Question 1

Decide whether the expression has been simplified correctly.
-$6 ^ { 0 } x = 6 x$

Accepted Answer

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

Question 2

Identify the expression as a polynomial or not a polynomial.
-$7 x ^ { 2 } y ^ { 3 } - 4 x ^ { 3 } y - 3 x$

Accepted Answer

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

Question 3

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$3 ( x + 8 ) = 3 x + 24$

Accepted Answer

A)  Closure 
B)  Commutative 
C)  Distributive 
D)  Associative 
A)  Closure 
B)  Commutative 
C)  Distributive 
D)  Associative

Question 4

Find the sum or difference.
-$$( 8 a + 11 c ) ( 8 a - 11 c )$$

Accepted Answer

A)  $8 a ^ { 2 } - 11 c ^ { 2 }$ 
B)  $64 a ^ { 2 } - 121 c ^ { 2 }$ 
C)  $64 a ^ { 2 } - 176 a c - 121 c ^ { 2 }$ 
D)  $64 a ^ { 2 } + 176 a c - 121 c ^ { 2 }$ 
A)  $8 a ^ { 2 } - 11 c ^ { 2 }$ 
B)  $64 a ^ { 2 } - 121 c ^ { 2 }$ 
C)  $64 a ^ { 2 } - 176 a c - 121 c ^ { 2 }$ 
D)  $64 a ^ { 2 } + 176 a c - 121 c ^ { 2 }$

Question 5

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { ( m n ) ^ { - 1 } } { m ^ { - 2 } + n ^ { - 2 } }$$

Accepted Answer

A)  $\frac { n } { n ^ { 2 } - m ^ { 2 } }$ 
B)  $\frac { m n } { n + m }$ 
C)  $\frac { m ^ { 2 } + n ^ { 2 } } { m n }$ 
D)  $\frac { m n } { n ^ { 2 } + m ^ { 2 } }$ 
A)  $\frac { n } { n ^ { 2 } - m ^ { 2 } }$ 
B)  $\frac { m n } { n + m }$ 
C)  $\frac { m ^ { 2 } + n ^ { 2 } } { m n }$ 
D)  $\frac { m n } { n ^ { 2 } + m ^ { 2 } }$

Question 6

Find the product or quotient.
-$$\frac { 5 x ^ { 2 } + 17 x - 40 } { 3 x - 18 } \cdot \frac { x ^ { 2 } - 6 x } { 25 x ^ { 2 } - 64 } \div \frac { 3 x + 15 } { 2 x ^ { 3 } }$$

Accepted Answer

A)  $\frac { 9 } { 2 x ^ { 4 } ( 5 x + 8 ) }$ 
B)  $\frac { 3 ( x + 5 ) ^ { 2 } } { 6 x ^ { 2 } ( 5 x + 8 ) }$ 
C)  $\frac { 2 x ^ { 4 } } { 9 ( 5 x + 8 ) }$ 
D)  $\frac { 2 x ^ { 3 } } { 9 ( 5 x + 8 ) }$ 
A)  $\frac { 9 } { 2 x ^ { 4 } ( 5 x + 8 ) }$ 
B)  $\frac { 3 ( x + 5 ) ^ { 2 } } { 6 x ^ { 2 } ( 5 x + 8 ) }$ 
C)  $\frac { 2 x ^ { 4 } } { 9 ( 5 x + 8 ) }$ 
D)  $\frac { 2 x ^ { 3 } } { 9 ( 5 x + 8 ) }$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { 4 } { \sqrt [ 3 ] { 3 } } - \frac { 36 } { \sqrt [ 3 ] { 24 } } + \frac { 1 } { \sqrt [ 3 ] { 81 } }$$

