Question 1

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$$

Accepted Answer

A)  True 
B)  False; $\left| ( - 5 ) ^ { 3 } \right| = 5 ^ { 3 }$ 
A)  True 
B)  False; $\left| ( - 5 ) ^ { 3 } \right| = 5 ^ { 3 }$

Question 2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 } { 5 } ( - 5 y + 15 x - 5 z )$$

Accepted Answer

A)  $- 4 y - 12 x - 4 z$ 
B)  $- 4 y - 12 x + 4 z$ 
C)  $- 4 y + 12 x + 4 z$ 
D)  $- 4 y + 12 x - 4 z$ 
A)  $- 4 y - 12 x - 4 z$ 
B)  $- 4 y - 12 x + 4 z$ 
C)  $- 4 y + 12 x + 4 z$ 
D)  $- 4 y + 12 x - 4 z$

Question 3

Factor the trinomial, if possible.
-$$x ^ { 2 } + 4 x y - 192 y ^ { 2 }$$

Accepted Answer

A)  $( x + 16 y ) ( x - 12 y )$ 
B)  prime 
C)  $( x - 16 y ) ( x + y )$ 
D)  $( x - 16 y ) ( x + 12 y )$ 
A)  $( x + 16 y ) ( x - 12 y )$ 
B)  prime 
C)  $( x - 16 y ) ( x + y )$ 
D)  $( x - 16 y ) ( x + 12 y )$

Question 4

Find the product or quotient.
-$$\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }$$

Accepted Answer

A)  $\frac { 8 ( x + 8 ) ^ { 2 } } { 15 x ^ { 2 } ( 9 x + 8 ) }$ 
B)  $\frac { 40 } { 3 x ^ { 4 } ( 9 x + 8 ) }$ 
C)  $\frac { 3 x ^ { 4 } } { 40 ( 9 x + 8 ) }$ 
D)  $\frac { 3 x ^ { 3 } } { 40 ( 9 x + 8 ) }$ 
A)  $\frac { 8 ( x + 8 ) ^ { 2 } } { 15 x ^ { 2 } ( 9 x + 8 ) }$ 
B)  $\frac { 40 } { 3 x ^ { 4 } ( 9 x + 8 ) }$ 
C)  $\frac { 3 x ^ { 4 } } { 40 ( 9 x + 8 ) }$ 
D)  $\frac { 3 x ^ { 3 } } { 40 ( 9 x + 8 ) }$

Question 5

Factor by grouping.
-$$6 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 6$$

Accepted Answer

A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 3 x ^ { 2 } - 2 \right)$ 
B)  $\left( 2 x ^ { 4 } - 3 \right) ( 3 x - 2 )$ 
C)  $\left( 6 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
D)  $\left( 2 x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } + 2 \right)$ 
A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 3 x ^ { 2 } - 2 \right)$ 
B)  $\left( 2 x ^ { 4 } - 3 \right) ( 3 x - 2 )$ 
C)  $\left( 6 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
D)  $\left( 2 x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } + 2 \right)$

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 144 } + \sqrt { 16 }$

Accepted Answer

A)  4 
B)  $4 \sqrt { 10 }$ 
C)  16 
D)  8 
A)  4 
B)  $4 \sqrt { 10 }$ 
C)  16 
D)  8

Question 7

Find the domain of the expression.
-$$\frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }$$

Accepted Answer

A)  $\left\{ \left\{ x \mid x \neq \frac { 4 } { 3 } , - 2 \right\} \right.$ 
B)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 4 } , - 2 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq - \frac { 3 } { 4 } , 2 \right\} \right.$ 
D)  all real numbers 
A)  $\left\{ \left\{ x \mid x \neq \frac { 4 } { 3 } , - 2 \right\} \right.$ 
B)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 4 } , - 2 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq - \frac { 3 } { 4 } , 2 \right\} \right.$ 
D)  all real numbers

Question 8

Evaluate the expression.
-Let $x = - 1 , y = 4$. Evaluate $\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }$

Accepted Answer

A)  $\frac { 24 } { 7 }$ 
B)  $- \frac { 16 } { 7 }$. 
C)  $- \frac { 16 } { 17 }$ 
D)  $- \frac { 16 } { 17 }$. 
A)  $\frac { 24 } { 7 }$ 
B)  $- \frac { 16 } { 7 }$. 
C)  $- \frac { 16 } { 17 }$ 
D)  $- \frac { 16 } { 17 }$.

