| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Sign Change & Interval Methods |
| Type | Interval Bisection with Other Methods |
| Difficulty | Standard +0.3 This is a straightforward application of two standard numerical methods (interval bisection and linear interpolation) to find a root. The function evaluation is simple, the methods are routine algorithmic procedures taught directly in F1, and the question requires no problem-solving insight—just careful execution of learned algorithms. Slightly easier than average due to its purely procedural nature. |
| Spec | 1.09a Sign change methods: locate roots1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
\begin{enumerate}
\item In the interval $2 < x < 3$, the equation
\end{enumerate}
$$6 - x ^ { 2 } \cos \left( \frac { x } { 5 } \right) = 0 , \text { where } x \text { is measured in radians }$$
has exactly one root $\alpha$.\\[0pt]
(a) Starting with the interval [2,3], use interval bisection twice to find an interval of width 0.25 which contains $\alpha$.\\[0pt]
(b) Use linear interpolation once on the interval [2,3] to find an approximation to $\alpha$. Give your answer to 2 decimal places.\\
\hfill \mbox{\textit{Edexcel F1 2015 Q5 [7]}}