Algebra Final Exam Review kg2012
1. Evaluate the expression
and b = 5
Page 1 of 6
2b(b  a)
when a  3
b
 v = 2.
2. Evaluate 3u + 6v when u = 3 and

17.5 m
3. Evaluate 2j + 3k when j = 2 and k = 5.
7m
4. Evaluate the expression 2x 2  6 when x  4.
6.1 m
5. Evaluate the expression 16 + 12x – x 3 when x =
3.


18. At an electronics store they sell about 760
cassette players a year and about 220 CD players a
year. If the rate of cassette player sales decreases by
40 each year and the rate of CD player sales
increases by 50 each year, in how many years will
the CD player sales be twice as much as the cassette
player sales? Use a table to determine your answer.
6. Evaluate the expression 4a
  4b when a = 3
and b = 2.
2
7. Add: (5x 5  5x 6  5) + (5x 6  5  3x 5 )

Solve the equation:
y 1
9
19.
2
Subtract:
8. (4 x 3  7x 2  6)  (7x 3  7x 2  8x  6)

9.  x 4  8x   3x  2  2x 4 






12. x  5x 2  4 x  5

13. Simplify the product: (4 fg3 ) 4 ( fg) 2
Simplify:
35x 6 y 5
14.
7x 5 y 7
21.

11. ( x  1 )( x  4 )

20. 3 4z  5  8z

Multiply:
10. x  5x  9

x x
 5
2 4
Solve:
3
y + 15  0
22.
12
23.

9x
 11x  28
3
24. Solve for t : 5 = t  6s


25. Solve for y 5x  3y = 5
 
Graph:
26. x  –1

9x 7 y 3
15.
3x 5 y 4
16. Simplify the expression
w
8x 2 y 2 (4 xy 2 ) 1

.
x 2 y
x2y
17. The two rectangles are similar. Find the width
of the larger rectangle.

27. x  7


28. Sketch a graph of the inequality 4  x .
29. Solve the inequality. 8x < 24
30. Solve x  11  12.


Algebra Final Exam Review kg2012
Page 2 of 6
37. Name the type of model suggested by the graph.
31. Solve the inequality 4  3x  x  3 .
y
10
1
32. Solve the inequality 2  x  3.
3

33. Solve the inequality 3  4 x  x  2.
 of model suggested by the graph.
34. Name the type
10 x
–10
y
10
–10
38. The table gives the number of inner tubes, I,
sold in a bike shop between 1985 and 1990.
Year, t
1985 1986 1987 1988 1989 1990
10 x
–10
Inner tubes, I
26
37
47
58
71
80
Find the type of model that best fits the data.
–10

35. Name the type of model suggested by the graph.
y
39. The table gives the number of inner tubes, I,
sold in a bike shop between 1985 and 1990.
Year, t
1985 1986 1987 1988 1989 1990
Inner tubes, I
10
8
21
33
67
132
258
Find the type of model that best fits the data.
10 x
–10

40. The table gives the number of inner tubes, I,
sold in a bike shop between 1985 and 1990.
Year, t
1985 1986 1987 1988 1989 1990
Inner tubes, I
8
18
35
65
132
–10
Determine which model best fits the data.
36. Name the type of model suggested by the graph.

y
10
10 x
–10
–10
41. At an electronics store they sell about 730
cassette players a year and about 180 CD players a
year. If the rate of cassette player sales decreases by
50 each year and the rate of CD player sales
increases by 60 each year, in how many years will
the CD player sales be twice as much as the cassette
player sales? Use a table to determine your answer.
42. Suzy can run 4 m/sec and Tim can run 6 m/sec.
How far ahead of Tim must Suzy be to not to fall
behind Tim in the first 10 seconds of running? Use
a graph to check your answer.
261

