Question 1

Factor the trinomial, if possible.
-$$x ^ { 2 } + 3 x y - 18 y ^ { 2 }$$

Accepted Answer

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

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$$3 \sqrt [ 3 ] { 125 x } + 3 \sqrt [ 3 ] { 64 x }$$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 189 x }$ 
B)  $9 \sqrt [ 3 ] { x }$ 
C)  $27 \sqrt [ 3 ] { x }$ 
D)  $27 x$ 
A)  $3 \sqrt [ 3 ] { 189 x }$ 
B)  $9 \sqrt [ 3 ] { x }$ 
C)  $27 \sqrt [ 3 ] { x }$ 
D)  $27 x$

Question 3

Find the domain of the expression.
-$$\frac { 8 } { p + 6 }$$

Accepted Answer

A)  $\{ p \mid p \neq - 6 \}$ 
B)  $\{ p \mid p \neq 8 \}$ 
C)  $\{ p \mid p \neq 6 \}$ 
D)  all real numbers 
A)  $\{ p \mid p \neq - 6 \}$ 
B)  $\{ p \mid p \neq 8 \}$ 
C)  $\{ p \mid p \neq 6 \}$ 
D)  all real numbers

Question 4

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-6 {2, 5, 8, 6, 4}

Accepted Answer

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

Question 5

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$\left( 2 x + \frac { 1 } { 6 } \right) \left( 8 x - \frac { 1 } { 3 } \right)$$

Accepted Answer

A)  $16 x ^ { 2 } + \frac { 2 } { 3 } x - \frac { 1 } { 18 }$ 
B)  $16 x ^ { 2 } + \frac { 2 } { 3 } x + \frac { 1 } { 18 }$ 
C)  $16 x ^ { 2 } - 2 x - \frac { 1 } { 18 }$ 
D)  $16 x ^ { 2 } - \frac { 2 } { 3 } x + \frac { 1 } { 18 }$ 
A)  $16 x ^ { 2 } + \frac { 2 } { 3 } x - \frac { 1 } { 18 }$ 
B)  $16 x ^ { 2 } + \frac { 2 } { 3 } x + \frac { 1 } { 18 }$ 
C)  $16 x ^ { 2 } - 2 x - \frac { 1 } { 18 }$ 
D)  $16 x ^ { 2 } - \frac { 2 } { 3 } x + \frac { 1 } { 18 }$

Question 6

Find the sum or difference.
-$$\left( 3 x ^ { 8 } + 10 x ^ { 6 } - 11 x ^ { 3 } + 3 \right) - \left( 5 x ^ { 8 } - 9 x ^ { 4 } + 3 x ^ { 3 } - 11 \right)$$

Accepted Answer

A)  $- 2 x ^ { 8 } + 10 x ^ { 6 } + 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
B)  $- 2 x ^ { 8 } + 10 x ^ { 6 } - 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
C)  $2 x ^ { 8 } + 10 x ^ { 6 } - 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
D)  $2 x ^ { 8 } + 10 x ^ { 6 } + 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
A)  $- 2 x ^ { 8 } + 10 x ^ { 6 } + 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
B)  $- 2 x ^ { 8 } + 10 x ^ { 6 } - 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
C)  $2 x ^ { 8 } + 10 x ^ { 6 } - 9 x ^ { 4 } - 14 x ^ { 3 } + 14$ 
D)  $2 x ^ { 8 } + 10 x ^ { 6 } + 9 x ^ { 4 } - 14 x ^ { 3 } + 14$

Question 7

Evaluate the expression.
-$$\text { Let } x = - 14 , y = 11 \text {. Evaluate } | y - x | \text {. }$$

Accepted Answer

A)  -25 
B)  3 
C)  -3 
D)  25 
A)  -25 
B)  3 
C)  -3 
D)  25

Question 8

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\{ 0,3,5,8 \}$ _____$\{ 3,5,8,9,10,11 \}$

Accepted Answer

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

Question 9

Solve the problem.
-$$[ ( 4 x + 3 ) + 7 y ] ^ { 2 }$$

Accepted Answer

A)  $16 x ^ { 2 } + 24 x + 9 + 56 x y + 42 y + 49 y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 12 x + 9 + 28 x y + 21 y + 49 y ^ { 2 }$ 
C)  $16 x ^ { 2 } + 56 x y + 49 y ^ { 2 }$ 
D)  $16 x ^ { 2 } + 24 x + 56 x y + 42 y + 49 y ^ { 2 }$ 
A)  $16 x ^ { 2 } + 24 x + 9 + 56 x y + 42 y + 49 y ^ { 2 }$ 
B)  $16 x ^ { 2 } + 12 x + 9 + 28 x y + 21 y + 49 y ^ { 2 }$ 
C)  $16 x ^ { 2 } + 56 x y + 49 y ^ { 2 }$ 
D)  $16 x ^ { 2 } + 24 x + 56 x y + 42 y + 49 y ^ { 2 }$

