Question 1

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$x ^ { 3 } - 7 y + 3 a$$

Accepted Answer

A)  $- 28$ 
B)  $- 37$ 
C)  $- 41$ 
D)  $- 25$ 
A)  $- 28$ 
B)  $- 37$ 
C)  $- 41$ 
D)  $- 25$

Question 2

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$( 8 \cdot 4 ) \cdot 6 = 8 \cdot ( 4 \cdot 6 )$

Accepted Answer

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

Question 3

Find the domain of the expression.
-$$\frac { x ^ { 2 } - 64 } { x ^ { 2 } - 6 x + 8 }$$

Accepted Answer

A)  $\{ x \mid x \neq 2$ and $x \neq 4 \}$ 
B)  $\{ x \mid x \neq - 2$ and $x \neq - 4 \}$ 
C)  $\{ x \mid x \neq - 8$ and $x \neq + 8 \}$ 
D)  $\{ x \mid x \neq 0 \}$ 
A)  $\{ x \mid x \neq 2$ and $x \neq 4 \}$ 
B)  $\{ x \mid x \neq - 2$ and $x \neq - 4 \}$ 
C)  $\{ x \mid x \neq - 8$ and $x \neq + 8 \}$ 
D)  $\{ x \mid x \neq 0 \}$

Question 4

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true.
-

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 5

Find the sum or difference.
-$$\frac { x ^ { 2 } + 10 x + 24 } { x + 6 }$$

Accepted Answer

A)  $x ^ { 2 } + 4$ 
B)  $x + 4$ 
C)  $x ^ { 3 } - 18$ 
D)  $x - 18$ 
A)  $x ^ { 2 } + 4$ 
B)  $x + 4$ 
C)  $x ^ { 3 } - 18$ 
D)  $x - 18$

Question 6

Determine the degree of the polynomial.
-$- x - 3 x ^ { 2 } - 6 x ^ { 3 } - 2 x ^ { 5 }$

Accepted Answer

A)  4 
B)  11 
C)  5 
D)  10 
A)  4 
B)  11 
C)  5 
D)  10

Question 7

Evaluate the expression.
-Let x = 18, y = -6. Evaluate |y - x|.

Accepted Answer

A)  -24 
B)  -12 
C)  12 
D)  24 
A)  -24 
B)  -12 
C)  12 
D)  24

Question 8

Perform the indicated operations.
-$$\frac { 6 } { 3 r ^ { 2 } - 5 r s - 2 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 13 r s + 2 s ^ { 2 } } + \frac { 7 } { 18 r ^ { 2 } + 3 r s - s ^ { 2 } }$$

Accepted Answer

A)  $\frac { 25 r - 26 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
B)  $\frac { 61 r - 26 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
C)  $\frac { 61 r - 14 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
D)  $\frac { 25 r - 14 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
A)  $\frac { 25 r - 26 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
B)  $\frac { 61 r - 26 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
C)  $\frac { 61 r - 14 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$ 
D)  $\frac { 25 r - 14 s } { ( 3 r + s ) ( r - 2 s ) ( 6 r - s ) }$

Question 9

Determine the degree of the polynomial.
-$2 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 8$

Accepted Answer

A)  4 
B)  15 
C)  6 
D)  7 
A)  4 
B)  15 
C)  6 
D)  7

Question 10

Evaluate the expression.
-$$- \left( \frac { 9 } { 49 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $- \frac { 9 } { 98 }$ 
B)  $\frac { 7 } { 3 }$ 
C)  $- \frac { 3 } { 7 }$ 
D)  not a real number 
A)  $- \frac { 9 } { 98 }$ 
B)  $\frac { 7 } { 3 }$ 
C)  $- \frac { 3 } { 7 }$ 
D)  not a real number

Question 11

Find the sum or difference.
-$$\left( 3 x + \frac { 1 } { 8 } \right) \left( 8 x - \frac { 1 } { 4 } \right)$$

