Question 1

Write an inequality using absolute value that represents the given condition.
-The distance between y and L is less than $\varepsilon$ (epsilon).

Accepted Answer

A)  $| y | < \varepsilon - L$ 
B)  $| y + L | < \varepsilon$ or $| L + y | < \varepsilon$ 
C)  $| y - L | < \varepsilon$ or $| L - y | < \varepsilon$ 
D)  $| y | < \varepsilon + L$ 
A)  $| y | < \varepsilon - L$ 
B)  $| y + L | < \varepsilon$ or $| L + y | < \varepsilon$ 
C)  $| y - L | < \varepsilon$ or $| L - y | < \varepsilon$ 
D)  $| y | < \varepsilon + L$ C

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The product property of radicals indicates that $\sqrt [ n ] { a } \cdot \sqrt [ n ] { b } =$ provided that $\sqrt [ n ] { a } \text { and } \sqrt [ n ] { b }$ represent real numbers.

Accepted Answer

$\sqrt [ n ] { a \cdot b }$

Question 3

For the following exercise, interval notation is given for several sets of real numbers. Graph the set and
write the corresponding set-builder notation.
-$( - \infty , 1.1 ]$

Accepted Answer

A) $\{x \mid x \leq 1.1\}$ B) $\{x \mid x \geq 1.1\}$ C) $\{ x \mid x > 1.1 \}$ D) $\{x \mid x<1.1\}$ A) $\{x \mid x \leq 1.1\}$ B) $\{x \mid x \geq 1.1\}$ C) $\{ x \mid x > 1.1 \}$ D) $\{x \mid x<1.1\}$ A

Question 4

Solve the problem.
-A tool rental store charges a flat fee of $\$ 8.50$ to rent a chain saw, and $\$ 4.00$ for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

Accepted Answer

A)  $\$ 36.50$ 
B)  $\$ 32.50$ 
C)  \$28.00 
D)  $\$ 12.50$ 
A)  $\$ 36.50$ 
B)  $\$ 32.50$ 
C)  \$28.00 
D)  $\$ 12.50$

Question 5

Subtract the polynomials and simplify.
-$$\left( \frac { 2 } { 7 } p ^ { 2 } - \frac { 1 } { 2 } p q + \frac { 3 } { 14 } q ^ { 2 } + 14 \right) - \left( \frac { 9 } { 14 } p ^ { 2 } + \frac { 4 } { 7 } p q - \frac { 5 } { 14 } q ^ { 2 } + 11 \right)$$

Accepted Answer

A)  $- \frac { 5 } { 14 } p ^ { 2 } - \frac { 15 } { 14 } p q + \frac { 4 } { 7 } q ^ { 2 } + 25$ 
B)  $- \frac { 5 } { 14 } p ^ { 2 } + \frac { 1 } { 14 } p q - \frac { 1 } { 7 } q ^ { 2 } + 25$ 
C)  $\frac { 13 } { 14 } p ^ { 2 } + \frac { 1 } { 14 } p q - \frac { 1 } { 7 } q ^ { 2 } + 25$ 
D)  $- \frac { 5 } { 14 } p ^ { 2 } - \frac { 15 } { 14 } p q + \frac { 4 } { 7 } q ^ { 2 } + 3$ 
A)  $- \frac { 5 } { 14 } p ^ { 2 } - \frac { 15 } { 14 } p q + \frac { 4 } { 7 } q ^ { 2 } + 25$ 
B)  $- \frac { 5 } { 14 } p ^ { 2 } + \frac { 1 } { 14 } p q - \frac { 1 } { 7 } q ^ { 2 } + 25$ 
C)  $\frac { 13 } { 14 } p ^ { 2 } + \frac { 1 } { 14 } p q - \frac { 1 } { 7 } q ^ { 2 } + 25$ 
D)  $- \frac { 5 } { 14 } p ^ { 2 } - \frac { 15 } { 14 } p q + \frac { 4 } { 7 } q ^ { 2 } + 3$

Question 6

Write the set as a single interval.
-$( - \infty , 5 ) \cap ( - 6,8 ) \cap [ 1,6 ]$

Accepted Answer

A)  $( - \infty , 8 )$ 
B)  $[ 1,5 )$ 
C)  $[ 1,6 ]$ 
D)  $( - 6,5 )$ 
A)  $( - \infty , 8 )$ 
B)  $[ 1,5 )$ 
C)  $[ 1,6 ]$ 
D)  $( - 6,5 )$

