| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| 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 equations question requiring standard techniques: finding a parameter value from given coordinates, then computing dy/dx using the chain rule. The algebra is routine with no conceptual surprises, making it slightly easier than average for A-level. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation |
5.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0c4a3759-ecaa-47c3-a071-ce25fd11159f-16_938_1257_125_486}
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\caption{Figure 2}
\end{center}
\end{figure}
Figure 2 shows a sketch of the curve $C$ with parametric equations
$$x = 1 + t - 5 \sin t , \quad y = 2 - 4 \cos t , \quad - \pi \leqslant t \leqslant \pi$$
The point $A$ lies on the curve $C$.
Given that the coordinates of $A$ are ( $k , 2$ ), where $k > 0$
\begin{enumerate}[label=(\alph*)]
\item find the exact value of $k$, giving your answer in a fully simplified form.
\item Find the equation of the tangent to $C$ at the point $A$.
Give your answer in the form $y = p x + q$, where $p$ and $q$ are exact real values.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2018 Q5 [7]}}