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Homework Practice Workbook
To the Student
This Homework Practice Workbook gives you additional problems for the concept exercises in
each lesson. The exercises are designed to aid your study of mathematics by reinforcing important
mathematical skills needed to succeed in the everyday world. The materials are organized by chapter
and lesson, with one Practice worksheet for every lesson in Glencoe Algebra 2.
To the Teacher
These worksheets are the same ones found in the Chapter Resource Masters for Glencoe Algebra 2.
The answers to these worksheets are available at the end of each Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.
Except as permitted under the United States Copyright Act, no part of this publication
may be reproduced or distributed in any form or by any means, or stored in a database
or retrieval system, without prior written permission of the publisher.
Send all inquiries to:
Glencoe/McGraw-Hill
8787 Orion Place
Columbus, OH 43240
ISBN: 978-0-07-890862-0
MHID: 0-07-890862-0
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 045 14 13 12 11 10 09 08
Homework Practice Workbook, Algebra 2
Contents
Lesson/Title
1-1
1-2
1-3
1-4
1-5
1-6
Page
Lesson/Title
Expressions and Formulas ………………….. 1
Properties of Real Numbers ………………… 3
Solving Equations ………………………………. 5
Solving Absolute Value Equations ……….. 7
Solving Inequalities …………………………….. 9
Solving Compound and Absolute
Value Inequalities …………………………….. 11
6-1 Operations with Polynomials ……………… 67
6-2 Dividing Polynomials ………………………… 69
6-3 Polynomial Functions ……………………….. 71
6-4 Analyzing Graphs of Polynomial
Functions ………………………………………… 73
6-5 Solving Polynomial Equations ……………. 75
6-6 The Remainder and Factor
Theorems………………………………………… 77
6-7 Roots and Zeros ………………………………. 79
6-8 Rational Zero Theorem……………………… 81
2-1
2-2
2-3
2-4
2-5
Relations and Functions ……………………. 13
Linear Relations and Functions ………….. 15
Rate of Change and Slope ………………… 17
Writing Linear Equations …………………… 19
Scatter Plots and Lines
of Regression ………………………………….. 21
2-6 Special Functions …………………………….. 23
2-7 Parent Functions and
Transformations ……………………………….. 25
2-8 Graphing Linear and Absolute
Value Inequalities …………………………….. 27
3-1
3-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3-3
3-4
3-5
4-1
4-2
4-3
4-4
4-5
4-6
Page
7-1 Operations on Functions …………………… 83
7-2 Inverse Functions and Relations ………… 85
7-3 Square Root Functions and
Inequalities………………………………………. 87
7-4 nth Roots ………………………………………… 89
7-5 Operations with Radical Expressions ….. 91
7-6 Rational Exponents ………………………….. 93
7-7 Solving Radical Equations and
Inequalities………………………………………. 95
Solving Systems of Equations by
Graphing …………………………………………. 29
Solving Systems of Equations
Algebraically ……………………………………. 31
Solving Systems of Inequalities by
Graphing …………………………………………. 33
Optimization with Linear
Programming …………………………………… 35
Systems of Equations in
Three Variables ……………………………….. 37
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
Introduction to Matrices …………………….. 39
Operations with Matrices …………………… 41
Multiplying Matrices ………………………….. 43
Transformations with Matrices……………. 45
Determinants and Cramer’s Rule ……….. 47
Inverse Matrices and Systems
of Equations …………………………………….. 49
9-1
9-2
9-3
9-4
9-5
9-6
5-1 Graphing Quadratic Functions……………. 51
5-2 Solving Quadratic Equations by
Graphing …………………………………………. 53
5-3 Solving Quadratic Equations by
Factoring …………………………………………. 55
5-4 Complex Numbers ……………………………. 57
5-5 Completing the Square ……………………… 59
5-6 The Quadratic Formula and the
Discriminant …………………………………….. 61
5-7 Transformations with Quadratic
Functions ………………………………………… 63
5-8 Quadratic Inequalities ……………………….. 65
10-1
10-2
10-3
10-4
10-5
10-6
10-7
iii
