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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 32

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]
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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