| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Compare Newton-Raphson with linear interpolation |
| Difficulty | Standard +0.3 This is a straightforward application of two standard numerical methods (Newton-Raphson and linear interpolation) to a given function. While the function involves fractional powers requiring careful differentiation, the question provides clear intervals, starting values, and only asks for one iteration of each method—making it slightly easier than average but requiring competent execution of routine techniques. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
6.
$$f ( x ) = \frac { 2 \left( x ^ { 3 } + 3 \right) } { \sqrt { x } } - 9 , \quad x > 0$$
The equation $\mathrm { f } ( x ) = 0$ has two real roots $\alpha$ and $\beta$, where $0.4 < \alpha < 0.5$ and $1.2 < \beta < 1.3$
\begin{enumerate}[label=(\alph*)]
\item Taking 0.45 as a first approximation to $\alpha$, apply the Newton-Raphson procedure once to $\mathrm { f } ( x )$ to find a second approximation to $\alpha$, giving your answer to 3 decimal places.\\[0pt]
\item Use linear interpolation once on the interval [1.2, 1.3] to find an approximation to $\beta$, giving your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2018 Q6 [9]}}