Graphing Exponential Functions ………… 97
Solving Exponential Equations
and Inequalities ……………………………….. 99
Logarithms and Logarithmic
Functions ………………………………………. 101
Solving Logarithmic Equations
and Inequalities ……………………………… 103
Properties of Logarithms …………………. 105
Common Logarithms ………………………. 107
Base e and Natural Logarithms ………… 109
Using Exponential and
Logarithmic Functions …………………….. 111
Multiplying and Dividing Rational
Expressions …………………………………… 113
Adding and Subtracting Rational
Expressions …………………………………… 115
Graphing Reciprocal Functions ………… 117
Graphing Rational Functions ……………. 119
Variation Functions …………………………. 121
Solving Rational Equations
and Inequalities ……………………………… 123
Midpoint and Distance Formulas …….. 125
Parabolas…………………………………….. 127
Circles …………………………………………. 129
Ellipses ……………………………………….. 131
Hyperbolas…………………………………… 133
Identifying Conic Sections ……………… 135
Solving Quadratic Systems ……………. 137
Lesson/Title
11-1
11-2
11-3
11-4
11-5
11-6
11-7
Page
Lesson/Title
Sequences as Functions ……………….. 139
Arithmetic Sequences and Series …… 141
Geometric Sequences and Series …… 143
Infinite Geometric Series ……………….. 145
Recursion and Iteration …………………. 147
The Binomial Theorem ………………….. 149
Proof by Mathematical Induction …….. 151
13-3
12-1 Experiments, Surveys, and
Observational Studies …………………… 153
12-2 Statistical Analysis ………………………… 155
12-3 Conditional Probability …………………… 157
12-4 Probability Distributions …………………. 159
12-5 The Normal Distribution …………………. 161
12-6 Hypothesis Testing ……………………….. 163
12-7 Binomial Distributions ……………………. 165
13-9
13-4
13-5
13-6
13-7
13-8
Page
Trigonometric Functions of
General Angles …………………………….. 171
Law of Sines ………………………………… 173
Law of Cosines …………………………….. 175
Circular Functions …………………………. 177
Graphing Trigonometric Functions ….. 179
Translations of Trigonometric
Graphs ………………………………………… 181
Inverse Trigonometric Functions …….. 183
14-1 Trigonometric Identities …………………. 185
14-2 Verifying Trigonometric Identities ……. 187
14-3 Sum and Difference of Angles
Formulas ……………………………………… 189
14-4 Double-Angle and Half-Angle
Formulas ……………………………………… 191
14-5 Solving Trigonometric Equations …….. 193
13-1
Trigonometric Functions in Right
Triangles ……………………………………… 167
13-2 Angles and Angle Measure ……………. 169
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
iv
NAME
DATE
1-1
PERIOD
Skills Practice
Expressions and Formulas
Evaluate each expression if a = -4, b = 6, and c = -9.
1. 3ab – 2bc
2. a3 + c2 – 3b
3. 2ac – 12b
4. b(a – c) – 2b
ac
2b
5. − + −
3b – 4 c
6. −
3ab
2c
+−
7. −
b2
8. −
ac – c
b
c
2b – (c – b)
a
b
1
Evaluate each expression if r = -1, n = 3, t = 12, v = 0, and w = – −
.
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 6r + 2n
10. 2nt – 4rn
11. w(n – r)
12. n + 2r – 16v
13. (4n)2
14. n2r – wt
15. 2(3r + w)
16. −
17. -w[t + (t – r)]
rv3
18. −
2
19. 9r2 + (n2 – 1)t
2w
20. 7n – 2v + −
r
3v + t
5n – t
n
21. TEMPERATURE The formula K = C + 273 gives the temperature in kelvins (K) for a
given temperature in degrees Celsius. What is the temperature in kelvins when the
temperature is 55 degrees Celsius?
5
22. TEMPERATURE The formula C = −
(F – 32) gives the temperature in degrees Celsius
9
for a given temperature in degrees Fahrenheit. What is the temperature in degrees
Celsius when the temperature is 68 degrees Fahrenheit?
Chapter 1
1
Glencoe Algebra 2
NAME
DATE
1-1
PERIOD
Practice
Expressions and Formulas
Evaluate each expression.
1. 3(4 – 7) – 11
2. 4(12 – 42)
3. 1 + 2 – 3(4) ÷ 2
4. 12 – [20 – 2(62 ÷ 3 × 22)]
5. 20 ÷ (5 – 3) + 52(3)
6. (-2)3 – (3)(8) + (5)(10)
7. 18 – {5 – [34 – (17 – 11)]}
8. [4(5 – 3) – 2(4 – 8)] ÷ 16
1
[6 – 42]
9. −
1
10. −
[-5 + 5(-3)]
2
4
(-8)2
5-9
-8(13 – 37)
6
12. − – (-1)2 + 4(-9)
11. −
3
1
, b = -8, c = -2, d = 3, and e = −
.
