| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Applied differentiation |
| Type | Connected rates of change |
| Difficulty | Standard +0.3 This is a straightforward related rates problem requiring chain rule differentiation and substitution. Part (i) is routine differentiation of a composite function. Part (ii) applies the standard related rates formula dV/dt = (dV/dh)(dh/dt), requiring only algebraic rearrangement. The arithmetic is clean (h=2 gives h^6+16=80) and the question follows a standard template, making it slightly easier than average for C3. |
| Spec | 1.07b Gradient as rate of change: dy/dx notation1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
Earth is being added to a pile so that, when the height of the pile is $h$ metres, its volume is $V$ cubic metres, where
$$V = (h^6 + 16)^{\frac{1}{2}} - 4.$$
\begin{enumerate}[label=(\roman*)]
\item Find the value of $\frac{dV}{dh}$ when $h = 2$. [3]
\item The volume of the pile is increasing at a constant rate of 8 cubic metres per hour. Find the rate, in metres per hour, at which the height of the pile is increasing at the instant when $h = 2$. Give your answer correct to 2 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q4 [6]}}