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Chapter 6
1. Graph the system and determine the number of solutions that it has. If it has one
solution, name it. 6.1
x–y=3
2x – y = -1
2. Alexis buys pizza and soda for ski club meetings. For the first meeting, she bought 4 pizzas and 10
sodas for $63. For the second meeting, she bought 3 pizzas and 8 sodas for $48. What is the cost of one
pizza? 6.1
3. Use the graph at the right to determine whether each
system is consistent or inconsistent and if it is independent
or dependent. 6.1
a. y = 2x + 2
y = 2x – 5
b. y = 2x – 5
4x - 2y = 10
4. Use substitution to solve the system of equations. 6.2
2x – y = -3
x = 2y
5. Use substitution to solve the system of equations. 6.2
y = -x + 3
2x + 2y = 6
6. Use elimination to solve the system of equations. 6.3
7a + 3b = 3
2a + 3b = 18
7. Use elimination to solve the system of equations. 6.4
5x – 7y = -2
-4x + 6y = 4
8. A boat travels 32 miles with the wind in 3 hours. The return trip into the wind took 4 hours. Find
the rate of the boat when there is no wind. 6.4
9. Selena rode her bike 7 more miles yesterday than she did today. She rode her bike a total
of 23 miles yesterday and today. How many miles did she ride her bike each day? 6.4
10. Determine the best method to solve the system of equations. Then solve the system. 6.5
3x + 3y = 15
4x + 3y = 18
-21
11. Find each sum for X =  15

 54
11 
31 -13  , and Z =
23  , Y = 13
0 
18 14
41
14
 -3

 28
11 
25  . If the sum does not
17 
exist, write impossible. 6.6
a. X + Y
b. X + Z
 0 -7 11


12. Find each difference for L = 21 3 41 , M =


 4 34 8 
difference does not exist, write impossible. 6.6
a. M – L
b. N – M
 7 -6 9 
19 5 22 , and N =


 -3 4 13 
14
12

 6
-3 
11 . If the
17 
 4 -10 
 , find –2J. 6.6
14 17 
13. If J = 
14. Use an augmented matrix to solve the system of equations. 6.7
4x + y = 17
–x – 2y = 8
15. Solve the system of inequalities by graphing. 6.8
y1
3x + y < -1
16. Solve the system of inequalities by graphing. 6.8
2x + y > 1
y  -2x – 2
17. For a child to be allowed to ride the Wild Slide Ride at an amusement park, the
child must be 5 to 9 years old, and be 30 to 50 inches in height. 6.8
a. Define the variables, and write a system of inequalities to represent this
situation. Then graph the system.
b. Name one possible solution.
Chapter 7
18. Determine whether each expression is a monomial. Write yes or no. Explain
your reasoning. 7.1
a. 6m
b.
3a
b
19. Simplify each expression. 7.1
a. (3a2)(-2a9)
b. (8r2s7)(6r3s2)
20. Simplify [(32)4]2. 7.1
21. Express the area of the circle as a monomial. 7.1
22. Simplify (-4c2d)3[(2c3d)4]2.
23. Simplify
7.1
x6y2z3
. Assume that no denominator equals zero. 7.2
x4yz
2
 3m 2 n 
24. Simplify 
 . Assume that the denominator does not equal zero. 7.2
p 