Algebra Final Exam Review kg2012
43. Nicole pays $325 in advance on her account at
the athletic club. Each time she uses the club, $10 is
deducted from the account. Find a linear function
that models the value remaining in her account after
x visits to the club. Find the value remaining in the
account after 7 visits.
Page 3 of 6
y
1
(–3, 0)
–4
–2
–1
1
x
–1
–2
44. The following situation can be modeled by the
equation y  1.5x  8 .
Graph the equation.
–3
–4
A candle is 8 inches tall and burns at a rate of 1.5

inches per hour.
Graph:
57. 6x  12 = 0
45. Find the y-intercept of the line. 2x  y  10
46. Find the y-intercept of the line. 2x  y  10
Graph:
47. x =  3



Graph:
58. 6x  12 = 0

59. Find an equation, in slope-intercept form, that
passes through point (–1, –4) with slope –3.


(0, –4)
48. y =  7
60. Find an equation for the line with undefined
slope and passing through the point (3, –3).
49. What is the x -intercept of the line
5x  2y = 10 ?
61. Find an equation for the line with undefined
slope and passing through the point (–8, –8).
50. State the x- and y-intercepts of y = 5x  6 .
62. Find an equation for the line with undefined
slope and passing through the point (1, 3).

51. Find the x-intercept of the line 3x  4 y  12 .

52. Write the equation of the line passing through
(2, –7), (2, 0), and (2, 5).

53. Find an equation, in slope-intercept form, that
passes through point (4, –7) with slope –2.
54. Write an equation of a line with slope 5 passing

through the point (3, –5).
55. Find an equation of the line passing through the
point (1, 4) with slope m  6.
56. What is the slope of the graph.

63. Find the y-intercept of the line containing the
point (–7, –6) with undefined slope.
64. Write an equation for the line containing
(3, 10) and (7, 22) .
65. Write the equation of the line in slope-intercept
form that passes through the points (7, –1) and (2,

9).
66. Write the equation of the line in slope-intercept
form that passes through the points (–3, 5) and (2, –
5).
67. Find an equation of the line containing the
points (8,  7) and (12,  16).
Graph:
68. –y < 3x  7







Algebra Final Exam Review kg2012
Graph:
69. y = x 2  2

Page 4 of 6
Which system of equations below will determine
the number of adult tickets, a, and the number of
child tickets, c, he bought?
70. Determine the number of solutions of the
equation.
3x 2  2x  6 = 0
79. The Modern Grocery has cashews that sell for
$3.50 a pound and peanuts that sell for $2.00 a
pound. How much of each must Albert, the grocer,
mix to get 60 pounds of mixture that he can sell for
$3.00 per pound? Express the problem as a system
of linear equations and solve using the method of
your choice.
71. Determine the number of solutions of the
equation.
x 2  2x  1 = 0
72. Determine the number of solutions of the
equation.
4 x 2  3x  4 = 0
73. Solve the linear system by any method.
3x  2y  3
6x  2y  3
80. Use an addition equation to solve for x.
14
6

x
Perimeter = 34
74. Solve the linear system by any method.
5x  2y  3
 x  6y  2
75. Solve the linear system by any method.
6x  4 y = 1
2x  5y = 1
Solve the equation:
81. 5n – 2(n – 2)  –11
82. 4n – 2(3 – n)  –13


76. A rental car agency charges $20 per day plus 14
cents per mile to rent a certain car. Another agency 
charges $22 per day plus 10 cents per mile to rent
the same car. How many miles will have to be
driven for the cost of a car from the first agency to
equal the cost of a car from the second agency?

