O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2024 · Q69 Marks
In this question, all lengths are in metres and all angles are in radians. The diagram shows a circle with centre O and radius 5. The points A, B, C and D lie on the circumference of the circle. Angle DOC = θ. Angle AOD = angle COB = 0.5. The length of the minor arc DC is 3.75. [Figure 6.1]
- (a)Show that θ = 0.75.[1]
- (b)Find the perimeter of the shaded region.[5]
- (c)Find the area of the shaded region.[3]
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 (May/June 2024). The mark or mark type is shown in brackets.
- [B1] 5θ=3.75 so θ = 0.75 AG Allow θ = 3.75/5 as a starting point
- [M1] For attempt to find the length of at least one chord. May be implied by a correct length.
- [A1] AB = 7.67(5) soi
- [A1] DC = 3.66(3) soi
- [B1] Arc length AD or BC : 5 × 0.5 soi oe Allow unsimplified
- [A1] 16.3
- [M2] (1/2 × 5² (1.75-sin1.75)) - (1/2 × 5² (0.75-sin 0.75))
- [A1] 8.7
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 →