| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Compound shape area |
| Difficulty | Moderate -0.3 This is a straightforward application of radian arc length and sector area formulas with clear diagrams and step-by-step guidance. Part (i) involves finding an angle from arc length (with 'show that' scaffolding) then calculating sector area. Part (ii) requires dividing arc lengths by seat width—purely computational with no conceptual challenges. Slightly easier than average due to the structured nature and standard techniques. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
In a concert hall, seats are arranged along arcs of concentric circles. The stage is part of a sector $ABO$ of radius 11 m.
(i) Show that angle $\text{COD} = 1.55$ radians, correct to 2 decimal places. Hence find the area of the stage. [6]
(ii) There are four rows of seats, with their backs along arcs, with centre $O$, of radii 7.4 m, 8.6 m, 9.8 m and 11 m. Each seat takes up 80 cm of the arc.
(A) Calculate how many seats can fit in the front row. [4]
(B) Calculate how many more seats can fit in the back row than the front row. [2]13
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\caption{Fig. 13.1}
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In a concert hall, seats are arranged along arcs of concentric circles, as shown in Fig. 13.1. As shown in Fig. 13.2, the stage is part of a sector ABO of radius 11 m . Fig. 13.2 also gives the dimensions of the stage.
\begin{enumerate}[label=(\roman*)]
\item Show that angle $\mathrm { COD } = 1.55$ radians, correct to 2 decimal places. Hence find the area of the stage.
\item There are four rows of seats, with their backs along arcs, with centre O, of radii $7.4 \mathrm {~m} , 8.6 \mathrm {~m} , 9.8 \mathrm {~m}$ and 11 m . Each seat takes up 80 cm of the arc.\\
(A) Calculate how many seats can fit in the front row.\\
(B) Calculate how many more seats can fit in the back row than the front row.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 2012 Q13 [12]}}