(Round your answer to the nearest hundredth of a
mile.) Express the problems as a system of linear
equations and solve using the method of your
choice.
77. A group of 80 people attend a ball game. There
were three times as many children as adults in the
group. Write a system of equations that you could
use to set up this problem, where a is the number of
adults and c is the number of children in the group.
Solve the system of equations for c, the number of
children in the group.
78. Mr. Frankel bought 7 tickets to a puppet show
and spent $32. He bought a combination of child
tickets for $2 each and adult tickets for $8 each.
83. 5 n  2(2  n)  7
Solve the equation:
y3
7
84.
4
85. The triangle below has a perimeter of 20. Solve
for x.
x
8
x+ 2
86. The triangle below has a perimeter of 23.2.
Solve for x.
x
x+ 2
8
87. The circle below has a circumference of 27
inches. Approximate the radius of the circle to two
Algebra Final Exam Review kg2012
decimal places.
98. Draw a box-and-whisker plot for the following
data.
38, 31, 38, 34, 38, 29, 36, 28, 24, 42, 35, 40, 20, 26,
38
r
88. The circle below has a circumference of 16
inches. Approximate the radius of the circle. Round
your result to two decimal places.
r
99. Draw a box-and-whisker plot for the data. 37,
32, 18, 31, 40, 36, 24
100. For the data set 44, 38, 21, 37, 48, 43, and 28
draw a box-and-whisker plot.
101. Sketch a box and whisker for 27, 22, 8, 21, 30,
26, 14
89. The trapezoid below has a perimeter of 20.
Solve for x.
x+ 2
x
3x + 2
8
90. The circle below has a circumference of 21.54
inches. Approximate the radius of the circle to two
decimal places.
r
91. Find the greatest common factor of the terms
4k 4 , 40k 5 , and 28k 2 .
92. Find the greatest common factor of the terms
7
2
12
 4 y , 12y
 , and 36y .
93. Factor out the greatest common monomial
factor. 18u 4 v 5  30u 5v 4


94. Factor out the greatest common monomial
3
2
 factor. 24u  40u
95. Solve the equation 4 x 2  7x  2  0.

Page 5 of 6
96. Solve the equation 30x 2  11x  30  0.

97. Solve the equation 3x  7x 2  0.


102. A single six-sided fair die is tossed. Find the
probability of obtaining a number greater than 3.
103. A six-sided die is rolled 210 times. Six comes
up 33 times.
A. What is the theoretical probability of rolling a
six?
B. What is the experimental probability of rolling a
six?
104. After the introduction of a new soft drink, a
taste test is conducted to see how it is being
received. Of those who participated, 56 said they
preferred the new soft drink, 100 preferred the old
soft drink, and 44 could not tell any difference.
What is the probability that a person in this survey
preferred the new soft drink?
105. Each square is made from toothpicks.
Assuming the pattern continues, plot the relation
between the number of squares and the number of
toothpicks.
1
2
3
106. Each trapezoid is made from toothpicks.
Assuming the pattern continues, plot the relation
between the number of trapezoids and the number
of toothpicks.
107. Each square is made from toothpicks.
Assuming the pattern continues, plot the relation
between the number of squares and the number of
Algebra Final Exam Review kg2012
toothpicks.
Page 6 of 6
111. What type of relationship – positive,
negative, or none – is shown by the scatter plot?
y
1
2
10
3
108. A monthly phone bill, b, in dollars, consists of
a $23 service fee plus $0.15 per minute, m, of long
distance calls. The amount of the bill is a function
of the minutes used, b = 23 + 0.15m.
A. Draw a graph for up to and including 120
minutes of long distance calls made in a month.
B. Estimate the bill if 90 minutes of long distance
calls are made.
109. The table shows the study times and test scores
for a number of students. Draw a scatter plot of
score versus time.
Study Time (min)
7
13 16 19 25 30 36 39
Test Score
57 58 65 67 67 68 74 76
110. For the following data:
A. Make a scatter plot of the data.
B. Draw a line of fit for your scatter plot.
C. Find an equation of your line of fit.
x 1
2
3 4 5
6
7
8
y 1.5 3.6 4.2 6 6.9 9.6 10.2 12

1
2
3
10 x
–10
–10
Algebra Final Exam Review kg2012
Reference: [1.1.1.1a]
[1] 4
Reference: [1.1.1.2]
[2] 21