Question 7

Express the set in interval notation.
-

Accepted Answer

A)  $( - \infty , 9 )$ 
B)  $( - \infty , 9 ]$ 
C)  $( 9 , \infty )$ 
D)  $[ - \infty , 9 ]$ 
A)  $( - \infty , 9 )$ 
B)  $( - \infty , 9 ]$ 
C)  $( 9 , \infty )$ 
D)  $[ - \infty , 9 ]$

Question 8

Write the word or phrase that best completes each statement or answers the question.
Write the expression by using rational exponents rather than radical notation.
-$$\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$$

Accepted Answer

A)  $\frac { 27 s ^ { 6 } } { 8 }$ 
B)  $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$ 
C)  $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$ 
D)  $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$ 
A)  $\frac { 27 s ^ { 6 } } { 8 }$ 
B)  $\frac { 27 s ^ { 12 } } { 8 r ^ { 6 } }$ 
C)  $\frac { 3 s ^ { 16 } r ^ { 8 } } { 2 }$ 
D)  $\frac { 3 s ^ { 12 } } { 2 r ^ { 6 } }$

Question 9

Simplify the radical. Assume that all variables represent positive real numbers.
-$9 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }$

Accepted Answer

A)  $\frac { 27 } { 64 } c ^ { 18 } d ^ { 20 } \sqrt [ 3 ] { c d }$ 
B)  $\frac { 9 } { 4 } c d \sqrt [ 3 ] { c ^ { 18 } d ^ { 20 } }$ 
C)  $\frac { 9 } { 4 } c ^ { 6 } d ^ { 6 } \sqrt [ 3 ] { d ^ { 2 } }$ 
D)  $\frac { 9 } { 64 } c ^ { 6 } d ^ { 7 }$ 
A)  $\frac { 27 } { 64 } c ^ { 18 } d ^ { 20 } \sqrt [ 3 ] { c d }$ 
B)  $\frac { 9 } { 4 } c d \sqrt [ 3 ] { c ^ { 18 } d ^ { 20 } }$ 
C)  $\frac { 9 } { 4 } c ^ { 6 } d ^ { 6 } \sqrt [ 3 ] { d ^ { 2 } }$ 
D)  $\frac { 9 } { 64 } c ^ { 6 } d ^ { 7 }$

Question 10

Simply the expression. Assume that all variable expressions represent positive real numbers.
-$$\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }$$

Accepted Answer

A)  $\frac { 31 \sqrt { 13 x } } { 26 x }$ 
B)  $\frac { 31 \sqrt { 13 x } } { 13 x }$ 
C)  $\frac { 234 \sqrt { 13 x } } { 26 x }$ 
D)  $\frac { 234 \sqrt { 13 x } } { 13 x }$ 
A)  $\frac { 31 \sqrt { 13 x } } { 26 x }$ 
B)  $\frac { 31 \sqrt { 13 x } } { 13 x }$ 
C)  $\frac { 234 \sqrt { 13 x } } { 26 x }$ 
D)  $\frac { 234 \sqrt { 13 x } } { 13 x }$

Question 11

Simplify the expression. Write your answer with positive exponents only.
-$$\left( x ^ { 9 } \right) ^ { 4 }$$

Accepted Answer

A)  $x ^ { 6,561 }$ 
B)  $x ^ { 13 }$ 
C)  $x ^ { 36 }$ 
D)  $x ^ { 5 }$ 
A)  $x ^ { 6,561 }$ 
B)  $x ^ { 13 }$ 
C)  $x ^ { 36 }$ 
D)  $x ^ { 5 }$

Question 12

Factor completely.
-$3 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }$

Accepted Answer

A)  $3 c ^ { 9 / 5 } ( c - 1 )$ 
B)  $\frac { 3 ( c - 1 ) } { c^{4 / 5} }$ 
C)  $3 c ^ { 4 / 5 } ( c - 1 )$ 
D)  $c ^ { 4 / 5 } ( 3 c - 3 )$ 
A)  $3 c ^ { 9 / 5 } ( c - 1 )$ 
B)  $\frac { 3 ( c - 1 ) } { c^{4 / 5} }$ 
C)  $3 c ^ { 4 / 5 } ( c - 1 )$ 
D)  $c ^ { 4 / 5 } ( 3 c - 3 )$

Question 13

Rationalize the denominator.
-$\frac { - 13 } { \sqrt { x } }$

Accepted Answer

A)  $\frac { - 13 \sqrt { x } } { x }$ 
B)  $\frac { x \sqrt { x } } { - 13 }$ 
C)  $\frac { 169 } { x }$ 
D)  Already rationalized. 
A)  $\frac { - 13 \sqrt { x } } { x }$ 
B)  $\frac { x \sqrt { x } } { - 13 }$ 
C)  $\frac { 169 } { x }$ 
D)  Already rationalized.

