| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differentiating Transcendental Functions |
| Type | Find normal line equation |
| Difficulty | Standard +0.3 This is a straightforward C2 question combining exponential functions, differentiation, and coordinate geometry. Part (a) involves substituting given conditions into the curve equation and its derivative to find two constants—standard simultaneous equations. Part (b) requires finding the normal equation, its intercepts, and calculating a triangle area using basic coordinate geometry. All steps are routine applications of standard techniques with no novel insight required, making it slightly easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.06a Exponential function: a^x and e^x graphs and properties1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07m Tangents and normals: gradient and equations |
The curve $C$ with equation $y = p + qe^x$, where $p$ and $q$ are constants, passes through the point $(0, 2)$. At the point $P$ (ln 2, $p + 2q$) on $C$, the gradient is 5.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $p$ and the value of $q$. [5]
\end{enumerate}
The normal to $C$ at $P$ crosses the $x$-axis at $L$ and the $y$-axis at $M$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Show that the area of $\triangle OLM$, where $O$ is the origin, is approximately 53.8 [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [10]}}