NAME ______________________________________________ DATE______________ PERIOD _____
1-1
Skills Practice
Variables and Expressions
Write an algebraic expression for each verbal expression.
1. the sum of a number and 10
2. 15 less than k
3. the product of 18 and q
4. 6 more than twice m
5. 8 increased by three times a number
6. the difference of 17 and 5 times a number
7. the product of 2 and the second power of y
8. 9 less than g to the fourth power
Evaluate each expression.
10. 34
11. 53
12. 33
13. 102
14. 24
15. 72
16. 44
17. 73
18. 113
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 82
Write a verbal expression for each algebraic expression.
19. 9a
20. 52
21. c ! 2d
22. 4 " 5h
23. 2b2
24. 7x3 " 1
25. p4 ! 6q
26. 3n2 " x
Chapter 1
8
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-2
Skills Practice
Order of Operations
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Evaluate each expression.
1. (5 ! 4) " 7
2. (9 # 2) " 3
3. 4 ! 6 " 3
4. 28 # 5 " 4
5. 12 ! 2 " 2
6. (3 ! 5) " 5 ! 1
7. 9 ! 4(3 ! 1)
8. 2 ! 3 " 5 ! 4
10. 10 ! 2 " 6 ! 4
11. 14 $ 7 " 5 # 32
12. 6 $ 3 " 7 ! 23
13. 4[30 # (10 # 2) " 3]
14. 5 ! [30 # (6 # 1)2]
15. 2[12 ! (5 # 2)2]
16. [8 " 2 # (3 ! 9)] ! [8 # 2 " 3]
Lesson 1-2
9. 30 # 5 " 4 ! 2
Evaluate each expression if x ! 6, y ! 8, and z ! 3.
17. xy ! z
18. yz # x
19. 2x ! 3y # z
20. 2(x ! z) # y
21. 5z ! ( y # x)
22. 5x # ( y ! 2z)
23. x2 ! y2 # 10z
24. z3 ! ( y2 # 4x)
y ! xz
2
25. %
Chapter 1
3y ! x2
z
26. %
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-3
1-3
Skills Practice
Open Sentences
1. 5a ! 9 " 26
2. 4a ! 8 " 16
3. 7a # 21 " 56
4. 3b # 15 " 48
5. 4b ! 12 " 28
6. ( ! 3 " 0
36
b
Find the solution of each equation using the given replacement set.
1
2
5
4
! 21
3
4
5
4
7. ( # x " ( ; ( , ( , 1, (
1
4
5
6
! 32
"
3 5 4
4 4 3
9. ( (x # 2) " ( ; ( , ( , ( , (
2
3
13
9
! 94
5 2 7
9 3 9
8. x # ( " ( ; ( , ( , ( , (
"
"
10. 0.8(x # 5) " 5.2; {1.2, 1.3, 1.4, 1.5}
Solve each equation.
11. 10.4 ! 6.8 " x
12. y " 20.1 ! 11.9
13. ( " a
46 ! 15
3 # 28
14. c " (
2(4) # 4
3(3 ! 1)
16. (( " n
15. (( " b
Lesson 1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
873946 Alg1 CH01 EP3
Find the solution of each equation if the replacement sets are A ! {4, 5, 6, 7, 8} and
B ! {9, 10, 11, 12, 13}.
6 # 18
31 ! 25
6(7 ! 2)
3(8) # 6
Find the solution set for each inequality using the given replacement set.
17. a # 7 $ 13; {3, 4, 5, 6, 7}
18. 9 # y $ 17; {7, 8, 9, 10, 11}
19. x ! 2 % 2; {2, 3, 4, 5, 6, 7}
20. 2x & 12; {0, 2, 4, 6, 8, 10}
21. 4b # 1 & 12; {0, 3, 6, 9, 12, 15}
22. 2c ! 5 % 11; {8, 9, 10, 11, 12, 13}
y
2
23. ( ' 5; {4, 6, 8, 10, 12}
Chapter 1
x
3
24. ( & 2; {3, 4, 5, 6, 7, 8}
23
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-4
1-4
Skills Practice
Identity and Equality Properties
Name the property used in each equation. Then find the value of n.
1. n ! 0 " 19
2. 1 # n " 8
3. 28 # n " 0
4. 0 ! n " 22
1
4
5. & # n " 1
6. n # 9 " 9
7. 5 " n ! 5
8. 2 # n " 2 # 3
10. (7 # 3) ! 4 " n ! 4
11. 5 ! 4 " n ! 4
12. n " 14 # 0
13. 3n " 1
14. 11 $ (18 % 2) " 11 $ n
Evaluate each expression. Name the property used in each step.
15. 7(16 % 42)
16. 2[5 $ (15 % 3)]
17. 4 $ 3[7 $ (2 # 3)]
18. 4[8 $ (4 # 2)] ! 1
19. 6 ! 9[10 $ 2(2 ! 3)]
20. 2(6 % 3 $ 1) # &
Chapter 1
Lesson 1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 2(9 $ 3) " 2(n)
1
2
31
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-5
Skills Practice
The Distributive Property
Rewrite each expression using the Distributive Property. Then simplify.
1. 4(3 ! 5)
2. 2(6 ! 10)
3. 5(7 " 4)
4. (6 " 2)8
5. (a ! 7)2
6. 7(h " 10)
7. 3(m ! n)
8. (x " y)6
9. 2(x " y ! 1)
10. 3(a ! b " 1)
Use the Distributive Property to find each product.
11. 5 # 89
12. 9 # 99
13. 15 # 104
14. 15 2 $
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
! 14 "
15. 12 1 $
! 13 "
! 18 "
16. 8 3 $
Simplify each expression. If not possible, write simplified.
17. 2x ! 8x
18. 17g ! g
19. 16m " 10m
20. 12p " 8p
21. 2x2 ! 6x2
22. 7a2 " 2a2
23. 3y2 " 2y
24. 2(n ! 2n)
25. 4(2b " b)
26. 3q2 ! q " q2
Chapter 1
38
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
3-6
1-6
Skills Practice
Evaluate each expression.
1. 16 ! 8 ! 14 ! 12
2. 36 ! 23 ! 14 ! 7
3. 32 ! 14 ! 18 ! 11
4. 5 " 3 " 4 " 3
5. 2 " 4 " 5 " 3
6. 5 " 7 " 10 " 4
7. 1.7 ! 0.8 ! 1.3
8. 1.6 ! 0.9 ! 2.4
9. 4 # ! 6 ! 5 #
1
2
1
2
Simplify each expression.
10. 2x ! 5y ! 9x
11. a ! 9b ! 6a
12. 2p ! 3q ! 5p ! 2q
13. r ! 3s ! 5r ! s
14. 5m2 ! 3m ! m2
15. 6k2 ! 6k ! k2 ! 9k
16. 2a ! 3(4 ! a)
17. 5(7 ! 2g) ! 3g
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an algebraic expression for each verbal expression. Then simplify,
indicating the properties used.
18. three times the sum of a and b increased by a
19. twice the sum of p and q increased by twice the sum of 2p and 3q
Chapter 1
45
Glencoe Algebra 1
Lesson 1-6
Commutative and Associative Properties
NAME ______________________________________________ DATE______________ PERIOD _____
1-7
Skills Practice
Logical Reasoning and Counterexamples
Identify the hypothesis and conclusion of each statement.
1. If it is Sunday, then mail is not delivered.
2. If you are hiking in the mountains, then you are outdoors.
3. If 6n ! 4 " 58, then n " 9.
Identify the hypothesis and conclusion of each statement. Then write the
statement in if-then form.
4. Martina works at the bakery every Saturday.
.
5. Ivan only runs early in the morning.
6. A polygon that has five sides is a pentagon.
7. Hector scored an 86 on his science exam.
8. Hector did not earn an A in science.
9. Hector scored 84 on the science exam.
10. Hector studied 10 hours for the science exam.
Find a counterexample for each statement.
11. If the car will not start, then it is out of gas.
12. If the basketball team has scored 100 points, then they must be winning the game.
13. If the Commutative Property holds for addition, then it holds for subtraction.
14. If 2n ! 3 # 17, then n $ 7.
Chapter 1
52
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Determine whether a valid conclusion follows from the statement If Hector scores
an 85 or above on his science exam, then he will earn an A in the class for the
given condition. If a valid conclusion does not follow, write no valid conclusion
and explain why.
NAME ______________________________________________ DATE______________ PERIOD _____
1-8
Skills Practice
Number Systems
Find each square root. If necessary, round to the nearest hundredth.
"
1. !144
2. !!36
"
3. "!0.25
"
4. ! '
5. "!17
"
6. !2.25
"
#$
49
100
Name the set or sets of numbers to which each real number belongs.
5
6
28
7
8. ! '
9. !29
"
10. !196
"
9
13
12. !1.8
"
11. '
Lesson 1-8
7. ! '
Graph each solution set.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. x # !1
$2 $1
14. x $ 1
0
1
2
3
4
5
6
15. x % 1.5
$4 $3 $2 $1
0
1
2
3
4
0
1
2
3
4
16. x & !2.5
$4 $3 $2 $1
0
1
2
3
4
$4 $3 $2 $1
Replace each ● with !, ", or # to make each sentence true.
4
9
1
90
"
17. ' ● 0.4
18. 0.0
"9
"●'
19. 6.2
"3
" ● !39
"
20. ' ● '
1
8
1
!8
"
Write each set of numbers in order from least to greatest.
7
3
2
9
", 2.3
"6
", '
21. !5
22. ' , 0.2
"1
", !0.05
"
23. !!12
", !3.4
"8
", !!11
"
24. 0.4
"3
", ' , '
Chapter 1
!6
" 3
5 7
59
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
1-9
Skills Practice
Functions and Graphs
1. The graph below represents the path of
a football thrown in the air. Describe
what is happening in the graph.
2. The graph below represents a puppy
exploring a trail. Describe what is
happening in the graph. Is the function
discrete or continuous?
Distance from
Trailhead
Height
Time
Time
3. WEATHER During a storm, it rained lightly for a while, then poured heavily, and then
stopped for a while. Then it rained moderately for a while before finally ending. Which
graph represents this situation?
A
B
C
Total
Rainfall
Total
Rainfall
Time
LAUNDRY For Exercises 4–7, use the table
that shows the charges for washing and
pressing shirts at a cleaners.
Time
Number of Shirts
2
4
6
8
Total Cost ($)
3
6
9
12 15 18
10 12
4. Identify the independent and dependent variables.
5. Write the ordered pairs the table represents.
6. Draw a graph of the data.
21
18
Total Cost ($)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Time
15
12
9
6
3
0
2
4 6 8 10 12 14
Number of Shirts
7. Use the data to predict the cost for washing and
pressing 16 shirts.
Chapter 1
67
Glencoe Algebra 1
Lesson 1-9
Total
Rainfall
NAME ______________________________________________ DATE______________ PERIOD _____
2-1
Skills Practice
Writing Equations
Translate each sentence into an equation.
1. Two added to three times a number m is the same as 18.
2. Twice a increased by the cube of a equals b.
3. Seven less than the sum of p and q is as much as 6.
4. The sum of x and its square is equal to y times z.
5. Four times the sum of f and g is identical to six times g.
Translate each sentence into a formula.
6. The perimeter P of a square equals four times the length of a side s.
7. The area A of a square is the length of a side s squared.
8. The perimeter P of a triangle is equal to the sum of the lengths of sides a, b, and c.
9. The area A of a circle is pi times the radius r squared.
10. The volume V of a rectangular prism equals the product of the length !, the width w,
and the height h.
Translate each equation into a verbal sentence.
12. 2p ! 4q " 20
13. 4(a ! b) " 9a
14. 8 # 6x " 4 ! 2x
1
2
15. $ ( f ! y) " f # 5
16. s2 # n2 " 2b
Write a problem based on the given information.
17. c " cost per pound of plain coffee beans
c ! 3 " cost per pound of flavored coffee beans
2c ! (c ! 3) " 21
Chapter 2
8
18. p " cost of dinner
0.15p " cost of a 15% tip
p ! 0.15p " 23
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. g ! 10 " 3g
NAME ______________________________________________ DATE______________ PERIOD _____
2-2
Skills Practice
Solving Equations by Using Addition and Subtraction
Solve each equation. Then check your solution.
1. y ! 7 " 8
2. w # 14 " !8
3. p ! 4 " 6
4. !13 " 5 # x
5. 98 " b # 34
6. y ! 32 " !1
7. s # (!28) " 0
8. y # (!10) " 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. j ! (!17) " 36
11. 14 " d # (!10)
12. u # (!5) " !15
13. 11 " !16 # y
14. c ! (!3) " 100
15. 47 " w ! (!8)
16. x ! (!74) " !22
17. 4 ! (!h) " 68
18. !56 " 20 ! (!e)
Lesson 2-2
9. !1 " s # (!19)
Write an equation for each problem. Then solve the equation and check your
solution.
19. A number decreased by 14 is !46. Find the number.
20. Thirteen subtracted from a number is !5. Find the number.
21. The sum of a number and 67 is equal to !34. Find the number.
22. What number minus 28 equals !2?
23. A number plus !73 is equal to 27. What is the number?
24. A number plus !17 equals !1. Find the number.
25. What number less 5 is equal to !39?
Chapter 2
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-3
Skills Practice
Solving Equations by Using Multiplication and Division
Solve each equation. Then check your solution.
1. 12z ! 108
2. "7t ! 49
3. 18e ! "216
4. "22 ! 11v
5. "6d ! "42
6. 96 ! "24a
c
4
a
16
7. # ! 16
8. # ! 9
d
3
10. " # ! "13
11. # ! "13
12. 31 ! " # n
9. "84 ! #
t
4
2
3
13. "6 ! # z
5
9
d
7
1
6
2
7
14. # q ! "4
a
10
2
5
15. # p ! "10
16. # ! #
17. "0.4b ! 5.2
18. 1.6m ! "4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an equation for each problem. Then solve the equation.
