| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Compare Newton-Raphson with linear interpolation |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing standard numerical methods. Part (a) requires simple substitution to verify sign change, part (b) is a single Newton-Raphson iteration with routine differentiation of standard functions, and part (c) is a single linear interpolation calculation. All techniques are direct applications of formulas with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
1.
$$\mathrm { f } ( x ) = 6 \sqrt { x } - x ^ { 2 } - \frac { 1 } { 2 x } , \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval $[ 3,4 ]$.
\item Taking 3 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 [3,4] to find another approximation to $\alpha$. Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2014 Q1 [10]}}