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WMA12/01 Jan 2020, Question 1: The Trapezium Rule

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

The question, in short

Use the given table of y = log₂(2x) at x = 2, 5, 8, 11, 14 with the trapezium rule to estimate integrals involving related logarithmic functions.

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 across x = 2 to 14 to estimate the integral of log₂(2x), to one decimal place.

  1. 1Strip width h = 3
  2. 2Area ≈ ½ × 3 × {2 + 4.81 + 2(3.32 + 4 + 4.46)}
  3. 3= 1.5 × 30.37 = 45.555
  4. 4≈ 45.6

Answer45.6

Part (bi) · 2 marks

Using the part (a) result, estimate the integral of log₂(4x²) divided by 5, explaining the method.

  1. 1log₂(4x²) = log₂((2x)²) = 2 log₂(2x)
  2. 2So the integrand is (2/5) log₂(2x)
  3. 3Estimate = 2/5 × 45.6
  4. 4= 18.24 ≈ 18.2

Answer18.2

Part (bii) · 2 marks

Using the part (a) result, estimate the integral of log₂(2/x), showing clearly how the method follows.

  1. 1log₂(2/x) = log₂ 4 − log₂(2x) = 2 − log₂(2x)
  2. 2∫₂¹⁴ 2 dx = 2 × 12 = 24
  3. 3Estimate = 24 − 45.6
  4. 4= −21.6

Answer−21.6

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Also searched as: WMA12 January 2020 · WMA12/01 · wma12 jan20 · IAS Maths Pure Mathematics 2 January 2020 · question 1.
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