Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 7 } { 5 } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 35 } } { 5 }$ 
B)  $\frac { \sqrt [ 3 ] { 875 } } { 5 }$ 
C)  $\frac { 175 } { 5 }$ 
D)  $\frac { \sqrt [ 3 ] { 175 } } { 5 }$ 
A)  $\frac { \sqrt [ 3 ] { 35 } } { 5 }$ 
B)  $\frac { \sqrt [ 3 ] { 875 } } { 5 }$ 
C)  $\frac { 175 } { 5 }$ 
D)  $\frac { \sqrt [ 3 ] { 175 } } { 5 }$

Question 2

Factor by any method.
-$25 x ^ { 2 } - 25 y ^ { 2 }$

Accepted Answer

A)  $25 ( x + y ) ( x - y )$ 
B)  $( 5 x + y ) ( 5 x - y )$ 
C)  $5 ( x + y ) ( x - y )$ 
D)  $25 ( x - y ) ^ { 2 }$ 
A)  $25 ( x + y ) ( x - y )$ 
B)  $( 5 x + y ) ( 5 x - y )$ 
C)  $5 ( x + y ) ( x - y )$ 
D)  $25 ( x - y ) ^ { 2 }$

Question 3

Find the product.
-$$( \mathrm { m } + 10 ) ( \mathrm { m } - 10 )$$

Accepted Answer

A)  $m ^ { 2 } - 20 m + 100$ 
B)  $m ^ { 2 } - 20 m - 100$ 
C)  $m ^ { 2 } - 100$ 
D)  $m ^ { 2 } - 20$ 
A)  $m ^ { 2 } - 20 m + 100$ 
B)  $m ^ { 2 } - 20 m - 100$ 
C)  $m ^ { 2 } - 100$ 
D)  $m ^ { 2 } - 20$

Question 4

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$5 x$

Accepted Answer

A)  None of these 
B)  Trinomial 
C)  Monomial 
D)  Binomial 
A)  None of these 
B)  Trinomial 
C)  Monomial 
D)  Binomial

Question 5

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 9 v ^ { 3 } + 8$

Accepted Answer

A)  Binomial 
B)  Monomial 
C)  None of these 
D)  Trinomial 
A)  Binomial 
B)  Monomial 
C)  None of these 
D)  Trinomial

Question 6

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-5 + 8 = 8 + 5

Accepted Answer

A)  Associative 
B)  Identity 
C)  Commutative 
D)  Inverse 
A)  Associative 
B)  Identity 
C)  Commutative 
D)  Inverse

Question 7

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

Accepted Answer

A)  $25 m ^ { 4 } + 30 m ^ { 3 } - 7 m ^ { 2 } + 25 m + 20$ 
B)  $25 m ^ { 4 } + 18 m ^ { 3 } - 7 m ^ { 2 } + 13 m + 20$ 
C)  $25 m ^ { 4 } + 30 m ^ { 3 } - 7 m ^ { 2 } + 13 m + 20$ 
D)  $25 m ^ { 4 } + 30 m ^ { 3 } - 27 m ^ { 2 } + 13 m + 20$ 
A)  $25 m ^ { 4 } + 30 m ^ { 3 } - 7 m ^ { 2 } + 25 m + 20$ 
B)  $25 m ^ { 4 } + 18 m ^ { 3 } - 7 m ^ { 2 } + 13 m + 20$ 
C)  $25 m ^ { 4 } + 30 m ^ { 3 } - 7 m ^ { 2 } + 13 m + 20$ 
D)  $25 m ^ { 4 } + 30 m ^ { 3 } - 27 m ^ { 2 } + 13 m + 20$

Question 8

Use set notation, and list all the elements of the set.
-$\{ 12,18,24 , \ldots , 54 \}$

Accepted Answer

A)  $\{ 12,18,24,30,36,42,48,54 \}$ 
B)  $\{ 12,18,24,31,37,43,49,55 \}$ 
C)  $\{ 12,18,23,29,35,41,47,53 \}$ 
D)  $\{ 12,18,24,30,36 \}$ 
A)  $\{ 12,18,24,30,36,42,48,54 \}$ 
B)  $\{ 12,18,24,31,37,43,49,55 \}$ 
C)  $\{ 12,18,23,29,35,41,47,53 \}$ 
D)  $\{ 12,18,24,30,36 \}$

Question 9

Perform the indicated operations.
-$$\frac { 5 } { 2 x - 4 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$$

