| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2012 |
| Session | Specimen |
| Marks | 4 |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Standard +0.3 This is a straightforward Newton-Raphson application requiring rearrangement to f(x)=0, differentiation using the chain rule (moderate but standard), and iterative calculation. The derivative is slightly more involved than basic polynomials, but the method is routine and the question provides the starting value and interval, making it slightly easier than average. |
| Spec | 1.09d Newton-Raphson method |
Attempt use of correct Newton-Raphson formula with appropriate $f(x)$ **M1**
Use e.g. $f'(x) = 1 - \dfrac{2}{(x+1)^3}$ **B1**
Use $x_0 = 2$ and continue until at least 2 iterates agree **M1**
Obtain final answer $1.879$ **A1**
**Total: 4 marks**7 Given that the equation $x = 2 - \frac { 1 } { ( x + 1 ) ^ { 2 } }$ has a root between $x = 1$ and $x = 2$, use the Newton-Raphson formula with $x _ { 0 } = 2$ to find this root correct to 3 decimal places.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2012 Q7 [4]}}