Question 14

Determine whether the statement is true or false.
-$- 3 . \overline { 51 } > - 3.5 \overline { 1 }$

Accepted Answer

A) True 
 B)False

Question 15

Evaluate the root without using a calculator or note that root is not a real number.
-$\sqrt [ 3 ] { 64 }$

Accepted Answer

A)  5 
B)  4 
C)  $- 4$ 
D)  Not a real number 
A)  5 
B)  4 
C)  $- 4$ 
D)  Not a real number

Question 16

Factor completely.
-$m ^ { 6 } + 124 m ^ { 3 } - 125$

Accepted Answer

A)  $( m + 5 ) \left( m ^ { 2 } + 5 m + 25 \right) ( m - 1 ) \left( m ^ { 2 } - m - 1 \right)$ 
B)  $( m + 4 ) \left( 2 m ^ { 2 } - 4 m + 26 \right)$ 
C)  $\left( m ^ { 3 } - 125 \right) \left( m ^ { 3 } - 1 \right)$ 
D)  $( m + 5 ) \left( m ^ { 2 } - 5 m + 25 \right) ( m - 1 ) \left( m ^ { 2 } + m + 1 \right)$ 
A)  $( m + 5 ) \left( m ^ { 2 } + 5 m + 25 \right) ( m - 1 ) \left( m ^ { 2 } - m - 1 \right)$ 
B)  $( m + 4 ) \left( 2 m ^ { 2 } - 4 m + 26 \right)$ 
C)  $\left( m ^ { 3 } - 125 \right) \left( m ^ { 3 } - 1 \right)$ 
D)  $( m + 5 ) \left( m ^ { 2 } - 5 m + 25 \right) ( m - 1 ) \left( m ^ { 2 } + m + 1 \right)$

Question 17

Determine whether the statement is true or false.
-$13 < - \sqrt { 13 }$

Accepted Answer

A) True 
 B)False

Question 18

Given the expression $b ^ { n }$ , the value of b is called the________ and n is called the ________.

Accepted Answer

base, expo

Question 19

Add or subtract as indicated and simplify if possible.
-$\frac { 5 } { x ^ { 2 } + 1 x - 6 } - \frac { 4 } { x ^ { 2 } + 0 x - 4 }$

Accepted Answer

A)  $\frac { 1 } { x - 2 } \left( \frac { x + 22 } { ( x + 3 ) ( x + 2 ) } \right)$ 
B)  $\frac { 1 } { ( x + 3 ) ( x + 2 ) }$ 
C)  1 
D)  $\frac { x } { ( x - 2 ) ( x + 3 ) ( x + 2 ) }$ 
A)  $\frac { 1 } { x - 2 } \left( \frac { x + 22 } { ( x + 3 ) ( x + 2 ) } \right)$ 
B)  $\frac { 1 } { ( x + 3 ) ( x + 2 ) }$ 
C)  1 
D)  $\frac { x } { ( x - 2 ) ( x + 3 ) ( x + 2 ) }$

Question 20

Write the answer as a single term and simplify.
-$$( x + 3 ) ^ { 1 / 4 } + \frac { x } { 5 ( x + 3 ) ^ { 3 / 4 } }$$

Accepted Answer

A)  $\frac { 5 + x } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
B)  $\frac { 6 x + 15 } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
C)  $1 + \frac { x } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
D)  $\frac { 6 x + 3 } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
A)  $\frac { 5 + x } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
B)  $\frac { 6 x + 15 } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
C)  $1 + \frac { x } { 5 ( x + 3 ) ^ { 3 / 4 } }$ 
D)  $\frac { 6 x + 3 } { 5 ( x + 3 ) ^ { 3 / 4 } }$

Write an inequality using absolute value that represents the given condition. -The distance between y and L is less than $\varepsilon$ (epsilon).