Question 10

Use set notation, and list all the elements of the set.
-{90, 84, 78, . . ., 30}

Accepted Answer

A)  {90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150} 
B)  {90, 84, 78, 72, 66, 60, 54, 48, 42, 36, 30} 
C)  {90, 84, 78, 66, 54, 42, 30} 
D)  {90, 84, 78, 71, 65, 59, 53, 47, 41, 35, 29} 
A)  {90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150} 
B)  {90, 84, 78, 72, 66, 60, 54, 48, 42, 36, 30} 
C)  {90, 84, 78, 66, 54, 42, 30} 
D)  {90, 84, 78, 71, 65, 59, 53, 47, 41, 35, 29}

Question 11

Identify the expression as a polynomial or not a polynomial.
-$\frac { 9 } { x ^ { 5 } } + \frac { 2 } { x ^ { 2 } } = 6$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Question 12

Factor the polynomial by substitution.
-$$8 x ^ { 4 } + 18 x ^ { 2 } + 9$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 1 \right) \left( 2 x ^ { 2 } + 9 \right)$ 
B)  $\left( 4 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } - 3 \right)$ 
C)  $\left( 4 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
D)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$ 
A)  $\left( 4 x ^ { 2 } + 1 \right) \left( 2 x ^ { 2 } + 9 \right)$ 
B)  $\left( 4 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } - 3 \right)$ 
C)  $\left( 4 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
D)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$

Question 13

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { - 4 } y ^ { 7 } } { x ^ { - 2 } y ^ { 5 } }$$

Accepted Answer

A)  $\frac { x ^ { 2 } } { y ^ { 2 } }$ 
B)  $\frac { y ^ { 2 } } { x ^ { 2 } }$ 
C)  $\frac { x ^ { 3 } } { y ^ { 3 } }$ 
D)  $\frac { y ^ { 3 } } { x ^ { 3 } }$ 
A)  $\frac { x ^ { 2 } } { y ^ { 2 } }$ 
B)  $\frac { y ^ { 2 } } { x ^ { 2 } }$ 
C)  $\frac { x ^ { 3 } } { y ^ { 3 } }$ 
D)  $\frac { y ^ { 3 } } { x ^ { 3 } }$

Question 14

Use these sets to find the following. Identify any disjoint sets.
-Let $U = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , M = \{ 3,5,7,9 \} , N = \{ 4,6,8,10,12 \} , Q = \{ 3,5,7,9,11,13 \}$, and $R = \{ 3,4,5,6 \}$.

$\mathrm { M } \cap \mathrm { N }$

Accepted Answer

A)  $\{ 3,4,5,6,7,8,9,10,12 \}$ 
B)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
C)  $\{ 5,6,7,8,12 \}$ 
D)  $\{ 4,5,6,7,8,9,10,11,12 \}$ 
A)  $\{ 3,4,5,6,7,8,9,10,12 \}$ 
B)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
C)  $\{ 5,6,7,8,12 \}$ 
D)  $\{ 4,5,6,7,8,9,10,11,12 \}$

Question 15

Determine the degree of the polynomial.
-$3 x ^ { 6 } - 9 x ^ { 7 } + 10 x ^ { 2 } - 8$

Accepted Answer

A)  6 
B)  4 
C)  15 
D)  7 
A)  6 
B)  4 
C)  15 
D)  7

Question 16

Find the distance between two points given their coordinates.
-Find the distance between points P and Q on a number line, with coordinates 2 and -4, respectively.

Accepted Answer

A)  d(P, Q) = 2 
B)  d(P, Q) = 6 
C)  d(P, Q) = -2 
D)  d(P, Q) = -6 
A)  d(P, Q) = 2 
B)  d(P, Q) = 6 
C)  d(P, Q) = -2 
D)  d(P, Q) = -6

Question 17

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

Accepted Answer

A)  $\pm 3$ 
B)  3 
C)  9 
D)  5 
A)  $\pm 3$ 
B)  3 
C)  9 
D)  5

Question 18

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 3 n ^ { 2 } \right) \cdot \left( - 6 n ^ { 5 } \right)$

Accepted Answer

A)  $- 3 n ^{10}$ 
B)  $- 3 n ^ { 7 }$ 
C)  $- 18 n ^{10}$ 
D)  $- 18 n ^ { 7 }$ 
A)  $- 3 n ^{10}$ 
B)  $- 3 n ^ { 7 }$ 
C)  $- 18 n ^{10}$ 
D)  $- 18 n ^ { 7 }$

Question 19

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\left( 6 x ^ { - 5 } \right) ^ { 2 } \left( x ^ { 2 } \right) ^ { - 1 }$$

