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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