Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 5 ] { \frac { \mathrm { r } ^ { 2 } } { 243 } }$$

Accepted Answer

A)  $\sqrt { \frac { 5 \mathrm { r } ^ { 2 } } { 243 } }$ 
B)  $\frac { \sqrt [ 5 ] { \mathrm { r } ^ { 2 } } } { 3 }$ 
C)  $\frac { \sqrt [ 5 ] { \mathrm { r } } } { 3 }$ 
D)  $\frac { \mathrm { r } } { 3 }$ 
A)  $\sqrt { \frac { 5 \mathrm { r } ^ { 2 } } { 243 } }$ 
B)  $\frac { \sqrt [ 5 ] { \mathrm { r } ^ { 2 } } } { 3 }$ 
C)  $\frac { \sqrt [ 5 ] { \mathrm { r } } } { 3 }$ 
D)  $\frac { \mathrm { r } } { 3 }$

Question 2

Factor by any method.
-$512 p ^ { 3 } - 1$

Accepted Answer

A)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$ 
B)  $( 8 p - 1 ) \left( 64 p ^ { 2 } + 1 \right)$ 
C)  $( 8 p - 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$ 
D)  $( 512 p - 1 ) \left( p ^ { 2 } + 8 p + 1 \right)$ 
A)  $( 8 p + 1 ) \left( 64 p ^ { 2 } - 8 p + 1 \right)$ 
B)  $( 8 p - 1 ) \left( 64 p ^ { 2 } + 1 \right)$ 
C)  $( 8 p - 1 ) \left( 64 p ^ { 2 } + 8 p + 1 \right)$ 
D)  $( 512 p - 1 ) \left( p ^ { 2 } + 8 p + 1 \right)$

Question 3

Perform the indicated operations.
-$$\frac { 49 x } { 3 ( 7 x + 1 ) } - \frac { 1 } { 3 x ( 7 x + 1 ) } + \frac { 12 } { x }$$

Accepted Answer

A)  $\frac { 7 ( x + 5 ) } { 21 x ^ { 2 } + 3 x }$ 
B)  $\frac { 49 x ^ { 2 } + 252 x + 35 } { 3 x }$ 
C)  $\frac { 49 x ^ { 2 } + 252 x + 35 } { 21 x ^ { 2 } + 3 x }$ 
D)  $\frac { 7 ( x + 5 ) } { 3 x }$ 
A)  $\frac { 7 ( x + 5 ) } { 21 x ^ { 2 } + 3 x }$ 
B)  $\frac { 49 x ^ { 2 } + 252 x + 35 } { 3 x }$ 
C)  $\frac { 49 x ^ { 2 } + 252 x + 35 } { 21 x ^ { 2 } + 3 x }$ 
D)  $\frac { 7 ( x + 5 ) } { 3 x }$

Question 4

Determine the degree of the polynomial.
-$t - 4 t ^ { 2 } + 5 t ^ { 3 } + 8$

Accepted Answer

A)  6 
B)  3 
C)  4 
D)  1 
A)  6 
B)  3 
C)  4 
D)  1

Question 5

Factor the trinomial, if possible.
-$$16 a ^ { 2 } + 32 a b + 16 b ^ { 2 }$$

Accepted Answer

A)  $16 ( a + b ) ^ { 2 }$ 
B)  $( 4 a - 4 b ) ^ { 2 }$ 
C)  $16 ( a - b ) ^ { 2 }$ 
D)  $( 4 a + 4 b ) ^ { 2 }$ 
A)  $16 ( a + b ) ^ { 2 }$ 
B)  $( 4 a - 4 b ) ^ { 2 }$ 
C)  $16 ( a - b ) ^ { 2 }$ 
D)  $( 4 a + 4 b ) ^ { 2 }$

Question 6

Solve the equation
-$$\frac { 6 m ^ { 2 } + 38 m - 28 } { m + 7 }$$

Accepted Answer

A)  $6 m - 4$ 
B)  $6 m + 4$ 
C)  $6 m - 4 + \frac { 2 } { m - 4 }$ 
D)  $m - 4$ 
A)  $6 m - 4$ 
B)  $6 m + 4$ 
C)  $6 m - 4 + \frac { 2 } { m - 4 }$ 
D)  $m - 4$

Question 7

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\varnothing$____$\varnothing$

Accepted Answer

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

Question 8

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-7 + (-7) = 0

Accepted Answer

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

Question 9

Tell whether the statement is true or false.
-Let $A = \{ 8,9,10,11,12,13 \} , B = \{ 10,12,14 \} , C = \{ 8,9,11,13 \} , D = \{ 8,13 \}$, and $\mathrm { U } = \{ 8,9,10,11,12,13,14 \}$
$$\varnothing \subseteq D$$

Accepted Answer

A) True 
 B)False

Question 10

Find the sum or difference.
-$$\left( 3 a ^ { 4 } - 8 a ^ { 3 } \right) + \left( 6 a ^ { 4 } + 5 a ^ { 3 } \right)$$

