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0580/22 May/Jun 2025, Question 20: Proportion to Powers of x

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 4 marks

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The question, in short

Given y proportional to 1 over the square root of x, with y = 2 at x = 9, work out y at x = 36 and the factor p by which y changes when x is multiplied by 4.

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Part (a) · 3 marks

Using the inverse square-root relationship and the pair x = 9, y = 2, determine y at x = 36.

  1. 1y = k/√x
  2. 22 = k/√9 = k/3, so k = 6
  3. 3x = 36: y = 6/√36 = 6/6 = 1

Answer1

Part (b) · 1 mark

Find p, the factor multiplying y when x grows by a factor of 4 under this inverse square-root proportionality.

  1. 1y = k/√(4x) = k/(2√x) = 1/2 × k/√x
  2. 2p = 1/2

Answer1/2

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Also searched as: 0580/22/M/J/25 · 0580_s25_qp_22 · 0580 s25 22 · question 20.
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