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4MA1/2H Jun 2018, Question 16: 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

Using a graph of R against t from 0 to 4 where R reaches 40 at t = 4 and R varies with t squared, derive an equation linking R and t, then use R = 8/(5x) to demonstrate a relationship between t and √x.

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

Part (a) · 3 marks

Use the curve's values to determine the constant of proportionality and write R as a formula involving t.

  1. 1R is proportional to t², so R = kt²
  2. 2From the graph, R = 40 when t = 4: 40 = k × 16
  3. 3k = 40 ÷ 16 = 5/2, so R = (5/2)t²

AnswerR = (5/2)t²

Part (b) · 2 marks

Substitute R = 8/(5x) into your formula and rearrange to prove t is inversely proportional to √x when t > 0.

  1. 1Set the two expressions for R equal: (5/2)t² = 8/(5x)
  2. 2t² = 8/(5x) × 2/5 = 16/(25x)
  3. 3t = 4/(5√x) = 0.8/√x, so t is inversely proportional to √x

Answert = 0.8 / √x

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