| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2022 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Standard +0.3 This is a straightforward Further Pure 1 question requiring standard differentiation (including negative and fractional powers), one iteration of Newton-Raphson, and linear interpolation. While the derivative involves multiple terms with fractional/negative indices, these are routine A-level techniques. The question is structured with clear guidance through parts (a)-(d), requiring no novel insight—just careful application of standard methods. Slightly above average difficulty due to the algebraic complexity of the derivative, but well within typical Further Maths expectations. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09a Sign change methods: locate roots1.09d Newton-Raphson method1.09f Trapezium rule: numerical integration |
2.
$$f ( x ) = 10 - 2 x - \frac { 1 } { 2 \sqrt { x } } - \frac { 1 } { x ^ { 3 } } \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval [0.4, 0.5]
\item Determine $\mathrm { f } ^ { \prime } ( x )$.
\item Using $x _ { 0 } = 0.5$ 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 3 decimal places.
The equation $\mathrm { f } ( x ) = 0$ has another root $\beta$ in the interval [4.8, 4.9]\\[0pt]
\item Use linear interpolation once on the interval [4.8, 4.9] to find an approximation to $\beta$, giving your answer to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2022 Q2 [9]}}