Accepted Answer

A)  $24 x ^ { 2 } - \frac { 1 } { 4 } x + \frac { 1 } { 32 }$ 
B)  $24 x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 32 }$ 
C)  $24 x ^ { 2 } - \frac { 7 } { 4 } x - \frac { 1 } { 32 }$ 
D)  $24 x ^ { 2 } + \frac { 1 } { 4 } x - \frac { 1 } { 32 }$ 
A)  $24 x ^ { 2 } - \frac { 1 } { 4 } x + \frac { 1 } { 32 }$ 
B)  $24 x ^ { 2 } + \frac { 1 } { 4 } x + \frac { 1 } { 32 }$ 
C)  $24 x ^ { 2 } - \frac { 7 } { 4 } x - \frac { 1 } { 32 }$ 
D)  $24 x ^ { 2 } + \frac { 1 } { 4 } x - \frac { 1 } { 32 }$

Question 12

Write in exponential form. Assume all variables are positive real numbers.
-$\sqrt [ 3 ] { x ^ { 5 } }$

Accepted Answer

A)  $5 x ^ { 3 }$ 
B)  $x ^ { 5 / 3 }$ 
C)  $x ^ { 3 / 5 }$ 
D)  $3 x ^ { 5 }$ 
A)  $5 x ^ { 3 }$ 
B)  $x ^ { 5 / 3 }$ 
C)  $x ^ { 3 / 5 }$ 
D)  $3 x ^ { 5 }$

Question 13

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 5 ^ { 4 } \right) ^ { 3 }$

Accepted Answer

A)  25 
B)  $25 ^ { 12 }$ 
C)  $5 ^ { 12 }$ 
D)  $5 ^ { 7 }$ 
A)  25 
B)  $25 ^ { 12 }$ 
C)  $5 ^ { 12 }$ 
D)  $5 ^ { 7 }$

Question 14

Factor out the greatest common factor. Simplify the factors, if possible.
-$$15 x ^ { 2 } + 6 x - 20 x - 8$$

Accepted Answer

A)  $( 15 x - 4 ) ( x + 2 )$ 
B)  $( 3 x - 4 ) ( 5 x + 2 )$ 
C)  $( 3 x + 4 ) ( 5 x - 2 )$ 
D)  $( 15 x + 4 ) ( x - 2 )$ 
A)  $( 15 x - 4 ) ( x + 2 )$ 
B)  $( 3 x - 4 ) ( 5 x + 2 )$ 
C)  $( 3 x + 4 ) ( 5 x - 2 )$ 
D)  $( 15 x + 4 ) ( x - 2 )$

Question 15

Find the sum or difference.
-$$( 8 m + 11 ) ^ { 2 }$$

Accepted Answer

A)  $64 \mathrm {~m} ^ { 2 } + 176 \mathrm {~m} + 121$ 
B)  $8 m ^ { 2 } + 121$ 
C)  $64 m ^ { 2 } + 121$ 
D)  $8 m ^ { 2 } + 176 m + 121$ 
A)  $64 \mathrm {~m} ^ { 2 } + 176 \mathrm {~m} + 121$ 
B)  $8 m ^ { 2 } + 121$ 
C)  $64 m ^ { 2 } + 121$ 
D)  $8 m ^ { 2 } + 176 m + 121$

Question 16

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

Accepted Answer

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

Question 17

Evaluate the expression.
-$$\left| - \frac { 8 } { 7 } \right|$$

Accepted Answer

A)  0 
B)  $- \frac { 8 } { 7 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $\pm \frac { 8 } { 7 }$ 
A)  0 
B)  $- \frac { 8 } { 7 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $\pm \frac { 8 } { 7 }$

