```AM ERICAN BOOK COMPAN Y’S
FOR
Passing the Minnesota
Mathematics Test
March 2006
Erica Day
Colleen Pintozzi
AMERICAN BOOK COMPANY
P. O. BOX 2638
WOODSTOCK, GA 30188-1383
TOLL FREE 1 (888) 264-5877 PHONE (770) 928-2834
TOLL FREE FAX 1 (866) 827-3240
Web site: www.americanbookcompany.com
306-040706
Strand II – Number Sense
Sub-strand A. Number Sense
II.A – Use real numbers, represented in a variety of ways, to quantify information and to solve
real-world and mathematical problems.
Sub-strand B. Computation and Operation
II.B.1 – Students will apply the correct order of operations and grouping symbols when using
calculators.
II.B.2 – Students will translate calculator notational conventions to mathematical notation.
II.B.3 – Students will recognize the impact of units such as degrees and radians on calculations.
II.B.4 – Students will recognize that applying an inverse function with a calculator may lead to
extraneous or incomplete solutions.
II.B.5 – Students will understand the limitations of calculators such as missing or additional features on graphs due to viewing parameters or misleading representations of zero or very large
numbers.
II.B.6 – Students will understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.
II.B.G7 – Students will apply the correct order of operations to simplify and evaluate numeric
expressions.
II.B.G8 – Students will use rational numbers in complex ways to solve multi-step real-world and
mathematical problems.
II.B.G9 – Students will use fractions, decimals and percents in multiple representations for estimation and computation to solve real-world and mathematical problems.
II.B.G10 – Students will use proportional reasoning to solve real-world and mathematical problems.
Strand III – Patterns, Functions and Algebra
Sub-strand A. Patterns and Functions
III.A.1 – Students will know the numeric, graphic and symbolic properties of linear, step, absolute
III.A.2 – Students will model exponential growth and decay.
III.A.3 – Students will analyze the effects of coefﬁcient changes on linear and quadratic functions
and their graphs.
III.A.4 – Students will apply basic concepts of linear, quadratic and exponential expressions or
equations in real- world problems.
III.A.5 – Students will distinguish functions from other relations using graphic and symbolic
methods.
III.A.G6 – Students will generate a table of values from a formula or equation. Students will graph
the result of a formula or linear equation in ordered pair format on a grid.
III.A.G7 – Students will translate a problem described verbally or by tables, diagrams or graphs,
into suitable mathematical language, solve the problem mathematically and interpret the result in
the original context.
1
Sub-strand B. Algebra (Algebraic Thinking)
III.B.1 – Students will translate among equivalent forms of expressions.
III.B.2 – Students will understand the relationship between absolute value and distance on the
number line. Students will graph simple expressions involving absolute value.
III.B.3 – Students will ﬁnd equations of a line.
III.B.4 – Students will translate among equivalent forms of linear equations and inequalities.
III.B.5 – Students will use a variety of models to represent functions and patterns in real-world
and mathematical problems.
III.B.6 – Students will apply the laws of exponents to perform operations on expressions with
integer exponents.
III.B.7 – Students will solve linear equations and inequalities in one variable with numeric, graphic
and symbolic methods.
III.B.8 – Students will determine solutions to quadratic equations in one variable with numeric,
graphic and symbolic methods.
III.B.9 – Students will use appropriate terminology and mathematical notation to deﬁne and represent recursion.
III.B.10 – Students will create and use recursive formulas to model and solve real-world and
mathematical problems.
III.B.11 – Students will solve systems of two linear equations and inequalities with 2 variables
using numeric, graphic and symbolic methods.
III.B.12 – Students will understand how slopes can be used to determine whether lines are parallel
or perpendicular and determine equations for parallel lines and perpendicular lines.
III.B.G13 – Students will use formulas with more than one variable to solve real-world and mathematical problems.
Strand IV – Data Analysis, Statistics and Probability
Sub-strand A. Data and Statistics
IV.A.1 – Students will analyze graphs and demonstrate understanding of the strengths and weaknesses of each format by choosing appropriately among them for a given situation.
IV.A.2 – Students will use measures of central tendency and variability to describe, compare and
draw conclusions about sets of data.
IV.A.3 – Students will determine approximate line of best-ﬁt and use the line to draw conclusions.
IV.A.4 – Students will know the inﬂuence of outliers on various measures and representations of
data about real- world and mathematical problems.
IV.A.5 – Students will distinguish between correlation and causation.
IV.A.6 – Students will interpret data credibility in the context of measurement error and display
distortion.
IV.A.7 – Students will compare outcomes of voting methods.
IV.A.G8 – Students will analyze histograms, bar graphs, circle graphs, stem-and-leaf plots and
box-and-whisker plots.
IV.A.G9 – Students will understand the meaning of and be able to compute minimum, maximum,
range, median, mean and mode of a data set.
2
Sub-strand B. Probability
IV.B.1 – Students will select and apply appropriate counting procedures to solve real-world and
mathematical problems.
IV.B.2 – Students will calculate probabilities and relate the results in real-world and mathematical
problems.
IV.B.3 – Students will use probability models in real-world and mathematical problems.
IV.B.4 – Students will determine the expected values of random variables for simple probability
models.
IV.B.5 – Students will know the effect of sample size on experimental and simulation probabilities.
IV.B.6 – Students will calculate probabilities.
Strand V – Spatial Sense, Geometry and Measurement
Sub-strand A. Spatial Sense
V.A.1 – Students will use models and visualization to understand and represent various threedimensional objects and their cross sections from different perspectives.
Sub-strand B. Geometry
V.B.1 – Students will know and use theorems about triangles and parallel lines in elementary
geometry to justify facts about various geometrical ﬁgures and solve real-world and mathematical
problems.
V.B.2 – Students will know and use theorems about circles to justify geometrical facts and solve
real-world and mathematical problems.
V.B.3 – Students will use properties of two- and three-dimensional ﬁgures to solve real-world and
mathematical problems.
V.B.4 – Students will apply the basic concepts of right triangle trigonometry to determine unknown
sides or unknown angles when solving real-world and mathematical problems.
V.B.5 – Students will use coordinate geometry.
V.B.6 – Students will use numeric, graphic and symbolic representations of transformations to
solve real-world and mathematical problems.
V.B.7 – Students will perform basic constructions with a straightedge and compass.
V.B.8 – Students will draw accurate representations of planar ﬁgures using a variety of tools.
Sub-strand C. Measurement
V.C. – Students will demonstrate an understanding of the interconnectedness of geometry, algebra
and measurement.
V.C.G1 – Students will make calculations involving time, length, area, volume, weight and mass
choosing appropriate units to calculate, measure and record.
V.C.G2 – Students will use formulas to solve real world and mathematical problems.
3
Diagnostic Test
Pages 1–19
Segment 1
1. C
3. A
5. D
7. B
9. C
11. D
13. B
15. D
17. B
2. D
4. C
6. B
8. C
10. A
12. B
14. D
16. B
18. D
20.(A)
Girls
310
864
5410
22
2 | 18 = 182 cm
Boys
15
16
17
18
19
19. C
19 | 8 = 198 cm
1
2
668
13577
48
(B) The median height of the girls in the sample is 169 cm. Half of the 300 girls in the school
would be expected to have heights of 169 cm or more.
300 ÷ 2 = 150
Approximate number of girls = 150 girls
Segment 2
21. A
23. A
25. A
27. B
29. C
31. D
33. C
35. D
37. A
22. B
24. A
26. C
28. D
30. C
32. C
34. A
36. A
38. B
39. 36
40. First, ﬁnd the rate of the ball in feet per second.
2 (2u feet) 2 (2) (3=14) (1 foot)
12=56 feet
2 revolutions
=
=
=
= 12=56 ft/sec
1 second
1 second
1 second
1 second
Next, convert feet per second to miles per hour.
1 mi
60 sec 60 min 8=56 mi
12=56 ft
×
×
×
=
1 sec
5280 ft
1 min
1 hr
1 hr
Speed = 8=56 miles/hour
Segment 3
41. A
43. A
45. C
47. B
49. C
51. B
53. B
55. A
57. D
42. C
44. A
46. D
48. A
50. C
52. B
54. B
56. C
58. A
59. 10
60.(A) The Pythagorean theorem f2 = d2 + e2 may be used to ﬁnd the hypotenuse (f) of the right
triangle from the length of the two legs (d and e).
(B) f2 = d2 + e2
f2 = 1052 + 1302
(C) f2 = d2 + e2
f2 = 1052 + 1302
fs2 = 27>s925
f2 = 27> 925
f = 167=1
Distance = 167=1 yards
4
Segment 4
61. C
64. B
67. A
70. C
73. A
76. C
79. C
82. A
62. C
65. C
68. D
71. B
74. B
77. A
80. C
83.
63. C
66. D
69. B
72. D
75. B
78. B
81. A
3
10
y
84.
9
A
B
8
7
6
5
4
3
2
1
−4 −3 −2 −1 0
1
2
3
4
5
6
x
−1
−2
−3
(A) slope = 2, |-intercept = (0> 7)
(B) | = 2{ + 7
85. 775
Chapter 1 Fractions, Decimals, and Percents
Page 21 Greatest Common Factor
1. 10:
1,2,5,10
15:
1,3,5,15
GCF: 5
7. 6:
1,2,3,6
42:
1,2,3,6,7,14,21,42
GCF: 6
2. 12:
1,2,3,4,6,12
16:
1,2,4,8,16
GCF: 4
8. 14:
1,2,7,14
63:
1,3,7,9,21,63
GCF: 7
3. 18:
1,2,3,6,9,18
36:
1,2,3,4,6,9,12,18,36
GCF: 18
9. 9:
1,3,9
51:
1,3,17,51
GCF: 3
4. 27:
1,3,9,27
45:
1,3,5,9,15,45
GCF: 9
10. 18:
1,2,3,6,9,18
45:
1,3,5,9,15,45
GCF: 9
5. 32:
1,2,4,8,16,32
40:
1,2,4,5,8,10,20,40
GCF: 8
11. 12:
1,2,3,4,6,12
20:
1,2,4,5,10,20
GCF: 4
6. 16:
1,2,4,8,16
48:
1,2,3,4,6,8,12,16,24,48
GCF: 16
12. 16:
1,2,4,8,16
40:
1,2,4,5,8,10,20,40
GCF: 8
5
Page 22 Least Common Multiple
1. 30
4. 21
7. 28
10. 42
13. 90
16. 45
2. 48
5. 24
8. 18
11. 36
14. 24
17. 15
3. 36
6. 24
9. 30
12. 35
15. 36
18. 44
Pages 22–23 Fraction Review
1. 5 12
11. 2 12
21.
21
8
31.
1
3
1
41. 11 12
51. 49
12. 3 23
22.
19
2
32.
1
3
42. 3 34
52. 11 23
13.
23.
73
9
33.
1
2
43. 3 13
20
53. 69
4. 2 29
17
8
14.
24.
51
7
34.
5. 4
33
4
4
7
44. 1 38
15.
25.
1
4
35.
3
7
7
45. 2 12
55. 10 12
6. 4 15
14
3
16.
26.
2
3
36.
1
4
1
46. 6 40
56.
9
16
7. 3 14
28
3
17.
27.
1
3
37. 9 18
47. 75
57.
9
16
8. 6
47
5
18.
28.
1
4
38. 11 78
48. 32
9. 3
27
4
58. 11 14
19.
44
7
29.
5
6
39. 14 14
49.
7
12
59. 16 12
20.
11
4
30.
4
5
40. 4 11
12
2. 2 23
3. 2 14
10. 2 47
50. 5 12
54. 3 34
60. 8 13
Page 23 Fraction Word Problems
1. 2 53
60
2. 4 12
3. 96
5. 13 13
4. 750
6. 1 56
Page 24 Changing Fractions to Decimals
1. 0=8
5. 0=1
2. 0=6
9. 0=6
13. 0=77
17. 0=1875
6. 0=625
10. 0=7
14. 0=9
18. 0=75
3. 0=5
7. 0=83
11. 0=36
15. 0=25
19. 0=8
4. 0=55
8. 0=16
12. 0=11
16. 0=375
20. 0=416
Page 25 Changing Mixed Numbers to Decimals
1. 5=6
5. 30=3
9. 6=8
13. 7=25
17. 10=1
2. 8=45
6. 3=5
10. 13=5
14. 12=3
18. 20=4
3. 15=6
7. 1=875
11. 12=8
15. 1=625
19. 4=9
4. 13=6
8. 4=09
12. 11=625
16. 2=75
20. 5=36
6
Page 25 Changing Decimals to Fractions
11
20
3
2.
5
1.
3
4
41
6.
50
3
25
9
4.
10
5.
3.
3
10
21
8.
50
7.
71
100
16
10.
25
9.
14
25
6
12.
25
11.
7
20
24
14.
25
13.
1
8
3
16.
8
15.
Page 26 Changing Decimals with Whole Numbers to Mixed Numbers
1. 7 18
5. 16 19
20
2. 99 12
13
3. 2 100
1
4. 5 10
7
9. 6 10
9
13. 13 10
6. 3 58
10. 45 17
40
14. 32 13
20
7. 4 21
50
11. 15 45
15. 17 14
8. 15 21
25
4
12. 8 25
16. 9 41
50
Page 26 Decimal Word Problems
1. \$11= 20
3. \$9= 99
5. \$645= 33
7. 1> 211
2. \$18= 75
4. \$2= 45
6. \$26= 24
8. 25=38
9. \$896=05
10. \$62=11
1. 16 oz for \$1=76
6. 4 for \$1=36
2. 5 lb for \$9=45
7. 3 for \$5=88
3. 10 for \$5=99
8. 50 for \$9=50
4. 6 for \$4=80
9. 12 for \$2=64
5. 20 oz for \$0=60
10. 54 for \$9=28
Page 28 Changing Percents to Decimals and Decimals to Percents
1. 0=18
8. 1=19
15. 0=73
22. 15%
29. 4=4%
36. 4=2%
2. 0=23
9. 0=07
16. 0=25
23. 87%
30. 58%
37. 31%
3. 0=09
10. 0=55
17. 4=10
24. 153%
31. 86%
38. 509%
4. 0=63
11. 0=80
18. 0=01
25. 22%
32. 29%
39. 75%
5. 0=04
12. 0=17
19. 0=50
26. 35%
33. 6%
40. 30%
6. 0=45
13. 0=66
20. 0=99
27. 37=5%
34. 48%
41. 290%
7. 0=02
14. 0=13
21. 1=07
28. 64=8%
35. 308=9%
42. 60%
7
Page 29 Changing Percents to Fractions
1
2
13
2.
100
11
3.
50
19
4.
20
1.
9
50
3
10.
100
1
11.
4
1
12.
20
13
25
63
6.
100
3
7.
4
91
8.
100
4
25
1
14.
100
79
15.
100
2
16.
5
9.
5.
13.
99
100
3
18.
10
21
19.
50
21
20.
25
17.
Page 29 Changing Fractions to Percents
1. 20%
4. 37=5%
7. 10%
10. 75%
13. 6=25%
16. 35%
2. 62=5%
5. 18=75%
8. 80%
11. 12=5%
14. 25%
17. 40%
3. 43=75%
6. 19%
9. 93=75%
12. 31=25%
15. 4%
18. 64%
Page 30 Changing Percents to Mixed Numbers
1. 1 12
13
2. 1 100
3. 2 11
50
4. 3 19
20
5. 2 13
25
2
9. 1 25
4
13. 5 25
99
17. 1 100
63
6. 1 100
53
10. 4 100
61
14. 1 100
18. 3
7. 2 34
1
11. 2 20
79
15. 1 100
91
8. 2 100
1
12. 4 20
16. 3 25
19. 1 14
20. 3 21
25
Page 30 Changing Mixed Numbers to Percents
1. 550%
4. 325%
7. 130%
10. 252%
13. 118=75%
16. 480%
2. 875%
5. 487=5%
8. 620%
11. 112=5%
14. 106=25%
17. 340%
3. 100%
6. 300%
9. 400%
12. 200%
15. 500%
18. 600%
Page 31 Changing to Percent Word Problems
1. 75%
4. 80%
7. 48%
10. 92%
13. 87=5%
16. 95%
2. 20%
5. 25%
8. 75%
11. 40%
14. 52%
17. 68%
3. 30%
6. 16%
9. 72%
12. 85%
15. 82=4%
18. 15%
Page 32 Finding the Percent of the Total
1. 34
3. 459
5. 475
7. 71=76
2. 9
4. 2> 070
6. 24
8. \$580=45
8
9. \$520> 000
10. 465
Page 33 Finding the Percent Increase or Decrease
1. 12%
2. 83%
3. 12 12 %
5. 54%
7. 19%
4. 20%
6. 13 12 %
8. 44%
Page 34 Sales Tax
1. \$44=94
6. \$1=87
2. \$18> 544=70
7. \$116=38
3. \$6=36
8. \$19=08
4. \$12=60
9. \$2=46
5. \$37=86
10. \$97=15
Chapter 1 Review
Pages 35–36
1. 3
2. 4
18. 4 34
36. 0=235
54. 165%
19. 8
37.
