A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2020 · Q87 Marks
In the diagram, ABC is an isosceles triangle with AB = BC = r cm and angle BAC = θ radians. The point D lies on AC and ABD is a sector of a circle with centre A. [Figure 8.1]
- (a)Express the area of the shaded region in terms of r and θ.[3]
- (b)In the case where r = 10 and θ = 0.6, find the perimeter of the shaded region.[4]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] Use of 180-2θ scores M0. Condone 2π-2θ
- [A1] ½r² sin(π−2θ) or ½r² sin 2θ or 2×½r cosθ r sinθ OE
- [B1FT] [Shaded area = triangle – sector] = their triangle area – ½r²θ (Condone use of 180 degrees for triangle area for B1)
- [B1] Arc BD = rθ = 6 cm SOI
- [*M1] Finding AC or ½ AC (= 8.25)
- [DM1] Subtracting r from their AC or r-rcosθ from their half AC (8.25-1.75)
- [A1] (Perimeter = 10 + 6 + 6.506 =) 22.5 AWRT
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →