Name___________________________________
Algebra 1 – Semester 2 Final Review Packet
3
5
1. Simplify. Leave your answer in exponential form. 6 ( 6 )
15
[A] 6
[B] 128
8
[C] 36
8
[D] 6
[B] 45
[C] 4 36
[D] 4 6
2. Simplify: (42 )3
[A] 411
3. Simplify the product:  6xy 2   x3 y 
2
[A] 36x8 y 5
3
[B] 6x8 y 5
[C] 6x11 y 7
[D] 36x11 y 7
4. Sara bought 7 fish. Every month the number of fish she has doubles. After m months she will have F
fish, where F  7  2m . How many fish will Sara have after 2 months if she keeps all of them and the
fish stay healthy?
[A] 196
[B] 28
[C] 11
2
[B] x
[C]
[D] 20
5. Simplify: x 5 ( x)3
[A]
1
x15
1
x2
15
[D] x
2
3
0
6. Simplify: x  2 x 10 x
5
[A] 20x
[B] 1
[C] 0
7. Rewrite the expression using positive exponents.
[A]
1
9x 2 y
[B]
x2 y
9
510
8. Which is equivalent to 12 ?
5
1
1
[A] 2
[B] 2
5
5
[C]
9 x2 y
1
2
[C] 5
5
[D] 2x
1
2
9 x y 1
[D] 9x 2 y
22
[D] 5
20 x6 y 6
5 y 3 x7
9. Simplify:
[A] 4y 3 x
[B]
y3
4 x
[C]
74
.
75
1
[B]
7
4 y 3
x
[D]
x
4 y 3
10. Evaluate the expression
[A] 7
4
9
[C] 7
[D] 7 5
11. Write 0.0000656 in scientific notation.
[A] 656  107
[B] 0.656  104
12. Multiply: ( 2.5  10 )( 3.0  10
9
23
[A] 7.5  10
14
[C] 656  106
[D] 6.56  105
5
[C] 5.5  10
5
[D] 7.5  10
)
[B] 7.5  10
13. It is about 24,900 miles around the center of the Earth. If you were to take five trips around the
world about how many miles would you travel? Represent the amount in scientific notation.
4
[A] 2.5  10
3
[B] 5.0  10
25
[C] 2.5  10
5
[D] 1.2  10
14. In a certain country, the population is 4.5 million. 22,500 people have formed a new political party. If
a person is picked at random from the country, what is the probability that the person belongs to the
party? Express your answer in scientific notation.
11
[A] 1.00  10
15. Simplify:
[C] 500
.  103
1
[A] 0.1
16. Evaluate: 2
[A]
4
[B] 2.3  10
[B] 2
[C] 1
[D] 0.5
4
64
1
2
[B]
1
16
[C]
1
4
[D]
1
8
17. Solve: x 2 = 4
[A] 2
[B]  2
[C]  16
[D] 16
4
[D] 5.0  10
18. Solve: 64 x 2 – 25 = 0
[A] No solution
19. Simplify:
5
8
[C]
25
64
[D]  40
32
[A] 2 4
20. Simplify
[B] 
[B] 4 2
[C] 2 2
[D] 16 2
[B]
[C] 5 2
[D] 5 5
10  5
[A] 5 10
15
21. Joey tried to throw a ball over a fence from an initial height (s) of 5 feet at a velocity (v) 32 ft/sec. If
2
the fence is 10 feet high (h), will the ball clear the fence? Use the equation h  16t  vt  s .
[A] Yes it will
[B] No it will not
[C] Cannot be determined
[D] Who is Joey?
2
22. A rocket is fired upward and follows the path h  30t  120t . How long will it take the rocket
to return to the ground?
[A] 2 seconds
[B] 4 seconds
[C] 30 seconds
23. Graph: y   x 2  2 x  2
[A]
[C]
[B]
[D]
[D] 5,280 seconds
24. Graph: y  x 2  2
[A]
[C]
[B]
[D]
25. Which is NOT true about the graph of y  x 2  5x  6 ?
[A] It has a maximum
[C] It has two x-intercepts
[B] It opens up
[D] It has two real solutions
26. Determine the coordinates of the vertex for the graph of y   x 2  6 x  4
[A] (-3, -31)
[B] (3, 5)
[C] (3, 23)
[D] (-3, -13)
[B] x = 3, 10
[C] x = -5, -6
[D] x = -15, 2
27. Solve x2 – 11x + 30 = 0.
[A] x = 5, 6
28. Determine the x-intercepts of the graph of:
y = 3x 2  3x  6
[A] (0, -1) and (0, 2)
[C] (0, -0.5) and (0, 0.5)
[B] (-6, 0) and (3,0)
[D] (1, 0) and (-2, 0)
29. A rocket is launched from atop a 33-foot cliff with an initial velocity of 98 feet per second. The
height of the rocket t seconds after launch is given by the equation h  16t 2  98t  33. Graph the
equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to
the nearest tenth of a second.
[A] 1.5 seconds
[B] 0.3 seconds
[C] 8.0 seconds
[D] 6.4 seconds
2
30. Solve by the quadratic formula: x  6 x  5
[A]
6  54 6  54
,
2
2
[C] 3  7,3  7
[B]
6  4 14 6  4 14
,
2
2
[D] 3  14,3  14
