| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2021 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Differential equations |
| Type | Geometric curve properties |
| Difficulty | Standard +0.3 This is a straightforward differential equations question requiring standard techniques: forming a DE from a geometric property, separating variables, and applying initial conditions. Part (c) involves recognizing a transformation, which is routine A-level work. The question is slightly easier than average as it's well-scaffolded with clear steps and uses standard methods throughout. |
| Spec | 1.08k Separable differential equations: dy/dx = f(x)g(y) |
A curve $C$ in the $x$-$y$ plane has the property that the gradient of the tangent at the point $P(x, y)$ is three times the gradient of the line joining the point $(3, 2)$ to $P$.
\begin{enumerate}[label=(\alph*)]
\item Express this property in the form of a differential equation. [2]
\end{enumerate}
It is given that $C$ passes through the point $(4, 3)$ and that $x > 3$ and $y > 2$ at all points on $C$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the equation of $C$ giving your answer in the form $y = f(x)$. [4]
\end{enumerate}
The curve $C$ may be obtained by a transformation of part of the curve $y = x^3$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Describe fully this transformation. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2021 Q7 [8]}}