| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 10 |
| Topic | Radians, Arc Length and Sector Area |
| Type | Segment area calculation |
| Difficulty | Moderate -0.3 This is a straightforward multi-part question testing standard techniques: cosine rule for finding AC, then sector area minus triangle area for the segment, and arc length plus chord for perimeter. All are routine A-level applications with no novel problem-solving required, though the multi-step nature and radian mode calculations place it slightly below average difficulty rather than being trivial. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
The diagram shows a triangle $ABC$, and a sector $ACD$ of a circle with centre $A$. It is given that $AB = 11$ cm, $BC = 8$ cm, angle $ABC = 0.8$ radians and angle $DAC = 1.7$ radians. The shaded segment is bounded by the line $DC$ and the arc $DC$.
\includegraphics{figure_7}
\begin{enumerate}[label=(\roman*)]
\item Show that the length of $AC$ is $7.90$ cm, correct to 3 significant figures. [3]
\item Find the area of the shaded segment. [3]
\item Find the perimeter of the shaded segment. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q7 [10]}}