| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with derivative given or simple |
| Difficulty | Moderate -0.8 This is a straightforward application of the Newton-Raphson formula with explicit guidance: the derivative is asked for in part (a), the starting value is given, and only one iteration is required. It's purely procedural with no problem-solving or insight needed, making it easier than average but not trivial since it involves careful calculation. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09d Newton-Raphson method |
1.
$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 5 x - 4$$
\begin{enumerate}[label=(\alph*)]
\item Use differentiation to find $\mathrm { f } ^ { \prime } ( x )$.
The equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval $1.4 < x < 1.5$
\item Taking 1.4 as a first approximation to $\alpha$, use the Newton-Raphson procedure once to obtain a second approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q1 [6]}}