Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 5 x } + 7 \sqrt { 125 x } + 4 \sqrt { 80 x }$

Accepted Answer

A)  $51 \sqrt { 5 x }$ 
B)  $52 \sqrt { 5 x }$ 
C)  $12 \sqrt { 210 x }$ 
D)  $11 \sqrt { 210 x }$ 
A)  $51 \sqrt { 5 x }$ 
B)  $52 \sqrt { 5 x }$ 
C)  $12 \sqrt { 210 x }$ 
D)  $11 \sqrt { 210 x }$

Question 2

Factor by grouping.
-$$12 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 15 b ^ { 3 }$$

Accepted Answer

A)  $\left( 12 a ^ { 2 } - 5 b ^ { 2 } \right) ( a - 3 b )$ 
B)  $\left( 3 a ^ { 2 } - 5 b \right) ( 4 a - 3 b )$ 
C)  $\left( 3 a ^ { 2 } - 5 b ^ { 2 } \right) ( 4 a - 3 b )$ 
D)  $\left( 3 a ^ { 2 } + 5 b ^ { 2 } \right) ( 4 a + 3 b )$ 
A)  $\left( 12 a ^ { 2 } - 5 b ^ { 2 } \right) ( a - 3 b )$ 
B)  $\left( 3 a ^ { 2 } - 5 b \right) ( 4 a - 3 b )$ 
C)  $\left( 3 a ^ { 2 } - 5 b ^ { 2 } \right) ( 4 a - 3 b )$ 
D)  $\left( 3 a ^ { 2 } + 5 b ^ { 2 } \right) ( 4 a + 3 b )$

Question 3

Determine the degree of the polynomial.
-$- 2 x ^ { 2 } + 3 x ^ { 3 } + 3 x ^ { 4 } + 1$

Accepted Answer

A)  4 
B)  10 
C)  2 
D)  9 
A)  4 
B)  10 
C)  2 
D)  9

Question 4

Find the product or quotient.
-$$\frac { 3 p - 3 } { p } \div \frac { 5 p - 5 } { 6 p ^ { 2 } }$$

Accepted Answer

A)  $\frac { 5 } { 18 } \mathrm { p }$ 
B)  $\frac { 18 } { 5 } p$ 
C)  $\frac { 15 p ^ { 2 } + 30 p + 15 } { 6 p ^ { 3 } }$ 
D)  $\frac { 18 p ^ { 3 } - 18 p ^ { 2 } } { 5 p ^ { 2 } - 5 p }$ 
A)  $\frac { 5 } { 18 } \mathrm { p }$ 
B)  $\frac { 18 } { 5 } p$ 
C)  $\frac { 15 p ^ { 2 } + 30 p + 15 } { 6 p ^ { 3 } }$ 
D)  $\frac { 18 p ^ { 3 } - 18 p ^ { 2 } } { 5 p ^ { 2 } - 5 p }$

Question 5

Evaluate the expression.
-99 - 4 ·16 + 5

Accepted Answer

A)  1995 
B)  116 
C)  40 
D)  1525 
A)  1995 
B)  116 
C)  40 
D)  1525

Question 6

Simplify the expression.
-$$\sqrt { 9 x ^ { 2 } }$$

Accepted Answer

A)  $3 x ^ { 2 }$ 
B)  $9 x$ 
C)  $- 3 x$ 
D)  $3 | \mathrm { x } |$ 
A)  $3 x ^ { 2 }$ 
B)  $9 x$ 
C)  $- 3 x$ 
D)  $3 | \mathrm { x } |$

Question 7

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 6 } { x - h } + \frac { 6 } { x } } { 2 x - h }$$

Accepted Answer

A)  $\frac { 1 } { x ( x - h ) }$ 
B)  $\frac { 6 } { x ( x - h ) }$ 
C)  $\mathrm { h }$ 
D)  $\frac { 6 } { x ( x + h ) }$ 
A)  $\frac { 1 } { x ( x - h ) }$ 
B)  $\frac { 6 } { x ( x - h ) }$ 
C)  $\mathrm { h }$ 
D)  $\frac { 6 } { x ( x + h ) }$

Question 8

Solve the problem.
-The formula $\mathrm { T } = 0.07 \mathrm { D } ^ { 1.5 }$ can be used to approximate the duration of a storm, where is the time in hours and D is the diameter of the storm in miles. A storm that is $16.2$ miles in diameter is heading toward a city. How long can the residents of the city expect the storm to last? Round you answer to the nearest hundredth of an hour.

