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1.9 Numerical Methods (A-level only)

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Question 56

A curve has the equation

y=ln⁡(3−2x)+x2−2xy = \ln(3 - 2x) + x^2 - 2xy=ln(3−2x)+x2−2x

The curve intersects the xxx-axis at exactly one point.

a.

Show that the xxx-coordinate of this point lies between 0 and 1.

[2]
b.

Use the Newton-Raphson method, with x0=1x_0 = 1x0​=1, to find the xxx-coordinate of this point, giving your answer correct to five decimal places. Show the result of each iteration.

[5]
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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