O-LevelMathematicsGeometry4024/21 · Oct/Nov 2020 · Q79 Marks
A, B, C and D are points on the circle, centre O. BÂD = 68° and CBO = 52°. Find CÔD.
- (a)A, B, C and D are points on the circle, centre O. BÂD = 68° and CBO = 52°. Find CÔD.[3]
- (b)(i)The cross-section of solid A is the sector of a circle of radius 6 cm and angle 40°. The height of solid A is 5 cm. Calculate the total surface area of solid A.[4]
- (b)(ii)Solid B is mathematically similar to solid A. The ratio volume of solid A : volume of solid B = 27 : 1. Calculate the surface area of solid B.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [3] 60° nfww B1 for ∠DOB = 136° soi B1 for ∠BCD = 112° soi M1 for ∠CDO = 360 – their 136 – their 112 – 52 Alternative method B1 ∠COB = 76° soi B1 ∠COD = 60° or ∠OCD = 60° soi M1 ZCDO = ∠OCD or ∠CDO = (180 – their 60) ÷ 2 Max 2 marks if answer incorrect
- [4] 106 to 106.1 M1 for [2x] 40/360 ×π×6^2 soi M1 for 40/360 ×2×π×6×5 soi M1 for [2x] 5 × 6 soi
- [2] 11.7 to 11.8 FT their (b)(i) ÷ 9 B1 for 1/√27 or 1/27 soi
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