Question 1

Find the sum or difference.
-$$\frac { - 35 x ^ { 6 } + 56 x ^ { 4 } - 42 x ^ { 2 } } { - 7 x ^ { 4 } }$$

Accepted Answer

A)  $5 x ^ { 2 } - 8 + \frac { 6 } { x }$ 
B)  $5 x - 8 + \frac { 6 } { x ^ { 2 } }$ 
C)  $5 x - 8 + \frac { 6 } { x }$ 
D)  $5 x ^ { 2 } - 8 + \frac { 6 } { x ^ { 2 } }$ 
A)  $5 x ^ { 2 } - 8 + \frac { 6 } { x }$ 
B)  $5 x - 8 + \frac { 6 } { x ^ { 2 } }$ 
C)  $5 x - 8 + \frac { 6 } { x }$ 
D)  $5 x ^ { 2 } - 8 + \frac { 6 } { x ^ { 2 } }$

Question 2

Find the product or quotient.
-$$\frac { z ^ { 2 } + 10 z + 21 } { z ^ { 2 } + 12 z + 27 } \div \frac { z ^ { 2 } + 7 z } { z ^ { 2 } + 6 z - 27 }$$

Accepted Answer

A)  $\frac { z - 3 } { z ^ { 2 } + 9 z }$ 
B)  $\frac { \mathrm { z } } { \mathrm { z } ^ { 2 } + 12 \mathrm { z } + 27 }$ 
C)  $z - 3$ 
D)  $\frac { z - 3 } { z }$ 
A)  $\frac { z - 3 } { z ^ { 2 } + 9 z }$ 
B)  $\frac { \mathrm { z } } { \mathrm { z } ^ { 2 } + 12 \mathrm { z } + 27 }$ 
C)  $z - 3$ 
D)  $\frac { z - 3 } { z }$

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt { \frac { 25 } { 24 } }$$

Accepted Answer

A)  $- \frac { 5 \sqrt { 6 } } { 12 }$ 
B)  $- \frac { 5 \sqrt { 6 } } { 6 }$ 
C)  $- 5 \sqrt { 6 }$ 
D)  $- 24$ 
A)  $- \frac { 5 \sqrt { 6 } } { 12 }$ 
B)  $- \frac { 5 \sqrt { 6 } } { 6 }$ 
C)  $- 5 \sqrt { 6 }$ 
D)  $- 24$

Question 4

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$- 3 x + 7 y + 5 a$$

Accepted Answer

A)  7 
B)  $- 43$ 
C)  $- 7$ 
D)  23 
A)  7 
B)  $- 43$ 
C)  $- 7$ 
D)  23

Question 5

Decide whether the expression has been simplified correctly.
-$x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Question 6

Use set notation, and list all the elements of the set.
-{15, 22, 29, . . ., 64}

Accepted Answer

A)  {15, 22, 29, 36, 43, 50, 57, 64} 
B)  {15, 22, 28, 35, 42, 49, 56, 63} 
C)  {15, 22, 29, 37, 44, 51, 58, 65} 
D)  {15, 22, 29, 36, 43} 
A)  {15, 22, 29, 36, 43, 50, 57, 64} 
B)  {15, 22, 28, 35, 42, 49, 56, 63} 
C)  {15, 22, 29, 37, 44, 51, 58, 65} 
D)  {15, 22, 29, 36, 43}

Question 7

Find the sum or difference.
-$$\frac { x ^ { 2 } + 11 x + 14 } { x + 9 }$$

Accepted Answer

A)  $x + 2 - \frac { 4 } { x + 9 }$ 
B)  $x + 3$ 
C)  $x + 2 + \frac { 4 } { x + 9 }$ 
D)  $\frac { x + 2 } { x + 9 }$ 
A)  $x + 2 - \frac { 4 } { x + 9 }$ 
B)  $x + 3$ 
C)  $x + 2 + \frac { 4 } { x + 9 }$ 
D)  $\frac { x + 2 } { x + 9 }$

