Math Management Software
Algebra 1
Second Edition
Texas Standards - Aligned
Library Guide
Renaissance Learning
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Welcome
Thank you for purchasing this Accelerated Math Library. Libraries include the objectives for a
specific grade level, math subject, state requirements, or textbook. Each library includes
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curriculum guidelines and the content of widely used math textbooks.
Libraries are the source of the problems that appear on the assignments and tests you print for
your classes. Within each library, closely related problems are grouped by objective. This
Library Guide includes the topics covered by the library, the objectives related to each topic,
and sample problems from each objective.
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please email us at [email protected].
Contents
Topic 1 - Numbers and Operations..................................................................1
Obj. 1 - Evaluate a numerical expression involving multiple
forms of rational numbers.......................................................................1
Obj. 2 - Simplify a complex fraction .......................................................1
Obj. 3 - Evaluate a multi-step numerical expression involving
absolute value ..........................................................................................2
Obj. 4 - Evaluate a fraction raised to an integer power ..........................3
Obj. 5 - Evaluate a numerical expression involving one
or more exponents and multiple forms of rational numbers .................3
Obj. 6 - Compare expressions involving unlike forms of
real numbers............................................................................................4
Topic 2 - Relations and Functions...................................................................6
Obj. 7 - Determine the independent or dependent variable
in a given situation ..................................................................................6
Obj. 8 - Determine if a relation is a function ..........................................7
Obj. 9 - Determine the domain or range of a function ...........................10
Obj. 10 - WP: Determine a reasonable domain or range for
a function in a given situation.................................................................11
Obj. 11 - Evaluate a function written in function notation
for a given value.......................................................................................14
Obj. 12 - Determine if a function is linear or nonlinear..........................15
Obj. 13 - Determine whether a graph or a table represents
a linear or nonlinear function .................................................................16
Obj. 14 - WP: Determine a graph that can represent a situation
involving a varying rate of change ..........................................................19
Obj. 15 - Use a scatter plot to organize data............................................21
Obj. 16 - Determine if a scatter plot shows a positive
relationship, a negative relationship, or no relationship
betweeen the variables............................................................................23
Obj. 17 - Make a prediction based on a scatter plot ................................24
Obj. 18 - Interpret the graph of a function in context.............................29
Topic 3 - Linear Equations and Inequalities ...................................................32
Obj. 19 - Simplify an algebraic expression by combining
like terms .................................................................................................32
Obj. 20 - Use the distributive property to simplify an
algebraic expression ................................................................................32
Obj. 21 - Solve a 1-variable linear equation that requires
simplification and has the variable on one side......................................32
Obj. 22 - Solve a 1-variable linear equation with the variable
on both sides............................................................................................33
Obj. 23 - WP: Determine a linear equation that can be used
to solve a percent problem ......................................................................34
Obj. 24 - Determine a linear equation in two variables
that represents a table of values..............................................................35
Obj. 25 - Determine if a table or an equation represents
a direct variation, an inverse variation, or neither .................................35
Obj. 26 - WP: Determine an equation representing a direct
variation or an inverse variation .............................................................37
Obj. 27 - WP: Solve a direct- or inverse-variation problem ...................38
Obj. 28 - Solve a 1-variable absolute value equation ..............................39
Obj. 29 - Solve a 1-variable linear inequality with the
variable on one side.................................................................................40
Obj. 30 - WP: Use a 2-step linear inequality in one variable
to represent a situation ...........................................................................41
Obj. 31 - WP: Solve a problem involving a 2-step linear
inequality in one variable ........................................................................41
Obj. 32 - Determine the graph of the solutions to a 2-step
linear inequality in one variable..............................................................42
Obj. 33 - Solve a 1-variable linear inequality with the
variable on both sides..............................................................................43
Obj. 34 - Solve a 1-variable compound inequality ..................................43
Obj. 35 - Rewrite an equation to solve for a specified
variable ....................................................................................................44
Obj. 36 - Determine the slope-intercept form or the standard
form of a linear equation.........................................................................45
Obj. 37 - Determine the slope of a line given its graph
or a graph of a line with a given slope.....................................................46
Obj. 38 - Determine the slope of a line given a table of
values .......................................................................................................47
Obj. 39 - Determine the slope of a line given two points
on the line ................................................................................................47
Obj. 40 - Determine the slope of a line given an equation
of the line .................................................................................................48
Obj. 41 - WP: Interpret the meaning of the slope of a line .....................49
Obj. 42 - Determine the x- or y-intercept of a line given
its graph ...................................................................................................51
Obj. 43 - Determine the x- or y-intercept of a line given
an equation ..............................................................................................51
Obj. 44 - Determine the x- or y- intercept of a line given
a table.......................................................................................................52
Obj. 45 - WP: Interpret the meaning of the y-intercept
of a graphed line ......................................................................................53
Obj. 46 - Determine the effect of a change in the slope
and/or y-intercept on the graph of a line................................................54
Obj. 47 - WP: Determine the effect of a change in the slope
and/or y-intercept of a line .....................................................................55
Obj. 48 - Determine the graph of a line using given information ..........58
Obj. 49 - Determine the graph of a linear equation given
in slope-intercept, point-slope, or standard form ..................................62
Obj. 50 - Determine an equation of a line given the slope
and y-intercept of the line .......................................................................66
Obj. 51 - Determine an equation that represents a graphed
line ...........................................................................................................67
Obj. 52 - Determine an equation for a line given the slope
of the line and a point on the line that is not the y-intercept .................69
Obj. 53 - Determine an equation of a line given two points
on the line ................................................................................................71
Obj. 54 - Determine if two lines are perpendicular or parallel
given the equations of the lines...............................................................72
Obj. 55 - Determine an equation for a line that goes through
a given point and is parallel or perpendicular to a given line.................73
Obj. 56 - Determine the graph of a 2-variable absolute
value equation .........................................................................................74
Obj. 57 - Solve a 2-variable linear inequality for the
dependent variable ..................................................................................77
Obj. 58 - Determine if an ordered pair is a solution to
a 2-variable linear inequality ..................................................................78
Obj. 59 - Determine the graph of a 2-variable linear inequality ............79
Obj. 60 - Determine a 2-variable linear inequality represented
by a graph ................................................................................................82
Obj. 61 - Determine the graph of the solutions to a problem
that can be described by a 2-variable linear inequality ..........................85
Obj. 62 - Solve a 1-variable absolute value inequality ............................90
Obj. 63 - Determine the graph of a 1-variable absolute
value inequality .......................................................................................91
Topic 4 - Systems of Linear Equations and Inequalities ................................95
Obj. 64 - Solve a system of linear equations in two variables
by graphing ..............................................................................................95
Obj. 65 - Solve a system of linear equations in two variables
by substitution.........................................................................................98
Obj. 66 - Solve a system of linear equations in two variables
by elimination..........................................................................................99
Obj. 67 - Determine the number of solutions to a system
of linear equations ...................................................................................99
Obj. 68 - Solve a system of linear equations in two variables
using any method ....................................................................................100
Obj. 69 - WP: Determine a system of linear equations that
represents a given situation ....................................................................102
Obj. 70 - WP: Solve a mixture problem that can be represented
by a system of linear equations ...............................................................103
Obj. 71 - WP: Solve a motion problem that can be represented
by a system of linear equations ...............................................................105
Obj. 72 - Solve a number problem that can be represented
by a linear system of equations ...............................................................106
Obj. 73 - Determine if a given ordered pair is a solution
to a system of linear inequalities.............................................................107
Obj. 74 - Determine the graph of the solution set of a
system of linear inequalities in two variables .........................................108
Obj. 75 - WP: Determine a system of linear inequalities
that represents a given situation.............................................................113
Obj. 76 - WP: Determine possible solutions to a problem
that can be represented by a system of linear inequalities.....................115
Topic 5 - Properties of Powers.........................................................................118
Obj. 77 - Determine an equivalent form of a variable expression
involving exponents.................................................................................118
Obj. 78 - Apply the product of powers property to a monomial
numerical expression ..............................................................................118
Obj. 79 - Apply the product of powers property to a monomial
algebraic expression ................................................................................119
Obj. 80 - Apply the power of a power property to a monomial
numerical expression ..............................................................................119
Obj. 81 - Apply the power of a power property to a monomial
algebraic expression ................................................................................120
Obj. 82 - Apply the power of a product property to a monomial
algebraic expression ................................................................................121
Obj. 83 - Apply the quotient of powers property to monomial
numerical expressions.............................................................................122
Obj. 84 - Apply the quotient of powers property to monomial
algebraic expressions...............................................................................122
Obj. 85 - Apply the power of a quotient property to monomial
algebraic expressions...............................................................................123
Obj. 86 - Compare monomial numerical expressions using
the properties of powers..........................................................................124
Obj. 87 - Apply properties of exponents to monomial algebraic
expressions ..............................................................................................125
Topic 6 - Polynomial Expressions...................................................................126
Obj. 88 - Apply terminology related to polynomials ..............................126
Obj. 89 - Multiply two monomial algebraic expressions........................126
Obj. 90 - Simplify a polynomial expression by combining
like terms .................................................................................................127
Obj. 91 - Add polynomial expressions.....................................................127
Obj. 92 - Subtract polynomial expressions .............................................128
Obj. 93 - Multiply a polynomial by a monomial .....................................129
Obj. 94 - Multiply two binomials of the form (x +/- a)(x
+/- b)........................................................................................................130
Obj. 95 - Multiply two binomials of the form (ax +/- b)(cx
+/- d) .......................................................................................................131
Obj. 96 - Multiply two binomials of the form (ax +/- by)(cx
+/- dy)......................................................................................................132
Obj. 97 - Square a binomial.....................................................................133
Obj. 98 - Multiply two nonlinear binomials ...........................................133
Obj. 99 - Multiply a trinomial by a binomial ..........................................134
Topic 7 - Factor Algebraic Expressions ...........................................................136
Obj. 100 - Factor the GCF from a polynomial expression ......................136
Obj. 101 - Factor trinomials that result in factors of
the form (x +/- a)(x +/- b).......................................................................137
Obj. 102 - Factor trinomials that result in factors of
the form (ax +/- b)(cx +/- d)...................................................................137
Obj. 103 - Factor trinomials that result in factors of
the form (ax +/- by)(cx +/- dy) ...............................................................138
Obj. 104 - Factor the difference of two squares ......................................139
Obj. 105 - Factor a perfect-square trinomial ..........................................140
Obj. 106 - Factor a polynomial that has a GCF and two linear
binomial factors.......................................................................................141
Topic 8 - Quadratic Equations and Functions ................................................143
Obj. 107 - Determine the graph of a given quadratic function ...............143
Obj. 108 - WP: Answer a question using the graph of a quadratic
function....................................................................................................148
Obj. 109 - WP: Determine the domain or range of a quadratic
function in a given situation....................................................................151
Obj. 110 - Determine the result of a change in a or c on
the graph of y = ax^2 + c.........................................................................154
Obj. 111 - Solve a quadratic equation by graphing the associated
quadratic function ...................................................................................155
Obj. 112 - Solve a quadratic equation by taking the square
root...........................................................................................................157
Obj. 113 - Determine the solution(s) of an equation given
in factored form .......................................................................................159
Obj. 114 - Solve a quadratic equation by factoring .................................160
Obj. 115 - Solve a quadratic equation using the quadratic
formula ....................................................................................................160
Obj. 116 - Use the discriminant to determine the number
of real solutions .......................................................................................161
Obj. 117 - WP: Use a given quadratic equation to solve
a problem.................................................................................................162
Topic 9 - Exponential Equations and Functions.............................................164
Obj. 118 - Determine the graph of an exponential function ...................164
Obj. 119 - WP: Evaluate an exponential growth or an exponential
decay function .........................................................................................169
Obj. 120 - Solve a problem involving exponential growth
or exponential decay................................................................................170
Topic 10 - Radical Expressions........................................................................172
Obj. 121 - Simplify a monomial numerical expression involving
the square root of a whole number .........................................................172
Obj. 122 - Multiply monomial numerical expressions involving
radicals.....................................................................................................172
Obj. 123 - Divide monomial numerical expressions involving
radicals.....................................................................................................173
Obj. 124 - Add and/or subtract numerical radical expressions..............173
Obj. 125 - Multiply a binomial numerical radical expression
by a numerical radical expression...........................................................174
Obj. 126 - Rationalize the denominator of a numerical radical
expression................................................................................................175
Obj. 127 - Simplify a monomial algebraic radical expression.................176
Obj. 128 - Rationalize the denominator of an algebraic
radical expression....................................................................................177
Obj. 129 - Add or subtract algebraic radical expressions .......................177
Obj. 130 - Multiply monomial algebraic radical expressions .................178
Obj. 131 - Divide monomial algebraic radical expressions .....................179
Topic 11 - Radical Equations and Functions ...................................................180
Obj. 132 - Solve a radical equation that leads to a linear
equation ...................................................................................................180
Obj. 133 - Solve a radical equation that leads to a quadratic
equation ...................................................................................................180
Obj. 134 - Determine the graph of a radical function .............................182
Obj. 135 - WP: Solve a problem involving a radical function .................185
Topic 12 - Rational Expressions ......................................................................187
Obj. 136 - Determine the excluded values of a rational
algebraic expression ................................................................................187
Obj. 137 - Simplify a rational expression involving polynomial
terms ........................................................................................................188
Obj. 138 - Multiply rational expressions.................................................188
Obj. 139 - Divide rational expressions ....................................................189
Obj. 140 - Divide a polynomial expression by a monomial ....................190
Obj. 141 - Divide a polynomial expression by a binomial .......................191
Obj. 142 - Determine the LCD of two rational expressions ....................192
Obj. 143 - Add or subtract two rational expressions with
like denominators....................................................................................193
Obj. 144 - Add or subtract two rational expressions with
unlike monomial denominators..............................................................194
Obj. 145 - Add or subtract two rational expressions with
unlike polynomial denominators ............................................................195
Topic 13 - Rational Equations and Functions .................................................197
Obj. 146 - Solve a proportion that generates a linear or
quadratic equation ..................................................................................197
Obj. 147 - Solve a rational equation involving terms with
monomial denominators.........................................................................198
Obj. 148 - Solve a rational equation involving terms with
polynomial denominators .......................................................................199
Obj. 149 - Determine the graph of a rational function ...........................200
Obj. 150 - WP: Solve a problem involving a rational equation...............205
Topic 1 - Numbers and Operations
Obj. 1 - Evaluate a numerical expression involving multiple forms of rational numbers
Evaluate (round the answer to the nearest thousandth, if necessary):
b g
5
1. 3 × – 3 + 4.7
8
2.
3.
[A] 5.325
LM6.3 − FG − 7 − 7IJ OP ÷ FG − 7 − 7IJ
N H 8 KQ H 8 K
F 1 1I
[A]
– 7G + 2 J + 4.9
H 2 4K
b g
3 1
4. 1 + 1 ÷ – 10 + 6.2
8
2
LM
N
b
1
5. 9.3 3 + 7.2 ÷ 7.2 − 7
5
FG
H
gOPQ
IJ
K
1
6. 5.2 − 8 2 + 5.6 + 5.6
4
[B] 5.825
[A] –2.2
–54.35
[C] –5.675
[B] –5.2
[B] –14.35
[D] –6.175
[C] –1.8
[C] 3.65
[D] 3.2
[D] 17.65
[A] 1.913
[B] –0.575
[C] 7.425
[D] 5.913
[A] 364.56
[B] 484.56
[C] –26.04
[D] –52.04
[A] –102
[B] –1.6
[C] –52
[D] –96.6
Obj. 2 - Simplify a complex fraction
Evaluate:
7.
1
6
2
3
[A]
8−
8.
5
8
1
3
1
4
[A] 4
[B] 3
19
24
[B] 3
11
15
1
[C] 1
2
5
[D] 1
[C] 1
11
24
[D] 12
4
15
Topic 1 - Numbers and Operations
Evaluate:
1
4
2
1−
3
[A] 1
2
3
−7
[A] − 1
1−
9.
10.
11.
12.
2
3
1
1+
2
5 2
+
8 3
3 5
+
5 6
[A]
[B]
2
3
4
9
[A] 1
1
4
[C] 2
1
4
[D] 4
2
21
[C] −
1
2
[D] −
2
3
[C]
2
3
[D] 3
9
10
[C]
155
172
[D] 2
[B] −
[B] 1
427
720
[B]
3
14
29
40
Obj. 3 - Evaluate a multi-step numerical expression involving absolute value
Evaluate:
13. 6 – 4 − 8
[A] – 16
[B] 16
[C] – 10
[D] 10
14. – 5 9 − 10 − 7
[A] – 12
[B] – 2
[C] 2
[D] 12
15. – 10 + 3 – 3 ×7
[A] – 73
[B] – 53
[C] 53
[D] 73
16. 6 – 7 − 11 + 8 2 + 12
17. – 13 − 12 4
18. – 23 – 5 + 5 – 8
[A] – 143
[A] 61
[A] – 155
[B] – 220
[B] – 137
[B] – 75
2
[C] 143
[C] – 61
[C] 155
[D] 220
[D] 137
[D] 75
Topic 1 - Numbers and Operations
Obj. 4 - Evaluate a fraction raised to an integer power
Evaluate:
19.
FG 5IJ
H 3K
20.
FG − 8IJ
H 3K
21.
FG 5IJ
H 9K
22.
FG − 6IJ
H 5K
23.
FG 1IJ
H 9K
24.
FG − 1IJ
H 3K
4
[A]
625
81
[B]
20
3
[C]
9
64
[B]
9
64
[C] −
–2
[A] −
0
[A]
1
9
3
[A] −
[B] 0
216
5
[B]
0
[A] −
1
3
216
125
[B] − 81
[B]
64
9
[C] 1
[C] −
−2
[A] 81
125
81
1
3
[C]
216
125
1
81
[C] 1
[D]
625
3
[D]
64
9
[D]
5
9
[D]
216
5
[D] −
1
9
[D] 0
Obj. 5 - Evaluate a numerical expression involving one or more exponents and multiple
forms of rational numbers
Evaluate (round the answer to the nearest thousandth, if necessary):
FG 0.6 + 1 1IJ ×b– 4g
H 8K
2
25.
–2
.
26. 15
F 3I
+G J
H 4K
3
[A] –119.4
[B] –104.44
[C] –190.44
[D] –41.4
[A] 9.926
[B] 14.75
[C] –14.25
[D] 12.926
–3
×4
3
Topic 1 - Numbers and Operations
Evaluate (round the answer to the nearest thousandth, if necessary):
27.
FG 3 3IJ
H 4K
28.
FG – 0.29 − 4 3IJ ÷ b– 5g
H
4K
29.
F 1I
– 7 + 0.21 ÷ G 2 J
H 5K
30.
FG 0.93 + 2 3IJ
H
5K
–2
×FGH 5 + 0.283 IJK
[A] 10.357
[B] 0.357
[C] 11.269
[D] 147.269
2
[A] 1.065
[B] –5.056
[C] –5.080
[D] 1.034
–4
[A] –7.382
[B] –2.081
[C] –0.081
[D] 27.618
[A] 0.010
[B] 1.458
[C] 1.454
[D] 0.006
–3
÷4
Obj. 6 - Compare expressions involving unlike forms of real numbers
31. Which statement is true?
[A] 3
–2
F 1I
<G J
H 9K
4
[B] 3
–2
F 1I
>G J
H 9K
4
–2
[C] 3
F 1I
=G J
H 9K
4
32. Which statement is true?
[A]
b– 0.3g < b– 117 g
–2
2
[B]
b– 0.3g > b– 117 g
–2
2
[C]
b– 0.3g = b– 117 g
–2
2
33. Which statement is true?
[A]
0.42 <
FG 4 IJ
H 7K
[B]
0.42 >
FG 4 IJ
H 7K
[B]
0.91 >
5
11
2
[C]
0.42 =
FG 4 IJ
H 7K
[C]
0.91 =
5
11
2
2
34. Which statement is true?
[A]
0.91 <
5
11
35. Which statement is true?
[A] 0.24 – 2 < 34
4
[B] 0.24 – 2 > 34
[C] 0.24 – 2 = 34
Topic 1 - Numbers and Operations
36. Which statement is true?
2
7
[A] 0.212 <
5
[B] 0.212 >
2
7
[C] 0.212 =
2
7
Topic 2 - Relations and Functions
Obj. 7 - Determine the independent or dependent variable in a given situation
1. Various numbers of ladybugs are placed into jars, each of which contains the same number
of aphids. Ladybugs eat aphids. The number of aphids remaining after 24 hours is measured
in each of the jars. Which phrase describes the independent variable in the experiment?
[A] the number of aphids remaining in each jar
[B] the time the ladybugs had to eat the aphids
[C] the number of ladybugs placed in each jar
[D] number of aphids originally placed in each jar
2. A botanist is experimenting to determine the best soil temperature for germinating bean
seeds. Several seeds are planted in soil kept at different temperatures and are given the same
exposure to sunlight and the same amount of water. What is the independent variable in this
situation?
[A] the height of the plants after 10 days
[B] the amount of water the seeds receive
[C] the number of seeds sprouting after 10 days
[D] the temperature of the soil
3. A baby elephant weighs 280 pounds at birth. On average the baby gains 4 pounds each day.
What is the dependent variable in this situation?
[A] the number of days since the elephant was born
[B] the weight of the baby elephant
[C] the height of the baby elephant
[D] the birth weight of the elephant
4. The owner of a small shopping mall charges a fixed monthly rent to stores in the mall as
well as a certain percentage of their gross sales. What is the dependent variable in this
situation?
[A] the size of the store
[B] the gross sales
[C] the number of customers
[D] the total charge for the month
5. A botanist is experimenting with the effect of fertilizer on the growth of corn plants. Which
phrase describes the dependent variable?
[A] the amount of fertilizer used
[B] the mass of the corn produced by the plant
[C] the amount of water given the plants
[D] the amount of sunlight the plants received
6
Topic 2 - Relations and Functions
6. The cost to rent a moving truck includes a fixed amount per day plus a fixed amount per
mile. A truck is rented for two days for a family to move to a new house. What is the
independent variable in this situation?
[A] the number of miles driven
[B] the cost per mile to rent the truck
[C] the total cost of renting the truck
[D] the number of hours required to move
Obj. 8 - Determine if a relation is a function
7. Which table represents a function?
[A]
x – 1 7 7 11
y – 2 2 6 10
[B]
x – 1 3 7 11
y – 2 2 – 2 10
[C]
x –1 3 7 –1
y – 2 2 6 10
[D]
x 11 3 7 11
y – 2 2 6 10
8. Which mapping shows a function?
[A]
3
3
3
3
[C]
[B]
Input Output
–3
1
4
7
3
3
3
[D]
Input Output
3
Input Output
–3
1
4
7
Input Output
–3
1
4
7
7
–3
1
4
7
3
Topic 2 - Relations and Functions
9. Which graph represents a function?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
10. Which change, if applied to the values in the table, would make the relation a function?
x –8 –8 –4 –2
y – 24 – 18 – 12 – 6
b
Change b – 4,
g b
g
– 12g to b – 4, – 4g .
b
g b
g
Change b – 2, – 6g to b – 2, – 24g .
[A] Change – 8, – 24 to – 8, – 13 .
[B] Change – 8, – 18 to – 6, – 18 .
[C]
[D]
8
Topic 2 - Relations and Functions
11. Which change in the mapping would make the relation a function?
Input
Output
–9
–4
2
5
2
7
6
9
[A] Change – 9 → – 4 to – 9 → 9.
[B] Change 6 → 9 to 7 → 10.
[C] Change 2 → 5 to 2 → 4.
[D] Change 2 → 7 to – 2 → 7.
12. Which graph represents a function?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
9
Topic 2 - Relations and Functions
Obj. 9 - Determine the domain or range of a function
bg
l0, 16, 32q
13. What is the domain of the function f x =
[A]
l5, 6, 7q
[B]
l
q
1
x + 4 when the range is 4, 8, 12 ?
4
[C]
l32, 48, 64q
[D]
l20, 36, 52q
14. What is the range of the function shown in the graph?
y
10
10 x
–10
–10
[A] – 4 < y < 4
[B] y ≥ –4
[C] y ≥ 4
[D] all real numbers
15. What is the domain of the function shown in the graph?
y
10
10 x
–10
–10
[A] 0 < x < 5
[B] – 5 < x < 5
[C] positive real numbers
[D] all real numbers
16. What is the domain of the function y = − 6 x − 5 when the range is – 11 ≤ y ≤ 19?
[A] – 114 ≤ x ≤ 66
[B] – 6 ≤ x ≤ 24
[C] – 4 ≤ x ≤ 1
10
[D] – 119 ≤ x ≤ 61
Topic 2 - Relations and Functions
17. What is the range of the function y = x 3 + 5 when the domain is 4 ≤ x ≤ 6?
[A] 59 ≤ y ≤ 211
[B] 64 ≤ y ≤ 216
[C] 17 ≤ y ≤ 23
[D] 69 ≤ y ≤ 221
18. What is the range of the function shown in the graph?
y
10
10 x
–10
–10
[A] y ≥ 1
[B] y ≤ 1
[C] – 4 < y < 3
[D] all real numbers
Obj. 10 - WP: Determine a reasonable domain or range for a function in a given situation
19. A theater’s maximum capacity is 425 people. The cost of admission to a play at the theater
is $29. The revenue function R = 29 n, in which n is the number of tickets sold, represents
the amount of income from admissions for one performance. What values of n represent a
reasonable domain for the revenue function in this situation?
[A] any real number such that 0 ≤ n ≤ 425
[B] any whole number such that 0 ≤ n ≤ 12,325
[C] any whole number such that 0 ≤ n ≤ 425
11
[D] any real number
Topic 2 - Relations and Functions
20. A telephone company charges $0.10 per minute for a long-distance phone call. Customers
are charged in 1-minute increments. The graph shows a function that can be used to find C,
the total cost in dollars of a long-distance phone call that lasts t seconds.
C
1.00
t
10
0
Which statement represents a reasonable range for the cost of a telephone call in this
situation?
[A] C is any whole number multiple of $0.10.
[B] C is any integer multiple of $0.10.
[C] C is any whole number of cents.
[D] C is any real number.
21. An egg is dropped from a height of 60 feet. The function h = −16t 2 + 60 can be used to find
h, the egg’s height in feet after t seconds. The graph of the function is shown below.
h
100
0
1
2
3
t
Which values of h represent a reasonable range for the function in this situation?
[A] h ≤ 60
[B] 0 ≤ h ≤ 60
[C] h ≤ 19
.
12
[D] any real number
Topic 2 - Relations and Functions
22. A ball is thrown upward at the rate of 115 feet per second from a height of 6 feet. The
function h t = −16t 2 + 115 t + 6 represents the ball’s height at t seconds. The graph shows
the function.
bg
h
300
0
10
t
Which values of t represent a reasonable domain for the function in this situation?
[A] 0 ≤ t ≤ 7.2
[C] t ≥ 0
[B] 6 ≤ t ≤ 213
[D] any real number
23. A store that is open 6 days per week pays part-time employees $8.50 per hour. Part-time
employees are allowed to work no more than 6 hours per day. A part-time employee’s
weekly wages can be found using the function w h = 8.50 h, in which h is the number of
hours worked. Which values of h represent a reasonable domain for the wage function in
this situation?
bg
[A] 0 ≤ h ≤ 36
[B] 0 ≤ h ≤ 6
[C] h ≥ 0
13
[D] 0 ≤ h ≤ 306
Topic 2 - Relations and Functions
24. A parking garage charges a flat rate of $14 per day for parking. The garage is open 5 a.m. to
midnight. The graph represents the function that may be used to find the cost of parking.
Cost ($)
20
10
5
Time (hours)
10
Which solution set represents a reasonable range for the function in this situation?
