Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { \sqrt { 49 } }$$

Accepted Answer

A)  $\sqrt [ 3 ] { 7 }$ 
B)  7 
C)  $\sqrt { 7 }$ 
D)  $\sqrt [ 5 ] { 49 }$ 
A)  $\sqrt [ 3 ] { 7 }$ 
B)  7 
C)  $\sqrt { 7 }$ 
D)  $\sqrt [ 5 ] { 49 }$ A

Question 2

Perform the indicated operations.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

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

Question 3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 5 } { y } } { \frac { 2 } { y + 5 } }$$

Accepted Answer

A)  $\frac { 5 ( y + 5 ) } { 2 y }$ 
B)  $\frac { 2 y } { 5 ( y + 5 ) }$ 
C)  $\frac { y + 5 } { 10 y }$ 
D)  $10 y ( y + 5 )$ 
A)  $\frac { 5 ( y + 5 ) } { 2 y }$ 
B)  $\frac { 2 y } { 5 ( y + 5 ) }$ 
C)  $\frac { y + 5 } { 10 y }$ 
D)  $10 y ( y + 5 )$ A

Question 4

Factor out the greatest common factor. Simplify the factors, if possible.
-$15 w x - 20 w y - 25 w z$

Accepted Answer

A)  $15 w ( x - 20 y - 25 z )$ 
B)  $5 w ( 3 x - 20 w y - 25 w z )$ 
C)  $5 w ( 3 x - 4 y - 5 z )$ 
D)  $5 ( 3 w x - 4 w y - 5 w z )$ 
A)  $15 w ( x - 20 y - 25 z )$ 
B)  $5 w ( 3 x - 20 w y - 25 w z )$ 
C)  $5 w ( 3 x - 4 y - 5 z )$ 
D)  $5 ( 3 w x - 4 w y - 5 w z )$

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 1715 } { 8 } }$$

Accepted Answer

A)  $\frac { 7 } { \sqrt { 8 } }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 7 \sqrt { 70 } } { 4 }$ 
D)  $\frac { \sqrt { 5 } } { 2 }$ 
A)  $\frac { 7 } { \sqrt { 8 } }$ 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 7 \sqrt { 70 } } { 4 }$ 
D)  $\frac { \sqrt { 5 } } { 2 }$

Question 6

Determine the degree of the polynomial.
-$- a + 8 a ^ { 3 } - 4 a ^ { 7 } + 2 a ^ { 2 }$

Accepted Answer

A)  7 
B)  4 
C)  13 
D)  12 
A)  7 
B)  4 
C)  13 
D)  12

Question 7

Decide whether the expression has been simplified correctly.
-$( a b ) ^ { 4 } = a b ^ { 4 }$

Accepted Answer

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

Question 8

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$5 x ^ { - 3 }$

Accepted Answer

A)  $- \frac { 1 } { 15 x }$ 
B)  $\frac { 5 } { x ^ { 3 } }$ 
C)  $\frac { 1 } { 125 x ^ { 3 } }$ 
D)  $- 15 x$ 
A)  $- \frac { 1 } { 15 x }$ 
B)  $\frac { 5 } { x ^ { 3 } }$ 
C)  $\frac { 1 } { 125 x ^ { 3 } }$ 
D)  $- 15 x$

Question 9

Solve the problem.
-$$4 x ( 3 x - 1 ) ( 3 x + 8 )$$

Accepted Answer

A)  $36 x ^ { 3 } + 84 x ^ { 2 } - 32 x$ 
B)  $9 x ^ { 3 } + 21 x ^ { 2 } - 8 x$ 
C)  $32 x ^ { 3 } + 86 x ^ { 2 } - 30 x$ 
D)  $34 x ^ { 2 } + 85 x - 32$ 
A)  $36 x ^ { 3 } + 84 x ^ { 2 } - 32 x$ 
B)  $9 x ^ { 3 } + 21 x ^ { 2 } - 8 x$ 
C)  $32 x ^ { 3 } + 86 x ^ { 2 } - 30 x$ 
D)  $34 x ^ { 2 } + 85 x - 32$

Question 10

Factor the polynomial by substitution.
-$$36 z ^ { 8 } + 21 z ^ { 5 } - 36 z ^ { 2 }$$

