| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Parametric differentiation |
| Type | Find tangent equation at parameter |
| Difficulty | Standard +0.3 This is a standard C4 parametric differentiation question with three routine parts: finding dy/dx using the chain rule, finding a tangent equation at a specific point, and converting to Cartesian form. All techniques are textbook exercises requiring careful differentiation of trig functions and algebraic manipulation, but no novel insight or problem-solving beyond applying learned methods. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
A curve has parametric equations
$$x = 2\cot t, \quad y = 2\sin^2 t, \quad 0 < t \leq \frac{\pi}{2}.$$
\begin{enumerate}[label=(\alph*)]
\item Find an expression for $\frac{dy}{dx}$ in terms of the parameter $t$. [4]
\item Find an equation of the tangent to the curve at the point where $t = \frac{\pi}{4}$. [4]
\item Find a cartesian equation of the curve in the form $y = f(x)$. State the domain on which the curve is defined. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q6 [12]}}