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WMA12/01 Oct 2024, Question 1: The Trapezium Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 5 marks

The question, in short

Use the given table of values for y = f(x) at x = 0.5, 1.75, 3, 4.25, 5.5 with the trapezium rule to estimate two definite integrals over 0.5 to 5.5.

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 y-values and the equal x-interval to estimate the integral of f(x) from 0.5 to 5.5, to one decimal place.

  1. 1Strip width h = (5.5 − 0.5) ÷ 4 = 1.25
  2. 2Area ≈ ½ × 1.25 × {3.479 + 5.182 + 2(6.101 + 7.448 + 6.823)}
  3. 3= 0.625 × 49.405 = 30.878…
  4. 4≈ 30.9 (1 d.p.)

Answer30.9

Part (b) · 2 marks

Using part (a), estimate the integral of f(x) + 4x from 0.5 to 5.5, showing your method clearly.

  1. 1∫(f(x) + 4x) dx = ∫f(x) dx + ∫4x dx
  2. 2∫ from 0.5 to 5.5 of 4x dx = [2x²] from 0.5 to 5.5 = 2(5.5)² − 2(0.5)² = 60
  3. 3Estimate = 30.9 + 60 = 90.9

Answer90.9

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Also searched as: WMA12 October 2024 · WMA12/01 · wma12 oct24 · IAS Maths Pure Mathematics 2 October 2024 · question 1.
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