| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Separable variables - standard (applied/contextual) |
| Difficulty | Standard +0.3 This is a straightforward differential equations question requiring standard techniques: forming a DE from a verbal description, verifying a solution by differentiation (routine chain rule), then using two initial conditions to find constants. All steps are mechanical with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.07t Construct differential equations: in context1.08k Separable differential equations: dy/dx = f(x)g(y)1.08l Interpret differential equation solutions: in context |
Question 3:
--- 3 (i) ---
3 (i)
--- 3 (ii) ---
3 (ii)The total value of the sales made by a new company in the first $t$ years of its existence is denoted by $£V$. A model is proposed in which the rate of increase of $V$ is proportional to the square root of $V$. The constant of proportionality is $k$.
\begin{enumerate}[label=(\roman*)]
\item Express the model as a differential equation.
Verify by differentiation that $V = (\frac{1}{2}kt + c)^2$, where $c$ is an arbitrary constant, satisfies this differential equation. [4]
\item The value of the company's sales in its first year is £10000, and the total value of the sales in the first two years is £40000. Find $V$ in terms of $t$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 2012 Q3 [8]}}