Name_________________________ Algebra I
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Final Exam Review
3
1. Evaluate: c  d when c = 4 and d = -3
2. Evaluate: (a - b)2 when a = -6 and b = -4
3. Evaluate: (-2x)3 when x = -3
4. Evaluate: -2x3 when x = -3
2
5. Evaluate: 16  8  2
6  5  3  3
2
6. Evaluate:
1
 26  32
7. Evaluate: 2
2
8. Evaluate: 2.5 0.5  5
53  2
2
9. Evaluate: 1  6  8
10. Find your average speed traveled if you traveled 90 miles in 1 ¼ hours.
11. Solve: 5q - 2 = 3
12. Solve. 2t - 1 = -8
13. Solve: n2 = 144
10 
14. Solve:
x
 12
7
15. Solve and graph: 4p - 1 > 8
16. Solve and graph: r + 2r < -27
17. Text: pg. 59 #19 - 21
18. Evaluate:
4.5

19. Evaluate:
20. Evaluate:
3
5
6.1  6.01
21. In the game that decides the high school football championship, your team needs to gain
14 yards to score a touchdown and win. Your team’s final four plays result in a 9-yard
gain, a 5-yard loss, a 4-yard gain, and a 5-yard gain. Did you win? Write an arithmetic
expression for this problem.
22. A pizzeria charges $8 for a large pizza and $.85 for each additional topping. Write an
expression for the total cost C of a large pizza as a function of the number of additional
toppings, n. What is the cost for a large pizza with 3 additional toppings?
23. Simplify: 14 - 8 + 17 - (-23)
24. Simplify: -8.5 - 3.9 + (-16.2)
7  3 1
 
12
 4 8
25. Simplify:
1.2  1.5 9.2 
6.2
 2.5 4.4   6.6 2.2


 
3.4
5.8  5.7 7.1
26. Add:
3 
 4 1   6


0
13   5
8 

2
8   2
7 
27. Subtract: 
28. Simplify: (-4)(-x)(x)(-x)
29. Simplify: (-b2)(-b3)(-b4)
3
 ( w2 )(7 w)
30. Simplify: 7
3
31. Evaluate: 9r  (2r ) when r = 2
32. Use the distributive property to simplify: 5y(3y - 2)
3
2
33. Simplify:  x  2 x( x  x )
42t 6

34. Simplify: 14 z 7t
8  (91  13) 
35. Simplify:
4
7
36. Simplify: 8x + 7 - 2x – 3
1
x
37. Solve: 30 = 16 + 5
38. Solve: 17 = 2(3x + 1) – x
39. Solve: 9x - 5(3x - 12) = 30
40. What property of multiplication is illustrated by 3(-2)(4) = 3(4)(-2)?
41. What property of addition is illustrated by (2 + 4) + x = 2 + (4 + x)?
42. Solve. Round to two decimal places: 12.67 + 42.35x = 5.34x + 26.58
1
y  3  5 x
43. Rewrite the equation so that y is a function of x: 4
8
4
44. Find the quotient:  5
45. Determine the x- and y- intercepts of 2x - 3y = 9
46. Graph the linear equation 3x - 2y = 4.
2
x  3y  5
47. Write the equation 3
in standard form.
48. Write the equation of the line parallel to y = -2x +5 which passes through the point (3, 2). Put the equation in standard form.
49. Write the equation of the line that passes through the points (10, 50) and (20, 45).
50. Your job as a marketing manager for a toy store requires you to do some research. You
want to study how the amount spent on toys in the United States has been changing since
1990. You find that in 1991 the amount spent was $32.8 billion and in 1995 the amount
was $42.7 billion. Write a linear model for the amount spent on toys since 1990. Predict
how much money was spent on toys in 2000.
51. Graph: 2 - y < 3 + 2x
52. Graph: x  -2
53. Solve the system by graphing:2x - y = -2
4x - y = -6
54. Solve the system by substitution: 2c + d = -2
4c - d = 20
55. Solve the system by linear combinations (elimination): 2x - y = 3
4x + 3y =21
56. You exercised on a treadmill for 1.5 hours. You ran at 4 miles per hour and then you
sprinted at 6 miles per hour. If the treadmill monitor says that you ran and sprinted 7
miles, how long did you run at each speed? Write a system of equations for this
situation. Solve the system of equations.
57. Solve the system: -2x + 4y = 1
3x - 6y = 9
58. Graph the solution set: x > 1
x+y<6
y2
59. A carpenter is buying supplies for a job. The carpenter needs 4 sheets of oak paneling
and 2 sheets of shower tileboard. The carpenter pays $99.62 for these supplies. For the
next job the carpenter buys 12 sheets of oak paneling and 6 sheets of shower tileboard
and pays $298.86. Write a system of equations to determine the cost one sheet of the oak
paneling and one sheet of the tileboard. Solve the system.
9
4
60. Simplify. Leave the answer in exponent form: 5  5
61. Simplify: (-2m4n)3
3
2
62. Simplify: (2t ) (t )
0
63. Simplify: (3x)
 4 x 2 
 1 
2x 
64. Simplify: 
2
65. Graph: y = 5(2)x
66. Graph: y = -2x2 + 8x – 5
67. Graph: y = x2 + 5x – 24
68. Write in standard notation: 3.45 x 10-6
69. Write in scientific notation: 45,830,000
70. Solve: 3n2 = 27
71. Solve: 6x2 + 2x + 4 = 0
72. Solve: 2x2 - 3x - 5 = 0
73. How many solutions are there to the equation 4x2 + 20x + 25 = 0?
74. Graph the solution set: y > 2x2 - 3x + 5
75. Multiply: (3x - 4)(2x2 + 7x - 3)
76. Multiply: (4x - 5)2
77. Factor: 25x2 – 196
78. Factor: 2x2 - 12x + 18
79. Factor: x3 + 2x2 - 16x - 32
80. Factor: 4x2 + 44x + 121
81. Solve: x2 - 60 = -11
82. Solve: 2x2 + 15x - 8 = 0
83. Solve: 12x2 + 3x = 0
2 t 1

