| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (sin/cos identities) |
| Difficulty | Standard +0.3 This is a standard parametric equations question requiring routine techniques: eliminating the parameter using a double angle identity, verifying points lie on a line (substitution), finding tangent equations using dy/dx from parametric derivatives, and finding an intersection point. All steps are textbook procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
The equation of a curve $C$ is given by the parametric equations
$$x = \cos 2\theta, \quad y = \cos\theta.$$
\begin{enumerate}[label=(\alph*)]
\item Find the Cartesian equation of $C$. [2]
\item Show that the line $x - y + 1 = 0$ meets $C$ at the point $P$, where $\theta = \frac{\pi}{3}$, and at the point $Q$, where $\theta = \frac{\pi}{2}$. Write down the coordinates of $P$ and $Q$. [5]
\item Determine the equations of the tangents to $C$ at $P$ and $Q$. Write down the coordinates of the point of intersection of the two tangents. [7]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2018 Q10 [14]}}