Accepted Answer

A)  $5.79 \mathrm { hr }$ 
B)  $6.09 \mathrm { hr }$ 
C)  $4.56 \mathrm { hr }$ 
D)  $3.99 \mathrm { hr }$ 
A)  $5.79 \mathrm { hr }$ 
B)  $6.09 \mathrm { hr }$ 
C)  $4.56 \mathrm { hr }$ 
D)  $3.99 \mathrm { hr }$

Question 9

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

Accepted Answer

A)  1 
B)  $\frac { 1 + a } { 1 - a }$ 
C)  $\frac { a } { 1 - a ^ { 2 } }$ 
D)  $1 - a ^ { 2 }$ 
A)  1 
B)  $\frac { 1 + a } { 1 - a }$ 
C)  $\frac { a } { 1 - a ^ { 2 } }$ 
D)  $1 - a ^ { 2 }$

Question 10

Factor by any method.
-$$z ^ { 6 } - 64 a ^ { 6 }$$

Accepted Answer

A)  $\left( z ^ { 2 } - 4 a ^ { 2 } \right) \left( z ^ { 4 } + 4 z ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
B)  $\left( z ^ { 3 } + 8 a ^ { 3 } \right) \left( z ^ { 3 } - 8 a ^ { 3 } \right)$ 
C)  $( z + 2 a ) ( z - 2 a ) \left( z ^ { 4 } + 4 z ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
D)  $( z + 2 a ) ( z - 2 a ) \left( z ^ { 2 } + 2 z a + 4 a ^ { 2 } \right) \left( z ^ { 2 } - 2 z a + 4 a ^ { 2 } \right)$ 
A)  $\left( z ^ { 2 } - 4 a ^ { 2 } \right) \left( z ^ { 4 } + 4 z ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
B)  $\left( z ^ { 3 } + 8 a ^ { 3 } \right) \left( z ^ { 3 } - 8 a ^ { 3 } \right)$ 
C)  $( z + 2 a ) ( z - 2 a ) \left( z ^ { 4 } + 4 z ^ { 2 } a ^ { 2 } + 16 a ^ { 4 } \right)$ 
D)  $( z + 2 a ) ( z - 2 a ) \left( z ^ { 2 } + 2 z a + 4 a ^ { 2 } \right) \left( z ^ { 2 } - 2 z a + 4 a ^ { 2 } \right)$

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$$16 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$$

Accepted Answer

A)  $- 9 \sqrt [ 3 ] { 2 }$ 
B)  $9 \sqrt [ 3 ] { 2 }$ 
C)  $16 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$ 
D)  $11 \sqrt [ 3 ] { 2 }$ 
A)  $- 9 \sqrt [ 3 ] { 2 }$ 
B)  $9 \sqrt [ 3 ] { 2 }$ 
C)  $16 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$ 
D)  $11 \sqrt [ 3 ] { 2 }$

Question 12

Factor the trinomial, if possible.
-$$( m + 5 n ) ^ { 2 } - 8 ( m + 5 n ) + 16$$

Accepted Answer

A)  $( m + 5 n + 4 ) ^ { 2 }$ 
B)  $( \mathrm { m } - \mathrm { n } - 20 ) ^ { 2 }$ 
C)  $( m - 5 n - 4 ) ^ { 2 }$ 
D)  $( m + 5 n - 4 ) ^ { 2 }$ 
A)  $( m + 5 n + 4 ) ^ { 2 }$ 
B)  $( \mathrm { m } - \mathrm { n } - 20 ) ^ { 2 }$ 
C)  $( m - 5 n - 4 ) ^ { 2 }$ 
D)  $( m + 5 n - 4 ) ^ { 2 }$

Question 13

Factor by any method.
-$$4 a ^ { 3 } - 25 a$$

Accepted Answer

A)  $\left( 2 a ^ { 2 } + 5 \right) ( 2 a - 5 )$ 
B)  $a ( 2 a + 5 ) ( 2 a - 5 )$ 
C)  $a ( 4 a + 1 ) ( a - 25 )$ 
D)  $a ( 2 a - 5 ) ^ { 2 }$ 
A)  $\left( 2 a ^ { 2 } + 5 \right) ( 2 a - 5 )$ 
B)  $a ( 2 a + 5 ) ( 2 a - 5 )$ 
C)  $a ( 4 a + 1 ) ( a - 25 )$ 
D)  $a ( 2 a - 5 ) ^ { 2 }$

Question 14

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

Accepted Answer

A)  d(R, S) = 6 
B)  d(R, S) = -6 
C)  d(R, S) = 2 
D)  d(R, S) = -2 
A)  d(R, S) = 6 
B)  d(R, S) = -6 
C)  d(R, S) = 2 
D)  d(R, S) = -2

Question 15

Tell whether the statement is true or false.
-$\{ 7,9,10,12 \} \cup \varnothing = \{ 7,9,10,12 \}$

Accepted Answer

A) True 
 B)False

Question 16

Write in exponential form. Assume all variables are positive real numbers.
-$- 4 \sqrt { 6 m ^ { 9 } }$