[A] 0 ≤ C ≤ 14
[B] 0 < t ≤ 19
[C]
l14q
[D] any real number
Obj. 11 - Evaluate a function written in function notation for a given value
bg
25. Evaluate f x = 2 x 2 when x = – 2.
[A] – 8
bg
x
when x = – 9.
x+4
bg
21
when x = 7.
x2
26. Evaluate f x =
27. Evaluate f x =
b g
bg b g
b g
bg
b g
bg
[A]
28. Find f – 3 when f x = x + 1 − 1.
29. Find f 10 when f x =
48
.
x−6
30. Find f – 4 when f x = 2 x .
2
[B] 16
[A] −
1
5
3
7
[B]
[B]
[A] – 5
[A] 3
[A] – 8
14
9
4
3
2
[C]
[C]
[B] 8
[B] 12
[B]
[C] – 4
1
8
7
3
[C] 3
[C]
[C]
1
16
1
12
9
5
[D] 8
[D] −
[D] 3
[D] 4
[D]
1
3
[D] 16
9
4
Topic 2 - Relations and Functions
Obj. 12 - Determine if a function is linear or nonlinear
31. Which function is linear?
[A] y =
3 5
−
5 x
[B] y =
3
x +5
[C] y =
7
x
1
x+7
[C] y =
7
x
x–6
5
[C] y =
5
x–6
[D] y =
x
7
32. Which function is linear?
[A] y = 7 x
[B] y =
[D] y = x 7
33. Which function is nonlinear?
[A] y = 5 x – 6
[B] y =
[D] y = x − – 5
34. Which function is linear?
[A] y = x + 3
[B] y = – 8 x + 3
[C] y =
–8
x+3
[D] y = – 8 x – 3
35. Which function is nonlinear?
[A] y =
x3
11
[B] y = x + 11
[C] y = 11x
[D] y =
x
11
[D] y =
x−7
2
36. Which function is nonlinear?
[A] y =
1 x
−
2 7
[B] y = −
x
7
[C] y =
15
2
x−7
Topic 2 - Relations and Functions
Obj. 13 - Determine whether a graph or a table represents a linear or nonlinear function
37. Which graph shows a linear function?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
10 x
–10
–10
[D]
y
10
10 x
–10
y
10
10 x
–10
–10
–10
38. Which table represents a linear function?
[A]
x
f x
2
–4
2
–5
2
–6
2
–7
[B]
x
f x
–4
2
–5
4
–6
8
–7
16
[C]
x
f x
–4
16
–5
25
–6
36
–7
49
[D]
x
f x
–4
2
–5
2
–6
2
–7
2
bg
bg
16
bg
bg
Topic 2 - Relations and Functions
39. Which graph shows a nonlinear function?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
10 x
–10
–10
[D]
y
10
10 x
–10
y
10
10 x
–10
–10
–10
40. Which table represents a linear function?
[A]
x
f x
–3
9
–4
16
–5
25
–6
36
[B]
x
f x
–3
3
–4
7
–5
11
–6
15
[C]
x
f x
–3
3
–4
7
–5
11
–3
15
[D]
x
f x
–3
3
–4
16
–5
64
–6
256
bg
bg
17
bg
bg
Topic 2 - Relations and Functions
41. Which graph shows a nonlinear function?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
10 x
–10
–10
[D]
y
10
10 x
–10
y
10
10 x
–10
–10
–10
42. Which table represents a nonlinear function?
[A]
x
f x
1
–2
–1
–5
–3
–8
–5
– 11
[B]
x
f x
1
1
–1
1
–3
3
–5
5
[C]
x
f x
1
8
–1
–2
–3
– 12
–5
– 22
[D]
x
f x
1
1
–1
1
–3
3
–1
5
bg
bg
18
bg
bg
Topic 2 - Relations and Functions
Obj. 14 - WP: Determine a graph that can represent a situation involving a varying rate of
change
43. Courtney was writing a report on the storage of nuclear waste. She found that thorium-230
decays to half its original mass in 75,400 years. It then decays to half of that amount in
another 75,400 years and to half of that amount in another 75,400 years. The decay goes on
continuously in this manner. Courtney created a graph to show how the amount of thorium230 changes over time. Which of these could be her graph?
[A]
[B]
[C]
[D]
44. On a farm, a grain storage bin is slowly filled with corn. After the bin is full, some of the
corn is dumped into a truck to take it to the market. Which graph represents the volume of
the corn in the bin?
19
Topic 2 - Relations and Functions
[A]
[B]
[C]
[D]
(44.)
20
Topic 2 - Relations and Functions
Obj. 15 - Use a scatter plot to organize data
45. The weather bureau measured wind speed every 5 minutes during a storm. The
measurements are shown below.
Time (min)
0 5 10 15 20 25
Wind Speed (mph) 51 55 48 44 44 40
Which scatter plot best represents the data?
Storm Wind Speed
[A]
Storm Wind Speed
[B]
60
60
55
55
50
50
45
45
40
40
35
35
30
0
5
10 15 20
Time (min)
30
25
Storm Wind Speed
[C]
60
55
55
50
50
45
45
40
40
35
35
0
5
10 15 20
Time (min)
30
25
5
10 15 20
Time (min)
25
Storm Wind Speed
[D]
60
30
0
0
5
10 15 20
Time (min)
25
46. The coach at Summerville Middle School recorded the number of students who entered the
1500-meter race for the last eight years.
Year
2000 2001 2002 2003 2004 2005 2006 2007
Number of Entrants 32
39
37
38
33
36
34
33
Which scatter plot best represents the data?
21
Topic 2 - Relations and Functions
1500-Meter Race Entrants
[A]
45
40
35
30
2000
2002
2004
Year
2006
1500-Meter Race Entrants
[B]
45
40
35
30
2000
2002
2004
Year
2006
1500-Meter Race Entrants
[C]
45
40
35
30
2000
2002
2004
Year
2006
1500-Meter Race Entrants
[D]
45
40
35
30
2000
2002
2004
Year
2006
(46.)
22
Topic 2 - Relations and Functions
Obj. 16 - Determine if a scatter plot shows a positive relationship, a negative relationship,
or no relationship between the variables
47. Does the scatter plot show a positive relationship, a negative relationship, or no relationship
between the variables?
y
x
[A] positive relationship
[B] negative relationship
[C] no relationship
48. Does the scatter plot show a positive relationship, a negative relationship, or no relationship
between the variables?
y
x
[A] positive relationship
[B] negative relationship
23
[C] no relationship
Topic 2 - Relations and Functions
Obj. 17 - Make a prediction based on a scatter plot
49. In a study, the weights and the lengths from nose to tail of 8 female cheetahs were recorded
and graphed on a scatter plot. Which is the most reasonable prediction for the weight of a
female cheetah that is 6 feet long?
Length and Weight of Female Cheetahs
112
108
104
100
96
92
88
84
80
76
4.6
[A] 100 lb
4.8
5.0
5.2 5.4 5.6
Length (ft)
5.8
[B] 95 lb
6.0
[C] 110 lb
24
[D] 120 lb
Topic 2 - Relations and Functions
50. A study was made of the math scores of high school seniors in various states on a college
entrance exam. The average math scores were compared to the percent of seniors in the state
who took the exam. The results for 10 states are shown in the scatter plot. Using this data,
which math score is the most reasonable prediction if 42% of the students took the exam?
Math Scores on College Entrance Exam
525
520
515
510
505
500
495
490
485
480
475
470
465
460
455
450
445
440
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41
Percent of Students Taking Exam
[A] 420
[B] 435
[C] 480
25
[D] 450
Topic 2 - Relations and Functions
51. A nutritionist did a study comparing the fat content to the calories in fast-food chicken
sandwiches. The scatter plot shows the grams of fat and calories for 10 chicken sandwiches.
Using this data, which is a reasonable prediction for the grams of fat in a chicken sandwich
that contains 400 calories?
Calories and Fat Content of Chicken Sandwiches
34
32
30
28
26
24
22
20
18
16
360 400 440 480 520 560 600 640 680
Calories
[A] 24
[B] 19
[C] 27
26
[D] 15
Topic 2 - Relations and Functions
52. A study was made comparing a student’s grade point average to the amount of time the
student spent watching television each week. The results are plotted in the scatter plot
below. Using this data, which is the most reasonable prediction of the number of hours of
television watched per week for a student whose grade point average is 3.2?
Grade Point Average Versus TV Time
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2
[A] 9 hr
6
10
14 18 22
Time (hr)
26
30
[B] 16 hr
[C] 13 hr
27
[D] 6 hr
Topic 2 - Relations and Functions
53. For the first 36 weeks after birth a Newfoundland puppy grows at a fairly regular rate. The
weight of a Newfoundland puppy was charted every two weeks until age 24 weeks. That
data was recorded on the scatter plot below. Using this data, which is the most reasonable
prediction of the age of the puppy when it weighs 80 pounds?
Weight Versus Age in a Newfoundland Puppy
80
70
60
50
40
30
20
10
0
2 4 6 8 10 12 14 16 18 20 22 24
Age (wk)
[A] 36 wk
[B] 32 wk
[C] 28 wk
[D] 25 wk
54. The scatter plot shows the monthly commissions earned by a furniture salesperson for the
first seven months one year. Using this data, which is the most reasonable prediction for the
commission the salesperson will earn in August?
Sales Commission
3750
3500
3250
3000
2750
2500
2250
Jan
Feb
Mar Apr May Jun
Jul
Aug
Month
[A] $2750
[B] $3250
[C] $3500
28
[D] $3200
Topic 2 - Relations and Functions
Obj. 18 - Interpret the graph of a function in context
55. The graph shows water consumption for one year. Which explanation best describes what
happened throughout the year?
[A] Water consumption was lowest at the beginning of the year during winter.
Consumption increased slowly through spring and summer. In the autumn, it decreased
as winter approached.
[B] Water consumption increased rapidly through the winter and slowly through spring and
summer. In the autumn, it decreased rapidly as winter approached.
[C] Water consumption was highest at the beginning of the year during winter.
Consumption decreased through the spring, then increased during the summer. In the
autumn, it decreased rapidly as winter approached.
[D] Water consumption was low at the beginning of the year during winter. Consumption
slowly decreased during spring and increased rapidly throughout the summer. At the
start of autumn, consumption decreased rapidly.
29
Topic 2 - Relations and Functions
56. Jahan is performing an experiment involving adding frozen corn to a pot of boiling water on
the stove. If the heat from the burner is kept at the same temperature throughout the
experiment, which graph best illustrates what happens to the temperature of the water after
the frozen corn is added?
[A]
[B]
[C]
[D]
30
Topic 2 - Relations and Functions
57. The graph below shows the passenger usage of a public transportation system during one
day last week. Which statement best describes what happened throughout the day?
[A] Passenger usage increased throughout the day.
[B] Passenger usage was highest at noon.
[C] Passenger usage was highest during the morning and evening when people were going
to and coming from work.
[D] Passenger usage was highest in the morning.
31
Topic 3 - Linear Equations and Inequalities
Obj. 19 - Simplify an algebraic expression by combining like terms
Simplify:
1. 9 x + 4 x − 7 x + 5 + 7
[A] − 2 x − 2
[B] 6 x + 12
[C] 11x − 2
[D] 11x + 7
[C] 11x + 5 y − 2
[D] 3x − 5 y − 2
2. 11y − 6 y + 4 − 6 + 7 x + 4 x
[B] 11x − 5 y + 2
[A] 3x + 5 y + 2
Obj. 20 - Use the distributive property to simplify an algebraic expression
Simplify:
b
g
[A] − 6 x − 2
3. – 10 4 x + 8
b
g
4. 12 x − 3 3x + 5
[B] − 40 x − 80
[A] 3x − 15
[C] − 6 x + 8
[C] 12 x − 15
[B] 12 x + 2
[D] − 40 x + 8
[D] 3x + 5
Obj. 21 - Solve a 1-variable linear equation that requires simplification and has the
variable on one side
Solve:
5. 7 x − 11 − 5x − 17 = 4
b
[A] x = −16
[B] x = −12
[C] x = 16
[D] x = 12
g
6. – 5 – 3x − 4 + 3x + 2 = – 4
[A] x = −
b
7
9
g
7. – 4 3x − 6 = – 13
b
[B] x =
13
9
[A] x = −
[C] x = −
11
12
[B] x =
13
9
37
12
[C] x =
[D] x =
11
12
7
9
[D] x = −
g
8. 6 6 x − 3 + 3x = – 4
[A] x = −
14
39
[B] x = −
22
39
[C] x =
32
14
39
[D] x =
22
39
37
12
Topic 3 - Linear Equations and Inequalities
Solve:
[A] x =
9. – 9 x + 9 + 11x = 6
b
15
2
[B] x = −
3
2
[C] x =
3
2
[D] x = −
15
2
g
10. – 6 + 2 – 7 x + 3 = 5
[A] x =
1
2
[B] x = −
1
2
[C] x =
5
14
[D] x = −
5
14
Obj. 22 - Solve a 1-variable linear equation with the variable on both sides
Solve:
11. – 5x − 7 = – 6 x − 1
b
[A] x = 6
g
[A] x =
12. 5 3x + 6 = 4 x + 3
13. – 7 x − 3 + 8 x = – 8 x − 9
b
[B] x = −
15
11
[B] x =
[A] x = −
6
7
6
5
[C] x =
27
11
[C] x = −
[B] x = −6
6
5
[D] x = −6
27
11
[C] x =
[D] x = −
2
3
[D] x = −
g
14. – 4 – 5x − 7 = – 3x
[A] x = −
28
17
[A] x = −
15. 4 x = 3x + 5
b
[B] x = −
28
23
5
7
[C] x =
[B] x = −5
28
17
[C] x = 5
[D] x =
28
23
[D] x =
g
16. – 6 – 5x + 4 − 5x = 4 x
[A] x = −
8
7
[B] x =
24
29
[C] x =
33
8
7
15
11
[D] x = −
24
29
5
7
2
3
Topic 3 - Linear Equations and Inequalities
Obj. 23 - WP: Determine a linear equation that can be used to solve a percent problem
17. Mr. Cohen purchased a used car for $4800. In one year, the car’s value depreciated by
$800. Which equation can be used to find p, the percent the car’s value depreciated in one
year?
FG p IJ = 800
H 100K
F p IJ = 4800
800G
H 100K
[A] 100 p =
4000
4800
[B] 4800
[C] 100 p =
800
4800
[D]
18. An art gallery receives a commission of 15% for each piece of artwork sold. If the art
gallery received a commission of $51 for selling a painting, which equation could be used
to find p, the amount the painting sold for?
[A] 51 p = 015
.
[B]
p
= 015
.
51
[C] 015
. p = 51
[D] 015
. + p = 51
19. A shopper paid $90 for a coat during a sale. The coat was priced at 75% of its original
price. Which equation can be used to find x, the original price of the coat?
[A]
x
= 0.75
90
[C] x − 0.75 = 90
[B] 90 x = 0.75
[D] 0.75x = 90
20. Eve’s bill for dinner at a restaurant was $18.35. She left a total of $21, including a tip.
Which equation can be used to find p, the percent Eve left for the tip?
[A] 18.35 p =
[C] 18.35 ×
21
100
FG 1+ p IJ = 21
H 100 K
F p IJ = 21
18.35G1 +
H 100K
[B] 18.35
p
= 21
100
[D]
34
Topic 3 - Linear Equations and Inequalities
21. Alexandra’s weekly wage is $564. Each week, Alexandra puts $50 into a savings account.
Which equation can be used to find what percentage, p, of her wage Alexandra saves each
week?
[A]
p
= 50 × 100
564
[B]
b50 × 100g + p = 564
p
= 50
100
[D]
b50 × 100g p = 564
[C] 564 ×
22. An electronics store sells a DVD player for 40% above its wholesale price. Which equation
can be used to find the wholesale price, w, of a DVD player that the store sells for $239?
[A] w + 0.4 w = 239
[B] 0.4 w = 239
[C]
w
= 0.4
239
[D] w − 0.4 w = 239
Obj. 24 - Determine a linear equation in two variables that represents a table of values
23. Which equation generates the values in the table?
x
y
– 3 –1
0
6
1
3
5
12
18
24
[A] y = 3x − 9
[B] y = 3x − 29
[C] y = 3x + 9
[D] y = 3x + 19
24. Which equation generates the values in the table?
x
–3
–1
1
3
5
y
25
9
– 7 – 23 – 39
[A] y = − 8 x − 1
[B] y = − 8 x − 44
[C] y = − 8 x + 34
[D] y = − 8 x + 1
Obj. 25 - Determine if a table or an equation represents a direct variation, an inverse
variation, or neither
25. Does the equation represent a direct variation, an inverse variation, or neither?
7
y=
3x
[A] direct variation
[B] inverse variation
35
[C] neither
Topic 3 - Linear Equations and Inequalities
26. Does the relationship between x and y shown in the table represent a direct variation, an
inverse variation, or neither?
x 4 20 44 200
y 1 5 11 50
[A] direct variation
[B] inverse variation
[C] neither
27. Does the relationship between x and y shown in the table represent a direct variation, an
inverse variation, or neither?
x 60 48 30 20
y 2 2.5 4 6
[A] direct variation
[B] inverse variation
[C] neither
28. Does the equation represent a direct variation, an inverse variation, or neither?
x
y=−
5
[A] direct variation
[B] inverse variation
[C] neither
29. Does the equation represent a direct variation, an inverse variation, or neither?
5
y = −2
x
[A] direct variation
[B] inverse variation
[C] neither
30. Does the relationship between x and y shown in the table represent a direct variation, an
inverse variation, or neither?
x 14 30 42 58
y 2 6 9 13
[A] direct variation
[B] inverse variation
36
[C] neither
Topic 3 - Linear Equations and Inequalities
Obj. 26 - WP: Determine an equation representing a direct variation or an inverse
variation
31. The total labor fee, t, that a tiler charges is proportional to the number of hours worked.
The tiler charges $390 for a job that takes 6 hours and $260 for a job that takes 4 hours. If
h represents the number of hours worked, which equation can be used to represent this
situation?
[A] t =
65
h
[B] h = 65t
[C] t = 65h
[D] h = t + 65
32. Natalie is completing a science fair project on water conservation by filling a bucket with
water from one of her house’s downspouts. During a rainstorm, at a flow rate of
0.05 liter per second, the bucket is filled in 400 seconds. During the next rain, the flow rate
is 0.4 liter per second, and the bucket is filled in 50 seconds. Which equation represents the
relationship between the flow rate, f, and the time, t, it takes to fill the bucket?
[A] t =
20
f
[B] t = 125 f
[C] t = 20 f
[D] t =
f
125
33. Crystal’s family is planning a trip to her grandmother’s house. Crystal calculated that the
trip will take 5 hours if they drive 55 miles per hour or 5.5 hours if they drive
50 miles per hour. Which equation shows the relationship between time, t, and speed, s?
[A] t = 275s
[B] t =
275
s
[C] s = 275t
[D] 275 − s = t
34. For a science project, Leah made two models of household light circuits. She used
identical miniature lightbulbs in each circuit. The first circuit had 4 lightbulbs and drew a
maximum current of 1.6 amps when all the bulbs were on. The second circuit had
6 lightbulbs and drew a maximum current of 2.4 amps when all the bulbs were on. If n is
the number of lightbulbs in a circuit, which equation represents I, the maximum current in
the circuit?
[A] I =
6
n
[B] I =
2
5n
[C] I = 0.4n
37
[D] I = 6.4n
Topic 3 - Linear Equations and Inequalities
35. Adrian is charged a set fee for each text message he sends from his cell phone. In April,
Adrian sent 379 messages and was charged $37.90. In May, he sent 168 messages and was
charged $16.80. Which equation shows the relationship between the number of text
messages sent, n, and the total monthly cost for text messaging, c?
[A] n = 010
. c
[B] c = 010
. n
[C] c =
0.10
n
[D] c = n + 010
.
36. In a machine, a gear that has a diameter of 9 inches requires a force of 36 pounds to make
it rotate at a constant rate. When the machine is redesigned, the gear is replaced by a gear
that has a diameter of 15 inches. The new gear requires a force of 21.6 pounds to make it
rotate at the same rate as the original gear. Which equation describes the relationship
between d, the diameter of a gear in inches, and f, the force required to rotate the gear at a
constant rate?
[A] f = 324d
[B]
f = 6d
[C]
f =
324
d
[D] f =
6
d
Obj. 27 - WP: Solve a direct- or inverse-variation problem
37. Isabella is charged a late fee of $1.50 for returning a CD 6 days late to the library. The late
fee is directly proportional to the number of days the CD is late. How much would Isabella
be charged for returning a CD 10 days late?
[A] $2.50
[B] $15.00
[C] $0.25
[D] $0.90
38. The cost per person for renting a bus varies inversely with the number of people renting the
bus. It costs $34 per person if 40 people rent the bus. To the nearest cent, how much will it
cost per person if 26 people rent the bus?
[A] $30.59
[B] $22.10
[C] $52.31
[D] $34.02
39. The time it takes Abbey to ride her bike to work varies inversely with her average speed. If
Abbey rides at an average speed of 11 miles per hour, it takes her 25 minutes to ride to
work. If Abbey wants to get to work in 21 minutes, what will her average speed (to the
nearest tenth) need to be?
[A] 13.1 mph
[B] 12.2 mph
[C] 15.0 mph
38
[D] 9.2 mph
Topic 3 - Linear Equations and Inequalities
40. The increase in the water pressure on a scuba diver in a lake varies directly with the depth
of the diver. When a diver is at a depth of 35 feet, the pressure is 15.05 pounds per square
inch (psi) greater than at the surface of the water. How much greater is the water pressure
at a depth of 95 feet than it is at the surface of the lake?
[A] 75.05 psi
[B] 40.85 psi
[C] 25.80 psi
[D] 30.64 psi
41. The total cost of peanuts bought from a bulk-foods bin is directly proportional to the
number of ounces purchased. Yumi can buy 16 ounces of peanuts for $9.60. What is the
greatest amount of peanuts Yumi can buy for $12?
[A] 20.0 oz
[B] 18.4 oz
[C] 12.7 oz
[D] 18.8 oz
42. At a handmade-furniture shop, the time that it takes to build a dresser is inversely
proportional to the number of people assigned to the task. If it takes 5 people 8 hours to
build a dresser, how long would it take 3 people to build the same kind of dresser?
[A] 9.9 hr
[B] 1.9 hr
[C] 13.3 hr
[D] 7.4 hr
Obj. 28 - Solve a 1-variable absolute value equation
Solve:
43. 5 = 4 x + 3
[A] x =
44.
1
or x = 2
2
[B] x =
1
or x = − 2
2
[C] x = −
1
or x = −2
2
[D] no solution
– 5x + 6 + 7 = 12
[A] x =
1
11
or x =
5
5
[B] x = −
1
11
or x =
5
5
[C] x =
1
11
or x = −
5
5
[D] no solution
45. 3 2 x − 4 = 2
[A] x = −
7
5
or x =
3
3
[B] x =
7
5
or x = −
3
3
39
[C] x =
7
5
or x =
3
3
[D] no solution
Topic 3 - Linear Equations and Inequalities
Solve:
– 3x − 15 = 11
46.
[A] x = −
26
4
or x =
3
3
[B] x =
26
4
or x = −
3
3
[C] x = −
26
4
or x = −
3
3
[D] no solution
47. 7 = – 9 x − 6 − 8
[A] x = −
7
or x = −1
3
[B] x =
7
or x = 1
3
[C] x = −
7
or x = 1
3
[D] no solution
48. −9 6 x − 9 = 9
[A] x = −
[C] x =
25
29
or x =
18
18
[B] x =
25
29
or x = −
18
18
25
29
or x =
18
18
[D] no solution
Obj. 29 - Solve a 1-variable linear inequality with the variable on one side
Solve:
49. −
x
−6≥3
8
[A] x ≤ –72
50. 4 x + 2 − 7 x + 5 < – 14
b
g
51. 3 – 5x − 20 > – 15
52. 29 ≤ 4 x + 4 + 9 x + 6
[B] x ≥ 24
[A] x >
[A] x < −3
[A] x ≤
7
3
[C] x ≥ –72
[B] x > 7
[B] x > −3
19
13
40
[B] x ≤ 3
[C] x < 7
[C] x < 5
[C] x ≥ 3
[D] x ≤ 24
[D] x <
7
3
[D] x > 5
[D] x ≥
19
13
Topic 3 - Linear Equations and Inequalities
Solve:
b
g
53. – 26 ≥ 6 – 7 − x + x
[A] x ≥ −
16
5
b
g
54. 72 < – 4 – 18 x + 3
[B] x ≤ −
16
5
[A] x <
5
6
[C] x ≤
[B] x >
7
6
68
5
[D] x ≥
[C] x >
5
6
68
5
[D] x <
7
6
Obj. 30 - WP: Use a 2-step linear inequality in one variable to represent a situation
55. A fencing company wants to have at least 150 of a frequently used type of fence post on
hand at all times. Each fence post costs the company $4.50. After completing a fencing
project the company has 86 fence posts in stock. Which inequality can be used to
determine how much the company might spend, S, to restock the fence posts?
b
g
b
[A] 4.5 S − 86 ≥ 150
[C]
g
[B] 4.5 S − 150 ≥ 86
S
+ 86 ≥ 150
4.5
[D]
S
+ 4.5 ≥ 150
86
56. A project may use at most 36 hours of employee time. The 6 employees working on the
project have already used 11 of the 36 hours. Which inequality can be used to determine h,
the number of hours each of the 6 employees may spend on the remainder of the project if
they each work the same number of hours?
[A] h + 11 ≤ 36
[B] 6h + 11 ≤ 36
[C] 11h + 6 ≤ 36
[D] 6h − 11 ≤ 36
Obj. 31 - WP: Solve a problem involving a 2-step linear inequality in one variable
57. A businessperson is given approval to spend an average of $18 per meal for the
7 meals she will have while traveling on company business. For the first 6 meals she has
115 + x
spent a total of $115. Solve the inequality
≤ 18 to find x, the amount she may
7
spend on her next meal and still remain within the given budget.
[A] x ≥ $12
[B] x ≥ $11
[C] x ≤ $11
41
[D] x ≤ $12
Topic 3 - Linear Equations and Inequalities
58. A radio station disc jockey is asking for donation pledges. The goal for the first hour of the
pledge drive is to receive at least $800 in pledges. By the middle of the hour, $200 has
been pledged. The station decides to offer a free CD as an incentive to anyone who pledges
$40 during the remainder of the hour. Solve the inequality 40n + 200 ≥ 800 for n, the
number of $40 pledges that will allow the station to meet its goal for the first hour of the
pledge drive.
[A] n ≤ 15
[B] n ≥ 15
[C] n ≥ 14
[D] n ≤ 14
Obj. 32 - Determine the graph of the solutions to a 2-step linear inequality in one variable
b
g
59. Which number line shows the solution of – 52 > –4 x + 17 ?
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
b
g
60. Which number line shows the solution of – 3 x + 13 < –63?
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
42
Topic 3 - Linear Equations and Inequalities
Obj. 33 - Solve a 1-variable linear inequality with the variable on both sides
Solve:
61. 12 x − 12 ≥ 7 x
b
x≥2
[A]
2
5
[B] x ≥
12
19
[C] x ≤ 2
2
5
[D] x ≤
12
19
g
62. – 4 5x + 6 < – 2 x + 6
[A] x > − 1
b
4
11
g
[B] x < − 1
b
4
11
[C] x < −
5
3
[D] x > −
5
3
g
63. 3 11x + 1 ≤ – 2 12 x + 5
[A] x ≤ −
13
57
[B] x ≥ −
13
57
[A] x <
24
37
64. 18 x − 20 > 19 x + 4
b
[C] x ≤ − 1
[B] x < − 24
4
9
[C] x >
[D] x ≥ − 1
24
37
4
9
[D] x > − 24
g
65. 5 4 x + 4 + 4 < – 3x + 6
[A] x > −
18
23
[B] x > 1
b
66. – 16 + x ≥ 7 − 2 – 9 x − 17
[A] x ≥ 3
13
17
[C] x < 1
13
17
[D] x < −
18
23
g
[B] x ≥ − 3
6
17
[C] x ≤ 3
[D] x ≤ − 3
6
17
Obj. 34 - Solve a 1-variable compound inequality
Solve:
67. x − 10 > – 9 or x + 8 < – 15
[A] – 23 < x < 1
[B] x < –23 or x > 1
43
[C] x < – 23
[D] all real numbers
Topic 3 - Linear Equations and Inequalities
Solve:
68. – 12 < – 3x + 15 < 9
[A] 2 < x < 9
b g
[B] x > 9 or x < 2
[C] 3 < x < 24
[D] x < – 24 or x > – 3
b g
69. – 4 x + 9 > 4 or – 6 x − 6 < – 12
[A] – 10 < x < 8
[B] x < 8
[C] x < –10 or x > 8
[D] all real numbers
b g
70. – 2 < – 2 x – 6 < 8
[A] x < – 20 or x > – 10
[B] 10 < x < 20
[C] x > 7 or x < 2
[D] 2 < x < 7
71. 2 x − 14 > – 12 or 7 x + 12 < – 14
[A] −
26
< x <1
7
[B] x > 1 or x < −
26
7
[C] x > 1
[D] all real numbers
72. – 6 < x + 4 < 8
[A] – 2 < x < 12
[B] x > 12 or x < – 2
[C] – 10 < x < 4
[D] x > 4 or x < – 10
Obj. 35 - Rewrite an equation to solve for a specified variable
73. Solve R = 3 p − 2l for p.
[A] p =
R + 21
3
74. Solve P =
[B] p =
R
+ 2l
3
[C] p =
R
2l − 3
[D] p = R + 2l − 3
Pbx
xy
[C] a =
P − xy
bx
[D] a =
xy − Pbx
P
[B] b =
2
ah
2A
h
[D] b =
xy
for a.
a + bx
[A] a = xy − bxP
1
75. Solve A = bh for b.
2
[B] a =
[A] b =
2h
A
44
[C] b =
A
2h
Topic 3 - Linear Equations and Inequalities
76. Solve S =
1600
for d.
d2
[A] d = S 1600
[B] d =
S
1600
1600
S
[C] d =
[D] d =
40
S
Obj. 36 - Determine the slope-intercept form or the standard form of a linear equation
77. What is the standard form of the equation y − 4 = −
[A] 2 x + 5 y = – 24
b g
2
x–2 ?
