| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Exact trigonometric values |
| Difficulty | Moderate -0.8 Part (i) is a standard geometric proof using an equilateral triangle that appears in most textbooks. Part (ii) is a routine trigonometric equation requiring knowledge of special angles and the CAST diagram. Both parts involve direct application of basic techniques with no problem-solving insight required, making this easier than average for A-level. |
| Spec | 1.05g Exact trigonometric values: for standard angles1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| clear diagram or explanation starting with equilateral triangle correctly showing 30 as half angle and sides 1 and 2 or multiples of these lengths; correct use of Pythagoras and adjacent and hypotenuse correctly identified to obtain given result \(\cos 30° = \frac{\sqrt{3}}{2}\) | B1, B1 | units for sides and angle not required; adjacent and hypotenuse may be identified on diagram; condone abbreviations |
| Answer | Marks | Guidance |
|---|---|---|
| \(\pm \frac{\pi}{6}\) or \(\frac{5\pi}{6}\) soi; \(\frac{11\pi}{6}\); \(\frac{7\pi}{6}\) | M1, A1, A1 | may be implied by correct answer or \(\pm 0.5235998775...\) or may appear on quadrant diagram or graph; condone \(\pm 30°\) or \(-150°\); ignore extra values outside the range; if full marks or SC1 awarded, subtract 1 for extra values in the range |
### Part (i)
clear diagram or explanation starting with equilateral triangle correctly showing 30 as half angle and sides 1 and 2 or multiples of these lengths; correct use of Pythagoras and adjacent and hypotenuse correctly identified to obtain given result $\cos 30° = \frac{\sqrt{3}}{2}$ | B1, B1 | units for sides and angle not required; adjacent and hypotenuse may be identified on diagram; condone abbreviations
### Part (ii)
$\pm \frac{\pi}{6}$ or $\frac{5\pi}{6}$ soi; $\frac{11\pi}{6}$; $\frac{7\pi}{6}$ | M1, A1, A1 | may be implied by correct answer or $\pm 0.5235998775...$ or may appear on quadrant diagram or graph; condone $\pm 30°$ or $-150°$; ignore extra values outside the range; if full marks or SC1 awarded, subtract 1 for extra values in the range\begin{enumerate}[label=(\roman*)]
\item Starting with an equilateral triangle, prove that $\cos 30° = \frac{\sqrt{3}}{2}$. [2]
\item Solve the equation $2 \sin \theta = -1$ for $0 \leq \theta \leq 2\pi$, giving your answers in terms of $\pi$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2013 Q4 [5]}}