SPS SPS SM Pure 2023 June — Question 6 5 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2023
SessionJune
Marks5
TopicRadians, Arc Length and Sector Area
TypeTriangle and sector combined - area/perimeter with given values
DifficultyModerate -0.3 This is a straightforward application of arc length and triangle perimeter formulas. Students need to find arc length AB (using s = rθ), length OB (given as radius), and BC (using cosine rule or recognizing the triangle geometry). All techniques are standard and the question is well-scaffolded with clear given information. Slightly easier than average due to being purely procedural with no conceptual challenges.
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_2} The shape \(AOCBA\), shown in Figure 2, consists of a sector \(AOB\) of a circle centre \(O\) joined to a triangle \(BOC\). The points \(A\), \(O\) and \(C\) lie on a straight line with \(AO = 7.5\) cm and \(OC = 8.5\) cm. The size of angle \(AOB\) is 1.2 radians. Find, in cm, the perimeter of the shape \(AOCBA\), giving your answer to one decimal place. [5]

\includegraphics{figure_2}

The shape $AOCBA$, shown in Figure 2, consists of a sector $AOB$ of a circle centre $O$ joined to a triangle $BOC$.

The points $A$, $O$ and $C$ lie on a straight line with $AO = 7.5$ cm and $OC = 8.5$ cm.

The size of angle $AOB$ is 1.2 radians.

Find, in cm, the perimeter of the shape $AOCBA$, giving your answer to one decimal place. [5]

\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q6 [5]}}