5
[C] y = −
[B] 2 x + 5 y = 24
2
24
x+
5
5
[D] 5 y = − 2 x + 24
7
8
78. What is the standard form of the equation y = − x − ?
9
9
[A] − 7 x = 9 y + 8
[B] − 9 y = 7 x + 8
[C] 7 x + 9 y = – 8
[D] 7 x + 9 y = 8
79. What is the slope-intercept form of the equation 6 x − 4 y + 18 = 0 ?
3
9
[A] y = − x −
2
2
[B] x =
2
y+3
3
3
9
[C] y = x +
2
2
[D] x =
2
y−3
3
80. What is the slope-intercept form of the equation 7 x − 6 y = – 9?
[A] y =
6
3
x+
7
2
[B] y =
7
3
x+
6
2
[C] y = − 7 x − 9
81. What is the slope-intercept form of the equation y − 5 = −
b g
2
x +8 ?
7
[A] x = −
7
19
y+
2
2
[B] − 2 x − 7 y = – 19
[C] y = −
2
19
x+
7
7
[D] – 7 y = 2 x − 19
45
[D] − 6 y = − 7 x − 9
Topic 3 - Linear Equations and Inequalities
82. What is the standard form of the equation
[A] 5x + 6 y = 30
x y
+ = 1?
6 5
[B] 6 y = − 5x + 30
[C] 5x = −6 y + 30
[D] y = −
5
x +5
6
Obj. 37 - Determine the slope of a line given its graph or a graph of a line with a given slope
4
83. Which line has a slope of ?
3
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
46
Topic 3 - Linear Equations and Inequalities
[A] −
84. What is the slope of the line?
5
6
[B]
5
6
[C]
6
5
[D] −
y
10
–10
10 x
–10
Obj. 38 - Determine the slope of a line given a table of values
85. If the values in the table were graphed, what would be the slope of the line?
Energy Remaining in a Battery
b g
y: Energy bJ g
x: Run Time hr
[A] – 341 J hr
4
8
9
12
8636 7272 6931 5908
[B] – 492 J hr
[C] – 2159 J hr
[D] – 909 J hr
86. If the values in the table were graphed, what would be the slope of the line?
Speed of Airplane
bg
y: Distance b mg
x: Time s
[A] 223 m s
6
11
16
20
1258 2303 3348 4184
[B] 205 m s
[C] 209 m s
[D] 324 m s
Obj. 39 - Determine the slope of a line given two points on the line
b g
b
g
87. What is the slope of the line passing through the points 4, 3 and – 7, – 9 ?
[A]
12
11
[B]
1
2
[C] 2
47
[D]
11
12
6
5
Topic 3 - Linear Equations and Inequalities
b
g
b
g
88. What is the slope of the line passing through the points – 4, – 4 and – 8, 2 ?
[A] −
2
3
[B] −
3
2
[C] 0
[D] undefined
b
g
b
g
89. What is the slope of the line passing through the points – 2, 7 and – 5, – 9 ?
[A]
3
16
[B]
16
3
[C] 0
[D] undefined
b
g b
g
90. What is the slope of the line passing through the points – 8, – 3 and 7, – 7 ?
[A] −
15
4
[B] −
4
15
[C] 0
[D] undefined
b g
b
g
91. What is the slope of the line passing through the points 1, 3 and 5, – 7 ?
[A] −
5
2
[B] −
2
5
[C] 0
[D] undefined
b g
b
g
92. What is the slope of the line passing through the points 0, 7 and 0, – 8 ?
[A] −
8
7
[B] −
7
8
[C] 0
[D] undefined
Obj. 40 - Determine the slope of a line given an equation of the line
93. What is the slope of the line y = −
[B] −
[A] 3
2
x + 3?
3
3
2
94. What is the slope of the line y − 3 = −
[A] −
3
8
[B]
[C]
1
3
[D] −
2
3
3
4
[D] −
8
3
b g
3
x–2 ?
8
15
4
[C]
48
Topic 3 - Linear Equations and Inequalities
95. What is the slope of the line 6 x + 8 y = 7?
[A]
3
4
[B] −
3
4
7
8
[D] −
7
8
[C]
1
3
[D] −
1
3
[A]
1
3
[B] 3
[C] −
[A]
7
2
2
7
[C]
96. What is the slope of the line − 10 x − 2 y = − 6 − 4 x?
[A] −3
[B] 3
97. What is the slope of the line
x y
− = 1?
3 9
7
98. What is the slope of the line y = 5x − ?
2
[B]
1
3
[C] 5
[D] 9
[D]
1
5
Obj. 41 - WP: Interpret the meaning of the slope of a line
99. A soil scientist designed an experiment to study water runoff. She added water to a tray of
soil, opened a drain, and measured the volume of water in the tray over time. The table
below shows the results.
Time (minutes) Volume of Water (liters)
1
36
2
26
3
16
4
6
Which statement describes the slope of the line?
[A] The volume of water decreased by 10 L every minute.
[B] The tray took 10 minutes to empty.
[C] The volume of water decreased by 1 L every 10 minutes.
[D] The tray can hold a total volume of 10 L.
49
Topic 3 - Linear Equations and Inequalities
100. The function c = 10t + 40 can be used to determine the cost to rent windsurfing gear from
a resort. The variable c represents cost in dollars, and the variable t represents time in
hours. Which statement describes the slope of the function?
[A] The customer can rent windsurfing gear for a maximum of 10 days.
[B] The cost of the rental is $10 per hour.
[C] The customer pays $10 to rent windsurfing gear.
[D] The cost includes a flat fee of $10 in addition to an hourly fee.
101. Claude jogs every morning. The graph shows the distance he travels.
100
90
80
70
60
50
40
30
20
10
10
20
30 40
Time (s)
50
What does the slope of the line represent?
[A] Claude jogs 100 m in 2.5 seconds.
[B] Claude jogs no more than 2.5 m.
[C] Claude jogs 2.5 m a day.
[D] Claude jogs at a rate of 2.5 m s .
50
Topic 3 - Linear Equations and Inequalities
Obj. 42 - Determine the x- or y-intercept of a line given its graph
102. What is the x-intercept of the line?
[A] –8
[B] –9
[C] –4
[D] –3
[A] –8
[B] –9
[C] –7
[D] –10
y
10
10 x
–10
–10
103. What is the y-intercept of the line?
y
10
10 x
–10
–10
Obj. 43 - Determine the x- or y-intercept of a line given an equation
104. What is the y-intercept of the graph of 3 y + 12 = –3?
[A] −
1
5
[B] –18
[C] –5
[D] –21
105. What is the y-intercept of the graph of x = 7 y − 2?
[A]
1
7
[B]
2
7
[C] 3
51
1
2
[D] –2
Topic 3 - Linear Equations and Inequalities
106. What is the x-intercept of the graph of 7 x + 3 y = 15?
[A] 2
1
7
[C] − 2
[B] 15
107. What is the y-intercept of the graph of 10 +
[A] 16
[B] − 3
1
5
1
3
[D] 5
x
= −4 y − 6?
5
[C] − 4
[D] –80
108. What is the x-intercept of the graph of 4 x = 12?
[A]
1
3
[B] 48
[C] 3
109. What is the x-intercept of the graph of 2 −
[A] –2
[B] − 24
[D] 8
2
x = 9 + 3 y?
7
1
2
[C] − 2
1
3
[D] − 7
Obj. 44 - Determine the x- or y- intercept of a line given a table
110. What is the x-intercept of a line with the given set of points?
x
y
– 1 2.5
6
20
7 22.5
8
[A]
25
b2, 0g
[B]
b– 5, 0g
[C]
52
b5, 0g
[D]
b– 2, 0g
Topic 3 - Linear Equations and Inequalities
111. What is the y-intercept of a line that passes through the given set of points?
x
y
– 6 27
4 – 13
7 – 25
9
[A]
– 33
b0, – 3g
[B]
b0, 3g
[C]
FG 0, 3IJ
H 4K
[D]
b0, – 4g
Obj. 45 - WP: Interpret the meaning of the y-intercept of a graphed line
112. Miss Hwang decided to organize a raffle to raise money for the school softball club. The
graph below shows how the number of raffle tickets sold is related to the amount of money
raised.
100
50
Number of Tickets Sold
–100
What does the point where the line intersects the vertical axis of the graph represent?
[A] The tickets sold for $85 each.
[B] Miss Hwang needed to sell at least 85 tickets.
[C] The cost of holding the raffle was $85.
[D] Miss Hwang raised $85 from the raffle.
53
Topic 3 - Linear Equations and Inequalities
113. The graph shows the relationship between the number of people and the cost for a dinner at
a hotel. What does the point where the line intersects the vertical axis of the graph
represent?
600
500
400
300
200
100
10 20 30 40 50
Number of People
[A] A maximum of 200 people can attend the dinner.
[B] The hotel charges a base fee of $200 in addition to the fee for each person.
[C] A minimum of 200 people must attend the dinner.
[D] The hotel charges $200 for each person who attends the event.
Obj. 46 - Determine the effect of a change in the slope and/or y-intercept on the graph of a
line
114. The line y = 5x − 2 is graphed on a graphing calculator. Then the slope of the line is
decreased by 3. What happens to the line?
[A] The slope remains positive, but the line is less steep.
[B] The slope changes from positive to negative, and the line is less steep.
[C] The slope changes from positive to negative, and the line is steeper.
[D] The slope remains positive, but the line is steeper.
115. The line y = −9 x + 8 is graphed on a graphing calculator. Then the y-intercept is increased
by 6. What happens to the line?
[A] The slope remains negative, but the line is less steep.
[B] The line moves up along the y-axis.
[C] The line moves down along the y-axis.
[D] The slope remains negative, but the line is steeper.
54
Topic 3 - Linear Equations and Inequalities
116. The line y = 9 x + 2 is graphed on a graphing calculator. Then the y-intercept is increased
by 7, and the slope is decreased by 11. What happens to the line?
[A] The slope changes from positive to negative, the line is steeper, and it moves up along
the y-axis.
[B] The slope changes from positive to negative, the line is steeper, and it moves down
along the y-axis.
[C] The slope changes from positive to negative, the line is less steep, and it moves up
along the y-axis.
[D] The slope changes from positive to negative, the line is less steep, and it moves down
along the y-axis.
Obj. 47 - WP: Determine the effect of a change in the slope and/or y-intercept of a line
117. Francelle wants to buy a large flat-screen television that costs $1188. She can pay for the
television in 12 months with no finance charges if she makes a down payment of $252 now
and then pays $78 each month. How many fewer monthly payments will be required if she
makes a down payment of $642 and pays $78 each month?
[A] 4
[B] 5
[C] 3
[D] 2
118. A tank at a chemical factory holds 3726 gallons of liquid when it is full. Once the tank is
full, the contents are pumped into containers for shipment. The amount of liquid in the
tank t minutes after the pumping starts can be described by the equation
A = 3726 − 46t . Suppose a new pump is installed before the next time the tank is emptied,
and after that change the equation becomes A = 3726 − 54t . What happens to the amount of
time it takes to empty the full tank?
[A] It increases by 12 minutes.
[B] It decreases by 14 minutes.
[C] It decreases by 12 minutes.
[D] It increases by 14 minutes.
55
Topic 3 - Linear Equations and Inequalities
119. The graph shows the amount currently charged by a landscaping company for fill dirt
delivered to a customer’s house. The company charges $14 per cubic yard of dirt plus a
delivery fee of $60.
y
Cost ($)
200
100
0
5
Cubic Yards
10
x
The owner of the landscaping service is considering raising the delivery fee to $69 and
lowering the fee for each cubic yard of dirt by $3. What would these changes do to the cost
of a delivery of 10 cubic yards of fill dirt?
[A] The cost would decrease by $6.
[B] The cost would increase by $21.
[C] The cost would increase by $6.
[D] The cost would decrease by $21.
120. Several times each week, Meda jogs for 5 minutes on her way to a park. Then she usually
runs at an average speed of 2.8 m s along a path that winds through the park for 4270 m.
Today, she jogged to the park at her usual speed, but when she got to the park entrance she
ran the rest of the route at an average speed of 35
. m s . How does Meda’s time to jog and
run through the park today compare to her usual time?
[A] Her time today was 5 minutes 5 seconds longer than her usual time.
[B] Her time today was 5 minutes 57 seconds longer than her usual time.
[C] Her time today was 5 minutes 57 seconds shorter than her usual time.
[D] Her time today was 5 minutes 5 seconds shorter than her usual time.
56
Topic 3 - Linear Equations and Inequalities
121. Airplane A is 43,000 feet above the ground and begins to descend at a rate of
1100 feet per minute. At the same time, airplane B is 27,000 feet above the ground and
begins to descend at a rate of 850 feet per minute. Which statement best represents the
time at which the planes reach 10,000 feet?
[A] Airplane B is first and takes 10 minutes less than airplane A.
[B] Airplane B is first and takes 7 minutes less than airplane A.
[C] Airplane A is first and takes 10 minutes less than airplane B.
[D] Airplane A is first and takes 7 minutes less than airplane B.
122. A ramp to the doorway of a building rises to a vertical height of 1.5 feet and has a slope of
1
. The ramp must be replaced to meet a specification for wheelchair access that requires a
8
1
slope of
. If the new ramp is not curved, what will be the horizontal distance the ramp
16
covers?
[A] 12 ft
[B] 24 ft
[C] 30 ft
57
[D] 28 ft
Topic 3 - Linear Equations and Inequalities
Obj. 48 - Determine the graph of a line using given information
123. Which graph shows the line that has x-intercept – 2 and y-intercept 6?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
58
Topic 3 - Linear Equations and Inequalities
b g
124. Which graph shows the line that goes through the point 1, 2 and has slope
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
125. Which graph shows the line that has slope – 2 and y-intercept – 2?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
59
2
?
3
Topic 3 - Linear Equations and Inequalities
126. Which graph shows the line that has x-intercept 1 and y-intercept 4?
[A]
[B]
y
10
10 x
–10
y
10
10 x
–10
–10
[C]
–10
[D]
y
10
10 x
–10
y
10
10 x
–10
–10
–10
b
g
127. Which graph shows the line that goes through the point – 5, – 4 and has slope 1?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
60
Topic 3 - Linear Equations and Inequalities
128. Which graph shows the line that has slope
[A]
1
and y-intercept – 2?
4
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
61
Topic 3 - Linear Equations and Inequalities
Obj. 49 - Determine the graph of a linear equation given in slope-intercept, point-slope, or
standard form
b g
129. Which graph shows y − 2 = 3 x + 3 ?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
62
Topic 3 - Linear Equations and Inequalities
130. Which graph shows y = − 8 x − 4?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
131. Which graph shows 4 x − 7 y = – 28?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
63
Topic 3 - Linear Equations and Inequalities
132. Which graph shows y − 4 = −
[A]
b g
2
x+2 ?
3
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
64
Topic 3 - Linear Equations and Inequalities
133. Which graph shows y =
[A]
8
x + 2?
9
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
134. Which graph shows x − y = 1?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
65
Topic 3 - Linear Equations and Inequalities
Obj. 50 - Determine an equation of a line given the slope and y-intercept of the line
135. Which equation represents a line with a slope of –2 and a y-intercept of –6?
[A] y = 2 x − 6
[B] y = −2 x + 6
[C] y = −2 x − 6
136. Which equation represents a line with a slope of −
[A] y = 9 x +
6
11
[B] y = −
6
x+9
11
[D] y = 6 x + 2
6
and a y-intercept of –9?
11
[C] y =
6
x−9
11
[D] y = −
137. Which equation represents a line with a slope of –3 and a y-intercept of
[A] 6 x + 18 y = 5
[B] 18 x − 6 y = –5
[C] 6 x − 18 y = –5
138. Which equation represents a line with a slope of −
[A] y = −
6
3
+
11x 8
[B] y =
6
3
x−
11
8
6
x−9
11
5
?
6
[D] 18 x + 6 y = 5
6
3
and a y-intercept of ?
11
8
[C] y = −
6
3
x+
11
8
[D] y =
3 3
−
8x 8
139. Which equation represents a line with a slope of 4 and a y-intercept of 4?
[A] 4 x − y = 4
[B] 4x − y = –4
[C] 4x + y = –4
140. Which equation represents a line with slope of −
[A] 3x + 7 y = 8
[B] 7 x − 3 y = 8
3
8
and y-intercept of ?
7
7
[C] 7 x + 3 y = –8
66
[D] 4 x + y = 4
[D] 3x − 7 y = 8
Topic 3 - Linear Equations and Inequalities
Obj. 51 - Determine an equation that represents a graphed line
b g
141. The line in the graph goes through the point 3, 4 . Which equation represents the line?
y
10
–10
10 x
–10
b g
[B] y − 3 = −
1
x−4
3
b g
[D] y − 4 = −
1
x−3
3
[A] y − 3 =
1
x−4
3
[C] y − 4 =
1
x−3
3
b g
b g
142. Which equation represents the line in the graph?
y
10
–10
10 x
–10
[A] 3x − y = –3
[C] x − 3 y = –3
[B] x + 3 y = –3
67
[D] 3x + y = –3
Topic 3 - Linear Equations and Inequalities
143. Which equation represents the line in the graph?
y
10
–10
10 x
–10
[A] y = −
3
x−2
2
[B] y = −
2
x−2
3
[C] y =
b
2
x−2
3
g
[D] y =
3
x−2
2
144. The line in the graph goes through the point 1, – 3 . Which equation represents the line?
y
10
–10
10 x
–10
b g
y − 1 = –4b x + 3g
b g
y + 1 = –4b x − 3g
[A] y + 3 = –4 x − 1
[B] y − 3 = –4 x + 1
[C]
[D]
68
Topic 3 - Linear Equations and Inequalities
145. Which equation represents the line in the graph?
y
10
–10
10 x
–10
[A] 5x − 7 y = 35
[C] 7 x − 5 y = 35
[B] 7 x + 5 y = 35
[D] 5x + 7 y = 35
146. Which equation represents the line in the graph?
y
10
–10
10 x
–10
[A] y = − 7 x − 3
[B] y = 7 x − 3
[C] y = − 3x − 7
[D] y = 3x − 7
Obj. 52 - Determine an equation for a line given the slope of the line and a point on the line
that is not the y-intercept
b g
147. Which equation represents the line with slope − 3 that passes through the point 5, 4 ?
[A] y = −3x − 11
[B] y = −3x − 19
[C] y = −3x + 11
69
[D] y = −3x + 19
Topic 3 - Linear Equations and Inequalities
148. Which equation represents the line with slope −
b
[A] y + 7 = −
3
x+3
2
b g
[B] y − 7 = −
3
x−3
2
[C] y + 7 = −
3
x−3
2
b g
[D] y − 7 = −
3
x+3
2
149. Which equation represents the line with slope
[A] y =
3
1
x+4
4
4
[B] y =
3
3
x+4
4
4
8
1
x − 16
3
3
b g
b g
[C] y =
8
1
[B] y = − x + 16
3
3
b g
3
that passes through the point 1, 5 ?
4
150. Which equation represents the line with slope −
[A] y =
3
3
x+5
4
4
[D] y =
3
3
x−2
4
4
FG IJ
H K
8
1
that passes through the point 6,
?
3
3
[C] y =
8
1
x + 16
3
3
8
1
[D] y = − x − 16
3
3
151. Which equation represents the line with slope – 10 that passes through the point
– 2, – 3 ?
b
g
b g
y + 3 = –10b x + 2g
b g
y − 3 = –10b x − 2g
[A] y + 3 = –10 x − 2
[B] y − 3 = –10 x + 2
[C]
[D]
152. Which equation represents the line with slope
b g
2
that passes through the point 9, 8 ?
3
b g
[B] y + 8 =
2
x+9
3
b g
[D] y + 8 =
2
x−9
3
[A] y − 8 =
2
x−9
3
[C] y − 8 =
2
x+9
3
70
g
3
that passes through the point – 3, 7 ?
2
b g
b g
Topic 3 - Linear Equations and Inequalities
Obj. 53 - Determine an equation of a line given two points on the line
b
g
b g
153. Which equation represents the line that passes through the points – 3, – 2 and 1, 10 ?
[A] y = − 3x − 7
[C] y = 3x − 7
[B] y = 3x + 7
[D] y = − 3x + 7
b
g
b g
154. Which equation represents the line that passes through the points – 1, 0 and 0, 3 ?
[A] 3x + y = – 3
[B] x − 3 y = 3
[D] 3x − y = – 3
[C] x + 3 y = 3
b
5
y + 2 = b x − 7g
3
g
b
g
g
b
g
155. Which equation represents the line that passes through the points – 2, 5 and – 7, 2 ?
b g
[B]
b g
[D] y + 2 =
[A] y − 2 =
5
x+7
3
[C] y − 2 =
3
x+7
5
b g
3
x−7
5
b
156. Which equation represents the line that passes through the points – 5, 0 and 0, – 8 ?
[A] 8 x + 5 y = – 40
[C] 8 x − 5 y = – 40
[B] 5x + 8 y = 40
[D] 5x − 8 y = 40
b
g
b
g
157. Which equation represents the line that passes through the points – 1, 6 and – 3, 14 ?
b y − 6g = 4b x + 1g
[C]
[D] b y − 6g = –4b x + 1g
Which equation represents the line that passes through the points b3, – 12g and b18, – 21g ?
[A]
158.
b y − 1g = –4b x + 6g
b y + 6g = –4b x − 1g
5
[A] y = − x − 7
3
[B]
3
1
[B] y = − x − 10
5
5
71
[C] y =
3
1
x − 10
5
5
[D] y =
5
x+7
3
Topic 3 - Linear Equations and Inequalities
Obj. 54 - Determine if two lines are perpendicular or parallel given the equations of the
lines
159. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
y = − 3x − 5
1
y = x+3
3
[A] parallel
[B] perpendicular
[C] neither
160. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
7x + y = –7
7x + y = 7
[A] parallel
[B] perpendicular
[C] neither
161. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
3x + y = 2
1
y = − x−7
3
[A] parallel
[B] perpendicular
[C] neither
162. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
5x – 5 y = 7
2 x – 5y = 8
[A] parallel
[B] perpendicular
[C] neither
163. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
2
y = x –5
3
3
y = − x +1
2
[A] parallel
[B] perpendicular
72
[C] neither
Topic 3 - Linear Equations and Inequalities
164. Determine whether the graphs of the two equations are parallel, perpendicular, or neither.
4 x + 3y = 3
3
y = x−7
4
[A] parallel
[B] perpendicular
[C] neither
Obj. 55 - Determine an equation for a line that goes through a given point and is parallel or
perpendicular to a given line
b
g
165. Which equation describes the line that passes through the point 6, – 1 and is parallel to
the graph of y = − 6 x − 3?
[A] y = 6 x − 35
[C] y = − 6 x + 35
[B] y = 6 x
[D] y = − 6 x
b
g
166. Which equation describes the line that passes through the point 2, – 5 and is
perpendicular to the line 5x − 7 y = 35?
[A] 7 x + 5 y = 11
[B] 5x − 7 y = 25
[C] 5x + 7 y = –25
[D] 7 x + 5 y = –11
b g
167. Which equation describes the line that passes through the point 1, 2 and is parallel to the
line 6 x − y = 3?
[A] 6 x + y = 4
[B] 6 x − y = 4
[D] 6 x − y = 11
[C] 6 x + y = 11
b g
168. Which equation describes the line that passes through the point 6, 8 and is perpendicular
3
3
to the graph of y = − x + ?
4
4
4
[A] y = x
3
4
[B] y = x + 16
3
4
[C] y = − x + 16
3
b
4
[D] y = − x
3
g
169. Which equation describes the line that passes through the point − 1, − 5 and is parallel to
the line 5x − y = −5?
[A] 5x + y = −24
[C] 5x − y = −24
[B] 5x − y = 0
73
[D] 5x + y = 0
Topic 3 - Linear Equations and Inequalities
b
g
170. Which equation describes the line that passes through the point 8, – 7 and is
4
4
perpendicular to the graph of y = − x − ?
3
3
3
[A] y = x − 1
4
3
[B] y = − x + 13
4
3
[C] y = − x − 1
4
3
[D] y = x − 13
4
Obj. 56 - Determine the graph of a 2-variable absolute value equation
171. Identify the graph of y = x + 2.
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
74
Topic 3 - Linear Equations and Inequalities
172. Identify the graph of y = x − 7 .
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
173. Identify the graph of y = 3 x .
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
75
Topic 3 - Linear Equations and Inequalities
174. Identify the graph of y = x + 2 .
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
175. Identify the graph of y = x − 8.
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
76
Topic 3 - Linear Equations and Inequalities
176. Identify the graph of y = – 4 x .
[A]
[B]
y
10
10 x
–10
y
10
10 x
–10
–10
[C]
–10
[D]
y
10
10 x
–10
y
10
10 x
–10
–10
–10
Obj. 57 - Solve a 2-variable linear inequality for the dependent variable
Solve for y:
177. − 3x − 4 y < 32
[A] y <
3
x −8
4
3
[B] y > − x − 8
4
[C] y >
3
x −8
4
9
[B] y > − x + 2
8
[C] y < −
[B] y < –2 x − 4
[C] y > 2 x − 4
3
[D] y < − x − 8
4
178. 2 x + 8 y < −11x + 16
[A] y > −
13
x+2
8
13
x+2
8
9
[D] y < − x + 2
8
179. − 16 + 3 y < 8 x + 7 y
[A] y < 2 x − 4
77
[D] y > –2 x − 4
Topic 3 - Linear Equations and Inequalities
Solve for y:
180. 35 + 7 y ≥ 3x
[A] y ≥
3
x −5
7
[B] y ≤
3
x −5
7
[C] y ≤ −
3
x +5
7
[B] y ≥
15
x−4
8
[C] y ≤
3
x−4
8
[D] y ≥
[C] y ≥
3
x−2
2
[D] y ≤ −
[D] y ≥ −
3
x +5
7
181. − 6 x − 8 y ≥ −9 x + 32
[A] y ≤
15
x−4
8
3
x−4
8
182. − 3x + 4 y ≥ −4 + 2 y
[A] y ≤
3
x−2
2
[B] y ≥ −
3
x−2
2
3
x−2
2
Obj. 58 - Determine if an ordered pair is a solution to a 2-variable linear inequality
183. Which ordered pair is a solution to − 6 x − 7 y > –14?
[A]
b 7, – 4 g
[B]
b– 1, 6g
[C]
b7, – 5g
[D]
b – 2, 9g
[D]
b10, 10g
b– 3, – 4g
[D]
b5, 5g
b– 1,
[D]
b8, 10g
[D]
b3, 7g
184. Which ordered pair is a solution to 8 x + 7 y < 14 x − 14?
[A]
b4, 3g
[B]
b 7,
g
– 10
[C]
b 7, 4g
185. Which ordered pair is a solution to 6 x + 3 y ≤ 6 y − 6?
[A]
b– 5, – 10g
[B]
b– 3, – 9g
[C]
186. Which ordered pair is a solution to 32 + 8 y ≥ −5x?
[A]
b – 7, – 4 g
[B]
b 7, – 9 g
[C]
g
– 10
187. Which ordered pair is a solution to 9 x − 36 ≥ −5x + 6 y?
[A]
b– 3, – 6g
[B]
b– 2, – 3g
[C]
78
b6, – 6g
Topic 3 - Linear Equations and Inequalities
188. Which ordered pair is a solution to − 6 + 9 y < −7 x + 6 y?
[A]
b3, – 8g
[B]
b3, – 5g
[C]
b1, 5g
[D]
b3, – 1g
Obj. 59 - Determine the graph of a 2-variable linear inequality
189. Which graph shows the solutions to y <
[A]
2
x + 3?