Accepted Answer

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

Question 11

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| - 1 | = | 1 |$$

Accepted Answer

A)  True 
B)  False; $| - 1 | = - | 1 | = - 1$ 
A)  True 
B)  False; $| - 1 | = - | 1 | = - 1$

Question 12

Solve the problem.
-$( w - 9 ) ^ { 2 }$

Accepted Answer

A)  $w ^ { 2 } + 81$ 
B)  $81 w ^ { 2 } - 18 w + 81$ 
C)  $w ^ { 2 } - 18 w + 81$ 
D)  $w + 81$ 
A)  $w ^ { 2 } + 81$ 
B)  $81 w ^ { 2 } - 18 w + 81$ 
C)  $w ^ { 2 } - 18 w + 81$ 
D)  $w + 81$

Question 13

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( 2 a ^ { 6 } b ^ { 8 } \right) \left( - 4 a ^ { 7 } b ^ { 4 } \right)$$

Accepted Answer

A)  $- 8 a ^ { 13 } b ^ { 12 }$ 
B)  $8 a ^ { 13 } b ^ { 13 }$ 
C)  $8 a ^ { 41 } b ^ { 8 }$ 
D)  $- 8 a ^ { 42 } b ^ { 8 }$ 
A)  $- 8 a ^ { 13 } b ^ { 12 }$ 
B)  $8 a ^ { 13 } b ^ { 13 }$ 
C)  $8 a ^ { 41 } b ^ { 8 }$ 
D)  $- 8 a ^ { 42 } b ^ { 8 }$

Question 14

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$5 ^ { 4 } \cdot 5 ^ { 6 }$$

Accepted Answer

A) $ 5^{10}$ 
B)  $25^{24}$ 
C)  $5^{24}$ 
D)  $10^{10}$ 
A) $ 5^{10}$ 
B)  $25^{24}$ 
C)  $5^{24}$ 
D)  $10^{10}$

Question 15

Factor the trinomial, if possible.
-$$2 x ^ { 2 } - 12 x + 16$$

Accepted Answer

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

Question 16

Identify the set as finite or infinite.
-$$\{ x \mid x \text { is a natural number larger than } 3 \}$$

Accepted Answer

A)  finite 
B)  infinite 
A)  finite 
B)  infinite

Question 17

Identify the set as finite or infinite.
-{3, 4, 5, . . .}

Accepted Answer

A)  finite 
B)  infinite 
A)  finite 
B)  infinite

Question 18

Perform the indicated operations.
-$$\frac { 3 } { 4 x - 8 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$$

Accepted Answer

A)  $\frac { 41 x ^ { 2 } + 99 x + 13 } { 12 x + 21 }$ 
B)  $\frac { 121 x ^ { 2 } + 99 x + 178 } { 12 x + 21 }$ 
C)  $\frac { 121 x ^ { 2 } + 99 x + 178 } { 60 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
D)  $\frac { 41 x ^ { 2 } + 99 x + 178 } { 60 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
A)  $\frac { 41 x ^ { 2 } + 99 x + 13 } { 12 x + 21 }$ 
B)  $\frac { 121 x ^ { 2 } + 99 x + 178 } { 12 x + 21 }$ 
C)  $\frac { 121 x ^ { 2 } + 99 x + 178 } { 60 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$ 
D)  $\frac { 41 x ^ { 2 } + 99 x + 178 } { 60 ( x - 2 ) ( x + 1 ) ( x + 2 ) }$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - \frac { 64 } { 27 } }$$

Accepted Answer

A)  $- \frac { 64 } { 27 }$ 
B)  $- \frac { 4 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 16 } { 9 }$ 
A)  $- \frac { 64 } { 27 }$ 
B)  $- \frac { 4 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 16 } { 9 }$

Question 20

Find the product or quotient.
-$$\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }$$

Accepted Answer

A)  $\frac { k } { k ^ { 2 } + 12 k + 36 }$ 
B)  $\frac { k } { k - 9 }$ 
C)  $\frac { 1 } { k - 9 }$ 
D)  $\frac { k ^ { 2 } + 6 k } { k - 9 }$ 
A)  $\frac { k } { k ^ { 2 } + 12 k + 36 }$ 
B)  $\frac { k } { k - 9 }$ 
C)  $\frac { 1 } { k - 9 }$ 
D)  $\frac { k ^ { 2 } + 6 k } { k - 9 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \sqrt { 49 } }$