Question 9

Decide whether the expression has been simplified correctly.
-$4 ^ { 0 } x = 0$

Accepted Answer

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

Question 10

Determine the degree of the polynomial.
-$3 a ^ { 2 } + 16 a ^ { 5 } - 8 a$

Accepted Answer

A)  7 
B)  5 
C)  3 
D)  8 
A)  7 
B)  5 
C)  3 
D)  8

Question 11

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }$$

Accepted Answer

A)  $x ^ { 25 / 3 }$ 
B)  $\frac { 1 } { x ^ { 17 / 3 } }$ 
C)  $\frac { 1 } { x ^ { 25 / 3 } }$ 
D)  $x ^ { 17 / 3 }$ 
A)  $x ^ { 25 / 3 }$ 
B)  $\frac { 1 } { x ^ { 17 / 3 } }$ 
C)  $\frac { 1 } { x ^ { 25 / 3 } }$ 
D)  $x ^ { 17 / 3 }$

Question 12

Write the expression in lowest terms.
-$$\frac { 5 x + 20 } { 3 x + 12 }$$

Accepted Answer

A)  1 
B)  $\frac { x + 4 } { x + 12 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $x + 4$ 
A)  1 
B)  $\frac { x + 4 } { x + 12 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $x + 4$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }$$

Accepted Answer

A)  $- \frac { \sqrt { 210 } } { 7 }$ 
B)  $\frac { 5 \sqrt { 6 } } { 7 }$ 
C)  $\frac { 5 \sqrt { 6 } } { 49 }$ 
D)  $\frac { 7 \sqrt { 6 } } { 7 }$ 
A)  $- \frac { \sqrt { 210 } } { 7 }$ 
B)  $\frac { 5 \sqrt { 6 } } { 7 }$ 
C)  $\frac { 5 \sqrt { 6 } } { 49 }$ 
D)  $\frac { 7 \sqrt { 6 } } { 7 }$

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$- \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right)$$

Accepted Answer

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

Question 15

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the
-In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $\mathrm { x } : \mathrm { y } = \frac { 0.37 \mathrm { x } } { 100.5 - \mathrm { x } }$. How many hours of study are needed to score $82 ?$

Accepted Answer

A)  $1.64 \mathrm { hr }$ 
B)  $16.40 \mathrm { hr }$ 
C)  $4.22 \mathrm { hr }$ 
D)  $101.04 \mathrm { hr }$ 
A)  $1.64 \mathrm { hr }$ 
B)  $16.40 \mathrm { hr }$ 
C)  $4.22 \mathrm { hr }$ 
D)  $101.04 \mathrm { hr }$

Question 16

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }$$

Accepted Answer

A)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 3 }$ 
B)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 9 }$ 
C)  $\frac { \sqrt { 21 } + 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 3 \sqrt { 21 } + 73 } { 14 }$ 
A)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 3 }$ 
B)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 9 }$ 
C)  $\frac { \sqrt { 21 } + 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 3 \sqrt { 21 } + 73 } { 14 }$

Question 17

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 4,5,6,7,8,9,10,11,12,13,14 \} , \mathrm { M } = \{ 4,6,8,10 \} , \mathrm { N } = \{ 5,7,9,11,13 \} , \mathrm { Q } = \{ 4,6,8,10,12,14 \}$, and $\mathrm { R } = \{ 4,5,6,7 \}$.

$( \mathrm { N } \cup \mathrm { R } ) \cap \mathrm { Q }$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\varnothing ; \mathrm { N }$ and $\mathrm { R }$ are disjoint sets. 
C)  $\{ 4,6 \}$ 
D)  $\{ 6 \}$ 
A)  $\{ 4 \}$ 
B)  $\varnothing ; \mathrm { N }$ and $\mathrm { R }$ are disjoint sets. 
C)  $\{ 4,6 \}$ 
D)  $\{ 6 \}$

Question 18

Factor the trinomial, if possible.
-$$16 x ^ { 2 } - 56 x - 32$$

Accepted Answer

A)  $( 2 x - 1 ) ( 8 x + 32 )$ 
B)  $8 ( 2 x + 1 ) ( x - 4 )$ 
C)  $( 16 x - 8 ) ( x + 4 )$ 
D)  $8 ( 2 x - 1 ) ( x + 4 )$ 
A)  $( 2 x - 1 ) ( 8 x + 32 )$ 
B)  $8 ( 2 x + 1 ) ( x - 4 )$ 
C)  $( 16 x - 8 ) ( x + 4 )$ 
D)  $8 ( 2 x - 1 ) ( x + 4 )$

