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 Louis’s stickers to that of Steve’s. (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) 𝟏.𝟐𝒌𝒎: 𝟐𝟒𝟎𝒄𝒎
𝟏.𝟐 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎 𝒄𝒎: 𝟐𝟒𝟎𝒄𝒎 𝟏𝟐𝟎𝟎𝟎𝟎𝒄𝒎: 𝟐𝟒𝟎𝒄𝒎
𝟓𝟎𝟎: 𝟏 (b) (3marks)
𝟑.𝟐𝒉𝒖𝒐𝒓𝒔: 𝟏.𝟓𝒅𝒂𝒚𝒔 𝟑.𝟐𝒉𝒓: 𝟏.𝟓 𝟐𝟒 𝒉𝒓 𝟑.𝟐𝒉𝒓: 𝟑𝟔𝒉𝒓
𝟒: 𝟒𝟓 (c) (3marks)
𝟓𝟔: 𝟖𝟎: 𝟏𝟔 𝟓𝟔𝟖 :
𝟖𝟎𝟖 :
𝟏𝟔𝟖
𝟕: 𝟏𝟎: 𝟐 (d) (3marks)
𝟎.𝟔𝟑: 𝟎.𝟐𝟖: 𝟎.𝟎𝟕 𝟎.𝟔𝟑 𝟏𝟎𝟎 : 𝟎.𝟐𝟖 𝟏𝟎𝟎 : 𝟎.𝟎𝟕 𝟏𝟎𝟎
𝟔𝟑: 𝟐𝟖: 𝟕 𝟔𝟑𝟕 :
𝟐𝟖𝟕 :
𝟕𝟕
𝟗: 𝟒: 𝟏 (e) (3marks)
𝟑𝟐 :𝟏𝟐𝟓 :
𝟏𝟒
𝟑𝟐 𝟐𝟎 :
𝟏𝟐𝟓 𝟐𝟎 :
𝟏𝟒 𝟐𝟎
𝟑𝟎:𝟒𝟖:𝟓 2. (a) (3marks)
𝟑𝟎𝒎𝒎: 𝟔𝟎𝟎𝟎𝒄𝒎 𝟑𝟎𝒎𝒎: 𝟔𝟎𝟎𝟎 𝟏𝟎 𝒎𝒎 𝟑𝟎𝒎𝒎: 𝟔𝟎𝟎𝟎𝟎𝒎𝒎
𝟏: 𝟐𝟎𝟎𝟎
Mathematics St. Bonaventure College and High School Form 2, Quiz 1 (Chapter 1: Rate and Ratio)
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(b) (3marks) 𝟐.𝟓𝒎𝒎: 𝟏𝒌𝒎
𝟐.𝟓𝒎𝒎:𝟏 𝟏𝟎𝟎𝟎 𝟏𝟎𝟎 𝟏𝟎 𝒎𝒎 𝟐.𝟓𝒎𝒎𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝒎𝒎
𝟏:𝟒𝟎𝟎𝟎𝟎𝟎 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)
𝟏𝒂 :𝟏𝒃 = 𝟑:𝟐
𝟏𝒂𝟏𝒃=𝟑𝟐
𝟏𝒂
𝒃𝟏 =
𝟑𝟐
𝒃𝒂 =
𝟑𝟐
∴ 𝒂:𝒃 = 𝟐:𝟑
