Question 1

List all the elements of set B that belong to the indicated set.
-$$B = \left\{ 11 , \sqrt { 5 } , - 7,0 , \frac { 0 } { 9 } , \sqrt { 9 } \right\}$$
Natural numbers

Accepted Answer

A)  $11 , \sqrt { 9 }$ 
B)  $11,0 , \frac { 0 } { 2 }$ 
C)  11,0 
D)  $11,0 , \sqrt { 9 }$

Question 2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 + \frac { 2 } { s } } { \frac { s } { 4 } + \frac { 1 } { 8 } }$$

Accepted Answer

A)  $\frac { 16 } { \mathrm {~s} }$ 
B)  1 
C)  16 
D)  $\frac { \mathrm { s } } { 16 }$

Question 3

Evaluate the expression.
-$\left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }$

Accepted Answer

A)  $\frac { 25 } { 6 }$ 
B)  not a real number 
C)  $\frac { 5 } { 36 }$ 
D)  $\frac { 5 } { 6 }$

Question 4

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 8,9,10,11,12,13 \} , \mathrm { B } = \{ 10,12,14 \} , \mathrm { C } = \{ 8,9,11,13 \} , \mathrm { D } = \{ 8,13 \}$, and $\mathrm { U } = \{ 8,9,10,11,12,13,14 \}$
$\varnothing \subseteq D$

Accepted Answer

A)  True 
B)  False

Question 5

Factor by any method.
-$$( m - n ) ^ { 2 } - 10 ( m - n ) + 25$$

Accepted Answer

A)  $( \mathrm { m } - \mathrm { n } - 25 ) ( \mathrm { m } - \mathrm { n } )$ 
B)  prime 
C)  $( m - n - 5 ) ( m - n + 5 )$ 
D)  $( \mathrm { m } - \mathrm { n } - 5 ) ^ { 2 }$

Question 6

Factor the trinomial, if possible.
-$5 x ^ { 2 } + 9 x + 2$

Accepted Answer

A)  $( 5 x - 1 ) ( x + 2 )$ 
B)  $( 5 x + 1 ) ( x - 2 )$ 
C)  $( 5 x + 2 ) ( x - 1 )$ 
D)  prime

Question 7

Find the product.
-$$( x - 7 ) ( x + 7 ) \left( x ^ { 2 } + 49 \right)$$

Accepted Answer

A)  $x ^ { 4 } - 49$ 
B)  $x ^ { 4 } - 196 x ^ { 2 } + 2401$ 
C)  $x ^ { 4 } - 2401$ 
D)  $x ^ { 4 } - 14 x ^ { 2 } - 49$

Question 8

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-6 ∙ 1 = 6

Accepted Answer

A)  Distributive 
B)  Identity 
C)  Closure 
D)  Inverse

Question 9

Evaluate the expression for x = -2, y = 3, and a = -4.
-x3 - 9y + 5a

Accepted Answer

A)  -42 
B)  -51 
C)  -39 
D)  -55

Question 10

Find the product or quotient.
-$\frac { 8 p - 8 } { p } \cdot \frac { 6 p ^ { 2 } } { 3 p - 3 }$

Accepted Answer

A)  $\frac { 48 p ^ { 3 } - 48 p ^ { 2 } } { 3 p ^ { 2 } - 3 p }$ 
B)  $16 \mathrm { p }$ 
C)  $\frac { 1 } { 16 } \mathrm { p }$ 
D)  $\frac { 24 p ^ { 2 } + 48 p + 24 } { 6 p ^ { 3 } }$

Question 11

Find the product or quotient.
-$\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 32 }$

Accepted Answer

A)  $\frac { 16 } { x }$ 
B)  $\frac { 64 x ^ { 2 } } { 4 x ^ { 3 } }$ 
C)  $\frac { 16 x ^ { 2 } } { x ^ { 3 } }$ 
D)  $\frac { x } { 16 }$

Question 12

Write in exponential form. Assume all variables are positive real numbers.
-$\sqrt [ 5 ] { x ^ { 4 } }$

Accepted Answer

A)  $x ^ { 5 / 4 }$ 
B)  $x ^ { 1 / 20 }$ 
C)  $x ^ { 4 / 5 }$ 
D)  $x ^ { 4 / 20 }$

Question 13

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-{ 0 }_____[ 0,5,6,7,8 }

Accepted Answer

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

Question 14

Identify the expression as a polynomial or not a polynomial.
-$3 x ^ { 2 } y ^ { 3 } - 8 x ^ { 3 } y + 9 x$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial

Question 15

Find the product.
-$$\left( - 4 m ^ { 3 } \right) \left( 5 m ^ { 2 } \right)$$

Accepted Answer

A)  $- 20 \mathrm {~m} ^ { 5 }$ 
B)  $- 20 \mathrm {~m}$ 
C)  $20 \mathrm {~m} ^ { 6 }$ 
D)  $20 \mathrm {~m}$

Question 16

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 4,5,6,7,8,9 \} , \mathrm { B } = \{ 6,8,10 \} , \mathrm { C } = \{ 4,5,7,9 \} , \mathrm { D } = \{ 4,9 \}$, and $\mathrm { U } = \{ 4,5,6,7,8,9,10 \}$.
$B \nsubseteq C$

Accepted Answer

A)  True 
B)  False

Question 17

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

Accepted Answer

A)   
B)

Question 18

Find the product.
-$$\left( 2 x ^ { 2 } + 3 x - 4 \right) \left( x ^ { 2 } - 4 x - 1 \right)$$

Accepted Answer

A)  $2 x ^ { 4 } - 5 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 4$ 
B)  $2 x ^ { 4 } - 8 x ^ { 3 } - 18 x ^ { 2 } + 13 x + 4$ 
C)  $2 x ^ { 4 } - 8 x ^ { 3 } - 14 x ^ { 2 } + 13 x + 4$ 
D)  $2 x ^ { 4 } - 5 x ^ { 3 } - 18 x ^ { 2 } + 13 x + 4$