Evaluate each expression if a = −
3
4
2
13. ab – d
14. (c + d)b
ab
2
15. −
c +d
16. −
ac
17. (b – de)e2
18. ac3 – b2de
19. -b[a + (c – d) 2]
ac4
c
20. −
-−
2
1
21. 9bc – −
e
22. 2ab2 – (d 3 – c)
d(b – c)
e
9
23. TEMPERATURE The formula F = −
C + 32 gives the temperature in degrees
5
Fahrenheit for a given temperature in degrees Celsius. What is the temperature in
degrees Fahrenheit when the temperature is -40 degrees Celsius?
24. PHYSICS The formula h = 120t – 16t2 gives the height h in feet of an object t seconds
after it is shot upward from Earth’s surface with an initial velocity of 120 feet per
second. What will the height of the object be after 6 seconds?
25. AGRICULTURE Faith owns an organic apple orchard. From her experience the last few
seasons, she has developed the formula P = 20x – 0.01×2 – 240 to predict her profit P in
dollars this season if her trees produce x bushels of apples. What is Faith’s predicted
profit this season if her orchard produces 300 bushels of apples?
Chapter 1
2
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
d
NAME
DATE
1-2
PERIOD
Skills Practice
Properties of Real Numbers
Name the sets of numbers to which each number belongs.
1. 34
2. -525
3. 0.875
12
4. −
5. – √
9
6. √
30
3
Name the property illustrated by each equation.
7. 3 x = x 3
9. 2(r + w) = 2r + 2w
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
( )
8. 3a + 0 = 3a
10. 2r + (3r + 4r) = (2r + 3r) + 4r
1
11. 5y −
5y = 1
12. 15x(1) = 15x
13. 0.6[25(0.5)] = [0.6(25)]0.5
14. (10b + 12b) + 7b = (12b + 10b) + 7b
Find the additive inverse and multiplicative inverse for each number.
15. 15
16. 1.25
4
17. – −
3
18. 3 −
5
4
Simplify each expression.
19. 3 x + 5 y + 2 x – 3y
20. x – y – z + y – x + z
21. -(3g + 3h) + 5g – 10h
22. a2 – a + 4a – 3a2 + 1
23. 3(m – z) + 5(2m – z)
24. 2x – 3y – (5x – 3y – 2z)
25. 6(2 w + v) – 4(2 v + 1w)
1
1
(15 d + 3 c) – −
(8 c – 10 d)
26. −
Chapter 1
3
3
2
Glencoe Algebra 2
NAME
DATE
1-2
PERIOD
Practice
Properties of Real Numbers
Name the sets of numbers to which each number belongs.
1. 6425
5.
25
−
√
36
2. √
7
3. 2π
4. 0
6. – √
16
7. -35
8. -31.8
Name the property illustrated by each equation.
9. 5x (4y + 3x) = 5x (3x + 4y)
11. 5(3x + y) = 5(3x + 1y)
10. 7x + (9x + 8) = (7x + 9x) + 8
12. 7n + 2n = (7 + 2)n
13. 3(2x)y = (3 2)(xy)
14. 3x 2y = 3 2 x y
15. (6 + -6)y = 0y
1
4y = 1y
16. −
17. 5(x + y) = 5x + 5y
18. 4n + 0 = 4n
4
Find the additive inverse and multiplicative inverse for each number.
19. 0.4
5
6
22. 5 −
Simplify each expression.
23. 5x – 3y – 2x + 3y
24. -11a – 13b + 7a – 3b
25. 8x – 7y – (3 – 6y)
26. 4c – 2c – (4c + 2c)
27. 3(r – 10s) – 4(7s + 2r)
1
1
28. −
(10a – 15b) + −
(8b + 4a)
29. 2(4z – 2x + y) – 4(5z + x – y)
5 3
1
−x + 12y – −
30. −
(2x – 12y)
5
2
(
6 5
)
4
31. TRAVEL Olivia drives her car at 60 miles per hour for t hours. Ian drives his car at
50 miles per hour for (t + 2) hours. Write a simplified expression for the sum of the
distances traveled by the two cars.
32. NUMBER THEORY Use the properties of real numbers to tell whether the following
()
()
1
1 . Explain
statement is true or false: If a and b ≠ 0 and a > b, it follows that a −
a >b −
b
your reasoning.
