| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Verify point and find gradient |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question with standard steps: substitute to find a constant, apply product and chain rules for implicit differentiation, then verify a stationary point. All techniques are routine C4 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07s Parametric and implicit differentiation |
6 A curve is defined by the equation $2 y + \mathrm { e } ^ { 2 x } y ^ { 2 } = x ^ { 2 } + C$, where $C$ is a constant. The point $P \left( 1 , \frac { 1 } { \mathrm { e } } \right)$ lies on the curve.
\begin{enumerate}[label=(\alph*)]
\item Find the exact value of $C$.
\item Find an expression for $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $x$ and $y$.
\item Verify that $P \left( 1 , \frac { 1 } { \mathrm { e } } \right)$ is a stationary point on the curve.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2011 Q6 [10]}}