| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Session | Specimen |
| Marks | 10 |
| 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 (linear interpolation and Newton-Raphson) with clear instructions and no conceptual challenges. Both parts require only direct substitution into formulas, differentiation of a simple function, and calculator work. Slightly easier than average due to the routine nature and explicit guidance. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09d Newton-Raphson method1.09f Trapezium rule: numerical integration |
2.
$$f ( x ) = 5 x ^ { 2 } - 4 x ^ { \frac { 3 } { 2 } } - 6 , \quad x \geqslant 0$$
The root $\alpha$ of the equation $\mathrm { f } ( x ) = 0$ lies in the interval $[ 1.6,1.8 ]$
\begin{enumerate}[label=(\alph*)]
\item Use linear interpolation once on the interval $[ 1.6,1.8 ]$ to find an approximation to $\alpha$. Give your answer to 3 decimal places.
\item Taking 1.7 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.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 Q2 [10]}}