Question 18

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- x ^ { - 4 }$

Accepted Answer

A)  $4 \mathrm { x }$ 
B)  $- 4 x$ 
C)  $\frac { 1 } { x ^ { 4 } }$ 
D)  $- \frac { 1 } { x ^ { 4 } }$ 
A)  $4 \mathrm { x }$ 
B)  $- 4 x$ 
C)  $\frac { 1 } { x ^ { 4 } }$ 
D)  $- \frac { 1 } { x ^ { 4 } }$

Question 19

Find the sum or difference.
-$\left( 5 m ^ { 2 } z ^ { 4 } \right) \left( 3 m ^ { 3 } z ^ { 2 } \right)$

Accepted Answer

A)  $15 \mathrm { mz } ^ { 6 }$ 
B)  $15 \mathrm { mz } ^ { 5 }$ 
C)  $15 \mathrm {~m} ^ { 5 } \mathrm { z } ^ { 6 }$ 
D)  $15 \mathrm {~m} ^ { 5 } \mathrm { z }$ 
A)  $15 \mathrm { mz } ^ { 6 }$ 
B)  $15 \mathrm { mz } ^ { 5 }$ 
C)  $15 \mathrm {~m} ^ { 5 } \mathrm { z } ^ { 6 }$ 
D)  $15 \mathrm {~m} ^ { 5 } \mathrm { z }$

Question 20

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-It is recommended that a woman who is pregnant should exercise such that her heart rate does not exceed 140 beats per minute. Use absolute value notation to write an expression that describes the difference between the heart rate achieved
By each of the following pregnant women and the recommended maximum heart rate. Then evaluate that expression.
(i) Abigail: 138 beats per minute
(ii) Mathilda: 147 beats per minute

Accepted Answer

A)  (i) Abigail: $| 138 + 140 | = 278$
(ii) Mathilda: $| 147 + 140 | = 287$ 
B)  (i) Abigail: $138 - 140 = - 2$
(i) Mathilda: $147 - 140 = 7$ 
C)  (i) Abigail: $| 140 - 138 | = - 2$
(ii) Mathilda: $| 140 - 147 | = - 7$ 
D)  (i) Abigail: $| 138 - 140 | = 2$
(ii) Mathilda: $| 147 - 140 | = 7$ 
A)  (i) Abigail: $| 138 + 140 | = 278$
(ii) Mathilda: $| 147 + 140 | = 287$ 
B)  (i) Abigail: $138 - 140 = - 2$
(i) Mathilda: $147 - 140 = 7$ 
C)  (i) Abigail: $| 140 - 138 | = - 2$
(ii) Mathilda: $| 140 - 147 | = - 7$ 
D)  (i) Abigail: $| 138 - 140 | = 2$
(ii) Mathilda: $| 147 - 140 | = 7$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $x ^ { 3 } - 7 y + 3 a$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $( 8 \cdot 4 ) \cdot 6 = 8 \cdot ( 4 \cdot 6 )$

Find the domain of the expression. - $\frac { x ^ { 2 } - 64 } { x ^ { 2 } - 6 x + 8 }$

Insert $\in \mathbf { O r } \notin$ in the blank to make the statement is true. - $Insert \in \mathbf { O r } \notin in the blank to make the statement is true. -$

Find the sum or difference. - $\frac { x ^ { 2 } + 10 x + 24 } { x + 6 }$

Determine the degree of the polynomial. - $- x - 3 x ^ { 2 } - 6 x ^ { 3 } - 2 x ^ { 5 }$

Evaluate the expression. -Let x = 18, y = -6. Evaluate |y - x|.