5
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
79
Topic 3 - Linear Equations and Inequalities
190. Which graph shows the solutions to 4 x − y ≤ 4?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
191. Which graph shows the solutions to − y − 2 x < 10?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
80
Topic 3 - Linear Equations and Inequalities
192. Which graph shows the solutions to y >
[A]
3
x − 4?
8
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
193. Which graph shows the solutions to the inequality x > 4?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
81
Topic 3 - Linear Equations and Inequalities
194. Which graph shows the solutions to − 2 y − 3x ≥ 18?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
Obj. 60 - Determine a 2-variable linear inequality represented by a graph
195. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[A] y ≤ −
2
x+3
3
2
[B] y > − x + 3
3
2
[C] y < − x + 3
3
82
[D] y ≥ −
2
x+3
3
Topic 3 - Linear Equations and Inequalities
196. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[B] y ≤ 2
[A] y < 2
[C] y > 2
[D] y ≥ 2
197. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[A] x − 5 y ≤ 5
[B] x − 5 y > 5
[C] − x + 5 y ≥ 5
83
[D] − x + 5 y > –5
Topic 3 - Linear Equations and Inequalities
198. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[A] − y + 2 x ≤ 4
[B] y − 2 x > 4
[C] − y + 2 x < 4
[D] y − 2 x ≤ 4
199. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[A] 3x + 2 y ≥ 18
[C] − 3x − 2 y > 18
[B] 3x + 2 y > –18
84
[D] − 3x − 2 y < –18
Topic 3 - Linear Equations and Inequalities
200. Which inequality is represented by the graph?
y
10
10 x
–10
–10
[A] y ≥ 3x + 3
[C] y ≤ 3x + 3
[B] y < 3x + 3
[D] y > 3x + 3
Obj. 61 - Determine the graph of the solutions to a problem that can be described by a 2variable linear inequality
201. A tourist is driving a car through a scenic area. The posted speed limit is 60 mph. Which
graph shows all the possibilities for the distance the car may travel if the driver never
exceeds the speed limit?
[A]
[B]
70
60
50
40
30
20
10
70
60
50
40
30
20
10
0
0
1
Time (hours)
1
Time (hours)
[C]
[D]
70
60
50
40
30
20
10
70
60
50
40
30
20
10
0
0
1
Time (hours)
1
Time (hours)
85
Topic 3 - Linear Equations and Inequalities
202. A pickup truck can safely transport up to 2000 pounds of cargo in its bed. One day, it is
being used to transport bricks and bags of mortar. Each brick weighs 6 pounds, and each
bag of mortar weighs 80 pounds. Let b represent the number of bricks and m the number of
bags of mortar. Which graph includes all possible combinations of bricks and bags of
mortar the truck can safely carry in one load?
[A] m
[B] m
40
36
32
28
24
20
16
12
8
4
40
36
32
28
24
20
16
12
8
4
100
200
300
400 b
[C] m
[D] m
40
36
32
28
24
20
16
12
8
4
40
36
32
28
24
20
16
12
8
4
100
200
300
400 b
100
200
300
400 b
100
200
300
400 b
203. A computer printer can print up to 25 pages per minute. The rate varies based on the type
of documents being printed. Which graph shows all the possibilities for the number of
pages the printer might produce?
[A]
1000
900
800
700
600
500
400
300
200
100
1 2 3 4 5 6 7 8 9 10
Time (minutes)
86
Topic 3 - Linear Equations and Inequalities
[B]
1000
900
800
700
600
500
400
300
200
100
1 2 3 4 5 6 7 8 9 10
Time (minutes)
[C]
1000
900
800
700
600
500
400
300
200
100
1 2 3 4 5 6 7 8 9 10
Time (minutes)
[D]
1000
900
800
700
600
500
400
300
200
100
1 2 3 4 5 6 7 8 9 10
Time (minutes)
(203.)
87
Topic 3 - Linear Equations and Inequalities
204. Which graph shows the values of two real numbers, x and y, if the sum of the two numbers
is at most 55?
[A]
[B]
y
100
100 x
–100
y
100
–100
[C]
–100
[D]
y
100
100 x
–100
100 x
–100
y
100
100 x
–100
–100
–100
205. An ice-cream shop makes a profit of $22 for each gallon of sherbet it sells. The shop
makes a profit of $18 for each gallon of ice cream it sells. Which graph shows all the
possible amounts of those two items the shop can sell each day to generate a profit of at
least $198?
[A]
25
20
15
10
5
0
5 10 15 20 25
Sherbet Sales (gal)
88
Topic 3 - Linear Equations and Inequalities
[B]
25
20
15
10
5
0
5 10 15 20 25
Sherbet Sales (gal)
[C]
25
20
15
10
5
0
5 10 15 20 25
Sherbet Sales (gal)
[D]
25
20
15
10
5
0
5 10 15 20 25
Sherbet Sales (gal)
(205.)
89
Topic 3 - Linear Equations and Inequalities
206. A produce stand at a farmers’ market charges $0.75 per pound for apples and $1.35 per
pound for pears. Let a equal the weight of the apples Cameron buys, and let p equal the
weight of the pears he buys. Which graph shows the possible weights of the apples and
pears he can buy without spending more than $26?
[A]
p
20
20
10
10
20
40
Weight of Apples (lb)
[C]
p
[B]
a
20
40
Weight of Apples (lb)
p
p
[D]
20
20
10
10
20
40
Weight of Apples (lb)
a
a
20
40
Weight of Apples (lb)
a
Obj. 62 - Solve a 1-variable absolute value inequality
Solve:
207.
5x ≥ 9
[A] x ≤ −
208.
9
9
or x ≥
5
5
[B] x ≤ –4 or x ≥ 4
[C] – 4 ≤ x ≤ 4
[D] −
9
9
≤x≤
5
5
− 8x − 1 < 8
[A] x < −
7
9
or x >
8
8
[B] −
7
9
<x<
8
8
90
[C] x < −
9
7
or x >
8
8
[D] −
9
7
<x<
8
8
Topic 3 - Linear Equations and Inequalities
Solve:
209.
2x + 3 − 4 ≤ 3
[A] – 5 ≤ x ≤ 2
[B] x ≤ –5 or x ≥ 2
[C] x ≤ –1 or x ≥ 5
[D] – 1 ≤ x ≤ 5
210. 2 x + 1 ≥ 5
[A] x ≤ –2 or x ≥ 3
211.
[B] – 2 ≤ x ≤ 2
[C] – 2 ≤ x ≤ 3
[D] x ≤ –2 or x ≥ 2
[B] – 7 ≤ x ≤ 7
[C] – 1 ≤ x ≤ 1
[D] x ≤ –7 or x ≥ 7
x + 3≤ 4
[A] x ≤ –1 or x ≥ 1
212. 2 | x − 4 | > 7
[A] x <
1
15
or x >
2
2
[B] x < −
1
15
or x >
2
2
[C]
1
15
<x<
2
2
Obj. 63 - Determine the graph of a 1-variable absolute value inequality
213. Which graph represents the solution set for the inequality?
2x > 6
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
91
[D] −
1
15
<x<
2
2
Topic 3 - Linear Equations and Inequalities
214. Which graph represents the solution set for the inequality?
4 x − 22 ≥ 10
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
215. Which graph represents the solution set for the inequality?
2x + 2 – 1< 3
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
92
Topic 3 - Linear Equations and Inequalities
216. Which graph represents the solution set for the inequality?
4 x – 16 ≥ 4
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
217. Which graph represents the solution set for the inequality?
x –2≤6
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
93
Topic 3 - Linear Equations and Inequalities
218. Which graph represents the solution set for the inequality?
3− x > 4
[A]
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
[B]
[C]
[D]
94
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 64 - Solve a system of linear equations in two variables by graphing
Solve the system of equations by graphing:
1. y = 4 x
y = 8x − 4
y
10
10 x
–10
–10
[A]
b1, 4g
[B]
b4, 1g
[C]
b0, 3g
[D] no solution
[C]
b – 2, 9g
[D] no solution
2. 5x + 13 y = 19
x + 11y = – 13
y
10
10 x
–10
–10
[A]
b8, – 1g
[B]
b 9, – 2 g
95
Topic 4 - Systems of Linear Equations and Inequalities
Solve the system of equations by graphing:
3. y = −2 x − 10
2 y = 3x + 1
y
10
10 x
–10
–10
[A]
b– 3, – 4g
[B]
b – 2, – 4 g
[C]
b– 4, – 3g
[D] infinitely many solutions
4. y = − x + 7
y = 3x − 9
y
10
10 x
–10
–10
[A]
b – 2, 2g
[B]
FG1 3 , 5 1 IJ
H 4 4K
[C]
96
b4, 3g
[D]
FG − 1 , 7 1 IJ
H 2 2K
Topic 4 - Systems of Linear Equations and Inequalities
Solve the system of equations by graphing:
5.
2
x+9= y
3
1
y+ x=9
2
y
10
10 x
–10
–10
[A]
b0, 9g
[B]
b9, 0g
[C]
b0, – 9g
[D]
b– 9, 0g
6. x + 2 y = 5
− 3x − 6 y = – 15
y
10
10 x
–10
–10
[A]
b– 6, 2g
[B]
b2, 6g
[C] no solution
97
[D] infinitely many solutions
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 65 - Solve a system of linear equations in two variables by substitution
Solve the system of linear equations using substitution:
7. y = 4 x −
1
2
3x = y − 2
[A]
8.
1
2
FG11 1 , − 2 1 IJ
H 2 2K
1
x + 5y = 9
2
x + 2 y = 10
[B]
FG 3, 1 IJ
H 2K
[C]
[D]
b8, 2g
FG11 1 , 3IJ
H 2 K
[B]
b1, 8g
[B]
FG 8 5 , − 1 5 IJ
H 9 9K
[C]
FG − 1 5 , 25 2 IJ
H 9 3K
[D]
FG − 1 5 , 8 5 IJ
H 9 9K
[B]
b63, 125g
[C]
b63, – 62g
[D]
b– 62, 125g
[B]
FG1 1 , 1 1 IJ
H 2 2K
[C]
FG1 1 , 2 IJ
H 2 3K
[D]
FG 2 , 2 IJ
H 3 3K
[A]
b8, 1g
FG 3, 11 1 IJ
H 2K
[C]
[D]
b8, 0g
9. – 10 x + 8 y = 84
10 x + y = – 7
[A]
10.
FG 8 5 , 25 2 IJ
H 9 3K
1
x + y = 32
2
16 x + 16 y = 16
[A]
b– 62, 63g
11. y = x
– 5y = – 6 − x
[A]
FG1 1 , − 1 1 IJ
H 2 2K
12. y = 44 x − 6
1
x= y
11
[A]
FG 2, 2 IJ
H 11K
[B]
FG 2 , 0IJ
H 11 K
98
[C]
FG 2 , – 6IJ
H 11 K
[D]
FG 2 , 2IJ
H 11 K
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 66 - Solve a system of linear equations in two variables by elimination
Solve by elimination:
13. 3x + 7 y = 8
12 x − 7 y = 22
[A]
FG 2 , 2IJ
H7 K
14. 4 x + 3 y = 63
4 x + 7 y = 83
[A]
FG 4 4 , 14 3IJ
H 5 5K
15. 2 x + 3 y = 0
9 x − 4 y = 105
[A]
b9, – 6g
FG1, 5 IJ
H 7K
[B]
[B]
[C]
FG17 1 , − 2IJ
H 4 K
b– 6, 9g
[B]
FG 2, 2 IJ
H 7K
[C]
[C]
[D]
b12, 5g
FG 2, − 2 IJ
H 7K
[D]
b– 9, – 6g
[D]
b5, 12g
b6, 9g
16. 5x + 12 y = 27
7 x + 6 y = 54
[A]
FG1 1 , 9IJ
H2 K
[B]
FG − 1 1 , 9IJ
H 2 K
[C]
FG 9, − 1 1 IJ
H 2K
[D]
FG − 9, − 1 1 IJ
H
2K
17. 3x + 15 y = 141
x + 5 y = 47
[A]
b– 3, 10g
18. −2 x + 7 y = 22
3x + 6 y = 0
b10, – 3g
[A] b – 4, – 2g
[B]
[D] b – 3, – 10g
b – 4, 9g
b– 5, 1g [C] b– 4, 2g [D] b2, – 4g
[C]
[B]
Obj. 67 - Determine the number of solutions to a system of linear equations
Without solving, determine the number of solutions for the system of linear equations:
19. y = – 15x + 6
162 = – 13x + 27 y
[A] one solution
[B] no solution
99
[C] infinitely many solutions
Topic 4 - Systems of Linear Equations and Inequalities
Without solving, determine the number of solutions for the system of linear equations:
20. – 4 y = − 40 x + 4
y = 10 x − 3
[A] one solution
[B] no solution
[C] infinitely many solutions
[B] no solution
[C] infinitely many solutions
5
y = – 10
4
− 8 x − 5 y = 40
21. 2 x +
[A] one solution
4
y=2
9
3
− 3x + y = 3
2
22. 9 x +
[A] one solution
[B] no solution
[C] infinitely many solutions
23. y = x + 5
8 y = 8 x + 40
[A] one solution
[B] no solution
[C] infinitely many solutions
24. − 3x − 7 y = – 17
− 63 y = 27 x
[A] one solution
[B] no solution
[C] infinitely many solutions
Obj. 68 - Solve a system of linear equations in two variables using any method
Solve using any method:
25. y = − 10 x − 5
− 30 x = 3 y + 15
[A]
FG − 3 1 , 2 1 IJ
H 2 2K
[B]
[C] no solution
FG − 3 1 , − 40IJ
H 2 K
[D] infinitely many solutions
100
Topic 4 - Systems of Linear Equations and Inequalities
Solve using any method:
26. 5x − 5 y = 9
2 x + y = 25
[A]
FG 8 14 , 9 8 IJ
H 15 15K
[B]
FG 7 2 , 8 14 IJ
H 15 15K
[C]
FG 8 14 , 7 2 IJ
H 15 15K
[D]
FG 7 2 , − 1 4 IJ
H 15 5 K
[B]
FG 4 1 , 6IJ
H2 K
[C]
b– 6, − 42g
[D]
FG − 4 1 , − 42IJ
H 2 K
[B]
FG − 3 1 , 4 IJ
H 5 5K
[C]
FG 3 1 , − 4 IJ
H 5 5K
[D]
FG 3 1 , 4 IJ
H 5 5K
[B]
b– 915. ,
27. – 6 x − 5 y = 3
– 24 x + 7 y = – 150
[A]
FG 4 1 , – 6IJ
H 2 K
28. 6 y = 8 − x
x
y=
4
[A]
FG − 3 1 , − 4 IJ
H 5 5K
29. − x − 0.2 y = 36
30 x − 6 y = 18
[A]
b– 17.7, – 915. g
[C] no solution
– 17.7
g
[D] infinitely many solutions
30. 33x + 18 y = 0
3x + 4 y = – 39
[A]
FG16 1 , 30 1 IJ
H 2 4K
[B]
FG 9, − 16 1IJ
H
2K
[C]
101
FG − 16 1 , − 30 1 IJ
H 2 4K
[D]
FG − 9, 16 1 IJ
H
2K
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 69 - WP: Determine a system of linear equations that represents a given situation
31. An office assistant made a total of 514 copies in one day. He made 80 fewer one-sided
copies than two-sided copies. Let x equal the number of one-sided copies, and let y equal the
number of two-sided copies. Which system of equations could be used to find the number of
each type of copy the assistant made?
[A] x + y = 594
2 x = 434
[B] x + y = 594
2 y = 434
[C] x + y = 514
y − x = 80
[D] x + y = 514
x − y = 80
32. The number of full-time employees of a paper manufacturing company is 2 more than 4
times the number of part-time employees. The company has 102 employees in all. Let x
equal the number of full-time employees, and let y equal the number of part-time
employees. Which system of equations could be solved to find the number of full-time
employees?
[A] x + y = 102
x = 4y + 2
[B] x + y = 102
y = 4x + 2
[C] x + 4 y = 100
y = 4x − 2
[D] x + 4 y = 100
x = 4y − 2
33. One month, a company spent $7046.40 to print and mail letters and postcards to its
customers. The company paid $0.69 per letter and $0.57 per postcard. The next month, the
company mailed the same number of letters and postcards, but paid $0.68 per letter and
$0.60 per postcard. The total cost for the second month was $7152.80. Let x equal the
number of letters mailed and y equal the number of postcards mailed. Which system of
equations could be solved to find the number of postcards mailed each month?
[A] 0.57 x + 0.69 y = 7046.40
0.60 x + 0.68 y = 7152.80
[B] 0.69 x + 0.68 y = 7046.40
0.57 x + 0.60 y = 7152.80
[C] 0.69 x + 0.57 y = 7046.40
0.68 x + 0.60 y = 7152.80
[D] 0.60 x + 0.57 y = 7046.40
0.68 x + 0.69 y = 7152.80
102
Topic 4 - Systems of Linear Equations and Inequalities
34. Ruby makes fleece scarves and sells them for $5.00 each. The supplies cost her $1.70 per
scarf. Last month, Ruby sold all but 6 of the scarves she made. Her net profit for the month
was $52.50. Let x equal the number of scarves Ruby sold and let y equal the number of
scarves she made. Which system of equations could be solved to find how many scarves
Ruby sold last month?
[A] 5.0 x − 17
. y = 52.5
x = y−6
[B] 17
. x − 5.0 y = 52.5
y = x−6
[C] 5.0 x − 17
. y = 52.5
y = x−6
[D] 17
. x − 5.0 y = 52.5
x = y−6
35. A call center representative logged a total of 92 calls in one day. The number of outbound
1
calls was 4 more than the number of inbound calls. Let x equal the number of outbound
3
calls and let y equal the number of inbound calls. Which system of equations can be solved
to find the number of outbound calls the representative made that day?
[A] 3x + y = 92
1
y = x+4
3
[B] x + y = 92
1
y = x+4
3
[C] 3x + y = 92
1
x = y+4
3
[D] x + y = 92
1
x = y+4
3
36. On one trip, a traveling salesperson was reimbursed $792 for 3 nights in a hotel and
36 meals with clients. On the next trip, she was reimbursed $1020 for 4 nights in a hotel and
45 meals with clients. Let x equal the amount the company pays per night for lodging and let
y equal the amount the company pays per meal. Which system of equations could be solved
to find how much the company reimburses the salesperson for lodging and meals?
[A] 3x + 36 y = 1020
4 x + 45 y = 792
[B] 3x + 36 y = 792
4 x + 45 y = 1020
[C] 36 x + 3 y = 792
45x + 4 y = 1020
[D] 36 x + 3 y = 1020
45x + 4 y = 792
Obj. 70 - WP: Solve a mixture problem that can be represented by a system of linear
equations
37. During a science experiment, Nico created a 14% alcohol solution by mixing 3 fluid ounces
of an 18% alcohol solution with a certain amount of an 8% alcohol solution. How many
fluid ounces of the 14% alcohol solution did he create?
[A] 5 fl oz
[B] 2 fl oz
[C] 11 fl oz
103
[D] 3 fl oz
Topic 4 - Systems of Linear Equations and Inequalities
38. Mr. Petek mixes a 95% sugar cinnamon-flavored solution with a 75% sugar cherry-flavored
solution to make 20 gallons of a new product. The new product is 82% sugar. How much of
the cherry-flavored solution did he use?
[A] 7 gal
[B] 11 gal
[C] 15 gal
[D] 13 gal
39. Mr. Ferrer works in the lab at a pharmaceutical company. He needs to make 22 liters of a
17% acid solution to test a new product. His supplier only ships a 23% and a 12% solution.
Mr. Ferrer decides to make the 17% solution by mixing the 23% solution with the
12% solution. How much of the 23% solution will Mr. Ferrer need to use?
[A] 10 L
[B] 22 L
[C] 12 L
[D] 5 L
40. Anika is making a nut mixture to sell at the local farmers’ market. She mixes 3 pounds of
pistachios with a nut mixture that is 40% pistachios. The resulting mixture is
58% pistachios. How many pounds of nut mixture does Anika make?
[A] 7 lb
[B] 3 lb
[C] 8 lb
[D] 10 lb
41. Ms. Costa is filling planter boxes with soil. She has soil that is 16% sand, and she buys
6 pounds of a commercial potting soil that is 34% sand. She mixes some of her soil with the
6 pounds of commercial potting soil. The resulting soil mixture is 28% sand. How many
pounds of her soil did Ms. Costa use?
[A] 6 lb
[B] 3 lb
[C] 5 lb
[D] 9 lb
42. A metal recycling plant has some scrap metal that is 40% copper. It also has some other
scrap metal that is 45% copper. The scrap metal is melted together and produces 1170 g of
metal that is 43% copper. How many grams of the 45% copper metal were mixed with the
40% copper metal?
[A] 702 g
[B] 527 g
[C] 468 g
104
[D] 1170 g
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 71 - WP: Solve a motion problem that can be represented by a system of linear
equations
43. Cathy is training for a bike race that will take place next month. On Saturday she rode her
bike 145 miles in a practice race. Cathy rode part of the race at an average speed of
25 miles per hour, and she averaged 15 miles per hour for the remaining part of the race. If
it took Cathy 7 hours to finish the practice race, how much time did she spend riding at a
rate of 25 miles per hour?
[A] 21 hr
[B] 3 hr
[C] 4 hr
[D] 5 hr
44. On Sunday, the Fischer family left home to drive to a resort in Maine for vacation. They
drove at an average rate of 50 miles per hour. On Friday, they drove back the same route,
traveling at an average rate of only 40 miles per hour because of road construction. If the
Fischer family spent a total of 9 hours driving to and from the resort in Maine, how many
miles did they travel from their house to the resort?
[A] 200 mi
[B] 180 mi
[C] 94 mi
[D] 405 mi
45. Last weekend Claudia traveled by train to visit her grandparents. On Friday she boarded an
express train that traveled at an average rate of 85 miles per hour. On Sunday she returned
home on a slower train that traveled at an average rate of 51 miles per hour. The total time
Claudia spent on the trains last weekend was 8 hours. How many hours did Claudia spend
on the train on Friday?
[A] 8 hr
[B] 4 hr
[C] 5 hr
[D] 3 hr
46. Mr. and Mrs. Abbott went on a cruise to a tropical island. They spent a total of 30 hours on
the cruise ship traveling to and from the island. On Wednesday the cruise ship left its port
and traveled at an average speed of 10 miles per hour to the island. On the return trip, the
ship traveled by the same route at an average speed of 20 miles per hour. How many miles
did the cruise ship travel from its port to the island?
[A] 200 mi
[B] 400 mi
[C] 450 mi
[D] 60 mi
47. On Wednesday morning, Mrs. Juarez flew a plane from her hometown to Seattle, flying at
an average speed of 260 miles per hour. Later that day, she flew the plane back to her
hometown. Together, the two flights lasted a total of 11 hours. If Mrs. Juarez flew at an
average speed of 312 miles per hour on the return trip, how long did the return trip take?
[A] 7 hr
[B] 11 hr
[C] 6 hr
105
[D] 5 hr
Topic 4 - Systems of Linear Equations and Inequalities
48. One evening Hana and Amal both drive to a concert in a city that lies between their
hometowns. Together they drive a total of 380 miles to the concert. Hana drives an average
of 5 miles per hour faster than Amal. If Hana and Amal both arrive at the concert after
4 hours, what is the average speed of Hana’s car?
[A] 76 mph
[B] 45 mph
[C] 55 mph
[D] 50 mph
Obj. 72 - Solve a number problem that can be represented by a linear system of equations
49. The sum of two integers is 2. Their difference is 12. What are the two integers?
[A] –7 and 9
[B] –5 and 7
[C] –19 and –7
[D] 7 and 19
50. One integer is 3 greater than another integer. The larger integer is also 29 greater than the
opposite of the smaller integer. What are the two integers?
[A] 16 and 19
[B] 13 and 42
[C] 13 and 16
[D] 39 and 42
51. The sum of an integer and twice a smaller integer is 25. If the smaller integer is subtracted
from twice the larger integer, the difference is 10. What are the two integers?
[A] 8 and 9
[B] 8 and 33
[C] 17 and 27
[D] 8 and 17
52. The sum of two integers is 29. The larger of the two integers is 2 more than 2 times the
smaller integer. What are the integers?
[A] 9 and 16
[B] 16 and 13
[C] –9 and 38
[D] 9 and 20
53. The sum of 3 times the larger of two integers and twice the smaller is –7. The difference
between the two integers is 6. What are the two integers?
[A] –5 and 1
[B] –11 and –5
[C] 1 and 7
[D] –1 and 5
54. The larger of two integers is 14 greater than twice the smaller integer. The smaller integer is
19 less than twice the larger integer. What are the two integers?
[A] –3 and 13
[B] 16 and 51
[C] –3 and 8
106
[D] –20 and –3
Topic 4 - Systems of Linear Equations and Inequalities
Obj. 73 - Determine if a given ordered pair is a solution to a system of linear inequalities
55. Which ordered pair is a solution of the system of linear inequalities?
x + 2 y > –4
2 x + y > –4
[A]
b9, – 8g
[B]
b– 7, 8g
[C]
b8, 9g
[D]
b5, – 5g
[D]
b– 1, 1g
[D]
b 7, 2g
[D]
b– 5, – 6g
[D]
b1, – 8g
56. Which ordered pair is a solution of the system of linear inequalities?
6 x − 5 y < –30
x + 4 y < –4
[A]
b– 8, – 2g
[B]
b– 9, 3g
[C]
b– 1, – 1g
57. Which ordered pair is a solution of the system of linear inequalities?
x − 2y ≤ 2
4
y ≥ − x+4
7
[A]
b– 2, 5g
[B]
b– 7, – 6g
[C]
b 2, 9g
58. Which ordered pair is a solution of the system of linear inequalities?
2 x + 3 y ≥ –12
1
y < x −1
4
[A]
b3, 4g
[B]
b5, – 1g
[C]
b– 9, – 1g
59. Which ordered pair is a solution of the system of linear inequalities?
y < −x + 5
x + 3y ≤ 6
[A]
b8, – 1g
[B]
b – 4, 4g
[C]
107
b8, 4g
Topic 4 - Systems of Linear Equations and Inequalities
60. Which ordered pair is a solution of the system of linear inequalities?
5x − 3 y > 15
2 x + 3 y < –6
[A]
b 4, – 2 g
[B]
b– 3, – 7g
[C]
b2, – 8g
[D]
b6, 9g
Obj. 74 - Determine the graph of the solution set of a system of linear inequalities in two
variables
61. Which graph shows the solution set for the system of linear inequalities?
3x + 5 y ≥ 15
3x + y ≥ 6
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
108
Topic 4 - Systems of Linear Equations and Inequalities
62. Which graph shows the solution set for the system of linear inequalities?
4 x − 3 y ≤ 12
x − 3 y ≤ –3
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
63. Which graph shows the solution set for the system of linear inequalities?
4
y > − x+4
5
x + 4y < 8
109
Topic 4 - Systems of Linear Equations and Inequalities
[A]
y
10
10 x
–10
–10
[B]
y
10
10 x
–10
–10
[C]
y
10
10 x
–10
–10
[D]
y
10
10 x
–10
–10
(63.)
