| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2010 |
| Session | January |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (exponential/logarithmic) |
| Difficulty | Moderate -0.3 This is a straightforward parametric equations question requiring standard techniques: finding dy/dx using the chain rule (dy/dt ÷ dx/dt) and eliminating the parameter. The exponential makes the Cartesian conversion slightly less routine than polynomial examples, but the methods are direct applications of C4 content with no problem-solving insight required. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| M H X I Q | B2 | 3 or 4 correct – award 1 mark |
### Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| M H X I Q | B2 | 3 or 4 correct – award 1 mark |3 A curve has parametric equations
$$x = \mathrm { e } ^ { 2 t } , \quad y = \frac { 2 t } { 1 + t }$$
(i) Find the gradient of the curve at the point where $t = 0$.\\
(ii) Find $y$ in terms of $x$.
\hfill \mbox{\textit{OCR MEI C4 2010 Q3 [2]}}