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1.12 I: Numerical methods (A-level only)

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Question 10

Figure 1 below shows the graph of y=ln⁡(4x+3)y = \ln(4x + 3)y=ln(4x+3) and the graph of y=xy = xy=x.

Figure for question 6

a.

Show that the equation ln⁡(4x+3)=x\ln(4x + 3) = xln(4x+3)=x has a root between 2 and 3.

[2]
b.

Use Figure 1, starting with x1=2x_1 = 2x1​=2, to determine whether the iteration formula

xn+1=ln⁡(4xn+3)x_{n+1} = \ln(4x_n + 3)xn+1​=ln(4xn​+3)

can be used to find an approximation for this root. Justify your answer.

[2]
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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