Chapter 1
4
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11
16
21. – −
20. -1.6
NAME
DATE
1-3
PERIOD
Skills Practice
Solving Equations
Write an algebraic expression to represent each verbal expression.
1. 4 times a number, increased by 7
2. 8 less than 5 times a number
3. 6 times the sum of a number and 5
4. the product of 3 and a number, divided by 9
5. 3 times the difference of 4 and a number
6. the product of -11 and the square of a number
Write a verbal sentence to represent each equation.
7. n – 8 = 16
8. 8 + 3x = 5
9. b + 3 = b2
10. − = 2 – 2y
y
3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Name the property illustrated by each statement.
11. If a = 0.5b, and 0.5b = 10, then a = 10.
12. If d + 1 = f, then d = f – 1.
13. If -7x = 14, then 14 = -7x.
14. If (8 + 7)r = 30, then 15r = 30.
Solve each equation. Check your solution.
15. 4m + 2 = 18
16. x + 4 = 5x + 2
17. 3t = 2t + 5
18. -3b + 7 = -15 + 2b
19. -5x = 3x – 24
20. 4v + 20 – 6 = 34
2a
21. a – −
=3
22. 2.2n + 0.8n + 5 = 4n
5
Solve each equation or formula for the specified variable.
23. I = prt, for p
1
x – 12, for x
24. y = −
x+y
25. A = − , for y
2
26. A = 2πr2 + 2πrh, for h
Chapter 1
5
4
Glencoe Algebra 2
NAME
DATE
1-3
PERIOD
Practice
Solving Equations
Write an algebraic expression to represent each verbal expression.
1. 2 more than the quotient of a number and 5
2. the sum of two consecutive integers
3. 5 times the sum of a number and 1
4. 1 less than twice the square of a number
Write a verbal sentence to represent each equation.
5. 5 – 2x = 4
6. 3y = 4y3
7. 3c = 2(c – 1)
m
8. −
= 3(2m + 1)
5
Name the property illustrated by each statement.
9. If t – 13 = 52, then 52 = t – 13.
10. If 8(2q + 1) = 4, then 2(2q + 1) = 1.
11. If h + 12 = 22, then h = 10.
12. If 4m = -15, then -12m = 45.
13. 14 = 8 – 6r
14. 9 + 4n = -59
3
5
1
-−
n=−
15. −
5
3
11
16. −
s+−
=−
17. -1.6r + 5 = -7.8
18. 6x – 5 = 7 – 9x
19. 5(6 – 4v) = v + 21
20. 6y – 5 = -3(2y + 1)
4
2
8
6
4
12
Solve each equation or formula for the specified variable.
2d + 1
3
21. E = mc2, for m
22. c = −, for d
23. h = vt – gt2, for v
1 2
24. E = −
Iw + U, for I
2
25. GEOMETRY The length of a rectangle is twice the width. Find the width if the
perimeter is 60 centimeters. Define a variable, write an equation, and solve the problem.
26. GOLF Luis and three friends went golfing. Two of the friends rented clubs for $6 each.
The total cost of the rented clubs and the green fees for each person was $76. What was
the cost of the green fees for each person? Define a variable, write an equation, and solve
the problem.
Chapter 1
6
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solution.
NAME
1-4
DATE
PERIOD
Skills Practice
Solving Absolute Value Equations
Evaluate each expression if w = 0.4, x = 2, y = -3, and z = -10.
1. |5w|
2. |-9y|
3. |9y – z|
4. – |17z|
5. – |10z – 31|
6. – |8x – 3y| + |2y + 5x|
7. 25 – |5z + 1|
8. 44 + |-2x – y|
9. 2 |4w|
10. 3 – |1 – 6w|
11. |-3x – 2y| – 4
12. 6.4 + |w – 1|
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Check your solutions.
13. |y + 3| = 2
14. |5a| = 10
15. |3k – 6| = 2
16. |2g + 6| = 0
17. 10 = |1 – c|
18. |2x + x| = 9
19. |p – 7| = -14
20. 2 |3w| = 12
21. |7x – 3x| + 2 = 18
22. 4 |7 – y| – 1 = 11
1
23. |3n – 2| = −
24. |8d – 4d| + 5 = 13
25. -5|6a + 2| = -15
26. |k| + 10 = 9
Chapter 1
7
2
Glencoe Algebra 2
NAME
1-4
DATE
PERIOD
Practice
Solving Absolute Value Equations
Evaluate each expression if a = -1, b = -8, c = 5, and d = -1.4.