19. The opposite of a number is "9. What is the number?
20. Fourteen times a number is "42. Find the number.
21. Eight times a number equals 128. What is the number?
22. Negative twelve times a number equals "132. Find the number.
23. Negative eighteen times a number is "54. What is the number?
24. One sixth of a number is "17. Find the number.
25. Negative three fifths of a number is "15. What is the number?
Chapter 2
22
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-4
Skills Practice
Solving Multi-Step Equations
Solve each problem by working backward.
1. A number is divided by 2, and then the quotient is added to 8. The result is 33. Find the
number.
2. Two is subtracted from a number, and then the difference is divided by 3. The result is
30. Find the number.
3. A number is multiplied by 2, and then the product is added to 9. The result is 49. What
is the number?
4. ALLOWANCE After Ricardo received his allowance for the week, he went to the mall
with some friends. He spent half of his allowance on a new paperback book. Then he
bought himself a snack for $1.25. When he arrived home, he had $5.00 left. How much
was his allowance?
5. 5x ! 3 " 23
6. 4 " 3a # 14
8. 6 ! 5c " #29
9. 8 # 5w " #37
n
3
11. $ # 8 " #2
d
6
14. # $ ! 12 " #7
x
4
12. 5 ! $ " 1
h
3
13. # $ # 4 " 13
16. $ ! 3 " #1
2
3
19. $ z # 8 " #3
c#5
4
22. $ " 2
18. $ g ! 6 " #12
4
5
21. $ " 3
20. $ m ! 2 " 6
10. 18 # 4v " 42
a
5
15. $ # 2 " 9
3
4
17. $ q # 7 " 8
7. 2y ! 5 " 19
w
7
5
2
b!1
3
Lesson 2-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Then check your solution.
Write an equation and solve each problem.
23. Twice a number plus four equals 6. What is the number?
24. Sixteen is seven plus three times a number. Find the number.
25. Find two consecutive integers whose sum is 35.
26. Find three consecutive integers whose sum is 36.
Chapter 2
29
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-5
Skills Practice
Solving Equations with the Variable on Each Side
Justify each step.
1.
4k ! 3 " 2k # 5
4k ! 3 ! 2k " 2k # 5 ! 2k
a.
2k ! 3 " 5
b.
2k ! 3 # 3 " 5 # 3
c.
2.
2k " 8
d.
8
2k
$"$
2
2
e.
k"4
f.
2(8u # 2) " 3(2u ! 7)
16u # 4 " 6u ! 21
a.
16u # 4 ! 6u " 6u ! 21 ! 6u
b.
10u # 4 " !21
c.
10u # 4 ! 4 " !21 ! 4
d.
10u " !25
e.
10u
!25
$"$
10
10
f.
u " !2.5
g.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation. Then check your solution.
3. 2m # 12 " 3m ! 31
4. 2h ! 8 " h # 17
5. 7a ! 3 " 3 ! 2a
6. 4n ! 12 " 12 ! 4n
7. 4x ! 9 " 7x # 12
8. !6y ! 3 " 3 ! 6y
9. 5 # 3r " 5r ! 19
10. !9 # 8k " 7 # 4k
11. 8q # 12 " 4(3 # 2q)
12. 3(5j # 2) " 2(3j ! 6)
13. 6(!3v # 1) " 5(!2v ! 2)
14. !7(2b ! 4) " 5(!2b # 6)
15. 3(8 ! 3t) " 5(2 # t)
16. 2(3u # 7) " !4(3 ! 2u)
17. 8(2f ! 2) " 7(3f # 2)
18. 5(!6 ! 3d) " 3(8 # 7d)
19. 6(w ! 1) " 3(3w # 5)
20. 7(!3y # 2) " 8(3y ! 2)
2
3
2
3
21. $ v ! 6 " 6 ! $ v
Chapter 2
1
2
5
8
7
8
7
2
22. $ ! $ x " $ x # $
36
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-6
Skills Practice
Ratios and Proportions
Use cross products to determine whether each pair of ratios forms a proportion.
Write yes or no.
1. " , "
4 20
5 25
2. " , "
5
9
6 24
7 28
4. " , "
5. " , "
7 42
16 90
6. " , "
3 21
14 98
8. " , "
7
11
8 72
9 81
3. " , "
7. " , "
13 26
19 38
12 50
17 85
Solve each proportion. If necessary, round to the nearest hundredth.
2
14
10. " ! "
9
g
15
10
12. " ! "
13. " ! "
6
z
3
5
14. " ! "
12
7
36
s
16. " ! "
42
56
6
f
18. " ! "
10
14
30
m
20. " ! "
11. " ! "
15. " ! "
17. " ! "
19. " ! "
9
c
27
39
21. " ! "
4
21
s
84
23. " ! "
5
b
3
9
3
a
1
6
5
e
35
21
6
23
7
b
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
a
9. " ! "
y
69
1
9
11
15
n
60
5
12
20
g
22
x
11
30
22. " ! "
24. " ! "
25. BOATING Hue’s boat used 5 gallons of gasoline in 4 hours. At this rate, how many
gallons of gasoline will the boat use in 10 hours?
Chapter 2
44
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-7
Skills Practice
Percent of Change
1. original: 25
new: 10
2. original: 50
new: 75
3. original: 55
new: 50
4. original: 25
new: 28
5. original: 50
new: 30
6. original: 90
new: 95
7. original: 48
new: 60
8. original: 60
new: 45
Lesson 2-7
State whether each percent of change is a percent of increase or a percent of
decrease. Then find each percent of change. Round to the nearest whole percent.
Find the total price of each item.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. dress: $69.00
tax: 5%
10. binder: $14.50
tax: 7%
11. hardcover book: $28.95
tax: 6%
12. groceries: $47.52
tax: 3%
13. filler paper: $6.00
tax: 6.5%
14. shoes: $65.00
tax: 4%
15. basketball: $17.00
tax: 6%
16. concert tickets: $48.00
tax: 7.5%
Find the discounted price of each item.
17. backpack: $56.25
discount: 20%
18. monitor: $150.00
discount: 50%
19. CD: $15.99
discount: 20%
20. shirt: $25.50
discount: 40%
21. sleeping bag: $125
discount: 25%
22. coffee maker: $102.00
discount: 45%
Chapter 2
51
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-8
Skills Practice
Solving Equations and Formulas
Solve each equation or formula for the variable specified.
1. 7t ! x, for t
2. e ! wp, for p
3. q " r ! r, for r
4. 4m " n ! m, for m
5. 7a " b ! 15a, for a
6. "5c # d ! 2c, for c
7. x " 2y ! 1, for y
8. m # 3n ! 1, for n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. ax " c ! b, for x
11. rt " 2n ! y, for t
12. bc # 3g ! 2k, for c
13. kn # 4f ! 9v, for n
14. 8c # 6j ! 5p, for c
x"c
2
16. $ ! d, for c
p#9
5
18. $ ! a, for b
15. $ ! d, for x
17. $ ! q, for p
Lesson 2-8
9. 7f # g ! 5, for f
x"c
2
b " 4z
7
Write an equation and solve for the variable specified.
19. Five more than a number g is six less than twice a number h. Solve for g.
20. One fourth of a number q is three more than three times a number w. Solve for q.
21. Eight less than a number s is three more than four times a number t. Solve for s.
Chapter 2
59
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
2-9
Skills Practice
Weighted Averages
SEASONING For Exercises 1–4, use the following information.
A health food store sells seasoning blends in bulk. One blend contains 20% basil. Sheila
wants to add pure basil to some 20% blend to make 16 ounces of her own 30% blend. Let b
represent the amount of basil Sheila should add to the 20% blend.
1. Complete the table representing the problem.
Ounces
Amount of Basil
20% Basil Blend
100% Basil
30% Basil Blend
2. Write an equation to represent the problem.
3. How many ounces of basil should Sheila use to make the 30% blend?
4. How many ounces of the 20% blend should she use?
HIKING For Exercises 5–7, use the following information.
5. Copy and complete the table representing the problem.
r
t
d ! rt
First group of hikers
Second group of hikers
6. Write an equation using t that describes the distances traveled.
7. How long will it be until the two groups of hikers meet?
SALES For Exercises 8 and 9, use the following information.
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To
make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts
that cost $3.00 per pound. He mixes 10 pounds at a time.
8. How many pounds of Virginia peanuts does Sergio use?
9. How many pounds of Spanish peanuts does Sergio use?
Chapter 2
66
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
At 7:00 A.M., two groups of hikers begin 21 miles apart and head toward each other. The
first group, hiking at an average rate of 1.5 miles per hour, carries tents, sleeping bags, and
cooking equipment. The second group, hiking at an average rate of 2 miles per hour, carries
food and water. Let t represent the hiking time.
NAME ______________________________________________ DATE______________ PERIOD _____
3-1
Skills Practice
Representing Relations
Express each relation as a table, a graph, and a mapping. Then determine the
domain and range.
873946 Alg1 CH03 EP7
1. {(!1, !1), (1, 1), (2, 1), (3, 2)}
y
O
x
2. {(0, 4), (!4, !4), (!2, 3), (4, 0)}
y
O
x
3. {(3, !2), (1, 0), (!2, 4), (3, 1)}
O
x
Express the relation shown in each table, mapping, or graph as a set of ordered
pairs. Then write the inverse of the relation.
4.
x
y
3
!5
!4
3
7
6
1
!2
Chapter 3
5.
X
Y
9
!5
4
7
6
8
2
8
6.
y
O
x
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
y
NAME ______________________________________________ DATE______________ PERIOD _____
3-2
Skills Practice
Representing Functions
Determine whether each relation is a function.
4.
X
Y
#6
#2
1
3
4
1
#3
#5
x
5.
y
X
Y
5
2
0
#3
4
1
#2
x
3.
6.
y
X
Y
4
6
7
2
#1
3
5
x
y
4
!5
2
7
3
7
!1
!10
5
!3
!1
1
0
!9
3
5
1
0
1
!7
!4
!2
3
5
9
1
5
2
7
3
7. {(2, 5), (4, !2), (3, 3), (5, 4), (!2, 5)}
8. {(6, !1), (!4, 2), (5, 2), (4, 6), (6, 5)}
9. y " 2x ! 5
11.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2.
10. y " 11
12.
y
O
x
13.
y
O
x
y
O
x
If f(x) ! 3x " 2 and g(x) ! x2 # x, find each value.
14. f(4)
15. f(8)
16. f(!2)
17. g(2)
18. g(!3)
19. g(!6)
20. f(2) # 1
21. f(1) ! 1
22. g(2) ! 2
23. g(!1) # 4
24. f(x # 1)
25. g(3b)
Chapter 3
15
Glencoe Algebra 1
Lesson 3-2
873946 Alg1 CH03 EP7
1.
NAME ______________________________________________ DATE______________ PERIOD _____
3-3
Skills Practice
Linear Functions
1. xy ! 6
2. y ! 2 " 3x
3. 5x ! y " 4
4. y ! 2x # 5
5. y ! "7 # 6x
6. y ! 3x2 # 1
7. y " 4 ! 0
8. 5x # 6y ! 3x # 2
9. $ y ! 1
1
2
Determine the x-intercept and y-intercept of each graph.
y
y
10.
11.
12.
y
x
x
O
O
x
O
13. y ! 4
14. y ! 3x
15. y ! x # 4
y
O
y
x
O
y
O
x
x
Graph each equation by using the x-intercept and y-intercept.
16. x " y ! 3
17. 10x ! "5y
y
O
Chapter 3
18. 4x ! 2y # 6
y
x
O
y
x
22
O
x
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph each equation by making a table.
873946 Alg1 CH03 EP7
Determine whether each equation is a linear equation. If so, write the equation in
standard form.
NAME ______________________________________________ DATE______________ PERIOD _____
3-4
Skills Practice
Arithmetic Sequences
1. 4, 7, 9, 12, …
2. 15, 13, 11, 9, …
3. 7, 10, 13, 16, …
4. !6, !5, !3, !1, …
5. !5, !3, !1, 1, …
6. !9, !12, !15, !18, …
873946 Alg1 CH03 EP7
Determine whether each sequence is an arithmetic sequence. If it is, state the
common difference.
Find the next three terms of each arithmetic sequence.
8. 22, 20, 18, 16, …
7. 3, 7, 11, 15, …
9. !13, !11, !9, !7, …
10. !2, !5, !8, !11, …
11. 19, 24, 29, 34, …
12. 16, 7, !2, !11, …
Find the nth term of each arithmetic sequence described.
14. a1 " !2, d " 5, n " 11
15. a1 " 10, d " !3, n " 15
16. a1 " !3, d " !3, n " 22
17. a1 " 24, d " 8, n " 25
18. a1 " 8, d " !6, n " 14
19. 8, 13, 18, 23, … for n " 17
20. !10, !3, 4, 11, … for n " 12
21. 12, 10, 8, 6, … for n " 16
22. 12, 7, 2, !3, … for n " 25
Write an equation for the nth term of each arithmetic sequence. Then graph the
first five terms of the sequence.
23. 7, 13, 19, 25, …
30
24. 30, 26, 22, 18, …
an
30
25. !7, !4, !1, 2, …
an
an
4
20
20
10
10
O
2
4
6n
!4
O
Chapter 3
2
4
6n
O
2
4
30
6n
!8
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. a1 " 6, d " 3, n " 12
NAME ______________________________________________ DATE______________ PERIOD _____
3-5
Skills Practice
Describing Number Patterns
Find the next two items for each pattern. Then find the 19th figure in the pattern.
2.
Find the next three terms in each sequence.
