| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with verification |
| Difficulty | Standard +0.3 This is a straightforward Newton-Raphson application requiring one iteration with verification via sign change. The function is simple to differentiate, calculations are manageable, and part (b) only requires checking f(x) values at nearby points to confirm 2dp accuracy. Slightly easier than average due to the routine nature and clear structure. |
| Spec | 1.09d Newton-Raphson method |
3.
$$\mathrm { f } ( x ) = x ^ { 2 } + \frac { 3 } { x } - 1 , \quad x < 0$$
The only real root, $\alpha$, of the equation $\mathrm { f } ( x ) = 0$ lies in the interval $[ - 2 , - 1 ]$.
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\item Taking - 1.5 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 2 decimal places.
\item Show that your answer to part (a) gives $\alpha$ correct to 2 decimal places.\\
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tion 3continued -
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\hfill \mbox{\textit{Edexcel F1 2016 Q3 [7]}}