| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (polynomial/rational) |
| Difficulty | Standard +0.3 This is a straightforward parametric equations question requiring standard techniques: differentiation using the chain rule (part i), interpretation of gradient (part ii), and elimination of parameter with a helpful hint provided (part iii). The algebraic manipulation is routine, making this slightly easier than average for A-level. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
10 A curve has parametric equations $x = t + \frac { 2 } { t }$ and $y = t - \frac { 2 } { t }$, for $t \neq 0$.\\
(i) Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $t$, giving your answer in its simplest form.\\
(ii) Explain why the curve has no stationary points.\\
(iii) By considering $x + y$, or otherwise, find a cartesian equation of the curve, giving your answer in a form not involving fractions or brackets.
\hfill \mbox{\textit{OCR H240/01 2018 Q10 [10]}}