11
20
55. 565%
3. 5
20.
38.
21
25
56.
4. 8
5
9
1
4
21.
39.
8
25
57.
5. 24
5
8
3
100
22. 2 47
40. 7 38
58.
17
25
6. 45
7. 20
8. 24
9. 1 13
10.
11.
12.
10 78
7
4 15
4
7
13. 4 78
14.
15.
16.
7
2 12
7 38
9
4 10
17. 4 23
23.
1
3
41. 9 35
1
59. 1 50
24.
5
12
42. 13 14
60. 90%
25. 19=019
43. 5=12
61. 31=25%
26. 19=943
44. 0=07
62. 12=5%
27. 164=964
45. 10=6
63. 25%
28. 8=927
46. 0=45
64. 12 56 miles
29. 1=757
47. 2=19
65. 17 12 gallons
30. 7=3
48. 0=22
66. 23
31. 0=1145
49. 0=0125
67. \$315> 840
32. 1=4943
50. 52%
68. \$13=50
33. 0=12587
51. 64%
69. \$16=00
34. 320
52. 109%
70. 60%
35. 142
53. 62=5%
9
Chapter 2 Exponents and Roots
Page 37 Understanding Exponents
1. 74
3. 123
5. 93
7. 512
2. 102
4. 44
6. 252
8. 144
9. 20
10. 625
Page 38 Multiplication with Exponents
1. 15> 625
9. 729
17. 576
25. 65> 536
2. 1> 679> 616
10. 1> 024
18. 729d15
26. 16e12
3. 4> 096
11. 81
19. 16> 384
27. 3> 125d10
4. 282> 475> 249
12. 16d4
20. 36e10
28. 64d6
5. 60> 466> 176
13. 6> 561
21. 15> 625
29. 6> 561
6. 256
14. 65> 536
22. 59> 049
30. 1> 000> 000> 000
7. 400
15. 1> 296
23. 9d2
31. 225
8. 1
16. 625
24. 6> 561
32. 117> 649
Page 39 Division with Exponents
5
{4
1
2.
4
4
3.
9
6
4. 2
d
5. 27
1
6.
25d2
7. 3
343
8.
512
1.
1
36d2
10. {2
1
4
18. 9
2
{2
1
15. 6
d
1
16.
64
9.
17.
14.
11. 3|2
12. 27d2
1
13.
32{10
1
1024| 5
4
20. 5
|
19.
Page 40 Square Root
1. 7
3. 5
5. 11
7. 10
2. 9
4. 4
6. 25
8. 17
Page 40 Simplifying Square Roots
s
s
1. 7 2
5. 2 2
s
s
2. 10 6
6. 3 7
s
s
3. 5 2
7. 4 3
s
s
4. 3 3
8. 5 3
10
9. 14
10. 6
s
9. 3 6
s
10. 2 10
s
11. 6 2
s
12. 4 5
11. 2
13. 8
12. 30
14. 3
s
13. 3 10
s
14. 5 7
s
15. 3 2
s
16. 2 5
15. 12
Page 41 Order of Operations
1. 20
5. 35
9. 8
13. 9
17. 10
2. 18
6. 4
10. 80
14. 1
18. 121
3. 1
7. 48
11. 34
15. 10
19. 19
4. 2
8. 23
12. 93
16. 8
20. 25
Page 42 Scientiﬁc Notation for Large Numbers
1. 4=23 × 109
7. 4=5 × 1011
13. 685> 000> 000
19. 58> 700> 000
7
8. 6=2 × 103
14. 13> 000> 000
20. 804> 700> 000
11
9. 8=7 × 107
15. 49> 080
21. 381> 000
4
10. 1=05 × 108
16. 7> 102> 000
22. 9> 500> 000> 000> 000
11. 1=083 × 1012
17. 2500
23. 1> 504> 000
12. 3=04 × 105
18. 911> 400
24. 7> 300> 000> 000
2. 6=43 × 10
3. 9=51 × 10
4. 1=23 × 10
10
5. 2=035 × 10
3
6. 9=0 × 10
Page 43 Scientiﬁc Notation for Small Numbers
1. 2=54 × 1036
7. 4=712 × 1038
13. 0=000000118
19. 0=0000000275
2. 5=08 × 1039
8. 2=5 × 1034
14. 0=000023
20. 0=000000407
3. 8=004 × 1036
9. 5=01 × 1038
15. 0=000000006205
21. 0=0052
4. 4=7 × 1034
10. 6 × 1037
16. 0=0000041
22. 0=00000701
5. 5=478 × 1039
11. 8=75 × 10311
17. 0=0007632
23. 0=000044
6. 5=9 × 1037
12. 4 × 1035
18. 0=000000000548
24. 0=0343
Chapter 2 Review
Page 44
1. 1
9. 0
17. 2
25. 1=05 × 105
2. 10
10. 7
18. 5
26. 0=00005204
3. 7
11. 22
19. 2
27. 10> 200> 000
4. 27
12. 26
20. 5=34 × 106
28. 810> 000
13. 4
21. 5=874 × 1038
29. 0=00020078
14. 3
22. 1=451 × 103
30. 0=0047
7. 11
15. 1
23. 4=1 × 1036
8. 28
16. 21
24. 4=148 × 1034
4
5. 3
6
6. 6
3
11
Chapter 3 Introduction to Algebra
Page 46 Substituting Numbers for Variables
1. 10
5. 50
2. 11
6. 10
3. 3
4. 16
9. 41
13. 26
17. 18
21. 3
10. 7
14. 40
18. 80
22. 34
7. 21
11. 63
15. 2
19. 15
23. 25
8. 7
12. 14
16. 2
20. 40
24. 111
18. } + 12
23. 2e
28. 10 q
19. 2e
24. 3|
29. 3 + s
20. { + 1
w
21.
4
|
22.
2
25. q + 4
30. 4p
26. w 6
18
27.
{
31. | 20
Page 48 Understanding Algebra Word Problems
13. { 3
|
14.
10
15. w + 5
1. C
7. E
2. D
8. B
3. A
9. A
4. B
10. B
16. q 14
5. D
11. E
17. 5n
6. C
12. C
32. 5{
Page 49 Setting Up Algebra Word Problems
1. 3q = 2> 700
5. s 54 = 320
2. 5| = 15
1
6. { + \$50 = \$262
2
3. 4 ({ 2) = 20
4.
w
= 45
5
7.
100
=q
5
8. 50 | = 82
9. \$200 + { = \$500
1
10. k + 17 = 35
2
11. \$2> 300 = 2{
z
12. = 32
4
13. 6 g = 12
14. 4 (| + 10) = 48
15. { 5 = 42
16.
36
= 12
e
Page 50 Changing Algebra Word Problems to Algebraic Equations
1. i + i 14 + i + 6 = 91
5. s = \$600 \$100 8z
2. u = 0=05 × \$11 × 40 × z
6. | = (6 × \$3=50) + w
3. s = \$2> 530 (0=40 × \$2> 530)
7. p = {(\$40=50 \$34=50)
4. i = 0=75{ + (0=06 × 0=75{)
Page 51 Substituting Numbers in Formulas
1. 132 in3
4. 24
7. 904=32 cm3
10. 267=95 cm3
2. 56> 520 in3
5. 25=12 cm
8. 25=12 cm2
11. 340=17 cm2
3. 56 board ft
6. 306 in2
9. 20 C
12
Page 52 Properties of Addition and Multiplication
3. Distributive Property
10. Commutative Property of Multiplication
4. Associative Property of Multiplication
5. Identity Property of Multiplication
12. Distributive Property
6. Inverse Property of Multiplication
13. Associative Property of Multiplication
7. Identity Property of Multiplication
Chapter 3 Review
Pages 53–54
1. 10
11. 13
21. z = \$8=00{ + 0=07|
2. 3
12. 7
22. D
3. 1
13. 4
23. A
4. 8
14. 7
24. C
5. 6
15. 5
25. C
6. 3
16. 3
26. 0=6e
7. 6
17. 1
27. { = v + 0=07v
8. 7
18. 4
28. 36 board feet
9. 6
19. z = \$450 + \$16=83y
29. 59 F
20. { = f + 0=06f
10. 8
Chapter 4 Introduction to Graphing
Page 55 Absolute Value
1. 9
4. 12
7. 3
10. 9
13. 6
2. 5
5. 64
8. 1
11. 8
14. 7
3. 25
6. 2
9. 4
12. 18
15. 2
Page 57 Graphing Fractional Values
1. D = 38 , E = 78 , F = 1 12 , G = 2 14
2. H = 45 , I = 25 , J =
3
,
10
K=
7
10
3. L = 8 25 , M = 7 35 , N = 6 45 , O = 5 15
4. P = 2 13 , Q = 3 23 , S = 4 13 , T = 5 23
5. U = 15 13 , V = 16 12 , W = 17 16 , X = 17 23
6. Y = 1 57 , Z = 47 , [ = 17 , \ =
6
7
13
Page 59 Recognizing Improper Fractions, Decimals, and Square Root Values on a Number Line
1.
−2
D
−1
0
C
F −2
−1
1 A
2
B
3
H
1
E
2
J
K
2.
−3
G
0
3.
0
I
1
2
L
3
4. J
7. E
10. L
13. V
16. P
19. M
5. K
8. D
11. H
14. N
17. S
20. U
6. I
9. F
12. G
15. Q
18. O
21. T
Page 60 Cartesian Coordinates
G
B
M
5
P 4
A
3
E
2
J
T
1
R
O
−5 −4 −3 −2 −1 0 1 Q 2
3
4
H
K
D
N
5
S −2
F
−3
L
−4
C
I
−5
Page 61 Identifying Ordered Pairs
1. (6> 2), II
7. (4> 4), IV
13. (5> 3), IV
2. (1> 2), I
8. (3> 1), I
14. (4> 5), III
3. (2> 6), II
9. (2> 6), I
15. (4> 5), I
4. (3> 2), III
10. (2> 3), II
16. (5> 4), II
5. (3> 1), II
11. (1> 7), III
17. (5> 3), III
6. (2> 2), IV
12. (6> 6), IV
18. (6> 1), III
14
Chapter 4 Review
Page 62
1.
4
2.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
−4 −3 1 −3
2
5
5
3
5
3.
6
77.2
6
8
9
10
4.
−2
−1
−3
0
−2.3 −2
−1
y
I
III
D = (3> 3), IV
E = (2> 2), III
F = (4> 3), I
G = (1> 3), II
see graph to the right
see graph to the right
see graph to the right
see graph to the right
3
2
14.
H
1
−4
12.
F
−3
−2
−1
0
13.
1
2
3G 4
x
−1
11.
E
−2
−3
−4
Chapter 5 Solving One-Step Equations and Inequalities
Page 63 One-Step Algebra Problems with Addition and Subtraction
1. q = 18
4. i = 15
7. z = 103
10. f = 28
13. g = 30
2. | = 43
5. { = 18
8. w = 46
11. n = 34
14. { = 41
3. y = 16
6. { = 9
9. p = 29
12. d = 28
15. | = 13
Page 65 One-Step Algebra Problems with Multiplication and Division
1. { = 7
5. { = 27
9. | = 6
13. } = 30
17. w = 9
2. z = 55
6. g = 11
10. | = 3
14. q = 45
18. p = 54
3. k = 15
7. z = 27
11. u = 28
15. } = 6
19. s = 8
4. { = 144
8. u = 14
12. w = 12
16. g = 14
20. d = 12
Page 65 One-Step Algebra Problems with Multiplication and Division
1. { =
3
2
7. { = 3
13. p = 12
2. | =
5
4
8. } = 16
14. k =
21
5
20. } = 15
3. w =
2
5
9. { = 18
15. | =
8
3
21. | =
4
9
27. z =
1
5
22. g =
12
7
28. { =
13
5
19. g =
3
4
4. e = 12
10. s =
5
3
16. w = 5
5. d = 8
11. q =
9
2
17. e =
2
3
23. z =
6. | = 2
12. { =
11
5
18. f =
14
5
24. j = 9
25. d = 3
26. s = 8
13
2
15
Page 67 Multiplying and Dividing with Negative Numbers
1. } = 3
13. { = 2
2. | = 100
14. p = 36
3. n = 9
15. f = 36
4. { = 6
16. g = 56
5. w = 28
17. | = 36
6. u = 20
18. z = 4
7. { = 8
19. y = 3
8. { = 18
20. } = 4
3
21. { =
4
7
22. | = 12
9. z = 55
10. | = 7
11. { = 36
12. w = 7
23. d = 44
1
24. e = 3
36
25. d = 13
26. e = 28
1
27. { =
4
28. | = 54
29. { = 23
30. { = 1
1
31. | =
9
32. g = 50
33. } = 26
34. f = 9
3
35. g = 2
3
36. g =
2
3
37. z = 8
38. s = 7
39. d = 2
40. s = 30
Page 67 Variables with a Coefﬁcient of Negative One
1. z = 14
7. s = 34
2. d = 20
8. p = 81
3. { = 15
9. z = 17
4. { = 25
10. y = 9
5. | = 16
11. n = 13
6. w = 62
12. t = 7
Page 68 Graphing Inequalities
1.
11. { 0
6.
−2
8
2.
12. { ? 4 or { 10
7.
5
13. 2 { 4
10
3.
14. { ? 8
8.
−5
1
4.
4
15. 10 ? { ? 4
9.
7
3
5.
5
4
16. { 1 or { 3
17. { 5
10.
1
16
1
−1
1
18. { A 6
Page 69 Solving Inequalities by Addition and Subtraction
1. { A 2
11. { ? 4
2. { ? 15
12. { 3
3. { 3
13. { 6
4. { 2
14. { A 32
5. { A 2
15. { 11
6. { 9
16. { 0
7. { ? 9
17. { ? 20
18. { A 13
8. { 9
19. { 8
9. { 4
20. { 27
10. { A 10
Page 70 Solving Inequalities by Multiplication and Division
1. { A 20
20
2. { 12
12
3. { 6
−6
4. { A 20
−20
5. { ? 32
−32
6. { 7
8. { 63
6
10. { A 8
8
11. { 27
−27
12. { A 3
3
13. { 40
40
14. { 3
7
7. { ? 6
9. { 6
3
−6
15. { A 48
−63
16. { A 4
−48
−4
17
Chapter 5 Review
Page 71
1. | = 5
11. n = 3
16. s = 38
2. { = 20
6. e = 67
7. f = 30
12. | = 14
17. { = 7
3. g = 25
8. } = 4
13. k = 11
18. p = 10
4. d = 48
9. g =
5. w = 2
4
13
14. s =
10. { = 28
1
7
19. n = 52
15. e = 44
21.
20. d =
7
18
31.
−3
9
22.
32.
−4
6
23.
33.
−2
−2
24.
34.
−15
4
25. { 3
35.
−6
26. 5 { ? 9
27. { ? 2 or { 0
36.
28. { A 10
37.
4
−2
29.
10
38.
30.
