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1.12 I: Numerical methods (A-level only)

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Question 7

g(x)=ln⁡(3x−1)+x2−6x>13\displaystyle g(x) = \ln(3x - 1) + x^2 - 6 \quad x > \frac{1}{3}g(x)=ln(3x−1)+x2−6x>31​

a.

Show that g(x)=0g(x) = 0g(x)=0 has a root in the interval [2.0,2.1][2.0, 2.1][2.0,2.1]

[2]
b.

Find g′(x)g'(x)g′(x)

[3]
c.

Using x0=2.0x_0 = 2.0x0​=2.0 as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer to 3 decimal places.

[3]
Markscheme

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

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

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), 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). Each one has a worked solution and a mark scheme showing where the marks go.

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