Accepted Answer

A)  $- \frac { 85 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $- \frac { 41 } { 9 } \sqrt [ 3 ] { 9 }$ 
C)  $\frac { 40 } { 9 } \sqrt [ 3 ] { 3 }$ 
D)  $- \frac { 46 } { 9 } \sqrt [ 3 ] { 3 }$ 
A)  $- \frac { 85 } { 18 } \sqrt [ 3 ] { 9 }$ 
B)  $- \frac { 41 } { 9 } \sqrt [ 3 ] { 9 }$ 
C)  $\frac { 40 } { 9 } \sqrt [ 3 ] { 3 }$ 
D)  $- \frac { 46 } { 9 } \sqrt [ 3 ] { 3 }$

Question 8

Simplify the expression. Assume all variables represent positive real numbers.
-$- \sqrt { 112 }$

Accepted Answer

A)  10 
B)  not a real number 
C)  $- 4 \sqrt { 7 }$ 
D)  $- 16 \sqrt { 7 }$ 
A)  10 
B)  not a real number 
C)  $- 4 \sqrt { 7 }$ 
D)  $- 16 \sqrt { 7 }$

Question 9

Find the sum or difference.
-$3 x ( 3 x - 1 ) ( 4 x + 9 )$

Accepted Answer

A)  $12 x ^ { 3 } + 23 x ^ { 2 } - 9 x$ 
B)  $32 x ^ { 3 } + 71 x ^ { 2 } - 25 x$ 
C)  $34 x ^ { 2 } + 70 x - 27$ 
D)  $36 x ^ { 3 } + 69 x ^ { 2 } - 27 x$ 
A)  $12 x ^ { 3 } + 23 x ^ { 2 } - 9 x$ 
B)  $32 x ^ { 3 } + 71 x ^ { 2 } - 25 x$ 
C)  $34 x ^ { 2 } + 70 x - 27$ 
D)  $36 x ^ { 3 } + 69 x ^ { 2 } - 27 x$

Question 10

Find the sum or difference.
-$$( 10 x - 7 y ) ^ { 2 }$$

Accepted Answer

A)  $100 x ^ { 2 } + 49 y ^ { 2 }$ 
B)  $10 x ^ { 2 } + 49 y ^ { 2 }$ 
C)  $100 x ^ { 2 } - 140 x y + 49 y ^ { 2 }$ 
D)  $10 x ^ { 2 } - 140 x y + 49 y ^ { 2 }$ 
A)  $100 x ^ { 2 } + 49 y ^ { 2 }$ 
B)  $10 x ^ { 2 } + 49 y ^ { 2 }$ 
C)  $100 x ^ { 2 } - 140 x y + 49 y ^ { 2 }$ 
D)  $10 x ^ { 2 } - 140 x y + 49 y ^ { 2 }$

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 4 ] { 81 a ^ { 4 } }$

Accepted Answer

A)  $3 a$ 
B)  $3 \sqrt { a }$ 
C)  $3 a ^ { 2 }$ 
D)  $81 a$ 
A)  $3 a$ 
B)  $3 \sqrt { a }$ 
C)  $3 a ^ { 2 }$ 
D)  $81 a$

Question 12

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$| 2 - 8 | = | 8 | - | 2 |$

Accepted Answer

A) True 
 B)False

Question 13

Insert   in the blank to make the statement true.
-$\{ 9,10,11 \}$ $\{ 0,9,10,11,12,13 \}$

Accepted Answer

A)    
B)    
A)    
B)

Question 14

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 125 \mathrm { k } ^ { 6 } }$$

Accepted Answer

A)  $5 \mathrm { k } ^ { 2 }$ 
B)  $5 \mathrm { k } ^ { 9 }$ 
C)  $125 \mathrm { k } ^ { 2 }$ 
D)  $- 5 \mathrm { k } ^ { 2 }$ 
A)  $5 \mathrm { k } ^ { 2 }$ 
B)  $5 \mathrm { k } ^ { 9 }$ 
C)  $125 \mathrm { k } ^ { 2 }$ 
D)  $- 5 \mathrm { k } ^ { 2 }$

