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4MA1/2H Jun 2019, Question 17: Proportion to Powers of x

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

Given y varies directly with x cubed and y = 20h at x = h, derive an equation linking y, x and h, then use the stated formula to find x when y = 67.5h.

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Part (a) · 3 marks

Use the direct proportion relationship and the given pair of values to write y as an expression involving x and h.

  1. 1y = kx³
  2. 2x = h, y = 20h: 20h = k × h³
  3. 3k = 20h ÷ h³ = 20/h²
  4. 4y = 20x³/h²

Answery = 20x³/h²

Part (b) · 2 marks

Starting from y = 20x³/h², solve for x when y = 67.5h, giving the result in simplest form.

  1. 1Use y = 20x³/h²: 67.5h = 20x³/h²
  2. 220x³ = 67.5h³
  3. 3x³ = 3.375h³
  4. 4x = ∛(3.375h³) = 1.5h

Answer1.5h

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