4
−5
Chapter 6 Solving Multi-Step Equations and Inequalities
Page 73 Two-Step Algebra Problems
1. { = 5
5. p = 9
9. k = 7
2. | = 7
6. { = 9
3. w = 7
4. s = 3
13. u = 11
17. | = 7
10. e = 3
14. | = 8
18. s = 4
7. { = 8
11. j = 7
15. i = 3
19. k = 4
8. g = 6
12. n = 6
16. w = 3
20. z = 5
Page 73 Two-Step Algebra Problems with Fractions
1. | = 9
4. { = 36
7. { = 20
10. p = 12
13. y = 49
16. | = 20
2. d = 14
5. e = 36
8. f = 40
11. s = 21
14. k = 30
17. } = 28
3. z = 45
6. } = 40
9. { = 44
12. w = 48
15. n = 70
18. e = 30
18
Page 74 More Two-Step Algebra Problems with Fractions
1. { = 19
5. g = 14
9. k = 11
13. w = 32
17. w = 27
21. | = 2
2. } = 23
6. z = 42
10. n = 37
14. e = 15
18. { = 20
22. } = 22
3. e = 16
7. { = 11
11. d = 27
15. i = 33
19. j = 19
23. z = 17
4. | = 30
8. f = 5
12. { = 62
16. z = 40
20. n = 31
24. k = 15
9. 3{ + 6
13. 15d 5
17. 8{ + 7
21. 10p + 3
Page 75 Combining Like Terms
1. 19{
5. 12z + 3
2. 3| + 8
6. 2{
10. 11e + 12
14. 9f 5
18. 4} + 5
3. 2{ + 13
7. 10z 15
11. 3k 3
15. g 3
19. 2| + 12
4. 10d 16
8. 12w + 30 12. 10n + 10 16. 3k 7
20. 12s 4
Page 75 Solving Equations with Like Terms
1. z = 2
3. | = 5
5. w = 8
7. f = 2
9. { = 3
11. | = 7
2. { = 2
4. d = 1
6. g = 2
8. p = 2
10. s = 1
12. d = 2
Page 76 Solving Equations with Like Terms
1. d = 4
6. e = 4
11. | = 3
16. s = 6
21. { = 3
26. s = 6
2. g = 15
7. p = 4
12. z = 1
17. } = 10
22. k = 11
27. g = 15
3. { = 1
8. { = 3
13. e = 3
18. | = 6
23. w = 6
28. z = 17
4. | = 3
9. s = 7
14. n = 5
19. z = 5
24. | = 5
29. | = 2
5. z = 2
10. s = 5
15. p = 3
20. { = 5
25. { = 2
30. p = 4
Page 77 Removing Parentheses
1. 7q + 42
7. 8{ + 12
13. 36w + 12
19. 16f 12
25. 20z 40
2. 16j 40
8. 28 + 42s
14. 12| + 27
20. 5z + 40
26. 27 + 21s
3. 55} 22
9. 20z 40
15. 8e + 24
21. 12{ + 6
27. 9n + 27
4. 6| 24
10. 66{ + 12
16. 7{ 14
22. 2} 4
28. 7e + 9
5. 9n + 15
11. 90 10|
17. 20 + 5|
23. 28s 28
29. 30w + 12
6. 4g 32
12. 9f 81
18. 8e + 8
24. 9w + 54
30. 7y 28
19
Pages 78–79 Multi-Step Algebra Problems
1. | = 6
7. e = 5
13. { = 4
19. { = 3
25. d = 2
31. { = 2
2. d = 8
8. | = 2
14. { = 3
20. f = 1
26. p = 4
32. { = 5
3. { = 9
9. { = 11
15. d = 8
21. d = 7
27. e = 12
33. { = 1
4. | = 3
10. q = 27
16. { = 19
22. { = 1
28. e = 12
34. f = 3
5. { = 5
11. { = 3
17. e = 4
23. | = 2
29. { = 3
35. | = 9
6. d = 14
12. d = 2
18. { = 1
24. | = 2
30. { = 7
36. { = 8
13. { 74
17. { ? 14
21. f ? 94
14. | A 6
18. | 16
22. d ? 2
15. | 3
13
23. e 3
20. | 24
24. { ? 2
Page 81 Multi-Step Inequalities
1. { 1
5. d ? 11
2. { 5
6. d A 0
3. e A 21
4. | A 12
7. { 1
8. { 7
9. { ? 48
10. { 9
11. e ? 13
12. { 6
16. f 12
19. { ?
Page 82 Solving Equations and Inequalities with Absolute Values
1. | = {4> 4}
8. j = {2> 2}
15. n ? 2, n A 2
2. 3 ? { ? 3
9. { = {4> 4}
16. s = {4> 4}
3. n = {2> 2}
10. 4 ? z ? 4
17. e ? 3, e A 3
4. 6 ? q ? 6
11. 2 ? u ? 2
18. t = {4> 4}
5. } = {3> 3}
12. w = {17> 17}
6. 2 ? p ? 2
19. | ? 12 , | A
13. 6 ? { ? 6
20. v = {4> 4}
7. { ? 5, { A 5
14. 4 f 4
21. h 10, h 10
1
2
Page 84 More Solving Equations and Inequalities with Absolute Values
ª
1. { = {7> 11}
21. m ? 42, m A 8
11. d = 8> 1 12
ª
1
2. e ? 2 , e A 4
22. l = 3> 8 23
12. 3 34 ? n ? 19 34
ª
3. 3 ? h ? 2 12
23. u ? 3, u A 9 12
13. g = 4> 2 12
ª
4. i ? 4 12 , i A 8
24. v = 12 13 > 4
14. y ? 11, y A 19
ª
5. e = 1> 3 89
25. w ? 16, w A 10
15. s = {2> 1}
7. z ? 13 17 , z A 12 47
16. 4 13 ? y ? 3
ª
17. p = 3 25 > 5
8. g = {10> 18}
18. h ? 5 12 , h A
6. 1 17 ? e ? 7
9. { ? 3 14 , { A 9
1
10. { A 2 10
, { ? 4
20
1
3
19. 13 ? m ? 9
ª
1
20. p = 45 > 1 15
26. 3 79 ? t ? 6
27. y ? 12 , y A 4
ª
28. l = 2 78 > 7
29. 13 ? s ? 5
30. 3 ? i ? 13
Page 85 Inequality Word Problems
1. { \$80
2. { \$200=00
3. { 147 lbs
4. { 89%
5. { \$379
Chapter 6 Review
Page 86
1. d = 9
12. { = 1
2. { = 72
13. z = 4
3. z = 5
14. t = 4
4. | = 50
15. n = 2
5. f = 18
16. 12{ + 21
6. e = 45
17. 22| + 55
7. g = 4
18. 54e + 48
8. { = 36
19. 24d + 16
9. z = 10
20. 10f + 6
10. { = 1
21. 35| + 5
11. i = 6
22. 3{ 15
1 7d
2
24. f = 11
23.
25. { = 5
26. { 2
27. { 1
28. q = 22
29. | ? 14
30. { 53
31. { A 4
32. u 1> 850
33. s 320
Chapter 7 Rates, Ratios, and Proportions
Page 87 Rate
1. 125 mph
4. 45 mph
7. 82 mph
10. 42 mph
2. 62 mph
5. 61 mph
8. 524 mph
11. 64 mph
3. 52 mph
6. 5 mph
9. 65 mph
12. 45 mph
Page 88 More Rates
1. 250 words/minute
5. 53 feet/second
2. 4 feet/second
6. \$21 million/year
3. 3 minutes
7. 7 points/quarter
4. 25=45 kilometers/day
8. 467 customers/hour
Page 89 Ratio Problems
1.
14
31
3.
5.
4
11
7.
23
45
2.
7
2
25
124
4.
1
26
6.
\$3=00
5
8.
4
3
21
Page 90 Solving Proportions
1. 15
4. 21
7. 18
10. 3
13. 3
16. 4
2. 15
5. 30
8. 4
11. 12
14. 1
17. 6
3. 9
6. 9
9. 30
12. 8
15. 49
18. 2
Page 91 Ratio and Proportion Word Problems
1. 7 hr
4. 5
7. 20
2. 15 ft
5. 500 sq ft
8. \$4.20
3. 320
6. 250 min
9. 1,500
Page 94 Direct and Indirect Variation
1. 10
5. 18
2. 8
6. 3
10. 4
14. 26=4 mph
3. 21
7. 9
11. 20 min
15. 7=5 min
4. 12
8. 18
12. 3 movies
16. 63 min
9. 10
13. \$6=95
Page 95 Maps and Scale Drawings
1. 1 in
3. 300 km
5. 6.5 cm
2. 22.5 km
4. 7 in
6. 15 ft
Chapter 7 Review
Page 96
4
47
12. 6 hours
1. 16
7.
2. 4
8. 7.5
13. 60 miles/hour
3. 2
9. 375 km
14. 340 feet/hour
4. 18
10. 9 yards
15. 80 songs/month
11. 376 widgets
16. 110 miles
5.
9
20
6. 162
22
Chapter 8 Polynomials
Page 97 Adding and Subtracting Monomials
1. 7{2
4. 2j
7. 6{
10. n
13. 3y 3
2. 13w
5. 15| 2
8. 3z2
11. 2{2
14. {3
3. 7|3
6. 2v5
9. 10} 4
12. 11w
15. 5| 4
1. 3|2 + 3| + 6
10. 7p2 3p + 2
19. 2{2 + 2{ 7
2. 7| 2 | + 2
11. 3{2 + 2
20. 12|2 6| + 6
3. 5{3 + {2 + 3{ + 1
12. w2 + 2w + 4
21. 3g5 + 2g4 6g3 + 5
4. 5s2 3s + 6
13. 3s4 3s2 s + 7
22. 10w5 + 6w3 + 17
5. z2 + z
14. 13v3 + 10v2 + 3v
23. 3s2 11s + 4
6. 4w2 + 3w 5
15. 10e2 + 13e + 11
24. 20e3 4e2 + 10e + 14
7. w4 + 2w3 + 5w + 4
16. 8f2 8f 4
25. z3 z + 7
8. v3 + v2 + 2
17. 7f3 + 6f2 + 4
26. 26} 2 + 11} 2
9. 4y3 y 2 + y 4
18. 7{3 + 3{2 + 3
Page 99 Subtracting Polynomials
1. {2 + 2{ + 1
7. 12{2 13{ 8
2. 4| 7
8. 9| 3 8| 2 | 19 14. 11|3 2| 2 |
20. 9y 2 + 10y 6
3. 12w3 8w2 + 8
9. 8k2 11k 3
15. j 2 + 3j + 8
21. 3e3 + 3e2 + 13
16. 2z3 + 4z2 + 5z
22. 11{3 + 9{2 4
17. 9{3 {2 11
23. 3|2 + 2| + 1
18. 3d2 d 1
24. 4} 2 13
4. 2z2 + 9z
10. 14n3 n2 13
5. d5 d3 d2 + 4d 11. 5{2 + 2
6. 7f4 + 15f2 2
12. 12s2 5s + 2
13. 8p 10
19. 3f2 + 8f + 17
Page 100 Multiplying Monomials
1. 54d6
2. 10{9
3. 12| 5
4. 20w4
5. 8s7
6. 72e3
7. 9f6
13. 20{7
19. 21w15
25. 3|5
31. 49v7
37. 30| 6
8. 18g10
14. 15q5
20. 12s11
26. 15e7
32. 2g4
38. 63{8
9. 30n5
15. 8z8
21. 2{6
27. 18f5
33. 22s6
39. d5
10. 7p6
16. 50v9
22. 35v7
28. 32w6
34. 15{10
40. 21n3
11. 22} 8
17. 16g10
23. 54d6
29. 80g8
35. 56} 8
41. 15w6
12. 18z9
18. 40| 8
24. 4{2
30. 6j9
36. 20z9
42. 27{10
23
Page 101 Finding the Greatest Common Factor of Polynomials
1. 6{2 ({2 + 3)
6. 6{2 ({2 2)
11. 9p3 (3 + 2p)
16. 8{2 (2 3{3 )
2. 7| (2|2 + 1)
7. 6| (3| 2)
12. 25{3 (4{ 1)
17. 5d2 (3d2 5)
3. 4e3 (e2 + 3)
8. 5d2 (3d 5)
13. 4e3 (e 3)
18. 8e3 (3 + 2e3 )
4. 5 (2d3 + 1)
9. 4{2 ({ + 4)
14. 6f (3f + 4)
19. 9| 2 (4| 2 + 1)
5. 2| 2 (| + 4)
10. 3e2 (2 + 7e3 )
15. 10|3 (2 + 3| 2 )
20. 7{ (6{2 + 7)
Page 102 Finding the Greatest Common Factor of Polynomials
1. 5d (d2 + 3d + 4)
13. 2p2 (2p3 + 4p2 + 6p + 3)
2. 6| 2 (3| 2 + | + 4)
14. 4{2 (4{3 + 5{2 3{ + 6)
3. {2 (12{3 + 21{ + 1)
15. 3|2 (6| 2 + 7| 3)
4. 3e2 (2e2 + e + 5)
16. 3q (q4 + 3q2 + 4q + 5)
5. 7f (2f2 + 4f + 1)
17. 2g (2g5 4g + 1)
6. 5e (3e3 e + 4)
18. 2 (5z2 + 2z + 1)
7. w (w2 + 3w 5)
19. 3w (2w2 w + 3)
8. 4d (2d2 d + 3)
20. 5s2 (5s3 2s 1)
9. 2e2 (8e3 6e2 5)
21. 9{ (2{3 + { 4)
10. 4{ (5{3 + 4{2 6{ + 7)
22. 6e (e3 2e 1)
11. 10e3 (4e4 + 3e2 5)
23. | (| 2 + 3| 9)
12. 5|2 (4| 2 3| + 6)
24. 2{2 (5{3 {2 + 2)
Page 102 Finding the Greatest Common Factor of Polynomials
1. 3d2 e2 (1 2de2 + 3e)
10. 3d2 e2 (7d2 e + 9e + 5d)
2. 6{3 | 3 (2{ + 3| 4)
11. 2zw (2z2 w + 3z 4w)
3. 5{2 | (4 5{|2 )
12. st (5t 2 2st 9s2 )
4. 4{| (3{ 5{| + 4|)
13. 7{w2 (7{2 w + 1 2w)
5. 4d2 e (2d + 3 + 5e2 )
14. 3g3 (3fg g 2f2 )
6. 6f (6f3 + 7f2 + 4f 3)
15. 2de (6de2 7 + 5e)
7. 14p2 q2 (pq2 2p + 3q)
16. 5{ (5{3 + 2 4{)
8. 4{| 2 (4{3 6{2 + 3{ 2)
17. e{ ({2 e{ + e2 )
9. 8f2 g2 (4fg2 7g + 8f2 )
18. 2nd (2n2 d + 11 + 8nd)
24
Page 103 Multiplying Two Binomials
1. | 2 4| 21
15. 30f2 + 37f + 10
29. 7| 2 26| + 15
2. 2{2 + 22{ + 36
16. | 2 9
30. 27{2 + 6{ 5
3. 12e2 25e + 12
17. 8z2 8z 30
31. 3w2 + 31w + 10
4. 6j2 52j 18
18. 7{2 27{ 4
32. 16z2 58z 63
5. 28n2 n + 15
19. 24w2 60w + 36
33. 8v2 + 30v 8
6. 24y 2 + 26y 8
20. 30e2 + 46e + 12
34. 32n2 + 28n 9
7. 40s2 + 38s + 6
21. 20} 2 + 18} + 4
35. k2 + 10k 24
8. 6k2 + 3k + 45
22. 11z2 + 25z 24
36. 21{2 + 58{ + 21
9. z2 11z + 28
23. 45g2 36g 81
37. 4y 2 36
10. 6{2 11{ 2
24. 9j 2 16j 4
38. 4{2 + 10{ 24
11. 10w2 + w 3
25. 8s2 + 26s + 21
39. 6n2 + 6n 12
12. 16| 2 81
26. p2 25
40. 6z2 + 28z + 22
13. 3d2 + 23d + 30
27. 16e2 24e + 8
41. 40| 2 74| + 30
14. 3} 2 20} + 32
28. 3} 2 + 14} + 15
42. 6g2 + 7g 13
Page 104 Finding the Numbers
1. 10> 4
6. 3> 5
11. 8> 7
16. 4> 4
2. 7> 3
7. 5> 5
12. 6> 3
17. 4> 5
3. 9> 9
8. 6> 8
13. 8> 5
18. 9> 4
4. 10> 2
9. 6> 6
14. 9> 7
19. 10> 5
5. 3> 4
10. 9> 8
15. 8> 2
20. 6> 5
Page 105 More Finding the Numbers
1. 5> 7
6. 11> 1
11. 6> 8
16. 8> 2
2. 5> 1
7. 9> 3
12. 4> 5
17. 8> 3
3. 6> 2
8. 10> 2
13. 2> 1
18. 2> 2
4. 4> 2
9. 8> 3
14. 5> 6
19. 6> 7
15. 3> 4
20. 4> 2
5. 5> 8
10. 7> 4
25
Page 107 Factoring Trinomials
1. ({ + 1) ({ 2)
10. (| + 5) (| 4)
19. (e + 3) (e 5)
2. (| 2) (| + 3)
11. (d + 2) (d 3)
20. (f 1) (f + 8)
3. (z + 4) (z 1)
12. (e + 1) (e 5)
21. (w 5) (w 6)
4. (w + 2) (w + 3)
13. (f + 2) (f 7)
22. (z + 9) (z + 4)
5. ({ + 4) ({ 2)
14. (f 4) (f + 3)
23. (p 8) (p + 6)
6. (n 3) (n 1)
15. (g + 3) (g 2)
24. (| + 7) (| + 7)
7. (w 2) (w + 5)
16. ({ 7) ({ + 4)
25. ({ + 2) ({ + 5)
8. ({ + 1) ({ 4)
17. (| + 6) (| 3)
26. (d 6) (d 1)
9. (| 3) (| 2)
18. (d 4) (d 5)
27. (g 9) (g + 3)
Page 108 More Factoring Trinomials
1. 2 ({ + 1) ({ + 2)
7. 5 (f + 2) (f 4)
13. 2 ({ 7) ({ 2)
2. 3 (| 2) (| 1)
8. 6 (g 1) (g + 6)
14. 4 (| 4) (| 1)
3. 2 (d + 3) (d 2)
9. 4 ({ + 5) ({ 3)
15. 7 (d + 2) (d 3)
4. 4 (e + 2) (e + 5)
10. 6 (d 4) (d + 1)
16. 6 (e 5) (e + 2)
5. 3 (| 3) (| + 1)
11. 5 (e + 3) (e + 5)
17. 11 (g + 4) (g + 2)
6. 10 ({ 4) ({ + 5)
12. 3 (f 4) (f + 2)
18. 3 ({ 5) ({ 3)
Page 108 More Factoring Trinomials
9. d (d 4) (d + 1)
17. 4| 4 (| 2) (| + 3)
10. 4{2 ({ 2) ({ + 3)
18. 2d (d 2) (d 5)
11. | 3 (| + 6) (| 7)
19. 6e3 (e 1) (e 3)
4. 3|2 (| + 1) (| 3)
12. e2 (e + 8) (e + 3)
20. {4 ({ + 1) ({ + 1)
5. 2{3 ({ + 5) ({ 1)
13. 4f (f + 3) (f 4)
21. 5g2 (g 2) (g 5)
14. 11d2 (d + 2) (d + 1)
22. d (d + 9) (d 6)
7. 2| (| 4) (| 4)
15. 2{3 ({ + 8) ({ 7)
23. 3| (| 7) (| 7)
8. 6e2 (e 5) (e + 2)
16. 10g (g + 2) (g 9)
24. 8{ ({ + 1) ({ + 2)
1. {2 ({ 4) ({ + 3)
2. 3f (f + 2) (f 4)
3. 5e (e + 4) (e 2)
6. 6g (g + 2) (g + 2)
26
Page 109 Simplifying Expressions with Exponents
1. | 2 + 6| + 9
7. 128y 2 + 64y 8
13. 25w2 + 30w + 9
2. 8{2 + 32{ + 32
8. 100s2 + 40s + 4
14. 48| 2 216| + 243
3. 96e2 144e + 54
9. 24k2 + 120k + 150
15. 8d2 + 96d + 288
4. 180j2 + 120j + 20
10. 6z2 84z + 294
16. 36} 2 192} + 256
5. 16n2 + 24n + 9
11. 72{2 + 24{ + 2
17. 75f2 + 60f + 12
6. 12k2 + 60k + 75
12. 81{2 + 36{ + 4
18. 36w2 + 216w + 324
1. 12d2
15. 20{3
28. 7n2 + 6n + 9
2. 63{3 | 9
16. 4s5
29. 6t 7 u6
3. 6} 3 18} 2
17. 12v5 w5
30. 7z2 60z + 32
4. 20e5
18. 8g2 + 46g + 63
31. 7st 2
5. 2{2
19. 12z3 + 28z2 20z
32. 2 (4{ 9)
Chapter 8 Review
Page 110
6. 2s 6
3
20. 14}
2
6
33. 6{ ({ 3)
7. 45w 270w 405w
21.
