| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Find intersection of exponential curves |
| Difficulty | Moderate -0.5 Part (i) requires simple substitution of x=0 into exponential functions. Part (ii) involves setting equations equal, rearranging to find x (which requires basic algebraic manipulation of exponentials), then substituting back to verify a given y-coordinate. This is a standard C3 exponential question with straightforward algebraic steps and no novel problem-solving required, making it 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 |
2.\\
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The diagram shows the curves $y = 3 + 2 \mathrm { e } ^ { x }$ and $y = \mathrm { e } ^ { x + 2 }$ which cross the $y$-axis at the points $A$ and $B$ respectively.\\
(i) Write down the coordinates of $A$ and $B$.
The two curves intersect at the point $C$.\\
(ii) Find an expression for the $x$-coordinate of $C$ and show that the $y$-coordinate of $C$ is $\frac { 3 \mathrm { e } ^ { 2 } } { \mathrm { e } ^ { 2 } - 2 }$.\\
\hfill \mbox{\textit{OCR C3 Q2 [7]}}