25. Simplify each expression. Assume that no denominator equals zero. 7.2
a. (16g2h3)0
b.
b2c0d5
bd2
26. Simplify each expression. Assume that no denominator equals zero. 7.2
a.
w 3 y 8
x 2
 2c 3 d  2
b.
12c 4d 6
c.
4 x 3 yz 5
16 xy 4 z 5
27. Express each number in scientific notation. 7.3
a. 0.000501
b. 162.1
28. Express each number in standard form. 7.3
a. 1  106
b. 8.31  10-3
29. Evaluate (4.1  10-5)(8.2  10-2). Express the result in both scientific notation and
standard form. 7.3
30. Evaluate
5.612  10 7
. Express the result in both scientific notation and standard form. 7.4
3.68  10 6
31. Find the sum. 7.5
(r2 + 11 + 7r) + (–2r + 10 + 8r2)
32. Find the difference. 7.5
(n3 + 3n – 9) – (n – 2n3 + 1)
33. Find 3x(2x2 + 8x – 1). 7.6
34. Simplify 5b(2b – 4) + 4(b2 – 6b – 3). 7.6
35. Find the product. 7.7
(3c – 1)(c + 2)
36. Find each product. 7.7
a. (x – 9)(x – 2)
b. (3a – 5)(5a – 2)
37. Find (r + 11)2. 7.8
38. Find (3s – t)2. 7.8
39. Find the area of the square at the right. Then, determine what
happens to the area of the square when the length of each side is
doubled. 7.8
a+b
a+b
40 .Find (10a2 + 3b2)(10a2 – 3b2).
7.8
Chapter 8
41. Factor –21xy4 completely. 8.1
42. Find the GCF of 25ab2c and 45ab.
8.1
43. Use the Distributive Property to factor the polynomial. 8.2
64r3s – 32r2s3 + 8r2s2
44. Factor 3a2 – 3a + 4 – 4a.
8.2
45. Solve each equation. Check your solutions. 8.2
a. (q + 2)(2q – 1) = 0
b. 3x2 + 9x = 0
46. Factor x2 + 16x + 63.
8.3
47. Factor x2 – 11x + 24.
8.3
48. Factor the polynomial. 8.3
x2 + x – 6
49. Solve x2 – 8x + 7 = 0. Check your solutions. 8.3
50. Factor 6x2 + 18x – 24.
8.4
51. Factor 3x2 – x + 1, if possible. If the polynomial cannot be factored using integers, write prime. 8.4
52. Factor each polynomial. 8.5
a. 64m2 – n2
b. 5x2y – 500y
53. Factor each polynomial. 8.5
a. 16 – m4
b. 256x4 – 1
54. Factor each polynomial. 8.5
a. 4w4 – 144
b. 2a3 – 10a2 – 8a + 40
55. In the equation x3 + 2x2 – x – 2 = y, which is a value of x when y = 0? 8.5
1
A) –1 B) 0 C) 2 D) 3
56. Factor x3 + 2x2 – x – 2. Then find the values of x. 8.5
57. Determine whether the trinomial is a perfect square trinomial. Write yes or no. If
so, factor it. 8.6
25n2 – 10n + 1
58. Factor the polynomial, if possible. If the polynomial cannot be factored, write prime. 8.6
3x2 – 12x + 12
59. Solve 16x2 + 8x + 1 = 0.
8.6
60. Solve the equation. Check the solutions. 8.6
(x + 1)2 = 10
Chapter 9
61. Use a table of values to graph y = x2 + 6x + 8. State the domain and range. 9.1
x
-6
-5
-4
-3
-2
-1
0
y
8
3
0
-1
0
3
8
62. Find the vertex, the equation of the axis of symmetry, and the y-intercept of the graph. 9.1
63. Find the vertex, the equation of the axis of symmetry, and the y-intercept of the function. 9.1
y = x2 – 6x + 3
64. Consider f(x) = x2 – 2x + 5. 9.1
a. Determine whether the function has a maximum or minimum value.
b. State the maximum or minimum value of the function.
c. State the domain and range of the function.
65. Graph y = x2 + 8x + 12.
9.1
66. Solve x2 + 8x + 12 = 0 by graphing. 9.2
67. Solve -2x2 + 3x – 4 = 0 by graphing. 9.2
68. Describe how the graph of each function is related to the graph of f(x) = x2.
a. g(x) = 1 + x2
b. h(x) = x2 – 7
y
g(x)
9.3
y
f(x)
f(x)
h(x)
69. Describe how the graph of each function is related to the graph of f(x) = x2.
a. g(x) = 4x2
y
9.3
1
b. h(x) = x2 – 3
2
y
70. Describe how the graph of g(x) = -x2 + 2 is related to the graph of f(x) = x2.
y
9.3
71. Find the value of c that makes x2 – 8x + c a perfect square trinomial. 9.4
72. Solve x2 + 4x + 5 = 0 by completing the square. 9.4
73. Solve 4x2 + 6 = 25x by using the Quadratic Formula. Round to the nearest tenth if
necessary. 9.5
74. Solve x 2 + 12x = -20.
9.5
