Download 1. Give two ways to write the algebraic expression p ÷ 10 in words. a

Math Olympics
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Give two ways to write the algebraic
7. Evaluate
the expression a ÷ b for a =
24 and b = 8.
a. 192
b. 16
c. 3
d. 4
expression p ÷ 10 in words.
a. the product of p and 10
p times 10
b. p subtracted from 10
p less than 10
c. the quotient of 10 and p
10 divided by p
d. the quotient of p and 10
p divided by 10
2.
3.
Julia wrote 14 letters to friends each
month for y months in a row. Write
an expression to show how many
total letters Julia wrote.
Mike scored 40 points in the first half
of the basketball game, and he
scored y points in the second half of
the game. Write an expression to
determine the number of points he
scored in all Then, find the number
of points he scored in all if he scored
2 points in the second half of the
game.
a. 40y; 42 points
b. 40 – y; 38
points c. ; 38 points d. 40 + y;
a. 14
42 points
–y
c. 14
+y
d.
Salvador’s class has collected 88
cans in a food drive. They plan to
sort the cans into x bags, with an
equal number of cans in each bag.
Write an expression to show how
many cans there will be in each bag.
a. 88x
4.
b. 14y
8.
b. 88
+x
c.
d. 88
9.
–x
Evaluate the expression m + o for m
= 9 and o = 7.
a. 15
b. 16
c. 2
d. 63
5.
Evaluate the expression q – v for q =
5 and v = 1.
a. 3
b. 4
c. 5
d. 6
6.
Evaluate the expression xy for x = 6
and y = 3.
a. 21
b. 24
c. 9
d. 18
Aaron has saved 72 sand dollars
and wants to give them away equally
to y friends. Write an expression to
show how many sand dollars each
of Aaron’s friends will receive. Then,
find the total number of sand dollars
each of Aaron’s friends will get if
Aaron gives them to 12 friends.
a. 72 – y; 60 sand dollars
b. 72 + y;
60 sand dollars c. ; 6 sand
dollars
10.
d. 72y;
6 sand dollars
Salvador reads 12 books from the
library each month for n months in a
row. Write an expression to show
how many books Salvador read in
all. Then, find the number of books
Salvador read if he read for 7
months.
a. 12
– n; 19 books
c. 12 + n; 19 books
books
12.
11.
; 84 books
d. 12n; 84
b.
Evaluate the expression
and
.
a. 23
b. 25
c. 32
d. 18
for
Subtract using a number line.
–5 – (–3)
– (–3)
–5
–8
–7
a. –3
13.
–6
–5
–4
b. 2
–3
–2
–1
c. –5
0
1
2
3
4
5
6
7
d. –2
Add.
34 + (–21)
a. 55
b. 13
a. –34ºF
d. –42ºF
c. –55
d. –13
14.
Evaluate x + (–9) for x = 35.
a. –44
b. –26
c. 26
d. 44
15.
Subtract.
–5 – (–8)
b. 13
a. –13
c. 3
Evaluate x – (–10) for x = 12.
a. –22
b. 2
c. 22
d. –2
17.
The highest temperature recorded in
the town of Westgate this summer
was 101ºF. Last winter, the lowest
temperature recorded was –9ºF.
Find the difference between these
extremes.
a. 92ºF
b. –92ºF
c. 110ºF
d. –110ºF
The temperature on the ground
during a plane’s takeoff was 4ºF. At
38,000 feet in the air, the
temperature outside the plane was
–38ºF. Find the difference between
these two temperatures.
b. 42ºF
c. 34ºF
19.
The elevator in the a downtown
skyscraper goes from the top floor
down to the lowest level of the
underground parking garage. If the
building is 470 feet tall and the
elevator descends 530 feet from top
to bottom, how far underground
does the parking garage go?
a. 990 feet
b. 60 feet
c. 1,000 feet
d. 50 feet
20.
Multiply.
–8 • 9
b. –72
a. 1
d. –3
16.
18.
8
c. –17
d. 72
21.
Evaluate –5u for u = –4.
a. –9
b. 25
c. –20
d. 20
22.
Divide.
–48 8
a. –384
b. 6
c. –56
d. –6
23.
Evaluate k (–11) for k = –33.
a. 363
b. 3
c. –22
d. –3
24.
Divide.
32.
8
a. 6 21
25.
26.
27.
5
a.
3
8
c. 8 21
b. 4 7
d. 6 14
33.
Divide.
0 ÷ 5.928
a. –5.928
d. 0
b. 5.928
Write 9 as a power of the base 3.
c. undefined
Carina hiked at Yosemite National
Park for 1.75 hours. Her average
speed was 3.5 mi/h. How many
miles did she hike?
a. 2 mi
b. 20 mi
c. 61.25 mi
d. 6.125 mi
b.
c.
d.
Suppose you have developed a
scale that indicates the brightness of
sunlight. Each category in the table
is 6 times brighter than the next
lower category. For example, a day
that is dazzling is 6 times brighter
than a day that is radiant. How many
times brighter is a dazzling day than
an illuminated day?
Sunlight Intensity
Category
Brightness
Dim
2
Illuminated
3
Radiant
4
Dazzling
5
Write the power represented by the
geometric model.
a. 36
times brighter b. 2 times
brighter c. 6 times brighter d. 216
times brighter
34.
5
a. 3
28.
29.
30.
31.
2
b. 5
3
Simplify
.
a. 27
b. 93
d. –12
c. –8
d. –16
.
Simplify
.
5
36
d. 12
c. 1
Simplify
a. –2
b. 16
b.
d. 2
c. 729
Simplify
.
a. –81
b. 81
a.
5
c. 5
c.
25
6
d.
25
36
If the population of an ant hill
doubles every 10 days and there are
currently 40 ants living in the ant hill,
what will the ant hill population be in
20 days?
a. 320 ants
b. 160 ants
c. 1,600
ants d. 80 ants
35.
To cover the path, 7 bags of gravel
are needed. b. The total area is
144 sq ft. The area of the vegetable
garden is 110.25 sq ft, and the area
of the path is 33.75 sq ft. To cover
the path, 4 bags of gravel are
needed. c. The total area is 144 sq
ft. The area of the vegetable garden
is 81 sq ft, and the area of the path
is 63 sq ft. To cover the path, 7 bags
of gravel are needed. d. The total
area is 144 sq ft. The area of the
vegetable garden is 72 sq ft, and the
area of the path is 72 sq ft. To cover
the path, 8 bags of gravel are
needed.
The design shows the layout of a
vegetable garden and the
surrounding path. The path is 1.5
feet wide. First, find the total area of
the vegetable garden and path.
Then, find the area of the vegetable
garden and the area of the path. If
one bag of gravel covers 10 square
feet, how many bags of gravel are
needed to cover the path?
12 ft
36.
Find the square root.
a. 14
12 ft
a. The
38.
39.
37.
b. 98
c. 38416
d. –14
The area of a square garden is 202
square feet. Estimate the side length
of the garden.
a. 16 ft
b. 12 ft
c. 17 ft
d. 14 ft
total area is 81 sq ft. The area
of the vegetable garden is 144 sq ft,
and the area of the path is 63 sq ft.
Write all classifications that apply to the real number .
a. rational number, terminating decimal
b. rational number, repeating decimal
c. irrational number
d. rational number
Write all classifications that apply to the real number
.
a. irrational number, integer b. irrational number c. rational number, terminating decimal, integer,
whole number, natural number d. rational number, terminating decimal
40.
A set of numbers is said to be closed
under a certain operation if, when
you perform the operation on any
two numbers in the set, the result is
also a number in the set. Is the set
of irrational numbers closed under
addition? Explain.
closed under addition. For example,
the sum of
and
is not an
irrational number. d. No, the set of
irrational numbers is not closed
under addition. The result of adding
any two irrational numbers is an
irrational number.
a. Yes,
42.
43.
45.
the set of irrational numbers
is closed under addition. For
example, the sum of 0.121221222..
and 0.131331333.. is 0.252552555...
which is an irrational number.
b. Yes, the set of irrational numbers
is closed under addition. The result
of adding any two irrational numbers
is an irrational number. c. No, the
set of irrational numbers is not
Simplify
.
a. 21
b. 75
c. 39
d. 93
Evaluate
for x = 9.
a. –68
b. 58
c. –5
d. 72
Simplify the expression
a. 14
46.
b. 23
c. 4
Simplify
a. –1
b. 2
44.
Evaluate 1 + x2 • 6 for x = 4.
a. 102
b. 97
c. 94
d. 150
48.
Use the numbers 2, 3, 5, and 8 to
write an expression that has a value
of
. You may use any operations,
and you must use each of the
numbers at least once.
d. 22
b.
d.
a.
47.
c. 22
.
d. 14
.
Translate the word phrase, the
product of 8.5 and the difference of
–4 and –8, into a numerical
expression.
a.
c.
41.
Tatia has coins in pennies, nickels,
dimes, and quarters. The total
amount of money she has in dollars
can be found using the expression
(P + 5N + 10D + 25Q) ÷ 100. Use
the table to find how much money
Tatia has.
P
20
a. $140.50
d. $1.90
N
16
D
4
b. $33.30
Q
2
b.
c.
d.
49.
Simplify the expression
.
5
a. 10 9
b. 10
5
c. 9 9
d. 9
50.
Write 11 • 59 using the Distributive
Property. Then simplify.
a. 11 • 50 + 11 • 9; 649
b. (11 +
50)(11 + 9); 1,220 c. 11 • 59 + 11 •
9; 748 d. 11 • 5 + 11 • 9; 154
51.
Write
using the Distributive
Property. Then simplify.
c. $0.42
a.
b.
60
52.
53.
d.
; 130
; 114 c.
; 168
;
b.
a.
c.
d.
Simplify by combining like terms.
The table shows, step-by-step, how to simplify the algebraic expression
. Justify Step 4.
Step
1.
2.
3.
4.
5.
6.
a. Multiply
Procedure
Justification
Distributive Property
b. Associative
Property
c. Combine
like terms
d. Commutative
Property
54.
Fill in the missing justifications.
Procedure
Justification
Definition of subtraction
?
?
?
Simplify
Definition of subtraction
a. Distributive Property; Associative Property; Commutative
b. Associative Property; Commutative Property; Distributive
c. Commutative Property; Distributive Property; Associative
d. Commutative Property; Associative Property; Distributive
55.
Graph the point (1, 4).
Property
Property
Property
Property
a.
56.
y
5
Name the quadrant where the point
(–3, 2) is located.
y
5
5 x
–5
–5
–5
b.
5
x
y
5
–5
a. Quadrant
c. Quadrant
5 x
–5
57.
–5
c.
III
IV
b. Quadrant I
d. Quadrant II
Name the quadrant where the point
(3, 0) is located.
y
y
5
5
5 x
–5
–5
5
x
–5
d.
y
–5
5
b. No quadrant
a. Quadrant III
(y-axis) c. No quadrant (x-axis)
d. Quadrant I
5 x
–5
–5
58.
59.
A phone company advertises a new
plan in which the customer pays a
fixed amount of $25 per month for
unlimited calls in the country, and
$0.10 per minute for international
calls. Find a rule for the monthly
payment a customer pays according
to the new plan. Write ordered pairs
for the monthly payment when the
customer uses 90, 120, 145, and
150 international minutes in a
month.
a.
; (34, 90), (37, 120),
(39.5, 145), (40, 150)
b.
; (90, 34), (120, 37),
(145, 39.5), (150, 40)
c.
; (34, 90), (37, 120),
(145, 39.5), (150, 40)
d.
; (34, 90), (37, 120),
(145, 39.5), (150, 40)
The points form an S shape.
b.
Create a table of ordered pairs for
the function
using the
values x = –2, –1, 0, 1, and 2. Graph
the ordered pairs and describe the
shape of the graph.
a.
The points form a straight line.
c.
The points form a U shape.
60.
The coordinates of three vertices of
,
,
a rectangle are
and
. Find the coordinates of
the fourth vertex. Then, find the area
of the rectangle.
a.
; Area = 80 square units
b.
; Area = 72 square units
c.
; Area = 80 square units
d.
; Area = 72 square units
61.
Give two ways to write the algebraic
expression 6p in words.
a. the quotient of 6 and p
6 divided by p
b. p subtracted from 6
p less than 6
c. 6 times p
6 groups of p
d. p more than 6
p added to 6
The points form a V shape.
d.
62.
Add using a number line.
3+3
3
3
–8
–7
a. 0
63.
64.
–6
–5
b. 6
Solve
a. p = 22
d. p = –10
Solve
–4
–3
–2
c. –6
–1
0
1
2
3
4
5
6
7
8
d. 3
.
b. p = –22
a. s
c. p
= 52
= 54
= 10
65.
.
b. s
= 42
Solve –14 + s = 32.
c. s
= 43
d. s
a. s
66.
= 46 b. s = 18 c. s = –46 d. s
= –18
A toy company's total payment for salaries for the first two months of 2005 is
$21,894. Write and solve an equation to find the salaries for the second month if
the first month’s salaries are $10,205.
a.
The salaries for the second month are $11,689.
b.
The salaries for the second month are $21,894.
c.
The salaries for the second month are $10,947.
d.
67.
The salaries for the second month are $32,099.
The range of a set of scores is 23,
71. The time between a flash of lightning
and the lowest score is 33. Write
and the sound of its thunder can be
and solve an equation to find the
used to estimate the distance from a
highest score. (Hint: In a data set,
lightning strike. The distance from
the range is the difference between
the strike is the number of seconds
the highest and the lowest values.)
between seeing the flash and
a.
hearing the thunder divided by 5.
