Question 1

Find the sum or difference.
-$$\frac { x ^ { 4 } + 7 x ^ { 2 } + 10 } { x ^ { 2 } + 1 }$$

Accepted Answer

A)  $x ^ { 2 } + 6 x + \frac { 3 } { 2 }$ 
B)  $x ^ { 2 } + 6$ 
C)  $x ^ { 2 } + 6 + \frac { 4 } { x ^ { 2 } + 1 }$ 
D)  $x ^ { 2 } + 6 x + 4$ 
A)  $x ^ { 2 } + 6 x + \frac { 3 } { 2 }$ 
B)  $x ^ { 2 } + 6$ 
C)  $x ^ { 2 } + 6 + \frac { 4 } { x ^ { 2 } + 1 }$ 
D)  $x ^ { 2 } + 6 x + 4$

Question 2

Evaluate the expression.
-$7776 ^ { 4 / 5 }$

Accepted Answer

A)  10,077,696 
B)  279,936 
C)  1,679,616 
D)  1296 
A)  10,077,696 
B)  279,936 
C)  1,679,616 
D)  1296

Question 3

Identify the set as finite or infinite.
-$\{ x \mid x \text { is a natural number larger than } 1 \}$

Accepted Answer

A)  infinite 
B)  finite 
A)  infinite 
B)  finite

Question 4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\left( \frac { 1 } { 3 } y \right) ( - 15 )$$

Accepted Answer

A)  $4 y$ 
B)  $3 y$ 
C)  $- 5 y$ 
D)  $5 \mathrm { y }$ 
A)  $4 y$ 
B)  $3 y$ 
C)  $- 5 y$ 
D)  $5 \mathrm { y }$

Question 5

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 3 ^ { 8 } } { 3 ^ { 2 } }$

Accepted Answer

A)  $\frac { 1 } { 3 ^ { 6 } }$ 
B)  96 
C)  36 
D)  6 
A)  $\frac { 1 } { 3 ^ { 6 } }$ 
B)  96 
C)  36 
D)  6

Question 6

Identify the set as finite or infinite.
-$$\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots , \right\}$$

Accepted Answer

A)  infinite 
B)  finite 
A)  infinite 
B)  finite

Question 7

Factor the trinomial, if possible.
-$12 z ^ { 2 } - 7 z - 12$

Accepted Answer

A)  $( 4 z - 3 ) ( 3 z + 4 )$ 
B)  $( 12 z + 3 ) ( z - 4 )$ 
C)  $( 4 z + 3 ) ( 3 z - 4 )$ 
D)  $( 12 z + 1 ) ( z - 12 )$ 
A)  $( 4 z - 3 ) ( 3 z + 4 )$ 
B)  $( 12 z + 3 ) ( z - 4 )$ 
C)  $( 4 z + 3 ) ( 3 z - 4 )$ 
D)  $( 12 z + 1 ) ( z - 12 )$

Question 8

Write the expression in lowest terms.
-$$\frac { z ^ { 2 } + 7 z + 6 } { z ^ { 2 } - 2 z - 3 }$$

Accepted Answer

A)  $\frac { z - 6 } { z + 3 }$ 
B)  $\frac { z + 7 } { z - 2 }$ 
C)  $\frac { z + 6 } { z - 3 }$ 
D)  $\frac { z + 1 } { z - 1 }$ 
A)  $\frac { z - 6 } { z + 3 }$ 
B)  $\frac { z + 7 } { z - 2 }$ 
C)  $\frac { z + 6 } { z - 3 }$ 
D)  $\frac { z + 1 } { z - 1 }$

Question 9

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-As the relative humidity increases, the temperature seems higher than it is. The formula $\mathrm { T } = 0.117 \mathrm { x } + 87.16$ approximates the apparent temperature for an actual temperature of $95 ^ { \circ } \mathrm { F }$, where $x$ is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of $100 \%$ ?

Accepted Answer

A)  $99 ^ { \circ } \mathrm { F }$ 
B)  $1020 ^ { \circ } \mathrm { F }$ 
C)  $87 ^ { \circ } \mathrm { F }$ 
D)  $187 ^ { \circ } \mathrm { F }$ 
A)  $99 ^ { \circ } \mathrm { F }$ 
B)  $1020 ^ { \circ } \mathrm { F }$ 
C)  $87 ^ { \circ } \mathrm { F }$ 
D)  $187 ^ { \circ } \mathrm { F }$

