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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 31

f(x)=x3+3x2−2xx>0f(x) = x^3 + 3x^2 - 2\sqrt{x} \quad x > 0f(x)=x3+3x2−2x​x>0

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [0.6,0.7][0.6, 0.7][0.6,0.7]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

Starting with x0=0.65x_0 = 0.65x0​=0.65, apply the Newton-Raphson procedure once to find an approximate solution to the equation f(x)=0f(x) = 0f(x)=0 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)

137 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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