1. |6a|
2. |2b + 4|
3. – |10d + a|
4. |17c| + |3b – 5|
5. -6 |10a – 12|
6. |2b – 1| – |-8b + 5|
7. |5a – 7| + |3c – 4|
8. |1 – 7c| – |a|
9. -3|0.5c + 2| – |-0.5b|
11. |a – b| + |b – a|
10. |4d| + |5 – 2a|
12. |2 – 2d| – 3|b|
Solve each equation. Check your solutions.
14. |x – 13| = 2
15. |2y – 3| = 29
16. 7|x + 3| = 42
17. |3u – 6| = 42
18. |5x – 4| = -6
19. -3 |4x – 9| = 24
20. -6|5 – 2y| = -9
21. |8 + p| = 2p – 3
22. |4w – 1| = 5w + 37
23. 4 |2y – 7| + 5 = 9
24. -2|7 – 3y| – 6 = -14
25. 2 |4 – s| = -3s
26. 5 – 3|2 + 2w| = -7
27. 5 |2r + 3| – 5 = 0
28. 3 – 5|2d – 3| = 4
29. WEATHER A thermometer comes with a guarantee that the stated temperature
differs from the actual temperature by no more than 1.5 degrees Fahrenheit. Write
and solve an equation to find the minimum and maximum actual temperatures when
the thermometer states that the temperature is 87.4 degrees Fahrenheit.
30. OPINION POLLS Public opinion polls reported in newspapers are usually given with a
margin of error. For example, a poll with a margin of error of ±5% is considered accurate
to within plus or minus 5% of the actual value. A poll with a stated margin of error of
63% predicts that candidate Tonwe will receive 51% of an upcoming vote. Write and solve
an equation describing the minimum and maximum percent of the vote that candidate
Tonwe is expected to receive.
Chapter 1
8
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. |n – 4| = 13
NAME
DATE
1-5
PERIOD
Skills Practice
Solving Inequalities
Solve each inequality. Then graph the solution set on a number line.
z
≥2
1. −
2. 3a + 7 ≤ 16
-4
-4 -3 -2 -1 0
-9 -8 -7 -6 -5 -4 -3 -2 -1
3. 16 < 3q + 4
-1 0
1
2
3
4
5
6
7
1
2
3
1
2
3
4
1
2
-4 -3 -2 -1 0
3
4
5
6
2
1
2
3
3
4
5
6
1
2
3
4
1
2
3
4
1
2
3
4
2
5
6
7
2
-4 -3 -2 -1 0
4
3
4
5
3
-4 -3 -2 -1 0
12. 4(5x + 7) ≤ 13
6
13. 1.7y - 0.78 > 5
1
1
10. 7t – (t – 4) ≤ 25
11. 0.7m + 0.3m ≥ 2m – 4
1
-2 -1 0
8. 7f – 9 > 3f – 1
9. -3k – 8 ≤ 5k
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
-4 -3 -2 -1 0
4
7. 2z < -9 + 5z
-2 -1 0
3
6. 4b - 9 ≤ 7
-4 -3 -2 -1 0
-2 -1 0
2
4. 20 - 3n > 7n
5. 3x ≥ -9
-2 -1 0
1
-4 -3 -2 -1 0
14. 4x – 9 > 2x + 1
4
5
6
-1 0
1
2
3
4
Define a variable and write an inequality for each problem. Then solve.
15. Nineteen more than a number is less than 42.
16. The difference of three times a number and 16 is at least 8.
17. One half of a number is more than 6 less than the same number.
18. Five less than the product of 6 and a number is no more than twice that same number.
Chapter 1
9
Glencoe Algebra 2
NAME
DATE
1-5
PERIOD
Practice
Solving Inequalities
Solve each inequality. Then graph the solution set on a number line.
1. 8x – 6 ≥ 10
-4 -3 -2 -1 0
2. 23 – 4u < 11
1
2
3
4
3. -16 - 8r ≥ 0
-4 -3 -2 -1 0
1
2
3
4
2
3
4
5
6
1
1
-4 -3 -2 -1 0
1
2
3
4
2
3
4
2
3
4
6. -3(4w - 1) > 18
2
3
4
7. 1 – 8u ≤ 3u – 10
-4 -3 -2 -1 0
1
4. 14s < 9s + 5
5. 9x - 11 > 6x – 9
-4 -3 – …
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