Accepted Answer

A)  $\frac { 6 ^ { 2 } } { x ^ { 2 } }$ 
B)  $\frac { 1 } { 6 ^ { - 10 } x ^ { 12 } }$ 
C)  $6 ^ { 2 } x ^ { 20 }$ 
D)  $\frac { 6 ^ { 2 } } { x ^ { 12 } }$ 
A)  $\frac { 6 ^ { 2 } } { x ^ { 2 } }$ 
B)  $\frac { 1 } { 6 ^ { - 10 } x ^ { 12 } }$ 
C)  $6 ^ { 2 } x ^ { 20 }$ 
D)  $\frac { 6 ^ { 2 } } { x ^ { 12 } }$

Question 20

Identify the set as finite or infinite.
-$$\{ \mathrm { x } \mid \mathrm { x } \text { is a fraction between } 0 \text { and } 1 \}$$

Accepted Answer

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

Factor the trinomial, if possible. - $x ^ { 2 } + 3 x y - 18 y ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $3 \sqrt [ 3 ] { 125 x } + 3 \sqrt [ 3 ] { 64 x }$

Find the domain of the expression. - $\frac { 8 } { p + 6 }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -6 {2, 5, 8, 6, 4}

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $\left( 2 x + \frac { 1 } { 6 } \right) \left( 8 x - \frac { 1 } { 3 } \right)$

Find the sum or difference. - $\left( 3 x ^ { 8 } + 10 x ^ { 6 } - 11 x ^ { 3 } + 3 \right) - \left( 5 x ^ { 8 } - 9 x ^ { 4 } + 3 x ^ { 3 } - 11 \right)$

Evaluate the expression. - $\text { Let } x = - 14 , y = 11 \text {. Evaluate } | y - x | \text {. }$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{ 0,3,5,8 \}$ _____ $\{ 3,5,8,9,10,11 \}$

Solve the problem. - $[ ( 4 x + 3 ) + 7 y ] ^ { 2 }$

Use set notation, and list all the elements of the set. -{90, 84, 78, . . ., 30}

Identify the expression as a polynomial or not a polynomial. - $\frac { 9 } { x ^ { 5 } } + \frac { 2 } { x ^ { 2 } } = 6$

Factor the polynomial by substitution. - $8 x ^ { 4 } + 18 x ^ { 2 } + 9$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 4 } y ^ { 7 } } { x ^ { - 2 } y ^ { 5 } }$

Use these sets to find the following. Identify any disjoint sets. -Let $U = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , M = \{ 3,5,7,9 \} , N = \{ 4,6,8,10,12 \} , Q = \{ 3,5,7,9,11,13 \}$ , and $R = \{ 3,4,5,6 \}$ . $\mathrm { M } \cap \mathrm { N }$

Determine the degree of the polynomial. - $3 x ^ { 6 } - 9 x ^ { 7 } + 10 x ^ { 2 } - 8$

Find the distance between two points given their coordinates. -Find the distance between points P and Q on a number line, with coordinates 2 and -4, respectively.

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 3 n ^ { 2 } \right) \cdot \left( - 6 n ^ { 5 } \right)$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\left( 6 x ^ { - 5 } \right) ^ { 2 } \left( x ^ { 2 } \right) ^ { - 1 }$

Identify the set as finite or infinite. - $\{ \mathrm { x } \mid \mathrm { x } \text { is a fraction between } 0 \text { and } 1 \}$

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 1: Review of Basic Concepts

Factor the trinomial, if possible. - x2+3xy−18y2x ^ { 2 } + 3 x y - 18 y ^ { 2 }x2+3xy−18y2

Simplify the expression. Assume all variables represent positive real numbers. - 3125x3+364x33 \sqrt [ 3 ] { 125 x } + 3 \sqrt [ 3 ] { 64 x }33125x​+3364x​

Find the domain of the expression. - 8p+6\frac { 8 } { p + 6 }p+68​

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -6 {2, 5, 8, 6, 4}

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - (2x+16)(8x−13)\left( 2 x + \frac { 1 } { 6 } \right) \left( 8 x - \frac { 1 } { 3 } \right)(2x+61​)(8x−31​)

Find the sum or difference. - (3x8+10x6−11x3+3)−(5x8−9x4+3x3−11)\left( 3 x ^ { 8 } + 10 x ^ { 6 } - 11 x ^ { 3 } + 3 \right) - \left( 5 x ^ { 8 } - 9 x ^ { 4 } + 3 x ^ { 3 } - 11 \right)(3x8+10x6−11x3+3)−(5x8−9x4+3x3−11)

Evaluate the expression. - Let x=−14,y=11. Evaluate ∣y−x∣. \text { Let } x = - 14 , y = 11 \text {. Evaluate } | y - x | \text {. } Let x=−14,y=11. Evaluate ∣y−x∣.

Insert ⊆\subseteq⊆ or ⊈\nsubseteq⊈ in the blank to make the statement true. - {0,3,5,8}\{ 0,3,5,8 \}{0,3,5,8} _____ {3,5,8,9,10,11}\{ 3,5,8,9,10,11 \}{3,5,8,9,10,11}

Solve the problem. - [(4x+3)+7y]2[ ( 4 x + 3 ) + 7 y ] ^ { 2 }[(4x+3)+7y]2