| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Differential equations |
| Type | Geometric curve properties |
| Difficulty | Standard +0.3 This is a straightforward differential equations question requiring separation of variables and application of boundary conditions. The question guides students through the process with clear steps, and the integration of 1/√y is a standard technique. While it requires multiple steps, the mathematical techniques are routine for C4 level with no novel problem-solving required. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
\begin{enumerate}
\item The gradient at any point $( x , y )$ on a curve is proportional to $\sqrt { y }$.
\end{enumerate}
Given that the curve passes through the point with coordinates $( 0,4 )$,\\
(i) show that the equation of the curve can be written in the form
$$2 \sqrt { y } = k x + 4$$
where $k$ is a positive constant.
Given also that the curve passes through the point with coordinates ( 2,9 ),\\
(ii) find the equation of the curve in the form $y = \mathrm { f } ( x )$.\\
\hfill \mbox{\textit{OCR C4 Q4 [8]}}