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1.12 I: Numerical methods (A-level only)

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Question 32
a.

Use the trapezium rule with four strips to find an estimate for

∫022x dx \int_0^2 2^x\,dx\,∫02​2xdx

Give your answer to four decimal places.

[3]
b.

Given that ∫022x dx=3ln⁡2\displaystyle\int_0^2 2^x\,dx = \frac{3}{\ln 2}∫02​2xdx=ln23​, find the percentage error in the estimate found in part (a). Give your answer to two significant figures.

[2]
c.

Explain, with reference to the shape of the curve y=2xy = 2^xy=2x, why the trapezium rule gives an overestimate here.

[2]
Markscheme

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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