Accepted Answer

A)  $- 4 \cdot 6 ^ { 1 / 2 } \mathrm {~m} ^ { 9 / 2 }$ 
B)  $96 \mathrm {~m} ^ { 2 / 9 }$ 
C)  $- 96 m ^ { 9 / 2 }$ 
D)  $( - 4 \cdot 6 ) ^ { 1 / 2 } m ^ { 9 / 2 }$ 
A)  $- 4 \cdot 6 ^ { 1 / 2 } \mathrm {~m} ^ { 9 / 2 }$ 
B)  $96 \mathrm {~m} ^ { 2 / 9 }$ 
C)  $- 96 m ^ { 9 / 2 }$ 
D)  $( - 4 \cdot 6 ) ^ { 1 / 2 } m ^ { 9 / 2 }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 5 ] { x ^ { 19 } y ^ { 9 } z ^ { 13 } }$$

Accepted Answer

A)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
B)  $x ^ { 15 } y ^ { 5 } z ^{10} \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
C)  $x y z \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
D)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { y ^ { 4 } z ^ { 3 } }$ 
A)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
B)  $x ^ { 15 } y ^ { 5 } z ^{10} \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
C)  $x y z \sqrt [ 5 ] { x ^ { 4 } y ^ { 4 } z ^ { 3 } }$ 
D)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { y ^ { 4 } z ^ { 3 } }$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 15 } \cdot \sqrt { 27 }$

Accepted Answer

A)  $- 15 \sqrt { 3 }$ 
B)  $9 \sqrt { 5 }$ 
C)  $15 \sqrt { 3 }$ 
D)  $- 9 \sqrt { 5 }$ 
A)  $- 15 \sqrt { 3 }$ 
B)  $9 \sqrt { 5 }$ 
C)  $15 \sqrt { 3 }$ 
D)  $- 9 \sqrt { 5 }$

Question 19

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

Accepted Answer

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

Question 20

Factor the trinomial, if possible.
-$$14 m ^ { 2 } + 53 m n + 14 n ^ { 2 }$$

Accepted Answer

A)  $( 2 m + 2 n ) ( 7 m + 7 n )$ 
B)  $( 2 m + 7 n ) ( 7 m + 2 n )$ 
C)  $( 2 m - 7 n ) ( 7 m - 2 n )$ 
D)  $\left( 2 m + 7 n ^ { 2 } \right) ( 7 m + 2 )$ 
A)  $( 2 m + 2 n ) ( 7 m + 7 n )$ 
B)  $( 2 m + 7 n ) ( 7 m + 2 n )$ 
C)  $( 2 m - 7 n ) ( 7 m - 2 n )$ 
D)  $\left( 2 m + 7 n ^ { 2 } \right) ( 7 m + 2 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 5 x } + 7 \sqrt { 125 x } + 4 \sqrt { 80 x }$

Factor by grouping. - $12 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 15 b ^ { 3 }$

Determine the degree of the polynomial. - $- 2 x ^ { 2 } + 3 x ^ { 3 } + 3 x ^ { 4 } + 1$

Find the product or quotient. - $\frac { 3 p - 3 } { p } \div \frac { 5 p - 5 } { 6 p ^ { 2 } }$

Evaluate the expression. -99 - 4 ·16 + 5

Simplify the expression. - $\sqrt { 9 x ^ { 2 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 6 } { x - h } + \frac { 6 } { x } } { 2 x - h }$

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

Factor by any method. - $z ^ { 6 } - 64 a ^ { 6 }$

Simplify the expression. Assume all variables represent positive real numbers. - $16 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$

Factor the trinomial, if possible. - $( m + 5 n ) ^ { 2 } - 8 ( m + 5 n ) + 16$

Factor by any method. - $4 a ^ { 3 } - 25 a$

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

Tell whether the statement is true or false. - $\{ 7,9,10,12 \} \cup \varnothing = \{ 7,9,10,12 \}$

Write in exponential form. Assume all variables are positive real numbers. - $- 4 \sqrt { 6 m ^ { 9 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 5 ] { x ^ { 19 } y ^ { 9 } z ^ { 13 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 15 } \cdot \sqrt { 27 }$

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

Factor the trinomial, if possible. - $14 m ^ { 2 } + 53 m n + 14 n ^ { 2 }$

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

Simplify the expression. Assume all variables represent positive real numbers. - 5x+7125x+480x\sqrt { 5 x } + 7 \sqrt { 125 x } + 4 \sqrt { 80 x }5x​+7125x​+480x​

Factor by grouping. - 12a3−9a2b−20ab2+15b312 a ^ { 3 } - 9 a ^ { 2 } b - 20 a b ^ { 2 } + 15 b ^ { 3 }12a3−9a2b−20ab2+15b3

Determine the degree of the polynomial. - −2x2+3x3+3x4+1- 2 x ^ { 2 } + 3 x ^ { 3 } + 3 x ^ { 4 } + 1−2x2+3x3+3x4+1

Find the product or quotient. - 3p−3p÷5p−56p2\frac { 3 p - 3 } { p } \div \frac { 5 p - 5 } { 6 p ^ { 2 } }p3p−3​÷6p25p−5​