| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Compare Newton-Raphson with linear interpolation |
| Difficulty | Moderate -0.3 This is a straightforward application of two standard numerical methods (linear interpolation and Newton-Raphson) with clear instructions and simple arithmetic. While it's Further Maths content, both procedures are routine calculations requiring only substitution into formulas with no problem-solving insight needed. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
4. $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 5 x - 3$
The equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval ( 2,3 ).
\begin{enumerate}[label=(\alph*)]
\item Use linear interpolation on the end points of this interval to obtain an approximation for $\alpha$.
\item Taking 2.5 as a first approximation to $\alpha$, apply the Newton - Raphson procedure once to $\mathrm { f } ( x )$ to obtain a second approximation to $\alpha$. Give your answer to 2 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q4 [9]}}