SPS SPS SM Pure 2022 June — Question 7 4 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2022
SessionJune
Marks4
TopicRadians, Arc Length and Sector Area
TypeSector with attached triangle
DifficultyModerate -0.5 This is a straightforward application of standard formulas: arc length for the sector and cosine rule for the triangle sides. It requires careful organization of given information and correct formula application, but involves no conceptual difficulty or problem-solving insight—slightly easier than average.
Spec1.05b Sine and cosine rules: including ambiguous case1.05d 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 and angle \(BFD = 1.82\) radians, find the perimeter of the stage, in metres, to one decimal place. [4]

\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 and angle $BFD = 1.82$ radians, find the perimeter of the stage, in metres, to one decimal place. [4]

\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q7 [4]}}