| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric differentiation |
| Type | Find tangent equation at parameter |
| Difficulty | Standard +0.3 This is a straightforward parametric differentiation question requiring standard application of dy/dx = (dy/dθ)/(dx/dθ) and chain rule, followed by routine tangent line calculation. The trigonometric simplification to get -tan θ is mechanical using double angle formulas. Slightly above average difficulty due to the algebraic manipulation required, but still a standard textbook exercise with no novel problem-solving needed. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
A curve is defined parametrically by
$$x = 2\theta + \sin 2\theta, \quad y = 1 + \cos 2\theta.$$
\begin{enumerate}[label=(\alph*)]
\item Show that the gradient of the curve at the point with parameter $\theta$ is $-\tan\theta$. [6]
\item Find the equation of the tangent to the curve at the point where $\theta = \frac{\pi}{4}$. [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q11 [10]}}