| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Arc length calculation |
| Difficulty | Easy -1.2 This is a straightforward application of the arc length formula s = rθ to find r, followed by basic trigonometry (cosine rule or right triangle) to find the chord length. Both parts require direct formula application with minimal problem-solving, making it easier than average but not trivial since it involves two distinct steps and working with radians. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 5 | 2 marks | M1 for \(6 = 1.2r\) |
| (ii) 5.646... to 2 s.f. or more | 3 marks | M2 for \(2x\) \(5x \sin 0.6\) or \(\sqrt{5^2 + 5^2 - 2(5)(5) \cos 1.2}\) or \(5 \sin 1.2/\sin 0.971\); M1 for these methods with 1 error |
(i) 5 | 2 marks | M1 for $6 = 1.2r$
(ii) 5.646... to 2 s.f. or more | 3 marks | M2 for $2x$ $5x \sin 0.6$ or $\sqrt{5^2 + 5^2 - 2(5)(5) \cos 1.2}$ or $5 \sin 1.2/\sin 0.971$; M1 for these methods with 1 error | 5 marks total7 In Fig. 7, A and B are points on the circumference of a circle with centre O . Angle $\mathrm { AOB } = 1.2$ radians.
The arc length AB is 6 cm .
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{15b8f97b-c058-409f-907f-cb0a6102abc4-3_371_723_1048_833}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{center}
\end{figure}
(i) Calculate the radius of the circle.\\
(ii) Calculate the length of the chord AB .
\hfill \mbox{\textit{OCR MEI C2 2006 Q7 [5]}}