8. 12z4 | 7
22. 15|
35. 5 (3d3 + 8)
9. 12j 2 + 36j + 27
23. 2d6 y 8
36. 4| 4 (5| 2 3)
10. 5g4
24. 144|2 240| + 100
37. 5d (1 3d)
11. 9{2 + 47{ + 10
25. 8{6 | 6
38. ({ + 7) ({ 1)
12. 16| 3 36| 2 + 8|
26. 20{2
39. 2 (e 3) (e + 2)
13. 16d6 e5
27. e2 10e 1
40. (w + 8) (w + 2)
7 7 5
j k
4
3
34. 8e (2e2 + 1)
14. 45z15
1. {3> 2}
8. {4> 2}
15. {6> 7}
2. {2> 4}
9. {3> 4}
16. {3> 2}
3. {5> 3}
10. {4> 7}
17. {4> 3}
4. {1> 4}
11. {2> 3}
18. {5> 3}
5. {2> 7}
12. {5> 2}
19. {2> 5}
6. {1> 4}
13. {8> 1}
20. {8> 2}
7. {5> 4}
14. {2> 1}
21. {2> 6}
ª
22. 4> 83
ª
23. 85 > 2
ª
24. 2> 47
ª
25. 23 > 4
ª
2
26. 3> 11
ª
27. 3> 25
ª
28. 43 > 5
ª
29. 10> 35
ª
30. 52 > 5
ª
31. 7> 32
ª
32. 6> 75
ª
33. 5> 43
34. 43 > 2
ª
35. 4> 57
36.
9
ª
>6
ª
37. 34 > 7
ª
38. 6> 58
39. 54 > 6
ª
40. 5> 38
ª
41. 23 > 13
ª
42. 34 > 12
27
Page 114 Solving the Difference of Two Squares
ª
ª
ª
1. 45 > 45
9. 16 > 16
5. 92 > 92
ª
2. {6> 6}
6. {5> 5}
10. 56 > 56
ª
ª
3. 83 > 83
7. 13 > 13
11. {4> 4}
ª
4. 10 > 10
8. >
12. 3 > 3
4 4
8 8
ª
13. 29 > 29
ª
14. 58 > 58
ª
15. 72 > 72
16. {9> 9}
ª
17. 37 > 37
21. {10> 10}
ª
22. 94 > 94
ª
23. 49 > 49
ª
24. 23 > 23
18. {8> 8}
ª
19. 23 > 23
ª
20. 32 > 32
Page 115 Solving Perfect Squares
1. {2}
5. {1}
2. {1}
6. {8}
3. {11}
4. {4}
13. {9> 5}
17. {1> 23}
10. {12> 6}
14. {1> 3}
18. {10=5> 5=5}
7. {5> 1}
11. {0=5> 9=5}
15. {15=9> 1=9}
8. {1> 9}
12. {13> 1}
16. {3> 15}
9. {0> 20}
Page 116 Completing the Square
1. {3> 1}
4. {2> 18}
7. {9> 3}
10. {3> 5}
13. {22> 2}
2. {1> 7}
5. {7> 7}
8. {6> 4}
11. {6> 10}
14. {5> 1}
3. {7> 1}
6. {0> 4}
9. {17> 5}
12. {4> 12}
15. {=5> 10=5}
Page 117 Using the Quadratic Formula
1. {3> 2}
6. {1> 4}
10. {4> 7}
14. {2> 1}
18. {4> 3}
2. {2> 4}
7. {5> 4}
11. {2> 3}
15. {6> 7}
19. {2> 5}
3. {5> 3}
8. {4> 2}
12. {5> 2}
16. {6> 1}
20. {8> 2}
4. {1> 4}
9. {3> 4}
13. {8> 1}
17. {4> 3}
21. {2> 6}
5. {2> 7}
Chapter 9 Review
Page 118
1. e = 54 > 54
2. e = 5> 6
3. { = 2> 3
4. { =
7 7
> 10
10
5. | =
13 > 2
8. { = 23 > 13
15. | = 6> 3
9. | = 1> 23
16. { = 11> 1
10. e = 4> 2
17. | = 4> 10
11. { = 5> 14
18. e = 6> 3
12. { = 14 > 1
19. | = 1> 13
6. | = 7> 3
13. | = 2> 5
20. d = 4> 12
7. | = 1> 8
14. { = 12 > 23
21. { = 9> 7
28
Chapter 10 Graphing and Writing Equations and Inequalities
Page 120 Graphing Linear Equations
1.
y
y
3.
y
4
6
1
3
−1 0
5
1
3
1
−1 0
1
−4 −3 −2 −1 0
2
1
2
3
4
5
6
7
x
y
2
3
3
−2
−5
−3
−6
−4
−7
y
6.
4
4
3
3
3
2
2
2
1
1
1
1
2
3
x
4
5
6
7
1
2
3
4
x
y
4
−4 −3 −2 −1 0
4
−3
−4
4.
2
−2
x
4
−1
−1
1
−1
2
4
2.
5.
7
1
−4 −3 −2 −1 0
2
3
x
4
−4 −3 −2 −1 0
−1
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
x
Page 120 Graphing Linear Equations
1.
y
4.
y
4
3
3
3
2
2
2
1
1
1
1
2
3
x
4
−4 −3 −2 −1 0
1
2
3
4
x
−4 −3 −2 −1 0
−1
−1
5.
y
y
8.
4
3
3
3
2
2
2
1
1
1
2
3
4
x
−4 −3 −2 −1 0
−1
−1
−2
−2
−3
−3
−4
−4
6.
y
4
3
2
1
−4 −3 −2 −1 0
−1
−2
−3
−4
1
2
3
4
x
1
2
3
x
4
−4 −3 −2 −1 0
9.
y
3
2
2
1
1
−4
x
−4
4
−3
4
−3
3
−2
3
−2
4
−1
2
−1
y
−4 −3 −2 −1 0
1
x
y
4
1
4
−4
4
−4 −3 −2 −1 0
3
−3
−4
−4
2
−2
−3
−3
1
−1
−2
−2
3.
y
4
−4 −3 −2 −1 0
2.
7.
4
1
2
3
4
x
−4 −3 −2 −1 0
1
2
3
4
x
−1
−2
−3
−4
29
Page 122 Graphing Horizontal and Vertical Lines
y
1.
6.
4
4
3
3
2
2
2
1
1
1
1
2
3
x
4
1
−4 −3 −2 −1 0
−1
−2
−3
−4
4
x
−2
−3
−3
−4
−4
y
7.
1
1
−4 −3 −2 −1 0
2
3
x
4
−2
3
2
2
1
1
2
3
4
x
−4 −3 −2 −1 0
y
4
3
3
2
2
1
1
1
2
3
x
4
1
−2
−3
−3
2
3
4
7
4
6
3
5
2
4
1
3
−4 −3 −2 −1 0
−4 −3 −2 −1 0
−4 −3 −2 −1 0
2
3
4
4
3
3
2
2
1
1
1
2
3
4
x
3
4
3
4
y
14.
4
3
2
1
2
3
4
x
1
−4 −3 −2 −1 0
−1
−2
−3
−4
y
4
−4 −3 −2 −1 0
2
−4
−3
10.
1
−4 −3 −2 −1 0
x
−3
−4
y
4
−2
−2
−1
3
−1
−1
1
2
1
x
y
x
1
x
y
−4
1
4
2
−2
2
3
3
−1
9.
2
4
−4 −3 −2 −1 0
y
1
−4
13.
−1
−4
x
−3
y
4
4
−2
−4
8.
3
−1
−3
−4
4.
1
−2
−3
−4 −3 −2 −1 0
4
3
−1
2
y
12.
4
−4 −3 −2 −1 0
−1
1
−4 −3 −2 −1 0
−1
2
30
3
−2
3
5.
2
−1
y
4
3.
y
11.
3
−4 −3 −2 −1 0
2.
y
4
15.
y
4
3
2
1
2
3
4
x
1
−4 −3 −2 −1 0
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
−1
1
2
x
x
Page 122 Finding the Distance Between Two Points
s
s
s
1. 10
7. 2 5
4. 2 2
s
s
s
2. 2 13
5. 74
8. 5 2
s
s
3. 5
6. 3 3
9. 2 10
s
10. 3 10
s
11. 8 2
s
12. 2 13
s
13. 6 2
s
14. 2 37
s
15. 65
Page 123 Finding the Midpoint of a Line Segment
1. (1> 7)
4. (4> 7)
7. (2> 8)
10. (1> 3)
13. (7> 11)
2. (2> 0)
5. (7> 10)
11. (6> 6)
14. (7> 1)
3. (6> 9)
6. (2> 5)
8. (1> 5)
¢
¡
9. 1 12 > 1
12. (9> 7)
15. (3> 2)
Page 127 Understanding Slope
y
1. slope = 1
y
4. slope = 0
7
4
6
5
3
(4, 5)
2
run = 1
rise
4 =1
3
2
1
1
2
3
4
−2
x
3
rise = 0
y
5. slope is undeﬁned
7
4
6
run = 1
3
rise =52
2
(2, 5)
4
3
2
run = 0
(3, 0)
1
2
3
4
−1
1
2
3
4
−2
x
−3
−1
−4
6. slope = 32
y
4
(−1, 2) 3
rise = 1
(3, 4)
1
−4 −3 −2 −1 0
(1, 3)
1
−4 −3 −2 −1 0
x
−4
y
3. slope = 15
4
(4, −2)
−3
−1
2. slope = 2
2
−1 (1, −2)
1
−4 −3 −2 −1 0
1
−4 −3 −2 −1 0
(2, 3)
(4, 1)
2
1
−4 −3 −2 −1 0
run = 5
1
2
3
4
y
(−1, 8)
8
rise = −3
7
6
x
run =52
4
−1
3
−2
2
−3
1
−4
−4 −3 −2 −1 0
(3, 2)
1
2
3
4
x
31
x
7. slope = 12
y
y
12. slope = 1
7
4 =1
run
6
5
2
(2, 4)
4 = −1
rise
(1, 2)
1
(4, 3)
3
1
−4 −3 −2 −1 0
run = 2
2
1
2
1
4
3
5
6
−3
13. slope = 1
y
6
y
4
(−4, 3)
(1, 5)
3
rise = −1
5
rise = 4−3
(−2, 1) 2
run = 1
3
1
(2, 2)
2run = 1
1
−4 −3 −2 −1 0
2
3
x
4
14. slope = 3
y
4
(3, 4)
rise =31
3
run = 1
2
(1, 2)
1
2
3
4
(5, 2)
rise = 3
1
x
−2 −1 0
−1
1
3
2
(4, 1)
−4
y
10. slope is undeﬁned
15. slope = 73
(3, 6)
6
y
4
5
3
run = 0
4
3
rise = −7
1
−4 −3 −2 −1 0
1
1
−4 −3 −2 −1 0
2
3
4
2
3
4
−1
x
−2
−1
run = 3 −3
−4
−2
y
16. slope = 6
4
y
6
3
run = 1
5
2
(3, 5)
4
1
32
2
1
(3, 2)
2
2
x
6
−3
−4
−4
5
−2
−3
−3
4
−1
−2
1
x
−4
4 run = 1
1
4
−3
y
−4 −3 −2 −1 0
3
−2
−2
2
2
−1
−1
9. slope = 1
1
−4 −3 −2 −1 0
1
−2
x
4
−4
8. slope = 3
−1
3
−2
x
7
−1
−1 0
2
−1
−1 0
11. slope = 0
(3, 4)
rise = 31
4
3
5
6
rise = 0
(3, −2)
7
x
rise = 6
3
2
1
(6, −2)
−4 −3 −2 −1 0
−1
−2
1
2 3 4
(2, −1)
x
x
Page 128 Slope-Intercept Form of a Line
y
1. | = 45 { 1
6. | = 85 { 2
4
3
2
6
5
1
-4 -3 -2 -1 0
y
1
2
3
x
4
4
3
-1
-2
2
-3
1
-4
−1 0
1
2
3
2. | = 12 { + 4
7. | = 2{ + 4
4
−4 −3 −2 −1 0
1
2
3
4
1
2
3
4
x
6
1
2
3
4
x
5
−1
4
−2
3
−3
2
−4
1
−4 −3 −2 −1 0
y
x
−1
1
−1 0
2
1
4
3
5
6
7
x
8. | = 43 { + 4
−1
y
7
−2
6
−3
5
−4
4
−5
3
−6
2
−7
1
−4 −3 −2 −1 0
y
x
−1
1
−1 0
1
2
3
4
5
6
7
x
9. | = 3{ + 6
y
−1
7
−2
6
−3
5
−4
4
−5
3
−6
2
−7
5. | = 3{
7
7
1
4. | =
6
y
2
13 {4
5
−2
y
3
3. | = 32 { 5
4
−1
30
1
y
10. | = 15 { 1
3
2
1
−1
−2
−3
−4
2
3
4
4
5
x
−1
4
−4 −3 −2 −1 0
1
−4 −3 −2 −1 0
1
2
3
4
x
y
4
3
2
1
−2 −1 0
1
2
3
6
x
−1
−2
−3
−4
33
11. | = 32 { + 3
16. | = 2{ + 4
y
y
7
4
6
3
5
2
4
1
3
−4 −3 −2 −1 0
2
1
1
−4 −3 −2 −1 0
2
3
2
3
x
4
−2
x
4
−3
−1
12. | = 34 { +
1
−1
1
2
−4
17. | = 6{ 4
y
4
4
3
3
2
2
1
1
−4 −3 −2 −1 0
y
1
2
3
4
−4 −3 −2 −1 0
x
1
2
3
4
x
2
3
−1
−1
−2
−2
−3
−3
−4
−4
13. | = 14 { 1
2
18. | = 12 { 2
y
y
4
4
3
3
2
2
1
1
−4 −3 −2 −1 0
1
2
3
4
−2
−2
−3
−3
−4
−4
1
2
19. | = 54 { + 4
y
y
4
4
3
3
2
2
1
1
1
−4 −3 −2 −1 0
2
3
x
4
−4 −3 −2 −1 0
20. | = 32 { + 3
y
4
3
4
y
7
3
6
2
5
1
34
2
4
−4
−4
1
2
3
4
x
4
3
2
−2
1
−3
−4 −3 −2 −1 0
−4
3
−3
−3
−1
2
−2
−2
−4 −3 −2 −1 0
1
−1
−1
15. | = 2{ 3
x
4
−1
−1
14. | = 12 { +
1
−4 −3 −2 −1 0
x
−1
1
x
x
Page 128 Verify That a Point Lies on a Line
1. yes
3. yes
5. yes
7. yes
9. yes
11. yes
2. yes
4. no
6. no
8. no
10. yes
12. no
Page 129 Graphing a Line Knowing a Point and Slope
1.
y
5.