Suppose you are 17 miles from a
The highest score is 10.
b.
lightning strike. Write and solve an
equation to find how many seconds
The highest score is 56.
c.
there would be between the flash
and thunder.
The highest score is –10.
d.
The highest score is 79.
68.
Solve
a. q
= 46
1
d. q = 8 5
69.
70.
.
b. q
= 205
Solve
d.
, so t is about 85 seconds.
b.
, so t is about 3.4 seconds.
72.
c. n
= 45
If
a. 3
d. n
73.
.
b.
, so t is about 22 seconds.
c.
= 36
d.
Solve 3n = 42.
a. n = 39
b. n = 15
= 14
a.
c. q
a.
, so t is about 0.3 seconds.
, find the value of
b. –5
c. 5
d. –3
Solve
a. a = –29
d. a = –15
.
b. a = 29
c.
74.
Solve
.
c. a
= 15
.
a.
d.
75.
80.
81.
82.
83.
c.
Solve
a.
d.
76.
b.
.
b.
If 8y – 8 = 24, find the value of 2y.
a. 8
b. 11
c. 2
d. 24
78.
The formula
gives the
profit p when a number of items n
are each sold at a cost c and
expenses e are subtracted. If
,
, and
,
what is the value of c?
a. 0.80
b. 1.55
c. 1.25
d. 0.95
79.
Solve
c.
Sara needs to take a taxi to get to
the movies. The taxi charges $4.00
for the first mile, and then $2.75 for
each mile after that. If the total
charge is $20.50, then how far was
Sara’s taxi ride to the movie?
a. 6 miles
b. 7 miles
c. 5.1 miles
d. 7.5 miles
Solve
1
a. n = 1 2
77.
.
a.
d.
b.
c.
.
b. n
= −4
1
2
c. n
= 3 12
d. n
= −1 16
Solve
. Tell whether the equation has infinitely many
solutions or no solutions.
a. Two solutions
b. No solutions
c. Infinitely many solutions
d. Only one
solution
A video store charges a monthly
84. A professional cyclist is training for
membership fee of $7.50, but the
the Tour de France. What was his
charge to rent each movie is only
average speed in kilometers per
$1.00 per movie. Another store has
hour if he rode the 194 kilometers
no membership fee, but it costs
from Laval to Blois in 4.7 hours? Use
$2.50 to rent each movie. How many
the formula
, and round your
movies need to be rented each
answer to the nearest tenth.
month for the total fees to be the
a. 189.3 kph
b. 911.8 kph
c. 115.3
same from either company?
kph d. 41.3 kph
a. 3 movies
b. 5 movies
c. 7
85. The formula for the resistance of a
movies d. 9 movies
conductor with voltage V and current
Find three consecutive integers such
that twice the greatest integer is 2
less than 3 times the least integer.
a. 2, 3, 4
b. 4, 5, 6
c. 6, 7, 8
d. 8,
9, 10
I is
a. I
. Solve for V.
= Vr
b.
c. V
d.
86.
Solve
for x.
= Ir
a.
b.
c.
87.
Solve
94.
95.
Solve the proportion
b.
d.
The fuel for a chain saw is a mix of
oil and gasoline. The ratio of ounces
of oil to gallons of gasoline is 7:19.
There are 38 gallons of gasoline.
How many ounces of oil are there?
a. 103.1 ounces
b. 20 ounces
c. 14 ounces
d. 3.5 ounces
Ramon drives his car 150 miles in 3
hours. Find the unit rate.
a. Ramon drives 50 miles per hour.
b. Ramon drives 1 mile per 50 hours.
c. Ramon drives 30 miles per hour.
d. Ramon drives 150 miles per 3
hours.
Find the value of MN if
ABCD LMNO
a. 22.4
91.
for y.
c.
89.
The local school sponsored a
mini-marathon and supplied 84
gallons of water per hour for the
runners. What is the amount of
water in quarts per hour?
a. 672 qt/h
b. 336 qt/h
c. 168 qt/h
d. 21 qt/h
d.
a.
88.
90.
cm
b. 12.6
cm
a. x =
d. x =
cm
b. x
= 26
c. x
= 0.03
92.
An architect built a scale model of a
shopping mall. On the model, a
circular fountain is 20 inches tall and
22.5 inches in diameter. If the actual
fountain is to be 8 feet tall, what is its
diameter?
a. 7 ft
b. 7.1 ft
c. 9 ft
d. 10.5 ft
93.
Complementary angles are two
angles whose measures add to 90°.
The ratio of the measures of two
complementary angles is 4:11. What
are the measures of the angles?
a. 51.4°, 38.6°
b. 26°, 64°
c. 24°,
66° d. 24°, 114°
cm, and
cm.
cm,
c. 22.8
36
25
.
d. 23.8
cm
On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The
shadow of a nearby eucalyptus tree is 35 feet long. Write and solve a proportion
to find the height of the tree.
; 25 feet
a.
; 49 feet
b.
; 245 feet
c.
; 175 feet
d.
96.
A right triangle has legs 15 inches
and 12 inches. Every dimension is
multiplied by to form a new right
triangle with legs 5 inches and 4
inches. How is the ratio of the areas
related to the ratio of corresponding
sides?
a. The ratio of the areas is the square
of the ratio of the corresponding
sides. b. The ratio of the areas is
equal to the ratio of the
corresponding sides. c. The ratio of
the areas is the cube of the ratio of
the corresponding sides. d. None
of the above
97.
Triangles C and D are similar. The
. The
area of triangle C is 47.6
base of triangle D is 6.72 in. Each
dimension of D is the
corresponding dimension of C. What
is the height of D ?
a. 20.4 in
b. 17 in
c. 5.6 in
d. 57.12 in
98.
Find 55% of 125.
a. 227.27
b. 68.75
d. 6875
c. 70.25
99.
What percent of 74 is 481? If
necessary, round your answer to the
nearest tenth of a percent.
a. 6.5%
b. 650%
c. 550%
d. 15.38%
100.
66 is 56% of what number? If
necessary, round your answer to the
nearest hundredth.
a. 0.85
b. 117.86
c. 1.18
d. 36.96
101.
A compound is made up of various
elements totaling 80 ounces. If the
total amount of lead in the
compound weighs 15 ounces, what
percent of the compound is made up
of lead? If necessary, round your
answer to the nearest hundredth of a
percent.
a. 81.25%
b. 18.75%
c. 5.33%
d. 0.19%
102.
103.
104.
105.
According to the United States
Census Bureau, the United States
population was projected to be
293,655,404 people on July 1, 2004.
The two most populous states were
California, with a population of
35,893,799, and Texas, with a
population of 22,490,022. About
what percent of the United States
population lived in California or
Texas? Round your answer to the
nearest percent.
a. 8%
b. 12%
c. 20%
d. 37%
Aaron works part time as a
salesperson for an electronics store.
He earns $6.75 per hour plus a
percent commission on all of his
sales. Last week Aaron worked 17
hours and earned a gross income of
$290.63. Find Aaron’s percent
commission if his total sales for the
week were $3,350. If necessary,
round your answer to the nearest
hundredth of a percent.
a. 1.03%
b. 0.05%
c. 5.25%
d. 6%
After 6 months the simple interest
earned annually on an investment of
$8000 was $975. Find the interest
rate to the nearest tenth of a
percent.
a. 0.2 %
b. 22.4%
c. 0.244%
d. 24.4%
Hidemi is a waiter. He waits on a
table of 4 whose bill comes to
$69.98. If Hidemi receives a 20% tip,
approximately how much will he
receive?
a. $14.00
d. $3.50
b. $84.00
c. $13.55
106.
Hannah had dinner at her favorite
restaurant. If the sales tax rate is 4%
and the sales tax on the meal came
to $1.25, what was the total cost of
the meal, including sales tax and a
20% tip?
a. $52.50
b. $45.63
c. $31.25
d. $38.75
107.
Find the percent change from 52 to
390. Tell whether it is a percent
increase or decrease. If necessary,
round your answer to the nearest
percent.
a. 650% decrease
b. 87% decrease
c. 650% increase
d. 87% increase
108.
Find the result when 28 is decreased
by 25%.
a. 21
b. 35
c. 7
d. 3
109.
The price of a train ticket from
Atlanta to Oklahoma City is normally
$117.00. However, children under
the age of 16 receive a 70%
discount. Find the sale price for
someone under the age of 16.
a. $35.10
b. $198.90
c. $81.90
d. $49.14
110.
A bookstore buys Algebra 1 books at
a wholesale price of $16 each. It
then marks up the price by 83%, and
sells the Algebra 1 books. What is
the amount of the markup? What is
the selling price?
a. The
amount of the markup is
$29.28, and the selling price is
$13.28. b. The amount of the
markup is $13.28, and the selling
price is $29.28. c. The amount of
the markup is $13.28, and the selling
price is $2.72. d. The amount of
the markup is $83, and the selling
price is $99.00.
111.
Mr. Chang sells holiday greeting
cards in his gift shop. Before the
holidays, he sells the cards at a
225% markup on the price he paid
his supplier. After the holidays, he
discounts the cards 60%. What is
the post-holiday price of two cards
he originally bought from his supplier
for $1.50 and $2.00, respectively?
a. $2.03;
c. $2.93;
112.
113.
Solve
a. x = 1
$2.70
$3.9
b. $1.35; $1.80
d. $1.95; $2.60
Solve
.
a. x = 0 or x = –14
d. x = 7 or x = –21
b. x
=7
c. x
=0
.
b. x
=
11
6
c. No
solution
d. x
114. Describe the solutions of
in words.
a. The value of y is a number less than or equal to 3.
b. The value of y is a number greater than 4.
c. The value of y is a number equal to 3 d. The
value of y is a number less than 4.
=
8
3
a.
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
–5
–4
–3
–2
–1
0
1
2
3
4
5
b.
115. Graph the inequality m < –3.4.
c.
d.
116. Write the inequality shown by the graph.
–7
–6
a. m ≤ –3
–5
–4
–3
–2
b. m > –3
–1
0
1
2
c. m ≥ –3
3
4
5
6
7
m
d. m < –3
117. To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent
the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will
result in a swimmer making the team. Graph the solution.
a.
0
100 200 300 400 500 600 700 800 900 1000
n
b.
0
100 200 300 400 500 600 700 800 900 1000
n
0
100 200 300 400 500 600 700 800 900 1000
n
0
100 200 300 400 500 600 700 800 900 1000
n
c.
d.
118. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can
spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then,
graph the inequality.
a.
;
s
–500
–400
b.
–300
–200
–100
0
100
200
300
400
500
300
400
500
300
400
500
300
400
500
;
s
–500
–400
c.
–300
–200
–100
0
100
200
;
s
–500
–400
d.
–300
–200
–100
0
100
200
;
s
–500
–400
–300
–200
–100
0
100
119. Solve the inequality n + 6 < –1.5 and graph the
solutions.
a. n < 4.5
–10 –8
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
b. n < –7.5
–10 –8
c. n < –7.5
–10 –8
120. Carlotta subscribes to the HotBurn music service.
She can download no more than 11 song files per
week. Carlotta has already downloaded 8 song files
this week. Write, solve, and graph an inequality to
show how many more songs Carlotta can
download.
a. s > 3
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
b. s ≥ 3
–6
–4
–2
0
2
4
6
8
10
d. n < 4.5
–10 –8
200
0
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
c. s ≤ 3
–6
–4
–2
0
2
4
6
8
10
0
d. s < 3
0
1
2
3
4
5
6
7
8
9
10
11
–9
b.
121. Denise has $365 in her saving account. She wants
to save at least $635. Write and solve an inequality
to determine how much more money Denise must
save to reach her goal. Let d represent the amount
of money in dollars Denise must save to reach her
goal.
a.
;
b.
;
c.
;
d.
;
5
–9
c.
5
8
–3
0
3
6
9
12
15
18
21
–6
–3
0
3
6
9
12
15
18
21
–6
–3
0
3
6
9
12
15
18
21
–6
–3
0
3
6
9
12
15
18
21
2
5
–9
d.
–6
2
5
1
5
122. Solve the inequality and graph the solution.
–9
a.
1
85
> 3 and graph the solutions.
123. Solve the inequality
a. x > 24
0
5
10
15
20
25
30
35
40
45
50
5
10
15
20
25
30
35
40
45
50
45
50
b. x > 24
0
c. x >
3
8
0
1
2
3
4
5
6
7
8
9
10
11
12
d. x > 24
0
5
10
15
20
25
30
35
40
124. Solve the inequality 2m ≤ 18 and graph the solutions.
a. m ≤ 9
–1
0
1
2
3
4
5
6
7
8
9
10
11
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
b. m ≤ 36
0
c. m ≤ 36
0
d. m ≤ 9
–1
0
1
2
3
4
5
6
7
8
9
≤ 2 and graph the
125. Solve the inequality
solutions.
a. z ≤ –8
10
11
129. Solve the inequality − n – 4 < 3 and graph the
solutions.
a. n < –7
–10 –8
–10 –8
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
b. z ≥ 8
c. z ≤ 8
d. z ≥ –8
126. Solve the inequality 2f ≥ –8 and graph the
solutions.
a. f ≥ –4
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
b. f ≤ –4
c. f ≤ 4
d. f ≥ 4
127. Marco’s Drama class is performing a play. He
wants to buy as many tickets as he can afford. If
tickets cost $2.50 each and he has $14.75 to spend,
how many tickets can he buy?
a. 0 tickets b. 5 tickets c. 6 tickets d. 4
tickets
128. What is the greatest possible integer solution of the
inequality
?
a. 5.33 b. 4 c. 6 d. 5
132. Solve and graph
.