t
84. Solve: 3t
x 2  7 x  12
2
85. Simplify: x  3x  18
5 x 2  30 x  45
 (5 x  15)
x2
86. Simplify:
5
  20  8 x 
87. Simplify: 10  4 x
x
5
 2
88. Simplify: x  2 x  35 x  2 x  35
2
4x 1
x6
 2
89. Simplify: 3 x  8 x  5 3 x  8 x  5
2
90. What property is being illustrated?
(7  5)  4  7  (5  4)
91. Write an equation to represent the following statement: “The product of four and five
less than the number x is twenty-six.”
92. Solve: ( y  1)(3 y  4)  ( y  3)(3 y  2)  0
93. What is the degree of the polynomial -5x + 9?
4
3
4
3
94. Simplify: (2 j  2)  (9 j  3)  (6 j  j )
95. Henry has eight more nickels than quarters. The total value of the coins is $10. How
many of each does he have?
96. Solve: 3  3x 12  9
97. Solve:
4x  2  3
98. Simplify:
60  2
99. Simplify:
2
7
100. One number is three less than another number. If twice the smaller number is increased
by the larger number, the result is eighteen. What is the smaller number?
101. Ben is five years older than Jay. Four years ago, Ben was twice as old as Jay was .How
old is Ben?
102. Graph the inequality on a number line. x > -3
103. Graph the inequality on a number line. x< 8
104. Solve the inequality and graph on a number line. 3x + 2 < 17
105. Solve the inequality and graph on a number line. a + 3 < 10
106. Solve the inequality and graph on a number line. x - 3 < 1
107. Solve the inequality and graph on a number line. 2 - x > 5
108. Solve the inequality and graph on a number line. 6 < x + 4 < 11
109. Solve the inequality and graph on a number line. x + 4 < 2 or x - 4 > -1
110. Solve the inequality and graph on a number line. 5 < 3 - a < 12
111. Solve the inequality and graph on a number line.
y 7
.
112. Solve the inequality and graph on a number line.
113. Solve the inequality and graph on a number line.
114. Solve the inequality and graph on a number line.
2 x  4  12
x  6  5
y 5  2
115. Solve and graph the linear inequality. y  5
116. Solve and graph the linear inequality. 3  x  0
117. Solve and graph the linear inequality. y  4 x  2
118. Solve and graph the linear inequality.
y  2x  5
119. Solve and graph the linear inequality. x  3 y  6
120. Tickets for South Pacific cost $5.00 for adults and $4.00 for children. In order to cover
expenses, at least $2500.00 worth of tickets must be sold.
a) Write an inequality to describe this situation.
b) If 175 adult and 435 student tickets are sold, will they cover their expenses?
121. The school counselor tells you that you need to score a combined math (m)
Verbal (v) score of 1200 on the SAT Test to get into Loyola College. Write an
inequality to describe this situation.
then. How old is Ben now?