4
3
3
2
2
1
−1 0
2.
1
2
3
4
5
6
7
4
3
2
1
x
2
1
−1 0
4
3
5
6
7
1
x
1
−4 −3 −2 −1 0
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
y
y
6.
10.
7
1
6
2
−1 0
5
1
−1
4
−2
2
3
4
5
6
7
x
−1
−2
3
−3
2
−4
1
−3
−4 −3 −2 −1 0
−4
3.
2
3
4
3
3
4
4
3
3
2
3
4
x
−4 −3 −2 −1 0
1
2
3
4
x
−4 −3 −2 −1 0
−1
−2
−3
−2
−3
−4
−3
−4
−4
8.
3
4
5
6
7
x
y
12.
4
2
−2
1
−3
−1 0
−4
−1
−5
−2
−6
−3
−7
−4
7
1
2
3
4
4
5
6
7
x
x
y
1
3
−1
6
−1
−2
1
5
y
11.
1
2
4
−7
1
1
x
−6
1
y
2
2
2
−1
1
1
2
−4 −3 −2 −1 0
4
−5
x
y
7.
4
−1 0
1
−1
y
3
y
3
1
2
−1
4
−1 0
4.
y
9.
4
−1 0
1
2
3
x
−1
1
2
3
4
5
6
7
x
−2
−3
−4
−5
−6
−7
35
y
13.
y
17.
7
7
6
6
5
5
4
4
3
3
2
2
1
1
−4 −3 −2 −1 0
2
3
4
1
x
y
1
6
−5 −4 −3 −2 −1 0
−1
4
−2
3
−3
2
−4
1
2
3
y
7
1
6
−1 0
5
−1
4
−2
3
−3
2
−4
1
4
5
6
7
8
1
2
4
3
5
6
7
x
−5
x
−6
−1
−7
y
16.
x
3
−7
19.
3
2
−6
y
2
x
4
−5
x
4
−1
1
1
5
1
0
3
y
18.
7
−4 −3 −2 −1 0
15.
2
−1
−1
14.
1
−4 −3 −2 −1 0
y
20.
7
1
−1 0
1
2
3
4
5
6
7
x
6
5
−1
4
−2
3
−3
2
−4
1
−5
0
−6
1
2
3
4
5
6
7
8
x
−1
−7
Page 130 Finding the Equation of a Line Using Two Points or a Point and Slope
1. | = 2{ 4
2. | =
1
{
3
+4
3. | = 14 { + 1
36
7. | = 43 { 4. | = { 5
5. | =
1
{
2
11
2
6. | = 53 { +
5
3
8. | = { + 7
7
3
9. | = 23 { +
1
3
10. | = 2{ 5
13. | = 2{ 1
11. | = 2{ + 7
14. | = 13 { +
12. | = 43 { 15. | = 32 { 2
2
3
10
3
Page 131 Graphing Inequalities
y
1.
5.
9.
4
4
3
3
3
2
2
2
1
−4 −3 −2 −1 0
2
3
x
4
1
−4 −3 −2 −1 0
1
2
3
4
x
1
−1 0
−1
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
y
y
6.
10.
1
2
3
4
1
3
3
−4 −3 −2 −1 0
2
2
−1
1
1
−2
1
2
4
3
5
6
x
7
−7 −6 −5 −4 −3 −2 −1 0
−1
−2
−3
−4
y
3.
7.
3
3
2
2
1
−4 −3 −2 −1 0
2
3
4
−2
−5
−3
−6
−4
−7
1
2
3
4
x
−4 −3 −2 −1 0
−2
−2
−3
−3
−3
−4
−4
−4
y
12.
4
4
3
3
3
2
2
2
2
3
4
x
1
−4 −3 −2 −1 0
4
1
2
3
4
1
2
3
4
x
1
2
3
4
x
x
y
4
1
3
2
−2
−4 −3 −2 −1 0
2
1
−1
1
1
x
4
−1
8.
7
y
−1
y
6
3
1
−4 −3 −2 −1 0
5
−3
−4
11.
4
x
x
−1
y
4
1
1
4
y
4
−1 0
4.
y
4
1
2.
y
1
−4 −3 −2 −1 0
−1
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
37
x
13.
y
4
2
3
3
1
2
2
−4 −3 −2 −1 0
1
1
2
3
1
x
4
−4 −3 −2 −1 0
2
3
4
−2
−2
−4
−3
−3
−5
−4
−4
−6
18.
4
4
3
3
2
2
2
1
1
1
2
3
4
x
−1 0
1
2
4
3
5
6
7
x
1
−4 −3 −2 −1 0
−1
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
19.
6
y
23.
4
5
4
1
−4 −3 −2 −1 0
1
−4 −3 −2 −1 0
2
3
4
x
−1
−2
y
20.
−1
4
−1 0
−4
y
24.
−1
−2
−2
−3
−3
−4
−4
2
3
4
5
6
x
7
y
4
3
2
1
1
−4 −3 −2 −1 0
1
−1
−4
2
3
x
−3
2
2
4
−2
3
1
3
1
−3
3
−4 −3 −2 −1 0
x
4
y
−2
4
x
2
−1
4
1
3
2
1
2
2
3
2
1
1
5
4
3
3
x
y
22.
3
y
15.
y
4
−2
−3
y
3
−1
x
−1
−4 −3 −2 −1 0
38
1
2
1
−1
4
16.
y
21.
4
−4 −3 −2 −1 0
14.
y
17.
1
2
3
4
x
−4 −3 −2 −1 0
−1
−2
−3
−4
1
2
3
4
x
Page 132 Graphing Inequalities
1.
y
5.
y
4
3
2
1
−1 0
1
2
3
4
5
6
7
x
−1
6.
4
3
2
1
−1 0
1
2
3
4
5
6
7
x
−1
−2
−3
3.
y
7.
4
4
3
3
2
1
1
−4 −3 −2 −1 0
−3
2.
−3
−4
−4
y
10.
4
3
3
2
2
1
−4 −3 −2 −1 0
1
2
3
4
x
−1
−2
−2
−3
−3
−4
−4
3
1
2
−4 −3 −2 −1 0
8.
4
1
2
3
4
x
−1
−2
−3
−4
1
2
3
4
x
−4 −3 −2 −1 0
−2
−3
−4
2
3
x
4
−4
12.
y
4
3
2
1
1
−1
1
−3
y
−4 −3 −2 −1 0
x
−2
2
1
−4 −3 −2 −1 0
4
−1
3
2
3
2
4
3
2
1
−3
y
1
x
3
−4
4.
4
4
−2
−1
3
y
11.
−1
x
2
1
−4 −3 −2 −1 0
−1
y
1
y
4
2
4
−4 −3 −2 −1 0
−3
4
3
x
4
−2
3
2
3
−2
5
1
2
−1
4
−4 −3 −2 −1 0
1
−1
6
1
y
2
−2
y
9.
1
2
3
4
x
−4 −3 −2 −1 0
1
2
3
4
−1
−2
−3
−4
39
x
Page 133 Graphing Inequalities
y
1.
5.
4
4
3
3
3
2
2
2
1
1
1
2
3
x
4
3
1
x
4
−2
−2
−2
−3
−3
−3
−4
−4
−4
y
6.
y
10.
4
4
3
3
3
2
2
2
1
2
3
1
x
4
−3
7.
2
3
4
−1
−2
−2
−3
−3
−4
−4
11.
6
3
5
2
2
1
1
1
1
3
2
5
4
6
7
x
−1
y
8.
4
3
2
1
−4 −3 −2 −1 0
−1
−2
−3
−4
1
2
3
4
x
1
2
3
4
1
2
3
4
1
2
3
4
x
3
1
−4 −3 −2 −1 0
2
x
4
4
3
4
y
y
7
4
3
1
−4 −3 −2 −1 0
−1
−4
y
1
−4 −3 −2 −1 0
x
2
y
4
−2
−1 0
1
−4 −3 −2 −1 0
−1
−1
40
2
−1
1
4.
1
−4 −3 −2 −1 0
−1
−4 −3 −2 −1 0
3.
y
9.
4
−4 −3 −2 −1 0
2.
y
2
3
x
4
−4 −3 −2 −1 0
−1
−1
−2
−2
−3
−3
−4
−4
y
12.
y
4
2
3
1
2
−4 −3 −2 −1 0
1
−4 −3 −2 −1 0
1
2
3
4
x
−1
−2
−1
−3
−2
−4
−3
−4
x
−5
−6
x
Chapter 10 Review
Page 134
y
1.
y
14.
4
3
3
6
2
2
5
1
1
−4 −3 −2 −1 0
2
3
2
3
4
4
x
3
2
−1
−1
−2
−2
1
−3
−3
−4 −3 −2 −1 0
−4
−4
16. | = 34 { + 2
y
17.
4
3
2
1
3
−4 −3 −2 −1 0
1
−1 0
1
2
3
4
4
3
5
6
7
18.
y
23.
4
y
3
2
1
2
−4 −3 −2 −1 0
1
−4 −3 −2 −1 0
8. (0> 14)
19.
4
3
4
−2
−2
−3
−3
−4
3
1
2
1
2
3
4
x
−4
20.
x
2
1
1
2
3
4
x
−4 −3 −2 −1 0
−2
−2
−3
−3
−4
−4
y
3
2
1
−1
−2
2
3
4
x
25. 5
s
26. 5 2
4
−4 −3 −2 −1 0
1
−1
−1
−3
4
3
1
−4 −3 −2 −1 0
−2
3
4
2
−1
2
y
24.
y
4
10. | = 32 { + 2
2
−1
3
−4 −3 −2 −1 0
1
1
−1
−4
y
x
4
−4
3
7. (5> 0)
3
−3
4
6
5
2
−2
x
−4
5. slope = 2
11. slope = 12
¡
¢
12. 65 > 0
2
−3
−4
9.
1
−2
−3
1
−1
−1
−2
x
4
3
4
2
−1
3
4
y
1
−4 −3 −2 −1 0
2
y
2
x
1
−1
22.
3. D
13. (0> 3)
1
−4 −3 −2 −1 0
15. C
6. slope =
7
1
x
4
2. B
4.
y
21.
4
1
2
3
4
x
27. (1> 7)
28. (2> 2)
−3
−4
41
Chapter 11 Applications of Graphs
Pages 136–137 Changing the Slope of \ -Intercept of a Line
1. P
4. P
7. NP
2. P
5. P
8. NP
3. NP
6. NP
9. P
y
10.
r
y
12.
4
l
3
r
2
1
1
−4 −3 −2 −1 0
2
3
4
3
2
2
1
1
1
−2
−3
−3
−4
−4
y
4
2
3
4
x
−4 −3 −2 −1 0
l
1
2
3
−1
−2
−3
−4
y = x
line l:
y = x + 2
line r:
slopes: Same: parallel lines
y-intercepts: l (0, 0) r (0, 2)
4
x
line l:
line r:
slopes:
x
y = −#x − y = x − 2
Line l is steeper than and
oriented in the opposite
direction as line r.
l (0, − ) r (0, −2)
y
4
l
3
2
2
1
1
1
2
3
−1
r
4
−3
y-intercepts:
15.
4
−4 −3 −2 −1 0
3
−4
3
1
2
−2
r
y
2
1
−1
y = −4x − 1
line l:
y = −3x − 1
line r:
Line l is slightly
slopes:
steeper than line r
y-intercepts: (0, −1) for both
13.
r
3
42
3
−2
−4 −3 −2 −1 0
4
l
−1
y = 2x
line l:
y = −2x
line r: Same steepness,
oriented
slopes: in different directions
y-intercepts: (0,0) for both
x
4
−4 −3 −2 −1 0
−1
11.
l
y
14.
−2
4
x
−4 −3 −2 −1 0
r
1
2
3
−1
−2
−3
−3
−4
−4
x=3
line l:
y = −3
line r:
Undefined for line l ,
slopes: 0 for line r
l: no y-intercept
y-intercepts: r: (0, −3)
l
y = −
x + 3
line l:
line r:
slopes: Same: parallel lines
y-intercepts: l (0, 3) r (0, −3)
4
x
Page 139 Equations of Perpendicular Lines
4. | = 13 { +
1.
5
3
5. | = 2{ + 10
6. | = { + 3
7. | = 32 { +
15
2
8. | = { 6
9. | = 14 { +
10. | = 6{ 7
8
13
4
11. | = 8{ 58
12. | = 54 { + 25
Slope of perpendicular line = 12
4
Equation of perpendicular line: | = 12 { 12 13. | = 3 { 12
7
7
2. | = 15 { + 75
14. | = 2{ + 92
3. | = 12 { + 72
15. | = 9{ + 6
Page 140 Writing an Equation From Data
1. | = 10> 000{ +
45> 000
2. | = 74 { +
3
2
3. | = 400{ +
4> 900
4. | = 11{ + 73
Page 142 Graphing Linear Data
6.
20
11. The slope represents
ounces per pound.
20
15
10
5
15
12.
10
25
5
1
2 3 4
Diameter
5
inches
4. slope = 3=14
5. The slope of circumference
over diameter gives the
value of .
1 2 3 4 5
Length of Side
0
7. Perimeter = 16 inches
8. slope = 4
9.
20
Days
0
10. 2=5 pounds
25
Perimeter
Circumference
25
15
10
5
0
70
1
2 3 4
Weeks
5
60
50
Ounces
1.
40
30
20
10
0
1
2
3 4
Pounds
5
43
Page 143 Identifying Graphs of Linear Equations
1. H
2. C
3. F
4. D
5. E
6. A
7. G
8. I
9. B
Page 144 Graphing Non-Linear Equations
1.
5.
9.
8
7
8
6
7
2
5
1 2
−2
−4
4
−6
−4 −3 −2 −1 0
6
5
4
3
1
2
3
1
4
−14
1
−4 −3 −2 −1 0
2.
3
2
2
−4 −3 −2 −1 0
1
2
3
1
−1
−2
−2
−3
−3
−4
−4
−5
−5
2
3
4
5
3
4
2
3
1
−4 −3 −2 −1 0
1
2
3
4
3
2
1
−3
−1
−2
−3
−4
−5
12.
4
−4 −3 −2 −1 0
4
3
2
2
3
4
5
1
1
2
3
6
3
1
2
7
4
2
4
−5
8.
1
3
−4
−5
3
2
−3
−4
4
−4 −3 −2 −1 0 1
−1
−2
−2
−2
4
−1
−1
4
3
4
−4 −3 −2 −1 0
3
2
11.
6
2
1
−4 −3 −2 −1 0
4
7.
−4 −3 −2 −1 0 1
−1
44
2
1
−1
1
4
3
−4 −3 −2 −1 0
2
4.
4
1
4
3.
3
4
3
1
2
10.
6.
4
4
−10
−12
2
1
3
−8
3
2
−4 −3 −2 −1 0
4
1
2
3
4
−4 −3 −2 −1 0
−1
−1
−2
−2
−3
−3
−4
−5
−4
−5
1
Page 146 Identifying Graphs of Real-World Situations
1. A
2. B
3. D
4. D
Page 147 Identifying Graphs of Real-World Situations
1. B
2. D
3. C
4. A
Chapter 11 Review
Pages 148–149
1. | = 125{ + 75
2. | = 50{ + 70
y
3.
4
13.
3
2
1
2
3
x
4
Interest
1
−4 −3 −2 −1 0
\$10
−1
−2
−3
−4
\$8
\$6
\$4
\$2
4. D
0
5. C
y
6.
4
3
15. slope =
2
1
−4 −3 −2 −1 0
2% 4% 6% 8% 10%
Interest Rate
1
2
3
4
4
5
16. The slope gives the amount of interest per
1% interest rate.
x
−1
17. y
−2
−3
−4
7. B
8. parabola
9.
20
18
x
16
14
KPH
12
10
8
6
4
2
0
2
4
6
8
10
12
14
MPH
45
Chapter 12 Systems of Equations and Systems of Inequalities
Page 151 Slopes of Collinear, Parallel, and Intersecting Lines
1. parallel
11. parallel
2. parallel
12. intersecting
3. collinear
13. parallel
4. intersecting
14. collinear
5. collinear
15. intersecting
6. intersecting
16. parallel
7. intersecting
17. intersecting
8. collinear
18. collinear
9. parallel
19. intersecting
10. intersecting
20. intersecting
Page 153 Solving Systems of Equation by Substitution
1. (4> 2)
11. (1> 3)
3. (3> 1)
6. (2> 2)
¢
¡
7. 12 > 13
8. (2> 1)
13. (0> 1)
4. (4> 5)
9. (0> 1)
14. (0> 1)
5. (3> 5)
10. (0> 1)
2. (2> 3)
12. (1> 1)
15. (3> 0)
Page 155 Solving Systems of Equations by Adding or Subtracting
1. (28> 10)
11. (1> 3)
3. (4> 5)
6. (2> 2)
¡ ¢
7. 32 > 1
8. (1> 4)
13. (0> 1)
4. (3> 10)
9. (0> 1)
14. (2> 1)
5. (6> 2)
10. (3> 1)
2. (2> 3)
46
12. (2> 4)
15. (3> 0)
Page 156 Graphing Systems of Inequalities
y
1.
