| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Find value where max/min occurs |
| Difficulty | Moderate -0.3 This is a standard harmonic form question requiring routine application of the R sin(x - α) formula using R = √(1² + (√3)²) = 2 and tan α = √3/1 = π/3, then reading off the maximum at x = α + π/2. While it involves multiple steps, the technique is algorithmic and commonly practiced in C4, making it slightly easier than average. |
| Spec | 1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Marathon = \(26 \times 1760 + 385 = 46145\) yards | M1 | Converting to yards |
| Speed = \(\frac{2 \times 1760}{8} = 440\) yards per minute | M1 | Finding speed in yards/min |
| Time = \(\frac{46145}{440} = 104.875...\) minutes \(\approx\) 1 hour 44 minutes 52 seconds | A1 | cao, accept equivalent forms |
# Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Marathon = $26 \times 1760 + 385 = 46145$ yards | M1 | Converting to yards |
| Speed = $\frac{2 \times 1760}{8} = 440$ yards per minute | M1 | Finding speed in yards/min |
| Time = $\frac{46145}{440} = 104.875...$ minutes $\approx$ 1 hour 44 minutes 52 seconds | A1 | cao, accept equivalent forms |
---1 Fig. 1 shows part of the graph of $y = \sin x - \sqrt { 3 } \cos x$.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c64062c4-4cbd-41b2-9b4d-60a43dceb700-2_467_629_468_717}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Express $\sin x - \sqrt { 3 } \cos x$ in the form $R \sin ( x - \alpha )$, where $R > 0$ and $0 \leqslant \alpha \leqslant \frac { 1 } { 2 } \pi$.\\
Hence write down the exact coordinates of the turning point P .
\hfill \mbox{\textit{OCR MEI C4 2006 Q1 [8]}}