Perform the indicated operations. - $\frac { 6 } { 3 r ^ { 2 } - 5 r s - 2 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 13 r s + 2 s ^ { 2 } } + \frac { 7 } { 18 r ^ { 2 } + 3 r s - s ^ { 2 } }$

Determine the degree of the polynomial. - $2 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 8$

Evaluate the expression. - $- \left( \frac { 9 } { 49 } \right) ^ { 1 / 2 }$

Find the sum or difference. - $\left( 3 x + \frac { 1 } { 8 } \right) \left( 8 x - \frac { 1 } { 4 } \right)$

Write in exponential form. Assume all variables are positive real numbers. - $\sqrt [ 3 ] { x ^ { 5 } }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 5 ^ { 4 } \right) ^ { 3 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $15 x ^ { 2 } + 6 x - 20 x - 8$

Find the sum or difference. - $( 8 m + 11 ) ^ { 2 }$

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

Evaluate the expression. - $\left| - \frac { 8 } { 7 } \right|$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- x ^ { - 4 }$

Find the sum or difference. - $\left( 5 m ^ { 2 } z ^ { 4 } \right) \left( 3 m ^ { 3 } z ^ { 2 } \right)$

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Exam 1: Review of Basic Concepts

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 - x3−7y+3ax ^ { 3 } - 7 y + 3 ax3−7y+3a

Identify the property illustrated by the statement. Assume all variables represent real numbers. - (8⋅4)⋅6=8⋅(4⋅6)( 8 \cdot 4 ) \cdot 6 = 8 \cdot ( 4 \cdot 6 )(8⋅4)⋅6=8⋅(4⋅6)

Find the domain of the expression. - x2−64x2−6x+8\frac { x ^ { 2 } - 64 } { x ^ { 2 } - 6 x + 8 }x2−6x+8x2−64​

Insert ∈Or∉\in \mathbf { O r } \notin∈Or∈/ in the blank to make the statement is true. -

Find the sum or difference. - x2+10x+24x+6\frac { x ^ { 2 } + 10 x + 24 } { x + 6 }x+6x2+10x+24​

Determine the degree of the polynomial. - −x−3x2−6x3−2x5- x - 3 x ^ { 2 } - 6 x ^ { 3 } - 2 x ^ { 5 }−x−3x2−6x3−2x5

Evaluate the expression. -Let x = 18, y = -6. Evaluate |y - x|.

Perform the indicated operations. - 63r2−5rs−2s2−66r2−13rs+2s2+718r2+3rs−s2\frac { 6 } { 3 r ^ { 2 } - 5 r s - 2 s ^ { 2 } } - \frac { 6 } { 6 r ^ { 2 } - 13 r s + 2 s ^ { 2 } } + \frac { 7 } { 18 r ^ { 2 } + 3 r s - s ^ { 2 } }3r2−5rs−2s26​−6r2−13rs+2s26​+18r2+3rs−s27​

Determine the degree of the polynomial. - 2x6−8x7+9x2−82 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 82x6−8x7+9x2−8

Evaluate the expression. - −(949)1/2- \left( \frac { 9 } { 49 } \right) ^ { 1 / 2 }−(499​)1/2

Find the sum or difference. - (3x+18)(8x−14)\left( 3 x + \frac { 1 } { 8 } \right) \left( 8 x - \frac { 1 } { 4 } \right)(3x+81​)(8x−41​)

Write in exponential form. Assume all variables are positive real numbers. - x53\sqrt [ 3 ] { x ^ { 5 } }3x5​

Simplify the expression. Assume all variables represent nonzero real numbers. - (54)3\left( 5 ^ { 4 } \right) ^ { 3 }(54)3

Factor out the greatest common factor. Simplify the factors, if possible. - 15x2+6x−20x−815 x ^ { 2 } + 6 x - 20 x - 815x2+6x−20x−8

Find the sum or difference. - (8m+11)2( 8 m + 11 ) ^ { 2 }(8m+11)2

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

Evaluate the expression. - ∣−87∣\left| - \frac { 8 } { 7 } \right|​−78​​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −x−4- x ^ { - 4 }−x−4

Find the sum or difference. - (5m2z4)(3m3z2)\left( 5 m ^ { 2 } z ^ { 4 } \right) \left( 3 m ^ { 3 } z ^ { 2 } \right)(5m2z4)(3m3z2)