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4MA1/2H Jun 2024, Question 19: Calculating with Bounds

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks

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The question, in short

Using G = c/(2f − 3h) with c = 8, f = 6.62, h = 1.2 given to stated accuracy, find the lower bound of G to 3 decimal places, showing working.

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Solution · 3 marks

  1. 1c = 8 to the nearest whole number, so 7.5 ≤ c < 8.5 and the lower bound of c is 7.5
  2. 2f = 6.62 to 2 d.p., so 6.615 ≤ f < 6.625 and the upper bound of f is 6.625
  3. 3h = 1.2 to 1 d.p., so 1.15 ≤ h < 1.25 and the lower bound of h is 1.15
  4. 4G = c ÷ (2f − 3h) is smallest when c is smallest and 2f − 3h is largest
  5. 5Largest value of 2f − 3h = 2 × 6.625 − 3 × 1.15 = 13.25 − 3.45 = 9.8
  6. 6Lower bound of G = 7.5 ÷ 9.8 = 0.76530612...
  7. 7Lower bound of G = 0.765 correct to 3 decimal places

Answer0.765

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