31. Use the quadratic formula to solve the equation : x 2  x  2
[A] x = -1, 2
[B] x = -4, 5
[C] x = 1, 2
[D] No solution
32. The number of new cars purchased in a city can be modeled by the equation C  2t 2  5t  20 where
C is the number of new cars and t = 0 corresponds to the number of new cars purchased in 1966. In what
year will the number of new cars reach 612?
[A] 1982
[B] 2032
[C] 1985
[D] 1997
[C] -7
[D] 1
33. Find the discriminant: 3x 2  5x  2 = 0
[A] 7
[B] 49
2
34. Tell if the equation has two solutions, one solution, or no solutions: x  2 x  1  0
[A] one solution
[C] no real solutions
[B] two solutions
[D] not enough information
35. Classify 4x by degree and number of terms.
[A] constant monomial
[C] linear monomial
[B] quartic monomial
[D] linear polynomial
36. Add: (2 x3  5 x  6)  ( x 4  3x  6)
3
[A] 3x  2 x
4
3
[B] x  2 x  2 x
c hb gc
37. Simplify: 5t 4  6  5t  2  7t 4  4t
[A] 12t 4  t  8
4
3
[C] x  2 x  2 x  12
3
[D] 3x  2 x  12
h
[B] 12t 4  t  4
[C] 12t 4  t  8
[D]  2t 4  t  4
38. Subtract: (5x3  7 x  5)  ( x3  x 2  5x  1)
3
2
[A] 4 x  x  2 x  4
3
2
[C] 4 x  x  12 x  6
3
2
[B] 6 x  x  12 x  6
3
2
[D] 4 x  x  2 x  4
39. Identify the leading coefficient:
[A] 3
3 f 4  f 6  f 2  13
[C] –1
[B] 1
[D] –13
3
2
40. Write the polynomial in standard form: 7  x  10 x  3x
3
2
[A] x  3 x  10 x  7
3
2
[C]  x  3x  10 x  7
2
3
[B] 10 x  7  3x  x
2
3
[D] 7  10 x  3x  x
2
4
41. Find the degree of the polynomial: 3x  x  3
[A] 4
[B] 2
[C] 3
[D]1
3
42. Classify x  1 and state its degree.
[A] monomial, 3
[B] binomial, 2
[C] binomial, 3
[D] monomial, 2
43. Classify the polynomial: x  4
[A] Constant
[B]Linear
[C] Quadratic
[D] None of the above
44. Multiply: (2 x  y )(2 x  y )
[A] 4 x 2  2 xy  y 2
[C] 4 x 2  2 xy  y 2
[B] 4 x  2 xy  y
[D] 4x 2  y 2
45. Multiply ( x  5)( x  3)
[A] x 2  5x  4
2
[B] x  2 x  15
2
[C] x  2 x  15
46. Multiply: (7 y 2  7 y  4)( y  4)
[A] 7 y 2  6 y
[C] 7 y 3  35 y 2  32 y  16
[B]  21y 3  21y 2  4 y  16
[D] 7 y 3  21y 2  24 y  16
2
[D] x  2 x  8
47. Multiply: 2 x 2 ( x3  2 x 2  3)
6
4
2
[A] 2 x  4 x  6 x
3
5
4
2
[C] x  2 x  4 x  6 x
3
2
[B] x  4 x  3
5
4
2
[D] 2 x  4 x  6 x
48. The sides of a rectangle have length x and width ( x  6) . Which equation below describes the area, A,
of the rectangle in terms of x?
49.
50.
[A] A = 4 x  12
2
[C] A  x  6
[B] A = 2 x  6
2
[D] A  x  6 x
A rectangle has side lengths 2 x  9 and 8x  5 . What is the perimeter of the rectangle?
[A] 16 x 2  62 x  45
[B] 20 x  8
[C] 10x  4
[D] 16 x 2  45
Find the product: (3x  5) 2
[A] 6x 10
2
[C] 9 x  30 x  25
2
[B] 9 x  30 x  25
2
[D] 6 x  30 x  25
c
51. Find the product: 3x 2  4
h
2
[A] 9x4 – 24x2 + 16
[C] 9x2 – 24x + 16
[B] 6x2 – 8
[D] 6x4 – 24x2 + 16
52. An expanding company is creating a model of the
design for their new work space. The work space will
be square, with a rectangular section designated for a help desk.
6
x
6
6
HELP
DESK
Determine the square footage of the work space without the
rectangular section when x = 10.
x
} 2 ft
[A] 420 ft
2
[B] 160 ft 2
[C] 388 ft
2
[D] 180 ft 2
6
8
2
53. Factor: x  13x  42
[A] ( x  6)( x  7)
[B] ( x  6)( x  7)
[C] ( x  6)( x  7)
[D] ( x  6)( x  7)
54. Factor: 2 x 2  7 x  6
[A] (2 x  4)( x  3)
b gb g
[B] 2 x  3 x  2
[C] ( x  4)( x  3)
[D] (2 x  2)( x  3)
55. Factor: 16x 2  16 x  3
b gb g [B] ( x  6)( x  8)
[A] 4 x  3 4 x  1
[C] (4 x  6)( 4 x  8)
[D] (4 x  3)( 4 x  1)
56. Find the missing term in the perfect square trinomial. ( x  3)2  x 2  6 x  _____
[A] 9
[B] 6
[C] 3
[D]
3
2
3
2
57. Solve: x  2 x  35 x  0
[A] x = 5, -7
[B] x = 0, 5, -7
58. Solve: 27s2  144s  192  0
3
[A] s = 
[B] No solution
8
59. Solve for y:
[A]
[C] x = -5, 7
[D] x = 0, -5, 7
[C] s =  24
[D] s = 
8
3
14 49