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
d. z ≥ 1
–10 –8
–10 –8
6
c. z ≤ –3
–10 –8
–10 –8
4
b. z ≤ 1
–10 –8
–10 –8
2
130. Solve the inequality z + 8 + 3z ≤ –4 and graph the
solutions.
a. z ≥ –3
–10 –8
–10 –8
0
d. n < 1
–10 –8
–10 –8
–2
c. n > 1
–10 –8
–10 –8
–4
b. n > –7
–10 –8
–10 –8
–6
131. A family travels to Bryce Canyon for three days.
On the first day, they drove 150 miles. On the
second day, they drove 190 miles. What is the least
number of miles they drove on the third day if their
average number of miles per day was at least 180?
a. 540 mi b. 180 mi c. 201 mi d. 200 mi
a. x > 5
–13 –12 –11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
b. x < 5
–13 –12 –11 –10 –9
c. x > 3
–13 –12 –11 –10 –9
d. x < –5
–13 –12 –11 –10 –9
133. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per
student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science
Center charge less than the Dino Discovery Museum?
a. 132 or more students b. 132 or fewer students c. More than 45 students d. Fewer than 45 students
134.
Solve the inequality and graph the solution.
a.
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
b.
c.
d.
135. Solve the inequality
7
9
a. z ≤ −2 16 b. z ≤ 3 16
d. no solutions
136. Solve
a.
.
c. all real numbers
b.
.
d.
c.
137. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are
at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on
a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions.
a.
–250
b.
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
–250
–200
–150
–100
–50
0
50
100
150
200
250
c.
d.
138. Solve and graph the solutions of the compound inequality
a.
AND
0
b.
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
.
AND
0
c.
AND
0
d.
AND
0
139. Solve and graph the compound inequality.
OR
a.
OR
–10 –9
b.
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
s
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
s
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
s
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
s
OR
–10 –9
c.
–8
OR
–10 –9
d.
–8
OR
–10 –9
–8
140. Write the compound inequality shown by the graph.
–10 –9
a.
–8
–7
–6
AND
–5
–4
–3
b.
–2
–1
0
1
AND
141. Which of the following is a solution of
a. 2 b. 14 c. 12 d. –6
2
3
4
5
6
c.
AND
7
8
9
10
OR
x
d.
?
OR
142. Solve the inequality
a.
and graph the solutions. Then write the solutions as a compound inequality.
–27 –24 –21 –18 –15 –12 –9
–6
–3
0
3
6
9
12
15
18
21
24
27
30
–30 –27 –24 –21 –18 –15 –12 –9
–6
–3
0
3
6
9
12
15
18
21
24
27
30
–27 –24 –21 –18 –15 –12 –9
–6
–3
0
3
6
9
12
15
18
21
24
27
30
–30 –27 –24 –21 –18 –15 –12 –9
–6
–3
0
3
6
9
12
15
18
21
24
27
30
b.
c.
d.
143. Solve and graph the solutions of
a. –9 < x < 21
–24 –22 –20 –18 –16 –14 –12 –10 –8
. Write the solutions as a compound inequality.
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
24
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
24
b. x < – 15 OR x > 15
–24 –22 –20 –18 –16 –14 –12 –10 –8
c. x > 21
–24 –22 –20 –18 –16 –14 –12 –10 –8
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
24
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
24
d. x < – 9 OR x > 21
–24 –22 –20 –18 –16 –14 –12 –10 –8
Numeric Response
144. An architect
charges $1800 for a first
draft of a three-bedroom house. If
the work takes longer than 8 hours,
the architect charges $105 for each
additional hour. What would be the
total cost for a first draft that took 14
hours to complete?
145.
The maximum speed of a greyhound
is 153 miles per hour less than 3
times the maximum speed of a
cheetah. If a greyhound’s maximum
speed is 42 miles per hour, what is
the maximum speed of a
greyhound? Check to make sure
your answer is reasonable.
146.
A car rental company increases daily
rental fees 15% in the summer to
cover increased fuel costs. They
then have a “25% off” promotion for
the fall. If a car rented for $36.00 per
day before the summer, what would
the per-day rental cost be during the
fall promotion?
147. What is the least possible integer solution of the
inequality
?
148. A volleyball team scored 14 more points in its first
game than in its third game. In the second game,
the team scored 28 points. The total number of
points scored was less than 80. What is the greatest
number of points the team could have scored in its
first game?
Matching
149.
150.
151.
154.
155.
Match each vocabulary term with its definition.
a. algebraic expression
b. numerical expression
c. like terms
d. absolute value
e. evaluate
f. variable
g. constant
a symbol used to represent a
152. a mathematical phrase that contains
quantity that can change
operations and numbers
a value that does not change
153. to find the value of an algebraic
expression by substituting a number
an expression that contains at least
for each variable and simplifying by
one variable
using the order of operations
Match each vocabulary term with its definition.
a. real numbers
b. additive inverse
c. opposites
d. multiplicative inverse
e. natural numbers
f. reciprocal
g. absolute value
numbers that are the same distance
156.
for any real number
from zero on opposite sides of the
157. the distance from zero on a number
number line
line
the opposite of a number
158. the reciprocal of the number
Match each vocabulary term with its definition.
a. coefficient
b. variable
c.
d.
e.
f.
g.
159.
160.
161.
164.
165.
166.
170.
171.
power
perfect square
square root
exponent
base
the number in a power that is used
162. an expression written with a base
as a factor
and an exponent or the value of
such an expression
a number that is multiplied to itself to
form a product
163. the number that indicates how many
times the base in a power is used as
a number whose positive square
a factor
root is a whole number
Match each vocabulary term with its definition.
a. real numbers
b. positive numbers
c. negative numbers
d. integers
e. irrational numbers
f. rational numbers
g. natural numbers
h. whole numbers
the set of numbers that can be
167. the set of rational and irrational
numbers
written in the form , where a and b
168. the set of whole numbers and their
are integers and
opposites
the set of counting numbers
169. the set of real numbers that cannot
the set of natural numbers and zero
be written as a ratio of integers
Match each vocabulary term with its definition.
a. repeating decimal
b. terminating decimal
c. reciprocal
d. absolute value
e. term
f. coefficient
g. like terms
h. order of operations
a rational number in decimal form
172. a part of an expression to be added
that has a block of one or more
or subtracted
digits that repeats continuously
173. terms with the same variables raised
to the same exponents
a number multiplied by a variable
174.
176.
177.
178.
181.
182.
Fourth, perform all addition and
A rule for evaluating expressions:
subtraction from left to right.
First, perform operations in
parentheses or other grouping
175. a rational number in decimal form
symbols.
that has a finite number of digits
Second, evaluate powers and roots.
after the decimal point
Third, perform all multiplication and
division from left to right.
Match each vocabulary term with its definition.
a. coordinate plane
b. ordered pair
c. origin
d. quadrant
e. y-axis
f. x-axis
g. axes
the intersection of the x- and y-axes
179. the two perpendicular number lines,
in a coordinate plane
also known as the x-axis and the
y-axis, used to define the location of
the vertical axis in a coordinate
a point in a coordinate plane
plane
180. a pair of numbers that can be used
the horizontal axis in a coordinate
to locate a point on a coordinate
plane
plane
Match each vocabulary term with its definition.
a. x-axis
b. x-coordinate
c. y-coordinate
d. input
e. output
f. y-axis
g. quadrant
h. coordinate plane
the second number in an ordered
183. the result of substituting a value for a
pair, which indicates the vertical
variable in a function
distance of a point from the origin on
184. a value that is substituted for the
the coordinate plane
independent variable in a relation or
function
the first number in an ordered pair,
which indicates the horizontal
185. one of the four regions into which
distance of a point from the origin on
the x- and y-axis divide the
the coordinate plane
coordinate plane
186.
187.
188.
189.
193.
194.
195.
a plane that is divided into four
the x-axis and a vertical line called
regions by a horizontal line called
the y-axis
Match each vocabulary term with its definition.
a. expression
b. solution of an equation
c. contradiction
d. identity
e. formula
f. inequality
g. equation
h. literal equation
a mathematical sentence that shows
190. a value or values that make the
that two expressions are equivalent
equation or inequality true
an equation that contains two or
191. a literal equation that states a rule
more variables
for a relationship among quantities
an equation that is true for all values
192. an equation that is not true for any
of the variables
value of the variable
Match each vocabulary term with its definition.
a. proportion
b. formula
c. ratio
d. unit rate
e. identity
f. conversion factor
g. rate
a rate in which the second quantity
196. an equation that states that two
in the comparison is one unit
ratios are equal
the ratio of two equal quantities,
197. a comparison of two numbers by
each measured in different units
division
a ratio that compares two quantities
measured in different units
Match each vocabulary term with its definition.
a. conversion factor
b. scale
c. scale drawing
d. scale factor
e. scale model
f. proportion
g. similar
198.
199.
200.
203.
204.
205.
208.
a drawing that uses a scale to
201. a three-dimensional model that uses
represent an object as smaller or
a scale to represent an object as
larger than the original object
smaller or larger than the actual
object
the ratio of any length in a drawing
to the corresponding actual length
202. the ratio of two equal quantities,
each measured in different units
in a dilation, the ratio of a linear
measurement of the image to the
corresponding measurement of the
preimage
Match each vocabulary term with its definition.
a. proportion
b. corresponding sides
c. indirect measurement
d. like terms
e. cross products
f. similar
g. corresponding angles
the product of the means bc and the
206. angles in the same relative position
product of the extremes ad in the
in two different polygons that have
the same number of angles
statement
207. a method of measuring an object by
sides in the same relative position in
using formulas, similar figures,
two different polygons that have the
and/or proportions
same number of sides
two figures that have the same
shape, but not necessarily the same
size
Match each vocabulary term with its definition.
a. commission
b. interest
c. rate
d. sales tax
e. markup
f. principal
g. tip
an amount of money added to a bill
209. the amount of money charged for
for service
borrowing money or the amount of
money earned when saving or
investing money
210.
211.
213.
214.
215.
219.
220.
221.
222.
223.
money paid to a person or company
212. an amount of money borrowed or
for making a sale
invested
a percent of the cost of an item that
is charged by governments to raise
money
Match each vocabulary term with its definition.
a. rate
b. markup
c. percent change
d. percent decrease
e. ratio
f. percent
g. percent increase
h. discount
a decrease given as a percent of the
216. an increase or decrease given as a
original amount
percent of the original amount
an increase given as a percent of
217. a ratio that compares a number to
the original amount
100
an amount by which an original price
218. the amount by which a wholesale
is reduced
cost is increased
Match each vocabulary term with its definition.
a. compound inequality
b. inequality
c. intersection
d. solution of an inequality
e. union
f. Venn diagram
g. equation
the set of all elements that are common to both sets,
denoted by
the set of all elements that are in either set, denoted
by
a statement that compares two expressions by using
one of the following signs: <, >, , , or
a value or values that make the inequality true
two inequalities that are combined into one
statement by the word and or or
Math Olympics
Answer Section
MULTIPLE CHOICE
1. ANS: D
The operation
means “divided by” or “quotient”.
p ÷ 10:
the quotient of p and 10
p divided by 10
Feedback
A
B
C
D
Check the operation in the algebraic expression.
Check the operation in the algebraic expression.
Check the order of the variable and constant.
Correct!
TOP: 1-1 Variables and Expressions
2. ANS: B
y represents the number of letters Julia wrote.
Think: y groups of 14 letters.
14y
Feedback
A
B
C
D
Think: how many groups of letters are there?
Correct!
Think: how many groups of letters are there?
To translate words into an algebraic expression, look for words
that indicate the action.
TOP: 1-1 Variables and Expressions
3. ANS: C
x represents the number of bags.
Think: How many groups of 88 are in x?
Feedback
A
B
Think: how many groups of cans are in the number of bags?
Think: how many groups of cans are in the number of bags?
C
D
Correct!
To translate words into an algebraic expression, look for words
that indicate the action.
TOP: 1-1 Variables and Expressions
4. ANS: B
m+o
9+7
16
Substitute 9 for m and 7 for o.
Simplify.
Feedback
A
B
C
D
Check your addition.
Correct!
This expression involves addition, not subtraction.
This expression involves addition, not multiplication.
TOP: 1-1 Variables and Expressions
5. ANS: B
Substitute the values for q and v into the expression, and then subtract.
Feedback
A
B
C
D
Check your subtraction.
Correct!
This expression involves subtraction, not division.
This expression involves subtraction, not addition.
TOP: 1-1 Variables and Expressions
6. ANS: D
Substitute the values for x and y into the expression, and then multiply.
Feedback
A
B
C
D
Check your multiplication.
Check your multiplication.
This expression involves multiplication, not addition.
Correct!
TOP: 1-1 Variables and Expressions
7. ANS: C
Substitute the values for a and b into the expression, and then divide.
Feedback
A
B
C
D
This expression involves division, not multiplication.
This expression involves division, not subtraction.
Correct!
Check your division.
TOP: 1-1 Variables and Expressions
8. ANS: D
The expression 40 + y models the number of points Mike scored in all
Evaluate 40 + y for y = 2.
40 + 2 = 42
If Mike scored 2 points in the second half of the game, then he scored 42 points in
all.
Feedback
A
B
C
D
Use a different operation.
Use a different operation.
Use a different operation instead of division.
Correct!
TOP: 1-1 Variables and Expressions
9. ANS: C
The expression
receive.
Evaluate
models the number of sand dollars each of Aaron’s friends will
for y = 12.
=6
If Aaron gives 72 sand dollars to 12 friends, each friend will get 6 sand dollars.
Feedback
A
B
C
D
Use a different operation.
Use a different operation.
Correct!
Use a different operation instead of multiplication.
TOP: 1-1 Variables and Expressions
10. ANS: D
The expression 12n models the number books Salvador read in all.
