| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of composite quotient/product |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question testing standard techniques (product rule, quotient rule, and tangent line equation). Part (a) is routine product rule application, part (b) is standard tangent finding, and part (c) is guided quotient rule with algebraic simplification using a trigonometric identity. All techniques are core C3 material with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find $\frac{dy}{dx}$ when $y = xe^{2x}$. [3]
\item Find an equation of the tangent to the curve $y = xe^{2x}$ at the point $(1, e^2)$. [2]
\end{enumerate}
\item Given that $y = \frac{2\sin 3x}{1 + \cos 3x}$, use the quotient rule to show that
$$\frac{dy}{dx} = \frac{k}{1 + \cos 3x}$$
where $k$ is an integer. [4]
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2011 Q2 [9]}}