| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | June |
| 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 integration and iteration question. Part (i) requires routine integration of exponentials and algebraic manipulation to reach the given form. Part (ii) is a standard fixed-point iteration with a given starting value. Both parts follow predictable C3 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
It is given that $\int_a^{3a} (e^{5x} + e^x) dx = 100$, where $a$ is a positive constant.
\begin{enumerate}[label=(\roman*)]
\item Show that $a = \frac{1}{5}\ln(300 + 3e^a - 2e^{3a})$. [5]
\item Use an iterative process, based on the equation in part (i), to find the value of $a$ correct to 4 decimal places. Use a starting value of 0.6 and show the result of each step of the process. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2009 Q4 [9]}}