| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Apply iteration to find root (pure fixed point) |
| Difficulty | Moderate -0.3 This is a standard C3 iterative methods question requiring sign change verification, calculator iteration (4 iterations), and error bound verification. All techniques are routine textbook procedures with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.09a Sign change methods: locate roots1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
2. $\quad \mathrm { f } ( x ) = x ^ { 3 } - 2 x - 5$.
\begin{enumerate}[label=(\alph*)]
\item Show that there is a root $\alpha$ of $\mathrm { f } ( x ) = 0$ for $x$ in the interval $[ 2,3 ]$.
The root $\alpha$ is to be estimated using the iterative formula
$$x _ { n + 1 } = \sqrt { \left( 2 + \frac { 5 } { x _ { n } } \right) } , \quad x _ { 0 } = 2$$
\item Calculate the values of $x _ { 1 } , x _ { 2 } , x _ { 3 }$ and $x _ { 4 }$, giving your answers to 4 significant figures.
\item Prove that, to 5 significant figures, $\alpha$ is 2.0946.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q2 [8]}}