| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Solve exponential equation via iteration |
| Difficulty | Moderate -0.3 This is a straightforward iterative methods question requiring repeated substitution into a given formula and sign-change verification. Part (a) is purely mechanical calculation with no problem-solving, and part (b) is a standard technique taught in C3. Slightly easier than average due to the routine nature of both parts, though it does require careful arithmetic and understanding of convergence/accuracy. |
| 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 Q2 [6]}}