Question 8

Evaluate the expression.
-$$- 8 [ - 1 + 2 ( - 9 + 3 ) ]$$

Accepted Answer

A)  104 
B)  44 
C)  48 
D)  $- 4$ 
A)  104 
B)  44 
C)  48 
D)  $- 4$

Question 9

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

Accepted Answer

A)  M, or $\{ 9,11,13,15 \}$ 
B)  $\varnothing$, ' $^ { \prime }$ and ( $\left. \mathrm { N } \cup \mathrm { N } \right)$ are disjoint sets. 
C)  $\{ 9,10,12,14,16,18 \}$ 
D)  $\mathrm { N }$, or $\{ 10,12,14,16,18 \}$ 
A)  M, or $\{ 9,11,13,15 \}$ 
B)  $\varnothing$, ' $^ { \prime }$ and ( $\left. \mathrm { N } \cup \mathrm { N } \right)$ are disjoint sets. 
C)  $\{ 9,10,12,14,16,18 \}$ 
D)  $\mathrm { N }$, or $\{ 10,12,14,16,18 \}$

Question 10

Factor out the greatest common factor. Simplify the factors, if possible.
-$$x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$$

Accepted Answer

A)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$ 
B)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
C)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$ 
D)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$ 
A)  $\left( x ^ { 2 } + 9 \right) ( x - 2 )$ 
B)  $( x + 9 ) \left( x ^ { 2 } - 2 x \right) ( x - 2 )$ 
C)  $\left( x ^ { 2 } - 2 x \right) + 9 ( x - 2 )$ 
D)  $x \left( x ^ { 2 } - 2 x + 9 \right) - 18$

Question 11

Factor out the greatest common factor. Simplify the factors, if possible.
-5x3 + 20x

Accepted Answer

A)  5x(x2 + 4) 
B)  5x(x2 + 4x) 
C)  5x2(x + 4) 
D)  5x(x2 + 15x) 
A)  5x(x2 + 4) 
B)  5x(x2 + 4x) 
C)  5x2(x + 4) 
D)  5x(x2 + 15x)

Question 12

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 5 y } }$

Accepted Answer

A)  $\frac { x \sqrt { 2 } - \sqrt { 5 x y } - \sqrt { 2 x y } + y \sqrt { 5 } } { 2 x + 5 y }$ 
B)  $\frac { \sqrt { 2 x } - \sqrt { 7 x y } + \sqrt { 5 y } } { 2 x - 5 y }$ 
C)  $\frac { \sqrt { 2 x } - \sqrt { 7 x y } + \sqrt { 5 y } } { 2 x + 5 y }$ 
D)  $\frac { x \sqrt { 2 } - \sqrt { 5 x y } - \sqrt { 2 x y } + y \sqrt { 5 } } { 2 x - 5 y }$ 
A)  $\frac { x \sqrt { 2 } - \sqrt { 5 x y } - \sqrt { 2 x y } + y \sqrt { 5 } } { 2 x + 5 y }$ 
B)  $\frac { \sqrt { 2 x } - \sqrt { 7 x y } + \sqrt { 5 y } } { 2 x - 5 y }$ 
C)  $\frac { \sqrt { 2 x } - \sqrt { 7 x y } + \sqrt { 5 y } } { 2 x + 5 y }$ 
D)  $\frac { x \sqrt { 2 } - \sqrt { 5 x y } - \sqrt { 2 x y } + y \sqrt { 5 } } { 2 x - 5 y }$

Question 13

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true.
-

Accepted Answer

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

Question 14

Find the sum or difference.
-$$\left( 3 \mathrm { k } ^ { 2 } + 4 \mathrm { k } - 3 \right) \left( \mathrm { k } ^ { 2 } - 5 \mathrm { k } + 1 \right)$$

