| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Compare Newton-Raphson with linear interpolation |
| Difficulty | Standard +0.3 This is a straightforward application of two standard numerical methods with explicit formulas. Part (a) requires computing f'(x) and applying the Newton-Raphson formula once, while part (b) uses the linear interpolation formula. Both are routine procedures with no problem-solving insight required, though the fractional power in f(x) adds minor algebraic complexity beyond the most basic examples. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
1.
$$f ( x ) = 3 x ^ { 2 } - \frac { 5 } { 3 \sqrt { x } } - 6 , \quad x > 0$$
The single root $\alpha$ of the equation $\mathrm { f } ( x ) = 0$ lies in the interval [1.5, 1.6].
\begin{enumerate}[label=(\alph*)]
\item Taking 1.5 as a first approximation to $\alpha$, apply the Newton-Raphson process once to $\mathrm { f } ( x )$ to obtain a second approximation to $\alpha$. Give your answer to 3 decimal places.\\[0pt]
\item Use linear interpolation once on the interval [1.5, 1.6] to find another approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2018 Q1 [7]}}