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4PM1/02 Jun 2021, Question 9: Connected Rates of Change and Small Changes

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 8 marks

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The question, in short

For a right prism with equilateral triangle cross-section side x cm and length 4x cm, heated so cross-sectional area grows at 0.03 cm²/s, find rates at x = 2.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 5 marks

Find dx/dt at x = 2, giving the answer to 3 significant figures.

  1. 1dA/dt = 0.03
  2. 2A = (1/2)x² sin 60° = (√3/4)x²
  3. 3dA/dx = (√3/2)x = √3 when x = 2
  4. 4dx/dt = (dA/dt)/(dA/dx) = 0.03/√3 = 0.0173 cm/s

Answerdx/dt = 0.0173 cm/s

Part (b) · 3 marks

Find the rate of increase of the volume of S in cm³/s when x = 2.

  1. 1V = (√3/4)x² × 4x = √3x³
  2. 2dV/dx = 3√3x² = 12√3 when x = 2
  3. 3dV/dt = 12√3 × (√3/100) = 0.36 cm³/s

Answer0.36 cm³/s

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