| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with derivative given or simple |
| Difficulty | Moderate -0.8 This is a straightforward application of the Newton-Raphson formula with a simple cubic function where the derivative is easily computed. It requires only one iteration with clear starting value, making it more routine than average but still requiring correct formula application and calculation accuracy. |
| Spec | 1.09d Newton-Raphson method |
The equation $x^3 - x^2 + 4x - 900 = 0$ has exactly one real root, $a$.
Taking $x = 10$ as a first approximation to $a$, use the Newton–Raphson method to find a second approximation, $x_2$, to $a$. Give your answer to four significant figures.
**(3 marks)**1 The equation
$$x ^ { 3 } - x ^ { 2 } + 4 x - 900 = 0$$
has exactly one real root, $\alpha$.
Taking $x _ { 1 } = 10$ as a first approximation to $\alpha$, use the Newton-Raphson method to find a second approximation, $x _ { 2 }$, to $\alpha$. Give your answer to four significant figures.\\
(3 marks)
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\hfill \mbox{\textit{AQA FP1 2013 Q1 [3]}}