| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Standard +0.3 This is a straightforward application of the Newton-Raphson formula requiring differentiation of a simple polynomial/rational expression (x^{-2} - 0.119 - 0.018x). While the derivative involves negative powers and the iteration requires careful arithmetic, it's a standard textbook exercise with a given starting value and clear stopping criterion. Slightly above average difficulty only due to the algebraic manipulation needed. |
| Spec | 1.09d Newton-Raphson method |
Obtain any equivalent form of correct derivative $\frac{-2}{x^3} - 0.018$ — B1
Attempt use of correct formula — M1
Use $x_0 = 2$ and continue at least as far as $x_1$ — dep M1
State $2.47$ — A1 **[4]**
SR 2.47 may be awarded B1 for any method or no method seen7 Taking $x = 2$ as a first approximation, use the Newton-Raphson process to find a root of the equation $\frac { 1 } { x ^ { 2 } } - 0.119 - 0.018 x = 0$. Give your answer correct to 3 significant figures.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2014 Q7 [4]}}