Math 9 Review (Chapters 3 and 4)
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1 Math 9 Review (Chapters 3 and 4) Problem 1. The number of insects in a colony doubles every month. There are currently 1000 insects in the colony. How many insects will there be after one year? 2. A culture of bacteria triples every hour. How many bacteria were there 3 h ago? 3. Two cubes have edge lengths of 4 cm and 6 cm, respectively. a) Determine an expression that represents the difference in volumes of the cubes. b) Calculate the difference in the volumes of the cubes. c) Determine an expression that represents the difference in the surface areas of the cubes. d) Calculate the difference in the surface areas of the cubes. 4. Some companies rely on word-of-mouth advertising. In this type of advertising, a customer tells a round of friends and relatives about the company s service. A customer of an interior decorating company tells three of her friends about her experience with the company. Each friend tells three more friends about the company, and so on. How many potential customers will the company have after the following number of rounds? a) the 4th round? b) the 6th round? c) the 12th round? 5. If 4 x = 7, use exponent laws to evaluate the following expressions: a) 4 3x b) 4 (x+2) 6. The product of the ages of a set of quadruplets is 16 times the sum of their ages. How old are the quadruplets? 7. A flower garden is shown below. What is the area of the garden? 8. The screen on a digital camera is 3.2 cm wide. After a picture is taken, the image is 1.6% the size of the actual object. If the image of a car is as wide as the screen, what is the actual width of the car, in metres? 9. A map of a nature reserve shows the location of three look-out points. On the map, the distance between Point A and Point B is 4.5 cm and the distance between Point B and Point C is 6.0 cm. Each centimetre on the map represents 15 km of actual distance. Calculate the actual distance between Point A and Point C.
2 10. An observer stands 18.2 m from the door of a house, and 2.6 m from the street. The observer is 1.3 m tall. Calculate the height of the house.
3 Math 9 Review (Chapters 3 and 4) Answer Section PROBLEM 1. ANS: Let P represent the population of insects. After one year, there will be insects in the colony. PTS: 1 DIF: Average OBJ: Section 3.4 NAT: N1 KEY: population growth problem solving 2. ANS: Let P represent the population of bacteria. There were approximately 3704 bacteria 3 h ago. PTS: 1 DIF: Difficult+ OBJ: Section 3.4 NAT: N1 KEY: population growth problem solving negative exponents 3. ANS: Example: a) b) = = 152 The difference in the volumes of the cubes is 152 cm 3. c) 6( ) or 6(6 2 ) 6(4 2 ) d) 6( ) = 6(20) = 120 The difference in the surface areas of the cubes is 120 cm 2. PTS: 1 DIF: Average OBJ: Section 3.3 NAT: N4 TOP: Order of Operations KEY: volume surface area cube order of operations problem solving 4. ANS: a) 3 4 = 81 After the 4th round, there are 81 potential customers.
4 b) 3 6 = 729 After the 6th round, there are 729 potential customers. c) 3 12 = After the 12th round, there are potential customers. PTS: 1 DIF: Easy OBJ: Section 3.4 NAT: N1 KEY: exponential form problem solving 5. ANS: a) b) PTS: 1 DIF: Difficult OBJ: Section 3.2 NAT: N2 TOP: Exponent Laws KEY: evaluate powers exponent laws 6. ANS: Let x represent the age of the quadruplets. The product of the ages of the quadruplets is x x x x,or x 4. Sixteen times the sum of the ages of the quadruplets is 16(x + x + x + x), or 16(4x). Divide both sides by x. The quadruplets are 4 years old. PTS: 1 DIF: Difficult OBJ: Section 3.2 NAT: N2 TOP: Exponent Laws KEY: quotient of powers evaluate powers problem solving 7. ANS: The garden has an area of 27 m 2. PTS: 1 DIF: Easy OBJ: Section 3.3 NAT: N4 TOP: Order of Operations KEY: area problem solving
5 8. ANS: Length of the image of the car is 3.2 cm (width of the screen) and is 1.6% of the actual size. The actual width of the car is 2 m. PTS: 1 DIF: Difficult OBJ: Section 4.1 NAT: SS4 TOP: Enlargements and Reductions KEY: scale factor reduction 9. ANS: Distance between Point A and Point C on the map Scale of the map = 1 cm:75 km The actual distance between Point A and Point C is km. PTS: 1 DIF: Difficult OBJ: Section 4.3 NAT: SS4 TOP: Similar Triangles KEY: similar triangles problem solving 10. ANS: The height of the house is 10.4 m. PTS: 1 DIF: Average OBJ: Section 4.3 NAT: SS4 TOP: Similar Triangles KEY: similar triangles problem solving
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