| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2009 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Express and solve equation |
| Difficulty | Moderate -0.3 This is a standard C4 harmonic form question with routine application of the R cos(θ + α) method followed by a straightforward equation solve. The technique is well-practiced and requires no novel insight, though it does involve multiple steps (finding R and α, then solving the resulting equation). Slightly easier than average due to being a textbook application. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks |
|---|---|
| \(\frac{1}{4} \times [3 + 1 + (-1) + (-2)] = 0.25\) * | M1, E1 |
$\frac{1}{4} \times [3 + 1 + (-1) + (-2)] = 0.25$ * | M1, E1 |
---|---|Express $4\cos\theta - \sin\theta$ in the form $R\cos(\theta + \alpha)$, where $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$.
Hence solve the equation $4\cos\theta - \sin\theta = 3$, for $0 \leq \theta \leq 2\pi$. [7]
\hfill \mbox{\textit{OCR MEI C4 2009 Q1 [7]}}