Question 19

Factor by any method.
-$24 k ^ { 3 } m - 375 m ^ { 4 }$

Accepted Answer

A)  $\left( 6 \mathrm {~km} - 15 \mathrm {~m} ^ { 2 } \right) \left( 4 \mathrm { k } ^ { 2 } + 25 \mathrm {~m} ^ { 2 } \right)$ 
B)  $3 m ( 8 k - 5 m ) \left( k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
C)  $3 m ( 2 k - 5 m ) \left( 4 k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
D)  $3 m \left( 2 k + 5 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 10 k m + 25 m ^ { 2 } \right)$ 
A)  $\left( 6 \mathrm {~km} - 15 \mathrm {~m} ^ { 2 } \right) \left( 4 \mathrm { k } ^ { 2 } + 25 \mathrm {~m} ^ { 2 } \right)$ 
B)  $3 m ( 8 k - 5 m ) \left( k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
C)  $3 m ( 2 k - 5 m ) \left( 4 k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
D)  $3 m \left( 2 k + 5 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 10 k m + 25 m ^ { 2 } \right)$

Question 20

Factor the trinomial, if possible.
-$$9 x ^ { 2 } - 39 x - 30$$

Accepted Answer

A)  $( 3 x + 2 ) ( 3 x - 15 )$ 
B)  $3 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 9 x + 6 ) ( x - 5 )$ 
D)  $3 ( 3 x - 2 ) ( x + 5 )$ 
A)  $( 3 x + 2 ) ( 3 x - 15 )$ 
B)  $3 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 9 x + 6 ) ( x - 5 )$ 
D)  $3 ( 3 x - 2 ) ( x + 5 )$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 4 } { 5 } ( - 5 y + 15 x - 5 z )$

Factor the trinomial, if possible. - $x ^ { 2 } + 4 x y - 192 y ^ { 2 }$

Find the product or quotient. - $\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }$

Factor by grouping. - $6 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 6$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 144 } + \sqrt { 16 }$

Find the domain of the expression. - $\frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }$

Evaluate the expression. -Let $x = - 1 , y = 4$ . Evaluate $\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }$

Decide whether the expression has been simplified correctly. - $4 ^ { 0 } x = 0$

Determine the degree of the polynomial. - $3 a ^ { 2 } + 16 a ^ { 5 } - 8 a$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }$

Write the expression in lowest terms. - $\frac { 5 x + 20 } { 3 x + 12 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right)$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }$

Factor the trinomial, if possible. - $16 x ^ { 2 } - 56 x - 32$

Factor by any method. - $24 k ^ { 3 } m - 375 m ^ { 4 }$

Factor the trinomial, if possible. - $9 x ^ { 2 } - 39 x - 30$

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

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣(−5)3∣=−∣(5)3∣\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|​(−5)3​=−​(5)3​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 45(−5y+15x−5z)\frac { 4 } { 5 } ( - 5 y + 15 x - 5 z )54​(−5y+15x−5z)

Factor the trinomial, if possible. - x2+4xy−192y2x ^ { 2 } + 4 x y - 192 y ^ { 2 }x2+4xy−192y2

Find the product or quotient. - 9x2+64x−645x−20⋅x2−4x81x2−64÷8x+643x3\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }5x−209x2+64x−64​⋅81x2−64x2−4x​÷3x38x+64​

Factor by grouping. - 6x4−4x2−9x2+66 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 66x4−4x2−9x2+6

Simplify the expression. Assume all variables represent positive real numbers. - 144+16\sqrt { 144 } + \sqrt { 16 }144​+16​

Find the domain of the expression. - 6x−7(4x−3)(x+2)\frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }(4x−3)(x+2)6x−7​

Evaluate the expression. -Let x=−1,y=4x = - 1 , y = 4x=−1,y=4 . Evaluate ∣x−3∣−∣5y∣∣3y+5x∣\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }∣3y+5x∣∣x−3∣−∣5y∣​

Decide whether the expression has been simplified correctly. - 40x=04 ^ { 0 } x = 040x=0

Determine the degree of the polynomial. - 3a2+16a5−8a3 a ^ { 2 } + 16 a ^ { 5 } - 8 a3a2+16a5−8a

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (x2/3)2(x3)7/3\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }(x3)7/3(x2/3)2​

Write the expression in lowest terms. - 5x+203x+12\frac { 5 x + 20 } { 3 x + 12 }3x+125x+20​

Simplify the expression. Assume all variables represent positive real numbers. - 2167−267+649\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }7216​​−726​​+49​6​​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −23(−154y−310x+34)- \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right)−32​(−415​y−103​x+43​)

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 37+2\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }7​+23​​

Factor the trinomial, if possible. - 16x2−56x−3216 x ^ { 2 } - 56 x - 3216x2−56x−32

Factor by any method. - 24k3m−375m424 k ^ { 3 } m - 375 m ^ { 4 }24k3m−375m4

Factor the trinomial, if possible. - 9x2−39x−309 x ^ { 2 } - 39 x - 309x2−39x−30