Question 1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( 4 x ) ^ { 0 }$

Accepted Answer

A)  4x 
B)  4 
C)  1 
D)  0 
A)  4x 
B)  4 
C)  1 
D)  0

Question 2

Tell whether the statement is true or false.
-{0, 4, 7, 12} = {7, 4, 12, 0}

Accepted Answer

A) True 
 B)False

Question 3

Solve the equation
-$$\frac { 25 y ^ { 4 } + 10 y ^ { 3 } + 2 y - 1 } { 5 y ^ { 2 } + 1 }$$

Accepted Answer

A)  $5 y ^ { 2 } + 2 y - 1$ 
B)  $5 y ^ { 2 } - 1$ 
C)  $5 y ^ { 2 } - 2 y + 1$ 
D)  $5 y ^ { 2 } + 2 y$ 
A)  $5 y ^ { 2 } + 2 y - 1$ 
B)  $5 y ^ { 2 } - 1$ 
C)  $5 y ^ { 2 } - 2 y + 1$ 
D)  $5 y ^ { 2 } + 2 y$

Question 4

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\{6,7,8\}$ _____$\{0,6,7,8,9,10\}$

Accepted Answer

A)  $\nsubseteq$ 
B)  $\subseteq$ 
A)  $\nsubseteq$ 
B)  $\subseteq$

Question 5

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-If a rock falls from a height of 60 meters above the ground, the height H (in meters) after x seconds can be approximated using the formula $\mathrm { H } = 60 - 4.9 \mathrm { x } ^ { 2 }$ . What is the height of the rock after 3
Seconds?

Accepted Answer

A)  -156.09 m 
B)  495.9 m 
C)  15.9 m 
D)  45.3 m 
A)  -156.09 m 
B)  495.9 m 
C)  15.9 m 
D)  45.3 m

Question 6

Factor by any method.
-$$20 x ^ { 2 } + 15 x + 24 x + 18$$

Accepted Answer

A)  $( 20 x + 6 ) ( x + 3 )$ 
B)  $( 20 x - 6 ) ( x - 3 )$ 
C)  $( 5 x + 6 ) ( 4 x + 3 )$ 
D)  $( 5 x - 6 ) ( 4 x - 3 )$ 
A)  $( 20 x + 6 ) ( x + 3 )$ 
B)  $( 20 x - 6 ) ( x - 3 )$ 
C)  $( 5 x + 6 ) ( 4 x + 3 )$ 
D)  $( 5 x - 6 ) ( 4 x - 3 )$

Question 7

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$$

Accepted Answer

A)  $\frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
B)  $\frac { 24 x + 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
C)  $\frac { 26 x - 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
D)  $\frac { 26 x + 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
A)  $\frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$ 
B)  $\frac { 24 x + 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
C)  $\frac { 26 x - 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$ 
D)  $\frac { 26 x + 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$

Question 8

Write in radical form. Assume all variables represent positive real numbers.
-$$( \mathrm { mn } ) ^ { 1 / 6 }$$

Accepted Answer

A)  $( m n ) ^ { - 6 }$ 
B)  $\frac { 1 } { \sqrt [ 6 ] { \mathrm { mn } } }$ 
C)  $\sqrt [ 6 ] { \mathrm { mn } }$ 
D)  $( \sqrt { m n } ) ^ { 6 }$ 
A)  $( m n ) ^ { - 6 }$ 
B)  $\frac { 1 } { \sqrt [ 6 ] { \mathrm { mn } } }$ 
C)  $\sqrt [ 6 ] { \mathrm { mn } }$ 
D)  $( \sqrt { m n } ) ^ { 6 }$

Question 9

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). $$\begin{array} { l r } 
\text { Month } & \text { Profit (Loss) in Dollars } \
\hline \text { January } & - 14,526 \
\text { February } & 1874 \
\text { March } & - 8977 \
\text { April } & - 14,107 \
\text { May } & 14,073 \
\text { June } & 14,632 \
\text { July } & - 13,834 \
\text { August } & - 13,170 \
\text { September } & - 4860 \
\text { October } & 6630 \
\text { November } & - 3338 \
\text { December } & - 974
\end{array}$$ The absolute value of the profit or loss was smallest in

Accepted Answer

A)  February 
B)  January 
C)  $\underline{ ? }$ December 
D)  June 
A)  February 
B)  January 
C)  $\underline{ ? }$ December 
D)  June

Question 10

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-Find the magnitude of the difference between a windchill factor of 80 and a windchill factor of -6.