Accepted Answer

A)  $\frac { 73 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
B)  $\frac { 73 x ^ { 2 } + 207 x + 13 } { 10 x + 17 }$ 
C)  $\frac { 113 x ^ { 2 } + 207 x + 194 } { 10 x + 17 }$ 
D)  $\frac { 113 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
A)  $\frac { 73 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
B)  $\frac { 73 x ^ { 2 } + 207 x + 13 } { 10 x + 17 }$ 
C)  $\frac { 113 x ^ { 2 } + 207 x + 194 } { 10 x + 17 }$ 
D)  $\frac { 113 x ^ { 2 } + 207 x + 194 } { 30 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$

Question 10

Perform the indicated operations.
-$$\frac { 81 x } { 2 ( 9 x + 1 ) } - \frac { 1 } { 2 x ( 9 x + 1 ) } + \frac { 23 } { x }$$

Accepted Answer

A)  $\frac { 81 x ^ { 2 } + 414 x + 45 } { 2 x }$ 
B)  $\frac { 9 ( x + 5 ) } { 18 x ^ { 2 } + 2 x }$ 
C)  $\frac { 9 ( x + 5 ) } { 2 x }$ 
D)  $\frac { 81 x ^ { 2 } + 414 x + 45 } { 18 x ^ { 2 } + 2 x }$ 
A)  $\frac { 81 x ^ { 2 } + 414 x + 45 } { 2 x }$ 
B)  $\frac { 9 ( x + 5 ) } { 18 x ^ { 2 } + 2 x }$ 
C)  $\frac { 9 ( x + 5 ) } { 2 x }$ 
D)  $\frac { 81 x ^ { 2 } + 414 x + 45 } { 18 x ^ { 2 } + 2 x }$

Question 11

Divide.
-$\frac { 16 x ^ { 7 } - 64 x ^ { 5 } + 40 x ^ { 3 } } { 8 x ^ { 5 } }$

Accepted Answer

A)  $2 x ^ { 2 } - 8 + \frac { 5 } { x }$ 
B)  $2 x ^ { 2 } - 8 + \frac { 5 } { x ^ { 2 } }$ 
C)  $2 x - 8 + \frac { 5 } { x ^ { 2 } }$ 
D)  $2 x - 8 + \frac { 5 } { x }$ 
A)  $2 x ^ { 2 } - 8 + \frac { 5 } { x }$ 
B)  $2 x ^ { 2 } - 8 + \frac { 5 } { x ^ { 2 } }$ 
C)  $2 x - 8 + \frac { 5 } { x ^ { 2 } }$ 
D)  $2 x - 8 + \frac { 5 } { x }$

Question 12

Write in radical form. Assume all variables represent positive real numbers.
-$( 10 x ) ^ { 1 / 3 }$

Accepted Answer

A)  $\frac { \sqrt { 10 x } } { 3 }$ 
B)  $- \sqrt [ 3 ] { 10 x }$ 
C)  $\sqrt [ 1 / 3 ] { 10 x }$ 
D)  $\sqrt [ 3 ] { 10 x }$ 
A)  $\frac { \sqrt { 10 x } } { 3 }$ 
B)  $- \sqrt [ 3 ] { 10 x }$ 
C)  $\sqrt [ 1 / 3 ] { 10 x }$ 
D)  $\sqrt [ 3 ] { 10 x }$

Question 13

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }$

Accepted Answer

A)  $\mathrm { y }$ 
B)  $\frac { 1 } { y }$ 
C)  $\mathrm { y } ^ { 1 / 2 }$ 
D)  $y ^ { 9 / 8 }$ 
A)  $\mathrm { y }$ 
B)  $\frac { 1 } { y }$ 
C)  $\mathrm { y } ^ { 1 / 2 }$ 
D)  $y ^ { 9 / 8 }$

Question 14

Solve the problem.
-In an economics study, three quantities $\mathrm { m } , \mathrm { p }$, and $\mathrm { q }$ have been found to be related by the equation $m = p ^ { 1 / 2 } \cdot q ^ { 1 / 2 }$. Find $m$, if $p = 36$ and $q = 16$.

Accepted Answer

A)  96 
B)  576 
C)  24 
D)  10 
A)  96 
B)  576 
C)  24 
D)  10

Question 15

Find the distance between two points given their coordinates.
-Find the distance between points $R$ and $S$ on a number line, with coordinates 7 and $- 4$, respectively.