75. State the value of the discriminant of 4x2 + 1 = –4x. Then determine the
number of real solutions of the equation. 9.5
76. Graph y = 5x. State the y-intercept. Find the y-intercept, and state the domain
and range. 9.6
77. Determine whether the set of data shown below displays exponential behavior. Write yes or no.
Explain why or why not. 9.6
0
1
2
3
4
5
x
y
50
46
42
38
34
30
78. In 1990, the population of Idaho was 1,006,749. Since then, that number has increased an average
of 2.85% per year. 9.7
a. Write an equation to represent the population of Idaho since 1990.
b. According to the equation, what was the population of Idaho in 2000?
79. Anna’s parents plan to invest $4,000 in an account for her with an interest rate of 9%
compounded monthly for 5 years. How much money will be in Anna’s account? 9.7
80. Determine whether the sequence is arithmetic, geometric, or neither. Explain. 9.8
6, 24, 96, 384, …
81. Find the next three terms in the geometric sequence. 9.8
–64, 32, –16, 8, …
82. Write an equation for the nth term of the geometric sequence 2, 6, 18, 54, …
9.8
83. Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a
quadratic function, or an exponential function. 9.9
a. (-6, 5), (-3, 4), (0, 3), (3, 2), (6, 1)
b. (-2, -4), (-1, 0), (0, 1), (1, 0), (2, -4)
c. (-2, 0.06), (-1, 0.25), (0, 1), (1, 4), (2, 16)
84. Determine which model best describes the data. Then
write an equation for the function that models the data. 9.9
x
y
–2
–3
–1
–1
0
1
1
3
2
5
Chapter 10
85. Graph f(x) = 8 x. State the domain and range. 10.1
86. Graph y = -6 x, and compare to the parent graph. State the domain and range. 10.1
87. Graph the function, and compare to the parent graph. State the domain and range. 10.1
h(x) = x + 6
88. Graph y = 3 x – 2, and compare to the parent graph. State the domain and range. 10.1
89. Simplify 124.
10.2
90. Simplify
5  18
10.2
91. Simplify
27a 5bc 2
10.2
92. Simplify
5
2 2+3
10.2
93. Simplify each expression. 10.3
a. -3 3 – 3 + 8 3
b. 7 11 – 4 3 + 6 11 – 2 3
94. Simplify -5 28 + 6 63 – 11 7
10.4
95, Simplify each expression. 10.3
5 2(3 3 - 2 2)
96. Solve
2x -3 – 2 = 7. Check your solution. 10.4
97. Solve
x+5 – 3 = x
10.4
98. Find the length of each missing side. If necessary, round to the nearest hundredth. 10.5
a.
c
12
b.
9
99. Determine whether 14, 15, and 19 can be sides of a right triangle. 10.5
100. Find the distance between the points at (–1, 5) and (8, –7). 10.6
101. Find the coordinates of the midpoint of the segment with endpoints at
(5, 0) and (–9, 6). 10.6
102. Determine whether the pair of triangles is
similar. Justify your answer. 10.7
14
22
28
21
33
42
103. Find the missing measures for the pair of similar
triangles. 10.7
104. Find the values of the three trigonometric ratios for angle A.
10.8
B
26
A
24
a
C
105. Find mT to the nearest degree. 10.8
Chapter 11
106. Determine whether each table or equation represents an inverse or a direct
variation. Explain. 11.1
a.
x
1
2
3
y
4
8
12
b.
xy
=1
3
107. Assume that y varies inversely as x. If y = –6 when x = 3, write an inverse
variation equation that relates x and y. 11.1
108. Assume that y varies inversely as x. If y = 7 when x = 24, find y when x = 10.
11.1
109. Graph an inverse variation in which y varies inversely as x and y = -1.5 when x = 40. 11.1
110. State the excluded value for each function. 11.2
a. y =
8
3x
b. y =
6
x–2
c. y =
–7
2x + 10
111. Identify the asymptotes of the function. Then graph the function. 11.2
y=
2
x–1
112. State the excluded value of the expression. 11.3
-b
b 2 -9
113. Find the roots of f(x) =
x2 – 8x – 7
x+2
11.3
When x = 1 or x = 7, the numerator becomes 0, so f(x) = 0. Therefore, the roots of the function are 1
and 7.
114. Find each product. 11.4
2x 3 y
7z
a.