y
3
7
6
[B] 10
1
2
[C]
6
7
[D] None of these
60. You can do 23 math problems in a half hour. Let p represent the number of problems you can do in
5.5 hours. Select the correct statement for the given conditions.
[A]
23
p

30 5.5
[B]
23 5.5

30
p
[C]
23 30

330 p
[D]
23
p

30 330
61. On a map 1 in represents 150 miles. If two cities are 375 miles apart in real life, how many inches
apart are they on the map?
[A] 2.5 inches
[B] 0.4 inches
[C] 56,250 inches
[D] Not enough information
62. 26% of 90 is what number?
[A] 2,340
[B] 23.4
[C] 346.15
[D] 28.89
[B] 0.095 %
[C] 42%
[D] 10.5%
[B] 0.25%
[C] 16%
[D] 4%
[C] 160
[D] 1.6
63. What percent of 21 is 2?
[A] 9.5%
64. What percent of 8 is 2?
[A] 25%
65. Eight is 20 percent of what number?
[A] 0.4
[B] 40
66. If there are 2,100 students at Libertyville High School and 24% of them are seniors, then how many
students are NOT seniors?
[A] 504 students
[B] 1,596 students
[C] 76 students
[D] 50,400 students
67. A survey was taken to determine the favorite subjects of 6th graders. The results are represented by
the graph below. About what percentage of students chose P.E. as their favorite subject?
Students Per Subject
Social
Studies
94
English
58
P.E.
31
Art 18
[A] 50%
[C] 31%
[B] 13%
[D] 14%
Math
47
68. Jim put $8000 in a savings account. At the end of a year the account had earned $600 in interest.
What was the yearly interest rate on the account?
[A] 15.5%
[B] 6.5%
[C] 7.5%
[D] 14.5%
69. Find an equation of variation when y varies inversely with x and y = 12 when x = 2.
[A] y = 6x
[B] y =
1
6x
1
[C] y = x
6
[D] y =
24
x
70. Multiply:
3x 2 2 y 5

y 18 yx
[A] 12xy 3
xy 4
3
[C] 3xy 3
[D]
xy 3
3
2 x 2  18 x  3

x3
3
71. Divide:
[A]
[B]
6 x 2  54
x3
[B]
2 x 2  18
x2  3
[C]
2( x  3) 2
3
[D] 6
72. If the perimeter of the figure below is 24 feet, what is the area of the figure?
6
x
8
x
15
x 1
9
x 1
[A] 17 ft 2
73. Subtract:
[A]
[B] 162 ft 2
[C] 130 ft 2
[B] 6x
[C]
[D] 27 ft 2
15 x 3x

