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WMA12/01 Jun 2025, Question 5: The Trapezium Rule

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks

The question, in short

Use the table of y values for y = 3(½)ˣ at seven x values to estimate definite integrals of related functions over x from −2 to 7.

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 seven tabulated y values to estimate the integral of 3(½)ˣ from −2 to 7, to one decimal place.

  1. 1Strip width h = 1.5
  2. 2Area ≈ (1.5/2) × {12 + 0.023 + 2(4.243 + 1.5 + 0.530 + 0.188 + 0.066)}
  3. 3= 0.75 × {12.023 + 2 × 6.527} = 0.75 × 25.077
  4. 4= 18.80775 ≈ 18.8

Answer18.8

Part (bi) · 1 mark

Using the part (a) answer, estimate the integral of 3(½)ˣ⁺² from −2 to 7, showing the method.

  1. 13(½)ˣ⁺² = (½)² × 3(½)ˣ = ¼ × 3(½)ˣ
  2. 2So the integral ≈ ¼ × 18.8 = 4.7

Answer4.7

Part (bii) · 2 marks

Using the part (a) answer, estimate the integral of 2⁻ˣ + 2x from −2 to 7, showing the method.

  1. 12⁻ˣ = (½)ˣ = ⅓ × 3(½)ˣ, so ∫₋₂⁷ 2⁻ˣ dx ≈ ⅓ × 18.8 = 6.27
  2. 2∫₋₂⁷ 2x dx = [x²]₋₂⁷ = 49 − 4 = 45
  3. 3Total ≈ 6.27 + 45 = 51.3

Answer51.3

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