(m)mif ass c2 tp - newark public schools
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Name: Date:
48 Chapter 5 Test A
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25 Suggested Time:
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CHAPTER TEST A
Direct and Inverse Proportion5
Concepts and Skills (Questions 1 to 6: 6 � 1 point � 6 points, Questions 7 and 8: 2 � 2 points � 4 points)
Tell whether each table, graph, or equation represents a direct proportion, an inverse proportion, or neither.
1. x 7 9 15
y 3.5 4.5 7.5
2.
1
0 1
2
2
3
3
4
4
y
x
3.
3
0
6
1
9
12
2
y
x
4. y � 4x � 3 5. 2y � 15
x
Find the constant of proportionality. Then write an equation relating x and y.
6. y is directly proportional to x, and y � 35 when x � 7.
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Assessments Course 2 49
Solve using proportional reasoning.
7. y is directly proportional to x, and y � 216 when x � 2.
a) Find y when x � 7.
b) Find x when y � 540.
8. r is inversely proportional to s, and s � 30 when r � 10.
a) Write an equation relating r and s.
b) Find s when r � 150.
Problem Solving (Question 9: 2 points, Questions 10 to 12: 3 � 3 points � 9 points, Question 13: 4 points)
Use a proportion to solve each question. Show your work.
9. The circumference, C, of a circle is directly proportional to the diameter, d, of a circle. They are related by the formula C � d.
a) Find the constant of proportionality in the formula.
b) What is the diameter of a circle with circumference 105 centimeters? Round your answer to the nearest tenth. Use 3.14 as an approximation for .
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Name: Date:
50 Chapter 5 Test A
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10. The volume of paint used, V liters, is directly proportional to the area, A square feet, that the paint can cover. 5 liters of paint can cover a wall with an area of 75 square feet.
a) Find the constant of proportionality.
b) Write an equation relating V and A.
c) How much paint would be needed to cover an area of 180 square feet?
11. Jane paints clay figurines to sell at a crafts fair. The graph shows that the number of figurines she paints, y, is directly proportional to the number of days she paints, x.
Painting Clay Figurines
Number of Days
Num
ber
of
Cla
y Fi
gur
ines
0x
y
5
1
10
2
15
3
20
4
25
5
30
6
a) Find the constant of proportionality.
b) What does the constant of proportionality represent in this situation?
c) How long will it take Jane to paint 30 figurines?
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Assessments Course 2 51
12. The table shows the daily houseboat rental rate, in P dollars, for x number of people.
Number of People (x) 1 2 3
Rental Rate (P dollars per person) 240 120 80
a) Describe the relationship between the number of people and the daily houseboat rental rate.
b) Write an equation relating x and P.
c) What is the rental rate, in dollars per person, if 6 people plan to rent the houseboat?
13. The time taken to cycle a particular distance varies inversely with the speed of the bicycle. Tim takes 3 hours to reach his destination traveling at a constant speed of 12 miles per hour.
a) Find the constant of proportionality.
b) What does the constant of proportionality represent in the context of the problem?
c) Write an equation relating speed and time.
d) How long would it take Tim to reach his destination if he travels at a constant speed of 15 miles per hour?
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Name: Date:
52 Chapter 5 Test B
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CHAPTER TEST B
Direct and Inverse Proportion5
Concepts and Skills (Questions 1 to 6: 6 � 1 point � 6 points, Questions 7 and 8: 2 � 2 points � 4 points)
Tell whether each table, graph, or equation represents a direct proportion, an inverse proportion, or neither.
1. x 2 4 8
y 15 712
334
2.
1
0 1
2
2
3
3
4
4
y
x
3. xy � 18 4. y � 2.25x
Find the constant of proportionality for each situation. Then write an equation relating x and y.
5. x is inversely proportional to y, and x � 9 when y � 4.
6. y is directly proportional to x in the table shown below.
x 2 3 5
y 5 712
1212
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Assessments Course 2 53
Solve using proportional reasoning.
7. p is directly proportional to m, and p � 128 when m � 8.
a) Find p when m � 10.
b) Find m when p � 80.
8. x is inversely proportional to y, and x � 18 when y � 4.
a) Write an equation relating x and y.
b) Find x when y � 30.
Problem Solving (5 � 3 points � 15 points)
Use a proportion to solve each question. Show your work.
9. The cost of a piece of ribbon, c, is directly proportional to the length of the ribbon, r. The cost of 8 meters of ribbon is $5.60.
a) Find the cost per meter of the ribbon.
b) Write an equation relating c and r.
c) Find the value of c when r is 9.
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Name: Date:
54 Chapter 5 Test B
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10. The table below shows the relationship between mass in grams and mass in ounces. The mass in grams is directly proportional to the mass in ounces.
Mass (x ounces) 2 4 6
Mass (y grams) 56.7 113.4 170.1
a) Find the constant of proportionality.
b) Write a direct proportion equation.
c) How many grams are in 7 ounces?
11. M varies inversely as N, and M � 60 when N � 2.
a) Find the constant of proportionality.
b) Write an equation relating N and M.
c) Find the value of M when N � 5.
