Moderate -0.8 This is a straightforward application of standard formulas for sector and semicircle areas. Students need to find the area of semicircle AYB and subtract the area of sector OAXB, using the given radius r and angle 2θ. The setup is clear, requires only direct formula application (sector area = ½r²(2θ), semicircle area = ½π(r/2)² after finding the semicircle's radius), and involves minimal algebraic manipulation—typical of early Pure 1 content with no problem-solving insight required.
\includegraphics{figure_2}
In the diagram, \(AYB\) is a semicircle with \(AB\) as diameter and \(OAXB\) is a sector of a circle with centre \(O\) and radius \(r\). Angle \(AOB = 2\theta\) radians. Find an expression, in terms of \(r\) and \(\theta\), for the area of the shaded region. [4]
\includegraphics{figure_2}
In the diagram, $AYB$ is a semicircle with $AB$ as diameter and $OAXB$ is a sector of a circle with centre $O$ and radius $r$. Angle $AOB = 2\theta$ radians. Find an expression, in terms of $r$ and $\theta$, for the area of the shaded region. [4]
\hfill \mbox{\textit{CAIE P1 2015 Q2 [4]}}