Evaluate 12n for n = 7.
12(7) = 84
If Salvador read for 7 months, then that means Salvador read 84 books.
Feedback
A
B
C
D
Use a different operation.
Use a different operation.
Use a different operation.
Correct!
TOP: 1-1 Variables and Expressions
11. ANS: A
Substitute 7 for m and 9 for n.
Simplify. Remember:
means 2 times m.
Feedback
A
B
C
D
Correct!
You switched the values of the variables.
First, substitute the given values. Then, simplify the
expression.
When there is no operation sign between a number and a
variable, it means it is multiplication.
TOP: 1-1 Variables and Expressions
12. ANS: D
The lower vector shows the minuend and the upper vector shows the subtrahend.
The number at which the upper vector stops is the difference of the two integers.
Feedback
A
B
C
D
Move left on a number line to subtract a positive integer; move
right to subtract a negative integer.
Move left on a number line to subtract a positive integer; move
right to subtract a negative integer.
Move left on a number line to subtract a positive integer; move
right to subtract a negative integer.
Correct!
TOP: 1-2 Adding and Subtracting Real Numbers
13. ANS: B
To add two integers with the same sign, find the sum of their absolute values and
use the sign of the two integers. To add two integers with different signs, find the
difference of their absolute values and use the sign of the integer with the greater
absolute value.
Feedback
A
B
C
D
When adding two integers with the same sign, find the sum of
their absolute values. When adding two integers with different
signs, find the difference of their absolute values.
Correct!
When adding two integers with the same sign, find the sum of
their absolute values. When adding two integers with different
signs, find the difference of their absolute values.
Check the sign of your answer.
TOP: 1-2 Adding and Subtracting Real Numbers
14. ANS: C
Substitute 35 for x, and then add the integers.
To add two integers with the same sign, find the sum of their absolute values and
use the sign of the two integers. To add two integers with different signs, find the
difference of their absolute values and use the sign of the integer with the greater
absolute value.
Feedback
A
B
C
D
Substitute for x, and then add the integers.
Check the sign of your answer.
Correct!
When adding two integers with the same sign, find the sum of
their absolute values. When adding two integers with different
signs, find the difference of their absolute values.
TOP: 1-2 Adding and Subtracting Real Numbers
15. ANS: C
Change the subtraction sign to an addition sign, and change the sign of the
second number.
Feedback
A
B
Change the subtraction sign to an addition sign, and change
the sign of the second number.
Change the subtraction sign to an addition sign, and change
C
D
the sign of the second number.
Correct!
Pay attention to the sign.
TOP: 1-2 Adding and Subtracting Real Numbers
16. ANS: C
Substitute 12 for x, and then subtract the integers.
To subtract, change the subtraction sign to an addition sign, and change the sign
of the second number.
Feedback
A
B
C
D
Pay attention to the sign.
Change the subtraction sign to an addition sign, and change
the sign of the second number.
Correct!
Change the subtraction sign to an addition sign, and change
the sign of the second number.
TOP: 1-2 Adding and Subtracting Real Numbers
17. ANS: C
Subtract the negative temperature from the positive temperature to calculate the
difference in the two readings.
Feedback
A
B
C
D
Check the signs.
Check the signs.
Correct!
Subtract the lower temperature from the higher one.
TOP: 1-2 Adding and Subtracting Real Numbers
18. ANS: B
Subtract the lower temperature from the higher temperature to calculate the
difference in the two readings.
Feedback
A
B
C
D
Subtract the lower temperature from the higher temperature.
Correct!
Subtract the lower temperature from the higher temperature.
Check the signs.
TOP: 1-2 Adding and Subtracting Real Numbers
19. ANS: B
Subtract the height of the building from the height of the elevator. The difference
represents how far underground the parking garage goes.
Feedback
A
B
C
D
Check your subtraction.
Correct!
Subtract the numbers instead of adding them.
Check your subtraction.
TOP: 1-2 Adding and Subtracting Real Numbers
20. ANS: B
Multiply the two integers. If the signs are the same, the product is positive; if the
signs are different, the product is negative.
Feedback
A
B
C
D
Multiply the integers, not add.
Correct!
Be sure to multiply the integers.
If the signs of the two integers are the same, the product will
be positive. If the signs are different, the product will be
negative.
TOP: 1-3 Multiplying and Dividing Real Numbers
21. ANS: D
Substitute –4 for u. Then multiply.
Feedback
A
B
C
D
Substitute the value in the variable, and then multiply.
Check your multiplication.
If the signs of the two integers are the same, the product will
be positive; if they are different, the product will be negative.
Correct!
TOP: 1-3 Multiplying and Dividing Real Numbers
22. ANS: D
Divide the two integers. If the signs are the same, the quotient is positive; if the
signs are different, the quotient is negative.
Feedback
A
B
This expression involves division, not multiplication.
If the signs of the two integers are the same, the quotient will
be positive. If the signs are different, the quotient will be
C
D
negative.
This expression involves division, not subtraction.
Correct!
TOP: 1-3 Multiplying and Dividing Real Numbers
23. ANS: B
Substitute –33 for k in the expression. Then divide the integers. If the signs are
the same, the quotient is positive; if the signs are different, the quotient is
negative.
Feedback
A
B
C
D
This expression involves division, not multiplication.
Correct!
This expression involves division, not subtraction.
If the signs of the two integers are the same, the product will
be positive. If the signs are different, the product will be
negative.
TOP: 1-3 Multiplying and Dividing Real Numbers
24. ANS: C
Write
as an improper fraction.
To divide by
Multiply.
8 218
multiply by
.
Simplify.
Feedback
A
B
C
D
First convert the mixed number to an improper fraction.
Multiply by the reciprocal.
Correct!
First convert the mixed number to an improper fraction. Then
multiply by the reciprocal.
TOP: 1-3 Multiplying and Dividing Real Numbers
25. ANS: D
The quotient of 0 and any nonzero number is 0.
Feedback
A
B
C
D
Multiply or divide by 0.
Multiply or divide by 0.
Only division by 0 is undefined.
Correct!
TOP: 1-3 Multiplying and Dividing Real Numbers
26. ANS: D
Distance = rate
time
Distance =
Substitute 3.5 for rate and 1.75 for time.
Multiply to find the distance.
Feedback
A
B
C
D
To find distance, multiply rate by time.
To find distance, multiply rate by time. Then estimate to check
if your answer is reasonable.
The decimal point is not in the correct place. Use estimation to
check if your answer is reasonable.
Correct!
TOP: 1-3 Multiplying and Dividing Real Numbers
27. ANS: C
The figure is 5 cubes tall, 5 cubes wide, and 5 cubes long. The factor 5 is used 3
times.
Feedback
A
B
C
D
The length, width, and height of the figure is 5.
Is the figure 2-dimensional or 3-dimensional?
Correct!
The length, width, and height of the figure is 5.
TOP: 1-4 Powers and Exponents
28. ANS: C
The exponent tells the number of times to multiply the base number by itself.
Multiply 9 by itself 3 times.
Feedback
A
B
Multiply the base number by itself as many times as the
exponent tells you.
Multiply using the base. The exponent just tells how many
C
D
times to multiply the base by itself.
Correct!
Multiply the number by itself rather than adding two different
numbers.
TOP: 1-4 Powers and Exponents
29. ANS: A
The exponent tells the number of times to multiply the base number by itself.
The negative sign in front of the expression multiplies the expression by –1.
Multiply 3 by itself 4 times, and then multiply your answer by –1.
Feedback
A
B
C
D
Correct!
Think of the negative sign in front as multiplying the expression
by -1.
Multiply the base number by itself rather than adding.
Multiply the base number by itself. The exponent tells how
many times to multiply the base by itself.
TOP: 1-4 Powers and Exponents
30. ANS: B
The exponent tells the number of times to multiply the base number by itself.
Multiply –4 by itself 2 times.
Feedback
A
B
C
D
Multiply the base number by itself rather than adding.
Correct!
This is the product of the base and the exponent. The
exponent tells how many times to multiply the base by itself.
Check the sign of your answer. The product of an even
number of negative factors is positive; the product of an odd
number of negative factors is negative.
TOP: 1-4 Powers and Exponents
31. ANS: D
The exponent tells how many times to multiply the fraction by itself.
Multiply by itself 2 times.
Feedback
A
The exponent tells how many times to multiply the fraction by
itself.
B
C
D
Raise both the numerator and denominator to the exponent.
Raise both the numerator and denominator to the exponent.
Correct!
TOP: 1-4 Powers and Exponents
32. ANS: B
The number given as a base should be multiplied by itself a certain number of
times in order to represent the value of the whole number given.
The product of two 3’s is 9.
Feedback
A
B
C
D
An exponent is written as a small number raised slightly above
the base number.
Correct!
The exponent tells how many times to multiply the base by
itself.
The number given as a base should be multiplied by itself a
certain number of times in order to represent the value of the
whole number given.
TOP: 1-4 Powers and Exponents
33. ANS: A
If each category represents sunlight that is 6 times brighter than the category
before, then a dazzling day would be 36 times brighter than an illuminated day
because:
a dazzling day is 6 times brighter than a radiant day,
a radiant day is 6 times brighter than an illuminated day,
and an illuminated day is 6 times brighter than a dim day.
Feedback
A
B
C
D
Correct!
The brightness number is just for identifying the category. You
need to use the number of times brighter as a factor.
You need to use the number of times brighter as a factor one
more time.
Check to see whether you used the number of times brighter
as a factor too many times.
TOP: 1-4 Powers and Exponents
34. ANS: C
If the population of the ant hill is 40 ants and it doubles every 10 days, then to find
its population in 20 days, make a chart to see what the population is after a
certain number of days.
In 10 days, the population is 40 ants.
In 2 • 10 days, the population is 402 ants.
In 3 • 10 days, the population is 403 ants.
In 4 • 10 days, the population is 404 ants.
Feedback
A
B
C
D
Make a chart to see what the population is after a certain
number of days.
Make a chart to see what the population is after a certain
number of days.
Correct!
Make sure that the ant population doubles.
TOP: 1-4 Powers and Exponents
35. ANS: C
Step 1 Find the total area of the vegetable garden and path.
Step 2 Find the area of the vegetable garden and the area of the path.
Find the side length of the vegetable garden.
Find the area of the vegetable garden.
To find the area of the path, subtract the area of the vegetable garden from the
total area.
Step 3 Find the number of gravel bags needed to cover the path.
So, 7 bags of gravel are needed to cover the path.
Feedback
A
B
C
D
You switched the area of the vegetable garden and the area of
the path.
To find the area of the path, subtract the area of the vegetable
garden from the total area.
Correct!
To find the area of the path, subtract the area of the vegetable
garden from the total area.
TOP: 1-4 Powers and Exponents
36. ANS: A
196 =
What number squared equals 196?
= 14
The sign to the left of the radical determines
whether the square root is positive or negative.
Feedback
A
B
C
D
Correct!
This is half of the number. The square root of a number,
multiplied by itself, equals that number.
Find the square root of the number under the radical sign, not
the square of that number.
The + or - sign to the left of the radical is the sign of the square
root.
TOP: 1-5 Square Roots and Real Numbers
37. ANS: D
202 is between 196 and 225. Since 202 is closer to 196, the best estimate for the
side length is 14 ft.
Feedback
A
B
C
D
Find the two perfect squares that the area is between.
Find the two perfect squares that the area is between.
Of the two perfect squares that the area is between, which is
closer to the area?
Correct!
TOP: 1-5 Square Roots and Real Numbers
38. ANS: B
Any number that can be written as a fraction is a rational number. Rational
numbers include terminating decimals and repeating decimals.
If a rational number simplifies to a whole number or its opposite, it is also an
integer.
If a rational number simplifies to a nonzero whole number, it is also a natural
number.
Feedback
A
B
C
D
To check whether the number is a terminating or repeating
decimal, divide the numerator by the denominator.
Correct!
Since this number can be written as a fraction, it is not an
irrational number.
There are more ways to classify the number. Check to see
whether it is a terminating or repeating decimal.
TOP: 1-5 Square Roots and Real Numbers
39. ANS: D
A rational number can be written as a fraction. Rational numbers include integers,
fractions, terminating decimals, and repeating decimals.
An irrational number cannot be expressed as either a terminating decimal or
repeating decimal.
Feedback
A
B
C
D
A rational number will either terminate or repeat, but an
irrational number will not. If the fraction simplifies to a nonzero
whole number, the number is also an integer and a natural
number.
A rational number will either terminate or repeat, but an
irrational number will not. If the fraction simplifies to a nonzero
whole number, the number is also an integer and a natural
number.
A rational number will either terminate or repeat, but an
irrational number will not. If the fraction simplifies to a nonzero
whole number, the number is also an integer and a natural
number.
Correct!
TOP: 1-5 Square Roots and Real Numbers
40. ANS: C
If there is an example of two irrational numbers whose sum is not an irrational
number, then the set of irrational numbers is not closed under addition. Add the
following irrational numbers:
0.121121112...
0.212212221...
The result is 0.33333... which is equal to , and is a rational number.
Another example is
and
. The sum is 0 which is a rational number.
Feedback
A
B
C
D
Find an example of two irrational numbers whose sum is not
an irrational number.
If there is an example of two irrational numbers whose sum is
not an irrational number, then the set of irrational numbers is
not closed under addition.
Correct!
The set of irrational numbers being closed under addition
means that when you add any two irrational numbers, the sum
is also an irrational number.
TOP: 1-5 Square Roots and Real Numbers
41. ANS: D
Use the order of operations:
1. Perform operations in parentheses.
2. Evaluate powers.
2. Multiply or divide from left to right.
3. Add or subtract from left to right.
Feedback
A
B
C
D
The exponent tells how many times to use the base as a factor
with itself.