Question 10

Insert   in the blank to make the statement true.
-

Accepted Answer

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

Question 11

Factor the trinomial, if possible.
-$$6 x ^ { 2 } + 17 x y + 12 y ^ { 2 }$$

Accepted Answer

A)  prime 
B)  $( 2 x - 3 y ) ( 3 x - 4 y )$ 
C)  $( 2 x + 3 y ) ( 3 x + 4 y )$ 
D)  $( 6 x + 3 y ) ( x + 4 y )$ 
A)  prime 
B)  $( 2 x - 3 y ) ( 3 x - 4 y )$ 
C)  $( 2 x + 3 y ) ( 3 x + 4 y )$ 
D)  $( 6 x + 3 y ) ( x + 4 y )$

Question 12

Evaluate the expression.
-Let $x = - 8 , y = 4$. Evaluate $| x | + | y |$.

Accepted Answer

A)  12 
B)  $- 4$ 
C)  $- 12$ 
D)  4 
A)  12 
B)  $- 4$ 
C)  $- 12$ 
D)  4

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { y ^ { 16 } } { 27 } }$

Accepted Answer

A)  $y ^ { 5 } - 3 \sqrt [ 3 ] { y }$ 
B)  $\frac { y ^ { 5 } \sqrt [ 3 ] { y } } { 3 }$ 
C)  $\frac { y ^ { 5 } + \sqrt [ 3 ] { y } } { 3 }$ 
D)  $3 y 5 \sqrt [ 3 ] { y }$ 
A)  $y ^ { 5 } - 3 \sqrt [ 3 ] { y }$ 
B)  $\frac { y ^ { 5 } \sqrt [ 3 ] { y } } { 3 }$ 
C)  $\frac { y ^ { 5 } + \sqrt [ 3 ] { y } } { 3 }$ 
D)  $3 y 5 \sqrt [ 3 ] { y }$

Question 14

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the expression number of oz × % alcohol × .075 ÷ body weight in lb - hours of drinking × .015.
Find the BAC to the nearest thousandth for a 142-lb woman, who, in 3 hours, has drunk 3 10-oz beers (30 oz),
Each having a 3.2% alcohol content.

Accepted Answer

A)  0.006 
B)  -0.028 
C)  -199.949 
D)  -0.215 
A)  0.006 
B)  -0.028 
C)  -199.949 
D)  -0.215

Question 15

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

Accepted Answer

A)  not a real number 
B)  $2 x ^ { 3 }$ 
C)  $2 x$ 
D)  $- 2 x$ 
A)  not a real number 
B)  $2 x ^ { 3 }$ 
C)  $2 x$ 
D)  $- 2 x$

Question 16

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( 5 \mathrm { t } ) ^ { 5 }$

Accepted Answer

A)  $5 t ^ { 5 }$ 
B)  $5 ^ { 5 } \mathrm { t } ^ { 5 }$ 
C)  $25 t ^ { 5 }$ 
D)  $5 ^ { 5 } \mathrm { t }$ 
A)  $5 t ^ { 5 }$ 
B)  $5 ^ { 5 } \mathrm { t } ^ { 5 }$ 
C)  $25 t ^ { 5 }$ 
D)  $5 ^ { 5 } \mathrm { t }$

Question 17

Find the sum or difference.
-$$\left( - 4 - 4 x ^ { 5 } + 3 x ^ { 7 } + 2 x ^ { 6 } \right) + \left( - 6 x ^ { 6 } - 2 x ^ { 5 } - 5 + 4 x ^ { 7 } \right)$$

Accepted Answer

A)  $7 x ^ { 7 } - 4 x ^ { 6 } - 6 x ^ { 5 } - 9$ 
B)  $7 x ^ { 14 } - 4 x ^ { 12 } - 6 x ^ { 10 } - 9$ 
C)  $- 10 x ^ { 7 } - 10 x ^ { 6 } - 2 x ^ { 5 } + 6$ 
D)  $- 3 x ^ { 36 } - 9$ 
A)  $7 x ^ { 7 } - 4 x ^ { 6 } - 6 x ^ { 5 } - 9$ 
B)  $7 x ^ { 14 } - 4 x ^ { 12 } - 6 x ^ { 10 } - 9$ 
C)  $- 10 x ^ { 7 } - 10 x ^ { 6 } - 2 x ^ { 5 } + 6$ 
D)  $- 3 x ^ { 36 } - 9$

Question 18

Find the domain of the expression.
-$$\frac { - 5 } { m + 4 }$$

Accepted Answer

A)  $\{ m \mid m \neq - 4 \}$ 
B)  all real numbers 
C)  $\{ m \mid m > - 5 \}$ 
D)  $\{ \mathrm { m } \mid \mathrm { m } \neq 4 \}$ 
A)  $\{ m \mid m \neq - 4 \}$ 
B)  all real numbers 
C)  $\{ m \mid m > - 5 \}$ 
D)  $\{ \mathrm { m } \mid \mathrm { m } \neq 4 \}$

