| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Roots of polynomials |
| Type | Factor theorem and finding roots |
| Difficulty | Standard +0.8 This is a numerical methods question involving transcendental functions (exponential and trigonometric). Part (a) requires applying the intermediate value theorem, which is straightforward. Part (b) requires linear interpolation, a standard A-level technique but less routine than basic calculus. The combination of transcendental functions and numerical methods places it moderately above average difficulty, though the execution is methodical rather than requiring deep insight. |
| Spec | 1.09a Sign change methods: locate roots |
$\mathrm { f } ( x ) = 2 ^ { x } - 10 \sin x - 2$, where $x$ is measured in radians
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { f } ( x ) = 0$ has a root, $\alpha$, between 2 and 3\\[0pt]
\item Use linear interpolation once on the interval [2,3] to find an approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q1 [5]}}