| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Find intersection of exponential curves |
| Difficulty | Standard +0.3 Part (i) is routine curve sketching of exponential functions requiring knowledge of transformations and asymptotes. Part (ii) involves solving e^x - 1 = 2e^{-x}, which requires multiplying by e^x to get a quadratic in e^x, then using the quadratic formula—a standard technique for this topic. The 8 marks reflect multiple steps rather than conceptual difficulty, making this slightly easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\roman*)]
\item On a single set of axes, sketch the curves $y = e^x - 1$ and $y = 2e^{-x}$.
[3]
\item Find the exact coordinates of the point of intersection of these curves.
[5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2011 Q5 [8]}}