| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2008 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - partial fractions |
| Difficulty | Challenging +1.8 This AEA question requires solving a differential equation by separation of variables with partial fractions, then using tangent conditions to find integration constants. Part (a) involves simultaneous equations with the derivative condition. Part (b) requires careful algebraic manipulation and handling of logarithms. The multi-step nature, algebraic complexity, and need to connect tangent geometry with differential equations makes this significantly harder than standard A-level calculus, though it follows recognizable techniques for strong students. |
| Spec | 1.07m Tangents and normals: gradient and equations1.08k Separable differential equations: dy/dx = f(x)g(y) |
The points $(x, y)$ on the curve $C$ satisfy
$(x + 1)(x + 2) \frac{dy}{dx} = xy$.
The line with equation $y = 2x + 5$ is the tangent to $C$ at a point $P$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of $P$. [4]
\item Find the equation of $C$, giving your answer in the form $y = f(x)$. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2008 Q2 [12]}}