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1.12 I: Numerical methods (A-level only)

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Question 10

Figure 1 below shows part of the curve y=2xsin⁡xy = 2x\sin xy=2xsinx, where x x\,x is measured in radians. The maximum point on the curve is PPP.

Figure for question 3

a.

Show that the xxx-coordinate of P P\,P satisfies the equation

tan⁡x+x=0\tan x + x = 0tanx+x=0

[3]
b.

Use the Newton-Raphson method, with a suitable initial value, to find the xxx-coordinate of PPP, giving your answer correct to four decimal places. Show the result of each iteration.

[4]
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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