The order of operations is correct, but check your signs.
After evaluating the exponents and evaluating within
parentheses, multiplication must be performed before addition
or subtraction.
Correct!
TOP: 1-6 Order of Operations
42. ANS: D
Use the order of operations:
1. Perform operations in parentheses.
2. Evaluate powers.
3. Multiply or divide from left to right.
4. Add or subtract from left to right.
Feedback
A
B
C
D
Use the order of operations.
Perform operations in parentheses first.
Divide before you add.
Correct!
TOP: 1-6 Order of Operations
43. ANS: C
Substitute 9 for x in the expression. Then use the order of operations to evaluate
the expression.
1. Perform operations in parentheses.
2. Evaluate powers.
3. Multiply or divide from left to right.
4. Add or subtract from left to right.
Feedback
A
B
C
D
Use the order of operations. Multiply before adding or
subtracting.
Use the order of operations. Multiply before adding or
subtracting.
Correct!
Use the order of operations. Multiply before adding or
subtracting.
TOP: 1-6 Order of Operations
44. ANS: B
Substitute 4 for x in the expression. Then use the order of operations to evaluate
the expression.
1. Perform operations in parentheses.
2. Evaluate powers.
3. Multiply or divide from left to right.
4. Add or subtract from left to right.
Feedback
A
B
C
D
Use the order of operations. Evaluate powers before
multiplying or adding.
Correct!
Use the order of operations. Evaluate powers before
multiplying or adding.
Use the order of operations. Evaluate powers before
multiplying or adding.
TOP: 1-6 Order of Operations
45. ANS: A
First, simplify the numerator of the fraction, and then divide the numerator by the
denominator. Next, subtract the terms in the absolute value, and then find the
absolute value.
=
Finally, add the two terms.
= 14
Feedback
A
B
C
D
Correct!
Only square the value that has an exponent, not both numbers
in the numerator.
Subtract within the absolute value bars before taking the
absolute value.
Simplify the numerator before dividing by the denominator.
TOP: 1-6 Order of Operations
46. ANS: D
Use parentheses so that the difference is
evaluated first.
Product means multiplication.
Feedback
A
B
C
D
"Product" indicates multiplication.
Use parentheses so the difference is evaluated first.
When finding a difference, subtract the second number from
the first.
Correct!
TOP: 1-6 Order of Operations
47. ANS: D
Use the formula (P + 5N + 10D + 25Q) ÷ 100. Substitute the values from the
table.
100
Total
100
100
Tatia has $1.90.
Feedback
A
B
C
D
First perform operations inside parentheses, and then divide.
Multiply before you add.
Multiply the number of coins of each type by its coin value
before performing the addition.
Correct!
TOP: 1-6 Order of Operations
48. ANS: C
You must use each of the numbers at least once, and you may use any
operations. Pay attention to the order of operations.
Feedback
A
B
C
D
Evaluate powers before performing subtraction.
Perform multiplication before subtraction.
Correct!
The number 8 must be used also.
TOP: 1-6 Order of Operations
49. ANS: B
Use the Commutative Property.
Use the Associative Property to make groups of
compatible numbers.
Simplify.
Feedback
A
B
C
D
The sum of two mixed numbers is the sum of the whole parts
plus the sum of the fractional parts.
Correct!
To add two fractions, first find a common denominator and
then add the numerators.
The sum of the fractional parts is greater than 1.
TOP: 1-7 Simplifying Expressions
50. ANS: A
Rewrite 59 as 50 + 9. Then multiply each term by 11 and add the products.
Feedback
A
B
C
D
Correct!
Multiply the first number by each digit in the second number,
then add the two products.
Multiply the first number by each digit in the second number,
then add the two products.
Multiply the first number by each digit in the second number,
then add the two products.
TOP: 1-7 Simplifying Expressions
51. ANS: B
Notice that 19 is very close to 20.
. Then use the Distributive Property.
Rewrite 19 as 20 +
Feedback
A
B
C
D
You've reversed multiplication and addition. Look at the
Distributive Property again.
Correct!
Use mental math. Notice that the two-digit factor is close to a
multiple of 10.
Use mental math. Notice that the two-digit factor is close to a
multiple of 10.
TOP: 1-7 Simplifying Expressions
52. ANS: A
Group like terms.
Add or subtract the coefficients.
Feedback
A
B
C
D
Correct!
Combine only like terms.
Check the signs of all the coefficients.
First, group like terms. Then, add or subtract the coefficients.
TOP: 1-7 Simplifying Expressions
53. ANS: D
The Commutative Property allows for you to add or subtract terms in any order.
Feedback
A
B
C
D
Multiplication is used in Step 3.
The Associative Property is used in Step 5.
Like terms are combined in Step 6.
Correct!
TOP: 1-7 Simplifying Expressions
54. ANS: D
Procedure
Justification
Definition of subtraction
Commutative Property
Associative Property
Distributive Property
Simplify
Definition of subtraction
Feedback
A
B
C
D
What is the difference between the Commutative Property and
the Distributive Property?
The Associative Property involves grouping of numbers. What
does the Commutative Property state?
What is the difference between the Associative Property and
the Distributive Property?
Correct!
TOP: 1-7 Simplifying Expressions
55. ANS: C
The x-coordinate of the ordered pair tells how many units to move left or right
from the origin. The y-coordinate of the ordered pair tells how many units to move
up or down from the origin.
Feedback
A
B
The first number in the ordered pair tells whether to move left
or right from (0, 0). The second number tells whether to move
up or down.
The first number in the ordered pair tells whether to move left
or right from (0, 0). The second number tells whether to move
up or down.
Correct!
The first number in the ordered pair tells whether to move left
or right from (0, 0). The second number tells whether to move
up or down.
C
D
TOP: 1-8 Introduction to Functions
56. ANS: D
If both x and y are positive, the point is in Quadrant I.
If x is negative and y is positive, the point is in Quadrant II.
If both x and y are negative, the point is in Quadrant III.
If x is positive and y is negative, the point is in Quadrant IV.
y
5
Quadrant II
Quadrant I
–5
5
Quadrant III
x
Quadrant IV
–5
Feedback
A
B
C
D
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. The signs of x and y determine which
quadrant the point is in.
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. The signs of x and y determine which
quadrant the point is in.
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. The signs of x and y determine which
quadrant the point is in.
Correct!
TOP: 1-8 Introduction to Functions
57. ANS: C
If x = 0, the point is on the y-axis.
If y = 0, the point is on the x-axis.
Feedback
A
B
C
D
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. If x = 0, the point is on the y-axis. If y = 0,
the point is on the x-axis.
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. If x = 0, the point is on the y-axis. If y = 0,
the point is on the x-axis.
Correct!
The coordinate plane is divided by the x-axis and the y-axis
into four quadrants. If x = 0, the point is on the y-axis. If y = 0,
the point is on the x-axis.
TOP: 1-8 Introduction to Functions
58. ANS: B
Let y represent the monthly payment and x represent the number of minutes of
international calls.
monthly
is $25
plus $0.10
for
international
payment
each
minute
=
25
+
0.10
y
x
Number of
international
minutes
x (input)
90
120
145
150
Rule
Monthly
payment
Ordered
pair
y (output)
$34.00
$37.00
$39.50
$40.00
(x, y)
(90, 34)
(120, 37)
(145, 39.5)
(150, 40)
Feedback
A
B
C
The monthly payment is determined by the number of
international minutes, so the number of international minutes is
the input and the monthly payment is the output.
Correct!
The monthly payment is determined by the number of
international minutes, so the number of international minutes is
D
the input and the monthly payment is the output.
The monthly payment is $25 plus $0.10 for each international
minute.
TOP: 1-8 Introduction to Functions
59. ANS: D
Make a table to find values of (x, y) for
x
y
(x, y)
–2
(–2, 6)
–1
(–1, 0)
0
(0, –2)
1
(1, 0)
2
(2, 6)
.
The points form a U shape.
Feedback
A
B
C
D
This is a cubic function. Use the given values for x to get the
values for y.
This is a linear function. Use the given values for x to get the
values for y.
This is an absolute value function. Use the given values for x
to get the values for y.
Correct!
TOP: 1-8 Introduction to Functions
60. ANS: B
Step 1 Plot the points.
y
5
4
B
3
C
2
1
1
–1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
A
–5
Step 2 Find the fourth vertex.
The fourth vertex will have the same x-coordinate as C(10,3) and the same
y-coordinate as A(1, –5).
x-coordinate: 10
y-coordinate: –5
The fourth vertex is D(10, –5).
y
5
4
C
B
3
2
1
1
–1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
–5
A
D
Step 3 Find the area of the rectangle.
square units
Feedback
A
B
C
The fourth vertex will have the same x-coordinate as point C
and the same y-coordinate as point A.
Correct!
First, plot the points. Then, use the formula for the area of the
D
rectangle.
The fourth vertex will have the same x-coordinate as point C
and the same y-coordinate as point A.
TOP: 1-8 Introduction to Functions
61. ANS: C
The operation means “times”, “multiplied by”, “product”, or “each groups of”.
6p:
6 times p
6 groups of p
Feedback
A
B
C
D
The algebraic expression does not show division.
Check the operation in the algebraic expression.
Correct!
Check the operation in the algebraic expression.
TOP: 1-1 Variables and Expressions
62. ANS: B
The lower vector shows the first addend, and the upper vector shows the second
addend. The number at which the upper vector stops is the sum of the two
integers.
Feedback
A
B
C
D
Move right on a number line to add a positive integer; move
left to add a negative integer.
Correct!
Move right on a number line to add a positive integer; move
left to add a negative integer.
Move right on a number line to add a positive integer; move
left to add a negative integer.
TOP: 1-2 Adding and Subtracting Real Numbers
63. ANS: A
Since 6 is subtracted from p, add 6 to both
sides to undo the subtraction.
Check:
To check your solution, substitute 22 for p in
the original equation.
Feedback
A
B
C
D
Correct!
Check the ones place.
Is subtraction the correct operation for solving this equation?
Check the tens place.
TOP: 2-1 Solving Equations by Adding or Subtracting
64. ANS: B
Since 6 is added to s, subtract 6 from both sides to
undo the addition.
Check:
To check your solution, substitute 42 for s in the
original equation.
Feedback
A
B
C
D
Check the tens place.
Correct!
Check the ones place.
Is addition the correct operation for solving this equation?
TOP: 2-1 Solving Equations by Adding or Subtracting
65. ANS: A
When something is added to the variable, add its opposite to both sides of the
equation to isolate the variable. Here, –14 is added to the variable, so add 14 to
both sides of the equation to isolate s.
Feedback
A
B
Correct!
Add the number that will isolate the variable.
C
D
Add the opposite to isolate the variable.
Add the number that will isolate the variable.
TOP: 2-1 Solving Equations by Adding or Subtracting
66. ANS: A
First month
salaries
Added
to
b
+
b + x = 21,894
10,205 + x =
21,894
–10,205
–10,205
Second
month
salaries
x
is
21,894
=
21,894
Write an equation to represent the
relationship.
Substitute 10,205 for b. Since 10,205 is added
to x, subtract 10,205 from both sides to undo
the addition.
The salaries for the second month are $11,689.
Feedback
A
B
C
D
Correct!
Subtract the same number from both sides of the equation.
Check your answer.
Use the same operation on both sides of the equation.
TOP: 2-1 Solving Equations by Adding or Subtracting
67. ANS: B
highest
score
h
minus
–
lowest
score
l
equals
score range
=
23
Write an equation to represent the
relationship.
Substitute 33 for l.
Solve the equation.
Feedback
A
The sum of the lowest value and the range is the highest
B
C
D
value.
Correct!
The range is the difference between the highest and the lowest
values, not the sum.
The range is the difference between the highest and the lowest
values, not the average.
TOP: 2-1 Solving Equations by Adding or Subtracting
68. ANS: B
Since q is divided by 5, multiply both sides by 5
to undo the division.
q = 205
Check:
To check your solution, substitute 205 for q in
the original equation.
Feedback
A
B
C
D
If the variable is connected to the number by division, then use
multiplication to solve for it.
Correct!
Instead of subtracting, multiply both sides by the denominator.
Multiply on both sides of the equation to isolate the variable.
TOP: 2-2 Solving Equations by Multiplying or Dividing
69. ANS: D
3n = 42
Since n is multiplied by 3, divide both sides by 3 to
undo the multiplication.
Check:
3n = 42
To check your solution, substitute 14 for n in the
original equation.
Feedback
A
B
C
D
Since the variable is multiplied, divide on both sides to undo
the multiplication.
Check your solution by substituting the variable in the original
equation.
To undo multiplication, use division.
Correct!
TOP: 2-2 Solving Equations by Multiplying or Dividing
70. ANS: A
The reciprocal of
multiplied by
is
. Since
is
, multiply both sides by
Feedback
A
B
C
D
Correct!
Multiply both sides of the equation by the reciprocal of the
fraction.
Multiply both sides of the equation by the reciprocal of the
fraction.
Multiply both sides of the equation by the reciprocal of the
fraction.
TOP: 2-2 Solving Equations by Multiplying or Dividing
71. ANS: A
Seconds divided by 5 equals distance.
Write an equation. Let d = distance from the
lightning strike in miles and t = number of
seconds between flash and thunder.
Substitute 17 for d, the distance from the
lightning strike.
Multiply both sides of the equation by 5 to undo
the division.
.
The number of seconds between flash and
thunder is about 85 seconds.
Feedback
A
B
C
D
Correct!
Divide the distance from the lightning strike by 5.
Divide the distance from the lightning strike by 5.
Divide the distance from the lightning strike by 5.