3. 1, 4, 10, 19, 31, …
4. 15, 14, 16, 15, 17, 16, …
5. 29, 28, 26, 23, 19, …
6. 2, 3, 2, 4, 2, 5, …
7. x, x ! 1, x ! 2, …
8. y, 4y, 9y, 16y, …
Write an equation in function notation for each relation.
9.
10.
y
x
O
12.
O
13.
y
11.
y
x
y
14.
y
y
O
Chapter 3
x
x
O
O
x
O
Lesson 3-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
873946 Alg1 CH03 EP7
1.
x
37
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
4-1
Skills Practice
Rate of Change and Slope
Find the slope of the line that passes through each pair of points.
1.
2.
y
3.
y
y
(2, 5)
(0, 1)
O
(0, 1)
O
(3, 1)
O
x
(1, –2)
x
(0, 0)
4. (2, 5), (3, 6)
5. (6, 1), (!6, 1)
6. (4, 6), (4, 8)
7. (5, 2), (5, !2)
8. (2, 5), (!3, !5)
9. (9, 8), (7, !8)
11. (!3, 10), (!3, 7)
12. (17, 18), (18, 17)
13. (!6, !4), (4, 1)
14. (10, 0), (!2, 4)
15. (2, !1), (!8, !2)
16. (5, !9), (3, !2)
17. (12, 6), (3, !5)
18. (!4, 5), (!8, !5)
19. (!5, 6), (7, !8)
Find the value of r so the line that passes through each pair of points has the
given slope.
20. (r, 3), (5, 9), m " 2
1
2
21. (5, 9), (r, !3), m " !4
3
4
22. (r, 2), (6, 3), m " #
23. (r, 4), (7, 1), m " #
24. (5, 3), (r, !5), m " 4
25. (7, r), (4, 6), m " 0
Chapter 4
8
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. (!5, !8), (!8, 1)
x
NAME ______________________________________________ DATE______________ PERIOD _____
4-2
Skills Practice
Slope and Direct Variation
Name the constant of variation for each equation. Then determine the slope of the
line that passes through each pair of points.
1.
2.
y
(3, 1)
(0, 0)
O
(0, 0)
x
O
(0, 0)
x
y ! – 32 x
y ! –2x
y ! 13 x
y
(–2, 3)
(–1, 2)
x
O
3.
y
Graph each equation.
3
4
5. y ! " # x
y
O
2
5
6. y ! # x
y
O
x
y
O
x
x
Write a direct variation equation that relates x and y. Assume that y varies
directly as x. Then solve.
8. If y ! 45 when x ! 15, find x
when y ! 15.
9. If y ! "4 when x ! 2, find y
when x ! "6.
10. If y ! "9 when x ! 3, find y
when x ! "5.
11. If y ! 4 when x ! 16, find y
when x ! 6.
12. If y ! 12 when x ! 18, find x
when y ! "16.
Write a direct variation equation that relates the variables. Then graph the
equation.
13. TRAVEL The total cost C of gasoline
is $1.80 times the number of gallons g.
24
18
20
15
Toys
21
16
12
12
9
8
6
4
3
2
4
Toys Shipped
T
28
0
Chapter 4
14. SHIPPING The number of delivered toys T
is 3 times the total number of crates c.
Gasoline Cost
C
Cost ($)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. If y ! "8 when x ! "2, find x
when y ! 32.
6 8 10 12 14 g
Gallons
0
15
1
2
3 4 5
Crates
6
7
c
Glencoe Algebra 1
Lesson 4-2
4. y ! 3x
NAME ______________________________________________ DATE______________ PERIOD _____
4-3
Skills Practice
Graphing Equations in Slope-Intercept Form
Write an equation of the line with the given slope and y-intercept.
1. slope: 5, y-intercept: !3
2. slope: !2, y-intercept: 7
3. slope: !6, y-intercept: !2
4. slope: 7, y-intercept: 1
5. slope: 3, y-intercept: 2
6. slope: !4, y-intercept: !9
7. slope: 1, y-intercept: !12
8. slope: 0, y-intercept: 8
Write an equation of the line shown in each graph.
9.
10.
y
11.
y
y
(0, 2)
(2, 1)
O
x
O
x
x
O
(0, –1)
(2, –4)
(0, –3)
(2, –3)
Graph each equation.
13. y " !2x ! 1
y
14. x # y " !3
y
y
O
O
O
x
x
x
Write a linear equation in slope-intercept form to model each situation.
15. A video store charges $10 for a rental card plus $2 per rental.
16. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year.
17. A Cairn terrier weighs 30 pounds and is on a special diet to lose 2 pounds per month.
18. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.
Chapter 4
22
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12. y " x # 4
NAME ______________________________________________ DATE______________ PERIOD _____
4-4
Skills Practice
Writing Equations in Slope-Intercept Form
Write an equation of the line that passes through each point with the given slope.
1.
2.
y
3.
y
y
(4, 1)
(–1, 4)
(–1, 2)
x
O
m ! –3
m!2
m!1
x
O
x
O
4. (1, 9), m ! 4
5. (4, 2), m ! "2
6. (2, "2), m ! 3
7. (3, 0), m ! 5
8. ("3, "2), m ! 2
9. ("5, 4), m ! "4
Write an equation of the line that passes through each pair of points.
11.
y
(–2, 3)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
O
x
O
12.
y
(1, 1)
(0, 3)
x
x
O
(–1, –3)
(3, –2)
y
(2, –1)
13. (1, 3), ("3, "5)
14. (1, 4), (6, "1)
15. (1, "1), (3, 5)
16. ("2, 4), (0, 6)
17. (3, 3), (1, "3)
18. ("1, 6), (3, "2)
Write an equation of the line that has each pair of intercepts.
19. x-intercept: "3, y-intercept: 6
20. x-intercept: 3, y-intercept: 3
21. x-intercept: 1, y-intercept: 2
22. x-intercept: 2, y-intercept: "4
23. x-intercept: "4, y-intercept: "8
24. x-intercept: "1, y-intercept: 4
Chapter 4
29
Glencoe Algebra 1
Lesson 4-4
10.
NAME ______________________________________________ DATE______________ PERIOD _____
4-5
Skills Practice
Writing Equations in Point-Slope Form
Write the point-slope form of an equation for a line that passes through each
point with the given slope.
1.
2.
y
m ! –1
3.
y
y
x
O
m!3
O
x
x
O
(–1, –2)
m!0
(1, –2)
4. (3, 1), m ! 0
5. ("4, 6), m ! 8
7. (4, "6), m ! 1
8. (3, 3), m ! $
4
3
(2, –3)
6. (1, "3), m ! "4
5
4
9. ("5, "1), m ! " $
Write each equation in standard form.
11. y # 9 ! "3(x " 2)
12. y " 7 ! 4(x # 4)
13. y " 4 ! "(x " 1)
14. y " 6 ! 4(x # 3)
15. y # 5 ! "5(x " 3)
16. y " 10 ! "2(x " 3)
17. y " 2 ! " $ (x " 4)
1
2
1
3
18. y # 11 ! $ (x # 3)
Write each equation in slope-intercept form.
19. y " 4 ! 3(x " 2)
20. y # 2 ! "(x # 4)
21. y " 6 ! "2(x # 2)
22. y # 1 ! "5(x " 3)
23. y " 3 ! 6(x " 1)
24. y " 8 ! 3(x # 5)
1
2
25. y " 2 ! $ (x # 6)
Chapter 4
1
3
26. y # 1 ! " $ (x # 9)
36
1
2
1
2
27. y " $ ! x # $
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. y # 1 ! x # 2
NAME ______________________________________________ DATE______________ PERIOD _____
4-6
Skills Practice
Statistics: Scatter Plots and Lines of Fit
Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.
1.
Calories Burned
During Exercise
2.
Library Fines
7
600
6
Fines (dollars)
Calories
500
400
300
200
100
0
3.
10 20 30 40 50 60
Time (minutes)
3
2
0
1
4.
12
10
8
6
2
3 4 5 6 7
Books Borrowed
8
8 10
20 40 60 80 100120140
Weight (pounds)
900
850
800
750
700
650
600
0
’95 ’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03
Year
Source: Editor & Publisher
BASEBALL For Exercises 5–7, use the scatter
plot that shows the average price of a
major-league baseball ticket from 1991 to 2005.
6. Use the points (1998, 13.60) and (2003, 19.00)
to write the slope-intercept form of an equation
for the line of fit shown in the scatter plot.
7. Predict the price of a ticket in 2009.
Chapter 4
20
Average Price ($)
5. Determine what relationship, if any, exists in
the data. Explain.
Baseball Ticket Prices
22
18
16
14
12
10
0
’96 ’97 ’98 ’99 ’00 ’01 ’02 ’03 ’04 ’05
Year
Source: Team Marketing Report, Chicago
44
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
2
Evening Newspapers
Number of Newspapers
14
Repetitions
4
1
Weight-Lifting
0
5
NAME ______________________________________________ DATE______________ PERIOD _____
4-7
Skills Practice
Geometry: Parallel and Perpendicular Lines
Write the slope-intercept form of an equation of the line that passes through the
given point and is parallel to the graph of each equation.
1.
2.
y
3.
y
y ! –x " 3
x
O
(–2, –3)
y ! 2x # 1
(–2, 2)
y
x
O
x
O
(1, –1)
y ! 12 x " 1
4. (3, 2), y ! 3x " 4
5. (#1, #2), y ! #3x " 5
6. (#1, 1), y ! x # 4
7. (1, #3), y ! #4x # 1
8. (#4, 2), y ! x " 3
9. (#4, 3), y ! $ x # 6
1
4
10. (4, 1), y ! # $ x " 7
11. (#5, #1), 2y ! 2x # 4
1
2
12. (3, #1), 3y ! x " 9
13. (#3, #2), y ! x " 2
14. (4, #1), y ! 2x # 4
16. (#4, 5), y ! #4x # 1
17. (#2, 3), y ! $ x # 4
3
4
1
4
5
3
15. (#1, #6), x " 3y ! 6
1
2
18. (0, 0), y ! $ x # 1
19. (3, #3), y ! $ x " 5
20. (#5, 1), y ! # $ x # 7
21. (0, #2), y ! #7x " 3
22. (2, 3), 2x " 10y ! 3
23. (#2, 2), 6x " 3y ! #9
24. (#4, #3), 8x # 2y ! 16
Chapter 4
52
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write the slope-intercept form of an equation of the line that passes through the
given point and is perpendicular to the graph of each equation.
NAME ______________________________________________ DATE______________ PERIOD _____
5-1
Skills Practice
Graphing Systems of Equations
Use the graph at the right to determine whether
each system has no solution, one solution, or
infinitely many solutions.
1. y ! x " 1
y ! "x # 1
y
x " y ! "4
2. x " y ! "4
y!x#4
3. y ! x # 4
2x " 2y ! 2
y!x#4
2x " 2y ! 2
x
O
y ! "x # 1
y!x"1
4. y ! 2x " 3
2x " 2y ! 2
y ! 2x " 3
Graph each system of equations. Then determine whether the system has no
solution, one solution, or infinitely many solutions. If the system has one solution,
name it.
5. 2x " y ! 1
y ! "3
6. x ! 1
2x # y ! 4
y
y
x
O
y
x
O
9. x # 3y ! "3
x " 3y ! "3
y
11. x " y ! 3
x
O
x
O
13. y ! 2x # 3
1
y ! "$x # 2
2
3y ! 6x " 6
y
y
y
x
x
O
Chapter 5
y
12. x # 2y ! 4
x " 2y ! 3
O
10. y " x ! "1
x#y!3
y
x
x
O
8
O
x
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. y ! x # 2
x " y ! "2
O
7. 3x # y ! "3
3x # y ! 3
NAME ______________________________________________ DATE______________ PERIOD _____
5-2
Skills Practice
Substitution
Use substitution to solve each system of equations. If the system does not have
exactly one solution, state whether it has no solution or infinitely many solutions.
1. y ! 4x
x"y!5
2. y ! 2x
x " 3y ! #14
3. y ! 3x
2x " y ! 15
4. x ! #4y
3x " 2y ! 20
5. y ! x # 1
x"y!3
6. x ! y # 7
x " 8y ! 2
7. y ! 4x # 1
y ! 2x # 5
8. y ! 3x " 8
5x " 2y ! 5
9. 2x # 3y ! 21
y!3#x
10. y ! 5x # 8
4x " 3y ! 33
12. x " 5y ! 4
3x " 15y ! #1
13. 3x # y ! 4
2x # 3y ! #9
14. x " 4y ! 8
2x # 5y ! 29
15. x # 5y ! 10
2x # 10y ! 20
16. 5x # 2y ! 14
2x # y ! 5
17. 2x " 5y ! 38
x # 3y ! #3
18. x # 4y ! 27
3x " y ! #23
19. 2x " 2y ! 7
x # 2y ! #1
20. 2.5x " y ! #2
3x " 2y ! 0
Chapter 5
16
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. x " 2y ! 13
3x # 5y ! 6
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
5-3
Skills Practice
Elimination Using Addition and Subtraction
1. x ! y " 1
x#y"3
2. !x # y " 1
x # y " 11
3. x # 4y " 11
x ! 6y " 11
4. !x # 3y " 6
x # 3y " 18
5. 3x # 4y " 19
3x # 6y " 33
6. x # 4y " !8
x ! 4y " !8
7. 3a # 4b " 2
4a ! 4b " 12
8. 3c ! d " !1
!3c ! d " 5
9. 2x ! 3y " 9
!5x ! 3y " 30
10. x ! y " 4
2x # y " !4
11. 3m ! n " 26
!2m ! n " !24
12. 5x ! y " !6
!x # y " 2
13. 6x ! 2y " 32
4x ! 2y " 18
14. 3x # 2y " !19
!3x ! 5y " 25
15. 7m # 4n " 2
7m # 2n " 8
16. 2x ! 5y " !28
4x # 5y " 4
Lesson 5-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Use elimination to solve each system of equations.