For the following exercise, interval notation is given for several sets of real numbers. Graph the set and write the corresponding set-builder notation. - $( - \infty , 1.1 ]$

Solve the problem. -A tool rental store charges a flat fee of $\$ 8.50$ to rent a chain saw, and $\$ 4.00$ for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

Subtract the polynomials and simplify. - $\left( \frac { 2 } { 7 } p ^ { 2 } - \frac { 1 } { 2 } p q + \frac { 3 } { 14 } q ^ { 2 } + 14 \right) - \left( \frac { 9 } { 14 } p ^ { 2 } + \frac { 4 } { 7 } p q - \frac { 5 } { 14 } q ^ { 2 } + 11 \right)$

Write the set as a single interval. - $( - \infty , 5 ) \cap ( - 6,8 ) \cap [ 1,6 ]$

Express the set in interval notation. -

Write the word or phrase that best completes each statement or answers the question. Write the expression by using rational exponents rather than radical notation. - $\left( \frac { 81 s ^ { 12 } r ^ { - 4 } } { 16 s ^ { - 4 } r ^ { 4 } } \right) ^ { 3 / 4 }$

Simplify the radical. Assume that all variables represent positive real numbers. - $9 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }$

Simply the expression. Assume that all variable expressions represent positive real numbers. - $\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }$

Simplify the expression. Write your answer with positive exponents only. - $\left( x ^ { 9 } \right) ^ { 4 }$

Factor completely. - $3 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }$

Rationalize the denominator. - $\frac { - 13 } { \sqrt { x } }$

Determine whether the statement is true or false. - $- 3 . \overline { 51 } > - 3.5 \overline { 1 }$

Evaluate the root without using a calculator or note that root is not a real number. - $\sqrt [ 3 ] { 64 }$

Factor completely. - $m ^ { 6 } + 124 m ^ { 3 } - 125$

Determine whether the statement is true or false. - $13 < - \sqrt { 13 }$

Given the expression $b ^ { n }$ , the value of b is called the and n is called the .

Add or subtract as indicated and simplify if possible. - $\frac { 5 } { x ^ { 2 } + 1 x - 6 } - \frac { 4 } { x ^ { 2 } + 0 x - 4 }$

Write the answer as a single term and simplify. - $( x + 3 ) ^ { 1 / 4 } + \frac { x } { 5 ( x + 3 ) ^ { 3 / 4 } }$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Filters

Exam 9: Review of Prerequisites

Write an inequality using absolute value that represents the given condition. -The distance between y and L is less than ε\varepsilonε (epsilon).

For the following exercise, interval notation is given for several sets of real numbers. Graph the set and write the corresponding set-builder notation. - (−∞,1.1]( - \infty , 1.1 ](−∞,1.1]

Solve the problem. -A tool rental store charges a flat fee of $8.50\$ 8.50$8.50 to rent a chain saw, and $4.00\$ 4.00$4.00 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week.

Write the set as a single interval. - (−∞,5)∩(−6,8)∩[1,6]( - \infty , 5 ) \cap ( - 6,8 ) \cap [ 1,6 ](−∞,5)∩(−6,8)∩[1,6]

Express the set in interval notation. -

Simplify the radical. Assume that all variables represent positive real numbers. - 9c18d206439 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }9364c18d20​​

Simply the expression. Assume that all variable expressions represent positive real numbers. - 1813x+13xx\frac { 18 } { \sqrt { 13 x } } + \frac { \sqrt { 13 x } } { x }13x​18​+x13x​​

Simplify the expression. Write your answer with positive exponents only. - (x9)4\left( x ^ { 9 } \right) ^ { 4 }(x9)4

Factor completely. - 3c9/5−3c4/53 c ^ { 9 / 5 } - 3 c ^ { 4 / 5 }3c9/5−3c4/5

Rationalize the denominator. - −13x\frac { - 13 } { \sqrt { x } }x​−13​

Determine whether the statement is true or false. - −3.51‾>−3.51‾- 3 . \overline { 51 } > - 3.5 \overline { 1 }−3.51>−3.51

Evaluate the root without using a calculator or note that root is not a real number. - 643\sqrt [ 3 ] { 64 }364​

Factor completely. - m6+124m3−125m ^ { 6 } + 124 m ^ { 3 } - 125m6+124m3−125

Determine whether the statement is true or false. - 13<−1313 < - \sqrt { 13 }13<−13​

Given the expression bnb ^ { n }bn , the value of b is called the________ and n is called the ________.

Add or subtract as indicated and simplify if possible. - 5x2+1x−6−4x2+0x−4\frac { 5 } { x ^ { 2 } + 1 x - 6 } - \frac { 4 } { x ^ { 2 } + 0 x - 4 }x2+1x−65​−x2+0x−44​

Write the answer as a single term and simplify. - (x+3)1/4+x5(x+3)3/4( x + 3 ) ^ { 1 / 4 } + \frac { x } { 5 ( x + 3 ) ^ { 3 / 4 } }(x+3)1/4+5(x+3)3/4x​