TOP: 2-2 Solving Equations by Multiplying or Dividing
72. ANS: B
Solve the equation.
Substitute 8 for x and simplify.
Feedback
A
B
C
D
Find the value of x by solving the equation. Then substitute it
for x in the given expression and simplify.
Correct!
Subtract the terms in the right order.
Find the value of x by solving the equation. Then substitute it
for x in the given expression and simplify.
TOP: 2-2 Solving Equations by Multiplying or Dividing
73. ANS: D
First x is multiplied by –2. Then 14 is added.
Work backward: Subtract 14 from both sides.
Since x is multiplied by –2, divide both sides by –2 to
undo the multiplication.
Feedback
A
B
To solve for the variable, work backward.
Substitute the solution in the original equation to check your
answer.
C
D
Check the signs.
Correct!
TOP: 2-3 Solving Two-Step and Multi-Step Equations
74. ANS: C
Since is subtracted from , add
both sides to undo the subtraction.
to
Since f is divided by 45, multiply both sides
by 45 to undo the division.
Simplify.
Feedback
A
B
C
D
First, add to undo the subtraction. Then, multiply to undo the
division.
Check your signs.
Correct!
First, add to undo the subtraction. Then, multiply to undo the
division.
TOP: 2-3 Solving Two-Step and Multi-Step Equations
75. ANS: A
Use the Commutative Property of Addition.
Combine like terms.
Since 10 is added to 17a, subtract 10 from
both sides to undo the addition.
Since a is multiplied by 17, divide both sides
by 17 to undo the multiplication.
Feedback
A
B
C
Correct!
Check your signs.
Combine like terms, and then solve.
D
Combine like terms, and then solve.
TOP: 2-3 Solving Two-Step and Multi-Step Equations
76. ANS: B
Let d be the distance (in miles) to the movies, then
is the number of miles
after the first mile. So a formula for the total charge could be
first mile +
charge
4.00
+
rate after
first mile
2.75
=
2.75
=
2.75
=
=
total
charge
20.50
20.50
4.00
16.5
Subtract
4.00 from
each side.
Divide both
sides by
2.75.
=
d
d
=
6
=
=
6+1
7
Add 1 to
both sides.
Feedback
A
B
C
D
Add one for the first mile.
Correct!
The mileage rate is the charge for each mile after the first mile.
Subtract the charge for the first mile.
TOP: 2-3 Solving Two-Step and Multi-Step Equations
77. ANS: A
8y – 8 = 24
+8 +8
8y = 32
8y =
8
y=
2(4) =
32
8
4
8
Add 8 to both sides of the equation.
Divide both sides by 8.
Apply 4 to 2y.
Feedback
A
B
C
D
Correct!
Add before multiplying.
To undo subtraction, add to both sides.
To undo multiplication, divide.
TOP: 2-3 Solving Two-Step and Multi-Step Equations
78. ANS: B
Substitute 3750 for p, 3000 for n, and 900 for
e.
Add 900 to both sides of the equation.
Divide both sides by 3000.
Feedback
A
B
C
D
Divide both sides of the equation by the coefficient of c.
Correct!
Add the same number to both sides of the equation.
Add the same number to both sides of the equation.
TOP: 2-3 Solving Two-Step and Multi-Step Equations
79. ANS: D
To collect the variable terms on one side,
subtract 50q from both sides.
Since 81 is subtracted from 2q, add 81 to both
sides to undo the subtraction.
Since q is multiplied by 2, divide both sides by 2
to undo the multiplication.
Feedback
A
B
Check your signs.
After adding to undo the subtraction, divide to undo the
C
D
multiplication.
First, collect the variable terms on one side. Then, add to undo
the subtraction.
Correct!
TOP: 2-4 Solving Equations with Variables on Both Sides
80. ANS: A
Combine like terms.
Add to undo the subtraction. Or subtract to
undo the addition. Then, divide to undo the
multiplication.
n = 1 12
Feedback
A
B
C
D
Correct!
Add to undo the subtraction. Or subtract to undo the addition.
Then, divide to undo the multiplication.
Add to undo the subtraction. Or subtract to undo the addition.
Then, divide to undo the multiplication.
Combine like terms, and then solve.
TOP: 2-4 Solving Equations with Variables on Both Sides
81. ANS: C
Combine like terms on each side of the equation before collecting variable terms
on one side.
If you get an equation that is always true, the original equation is an identity, and it
has infinitely many solutions.
If you get a false equation, the original equation is a contradiction, and it has no
solutions.
Feedback
A
B
First, combine like terms on each side of the equation. Then
collect variable terms on one side. Now, if you get an equation
that is always true, it means that the original equation has
infinitely many solutions. If you get a false equation, the
original equation has no solutions.
If you get an equation that is always true, the original equation
is an identity, and it has infinitely many solutions. If you get a
C
D
false equation, the original equation is a contradiction and it
has no solutions.
Correct!
If you get an equation that is always true, the original equation
is an identity, and it has infinitely many solutions. If you get a
false equation, the original equation is a contradiction and it
has no solutions.
TOP: 2-4 Solving Equations with Variables on Both Sides
82. ANS: B
Let m represent the number of movies rented each month.
Here are the costs for each company (in dollars).
7.5 + m =
2.5m
To collect the variable terms on one side, subtract m from both sides.
7.5 – m = 2.5m – m
7.5
=
1.5 m
Divide both sides by 1.5.
=
m
5
=
m
Feedback
A
B
C
D
You divided $7.50 by $2.50. Before dividing by 2.50, subtract
the $1.00 charge from the $2.50.
Correct!
You divided $7.50 by $1.00. Subtract the $1.00 charge from
the $2.50 and then divide.
Set up this equation 7.5 + m = 2.5m, where m is the number of
movies.
TOP: 2-4 Solving Equations with Variables on Both Sides
83. ANS: C
Let g represent the greatest integer.
The expressions for the three consecutive integers from least to greatest:
, g.
twice
the greatest
3 times
the least
integer
integer
g
(
)
,
To create an equation, use the additional data
that 2g is 2 less than
.
Solve the equation.
g
8
The three consecutive numbers are 6, 7, and 8.
Feedback
A
B
C
D
If an expression is x less than a second expression, add x to
the first expression to make it equal to the second one.
If the variable represents the least number, add 2 to the
variable value to find the greatest number. Add 1 to find the
second number.
Correct!
If the variable represents the greatest number, subtract 2 from
the variable value to find the least number. Subtract 1 to find
the second number.
TOP: 2-4 Solving Equations with Variables on Both Sides
84. ANS: D
Divide both sides by t.
Substitute the known values.
Simplify. Round to the nearest tenth.
Feedback
A
B
C
D
Solve the equation
Solve the equation
Solve the equation
Correct!
.
.
.
TOP: 2-5 Solving for a Variable
85. ANS: C
Locate V in the equation.
Since V is divided by I, multiply both sides by I to
undo the division.
Feedback
A
B
C
D
Multiply both sides by I to isolate r.
Multiply both sides by I to isolate r.
Correct!
Multiply both sides by I to isolate r.
TOP: 2-5 Solving for a Variable
86. ANS: D
Add z to both
sides.
Divide both sides
by 4.
Feedback
A
B
C
D
To undo subtraction, add to both sides.
Both terms need to be divided by the coefficient of x.
To undo multiplication, divide.
Correct!
TOP: 2-5 Solving for a Variable
87. ANS: B
Subtract 2 from both sides.
Subtract the
Rewrite 3.8 as
Multiply by
Distribute.
Simplify.
Feedback
.
term from both sides.
.
A
B
C
D
Divide all terms by 3.8.
Correct!
Multiply by the reciprocal of 3.8.
Keep the x term in the equation.
TOP: 2-5 Solving for a Variable
88. ANS: C
Write a ratio comparing ounces of oil to
gallons of gasoline.
Write a proportion. Let x be the amount of oil
in ounces.
Since x is divided by 38, multiply both sides of
the equation by 38.
There are 14 ounces of
oil.
Feedback
A
B
C
D
Set up a proportion, and use cross products.
First, set up two ratios that compare the ounces of oil to the
gallons of gasoline. Then, solve for the unknown amount of oil.
Correct!
Write a proportion, and use cross products.
TOP: 2-6 Rates Ratios and Proportions
89. ANS: A
Write a proportion to find an equivalent
ratio with a second quantity of 1.
Divide on the left side to find x.
The unit rate is
.
Ramon drives 50 miles
per hour.
Feedback
A
Correct!
B
C
D
Divide miles by hours, not hours by miles.
Check that you divided correctly when finding the unit rate.
This is not a unit rate.
TOP: 2-6 Rates Ratios and Proportions
90. ANS: B
•
To convert the first quantity in a rate, multiply
by a conversion factor with that unit in the
first quantity.
336 quarts per
hour
Feedback
A
B
C
D
There are 4 quarts in a gallon.
Correct!
There are 4 quarts in a gallon.
To convert the first quantity in a rate, multiply by a conversion
factor with that unit in the first quantity.
TOP: 2-6 Rates Ratios and Proportions
91. ANS: D
Use cross products.
Divide both sides by 6.
Feedback
A
B
C
D
Use cross products to solve.
Cross multiply.
Multiply the numerator of one fraction by the denominator of
the other fraction.
Correct!
TOP: 2-6 Rates Ratios and Proportions
92. ANS: C
Write the scale as a fraction.
Let x be the actual diameter.
Use cross products to solve.
Feedback
A
B
C
D
Use cross products to solve.
Use the proportion (model height)/(actual height) = (model
diameter)/(actual diameter).
Correct!
Set up a proportion and solve.
TOP: 2-6 Rates Ratios and Proportions
93. ANS: C
Let a represent the measure of one of the complementary angles and
represent the measure of the second angle.
ratio of the measures of
the angles
is
4:11
=
Solve
.
Use cross products.
Distribute.
Add 4a to both sides.
Simplify.
Solve the equation.
Substitute 24 for a to find the measure of the
second angle.
The measures of the complementary angles are 24° and 66°.
Feedback
A
B
Check if the signs of all the terms in the equation are correct
when you simplify.
Write an equation that uses the given ratio and the sum of the
C
D
angles' measures.
Correct!
Subtract the measure of the angle you found from 90 to get the
second angle.
TOP: 2-6 Rates Ratios and Proportions
94. ANS: A
A corresponds to L, B corresponds to M, C corresponds to N, and D corresponds
to O.
Use cross products.
Since x is multiplied by 21, divide both sides
by 21 to undo the multiplication.
_MN is 22.4
cm.
Feedback
A
B
C
D
Correct!
Set up a proportion, and solve for the missing length.
Set up a proportion, and solve for the missing length.
Set up a proportion, and solve for the missing length.
TOP: 2-7 Applications of Proportions
95. ANS: A
Use cross products.
Since x is multiplied by 7, divide both sides
by 7 to undo the multiplication.
The tree is 25 feet
tall.
Feedback
A
B
C
D
Correct!
Check that the proportion is set up correctly.
Set up a proportion and solve.
Divide the cross products by the length of the kangaroo's
shadow.
TOP: 2-7 Applications of Proportions
96. ANS: A
Find the areas of the two right triangles:
,
Then, find the ratio of the sides and the ratio of the corresponding areas.
ratio of the sides:
ratio of the areas:
The ratio of the areas is the square of the ratio of the corresponding sides.
Feedback
A
B
C
D
Correct!
First, find the ratio of the corresponding sides and the ratio of
the areas. Then, compare the two ratios.
First, find the ratio of the corresponding sides. Then, find the
ratio of the areas. How is the second number you found
related to the first number?
First, find the ratio of the corresponding sides and the ratio of
the areas. Then, compare the two ratios.
TOP: 2-7 Applications of Proportions
97. ANS: A
Step 1 Find the base of C.
Base C
Base D
6.72
(6.72)
5.6
Base C
Base C
Base C
Step 2 Find the height of C.
Area C
(Base C)(Height C)
Substitute 6.72 for the base of D.
Multiply by
.
47.6
47.6
17
(5.6)(Height C)
(2.8)(Height C)
Height C
Substitute 5.6 for the base of C.
Multiply.
Divide by 2.8.
Step 3 Find the height of D.
Height D
Height C
Height D
Height D
(17)
20.4
Substitute 17 for the height of D.
Feedback
A
B
C
D
Correct!
This is the height of C. Now find the height of D.
This is the base of C. Use this to find the height of C, and then
the height of D.
Find the base of C, then the height of C, then the height of D.
TOP: 2-7 Applications of Proportions
98. ANS: B
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the part.
Find the cross products.
Since x is multiplied by 100, divide both
sides by 100 to undo the multiplication.
_55% of 125 is
68.75.
Method 2 Use an equation.
Write an equation. Let x represent the part.
Write the percent as a decimal and
multiply.
55% of 125 is 68.75.
Feedback
A
B
C
D
Divide the percent by 100, and then multiply.
Correct!
First, write the percent as a decimal. Then, multiply.
Divide the percent by 100, and then multiply.
TOP: 2-8 Percents
99. ANS: B
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the percent.
Find the cross products.
Since x is multiplied by 74, divide both sides
by 74 to undo the multiplication.
_481 is 650% of
74.
Method 2 Use an equation.
Write an equation. Let x represent the
percent.
Since x is multiplied by 74, divide both sides
by 74 to undo the multiplication.
The answer is a decimal.
Write the decimal as a percent.
_481 is 650% of 74.
Feedback
A
B
C
D
Set up an equation where the percent is a variable, "of" means
to multiply, and "is" means "=". Then, solve for the variable.
Correct!
Use the percent proportion: part is to whole as percent is to
100. Then, find the cross products.
Use the percent proportion: part is to whole as percent is to
100. Then, find the cross products.
TOP: 2-8 Percents
100. ANS: B
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
Find the cross products.