17. The sum of two numbers is 28 and their difference is 4. What are the numbers?
18. Find the two numbers whose sum is 29 and whose difference is 15.
19. The sum of two numbers is 24 and their difference is 2. What are the numbers?
20. Find the two numbers whose sum is 54 and whose difference is 4.
21. Two times a number added to another number is 25. Three times the first number minus
the other number is 20. Find the numbers.
Chapter 5
23
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
5-4
Skills Practice
Elimination Using Multiplication
Use elimination to solve each system of equations.
1. x ! y " #9
5x # 2y " 32
2. 3x ! 2y " #9
x # y " #13
3. 2x ! 5y " 3
#x ! 3y " #7
4. 2x ! y " 3
#4x # 4y " #8
5. 4x # 2y " #14
3x # y " #8
6. 2x ! y " 0
5x ! 3y " 2
7. 5x ! 3y " #10
3x ! 5y " #6
8. 2x ! 3y " 14
3x # 4y " 4
9. 2x # 3y " 21
5x # 2y " 25
10. 3x ! 2y " #26
4x # 5y " #4
11. 3x # 6y " #3
2x ! 4y " 30
12. 5x ! 2y " #3
3x ! 3y " 9
14. Four times a number minus twice another number is #16. The sum of the two numbers
is #1. Find the numbers.
Determine the best method to solve each system of equations. Then solve the system.
15. 2x ! 3y " 10
5x ! 2y " #8
16. 8x # 7y " 18
3x ! 7y " 26
17. y " 2x
3x ! 2y " 35
18. 3x ! y " 6
3x ! y " 3
19. 3x # 4y " 17
4x ! 5y " 2
20. y " 3x ! 1
3x # y " #1
Chapter 5
30
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. Two times a number plus three times another number equals 13. The sum of the two
numbers is 7. What are the numbers?
NAME ______________________________________________ DATE______________ PERIOD _____
5-5
Skills Practice
Applying Systems of Linear Equations
1. 5x ! 3y " 16
3x – 5y " #4
2. 3x – 5y " 7
2x ! 5y " 13
3. y " 3x # 24
5x # y " 8
4. #11x – 10y " 17
5x – 7y " 50
5. 4x ! y " 24
5x # y " 12
6. 6x – y " #145
x " 4 – 2y
7. VEGETABLE STAND A roadside vegetable stand sells pumpkins for $5 each and
squashes for $3 each. One day they sold 6 more squash than pumpkins, and their sales
totaled $98. Write and solve a system of equations to find how many pumpkins and
squash they sold?
8. INCOME Ramiro earns $20 per hour during the week and $30 per hour for overtime
on the weekends. One week Ramiro earned a total of $650. He worked 5 times as many
hours during the week as he did on the weekend. Write and solve a system of equations
to determine how many hours of overtime Ramiro worked on the weekend.
9. BASKETBALL Anya makes 14 baskets during her game. Some of these baskets were
worth 2-points and others were worth 3-points. In total, she scored 30 points. Write and
solve a system of equations to find how 2-points baskets she made.
Chapter 5
37
Glencoe Algebra 1
Lesson 5-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Determine the best method to solve each system of equations. Then solve
the system.
NAME ______________________________________________ DATE______________ PERIOD _____
6-1
Skills Practice
Solving Inequalities by Addition and Subtraction
Match each inequality with its corresponding graph.
1. x ! 11 " 16 c
a.
2. x # 6 $ 1 e
0
b.
0
1
2
3
4
4
5
6
7
8
#8 #7 #6 #5 #4 #3 #2 #1
0
#4 #3 #2 #1
3. x ! 2 % #3 a
c.
0
4. x ! 3 & 1 b
1
2
3
d.
5. x # 1 $ #7 d
e.
0
1
2
3
4
5
6
7
8
Solve each inequality. Then check your solution, and graph it on a number line.
6. d # 5 % 1 {d ! d ! 6}
0
1
2
3
4
5
6
7
8
8. a # 7 " #13 {a ! a $ #6}
#8 #7 #6 #5 #4 #3 #2 #1
1
2
3
#8 #7 #6 #5 #4 #3 #2 #1
1
2
3
4
9. w # 1 $ 4 {w ! w " 5}
0
1
2
3
4
5
6
7
8
11. #9 % b # 4 {b ! b % #5}
4
12. #2 & x ! 4 {x ! x ! #6}
0
#8 #7 #6 #5 #4 #3 #2 #1
0
13. 2y $ y ! 2 {y ! y " 2}
0
#4 #3 #2 #1
0
1
2
3
4
Define a variable, write an inequality, and solve each problem. Then check your
solution. 14–18. Sample answer: Let n & the number.
14. A number decreased by 10 is greater than #5. n # 10 $ #5; {n ! n $ 5}
15. A number increased by 1 is less than 9. n ' 1 " 9; {n ! n " 8}
16. Seven more than a number is less than or equal to #18. n ' 7 ! #18; {n ! n ! #25}
17. Twenty less than a number is at least 15. n # 20 % 15; {n ! n % 35}
18. A number plus 2 is at most 1. n ' 2 ! 1; {n ! n ! #1}
Chapter 6
8
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0
#4 #3 #2 #1
0
10. 4 & k ! 3 {k ! k ! 1}
#4 #3 #2 #1
7. s ! 9 $ 8 {s ! s " #1}
873949 Alg1 CH06 EP3
#8 #7 #6 #5 #4 #3 #2 #1
NAME ______________________________________________ DATE______________ PERIOD _____
6-2
Skills Practice
Solving Inequalities by Multiplication and Division
Match each inequality with its corresponding statement.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
3
a. Three times a number is at most nine.
2. & n " 9 f
b. One third of a number is no more than nine.
3. 3n # 9 a
c. Negative three times a number is more than nine.
4. $3n % 9 c
d. Three times a number is less than nine.
1
3
5. & n # 9 b
e. Negative three times a number is at least nine.
6. $3n " 9 e
f. One third of a number is greater than or equal to nine.
Solve each inequality. Then check your solution.
7. 14g % 56
{g ! g ! 4}
11. $15p # $90
{p ! p # 6}
t
12
15. $ & " 6
{t ! t " $72}
19. $y ! 36
{y ! y ! $36}
8. 11w # 77
9. 20b " $120
{w ! w " 7}
s
4
12. & ! 9
{b ! b # $6}
a
9
13. & " $15
{s ! s % 36}
16. 5z ! $90
{a ! a # $135}
17. $13m % $26
{z ! z % $18}
20. $16c " $224
{m ! m % 2}
h
10
21. $ & # 2
{c ! c " 14}
{h ! h # $20}
10. $8r ! 16
{r ! r ! $2}
p
7
14. $ & % $9
{p ! p % 63}
k
5
18. & # $17
{k ! k " $85}
d
12
22. 12 % &
{d ! d % 144}
Define a variable, write an inequality, and solve each problem. Then check your
solution. 23–27. Sample answer: Let n & the number.
23. Four times a number is greater than $48. 4n ! $48; {n ! n ! $12}
1
24. One eighth of a number is less than or equal to 3. '
8 n " 3; {n ! n " 24}
25. Negative twelve times a number is no more than 84. $12n " 84; {n ! n # $7}
1
26. Negative one sixth of a number is less than $9. $ '
6 n % $9; {n ! n ! 54}
27. Eight times a number is at least 16. 8n # 16; {n ! n # 2}
Chapter 6
15
Glencoe Algebra 1
Lesson 6-2
873949 Alg1 CH06 EP3
1. 3n ! 9 d
NAME ______________________________________________ DATE______________ PERIOD _____
6-3
Skills Practice
Solving Multi-Step Inequalities
2. 5(k # 8) ! 7 $ 23
5k # 40 ! 7 $ 23
5k # 33 $ 23
5k # 33 ! 33 $ 23 ! 33
5k $ !10
3
% t ! 3 " !15
4
1.
3
% t ! 3 # 3 " !15 # 3
4
3
% t " !12
4
! "
4 3
4
% % t " % (!12)
3 4
3
?
a.
!10
5k
%$%
5
5
?
b.
a.
?
b.
?
c.
?
k $ !2
t " !16
a. Distributive Property
b. Subtract 33 from each side.
c. Divide each side by 5.
a. Add 3 to each side.
4
b. Multiply each side by !
3.
Solve each inequality. Then check your solution.
3. !2b # 4 & !6
4. 3x # 15 $ 21
{b # b " 5}
{x # x # 2}
2
5
t
5
6. % a ! 4 ' 2
7. !%% # 7 & !4
{a # a " 15}
2
3
{t # t " 55}
10. 2p # 5 " 3p ! 10
{f # f % 18}
{p # p # 15}
12. 2(!3m ! 5) " !28
13. !6(w # 1) ' 2(w # 5)
{m # m # 3}
{w # w % &2}
{d # d $ 8}
3
4
8. % j ! 10 " 5
{j # j $ 20}
11. 4k # 15 & !2k # 3
{k # k % &2}
14. 2(q ! 3) # 6 $ !10
{q # q # &5}
Define a variable, write an inequality, and solve each problem. Then check your
solution. 15–20. Sample answer: Let n ' the number.
n
3
15. Four more than the quotient of a number and three is at least nine. ! ( 4 $ 9;
{n # n $ 15}
16. The sum of a number and fourteen is less than or equal to three times the number.
n ( 14 # 3n; {n # n $ 7}
17. Negative three times a number increased by seven is less than negative eleven.
&3n ( 7 " &11; {n # n % 6}
18. Five times a number decreased by eight is at most ten more than twice the number.
5n & 8 # 2n ( 10; {n # n # 6}
5
6
19. Seven more than five sixths of a number is more than negative three. ! n ( 7 % &3;
{n # n % &12}
20. Four times the sum of a number and two increased by three is at least twenty-seven.
4(n ( 2) ( 3 $ 27; {n # n $ 4}
Chapter 6
22
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. ! % f # 3 ' !9
d
2
5. % ! 1 " 3
873949 Alg1 CH06 EP3
Justify each indicated step.
NAME ______________________________________________ DATE______________ PERIOD _____
6-4
Skills Practice
Solving Compound Inequalities
Graph the solution set of each compound inequality.
!4 !3 !2 !1
0
2. z " 3 and z # $2
1
2
3
4
3. k ! 1 and k ! 5
0
1
2
3
4
5
!4 !3 !2 !1
0
1
2
3
4
4. y % $1 or y # 1
6
7
8
!4 !3 !2 !1
0
1
2
3
4
2
3
4
5
6
0
1
2
3
4
Write a compound inequality for each graph.
5.
6.
!4 !3 !2 !1
0
1
2
3
4
!2 !1
!3 " x # 3
0
1
1#x#4
7.
8.
!4 !3 !2 !1
0
1
2
3
4
!4 !3 !2 !1
x " !2 or x $ 1
x " !1 or x % 2
Solve each compound inequality. Then graph the solution set.
9. m & 3 # 5 and m & 3 % 7
{m ! 2 # m " 4}
!2 !1
0
1
2
3
4
5
{f ! !2 " f " !1}
0
1
2
3
1
2
3
4
0
1
2
3
4
5
6
12. w & 3 " 0 or w & 7 # 9
{w ! w # !3 or w $ 2}
!4 !3 !2 !1
0
1
2
3
4
14. p $ 2 " $2 or p $ 2 ! 1
{b ! !2 " b " 6}
0
!2 !1
4
13. $6 % b $ 4 % 2
!2 !1
{y ! y " 1 or y $ 6}
6
11. 4 % f & 6 and f & 6 % 5
!4 !3 !2 !1
10. y $ 5 % $4 or y $ 5 # 1
{p ! p # 0 or p % 3}
5
6
!4 !3 !2 !1
0
1
2
3
4
Define a variable, write an inequality, and solve each problem. Then check your
solution. 15–17. Sample answer: Let n & the number.
15. A number plus one is greater than negative five and less than three.
!5 " n ' 1 " 3; {n ! !6 " n " 2}
16. A number decreased by two is at most four or at least nine.
n ! 2 # 4 or n ! 2 $ 9; {n ! n # 6 or n $ 11}
17. The sum of a number and three is no more than eight or is more than twelve.
n ' 3 # 8 or n ' 3 % 12; {n ! n # 5 or n % 9}
Chapter 6
29
Glencoe Algebra 1
Lesson 6-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
873949 Alg1 CH06 EP3
1. b ! 3 or b " 0
NAME ______________________________________________ DATE______________ PERIOD _____
6-5
Skills Practice
Solving Open Sentences Involving Absolute Value
1. x ! 4 c
a.
2. x " 6 ! 3 a
b.
3. 2x # 4 ! 8 d
3
4
7
8
9
10
!7 !6 !5 !4 !3 !2 !1
0
1
2
3
1
2
3
4
5
!7 !6 !5 !4 !3 !2 !1
0
1
2
3
1
2
c.
!5 !4 !3 !2 !1
4. x # 2 ! 3 b
5
6
0
0
d.
Express each statement as an open sentence using absolute value.
5. Jordan’s highest and lowest test scores are 7 percentage points from 89%. |p ! 89| = 7
6. The normal human body temperature varies 1.5ºF from the average 98.6ºF.
! t ! 98.6 ! " 1.5
7. Last year, 224 students attended the Homecoming game. This year, the Student Council
expects student attendance to be within 36 of the previous years’ attendance.
! s ! 224 ! " 36
Solve each open sentence. Then graph the solution set.
9. 2f " 9! 1 {4, 5}
!10 !9 !8 !7 !6 !5 !4 !3 !2 !1
10. g " 4 ! 3 {1, 7}
0
1
2
3
4
5
6
0
1
1
2
3
4
5
6
7
8
9 10
3
4
5
!10 !9 !8 !7 !6 !5 !4 !3 !2 !1
0
11. w # 3! 1 {!4, !2}
7
8
9 10
12. 3s ! 12 {!4, 4}
!5 !4 !3 !2 !1
0
0
!5 !4 !3 !2 !1
0
1
2
13. c # 6! 2 {!8, !4}
2
3
4
5
For each graph, write an open sentence involving absolute value.