Perform the indicated operations. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 5 } { y } } { \frac { 2 } { y + 5 } }$

Factor out the greatest common factor. Simplify the factors, if possible. - $15 w x - 20 w y - 25 w z$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 1715 } { 8 } }$

Determine the degree of the polynomial. - $- a + 8 a ^ { 3 } - 4 a ^ { 7 } + 2 a ^ { 2 }$

Decide whether the expression has been simplified correctly. - $( a b ) ^ { 4 } = a b ^ { 4 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $5 x ^ { - 3 }$

Solve the problem. - $4 x ( 3 x - 1 ) ( 3 x + 8 )$

Factor the polynomial by substitution. - $36 z ^ { 8 } + 21 z ^ { 5 } - 36 z ^ { 2 }$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 1 | = | 1 |$

Solve the problem. - $( w - 9 ) ^ { 2 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 2 a ^ { 6 } b ^ { 8 } \right) \left( - 4 a ^ { 7 } b ^ { 4 } \right)$

Simplify the expression. Assume all variables represent nonzero real numbers. - $5 ^ { 4 } \cdot 5 ^ { 6 }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 12 x + 16$

Identify the set as finite or infinite. - $\{ x \mid x \text { is a natural number larger than } 3 \}$

Identify the set as finite or infinite. -{3, 4, 5, . . .}

Perform the indicated operations. - $\frac { 3 } { 4 x - 8 } - \frac { 2 } { 3 x + 3 } + \frac { 3 } { 5 x + 10 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - \frac { 64 } { 27 } }$

Find the product or quotient. - $\frac { k ^ { 2 } + 11 k + 30 } { k ^ { 2 } + 12 k + 36 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 4 k - 45 }$

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

Simplify the expression. Assume all variables represent positive real numbers. - 493\sqrt [ 3 ] { \sqrt { 49 } }349​​

Perform the indicated operations. - xx2−16−8x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 8 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+48​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 5y2y+5\frac { \frac { 5 } { y } } { \frac { 2 } { y + 5 } }y+52​y5​​

Factor out the greatest common factor. Simplify the factors, if possible. - 15wx−20wy−25wz15 w x - 20 w y - 25 w z15wx−20wy−25wz

Simplify the expression. Assume all variables represent positive real numbers. - 17158\sqrt { \frac { 1715 } { 8 } }81715​​

Determine the degree of the polynomial. - −a+8a3−4a7+2a2- a + 8 a ^ { 3 } - 4 a ^ { 7 } + 2 a ^ { 2 }−a+8a3−4a7+2a2

Decide whether the expression has been simplified correctly. - (ab)4=ab4( a b ) ^ { 4 } = a b ^ { 4 }(ab)4=ab4

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 5x−35 x ^ { - 3 }5x−3

Solve the problem. - 4x(3x−1)(3x+8)4 x ( 3 x - 1 ) ( 3 x + 8 )4x(3x−1)(3x+8)

Factor the polynomial by substitution. - 36z8+21z5−36z236 z ^ { 8 } + 21 z ^ { 5 } - 36 z ^ { 2 }36z8+21z5−36z2

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−1∣=∣1∣| - 1 | = | 1 |∣−1∣=∣1∣

Solve the problem. - (w−9)2( w - 9 ) ^ { 2 }(w−9)2

Simplify the expression. Assume all variables represent nonzero real numbers. - (2a6b8)(−4a7b4)\left( 2 a ^ { 6 } b ^ { 8 } \right) \left( - 4 a ^ { 7 } b ^ { 4 } \right)(2a6b8)(−4a7b4)

Simplify the expression. Assume all variables represent nonzero real numbers. - 54⋅565 ^ { 4 } \cdot 5 ^ { 6 }54⋅56

Factor the trinomial, if possible. - 2x2−12x+162 x ^ { 2 } - 12 x + 162x2−12x+16

Identify the set as finite or infinite. - {x∣x is a natural number larger than 3}\{ x \mid x \text { is a natural number larger than } 3 \}{x∣x is a natural number larger than 3}