| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch single standard trig graph (sin/cos/tan) |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometry question requiring a standard sketch of cos(2x), identifying intercepts by inspection (x-intercepts at π/4, 3π/4 where cos(2x)=0, y-intercept at (0,1)), and solving a basic equation cos(2x)=0.5 using inverse cosine. All parts are routine recall and application of standard techniques with no problem-solving insight required, making it easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks |
|---|---|
| Graph of curve with correct shape showing one complete oscillation with maximum at origin | B2 |
| Answer | Marks |
|---|---|
| \((0, 1), (\frac{\pi}{2}, 0), (\frac{3\pi}{4}, 0)\) | B3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(x = \frac{\pi}{6}, \frac{5\pi}{6}\) | B1 M1 | A1 |
## (i)
Graph of curve with correct shape showing one complete oscillation with maximum at origin | B2 |
## (ii)
$(0, 1), (\frac{\pi}{2}, 0), (\frac{3\pi}{4}, 0)$ | B3 |
## (iii)
$\cos 2x = 0.5$
$2x = \frac{\pi}{3}, 2\pi - \frac{\pi}{3}$
$2x = \frac{\pi}{3}, \frac{5\pi}{3}$
$x = \frac{\pi}{6}, \frac{5\pi}{6}$ | B1 M1 | A1 | (8)
---$$f(x) = \cos 2x, \quad 0 \leq x \leq \pi.$$
\begin{enumerate}[label=(\roman*)]
\item Sketch the curve $y = f(x)$. [2]
\item Write down the coordinates of any points where the curve $y = f(x)$ meets the coordinate axes. [3]
\item Solve the equation $f(x) = 0.5$, giving your answers in terms of $\pi$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 Q6 [8]}}