14.
!5 !4 !3 !2 !1
0
1
2
3
4
5
15.
!5 !4 !3 !2 !1
!x! "2
16.
!10 !9 !8 !7 !6 !5 !4 !3 !2 !1
1
2
3
4
5
5
6
7
8
9
10
!x#1! "4
0
17.
!x#5! "4
Chapter 6
0
0
1
2
3
4
!x!7! "3
36
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. d # 5 ! 1 {!6, !4}
873949 Alg1 CH06 EP3
Match each open sentence with the graph of its solution set.
NAME ______________________________________________ DATE______________ PERIOD _____
6-6
Skills Practice
Solving Inequalities Involving Absolute Value
Match each open sentence with the graph of its solution set.
1. x ! 2 c
873949 Alg1 CH06 EP3
!10 !9 !8 !7 !6 !5 !4 !3 !2 !1
2. x " 5 # 3 a
Lesson 6-6
a.
0
b.
3. x $ 2 % 3 d
!5 !4 !3 !2 !1
0
1
2
3
4
5
!5 !4 !3 !2 !1
0
1
2
3
4
5
0
1
2
3
4
5
6
c.
4. x " 1 & 4 b
d.
!4 !3 !2 !1
Express each statement using an inequality involving absolute value. Do not solve.
5. The weatherman predicted that the temperature would be within 3° of 52°F.
! t ! 52 ! " 3
6. Serena will make the B team if she scores within 8 points of the team average of 92.
! p ! 92 ! " 8
7. The dance committee expects attendance to number within 25 of last year’s 87 students.
! a ! 87 ! " 25
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each open sentence. Then graph the solution set.
8. s " 1 % 5 {s ! !6 " s " 4}
!6 !5 !4 !3 !2 !1
0
1
2
3
9. c $ 3& 1 {c ! 2 # c # 4}
4
!3 !2 !1
0
1
2
3
4
5
6
7
10. n " 2 # 1 {n ! n " !3 or n $ !1} 11. t " 6 ! 4 {t ! t # !10 or t % !2}
!6 !5 !4 !3 !2 !1
0
1
2
3
4
12. w $ 2 ! 2 {w ! w # 0 or w % 4}
!4 !3 !2 !1
0
1
2
3
4
5
!10!9 !8 !7 !6 !5 !4 !3 !2 !1
0
13. k $ 5 % 4 {k ! 1 " k " 9}
6
0
1
2
3
4
5
6
7
8
9 10
For each graph, write an open sentence involving absolute value.
14.
15.
!5 !4 !3 !2 !1
0
1
2
3
4
5
!7 !6 !5 !4 !3 !2 !1
!x! &1
16.
!5 !4 !3 !2 !1
1
2
3
2
3
4
5
!x'3! %2
0
1
2
3
4
5
17.
!5 !4 !3 !2 !1
!x!4! "1
Chapter 6
0
0
1
!x! $4
43
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
6-7
Skills Practice
Graphing Inequalities in Two Variables
Determine which ordered pairs are part of the solution set for each inequality.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. y # x $ 3, {(2, "3), ("2, "1), (1, 6), (3, 4)} {(1, 6)}
3. y % x " 1, {(3, 1), ("2, "4), (4, "2), ("3, 3)} {(3, 1), (!2, !4), (4, !2)}
Match each inequality with its graph.
4. y " 2x % 2 b
a.
b.
y
y
5. y & "3x d
O
6. 2y " x # 4 a
O
x
x
7. x $ y ! 1 c
c.
d.
y
O
y
O
x
x
Graph each inequality.
8. y % "1
9. y # x " 5
y
10. y ! 3x
y
y
O
O
x
x
11. y & 2x $ 4
O
12. y $ x ! 3
13. y " x # 1
y
y
y
O
O
O
Chapter 6
x
x
x
x
51
Glencoe Algebra 1
Lesson 6-7
873949 Alg1 CH06 EP2
1. y ! 3x, {(1, 5), (1, 0), ("1, 0), (5, 1)} {(1, 5), (!1, 0)}
NAME ______________________________________________ DATE______________ PERIOD _____
6-8
Skills Practice
Graphing Systems of Inequalities
Solve each system of inequalities by graphing.
2. y ! 2
x % "2
3. y ! x # 3
y $ "1
y
O
y
O
x
4. x % 2
y"x$2
y
x
O
5. x # y $ "1
x#y&3 !
y
6. y " x ! 4
x#y!2
y
y
O
O
x
O
x
x
x
7. y ! x # 1
y & "x # 1
8. y & "x # 2
y % 2x " 2
y
y
O
O
x
9. y % 2x # 4
y&x#1
Lesson 6-8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
873949 Alg1 CH06 EP3
1. x ! "1
y $ "3
y
x
O
x
Write a system of inequalities for each graph.
10.
11.
y
O
x
y " x # 2, y $ x % 3
Chapter 6
12.
y
O
y & %x, y & x
59
x
y
O
x
y $ x # 1, y ' 1
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
7-1
Skills Practice
Multiplying Monomials
Determine whether each expression is a monomial. Write yes or no. Explain.
1. 11
EP4
2. a ! b
p2
q
3. #2
873950 Alg1 CH07
4. y
5. j 3k
6. 2a " 3b
Simplify.
8. x(x2)(x7)
9. (y2z)(yz2)
10. (!2k2)(!3k)
11. (e2f 4)(e2f 2)
12. (cd2)(c3d2)
13. (2x2)(3x5)
14. (5a7)(4a2)
15. (4xy3)(3x3y5)
16. (7a5b2)(a2b3)
17. (!5m3)(3m8)
18. (!2c4d)(!4cd)
19. (102)3
20. (p3)12
21. (!6p)2
22. (!3y)3
23. (3pq2)2
24. (2b3c4)2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. a2(a3)(a6)
GEOMETRY Express the area of each figure as a monomial.
25.
26.
27.
x2
x5
Chapter 7
cd
cd
4p
9p 3
8
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
7-2
Skills Practice
Dividing Monomials
65
6
2. "
8
EP4
3. "2
x4
x
4. "
3 4
873950 Alg1 CH07
Simplify. Assume that no denominator is equal to zero.
912
9
5. "3
m
m
6. "6
12n5
36n
8. "
4
a3b5
ab
10. "
3 2
!21w5u2
7w u
12. ""
2
13. "
2
! 4p
7s "
14. 4!4
15. 8!2
16. "
1. "4
r3s2
r s
9d7
3d
7. "
11. ""
4 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7 2
32x3y2z5
!8xyz
! 35 "
! 119 "
!1
19. k0(k4)(k!6)
!2
h3
18. "
h!6
20. k!1(!!6)(m3)
q
! 16p
2p q "
5 2 0
f!7
f
22. "
3 3
f!5g 4
h
24. "
5xy!11
!15w0u!1
5u
26. ""
5 6
21. "
4
23. "
!2
25. ""
3
Chapter 7
Lesson 7-2
m7n2
m n
9. "
2
17. "
w4u3
w u
15x6y!9
48x6y7z5
!6xy z
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
7-3
Skills Practice
Polynomials
3x
7
4. #
2. 4by ! 2b " by
3. "32
5. 5x2 " 3x"4
6. 2c2 ! 8c ! 9 " 3
GEOMETRY Write a polynomial to represent the area of each shaded region.
7.
8.
r
y
b
x
a
Find the degree of each polynomial.
9. 12
12. 4a3 " 2a
10. 3r4
11. b ! 6
13. 5abc " 2b2 ! 1
14. 8x5y4 " 2x8
15. 3x ! 1 ! 2x2
16. 5x " 6 ! 3x2
17. 9x2 ! 2 ! x3 ! x
18. "3 ! 3x3 " x2 ! 4x
19. 7r5x ! 21r4 " r2x2 " 15x3
20. 3a2x4 ! 14a2 " 10x3 ! ax2
Arrange the terms of each polynomial so that the powers of x are in descending
order.
21. x2 ! 3x3 ! 27 " x
22. 25 " x3 ! x
23. x " 3x2 ! 4 ! 5x3
24. x2 ! 64 " x ! 7x3
25. 2cx ! 32 " c3x2 ! 6x3
26. 13 " x3y3 ! x2y2 ! x
Chapter 7
22
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Arrange the terms of each polynomial so that the powers of x are in ascending
order.
873950 Alg1 CH07
1. 5mn ! n2
EP4
State whether each expression is a polynomial. If the expression is a polynomial,
identify it as a monomial, a binomial, or a trinomial.
NAME ______________________________________________ DATE______________ PERIOD _____
7-4
Skills Practice
Adding and Subtracting Polynomials
2. (6s ! 5t) ! (4t ! 8s)
3. (5a ! 9b) " (2a ! 4b)
4. (11m " 7n) " (2m ! 6n)
5. (m2 " m) ! (2m ! m2)
6. (x2 " 3x) " (2x2 ! 5x)
7. (d2 " d ! 5) " (2d ! 5)
8. (2e2 " 5e) ! (7e " 3e2)
9. (5f ! g " 2) ! ("2f ! 3)
873950 Alg1 CH07
1. (2x ! 3y) ! (4x ! 9y)
EP4
Find each sum or difference.
10. (6k2 ! 2k ! 9) ! (4k2 " 5k)
12. (b2 ! ab " 2) " (2b2 ! 2ab)
13. (7z2 ! 4 " z) " ("5 ! 3z2)
14. (5 ! 4n ! 2m) ! ("6m " 8)
15. (4t2 ! 2) ! ("4 ! 2t)
16. (3g 3 ! 7g) " (4g ! 8g 3)
17. (2a2 ! 8a ! 4) " (a2 " 3)
18. (3x2 " 7x ! 5) " ("x2 ! 4x)
19. (7z2 ! z ! 1) " ("4z ! 3z2 " 3)
20. (2c2 ! 7c ! 4) ! (c2 ! 1 " 9c)
21. (n2 ! 3n ! 2) " (2n2 " 6n " 2)
22. (a2 ! ab " 3b2) ! (b2 ! 4a2 " ab)
23. (!2 " 5! " 6) ! (2!2 ! 5 ! !)
24. (2m2 ! 5m ! 1) " (4m2 " 3m " 3)
25. (x2 " 6x ! 2) " ("5x2 ! 7x " 4)
26. (5b2 " 9b " 5) ! (b2 " 6 ! 2b)
27. (2x2 " 6x " 2) ! (x2 ! 4x) ! (3x2 ! x ! 5)
Chapter 7
30
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. (x3 " x ! 1) " (3x " 1)
NAME ______________________________________________ DATE______________ PERIOD _____
7-5
Skills Practice
Multiplying a Polynomial by a Monomial
873950 Alg1 CH07
EP4
Find each product.
1. a(4a ! 3)
2. "c(11c ! 4)
3. x(2x " 5)
4. 2y(y " 4)
5. "3n(n2 ! 2n)
6. 4h(3h " 5)
7. 3x(5x2 " x ! 4)
8. 7c(5 " 2c2 ! c3)
9. "4b(1 " 9b " 2b2)
11. 2m2(2m2 ! 3m " 5)
10. 6y("5 " y ! 4y2)
12. "3n2("2n2 ! 3n ! 4)
13. w(3w ! 2) ! 5w
14. f (5f " 3) " 2f
15. "p(2p " 8) " 5p
16. y2("4y ! 5) " 6y2
17. 2x(3x2 ! 4) " 3x3
18. 4a(5a2 " 4) ! 9a
19. 4b("5b " 3) " 2(b2 " 7b " 4)
20. 3m(3m ! 6) " 3(m2 ! 4m ! 1)
Solve each equation.
21. 3(a ! 2) ! 5 # 2a ! 4
22. 2(4x ! 2) " 8 # 4(x ! 3)
23. 5( y ! 1) ! 2 # 4( y ! 2) " 6
24. 4(b ! 6) # 2(b ! 5) ! 2
25. 6(m " 2) ! 14 # 3(m ! 2) " 10
26. 3(c ! 5) " 2 # 2(c ! 6) ! 2
Chapter 7
37
Lesson 7-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Simplify.
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
7-6
Skills Practice
Multiplying Polynomials
3. (b ! 3)(b ! 4)
4. (t ! 4)(t " 3)
5. (r ! 1)(r " 2)
6. (z " 5)(z ! 1)
7. (3c ! 1)(c " 2)
8. (2x " 6)(x ! 3)
9. (d " 1)(5d " 4)
10. (2! ! 5)(! " 4)
11. (3n " 7)(n ! 3)
12. (q ! 5)(5q " 1)
13. (3b ! 3)(3b " 2)
14. (2m ! 2)(3m " 3)
15. (4c ! 1)(2c ! 1)
16. (5a " 2)(2a " 3)
17. (4h " 2)(4h " 1)
18. (x " y)(2x " y)
19. (e ! 4)(e2 ! 3e " 6)
20. (t ! 1)(t2 ! 2t ! 4)
21. (k ! 4)(k2 ! 3k " 6)
22. (m ! 3)(m2 ! 3m ! 5)
873950 Alg1 CH07
2. (x ! 2)(x ! 2)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. (m ! 4)(m ! 1)
EP4
Find each product.
GEOMETRY Write an expression to represent the area of each figure.
23.
24.
2x ! 4
4x " 1
2x ! 5
Chapter 7
44
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
7-7
Skills Practice
Special Products
2. (x ! 4)(x ! 4)
3. ( y " 7)2
4. (t " 3)(t " 3)
5. (b ! 1)(b " 1)
6. (a " 5)(a ! 5)
7. (p " 4)2
8. (z ! 3)(z " 3)
9. (! ! 2)(! ! 2)
873950 Alg1 CH07
1. (n ! 3)2
EP4
Find each product.
