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EXAM REVIEW - FORM IR

I. Signed Number Evaluation:
Evaluate:
18
2. 2(—5) — 42
—3
42

s. 23 +4(-5+1) 6. 9 6(3)

Numerical Evaluation:
Evaluate each expression when x = 2, y = — 3, and z

9. 7-y2z 10.11. y3 +2xy -5x2

8. 3K —y

111. Formula Substitution:

Evaluate the following expressions:

12. If C —(F-32), find C when 23 0 13. If m = 24 and v 1 find k for k 2

d
14. If d=10 and t , then find V for V=—

IV. Function Notation

Given the functions: f(x) = —2x3 — — 4x+1 and g(x)=5-3x. Find the following
values:
15. f(0) 16. f(-l)17. f(l) 18. g(2) 19. 9(-3)

V. Multiplication of Terms and Powers:

Multiply:

20. -5xy2 (3x3 ) 21. (7df2 22. (-5x3y)2 23.

Division of Terms:
Reduce:
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24. -15a3b2 25. — 32q3rs 26. —12mn3 27 — 24r2s 3 t2 28. 40x5y7z2

- 5a3b 16qs 12mn3 —30r4s3 — 12yllz

VII. The Distributive Law: Multiply:

29. 7x(3x — 4) 30. 31. — 5r2 s(3r2 — 4s —9)

Divide:

32. 8y5 -4/ 33. 12m3 -15m2 +3m 34. 21r2 s — 14r2 s 3 t — 28r3s2

2y2 — 3m 7r2s

VIII. Combined Operations:

Rewritc and simplify:
35. Subtract + 4 from 4x 36. Subtract 2a2 — 4a from 3a + a2

61. 62. 63. 64.

2
37. Subtract 6x 3x 1 from 45<-1

Multiply and Combine:

38. 3rs(rs) — r2s 2 39. 7q — (4q q) 40. (02b + 4b) + (2ab2 — 3b)

41. 42. 5X — 3(2X — 7) + 9 43.

IX. Multiplication of Polynomials:

Multiply:

44. (2x- -3) 45. (y -7)2 46. (2y + 4) 47. (2m- 7)

48. (x -2x +3) 49. + -x -2) 50, (x + x-2)

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X. Factoring: (Greatest Common Factor,
Trinomial, Difference of Squares, and
Combined)

Factor Completely:
51. 4z2 — 8z 52.
2bx — 6by + 4bz 53. — 12ax 3 y — 18ax zy 2 +
24ax 2

54. 55. 56. 4a 2 --36 57. -144

5c2 —25c + 30
59. 60. 3x 2 y - 6xy -105y
XI. Reducing Fractions:
Factor and Reduce:
— 3x a2 —8a +16 b2 -81 65. 66. 67.
-2x-3 a — 3a — 4 b 2 -11b+18
XII.Multiplication of Fractions: Multiply:
— 21r2s —14t2
68.69. (6ab3(
8t 3rs 2102b
14b2
4x2y — 3wz2 2xy 71.
9w2z 8xy 3 5wz

XIII. Division of Fractions:

Divide:
2
1402b -21a2b2 9x2y 74. 2a 3a 75. —2x
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2x x 3 5 4 1
76. 78. 79.
6y 6x
8 8
XV. Radicals: Simplify:
81. 82. 83.

Multiply:
ä 86.
84. (G 16F) 85.
Add or subtract the following:
87. 3fi-5ä 88. 89. 90. 20
Multiply or Divide and simplify completely:

91. -5(2ä) 92. 93.

94.
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95. 96.97.
98. 99.
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XVI. One Variable First Degree or Linear Equations:
102.

105.

108. — 6
100. 6a-a 101. 8+3t-

103. 6z-5-7z=10-2Z+3 104. -2k +3-

3k

XVII. Fractional
Equations:
Solve: 7 9
8d 107.
106. = -16

110.
Solve and Check:

2
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109.15y -S 5 2

XVIII. Decimal
Equations:
Solve: 113. .04x-o.11 = .25
111.
112. 3-.2w 4.2
114. .6Y+O.13=1.93 115.

XIX. 116.
x +0.15 = -0.25 0.0<+0.4

Linear Inequalities
Solve the following inequalities and sketch the solution 119.
on 6X+7>4x-3a number line: 120. 117. 118.

XX. Literal Equations and

Formula
Rearrangement:

Solve each equation for the indicated variable:

121. Solve for y: 3x—2y = 122. Solve = P22
5 for P1

2
124. Solve for m: tnv
V = K
V

123. Solve for g: + gt

XXI. Ouadratic Equations:

Solve and Check:
125
XXIL Checking a solution:
Check if the number in parenthesis is a solution to the given equations:

1 = —15y129. 9z2 -25- 0 130. 49 - 81x 2

128. 5y
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131. (X: 3) 132. (x -1)

133. (x 6) 134. (x = -2)

XXIII. Systems of Two Variable Linear Equations: Solve
Graphically: y=2x5x-2Y+8=O 135.136.137.
3x+Y=-7
Solve Algebraically:
2x + 5y = —4
140.
138. 139.

3x +5y = —4

XXIV. Translating Expressions:

Translate into an algebraic expression using a variable:
141. 5 less than twice an unknown number. 142. the price of x pants at $45 and y shirts at
$23

143. 3 times a number increased by 7 144. 4 times the difference of a number and 1 1

XXV. Word Problems: Show all work and answers:

145. If twice an unknown number is added to thirteen, the sum is twenty-five. Write an
equation that expresses the relationship in this sentence and find the unknown number.

