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1.10 Numerical Methods (A-level only)

1.10 Numerical Methods (A-level only)

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Question 4

Figure 1 below shows the sector AOB AOB\,AOB of a circle. The angle AOB AOB\,AOB is θ \theta\,θ radians.

Figure for question 2

The area of the triangle AOB AOB\,AOB is 34\displaystyle \frac{3}{4}43​ of the area of the sector AOBAOBAOB.

a.

Show that sin⁡θ−34θ=0\displaystyle \sin\theta - \frac{3}{4}\theta = 0sinθ−43​θ=0.

[3]
b.

Use the Newton-Raphson method with θ0=2\theta_0 = 2θ0​=2 to find θ4 \theta_4\,θ4​ as an approximation for θ\thetaθ. Give your answer to four decimal places, and show the result of each iteration.

[4]
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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