Since x is multiplied by 56, divide both
sides by 56 to undo the multiplication.
_56% of 66 is
117.86.
Method 2 Use an equation.
Write an equation. Let x represent the
whole.
Write the percent as a decimal.
Since x is multiplied by 0.56, divide both
sides by 0.56 to undo the multiplication.
_56% of 66 is
117.86.
Feedback
A
B
C
D
Use the percent proportion: part is to whole as percent is to
100. Then, find the cross products.
Correct!
Set up an equation where the percent is a variable, "of" means
to multiply, and "is" means "=". Then, solve for the variable.
Set up an equation where the percent is a variable, "of" means
to multiply, and "is" means "=". Then, solve for the variable.
TOP: 2-8 Percents
101. ANS: B
Use the percent proportion.
Let x represent the percent.
Find the cross products.
Since x is multiplied by 80, divide both sides
by 80 to undo the multiplication.
18.75% of the compound is made up of lead.
Feedback
A
B
C
D
Use the percent proportion: part is to whole as percent is to
100. Then, find the cross products.
Correct!
Use the percent proportion: part is to whole as percent is to
100. Then, cross multiply.
In your final answer, convert the decimal to a percent.
TOP: 2-8 Percents
102. ANS: C
Feedback
A
B
C
D
This is the percent of the population who lived in Texas. Find
the percent of the population who lived in both California and
Texas.
This is the percent of the population who lived in California.
Find the percent of the population who lived in both California
and Texas.
Correct!
Find the total in California and Texas, and then divide that by
the total population.
TOP: 2-8 Percents
103. ANS: C
Write the formula for gross income.
gross income (income number of hours)
Write the formula for commission.
commission
gross income
(income
number of hours)
% of total sales
Substitute value given in the problem.
Let x represent the percent commission.
Multiply
Subtract.
Since x is multiplied by 3,350, divide
both sides by 3,350 to undo the
multiplication.
The answer is a decimal.
_5.25% = x
Write the
decimal as a percent.
_Aaron’s percent commission is 5.25%.
Feedback
A
B
C
D
Use the formula for gross income: gross income = (income *
number of hours) + commission, and solve for the percent
commission.
In your final answer, convert the decimal to a percent.
Correct!
The percent commission is the percent of the total sales.
TOP: 2-9 Applications of Percents
104. ANS: D
I=Prt
975 = (8000)(r)
Write the formula for simple interest.
Substitute the given values.
975 = 4000r
Multiply (8000)
.
Since r is multiplied by 3500, divide both
sides by 3500 to undo the multiplication.
0.244 = r
The interest rate is
24.4%.
Feedback
A
Use the formula for simple interest, I = Prt.
B
C
D
Use the formula for simple interest, I = Prt.
Use the formula for simple interest, I = Prt.
Correct!
TOP: 2-9 Applications of Percents
105. ANS: A
Round $69.98 to $70.00.
20% = 10% + 10%
10% of $70 = $7.00
10% of $70 = $7.00
$7.00 + $7.00 = $14.00
Feedback
A
B
C
D
Correct!
First, round the amount to the nearest dollar. Then, multiply to
find 10% of that amount.
First, round the amount to the nearest dollar. Then, multiply to
find 10% of that amount.
First, round the amount to the nearest dollar. Then, multiply to
find 10% of that amount.
TOP: 2-9 Applications of Percents
106. ANS: D
Step 1 Find the cost of the meal before the tip and sales tax.
Write the formula for the sales
tax.
Substitute known values.
Solve for c, the cost of the meal.
Step 2 Find the total cost of the meal, including tip and sales tax.
Write the formula for the total
cost.
Substitute the known values.
Feedback
A
B
C
D
First, calculate the cost of the meal before sales tax and tip.
Then, find the total cost including sales tax and tip.
First, calculate the cost of the meal before sales tax and tip.
Then, find the total cost including sales tax and tip.
This is the cost of the meal before sales tax and tip. You need
to include the sales tax and tip.
Correct!
TOP: 2-9 Applications of Percents
107. ANS: C
Substitute the given values.
If the first number is less than the second number, there is a percent of increase.
If the first number is greater than the second number, there is a percent of
decrease.
Feedback
A
B
C
D
If the first number is less than the second number, there is a
percent of increase. If the first number is greater than the
second number, there is a percent of decrease.
The percent change is the amount of increase or decrease
divided by the original amount.
Correct!
The percent change is the amount of increase or decrease
divided by the original amount.
TOP: 2-10 Percent Increase and Decrease
108. ANS: A
To find the amount of decrease, multiply 28 by 0.25. Then, subtract the decrease
from 28 to find the result of the decrease.
Feedback
A
B
Correct!
For a percent increase, add the percent change to the original
amount. For a percent decrease, subtract the percent change
C
D
from the original amount.
To find the result, add the percent change to or subtract the
percent change from the original amount.
First, calculate the percent change. Then, add it to or subtract
it from the original amount.
TOP: 2-10 Percent Increase and Decrease
109. ANS: A
Method 1 A discount is percent decrease. So find $117.00 decreased by 70%.
Find 70% of $117.00. This is the amount of
the discount.
Subtract 81.90 from 117.00. This is the sale
price for children under the age of 16.
Method 2 Subtract percent discount from 100%.
Children under the age of 16 pay 30% of
the regular price, $117.00.
Find 30% of 117.00. This is the sale price
for children under the age of 16.
Feedback
A
B
C
D
Correct!
Check that the price is an increase or decrease.
Find the discounted price, not the discount.
Start by determining the discount.
TOP: 2-10 Percent Increase and Decrease
110. ANS: B
A markup is a percent increase. So find $16 increased by 83%.
Find 83% of 16. This is the amount of the
markup.
Add to 16. This is the selling price.
The amount of the markup is $13.28, and the selling price is $29.28.
Feedback
A
B
C
You reversed the order of the numbers. A markup is an
amount by which a wholesale cost is increased.
Correct!
A markup is an amount by which a wholesale cost is
D
increased. It's not a discount.
To find the amount of the markup, you need to multiply the
markup percent by the wholesale amount.
TOP: 2-10 Percent Increase and Decrease
111. ANS: D
Step 1 Calculate the pre-holiday price.
Supplier’s price + markup =
The selling price before the
selling price
holidays is 325% of the supplier’s
price.
For each card, find 325% of the supplier’s price. This is the
pre-holiday price.
First card:
Second card:
Step 2 Calculate the post-holiday price.
The selling price after the holidays
is 40% of the pre-holiday price.
For each card, find 40% of the pre-holiday price. This is the
post-holiday price.
First card:
Second card:
Feedback
A
B
C
D
To find the pre-holiday price, find the markup percent of the
supplier's price and add it to the supplier's price.
To find the pre-holiday price, find the markup percent of the
supplier's price and add it to the supplier's price.
To find the post-holiday price, subtract the discount percent
from 100% and multiply the result by the pre-holiday price.
Correct!
TOP: 2-10 Percent Increase and Decrease
112. ANS: A
Divide both sides by 2.
What numbers are 7 units from 0?
Case 1:
x+7=7
Case 2: Rewrite the equation as two cases.
x + 7 = The solutions are x = 0 or x = –14.
–7
Feedback
A
B
C
D
Correct!
Divide before you add or subtract. There are two cases to
solve.
Absolute value means distance from zero. Solve the second
case when the number inside the absolute value is negative.
Divide before you add or subtract.
TOP: 2-Ext Solving Absolute-Value Equations
113. ANS: C
First, isolate the absolute value expression.
Subtract 8 from both
sides.
The absolute value expression is equal to a negative number, which is
impossible. The equation has no solution.
Feedback
A
B
C
D
An absolute value must be greater than or equal to 0.
Isolate the absolute value by subtracting the term outside
absolute value bars.
Correct!
Subtract the term outside the absolute value bars.
TOP: 2-Ext Solving Absolute-Value Equations
114. ANS: D
Test values of y that are positive, negative, and 0.
When the value of y is a number less than 4, the value of
When the value of y is 4, the value of
is equal to 10.
When the value of y is a number greater than 4, the value of
It appears that the solutions of
is less than 10.
are numbers less than 4.
is greater than 10.
Feedback
A
B
C
D
Test the value you found with the equal sign. Do you get a true statement?
Test some values and find out if you get a true statement. Then, check the inequality
symbol.
Is this the only solution? Test some more values, including fractions.
Correct!
TOP: 3-1 Graphing and Writing Inequalities
115. ANS: B
The graph should start at the given value. A > or < graph has an empty circle at that value. A or graph has a
solid circle at that value. A > or graph has an arrow to the right, and a < or graph has an arrow to the left.
Feedback
A
B
C
D
Check the direction the arrow should be pointing.
Correct!
Check the direction the arrow should be pointing.
A "greater than" or "less than" graph has an empty circle. A "greater than or equal to" or
"less than or equal to" graph has a solid circle.
TOP: 3-1 Graphing and Writing Inequalities
116. ANS: C
Use the variable m. The arrow points to the right, so use either > or ≥. The solid circle at –3 means that –3 is a
solution, so use ≥.
Feedback
A
B
C
D
The arrow should point in the same direction as the inequality symbol.
The endpoint is not a solution.
Correct!
The endpoint is not a solution.
TOP: 3-1 Graphing and Writing Inequalities
117. ANS: D
The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should
include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line.
Feedback
A
B
C
D
The number of yards must be greater than or equal to 500, not less than 500.
The number of yards must be greater than or equal to 500, not less than 500.
The number 500 should be included in the solution.
Correct!
TOP: 3-1 Graphing and Writing Inequalities
118. ANS: C
Sam has $450, but must save $180 of that for his camping trip.
If s is the amount he can spend on music, then
So,
.
s
–500
–400
–300
–200
–100
0
100
200
300
400
500
Feedback
A
B
The amount Sam can spend on music cannot be more than the amount he earned.
The amount Sam can spend on music cannot be more than what he saved after his
camping trip.
Correct!
Sam has $450, but must save $180 for his trip. The remaining amount is how much he
can spend on music.
C
D
TOP: 3-1 Graphing and Writing Inequalities
119. ANS: C
n + 6 < –1.5
–6
–6
Subtract 6 on both sides to isolate n.
n < –7.5
–10 –8
–6
–4
–2
0
2
4
6
8
10
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
Feedback
A
Use a solid circle for a "greater than or equal to" or "less than or equal to" graph. Use an
empty circle for a "greater than" or "less than" graph.
Check that the arrow is pointing in the correct direction.
Correct!
Check that you used the correct inverse operation.
B
C
D
TOP: 3-2 Solving Inequalities by Adding and Subtracting
120. ANS: C
number already downloaded
+
additional songs
≤
8
+
s
≤
Subtract 8 from both sides to undo the addition.
s
≤
weekly limit
11
3
Since you can only download whole songs, graph the nonnegative integers less than or equal to 3.
0
1
2
3
4
5
6
7
8
9
10
11
Feedback
A
B
C
D
Check the inequality symbol.
Check the graph, as it not reasonable to have a fractional number of songs.
Correct!
Check the graph, as it not reasonable to have a fractional number of songs.
TOP: 3-2 Solving Inequalities by Adding and Subtracting
121. ANS: A
Let d represent the amount of money in dollars Denise must save to reach her goal.
$365
plus
additional amount of money is at least
$635
in dollars
365
+
d
635
Since 365 is added to d, subtract 365 from both sides to undo the
addition.
365
365
Check the endpoint 270 and a number that is greater than the endpoint.
Feedback
A
B
C
D
Correct!
You should be solving an inequality, not an equation.
Subtract from both sides of the inequality.
Check the endpoint to see if you get a true statement.
TOP: 3-2 Solving Inequalities by Adding and Subtracting
122. ANS: B
Step 1: Rewrite both mixed numbers as improper fractions.
and
Step 2: Solve the inequality.
Rewrite the inequality.
Subtract
from both sides.
Rewrite the fractions with a common denominator.
2
= 55
Simplify.
Step 3: Graph the inequality.
–9
–6
–3
0
3
6
9
12
15
18
21
Feedback
A
B
C
D
To solve the inequality, subtract the first mixed number from both sides of the
inequality.
Correct!
Check the direction of the inequality.
To solve the inequality, subtract the first mixed number from both sides of the
inequality.
TOP: 3-2 Solving Inequalities by Adding and Subtracting
123. ANS: A
>3
Multiply both sides by 8 to isolate x.
> 3(8)
x > 24
0
5
10
15
20
25
30
35
40
45
50
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
Feedback
A
B
Correct!
Use a solid circle when the value is included in the graph. Use an empty circle when the
value is not included.
To solve the inequality, use multiplication to undo the division.
Check that the arrow is pointing in the correct direction.
C
D
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
124. ANS: D
2m ≤ 18
≤
Divide both sides by 2 to isolate m.
m≤9
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
–1
0
1
2
3
4
5
6
7
8
9
10
11
Feedback
A
B
C
D
Check that the arrow is pointing in the correct direction.
To solve the inequality, use division to undo the multiplication.
Use a solid circle when the value is included in the graph. Use an empty circle when the
value is not included.
Correct!
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
125. ANS: D
≤2
Multiply both sides by –4 to isolate z. When you multiply by a
negative number, reverse the inequality symbol.
≥ 2(–4)
z ≥ –8
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
–10 –8
–6
–4
–2
0
2
4
6
8
10
Feedback
A
B
C
D
When multiplying by a negative number, reverse the inequality symbol.
Check the signs.
Check the signs.
Correct!
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
126. ANS: A
2f ≥ –8
≥
Divide both sides by 2 to isolate f.
f ≥ –4
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
–10 –8
–6
–4
–2
0
2
4
6
8
10
Feedback
A
B
C
D
Correct!