Question 15

Factor the trinomial, if possible.
-$3 x ^ { 2 } + 7 x + 20$

Accepted Answer

A)  $( 3 x + 4 ) ( x - 5 )$ 
B)  prime 
C)  $( 3 x + 5 ) ( x - 4 )$ 
D)  $( 3 x - 5 ) ( x + 4 )$ 
A)  $( 3 x + 4 ) ( x - 5 )$ 
B)  prime 
C)  $( 3 x + 5 ) ( x - 4 )$ 
D)  $( 3 x - 5 ) ( x + 4 )$

Question 16

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$5 z - 4$

Accepted Answer

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

Question 17

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

Accepted Answer

A)  $\{ 4,6,8,10,12 \}$ 
B)  $\{ 3,5,7,9,11,13 \}$ 
C)  $\{ 4,5,6,7,8,9 \}$ 
D)  $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets. 
A)  $\{ 4,6,8,10,12 \}$ 
B)  $\{ 3,5,7,9,11,13 \}$ 
C)  $\{ 4,5,6,7,8,9 \}$ 
D)  $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets.

Question 18

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$\frac { y + 2 x } { y - 4 a }$$

Accepted Answer

A)  $- \frac { 1 } { 19 }$ 
B)  $- \frac { 1 } { 23 }$ 
C)  0 
D)  $- \frac { 3 } { 19 }$ 
A)  $- \frac { 1 } { 19 }$ 
B)  $- \frac { 1 } { 23 }$ 
C)  0 
D)  $- \frac { 3 } { 19 }$

Question 19

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$( - 2 ) ^ { 0 }$

Accepted Answer

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

Question 20

Factor the polynomial by substitution.
-$$6 ( \mathrm { p } + 1 ) ^ { 2 } + 7 ( \mathrm { p } + 1 ) + 2$$

Accepted Answer

A)  $( 2 p + 3 ) ( 3 p + 5 )$ 
B)  $( 2 p + 1 ) ( 3 p + 2 )$ 
C)  $( 2 p + 2 ) ( 3 p + 3 )$ 
D)  $( 2 p + 4 ) ( 3 p + 4 )$ 
A)  $( 2 p + 3 ) ( 3 p + 5 )$ 
B)  $( 2 p + 1 ) ( 3 p + 2 )$ 
C)  $( 2 p + 2 ) ( 3 p + 3 )$ 
D)  $( 2 p + 4 ) ( 3 p + 4 )$

Decide whether the expression has been simplified correctly. - $6 ^ { 0 } x = 6 x$

Identify the expression as a polynomial or not a polynomial. - $7 x ^ { 2 } y ^ { 3 } - 4 x ^ { 3 } y - 3 x$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $3 ( x + 8 ) = 3 x + 24$

Find the sum or difference. - $( 8 a + 11 c ) ( 8 a - 11 c )$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { ( m n ) ^ { - 1 } } { m ^ { - 2 } + n ^ { - 2 } }$

Find the product or quotient. - $\frac { 5 x ^ { 2 } + 17 x - 40 } { 3 x - 18 } \cdot \frac { x ^ { 2 } - 6 x } { 25 x ^ { 2 } - 64 } \div \frac { 3 x + 15 } { 2 x ^ { 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 4 } { \sqrt [ 3 ] { 3 } } - \frac { 36 } { \sqrt [ 3 ] { 24 } } + \frac { 1 } { \sqrt [ 3 ] { 81 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { 112 }$

Find the sum or difference. - $3 x ( 3 x - 1 ) ( 4 x + 9 )$

Find the sum or difference. - $( 10 x - 7 y ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { 81 a ^ { 4 } }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| 2 - 8 | = | 8 | - | 2 |$

Insert $Insert in the blank to make the statement true. - \{ 9,10,11 \} \{ 0,9,10,11,12,13 \}$ in the blank to make the statement true. - $\{ 9,10,11 \}$ $\{ 0,9,10,11,12,13 \}$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 125 \mathrm { k } ^ { 6 } }$

