Question 1

Factor the trinomial, if possible.
-$$x ^ { 2 } + 2 x y - 99 y ^ { 2 }$$

Accepted Answer

A)  $( x - 11 y ) ( x + 9 y )$ 
B)  prime 
C)  $( x + 11 y ) ( x - 9 y )$ 
D)  $( x - 11 y ) ( x + y )$ 
A)  $( x - 11 y ) ( x + 9 y )$ 
B)  prime 
C)  $( x + 11 y ) ( x - 9 y )$ 
D)  $( x - 11 y ) ( x + y )$

Question 2

Factor by any method.
-$$8 a ^ { 3 } - 27 b ^ { 3 }$$

Accepted Answer

A)  $\left( 2 a + 3 b ^ { 2 } \right) \left( 4 a ^ { 2 } - 6 a b + 9 b ^ { 2 } \right)$ 
B)  $( 8 a - 3 b ) \left( a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
C)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 9 b ^ { 2 } \right)$ 
D)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
A)  $\left( 2 a + 3 b ^ { 2 } \right) \left( 4 a ^ { 2 } - 6 a b + 9 b ^ { 2 } \right)$ 
B)  $( 8 a - 3 b ) \left( a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
C)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 9 b ^ { 2 } \right)$ 
D)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$

Question 3

Perform the indicated operations.
-$$\frac { 9 } { 11 x } - \frac { 7 } { 11 x }$$

Accepted Answer

A)  $\frac { 11 } { 2 x }$ 
B)  1 
C)  $\frac { 1 } { 11 \mathrm { x } }$ 
D)  $\frac { 2 } { 11 x }$ 
A)  $\frac { 11 } { 2 x }$ 
B)  1 
C)  $\frac { 1 } { 11 \mathrm { x } }$ 
D)  $\frac { 2 } { 11 x }$

Question 4

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 3 a ^ { 3 } \right) \cdot \left( 5 a ^ { 8 } \right)$

Accepted Answer

A)  $15 a ^{11}$ 
B)  $8 ^ { 24 }$ 
C)  15 a24 
D)  811 
A)  $15 a ^{11}$ 
B)  $8 ^ { 24 }$ 
C)  15 a24 
D)  811

Question 5

Tell whether the statement is true or false.
-$\{ 8,10,11,13 \} \cup \varnothing = \{ 8,10,11,13 \}$

Accepted Answer

A) True 
 B)False

Question 6

Find the sum or difference.
-$$[ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ]$$

Accepted Answer

A)  $25 x ^ { 2 } + y ^ { 2 } - 9 z ^ { 2 }$ 
B)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
C)  $25 x ^ { 2 } + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
D)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } - 9 z ^ { 2 }$ 
A)  $25 x ^ { 2 } + y ^ { 2 } - 9 z ^ { 2 }$ 
B)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
C)  $25 x ^ { 2 } + y ^ { 2 } + 30 x z + 6 y z - 9 z ^ { 2 }$ 
D)  $25 x ^ { 2 } - 10 x y + y ^ { 2 } - 9 z ^ { 2 }$

Question 7

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$, and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$ $\emptyset \subseteq \mathrm { D }$

Accepted Answer

A) True 
 B)False

Question 8

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

Accepted Answer

A)  16 
B)  1 
C)  $\frac { 16 } { x }$ 
D)  $\frac { x } { 16 }$ 
A)  16 
B)  1 
C)  $\frac { 16 } { x }$ 
D)  $\frac { x } { 16 }$

Question 9

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

Accepted Answer

A)  $\frac { 27 - 10 \sqrt { 2 } } { 23 }$ 
B)  $- 1$ 
C)  $\frac { 27 + 10 \sqrt { 2 } } { 23 }$ 
D)  $\frac { 23 - 10 \sqrt { 2 } } { 27 }$ 
A)  $\frac { 27 - 10 \sqrt { 2 } } { 23 }$ 
B)  $- 1$ 
C)  $\frac { 27 + 10 \sqrt { 2 } } { 23 }$ 
D)  $\frac { 23 - 10 \sqrt { 2 } } { 27 }$

Question 10

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-Find the magnitude of the difference between a windchill factor of 82 and a windchill factor of $- 45$.

