| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Apply iteration to find root (pure fixed point) |
| Difficulty | Standard +0.3 This is a straightforward iterative sequence question requiring basic calculator work to find the limit (part i), then algebraic manipulation to find the equation satisfied by α (part ii). Both parts follow standard C3 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
The sequence defined by
$$x_1 = 3, \quad x_{n+1} = \sqrt{31 - \frac{5}{2}x_n}$$
converges to the number $\alpha$.
\begin{enumerate}[label=(\roman*)]
\item Find the value of $\alpha$ correct to 3 decimal places, showing the result of each iteration. [3]
\item Find an equation of the form $ax^3 + bx + c = 0$, where $a$, $b$ and $c$ are integers, which has $\alpha$ as a root. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q2 [6]}}