Reference: [1.2.1.14a]
[4] 26

Reference: [1.2.1.15]
[5] 25


Reference: [10.2.1.27]
[11] x²-3x-4
Reference: [8.1.1.4]
[13] 256f6g14

Reference: [3.3.1.33]
[22] -60
Reference: [3.3.1.34]
[23] x  2
Reference: [3.7.2.82b]
[24] t = 5  6s
 
5
6
220 270 320 370 420 470 520
Reference: [3.3.1.31]
20
[21]
3

4
CD sales

Reference: [10.2.1.39]
[12] x³-9x²+25x-25
3
760 720 680 640 600 560 520
Reference: [13.14.418]
2
[20]
3
Reference: [10.1.1.21]
[9] 3x 4  11x  2
2
cassette sales
Reference: [13.14.417]
[19] 17

Reference: [10.1.1.19]
[8] -3x³+14x²-8x+12
Reference: [10.2.1.28]
[10] x 2  4 x  45
Reference: [13.14.415]
[17] 15.25 m
Reference: [13.14.419]
[18] 10 years
year
0
1
Reference: [1.2.1.18]
[6] 400

Reference: [8.3.1.34]
[15] – 3x²/y
Reference: [8.3.1.37]
2x
[16] 6
y
Reference: [1.1.1.3]
[3] 19
Reference: [10.1.1.12]
[7] 10x 6  2x 5  10
Page 7 of 6
5x
[14]  2
y
Algebra Final Exam Review kg2012
Page 8 of 6
Reference: [9.8.1.96]
[35] linear
Reference: [3.7.2.83b]
5x  5
[25] y =
3

Reference: [9.8.1.96]
[36] exponential
Reference: [9.8.1.96]
[37] quadratic
Reference: [6.1.1.1]
[26]
–10
–8
–6
–4
–2
0
2
4
6
8
Reference: [9.8.2.97]
[38] linear
10
Reference: [6.1.1.2]
[27] [C]
–10
–5
Reference: [9.8.2.97]
[39] exponential
0
5
10
Reference: [9.8.2.98]
[40] exponential
Reference: [6.1.1.3]
[28]
0
1
2
3 4
5
6
x
Reference: [3.5.2.62]
[41] 8 years
year
0
Reference: [6.1.2.13]
[29] x < 3

2
Reference: [6.2.1.21]
1
[31] x 
4

Reference: [9.8.1.95]
[34] absolute value
5
6
CD sales
180 240 300 360 420 480 540
Reference: [3.5.2.63]
Dis tance
Reference: [6.2.1.22]
[32] x < –3
Reference: [6.2.1.23]
5
[33] x  
3
4
730 680 630 580 530 480 430
50

3
cassette sales
Reference: [6.1.2.15]
[30] x  1


1
[42]
20 meters
Seconds
Reference: [4.8.2.99]
[43] V(x) = 325 – 10x; $255
10
Algebra Final Exam Review kg2012
Reference: [4.6.2.85]
6
[50] x-intercept: ; y-intercept: –6
5
y
10
Reference: [4.3.1.38]

[51] 4
Height
(in.)
0
Number of
hours
[44]
Reference: [4.2.2.24]
[52] x = 2
10 x
Reference: [5.2.1.13]
[53] y=-2x+1
Reference: [13.14.427a]
[45] y-intercept: 10
Reference: [5.2.1.15]
[54] y = 5x  20
Reference: [13.14.427a]
[46] y-intercept: 10

Reference: [5.3.1.30a]
4
[56] y   x  4
3
Reference: [4.2.2.23]
y


Reference: [5.2.1.16]
[55] y=-6x+10
 x

Reference: [4.2.2.33]
y
[47]
10

y
10
10 x
–10
[57]
[48]
10 x
–10
–10
–10
Reference: [4.3.1.36]
[49] 2
Reference: [4.3.1.37]
Reference: [4.2.2.34]
Page 9 of 6
Algebra Final Exam Review kg2012
Page 10 of 6
y
y

10

10 x
–10
[58]
[68]
10

[69]
Reference: [13.14.466]
[72] 2
Reference: [5.2.1.18]
[63] none
Reference: [7.4.1.29]
1
2
,
[73]
3
2

