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1.10 Numerical Methods (A-level only)

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Question 30

k(x)=2ln⁡(x+1)+x2−8x>−1k(x) = 2\ln(x + 1) + x^2 - 8 \quad x > -1k(x)=2ln(x+1)+x2−8x>−1

a.

Show that k(x)=0k(x) = 0k(x)=0 has a root in the interval [2.3,2.4][2.3, 2.4][2.3,2.4]

[2]
b.

Find k′(x)k'(x)k′(x)

[3]
c.

Using x0=2.3x_0 = 2.3x0​=2.3 as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer to 3 decimal places.

[3]
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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