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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 105
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

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 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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