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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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