Name__________________________________ Period_____
7th Accelerated Chapter 1 Review
Part I-Multiple Choice
____
1. A cereal company determines that 3 out of 5 people who bought cereal bought raisin bran. If 3500 shoppers were
surveyed, how many bought raisin bran?
a.
b.
c.
d.
____
700
1167
2100
5833
2. Which statement is not true for the graph shown?
a. The relationship between time and distance is directly proportional.
b. The point (3, 165) means the car traveled 3 miles in 165 minutes.
c.
The constant of proportionality represents
.
d. The point (0, 0) represents the beginning of the trip.
____
3. The relationship between the number of girls who are in the middle school and high school jazz bands is
proportional. What is the constant of proportionality?
a.
b.
c.
Jazz Band
Number of Girls
Total Members
Middle School
6
15
High School
8
20
d.
____
4. A real estate agent received a $17,500 commission on the sale of a $350,000 house on Walnut Street. The same
agent received a $20,000 commission on the sale of a house on Center Avenue. What was the sale price of the
house on Center Avenue?
a.
b.
c.
d.
____
5. A shoe company took a survey of 150 people and found out that 1 out of 3 people like to wear sneakers. The
company took another survey of 300 people and again found that 1 out of 3 people like to wear sneakers. How did
the number of people who like to wear sneakers change from the first survey to the second survey?
a.
b.
c.
d.
____
$100,000
$370,000
$400,000
$450,000
The number who like to wear sneakers increased by 150.
The number who like to wear sneakers decreased by 150.
The number who like to wear sneakers increased by 50.
The number who like to wear sneakers stayed the same.
6. The graph shows that the amount of water in a person’s body varies directly with the person’s mass. What is the
ratio of the vertical distance to the horizontal distance on the graph between the points (15, 10) and (30, 20)?
a.
b.
c.
d.
____
7. The graph shows the distance a ghost crab can run over time.
Let d equal the distance in meters and t equal the time in seconds. Which is the direct variation equation for this
relationship?
a.
b.
c.
d.
____
8. An engineer filled a tank with water and made a graph of the number of gallons of water in the tank after a given
period of time.
Which rate is equal to the equivalent ratios of points on this graph?
a.
b.
c.
d.
____
9. If you solve using the equation for the constant of proportionality,
, with
value of x?
a.
b.
c.
d.
____ 10. If u varies directly with v, with k  0.6, what is the value of u when v  7.8?
a.
b.
c.
d.
u  13
u  0.77
u  0.468
u  4.68
____ 11. Which of the following graphs shows a direct variation?
a.
c.
b.
d.
and
, what is the
____ 12. The weight of a person on Venus varies directly with his or her weight on Earth. A person weighing 120 pounds
on Earth weighs 106 pounds on Venus. How much would a person weighing 180 pounds on Earth weigh on
Venus?
a.
b.
c.
d.
120 pounds
159 pounds
176 pounds
226 pounds
____ 13. A painter mixes cans of green and white paint to make the shade needed for painting a bedroom. The table shows
the proportions he can use for the color he wants.
Which is the direct variation equation for this relationship?
Green Cans
6
10
16
18
White Cans
9
15
24
27
a.
b.
c.
d.
____ 14. If two quantities vary directly, which must be true of a graph showing the relationship between them?
a.
b.
c.
d.
The graph is a curve.
The graph increases from left to right.
The points on the graph are connected.
The points of the graph form a straight line, and the line must pass through the origin.
____ 15. Tanya polled boys and girls in her grade to determine how many prefer math to other subjects. Her results are
shown in the table.
Students
Prefer Math
Total Students
Boys
14
30
Girls
16
32
Which is a true statement?
a. The relationship is proportional because 16  4  2 and 32  30  2.
b. The relationship is proportional because 30  14  16 and 32  16  16.
c.
The relationship is not proportional because
.
d.
The relationship is not proportional because
.
____ 16. In the graph, the amount of sales tax is directly proportional to the price of an item.
Which equation represents this relationship?
a.
b.
c.
d.
t  0.05 p
t  0.06 p
t  0.96 p
t  1.6 p
____ 17. Which graph displays equivalent ratios?
a.
c.
b.
d.
____ 18. The amount of chlorine needed to treat a swimming pool is directly proportional to the volume of the pool.
Chlorine (c)
Volume of Pool (p)
5
2500
10
5000
15
7500
What is the constant of proportionality for this relationship?
a. 0.002
b. 0.02
c. 0.2
d.
____ 19. The number of campers who sign up for archery each week is listed in the table. If the relationship is proportional,
how many campers will sign up for archery in Week 3?
a.
b.
c.
d.
Week
Archery Sign-Up
Total Campers
1
36
120
2
45
150
3
?
130
54
40
41
39
____ 20. Determine the constant of proportionality for the graph.
a.
b. 2
c. 5
d. 10
Part II-Write the correct answer.
21. Determine if the graph shows two quantities that vary directly.
If possible, determine the constant of proportionality.__________
Explain your reasoning.
______________________________________________________
______________________________________________________
______________________________________________________
_
__________________________________________________
22. A recent survey of middle school students found that 1 out of 12 students like spinach, 1 out of 9 students like
green beans, and 1 out of 4 students like carrots.
a.
Complete the table using the information in the survey.
Total
Number of
Students
36
72
108
144
180
Spinach
Green Beans
Carrots
b.
