| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Fixed Point Iteration |
| Type | Derive equation from integral condition |
| Difficulty | Standard +0.3 This is a straightforward C3 integration and iteration question. Part (i) requires standard integration of exponential and polynomial functions, then algebraic manipulation. Part (ii) is routine iteration with a given formula. Both parts follow standard textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08d Evaluate definite integrals: between limits1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
\begin{enumerate}[label=(\roman*)]
\item Given that $\int_0^a (6e^{2x} + x) \, dx = 42$, show that $a = \frac{1}{2} \ln(15 - \frac{1}{6}a^2)$. [5]
\item Use an iterative formula, based on the equation in part (i), to find the value of $a$ correct to 3 decimal places. Use a starting value of 1 and show the result of each iteration. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q6 [9]}}