5.
y
4
3
2
1
1
−4 −3 −2 −1 0
2
3
x
4
−2
−3
−4
2.
6.
7
6
5
4
3
1
1
−4 −3 −2 −1 0
2
3
4
x
−1
3.
y
7.
3
2
2
1
1
4
−3
−4
y
10.
4
3
3
2
2
1
1
−3
−4
−4
y
11.
−4 −3 −2 −1 0
−3
−4
−4
2
−3
−4
2
3
4
x
1
2
3
4
−2
−3
−4
3
4
x
y
−4 −3 −2 −1 0
1
2
3
4
1
2
3
4
x
−1
−2
−3
−4
12.
y
4
3
2
1
1
−1
2
1
x
y
−4 −3 −2 −1 0
1
2
2
1
4
3
3
1
3
4
4
3
2
−4 −3 −2 −1 0
−2
1
8.
x
−3
−3
−2
4
−2
−2
−1
3
−1
−2
−4 −3 −2 −1 0
2
−1
−1
4
1
x
1
y
4
−1
y
−4 −3 −2 −1 0
−4
2
x
x
−2
2
3
4
−3
3
2
3
−2
3
1
2
−1
4
−4 −3 −2 −1 0
1
−1
4
1
4.
4
−4 −3 −2 −1 0
2
y
3
−4 −3 −2 −1 0
−1
y
9.
4
1
2
3
4
x
−4 −3 −2 −1 0
−1
−2
−3
−4
47
x
Page 157 Solving Word Problems with Systems of Equations
1. 90, 120
2. 42, 84
3. 9 times
4. 122
Chapter 12 Review
Page 158
1. (1> 1)
4. (2> 2)
7. (2> 0)
2. (1> 0)
5. (3> 0)
8. (5> 1)
3. (0> 1)
6. (6> 15)
9. (3> 4)
13.
y
y
17.
4
4
4
3
3
3
2
2
2
1
1
1
−4 −3 −2 −1 0
14.
¡ ¢
10. 1> 34
¡
¢
11. 15
>4
2
¡ ¢
12. 5> 73
y
15.
5. 45
1
2
3
4
x
−6 −5 −4 −3 −2 −1 0
−1
−1
−2
−2
−3
−3
−4
−4
y
1
2
x
−4
y
18.
4
3
3
3
2
2
2
1
1
1
2
3
4
x
1
−4 −3 −2 −1 0
2
3
4
x
−4 −3 −2 −1 0
−1
−1
−1
−2
−2
−2
−3
−3
−3
−4
−4
−4
19. 72 \$10’s, 13 \$5’s
20. 40 tickets
21. 1 time
1
22. \$0=80
Chapter 13 Relations and Functions
Page 159 Relations
1. Domain: {2> 9> 3> 6}
Range: {5> 12> 8> 7}
6. Domain: {8> 23> 4> 16> 3}
Range: {16> 7> 9> 8> 6}
2. Domain: {12> 3> 7> 26}
Range: {4> 12> 19}
7. Domain: {7> 3> 4> 6> 8}
Range: {4> 16> 17> 8> 12}
3. Domain: {4> 7> 16> 5}
Range: {3> 14> 34> 11}
8. Domain: {1> 3> 7> 2> 6}
Range: {2> 6> 14> 8> 2}
4. Domain: {2> 33> 98> 43> 67}
Range: {45> 43> 9> 61> 54}
9. Domain: {0> 8> 3> 8> 7}
Range: {9> 5> 12> 3> 18}
5. Domain: {78> 29> 84> 16> 98}
Range: {14> 67> 49> 18> 46}
10. Domain: {58> 44> 74> 6> 63}
Range: {14> 97> 32> 18> 44}
48
x
4
−3
4
1
3
−2
4
−4 −3 −2 −1 0
2
−1
y
16.
1
−4 −3 −2 −1 0
2
3
4
x
Page 160 Relations
1. {5> 10> 15> 20}
5. {1> 1> 5> 7}
2. {3> 2> 1> 0> 1}
6. {22> 12> 2> 8> 18}
10. {1> 2> 8> 11}
3. {2> 5> 11> 14}
7. {7> 4> 1> 4> 7}
11. {2> 6> 14> 18}
4. {2> 1> 0> 1> 2}
8. {1> 2> 3> 4}
12. {3> 1> 1> 1> 3}
9. {2> 4> 6> 8}
Page 161 Functions
1. F
3. NF
5. NF
7. F
2. F
4. F
6. F
8. NF
9. F
11. NF
13. F
15. NF
17. NF
19. NF
10. F
12. NF
14. F
16. F
18. NF
20. NF
Page 162 Function Notation
1. 29
3. 4
5. 23
7. 31
9. 3
2. 10
4. 16
6. 4
8. 60
10. 11
Page 164 Recognizing Functions
1. Function
3. Function
5. Not a Function
2. Not a Function
4. Function
6. Function
Page 165 Function Tables
1. rule: 2 (q 5):
q
i (q)
1
10
2
8
3
6
4
4
2. rule: 3{ ({ 4)
{
i({)
0
0
1
9
2
12
3
9
3. rule:
q
0
2
4
6
8
2q
2
i (q)
1
0
1
2
3
4. rule: 2{ ({ 1)
{
i({)
1
0
2
4
3
12
4
24
5. rule:
q
1
2
3
4
1
q+3
i (q)
1
4
1
5
1
6
1
7
6. rule: 4{ {
i ({)
{
2
6
1
3
0
0
1
3
2
6
7. rule: q (q + 2)
q
i (q)
1
3
2
8
3
15
4
24
8. rule: 2{ 3
{
i ({)
1
1
2
1
3
3
4
5
9. rule: 3 2q
i (q)
q
2
7
1
5
0
3
1
1
2
1
49
Pages 166–167 Relations That Can Be Represented By Functions
1. 4,044 atoms
3.(A) 5,381,290
(B) 3,591,580
2. 5 milligrams
4.(A) 2,726 bacteria
(B) 56,569 bacteria
5. \$3,514.37
6. Bank 2
Page 169 Exponential Growth and Decay
3. P (w) = 1000 (1=04)w
1. I (w) = 15 (1=01)w
15.15
15.30
15.45
15.61
w
2. V (w) = 350 (0=85)
t
S(t)
1
297.50
3
214.94
5
155.30
7
112.20
t
M(t)
t
C(t)
2
1081.60
5
165.63
4
1169.86
10
5.18
6
1265.32
15
8
1368.57
20
exponential growth
exponential growth
5. F (w) = 5300 (0=5)w
4. E (w) = 2 (2=50)w
exponential decay
6. U (w) = 80
3
B(t)
t
R(t)
1
5.00
2
8.89
2
12.50
4
0.99
3
31.25
6
0.11
4
78.13
8
0.01
exponential growth
exponential decay
7. Town B is experiencing decay. Town A is experiencing growth.
8. population
9. The graph represents population, and population cannot be negative.
10. year 8
Page 171 Step Functions
50
¡ 1 ¢w
t
exponential decay
1.
0.01
2.
3.
6.
4.
(A) \$0=50
(B) \$0=50
(C) \$1=00
7.
5.
(A) \$200
(B) \$800
(C) \$1> 600
Chapter 13 Review
Page 172
1. {1> 2> 4> 6}
4. F
2. {2> 4> 6> 8} 5. F
3. {0> 5> 10> 15> 20} 6. NF
15. rule:
q
0
1
2
3
4
1
2
(4 2q)
i (q)
2
1
0
1
2
7. NF
10. 9
8. F
11.
1
7
13. 24
14. 32
12. 3
9. 6
16. rule: 2q (q + 1)
17. rule: 6q 3
i (q)
i (q)
q
q
0
0
2
9
1
3
4
15
2
4
12
21
3
5
24
27
4
6
40
33
51
Chapter 14 Patterns
Page 174 Number Patterns
1.
2.
3.
4.
5.
6.
7.
8.
Sequence
Pattern
Next Number
20th number in the sequence
2> 1> 0> 1> 2
5> 6> 7> 8> 9
3> 7> 9> 11> 15> 19
3> 6> 9> 12> 15
3> 5> 7> 9> 11
2> 4> 8> 16> 32
1> 8> 27> 64> 125
0> 1> 2> 3> 4
q3
q+4
4q 1
3q
2q + 1
2q
q3
1q
3
10
23
18
13
64
216
5
17
24
79
60
41
1> 048> 576
8> 000
19
Page 175 Inductive Reasoning and Patterns
1.(A) Expect 80 visitors in the ﬁfth week.
(B) Expect 5 × 2q31 visitors in the qth week.
(C) It will take 8 weeks to get over 500 visitors in one week.
2. Predict 4> 000 in 2009.
3. Predict 1,464 in 2000 (1.1 times 1999 scores)
4. Each week the increase in height is 12 what it was the week before, so the April 29 reading
would be 22=5 + =75 = 23=25 inches.
5. Each week the decrease in height is 12 the previous week’s, so the temperature at 2:00 would
be 32 degrees and at 2:15 would be 30 degrees.
Page 177 Inductive Reasoning and Patterns
1.(A) 19 posts
(B) q + 1
(C) 310 feet
2.(A) 300 + 10q
(B) 300 + 40q
(C) 30 months
(ten 3-month periods)
3.(A) 100 + 2q
(B) 50 pair
4. 40 + 4 (q 50)
Page 178 Using Problem Solving Skills
1. 29
2. 26
3. 19
1. q 1
5. 3q
9. 22q
2. 19
6. 90
10. 14 batches
3. 2q 1
7. 4=95 + 0=95q
11. 378
4. 49
8. 15 hours
Chapter 14 Review
Page 179
52
Chapter 15 Statistics
Page 180 Range
1. 23
2. 44
3. 84
4. 54
5. 62
6. 35
Page 180 Mean
1. 86
2. 13=9
3. 4=5
4. 41=6
Page 181 Finding Data Missing From the Mean
1. 97%
4. 8 pounds
7. 15 ounces
2. \$92=00
5. 23 pounds
8. 4 ounces
6. 96 pounds
9. 10 points
Page 182 Median
1. 11
2. 38
3. 10=5
4. 51
5. 25
6. 5
2. 16
3. 4
4. 7
5. 22
6. 95
5. 90
6. 98
Page 182 Mode
1. 56
Page 183 Stem-and-Leaf Plots
1.
2. 69
Stem
1
2
3
4
5
6
Leaves
0,5,6
0,1,2,4,5,8,9
1,2,2,2,2,3,4,4,5,5,5,6,6,6,8,9
0,0,1,1,1,1,2,2,3,5,5,5,6,7,7,8,8,9,9
0,0,1,1,2,2,2,2,2,5,5,5,6,8,9,9
3,5,9
3. 10
4. 52
5. 26
6. 10
Page 184 More Stem-and-Leaf Plots
1. 58
2. 50
3. 58
4. 42
7.
I-85
7,6
9,9,9,9,8,7,5,5,5,4,3,2,0
9,8,7,5,5,4,3,1,1,0
1,0
2
8. 61.5
9. 69
Stem I-75
5
6
7
8
9
3,5,6,6,7,7,8,8,8,9,9
0,1,1,2,2,3,3,3,3,4,5,7,7,9,9
0,2
10. 63
11. 69
12. 92
53
Page 185 Quartiles and Extremes
lower extreme
lower quartile
1.
0
1
2.
15
16
3.
62
76
4.
74
74
5.
3
4
6.
190
191
7.
6
8
8.
21
23
median
2
20
81
76
6
192
10
26
upper quartile
3
22
89
77
7
195
12
30
upper extreme
5
23
94
78
8
196
15
35
Page 186 Box-and-Whisker Plots
1.
10
20
30
40
50
60
2.
0
10
20
30
40
Page 188 Scatter Plots
1. no relationship
3. no relationship
5. positive
2. negative
4. positive
6. negative
2. H = about 450 ft
Page 189 The Line of Best Fit
1. Graph B is misleading because the |-axis does not begin at 0.
2. 5
3. 2
4. 2
5. mean
6. median
7. Yes, the mean is affected by an outlier if one teenager purchases 58 games. The outlier inﬂates
the average number of games purchased per teenager.
8. Graph A is misleading because it does not start at 0.
54
Chapter 15 Review
Page 192
Data Set
Number
Mean
Median
Mode
Range
21
20
20
6
18
13
\$275.00
\$280.00
42
\$280.00
4. 115 points
\$198.00
6. 93 inches
5. \$400
10. 322 13 F
6. 14 pizzas
11. 349 F
7. 13 13 ounces
12. 104 F because it is an outlier
8. 10 points
Chapter 16 Data Interpretation
Pages 193–194 Tally Charts and Frequency Tables
1.
Speed
Tally
Frequency
0
3
7
18
19
15
2
0-9
10-19
20-29
30-39
40-49
50-59
60-69
2.
Tally
Frequency
A
7
B
17
C
20
D
9
F
3
55
Pages 194–195 Histograms
1.
HISTOGRAM OF CAR SPEEDS
60-69 mph
50-59 mph
40-49 mph
30-39 mph
20-29 mph
10-19 mph
5
10
15
20
25
Number of Cars
2.
A
B
C
D
F
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Number of Students
Page 195 Bar Graphs
1. China
4. India
7. C
2. 3
5. 30
8. 96
3. 800 Million
6. 7
9. 52
Page 196 Circle Graphs
1. \$16
6. 150
2. \$20
7. 280
3. \$40
8. 50
4. \$4
9. 150
5. 300
56
10. 70
1. True
3. 18th and Miami
5. 1st and Hyatt
2. 9:35
4. 18 min
6. False
7. 7:47
Page 199 Voting Methods
1.(A) blue
(B) purple
(C) rank #3 is yellow
rank #4 is green
2. candidate 3
3.(A) Pizza
(B) second is hot dogs
third is hamburgers
Chapter 16 Review
Pages 200–201
Frequency
7
6
5
4
2
4
6
7
3
2
1
0
10
12
6
5
3. 33
12.
Population
4. 2
5. 40
6. 11.2 million metric tons
Time
7. 37.6 million metric tons
13.
8. 14.8 million metric tons
Histogram: Pets per Student
7
6
5
4
3
2
1
0
Population
2.
Number
of Pets
Number of Pets Per Student
1.
9. 1.8 billion
10. 144 million
11. Africa
0
1
2 3
Time
4 5 6 7 8 9 10 11 12 13
Number of Students
Chapter 17 Probability
Page 204 Probability
1. 2%
3. 29%
5. 50%
7. 21%
2. 33%
4. 31%
6. 13=3%
8. 50%
9. 50%
11. 0=8%
10. 5%
12. 25%
Page 206 Independent and Dependent Events
3
22
1
2.
6
1.
1
2
5
4.
11
3.
1
3
1
6.
11
5.
7
23
1
8.
25
7.
1
5
2
10.
21
9.
57
Page 208 Tree Diagrams
1.
5
64
4.
3
50
7.
3
25
10.
1
9
13.
1
8
2.
4
25
5.
1
6
8.
2
49
11.
4
225
14.
2
9
3.
10
81
6.
10
121
9.
1
12
12.
1
16
15.
