WMA12/01 Oct 2020, Question 2: The Trapezium Rule
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 4 marks
The question, in short
For y = 2ˣ ÷ √(5x² + 3), fill in missing table values at x = 0 and x = 0.5, then estimate the integral from −0.25 to 0.75 using the trapezium rule with all tabulated y values.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 1 mark
Work out y at x = 0 and x = 0.5, rounding each to 3 decimal places.
- 1x = 0: y = 2⁰/√3 = 1/√3 = 0.577
- 2x = 0.5: y = 2^0.5/√(5 × 0.25 + 3) = 1.4142/√4.25 = 0.686
Answerx = 0: y = 0.577; x = 0.5: y = 0.686
Part (b) · 3 marks
Apply the trapezium rule across x = −0.25 to 0.75 using every y value from the finished table to approximate the integral.
- 1Strip width h = 0.25
- 2Area ≈ ½ × 0.25 × {0.462 + 0.698 + 2(0.577 + 0.653 + 0.686)}
- 3= 0.125 × {1.160 + 3.832}
- 4= 0.125 × 4.992 = 0.624
Answer0.624
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