2y 2y
6x
y
74. The production rate of a small factory is modeled by
factory is modeled by
12x
y
[D] Undefined
( x  20)
, while the production rate of another
3x( x  3)
(6 x  19)
. What would be a model for the combined production rate of the two
3x( x  3)
factories?
[A]
( 7 x  39)
3x 2  6
[B]
( x  20)
(6 x  19)
[C]
(7 x  39)
3x ( x  3)
[D]
(6 x 2  39)
3x 2  6
75. Add:
5x
x

x 1 x 1
6x2  4x
x 1
[A]
[B]
2 x(3 x  2)
x2 1
[C]
6x
x2 1
[D]
6x
x 1
4
1
cm was cut into two pieces. If one piece is
cm, express the length of
x4
x4
the other board as a rational expression.
76. A board of length
3x  20
( x  4)( x  4)
[A]
[B]
3x  20
( x  4) 2
[C]
5x  20
( x  4) 2
[D]
5x  20
( x  4)( x  4)
8
4
dollars was cut in half. If one part is
x4
x4
dollars, express the amount of the other part as a rational expression.
77. A restaurant bill represented by the expression
12 x  48
( x  4) 2
[A]
[B]
4 x  48
( x  4) 2
[C]
12 x  48
( x  4)( x  4)
[D]
4 x  48
( x  4)( x  4)
x 2  8x  4
x
78. Divide:
[A] x 12
79. Simplify:
[B] x  8 +
4
x
[C] x 2  8 x +
4
x
[D] x  8
x2  6x  7
x 1
[A] 5x  7
[B] x 13
[C] x  7
[D] ( x  1)( x  7)
[B] s2  5s  25
[C] s2  5s  25
[D] 𝑠 2 + 5𝑠
80. (𝑠 3 − 25𝑠) ÷ (𝑠 − 5)
[A] 𝑠 2 + 25
81. Add
x
1
to
.
x  16
x4
[A]
2
x 1
x  x  20
2
[B]
2x  4
x4
[C]
2x  4
( x  4)( x  4)
[D]
x2
x2  8
82. Add:
x2  x
3

2
2 x  12 x  10 2 x  10
[A]
x3
2
[B]
x3
2( x  1)( x  5)
[C]
x2  x  3
2( x  1)( x  5)
[D]
x3
2( x  5)
2
83. Divide: x  8 by 2 x  12 x  32
[A]
1
2( x  2)
[B] 2x  4
[C]
x 8
( x  16)( x  4)
[D]
x 8
x2
84. Solve the equation and check your answer.
[A] 18
85. Solve:
[B] 96
[C] 99
x
11
x2
+
= 2
x  18
x9
x  27 x  162
[D] 103
x
6
1


x  36 x  6 x  6
2
[A] 2
[B] 1
[C]
4
3
[D] -7
86. Write an equation that can be used to solve the problem. Solve the equation and answer the question.
A sight-seeing boat travels at an average speed of 18 miles per hour in the calm water of a large lake. The
same boat is used for sight-seeing in a nearby river. In the river, the boat travels 2.9 miles downstream
(with the current) in the same amount of time it takes to travel 2.3 miles upstream (against the current).
Find the current of the river.
[A]
2.9c – 2.3c
; 2.08 mph

18
3
[C]
2.9
2.3
; 2.08 mph

18  c 18  c
[B]
2.9c – 2.3c
; 0.98 mph

18
3
[D]
2.9
2.3
; 0.98 mph

18  c 18  c
87. After taking 5 quizzes, your average is 71 out of 100. What must your average score be on the next
five quizzes to increase your average to 76?
[A] 81
[B] 73
[C] 83
[D] 78
88. Solve:
5
2

