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1.12 I: Numerical methods (A-level only)

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Question 7

f(x)=x3+2x2−5xx>0f(x) = x^3 + 2x^2 - 5\sqrt{x} \quad x > 0f(x)=x3+2x2−5x​x>0

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.3,1.4][1.3, 1.4][1.3,1.4]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

Starting with x0=1.35x_0 = 1.35x0​=1.35, 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]

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.

Question bank