| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Find dy/dx at a point |
| Difficulty | Moderate -0.3 This is a straightforward parametric curves question requiring standard techniques: finding dy/dx using the chain rule (dy/dt ÷ dx/dt) and eliminating the parameter to convert to Cartesian form. Both parts are routine C4 exercises with no conceptual challenges—slightly easier than average due to the simple algebraic manipulation involved. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
A curve $C$ has parametric equations
$$x = 2t + 5, \quad y = 3 + \frac{4}{t}, \quad t \neq 0$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\frac{dy}{dx}$ at the point on $C$ with coordinates $(9, 5)$.
[4]
\item Find a cartesian equation of the curve in the form
$$y = \frac{ax + b}{cx + d}$$
where $a$, $b$, $c$ and $d$ are integers.
[3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2013 Q3 [7]}}