| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2016 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Connected Rates of Change |
| Type | Pile or heap: height rate from volume rate |
| Difficulty | Standard +0.3 This is a straightforward related rates problem requiring chain rule differentiation of a composite function and then applying dV/dt = (dV/dh)(dh/dt). Part (i) is routine differentiation practice, and part (ii) is a standard textbook application of related rates with clear setup and simple arithmetic. Slightly above average difficulty due to the composite function and two-part structure, but no novel insight required. |
| Spec | 1.07l Derivative of ln(x): and related functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
The volume $V$ m³ of a pile of grain of height $h$ metres is modelled by the equation
$$V = 4\sqrt{h^3 + 1} - 4.$$
\begin{enumerate}[label=(\roman*)]
\item Find $\frac{dV}{dh}$ when $h = 2$. [4]
\end{enumerate}
At a certain time, the height of the pile is 2 metres, and grain is being added so that the volume is increasing at a rate of 0.4 m³ per minute.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find the rate at which the height is increasing at this time. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2016 Q5 [7]}}