10. (r " 1)(r " 1)
12. (2m " 3)(2m ! 3)
13. (6 ! u)2
14. (r ! s)2
15. (3q ! 1)(3q " 1)
16. (c " e)2
17. (2k " 2)2
18. (w ! 3h)2
19. (3p " 4)(3p ! 4)
20. (t ! 2u)2
21. (x " 4y)2
22. (3b ! 7)(3b " 7)
23. (3y " 3g)(3y ! 3g)
24. (s2 ! r2)2
25. (2k ! m2)2
26. (3u2 " n)2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. (3g ! 2)(3g " 2)
27. GEOMETRY The length of a rectangle is the sum of two whole numbers. The width of
the rectangle is the difference of the same two whole numbers. Using these facts, write a
verbal expression for the area of the rectangle.
Chapter 7
52
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-1
Skills Practice
Monomials and Factoring
Find the factors of each number. Then classify each number as prime or
composite.
1. 10
2. 31
3. 16
4. 52
5. 38
6. 105
Find the prime factorization of each integer.
7. !16
9. 24
11. 112
8. 20
10. 36
12. !72
Factor each monomial completely.
14. !27x3y2
15. 28pq2
16. 44m2ns3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. 10a4
Find the GCF of each set of monomials.
17. 12, 18
18. 20, 27
19. 30, 48
20. 24, 81
21. 20, 36, 64
22. 42, 60, 78
23. 16c, 21b2d
24. 18a, 48a4
25. 32xyz, 48xy4
26. 12m3n2, 44mn3
Chapter 8
8
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-2
Skills Practice
Factoring Using the Distributive Property
Factor each polynomial.
1. 7x ! 49
2. 8m " 6
3. 5a2 " 15
4. 10q " 25q2
5. 8ax " 56a
6. 81r ! 48rs
7. t2h ! 3t
8. a2b2 ! a
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 3p2q2 ! 6pq ! p
11. 4a2b2 ! 16ab ! 12a
12. 10m3n3 " 2mn2 ! 14mn
13. x2 ! 3x ! x ! 3
14. b2 " 2b ! 3b " 6
15. 2s2 ! 2s ! 3s ! 3
16. 2a2 " 4a ! a " 2
17. 6t2 " 4t " 3t ! 2
18. 9x2 " 3xy ! 6x " 2y
Lesson 8-2
9. x ! x2y ! x3y2
Solve each equation. Check your solutions.
19. x(x " 8) # 0
20. b(b ! 12) # 0
21. (m " 3)(m ! 5) # 0
22. (a " 9)(2a ! 1) # 0
23. x2 " 5x # 0
24. y2 ! 3y # 0
25. 3a2 # 6a
26. 2x2 # 3x
Chapter 8
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-3
Skills Practice
Factoring Trinomials: x2 ! bx ! c
Factor each trinomial.
1. t2 ! 8t ! 12
2. n2 ! 7n ! 12
3. p2 ! 9p ! 20
4. h2 ! 9h ! 18
5. n2 ! 3n " 18
6. x2 ! 2x " 8
7. y2 " 5y " 6
8. g2 ! 3g " 10
9. s2 ! 4s " 12
10. x2 " x " 12
12. y2 " 6y ! 8
13. x2 " 8x ! 15
14. b2 " 9b ! 8
15. c2 " 15c ! 56
16. "4 " 3m ! m2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. w2 " w " 6
Solve each equation. Check your solutions.
17. x2 " 6x ! 8 # 0
18. b2 " 7b ! 12 # 0
19. m2 ! 5m ! 6 # 0
20. d 2 ! 7d ! 10 # 0
21. y2 " 2y " 24 # 0
22. p2 " 3p # 18
23. h2 ! 2h # 35
24. a2 ! 14a # "45
25. n2 " 36 # 5n
26. w2 ! 30 # 11w
Chapter 8
22
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-4
Skills Practice
Factoring Trinomials: ax2 ! bx ! c
1. 2x2 ! 5x ! 2
2. 3n2 ! 5n ! 2
3. 2s2 ! 9s " 5
4. 3g2 " 7g ! 2
5. 2t2 " 11t ! 15
6. 2x2 ! 3x " 6
7. 2y2 ! y " 1
8. 4h2 ! 8h " 5
9. 4x2 " 3x " 3
10. 4b2 ! 15b " 4
11. 9p2 ! 6p " 8
12. 6q2 " 13q ! 6
13. 3a2 ! 30a ! 63
14. 10w2 " 19w " 15
Solve each equation. Check your solutions.
15. 2x2 ! 7x ! 3 # 0
16. 3w2 ! 14w ! 8 # 0
17. 3n2 " 7n ! 2 # 0
18. 5d2 " 22d ! 8 # 0
19. 6h2 ! 8h ! 2 # 0
20. 8p2 " 16p # 10
21. 9y2 ! 18y " 12 # 6y
22. 4a2 " 16a # "15
23. 10b2 " 15b # 8b " 12
24. 6d2 ! 21d # 10d ! 35
Chapter 8
29
Lesson 8-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Factor each trinomial, if possible. If the trinomial cannot be factored using
integers, write prime.
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-5
Skills Practice
Factoring Differences of Squares
1. a2 ! 4
2. n2 ! 64
3. 1 ! 49c2
4. !16 " p2
5. k2 " 25
6. 36 ! 100w2
7. t2 ! 81u2
8. 4h2 ! 25g2
9. 64m2 ! 9y2
10. 4c2 ! 5d2
11. !49r2 " 4t2
12. 8x2 ! 72p2
13. 20q2 ! 5r2
14. 32a2 ! 50b2
Solve each equation by factoring. Check your solutions.
15. 16x2 ! 9 # 0
16. 25p2 ! 16 # 0
17. 36q2 ! 49 # 0
18. 81 ! 4b2 # 0
19. 16d2 # 4
20. 18a2 # 8
9
25
21. s2 ! $ # 0
1
25
23. $ h2 ! 16 # 0
Chapter 8
49
64
22. k2 ! $ # 0
Lesson 8-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Factor each polynomial, if possible. If the polynomial cannot be factored, write
prime.
1
16
24. $ y2 # 81
37
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
8-6
Skills Practice
Determine whether each trinomial is a perfect square trinomial. If so, factor it.
2. r2 " 4r " 4
1. c2 ! 6c " 9
3. g2 ! 14g " 49
4. 2w2 ! 4w " 9
5. 4d2 ! 4d " 1
6. 9n2 " 30n " 25
Factor each polynomial, if possible. If the polynomial cannot be factored, write
prime.
7. 2x2 ! 72
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 36t2 ! 24t " 4
8. 6b2 " 11b " 3
10. 4h2 ! 56
11. 17a2 ! 24ac
12. q2 ! 14q " 36
13. y2 " 24y " 144
14. 6d2 ! 96
15. 4k2 " 12k " 9
16. 6x2 " 28x ! 10
Solve each equation. Check your solutions.
17. x2 ! 18x " 81 # 0
18. 4p2 " 4p " 1 # 0
19. 9g2 ! 12g " 4 # 0
20. y2 ! 16y " 64 # 81
21. 4n2 ! 17 # 19
22. x2 " 30x " 150 # !75
23. (k " 2)2 # 16
24. (m ! 4)2 # 7
Chapter 8
45
Glencoe Algebra 1
Lesson 8-6
Perfect Squares and Factoring
NAME ______________________________________________ DATE______________ PERIOD _____
9-1
Skills Practice
Graphing Quadratic Functions
Use a table of values to graph each function.
1. y ! x2 " 4
2. y ! "x2 # 3
y
y
O
O
x
x
3. y ! x2 " 2x " 6
4. y ! "x2 " 4x # 1
y
O
y
x
O
x
Write the equation of the axis of symmetry, and find the coordinates of the vertex
of the graph of each function. Identify the vertex as a maximum or minimum.
Then graph the function.
6. y ! x2 " 2x " 5
y
7. y ! "x2 # 4x " 1
y
O
y
x
O
O
x
8. y ! "x2 " 2x # 2
9. y ! 2x2 # 4x " 2
y
O
x
10. y ! "2x2 " 4x # 6
y
y
x
O
x
O
Chapter 9
8
x
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. y ! 2x2
NAME ______________________________________________ DATE______________ PERIOD _____
9-2
Skills Practice
Solving Quadratic Equations by Graphing
Solve each equation by graphing.
1. x2 ! 2x " 3 # 0
2. c2 " 6c " 8 # 0
f(x)
f (c)
O
O
x
3. a2 ! 2a # !1
c
4. n2 ! 7n # !10
f (a)
O
O
Lesson 9-2
f (n)
n
a
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation by graphing. If integral roots cannot be found, estimate the
roots by stating the consecutive integers between which the roots lie.
5. p2 " 4p " 2 # 0
6. x2 " x ! 3 # 0
f (x)
f (p)
O
O
p
7. d2 " 6d # !3
8. h2 " 1 # 4h
f (d )
O
f (h)
d
O
Chapter 9
x
15
h
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
9-3
Skills Practice
Solving Quadratic Equations by Completing the Square
Solve each equation by taking the square root of each side. Round to the nearest
tenth if necessary.
1. c2 ! 12c " 36 # 4
2. w2 ! 10w " 25 # 16
3. b2 " 16b " 64 # 9
4. y2 " 2y " 1 # 3
5. r2 " 4r " 4 # 7
6. a2 ! 8a " 16 # 12
Find the value of c that makes each trinomial a perfect square.
7. g2 " 6g " c
9. a2 ! 14a " c
11. s2 ! 18s " c
8. y2 " 4y " c
10. n2 ! 2n " c
12. p2 " 20p " c
13. x2 " 4x ! 12 # 0
14. v2 ! 8v " 15 # 0
15. q2 " 6q # 7
16. r2 ! 2r # 15
17. m2 ! 14m " 30 # 6
18. b2 " 12b " 21 # 10
19. z2 ! 4z " 1 # 0
20. y2 ! 6y " 4 # 0
21. r2 ! 8r " 10 # 0
22. p2 ! 2p # 5
23. 2a2 " 20a # !2
24. 0.5g2 " 8g # !7
Chapter 9
22
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve each equation by completing the square. Round to the nearest tenth if
necessary.
NAME ______________________________________________ DATE______________ PERIOD _____
9-4
Skills Practice
Solving Quadratic Equations by Using the Quadratic Formula
Solve each equation by using the Quadratic Formula. Round to the nearest tenth
if necessary.
1. u2 ! 49 " 0
2. n2 ! n ! 20 " 0
3. s2 ! 5s ! 36 " 0
4. b2 # 11b # 30 " 0
5. c2 ! 7c " !3
6. p2 # 4p " !1
7. a2 ! 9a # 22 " 0
8. x2 # 6x # 3 " 0
10. 2h2 ! 3h " !1
11. 2p2 # 5p # 4 " 0
12. 2g2 # 7g " 9
13. 3t2 # 2t ! 3 " 0
14. 3x2 ! 7x ! 6 " 0
State the value of the discriminant for each equation. Then determine the number
of real roots of the equation.
15. q2 # 4q # 3 " 0
16. m2 # 2m # 1 " 0
17. a2 ! 4a # 10 " 0
18. w2 ! 6w # 7 " 0
19. z2 ! 2z ! 7 " 0
20. y2 ! 10y # 25 " 0
21. 2d 2 # 5d ! 8 " 0
22. 2s2 # 6s # 12 " 0
23. 2u2 ! 4u # 10 " 0
24. 3h2 # 7h # 3 " 0
Chapter 9
29
Lesson 9-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 2x2 # 5x ! 7 " 0
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
9-5
Skills Practice
Exponential Functions
Graph each function. State the y-intercept. Then use the graph to determine the
approximate value of the given expression. Use a calculator to confirm the value.
! 13 " ! 13 "
x
1. y ! 2x; 22.3
2. y ! $ ; $
y
"1.6
y
x
O
x
O
Graph each function. State the y-intercept.
3. y ! 3(2x)
4. y ! 3x # 2
y
y
x
O
Determine whether the data in each table display exponential behavior. Explain
why or why not.
5.
7.
x
"3
"2
"1
0
y
9
12
15
18
x
4
8
12
16
y
20
40
80
160
Chapter 9
6.
8.
36
x
0
5
10
15
y
20
10
5
2.5
x
50
30
10
"10
y
90
70
50
30
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x
O
NAME ______________________________________________ DATE______________ PERIOD _____
9-6
Skills Practice
Growth and Decay
POPULATION For Exercises 1 and 2, use the following information.
The population of New York City increased from 8,008,278 in 2000 to 8,168,388 in 2005. The
annual rate of population increase for the period was about 0.4%. Source: www.nyc.gov
1. Write an equation for the population t years after 2000.
2. Use the equation to predict the population of New York City in 2015.
SAVINGS For Exercises 3 and 4, use the following information.
The Fresh and Green Company has a savings plan for its employees. If an employee makes
an initial contribution of $1000, the company pays 8% interest compounded quarterly.
3. If an employee participating in the plan withdraws the balance of the account after
5 years, how much will be in the account?
4. If an employee participating in the plan withdraws the balance of the account after
35 years, how much will be in the account?
MANUFACTURING For Exercises 6 and 7, use the following information.
Zeller Industries bought a piece of weaving equipment for $60,000. It is expected to
depreciate at an average rate of 10% per year.
6. Write an equation for the value of the piece of equipment after t years.
7. Find the value of the piece of equipment after 6 years.
8. FINANCES Kyle saved $500 from a summer job. He plans to spend 10% of his savings
each week on various forms of entertainment. At this rate, how much will Kyle have left
after 15 weeks?
9. TRANSPORTATION Tiffany’s mother bought a car for $9000 five years ago. She wants
to sell it to Tiffany based on a 15% annual rate of depreciation. At this rate, how much
will Tiffany pay for the car?
