| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Segment area calculation |
| Difficulty | Moderate -0.3 This is a straightforward sector problem requiring standard formulas (arc length s=rθ, sector area, triangle area) with basic algebraic manipulation. Part (a) involves solving a simple linear equation from the perimeter condition, and part (b) applies the formula for segment area (sector minus triangle). While it requires multiple steps, all techniques are routine C2 content with no conceptual challenges. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(P = 2r + (r \times 2.5) = \frac{9}{2}r = 36\) | M1 | |
| \(OA = r = 8\) cm | A1 | |
| (b) \(=(\frac{1}{2} \times 8^2 \times 2.5) - (\frac{1}{2} \times 8^2 \times \sin 2.5) = 60.8\) cm² (3sf) | M2 A1 | (5 marks) |
**(a)** $P = 2r + (r \times 2.5) = \frac{9}{2}r = 36$ | M1 |
$OA = r = 8$ cm | A1 |
**(b)** $=(\frac{1}{2} \times 8^2 \times 2.5) - (\frac{1}{2} \times 8^2 \times \sin 2.5) = 60.8$ cm² (3sf) | M2 A1 | (5 marks)\includegraphics{figure_1}
Figure 1 shows the sector $OAB$ of a circle, centre $O$, in which $\angle AOB = 2.5$ radians.
Given that the perimeter of the sector is 36 cm,
\begin{enumerate}[label=(\alph*)]
\item find the length $OA$, [2]
\item find the area of the shaded segment. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q2 [5]}}