110
Topic 4 - Systems of Linear Equations and Inequalities
64. Which graph shows the solution set for the system of linear inequalities?
3x − y < 6
y < − x +1
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
65. Which graph shows the solution set for the system of linear inequalities?
2 x + 3y > 6
4 x + y < –4
111
Topic 4 - Systems of Linear Equations and Inequalities
[A]
y
10
10 x
–10
–10
[B]
y
10
10 x
–10
–10
[C]
y
10
10 x
–10
–10
[D]
y
10
10 x
–10
–10
(65.)
112
Topic 4 - Systems of Linear Equations and Inequalities
66. Which graph shows the solution set for the system of linear inequalities?
y ≤ 8x + 8
5x − 8 y ≥ 40
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
Obj. 75 - WP: Determine a system of linear inequalities that represents a given situation
67. An office manager needs to replace at least 7 chairs. Chairs without armrests cost $138
each, and chairs with armrests cost $208 each. She can spend at most $1300. If x represents
the number of chairs without armrests and y represents the number of chairs with armrests,
which system of inequalities has a solution that includes all the possible choices she can
make?
[A] x + y ≤ 7
b
[B] x + y < 7
208 x + 138 y < 1300
g
346 x + y ≤ 1300
[C] x + y ≥ 7
138 x + 208 y ≤ 1300
[D] x + y ≥ 7
208 x + 138 y ≤ 1300
113
Topic 4 - Systems of Linear Equations and Inequalities
68. The owner of a restaurant wants to buy two different types of coffee beans. One type costs
$14 per pound, and the other type costs $10 per pound. Based on previous customer sales,
3
he wants less than as much of the more expensive coffee, x, as he does the less expensive
4
type, y. The most he wants to spend for the two types of coffee is $300. Which system of
inequalities describes this situation?
3
[A] x < y
4
14 x + 10 y ≤ 300
3
[B] y < x
4
10 x + 14 y ≤ 300
3
[C] x ≤ y
4
24 x + y ≤ 300
3
[D] y ≥ x
4
24 x + y < 300
b
g
b
g
69. A company sells jars of cashew nuts mixed with peanuts. The weight of the peanuts in the
jar, y, must be at least 2.5 ounces less than the total weight of the cashew nuts in the jar, x.
The peanuts cost the company 8¢ per ounce, and the cashew nuts cost 41¢ per ounce. The
company wants its cost for the nuts in each jar to be less than $3.08. Which system of
inequalities represents this situation?
[A] y < x − 2.5
8 x + 41y < 308
[B] x ≤ y − 2.5
8 x + 41y < 308
[C] x < y − 2.5
41x + 8 y < 308
[D] y ≤ x − 2.5
41x + 8 y < 308
70. A manufacturing company’s processes result in at least 7 tons of plastic and metal waste
each month. To make recycling the waste profitable, the manufacturing company only
recycles the waste if they are paid at least $1300. One month, the company sells the plastic
waste to a recycling company for $130 per ton and the metal waste for $230 per ton. Let x
represent the weight, in tons, of the plastic waste, and let y represent the weight, in tons, of
the metal waste. Which system of inequalities represents this situation?
[A] x + y ≥ 7
130 x + 230 y < 1300
[B] x + y > 7
[C] x + y ≥ 7
130 x + 230 y ≥ 1300
[D] x + y > 7
230 x + 130 y ≥ 1300
b
g
360 x + y > 1300
114
Topic 4 - Systems of Linear Equations and Inequalities
71. An insurance agency wants to buy imprinted pens and notepads to give away to customers.
The company that supplies the items will ship them for free with a minimum purchase of at
least 400 items in all. The pens cost $1.35 each, and the notepads cost $0.35 each. The
insurance agency wants to spend less than $239 in all. Let x equal the number of pens in an
order, and let y equal the number of notepads in the same order. Which system of
inequalities describes this situation if the agency orders at least 400 items?
[A] 135
. x + 0.35 y > 400
x + y ≥ 239
[B] 0.35x + 135
. y < 239
x + y > 400
[C] 135
. x + 0.35 y < 239
x + y ≥ 400
[D] 0.35x + 135
. y > 400
x + y ≥ 239
72. An office manager needs to buy bagels and muffins for a morning staff meeting at the office
where he works. Bagels cost $0.59 each and muffins cost $0.89 each. He has been given
approval to spend up to $70. Based on his experience at previous meetings, he wants to buy
at least 10 more muffins than bagels. If x equals the number of bagels and y equals the
number of muffins, which system of inequalities describes the office manager’s options?
[A] x − y > 10
0.59 x + 0.89 y < 70
[B] y − x ≥ 10
0.59 x + 0.89 y ≤ 70
[C] x − y < 10
0.89 x + 0.59 y ≤ 70
[D] y − x > 10
0.89 x + 0.59 y < 70
Obj. 76 - WP: Determine possible solutions to a problem that can be represented by a
system of linear inequalities
73. A business owner wants to run no more than 20 ads per month in a local newspaper. A
weekday ad costs $140, and a weekend ad costs $180. The most the business owner wants
to spend for all the ads is $3200. Which combination of ads fits these conditions?
[A] 8 weekday ads and 8 weekend ads
[B] 12 weekday ads and 10 weekend ads
[C] 9 weekday ads and 11 weekend ads
[D] 10 weekday ads and 12 weekend ads
115
Topic 4 - Systems of Linear Equations and Inequalities
74. A small company silk-screens T-shirts for local high schools with the school name and logo.
The company carries two styles of shirts, long sleeved and short sleeved. The company
needs to have some of each style of shirt available for orders, and wants at least 500 shirts
on hand valued at no more than $2200. Their cost for one short-sleeved shirt is $2.25 and
for one long-sleeved shirt is $6.50. Which possible combination of shirts will fit these
conditions?
[A] 290 short-sleeved shirts
290 long-sleeved shirts
[B] 190 short-sleeved shirts
310 long-sleeved shirts
[C] 250 short-sleeved shirts
250 long-sleeved shirts
[D] 270 short-sleeved shirts
270 long-sleeved shirts
75. A small cruise ship carries at most 200 passengers. Two types of rooms are available for a
ten-day cruise to Nova Scotia. One room costs $2200 per person, and the other costs
$3200 per person. The cruise line must sell at least $429,000 worth of rooms to make the
cruise profitable. Which combination of types of rooms booked represents a profitable
cruise?
[A] 120 passengers booked a $2200 room
65 passengers booked a $3200 room
[B] 110 passengers booked a $2200 room
50 passengers booked a $3200 room
[C] 105 passengers booked a $2200 room
60 passengers booked a $3200 room
[D] 115 passengers booked a $2200 room
50 passengers booked a $3200 room
76. A farmer rotates growing soybeans, wheat, and corn on her farm to help keep her crops
disease free. Each year a different combination of crops is grown. This year she will plant at
most 320 acres of wheat and soybeans. The wheat crop is expected to produce $396 worth
of wheat per acre, and the soybean crop is expected to produce $414 worth of soybeans per
acre. The farmer needs to sell a minimum of $130,000 worth of these crops to cover the
farm expenses. Which combination of wheat and soy could she plant and produce enough
income to cover the farm expenses?
[A] 160 acres of wheat
160 acres of soybeans
[B] 128 acres of wheat
176 acres of soybeans
[C] 112 acres of wheat
208 acres of soybeans
[D] 80 acres of wheat
224 acres of soybeans
116
Topic 4 - Systems of Linear Equations and Inequalities
77. An artist produces two types of goblets, hand painted and hand blown. She sells the handpainted goblets for $20 each and the hand-blown goblets for $14 each. She is able to
produce at most 425 goblets per month. Which combination of goblets would produce an
income of at least $6840?
[A] 165 hand-painted goblets
260 hand-blown goblets
[B] 160 hand-painted goblets
250 hand-blown goblets
[C] 155 hand-painted goblets
260 hand-blown goblets
[D] 170 hand-painted goblets
230 hand-blown goblets
78. An appliance store carries two models of trash compactors. Model A costs the company
$260, and Model B costs $480. The manager of the store decides to stock at least
19 compactors, but does not want to have any more than $6300 worth. Which combination
of compactors fits these conditions?
[A] 14 Model A compactors
7 Model B compactors
[B] 15 Model A compactors
7 Model B compactors
[C] 14 Model A compactors
5 Model B compactors
[D] 13 Model A compactors
7 Model B compactors
117
Topic 5 - Properties of Powers
Obj. 77 - Determine an equivalent form of a variable expression involving exponents
1. Which expression is equivalent to 5cd 2 ?
[A] 10×c ×d ×d
[B] 5×c ×c ×d ×d
d i
[C] 10×c ×c ×d ×d
[D] 5×c ×d ×d
[C] 4 ×c 7 ×c 7
[D] 4 ×c 2 ×c 2
2
2. Which expression is equivalent to 4c 7 ?
[A] 4c 2 ×4c 2
[B] 4c 7 ×4c 7
3. Which expression is equivalent to 6×m ×m ×n ×n ×n?
[A] 6m2 n 3
[B] 62 m2 n 3
[C]
c6m nh
2
3
c h
[D] 6 m2 n
3
Obj. 78 - Apply the product of powers property to a monomial numerical expression
4. Which expression is equivalent to 9 3 ×9 4 ?
[A] 8112
[B] 9 7
[C] 817
b g ×b– 2g
5. Which expression is equivalent to – 2
[A] 414
[B]
–6
1
–8
?
[C]
b – 2g
14
[D] 912
1
4 48
[D] −
1
214
b g ×b– 9g ?
6. Which expression is equivalent to – 9
[A]
1
b – 9g
42
[B] −
–14
3
1
8142
[C]
1
b – 9g
11
[D]
1
8111
[D]
b– 6g
b g b g
7. Which expression is equivalent to – 6 × – 6 ?
4
[A] 3620
5
[B] 369
[C]
118
b– 6g
20
9
Topic 5 - Properties of Powers
b g b g
8. Which expression is equivalent to – 13 × – 13 ?
0
[A] 169
[B] –13
4
b g ×b– 13g
9. Which expression is equivalent to – 13
1
[A]
b– 13g
[B]
88
b– 13g
b– 13g
[C]
11
3
–8
4
[D] 169 4
?
1
16988
[C]
[D] 169 3
Obj. 79 - Apply the product of powers property to a monomial algebraic expression
Simplify:
10.
c x hc x h
−7
−4
[A]
11. FGH 4 x –5 IJK FH – 3x – 3 IK
12.
c7 x y hc− 8x
13.
c x hc x h
−1
−12
−1
−1
y −3
3
15.
c5x hc− 8x
−3
y
[B] x 28
[B] −
[A] – 12 x15
14. FGH – 8 x –11 IJK x 9
−2
1
x 11
−3
h
h
[A] − xy 3
12
x8
[B] −
[A] x 9
[B] x 36
[A] – 8 x 99
[B] −
3x 6
[A] − 3
y
[C] x11
[D]
1
x 28
[C] x15
[D]
1
x8
1
x y4
[C] −
2
[C]
8
x2
1
x9
[C] −
40 x 6
[B] − 3
y
56
x2 y4
[D]
8
x 99
[C] −
[D] − 56 xy 3
40
x5 y3
1
x 36
[D] – 8 x 2
[D] −
3
x y3
5
Obj. 80 - Apply the power of a power property to a monomial numerical expression
d i
5
16. Which expression is equivalent to 5 3 ?
[A] 58
119
[B] 55
[C] 515
[D] 535
Topic 5 - Properties of Powers
b g
17. Which expression is equivalent to – 4
[A] −
1
47
[B]
[C]
b – 4g
12
b g
1
7 54
[B]
6 –9
b – 7g
8 2
[C]
d i
1
22
–2
[D]
12
1
[D]
b– 5g
[D]
b– 5g
[D]
1
216
b – 7g
15
16
10
?
[B] 216
[C] 210
d i
b – 4g
?
[B] – 516
20. Which expression is equivalent to 2 –8
7
1
715
[C] −
54
b g
[A]
b – 4g
?
1
19. Which expression is equivalent to – 5
[A] – 510
?
1
18. Which expression is equivalent to – 7
[A] −
–3 –4
6
21. Which expression is equivalent to 9 – 3 ?
[A]
1
918
[B] 9 9
[C]
1
93
[D] 918
Obj. 81 - Apply the power of a power property to a monomial algebraic expression
Simplify:
22.
cx h
[A] x10
[B] x 7
[C] 10x
23.
da i
[A]
1
a8
[B] a 6
[C]
2 5
–4 –2
120
1
a6
[D] 7x
[D] a 8
Topic 5 - Properties of Powers
Simplify:
24.
dy i
[A] y
[B]
25.
dh i
[A] 42h
[B] h 42
26.
cx h
[A] x 72
[B]
27.
dr i
[A]
3 –2
6 7
– 9 –8
–8 6
1
r2
1
y
1
x 17
[B] r 48
1
y6
[C] y 6
[D]
[C] h13
[D] 13h
1
x 72
[D] x17
[C]
[C] r 2
[D]
1
r 48
Obj. 82 - Apply the power of a product property to a monomial algebraic expression
Simplify:
28.
d 2a i
[A] 6a 2
29.
b xyg
[A]
30.
b 3x y g
31.
b gd i
–1 3
–2
–5
2
3
[A] 9 x 3 y 3
6a –5
b g
32. – 4 pq
33.
3
c– 9 x yh
3
1
x y5
5
3
–2
[B]
[C] 2a 2
[D]
1
x y4
[B] x 4 y 4
[C]
[B] 9 x 3 y 2
[C] 3x 2 y 2
[A] – 9a 5
[A] – 4 pq 3
8
a3
[C] −
[B] 9a 5
[B] 64 p 3q 3
[A] – 729x 9 y 3
2a 10
9
[C] – 4 p 3q 3
[B] – 729x 6 y 3
121
4
[C] – 27 x 9 y 3
6
a3
[D] x 5 y 5
[D] 9 x 2 y 2
[D]
2a 10
9
[D] – 12 pq 3
[D] – 27 x 6 y 3
Topic 5 - Properties of Powers
Obj. 83 - Apply the quotient of powers property to monomial numerical expressions
Simplify:
3
5
34. 9
5
[A] 56
[B] 512
[C]
1
512
[D]
1
56
[A]
1
48
[B] 4 4
[C] 48
[D]
1
44
[A]
1
36
[B] 36
[C] 38
[D]
1
38
–2
4
35.
4–6
–1
36.
3
37
37.
12
12 6
11
[A]
1
1217
[B]
1
125
[C] 12 5
[D] 1217
[A]
1
12 3
[B]
1
1288
[C] 12 88
[D] 12 3
–11
12
38.
12 –8
2
9
39.
9 –1
[B] 9 3
[A] 9
[C]
1
9
[D]
1
93
Obj. 84 - Apply the quotient of powers property to monomial algebraic expressions
Simplify:
40.
x −8
x −1
13x −3
41.
x5
42.
36 y − 4
9 x − 4 y −1
[A] x 9
[B] x 7
[C]
[A]
13
x2
[B] 13x 8
[A]
4x4
y5
[B]
4 y3
x4
122
1
x9
[D]
1
x7
[C] 13x 2
[D]
13
x8
4x4
y3
[D]
4 y5
x4
[C]
Topic 5 - Properties of Powers
Simplify:
43.
− 70 x 7
− 14 x −8
[A]
24 x − 4 y
44.
− 4 x −5 y 4
45.
5
x 15
[B]
[A]
4x2
y5
[C] 5x15
6y3
[B] −
x
6
[A] − 9 5
x y
24 x 7 y −5
6x 5
5
x
[B]
4 x 12
y5
[D] 5x
[C] − 6 x 9 y 5
[C]
4 y5
x 12
[D] −
[D]
6x
y3
4 y5
x2
Obj. 85 - Apply the power of a quotient property to monomial algebraic expressions
Simplify:
46.
Fa I
GH b JK
47.
FG m IJ
H − 5n K
48.
FG 8a IJ
H 2b c K
49.
FG 6z IJ
H 2w K
50.
FG − 28a b IJ
H 4c d K
9
8
a 17
[A] 12
b
4
5
–4
[A]
4
[A]
2 4
−3
3
[A]
−1
4 5
5
625n 4
m20
16a 4
b2 c4
27 w 3
z9
a 72
[B]
b4
a 17
[C]
b4
[B] 625m5n 4
[C]
[B]
[B] −
16a 4
b8c16
9z 9
w3
a 72
[D] 32
b
625
m20n
[C]
[C] −
[D]
256a 4
b2 c4
9w3
z9
[D]
[D]
625m5
n
256a 4
b8c16
27 z 9
w3
4
−3
28a 8b 9 d 3
[A]
c5
28a 8b 9 d
[B]
c9
2401a 16b 20d 12
[C]
c 20
123
2401a 16b 20d 2
[D]
c5
Topic 5 - Properties of Powers
Simplify:
FG 28a b IJ
H 4c K
−6 6
51.
2
49a 12
[A] 12 12
b c
−6
a 12
[C] −
49b12 c12
49b12
[B] − 12 12
a c
49b12 c12
[D]
a 12
Obj. 86 - Compare monomial numerical expressions using the properties of powers
15
52. Which statement is true?
d i
4
< 43
3
4
15
d i
15
d i
[B]
4
> 43
3
4
[B]
d5 i > d5 i ×d5 i
[C]
d5 i = d5 i ×d5 i
[B]
3
> 3–13 × 3–12
–13
3
[C]
3
= 3–13 × 3–12
–13
3
[A]
4
4
4
= 43
3
4
[C]
4
53. Which statement is true?
[A]
d5 i < d5 i ×d5 i
3 –5
–7
–8
3 –5
–7
–8
3 –5
–7
–8
54. Which statement is true?
–14
[A]
d id i
3
< 3–13 × 3–12
–13
3
55. Which statement is true?
–14
[A]
d2 i
–5 3
d id i
–18
2
< –2
2
[B]
–14
d2 i
–5 3
d id i
–18
2
> –2
2
[C]
d2 i
–5 3
56. Which statement is true?
[A]
d6 i ×d6 i < d6 i
3
7
5 2
[B]
d6 i ×d6 i > d6 i
[B]
d id i
3
7
5 2
[C]
d6 i ×d6 i = d6 i
[C]
d2 i ×d2 i
3
7
5 2
57. Which statement is true?
[A]
d id i
20
2
2 ×2 < 8
2
5
7
20
2
2 ×2 > 8
2
5
7
124
5
7
20
2
= 8
2
–18
2
= –2
2
Topic 5 - Properties of Powers
Obj. 87 - Apply properties of exponents to monomial algebraic expressions
Simplify:
58.
c
6 x 3 – 3x 2 y 8
h
3
24 x 9 y 2
[A]
– 27 x 6 y 22
4
c
59. − x 0 y –5 3x –1 y 3
[B]
h
4
c6m h
3 3
60.
61.
c– 15m hm
–8
[A] −
2
[A]
c h
[A] − 20b15
5 –1
–7
0 –1
2
c− 2wz hc4z h
c− 5w h
−2
−3
−4 0
3y 7
x
72m25
[A] −
5
c4 gh h c3h g h
62. – 5b 6 4b 7
63.
– 27 x 9 y 22
4
[A]
[B] −
– 3 y 22
4
81
x 4 y8
72
[B] − 16
5m
1
gh 4
– 8z 5
w2
[C]
[B]
[B]
h2
12 g
1
− 20b 2
[B]
125
– 8w 2
z5
[D]
[C] −
81y 7
x4
72m15
[C] −
5
[C]
12h 2
g
[C] − 80b 20
[C]
– 8w
z5
– 27 y 22
4
[D] −
3y 7
x4
72m12
[D] −
5
[D]
4h 2
3g
[D] − 20b 20
[D] − 8w 2 z 5
Topic 6 - Polynomial Expressions
Obj. 88 - Apply terminology related to polynomials
1. Which word is used to classify the expression − 2d + 2?
[A] quadratic
[B] linear
[C] constant
[D] cubic
[C] 5 − 2 y
[D] − 2 y + 5
2. Which polynomial is in standard form?
[A] 5 − 3 − 2 y
[B] − 2 y + 5 − 3
3. Based on its number of terms, what is the polynomial p 3 + p 2 + 5 p called?
[A] trinomial
[B] binomial
[C] cubic
[D] quadratic
4. What is the leading coefficient of 5z 3 + z 2 − 8z − 7?
[A] 1
[B] 5
[C] – 8
[D] 3
[C] – 4
[D]
5. Which expression is a polynomial?
[A] – 9 y
[B]
2
z
9x2
7y
6. How many terms will be in the polynomial 9 x + 3 − 4 x if it is written in standard form?
[A] 2
[B] 3
[C] 1
[D] 9
Obj. 89 - Multiply two monomial algebraic expressions
Simplify:
7.
8.
b– 3agb5bg
8b6a gbbg
[A] – 15 + ab
[A] 48a + 48b
[B] – 3a + 5b
[B] 14ab
126
[C] – 15ab
[D] 2ab
[C] 14a + 14b
[D] 48ab
Topic 6 - Polynomial Expressions
Obj. 90 - Simplify a polynomial expression by combining like terms
Simplify:
9. x 2 + 5x − 6 x 2 − 9 x
[A] − 5x 2 − 4 x
b
[C] 6 x 2 − 15x
[B] 6 x 2 + 3x
[D] − 5x 2 + 14 x
g
10. – 5 − 3a + 7 + 2a − 5a 2 − 3
[A] − 5a 2 − a − 38
[B] − 5a 2 + 17a − 38
c
11. 4 6 x − 9 x 2 − 9 x + 4 x 2
[C] − 5a 2 + 17a + 4
[D] − 5a 2 − a + 4
h
[A] − 5x 2 − 12 x
[B] − 5x 2 − 3x
[C] − 20 x 2 − 3x
[D] − 20 x 2 − 12 x
12. − 3 − 4 x 3 + 8 x 2 + 7 x 3 − 6 − 5x 2
[A] − 7 x 3 + 15x 2 − 11
c
[B] − 7 x 3 + 3x 2 + 1
[C] 3x 3 + 3x 2 − 9
[D] 3x 3 + 2 x 2 − 8
h
13. w + 6 − 2 w 2 − 2 + 9 w 3 − 1
[A] 9 w 3 − 12 w 2 + w − 13
[B] 9 w 3 − 12 w 2 + w − 12
[C] 9 w 3 − 12 w 2 + w − 3
[D] 9 w 3 − 2 w 2 + w − 13
c
14. − 36q + 3q 3 − 4q 2 − 7 + 4 9q 3 + 9q + 4
h
[A] 36q 3 − 4q 2 + 9
[B] 39q 3 − 4q 2 + 36q + 16
[C] 36q 3 − 4q 2 + 36q + 16
[D] 39q 3 − 4q 2 + 9
Obj. 91 - Add polynomial expressions
Simplify:
15.
c 3 x − 2 x + 4 h + c9 x + 7 x h
5
[A] − 6 x 5 − 9 x + 4
5
[B] 12 x 5 − 2 x + 4
[C] − 6 x 5 − 2 x + 4
127
[D] 12 x 5 + 5x + 4
Topic 6 - Polynomial Expressions
Simplify:
16.
17.
c3b
h c
− 3b5 + 3 + 7b 5 + 9 + 7b 4 + 3b 2
4
[A] 4b5 + 10b 4 + 3b 2 − 6
[B] 10b 5 + 6b 4 + 3b 2 − 6
[C] 4b5 + 10b 4 + 3b 2 + 12
[D] 10b 5 + 6b 4 + 3b 2 + 12
c9 p
2
h c
+ 4 p − 9 + 7 p2 − 8 p + 2
[A] 16 p 2 + 12 p − 7
18.
19.
20.
h
c 4t
5
h
[B] 16 p 2 − 4 p − 7
h c
+ 6t 4 + 8t 2 − 3 + 8t 5 − 6t 4
[C] 16 p 2 + 12 p − 11
[D] 16 p 2 − 4 p − 11
h
[A] 12t 5 + 12t 4 + 8t 2 − 9
[B] 12t 5 + 12t 4 + 8t 2 − 3
[C] 12t 5 + 8t 2 − 3
[D] 12t 5 + 8t 2 − 9
c− 3w
2
h c
− 7 w 4 − 3 + − 5w + 9 w 4
h
[A] 2 w 4 − 8w 2 − 3
[B] 2 w 4 − 3w 2 − 5w − 3
[C] 6w 4 − 3w 2 − 5w − 3
[D] 6w 4 + 2 w 2 − 3
c3 p − 3 − 7 p − 9 p h + c − 5 p − 9 p + 5 − 9 p h
3
5
2
5
3
2
[A] − 2 p5 − 12 p 3 − 18 p 2 + 2
[B] − 12 p 5 − 6 p 3 − 18 p 2 − 12
[C] − 2 p5 − 2 p 3 − 18 p 2 − 12
[D] − 12 p 5 − 6 p 3 − 18 p 2 + 2
Obj. 92 - Subtract polynomial expressions
Simplify:
21.
c− 4 y + 2 y + 6h − c− 3y − 5yh
5
[A] − y 5 + 7 y + 6
5
[B] − y 5 − 3 y − 6
[C] − 7 y 5 + 7 y − 6
128
[D] − 7 y 5 − 3 y + 6
Topic 6 - Polynomial Expressions
Simplify:
22.
23.
24.
25.
c6 g + 7 g
2
h c
− 8g 4 − 8g + 9 g 2 + 6g 4 + 9 g 3
[A] − 14 g 4 + 9 g 3 − 2 g 2 − 2 g
[B] − 14 g 4 + 9 g 3 + 16 g 2 + 14 g
[C] − 14 g 4 − 9 g 3 − 2 g 2 − 2 g
[D] − 14 g 4 − 9 g 3 + 16 g 2 + 14 g
cm − m − 2m − 8h − c3m − 8m + 1h
3
2
3
[A] 4m3 − m2 − 10m − 7
[B] − 2m3 − m2 + 6m − 7
[C] − 2m3 − m2 + 6m − 9
[D] 4m3 − m2 + 6m − 9
c− 3d
4
h c
+ 2d 3 − 2d 2 + 3d − − 2d 3 − 2d 2 + d
h
[A] − 3d 4 + 2d
[B] − 3d 4 + 4d 3 + 2d
[C] − 3d 4 − 4d 2 + 4d
[D] − 3d 4 + 4d 3 − 4d 2 + 4d
c− 9n − 7n h − c8n − 8 − 6n h
2
2
[A] − n 2 − 17n + 8
26.
h
c3z
3
[B] − 15n 2 − 15n − 8
h c
+ 7 z + 7 z 2 + 4 z 4 − 7 z + 6z 2 − 9 z 4 − 9 z 3
[C] − 13n 2 + 17n + 8
[D] − 15n 2 − n − 8
h
[A] − 5z 4 − 6z 3 + 13z 2 + 14 z
[B] 13z 4 − 6z 3 + z 2
[C] 13z 4 + 12 z 3 + z 2
[D] − 5z 4 − 6z 3 + 13z 2
Obj. 93 - Multiply a polynomial by a monomial
Simplify:
b
27. 3d 5d − 2
c
g
28. − 7 x 3 3x 2 + 6 x
[A] 15d 2 + d
[B] 15d 2 − 6d
[C] 8d 2 − 6d
[D] 8d 2 + d
h
[A] − 21x 5 − 42 x 4
[B] − 21x 6 − 42 x 3
129
[C] 21x 6 + 42 x 3
[D] 21x 5 + 42 x 4
Topic 6 - Polynomial Expressions
Simplify:
c
29. − 2b 2 c 2 2c 4 + 3d 2 + 4c
h
[A] − 4b 2 c8 − 6b 2 c 2 d 2 − 8b 2 c 2
[B] b 2 c 2 d 2 + 2b 2 c 2
[C] − 4b 2 c 6 − 6b 2 c 2 d 2 − 8b 2 c 3
[D] b 2 c 2 d 2 + 2b 2 c 3
c
30. 2 z 5 9 z 2 + 3z − 4
h
[A] 11z 10 + 5z 5 − 2 z 5
[B] 18z 7 + 6z 6 − 8z 5
[C] 18z10 + 6z 5 − 8z 5
[D] 11z 7 + 5z 6 − 2 z 5
c
31. − 9d 4 2d 3 − 6d 2 − 7
h
[A] − 18d 12 + 54d 8 + 63d 4
[B] 18d 7 − 54d 6 − 63d 4
[C] 18d 12 − 54d 8 − 63d 4
[D] − 18d 7 + 54d 6 + 63d 4
c
32. 4 xy 4 2 x 3 + 2 xy 2
h
[A] 8 x 3 y 4 + 8 xy 8
[B] 8 x 4 y 4 + 8 x 2 y 6
[C] 8 x 4 y 4 + 8 xy 8
[D] 8 x 3 y 4 + 8 x 2 y 6
Obj. 94 - Multiply two binomials of the form (x +/- a)(x +/- b)
Simplify:
33.
bm + 1gbm + 5g
34.
bc + 7gbc − 4g
[A] c 2 + 11c − 28
35.
bd − 5gbd − 6g
36.
bq + 9gbq + 9g
[A] q 2 + 18
[A] m2 + 6m + 5
[B] m2 + 5m + 5
[B] c 2 + 3c − 28
[A] d 2 + d + 30
[C] m2 + 6
[C] c 2 − 11c − 28
[B] d 2 − 11
[B] q 2 + 9q + 81
130
[D] c 2 + 3c + 28
[C] d 2 − 11d + 30
[C] q 2 + 81
[D] m2 + 5
[D] d 2 + 30
[D] q 2 + 18q + 81
Topic 6 - Polynomial Expressions
Simplify:
37.