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Assessments Course 2 55
12. The graph below shows the exchange rate between U.S. dollars (USD) and Thailand baht (THB).
Currency Exchange Rates
U.S. Dollars
Thai
land
Bah
t
x
y
70 62 4 531
30
150
180
210
90
60
120
a) What is the exchange rate when you convert U.S. dollars to Thailand baht?
b) Sam wants to exchange 120 Thailand baht for U.S. dollars. Find the amount of U.S. dollars he will receive.
c) Dave wishes to exchange 7 U.S. dollars for Thailand baht. Find the amount of Thailand baht he will receive.
13. The number of students, n, is inversely proportional to the time, t days, required to complete a project. It takes 12 students 20 days to complete a project.
a) Find the constant of proportionality.
b) Write an inverse proportion equation.
c) Find the number of days it would take for 15 students to complete the same project.
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Assessments Course 2 179
5. q � �113
10�11��2
13
6. x �2
�4 �3 �2 �1�5
7. y � 312
6543312
8. p �5
�8 �7 �6 �5 �4
9. 39 in. 10. $611. b � 4112. 51 bags of popcorn13. At least 22 points14. At least 4 computers
Chapter 5 Pre-Test
1. 4 : 5 2. 5 : 8 3. Yes 4. Yes 5. No 6. No 7. Yes; Sample: 14 : 30; 21 : 45 8. No; Sample: 3 : 9; 1 : 3
9. Yes; Sample: 2224
; 3336
10. Yes; Sample: 1018
; 1527
11. 5.7 m/s
12. A: $0.26/fl oz; B: $0.23/fl oz; B is the better buy.
13. A: $1.07 per oz; B: $1.06 per oz; B is the better buy.
14. A(4, 3); B(3, 4); C(1, 2); D(5, 1)
15. 780 girls
16. $21.25
Chapter 5 Test A
1. Direct proportion 2. Neither 3. Inverse proportion
4. Neither
10.
0 1 2 3 414
11.
�7 �6 �5 �4 �3
12.
14 15 16 17 18
13. � 14. �
15. � 16. �
17. x ≤ 50,000 18. x ≥ 45
19. x ≤ 300 20. x � 10
21. x ≥ 18 22. x � 95
23. x � 150 24. x � 500
25. x ≤ 2,000
Chapter 4 Test A
1. x � 4 2. m � 20
3. r � 5 4. a � 2
5. y �12
�4 �3 �2 �1 0�12
6. x � 34
�3 �2 �1 0 1
34
7. y 12
43210 1
2
8. x � 1
43210
9. $0.55 10. 45 people
11. x � 32 12. At least 97
13. At most 33 students
14. x � 30
Chapter 4 Test B
1. m � 3 2. x � 2
3. y � �40 4. p � 6
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180 Answers
5. Direct proportion
6. 5; y � 5x 7. a) y � 756
b) x � 5
8. a) sr � 300 b) s � 2
9. a) , 227
or 3.14
b) 33.4 cm
10. a) 1
15
b) V � 1
15 A
c) 12 L
11. a) 5 b) It represents the number of clay figurines
she paints per day. c) 6 days
12. a) The value of x increases as the value of P decreases, and the product of x and P is a constant value. Hence, the rental rate is inversely proportional to the number of people renting the houseboat.
b) xP � 240 c) $40
13. a) 36 b) It represents the distance traveled. c) st � 36 d) 2.4 h
Chapter 5 Test B
1. Inverse proportion
2. Neither
3. Inverse proportion
4. Direct proportion
5. 36; xy � 36
6. 2.5; y � 2.5x 7. a) p � 160 b) m � 5
8. a) xy � 72 b) x � 2.4
9. a) $0.70 b) c � 0.7r c) c � 6.3
10. a) 28.35 b) y � 28.35x c) 198.45 g
11. a) 120 b) NM � 120 c) M � 24
12. a) 30 Thailand baht per U.S. dollar b) 4 USD c) 210 THB
13. a) 240 b) nt � 240 c) 16 days
Mid-Course Test A
1. B 2. C
3. D 4. B
5. C 6. B
7. B 8. A
9. D 10. A
11. 2,100 mi
12. 0.55p � 12q13. y 6
14. x � 1
15. 11x
16. 3 45
� p
17. 4 � 4 871, � 32.4 � �2325
� �638
18. 12°F
19. a) 3,240 ft b) 194,400 ft
20. $(2.4x � 0.45y � 2.2)
21. 190
22. x � 6
23. a) One floor above ground level b) $270
24. a) 18
34
168 76x x� ( )− �
b) 80 g c) 8 g
25. a) Direct proportion b) 3; The cost of 1 pen is $3.
c) y � 3x d) It means the cost of 4 pens is $12. e) 8 pens
26. a) i) Mount Whitney, California ii) Death Valley, California b) 6,317 ft c) Death Valley, California d) Houston, Texas
27. 13 nickel coins
28. a) (258 � 2.1v) mi b) 132 mi
29. 7
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