Question 19

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { x } { 8 } } { \frac { 9 } { x + 8 } }$

Accepted Answer

A)  $\frac { x + 8 } { 72 x }$ 
B)  $72 x ( x + 8 )$ 
C)  $\frac { x ( x + 8 ) } { 72 }$ 
D)  $\frac { 9 x } { 8 ( x + 8 ) }$

Question 20

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-{ 4 }____{ 2,4,6,8 }

Accepted Answer

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

Exam 12: Review of Basic Concepts

List all the elements of set B that belong to the indicated set. - $B = \left\{ 11 , \sqrt { 5 } , - 7,0 , \frac { 0 } { 9 } , \sqrt { 9 } \right\}$ Natural numbers

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 4 + \frac { 2 } { s } } { \frac { s } { 4 } + \frac { 1 } { 8 } }$

Evaluate the expression. - $\left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 8,9,10,11,12,13 \} , \mathrm { B } = \{ 10,12,14 \} , \mathrm { C } = \{ 8,9,11,13 \} , \mathrm { D } = \{ 8,13 \}$ , and $\mathrm { U } = \{ 8,9,10,11,12,13,14 \}$ $\varnothing \subseteq D$

Factor by any method. - $( m - n ) ^ { 2 } - 10 ( m - n ) + 25$

Factor the trinomial, if possible. - $5 x ^ { 2 } + 9 x + 2$

Find the product. - $( x - 7 ) ( x + 7 ) \left( x ^ { 2 } + 49 \right)$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -6 ∙ 1 = 6

Evaluate the expression for x = -2, y = 3, and a = -4. -x3 - 9y + 5a

Find the product or quotient. - $\frac { 8 p - 8 } { p } \cdot \frac { 6 p ^ { 2 } } { 3 p - 3 }$

Find the product or quotient. - $\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 32 }$

Write in exponential form. Assume all variables are positive real numbers. - $\sqrt [ 5 ] { x ^ { 4 } }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -{ 0 }_____[ 0,5,6,7,8 }

Identify the expression as a polynomial or not a polynomial. - $3 x ^ { 2 } y ^ { 3 } - 8 x ^ { 3 } y + 9 x$

Find the product. - $\left( - 4 m ^ { 3 } \right) \left( 5 m ^ { 2 } \right)$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 4,5,6,7,8,9 \} , \mathrm { B } = \{ 6,8,10 \} , \mathrm { C } = \{ 4,5,7,9 \} , \mathrm { D } = \{ 4,9 \}$ , and $\mathrm { U } = \{ 4,5,6,7,8,9,10 \}$ . $B \nsubseteq C$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. - $Insert \in \mathbf { Or } \notin in the blank to make the statement is true. - A) B)$

Find the product. - $\left( 2 x ^ { 2 } + 3 x - 4 \right) \left( x ^ { 2 } - 4 x - 1 \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { x } { 8 } } { \frac { 9 } { x + 8 } }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -{ 4 }____{ 2,4,6,8 }

Exam 12: Review of Basic Concepts

List all the elements of set B that belong to the indicated set. - B={11,5,−7,0,09,9}B = \left\{ 11 , \sqrt { 5 } , - 7,0 , \frac { 0 } { 9 } , \sqrt { 9 } \right\}B={11,5​,−7,0,90​,9​} Natural numbers

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 4+2ss4+18\frac { 4 + \frac { 2 } { s } } { \frac { s } { 4 } + \frac { 1 } { 8 } }4s​+81​4+s2​​

Evaluate the expression. - (2536) 1/2\left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }(3625​) 1/2

Factor by any method. - (m−n) 2−10(m−n) +25( m - n ) ^ { 2 } - 10 ( m - n ) + 25(m−n) 2−10(m−n) +25

Factor the trinomial, if possible. - 5x2+9x+25 x ^ { 2 } + 9 x + 25x2+9x+2

Find the product. - (x−7) (x+7) (x2+49) ( x - 7 ) ( x + 7 ) \left( x ^ { 2 } + 49 \right) (x−7) (x+7) (x2+49)

Identify the property illustrated by the statement. Assume all variables represent real numbers. -6 ∙ 1 = 6

Evaluate the expression for x = -2, y = 3, and a = -4. -x3 - 9y + 5a

Find the product or quotient. - 8p−8p⋅6p23p−3\frac { 8 p - 8 } { p } \cdot \frac { 6 p ^ { 2 } } { 3 p - 3 }p8p−8​⋅3p−36p2​

Find the product or quotient. - 2x24÷x332\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 32 }42x2​÷32x3​

Write in exponential form. Assume all variables are positive real numbers. - x45\sqrt [ 5 ] { x ^ { 4 } }5x4​

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -{ 0 }_____[ 0,5,6,7,8 }

Identify the expression as a polynomial or not a polynomial. - 3x2y3−8x3y+9x3 x ^ { 2 } y ^ { 3 } - 8 x ^ { 3 } y + 9 x3x2y3−8x3y+9x

Find the product. - (−4m3) (5m2) \left( - 4 m ^ { 3 } \right) \left( 5 m ^ { 2 } \right) (−4m3) (5m2)

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -

Find the product. - (2x2+3x−4) (x2−4x−1) \left( 2 x ^ { 2 } + 3 x - 4 \right) \left( x ^ { 2 } - 4 x - 1 \right) (2x2+3x−4) (x2−4x−1)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - x89x+8\frac { \frac { x } { 8 } } { \frac { 9 } { x + 8 } }x+89​8x​​

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -{ 4 }____{ 2,4,6,8 }