| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2012 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Connected Rates of Change |
| Type | Balloon or expanding shape |
| Difficulty | Standard +0.3 This is a straightforward application of differentiation to an exponential model. Part (i) requires direct substitution and finding dr/dt using the chain rule. Part (ii) requires relating dA/dt to dr/dt using A = πr², which is a standard related rates problem. All techniques are routine for C3 level with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.06i Exponential growth/decay: in modelling context1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
Oil is leaking into the sea from a pipeline, creating a circular oil slick. The radius $r$ metres of the oil slick $t$ hours after the start of the leak is modelled by the equation
$$r = 20(1 - e^{-0.2t}).$$
\begin{enumerate}[label=(\roman*)]
\item Find the radius of the slick when $t = 2$, and the rate at which the radius is increasing at this time. [4]
\item Find the rate at which the area of the slick is increasing when $t = 2$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 2012 Q6 [8]}}