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1.10 Numerical Methods (A-level only)

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Question 49
a.

Use the trapezium rule with 3 strips to estimate the value of

∫0π2cos⁡(x2)dx\displaystyle \int_0^{\pi} 2\cos\left(\frac{x}{2}\right)dx∫0π​2cos(2x​)dx

Give your answer to four decimal places.

[4]
b.

Find the exact value of ∫0π2cos⁡(x2)dx\displaystyle\int_0^{\pi} 2\cos\left(\frac{x}{2}\right)dx∫0π​2cos(2x​)dx.

[2]
c.

Hence find the percentage error in the estimate found in part (a), giving your answer to three significant figures.

[1]
Markscheme

1.10 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.10 Numerical Methods (A-level only)

133 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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