Skip to content

Course home

Sign up

1.12 I: Numerical methods (A-level only)

EasyMediumHard
1234567891011121314151617181920212223242526272829303132
Question 19

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

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank