Question 1

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$- \left( \frac { 2 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }$$

Accepted Answer

A)  $\frac { 8 x ^ { 9 } } { y ^ { 6 } }$ 
B)  $\frac { y ^ { 2 } } { 8 x ^ { 9 } }$ 
C)  1 
D)  $- 1$ 
A)  $\frac { 8 x ^ { 9 } } { y ^ { 6 } }$ 
B)  $\frac { y ^ { 2 } } { 8 x ^ { 9 } }$ 
C)  1 
D)  $- 1$

Question 2

Evaluate the expression.
-$$\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }$$

Accepted Answer

A)  not a real number 
B)  $- \frac { 6 } { 7 }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 49 } { 72 }$ 
A)  not a real number 
B)  $- \frac { 6 } { 7 }$ 
C)  $\frac { 7 } { 6 }$ 
D)  $\frac { 49 } { 72 }$

Question 3

Evaluate the expression.
-$11 + 8 ^ { 2 } - ( - 10 ) \cdot 4$

Accepted Answer

A)  35 
B)  115 
C)  148 
D)  260 
A)  35 
B)  115 
C)  148 
D)  260

Question 4

Evaluate the expression.
-Let $x = 4$ and $y = - 5$. Evaluate $\frac { | x | } { x } + \frac { | y | } { y }$.

Accepted Answer

A)  2 
B)  1 
C)  0 
D)  $- 1$ 
A)  2 
B)  1 
C)  0 
D)  $- 1$

Question 5

Factor the trinomial, if possible.
-$$( m - 5 n ) ^ { 2 } - 12 ( m - 5 n ) + 36$$

Accepted Answer

A)  $( m - 5 n ) ^ { 2 }$ 
B)  $( m - 5 n + 6 ) ( m + 5 n - 6 )$ 
C)  $( m + 5 n + 6 ) ^ { 2 }$ 
D)  $( m - 5 n - 6 ) ^ { 2 }$ 
A)  $( m - 5 n ) ^ { 2 }$ 
B)  $( m - 5 n + 6 ) ( m + 5 n - 6 )$ 
C)  $( m + 5 n + 6 ) ^ { 2 }$ 
D)  $( m - 5 n - 6 ) ^ { 2 }$

Question 6

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
B)  $x ^ { 34 / 5 }$ 
C)  $x ^ { 22 / 5 }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$ 
A)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
B)  $x ^ { 34 / 5 }$ 
C)  $x ^ { 22 / 5 }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$

Question 7

Factor out the greatest common factor. Simplify the factors, if possible.
-$5 m ( 2 - m ) + 8 n ( 2 - m )$

Accepted Answer

A)  $m ( 5 + 8 n ) ( 2 - m )$ 
B)  $5 ( m + n ) ( 2 - m )$ 
C)  $( 5 m - 8 n ) ( 2 - m )$ 
D)  $( 5 m + 8 n ) ( 2 - m )$ 
A)  $m ( 5 + 8 n ) ( 2 - m )$ 
B)  $5 ( m + n ) ( 2 - m )$ 
C)  $( 5 m - 8 n ) ( 2 - m )$ 
D)  $( 5 m + 8 n ) ( 2 - m )$

Question 8

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt [ 3 ] { \mathrm { x } ^ { 2 } \mathrm { y } } \cdot \sqrt [ 3 ] { \mathrm { x } } } { \sqrt [ 3 ] { \mathrm { y } ^ { 2 } } }$$

Accepted Answer

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

Question 9

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

Accepted Answer

A)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 3 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $13 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
C)  $7 x \sqrt [ 4 ] { x ^ { 7 } }$ 
D)  $7 x \sqrt [ 4 ] { x ^ { 3 } }$ 
A)  $10 \sqrt [ 4 ] { x ^ { 7 } } - 3 x \sqrt [ 4 ] { x ^ { 3 } }$ 
B)  $13 \sqrt [ 4 ] { \mathrm { x } ^ { 3 } }$ 
C)  $7 x \sqrt [ 4 ] { x ^ { 7 } }$ 
D)  $7 x \sqrt [ 4 ] { x ^ { 3 } }$

Question 10

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$x ^ { 11 } \cdot x ^ { 7 }$$

Accepted Answer

A)  $( 2 x ) ^ { 77 }$ 
B)  $( 2 x ) ^ { 18 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 77 }$ 
A)  $( 2 x ) ^ { 77 }$ 
B)  $( 2 x ) ^ { 18 }$ 
C)  $x ^ { 18 }$ 
D)  $x ^ { 77 }$

Question 11

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$$( x - 6 ) ( 5 x - 2 )$$

Accepted Answer

A)  $5 x ^ { 2 } - 32 x - 32$ 
B)  $5 x ^ { 2 } - 34 x + 12$ 
C)  $5 x ^ { 2 } + 12 x - 32$ 
D)  $5 x ^ { 2 } - 32 x + 12$ 
A)  $5 x ^ { 2 } - 32 x - 32$ 
B)  $5 x ^ { 2 } - 34 x + 12$ 
C)  $5 x ^ { 2 } + 12 x - 32$ 
D)  $5 x ^ { 2 } - 32 x + 12$

Question 12

Identify the set as finite or infinite.
-$$\{ x \mid x \text { is an even natural number } \}$$

Accepted Answer

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

Question 13

Decide whether the expression has been simplified correctly.
-$\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 12 }$

Accepted Answer

A)  Simplified correctly 
B)  Not simplified correctly 
A)  Simplified correctly 
B)  Not simplified correctly

Question 14

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.
-$( 6 y - 5 ) \left( 36 y ^ { 2 } + 30 y + 25 \right)$

Accepted Answer

A)  $216 y ^ { 3 } + 125$ 
B)  $216 y ^ { 3 } + 150 y ^ { 2 } - 125$ 
C)  $216 y ^ { 3 } - 125$ 
D)  $36 y ^ { 3 } + 125$ 
A)  $216 y ^ { 3 } + 125$ 
B)  $216 y ^ { 3 } + 150 y ^ { 2 } - 125$ 
C)  $216 y ^ { 3 } - 125$ 
D)  $36 y ^ { 3 } + 125$

Question 15

Determine which property of absolute value justifies the statement.
-$| - x | = | x |$

Accepted Answer

A)  Property 2: the absolute value of a number and its opposite are equal. 
B)  Property 5: the triangle inequality 
C)  Property 2: the opposite of the absolute value of a number is equal to the absolute value of the number. 
D)  Property 1: the opposite of a number is equal to the absolute value of the number . 
A)  Property 2: the absolute value of a number and its opposite are equal. 
B)  Property 5: the triangle inequality 
C)  Property 2: the opposite of the absolute value of a number is equal to the absolute value of the number. 
D)  Property 1: the opposite of a number is equal to the absolute value of the number .

Question 16

Find the product or quotient.
-$$\frac { k ^ { 2 } + 9 k + 18 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 7 k + 12 }$$

Accepted Answer

A)  $\frac { k } { k ^ { 2 } + 12 k + 36 }$ 
B)  $\frac { \mathrm { k } } { \mathrm { k } + 4 }$ 
C)  $\frac { \mathrm { k } ^ { 2 } + 6 \mathrm { k } } { \mathrm { k } + 4 }$ 
D)  $\frac { 1 } { k + 4 }$ 
A)  $\frac { k } { k ^ { 2 } + 12 k + 36 }$ 
B)  $\frac { \mathrm { k } } { \mathrm { k } + 4 }$ 
C)  $\frac { \mathrm { k } ^ { 2 } + 6 \mathrm { k } } { \mathrm { k } + 4 }$ 
D)  $\frac { 1 } { k + 4 }$

Question 17

Write the expression in lowest terms.
-$$\frac { 3 x ^ { 2 } + 13 x + 12 } { 4 x ^ { 2 } + 13 x + 3 }$$

Accepted Answer

A)  $\frac { 3 x + 4 } { 4 x + 1 }$ 
B)  $\frac { x + 5 } { x + 2 }$ 
C)  $\frac { x - 4 } { x - 1 }$ 
D)  $\frac { 3 x + 3 } { 4 x - 3 }$ 
A)  $\frac { 3 x + 4 } { 4 x + 1 }$ 
B)  $\frac { x + 5 } { x + 2 }$ 
C)  $\frac { x - 4 } { x - 1 }$ 
D)  $\frac { 3 x + 3 } { 4 x - 3 }$

Question 18

Tell whether the statement is true or false.
-$$\{ 10,13,14,16 \} \cap \{ 13,14,17,18 \} = \{ 13,14 \}$$

Accepted Answer

A) True 
 B)False

Question 19

Solve the problem.
-$$( 3 x + 7 y ) ( 3 x - 3 y + 1 )$$

Accepted Answer

A)  $9 x ^ { 2 } + 21 x y + 3 x - 21 y ^ { 2 } + 7 y$ 
B)  $9 x ^ { 2 } + 12 x y + 12 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 9 x y + 3 x - 21 y ^ { 2 }$ 
D)  $9 x ^ { 2 } + 12 x y + 3 x - 21 y ^ { 2 } + 7 y$ 
A)  $9 x ^ { 2 } + 21 x y + 3 x - 21 y ^ { 2 } + 7 y$ 
B)  $9 x ^ { 2 } + 12 x y + 12 y ^ { 2 }$ 
C)  $9 x ^ { 2 } - 9 x y + 3 x - 21 y ^ { 2 }$ 
D)  $9 x ^ { 2 } + 12 x y + 3 x - 21 y ^ { 2 } + 7 y$

Question 20

Factor by any method.
-$$8 c ^ { 3 } + 729$$

Accepted Answer

A)  $( 8 c + 9 ) \left( c ^ { 2 } - 18 c + 81 \right)$ 
B)  $( 2 c - 9 ) \left( 4 c ^ { 2 } + 18 c + 81 \right)$ 
C)  $( 2 c + 9 ) \left( 4 c ^ { 2 } + 81 \right)$ 
D)  $( 2 c + 9 ) \left( 4 c ^ { 2 } - 18 c + 81 \right)$ 
A)  $( 8 c + 9 ) \left( c ^ { 2 } - 18 c + 81 \right)$ 
B)  $( 2 c - 9 ) \left( 4 c ^ { 2 } + 18 c + 81 \right)$ 
C)  $( 2 c + 9 ) \left( 4 c ^ { 2 } + 81 \right)$ 
D)  $( 2 c + 9 ) \left( 4 c ^ { 2 } - 18 c + 81 \right)$

Simplify the expression. Assume all variables represent nonzero real numbers. - $- \left( \frac { 2 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }$

Evaluate the expression. - $\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }$

Evaluate the expression. - $11 + 8 ^ { 2 } - ( - 10 ) \cdot 4$

Evaluate the expression. -Let $x = 4$ and $y = - 5$ . Evaluate $\frac { | x | } { x } + \frac { | y | } { y }$ .

Factor the trinomial, if possible. - $( m - 5 n ) ^ { 2 } - 12 ( m - 5 n ) + 36$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 m ( 2 - m ) + 8 n ( 2 - m )$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { \mathrm { x } ^ { 2 } \mathrm { y } } \cdot \sqrt [ 3 ] { \mathrm { x } } } { \sqrt [ 3 ] { \mathrm { y } ^ { 2 } } }$

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $x ^ { 11 } \cdot x ^ { 7 }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $( x - 6 ) ( 5 x - 2 )$

Identify the set as finite or infinite. - $\{ x \mid x \text { is an even natural number } \}$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 12 }$

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. - $( 6 y - 5 ) \left( 36 y ^ { 2 } + 30 y + 25 \right)$

Determine which property of absolute value justifies the statement. - $| - x | = | x |$

Find the product or quotient. - $\frac { k ^ { 2 } + 9 k + 18 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 7 k + 12 }$

Write the expression in lowest terms. - $\frac { 3 x ^ { 2 } + 13 x + 12 } { 4 x ^ { 2 } + 13 x + 3 }$

Tell whether the statement is true or false. - $\{ 10,13,14,16 \} \cap \{ 13,14,17,18 \} = \{ 13,14 \}$

Solve the problem. - $( 3 x + 7 y ) ( 3 x - 3 y + 1 )$

Factor by any method. - $8 c ^ { 3 } + 729$

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 nonzero real numbers. - −(2x3y2)0- \left( \frac { 2 x ^ { 3 } } { y ^ { 2 } } \right) ^ { 0 }−(y22x3​)0

Evaluate the expression. - (−4936)−1/2\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }(−3649​)−1/2

Evaluate the expression. - 11+82−(−10)⋅411 + 8 ^ { 2 } - ( - 10 ) \cdot 411+82−(−10)⋅4

Evaluate the expression. -Let x=4x = 4x=4 and y=−5y = - 5y=−5 . Evaluate ∣x∣x+∣y∣y\frac { | x | } { x } + \frac { | y | } { y }x∣x∣​+y∣y∣​ .

Factor the trinomial, if possible. - (m−5n)2−12(m−5n)+36( m - 5 n ) ^ { 2 } - 12 ( m - 5 n ) + 36(m−5n)2−12(m−5n)+36

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x3/5x6/5⋅x−5\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }x6/5⋅x−5x3/5​

Factor out the greatest common factor. Simplify the factors, if possible. - 5m(2−m)+8n(2−m)5 m ( 2 - m ) + 8 n ( 2 - m )5m(2−m)+8n(2−m)

Simplify the expression. Assume all variables represent positive real numbers. - x2y3⋅x3y23\frac { \sqrt [ 3 ] { \mathrm { x } ^ { 2 } \mathrm { y } } \cdot \sqrt [ 3 ] { \mathrm { x } } } { \sqrt [ 3 ] { \mathrm { y } ^ { 2 } } }3y2​3x2y​⋅3x​​

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

Simplify the expression. Assume all variables represent nonzero real numbers. - x11⋅x7x ^ { 11 } \cdot x ^ { 7 }x11⋅x7

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - (x−6)(5x−2)( x - 6 ) ( 5 x - 2 )(x−6)(5x−2)

Identify the set as finite or infinite. - {x∣x is an even natural number }\{ x \mid x \text { is an even natural number } \}{x∣x is an even natural number }

Decide whether the expression has been simplified correctly. - (x6)2=x12\left( x ^ { 6 } \right) ^ { 2 } = x ^ { 12 }(x6)2=x12

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. - (6y−5)(36y2+30y+25)( 6 y - 5 ) \left( 36 y ^ { 2 } + 30 y + 25 \right)(6y−5)(36y2+30y+25)

Determine which property of absolute value justifies the statement. - ∣−x∣=∣x∣| - x | = | x |∣−x∣=∣x∣

Find the product or quotient. - k2+9k+18k2+12k+36⋅k2+6kk2+7k+12\frac { k ^ { 2 } + 9 k + 18 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } + 7 k + 12 }k2+12k+36k2+9k+18​⋅k2+7k+12k2+6k​

Write the expression in lowest terms. - 3x2+13x+124x2+13x+3\frac { 3 x ^ { 2 } + 13 x + 12 } { 4 x ^ { 2 } + 13 x + 3 }4x2+13x+33x2+13x+12​

Tell whether the statement is true or false. - {10,13,14,16}∩{13,14,17,18}={13,14}\{ 10,13,14,16 \} \cap \{ 13,14,17,18 \} = \{ 13,14 \}{10,13,14,16}∩{13,14,17,18}={13,14}

Solve the problem. - (3x+7y)(3x−3y+1)( 3 x + 7 y ) ( 3 x - 3 y + 1 )(3x+7y)(3x−3y+1)

Factor by any method. - 8c3+7298 c ^ { 3 } + 7298c3+729