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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 29

The curve C C\,C with equation y=exy = e^xy=ex intersects the line L L\,L with equation y=3x+5y = 3x + 5y=3x+5 at the point QQQ.

a.

Show that the x x\,x coordinate of Q Q\,Q satisfies the equation x=ln⁡(3x+5)x = \ln(3x + 5)x=ln(3x+5).

[2]
b.

Using the iterative relation xn+1=ln⁡(3xn+5)x_{n+1} = \ln(3x_n + 5)xn+1​=ln(3xn​+5) with x0=2.8x_0 = 2.8x0​=2.8, calculate the values of x1x_1x1​, x2 x_2\,x2​ and x3x_3x3​, giving each 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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