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4MA1/2H Jun 2022, Question 18: Calculating with Bounds

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

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The question, in short

Given X = (2a − b)/f with a = 7.5, b = 3.42, f = 2 each rounded to stated accuracy, find the upper bound of X, showing working.

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Solution · 3 marks

  1. 1a = 7.5 to 1 d.p., so 7.45 ≤ a < 7.55 and the upper bound of a is 7.55
  2. 2b = 3.42 to 2 d.p., so 3.415 ≤ b < 3.425 and the lower bound of b is 3.415
  3. 3f = 2 to the nearest whole number, so 1.5 ≤ f < 2.5 and the lower bound of f is 1.5
  4. 4X = (2a − b) ÷ f is largest when 2a − b is largest and f is smallest
  5. 5Largest value of 2a − b = 2 × 7.55 − 3.415 = 15.1 − 3.415 = 11.685
  6. 6Upper bound of X = 11.685 ÷ 1.5 = 7.79

Answer7.79

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