OCR MEI C3 2011 January — Question 5 8 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2011
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicExponential Functions
TypeFind intersection of exponential curves
DifficultyStandard +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.
Spec1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b

  1. On a single set of axes, sketch the curves \(y = e^x - 1\) and \(y = 2e^{-x}\). [3]
  2. Find the exact coordinates of the point of intersection of these curves. [5]

\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]}}