= 0
m2 m4
[A] 8
[B] none of these
[C] 
24
7
[D]
16
3
89. Which functions are equivalent?
3(9 x  4)
I.
3x  2
[A] All three
90. The function f(x) =
[B] None
[C] I and II
[D] II and III
x4
is undefined for what value(s) of x?
x3
[A] x = -4
91.
II. 9 x  6
27 x3  12 x
II.
x(3x  2)
[B] x = -3
[C] x = -3, -4
[D] None
Simplify: 2 8  3  3 2
[A] 7 2  3
[A] 3 2
[A]
94. Solve:
[A]
95. Solve:
[C] 4 2  3  3
[D] 6 7
[C] 3 2  3
[D] 3 2  3
18  27  12
92. Simplify:
93. Solve:
[B] 4 13
[B] 2 6
3x  5  6  11
10
3
[B]
40
3
[C] 10
[D] no solution
4 x2 1  3
2.5
[B]
0.5
[C]
3
2
[D] -1, 1
x  12  3  x  3
[A] –3, 4
[B] 3, –4
[C] 4
[D] no solution
96. If 2x  4 is twice as large as its square root. What are the possible value(s) for x?
[A]
15
8
[B] –2, 0
[C] 0
[D] None
97. The following equation describes the number of meters, x, which must be added to a string that
measures 13 meters so that a pendulum will have a complete swing (back and forth) that lasts 8 seconds.
13  x = 39
.
How much longer should the string be so that the complete swing of the pendulum will be 8 seconds?
[A] 9.1 m
[B] 15 m
[C] 1.521 m
[D] 2.21 m
98. Name the most efficient method to solve the quadratic equation: ( x  6) 2 = 7
[A] Solve for x2 and use the square root method.
[B] The square root method
[C] The quadratic formula
[D] Factoring and the zero-product principle
99. Given the right triangle below, what is the length of the hypotenuse?
[A] 5 8
8 cm
[B] 8 5
[C] 16 10
16 cm
[D] 64 5
100. Which set of side lengths cannot form a right triangle?
[A]
3
5
mm, 2 mm,
mm
2
2
[B] 6 mm, 8 mm, 10 mm
[C] 3 mm, 4 mm, 5 mm
[D] 4 mm, 4 mm, 5 mm
101. A cable 25 feet long runs from the top of a utility pole to a point on the ground 12 feet from the base
of the pole. How tall is the utility pole?
[A] 27.73 ft
[B] 13 ft
[C] 18 ft
[D] 21.93 ft
102. Find the distance between the two points: (–4, –2), (2, 3)
[A]
61
[B]
3
[C] 2
[D] (-2, 1)
103. Find the distance between the two points: (–5, 3), (4, –1)
[A]
97
[B] 5
[C]
1
2
[D] (-1, 2)
104. The midpoint of QT has coordinates (3, –4). The coordinate of point Q are (2,3). What are the
coordinates of point T?
5 1
[A]  ,  
2 2
[B] (–1, –7)
[C] (4, –12)
[D] (4, –11)
Part II Free Response:
1. The average salary (in thousands of dollars) for a professional baseball player in the United States
can be approximated by y  283(1.2) x , where x = 0 represents the year 2004.
a. Find the average salary in 2012.
a._______________
b. In exponential form, what is the ratio of an average salary
in 2012 to 2004?
b._______________
 15 x8 y 5 w12 
 5 2 10 
 5y z x 
2
2.
Simplify:
3.
Graph the following quadratic equation:
y  x2  4 x  3
a)
Axis of Symmetry:
b)
Vertex:
c) Table:
X
Y
d)
Roots:
2. __________________________
( x  5)(3x 2  8 x  1)
4.
Find the product:
5.
Factor completely:
6.
Solve the following equation:
7.
Solve the following equation (Hint: there ARE solutions)
3x3  15 x 2  6 x  30
4 x 2  1 6x  1 6 0
4. __________________________
5. __________________________
6. __________________________
7. __________________________
x 2  4 x  16  0
8.
Solve the proportion:
5
4x

x 1 x
8. __________________________
5
4
6

 2
x  6 x 6 x  3 6
9.
Solve the following equation:
10.
Solve the following equation:
11.
Solve for x:
12.
Find the distance and midpoint between (3, -5) and (-6, 8). 12.
x  1 0x  2 4
9. __________________________
10. _________________________
11. _________________________
Dist: _________________
Mid pt: _________________