| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| 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/segment question testing standard formulas (area = ½r²θ, segment = sector - triangle). Part (a) is simple algebraic manipulation, (b) applies the perimeter formula, and (c) requires subtracting triangle area from sector area. All techniques are routine C2 content with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
Figure 1 shows the sector $OAB$ of a circle of radius $r$ cm. The area of the sector is 15 cm$^2$ and $\angle AOB = 1.5$ radians.
\begin{enumerate}[label=(\alph*)]
\item Prove that $r = 2\sqrt{5}$. [3]
\item Find, in cm, the perimeter of the sector $OAB$. [2]
\end{enumerate}
The segment $R$, shaded in Fig 1, is enclosed by the arc $AB$ and the straight line $AB$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate, to 3 decimal places, the area of $R$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [8]}}