Factor the trinomial, if possible. - $3 x ^ { 2 } + 7 x + 20$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $5 z - 4$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $\frac { y + 2 x } { y - 4 a }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 2 ) ^ { 0 }$

Factor the polynomial by substitution. - $6 ( \mathrm { p } + 1 ) ^ { 2 } + 7 ( \mathrm { p } + 1 ) + 2$

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Exam 1: Review of Basic Concepts

Decide whether the expression has been simplified correctly. - 60x=6x6 ^ { 0 } x = 6 x60x=6x

Identify the expression as a polynomial or not a polynomial. - 7x2y3−4x3y−3x7 x ^ { 2 } y ^ { 3 } - 4 x ^ { 3 } y - 3 x7x2y3−4x3y−3x

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 3(x+8)=3x+243 ( x + 8 ) = 3 x + 243(x+8)=3x+24

Find the sum or difference. - (8a+11c)(8a−11c)( 8 a + 11 c ) ( 8 a - 11 c )(8a+11c)(8a−11c)

Perform the indicated operation and write your answer with positive integer exponents. - (mn)−1m−2+n−2\frac { ( m n ) ^ { - 1 } } { m ^ { - 2 } + n ^ { - 2 } }m−2+n−2(mn)−1​

Find the product or quotient. - 5x2+17x−403x−18⋅x2−6x25x2−64÷3x+152x3\frac { 5 x ^ { 2 } + 17 x - 40 } { 3 x - 18 } \cdot \frac { x ^ { 2 } - 6 x } { 25 x ^ { 2 } - 64 } \div \frac { 3 x + 15 } { 2 x ^ { 3 } }3x−185x2+17x−40​⋅25x2−64x2−6x​÷2x33x+15​

Simplify the expression. Assume all variables represent positive real numbers. - 433−36243+1813\frac { 4 } { \sqrt [ 3 ] { 3 } } - \frac { 36 } { \sqrt [ 3 ] { 24 } } + \frac { 1 } { \sqrt [ 3 ] { 81 } }33​4​−324​36​+381​1​

Simplify the expression. Assume all variables represent positive real numbers. - −112- \sqrt { 112 }−112​

Find the sum or difference. - 3x(3x−1)(4x+9)3 x ( 3 x - 1 ) ( 4 x + 9 )3x(3x−1)(4x+9)

Find the sum or difference. - (10x−7y)2( 10 x - 7 y ) ^ { 2 }(10x−7y)2

Simplify the expression. Assume all variables represent positive real numbers. - 81a44\sqrt [ 4 ] { 81 a ^ { 4 } }481a4​

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣2−8∣=∣8∣−∣2∣| 2 - 8 | = | 8 | - | 2 |∣2−8∣=∣8∣−∣2∣

Insert in the blank to make the statement true. - {9,10,11}\{ 9,10,11 \}{9,10,11} {0,9,10,11,12,13}\{ 0,9,10,11,12,13 \}{0,9,10,11,12,13}

Simplify the expression. Assume all variables represent positive real numbers. - 125k63\sqrt [ 3 ] { 125 \mathrm { k } ^ { 6 } }3125k6​

Factor the trinomial, if possible. - 3x2+7x+203 x ^ { 2 } + 7 x + 203x2+7x+20

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 5z−45 z - 45z−4

Evaluate the expression for x x=−2,y=3, and a=−4x = - 2 , y = 3 , \text { and } a = - 4x=−2,y=3, and a=−4 - y+2xy−4a\frac { y + 2 x } { y - 4 a }y−4ay+2x​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−2)0( - 2 ) ^ { 0 }(−2)0

Factor the polynomial by substitution. - 6(p+1)2+7(p+1)+26 ( \mathrm { p } + 1 ) ^ { 2 } + 7 ( \mathrm { p } + 1 ) + 26(p+1)2+7(p+1)+2