Question 1

Factor by any method.
-$$25 z ^ { 4 } + 5 z ^ { 2 } - 12$$

Accepted Answer

A)  $\left( 5 z ^ { 4 } + 4 \right) ( 5 z - 3 )$ 
B)  $\left( 5 z ^ { 2 } + 4 \right) \left( 5 z ^ { 2 } - 3 \right)$ 
C)  $\left( 5 z ^ { 2 } + 3 \right) \left( 5 z ^ { 2 } - 4 \right)$ 
D)  $\left( 5 z ^ { 4 } + 3 \right) ( 5 z - 4 )$ 
A)  $\left( 5 z ^ { 4 } + 4 \right) ( 5 z - 3 )$ 
B)  $\left( 5 z ^ { 2 } + 4 \right) \left( 5 z ^ { 2 } - 3 \right)$ 
C)  $\left( 5 z ^ { 2 } + 3 \right) \left( 5 z ^ { 2 } - 4 \right)$ 
D)  $\left( 5 z ^ { 4 } + 3 \right) ( 5 z - 4 )$

Question 2

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 3 \sqrt { x } } { \sqrt { x } - 3 \sqrt { y } }$$

Accepted Answer

A)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x - 9 y }$ 
B)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x - 3 y }$ 
C)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x + 3 y }$ 
D)  $\frac { 3 \sqrt { x } ( \sqrt { x } - 3 \sqrt { y } ) } { x + 9 y }$ 
A)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x - 9 y }$ 
B)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x - 3 y }$ 
C)  $\frac { 3 \sqrt { x } ( \sqrt { x } + 3 \sqrt { y } ) } { x + 3 y }$ 
D)  $\frac { 3 \sqrt { x } ( \sqrt { x } - 3 \sqrt { y } ) } { x + 9 y }$

Question 3

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }$$

Accepted Answer

A)  $\frac { a ^ { 8 } } { b ^ { 5 } }$ 
B)  $\frac { a ^ { 8 } } { b ^ { 10 } }$ 
C)  $\frac { a ^ { 5 } } { b ^ { 10 } }$ 
D)  $\frac { a ^ { 10 } } { b ^ { 8 } }$ 
A)  $\frac { a ^ { 8 } } { b ^ { 5 } }$ 
B)  $\frac { a ^ { 8 } } { b ^ { 10 } }$ 
C)  $\frac { a ^ { 5 } } { b ^ { 10 } }$ 
D)  $\frac { a ^ { 10 } } { b ^ { 8 } }$

Question 4

Determine which property of absolute value justifies the statement.
-$| x + y | \leq | x | + | y |$

Accepted Answer

A)  Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers. 
B)  Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of their absolute values (the triangle inequality). 
C)  Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers. 
D)  Property 5: the sum of the absolute values of two numbers is less than or equal to the absolute value of their sum (the triangle inequality). 
A)  Property 4: the absolute value of the sum of the numbers is less than or equal to the sum of the two numbers. 
B)  Property 5: the absolute value of the sum of two numbers is less than or equal to the sum of their absolute values (the triangle inequality). 
C)  Property 4: the sum of two numbers is less than or equal to the absolute value of the sum of the numbers. 
D)  Property 5: the sum of the absolute values of two numbers is less than or equal to the absolute value of their sum (the triangle inequality).

Question 5

Evaluate the expression.
-$$\left( \frac { 1 } { 100 } \right) ^ { 5 / 2 }$$

Accepted Answer

A)  not a real number 
B)  $\frac { 1 } { 100,000 }$ 
C)  $- 250$ 
D)  $- 100,000$ 
A)  not a real number 
B)  $\frac { 1 } { 100,000 }$ 
C)  $- 250$ 
D)  $- 100,000$

Question 6

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 7

Use set notation, and list all the elements of the set.
-The natural numbers between 3 and 5. 6)

Accepted Answer

A)  {3, 5} 
B)  {3, 4, 5} 
C)  {0, 1, 2, 3} 
D)  {4} 
A)  {3, 5} 
B)  {3, 4, 5} 
C)  {0, 1, 2, 3} 
D)  {4}

Question 8

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$\frac { x ^ { 2 } } { y } < 0$

Accepted Answer

A)  x and y have different signs. 
B)  x and y must be negative. 
C)  x must be negative. 
D)  y must be negative. 
A)  x and y have different signs. 
B)  x and y must be negative. 
C)  x must be negative. 
D)  y must be negative.

