| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with verification |
| Difficulty | Standard +0.3 This is a straightforward Newton-Raphson question requiring one iteration of the standard formula followed by verification using sign changes or bounds. The function is simple to differentiate, the arithmetic is manageable, and the verification in part (b) is a standard technique. While it requires careful calculation and understanding of convergence, it involves no novel insight and is typical of Further Pure 1 material, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
3.
$$\mathrm { f } ( x ) = x ^ { 2 } + \frac { 3 } { x } - 1 , \quad x < 0$$
The only real root, $\alpha$, of the equation $\mathrm { f } ( x ) = 0$ lies in the interval $[ - 2 , - 1 ]$.
\begin{enumerate}[label=(\alph*)]
\item Taking - 1.5 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 2 decimal places.
\item Show that your answer to part (a) gives $\alpha$ correct to 2 decimal places.\\
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\hfill \mbox{\textit{Edexcel F1 2018 Q3 [7]}}