O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2018 · Q67 Marks
In the diagram AOB and DOC are sectors of a circle centre O. The angle AOB is x radians. The length of the arc AB is 40 cm and the radius OB is 16 cm. [Figure 6.1]
- (i)Find the value of x.[2]
- (ii)Find the area of sector AOB.[2]
- (iii)Given that the area of the shaded region ABCD is 140 cm², find the length of OC.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [1] (i) 16x = 40 oe
- [1] (i) x = 2.5 oe (radians)
- [1] (ii) 1/2 (16)² (2.5) oe
- [1] (ii) 320
- [1] (iii) 1/2 r² (their 2.5) = (their 320) - 140 oe
- [1] (iii) FT provided their 320 > 140
- [1] (iii) correct simplification to r²=...
- [1] (iii) 12
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