146. When three times an unknown number is subtracted from 20, the result is the unknown
number.
Write an equation that expresses the relationship in this sentence and find the unknown
number.

147. If five times a number is subtracted from 23, the result is equal to twice the number
increased by nine. Write an equation that expresses the relationship in this sentence
and find the unknown number.

148. A $1200 TV is on sale for 15% off. What is the sale price?

149. Perl buys a new car, with a down payment of 15% of the price of the car. The down
payment is $3150. What is the original price of the car?
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150. John can travel 300 miles in five hours. How long will it take him to travel 540 miles?

151. A plane has a cruising range of 900 miles on its main fuel tank, which holds 50 gallons
of fuel. At this rate, how many gallons of fuel would be used in a flight of 252 miles?

152. The average pass rate in a class of 35 students is 10 students. How many students will
pass in a class of 98 students?

153. Jack can fly at 140 mph in his small plane. If a trip to Ohio takes him hours, how many
miles was the trip?
XXVI. Slope and Lines

Write each line in slope-intercept form, state the slope, the y-intercept and then sketch
the graph.
146. 2x + y = 4 155. -4x-3y = 12 156. -x-2y = -5 -157. 3x-2y 10

XXVII. Scientific Notation

Perform each operation:

158. (1.2 x 10 8 )
5
6.3x10159.160. (3.2 10-4 ) 4 x
2x10 9 2.1 x 10- 10-11
"10-4 4 1.6 x
103
9 4
161. 2x10-,3 162. (5.4 x 10-7 (3x 10-2 163. (8x10 5xi0
8x10 - 2x10- 1.8 10-3 1.5x10 1.25x10
6 7
4 5

XXVIII. Pythagorean Theorem:

Solve for the indicated sides by using the Pythagorean
Theorem:

b
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164. In the right triangle, if a 6 and b 8, find c. 165. In the right triangle, if c 13 and b = 12, find a.

166. In the right triangle, if a = 6 and b = 6, find c. 167. In the right triangle, if c = 8 and a = 4, find b.

ANSWERS TO MA063 AND MA065 FINAL EXAM REVIEW FORM IR

2. -3 3. —16 4. 14

6. -19 10. 35

11. -59 12. c 13. V 15. 1

16. 4 17. -8 18. -1 19. 14 20. -15x

21. —14d3e 3 f4 22. 25x6y 2 23. 18x3 y 24. 3b 25. -2q

10x5z
26.- 1 27. — 28. 29. 21x 2 -28x 30. 2y5 -10y 4 +8y3
5r2 3y4

31. —15r4s + 20r2s2 + 45r2s 32. 4y3 -2y 33. —4m 2 +5m-1 34e

35. 36. -a2 37. —8x 2 +8x-2 38. 10r2s 2 39. 4q

40. a
2
b +b + 2ab2 41. 6x 2 42.-x+30 43. 2x 3 -15* -5x-11

2
+ x -F 21 45. Y2 —14y + 49 46. 6y2 +23y +20 47. 4m2 —49

48. x 3 -X+6 49. 2x 3 + x2 50. 3x 3 -6X+8 51. 4z(z —2)

52. 2b(x-3y +2z) 53. —6ax2 (2xy +3y2 —4) OR 6ax2 (—2xy —3y2 +4) 54. +

55. 56. 57. 58.

59. 60. 3y(x 61. 62. (4x

63. 64. (2x -1) 65. x 66.

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b+9 49 2t2
2
67. 68. 69. — 9a3b2 70. 71. -
b—2 4

- 14 3x2— 75. 1 76. - 1

72. 73. 74.
9bx 16a2by 3b 9xy3

5x 78. 9y — 5x 79. 8+X 80. - 12x 81. -18a

6y 6xy
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82. 8w5 — 14b 84. 3x2 Jü 85. 40y3 Ji

87. -2Ji 89• 90. 86. 70a3b5 JSäG

95. Ji
92. 6 a 93. 91.
97. 6 98. 10 99. 15 100. E 2
96. 5Jä
102. h = 4 103. z 18 104. 105.
101. t=-2

1 109. Ito. x=b 106. d=-10

107. x-- 108. 2
2 2 111.
112 w 113. 114. y-3 115.
116.
119. 117. 128.
-3-2 -1 0 1 2 3 4 5 -6-54-3-2 -1 0 1 2 3 4 5
- 1012345
-43-2- 132. Yes, since 6 = 6
-5 147. 23-5x V-k
122. 123. g
136.
121.
2 5
140.
125. 126
127.
7 131. No, since 14
5 5 130. 7 144.
129. z 9 9
145. 146. 20-3x x,
134. No, since 135. 2
133, Yes, since 9 = 9 4uå110ns 15228 students
150. 9 hours 139. 149. $21,000
137. 138.

153. 490 miles

141. 142. 45 x+23y 143.
148. $1020
120.
154. y = —2X+4
slope: —2 y-
•-4-3 -2-1 0 1 2 3 4 5 6 intercept: (O, 4)

124. m ¯ä
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155. = ——x—4

-6

y-intercept: (O,
y

157. y = —X —5
slope: — y-
intercept: (O,
5)

156. Y— %)

IR

158. 2.4x10 16 159. 5x10 2 160. 8x10 18 161. 5x10 4 162.

163. 164. 10 165. 5 166. 6Jä 0167. 4