| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2021 |
| Session | October |
| Marks | 9 |
| 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 (sign change, Newton-Raphson, linear interpolation) with routine differentiation. All techniques are direct applications of learned procedures with no novel problem-solving required, making it slightly easier than average for Further Maths F1. |
| 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 |
| VIIN SIHILNI III IM ION OC | VIAV SIHI NI III HM ION OO | VIAV SIHI NI III IM I ON OC |
2.
$$f ( x ) = 7 \sqrt { x } - \frac { 1 } { 2 } x ^ { 3 } - \frac { 5 } { 3 x } \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root, $\alpha$, in the interval [2.8, 2.9]
\item \begin{enumerate}[label=(\roman*)]
\item Find $\mathrm { f } ^ { \prime } ( x )$.
\item Hence, using $x _ { 0 } = 2.8$ as a first approximation to $\alpha$, apply the Newton-Raphson procedure once to $\mathrm { f } ( x )$ to calculate a second approximation to $\alpha$, giving your answer to 3 decimal places.\\[0pt]
\end{enumerate}\item Use linear interpolation once on the interval [2.8, 2.9] to find another approximation to $\alpha$. Give your answer to 3 decimal places.
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VIIN SIHILNI III IM ION OC & VIAV SIHI NI III HM ION OO & VIAV SIHI NI III IM I ON OC \\
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\hfill \mbox{\textit{Edexcel F1 2021 Q2 [9]}}