Chapter 9
44
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. HOUSING Mr. and Mrs. Boyce bought a house for $96,000 in 1995. The real estate
broker indicated that houses in their area were appreciating at an average annual rate
of 4%. If the appreciation remained steady at this rate, what was the value of the Boyce’s
home in 2005?
NAME ______________________________________________ DATE______________ PERIOD _____
10-1
Skills Pracice
Simplifying Radical Expressions
Simplify.
1. !28
"
2. !40
"
3. !72
"
4. !99
"
5. !2
" ! !10
"
6. !5
" ! !60
"
7. 3!5
" ! !5
"
8. !6
" ! 4!24
"
9. 2!3
" ! 3!15
"
10. !"
16b4
11. !"
81c2d4"
12. !"
40x4y6"
13. !"
75m5n2"
14.
#$
15.
#$
1
"
6
16.
#$ ! #$
17.
#$
q
"
12
18.
#$
19.
#$
20.
#$
21. "
2
4 $ !5
"
22. "
23. "
5
7 $ !7
"
24. "
Chapter 10
8
12
"
b2
6
"
7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
"
3
1
"
3
4h
"
5
45
"
4m4
3
2 # !3
"
4
3 # !2
"
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
10-2
Skills Practice
Operations with Radical Expressions
Simplify.
1. 7!7
" ! 2!7
"
2. 3!13
" " 7!13
"
3. 6!5
" ! 2!5
" " 8!5
"
4. !15
" " 8!15
" ! 12!15
"
5. 12!c" ! 9!c"
6. 9!6a
" ! 11!6a
" " 4!6a
"
7. !44
" ! !"
11
8. !28
" " !63
"
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. 8!54
" ! 4!6
"
Lesson 10-2
9. 4!3
" " 2!12
"
11. !27
" " !48
" " !12
"
12. !72
" " !50
" ! !8
"
13. !180
" ! 5!5
" " !20
"
14. 2!24
" " 4!54
" " 5!96
"
15. 5!8
" " 2!20
" ! !8
"
16. 2!13
" " 4!2
" ! 5!13
" " !2
"
Find each product.
17. !2
" (!8
" " !6
")
18. !5
" (!10
" ! !3
")
19. !6
" (3!2
" ! 2!3
")
20. 3!3
" (2!6
" " 4!10
")
21. (4 " !3
" )(4 ! !3
")
22. (2 ! !6
") 2
23. (!8
" " !2
" )(!5
" " !3
")
24. (!6
" " 4!5
" )(4!3
" ! !10
")
Chapter 10
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
10-3 Skills Practice
Radical Equations
Solve each equation. Check your solution.
1. !f" ! 7
2. !"x
"!5
" ! 10
3. !5p
4. !4y
"!6
" ! !u
"
5. 2!2
6. 3!5
" ! !"n
"
7. !g
""6!3
8. !5a
"#2!0
2c " 1 ! 5
9. !"
10. !"
3k " 2
"!4
x#4"2!1
11. !"
!d
"
12. !"
4x " 4 " 4 ! 0
#$ ! 3
14.
x#2
15. x ! !"
16. d ! !"
12 " d
"
17. !"
6x " 9 ! x
18. !"
6p " 8
"!p
x#5!x"1
19. !"
20. !"
8"c!c"8
r"3#5!r
21. !"
22. !"
y"1#3!y
5n # 4
"!n#2
23. !"
24. !"
3z " 6 ! z " 2
Chapter 10
22
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
m
$
3
13. $
!4
3
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
10-4 Skills Practice
The Pythagorean Theorem
Find the length of each missing side. If necessary, round to the nearest
hundredth.
1.
c
2.
21
15
6.
c
240
4
29
b
16
b
5.
33
34
39
72
4.
3.
a
250
9
a
If c is the measure of the hypotenuse of a right triangle, find each missing
measure. If necessary, round to the nearest hundredth.
7. a ! 21, b ! 28, c ! ?
8. a ! 6, c ! 10, b ! ?
9. a ! 15, b ! 36, c ! ?
10. a ! 16, c ! 20, b ! ?
12. b ! 6, c ! 12, a ! ?
13. a ! 11, b ! 4, c ! ?
14. a ! 8, b ! 10, c ! ?
15. a ! 19, b ! !39
", c ! ?
16. a ! !12
", b ! 6, c ! ?
17. c ! !130
", a ! 7, b ! ?
18. a ! !6
", b ! !19
", c ! ?
Determine whether the following side measures form right triangles. Justify your
answer.
19. 7, 24, 25
20. 15, 30, 34
21. 16, 28, 32
22. 18, 24, 30
23. 15, 36, 39
24. 5, 7, !74
"
Chapter 10
30
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. a ! 5, b ! 12, c ! ?
NAME ______________________________________________ DATE______________ PERIOD _____
10-5 Skills Practice
The Distance Formula
Find the distance between each pair of points with the given coordinates. Express
answers in simplest radical form and as decimal approximations rounded to the
nearest hundredth if necessary.
1. (9, 7), (1, 1)
2. (5, 2), (8, !2)
3. (1, !3), (1, 4)
4. (7, 2), (!5, 7)
5. (!6, 3), (10, 3)
6. (3, 3), (!2, 3)
7. (!1, !4), (!6, 0)
8. (!2, 4), (5, 8)
9. (!3, 4), (!2, 8)
10. (5, !6), (7, !9)
12. (5, 2), (3, 10)
13. (12, !1), (4, !11)
14. (!3, !1), (!11, 3)
15. (9, 3), (6, !6)
16. (0, !4), (8, 4)
Find the possible values of a if the points with the given coordinates are the
indicated distance apart.
17. (!2, !5), (a, 7); d " 13
18. (8, !2), (5, a); d " 3
19. (4, a), (1, 6); d " 5
20. (a, 3), (5, !1); d " 5
21. (1, 1), (a, 1); d " 4
22. (2, a), (2, 3); d " 10
23. (a, 2), (!3, 3); d " !2
"
24. (!5, 3), (!3, a); d " !5
"
Chapter 10
38
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. (4, 2), (8, 6)
NAME ______________________________________________ DATE______________ PERIOD _____
10-6
Skills Practice
Similar Triangles
1.
2.
E
B
40!
A
3.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
45!
W
F
57!
V
G
K
40!
J
40!
Y
60!
C
F
E
U
50!
D
Lesson 10-6
Determine whether each pair of triangles is similar. Justify your answer.
60! 60!
X
4.
K
G
H
Z
F
65!
63!
52!
J
52!
E
For each set of measures given, find the measures
of the missing sides if !PQR ! !STU.
H
Q
5. r ! 4, s ! 6, t ! 3, u ! 2
P
T
p
r
q
s
u
R S
t
U
6. t ! 8, p ! 21, q ! 14, r ! 7
7. p ! 15, q ! 10, r ! 5, s ! 6
8. p ! 48, s ! 16, t ! 8, u ! 4
3
2
1
2
9. q ! 6, s ! 2, t ! " , u ! "
1
3
10. p ! 3, q ! 2, r ! 1, u ! "
11. p ! 14, q ! 7, u ! 2.5, t ! 5
21
8
9
4
12. r ! 6, s ! 3, t ! " , u ! "
Chapter 10
45
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-1
Skills Practice
Inverse Variation
Graph each variation if y varies inversely as x.
1. y ! 2 when x ! 5
8
2. y ! "6 when x ! "6
y
16
4
!8
8
!4 O
4
!16 !8 O
8x
!4
!8
!8
!16
3. y ! "4 when x ! "12
16
8
16 x
4. y ! 15 when x ! 3
y
20
8
!16 !8 O
y
y
10
8
!20 !10 O
16 x
!8
!10
!16
!20
10
20 x
5. If y ! 4 when x ! 8,
find y when x ! 2.
6. If y ! "7 when x ! 3,
find y when x ! "3.
7. If y ! "6 when x ! "2,
find y when x ! 4.
8. If y ! "24 when x ! "3,
find x when y ! "6.
9. If y ! 15 when x ! 1,
find x when y ! "3.
10. If y ! 48 when x ! "4,
find y when x ! 6.
11. If y ! 34 when x ! 4,
find y when x ! "17.
12. If y ! 72 when x ! "3,
find y when x ! 36.
13. If y ! 4 when x ! 1.5,
find x when y ! 5.
14. If y ! 20 when x ! 5.2,
find x when y ! 10.
1
2
15. If y ! "4 when x ! # , find x when y ! 2.
1
3
16. If y ! 12 when x ! # , find x when y ! "8.
Chapter 11
8
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write an inverse variation equation that relates x and y. Assume that y varies
inversely as x. Then solve.
NAME ______________________________________________ DATE______________ PERIOD _____
11-2
Skills Practice
Rational Expressions
State the excluded values for each rational expression.
2p
p!7
2. #
k"2
k !4
4. #
2
y2 ! 9
y " 3y ! 18
6. ##
2
1. #
3. #
2
5. ##
2
4n " 1
n"4
3x " 15
x ! 25
b2 ! 2b ! 8
b " 7b " 10
Simplify each expression. State the excluded values of the variables.
16x3y2
36x y
10. #
3
n"6
3n " 18
12. #
y2 ! 64
y"8
14. ##
z"1
z !1
16. ##
2
2d " 10
d ! 2d ! 35
18. ##
2
t2 " 5t " 6
t " 6t " 8
20. ##
2
x2 " 10x " 24
x ! 2x ! 24
22. ##
2
9. #
5 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12m2n
24mn
8. #3
11. #
13. #
15. #
2
17. ##
2
19. ##
2
21. ##
2
Chapter 11
Lesson 11-2
21bc
28bc
7. #2
8a2b3
40a b
4x ! 4
4x " 4
y2 ! 7y ! 18
y!9
x"6
x " 2x ! 24
3s ! 9
s ! 7s " 12
a2 " 3a ! 4
a " 2a ! 8
b2 ! 6b " 9
b ! 9b " 18
15
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-3 Skills Practice
Multiplying Rational Expressions
Find each product.
14
c
c5
2c
3m2
2n
n2
12
2x2y
3x y
3xy
4y
1. "
2 ! "
2. " ! "
2a2b
b c
"
4. "
2 !
b
a
3. "
!"
2
9n2
2(4m # 6)
3(4m # 6)
18n
( y # 3)( y $ 3)
4
8
y$3
(a # 7)(a $ 7)
a(a $ 5)
a$5
a$7
6. "" ! "
7. "" ! "
b#3
b$4
4
1#c
12. " ! "
a$2
a #a#6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
y$5
y#6
a#3
a$1
14. ""
!"
2
x2
x $ 5x $ 4
x2 $ x # 20
x
15. " ! ""
2
y2 $ 2y $ 1
y#1
4(b $ 4)
(b # 4)(b # 3)
1 # c2
12
x$2
x#2
13. "
!"
2
x$4
x
2(8x $ 3)
x#2
10. "" ! "
11. " ! "
y2 # 36
y # 25
(x # 2)(x $ 2)
x(8x $ 3)
8. "" ! ""
9. "" ! "
x2 # 4
5
n#2
n$2
4(n $ 2)
n(n # 2)
5. "" ! ""
x
x$5
16. ""
!"
2
3y # 3
y$1
2n $ 12
n#2
17. "" ! "
n2 # 8n $ 12
n$6
18. " ! ""
Find each product.
30 miles
1 hour
5280 feet
1 mile
1 hour
60 minutes
1 minute
60 seconds
19. "" ! "" ! "" ! ""
200 dollars
1 ton
100 cents
1 dollar
1 ton
2000 pounds
1 pound
16 ounces
20. "" ! "" ! "" ! ""
Chapter 11
22
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-4
Skills Practice
Dividing Rational Expressions
Find each quotient.
c3
d
d3
c
x3
y
1. %3 ! %
3
6e3
4f
2e2
12f
4m3
np
3. %2 ! %2
3b " 3
c2 # 4
8. %
! (b # 5)
2b
2x " 2
2n " 6
9. %
!%
x"5
x"4
n"3
10. %
!%
n#4
n#4
a"2
11. %
!%
a#2
4a # 8
5y " 15
2y " 6
12. %
!%
y"6
y#3
Complete.
13. 108 ft2 $
yd2
14. 0.2 m2 $
cm2
15. 26 m/s $
km/h
16. 930 gal/h $
qt/min
Lesson 11-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x#5
6. %
! (x # 5)
x"3
b2 # 25
7. %
! (c " 2)
c
3a " 6
2m
np
%
4. %
2 !
5. %
! (b " 1)
b"2
x"1
x3
y
2. %2 ! %
Find each quotient.
x2 # x # 12
6
x"3
x#4
17. %% ! %
a2 # 5a # 6
3
a#6
a"1
18. %% ! %
y2 " 10y " 25
3y # 9
y"5
y#3
m2 " 2m " 1
10m # 10
m"1
20
20. %% ! %
b"4
b # 8b " 16
2b " 8
b#8
22. % ! %%
19. %% ! %
21. %%
!%
2
Chapter 11
6x " 6
x#1
29
x2 " 3x " 2
2x # 2
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-5
Skills Practice
Dividing Polynomials
Find each quotient.
1. (20x2 ! 12x) " (4x)
2. (18n2 ! 6n) " (3n)
3. (b2 # 12b ! 5) " (2b)
4. (8r2 ! 5r # 20) " (4r)
7. (x2 # 5x # 6) " (x # 6)
8. (a2 # 10a ! 16) " (a # 2)
9. (n2 # n # 20) " (n ! 4)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
15k2u # 10ku ! 25u2
5ku
6. $$$
10. ( y2 ! 4y # 21) " ( y # 3)
11. (h2 # 6h ! 9) " (h # 2)
12. (b2 ! 5b # 2) " (b ! 6)
13. ( y2 ! 6y ! 1) " ( y ! 2)
14. (m2 # 2m # 5) " (m # 3)
2c2 # 5c # 3
2c ! 1
16. $$
x3 # 3x2 # 6x # 20
x#5
18. $$$
19. $$
n3 # 6n # 2
n!1
20. $$
Chapter 11
37
15. $$
17. $$$
2r2 ! 6r # 20
2r # 4
p3 # 4p2 ! p ! 6
p#2
Lesson 11-5
12p3q2 ! 18p2q # 6pq
6p q
5. $$$
2
y3 # y2 # 40
y#4
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-6 Skills Practice
Rational Expressions with Like Denominators
Find each sum.
