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1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only)

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Question 39

f(x)=x3−2x2+4x−5x>0f(x) = x^3 - 2x^2 + 4\sqrt{x} - 5 \quad x > 0f(x)=x3−2x2+4x​−5x>0

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.8,1.9][1.8, 1.9][1.8,1.9]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

Starting with x0=1.85x_0 = 1.85x0​=1.85, apply the Newton-Raphson procedure once to find an approximate solution to the equation f(x)=0f(x) = 0f(x)=0 giving your answer to 3 decimal places.

[3]
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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