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)  $11,0 , \sqrt { 9 }$ 
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)  $\frac { \mathrm { s } } { 16 }$ 
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)  $\frac { 5 } { 6 }$ 
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 
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)  $( \mathrm { m } - \mathrm { n } - 5 ) ^ { 2 }$ 
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 
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)  $x ^ { 4 } - 14 x ^ { 2 } - 49$ 
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 
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 
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)  $\frac { 24 p ^ { 2 } + 48 p + 24 } { 6 p ^ { 3 } }$ 
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)  $\frac { x } { 16 }$ 
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)  $x ^ { 4 / 20 }$ 
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)   $\notin$ 
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 
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)  $20 \mathrm {~m}$ 
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 
A)  True 
B)  False

Question 17

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

Accepted Answer

A)    
B)   
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)  $2 x ^ { 4 } - 5 x ^ { 3 } - 18 x ^ { 2 } + 13 x + 4$ 
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)  $\frac { 9 x } { 8 ( x + 8 ) }$ 
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)  $\notin$ 
A)  $\in$ 
B)  $\notin$

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

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 }

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 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)