Updated Spring 2009
MTH 098
1
ELEMENTARY ALGEBRA WITH GEOMETRY
FINAL EXAM REVIEW
Evaluate.
1.
−2ab
a 2 − 2ac
when a = 2, b = –2, and c = –3
2.
–2ac – 3(a + b)2 when a = 1, b = 3, and c = –4
3.
–a2 – 2ac ÷ (–b) when a = 6, b = –3, and c = 4
Solve the equations for the variable.
4.
3a + 5 = 5a + 7
5.
3x – 7 = 4 – 2(3x + 4)
6.
2(3 – 4x) + 4 = 2 – 3(4 – 4x)
7.
2
x+5=3
3
8.
Solve for a:
9.
Solve for y:
5a + 3b = 10
–x + 2y = 4
Simplify, leaving positive exponents in the answer.
10. (x3y4)2
11. (3a–1b2)–2
12. (2x–3) (x4y–1)2
13.
14. −
35a 3b 6
7ab 4
15.
−36a 3b
−12a 2 b
80a 8b11
16a 10b 9
Simplify.
16.
18.
3x − 12
5x − 20
3x 2 − 7 x − 20
16 − x 2
17.
x+3
x 2 − 5x − 24
Updated Spring 2009
2
Perform the indicated operation, leaving answers in simplest form.
19. (2b + 5) (3b – 2)
20. (5x + 3) (2x + 7)
21. (x – 6) (2x – 1)
22. (x + 7) (x – 7)
23. (4x – 1) (4x + 1)
24. (y + 2)2
25. (3x – 4)2
26. (2x2 – 3x + 6) + (3x2 + 8x – 9)
27. (3a2 – 2a + 9) – ( –2a2 + 5a + 12)
28. (–7y2 + 2y + 3) – (3y3 – 5y + 8)
29. (x2y3) (x3y4)
30. (5a2b) (–3a3b2)
31. x2 (x2 + 3x – 2)
32.
33.
10a 3 − 15a 2 + 20a
−5a
34.
35.
16 x 3 12ab 2
⋅
24a 2 b 8 x 2
36.
37.
12a 2 b 3
18 x 3 y
÷
16ab 2
9x2 y3
38.
39.
x2 − 4y2
x2 + 4x
⋅
5x + 20 5x 2 − 9 xy − 2 y 2
40.
41.
4
+5
x
42.
43.
7b + 2 4
−
b
b2
3x 3 − 6 x 2 + 9 x
3x
12a 4 − 16a 3 + 8a 2
4a 3
x 2 − x − 20
x2 y3
x 2 + 3x + 2
xy 2
⋅
x3y2
x 2 − 10 x + 25
÷
x2 + 4x + 4
x2 y2
2
5
+
3x x 2
7x − 2
2
x + 3x − 28
−
6x − 9
2
x + 3x − 28
Factor completely.
44. 5a2 – 25a
45. 6x3 – 42x2 + 54
46. 8x2y2 – 4xy
47. 8a3b + 12a2b2 – 4a3b2
Updated Spring 2009
3
48. x2 – 25
49. 9x2 – 64y2
50. b2 – 81c2
51. x(a – b) + 2 (a – b)
52. x2 + 4x – 3ax – 12a
53. 8y2 + 4y + 6y + 3
54. a2 – 4a – 21
55. p2 + 5p – 24
56. x2 + 5x – 14
57. ax2 + 17ax + 52a
58. x3 – 3x2 – 70x
59. 12x2 – 11x – 15
60. 8x2 – 10x + 3
61. 50x2 + 65x – 15
62. 9x2 + 12xy + 4y2
63. 3a3 – 42a2 + 147a
Solve the equations.
64. 3x2 + 5x = 0
65. x2 + 2x – 15 = 0
66. x (x – 5) = 50
67.
1 4 5
− =
2 x 6
69.
x +1 x
=
3
9
68.
x − 4 x + 12
=
3
4
Solve the inequalities and graph on a number line.
70. x + 2 ≤ 5
71. – 4y ≥ 16
72. 2x + 3 ≤ 5x – 6
73. 11 – 4x < 19
74. 4 (2x – 5) > 12x + 4
Simplify. Leave your answer in simplest radical form, if necessary.
75.
49
76. − x10
77.
27
78.
79.
64x 5 y10
80.
3
8x 3 y 6
48x 2 y 7
Updated Spring 2009
4
Find the midpoint of the line segment joining the given points and the distance between
the given points.
81. (– 4, 9) and (5, –3)
82. (0, 2) and (3, –2)
83. (7, 9) and (1, 1)
Find the slope of the line containing the given points.
84. (0, 5) and (3, – 4)
85. (2, –1) and (–6, 5)
86. Find the slope of a line parallel to a line with slope −
4
.
3
87. Find the slope of a line perpendicular to a line with slope
1
.
2
1
88. Find the slope of a line parallel to the line y = 5 x – 10.
89. Find the slope of a line perpendicular to the line y = –3x + 2.
For the following linear equations, write each equation in the form y = mx + b, find the
slope and the x- and y-intercepts, and graph.
90. 2x + 3y = 6
91. x + 3y = –3
92. 5x – y = 5
Graph the equations and find the slope of each line.
93. y = 5
94. x = –2
Find the length of the missing side of the right triangle.
95.
96.
3 cm
17 cm
4 cm
15 cm
Updated Spring 2009
5
97. If l1 and l2 are parallel, find angles x, y and z.
x
y
l1
z
110°
l2
98. If l1 and l2 are parallel, find angles a, b and c.
x + 160°
l1
a
b
c
l2
80° – x
Solve the system of linear equations algebraically (use either substitution or addition).
99. 3x – 2y = –3
x + 5y = –18
100.
5x + 5y = 5
y=3–x
101. 3x – 5y = –11
2x + 2y = 14
102 . 2x – 3y = 14
4x – 6y = 28
For the following word problems, identify the variable used, set up an equation and solve
algebraically.
103.
Find the length of a rectangle whose perimeter is 104 meters and whose width is
17 meters.
104.
Find two complementary angles such that the larger angle is 10 degrees more than
three times the smaller angle.
105.
The larger of two supplementary angles is 5 times the smaller angle. Find the
larger angle.
Updated Spring 2009
106.
6
A birdseed mixture is made by combining sunflower seeds with cracked corn. If
the sunflower seeds sell for $0.70 per pound and the cracked corn costs $0.45 per
pound, how much of each should be used for 10 pounds of a birdseed mixture that
sells for $0.65 per pound?
107.
The height of a triangle is 10 feet and the base is 12 feet. Find the area of the
triangle.
108.
One number is eight less than another number. The sum of the two numbers is
50. Find the smaller number.
109.
The sum of three consecutive odd integers is 117. Find the three integers.
110.
A company invested $10,000 in two money market accounts for one year, one
earning 9% simple interest, the other 7.5% simple interest. How much did they
invest in each account if the total interest earned was $855?
111.
Calvin traveled 160 miles from Rochester to Binghamton in 3 hours. Find his
rate, to the nearest tenth.
112.
In an isosceles triangle, two sides are equal. The third side is 8 inches less than
one of the equal sides. The perimeter is 46 inches. Find the length of one of the
equal sides.
113.
A man 6 feet tall casts a shadow 2 feet long at the same time a nearby building
casts a shadow 38 feet long. Find the height of the building.
114.
Denny takes 3 hours to rake the leaves from his lawn. His son Jordan takes 5
hours. How long does it take if they work together?