| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Parametric differentiation |
| Type | Gradient condition leads to trig equation |
| Difficulty | Standard +0.8 This is a multi-part parametric differentiation question requiring finding dy/dx, then deriving a tangent equation through an external point, algebraically manipulating to show a given trigonometric identity, and finally solving that equation. The algebraic manipulation in part (b) and solving the linear trigonometric equation in part (c) require solid technique beyond routine exercises, placing it moderately above average difficulty. |
| Spec | 1.07s Parametric and implicit differentiation |
12 The parametric equations of a curve are given by $x = 2 \cos \theta$ and $y = 3 \sin \theta$ for $0 \leq \theta < 2 \pi$.
\begin{enumerate}[label=(\alph*)]
\item Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ in terms of $\theta$.
The tangents to the curve at the points P and Q pass through the point $( 2,6 )$.
\item Show that the values of $\theta$ at the points P and Q satisfy the equation $2 \sin \theta + \cos \theta = 1$.
\item Find the values of $\theta$ at the points $P$ and $Q$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 Q12 [11]}}