1
8
Page 210 Simulations
1.(A)
101
250
1
3
2.(A)
(B)
3
8
(B)
(C)
14
125
1
6
(C)
(D)
1
8
7
50
(D) the simulation accurately portrays rolling
a six-sided cube
(E) Yes
Page 211 Intersection of Sets
1. {Jan, Dan}
6. {98> 95}
10. {6> 2}
14. >
2. {purple}
7. {orange}
11. {2> 9}
15. {Kate}
3. {2> 4> 6> 8> 10}
8. {7> 2}
12. {2}
16. >
4. {a, e, i}
9. {2}
13. {Phil}
17. {Jan}
5. {maple}
Page 212 Union of Sets
1. {apples, pears, oranges, bananas}
2. {5> 10> 15> 20> 25> 30> 40}
3. {Ted, Steve, Kevin, Michael, George, Kenny}
4. {raisins, prunes, apricots, peanuts, almonds, coconut}
5. {sales, marketing, accounting, receiving, shipping}
6. {beef, pork, chicken, tuna, shark}
7. {1> 2> 3> 4> 5> 6> 7> 8}
8. {1> 4> 5> 6> 7> 8> 9}
9. {1> 2> 3> 4> 5> 6> 9}
10. {1> 2> 3> 4> 5> 6> 7> 8> 9}
11. {Carol, Mike, Jill, Jack, Fred, Kate, Bill}
12. {Carol, Mike, Jack, Fred, Jill, Lamar, Bill}
13. {Jack, Kate, Bill, Jill, Lamar, Fred}
14. {Carol, Mike, Jill, Jack, Fred, Kate, Bill, Lamar}
58
Chapter 17 Review
Pages 213–215
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
3
10
1
3
5
6
27
512
1
8> 000
1
16
1
81
3> 125
59> 049
64
729
1
59> 049
1
59> 049
5
4
2
, dependent
9
6
, independent
29
1
15. , independent
3
16. {15}
17. {Felix, Mark, Kate, Carol, Jack}
18. {p, r, f, t}
19. >
20. {red, white, blue, black, grey}
21. {1> 2> 3> 4> 5> 6> 8> 10> 12}
22. D
23. L
24. A
25. K
26. I
27. N
28. O
29. E
30. M
31. J
32. F
33. H
34. B
35. G
36. C
Chapter 18 Permutations and Combinations
Page 218 Permutations
1. 120
3. 5,040
5. 24
7. 120
2. 720
4. 6
6. 24
8. 6
9. 6
11. 40,320
10. 24
59
Page 219 More Permutations
1. 1,680
4. 40,320
7. 1,320
2. 60
5. 95,040
8. 992
3. 116,280
6. 55,440
9. 15,600
Page 220 Combinations
1. 15
3. 1,140
5. 210
7. 1,001
2. 310,124
4. 28
6. 53,130
8. 66
7. 60
Page 221 More Combinations
1. 48
3. 96
5. 120
2. 280
4. 90
6. 36
Chapter 18 Review
Page 222
1. 5,040
3. 792
5. 45
7. 5,040
2. 792
4. 60
6. 180
8. 288
9. 300
10. 190
Chapter 19 Time Problems
Page 223 Converting Units of Time
1. 6 years 6 months
7. 6 hours 15 minutes
2. 5 hours 24 minutes
8. 6 days 7 hours 18 minutes
3. 2 minutes 16 seconds
9. 6 weeks 2 days 12 hours
4. 4 weeks 1 day
10. 2 hours 56 minutes 26 seconds
5. 2 weeks 3 days
11. 13 hours 27 minutes 27 seconds
6. 4 minutes 20 seconds
12. 8 years 1 month
Page 224 Adding Units of Time
1. 18 hours 5 minutes
6. 1 week 3 days 9 hours 28 minutes
2. 5 hours 5 minutes
7. 4 weeks 1 day
3. 1 week 4 days 6 hours
8. 6 years
4. 9 minutes 15 seconds
9. 1 hour 23 minutes 7 seconds
5. 13 years 5 months
60
10. 22 hours 11 minutes
Page 225 Subtracting Units of Time
1. 1 day 19 hours
10. 2 hours 25 minutes
2. 30 minutes
11. 2 hours 15 minutes
3. 2 minutes 40 seconds
12. 1 hours 33 minutes
4. 1 hour 45 minutes
13. 4 minutes 50 seconds
5. 32 minutes 32 seconds
14. 3 days 18 hours 35 minutes
6. 2 days 16 hours
15. 3 week 6 days
7. 6 months
16. 1 hour 35 minutes
8. 1 day 15 hours
17. 1 hour 15 minutes
9. 1 day 7 hours 55 minutes
18. 1 hour 40 minutes
Page 226 Changing Minutes to Hours
1.
2.
3.
4.
5.
6.
7.
1
2
5
6
1
4
1
3
3
4
1
6
7
12
8.
11
12
15. 2 13
22. 3 23
29. 3 13
9.
2
3
16. 1 14
23. 7 12
30. 5 13
10.
5
12
17. 1 56
5
24. 3 12
31. 1 13
18. 5
25. 4 34
32. 3
1
11. 2 12
12. 2 16
19. 6 12
13. 6
5
20. 1 12
14. 2 12
21. 3 16
26. 5 34
27. 2 14
33. 4 16
34. 5
28. 4 23
35. 7 16
Page 227 Changing Hours to Digital Time
1. 1:30
5. 4:20
9. 1:15
13. 7:20
17. 4:10
2. 2:45
6. 6:45
10. 4:40
14. 2:06
18. 5:20
3. 3:15
7. 2:40
11. 8:30
15. 5:05
19. 8:15
4. 6:30
8. 5:30
12. 9:45
16. 6:40
20. 7:45
Page 227 Time Word Problems
1. 10:45 a.m.
4. 2:40 p.m.
2. 5:45 p.m.
5. 11:10 a.m.
3. 10:15 p.m.
6. 5:15 p.m.
61
Page 228 Two-Step Time Problems
1. 3:15 p.m.
3. 3:20 p.m.
5. 5:15 p.m.
7. 3:00 p.m.
9. 6:50 p.m.
2. 2:15 p.m.
4. 3:45 p.m.
6. 3:20 p.m.
8. 5:25 p.m.
10. 1:15 p.m.
Page 229 Calculating Starting Times
1. 12:45 p.m.
3. 5:15 p.m.
5. 9:50 a.m.
7. 10:25 a.m.
9. 4:25 p.m.
11. 2:35 p.m.
2. 3:35 p.m.
4. 1:50 p.m.
6. 1:40 p.m.
8. 12:45 p.m. 10. 7:20 p.m.
12. 1:30 p.m.
3. 7 23 hours
5. 1 56 hours
7. 7 13 hours
9. 7 34 hours
11. 6 12 hours
4. 2 34 hours
6. 8 16 hours
8. 1 56 hours
10. 6 14 hours
Page 230 Calculating Hours
1. 7 34 hours
2. 4 12 hours
12.
5
6
hours
Chapter 19 Review
Page 231
5
1. 2 12
hours
3. 11:10 a.m.
5. 10 months
7. 1:45 p.m.
2. 2:15 p.m.
4. 7 14 hours
6. 3:05 p.m.
8. 3 23 hours
5. E
7. D
9. 12:50 p.m.
1
10. 3 12
hours
Chapter 20 Measurement
Page 233 Approximate English Measure
1. C
2. F
3. E
4. G
6. G
8. B
9. F
10. A
Page 235 Estimating Metric Measurements
1. B
3. A
5. C
7. D
9. D
11. A
13. B
2. A
4. D
6. A
8. C
10. B
12. C
14. C
Page 236 Converting Units within the Metric System
1. 0=035 g
8. 2=5 cg
15. 0=723 mm
2. 6> 000 m
9. 17> 500 mL
16. 3 L
3. 0=0215 L
10. 0=0042 kg
17. 5> 060 mg
4. 0=49 cm
11. 6 dL
18. 0=1058 cL
5. 5> 350> 000 mL
12. 41> 700 cg
19. 4=3 km
6. 0=0000321 kg
13. 0=182 L
20. 205=7 cm
7. 0=1564 km
14. 812 cm
21. 0=5643 kg
62
Chapter 20 Review
Page 237
1. pound
6. 4> 200
11. 0=12 km
16. 5> 000 mL
2. inches
7. 126
12. 9> 000 mg
17. 5 g
3. liters
8. 6=8
13. 20 L
18. 0=055 L
14. 0=0015 g
19. 0=3 m
4. milligrams
9.
5. 32
2 14
10. 0=00073
15. 150 mm
Chapter 21 Angles and Triangles
Page 239 Corresponding, Alternate Interior, and Alternate Exterior Angles
1. I
4. S
7. V
10. E
13. S
2. C
5. S
8. I
11. V
14. V
3. E
6. C
9. C
12. S
15. S
Page 241 Congruent Figures
1. congruent, all corresponding angles and sides are congruent
2. not congruent, corresponding angles are not congruent
3. congruent, all corresponding angles and sides are congruent
4. not congruent, corresponding angles are not congruent
5. not congruent, corresponding sides are not equal
6. not congruent, corresponding sides are not congruent
Page 242 Similar and Congruent
1. N
3. C
5. N
7. S
9. C
11. S
13. C
2. S
4. C
6. C
8. C
10. N
12. N
14. N
Page 244 Similar Triangles
1. 10
3. 9
5. 4
7. 12
2. 24
4. 8
6. 9
8. 12
Page 245 Pythagorean Theorem
1. 7=07
4. 8=06
7. 10=44
2. 8=94
5. 6=71
8. 9=90
3. 4=47
6. 6=40
9. 5=00
63
Page 246 Finding the Missing Leg of a Right Triangle
1. 12
4. 24
7. 4
2. 8
5. 60
s
6. 10 7
8. 36
3. 9
9. 84
Page 248 Applications of the Pythagorean Theorem
1. 70.71 feet
2. 258.14 feet
Page 250 Special Right Triangles
1. 8
2.
I
9 2
2
3. 7
s
4. 3
3. 41.23 yards
s
5. 3 3
4. 22.36 yards
9. d =
s
10. d = 2 3
s
11. d = 4 3
6. 10
7. d =
1
3
e=
8. d =
4
5
e=
I
2 2
3
I
3
3
I
4 2
5
12. d = 16
Page 252 Introduction to Trigonometric Ratios
1. sin D = 45 = 0=8
cos D = 35 = 0=6
tan D = 43 = 1=333
sin E = 35 = 0=6
cos E = 45 = 0=8
tan E = 34 = 0=75
2. sin D = 20
= 0=690
29
21
cos D = 29 = 0=724
= 0=952
tan D = 20
21
21
sin E = 29 = 0=724
= 0=690
cos E = 20
29
= 1=05
tan E = 21
20
9
3. sin D = 41
= 0=220
40
cos D = 41 = 0=976
9
= 0=225
tan D = 40
= 0=976
sin E = 40
41
9
cos E = 41 = 0=220
= 4=444
tan E = 40
9
64
8
4. sin D = 17
= 0=471
15
cos D = 17 = 0=882
8
tan D = 15
= 0=533
15
sin E = 17 = 0=882
8
cos E = 17
= 0=471
15
tan E = 8 = 1=875
5. sin D =
I
3 10
= 0=949
10
I
10
= 0=316
10
cos D =
tan D = I
3
sin E = 1010 = 0=316
I
cos E = 3 1010 = 0=949
tan E = 13 = 0=333
6. sin D =
cos D =
I
3
= 0=866
2
1
= 0=5
2
s
tan D = 3 = 1=732
sin E = 12 = 0=5
cos E =
tan E =
I
3
2
I
3
3
= 0=866
= 1=732
e=
I
2 2
3
e=3
s
e=8 3
s
e=8 2
Page 253 Introduction to Trigonometric Ratios
1. 24
6. 180
11. 45
2. 45
7. 37 or 323
12. 84
3. 44
8. 90
13. 0
4. 45
9. 69
14. 114
10. 89
15. 90
5. 56 or 304
Page 253 Introduction to Trigonometric Ratios
1. sin D = 0=766
cos D = 0=643
tan D = 1=192
sin E = 0=643
cos E = 0=766
tan E = 0=839
3. sin D = 0=208
cos D = 0=978
tan D = 0=213
sin E = 0=978
cos E = 0=208
tan E = 4=705
5. sin D = 0=951
cos D = 0=309
tan D = 3=078
sin E = 0=309
cos E = 0=951
tan E = 0=325
2. sin D = 0=707
cos D = 0=707
tan D = 1=000
sin E = 0=707
cos E = 0=707
tan E = 1=000
4. sin D = 0=469
cos D = 0=883
tan D = 0=532
sin E = 0=883
cos E = 0=469
tan E = 1=881
6. sin D = 0=809
cos D = 0=588
tan D = 1=376
sin E = 0=588
cos E = 0=809
tan E = 0=727
Page 254 Introduction to Trigonometric Ratios
1. _E = 45
e = 14=142
f = 10
3. _E = 60
e = 13=856
f = 16
5. _D = 80
d = 4=924
e = 0=868
2. _D = 50
e = 16=782
f = 26=108
4. _D = 77=5
d = 4=511
f = 4=620
6. _E = 40
d = 6=500
e = 5=454
Page 255 Introduction to Trigonometric Ratios
1. { = 232=992 ft
| = 199=714 ft
2. 0.911
3. 27.181
65
Chapter 21 Review
Pages 256–257
1. 48
13. C
2. 4 cm
14. S
3. 7.81
15. V
4. 12
16. S
5. 5
17. S
6. 30
18. E
7. 45 or 315
19. S
8. _E = 51 , e = 3=705, f = 4=767
20. I
9. _E = 45 , d = 6, f = 8=485
21. S
10.(A) 1.265 mi
(B) 18.435
22. I
23. C
11. g = 437 yards
24. C
12. V
25. V
Chapter 22 Plane Geometry
Page 259 Perimeter
1. 26 in
2. 17 ft
3. 168 cm
4. 38 cm
5. 44 in
6. 32 in
Page 260 Area of Squares and Rectangles
1. 100 ft2
3. 36 in2
5. 36 ft2
7. 8 ft2
2. 10 cm2
4. 180 in2
6. 50 cm2
8. 40 in2
9. 144 ft2
10. 84 cm2
11. 8 ft2
12. 42 cm2
Page 261 Area of Triangles
1. 6 in2
3. 21 ft2
5. 3 ft2
7. 52.5 m2
9. 2 ft2
11. 75 ft2
2. 36 cm2
4. 72 cm2
6. 160 cm2
8. 31.5 in2
10. 12 ft2
12. 15 m2
Page 262 Area of Trapezoids and Parallelograms
1. 132 in
4. 170 cm
7. 78 in
2. 48 in
5. 154 in
8. 120 cm
3. 18 in
6. 60 cm
9. 56 cm
66
Page 263 Area of a Rhombus or a Kite
1. 42 in2
3. 52=5 ft2
5. 49 in2
7. 50 in2
2. 15 cm2
4. 4 ft2
6. 17=5 in2
8. 6 ft2
9. 400 ft2
10. 9=375 ft2
Page 264 Area of Polygons
1. 48 in2
4. 120 ft2
7. 84 in2
2. 60 ft2
5. 800 cm2
8. 2> 250 ft2
3. 87=5 cm2
6. 1=28 in2
9. 52=5 ft2
Page 265 Parts of a Circle
Note: A line segment named as DE can also be correctly named as ED, an angle named as _DEF
can also be correctly named as _FED, and an arc named as DEF can also be corrected named as
FED. The answers below give only one of the two possible names for each question.
1. W V and VU
2. ]VU
Page 267 Central Angles
1. blue
108
red
90
yellow
36
green
126
3. S
2.
blue
108°
red
90° green
126°
4. _W VU
5. _\ S ]
5. 90
yellow
36°
6. 60
7. 180
3. Mr. Perry
Mrs. Nance
Miss Murphy
Mr. Bard
Mr. Olson
All Others
35%
25%
20%
12%
5%
3%
126
90
72
43.2
18
10.8
4. Mr. Perry
Mrs. Nance
Miss Murphy
Mr. Bard
Mr. Olson
All Others
8. 270
9. 30
10. 60
Page 268 Arc Lengths
1. 37
2. 26
3. 26
5. 180
4. 117
6. 243
7. 180
9. 45
11. 65
13. 180
8. 154
10. 25
12. 90
14. 90
15. 90
16. 140
Page 269 Circumference
1. 50.24 in
3. 6.28 cm
5. 25.12 ft
7. 37 57 in
2. 43.96 ft
4. 37.68 m
6. 18 67 ft
8. 18 67 m
9. 31 37 cm
10. 50 27 in
67
Page 270 Area of a Circle
1. 78.5 in2 , 78 47 in2
7. 16 cm, 200.96 cm2 , 201 17 cm2
2. 200.96 ft2 , 201 17 ft2
8. 10 ft, 314 ft2 , 314 27 ft2
3. 50.24 cm2 , 50 27 cm2
9. 28 m, 615.44 m2 , 616 m2
4. 28.26 m2 , 28 27 m2
10. 9 cm, 254.34 cm2 , 254 47 cm2
5. 18 ft, 254.34 ft2 , 254 47 ft2
11. 24 ft, 452.16 ft2 , 452 47 ft2
6. 2 in, 12.56 in2 , 12 47 in2
12. 3 in, 28.26 in2 , 28 27 in2
Page 271 Area of Sectors
1.
1
12
5.
1
8
9.
1
24
13. 7.85 cm2
2.
1
180
6.
1
5
10.
3
10
14. 65.4 in2
3.
2
45
7.
1
3
11.
1
6
15. 56.52 cm2
4.
13
90
8.
3
4
12.
