| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (exponential/logarithmic) |
| Difficulty | Standard +0.3 This is a standard C4 parametric equations question requiring routine techniques: chain rule for dy/dx, substitution of a parameter value, normal equation, and elimination to find Cartesian form. The exponential functions are straightforward to manipulate, and the final form is given. Slightly above average due to multiple parts and algebraic manipulation, but all techniques are textbook standard. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
4 A curve is defined by the parametric equations $x = 8 \mathrm { e } ^ { - 2 t } - 4 , y = 2 \mathrm { e } ^ { 2 t } + 4$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $t$.
\item The point $P$, where $t = \ln 2$, lies on the curve.
\begin{enumerate}[label=(\roman*)]
\item Find the gradient of the curve at $P$.
\item Find the coordinates of $P$.
\item The normal at $P$ crosses the $x$-axis at the point $Q$. Find the coordinates of $Q$.
\end{enumerate}\item Find the Cartesian equation of the curve in the form $x y + 4 y - 4 x = k$, where $k$ is an integer.\\
(3 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2013 Q4 [12]}}