| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Compare Newton-Raphson with linear interpolation |
| Difficulty | Moderate -0.3 This is a straightforward application of two standard numerical methods (Newton-Raphson and linear interpolation) with clear starting values and step-by-step instructions. Part (i)(a) is routine sign-checking, (i)(b) requires two iterations of a formula students practice extensively, and (ii) is direct substitution into the linear interpolation formula. While it requires careful arithmetic, there's no problem-solving or conceptual challenge beyond executing well-rehearsed procedures. |
| Spec | 1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
1.(i)
$$f ( x ) = x ^ { 3 } + 4 x - 6$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval[1,1.5]
\item Taking 1.5 as a first approximation,apply the Newton Raphson process twice to $\mathrm { f } ( x )$ to obtain an approximate value of $\alpha$ .Give your answer to 3 decimal places. Show your working clearly.\\
(ii)
$$g ( x ) = 4 x ^ { 2 } + x - \tan x$$
where $x$ is measured in radians.
The equation $\mathrm { g } ( x ) = 0$ has a single root $\beta$ in the interval[1.4,1.5]\\
Use linear interpolation on the values at the end points of this interval to obtain an approximation to $\beta$ .Give your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2021 Q1 [10]}}