Accepted Answer

A)  -86 
B)  74 
C)  -74 
D)  86 
A)  -86 
B)  74 
C)  -74 
D)  86

Question 11

Calculate the value mentally.
-$0.1 ^ { 1 / 2 } \cdot 160 ^ { 1 / 2 }$

Accepted Answer

A)  8 
B)  4 
C)  2 
D)  16 
A)  8 
B)  4 
C)  2 
D)  16

Question 12

Evaluate the expression.
-$| - 7 |$

Accepted Answer

A)  -7 
B)  ±7 
C)  7 
D)  0 
A)  -7 
B)  ±7 
C)  7 
D)  0

Question 13

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { \mathrm { mn } ^ { - 1 } - \mathrm { nm } - 1 } { \mathrm {~m} ^ { 2 } - \mathrm { n } ^ { 2 } }$$

Accepted Answer

A)  $\frac { 1 } { m n }$ 
B)  $\frac { 1 } { m + n }$ 
C)  $m + n$ 
D)  $\mathrm { mn }$ 
A)  $\frac { 1 } { m n }$ 
B)  $\frac { 1 } { m + n }$ 
C)  $m + n$ 
D)  $\mathrm { mn }$

Question 14

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { - 15 } } { x ^ { - 7 } }$$

Accepted Answer

A)  $- x ^ { 22 }$ 
B)  $x ^ { 8 }$ 
C)  $\frac { 1 } { x ^ { 22 } }$ 
D)  $\frac { 1 } { x ^ { 8 } }$ 
A)  $- x ^ { 22 }$ 
B)  $x ^ { 8 }$ 
C)  $\frac { 1 } { x ^ { 22 } }$ 
D)  $\frac { 1 } { x ^ { 8 } }$

Question 15

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( \frac { 4 x ^ { 2 } y ^ { 4 } } { z ^ { 3 } } \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { 4 x ^ { 6 } y ^ { 12 } } { z ^ { 6 } }$ 
B)  $\frac { 64 x ^ { 6 } y ^ { 12 } } { z ^ { 9 } }$ 
C)  $\frac { 4 x ^ { 6 } y ^ { 12 } } { z ^ { 9 } }$ 
D)  $\frac { 64 x ^ { 5 } y ^ { 7 } } { z ^ { 6 } }$ 
A)  $\frac { 4 x ^ { 6 } y ^ { 12 } } { z ^ { 6 } }$ 
B)  $\frac { 64 x ^ { 6 } y ^ { 12 } } { z ^ { 9 } }$ 
C)  $\frac { 4 x ^ { 6 } y ^ { 12 } } { z ^ { 9 } }$ 
D)  $\frac { 64 x ^ { 5 } y ^ { 7 } } { z ^ { 6 } }$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { 16 a ^ { 4 } }$$

Accepted Answer

A)  $2 a ^ { 2 }$ 
B)  $2 a$ 
C)  $16 a$ 
D)  $2 \sqrt { a }$ 
A)  $2 a ^ { 2 }$ 
B)  $2 a$ 
C)  $16 a$ 
D)  $2 \sqrt { a }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 100 } - \sqrt { 144 }$

Accepted Answer

A)  $- 2$ 
B)  $- \sqrt { 2 }$ 
C)  $- 1$ 
D)  $- 2 \sqrt { 11 }$ 
A)  $- 2$ 
B)  $- \sqrt { 2 }$ 
C)  $- 1$ 
D)  $- 2 \sqrt { 11 }$

