O-LevelAdditional MathematicsCircular measure4037/22 · May/June 2016 · Q67 Marks
The diagram shows a sector of a circle with centre O and radius 5 cm. The length of the arc AB is 7 cm. Angle AOB is θ radians. [Figure 6.1]
- (i)Explain why θ must be greater than 1 radian.[1]
- (ii)Find the value of θ.[2]
- (iii)Calculate the area of the sector AOB.[2]
- (iv)Calculate the area of the shaded segment.[2]
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 2016). The mark or mark type is shown in brackets.
- [B1] Valid explanation e.g. arc length is greater than the radius or 7 is greater than 5
- [M1] 7=5θ
- [A1] θ = 1.4 oe implies M1
- [M1] 1/2 × 5² × their1.4 oe
- [A1] 17.5 oe
- [M1] [triangle area =] 1/2 × 5² × sin their1.4 or 12.3 to 12.32 or for [1/2 × base × height=] 1/2 ×6.4[4...]×3.8[2...] oe may be embedded in a difference calculation
- [A1] 5.18 to 5.2 inclusive implies M1
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 →