| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Parametric curves and Cartesian conversion |
| Type | Convert to Cartesian (sin/cos identities) |
| Difficulty | Moderate -0.3 This is a straightforward parametric-to-Cartesian conversion question. Part (a) requires applying the compound angle formula for cos(t + π/6), which is standard bookwork. Part (b) involves simple algebraic manipulation using the identity cos²t + sin²t = 1. Both parts follow predictable patterns with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 |
\includegraphics{figure_3}
Figure 3 shows a sketch of the curve $C$ with parametric equations
$$x = 4\cos\left(t + \frac{\pi}{6}\right), \quad y = 2\sin t, \quad 0 \leq t < 2\pi$$
\begin{enumerate}
\item[(a)] Show that
$$x + y = 2\sqrt{3}\cos t$$ \hfill [3]
\item[(b)] Show that a cartesian equation of $C$ is
$$(x + y)^2 + ay^2 = b$$
where $a$ and $b$ are integers to be determined. \hfill [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2014 Q5 [5]}}