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1.12 I: Numerical methods (A-level only)

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Question 6

The curve C C\,C with equation y=exy = e^xy=ex meets the line L L\,L with equation y=4x+3y = 4x + 3y=4x+3 at the point PPP.

a.

Show that the x x\,x coordinate of P P\,P satisfies x=ln⁡(4x+3)x = \ln(4x + 3)x=ln(4x+3).

[2]
b.

Use the iteration formula xn+1=ln⁡(4xn+3)x_{n+1} = \ln(4x_n + 3)xn+1​=ln(4xn​+3) with x0=2x_0 = 2x0​=2 to find, to 3 decimal places, the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​.

[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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