Accepted Answer

A)  $6 a ^ { 14 }$ 
B)  $9 a ^ { 8 } - 3 a ^ { 6 }$ 
C)  $6 a ^ { 7 }$ 
D)  $9 a ^ { 4 } - 3 a ^ { 3 }$ 
A)  $6 a ^ { 14 }$ 
B)  $9 a ^ { 8 } - 3 a ^ { 6 }$ 
C)  $6 a ^ { 7 }$ 
D)  $9 a ^ { 4 } - 3 a ^ { 3 }$

Question 11

Evaluate the expression.
-$64 - 6 \cdot 10 + 170 \div ( - 17 )$

Accepted Answer

A)  -14 
B)  570 
C)  -6 
D)  -614 
A)  -14 
B)  570 
C)  -6 
D)  -614

Question 12

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

Accepted Answer

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

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 125 x ^ { 4 } y ^ { 5 } }$$

Accepted Answer

A)  $5 x y \sqrt [ 3 ] { x y }$ 
B)  $5 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $5 x y ^ { 2 } \sqrt [ 3 ] { x y }$ 
D)  $5 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
A)  $5 x y \sqrt [ 3 ] { x y }$ 
B)  $5 x y \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $5 x y ^ { 2 } \sqrt [ 3 ] { x y }$ 
D)  $5 x ^ { 2 } y ^ { 2 } \sqrt [ 3 ] { x y ^ { 2 } }$

Question 14

Factor the trinomial, if possible.
-$$- 2 x ^ { 2 } - 4 x + 48$$

Accepted Answer

A)  $- 2 ( x + 4 ) ( x + 6 )$ 
B)  $- 2 ( x - 4 ) ( x + 6 )$ 
C)  $2 ( x - 4 ) ( x + 6 )$ 
D)  $- 2 ( x + 4 ) ( x - 6 )$ 
A)  $- 2 ( x + 4 ) ( x + 6 )$ 
B)  $- 2 ( x - 4 ) ( x + 6 )$ 
C)  $2 ( x - 4 ) ( x + 6 )$ 
D)  $- 2 ( x + 4 ) ( x - 6 )$

Question 15

Find the sum or difference.
-$$\left( - 3 x ^ { 4 } + 2 x ^ { 6 } + 7 + 3 x ^ { 5 } \right) - \left( - 3 + 6 x ^ { 5 } + 6 x ^ { 6 } + 7 x ^ { 4 } \right)$$

Accepted Answer

A)  $8 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 10$ 
B)  $- 4 x ^ { 6 } - 3 x ^ { 5 } - 10 x ^ { 4 } + 10$ 
C)  $- 4 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 4$ 
D)  $8 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 4$ 
A)  $8 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 10$ 
B)  $- 4 x ^ { 6 } - 3 x ^ { 5 } - 10 x ^ { 4 } + 10$ 
C)  $- 4 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 4$ 
D)  $8 x ^ { 6 } + 9 x ^ { 5 } + 4 x ^ { 4 } + 4$

Question 16

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$| 4 - 10 | = | 4 | - | 10 |$

Accepted Answer

A)  True 
B)  False; $| 4 - 10 | = | 10 | - | 4 |$ 
A)  True 
B)  False; $| 4 - 10 | = | 10 | - | 4 |$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { 4 } { \sqrt [ 3 ] { 2 } } - \frac { 31 } { \sqrt [ 3 ] { 16 } } + \frac { 1 } { \sqrt [ 3 ] { 54 } }$$

Accepted Answer

A)  $- \frac { 67 } { 12 } \sqrt [ 3 ] { 4 }$ 
B)  $- \frac { 35 } { 6 } \sqrt [ 3 ] { 4 }$ 
C)  $- \frac { 77 } { 12 } \sqrt [ 3 ] { 2 }$ 
D)  $\frac { 65 } { 12 } \sqrt [ 3 ] { 2 }$ 
A)  $- \frac { 67 } { 12 } \sqrt [ 3 ] { 4 }$ 
B)  $- \frac { 35 } { 6 } \sqrt [ 3 ] { 4 }$ 
C)  $- \frac { 77 } { 12 } \sqrt [ 3 ] { 2 }$ 
D)  $\frac { 65 } { 12 } \sqrt [ 3 ] { 2 }$

Question 18

Factor by any method.
-$6 x 10 + 8 x ^ { 5 } y 5 + 9 x ^ { 5 } y ^5 + 12 y ^{10}$

