| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 9 |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector with attached triangle |
| Difficulty | Moderate -0.3 This is a straightforward application of standard formulas: arc length and sector area (given radius and angle), plus basic triangle calculations using sine/cosine rules. The multi-part structure and context add some complexity, but all required formulas are standard A-level content with no novel problem-solving required. Slightly easier than average due to direct application of memorized formulas. |
| Spec | 1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
Figure 1 shows the plan view of a design for a stage at a concert.
The stage is modelled as a sector $BCDF$, of a circle centre $F$, joined to two congruent triangles $ABF$ and $EDF$.
Given that
- $AFE$ is a straight line
- $AF = FE = 10.7$m
- $BF = FD = 9.2$m
- angle $BFD = 1.82$ radians
find
\begin{enumerate}[label=(\alph*)]
\item the perimeter of the stage, in metres, to one decimal place, [5]
\item the area of the stage, in m², to one decimal place. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q2 [9]}}