| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 4 |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with derivative given or simple |
| Difficulty | Moderate -0.3 This is a straightforward application of the Newton-Raphson method with a simple cubic function where the derivative is easily found (3x² + 2). The starting value is given, and students just need to iterate the standard formula until convergence to 3 decimal places. This is slightly easier than average as it's a direct procedural application with no complications or interpretation required. |
| Spec | 1.09d Newton-Raphson method |
**Question 8**
- State derivative — B1
- Use of the correct Newton-Raphson formula — M1
- State $1$ and at least one other correct value $(1.8, 1.59249, 1.56922, 1.56895, 1.56895)$ — A1
- State $1.569$ — A1
**Total: 4 marks**8 Given that the equation $x ^ { 3 } + 2 x - 7 = 0$ has a root between $x = 1$ and $x = 2$, use the Newton-Raphson formula with $x _ { \mathrm { o } } = 1$ to find this root correct to 3 decimal places.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q8 [4]}}