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4024/12 May/Jun 2021, Question 18: Inverse Proportion: y = k/x

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

Given y varies inversely as x cubed, with y = 24 at x = 1/2, derive the equation linking y and x, then evaluate y at x = 1/3.

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Part (a) · 2 marks

Use the inverse cube relationship and the pair x = 1/2, y = 24 to work out the constant and state y in terms of x.

  1. 1y = k/x³
  2. 224 = k ÷ (1/2)³ = 8k, so k = 3
  3. 3y = 3/x³

Answer3/x³

Part (b) · 1 mark

Using the inverse cube relationship with x = 1/3, calculate the resulting y value.

  1. 1y = 3 ÷ (1/3)³ = 3 × 27
  2. 2y = 81

Answer81

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Also searched as: 4024/12/M/J/21 · 4024_s21_qp_12 · 4024 s21 12 · question 18.
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