As the total number of students increased by 36, how did the number of students who like spinach
increase?________________________
c.
As the total number of students increased by 36, how did the number of students who like green beans
increase?________________________
d.
As the total number of students increased by 36, how did the number of students who like carrots
increase?________________________
e.
How does the increase in total students as a multiple of 36 make the calculations more straightforward?
Why 36?________________________
A recent survey determined that 5 out of 7 teens own portable music devices.
23. If 3500 teens were surveyed, how many owned portable music devices?________________
24. Analyze the tables shown. Determine whether each relationship is proportional. Explain your reasoning.
a.
The table shows the number of 6th graders who play soccer in the district.
6th
Soccer Total 6th
Graders Players Graders
Girls
204
340
Boys
186
310
_________________________________________________________
_________________________________________________________
_
The table shows the number of each kind of boat rented during two months from Sam’s Rentals.
b.
Month
Kayak
Sailboat
July
875
350
_________________________________________________________
August
972
405
_________________________________________________________
25. The cost (c) to hire a dog trainer is directly proportional to the amount of time (h) in hours spent training the dog.
a.
Write an equation representing the proportional relationship between c and h using the information
given with k as the constant of propotionality.
______________________________________
b.
Sue spent $660 on 12 hours of obedience training for her dog Muffin. Jon wants to use the same dog
trainer for his dog Tex, but he only has $440 to spend.
How many hours of training can he get for Tex?_________________
Explain your reasoning.
___________________________________________________________________________________
____________________________________________________________________________________
7th Accelerated
Answer Section
Review
Mrs. Willis
1. ANS: C
PTS: 1
REF: 2.3
NAT: 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
KEY: constant of proportionality
2. ANS: B
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
3. ANS: B
PTS: 1
REF: 2.3
NAT: 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
KEY: constant of proportionality
4. ANS: C
PTS: 1
REF: 2.4
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.3
TOP: Standardized Test
5. ANS: C
PTS: 1
REF: 2.1
NAT: 7.RP.1 | 7.RP.2.a | 7.RP.2.d
TOP: Standardized Test
KEY: direct variation (direct proportional) | origin
6. ANS: A
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
7. ANS: B
PTS: 1
REF: 2.5
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.2.d
TOP: Standardized Test
8. ANS: C
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
9. ANS: C
PTS: 1
REF: 2.6
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
10. ANS: D
PTS: 1
REF: 2.6
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
11. ANS: D
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
12. ANS: B
PTS: 1
REF: 2.6
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
13. ANS: A
PTS: 1
REF: 2.7
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.2.d
TOP: Standardized Test
14. ANS: D
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
15. ANS: D
PTS: 1
REF: 2.4
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.3
TOP: Standardized Test
16. ANS: B
PTS: 1
REF: 2.5
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.2.d
TOP: Standardized Test
17. ANS: A
PTS: 1
REF: 2.2
NAT: 7.RP.2.a
TOP: Standardized Test
18. ANS: A
PTS: 1
REF: 2.3
NAT: 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
KEY: constant of proportionality
19. ANS: D
PTS: 1
REF: 2.3
NAT: 7.RP.2.b | 7.RP.2.c
TOP: Standardized Test
KEY: constant of proportionality
20. ANS: A
PTS: 1
REF: 2.5
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.2.d
TOP: Standardized Test
21. ANS:
The graph does not show a direct variation because it does not go through the point (0, 0).
PTS: 1
TOP: Post Test
REF: 2.4
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c | 7.RP.3
22. ANS:
a.
Total Number of
Students
Spinach
Green Beans
Carrots
36
3
4
9
72
6
8
18
108
9
12
27
144
12
16
36
180
15
20
45
b.
The number who like spinach increased by 3.
c.
The number who like green beans increased by 4.
d.
The number who like green beans increased by 9.
e.
Using 36 makes all the answers whole number answers because 36 is the least common multiple of 3,
4, and 9.
PTS: 1
TOP: End Ch Test
23. ANS:
REF: 2.1
NAT: 7.RP.1 | 7.RP.2.a | 7.RP.2.d
KEY: direct variation (direct proportional) | origin
Of the 3500 teens surveyed, 2500 owned portable music devices.
PTS: 1
TOP: End Ch Test
24. ANS:
a.
REF: 2.3
NAT: 7.RP.2.b | 7.RP.2.c
KEY: constant of proportionality
Yes. The relationship is proportional because
proportionality,
.
and
. There is a constant of
b.
No. The relationship is not proportional because
is not equal to
. I used the means and
extremes method and discovered that 350  972 is not equal to 875  405. Therefore, there is no
constant of proportionality.
PTS: 1
25. ANS:
a.
c  kh
REF: 2.2
NAT: 7.RP.2.a
TOP: End Ch Test
b.
Therefore, the constant of proportionality is 55.
Jon can get 8 hours of training for his dog Tex.
To determine the number of hours of training that Jon could get for Tex, I first had to calculate the
constant of proportionality. I determined the constant of proportionality by using the ratio of the cost
of Muffin’s training to the number of hours of training she received, which is
. Then, I set up an
equation to show the direct proportional relationship to determine the number of hours of training Jon
could get for Tex with $440.
PTS: 1
TOP: End Ch Test
REF: 2.6
NAT: 7.RP.2.a | 7.RP.2.b | 7.RP.2.c