| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Standard +0.8 This question requires differentiating a term with negative fractional power (x^(-5/2)), applying the Newton-Raphson formula correctly, and careful arithmetic with the complex expression. While the method itself is standard A-level, the algebraic manipulation needed elevates it above average difficulty for Further Maths students. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
2.
$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + \frac { 1 } { 2 \sqrt { x ^ { 5 } } } + 2 , \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval $[ 2,3 ]$.
\item Taking 3 as a first approximation to $\alpha$, apply the Newton-Raphson process once to $\mathrm { f } ( x )$ to find a second approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2015 Q2 [7]}}