| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (polynomial/rational) |
| Difficulty | Moderate -0.3 Part (a) is a routine elimination of parameter using substitution (y=3/t gives t=3/y, substitute into x equation). Part (b) requires standard dy/dx calculation via chain rule and tangent equation, then verification by substitution. All techniques are standard C4 procedures with no novel insight required, making this slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
5 A curve is defined by the parametric equations
$$x = 8 t ^ { 2 } - t , \quad y = \frac { 3 } { t }$$
\begin{enumerate}[label=(\alph*)]
\item Show that the cartesian equation of the curve can be written as $x y ^ { 2 } + 3 y = k$, stating the value of the integer $k$.\\
(2 marks)
\item \begin{enumerate}[label=(\roman*)]
\item Find an equation of the tangent to the curve at the point $P$, where $t = \frac { 1 } { 4 }$.
\item Verify that the tangent at $P$ intersects the curve when $x = \frac { 3 } { 2 }$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q5 [11]}}