Accepted Answer

A)  $d ( R , S ) = 11$ 
B)  $d ( R , S ) = - 11$ 
C)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 3$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 3$ 
A)  $d ( R , S ) = 11$ 
B)  $d ( R , S ) = - 11$ 
C)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 3$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 3$

Question 16

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$( - 2 ) ^ { - 1 }$$

Accepted Answer

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

Question 17

Insert ⊆ or ⊈ in the blank to make the statement true.
-∅ ___ {8, 11, 15, 0, 12, 16}

Accepted Answer

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

Question 18

Find the product.
-$$( 10 x - 11 y ) ^ { 2 }$$

Accepted Answer

A)  $100 x ^ { 2 } - 220 x y + 121 y ^ { 2 }$ 
B)  $10 x ^ { 2 } - 220 x y + 121 y ^ { 2 }$ 
C)  $100 x ^ { 2 } + 121 y ^ { 2 }$ 
D)  $10 x ^ { 2 } + 121 y ^ { 2 }$ 
A)  $100 x ^ { 2 } - 220 x y + 121 y ^ { 2 }$ 
B)  $10 x ^ { 2 } - 220 x y + 121 y ^ { 2 }$ 
C)  $100 x ^ { 2 } + 121 y ^ { 2 }$ 
D)  $10 x ^ { 2 } + 121 y ^ { 2 }$

Question 19

Tell whether the statement is true or false.
-$13 \in\{-9,14,15,18\}$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 20

Factor by any method.
-$$y ^ { 2 } - \frac { 100 } { 121 }$$

Accepted Answer

A)  $\left( y + \frac { 100 } { 11 } \right) \left( y - \frac { 100 } { 11 } \right)$ 
B)  $\left( y ^ { 2 } + \frac { 10 } { 11 } \right) \left( y ^ { 2 } - \frac { 10 } { 11 } \right)$ 
C)  $\left( y - \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
D)  $\left( y + \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
A)  $\left( y + \frac { 100 } { 11 } \right) \left( y - \frac { 100 } { 11 } \right)$ 
B)  $\left( y ^ { 2 } + \frac { 10 } { 11 } \right) \left( y ^ { 2 } - \frac { 10 } { 11 } \right)$ 
C)  $\left( y - \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$ 
D)  $\left( y + \frac { 10 } { 11 } \right) \left( y - \frac { 10 } { 11 } \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 7 } { 5 } }$

Factor by any method. - $25 x ^ { 2 } - 25 y ^ { 2 }$

Find the product. - $( \mathrm { m } + 10 ) ( \mathrm { m } - 10 )$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $5 x$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 9 v ^ { 3 } + 8$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -5 + 8 = 8 + 5

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

Use set notation, and list all the elements of the set. - $\{ 12,18,24 , \ldots , 54 \}$

Perform the indicated operations. - $\frac { 5 } { 2 x - 4 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$

Perform the indicated operations. - $\frac { 81 x } { 2 ( 9 x + 1 ) } - \frac { 1 } { 2 x ( 9 x + 1 ) } + \frac { 23 } { x }$

Divide. - $\frac { 16 x ^ { 7 } - 64 x ^ { 5 } + 40 x ^ { 3 } } { 8 x ^ { 5 } }$

Write in radical form. Assume all variables represent positive real numbers. - $( 10 x ) ^ { 1 / 3 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { y ^ { 9 / 8 } } { y ^ { 5 / 8 } }$

Solve the problem. -In an economics study, three quantities $\mathrm { m } , \mathrm { p }$ , and $\mathrm { q }$ have been found to be related by the equation $m = p ^ { 1 / 2 } \cdot q ^ { 1 / 2 }$ . Find $m$ , if $p = 36$ and $q = 16$ .

Find the distance between two points given their coordinates. -Find the distance between points $R$ and $S$ on a number line, with coordinates 7 and $- 4$ , respectively.

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 2 ) ^ { - 1 }$

Insert ⊆ or ⊈ in the blank to make the statement true. -∅ ___ {8, 11, 15, 0, 12, 16}

Find the product. - $( 10 x - 11 y ) ^ { 2 }$

Tell whether the statement is true or false. - $13 \in\{-9,14,15,18\}$

Factor by any method. - $y ^ { 2 } - \frac { 100 } { 121 }$

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

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Exam 12: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 753\sqrt [ 3 ] { \frac { 7 } { 5 } }357​​

Factor by any method. - 25x2−25y225 x ^ { 2 } - 25 y ^ { 2 }25x2−25y2

Find the product. - (m+10)(m−10)( \mathrm { m } + 10 ) ( \mathrm { m } - 10 )(m+10)(m−10)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 5x5 x5x

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −9v3+8- 9 v ^ { 3 } + 8−9v3+8