21z
10x 2
a 2 -a -2 a +3
b.

a +1
a +3
115. Find
2ab b

7
7
11.4
116. Find the quotient. 11.4
2x + 4 x + 2
x+1 ÷x+1
117. Find
k 2 -6k +5 k -5

k +1
k +1
11.4
118. Find the quotient. 11.5
(14a 2 – 7a + 21)  7a
119. Find (2r 2 – 5r + 3)  (r – 1) 11.5
120. Find (6x 2 + 5x – 3)  (3x + 1) by using long division. 11.5
121. Find (2x 3 - x 2 + 1)  (x + 1) 11.5
122. Find
x + 1 2x – 7
+
x–2 x–2
11.6
123. Find
1
3k -1
–
5-2k
2k -5
11.6
124. Find the LCM of the pair of polynomials. 11.6
21r 3 st and 12r 2 s 2
125. Find
4
x
+ 2
x -2x -3
x -9
126. Find
2
1
–
2r +14 r -3
2
127. Write
11.6
11.6
m-2
+ 1 as a rational expression. 11.7
5m
128. Simplify each expression. 11.7
a.
b.
a+7
b
a2 – 49
3b
x 2 -x
x 2 -x + 12
x -1
2x - 8
4
129. Solve m =
8
. Check the solution. 11.8
m–6
130. Solve p -
2p
6
=
p +3
p +3
11.8
Chapter 12
131. A shopping mall wants to know if they should put a movie theater in the mall. Every
hour, the mall manager questions 20 of the people coming into the mall. 12.1
a. Identify the sample, and suggest the population from which it was selected.
b. Classify the type of data collection used by the mall manager.
132. Identify each sample as biased or unbiased. Explain your reasoning. 12.1
a. A sub sandwich store owner wants to make sure that his employees are weighing the meat
correctly to put on the sandwiches. He watches the meat being weighed by one employee for one
hour during the day.
b. Every tenth student entering the school is surveyed to determine the favorite classes at school.
133. The heights of ten dogs in pounds are shown below. Which measure of central
tendency represents the data? Justify your answer. Then find the measure. 12.2
{22, 20, 23, 21, 24, 22, 24, 25, 20, 23}
134. Given the following portion of a survey report, evaluate the validity of the information
and conclusion. 12.2
Results
Question:
On what days most do you prefer to ice skate?
Sunday
8%
Sample:
On a Thursday, every 12th person that entered
Monday
0%
the ice skating rink was asked what days he or
Tuesday
12%
Wednesday
6%
she preferred to skate.
Thursday
31%
Conclusion: The rink should remain open on Thursdays.
Friday
Saturday
25%
18%
135. Identify the sample and the population for each situation. Then describe the sample
statistic and the population parameter. 12.3
a. At a tree farm, a randomly selected tree is measured to determine the height. Every 10th
tree in the rows of trees is measured. The median height of the trees is calculated.
b. A stratified random sample of amusement park employees is selected from an amusement
park. The mean number of hours worked per week is calculated for the sample.
136. Avery kept track of how much she spent on guinea pig supplies at each trip to the pet
store. She spent the following amounts, rounded to the nearest dollar: {$4, $12, $3, $5, $6}.
Find the mean absolute deviation. 12.3
137. Find the mean, variance, and standard deviation of {7, 8, 10, 15, 22}. 12.3
138. A cycling store has 8 new helmets. How many ways can 5 of the helmets be displayed in
the window? 12.4
139. A literature teacher needs to choose 6 books out of 12 for her literature class to read. The
12 books consist of 4 British literature, 5 contemporary literature, and 3 Western literature
books. How many different ways can the teacher choose 6 books? 12.4
140. A bag contains 12 marbles. Three are green, two are blue, 6 are yellow and 1 is red. Jama
chooses one marble, records the color, and places it back into the bag. She then chooses
another marble. Find the probability that Jama chooses a green marble each time. 12.5
141. There are 26 students in Mr. Collins’ English class. Twelve are seniors and fourteen are
juniors. Eight of the seniors are boys and six of the juniors are boys. What is the probability
that a randomly selected student is a boy or a senior? 12.5
142. A toothpick company wants to put 250 toothpicks into each box. However, the number of
toothpicks in each box varies from 248 to 252. Fifty boxes are taken off of the shelf and the
number of toothpicks is counted. The results are shown in the table. 12.6
Number of
Toothpicks
248
249
250
251
252
Number of
Boxes
5
13
22
3
7
a. Find the probability that a randomly chosen box has 250 toothpicks.
b. Find the probability that a randomly chosen box has at most 250 toothpicks.
143. Dillon divided a spinner into 4 equal parts. He colored each part a different color (red,
yellow, orange, and blue). He spun the spinner 20 times and recorded his results. He then
performed this experiment two more times. The results are shown in the table below. 12.7
Result
Red
Yellow
Orange
Blue
Experiment
#1
7
6
4
3
Experiment
#2
3
5
6
6
Experiment
#3
3
4
5
8
a. What is the experimental probability of spinning orange in the first experiment?
b. What is the experimental probability of spinning orange in all three tests?
144. A multiple-choice test that has 5 questions. Each question has 3 possible answers, A, B, or
C. Kelly would like to figure out the most likely mix of answers. Assume that P(A) = P(B) =
1
. 12.7
3
a. What objects can be used to model the possible outcomes of the answers?
P(C) =
b. Find the theoretical probability that there will be all A’s.
c. The results of a simulation Kelly performed are shown in
the table. What is the experimental probability that there
will be 4 B’s?
d. How does this compare to the theoretical probability of
there being 4 B’s?