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4MA1/2H Jun 2023, 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

Given Q is directly proportional to √t and a graph of Q against t for 0 < t < 8, find the formula linking Q and t, then find the percentage increase in t when Q rises by 20%.

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

Part (a) · 3 marks

Use the graph to find the constant of proportionality, then write Q as a formula in terms of t.

  1. 1Q is directly proportional to √t, so Q = k√t
  2. 2From the graph, when t = 4, Q = 6
  3. 36 = k × √4
  4. 46 = 2k, so k = 3
  5. 5Q = 3√t

AnswerQ = 3√t

Part (b) · 2 marks

Using Q proportional to √t, work out the percentage increase in t when Q increases by 20%.

  1. 1Q = 3√t, so √t = Q ÷ 3
  2. 2Squaring both sides, t = Q² ÷ 9, so t is proportional to Q²
  3. 3Q is multiplied by 1.2, so t is multiplied by 1.2²
  4. 41.2² = 1.44
  5. 51.44 × t − t = 0.44 × t
  6. 6Percentage increase in t = 44%

Answer44

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