| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch two trig curves and count intersections/solutions |
| Difficulty | Easy -1.3 This is a straightforward question testing basic trigonometric graph sketching and solving a simple equation. Part (i) requires sketching two standard cosine curves with different frequencies—a routine task requiring only recall of transformations. Part (ii) involves solving cos 2x = 0.5, which requires finding reference angles and accounting for the factor of 2, but is a standard textbook exercise with no problem-solving insight needed. The 5 total marks and mechanical nature place this well below average difficulty. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (i) sketch of correct shape correct period and amplitude | G1 | Not ruled lines |
| G1 | need 1 and –1 indicated; nos. on horiz axis not needed if one period shown | |
| period halved for \(y = \cos 2x\); amplitude unchanged | G1 | |
| (iii) \(30, 150, 210, 330\) | B2 | B1 for 2 of these, ignore extras outside range |
(i) sketch of correct shape correct period and amplitude | G1 | Not ruled lines |
| G1 | need 1 and –1 indicated; nos. on horiz axis not needed if one period shown |
period halved for $y = \cos 2x$; amplitude unchanged | G1 | |
(iii) $30, 150, 210, 330$ | B2 | B1 for 2 of these, ignore extras outside range | $5$ |\begin{enumerate}[label=(\roman*)]
\item Sketch the graph of $y = \cos x$ for $0° \leq x \leq 360°$.
On the same axes, sketch the graph of $y = \cos 2x$ for $0° \leq x \leq 360°$. Label each graph clearly. [3]
\item Solve the equation $\cos 2x = 0.5$ for $0° \leq x \leq 360°$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2006 Q7 [5]}}