When dividing by a positive number, keep the same inequality symbol. When dividing
by a negative number, reverse the inequality symbol.
Check the signs.
Check the signs.
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
127. ANS: B
Divide both sides by the ticket price. The inequality symbol does not
change.
Simplify.
5 is the largest whole number less than 5.9.
Feedback
A
B
C
D
Divide the total amount by the ticket price and round down to the nearest whole
number.
Correct!
Round down, not up, to the nearest whole number.
Divide the total amount by the ticket price and round down to the nearest whole
number.
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
128. ANS: D
2.847 is about 3, and 15.168 about 15.
With estimation,
becomes
. So, the greatest possible integer solution is 5.
Feedback
A
The solution needs to be an integer.
B
C
D
Round the numbers in the inequality to the nearest integer, and then divide.
Round the numbers in the inequality to the nearest integer, and then divide.
Correct!
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
129. ANS: B
Use inverse operations to undo the operations in the inequality one at a time.
−n – 4 < 3
n > –7
–10 –8
–6
–4
–2
0
2
4
6
8
10
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
Feedback
A
B
C
D
If you divide both sides of the inequality by a negative number, reverse the inequality
symbol. If you divide by a positive number, do not reverse the inequality symbol.
Correct!
Use inverse operations to undo the operations in the inequality one at a time.
Check your calculations when using inverse operations to isolate the variable.
TOP: 3-4 Solving Two-Step and Multi-Step Inequalities
130. ANS: C
z + 8 + 3z ≤ –4
Combine like terms.
4z + 8 ≤ –4
Subtract 8 from both sides.
4z ≤ –12
Divide both sides by 4. When you divide by a negative number,
reverse the inequality symbol. When you divide by a positive
z ≤ –3
number, keep the same inequality symbol.
–10 –8
–6
–4
–2
0
2
4
6
8
10
Use a solid circle when the value is included in the graph, such as with ≥ or ≤. Use an empty circle when the value
is not included, such as with > or <.
Feedback
A
B
C
D
If you divide both sides of the inequality by a negative number, reverse the inequality
symbol. If you divide by a positive number, keep the same inequality symbol.
Use inverse operations to isolate the variable.
Correct!
Check your calculations.
TOP: 3-4 Solving Two-Step and Multi-Step Inequalities
131. ANS: D
Let d represent the distance the family drove on the third day. The average number of miles is the sum of the miles
of each day divided by 3.
( 150
plus
190
plus
d)
divided
3
is at
180
by
least
( 150
+
190
+
d)
÷
3
180
Since
is divided by 3, multiply both sides by 3
to undo the division.
Combine like terms.
Since 340 is added to d, subtract 340 from both sides to undo
the addition.
The least number of miles the family drove on the third day is 200.
Feedback
A
B
C
D
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
Correct!
TOP: 3-4 Solving Two-Step and Multi-Step Inequalities
132. ANS: B
Subtract 3x from both sides to collect the x terms on one side of the
inequality symbol.
Divide both sides by 3.
3x < 15
x<5
–13 –12 –11 –10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Feedback
A
B
C
D
Only change < to > when you divide or multiply by a negative number.
Correct!
Check your calculations.
Check your positive and negative signs.
TOP: 3-5 Solving Inequalities with Variables on Both Sides
133. ANS: C
Science
plus
$3
per
student
is less
Center fee
than
$135
+
$3
s
<
135 + 3s < 6s
– 3s – 3s
135
< 3s
<
$12
$6
per
student
s
45 < s
If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students.
Feedback
A
B
C
D
The per-student fees need to be multiplied by the number of students.
The per-student fees need to be multiplied by the number of students.
Correct!
This is the number of students where the Dino Discovery Museum charges less.
TOP: 3-5 Solving Inequalities with Variables on Both Sides
134. ANS: B
On the left side, combine the two terms. On the right side, distribute 1.5.
≤
≤
Subtract the 1.5x from both sides of the inequality.
6
≤
Divide both sides of the inequality by
3
. Reverse the inequality symbol.
Feedback
A
B
C
D
Check your signs. When you subtract 1.5 from both sides you should have a negative
coefficient.
Correct!
Check your signs. When you subtract 1.5 from both sides you should have a negative
coefficient. When multiplying or dividing by a negative number, reverse the inequality
symbol.
Reverse the inequality symbol when multiplying or dividing both sides of an inequality
by a negative number.
TOP: 3-5 Solving Inequalities with Variables on Both Sides
135. ANS: C
When the inequality is simplified, if the result is a statement that is always true, then the solution set includes all
real numbers. If the result is a statement that is always false, then there are no solutions to the inequality.
Feedback
A
B
C
D
Check that you have simplified the inequality correctly.
Check that you have simplified the inequality correctly.
Correct!
Check whether any real number will make the inequality true or whether no real
numbers will make the inequality true.
TOP: 3-5 Solving Inequalities with Variables on Both Sides
136. ANS: D
Combine like terms.
Simplify.
Divide both sides by 0.5.
Feedback
A
B
C
D
The inequality symbol will only change if you multiply or divide by a negative number.
Combine only like terms.
When moving a term from one side of the inequality to the other side, subtract from
both sides.
Correct!
TOP: 3-5 Solving Inequalities with Variables on Both Sides
137. ANS: A
Let n represent the possible number of people in the flight.
100
is less than or equal to
n
is less than or equal to
100
n
–250
–200
–150
–100
–50
0
50
100
150
240
240
200
250
Feedback
A
B
C
D
Correct!
The phrase "at least" means the number 100 is included in the solution.
Check your inequality symbols. Is it possible for a number to be less than or equal to
100 AND greater than or equal to 240?
A compound inequality is the result of combining two simple inequalities into one
statement by the words AND or OR.
TOP: 3-6 Solving Compound Inequalities
138. ANS: C
AND
Write the compound inequality using AND.
Solve each simple inequality.
Divide to undo the multiplication.
AND
First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two graphs
overlap.
Feedback
A
B
C
D
Check the endpoints to see whether they are included in the solutions.
Check the endpoints to see whether they are included in the solutions.
Correct!
Check the inequality symbols. A number cannot be less than 1 AND greater than or
equal to 4.
TOP: 3-6 Solving Compound Inequalities
139. ANS: D
First solve each simple inequality to obtain
of the graph of
and the graph of
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
OR
. The graph of the compound inequality is the union
. Find the union by combining the two regions.
2
3
4
5
6
7
8
9
s
10
Feedback
A
B
C
D
Use a solid circle if and only if the endpoint is contained in the solution set.
Find the union of the two regions. Use a solid circle if and only if the endpoint is
contained in the solution set.
Find the union of the two regions.
Correct!
TOP: 3-6 Solving Compound Inequalities
140. ANS: C
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
x ≤ –5
The numbers to the left of –5
are shaded.
A solid circle is used.
This part of the inequality
uses ≤.
0
1
2
3
4
5
6
OR
The shaded area is not
between two numbers so
the compound inequality
uses OR.
7
8
9
10
x
x>3
The numbers to the right of 3 are
shaded.
An empty circle is used.
This part of the inequality uses >.
Feedback
A
B
C
D
The shaded portion is not between two numbers.
The shaded portion is not between two numbers.
Correct!
There is a closed dot at –5.
TOP: 3-6 Solving Compound Inequalities
141. ANS: A
Test each value to see which is a solution of
AND
.
If x = 14, then
AND
. The first inequality is false, so the compound inequality is false.
If x = 12, then
AND
. The first inequality is false, so the compound inequality is false.
If x = –6, then
AND
. The second inequality is false, so the compound inequality is false.
If x = 2, then
AND
. Both inequalities are true, so the compound inequality is true.
Feedback
A
B
C
D
Correct!
Substitute the solution into the inequalities to check that the compound inequality is
true.
Check the inequality symbols.
As the compound inequality is an "AND" statement, check that both inequalities are
true.
TOP: 3-6 Solving Compound Inequalities
142. ANS: C
Add 9 to isolate the absolute-value expression.
Think: What numbers have an absolute value less than 8?
is between –8 and 8, inclusive.
Solve the two inequalities.
Write the solution as a compound inequality.
AND
AND
–27 –24 –21 –18 –15 –12 –9
–6
–3
0
3
6
9
12
15
18
21
24
27
30
Feedback
A
B
C
D
Isolate the variable to find the solution of the original inequality.
Check the inequality symbols.
Correct!
The inequality contains an absolute-value expression, so the solution should be a
compound inequality.
TOP: 3-Ext Solving Absolute-Value Inequalities
143. ANS: D
x – 6 < –15 OR x – 6 > 15
x < – 9 OR x > 21
Add 3 to both sides to undo the subtraction and isolate the
absolute value.
Think: “What numbers have an absolute value less than –15
or greater than 15?”
Solve the two inequalities.
–26 –24 –22 –20 –18 –16 –14 –12 –10 –8
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
Feedback
A
B
C
D
First, isolate the absolute value. Then, solve two separate inequalities.
First, isolate the absolute value. Then, solve two separate inequalities.
First, isolate the absolute value. Then, solve two separate inequalities.
Correct!
TOP: 3-Ext Solving Absolute-Value Inequalities
NUMERIC RESPONSE
144. ANS:
$2430
TOP: 1-3 Multiplying and Dividing Real Numbers
145. ANS:
65
20
22
24
26
TOP: 2-3 Solving Two-Step and Multi-Step Equations
146. ANS: $31.05
147. ANS: 5
TOP: 3-3 Solving Inequalities by Multiplying and Dividing
148. ANS: 18
TOP: 3-4 Solving Two-Step and Multi-Step Inequalities
MATCHING
149.
150.
151.
152.
153.
ANS:
ANS:
ANS:
ANS:
ANS:
F
G
A
B
E
TOP:
TOP:
TOP:
TOP:
TOP:
1-1 Variables and Expressions
1-1 Variables and Expressions
1-1 Variables and Expressions
1-1 Variables and Expressions
1-1 Variables and Expressions
154.
155.
156.
157.
158.
ANS:
ANS:
ANS:
ANS:
ANS:
C
B
F
G
D
TOP:
TOP:
TOP:
TOP:
TOP:
1-2 Adding and Subtracting Real Numbers
1-2 Adding and Subtracting Real Numbers
1-3 Multiplying and Dividing Real Numbers
1-2 Adding and Subtracting Real Numbers
1-3 Multiplying and Dividing Real Numbers
159.
160.
161.
162.
163.
ANS:
ANS:
ANS:
ANS:
ANS:
G
E
D
C
F
TOP:
TOP:
TOP:
TOP:
TOP:
1-4 Powers and Exponents
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
1-4 Powers and Exponents
1-4 Powers and Exponents
164.
165.
166.
167.
168.
169.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
F
G
H
A
D
E
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
1-5 Square Roots and Real Numbers
170.
171.
172.
173.
174.
175.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
A
F
E
G
H
B
TOP:
TOP:
TOP:
TOP:
TOP:
TOP:
1-5 Square Roots and Real Numbers
1-7 Simplifying Expressions
1-7 Simplifying Expressions
1-7 Simplifying Expressions
1-6 Order of Operations
1-5 Square Roots and Real Numbers
176.
177.
178.
179.
ANS:
ANS:
ANS:
ANS:
C
E
F
G
TOP:
TOP:
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1-8 Introduction to Functions
1-8 Introduction to Functions
1-8 Introduction to Functions
1-8 Introduction to Functions
180. ANS: B
TOP: 1-8 Introduction to Functions
181.
182.
183.
184.
185.
186.
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
C
B
E
D
G
H
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1-8 Introduction to Functions
1-8 Introduction to Functions
1-8 Introduction to Functions
1-8 Introduction to Functions
1-8 Introduction to Functions
187.
188.
189.
190.
191.
192.
ANS:
ANS:
ANS:
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G
H
D
B
E
C
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2-1 Solving Equations by Adding or Subtracting
2-5 Solving for a Variable
2-4 Solving Equations with Variables on Both Sides
2-1 Solving Equations by Adding or Subtracting
2-5 Solving for a Variable
2-4 Solving Equations with Variables on Both Sides
193.
194.
195.
196.
197.
ANS:
ANS:
ANS:
ANS:
ANS:
D
F
G
A
C
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2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
198.
199.
200.
201.
202.
ANS:
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C
B
D
E
A
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2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
2-7 Applications of Proportions
2-6 Rates Ratios and Proportions
2-6 Rates Ratios and Proportions
203.
204.
205.
206.
207.
ANS:
ANS:
ANS:
ANS:
ANS:
E
B
F
G
C
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2-6 Rates Ratios and Proportions
2-7 Applications of Proportions
2-7 Applications of Proportions
2-7 Applications of Proportions
2-7 Applications of Proportions
208.
209.
210.
211.
212.
ANS:
ANS:
ANS:
ANS:
ANS:
G
B
A
D
F
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2-9 Applications of Percents
2-9 Applications of Percents
2-9 Applications of Percents
2-9 Applications of Percents
2-9 Applications of Percents
213.
214.
215.
216.
217.
218.
ANS:
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ANS:
ANS:
ANS:
D
G
H
C
F
B
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2-10 Percent Increase and Decrease
2-10 Percent Increase and Decrease
2-10 Percent Increase and Decrease
2-10 Percent Increase and Decrease
2-8 Percents
2-10 Percent Increase and Decrease
219. ANS: C
TOP: 3-6 Solving Compound Inequalities
220.
221.
222.
223.
ANS:
ANS:
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ANS:
E
B
D
A
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3-6 Solving Compound Inequalities
3-1 Graphing and Writing Inequalities
3-1 Graphing and Writing Inequalities
3-6 Solving Compound Inequalities