| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Shaded region between arcs |
| Difficulty | Standard +0.3 This is a standard C2 radians question requiring sector area formula (½r²θ), arc length formula (rθ), and chord length using cosine rule. All techniques are routine applications of memorized formulas with straightforward arithmetic. The multi-part structure and 10 marks indicate moderate length, but no problem-solving insight is needed—just methodical application of standard formulas, 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_6}
Figure 1 shows a gardener's design for the shape of a flower bed with perimeter $ABCD$.
$AD$ is an arc of a circle with centre $O$ and radius 5 m.
$BC$ is an arc of a circle with centre $O$ and radius 7 m.
$OAB$ and $ODC$ are straight lines and the size of $\angle AOD$ is $\theta$ radians.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $\theta$, an expression for the area of the flower bed. [3]
\end{enumerate}
Given that the area of the flower bed is 15 m$^2$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item show that $\theta = 1.25$, [2]
\item calculate, in m, the perimeter of the flower bed. [3]
\end{enumerate}
The gardener now decides to replace arc $AD$ with the straight line $AD$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find, to the nearest cm, the reduction in the perimeter of the flower bed. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q15 [10]}}