Contents List of Figures
xi
List of Tables
xiii
I PROBLEMS STATEMENTS
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1 ALGEBRAIC APPLICATION 1.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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List of Figures
xi
List of Tables
xiii
Part I PROBLEMS STATEMENTS
1
1 ALGEBRAIC APPLICATION 1.1 Examples Example 1.1 On Saturday afternoon, Armand sent 𝑚 text messages each hour for 5 hours, and Tyrone sent 𝑝 text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
A 9𝑚𝑝
B 20𝑚𝑝
C 5𝑚 + 4𝑝
D 4𝑚 + 5𝑝
E 𝑚𝑝
Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. ..............................................................................
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1.1. EXAMPLES
Example 1.2 5 years ago, Tina was 2𝑝 years old. Next year, Tina’s brother, Jack, will be 7 years older than Tina. Find their total age in 10 years’ time. Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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Example 1.3 The figure shows a triangle, 𝑃𝑄𝑅. 𝑃
4𝑥 cm
𝑄
𝑅
24cm a) Find the total area of the shaded parts in terms of 𝑥. b) If 𝑥 = 7, find the total area of the shaded parts.
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CHAPTER 1. ALGEBRAIC APPLICATION
Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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..................................... Example 1.4 Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. For what number of shirts would the cost be the same?
Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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1.1. EXAMPLES
Example 1.5 Town A and Town B are 378 km apart. At 9.45 a.m, Roy set off from Town B to Town A at an average speed of 88 km/h. 15 minutes later, Sam set off from Town A to Town B at an average speed of 90 km/h. a) How far from Town A was Roy at 10 a.m? b) At what time did Sam and Roy pass at each other? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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..................................... Example 1.6 A mixture, weighing 100kg is made up of 2 chemicals 𝐴 and 𝐵 in the ratio 7 : 3. When some volume of Chemical 𝐴 evaporates, the content of Chemical 𝐴 is reduced to 60% of the new mixture. What is the mass of the mixture now?
Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. ..............................................................................
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CHAPTER 1. ALGEBRAIC APPLICATION
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1.2 Exercises Exercise 1. a) A zoo has 3 times as many gorillas as tigers. There are 3 more tigers than zebras at the zoo. If 𝑧 represents the number of zebras, in terms of 𝑧, how many gorillas are in the zoo? b) The total perimeter of an equilateral triangle and a square is (38𝑝 + 81)𝑐𝑚. If the length of a side of the equilateral triangle is (2𝑝 + 7)𝑐𝑚, find the length of a side of the square. Give your answer in terms of 𝑝. Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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1.2. EXERCISES
Exercise 2. The breadth of a rectangle is (3𝑦+5)𝑐𝑚. The perimeter of the rectangle is (24𝑦 + 10)𝑐𝑚. a) Find the length of the rectangle. b) Find the area of the rectangle if 𝑦 = 3. Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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Exercise 3. Susan jogged from home to the sport complex at a constant speed of 6 km/h. 10 minutes later, her sister, Susie, started riding a bicycle along the same route towards the sports complex at a constant speed of 18 km/h. If they arrived at sports complex at the same time, how many seconds does it take Susan to jog from home to the sport complex? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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CHAPTER 1. ALGEBRAIC APPLICATION
Exercise 4. Jack and Bill had $440 altogether. Bill had $20 more than Jack. When 1 Jack spent the amount of money spent by Bill, he had 3 times as much money 3 as Bill. How much money did Bill spend? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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Exercise 5. Daniel had some money. He spent $695 on an i-phone. He then 2 spent of the remaining money on a pair of shoes. The amount of money spent 5 was $65 less than the amount of money he had left. How much did Daniel have at first? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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1.2. EXERCISES
Exercise 6. 0.7 of the balls in a bag are black, 0.2 of the remainder are pink and the remainder are red. If there are 184 more black balls than red balls, how many balls are there in the bag together? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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Exercise 7. The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both plan trips there. The senior class at High School A rents and fills 8 vans and 8 buses with 240 students. High School B rents and fills 4 vans and 1 bus with 54 students. Every van and every bus has the same number of students. Find the number of students in each bus. Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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CHAPTER 1. ALGEBRAIC APPLICATION
Exercise 8. A rectangle has length 𝑥 and width 𝑦. A triangle has base 16 and height 𝑥. If the area of the rectangle is equal to the area of the triangle, then find the value of 𝑦. Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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Exercise 9. Phoebe has some 32-cent stamps, some 29-cent stamps, and some 3-cent stamps. The number of 29-cent stamps is 10 less than the number of 32-cent stamps, while the number of 3-cent stamps is 5 less than the number of 29-cent stamps. The total value of the stamps is $9.45. How many 32-cent stamp does she have? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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1.2. EXERCISES
Exercise 10. Father is aged three times more than his son, Sunny. After 8 years, he would be two and a half times of Sunny’s age. After further 8 years, how many times would he be of Sunny’s age? Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................... .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. .............................................................................. ..............................................................................
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