| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Solve exponential equation via iteration |
| Difficulty | Standard +0.3 This is a straightforward fixed point iteration question requiring mechanical application of the formula and sign-change verification. Part (a) involves simple calculator work with logarithms (4 marks for iteration), and part (b) is routine interval checking. Slightly easier than average as it requires no derivation of the iteration formula, no convergence analysis, and minimal problem-solving—just careful arithmetic and standard verification technique. |
| Spec | 1.09a Sign change methods: locate roots1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
The root of the equation $f(x) = 0$, where
$$f(x) = x + \ln 2x - 4$$
is to be estimated using the iterative formula $x_{n+1} = 4 - \ln 2x_n$, with $x_0 = 2.4$.
\begin{enumerate}[label=(\alph*)]
\item Showing your values of $x_1, x_2, x_3, \ldots$, obtain the value, to 3 decimal places, of the root. [4]
\item By considering the change of sign of $f(x)$ in a suitable interval, justify the accuracy of your answer to part (a). [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q3 [6]}}