| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Paper | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Apply iteration to find root (pure fixed point) |
| Difficulty | Easy -1.8 This is a purely mechanical calculation requiring repeated substitution into a given formula with no problem-solving, conceptual understanding, or interpretation needed. Students simply apply the iteration formula three times using a calculator—significantly easier than average A-level questions which typically require some mathematical reasoning or technique selection. |
| Spec | 1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
| \(n\) | \(x _ { n }\) |
| 0 | 0.5 |
| 1 | 0.8 |
| 2 | 0.512 |
| 3 | |
| 4 | |
| 5 |
3 Complete this table to show the next 3 values of the iteration
$$x _ { n + 1 } = k x _ { n } \left( 1 - x _ { n } \right)$$
in the case when $k = 3.2$ and $x _ { 0 } = 0.5$. Give your answers to calculator accuracy.
\begin{center}
\begin{tabular}{ | l | l | }
\hline
$n$ & \multicolumn{1}{|c|}{$x _ { n }$} \\
\hline
0 & 0.5 \\
\hline
1 & 0.8 \\
\hline
2 & 0.512 \\
\hline
3 & \\
\hline
4 & \\
\hline
5 & \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{OCR MEI C4 Q3}}