Question 9

Factor by any method.
-$$20 z ^ { 6 } + 3 z ^ { 3 } - 9$$

Accepted Answer

A)  $\left( 4 z ^ { 3 } + 3 \right) \left( 5 z ^ { 3 } - 3 \right)$ 
B)  $\left( 5 z ^ { 3 } + 3 \right) \left( 4 z ^ { 3 } - 3 \right)$ 
C)  $\left( 4 z ^ { 3 } + 1 \right) \left( 5 z ^ { 3 } - 9 \right)$ 
D)  $20 \left( z ^ { 3 } - 3 \right) \left( z ^ { 3 } + 3 \right)$ 
A)  $\left( 4 z ^ { 3 } + 3 \right) \left( 5 z ^ { 3 } - 3 \right)$ 
B)  $\left( 5 z ^ { 3 } + 3 \right) \left( 4 z ^ { 3 } - 3 \right)$ 
C)  $\left( 4 z ^ { 3 } + 1 \right) \left( 5 z ^ { 3 } - 9 \right)$ 
D)  $20 \left( z ^ { 3 } - 3 \right) \left( z ^ { 3 } + 3 \right)$

Question 10

Solve the problem.
-$$( n - 1 ) ( n - 1 ) ( n + 1 ) ( n + 1 )$$

Accepted Answer

A)  $n ^ { 4 } - 2 n ^ { 2 } + 1$ 
B)  $n ^ { 4 } + 2 n - 1$ 
C)  $n ^ { 4 } - 2 n + 1$ 
D)  $n ^ { 4 } + 2 n ^ { 2 } - 1$ 
A)  $n ^ { 4 } - 2 n ^ { 2 } + 1$ 
B)  $n ^ { 4 } + 2 n - 1$ 
C)  $n ^ { 4 } - 2 n + 1$ 
D)  $n ^ { 4 } + 2 n ^ { 2 } - 1$

Question 11

Evaluate the expression.
-$8 [ 1 - 7 ( - 6 - 7 ) ]$

Accepted Answer

A)  620 
B)  99 
C)  624 
D)  736 
A)  620 
B)  99 
C)  624 
D)  736

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { \frac { 256 } { y } }$$

Accepted Answer

A)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 3 } } } { \mathrm { y } }$ 
B)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 2 } } } { \mathrm { y } }$ 
C)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } } } { \mathrm { y } }$ 
D)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 3 } } } { y ^ { 2 } }$ 
A)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 3 } } } { \mathrm { y } }$ 
B)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 2 } } } { \mathrm { y } }$ 
C)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } } } { \mathrm { y } }$ 
D)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 3 } } } { y ^ { 2 } }$

Question 13

Evaluate the expression.
-$1024 ^ { 4 / 5 }$

Accepted Answer

A)  262,144 
B)  16,384 
C)  256 
D)  65,536 
A)  262,144 
B)  16,384 
C)  256 
D)  65,536

Question 14

Solve the problem.
-The cost of manufacturing clocks is given by $\mathrm { c } = 36 ( \mathrm { n } + 144 ) ^ { 1 / 2 }$, where $\mathrm { c }$ is the cost in dollars and $\mathrm { n }$ is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $\$ 36$ 
B)  $\$ 432$ 
C)  $\$ 5184$ 
D)  $\$ 72$ 
A)  $\$ 36$ 
B)  $\$ 432$ 
C)  $\$ 5184$ 
D)  $\$ 72$

Question 15

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 9,10,11,12,13,14,15,16,17,18,19 \} , \mathrm { M } = \{ 9,11,13,15 \} , \mathrm { N } = \{ 10,12,14,16,18 \}$, $Q = \{ 9,11,13,15,17,19 \}$, and $R = \{ 9,10,11,12 \}$.
$M \cap R$

Accepted Answer

A)  $\{ 9,10,11,12 \}$ 
B)  $\{ 9,10,11,12,13,15 \}$ 
C)  $\{ 9,11 \}$ 
D)  $\varnothing ; \mathrm { M }$ and $\mathrm { R }$ are disjoint sets. 
A)  $\{ 9,10,11,12 \}$ 
B)  $\{ 9,10,11,12,13,15 \}$ 
C)  $\{ 9,11 \}$ 
D)  $\varnothing ; \mathrm { M }$ and $\mathrm { R }$ are disjoint sets.

Question 16

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\{ 9,10,11,14 \}$ _____$\{ 9,13,11,12,10,14 \}$

Accepted Answer

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

Question 17

Determine the degree of the polynomial.
-$- x - 2 x ^ { 2 } - 3 x ^ { 3 } - 4 x ^ { 5 }$

Accepted Answer

A)  4 
B)  5 
C)  10 
D)  11 
A)  4 
B)  5 
C)  10 
D)  11

Question 18

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 12 , \sqrt { 7 } , - 23,0 , \frac { 0 } { 2 } , \sqrt { 16 } , \frac { - 2 } { 0 } , 0.18 \right\}$$
Rational numbers

