| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve double/multiple angle equation |
| Difficulty | Moderate -0.8 This is a straightforward C2 question requiring a standard sketch of cos(2x), identifying intercepts by inspection, and solving a basic trigonometric equation using standard angles. All parts involve routine procedures with no problem-solving insight needed, making it easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (a) [Sketch showing curve with one maximum and one minimum] | B2 | |
| (b) \((0, 1), (\frac{\pi}{6}, 0), (\frac{2\pi}{3}, 0)\) | B3 | |
| (c) \(\cos 2x = 0.5\) | ||
| \(2x = \frac{\pi}{3}, 2\pi - \frac{\pi}{3}\) | B1 M1 | |
| \(2x = \frac{\pi}{3}, \frac{5\pi}{3}\) | ||
| \(x = \frac{\pi}{6}, \frac{5\pi}{6}\) | M1 A1 | (9 marks) |
(a) [Sketch showing curve with one maximum and one minimum] | B2 |
(b) $(0, 1), (\frac{\pi}{6}, 0), (\frac{2\pi}{3}, 0)$ | B3 |
(c) $\cos 2x = 0.5$ | |
$2x = \frac{\pi}{3}, 2\pi - \frac{\pi}{3}$ | B1 M1 |
$2x = \frac{\pi}{3}, \frac{5\pi}{3}$ | |
$x = \frac{\pi}{6}, \frac{5\pi}{6}$ | M1 A1 | (9 marks)6.
$$f ( x ) = \cos 2 x , \quad 0 \leq x \leq \pi .$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = \mathrm { f } ( x )$.
\item Write down the coordinates of any points where the curve $y = \mathrm { f } ( x )$ meets the coordinate axes.
\item Solve the equation $\mathrm { f } ( x ) = 0.5$, giving your answers in terms of $\pi$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [9]}}