| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Moderate -0.3 This is a straightforward computational question requiring standard application of interval bisection (2 iterations) and one Newton-Raphson iteration. Both are routine A-level techniques with no conceptual challenges—students simply follow algorithms with calculator work. The function evaluation is slightly tedious but mechanical, making this slightly easier than average. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
5.
$$f ( x ) = 30 + \frac { 7 } { \sqrt { x } } - x ^ { 5 } , \quad x > 0$$
The only real root, $\alpha$, of the equation $\mathrm { f } ( x ) = 0$ lies in the interval [2,2.1].\\[0pt]
\begin{enumerate}[label=(\alph*)]
\item Starting with the interval [2,2.1], use interval bisection twice to find an interval of width 0.025 that contains $\alpha$.
\item Taking 2 as a first approximation to $\alpha$, apply the Newton-Raphson process once to $\mathrm { f } ( x )$ to find a second approximation to $\alpha$, giving your answer to 2 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q5 [9]}}