Name:
Date:
CHAPTER TEST A
5
Direct and Inverse Proportion
Concepts and Skills
25
Suggested Time:
30 min
(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.
x
7
9
15
y
3.5
4.5
7.5
y
2.
y
3.
4
12
3
9
2
6
1
3
0
1
4. y 4x 3
2
3
4
x
0
5. 2y 1
2
1
x
5
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.
48
x
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1.
Chapter 5 Test A
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Name:
Date:
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.
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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 U 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 U .
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Name:
Date:
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.
y
30
25
20
15
10
5
0
1
2
3
4
5
6
x
Number of Days
50
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?
© Marshall Cavendish International (Singapore) Private Limited.
Number of Clay Figurines
Painting Clay Figurines
Chapter 5 Test A
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Name:
Date:
12. The table shows the daily houseboat rental rate, in P dollars, for x number
of people.
Number of People (x)
Rental Rate (P dollars per person)
1
2
3
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?
© Marshall Cavendish International (Singapore) Private Limited.
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:
CHAPTER TEST B
5
Direct and Inverse Proportion
Concepts and Skills
25
Suggested Time:
30 min
(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
y
15
4
7
1
2
8
3
3
4
y
2.
4
3
2
1
1
2
3
x
4
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.
52
x
2
y
5
3
7
1
2
5
12
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0
1
2
Chapter 5 Test B
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Name:
Date:
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)
© Marshall Cavendish International (Singapore) Private Limited.
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:
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?
54
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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11. M varies inversely as N, and M 60 when N 2.
Chapter 5 Test B
(M)MIFAss_C2_05.indd 54
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Name:
Date:
12. The graph below shows the exchange rate between U.S. dollars (USD) and
Thailand baht (THB).
y
Currency Exchange Rates
210
Thailand Baht
180
150
120
90
60
30
0
1
2
3
4
5
6
7
x
© Marshall Cavendish International (Singapore) Private Limited.
U.S. Dollars
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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10.
5. q 1
1
4
0
1
2
3
1
3
4
11.
2 1
7
6
5
4
3
14
15
16
17
18
1
1
3
0
1
6. x f 2
12.
13.
15.
17.
19.
21.
23.
25.
14.
16.
18.
20.
22.
24.
x ≤ 50,000
x ≤ 300
x ≥ 18
x 150
x ≤ 2,000
x ≥ 45
x 10
x 95
x 500
1. x 4
3. r 5
2. m 20
4. a 2
1
2
4
3
2
1
1
7. y 3
2
3
3
1
2
4
5
6
8. p f 5
8
Chapter 4 Test A
5. y f 5
9.
11.
12.
13.
14.
7
6
5
4
39 in.
10. $6
b 41
51 bags of popcorn
At least 22 points
At least 4 computers
Chapter 5 Pre-Test
4
6. x © Marshall Cavendish International (Singapore) Private Limited.
2
1 2
1
0
1
2
0
3
4
3
7. y v
3
3
41
1
2
0
1
2
1
2
3
4
1
2
3
4
8. x 1
0
9.
11.
13.
14.
$0.55
10. 45 people
x 32
12. At least 97
At most 33 students
x 30
1.
3.
5.
7.
8.
4:5
2.
Yes
4.
No
6.
Yes; Sample: 14 : 30; 21
No; Sample: 3 : 9; 1 : 3
5:8
Yes
No
: 45
22 33
;
24 36
10 15
10. Yes; Sample:
;
18 27
9. Yes; Sample:
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
Chapter 4 Test B
1. m 3
3. y 40
2. x 2
4. p 6
1.
2.
3.
4.
Direct proportion
Neither
Inverse proportion
Neither
Assessments Course 2
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6/15/12 10:15 AM
U,
9. a)
b)
22
or 3.14
7
33.4 cm
1
15
10. a)
V
b)
c)
11. a)
b)
1
A
15
12 L
5
It represents the number of clay figurines
she paints per day.
6 days
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.
xP 240
$40
36
It represents the distance traveled.
st 36
2.4 h
c)
12. a)
b)
c)
13. a)
b)
c)
d)
Chapter 5 Test B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
180
Inverse proportion
Neither
Inverse proportion
Direct proportion
36; xy 36
2.5; y 2.5x
a) p 160
b) m 5
a) xy 72
b) x 2.4
a) $0.70
b) c 0.7r
c) c 6.3
a) 28.35
b) y 28.35x
c) 198.45 g
a) 120
b) NM 120
c) M 24
12. a)
b)
c)
13. a)
b)
c)
30 Thailand baht per U.S. dollar
4 USD
210 THB
240
nt 240
16 days
Mid-Course Test A
1.
3.
5.
7.
9.
11.
12.
13.
14.
15.
B
D
C
B
D
2,100 mi
0.55p 12q
yv6
x1
11x
2.
4.
6.
8.
10.
C
B
B
A
A
4
5
16. 3 p
17. U4 4, 871 32.4 63
23
8
25
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)
1
3
x (168 − x ) 76
8
4
b)
c)
25. a)
b)
c)
d)
e)
26. a)
80 g
8g
Direct proportion
3; The cost of 1 pen is $3.
y 3x
It means the cost of 4 pens is $12.
8 pens
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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5. Direct proportion
6. 5; y 5x
7. a) y 756
b) x 5
8. a) sr 300
b) s 2
Answers
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