𝑺𝒊𝒎𝒊𝒍𝒂𝒓𝒍𝒚,𝟏𝒂 :𝟏𝒄 = 𝟓:𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝒂: 𝒄 = 𝟒:𝟓
a ∶ b = 2 ∶ 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) ∵ 𝑻𝒓𝒂𝒑𝒆𝒛𝒊𝒖𝒎 𝑨𝑩𝑪𝑫 𝒂𝒏𝒅 𝑷𝑸𝑹𝑺 𝒂𝒓𝒆 𝒔𝒊𝒎𝒊𝒍𝒂𝒓 𝒇𝒊𝒈𝒖𝒓𝒆𝒔, 𝒕𝒉𝒆𝒏 𝒘𝒆 𝒉𝒂𝒗𝒆 ∵ 𝑪𝑫: 𝑹𝑺 = 𝟒: 𝟑 𝑨𝑫: 𝑷𝑺 = 𝑫𝑯: 𝑺𝑲 = 𝑩𝑪: 𝑸𝑹 = 𝟒: 𝟑 𝑨𝑫𝑷𝑺 =
𝑫𝑯𝑺𝑲 =
𝑩𝑪𝑸𝑹 =
𝟒𝟑
𝒙𝟏𝟐 =
𝟐𝟎𝒛 =
𝟑𝟐𝒚 =
𝟒𝟑
∴ 𝒙 = 𝟏𝟔,𝒚 = 𝟐𝟒, 𝒛 = 𝟏𝟓 (b) ∵ 𝑻𝒓𝒂𝒑𝒆𝒛𝒊𝒖𝒎 𝑨𝑩𝑪𝑫 𝒂𝒏𝒅 𝑷𝑸𝑹𝑺 𝒂𝒓𝒆 𝒔𝒊𝒎𝒊𝒍𝒂𝒓 𝒇𝒊𝒈𝒖𝒓𝒆𝒔, 𝒂𝒏𝒅𝑪𝑫: 𝑹𝑺 = 𝟒: 𝟑 ∴ 𝒂𝒓𝒆𝒂 𝒐𝒇 𝑨𝑩𝑪𝑫: 𝒂𝒓𝒆𝒂 𝒐𝒇 𝑷𝑸𝑹𝑺 = 𝟒𝟐: 𝟑𝟐 = 𝟏𝟔: 𝟗
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 ∴ 𝒚𝒆𝒍𝒍𝒐𝒘: 𝒑𝒊𝒏𝒌 ∶ 𝒑𝒖𝒓𝒑𝒍𝒆 = 𝟏𝟓 ∶ 𝟐𝟎 ∶ 𝟖 (b)
𝒚𝒆𝒍𝒍𝒐𝒘 = 𝟐𝟏𝟓×𝟏𝟓
𝟏𝟓+ 𝟐𝟎+ 𝟖 = 𝟕𝟓
𝒑𝒊𝒏𝒌 = 𝟐𝟏𝟓×𝟐𝟎
𝟏𝟓+ 𝟐𝟎+ 𝟖 = 𝟏𝟎𝟎
𝒑𝒖𝒓𝒑𝒍𝒆 = 𝟐𝟏𝟓× 𝟖𝟏𝟓!𝟐𝟎!𝟖
= 𝟒𝟎
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-‐x stickers and Steve has 56+x stickers:
𝟖𝟒− 𝒙𝟓𝟔+ 𝒙 =
𝟏𝟏𝟗
𝟖𝟒− 𝒙 𝟗 = 𝟓𝟔+ 𝒙 𝟏𝟏 𝟕𝟓𝟔− 𝟗𝒙 = 𝟔𝟏𝟔+ 𝟏𝟏𝒙 𝟐𝟎𝒙 = 𝟏𝟒𝟎
𝒙 =𝟏𝟒𝟎𝟐𝟎 = 𝟕
∴ 𝑳𝒐𝒖𝒊𝒔 𝒈𝒊𝒗𝒆𝒔 𝟕 𝒔𝒕𝒊𝒄𝒌𝒆𝒓𝒔 𝒕𝒐 𝑺𝒕𝒆𝒗𝒆, 𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆,𝑳𝒐𝒖𝒊𝒔 𝒉𝒂𝒔 𝟖𝟒− 𝟕= 𝟕𝟕 𝒔𝒕𝒊𝒌𝒆𝒓𝒔 𝒂𝒏𝒅 𝑺𝒕𝒆𝒗𝒆 𝒉𝒂𝒔 𝟓𝟔+ 𝟕 = 𝟔𝟑 𝒔𝒕𝒊𝒄𝒌𝒆𝒓𝒔.
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