Accepted Answer

A)  37 
B)  127 
C)  $- 37$ 
D)  $- 127$ 
A)  37 
B)  127 
C)  $- 37$ 
D)  $- 127$

Question 11

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 2,3,4,5,6,7,8,9,10,11,12 \} , \mathrm { M } = \{ 2,4,6,8 \} , \mathrm { N } = \{ 3,5,7,9,11 \} , \mathrm { Q } = \{ 2,4,6,8,10,12 \}$, and $\mathrm { R } = \{ 2,3,4,5 \}$.
$\mathrm { M } \cap \mathrm { N }$

Accepted Answer

A)  $\{ 4,5,6,7,11 \}$ 
B)  $\varnothing , \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
C)  $\{ 3,4,5,6,7,8,9,10,11 \}$ 
D)  $\{ 2,3,4,5,6,7,8,9,11 \}$ 
A)  $\{ 4,5,6,7,11 \}$ 
B)  $\varnothing , \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
C)  $\{ 3,4,5,6,7,8,9,10,11 \}$ 
D)  $\{ 2,3,4,5,6,7,8,9,11 \}$

Question 12

Find the product or quotient.
-$$\frac { k ^ { 2 } + 9 k + 14 } { k ^ { 2 } + 11 k + 18 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } - 2 k - 63 }$$

Accepted Answer

A)  $\frac { k ^ { 2 } + 9 k } { k - 9 }$ 
B)  $\frac { 1 } { \mathrm { k } - 9 }$ 
C)  $\frac { k } { k ^ { 2 } + 11 k + 18 }$ 
D)  $\frac { k } { k - 9 }$ 
A)  $\frac { k ^ { 2 } + 9 k } { k - 9 }$ 
B)  $\frac { 1 } { \mathrm { k } - 9 }$ 
C)  $\frac { k } { k ^ { 2 } + 11 k + 18 }$ 
D)  $\frac { k } { k - 9 }$

Question 13

Factor the trinomial, if possible.
-$2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

Accepted Answer

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

Question 14

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 15

Factor by any method.
-Find all values of b that will make the polynomial a perfect square trinomial. $4 x ^ { 2 } + 24 x + b$

Accepted Answer

A)  3 
B)  48 
C)  $3 , - 3$ 
D)  36 
A)  3 
B)  48 
C)  $3 , - 3$ 
D)  36

Question 16

Find the sum or difference.
-$$( x + 2 y ) ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } + 8 y ^ { 3 }$ 
B)  $3 ( x + 2 y )$ 
C)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$ 
A)  $x ^ { 3 } + 8 y ^ { 3 }$ 
B)  $3 ( x + 2 y )$ 
C)  $x ^ { 3 } + 6 x ^ { 2 } y + 12 x y ^ { 2 } + 8 y ^ { 3 }$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } y + 4 x y + 4 x y ^ { 2 } + 8 y ^ { 2 } + 8 y ^ { 3 }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Accepted Answer

A)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $6x \sqrt [ 4 ] { x ^ { 7 } }$ 
C)  $14 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
D)  $6 x \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
A)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $6x \sqrt [ 4 ] { x ^ { 7 } }$ 
C)  $14 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
D)  $6 x \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$$( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } - 8 \sqrt [ 3 ] { 5 } + 13$ 
B)  $- 3$ 
C)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } + 8 \sqrt [ 3 ] { 5 } - 3$ 
D)  13 
A)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } - 8 \sqrt [ 3 ] { 5 } + 13$ 
B)  $- 3$ 
C)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } + 8 \sqrt [ 3 ] { 5 } - 3$ 
D)  13

Question 19

Find the product. Assume variables represent positive real numbers.
-$$\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)$$

Accepted Answer

A)  $1 - \mathrm { m } ^ { 1 / 3 } + \mathrm { m } ^ { - 1 / 3 } - \mathrm { m }$ 
B)  $\mathrm { m } 1 / 3 - \mathrm { m } - 1 / 3$ 
C)  $- \mathrm { m } 1 / 3 + \mathrm { m } ^ { - 1 / 3 }$ 
D)  $\mathrm { m } - \mathrm { m } 1 / 3 + \mathrm { m } - 1 / 3 - 1$ 
A)  $1 - \mathrm { m } ^ { 1 / 3 } + \mathrm { m } ^ { - 1 / 3 } - \mathrm { m }$ 
B)  $\mathrm { m } 1 / 3 - \mathrm { m } - 1 / 3$ 
C)  $- \mathrm { m } 1 / 3 + \mathrm { m } ^ { - 1 / 3 }$ 
D)  $\mathrm { m } - \mathrm { m } 1 / 3 + \mathrm { m } - 1 / 3 - 1$

Question 20

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

Accepted Answer

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

Factor the trinomial, if possible. - $x ^ { 2 } + 2 x y - 99 y ^ { 2 }$

Factor by any method. - $8 a ^ { 3 } - 27 b ^ { 3 }$

Perform the indicated operations. - $\frac { 9 } { 11 x } - \frac { 7 } { 11 x }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 3 a ^ { 3 } \right) \cdot \left( 5 a ^ { 8 } \right)$

Tell whether the statement is true or false. - $\{ 8,10,11,13 \} \cup \varnothing = \{ 8,10,11,13 \}$

Find the sum or difference. - $[ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ]$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$ , and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$ $\emptyset \subseteq \mathrm { D }$

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

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

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of 82 and a windchill factor of $- 45$ .