38.
b y − 14gb y + 14g
[A] y 2 − 196
[B] y 2 + 196
bd − 4gbd − 4g
[A] d 2 + 16
[C] y 2 + 28 y + 196
[B] d 2 − 8d + 16
[D] y 2 + 28 y − 196
[C] d 2 − 8d − 16
[D] d 2 − 8
Obj. 95 - Multiply two binomials of the form (ax +/- b)(cx +/- d)
Simplify:
39.
b3x + 5gb4 x + 3g
[A] 12 x 2 + 15
40.
[B] 7 x 2 + 8
[B] 10a 2 − 34a + 28
[B] 21b 2 + 36b + 60
[D] 20 g 2 + 3g + 2
[C] 10a 2 − 34a − 11
[D] 10a 2 − 6a + 28
[C] 21b 2 + 60b + 36
[D] 21b 2 + 36
b5z − 14gb4z + 13g
[A] 20z 2 + 9 z + 182
44.
[C] 20 g 2 + 2
b7b + 6gb3b + 6g
[A] 10b 2 + 12
43.
[B] 20 g 2 − 35
b5a − 7gb2a − 4g
[A] 10a 2 − 6a − 11
42.
[D] 12 x 2 + 15x + 29
b5g + 7gb4 g − 5g
[A] 20 g 2 + 3g − 35
41.
[C] 12 x 2 + 29 x + 15
[B] 20z 2 + 9 z − 182
[C] 20z 2 − 182
[D] 20z 2 + 182
b7c − 3gb3c − 3g
[A] 21c 2 + 9
[B] 21c 2 − 6
[C] 21c 2 − 30c − 9
131
[D] 21c 2 − 30c + 9
Topic 6 - Polynomial Expressions
Obj. 96 - Multiply two binomials of the form (ax +/- by)(cx +/- dy)
Simplify:
45.
46.
b5x + 7 ygb3x + 4 yg
[A] 8 x 2 + 11y 2
[B] 15x 2 + 28 x y + 41y 2
[C] 15x 2 + 28 y 2
[D] 15x 2 + 41x y + 28 y 2
b4a + 5bgb2a − 7bg
[A] 8a 2 − 35b 2
47.
[B] 8a 2 − 18ab − 35b 2
49.
50.
[D] 8a 2 + 18ab − 35b 2
b2a − 3bgb5a − 2bg
[A] 10a 2 + 19ab + 6b 2
48.
[C] 6a 2 − 35b 2
[B] 10a 2 + 6b 2
[C] 10a 2 − 19ab + 6b 2
b4 y + 7zgb6 y + 7zg
[A] 24 y 2 + 70 yz + 49 z 2
[B] 10 y 2 + 14 z 2
[C] 24 y 2 + 49 z 2
[D] 24 y 2 + 49 yz + 70z 2
b9 p − 5qgb8 p + 5qg
[A] 72 p 2 − 5 pq − 25q 2
[B] 72 p 2 − 25q 2
[C] 17 p 2 − 25q 2
[D] 72 p 2 + 5 pq − 25q 2
b8a − 3bgb7a − 4bg
[A] 15a 2 + 12b 2
[B] 56a 2 − 53ab + 12b 2
[C] 56a 2 + 12b 2
[D] 56a 2 + 53ab + 12b 2
132
[D] 7a 2 − 5b 2
Topic 6 - Polynomial Expressions
Obj. 97 - Square a binomial
Simplify:
51.
b p + 9g
52.
b4b + 6cg
53.
[A] p 2 + 81 p + 18
2
[C] p 2 + 18 p + 81
[A] 16b 2 + 24bc + 36c 2
[B] 16b 2 + 20bc + 36c 2
[C] 16b 2 + 36c 2
[D] 16b 2 + 48bc + 36c 2
b7w + 3g
2
54.
br − 8g
55.
b3 p − 5qg
[B] 49 w 2 + 42 w + 9
[A] r 2 + 64
2
[C] 49 w 2 + 9
[B] r 2 + 16r + 64
[C] r 2 + 16
[D] 49 w 2 + 6
[D] r 2 − 16r + 64
2
[A] 9 p 2 + 25q 2
[B] 9 p 2 − 30 pq + 25q 2
[C] 9 p 2 − 15 pq + 25q 2
[D] 9 p 2 − 16 pq + 25q 2
b3c − 6g
[A] 9c 2 − 36c + 36
2
[B] 9c 2 − 12
[C] 9c 2 + 36c + 36
Obj. 98 - Multiply two nonlinear binomials
Simplify:
57.
d7c + 5id4c + 3i
3
[D] p 2 81
2
[A] 49 w 2 + 21w + 9
56.
[B] p 2 + 18
4
[A] 28c12 + 15
[B] 28c 7 + 15
[C] 28c 7 + 20c 4 + 21c 3 + 15
[D] 28c12 + 20c 4 + 21c 3 + 15
133
[D] 9c 2 + 36
Topic 6 - Polynomial Expressions
Simplify:
58.
d4 x − 3id3x + 2i
3
3
[A] 12 x 6 − 6
59.
60.
61.
[B] 12 x 6 − 1
[D] 12 x 6 − x 3 − 6
d8q − 7qid9q − 4i
2
4
[A] 72q 8 + 28q
[B] 72q 6 − 63q 5 − 32q 2 + 28q
[C] 72q 6 + 28q
[D] 72q 8 − 63q 5 − 32q 2 + 28q
d3b
3
id
+ 7b 7b 4 − 3b
i
[A] 21b 7 − 21b 2
[B] 21b 7 + 49b5 − 9b 4 − 21b 2
[C] 21b12 − 21b 2
[D] 21b12 − 49b5 + 9b 4 − 21b 2
d5y + 1id5y + 1i
4
4
[A] 10 y 8 + 2
62.
[C] 12 x 6 − 9 x 3 − 6
d7h − 3id9h
2
2
[B] 10 y 8 + 5 y 4 + 2
− 12
[C] 25 y 8 + 1
[D] 25 y 8 + 10 y 4 + 1
i
[A] 63h 4 – 27h 2 + 36
[B] 63h 4 + 36
[C] 16h 4 − 15
[D] 63h 4 − 111h 2 + 36
Obj. 99 - Multiply a trinomial by a binomial
Simplify:
63.
b x + 3gc x
2
h
− 5x + 6
[A] x 3 − 5x 2 + 6 x + 18
[B] x 3 − 2 x 2 − 9 x + 18
[C] x 3 − 2 x 2 − 15x + 18
[D] x 3 − 5x 2 − 9 x + 18
134
Topic 6 - Polynomial Expressions
Simplify:
64.
65.
66.
67.
68.
b x − 3gc9 x
2
+ 27 x − 2
h
[A] 9 x 3 + 27 x 2 − 83x + 6
[B] 9 x 3 + 27 x 2 − 3x + 6
[C] 9 x 3 − 83x + 6
[D] 9 x 3 − 81x + 6
c− 20x
2
g
hb
+ 21x − 4 4 x − 1
[A] − 80 x 3 + 84 x 2 − 16 x + 4
[B] − 80 x 3 + 84 x 2 − 37 x + 4
[C] − 80 x 3 + 104 x 2 − 37 x + 4
[D] − 80 x 3 + 104 x 2 − 21x + 4
b2 x + 1gc− 4 x
2
− 20 x − 24
h
[A] − 8 x 3 − 40 x 2 − 68 x − 24
[B] − 8 x 3 − 44 x 2 − 68 x − 24
[C] − 8 x 3 − 40 x 2 − 48 x − 24
[D] − 8 x 3 − 44 x 2 − 20 x − 24
c9 x
2
hb g
− 15x − 6 x − 3
[A] 9 x 3 − 15x 2 − 6 x + 18
[B] 9 x 3 − 15x 2 + 39 x + 18
[C] 9 x 3 − 42 x 2 + 45x + 18
[D] 9 x 3 − 42 x 2 + 39 x + 18
b2 x + 3gc x
2
h
+ 10 x + 21
[A] 2 x 3 + 23x 2 + 72 x + 63
[B] 2 x 3 + 72 x 2 + 23x + 63
[C] 2 x 3 + 42 x 2 + 20 x + 63
[D] 2 x 3 + 20 x 2 + 42 x + 63
135
Topic 7 - Factor Algebraic Expressions
Obj. 100 - Factor the GCF from a polynomial expression
1. Factor the expression using the greatest common factor.
33w5 − 22
c
h
c
[A] 2 2 w5 − 3
h
c
[B] 2 17 w5 − 11
[C] 11 3w5 − 22
h
c
[D] 11 3w5 − 2
h
2. Factor the expression using the greatest common factor.
− 48 x 6 − 12 x 4 − 60 x 2
c
[A] – 12 4 x 6 + x 4 + 5x 2
h
c
c
h
[B] – 12 x 2 4 x 4 + x 2 + 5
h
c
[C] – 12 x 2 4 x 4 + 5x 2 + 1
h
[D] – 12 4 x 6 + 5x 4 + 1
3. Factor the expression using the greatest common factor.
− 12c8d 7 − 12c 2 d 9 + 6c 6d 2
c
[A] − 6c 2 d 2 12c8d 7 + 12c 2 d 9 − 6c 6 d 2
c
[C] – 6 12c8d 7 + 12c 2 d 9 − 6c 6d 2
h
c
h
c
[D] − 6c 2 d 2 2c 6 d 5 + 2d 7
4. Factor the expression using the greatest common factor.
− 5d 4 − 3d 3
c
[A] − d 5d 3 + 3d 2
h
c
[B] − d 2 5d 2 + 3d
h
b
g
h
− 11h
[A] − v 14v 6 − 3v 3 − 11
[C]
6
− 3v 4
c
− vc14v
[D] − d 3 5d + 3d
h
− 11v h
[B] − v 14v 7 − 3v 4 − 11v
[D]
6
− 3v 3
6. Factor the expression using the greatest common factor.
70k 2 m5 − 10m3
c
h
10m c70k m − 10m h
c
[A] 10m3 7 k 2 − m3
[C]
3
2
5
h
[B] 10m3 7 k 2 m2 − 1
c
[D] 10 7 k 2 m5 − m3
3
136
4
b
[C] − d 3 5d + 3
5. Factor the expression using the greatest common factor.
− 14v 7 + 3v 4 + 11v
c
− vc14v
h
−c h
[B] – 6 2c8d 7 + 2c 2 d 9 − c 6d 2
h
g
Topic 7 - Factor Algebraic Expressions
Obj. 101 - Factor trinomials that result in factors of the form (x +/- a)(x +/- b)
Factor:
7. b 2 + 13b + 12
[A]
bb – 1gbb – 12g
[B]
bb – 3gbb – 4g
[C]
bb + 3gbb + 4g
[D]
bb + 1gbb + 12g
[B]
bn – 1gbn – 3g
[C]
bn – 3gbn + 1g
[D]
bn – 1gbn + 3g
[B]
bu – 2gbu + 3g
[C]
bu – 6gbu + 1g
[D]
bu – 1gbu + 6g
[B]
bc + 3gbc + 16g
[C]
bc + 6gbc + 8g
[D]
bc + 4gbc + 12g
[B]
bd – 6gbd – 14g
[C]
bd – 7gbd – 12g
[B]
b x – 8gb x + 6g
8. n 2 − 4n + 3
[A]
bn + 1gbn + 3g
9. u 2 − u − 6
[A]
bu – 3gbu + 2g
10. c 2 + 14c + 48
[A]
bc – 4gbc – 12g
11. d 2 − 20d + 84
[A]
bd – 3gbd – 24g
12. x 2 + 8 x − 48
[A]
b x – 4gb x + 12g
[C]
b x – 6gb x + 8g
[D]
[D]
bd – 7gbd + 12g
b x – 12gb x + 4g
Obj. 102 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)
Factor:
13. 8c 2 + 26c + 15
[A]
[C]
b4c + 15gb2c + 1g
b4c + 1gb2c + 15g
[B]
[D]
137
b4c + 5gb2c + 3g
b4c + 3gb2c + 5g
Topic 7 - Factor Algebraic Expressions
Factor:
14. 12 g 2 − 77 g + 30
[A]
[C]
b12 g − 6gb g − 5g
b12 g − 5gb g − 6g
[B]
[D]
15. 27n 2 + 39n − 10
[A]
[C]
b9n − 10gb3n + 1g
b9n + 5gb3n − 2g
[B]
[D]
16. 28v 2 + 53v + 7
[A]
[C]
b4v + 7gb7v + 1g
b4v − 1gb7v − 7g
[B]
[D]
17. 45d 2 + 97d + 40
[A]
[C]
b9d + 5gb5d + 8g
b9d + 2gb5d + 20g
[B]
[D]
18. 9v 2 − 9v − 40
[A]
[C]
b3v − 4gb3v + 10g
b3v + 5gb3v − 8g
[B]
[D]
b6g − 1gb2 g − 3g
b6g − 3gb2 g − 1g
b9n − 2gb3n + 5g
b9n + 1gb3n − 10g
b4v − 7gb7v − 1g
b4v + 1gb7v + 7g
b9d + 8gb5d + 5g
b9d + 4gb5d + 10g
b3v − 8gb3v + 5g
b3v + 2gb3v − 20g
Obj. 103 - Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy)
Factor:
19. 20c 2 + 21cd + 4d 2
[A]
[C]
b5c + d gb4c + 4d g
b4c + 4d gbc + 5d g
[B]
[D]
138
b5c + 4d gb4c + d g
b4c + 5d gbc + 4d g
Topic 7 - Factor Algebraic Expressions
Factor:
20. 56h 2 − 111hk + 54 k 2
[A]
[C]
b6h + 8k gb9h + 7k g
b6h + 7k gb9h + 8k g
[B]
[D]
21. 15u 2 − 16uv − 15v 2
[A]
[C]
b5u + 5vgb3u − 3vg
b5u + 3vgb3u − 5vg
[B]
[D]
b7h − 9k gb8h − 6k g
b7h − 6k gb8h − 9k g
b3u + 3vgb5u − 5vg
b3u + 5vgb5u − 3vg
22. 35 y 2 + 52 yz + 12 z 2
[A]
[C]
b2 y + 7zgb6 y + 5zg
b2 y + 5zgb6 y + 7zg
[B]
[D]
23. 36c 2 + 7cd − 4d 2
[A]
[C]
b4c − 4d gb9c + d g
bc − 4d gb4c + 9d g
[B]
[D]
24. 18k 2 + 73km − 36m2
[A]
[C]
b9k − 9mgb2k + 4mg
b9k − 4mgb2k + 9mg
b7 y + 2zgb5y + 6zg
b7 y + 6zgb5y + 2zg
bc − 9d gb4c + 4d g
b4c − d gb9c + 4d g
[D]
b4k − 9mgb9k + 2mg
b4k − 2mgb9k + 9mg
[C]
bb − 9gbb + 1g
[B]
Obj. 104 - Factor the difference of two squares
Factor:
25. b 2 − 9
[A]
b9 − bgb1 + bg
[B]
bb − 3gbb + 3g
139
[D]
b3 − bgb3 + bg
Topic 7 - Factor Algebraic Expressions
Factor:
26. h 2 − 36k 2
[A]
[C]
bh + 2k gbh − 18k g
bh + 4k gbh − 9k g
[B]
[D]
27. 9 x 2 − 25
[A]
b5 − 3xgb5 − 3xg
[B]
b5 + 3xgb5 − 3xg
[C]
28. 16t 2 − 9u 2
[A]
[C]
b4t − 3ugb4t + 3ug
b3u − 4t gb3u + 4t g
[B]
[D]
bh + 3k gbh − 12k g
bh + 6k gbh − 6k g
b3x + 5gb3x − 5g
[D]
b3x + 5gb3x + 5g
b3u + 4t gb3u + 4t g
b4t − 3ugb4t − 3ug
29. 361 − p 2
[A]
[C]
b p − 1gb p + 361g
b1 − pgb361 + pg
[B]
[D]
30. 169 − 225a 2
[A]
[C]
b13 − 15agb13 − 15ag
b15a + 13gb15a + 13g
b p − 19gb p + 19g
b19 − pgb19 + pg
[D]
b13 − 15agb13 + 15ag
b15a − 13gb15a + 13g
[C]
bb − 5gbb − 5g
[B]
Obj. 105 - Factor a perfect-square trinomial
Factor:
31. b 2 − 10b + 25
[A]
bb − 25gbb − 1g
[B]
bb − 25gbb + 1g
140
[D]
bb − 5gbb + 5g
Topic 7 - Factor Algebraic Expressions
Factor:
32. 49 p 2 − 14 p + 1
[A]
[C]
b49 p + 1gb p − 1g
b49 p − 1gb p − 1g
[B]
[D]
33. 4u 2 + 12uv + 9v 2
[A]
[C]
b3u + 2vgb3u + 2vg
b2u + 3vgb2u + 3vg
[B]
[D]
b7 p − 1gb7 p − 1g
b7 p + 1gb7 p − 1g
b2u + 3vgb2u − 3vg
b3u + 2vgb3u − 2vg
34. 169 + 26 y + y 2
[A]
[C]
b y + 169gb y + 1g
b y + 13gb y + 13g
[B]
[D]
35. 9c 2 + 24c + 16
[A]
b3c − 4gb3c − 4g
[B]
b3c + 4gb3c + 4g
[C]
36. 49 k 2 + 14 km + m2
[A]
[C]
b7k + mgb7k + mg
b7k + mgb7k − mg
[B]
[D]
b y − 169gb y − 1g
b y − 13gb y − 13g
b9c − 1gbc − 16g
[D]
b9c + 1gbc + 16g
bk + 7mgbk − 7mg
bk + 7mgbk + 7mg
Obj. 106 - Factor a polynomial that has a GCF and two linear binomial factors
Factor:
37. 10c 2 + 35c − 20
b gb g
– 5bc + 4gb2c − 1g
b gb g
5bc + 4gb2c − 1g
[A] – 5 c − 4 2c + 1
[B] 5 c − 4 2c + 1
[C]
[D]
141
Topic 7 - Factor Algebraic Expressions
Factor:
38. 3t 6 − 192t 4
b gb g
− 3t bt + 8gbt − 8g
[C]
4
[D]
39. − 2a 6 + 4a 5 + 70a 4
b gb g
2a ba − 5gba − 7g
[A] − 2a 4 a + 5 a + 7
[C]
4
b gb g
− 2a ba − 5gba + 7g
[B] − 2a 4 a + 5 a − 7
4
[D]
40. 35h 4 + 4h 3 − 15h 2
b gb g
h b7h + 5gb5h − 3g
[A] h 2 7h − 5 5h + 3
[C]
b gb g
3t bt + 8gbt − 8g
[B] − 3t 4 t + 8 t + 8
[A] 3t 4 t + 8 t + 8
4
b gb g
h b5h − 5gb7h + 3g
[B] h 2 5h + 5 7h − 3
2
[D]
2
41. − 16q 4 − 48q 3 − 36q 2
b gb g
− 4q b2q − 3gb2q − 3g
[A] − 4q 2 16q − 9 q − 1
[C]
2
[D]
42. − 81c 4 + 153c 3 + 168c 2
b gb g
− 3c b3c + 8gb9c − 7g
[A] − 3c 2 3c + 7 9c − 8
[C]
b gb g
− 4q b16q + 1gbq + 9g
[B] − 4q 2 2q + 3 2q + 3
2
b gb g
− 3c b3c − 8gb9c + 7g
[B] − 3c 2 3c − 7 9c + 8
2
[D]
142
2
Topic 8 - Quadratic Equations and Functions
Obj. 107 - Determine the graph of a given quadratic function
1. Which graph shows y = − x 2 + 3?
[A]
[B]
y
10
–10
10 x
y
10
–10
–10
[C]
–10
[D]
y
10
–10
10 x
y
10
–10
–10
2. Which graph shows y =
10 x
10 x
–10
5 2
x + 6x?
2
143
Topic 8 - Quadratic Equations and Functions
[A]
y
10
–10
10 x
–10
[B]
y
10
–10
10 x
–10
[C]
y
10
–10
10 x
–10
[D]
y
10
–10
10 x
–10
(2.)
144
Topic 8 - Quadratic Equations and Functions
3. Which graph shows y = − x 2 + 2 x − 2?
[A]
[B]
y
10
–10
10 x
y
10
–10
–10
[C]
–10
[D]
y
10
–10
10 x
10 x
y
10
–10
–10
10 x
–10
145
Topic 8 - Quadratic Equations and Functions
bg
4. Which graph shows f x = −
1 2
x ?
4
bg
[A]
–10
bg
[B]
f x
10
10 x
f x
10
–10
–10
–10
bg
[C]
bg
[D]
f x
10
–10
10 x
10 x
f x
10
–10
–10
10 x
–10
5. Which graph shows y = − 3x 2 + 3?
[A]
[B]
y
10
–10
10 x
y
10
–10
–10
[C]
–10
[D]
y
10
–10
10 x
10 x
y
10
–10
–10
10 x
–10
146
Topic 8 - Quadratic Equations and Functions
6. Which graph shows y =
[A]
2 2
x + x – 3?
3
[B]
y
10
–10
10 x
y
10
–10
–10
[C]
–10
[D]
y
10
–10
10 x
10 x
y
10
–10
–10
10 x
–10
147
Topic 8 - Quadratic Equations and Functions
Obj. 108 - WP: Answer a question using the graph of a quadratic function
7. Students prepared for an experiment in physics class by drawing a graph of the height of a
golf ball thrown upward from a height of 16 feet, assuming there is no air resistance.
80
60
40
20
0
2
4
6
8
Time (seconds)
10
According to the graph, about how much time should pass before the golf ball reaches the
ground?
[A] 2.6 s
[B] 2.2 s
[C] 4.8 s
[D] 5.2 s
8. Ms. Webb has 20 feet of fencing. She wants to use all of the fencing to enclose a rectangular
flower bed. The graph below shows how the area of the flower bed depends on the length of
one of its sides.
24
20
16
12
8
4
0
2
4
6
8
Length (feet)
10
What side length will give the flower bed the maximum area?
[A] 5 ft
[B] 12.5 ft
[C] 10 ft
148
[D] 25 ft
Topic 8 - Quadratic Equations and Functions
9. Abbott’s Flower Company specializes in supplying sunflowers to florists. The graph models
the relationship between the number of sunflowers the company sells and its profit from
those sales.
50
40
30
20
10
0
–10
–20
–30
–40
–50
5
10
15
20
Number of Sunflowers Sold (thousands)
About how many sunflowers need to be sold to break even?
[A] 19,000
[B] 5000
[C] 38,000
[D] 45,000
10. In 2008, a car that was manufactured in 1982 had a value of $9500. The value of the car
between 2008 and 2028 is modeled by the graph below. The model of the car’s value
predicts that the car will decrease in value for several years, but will increase in value later
as it becomes popular with car collectors.
20
15
10
5
2008 2013 2018 2023 2028
Year
According to the model, in what year will the value of the car reach its lowest point?
[A] 2017
[B] 2015
[C] 2010
149
[D] 2019
Topic 8 - Quadratic Equations and Functions
11. Mason is training for the javelin-throw event. A coach created a graph that shows the height
of the javelin over time for Mason’s best throw.
14
12
10
8
6
4
2
0
1
2
3
4
Time (seconds)
5
About how far above its initial height was the javelin at its highest point?
[A] 14 m
[B] 10 m
[C] 2 m
[D] 12 m
12. A marketing manager at a company that produces and sells cooking oils uses mathematical
models to determine the prices for the company’s products. The graph below shows how the
weekly revenue is predicted to vary depending on the price set for the smallest bottles of
olive oil that the company sells.
10
8
6
4
2
0
1 2 3 4 5
Price per Bottle ($)
6
What is the maximum revenue predicted by this model?
[A] $6
[B] $7680
[C] $5
150
[D] $8000
Topic 8 - Quadratic Equations and Functions
Obj. 109 - WP: Determine the domain or range of a quadratic function in a given situation
13. Abigail throws a softball and her brother catches it. The graph shows the relationship
between t, the time in seconds, and h, the ball’s height in feet. Which inequality best
describes the domain of the relation?
h
10
5
0
1
2
t
Time (seconds)
[A] 4.2 ≤ h ≤ 5.7
[C] 0 ≤ t ≤ 0.7
[B] 0 ≤ h ≤ 7.0
[D] 0 ≤ t ≤ 2.0
14. Mr. Abaza manages the budget for a museum. The museum is selling tickets to a new
exhibit about Africa. Mr. Abaza determines that the weekly profit the museum can earn
selling family-admission tickets at a price of n dollars can be estimated using the function
P = −9n 2 + 240n. Over what domain does the function predict increasing profits from the
sale of family-admission tickets?
P
3000
2500
2000
1500
1000
500
0
10
20 30 40 50
Family-admission
Ticket Price ($)
[A] 0 ≤ P ≤ 1599
60 n
[B] P ≥ 0
[C] 0 ≤ n ≤ 13
151
[D] all real numbers
Topic 8 - Quadratic Equations and Functions
15. A baseball player hits a fly ball that lands on the ground in center field. The ball’s height in
feet, h, is given by the function h = − 16t 2 + 108t + 3.75. The graph of the function is shown
below. Which inequality best describes the range of the function as it applies to the
baseball?
h
200
150
100
50
0
1
2
3 4 5 6
Time (seconds)
[A] 3.75 ≤ h ≤ 186
7 t
[B] t ≥ 0
[C] 0 ≤ h ≤ 186
[D] 0 ≤ t ≤ 6.8
16. For one type of kitchen cabinet, the manufacturer determines that the function
n = − 6 p 2 + 1008 p − 120 can be used to estimate n, the number of those cabinets that can be
sold at a price of p dollars each. The cabinets will never be sold for less than the amount it
costs to manufacture and distribute them, which is an average of $109 per cabinet. Which
inequality best describes the domain over which the function should be used to estimate the
number of cabinets that can be sold?
n
50,000
40,000
30,000
20,000
10,000
0
[A] 0 ≤ p ≤ 168
50
100 150
Price ($)
200
[B] 109 ≤ p ≤ 168
p
[C] 0 ≤ n ≤ 42,000
152
[D] 109 ≤ n ≤ 42,000
Topic 8 - Quadratic Equations and Functions
17. A company that makes scented candles estimates that its net profit can be modeled by the
function P = − 0.005x 2 + 44 x − 8000 if the range of the function is restricted to nonnegative
values. P represents the net profit, and x represents the number of boxes of candles
produced. A graph of the function is shown below. Which inequality best describes the
range of the function used by the company?
