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4MA1/1HR Jun 2023, Question 17: Inverse Proportion: y = k/x

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Given F varies inversely as r squared, with F = 36 at r = 4, derive the equation linking F and r, then evaluate F at r = 48.

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Part (a) · 3 marks

Use the inverse-square relationship and the pair F = 36, r = 4 to determine the constant and write F in terms of r.

  1. 1F = k / r²
  2. 236 = k / 4²
  3. 336 = k / 16
  4. 4k = 36 × 16
  5. 5k = 576
  6. 6F = 576 / r²

AnswerF = 576 / r²

Part (b) · 1 mark

Using the inverse-square relationship with F = 36 at r = 4, calculate F for r = 48.

  1. 1F = 576 / 48²
  2. 2F = 576 / 2304
  3. 3F = 0.25

Answer0.25

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