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 2,3,4,5,6,7,8,9,10,11,12 \} , \mathrm { M } = \{ 2,4,6,8 \} , \mathrm { N } = \{ 3,5,7,9,11 \} , \mathrm { Q } = \{ 2,4,6,8,10,12 \}$ , and $\mathrm { R } = \{ 2,3,4,5 \}$ . $\mathrm { M } \cap \mathrm { N }$

Find the product or quotient. - $\frac { k ^ { 2 } + 9 k + 14 } { k ^ { 2 } + 11 k + 18 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } - 2 k - 63 }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

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

Factor by any method. -Find all values of b that will make the polynomial a perfect square trinomial. $4 x ^ { 2 } + 24 x + b$

Find the sum or difference. - $( x + 2 y ) ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$

Find the product. Assume variables represent positive real numbers. - $\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)$

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

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Factor the trinomial, if possible. - x2+2xy−99y2x ^ { 2 } + 2 x y - 99 y ^ { 2 }x2+2xy−99y2

Factor by any method. - 8a3−27b38 a ^ { 3 } - 27 b ^ { 3 }8a3−27b3

Perform the indicated operations. - 911x−711x\frac { 9 } { 11 x } - \frac { 7 } { 11 x }11x9​−11x7​

Simplify the expression. Assume all variables represent nonzero real numbers. - (3a3)⋅(5a8)\left( 3 a ^ { 3 } \right) \cdot \left( 5 a ^ { 8 } \right)(3a3)⋅(5a8)

Tell whether the statement is true or false. - {8,10,11,13}∪∅={8,10,11,13}\{ 8,10,11,13 \} \cup \varnothing = \{ 8,10,11,13 \}{8,10,11,13}∪∅={8,10,11,13}

Find the sum or difference. - [(5x−y)+3z][(5x−y)−3z][ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ][(5x−y)+3z][(5x−y)−3z]

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 4+2xx4+18\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }4x​+81​4+x2​​

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 5−25+2\frac { 5 - \sqrt { 2 } } { 5 + \sqrt { 2 } }5+2​5−2​​

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of 82 and a windchill factor of −45- 45−45 .

Find the product or quotient. - k2+9k+14k2+11k+18⋅k2+9kk2−2k−63\frac { k ^ { 2 } + 9 k + 14 } { k ^ { 2 } + 11 k + 18 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } - 2 k - 63 }k2+11k+18k2+9k+14​⋅k2−2k−63k2+9k​

Factor the trinomial, if possible. - 2x2−6xy−8y22 x ^ { 2 } - 6 x y - 8 y ^ { 2 }2x2−6xy−8y2

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

Factor by any method. -Find all values of b that will make the polynomial a perfect square trinomial. 4x2+24x+b4 x ^ { 2 } + 24 x + b4x2+24x+b

Find the sum or difference. - (x+2y)3( x + 2 y ) ^ { 3 }(x+2y)3

Simplify the expression. Assume all variables represent positive real numbers. - 10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7​−4x4x3​

Simplify the expression. Assume all variables represent positive real numbers. - (53−2)(523+253+4)( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)(35​−2)(352​+235​+4)

Find the product. Assume variables represent positive real numbers. - (m1/6+m−1/6)(m−1/6−m1/6)\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)(m1/6+m−1/6)(m−1/6−m1/6)

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

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Factor the trinomial, if possible. - $x ^ { 2 } + 2 x y - 99 y ^ { 2 }$

Factor by any method. - $8 a ^ { 3 } - 27 b ^ { 3 }$

Perform the indicated operations. - $\frac { 9 } { 11 x } - \frac { 7 } { 11 x }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 3 a ^ { 3 } \right) \cdot \left( 5 a ^ { 8 } \right)$

Tell whether the statement is true or false. - $\{ 8,10,11,13 \} \cup \varnothing = \{ 8,10,11,13 \}$

Find the sum or difference. - $[ ( 5 x - y ) + 3 z ] [ ( 5 x - y ) - 3 z ]$

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

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

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of 82 and a windchill factor of $- 45$ .

Find the product or quotient. - $\frac { k ^ { 2 } + 9 k + 14 } { k ^ { 2 } + 11 k + 18 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } - 2 k - 63 }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

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

Factor by any method. -Find all values of b that will make the polynomial a perfect square trinomial. $4 x ^ { 2 } + 24 x + b$

Find the sum or difference. - $( x + 2 y ) ^ { 3 }$

Simplify the expression. Assume all variables represent positive real numbers. - $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$

Find the product. Assume variables represent positive real numbers. - $\left( m 1 / 6 + m ^ { - 1 / 6 } \right) \left( m ^ { - 1 / 6 } - m ^ { 1 / 6 } \right)$

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