Question 19

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 5 , \sqrt { 7 } , - 16,0 , \frac { 0 } { 8 } , \sqrt { 9 } , \frac { - 5 } { 0 } , 0.59 \right\}$$
Rational numbers

Accepted Answer

A)  $5 , - 16,0 , \frac { 0 } { 8 } , \sqrt { 9 } , 0.59$ 
B)  $\sqrt { 7 } , \frac { 0 } { 8 } , 0.59$ 
C)  $\sqrt { 7 } , \sqrt { 9 }$ 
D)  $5,0 , \sqrt { 9 }$ 
A)  $5 , - 16,0 , \frac { 0 } { 8 } , \sqrt { 9 } , 0.59$ 
B)  $\sqrt { 7 } , \frac { 0 } { 8 } , 0.59$ 
C)  $\sqrt { 7 } , \sqrt { 9 }$ 
D)  $5,0 , \sqrt { 9 }$

Question 20

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 3 } } { y } > 0$$

Accepted Answer

A)  $x$ and $y$ must be positive. 
B)  $x$ and $y$ have the same sign. 
C)  $x$ and $y$ have different signs. 
D)  $x$ and $y$ must be negative. 
A)  $x$ and $y$ must be positive. 
B)  $x$ and $y$ have the same sign. 
C)  $x$ and $y$ have different signs. 
D)  $x$ and $y$ must be negative.

Find the sum or difference. - $\frac { x ^ { 4 } + 7 x ^ { 2 } + 10 } { x ^ { 2 } + 1 }$

Evaluate the expression. - $7776 ^ { 4 / 5 }$

Identify the set as finite or infinite. - $\{ x \mid x \text { is a natural number larger than } 1 \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\left( \frac { 1 } { 3 } y \right) ( - 15 )$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 ^ { 8 } } { 3 ^ { 2 } }$

Identify the set as finite or infinite. - $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots , \right\}$

Factor the trinomial, if possible. - $12 z ^ { 2 } - 7 z - 12$

Write the expression in lowest terms. - $\frac { z ^ { 2 } + 7 z + 6 } { z ^ { 2 } - 2 z - 3 }$

Insert in the blank to make the statement true. -

Factor the trinomial, if possible. - $6 x ^ { 2 } + 17 x y + 12 y ^ { 2 }$

Evaluate the expression. -Let $x = - 8 , y = 4$ . Evaluate $| x | + | y |$ .

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { y ^ { 16 } } { 27 } }$

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 5 \mathrm { t } ) ^ { 5 }$

Find the sum or difference. - $\left( - 4 - 4 x ^ { 5 } + 3 x ^ { 7 } + 2 x ^ { 6 } \right) + \left( - 6 x ^ { 6 } - 2 x ^ { 5 } - 5 + 4 x ^ { 7 } \right)$

Find the domain of the expression. - $\frac { - 5 } { m + 4 }$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 5 , \sqrt { 7 } , - 16,0 , \frac { 0 } { 8 } , \sqrt { 9 } , \frac { - 5 } { 0 } , 0.59 \right\}$ Rational numbers

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 3 } } { y } > 0$

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Exam 1: Review of Basic Concepts

Find the sum or difference. - x4+7x2+10x2+1\frac { x ^ { 4 } + 7 x ^ { 2 } + 10 } { x ^ { 2 } + 1 }x2+1x4+7x2+10​

Evaluate the expression. - 77764/57776 ^ { 4 / 5 }77764/5

Identify the set as finite or infinite. - {x∣x is a natural number larger than 1}\{ x \mid x \text { is a natural number larger than } 1 \}{x∣x is a natural number larger than 1}

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (13y)(−15)\left( \frac { 1 } { 3 } y \right) ( - 15 )(31​y)(−15)

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 3832\frac { 3 ^ { 8 } } { 3 ^ { 2 } }3238​

Identify the set as finite or infinite. - {1,13,19,127,…,}\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \ldots , \right\}{1,31​,91​,271​,…,}

Factor the trinomial, if possible. - 12z2−7z−1212 z ^ { 2 } - 7 z - 1212z2−7z−12

Write the expression in lowest terms. - z2+7z+6z2−2z−3\frac { z ^ { 2 } + 7 z + 6 } { z ^ { 2 } - 2 z - 3 }z2−2z−3z2+7z+6​