution
  1. y = k⁄√x
  2. Substitute: c4 = k⁄√c2 = k⁄c, so k = c5

Answer: y = c5⁄√x

44 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q17

F is inversely proportional to the square of r. F = 36 when r = 4.

(a) Find a formula for F in terms of r. (3)

(b) Work out the value of F when r = 48. (1)

Show solution

Part (a)

  1. F = k⁄r2
  2. Substitute: 36 = k⁄16, so k = 36 × 16 = 576

Answer: F = 576⁄r2

Part (b)

  1. F = 576⁄482 = 576⁄2304

Answer: 0.25

54 marksHigherJune 2025 · Paper 1H (4MA1/1H) · Q18

y is inversely proportional to x3. y = 4 when x = 3. Work out the value of x when y = 864.

Show solution
  1. Inversely proportional to x3 means y = k⁄x3 for some constant k.
  2. Use y = 4 when x = 3: 4 = k⁄27, so k = 108 and y = 108⁄x3
  3. Substitute y = 864: 864 = 108⁄x3, so x3 = 108 ÷ 864 = 0.125
  4. x = ∛0.125

Answer: x = 0.5

65 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q18

F is inversely proportional to the cube of r. F = 6 when r = 2.

(a) Find a formula for F in terms of r. (3)

(b) Find the value of r when F = 3072. (2)

Show solution

Part (a)

  1. Inversely proportional to the cube means F = k⁄r3
  2. Substitute F = 6 and r = 2: 6 = k⁄8, so k = 48

Answer: F = 48⁄r3

Part (b)

  1. 3072 = 48⁄r3, so r3 = 48 ÷ 3072 = 1⁄64
  2. r = ∛(1⁄64) = 1⁄4

Answer: r = 0.25

76 marksHigherJanuary 2023 · Paper 1HR (4MA1/1HR) · Q19

P is inversely proportional to y2. When y = 4, P = a.

(a) Find a formula for P in terms of y and a. (3)

Given also that y is directly proportional to √x and when x = a, P = 4a

(b) find a formula for P in terms of x and a. (3)

Show solution

Part (a)

  1. P = k⁄y2
  2. a = k⁄16, so k = 16a

Answer: P = 16a⁄y2

Part (b)

  1. When P = 4a: 4a = 16a⁄y2, so y2 = 4 and y = 2 (this is when x = a)
  2. y = m√x: 2 = m√a, so m = 2⁄√a and y = 2√x⁄√a
  3. y2 = 4x⁄a. Substitute into part (a): P = 16a ÷ 4x⁄a = 16a2⁄4x

Answer: P = 4a2⁄x

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