O-LevelMathematicsMensuration4024/22 · May/June 2023 · Q811 Marks
(a) [Figure 8.1] The length of the rectangle R is twice its width. Rectangle R has a perimeter of 20.4 cm. (b) [Figure 8.2] A piece of card is a sector of a circle with sector angle 75° and radius 8 cm.
- (a)(i)Find the length and width of the rectangle R.[2]
- (a)(ii)Rectangle S is mathematically similar to rectangle R. Rectangle S has a perimeter of 30.6 cm. Calculate the length of rectangle S.[2]
- (b)(i)Find an expression, in terms of π, for the arc length of the sector. Give your answer in its simplest form.[2]
- (b)(ii)[Volume of a cone = 1/3πr²h] The piece of card forms the curved surface area of a cone. The cone is filled to the top with water. Calculate the volume of water in the cone.[5]
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Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [2] B1 for length = 6.8 or width = 3.4
- length = 6.8 width = 3.4
- After 0 scored SC1 for length = 3.4 and width = 6.8
- [2] FT 1.5× their length
- B1 for (30.6/20.4) or (length/6.8) oe or (20.4/30.6) or (length/width) oe
- or M1 for 20.4/their6.8 = 30.6/l oe or (30.6/20.4) × 2 oe
- 10.2 nfww
- [2] M1 for (75/360) × 2 × π × 8 oe
- 10π/3 or 3 1/3 π or (10/3)π final answer
- [5] M1 for (their arc length)/(2π) or (75/360) × π × 8² oe
- M2 for √8²-their r² oe
- or M1 for 8² – their r²
- M1 for 1/3 × π × their r² × their7.82
- 22.7 to 22.9
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