| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Simultaneous equations with arc/area |
| Difficulty | Standard +0.3 This is a straightforward sector geometry problem requiring standard formulas. Part (a) involves setting up an equation using the area formula for sectors (difference of two sector areas equals the shaded area), then solving a quadratic. Part (b) applies arc length formulas. The setup is clear from the diagram, and all techniques are routine A-level content with no novel insight required. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
The diagram below shows a badge $ODC$. The shape $OAB$ is a sector of a circle centre $O$ and radius $r$ cm. The shape $ODC$ is a sector of a circle with the same centre $O$. The length $AD$ is $5$ cm and angle $AOB$ is $\frac{\pi}{5}$ radians. The area of the shaded region, $ABCD$, is $\frac{13\pi}{2}$ cm$^2$.
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $r$. [4]
\item Calculate the perimeter of the shaded region. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2024 Q3 [7]}}