SPS SPS SM Pure 2023 September — Question 7 5 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2023
SessionSeptember
Marks5
TopicRadians, Arc Length and Sector Area
TypeShaded region between arcs
DifficultyModerate -0.3 This is a straightforward application of sector area formulas requiring students to find the angle from arc length, calculate two sector areas, and subtract. The steps are routine: θ = s/r = 48/60 = 0.8 rad, then Area = ½r²θ for both sectors and subtract. While it involves multiple steps, each is a standard formula application with no conceptual difficulty or problem-solving insight required.
Spec1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta

\includegraphics{figure_7} The figure above shows a circular sector \(OAB\) whose centre is at \(O\). The radius of the sector is 60 cm. The points \(C\) and \(D\) lie on \(OA\) and \(OB\) respectively, so that \(|OC| = |OD| = 24\) cm. Given that the length of the arc \(AB\) is 48 cm, find the area of the shaded region \(ABDC\), correct to the nearest cm\(^2\). [5 marks]

\includegraphics{figure_7}

The figure above shows a circular sector $OAB$ whose centre is at $O$.

The radius of the sector is 60 cm.

The points $C$ and $D$ lie on $OA$ and $OB$ respectively, so that $|OC| = |OD| = 24$ cm.

Given that the length of the arc $AB$ is 48 cm, find the area of the shaded region $ABDC$, correct to the nearest cm$^2$.

[5 marks]

\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q7 [5]}}