P
100
90
80
70
60
50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10
x
Number of Boxes of Candles
(in thousands)
[A] 200 ≤ x ≤ 8600
[C] 0 ≤ P ≤ 89,000
[B] P ≤ 10,000
153
[D] x ≤ 9000
Topic 8 - Quadratic Equations and Functions
18. The main cables of a suspension bridge form a parabola. Each cable hangs between two
vertical towers that are 350 feet apart. For any point on a main cable between the towers, the
height of that point above the roadbed of the bridge can be found using the function
h = 0.0016 x 2 − 0.5529 x + 56, where x is the distance in feet from one tower. Which
inequality best describes the range of the function if the domain is restricted to the distance
between the towers?
h
100
90
80
70
60
50
40
30
20
10
0
100
200
300
x
Distance from Tower (feet)
[A] 8 ≤ h ≤ 56
[B] 0 ≤ h ≤ 56
[C] 0 ≤ h ≤ 350
[D] h ≥ 8
Obj. 110 - Determine the result of a change in a or c on the graph of y = ax^2 + c
19. How is the graph of y = 3x 2 + 9 different from the graph of y = 3x 2 + 8?
[A] The graph of y = 3x 2 + 9 is 1 unit to the left of the graph of y = 3x 2 + 8.
[B] The graph of y = 3x 2 + 9 is 1 unit higher than the graph of y = 3x 2 + 8.
[C] The graph of y = 3x 2 + 9 is 1 unit to the right of the graph of y = 3x 2 + 8.
[D] The graph of y = 3x 2 + 9 is 1 unit lower than the graph of y = 3x 2 + 8.
154
Topic 8 - Quadratic Equations and Functions
bg
bg
20. What is the difference between the graphs of f x = −4 x 2 + 4 and g x = 3x 2 + 4?
[B] f b x g is narrower than g b x g.
bg
bg
f b x g is narrower than gb x g and opens in the opposite direction.
f b x g is wider than gb x g and opens in the opposite direction.
[A] f x is wider than g x .
[C]
[D]
Obj. 111 - Solve a quadratic equation by graphing the associated quadratic function
21. Solve − 2 x 2 − x − 2 = 0 by graphing the function y = − 2 x 2 − x − 2.
y
10
10 x
–10
–10
[A] x = –2
[B] x = 1 or x = 2
[C] x = –1
[D] no real solution
22. Solve x 2 + 18 x + 81 = 0 by graphing the function y = x 2 + 18 x + 81.
y
10
10 x
–10
–10
[A] x = 9
[B] x = –9
[C] x = –9 or x = 9
155
[D] no real solution
Topic 8 - Quadratic Equations and Functions
23. Solve x 2 − 5x − 14 = 0 by graphing the function y = x 2 − 5x − 14.
y
10
10 x
–10
–10
[A] x = 1 or x = 14
[B] x = –7 or x = 2
[C] x = –2 or x = 7
[D] no real solution
24. Solve 3x 2 − 6 x + 3 = 0 by graphing the function y = 3x 2 − 6 x + 3.
y
10
10 x
–10
–10
[A] x = –1
[B] x = –2
[C] x = 2
156
[D] x = 1
Topic 8 - Quadratic Equations and Functions
25. Solve 3x 2 + 12 x = 0 by graphing the function y = 3x 2 + 12 x.
y
10
10 x
–10
–10
[A] x = 0 or x = 4
[B] x = –4 or x = –1
[C] x = –4
[D] x = –4 or x = 0
26. Solve − 5x 2 − 45x − 100 = 0 by graphing the function y = − 5x 2 − 45x − 100.
y
10
10 x
–10
–10
[A] x = –20 or x = –1
[B] x = –5 or x = –4
[C] x = 20
[D] x = 4 or x = 5
Obj. 112 - Solve a quadratic equation by taking the square root
Solve:
27. x 2 − 4 = 8
[A] x = 3 2 or x = −3 2
[B] x = 2 or x = −2
[C] x = 2 3 or x = −2 3
[D] no real number solutions
157
Topic 8 - Quadratic Equations and Functions
Solve:
28. 4 x 2 = 45
[A] x =
5 3
5 3
or x = −
4
4
[B] x =
3 5
3 5
or x = −
2
2
[C] x =
3 5
3 5
or x = −
4
4
[D] no real number solutions
29. 2 x 2 − 10 = – 5
[A] x =
30
30
or x = −
2
2
[B] x =
[C] x = 5 or x = − 5
10
10
or x = −
2
2
[D] no real number solutions
30. x 2 − 45 = 0
[A] x = 4 5 or x = −4 5
[B] x = 5 3 or x = −5 3
[C] x = 3 5 or x = −3 5
[D] no real number solutions
31. 11x 2 – 27 = 0
3 33
3 33
or x = −
11
11
[A] x = 3 33 or x = −3 33
[B] x =
[C] x = 3 3 or x = −3 3
[D] no real number solutions
32. 16 x 2 + 11 = – 25
[A] x =
3
3
or x = −
2
2
[B] x =
[C] x =
2
2
or x = −
3
3
[D] no real number solutions
158
9
9
or x = −
4
4
Topic 8 - Quadratic Equations and Functions
Obj. 113 - Determine the solution(s) of an equation given in factored form
Solve:
33.
bb + 6gbb + 1g = 0
[A] b = –6 or b = 1
34.
[C] b = –6 or b = –1
[D] b = 6 or b = 1
b8h + 5gbh + 6g = 0
[A] h = −
[C] h =
35.
[B] b = 6 or b = –1
5
or h = 6
8
[B] h =
5
or h = 6
8
b6q + 3gb6q + 3g = 0
5
or h = –6
8
[D] h = −
[A] q = –2
[B] q = −
1
2
5
or h = –6
8
[C] q =
1
2
[D] q = 2
b g
36. w w + 1 = 0
[A] w = 0 or w = 1
[B] w = –1 or w = 1
[C] w = –1 or w = 2
[D] w = 0 or w = –1
b g
37. – 4a a + 8 = 0
[A] a = 0 or a = –8
38.
[B] a = 0 or a = 8
[C] a = 8 or a = –4
b2k – 9gb3k – 6g = 0
[A] k =
9
or k = –2
2
[C] k = −
[B] k = −
9
or k = 2
2
[D] k =
159
9
or k = –2
2
9
or k = 2
2
[D] a = 8 or a = 4
Topic 8 - Quadratic Equations and Functions
Obj. 114 - Solve a quadratic equation by factoring
39. Solve 9 x 2 − 12 x + 4 = 0 by factoring.
[A] x =
2
2
or x = −
3
3
[B] x = –3 or x = −
4
9
2
3
[C] x =
[D] x = −
2
3
40. Solve 2 x 2 − 44 x + 242 = 0 by factoring.
[A] x = –22
[B] x = –121 or x = –1
[C] x = 11
[D] x = 121
41. Solve x 2 − 11x + 24 = 0 by factoring.
[A] x = –24
[B] x = –8 or x = –3
[C] x = –24 or x = –1
[D] x = 3 or x = 8
42. Solve 15x 2 + 57 x − 12 = 0 by factoring.
[A] x = –4
[B] x = –4 or x =
1
5
[C] x = −
1
5
[D] x = −
1
or x = 4
5
43. Solve 3x 2 − 42 x + 144 = 0 by factoring.
[A] x = –48 or x = –1
[B] x = –8 or x = –6
[C] x = 48
[D] x = 6 or x = 8
44. Solve 6 x + 80 = 2 x 2 by factoring.
[A] x = –40
[B] x = 1 or x = 40
[C] x = –8 or x = 5
[D] x = –5 or x = 8
Obj. 115 - Solve a quadratic equation using the quadratic formula
45. Solve 8 x 2 − 50 x + 75 = 0 by using the quadratic formula.
[A] x = –2.5 or x = –3.75
[B] x = 2.5 or x = 3.75
[C] x = 2.5 or x = –3.75
[D] x = –2.5 or x = 3.75
46. Solve p 2 = − p + 1 by using the quadratic formula.
[A] p = 162
. or p = –0.62
[B] p = –0.62 or p = –1.62
[C] p = 0.62 or p = –1.62
[D] p = 0.62 or p = 162
.
160
Topic 8 - Quadratic Equations and Functions
47. Solve 5 y 2 − 2 y − 5 = 0 by using the quadratic formula.
[A] y = 8.20 or y = –12.20
[B] y = –6.10 or y = –4.10
[C] y = 2.24 or y = –1.84
[D] y = 122
. or y = –0.82
48. Solve 3 y 2 − 8 = 9 y by using the quadratic formula.
[A] y = 7.43 or y = –1.43
[B] y = 3.72 or y = 0.72
[C] y = 3.72 or y = –0.72
[D] y = –7.43 or y = –1.43
49. Solve 10 y 2 = 49 y + 306 by using the quadratic formula.
[A] y = 8.5 or y = –3.6
[B] y = –8.5 or y = 3.6
[C] y = –8.5 or y = –3.6
[D] y = 8.5 or y = 3.6
50. Solve 6 p 2 − 8 p − 7 = 0 by using the quadratic formula. Round the answer to the nearest
hundredth.
[A] p = 121
. , p = –3.87
[B] p = 194
. , p = –0.60
[C] p = 387
. , p = –1.21
[D] p = 0.60, p = –1.94
Obj. 116 - Use the discriminant to determine the number of real solutions
51. Use the discriminant to determine the number of real solutions for the equation
2 x 2 − 3x = – 6.
[A] 0
[B] 1
[C] 2
52. Use the discriminant to determine the number of real solutions for the equation
4 x 2 + 64 = 32 x.
[A] 0
[B] 1
[C] 2
53. Use the discriminant to determine the number of real solutions for the equation
2n 2 − 13n − 9 = 0.
[A] 0
[B] 1
[C] 2
161
Topic 8 - Quadratic Equations and Functions
54. Use the discriminant to determine the number of real solutions for the equation
6z 2 + 3z + 6 = 0.
[A] 0
[B] 1
[C] 2
55. Use the discriminant to determine the number of real solutions for the equation
6q 2 + 24q + 24 = 0.
[A] 0
[B] 1
[C] 2
56. Use the discriminant to determine the number of real solutions for the equation 6 x 2 − 1 = 7 x.
[A] 0
[B] 1
[C] 2
Obj. 117 - WP: Use a given quadratic equation to solve a problem
57. A company makes and sells swing sets. The equation P = – 0.5x 2 + 222 x − 1680 can be used
to model the company’s monthly net profit, P, where x is the price the company charges per
swing set. What is the highest price the company could charge for each swing set if it wants
to make a monthly net profit of $16,000?
[A] $340
[B] $1026
[C] $2444
[D] $104
58. As a bird flies upward, it drops a berry at a height of 750 feet above the ground. The
equation h t = − 16t 2 + 4t + 750 describes the height, h, of the berry in feet t seconds after it
is dropped. Ignoring air resistance, how long does it take the berry to hit the ground?
bg
[A] 7.92 s
[B] 13.95 s
[C] 6.97 s
[D] 3.96 s
59. A driver stomped on his brake pedal and stopped in time to avoid an accident. The equation
D = 0.04v 2 can be used to determine the distance the car traveled after the brakes were
applied, where D is the distance in feet and v is the car’s initial velocity in miles per hour.
From skid marks on the road, it was determined the car traveled 180 feet after the brakes
were applied. Approximately how fast was the driver going when he applied the brakes?
[A] 64 mph
[B] 67 mph
[C] 52 mph
162
[D] 72 mph
Topic 8 - Quadratic Equations and Functions
60. An egg is dropped from a height of 115 feet. Ignoring air resistance, the velocity of the egg
increases at the rate of 32 feet per second each second as it falls. The function
1
H v = − v 2 + 115 can be used to find the height, H, of the egg in feet when it has
64
reached a velocity of v feet per second. What is the velocity of the egg to the nearest foot per
second when it is 5 feet above the ground?
bg
[A] 84 ft s
[B] 88 ft s
[C] 110 ft s
[D] 86 ft s
61. Ali built a pumpkin catapult for a pumpkin-tossing contest. He places a 6-pound pumpkin
into the catapult and launches the pumpkin across a field, at a 45° angle to the ground. At
1 2
d + d + 14 can be used to find the height, h, of the
that angle, the equation h d = −
600
pumpkin in feet when it has traveled a horizontal distance of d feet. How far from its
launching point will the pumpkin be when it hits the ground?
bg
[A] 1207 ft
[B] 614 ft
[C] 1227 ft
[D] 314 ft
62. A batter hits a baseball and runs toward first base. Nichelle runs toward the ball to catch it
before it hits the ground. Ignoring wind resistance, the equation h t = −16t 2 + 63t + 2.5 can
be used to find h, the height of the ball in feet, using t, the time in seconds after it is hit.
How many seconds after the ball is hit does Nichelle have before the ball hits the ground?
bg
[A] 2.5 s
[B] 2.3 s
[C] 4.0 s
163
[D] 7.9 s
Topic 9 - Exponential Equations and Functions
Obj. 118 - Determine the graph of an exponential function
F 8I
Which graph shows y = – 5 G J + 4?
H 9K
x
1.
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
164
Topic 9 - Exponential Equations and Functions
b g
2. Which graph shows y = 5 31
. ?
[A]
x
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
165
Topic 9 - Exponential Equations and Functions
F 2I
Which graph shows y = G J + 2?
H 5K
x
3.
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
166
Topic 9 - Exponential Equations and Functions
4.
F 7I
Which graph shows y = 5 G J
H 8K
[A]
x
?
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
167
Topic 9 - Exponential Equations and Functions
bg bg
5. Which graph shows f x = 3 2 + 1?
x
bg
[A]
10 x
–10
bg
[B]
f x
10
f x
10
–10
–10
bg
[C]
bg
[D]
f x
10
10 x
–10
10 x
–10
f x
10
10 x
–10
–10
–10
168
Topic 9 - Exponential Equations and Functions
6.
F 9I
Which graph shows f b x g = G J
H 2K
x
?
bg
[A]
bg
[B]
f x
10
10 x
–10
f x
10
10 x
–10
–10
–10
bg
[C]
bg
[D]
f x
10
10 x
–10
f x
10
10 x
–10
–10
–10
Obj. 119 - WP: Evaluate an exponential growth or an exponential decay function
7. Karl invests $4000 in a savings account that yields 4.5% interest compounded annually. Use
t
4.5
the formula A = c 1+
, where c is the amount invested and t is the time in years, to
100
predict how much his investment will be worth after 11 years if the interest rate remains
constant.
FG
H
[A] $5800
IJ
K
[B] $6491
[C] $4876
[D] $6913
8. A colony of about 2,000,000 bacteria is treated with an experimental antibiotic. Every hour,
t
15
, where a is the initial number of
15% of the bacteria die. Use the formula N = a 1 −
100
bacteria and t is the time in hours, to estimate the number of bacteria still alive after 4 hours.
FG
H
[A] 956,000
[B] 175,000
IJ
K
[C] 887,000
169
[D] 1,044,000
Topic 9 - Exponential Equations and Functions
9. Mark competed in a checkers competition where there were 96 entrants. In each round of
the competition, half of the entrants were eliminated. To find the number of entrants
b g
remaining after a round, use the formula P = e 0.5 , where P is the number of players left, e
is the number of entrants, and r is the number of rounds. How many players were left after
3 rounds?
[A] 84
[B] 48
r
[C] 12
[D] 24
10. A bird sanctuary has 16 flamingoes and is planning a breeding program to increase the
number of birds. The program aims to increase the number of flamingoes by 12% each year.
b g
The number of flamingoes, N, can be found using the formula N = c 112
.
, where c is the
initial number of flamingoes and t is the number of years. How many flamingoes will there
be after 6 years?
[A] 32
[B] 37
[C] 18
t
[D] 108
11. The price of 5 pounds of sugar generally increases by 2% each year. The change in the price
t
2
of 5 pounds of sugar is modeled by the formula P = c 1 +
, where P is the current
100
price and c is the price t years ago. According to this model, if 5 pounds of sugar cost $2.90
this year, how much would 5 pounds of sugar have cost 5 years ago?
FG
H
[A] $0.57
[B] $2.79
IJ
K
[C] $3.20
[D] $2.63
12. Mr. Madan bought a laptop for his small business for $1599. The value of the laptop
b
g
depreciates at a rate of 13% each year. Use the formula V = c 1 − 013
.
, where V is the
depreciated value, c is the initial cost, and t is the time in years, to determine the value of the
laptop after 5 years.
[A] $1391
[B] $802
[C] $797
t
[D] $262
Obj. 120 - Solve a problem involving exponential growth or exponential decay
13. Mrs. Berg wants to invest in a piece of land that costs $85,000. She expects the land to
increase in value by 1.5% each year. To the nearest thousand dollars, how much would she
expect it to be worth after 20 years?
[A] $1,726,000
[B] $114,000
[C] $63,000
170
[D] $2,550,000
Topic 9 - Exponential Equations and Functions
14. A zoologist is using a computer model to study a population of salmon. According to the
model, the number of salmon will decline each year to 97% of the previous year. There are
currently 500 salmon in the population. To the nearest ten, how many salmon are predicted
to be in that population in 6 years?
[A] 600
[B] 420
[C] 410
[D] 490
15. The half-life of a radioactive element is the time it takes for 50% of its atoms to decay into
something else. The half-life of bismuth-210 is about 5 days. About how many grams of
bismuth-210 would remain from a sample of 17 g after 6 half-lives?
[A] 16.73 g
[B] 5.67 g
[C] 0.27 g
[D] 1.49 g
16. Mr. Echohawk is creating a fractal to teach his students about patterns. The fractal starts
with 2 rectangles in stage 0. The number of rectangles in each of the following stages is
4 times the number of rectangles in the previous stage. Using exponential equations,
determine how many rectangles there would be in stage 7 of the pattern.
[A] 4802
[B] 131,072
[C] 512
[D] 32,768
17. Louise added walking to her weekly exercise program. Each week, she recorded the total
number of minutes she walked. After the first week, she increased the time she spent
walking by 3% each week. After 12 weekly increases, Louise had increased her walking
time to 121 minutes for the week. How many minutes did she walk in the first week?
[A] 81 min
[B] 80 min
[C] 180 min
[D] 85 min
18. The publisher of a travel magazine found that last year subscription sales declined by
approximately 3% each month. Last year the magazine had about 133,000 subscribers at the
end of October. To the nearest hundred, about how many subscribers did the magazine have
at the start of January last year?
[A] 180,400
[B] 99,000
[C] 178,700
171
[D] 98,100
Topic 10 - Radical Expressions
Obj. 121 - Simplify a monomial numerical expression involving the square root of a whole
number
Simplify:
1.
24
2. 3 72
[A] 3 6
[B] 2 12
[C] 2 6
[D] 6 2
[A] 24 3
[B] 18 2
[C] 27 2
[D] 18 6
3.
252
12
[A]
4.
686
[A] 7 14
[B] 49 14
[C] 7 2
[D] 49 2
[A] 4 35
[B] 20 35
[C] 100 7
[D] 20 7
[C] 4 3
[D]
5. 4 875
6.
192
8
[A]
6 7
2
[B]
16 3
2
[B]
7
12
4 3
2
[C]
7
2
[D]
42
2
3
Obj. 122 - Multiply monomial numerical expressions involving radicals
Simplify:
7.
5 × 10
8. 9 7 ×5 56
9.
10.
2
1
11 × 99
3
2
18 × 12
11. 3 15 ×4 20
[A] 5 10
[B] 2 5
[A] 126 2
[C] 25 2
[D] 5 2
[B] 4410 2
[C] 630 2
[D] 70 2
[B] 11
[C] 1
[D] 22
[A] 18 2
[B] 18 6
[C] 6 6
[D] 6 2
[A] 24 3
[B] 120 3
[C] 30 3
[D] 40 3
[A]
33
2
172
Topic 10 - Radical Expressions
Simplify:
12.
7
2
72 ×
27
10
35
[A]
18
6
25
[B]
108
6
35
[C]
189
6
5
[D]
2
6
25
Obj. 123 - Divide monomial numerical expressions involving radicals
Simplify:
13.
10 55
2 5
[A] 20
[B] 5 22
[C] 3 30
[D] 5 11
14.
2 150
3
[A] 100
[B] 5 2
[C] 10 2
[D] 7 3
15.
12 180
8 10
[A] 3 3
[B]
16.
360
10
[A] 36
17.
3 14
7
18.
65
5
3 170
2
[C]
3 2
2
[B] 6
[C]
6
[A] 21 14
[B] 3 7
[C] 3 2
[D] 6
[A] 60
[B] 13
[C] 2 15
[D]
[D]
9 2
2
[D] 5 14
13
Obj. 124 - Add and/or subtract numerical radical expressions
Simplify:
19. – 8 2 − 6 2
[A] 14 2
[B] – 14 2
173
[C] 96
[D] –96
Topic 10 - Radical Expressions
Simplify:
20. 3 2 + 7 30 + 6 98
[A] 9 2 − 7 30
[B] 45 2 − 7 30
[C] 45 2 + 7 30
[D] 9 2 + 7 30
21. 5 45 + 20
[A] 17 5
[B] 19 5
[C] 47 5
[D] 16 5
22. – 8 5 + 2 5
[A] – 6 10
[B] – 10 10
[C] – 6 5
[D] – 10 5
23. 9 5 + 27 − 6 125
[A] – 21 5 − 3 3
24. – 5 72 + 4 32
[B] 3 5 + 3 3
[A] – 14 2
[C] – 21 5 + 3 3
[B] – 2 2
[D] 3 5 − 3 3
[C] – 46 2
[D] – 18 2
Obj. 125 - Multiply a binomial numerical radical expression by a numerical radical
expression
Simplify:
d
25. 3 17 7 + 6
i
[A] 21 17 + 6 23
[B] 7 + 3 102
26.
d2 − 2 id1 − 2 i
[A] 2 − 2 2
[B] 4 − 3 2
27.
d5 − 2 id5 + 2 i
[A] 25 − 2
[B] 21
28.
6 10 6 − 13
d
[A] 60 − 13
[C] 21 17 + 2 6
[D] 21 17 + 3 102
[C] 2 + 2 2
[C] 23
[D] 4 + 3 2
[D] 25 + 2
i
[B] 60 + 13
[C] 60 + 78
174
[D] 60 − 78
Topic 10 - Radical Expressions
Simplify:
29.
30.
d10
id
i
3−3 −7 5+6
[A] – 18 + 21 5 − 60 3 + 70 15
[B] 18 − 21 5 − 60 3 − 70 15
[C] – 18 + 70 15
[D] 18 − 70 15
d– 6 + 5 2 id– 6 + 5 2 i
[A] 86 + 60 2
[B] 86 − 60 2
[C] 36 + 25 2
[D] 36 − 25 2
Obj. 126 - Rationalize the denominator of a numerical radical expression
Rationalize the denominator:
31.
– 11
2
32. −
33.
[B]
– 11 2
4
[C]
– 11 2
2
[D]
− 22
2
13
14 − 3
[A]
– 13 14 + 3
17
[B]
– 13 14 – 13 3
17
[C]
– 13 14 + 3
11
[D]
– 13 14 – 13 3
11
[C]
–7 2 + 3
7
− 14 + 3
7
[A]
34.
[A] – 11 2
– 7 2 + 21
7
7 − 10
15 − 7
[A]
[B]
– 7 2 + 21
49
– 143 + 5 7
232
[B]
157
232
175
[C]
– 143 + 5 7
218
[D]
[D]
–7 2 + 3
49
– 143 − 5 7
218
Topic 10 - Radical Expressions
Rationalize the denominator:
35. −
36.
3
5 6
[A] −
1
50
[B] −
2
10
[C] −
2
60
[D] −
3
5
–8 5
– 2 13 – 7
[A]
16 65 – 56 5
3
[B]
– 16 65 – 7
33
[C]
16 65 + 7
3
[D]
– 16 65 + 56 5
33
Obj. 127 - Simplify a monomial algebraic radical expression
Simplify (assume the variables represent positive values):
37.
16z 5
[A] 8z 2 z
[B] 16z 2 z
[C] 4 z 2 z
[D] 4 z 4 z
38.
10 x 4
[A] 5x 4 2
[B] 2 x 2 5
[C] x 4 10
[D] x 2 10
39.
112 p 4 q 5
[A] 14 p 2 q 2 q
40.
165 y 7
41.
48 x 2 y 4
42.
98 p5q 7
[B] 4 p 3q 2 7 pq
[A] y 3 165 y
[A] 7 p 4 q 3 2 pq
[C] 4 p 2 q 2 7q
[B] 11y 3 15 y
[A] 4 xy 2 3x
[B] 6 xy 2
[B] 49 p 2 q 3 2 pq
[C] y 7 165
[C] 16 xy 2 3
[C] 7 p 2 q 3 2 pq
176
[D] 16 p 2 q 2 7q
[D] 3 y 3 55 y
[D] 4 xy 2 3
[D] 2 p 2 q 3 7 pq
Topic 10 - Radical Expressions
Obj. 128 - Rationalize the denominator of an algebraic radical expression
Rationalize the denominator (assume the variables represent positive values):
43. −
2 17
x
[A] −
68
x
[B] −
2 17x
x
[C] −
2 17 x
x2
[D] −
68
x2
44. −
7 14
[A] −
686
81x 22
[B] −
686
81x 11
[C] −
7 14 x
9 x 17
[D] −
7 14 x
9x6
45.
6 x5
19
46. −
47.
48.
9 x 11
8 x
2
10 2
15x
4 7
7 2x5
[A]
6 x 2 19 x
361
[A] − 8 x 2
6 x 4 19
19
[C] 6 x 4 19
[D]
[B] − 4 2x
[C] − 2 2x
[D] − 4 x 2
[B]
6 x 2 19 x
19
[A]
40
3x
[B]
8
9x2
[C]
2 30 x
3x
[D]
2 30 x
45x 2
[A]
2 14 x
7x3
[B]
8
7 x5
[C]
2 14 x
7x2
[D]
2 7
7x5
Obj. 129 - Add or subtract algebraic radical expressions
Simplify (assume the variables represent positive values):
49. − 125w − 9 20w
[A] – 61 10w
[B] – 61 5w
[C] – 23 5w
[D] – 23 10w
[B] – 7 x 2 3
[C] – 29 3x 4
[D] – 29 6 x 4
50. − x 2 12 − 75x 4
[A] – 7 x 2 6
177
Topic 10 - Radical Expressions
Simplify (assume the variables represent positive values):
51. − 6 x 2 7 − 10 63x 4
52.
[A] – 96 14 x 4
[B] – 36 x 2 14
3x + 13 48 x
[A] 53 3x
[B] 209 6x
[C] 53 6x
[D] 209 3x
[A] 71 2x
[B] 37 2x
[C] 37 x
[D] 71 x
53. − 64 x + 15 9 x
[C] – 96 7 x 4
[D] – 36 x 2 7
54. – 12 x 3 100 y 7 + 11y 3 9 x 6 y
[A] – 1101x 3 y 3 y
[B] – 87 x 3 y 3 y
[C] – 87 x 3 y 3 2
[D] – 1101x 3 y 3 2
Obj. 130 - Multiply monomial algebraic radical expressions
Simplify (assume the variables represent positive values):
55.
x × x
56.
2z × 2z
57.
y × y4
58.
y × y17
59.
15 y × 12 y
5
11
9
[A] x 6
7
11
[A] 6 y 12 5
60.
10 y 11 × 6 y 6
[A]
[A]
[B] 2 z10
2 z16
[A] y 2 y
y0
[B]
y9
x6
[B]
[C]
x8
[C] z 7 2 z 2
[C] y y
[B] y 9
[C]
y7
[D] x 8
[D] 2 z 8
[D]
y2
[D] y 7
9
[B] 15 y 10 179
[A] 10 y 9
[C] 15 y 12 179
[B] 2 y 8 15 y
178
[C] 10 y 8
[D] 6 y 10 5
[D] 2 y 9 15 y
Topic 10 - Radical Expressions
Obj. 131 - Divide monomial algebraic radical expressions
Simplify (assume the variables represent positive values):
61.
z4
z
62.
2
14 z11
7z
63.
64.
65.
66.
5
80z 8
5
8y3
2 y5
10 x 9
125x 2
75 y 7
3y
3
[A] z 2
[B] z 2 z
[C] z
[D] z z
[A] z 3 2 z
[B] z 3 2
[C] z 2 7 z
[D] z 2 7
[A] z 5 5
[B] 4 z 4 z
[C] 4 z 4
[D] z 5 5z
[A]
2
y
[B]
y
3
[C]
y
2
[D]
3
y
[A]
x3 2
5
[B]
x3 5
2
[C]
x 2 5x
2
[D]
x3 2x
5
[A] 5 y 2 y
[B] 5 y 2
179
[C] y 3 y
[D] y 3
Topic 11 - Radical Equations and Functions
Obj. 132 - Solve a radical equation that leads to a linear equation
Solve:
1. − x − 6 = –8
[B] x = −2
[A] x = 4
2.
