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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 3
a.

Sketch the graphs of y=ln⁡xy = \ln xy=lnx and y=1xy = \dfrac{1}{x}y=x1​ for x>0 x > 0\,x>0 on the same axes.

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b.

Explain why the equation ln⁡x=1x\ln x = \dfrac{1}{x}lnx=x1​ has exactly one solution.

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c.

By considering a suitable change of sign, show that the solution lies between 1.7 and 1.8.

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d.

Use the iterative formula

xn+1=e1xn\displaystyle x_{n+1} = e^{\frac{1}{x_n}}xn+1​=exn​1​

with x1=1.8x_1 = 1.8x1​=1.8 to find x2x_2x2​, x3 x_3\,x3​ and x4x_4x4​, giving your answers to four decimal places.

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Markscheme

1.9 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9 Numerical Methods (A-level only)

125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 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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