1
4
16. 3.49 ft2
Page 273 Two-Step Area Problems
1. 525 ft2
3. 452 cm2
5. 422 in2
7. 2,500 cm2
2. 112 in2
4. 73 ft2
6. 12.5 m2
8. 216 m2
Page 275 Geometric Relationships of Plane Figures
1. 4 times larger
3. 4 times larger
5. 25
7. 8
2. 2 times larger
4. 9 times larger
6. 3{
8. 2 in by 2 in
Chapter 22 Review
Page 276
1. 170 in2
6. 60, 45
2. 20 in
7. 66 cm2
3. S = 16 ft, D = 12 ft2
8. F = 44 cm, D = 154 cm2
#
\$
9. D
4. F = 6=28 ft, D = 3=14 ft2
5. 64 in2
68
10. 4 times larger
Chapter 23 Solid Geometry
Page 278 Volume of Rectangular Prisms and Cubes
1. 72 ft3
4. 1,200 m3
7. 675 in3
2. 1,872 mm3
5. 90 ft3
8. 343 in3
3. 240 cm3
6. 4,480 in3
9. 64 ft3
Page 280 Volume of Spheres, Cones, Cylinders, and Pyramids
1. 401.92 in3
3. 523.33 m3
5. 126 m3
7. 33.49 m3
2. 18 cm3
4. 33.49 ft3
6. 188.4 mm3
8. 160 in3
9. 1,469.52 m3
10. 27 ft3
Page 281 Two-Step Volume Problems
1. 1,536 in3
3. 4,383 cm3
5. 165 cm3
2. 297 in3
4. 175.84 in3
6. 932.58 m3
Page 283 Surface Area of Cubes and Rectangular Prisms
1. 24 ft2
3. 30 m2
5. 176 ft2
7. 280 in2
9. 150 m2
2. 610 cm2
4. 294 mm2
6. 258 cm2
8. 136 ft2
10. 356 cm2
Page 284 Surface Area of Pyramids
1. 16 ft2
4. 176 cm2
7. 88 m2
2. 180 mm2
5. 33 m2
8. 125 in2
3. 400 m2
6. 261 in2
9. 8.75 ft
Page 285 Surface Area of Cylinders
1. 87.92 m2
4. 75.36 in2
7. 351.68 ft2
2. 351.68 ft2
5. 175.85 ft2
8. 282.6 cm2
3. 226.08 cm2
6. 1,381.6 m2
9. 31.4 m2
Page 286 Surface Area of Spheres
1. 50.24 in2
4. 200.96 cm2
7. 615.44 cm2
10. 1.4 ft2
2. 452.16 m2
5. 7,850 mm2
8. 0.502 km2
11. 1,256 mm2
3. 7.065 yd2
6. 0.785 ft2
9. 28.26 in2
12. 78.5 yd2
69
Page 286 Surface Area of Cones
1. 15.7 cm2
3. 2,703.54 mm2
5. 176.63 ft2
2. 68.69 in2
4. 264.61 yd2
6. 56.52 m2
Page 291 Using Nets To Find Surface Area
1. 54 in2
3. 502.4 cm2
5. 17.53 cm2
2. 131 cm2
4. 518 ft2
6. 15.072 cm2
Page 292 Solid Geometry Word Problems
1. Y = 25> 000> 000 yd3
2. Y = 9=42 ft3
3. Y = 7> 234=56 cm3
4. Y = 5=23 in3
7. VD = 207=24 ft2
5. Y = 5> 184 in3
8. VD = 756 cm2
6. VD = 250 cm2
9. VD = 24 ft2 , Y = 8 ft3
Page 294 Front, Top, Side, and Corner Views of Solids Objects
4.
1. B
2. C
3. A
Chapter 23 Review
Pages 295–296
1. Y = 18 cm3 , VD = 42 cm2
10. 64 in3
2. Y = 3> 080 in3 , VD = 1> 188 in2
11. 50.24 in3
3. Y = 48 m3 , VD = 96 m2
12. 2,750 ft3
4. Y = 56=52 ft3
13. 2,200 cm2
5. 56 m3
14. 52 ft2
6. 1,437 13 in3 , VD = 616 in2
15. 1,728 one-inch cubes
3
7. 36,000 in
16. 80 in3
8. 512
17. 1,518 m3
9. 8 times larger
18.
Front
70
Side
Top
Chapter 24 Transformations
Page 298 Drawing Geometric Figures on a Cartesian Coordinate Plane
1. D = (1> 1)
E = (2> 4)
F = (2> 2)
G = (2> 0)
2. H = (6> 2)
I = (3> 2)
J = (3> 4)
K = (6> 4)
3. L = (3> 5)
M = (5> 1)
N = (6> 7)
5. S = (5> 3)
T = (0> 0)
U = (0> 3)
4. O = (6> 6)
P = (1> 6)
Q = (2> 3)
R = (3> 3)
6. V = (1> 7)
W = (0> 5)
Y = (2> 4)
[ = (4> 5)
\ = (3> 7)
Page 299 More Drawing Geometric Figures on a Cartesian Coordinate Plane
1. square
3. parallelogram
5. pentagon
7. triangle
2. isosceles triangle
4. right triangle
6. square
8. rectangle
Pages 301–302 Reﬂections
y
B
1. A´ = (4> 2) B´ = (2> 4) C´ = (0> 4)
2. A´´ = (4> 2) B´´ = (2> 4) C´´ = (0> 4)
5
C C''
4
p
B''
3
A
A''
2
1
−5 −4 −3 −2 −1 0
1
2
C''' x
4 5
3
−1
A'
B'''
−2
3. A´´´ = (2> 4) B´´´ = (4> 2) C´´´ = (4> 0)
C' −3
B'
−4 A'''
−5
s
y
5
F'
D'
4
F
4. D´ = (2> 3) F´ = (3> 4) G´ = (4> 1) H´ = (2> 1)
D
3
2
H'
G'
1
−5 −4 −3 −2 −1 0
D'''
F'''
H''' −1
−2
−3
G''' −4
H
1 2
H''
G
3
4
G''
D''
5
x
5. D´´ = (2> 3) F´´ = (3> 4) G´´ = (4> 1) H´´ = (2> 1)
6. D´´´ = (3> 2) F´´´ = (4> 3) G´´´ = (1> 4) H´´´ = (1> 2)
F''
−5
y
7. M´ = (3> 4) N´ = (1> 2) O´ = (1> 1) P´ = (4> 3)
8. M´´ = (3> 4) N´´ = (1> 2) O´´ = (1> 1) P´´ = (4> 3)
9. M´´´ = (4> 3) N´´´ = (2> 1) O´´´ = (1> 1) P´´´ = (3> 4)
5
M
P
N
3
2
P'
N'
O 1
O'
−5 −4 −3 −2 −1 0 1
O'''
O'' −1
2 3
N'''
N'' −2
P''
−4
4
5
x
M'''
−3
M''
w
M'
4
P'''
−5
71
Page 304 Translations
y
A
B A'
D
5
4
C
D' 2
C'
1
A''
A'''
−5 −4 −3 −2 −1 0 1
B''
1. A´ = (1> 4) B´ = (2> 3) C´ = (2> 1) D´ = (0> 2)
B'
3
2
3 4s5
B'''
−1
2. A´´ = (5> 0) B´´ = (2> 1) C´´ = (2> 3) D´´ = (4> 2)
x
3. A´´´ = (0> 0) B´´´ = (3> 1) C´´´ = (3> 3) D´´´ = (1> 2)
−2 D'''
D''
C''
−3
C'''
−4
y
−5
5
4
4. F´ = (5> 1) G´ = (3> 2) H´ = (2> 1)
F'' 2
F'
5. F´´ = (0> 2) G´´ = (2> 3) H´´ = (3> 0)
G''
3
G'
1
−5 −4 −3 −2 −1 0
H'
1
−1
2
H''
3 4
G
F
−2
−3
H
−4
−5
Page 305 Rotations
1. A´ = (1> 1)
B´ = (4> 4)
C´ = (2> 4)
D´ = (1> 2)
2. A´´ = (1> 1)
B´´ = (4> 4)
C´´ = (4> 2)
D´´ = (2> 1)
3. A´´´ = (1> 1)
B´´´ = (4> 4)
C´´´ = (2> 4)
D´´´ = (1> 2)
y
B'''
5
C'''
B
4
D'''
A'''
3
C
2
1A
−5 −4 −3 −2 −1 0 1
A'
D''
A'' −1
C''
−2
D'
−3
−4
B''
D
2
3
4s5
x
B'
C'
−5
y
5
4
M'
3
M
N2
1
N'''
−5 −4 −3 −2 −1O 0
1
N'
2
3
4
5
x
4. M´ = (2> 3)
N´ = (1> 0)
5. M´´ = (3> 2)
N´´ = (0> 1)
6. M´´´ = (2> 3)
N´´´ = (1> 0)
N'' −1
−2
M'''
M''
−3
−4
−5
Page 306 Transformation Practice
1. A´ = (4> 3)
B´ = (4> 4)
C´ = (2> 4)
D´ = (2> 2)
2. A´´ = (2> 1)
B´´ = (3> 1)
C´´ = (3> 3)
D´´ = (1> 3)
3. A´´´ = (2> 1)
B´´´ = (1> 1)
C´´´ = (1> 1)
D´´´ = (3> 1)
72
y
B' m
C'
A'
5
4
3
D'
B
2A
C'''
1
C
D
D'''
−5 −4 −3 −2 −1 0 1 2 3
A''
B''
−1 B''' A'''
−2
C''
D'’ −3
−4
−5
4
5
x
5
x
Page 307 Dilations
C
Page 308 Dilations
1. A´ = (12> 4) B´ = (4> 16)
C´ = (4> 16) D´ = (12> 4)
4. A´ = (2> 14) B´ = (2> 14)
C´ = (10> 10) D´ = (10> 1)
E´ = (2> 6) F´ = (2> 6)
G´ = (10> 1) H´ = (10> 10)
y
B′
C′
16
14
12
10
8
6
B 4C
A′
y
A′
D′
D
A
-16-14 -12
8 10 12 14 16
H′
x
A
-2
G′
B′
C′
8B
6
4
H
¡
¢
¡ ¢
2. A´ = ¡ 2> 53¢ B´ = ¡1> 53
¢
C´ = 1> 43 D´ = 2> 43
A
14
12
10
D
G
F′
x
E
E′
¡
¢
¡
¢
1
1
5. A´ = ¡ 12> 10
B´
=
6>
10
¢2
¡
¢ 2
C´ = 3> 4 12 D´ = 9> 4 12
y
B′
B′
A′
C′
D′
D′
8 10
-2
F
B
A′
C
B
A
D
C
D′
D
10
8
6
C′
4
C
-12
8
x
-2
3. A´ = ¡(8> 0)
¢ B´ = (0> 8)
C´ = 6 25 > 4
6. A´ = (2> 6) B´ = (3> 1) C´ = (7> 1)
y
B
B′
A
10
8
6
4
C′
C
A′
8 10
A A′
x
-2
C
9.
y
7. 3.5
A′
8
6
4
A
B′
B
C
C′
A
B′ B
B
y
11. Not a dilation
B′
8 10
D
2
3
C′
x
B′
A′
A′
A
-2C
B
8
6
4
C′
-2
C
8 10
D′
D
D′
8.
1
3
C′
y
10. 5
A′
24
22
20
A
B′
A′
C′
C
A′
18
16
F′
A
D′
E′
-14 -12
F
E -2
14
12
10
8
6
4
0
y
12. Not a dilation
B′
30
28
26
B
A 8
6
4
B′
B
C′
B
C
D
D′
D′
8 10 12 14
D
-2
C′
x
C
x
D
73
x
Chapter 24 Review
Pages 309–310
10. (4> 5)
y
1.
C 5C'
4
B
11. (4> 2)
B'
12. (3> 2)
3
2
13. A
1
D
−5 −4 −3 −2 −1 0
A
D'
1 2
3
A'
x
4 5
14. (6> 8), (12> 20), (6> 10)
¢
¡ ¢ ¡ ¢ ¡
15. 3> 52 , 2> 52 , 32 > 72
¡
¢ ¡
¢ ¡ 9 9¢ ¡
¢
16. 12> 21
, 3> 21
, 2 > 2 , 9> 92
2
2
2. (4> 0)
3. (3> 4)
17. (4> 4)
4. (0> 4)
18. (4> 2)
5. (2> 0)
6.
y
10
9
19. (1> 2)
P
8
S
7
6
5
4
20. (2> 2)
Q
22. (1> 3)
Q'
P'
U
21. (1> 2)
R
T
S'
U'
T'
23. (2> 3)
R'
24. see graph below
3
2
25. see graph below
1
0
1
2
3
4
5 6
7
8
9 10
26. see graph below
x
7. (3> 6)
27. see graph below
8. (6> 6)
28. parallelogram
9. (6> 5)
y
4
3
2
1
−4 −3 −2 −1 0
−1
−2
−3
74
24.
H
1
25.
I
2
27.
K
3
4
26.
J
x
Practice Test 1
Pages 313–330
Segment 1
1. A
3. D
5. A
7. D
9. B
11. C
13. B
15. A
17. C
19. D
2. D
4. C
6. D
8. A
10. D
12. D
14. D
16. B
18. C
20. F = g = 3=14 × 36 = 113=04
There are 24 panels, so the entire circumference of 113=04 feet is divided into 24 arcs with a
length of 113=4
= 4=71 feet.
24
The length of the arc is 4=71 feet.
Segment 2
21. D
23. B
25. D
27. B
29. D
31. D
33. B
35. C
37. C
22. C
26. A
28. A
30. D
32. D
34. D
36. B
38. 17
24. C
39.(A) 3{ + 5| = 736
{ + | = 190
(B) 3{ + 5| = 736 \$
3{ + 5|
{ + | = 190
3{ 3|
0{ + 2|
2|
|
{ = 107 and | = 83
=
736 \$ { + |
{ + 83
= 570
{
=
166
{
=
166
=
83
=
=
=
=
190
190
190 83
107
40.(A) The median speed is 20 mph, the middle point on the box-and-whisker plot. The range is
39 10 = 29 mph, the difference between the highest and lowest recorded speeds.
(B) Three of the four quartiles are to the right of 15, so 34 or 75% of the drivers exceeded the 15
mph speed limit.
(C) Since 20 mph is the median speed, approximately half of the 36 drivers would be
expected to be driving 20 mph or faster. The expected number of tickets issued would be
36 ÷ 2 = 18. The approximate expected number of warning tickets issued is 18.
Segment 3
41. B
43. B
45. D
47. C
49. C
51. A
53. C
55. B
57. D
42. C
46. D
48. B
50. C
52. B
54. B
56. A
58. C
44. A
59. 70
y
60.(A)
Perimeter
10
8
6
4
2
0
1
(B) slope = 3
2
3
4
5
x
Length
75
Segment 4
61. D
64. B
67. D
70. B
73. B
76. C
79. C
82. D
62. B
65. C
68. B
71. C
74. A
77. D
80. B
83. A
63. C
66. D
69. A
72. C
75. B
78. D
81. B
84.
11
50
85.(A) To ﬁnd the image of the points, multiply the { and |-coordinates by the scale factor 2.
y
(B)
A′ (-4, 8)
F
A (-2, 4)
F
C (-4, -1)
C′ (-8, -2)
8
7
6
5
4
3
2
1
B (2, 1)
x
-1
-2
-3
-4
-5
-6
-7
Practice Test 2
Pages 331–349
Segment 1
1. A
3. D
5. B
7. A
9. C
11. B
13. B
15. B
17. B
2. B
4. D
6. D
8. B
10. D
12. D
14. C
16. D
18. A
19. A
20.(A) Y = 13 ozk
(B) Y = 13 (4) (4) (2) = 10 23 cubic yards
Segment 2
21. B
23. A
25. A
27. B
29. D
31. B
33. D
35. C
37. A
22. A
24. C
26. A
28. A
30. B
32. C
34. B
36. B
38. 2
Number
of words
610
Number
Words per
of minutes minute
53
11.5
40.(A)
76
Week
Number
1
2
890
53
3
810
42
4
770
32
5
1420
46
6
1490
42
16.8
16.8
19.3
19.3
24.1
24.1
30.9
30.9
35.5
35.5
39.
30%
(B)
Typing Rate
50
40
30
20
10
&
&
& &
&
&
0
Week Number
(C) week 8
Segment 3
41. A
43. B
45. C
47. A
49. A
51. C
53. C
55. C
57. A
42. B
44. C
46. D
48. B
50. C
52. A
54. A
56. B
58. 44
59.(A) slope =
(B)
3
4
and |-intercept = (0> 3)
y
5
4
3
2
1
−5 −4 −3 −2 −1 0
1
2
3
4
5
x
−1
−2
−3
−4
−5
60. Since there are 360 degrees in an entire circle, there is
1
× 360 = 72
5
Measure of _S = 72
1
5
of 360 degrees in
1
5
of a circle.
Segment 4
61. B
64. D
67. B
70. C
73. B
76. C
79. B
82. A
62. C
65. A
68. B
71. C
74. C
77. C
80. C
83. D
63. C
66. C
69. C
72. A
75. C
78. A
81. B
84. A
85. Krista’s claim is not valid. Although only 9 of the units she assembled were defective, she
assembled fewer units than each of the other workers. Approximately 7% of the units Krista
assembled were defective, whereas only about 5% of the other workers’ units were defective.
77
78
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