2y
5
y
5
2. # ! #
3k
14
5k
14
4. # ! #
1. # ! #
3. # ! #
4r
9
5r
9
t
9
t"5
9
g!2
4
g"8
4
2p
p!1
2
p!1
x!2
3
x!5
3
6. # ! #
2q
q!2
3
q!2
8. # ! #
u"2
u!1
4u ! 7
u!1
5. # ! #
7. # ! #
9. # ! #
2b ! 1
b!3
5b " 4
b!3
11. # ! #
2y " 2
y"4
y!1
y"4
5d " 3
d"1
2d " 4
d"1
10. # ! #
12. # ! #
7n
10
3n
10
3p
2
p
2
6x
5
3x
5
14. # " #
8a
11
7a
11
16. # " #
13. # " #
15. # " #
t!3
7
t
7
18. # " #
y"6
4
y!2
4
20. # " #
x
x"1
1
x"1
22. # " #
3s
s"5
3s
5"s
24. # " #
17. # " #
19. # " #
21. # " #
23. # " #
Chapter 11
c!8
4
4
m!7
44
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find each difference.
c!6
4
"2
m!7
3r
r!3
r
r!3
5a
a"4
7
4"a
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-7
Skills Practice
Rational Expressions with Unlike Denominators
Find the LCM for each pair of expressions.
2. n ! 2, n " 3
3. 2r " 1, r ! 4
4. t ! 4, 4t ! 16
5. x2 " 2x " 3, (x " 3)2
6. c2 ! 2c " 8, c " 2
Lesson 11-7
1. 4x2y, 12xy2
Find each sum.
3
y
4
y
3
8a
7. # ! #2
m"2
m
m!3
2m
9. # ! #
2
b"4
b
b"1
11. # ! #
3x ! 15
x " 25
x
x!5
13. #
!#
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
2a
8. #2 ! #
5
y!2
1
y"6
k
k"5
k"1
k!5
10. # ! #
12. # ! #
x"3
x " 4x ! 4
x!2
x"2
14. ##
!#
2
Find each difference.
5
4r
2
r
5x
3y
15. # " #2
x
x!2
2x
9y
16. #2 " #
4
x"1
17. # " #
d"1
d"2
3
d!5
"5
s!4
"4
s ! 4s
18. # " #
a
2a " 1
2
a!3
20. # " #
2
6
b "1
b
b!1
22. ##
" ##
2
2
19. # " #
21. #
"#
2
Chapter 11
2u
u ! 3u " 4
51
u"1
u ! 8u ! 16
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
11-8 Skills Practice
Mixed Expressions and Complex Fractions
Write each mixed expression as a rational expression.
4
h
6
p
1. 6 ! #
2. 7 ! #
2q
r
b
c
4. 8q " #
3. 4b ! #
6
f!2
4
d"5
5. 2 ! #
6. 5 " #
12
b!3
6
m"7
7. b2 ! #
8. m " #
a"2
a
r!9
2r
9. 2a ! #
10. 4r " #
Simplify each expression.
2
3##
3
12. #
2
5##
14.
a2
##
b3
#
a
##
b
15.
x2y
#c#
#
xy3
##
c2
17.
w!4
##
w
##
w2 " 16
##
w
18.
x2 " 1
#x#
#
x"1
##
x2
4
k2 ! 5k ! 6
#
#
k2 " 9
20. ##
k!2
Chapter 11
13.
r
##
s2
#
r2
#s#
16.
s"2
##
s!3
#
s"2
##
3
5
b2 " 4
#
#
b2 ! 7b ! 10
19. ##
b"2
12
9
g ! ##
g!8
21. ##
g!6
p ! ##
p"6
22. ##
p"3
58
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
2##
2
11. #
3
4##
NAME ______________________________________________ DATE______________ PERIOD _____
11-9
Skills Practice
Solving Rational Equations
Solve each equation. State any extraneous solutions.
2
c#3
3
q
7
m#1
12
m#2
3. $ ! $
5. $ ! $
3m
2
1
4
1
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
3
5g
6
c#3
c
m " 11
m#4
s"5
5
s"3
10
1
2
10. $ # $ ! $
3b " 4
b
11. $ # $ ! 7
m"4
m
b#4
b#2
8. $ # $ ! $
9. $ " $ ! " $
c#2
c
b"2
b
7g
9
10m
8
2a
3
5
s#8
6. $ ! $
7. $ " $ ! $
2a # 5
6
3
s#2
4. $ ! $
y#1
y"5
y
y"2
5
q#4
2. $ ! $
b"7
b
12. $ " $ ! 1
1
m
13. $ " $ ! $
f#2
f
f#1
f#5
u#1
u"2
u
u#1
5
s"4
s
2s " 8
2"q
q"1
q2
1"q
1
f
14. $ " $ ! $
r#3
r"1
r
r"3
16. $ " $ ! 0
"2
x#1
2
x
18. $ " $ ! 1
2
4"t
t2
t"4
20. $ # $ ! 2
15. $ " $ ! 0
17. $ # $ ! 1
19. $ # $ ! "1
b"5
b#2
"4
b#2
21. $ " 2 ! $
Chapter 11
Lesson 11-9
5
c
1. $ ! $
3
2a
2a
a"3
22. $ # $ ! 2
65
Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
12-1
Skills Practice
Sampling and Bias
Identify each sample, suggest a population from which it was selected, and state
whether it is unbiased (random) or biased. If unbiased, classify the sample as simple,
stratified, or systematic. If biased, classify as convenience or voluntary response.
1. LANDSCAPING A homeowner is concerned about the quality of the topsoil in the back
yard. The back yard is divided into 5 equal sections, and then a 1-inch plug of topsoil is
randomly removed from each of the 5 sections. The soil is taken to a nursery and
analyzed for mineral content.
2. HEALTH A hospital’s administration is interested in opening a gym on the premises for
all its employees. They ask each member of the night-shift emergency room staff if he or
she would use the gym, and if so, what hours the employee would prefer to use it.
3. POLITICS A senator wants to know her approval rating among the constituents in her
state. She sends questionnaires to the households of 1000 registered voters in her party.
4. MANUFACTURING A company that produces motherboards for computers randomly
selects 25 boxed motherboards out of a shipment of 1500, and then tests each selected
motherboard to see that it meets specifications.
6. MUSIC To determine the music preferences of their customers, the owners of a music
store ask 10 customers who have expressed interest to participate in an in-store
interview in which they listen to new CDs from artists in all music categories.
7. LIBRARIES A community library asks every tenth patron who enters the library to
name the type or genre of book he or she is most likely to borrow. They conduct the
interviews from opening to closing on three days of the week. They will use the data for
new acquisitions.
8. COMPUTERS To determine the number of students who use computers at home, the
high school office chooses 10 students at random from each grade, and then interviews
the students.
Chapter 12
8
Glencoe Algebra 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. GOVERNMENT The first 100 people entering a county park on Thursday are asked
their opinions on a proposed county ordinance that would allow dogs in county parks to
go unleashed in certain designated areas.
NAME ______________________________________________ DATE______________ PERIOD _____
12-2
Skills Practice
Counting Outcomes
Draw a tree diagram to show the sample space for each event. Determine the
number of possible outcomes.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. selecting monogrammed or plain stationery, in white or buff, with lined or unlined
envelopes
Find the value of each expression.
3. 1!
4. 3!
5. 6!
6. 9!
7. Two dice are rolled. How many outcomes are possible?
8. If students can choose between 7 elective subjects, 6 class periods, and 5 teachers, how
many elective classes are possible?
9. How many different ways can a carpenter build a bookcase using one each of 4 types of
wood, 3 stains, 5 widths, and 6 heights?
Chapter 12
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Glencoe Algebra 1
Lesson 12-2
1. planting a garden with roses, zinnias, or cosmos, in yellow, red, orange, or purple
NAME ______________________________________________ DATE______________ PERIOD _____
12-3 Skills Practice
Permutations and Combinations
Determine whether each situation involves a permutation or combination. Explain
your reasoning.
1. dinner guests seated around a table
2. a pattern of different widths of bars and spaces for a bar code
3. selecting two yellow marbles out of a sack of yellow and blue marbles
4. placing one can of each of 15 different types of soup along a store shelf
5. selecting four candles from a box of ten
6. the placement of the top ten finishers in a school’s spelling bee
7. choosing two colors of paint out of twenty to paint the walls and trim of a bedroom
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. choosing a set of twelve pencils from a selection of thirty-six
Evaluate each expression.
9. 5 P2
10. 6 P4
11. 7 P3
12. 9 P4
13. 7 P5
14. 5 P3
15. 6C2
16. 9C7
17. 8C4
18. 7C5
19. 12C2
20. 13C7
21. 11C2
22. 5 P4
23. 14C5
24. 11C6
25. (4 P2)(3 P2)
26. (8C6)(5 P1)
Chapter 12
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Glencoe Algebra 1
NAME ______________________________________________ DATE______________ PERIOD _____
12-4
Skills Practice
Probability of Compound Events
A bag contains 2 green, 9 brown, 7 yellow, and 4 blue marbles. Once a marble is
selected, it is not replaced. Find each probability.
1. P(brown, then yellow)
2. P(green, then blue)
3. P(yellow, then yellow)
4. P(blue, then blue)
5. P(green, then not blue)
6. P(brown, then not green)
A die is rolled and a spinner like the one at
the right is spun. Find each probability.
A
D
7. P(4 and A)
B
C
8. P(an even number and C)
9. P(2 or 5 and B or D)
10. P(a number less than 5 and B, C, or D)
11. P(jack or ten)
12. P(red or black)
13. P(queen or club)
14. P(red or ace)
15. P(diamond or black)
16. P(face card or spade)
Tiles numbered 1 through 20 are placed in a box. Tiles numbered 11 through 30
are placed in a second box. The first tile is randomly drawn from the first box.
The second tile is randomly drawn from the second box. Find each probability.
17. P(both are greater than 15)
18. The first tile is odd and the second tile is less than 25.
19. The first tile is a multiple of 6 and the second tile is a multiple of 4.
20. The first tile is less than 15 and the second tile is even or greater than 25.
Chapter 12
29
Glencoe Algebra 1
Lesson 12-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
One card is drawn from a standard deck of 52 cards. Find each probability.
NAME ______________________________________________ DATE______________ PERIOD _____
12-5
Skills Practice
Probability Distributions
For Exercises 1–3, the spinner shown is spun three times.
1. Write the sample space with all possible outcomes.
GREEN
BLUE
RED
BLUE
GREEN
YELLOW
2. Find the probability distribution X, where X represents the number of
times the spinner lands on green for X ! 0, X ! 1, X ! 2, and X ! 3.
3. Make a probability histogram.
0.4
Spinner Probability
Distribution
0.3
P(X) 0.2
0.1
0
0
1
2
3
X ! Number of Times
Spinner Lands on Green
For Exercises 4–7, the spinner shown is spun two times.
4. Write the sample space with all possible outcomes.
6. Make a probability histogram.
Spinner Probability
Distribution
0.6
0.5
0.4
P(X) 0.3
0.2
0.1
0
0
1
2
X ! Number of Times
Spinner Lands on Yellow
BUSINESS For Exercises 7–9, use the table
that shows the probability distribution of
the number of minutes a customer spends at
the express checkout at a supermarket.
X ! Minutes
Probability
1
2
3
4
5"
0.09 0.13 0.28 0.32 0.18
7. Show that this is a valid probability distribution.
8. What is the probability that a customer spends less than 3 minutes at the checkout?
9. What is the probability that the customer spends at least 4 minutes at the checkout?
Chapter 12
37
Glencoe Algebra 1
Lesson 12-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Find the probability distribution X, where X represents the number of
times the spinner lands on yellow for X ! 0, X ! 1, and X ! 2.
NAME ______________________________________________ DATE______________ PERIOD _____
12-6
Skills Practice
For Exercises 1–3, use a standard deck of 52 cards. Select a card at random, record
the suit of the card (heart, diamond, club, or spade), and then replace the card.
Repeat this procedure 26 times.
1. Based on your results, what is the experimental probability of selecting a heart?
2. Based on your results, what is the experimental probability of selecting a diamond or a
.
spade?
3. Compare your results to the theoretical probabilities.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. There are 3 siblings in the Bencievenga family. What could you use to simulate the
genders of the 3 siblings?
5. A random survey of 23 students revealed that 2 students walk to school, 12 ride the bus,
6 drive a car, and 3 ride with a parent or other adult. What could you use for a
simulation to determine the probability that a student selected at random uses any one
type of transportation?
BIOLOGY For Exercises 6–9, use the following information.
Stephen conducted a survey of the students in
his classes to observe the distribution of eye
color. The table shows the results of his survey.
Eye Color
Number
Blue Brown Green Hazel
12
58
2
8
6. Find the experimental probability distribution for each eye color.
7. Based on the survey, what is the experimental probability that a student in Stephen’s
classes has blue or green eyes?
8. Based on the survey, what is the experimental probability that a student in Stephen’s
classes does not have green or hazel eyes?
9. If the distribution of eye color in Stephen’s grade is similar to the distribution in his
classes, about how many of the 360 students in his grade would be expected to have
brown eyes?
Chapter 12
45
Glencoe Algebra 1
Lesson 12-6
Probability Simulations
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