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1.12 I: Numerical methods (A-level only)

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Question 33

f(x)=12x2+5cos⁡(x)\displaystyle f(x) = \frac{1}{2}x^2 + 5\cos(x)f(x)=21​x2+5cos(x)

a.

Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [2.5,2.6][2.5, 2.6][2.5,2.6]

[5]
b.

Starting with x0=2.55x_0 = 2.55x0​=2.55, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [2.5,2.6][2.5, 2.6][2.5,2.6]. Give your answer to 3 decimal places.

[4]

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

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

Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

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