Accepted Answer

A)  $3 k ^ { 4 } - 15 k ^ { 3 } - 17 k ^ { 2 } + 19 k - 3$ 
B)  $3 \mathrm { k } ^ { 4 } - 11 \mathrm { k } ^ { 3 } - 17 \mathrm { k } ^ { 2 } + 19 \mathrm { k } - 3$ 
C)  $3 k ^ { 4 } - 15 k ^ { 3 } - 20 k ^ { 2 } + 19 k - 3$ 
D)  $3 k ^ { 4 } - 11 k ^ { 3 } - 20 k ^ { 2 } + 19 k - 3$ 
A)  $3 k ^ { 4 } - 15 k ^ { 3 } - 17 k ^ { 2 } + 19 k - 3$ 
B)  $3 \mathrm { k } ^ { 4 } - 11 \mathrm { k } ^ { 3 } - 17 \mathrm { k } ^ { 2 } + 19 \mathrm { k } - 3$ 
C)  $3 k ^ { 4 } - 15 k ^ { 3 } - 20 k ^ { 2 } + 19 k - 3$ 
D)  $3 k ^ { 4 } - 11 k ^ { 3 } - 20 k ^ { 2 } + 19 k - 3$

Question 15

Factor by any method.
-$$( r + s ) ^ { 2 } - 16$$

Accepted Answer

A)  $\left( r ^ { 2 } + 4 \right) \left( s ^ { 2 } - 4 \right)$ 
B)  $( r - s + 4 ) ( r - s - 4 )$ 
C)  $( r + s + 4 ) ( r + s - 4 )$ 
D)  $( r + s + 4 ) ( r - s - 4 )$ 
A)  $\left( r ^ { 2 } + 4 \right) \left( s ^ { 2 } - 4 \right)$ 
B)  $( r - s + 4 ) ( r - s - 4 )$ 
C)  $( r + s + 4 ) ( r + s - 4 )$ 
D)  $( r + s + 4 ) ( r - s - 4 )$

Question 16

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { x ^ { - 7 } } { x ^ { - 19 } }$

Accepted Answer

A)  $x ^ { 12 }$ 
B)  $- \mathrm { x } ^ { 12 }$ 
C)  $\frac { 1 } { x ^ { 12 } }$ 
D)  $\frac { 1 } { x ^ { 26 } }$ 
A)  $x ^ { 12 }$ 
B)  $- \mathrm { x } ^ { 12 }$ 
C)  $\frac { 1 } { x ^ { 12 } }$ 
D)  $\frac { 1 } { x ^ { 26 } }$

Question 17

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 5,6,7,8,9,10 \} , \mathrm { B } = \{ 7,9,11 \} , \mathrm { C } = \{ 5,6,8,10 \} , \mathrm { D } = \{ 5,10 \}$, and $\mathrm { U } = \{ 5,6,7,8,9,10,11 \}$
$$\{ 0,6,10 \} \subseteq C$$

Accepted Answer

A) True 
 B)False

Question 18

Tell whether the statement is true or false.
-$7 \in \{ - 3,8,9,12 \}$

Accepted Answer

A) True 
 B)False

Question 19

Write in radical form. Assume all variables represent positive real numbers.
-$\left( 5 m ^ { 4 } + 4 k ^ { 2 } \right) ^ { 4 / 3 }$

Accepted Answer

A)  $\left( \sqrt [ 3 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 4 }$ 
B)  $\frac { 1 } { \left( \sqrt [ 3 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 4 } }$ 
C)  $\frac { 1 } { \left( \sqrt [ 4 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 3 } }$ 
D)  $\left( \sqrt [ 4 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 3 }$ 
A)  $\left( \sqrt [ 3 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 4 }$ 
B)  $\frac { 1 } { \left( \sqrt [ 3 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 4 } }$ 
C)  $\frac { 1 } { \left( \sqrt [ 4 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 3 } }$ 
D)  $\left( \sqrt [ 4 ] { 5 m ^ { 4 } + 4 k ^ { 2 } } \right) ^ { 3 }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { x } { 8 } } { \frac { 3 } { x + 4 } }$

Accepted Answer

A)  $24 x ( x + 4 )$ 
B)  $\frac { x ( x + 4 ) } { 24 }$ 
C)  $\frac { x + 4 } { 24 x }$ 
D)  $\frac { 3 x } { 8 ( x + 4 ) }$ 
A)  $24 x ( x + 4 )$ 
B)  $\frac { x ( x + 4 ) } { 24 }$ 
C)  $\frac { x + 4 } { 24 x }$ 
D)  $\frac { 3 x } { 8 ( x + 4 ) }$

