| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric differentiation |
| Type | Find dy/dx expression in terms of parameter |
| Difficulty | Moderate -0.3 This is a straightforward chain rule application requiring standard differentiation of power and exponential functions, then using dy/dx = (dy/dt)/(dx/dt). The calculations are routine with no conceptual challenges beyond applying the chain rule formula, making it slightly easier than average for C3. |
| Spec | 1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
\begin{enumerate}[label=(\roman*)]
\item Given that $x = (4t + 9)^{\frac{1}{2}}$ and $y = 6e^{\frac{2t+1}{4}}$, find expressions for $\frac{dx}{dt}$ and $\frac{dy}{dx}$. [4]
\item Hence find the value of $\frac{dy}{dt}$ when $t = 4$, giving your answer correct to 3 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [7]}}