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MATH 1033 Review Questions for the Final Exam
Factoring Sections 5.4 – 5.6 
In questions 78 – 82 identify one factor of each polynomial.
_____ 78.
_____ 79.
_____ 80.
_____ 81.
_____ 82.
83. Factor completely:
84. Factor completely:
Solve Quadratic Equations by Factoring Section 5.7 
85. Solve the equation:
86. Solve the equation:
Operations with Rational Expression Section 6.1 – 6.2 
87. Simplify:
88. Simplify:
89. Simplify:
90. Simplify:
91. Simplify:
92. Simplify:
93. Simplify:
94. Simplify:
Simplifying Complex Fractions Section 6.3 
95. Simplify:
96. Simplify:
Simplifying Rational Equations Section 6.4 – 6.5 
97. Solve:
98. Solve:
99. The speed of a bicyclist is 12 mph faster than the speed of a walker. If the bicyclist travels 28 miles in the same amount of time that the walker travels 8 miles, find the speed of the walker and the bicyclist.
Variation and Problem Solving Section 6.6 
100. Write each statement as an equation. Use k as the constant of variation.
Statement  Equation with k as the constant of variation 
a) p varies directly as q  
b) m varies inversely as n  
c) y varies directly as a and inversely as b  
d) y varies jointly as x and z 
101. If y varies directly as x, find the constant of
variation.
y = 16 when x = 48
k= ______
102. If y varies inversely as x, find the constant of
variation.
y = 40 when x = 4
k= ______
Simplifying Radicals and Fractional Exponents Sections 7.1 – 7.3 
103. Use the definition of rational exponents to write the expression with the appropriate root:
In questions 104 – 106 use the properties of exponents to simplify each expression.
In questions 107 – 110 assume all variables represent
positive real numbers.
107. Simplify the radical:
108. Simplify the radical:
109. Simplify the radical:
110. Simplify the radical:
Adding and Subtracting with Radical Expressions Section 7.4 
111. Add or subtract as indicated:
112. Add or subtract as indicated:
Rationalize the Denominator Section 7.5 
113. Rationalize the denominator of
114. Rationalize the denominator of
Solving Radical Equations Section 7.6 
Solve each equation. Remember to check your solutions .
115. Solve:
116. Solve:
Complex Numbers Section 7.7 
117. Write using i notation:
In questions 118 – 119 add or subtract as indicated. Write your answer in the form
Multiply . Write your answer in the form
121. Divide . Write your answer in the form
122. Simplify each expression.
123. Evaluate the quadratic formula for a = 3, b = –13 and c = 4.
124. Solve using the quadratic formula and simplify your answer:
125. Solve using the quadratic formula and simplify your answer:
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