Reference: [7.4.1.30]
1 
1
,
[74]
2
4 

Reference: [7.4.1.31]
 1 4 
[75]  ,
 38 19 

Reference: [7.4.2.32]
[76] c = 20 + 0.14m
c = 22 + 0.10m
50 miles
Reference: [5.3.1.31]
[65] y  2x  13
Reference: [5.3.1.32]
[66] y  2x  1

Reference: [5.3.1.33]
[67] 9x-4y=-44
Reference: [13.14.443]
–10
Reference: [13.14.466]
[71] 1
Reference: [5.2.1.17]
[62] x = 1

10 x
Reference: [13.14.466]
[70] 2
Reference: [5.2.1.17]
[61] x =  8
Reference: [5.3.1.29]
[64] y =  3x  1

y
–10
Reference: [5.2.1.17]
[60] x = 3


Reference: [13.14.464]
–10
Reference: [5.2.1.13]
[59] y=-3x-7

 x
Algebra Final Exam Review kg2012
Page 11 of 6
Reference: [7.4.2.33]
[77] Sample Acceptable Response:
a  c = 80
c = 3a
by substitution:
a  3a = 80
4a
80
=
4
4
a = 20
c = 3(20) = 60 children




Reference: [3.7.1.76]
[86] 6.6
Reference: [3.7.1.77]
[87] 4.30 in.
Reference: [3.7.1.78]
[88] 2.55 in.
Reference: [7.4.2.34]
[78] 8a+2c=32
a+c=7
Reference: [3.7.1.79]
[89] 1.6
Reference: [7.5.2.49]
x  y  60
[79]
3.50x + 2.00y  180
x = 40 pounds of cashews
y = 20 pounds of peanuts
Reference: [3.7.1.80]
[90] 3.43 in.
Reference: [10.8.1.90]
[91] 4k 2

Reference: [3.1.1.3]
[80] 14

Reference: [10.8.1.91]
[92] 4 y 2

Reference: [10.8.1.96]
[93] 6u4v 4 (3v  5u)

Reference: [10.8.1.97]
[94] 8u2 (3u  5)
Reference: [3.3.1.25]
[81] –5
Reference: [3.3.1.26]
7
[82] –
6


Reference: [3.3.1.27]
3
[83] 
7

Reference: [3.3.1.29]
[84] 25
Reference: [10.6.2.83]
1
[95] –2,
4
Reference: [10.6.2.82]

6 5
[96]  ,
5 6
Reference: [3.7.1.73]
[85] 5

Algebra Final Exam Review kg2012
Reference: [10.6.2.81]
3
[97] 0,
7

Page 12 of 6

Number 
of
Toothpicks
Reference: [6.7.1.110]
[98]

0
19
23
27
31
35
39
43
47





















Number of Squares
[105]
Reference: [4.6.2.86]
Reference: [6.7.1.111]
[99] [A]

Reference: [6.7.2.112]
[100] yes
Number 
of
Toothpicks

Reference: [6.7.2.113]
[101] [A]
Reference: [2.8.1.90]
1
[102]
2
0
Number of Trapezoids
[106]
Reference: [4.6.2.86]

Reference: [2.8.1.91]
1
11
[103] A.
B.
6
70

Number 
of
Toothpicks
Reference: [2.8.1.94]


[104] 7/25 [B]

Reference: [4.6.2.86]
0
[107]
Number of Squares
Algebra Final Exam Review kg2012
Reference: [3.6.2.72]
Page 13 of 6
50
40
Cos t
30
($)
20
10
0
50
100
Minutes
[108] A.
B. $36.50
Reference: [4.1.2.12]
[109]
85
80
Test 75
Score 70
65
60
55
50
Effect of Study on Test Score
10
20
30
40
Time (min)
50
Reference: [13.14.433]
y
[110]
y = 1.5x

Reference: [13.13.390]
[111] none
x
60