Find the sum or difference. - $\frac { - 35 x ^ { 6 } + 56 x ^ { 4 } - 42 x ^ { 2 } } { - 7 x ^ { 4 } }$

Find the product or quotient. - $\frac { z ^ { 2 } + 10 z + 21 } { z ^ { 2 } + 12 z + 27 } \div \frac { z ^ { 2 } + 7 z } { z ^ { 2 } + 6 z - 27 }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 25 } { 24 } }$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $- 3 x + 7 y + 5 a$

Decide whether the expression has been simplified correctly. - $x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }$

Use set notation, and list all the elements of the set. -{15, 22, 29, . . ., 64}

Find the sum or difference. - $\frac { x ^ { 2 } + 11 x + 14 } { x + 9 }$

Evaluate the expression. - $- 8 [ - 1 + 2 ( - 9 + 3 ) ]$

Factor out the greatest common factor. Simplify the factors, if possible. - $x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18$

Factor out the greatest common factor. Simplify the factors, if possible. -5x3 + 20x

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 2 x } + \sqrt { 5 y } }$

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. - $Insert \in \mathbf { O r } \notin in the blank to make the statement is true. -$

Find the sum or difference. - $\left( 3 \mathrm { k } ^ { 2 } + 4 \mathrm { k } - 3 \right) \left( \mathrm { k } ^ { 2 } - 5 \mathrm { k } + 1 \right)$

Factor by any method. - $( r + s ) ^ { 2 } - 16$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 7 } } { x ^ { - 19 } }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 5,6,7,8,9,10 \} , \mathrm { B } = \{ 7,9,11 \} , \mathrm { C } = \{ 5,6,8,10 \} , \mathrm { D } = \{ 5,10 \}$ , and $\mathrm { U } = \{ 5,6,7,8,9,10,11 \}$ $\{ 0,6,10 \} \subseteq C$

Tell whether the statement is true or false. - $7 \in \{ - 3,8,9,12 \}$

Write in radical form. Assume all variables represent positive real numbers. - $\left( 5 m ^ { 4 } + 4 k ^ { 2 } \right) ^ { 4 / 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { x } { 8 } } { \frac { 3 } { x + 4 } }$

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Exam 1: Review of Basic Concepts

Find the sum or difference. - −35x6+56x4−42x2−7x4\frac { - 35 x ^ { 6 } + 56 x ^ { 4 } - 42 x ^ { 2 } } { - 7 x ^ { 4 } }−7x4−35x6+56x4−42x2​

Find the product or quotient. - z2+10z+21z2+12z+27÷z2+7zz2+6z−27\frac { z ^ { 2 } + 10 z + 21 } { z ^ { 2 } + 12 z + 27 } \div \frac { z ^ { 2 } + 7 z } { z ^ { 2 } + 6 z - 27 }z2+12z+27z2+10z+21​÷z2+6z−27z2+7z​

Simplify the expression. Assume all variables represent positive real numbers. - −2524- \sqrt { \frac { 25 } { 24 } }−2425​​

Evaluate the expression for x x=−2,y=3, and a=−4x = - 2 , y = 3 , \text { and } a = - 4x=−2,y=3, and a=−4 - −3x+7y+5a- 3 x + 7 y + 5 a−3x+7y+5a

Decide whether the expression has been simplified correctly. - x3⋅x2=x6x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }x3⋅x2=x6

Use set notation, and list all the elements of the set. -{15, 22, 29, . . ., 64}

Find the sum or difference. - x2+11x+14x+9\frac { x ^ { 2 } + 11 x + 14 } { x + 9 }x+9x2+11x+14​

Evaluate the expression. - −8[−1+2(−9+3)]- 8 [ - 1 + 2 ( - 9 + 3 ) ]−8[−1+2(−9+3)]

Factor out the greatest common factor. Simplify the factors, if possible. - x3−2x2+9x−18x ^ { 3 } - 2 x ^ { 2 } + 9 x - 18x3−2x2+9x−18