4x + 2 + 1 = 3
[A] x =
7
2
3.
7 x + 8 = 5x + 9
[A] x =
1
2
4. – 6 9x = –9
[A] x =
1
6
[B] x =
3
2
[B] x =
[B] x = −
[C] x = 2
[D] no real solution
1
2
[D] no real solution
[C] x =
17
2
1
6
[C] x =
[C] x =
17
12
1
4
[D] x =
1
12
[D] no real solution
5. 9 4 x = 3 2 x + 8
[A] x =
4
17
[B] x =
37
153
[C] x =
18
77
[B] x =
11
8
[C] x = 5
[D] no real solution
6. − 8 x + 6 = –2 2 x + 7
[A] x = 2
[D] no real solution
Obj. 133 - Solve a radical equation that leads to a quadratic equation
Solve:
7. 7 x = 8 x
[A] x =
9
49
8. − 6 x + 6 = 8 x − 8
[B] x = 0 or x =
[A] x = 1
8
49
[C] x = 0
[B] x =
180
29
24
[D] no real solution
[C] x =
11
9
[D] x =
89
72
Topic 11 - Radical Equations and Functions
Solve:
9.
5 x − 7 = −9 x
[A] x =
7
162
[B] x =
[A] x = −
10. 2 x = − 5x – 5
11.
1
54
[C] x =
5
4
[B] x = −5
5
162
[D] no real solution
[C] x =
5
4
[D] x = 5
6z + 7 = z + 2
[A] z = 1
[B] z = 3
[C] z = –1 or z = 3
[D] z = –3 or z = 1
12. – 6 4 x = −9 x
[A] x = 0 or x =
8
3
[B] x = 0
[C] x = 0 or x = −
181
8
27
[D] x = 0 or x =
16
9
Topic 11 - Radical Equations and Functions
Obj. 134 - Determine the graph of a radical function
13. Which graph represents the function y = x – 2 ?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
182
Topic 11 - Radical Equations and Functions
14. Which graph represents the function y = 14
. 5x – 3 ?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
bg
15. Which graph represents the function f x = − 2 x − 3 ?
bg
[A]
–10
bg
[B]
f x
10
10 x
f x
10
–10
–10
–10
bg
[C]
bg
[D]
f x
10
–10
10 x
10 x
f x
10
–10
–10
10 x
–10
183
Topic 11 - Radical Equations and Functions
bg
16. Which graph represents the function f x = x − 2 ?
bg
[A]
–10
bg
[B]
f x
10
10 x
f x
10
–10
–10
–10
bg
[C]
bg
[D]
f x
10
–10
10 x
10 x
f x
10
–10
–10
10 x
–10
17. Which graph represents the function y = 19
. x?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
184
Topic 11 - Radical Equations and Functions
18. Which graph represents the function y = x − 2 + 2?
[A]
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
Obj. 135 - WP: Solve a problem involving a radical function
19. At a height of h meters, the maximum distance in kilometers, d, that a person can see is
represented by the equation d = 13h . An observer is standing on the observatory deck of a
skyscraper. The maximum distance the observer can see out the window is 57 km. To the
nearest meter, how tall is the observatory deck of the skyscraper?
[A] 19 m
[B] 250 m
[C] 27 m
[D] 901 m
20. The amount of money that a company makes is dependent upon the number of units it can
produce and the number of production workers it hires. The gross amount of money made
by the company can be found using M = 3000 15,508 + w , where M is the gross amount
made and w is the number of production workers hired. If the company made $384,000 one
month, how many production workers did the company have that month?
[A] 876
[B] 15,636
[C] 117
185
[D] 63,772
Topic 11 - Radical Equations and Functions
21. A baseball player hit a ball and popped it up. The ball went straight up into the air and then
came straight down into the catcher’s mitt. The speed of the ball when it hit the mitt can be
15
approximated using v =
64 h − 6 , where v is the speed of the ball in miles per hour,
22
and h is the highest point the ball reached in feet. How high did the ball go, to the nearest
foot, if a radar gun clocked the speed of the ball at 52 mph as it hit the mitt?
b g
[A] 91 ft
[B] 26 ft
[C] 97 ft
[D] 7 ft
22. A council is formed by electing members from certain cities. The number of council
4 P
, where M is the number of council
members each city sends can be found using M =
43
members and P is the population of the city. If a city has 48 council members, how many
people might live in the city?
[A] 266,256
[B] 2,130,048
[C] 2,840,064
[D] 473,344
23. In an automobile crash test, a car is placed at rest on a machine and then accelerated at a
2x
, where x is the
constant rate. The time of the test, t, can be approximated by t =
2.45
distance the car has traveled in meters. If the car has been on the machine for 4 seconds,
about how far has it traveled? Round the answer to the nearest hundredth of a meter if
necessary.
[A] 163 m
[B] 24.01 m
[C] 19.6 m
[D] 1.81 m
24. In a science museum exhibit, an air blower pushes balls up through a tube mounted to the
wall. When a ball leaves the tube, it falls to the ground with an initial speed of 10 m s. After
a ball has left the tube, the speed of the ball, v, can be expressed in terms of the distance it
2
has traveled in meters, x, using the formula v = 10 +19.6 x . To the nearest meter, if the
speed of the ball is 15 m s, how far has the ball fallen?
[A] 19 m
[B] 6 m
[C] 369 m
186
[D] 20 m
Topic 12 - Rational Expressions
Obj. 136 - Determine the excluded values of a rational algebraic expression
1. What are all the values of x, if any, for which the expression is undefined?
5x
2x + 6
[A] −3
[B] –6
[C] 0
[D] The expression is never undefined.
2. What are all the values of x, if any, for which the expression is undefined?
8x
2
x − 2x − 8
[A] 4, –2, 0
[B] 4, –2
[C] 0
[D] –4, 2
3. What are all the values of x, if any, for which the expression is undefined?
4
2
x − 10 x + 25
[A] 5
[B] 0
[C] –5
[D] 0, 5
4. What are all the values of x, if any, for which the expression is undefined?
3x − 3
2
[A] 0
[B] 1
[C] 2
[D] The expression is never undefined.
5. What are all the values of x, if any, for which the expression is undefined?
2 x 2 + 12 x
–6
[A] 0, –6
[B] –6
[C] 0
[D] The expression is never undefined.
6. What are all the values of x, if any, for which the expression is undefined?
4x
2
4 x − 20 x
[A] 5, 0
[B] –5
[C] 5
187
[D] 0
Topic 12 - Rational Expressions
Obj. 137 - Simplify a rational expression involving polynomial terms
Simplify:
7.
4s
– 16s 2 + 80
4 x 2 − 4 x − 24
8.
28 x − 84
9.
[A]
s
4 s2 + 5
[B] −
[A]
x+2
7
[B]
2 x 2 − 26 x + 80
9 x 2 − 225
c
[A]
h
b g
b g
− 6 y − 18
5 y + 15
[A] −
6
5
11.
8x + 8
1−4 x 2 +4
[A] −
2
x +1
12.
4 x 3 + 24 x 2 + 32 x
20 x 2 − 40 x − 480
[A]
b gb g
b gb g
x x+2 x+4
5 x−4 x+6
[B]
[B]
c
b g
b g
2 x −8
9 x +5
b g
b g
–6 y+3
5 y−3
[C]
2
x −1
b x + 2gb x + 4g
5b x − 4gb x + 6g
c
[C]
6
5
[C]
[C]
s
4 s2 − 5
h
x−2
7
[C]
[B]
[B] −
[C] −
h
x−2
28
2 x +8
9 x +5
10.
s
4 s2 + 5
[D]
x −8
x +5
[D]
2
x +1
b g
b g
x x+2
5 x−6
c
h
x+2
28
x +8
x+5
[D]
1
5
[D]
[D]
s
4 s2 − 5
[D]
2
x −1
x+2
5 x−6
b g
Obj. 138 - Multiply rational expressions
Simplify:
13.
4 x 5 6x
×
3x 4 x 4
[A]
8x 7
9
[B] 2x
14.
7 x + 5 6x 2
×
8x 3 4 x − 1
[A]
42 x 3 + 5
32 x 4 − 1
[B]
b
b
[C] 2
g
4x 7x + 5
3 4x − 1
188
g
[C]
[D] 4x
b
b
g
g
3 7x + 5
4 4x − 1
[D]
b
g
g
3 7x + 5
4x 4x − 1
b
Topic 12 - Rational Expressions
Simplify:
15.
x 2 − x − 90
x−4
× 2
2
7x
4 x − 56 x + 160
[A]
x+9
28 x 2
[B]
16.
10 x 3 4 xy
×
10 y 4 5x 4
17.
3x − 3 x + 1
×
– 2 x + 3 12 x
[A]
18.
[A]
b x − 3gb x + 1g
− 4 xb2 x − 3g
x − 10
7x2
4
5xy 3
[B]
[C]
[B]
4
5y 3
b x − 3gb x + 1g
xb− 2 x + 3g
x+9
28 x
[D]
[C]
5x 6
4 y5
[C]
b x − 1gb x + 1g
− 4 xb2 x − 3g
[C]
b x + 6gb x + 7g
xb x + 10g
b x + 9gb x − 4g
4FGH 7 x IJK b x + 4g
2
[D]
4x
5y 3
[D]
b x − 1gb x + 1g
xb− 2 x + 3g
[D]
b x + 6g b x + 7g
xb x + 10g
2 x 2 + 26 x + 84 x 2 + 4 x − 12
×
x 2 + 8 x − 20
2x
[A]
b x + 6g
2
2x
[B]
b x + 7g
xb x + 10g
2
Obj. 139 - Divide rational expressions
Simplify:
19.
q 4 r 5 q 3r 7
÷ 5
s4
s
20.
2 x + 6 3x − 8
÷
5x 3
6x
b g
b g
5x 2 3x − 8
[A]
12 x + 3
[A]
qs 2
r2
[B]
[B]
qs
r2
6 x FGH 5x 3 IJK
b2 x + 6gb3x − 8g
189
[C]
q 7 r 12
s9
b g
b g
12 x + 3
[C]
5x 2 3x − 8
[D]
s9
q 7 r 12
12 x 2 + 6
[D]
15x 4 − 8
Topic 12 - Rational Expressions
Simplify:
21.
x 2 + 10 x + 24 x 2 + 13x + 36
÷
4 x + 28
− 12 x
x+6
x+7 x+9
b gb g
[A]
[B]
22.
5x 4 y 3 x 5 z
÷ 6
z7
y
23.
2p− 2
÷ 16 p − 16
14 p + 14
[A]
b
5y 7
3xz 8
[B]
[C]
– 3x
x+4
y5z 6
15x 9
[D]
[C]
5y 6
3xz 7
b g
b gb g
– 3x x + 6
x+7 x+9
[D]
15x 9
y5z 6
g
b g
[A] 112 p − 1
24.
b g
b gb g
–3 x+6
x+7 x+9
b g
[B] 112 p + 1
4 x 2 + 20 x
x 2 − x − 30
÷
x 2 − 36
x 2 + 14 x + 48
b g
[A] 4 x x + 8
[B]
[C]
b g
b x − 6g
4x x + 8
[C]
2
1
112 p + 1
[D]
1
112 p − 1
b g
b x − 6g
[D]
1
4x x + 8
b g
4 x +8
2
b g
b g
Obj. 140 - Divide a polynomial expression by a monomial
Simplify:
25.
c5 p
26.
c5a
h b g
2
+4p ÷ − p
4
− 4a 2 − 2 ÷ 3a
[A] −5 p − 4
[B] −5 p −1
[C] 5 p − 4
h
[A]
5 3 4
2
a + a+
3
3
3a
[B]
5 3 4
2
a − a−
3
3
3a
[C]
5 3 4
2
a − a+
3
3
3a
[D]
5 3 4
2
a + a−
3
3
3a
190
[D] 5 p + 4
Topic 12 - Rational Expressions
Simplify:
27.
28.
29.
30.
c5x + 7 x
5
4
h c
− 3x 3 − 4 ÷ − 9 x 2
h
[A] −
5 3 7 2 1
4
x − x + x+ 2
9
9
3
9x
[B] −
5 3 7 2 1
4
x − x + x− 2
9
9
3
9x
[C] −
5 3 7 2 1
4
x + x + x+ 2
9
9
3
9x
[D] −
5 3 7 2 1
4
x − x − x+ 2
9
9
3
9x
c− 7b
+ 3b 3 − 6b 2 ÷ 3b
4
h
[A] − 7b 3 + 3b 2 − 6b
[B] − 7b 3 + 3b 2 + 6b
7
[C] − b 3 + b 2 + 2b
3
7
[D] − b 3 + b 2 − 2b
3
c5z + 2z
5
3
h
+ 2z 2 − z ÷ z
[A] 5z 4 + 2 z 2 − 2 z − 1
[B] 5z 4 + 2 z 2 + 2 z + 1
[C] 5z 4 + 2 z 2 + 2 z − 1
[D] 5z 4 − 2 z 2 + 2 z − 1
c− 3q
3
h
− 4q ÷ 5q 3
1 4
[A] − − 2
5 5q
3 4
[B] − − 2
5 5q
3 4
[C] − + 2
5 5q
[D] − 1 −
4
q2
Obj. 141 - Divide a polynomial expression by a binomial
Simplify:
31.
c2 x
2
h b g
+ 26 x + 80 ÷ x + 5
[A] 2 x + 8
[B] 2 x + 5
[C]
191
2 x + 16
x +5
[D] 2 x + 16
Topic 12 - Rational Expressions
Simplify:
32.
33.
c 3x
4
h b g
− 15x 2 + 12 ÷ x − 2
[A] 3x 3 + 6 x 2 − 3x − 6
[B] 3x 3 + 6 x 2 + 3x + 6
[C] 3x 3 − 6 x 2 − 3x − 6
[D] 3x 3 + 6 x 2 − 3x + 6
c− 8x
2
h b
− 3x 3 + 140 x + 96 ÷ − 3x − 2
[B] x 3 + 2 x 2 − 48 x
[A] x 2 + 14 x + 48
34.
cx
35.
c9 x
36.
2
h b
+ x − 90 ÷ − x + 9
4
g
g
[A] x − 10
h b
[C] x 2 + 2 x − 48
[B] − x + 10
[D] − 3x 2 − 6 x + 144
[C] − x − 10
g
+ 24 x 3 + 27 x 2 − 10 ÷ 3x + 3
22
3x + 3
[A] 3x 3 + 5x 2 + 4 x − 4
[B] 3x 2 + 5x + 4 −
[C] 3x 2 + 5x + 4
[D] 3x 3 + 5x 2 + 4 x − 4 +
cx
2
[D] x + 10
h b
2
3x + 3
g
+ 3x 4 + 27 + 4 x 3 ÷ − x − 1
[A] − 3x 2 − x +
[C] 3x 3 + x 2 +
27
− x −1
[B] − 3x 3 − x 2 +
27
− x −1
27
− x −1
[D] 3x 3 + 7 x 2 + 8 x + 8 +
35
− x −1
Obj. 142 - Determine the LCD of two rational expressions
37. What is the LCD of
[A] 36 x 6 y
1
− 7y
and
?
6
36 x
6x y
[C] 216 x 7 y
[B] 6x
192
[D] 6 x 5 y
Topic 12 - Rational Expressions
38. What is the LCD of
b g
[A] 3x x − 5
1
4x
and
?
x − 5x
3x − 15
2
b g
[B] 3x x − 5
2
39. What is the LCD of
8
9
and
?
− 5x + 80 x
x+4
3
b gb g
c− 5x + 80xhb x + 4g
[A] – 5x x + 4 x − 4
[C]
[D] x − 5
[C] 3x
b gb
– 5 x b x − 4g
g
[B] – 5x x + 4 x − 16
3
[D]
a 2b 6
– 3c
40. What is the LCD of
?
7 and
4c
a 6b
[A] a 6bc 7
41. What is the LCD of
b gb g
[B] – 3a 2b 6c
x −8
14 x
and
?
3x + 24
15x + 15
[A] 15 x + 8 x + 1
42. What is the LCD of
b g
[C] 4a 6bc 7
[B]
b x + 8gb x + 1g
b
c5x
2
g
[C] 3 15x + 15
[D]
b3x + 24gb15x + 15g
1
− 7x
and
?
2
5x − 15x − 20
20 x + 120 x + 100
2
b gb g
20b x − 4gb x + 1gb x + 5g
[B] 20 x − 4 x + 5
[A] 4 x + 1
[C]
[D] 4abc
hc
h
− 15x − 20 20 x 2 + 120 x + 100
[D]
Obj. 143 - Add or subtract two rational expressions with like denominators
Simplify:
43.
− 3x 5x + 10
+
2x − 8 2x − 8
[A]
− 8 x + 10
2x − 8
44.
4y
6y + 4
−
9 − 6y 9 − 6y
[A]
y−4
9 − 3y
[B]
[B]
193
x+5
4x − 1
4− y
9 − 3y
[C]
[C] −
4 x + 10
2x − 8
4 + 2y
9 − 6y
[D]
[D]
x +5
x−4
2y − 4
9 − 6y
Topic 12 - Rational Expressions
Simplify:
45.
− 5 − 7n + 3
+
3n 3
3n 3
[A]
− 7n − 8
3n 3
46.
8 − 27 y 4 − 7 y
−
12 y − 8 12 y − 8
[A]
1 − 5y
3y − 2
47.
8x + 4
4x − 1
+
20 x + 14 20 x + 14
[A]
48. −
12 x − 3
20 x + 14
[B]
− 7n − 2
3n 3
[C]
[B] −
1 + 34 y
12 y − 8
[C]
− 12n + 3
3n 3
12 − 5 y
3y − 2
−2
3n 3
[D]
[D]
20 y + 1
12 y − 8
[B]
12 x + 3
20 x + 14
[C]
4x + 3
20 x + 14
[D]
− 4x − 3
20 x + 14
[B]
− 39 z 2 + 5
25z
[C]
− 39 z 2 − 13
50z
[D]
39 z 2 − 13
25z
9
− 39 z 2 + 4
−
25z
25z
[A]
39 z 2 + 13
25z
Obj. 144 - Add or subtract two rational expressions with unlike monomial denominators
Simplify:
49.
1
–3
+
3
12 g 16 g
[A]
4 − 9g2
48 g 3
− 12 y − 7 z 4
[A]
30 yz 5
–2
7
50.
−
5z 30 yz 5
51.
–8 8
−
12a 5b
[A]
7
30
52.
9c c
−
5 35
[A]
64c
35
[B]
− 3g 2
16 g 3
[B]
19
[B] −
15z
− 8a + 8b
15ab
[B]
[C]
62c
35
194
[C]
1− 4g2
16 g 3
− 12 yz 4 − 7
[C]
30 yz 5
− 10b − 24a
15ab
[C]
8c
35
− 5g 2
48 g 3
[D]
[D]
[D]
[D]
− 22 y
15z
14
15ab
62c 2
35
Topic 12 - Rational Expressions
Simplify:
53.
3 –1
+
x 2 5y
54.
2m
7
−
3
25v 30mv 2
[A]
[A]
5m2 v 2 − 21
75mv
15 y − x 2
5x 2 y
[B]
[B]
3y − x 2
x2 y
12m − 35
150v 2
[C]
[C]
14
5
12m2 − 35v
150mv 3
3x 2 − 5 y
5x 2 y
[D]
[D] −
23m
150v 2
Obj. 145 - Add or subtract two rational expressions with unlike polynomial denominators
Simplify:
55.
–9
–3
+
x −2 x +2
[A]
56.
b gb g
[B]
− 12 x − 12
x−2 x+2
b gb g
[C]
− x −1
x−2 x+2
b gb g
[D]
− 12 x + 12
x−2 x+2
b gb g
4
3t
− 2
t + 4t − 45 3t + 29t +18
2
[A]
[C]
57.
− 6x
x−2 x+2
− 3t 2 + 27t + 8
t − 5 t + 9 3t + 2
g
[B]
− 3t 2 − 3t + 8
t − 5 t + 9 3t + 2
g
[D]
b gb gb
b gb gb
9t + 23
t − 5 t + 9 3t + 2
g
43t
t − 5 t + 9 3t + 2
g
b gb gb
b gb gb
p
p +2
−
p −1 1− p 2
2
[A] −
2
p +1 p −1
b gb g
[B]
2
p + 1 1 − p2
b gc
h
195
[C]
2
p −1
[D] −
2
p +1
Topic 12 - Rational Expressions
Simplify:
58.
30
9
+ 2
x − 8 x − 17 x + 72
[A]
59.
60.
30 x − 261
x −8 x −9
b gb g
[B]
39 x − 9
x −8 x −9
b gb g
[C]
30 x − 231
x −8 x −9
b gb g
39 x − 333
x −8 x −9
[D]
b gb g
[D]
2 x + 22
x–4 x+6
– 7a
3
−
a − 6 5a + 4
− 66a + 18
a − 6 5a + 4
− 35a 2 + 31a − 18
[B]
a − 6 5a + 4
b gb
[A]
b gb
[C]
− 35a 2 − 31a + 18
a − 6 5a + 4
b gb
g
g
[D]
g
− 35a 2 + a − 6
a − 6 5a + 4
b gb
g
x + 16
x+4
+ 2
x + 12 x + 32 x + 14 x + 48
2
[A]
2 x + 22
x+4 x+6
b gb g
[B]
2 x + 14
x+4 x+6
b gb g
[C]
196
2 x + 14
x–4 x+6
b gb g
b gb g
Topic 13 - Rational Equations and Functions
Obj. 146 - Solve a proportion that generates a linear or quadratic equation
Solve:
1.
7 r −3
=
3 –2
2.
4y
–8
=
–4 y−2
3.
[A] r = − 1
2
3
[B] r = − 3
6
7
[C] r = − 7
2
3
[D] r = 2
[A] y = 4 or y = 2
[B] y = 4 or y = −2
[C] y = −4 or y = 2
[D] y = −4 or y = −2
1
7
z +8
9
=
–2
z−3
[A] z = – 1 or z = 6
4.
5
a +8
=
–2 a−6
5.
–4
9
=
− 5y − 1 y − 9
[B] z = – 1 or z = – 6
[A] a = 4
2
3
[C] z = 1 or z = – 6
[B] a = 4
[A] y = − 37
[B] y = 0
[C] a = 2
[C] y = −
27
41
2r 2 – 5
6.
=
–7
9
[A] r =
14
14
, −
3 70
3 70
[B] r =
70
70
, −
6
6
[C] r =
6
6
, −
70
70
[D] r =
3 70
3 70
, −
14
14
197
[D] z = 1 or z = 6
[D] a = − 6
4
7
[D] y = − 1
4
41
Topic 13 - Rational Equations and Functions
Obj. 147 - Solve a rational equation involving terms with monomial denominators
Solve:
7.
7x + 2 4x + 5
−
=7
3
7
8.
4
3
−
=2
3x 4 x
9.
1
1
1
−
=
2
3x 10 x 30
10.
11.
[A] x =
7
24
8
37
[B] x = 5
[B] x =
7
6
[C] x = 4
[C] x =
6
7
[A] x = 5 or x = 2
[B] x = –5 or x = 2
[C] x = 5 or x = –2
[D] x = –5 or x = –2
6 1
+ =1
x2 x
[A] x = 2 or x = –3
[B] x = 2 or x = 3
[C] x = –2 or x = 3
[D] x = –2 or x = –3
x 4 1
=
−
4 3x 6
[A] x =
8
or x = –2
3
[C] x = −
12.
[A] x =
[B] x = −
8
or x = –2
3
8
or x = 2
3
[D] x =
8
or x = 2
3
[B] x =
1
1
or x = −
3
2
3x
1
1
+
=
5 10 x 2
[A] x = −
[C] x =
1
1
or x =
3
2
1
1
or x =
3
2
[D] x = −
198
1
1
or x = −
3
2
[D] x =
[D] x =
118
61
24
7
Topic 13 - Rational Equations and Functions
Obj. 148 - Solve a rational equation involving terms with polynomial denominators
Solve:
13.
14.
2 1
9
+ =
x 2 x +5
[A] x = 4 or x = 5
[B] x = 4 or x = –5
[C] x = –4 or x = 5
[D] x = –4 or x = –5
6
2x + 2
12
+
= 2
x −1 x +1
x −1
[A] x = –4 or x = 1
15.
[C] x = –4
[D] no solution
4
6
3
+
= 2
x−3 x+3 x −9
[A] x =
16.
[B] x = –4 or x = 4
9
10
[B] x = −
10
9
[C] x = −
9
10
[D] no solution
12
12
+
=7
x − 2 x −1
[A] x = −
[C] x =
10
or x = 5
7
[B] x =
10
or x = –5
7
17.
x−2
1
4
−
=
x+3 x+3 3
18.
6
12
+ 2
=2
1− x x − 1
[A] x = 4 or x = –1
10
or x = 5
7
[D] x = −
[A] x = −21
[B] x =
[B] x = –4 or x = 1
199
1
21
10
or x = –5
7
[C] x = 21
[C] x = 1
[D] x = −
[D] x = –4
1
21
Topic 13 - Rational Equations and Functions
Obj. 149 - Determine the graph of a rational function
19. Which graph shows y =
[A]
4
– 2?
x
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
200
Topic 13 - Rational Equations and Functions
20. Which graph shows y =
[A]
5
+ 5?
x+3
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
201
Topic 13 - Rational Equations and Functions
21. Which graph shows y = −
[A]
2
– 1?
x–4
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
202
Topic 13 - Rational Equations and Functions
22. Which graph shows y = −
[A]
4
– 1?
x
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
203
Topic 13 - Rational Equations and Functions
23. Which graph shows y = −
[A]
5
– 3?
x+4
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
204
Topic 13 - Rational Equations and Functions
24. Which graph shows y =
[A]
3
+ 5?
x–2
[B]
y
10
10 x
–10
y
10
–10
[C]
–10
[D]
y
10
10 x
–10
10 x
–10
y
10
10 x
–10
–10
–10
Obj. 150 - WP: Solve a problem involving a rational equation
25. Each quiz Micah takes in his French class is worth 10 points. Micah has taken 19 quizzes in
the class so far, earning a total of 140 points. If he scores 10 points on each of the next
quizzes, how many more quizzes will he have to take to have an average quiz score of
8 points?
[A] 6
[B] 8
[C] 70
[D] 7
26. Two sisters share a bedroom. The older sister can sweep and mop the floor in 15 minutes.
The younger sister can sweep and mop the floor in 30 minutes. To the nearest minute, how
long would it take the sisters to sweep and mop the floor if they worked together?
[A] 20 min
[B] 10 min
[C] 5 min
205
[D] 23 min
Topic 13 - Rational Equations and Functions
27. Sasha and Matt are painting houses this summer for extra work. Sasha worked alone on one
house for 9 days. The next morning Matt joined Sasha to work on the house. Working
together, they finished the house in 5 more days. If Matt could have painted the entire house
by himself in 19 days, how many days would it have taken Sasha to paint the house alone?
Round the answer to the nearest whole number, if necessary.
[A] 19
[B] 11
[C] 28
[D] 27
28. Seanna likes to run in her neighborhood. Some days, she goes on a short route that takes
20 minutes. On other days, she runs on a longer route that takes 50 minutes. The longer
route is 1620 yards longer than twice the short route. She runs at the same average speed on
both routes. How long is the short route?
[A] 1013 yd
[B] 2700 yd
[C] 1080 yd
[D] 3240 yd
29. A lawn care worker has two customers in the same neighborhood. The first customer’s lawn
is three times the area of the second customer’s lawn plus 16,000 square feet. If it takes him
five times as long to mow the first customer’s lawn as it does the second customer’s lawn at
the same rate, how large is the first customer’s lawn?
[A] 40,000 ft 2
[B] 5714 ft 2
[C] 8000 ft 2
[D] 33,142 ft 2
30. Ida is going to participate in a run-and-bike event. Her goal is to complete the running
portion of the event at a rate of 12 km/hr and the biking portion at a rate of 24 km/hr. If she
meets her goal, she will finish the event in 2.9 hours. The biking portion is 10 km longer
than the running portion. To the nearest kilometer, how long is the biking portion?
[A] 27 km
[B] 30 km
[C] 20 km
206
[D] 17 km
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