| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Find derivative of quotient |
| Difficulty | Moderate -0.3 Both parts are straightforward applications of standard differentiation rules: (a) product rule with a polynomial and trig function, (b) quotient rule followed by substitution. These are routine C3 exercises requiring only direct application of learned techniques with no problem-solving or insight needed, making them slightly easier than average. |
| Spec | 1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07q Product and quotient rules: differentiation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
2
\begin{enumerate}[label=(\alph*)]
\item Given that $y = x ^ { 4 } \tan 2 x$, find $\frac { \mathrm { d } y } { \mathrm {~d} x }$.\\
(3 marks)
\item Find the gradient of the curve with equation $y = \frac { x ^ { 2 } } { x - 1 }$ at the point where $x = 3$.\\
(3 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2013 Q2 [6]}}