Numerical methods

Sample questions

Original practice questions written in the style of the exam.

1. Question 16 marks

   $f(x) = x^3 - 2x - 5$

   (a) Show that the equation $f(x) = 0$ has a root $\alpha$ in the interval $[2, 3]$.

   (b) Taking $x_0 = 2$ as a first approximation, apply the Newton–Raphson method twice to find $x_2$, giving your answer to 4 decimal places.

   Mark scheme

   • M1 Evaluates $f(2) = -1$ and $f(3) = 16$ (1)
   • A1 States change of sign and $f$ continuous, so a root lies in $$ (1)