Accepted Answer

A)  $\left( 2 x ^ { 5 } + 3 y \right) \left( 3 x ^ { 5 } + 4 y ^ { 10 } \right)$ 
B)  $\left( 2 x ^ { 5 } - 3 y ^ { 5 } \right) \left( 3 x ^ { 5 } - 4 y ^ { 5 } \right)$ 
C)  $\left( 6 x ^ { 5 } + 3 y ^ { 5 } \right) \left( x ^ { 5 } + 4 y ^ { 5 } \right)$ 
D)  $\left( 2 x ^ { 5 } + 3 y ^ { 5 } \right) \left( 3 x ^ { 5 } + 4 y ^ { 5 } \right)$ 
A)  $\left( 2 x ^ { 5 } + 3 y \right) \left( 3 x ^ { 5 } + 4 y ^ { 10 } \right)$ 
B)  $\left( 2 x ^ { 5 } - 3 y ^ { 5 } \right) \left( 3 x ^ { 5 } - 4 y ^ { 5 } \right)$ 
C)  $\left( 6 x ^ { 5 } + 3 y ^ { 5 } \right) \left( x ^ { 5 } + 4 y ^ { 5 } \right)$ 
D)  $\left( 2 x ^ { 5 } + 3 y ^ { 5 } \right) \left( 3 x ^ { 5 } + 4 y ^ { 5 } \right)$

Question 19

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-6 + 0 = 6

Accepted Answer

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

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { 384 x ^ { 2 } }$$

Accepted Answer

A)  $8 \times \sqrt { 6 }$ 
B)  $8 \sqrt { 6 x }$ 
C)  $6 x ^ { 2 } \sqrt { 8 }$ 
D)  $384 x$ 
A)  $8 \times \sqrt { 6 }$ 
B)  $8 \sqrt { 6 x }$ 
C)  $6 x ^ { 2 } \sqrt { 8 }$ 
D)  $384 x$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 5 ] { \frac { \mathrm { r } ^ { 2 } } { 243 } }$

Factor by any method. - $512 p ^ { 3 } - 1$

Perform the indicated operations. - $\frac { 49 x } { 3 ( 7 x + 1 ) } - \frac { 1 } { 3 x ( 7 x + 1 ) } + \frac { 12 } { x }$

Determine the degree of the polynomial. - $t - 4 t ^ { 2 } + 5 t ^ { 3 } + 8$

Factor the trinomial, if possible. - $16 a ^ { 2 } + 32 a b + 16 b ^ { 2 }$

Solve the equation - $\frac { 6 m ^ { 2 } + 38 m - 28 } { m + 7 }$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\varnothing$ ____ $\varnothing$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -7 + (-7) = 0

Tell whether the statement is true or false. -Let $A = \{ 8,9,10,11,12,13 \} , B = \{ 10,12,14 \} , C = \{ 8,9,11,13 \} , D = \{ 8,13 \}$ , and $\mathrm { U } = \{ 8,9,10,11,12,13,14 \}$ $\varnothing \subseteq D$

Find the sum or difference. - $\left( 3 a ^ { 4 } - 8 a ^ { 3 } \right) + \left( 6 a ^ { 4 } + 5 a ^ { 3 } \right)$

Evaluate the expression. - $64 - 6 \cdot 10 + 170 \div ( - 17 )$

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

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 125 x ^ { 4 } y ^ { 5 } }$

Factor the trinomial, if possible. - $- 2 x ^ { 2 } - 4 x + 48$

Find the sum or difference. - $\left( - 3 x ^ { 4 } + 2 x ^ { 6 } + 7 + 3 x ^ { 5 } \right) - \left( - 3 + 6 x ^ { 5 } + 6 x ^ { 6 } + 7 x ^ { 4 } \right)$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| 4 - 10 | = | 4 | - | 10 |$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 4 } { \sqrt [ 3 ] { 2 } } - \frac { 31 } { \sqrt [ 3 ] { 16 } } + \frac { 1 } { \sqrt [ 3 ] { 54 } }$

Factor by any method. - $6 x 10 + 8 x ^ { 5 } y 5 + 9 x ^ { 5 } y ^5 + 12 y ^{10}$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -6 + 0 = 6

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 384 x ^ { 2 } }$

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 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - r22435\sqrt [ 5 ] { \frac { \mathrm { r } ^ { 2 } } { 243 } }5243r2​​

Factor by any method. - 512p3−1512 p ^ { 3 } - 1512p3−1

Perform the indicated operations. - 49x3(7x+1)−13x(7x+1)+12x\frac { 49 x } { 3 ( 7 x + 1 ) } - \frac { 1 } { 3 x ( 7 x + 1 ) } + \frac { 12 } { x }3(7x+1)49x​−3x(7x+1)1​+x12​

Determine the degree of the polynomial. - t−4t2+5t3+8t - 4 t ^ { 2 } + 5 t ^ { 3 } + 8t−4t2+5t3+8

Factor the trinomial, if possible. - 16a2+32ab+16b216 a ^ { 2 } + 32 a b + 16 b ^ { 2 }16a2+32ab+16b2

Solve the equation - 6m2+38m−28m+7\frac { 6 m ^ { 2 } + 38 m - 28 } { m + 7 }m+76m2+38m−28​

Insert ⊆\subseteq⊆ or ⊈\nsubseteq⊈ in the blank to make the statement true. - ∅\varnothing∅ ____ ∅\varnothing∅