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WMA12/01 Jan 2022, Question 1: The Trapezium Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Use the table of y values for y = 2^(5 − √x) at x = 5 to 7 to estimate definite integrals, giving the part (a) answer to 2 decimal places.

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

Part (a) · 3 marks

Apply the trapezium rule with all five tabulated y values to estimate the integral from 5 to 7, to 2 decimal places.

  1. 1Strip width h = 0.5
  2. 2Area ≈ ½ × 0.5 × {6.792 + 5.113 + 2(6.298 + 5.858 + 5.466)}
  3. 3= 0.25 × {11.905 + 35.244} = 0.25 × 47.149 = 11.787…
  4. 4Estimate = 11.79 (2 d.p.)

Answer11.79

Part (bi) · 2 marks

Use the part (a) result to estimate the integral of 2^(6 − √x) from 5 to 7, explaining the method.

  1. 12^(6 − √x) = 2 × 2^(5 − √x)
  2. 2So the integral ≈ 2 × 11.79 = 23.58

Answer23.58

Part (bii) · 2 marks

Use the part (a) result to estimate the integral of 3 + 2^(5 − √x) from 5 to 7, showing the method.

  1. 1∫₅⁷ 3 dx = 3 × (7 − 5) = 6
  2. 2So the integral ≈ 11.79 + 6 = 17.79

Answer17.79

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Also searched as: WMA12 January 2022 · WMA12/01 · wma12 jan22 · IAS Maths Pure Mathematics 2 January 2022 · question 1.
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