Question 18

Evaluate the expression.
-$$\left( \frac { 4 } { 49 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $\frac { 4 } { 7 }$ 
B)  not a real number 
C)  $\frac { 2 } { 49 }$ 
D)  $\frac { 2 } { 7 }$ 
A)  $\frac { 4 } { 7 }$ 
B)  not a real number 
C)  $\frac { 2 } { 49 }$ 
D)  $\frac { 2 } { 7 }$

Question 19

Answer the question.
-$$n ^ { 2 } \left( 3 n - \frac { 1 } { 10 } \right) \left( 10 n + \frac { 1 } { 5 } \right)$$

Accepted Answer

A)  $30 n ^ { 4 } - \frac { 8 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
B)  $30 n ^ { 4 } + \frac { 2 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
C)  $30 n ^ { 4 } - \frac { 2 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
D)  $30 n ^ { 4 } - \frac { 2 } { 5 } n ^ { 3 } + \frac { 1 } { 50 } n ^ { 2 }$ 
A)  $30 n ^ { 4 } - \frac { 8 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
B)  $30 n ^ { 4 } + \frac { 2 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
C)  $30 n ^ { 4 } - \frac { 2 } { 5 } n ^ { 3 } - \frac { 1 } { 50 } n ^ { 2 }$ 
D)  $30 n ^ { 4 } - \frac { 2 } { 5 } n ^ { 3 } + \frac { 1 } { 50 } n ^ { 2 }$

Question 20

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| - 1 | = - | 1 |$$

Accepted Answer

A)  True 
B)  False; $| - 1 | = - ( - 1 ) = 1$ 
A)  True 
B)  False; $| - 1 | = - ( - 1 ) = 1$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 4 x ) ^ { 0 }$

Tell whether the statement is true or false. -{0, 4, 7, 12} = {7, 4, 12, 0}

Solve the equation - $\frac { 25 y ^ { 4 } + 10 y ^ { 3 } + 2 y - 1 } { 5 y ^ { 2 } + 1 }$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{6,7,8\}$ _____ $\{0,6,7,8,9,10\}$

Factor by any method. - $20 x ^ { 2 } + 15 x + 24 x + 18$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$

Write in radical form. Assume all variables represent positive real numbers. - $( \mathrm { mn } ) ^ { 1 / 6 }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of 80 and a windchill factor of -6.

Calculate the value mentally. - $0.1 ^ { 1 / 2 } \cdot 160 ^ { 1 / 2 }$

Evaluate the expression. - $| - 7 |$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { \mathrm { mn } ^ { - 1 } - \mathrm { nm } - 1 } { \mathrm {~m} ^ { 2 } - \mathrm { n } ^ { 2 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 15 } } { x ^ { - 7 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { 4 x ^ { 2 } y ^ { 4 } } { z ^ { 3 } } \right) ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 16 a ^ { 4 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 100 } - \sqrt { 144 }$

Evaluate the expression. - $\left( \frac { 4 } { 49 } \right) ^ { 1 / 2 }$

Answer the question. - $n ^ { 2 } \left( 3 n - \frac { 1 } { 10 } \right) \left( 10 n + \frac { 1 } { 5 } \right)$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 1 | = - | 1 |$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (4x)0( 4 x ) ^ { 0 }(4x)0

Tell whether the statement is true or false. -{0, 4, 7, 12} = {7, 4, 12, 0}

Solve the equation - 25y4+10y3+2y−15y2+1\frac { 25 y ^ { 4 } + 10 y ^ { 3 } + 2 y - 1 } { 5 y ^ { 2 } + 1 }5y2+125y4+10y3+2y−1​

Insert ⊆\subseteq⊆ or ⊈\nsubseteq⊈ in the blank to make the statement true. - {6,7,8}\{6,7,8\}{6,7,8} _____ {0,6,7,8,9,10}\{0,6,7,8,9,10\}{0,6,7,8,9,10}

Factor by any method. - 20x2+15x+24x+1820 x ^ { 2 } + 15 x + 24 x + 1820x2+15x+24x+18

Write in radical form. Assume all variables represent positive real numbers. - (mn)1/6( \mathrm { mn } ) ^ { 1 / 6 }(mn)1/6