Accepted Answer

A)  $\sqrt { 7 } , \sqrt { 16 }$ 
B)  $12 , - 23,0 , \frac { 0 } { 2 } , \sqrt { 16 } , 0.18$ 
C)  $12,0 , \sqrt { 16 }$ 
D)  $\sqrt { 7 } , \frac { 0 } { 2 } , 0.18$ 
A)  $\sqrt { 7 } , \sqrt { 16 }$ 
B)  $12 , - 23,0 , \frac { 0 } { 2 } , \sqrt { 16 } , 0.18$ 
C)  $12,0 , \sqrt { 16 }$ 
D)  $\sqrt { 7 } , \frac { 0 } { 2 } , 0.18$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - 64 a ^ { 8 } b ^ { 5 } }$$

Accepted Answer

A)  $- 4 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
B)  $4 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
C)  not a real number 
D)  $4 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$ 
A)  $- 4 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
B)  $4 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
C)  not a real number 
D)  $4 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$

Question 20

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { a \sqrt { x } - 7 } { a \sqrt { x } + 7 }$$

Accepted Answer

A)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } - 49 } { a ^ { 2 } x + 49 }$ 
B)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } + 49 } { a ^ { 2 } x + 49 }$ 
C)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } + 49 } { a ^ { 2 } x - 49 }$ 
D)  $\frac { a ^ { 2 } x + 14 a \sqrt { x } - 49 } { a ^ { 2 } x - 49 }$ 
A)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } - 49 } { a ^ { 2 } x + 49 }$ 
B)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } + 49 } { a ^ { 2 } x + 49 }$ 
C)  $\frac { a ^ { 2 } x - 14 a \sqrt { x } + 49 } { a ^ { 2 } x - 49 }$ 
D)  $\frac { a ^ { 2 } x + 14 a \sqrt { x } - 49 } { a ^ { 2 } x - 49 }$

Factor by any method. - $25 z ^ { 4 } + 5 z ^ { 2 } - 12$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 3 \sqrt { x } } { \sqrt { x } - 3 \sqrt { y } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }$

Determine which property of absolute value justifies the statement. - $| x + y | \leq | x | + | y |$

Evaluate the expression. - $\left( \frac { 1 } { 100 } \right) ^ { 5 / 2 }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. - $Insert \in or \notin in the blank to make the statement is true. -$

Use set notation, and list all the elements of the set. -The natural numbers between 3 and 5. 6)

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 2 } } { y } < 0$

Factor by any method. - $20 z ^ { 6 } + 3 z ^ { 3 } - 9$

Solve the problem. - $( n - 1 ) ( n - 1 ) ( n + 1 ) ( n + 1 )$

Evaluate the expression. - $8 [ 1 - 7 ( - 6 - 7 ) ]$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 256 } { y } }$

Evaluate the expression. - $1024 ^ { 4 / 5 }$

Solve the problem. -The cost of manufacturing clocks is given by $\mathrm { c } = 36 ( \mathrm { n } + 144 ) ^ { 1 / 2 }$ , where $\mathrm { c }$ is the cost in dollars and $\mathrm { n }$ is the number produced. What is the cost when no clocks are produced?

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 9,10,11,12,13,14,15,16,17,18,19 \} , \mathrm { M } = \{ 9,11,13,15 \} , \mathrm { N } = \{ 10,12,14,16,18 \}$ , $Q = \{ 9,11,13,15,17,19 \}$ , and $R = \{ 9,10,11,12 \}$ . $M \cap R$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{ 9,10,11,14 \}$ _____ $\{ 9,13,11,12,10,14 \}$

Determine the degree of the polynomial. - $- x - 2 x ^ { 2 } - 3 x ^ { 3 } - 4 x ^ { 5 }$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 12 , \sqrt { 7 } , - 23,0 , \frac { 0 } { 2 } , \sqrt { 16 } , \frac { - 2 } { 0 } , 0.18 \right\}$ Rational numbers

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 64 a ^ { 8 } b ^ { 5 } }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { a \sqrt { x } - 7 } { a \sqrt { x } + 7 }$

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

Factor by any method. - 25z4+5z2−1225 z ^ { 4 } + 5 z ^ { 2 } - 1225z4+5z2−12

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 3xx−3y\frac { 3 \sqrt { x } } { \sqrt { x } - 3 \sqrt { y } }x​−3y​3x​​

Simplify the expression. Assume all variables represent nonzero real numbers. - (a4b5)2\left( \frac { a ^ { 4 } } { b ^ { 5 } } \right) ^ { 2 }(b5a4​)2

Determine which property of absolute value justifies the statement. - ∣x+y∣≤∣x∣+∣y∣| x + y | \leq | x | + | y |∣x+y∣≤∣x∣+∣y∣

Evaluate the expression. - (1100)5/2\left( \frac { 1 } { 100 } \right) ^ { 5 / 2 }(1001​)5/2

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -