Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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Name: ( ) Class: ( )
Answer all questions. Total marks of this paper are 100. Time: 35minutes 1. Simplify the following ratios. (15 marks, 3 marks for each)
(a) 1.2km: 240cm (b) 3.2hours: 1.5days (c) 56:80:16 (d) 0.63:0.28:0.07
(e) !!: !"!: !!
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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2. Express each of the scales below in the form 1:n. (a) 30mm: 6000cm (4 marks) (b) 2.5mm: 1km (5 marks)
3. Find a: b: c in each of the following. (16 marks, 8 marks for each) (a) a:b = 2:3, a:c = 4:9
(b) !!: !!= 3: 2, !
!: !!= 5: 4
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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4. Trapeziums ABCD and PQRS shown on the right are two similar figures. If CD:RS=4:3, find (a) the values of x, y and z. (b) area of ABCD : area of PQRS (15 marks, part a: 9 marks, part b: 6 marks)
5. A boutique sells a brand of dresses in three different colors, which are yellow, pink and purple. The ratio of the number of purple dresses to that of pink dresses is 2:5, while the ratio of the number of pink dresses to that of yellows dresses is 4:3. (a) Find the number of yellow dresses: the number of pink dresses: the number of purple dresses. (b) If the total number of thus brand of dresses in the boutique is 215, find the number of dresses for each color. (20 marks, part a: 10 marks, part b: 10 marks)
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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6. Louis and Steve have 84 and 56 cartoon stickers respectively. (a) Find the ratio of the number of Louisโs stickers to that of Steveโs. (b) Louis gives some stickers to Steve and then the ratio in (a) becomes 11:9. How many stickers does each have now? (25 marks, part a: 10 marks, part b: 15 marks)
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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Suggested Solution
1. (a) (3marks) ๐.๐๐๐: ๐๐๐๐๐
๐.๐ ๐๐๐๐ ๐๐๐ ๐๐: ๐๐๐๐๐ ๐๐๐๐๐๐๐๐: ๐๐๐๐๐
๐๐๐: ๐ (b) (3marks)
๐.๐๐๐๐๐๐: ๐.๐๐ ๐๐๐ ๐.๐๐๐: ๐.๐ ๐๐ ๐๐ ๐.๐๐๐: ๐๐๐๐
๐: ๐๐ (c) (3marks)
๐๐: ๐๐: ๐๐ ๐๐๐ :
๐๐๐ :
๐๐๐
๐: ๐๐: ๐ (d) (3marks)
๐.๐๐: ๐.๐๐: ๐.๐๐ ๐.๐๐ ๐๐๐ : ๐.๐๐ ๐๐๐ : ๐.๐๐ ๐๐๐
๐๐: ๐๐: ๐ ๐๐๐ :
๐๐๐ :
๐๐
๐: ๐: ๐ (e) (3marks)
๐๐ :๐๐๐ :
๐๐
๐๐ ๐๐ :
๐๐๐ ๐๐ :
๐๐ ๐๐
๐๐:๐๐:๐ 2. (a) (3marks)
๐๐๐๐: ๐๐๐๐๐๐ ๐๐๐๐: ๐๐๐๐ ๐๐ ๐๐ ๐๐๐๐: ๐๐๐๐๐๐๐
๐: ๐๐๐๐
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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(b) (3marks) ๐.๐๐๐: ๐๐๐
๐.๐๐๐:๐ ๐๐๐๐ ๐๐๐ ๐๐ ๐๐ ๐.๐๐๐๐๐๐๐๐๐๐๐๐
๐:๐๐๐๐๐๐ 3. (a)
a : b = 2 : 3 a : c = 4 : 9 a : b = 2 x 2 : 3 x 2 b : c = 4 : 9 a : b : c = 4 : 6 : 9 (b)
๐๐ :๐๐ = ๐:๐
๐๐๐๐=๐๐
๐๐
๐๐ =
๐๐
๐๐ =
๐๐
โด ๐:๐ = ๐:๐
๐บ๐๐๐๐๐๐๐๐,๐๐ :๐๐ = ๐:๐ ๐๐ ๐๐๐๐๐ ๐๐ ๐: ๐ = ๐:๐
a โถ b = 2 โถ 3 a : c = 4 : 5 a : b = 2 x 2 : 3 x 2 b : c = 4 : 5 a : b : c = 4 : 6: 5
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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4. (a) โต ๐ป๐๐๐๐๐๐๐๐ ๐จ๐ฉ๐ช๐ซ ๐๐๐ ๐ท๐ธ๐น๐บ ๐๐๐ ๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐, ๐๐๐๐ ๐๐ ๐๐๐๐ โต ๐ช๐ซ: ๐น๐บ = ๐: ๐ ๐จ๐ซ: ๐ท๐บ = ๐ซ๐ฏ: ๐บ๐ฒ = ๐ฉ๐ช: ๐ธ๐น = ๐: ๐ ๐จ๐ซ๐ท๐บ =
๐ซ๐ฏ๐บ๐ฒ =
๐ฉ๐ช๐ธ๐น =
๐๐
๐๐๐ =
๐๐๐ =
๐๐๐ =
๐๐
โด ๐ = ๐๐,๐ = ๐๐, ๐ = ๐๐ (b) โต ๐ป๐๐๐๐๐๐๐๐ ๐จ๐ฉ๐ช๐ซ ๐๐๐ ๐ท๐ธ๐น๐บ ๐๐๐ ๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐, ๐๐๐ ๐ช๐ซ: ๐น๐บ = ๐: ๐ โด ๐๐๐๐ ๐๐ ๐จ๐ฉ๐ช๐ซ: ๐๐๐๐ ๐๐ ๐ท๐ธ๐น๐บ = ๐๐: ๐๐ = ๐๐: ๐
5. (a) purple : pink = 2 : 5 pink : yellow = 4 : 3 purple : pink = 2 x 4 : 5 x 4 pink : yellow = 4 x 5 : 3 x 5 purple : pink: yellow = 8 : 20 : 15 โด ๐๐๐๐๐๐: ๐๐๐๐ โถ ๐๐๐๐๐๐ = ๐๐ โถ ๐๐ โถ ๐ (b)
๐๐๐๐๐๐ = ๐๐๐ร๐๐
๐๐+ ๐๐+ ๐ = ๐๐
๐๐๐๐ = ๐๐๐ร๐๐
๐๐+ ๐๐+ ๐ = ๐๐๐
๐๐๐๐๐๐ = ๐๐๐ร ๐๐๐!๐๐!๐
= ๐๐
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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6. (a) Louis: Steve = 84: 56 = 3: 2 (b) Let Louis gives x stickers to Steve, then Louis has 84-ยญโx stickers and Steve has 56+x stickers:
๐๐โ ๐๐๐+ ๐ =
๐๐๐
๐๐โ ๐ ๐ = ๐๐+ ๐ ๐๐ ๐๐๐โ ๐๐ = ๐๐๐+ ๐๐๐ ๐๐๐ = ๐๐๐
๐ =๐๐๐๐๐ = ๐
โด ๐ณ๐๐๐๐ ๐๐๐๐๐ ๐ ๐๐๐๐๐๐๐๐ ๐๐ ๐บ๐๐๐๐, ๐๐๐๐๐๐๐๐๐,๐ณ๐๐๐๐ ๐๐๐ ๐๐โ ๐= ๐๐ ๐๐๐๐๐๐๐ ๐๐๐ ๐บ๐๐๐๐ ๐๐๐ ๐๐+ ๐ = ๐๐ ๐๐๐๐๐๐๐๐.