| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Moderate -0.3 This is a straightforward application of the Newton-Raphson method with standard calculus. Part (a) is routine substitution to verify sign change, part (b) requires differentiating powers (including fractional indices), and part (c) is a single iteration of the Newton-Raphson formula. While it's Further Maths content, the question is highly procedural with no problem-solving insight required, making it slightly easier than an average A-level question. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
$$\text{f}(x) = 3\sqrt{x} + \frac{18}{\sqrt{x}} - 20.$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation f$(x) = 0$ has a root $a$ in the interval $[1.1, 1.2]$.
[2]
\item Find $f'(x)$.
[3]
\item Using $x_0 = 1.1$ as a first approximation to $a$, apply the Newton-Raphson procedure once to f$(x)$ to find a second approximation to $a$, giving your answer to 3 significant figures.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP1 Q5 [9]}}