Question 1

Find the sum or difference.
-$$( 4 x + 3 ) ^ { 3 }$$

Accepted Answer

A)  $64 x ^ { 3 } + 144 x ^ { 2 } + 144 x + 27$ 
B)  $16 x ^ { 6 } + 12 x ^ { 3 } + 729$ 
C)  $64 x ^ { 3 } + 144 x ^ { 2 } + 108 x + 27$ 
D)  $16 x ^ { 2 } + 24 x + 9$ 
A)  $64 x ^ { 3 } + 144 x ^ { 2 } + 144 x + 27$ 
B)  $16 x ^ { 6 } + 12 x ^ { 3 } + 729$ 
C)  $64 x ^ { 3 } + 144 x ^ { 2 } + 108 x + 27$ 
D)  $16 x ^ { 2 } + 24 x + 9$

Question 2

Write the expression in lowest terms.
-$\frac { 19 \mathrm { k } ^ { 2 } } { 13 \mathrm { k } }$

Accepted Answer

A)  $\frac { 19 } { 13 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 3 } { 2 } k$ 
D)  $\frac { 19 } { 13 } \mathrm { k }$ 
A)  $\frac { 19 } { 13 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 3 } { 2 } k$ 
D)  $\frac { 19 } { 13 } \mathrm { k }$

Question 3

Write in exponential form. Assume all variables are positive real numbers.
-$\sqrt [ 7 ] { x ^ { 4 } }$

Accepted Answer

A)  $x ^ { 7 / 4 }$ 
B)  $x ^ { 4 / 28 }$ 
C)  $x ^ { 4 / 7 }$ 
D)  $x ^ { 1 / 28 }$ 
A)  $x ^ { 7 / 4 }$ 
B)  $x ^ { 4 / 28 }$ 
C)  $x ^ { 4 / 7 }$ 
D)  $x ^ { 1 / 28 }$

Question 4

Identify the expression as a polynomial or not a polynomial.
-$0.6 x ^ { 9 } - 8.2$

Accepted Answer

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

Question 5

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$| - 12 | = - | 12 |$

Accepted Answer

A) True 
 B)False

Question 6

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 9 } { y } }$

Accepted Answer

A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  0 
D)  2 
A)  $\frac { 4 } { 3 }$ 
B)  $\frac { 5 } { 2 }$ 
C)  0 
D)  2

Question 7

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$\frac { 1 } { ( a + 2 ) } \cdot ( a + 2 ) = 1 , \text { if } a + 2 \neq 0$

Accepted Answer

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

Question 8

Find the sum or difference.
-$$\left( 7 x ^ { 6 } + 6 x ^ { 8 } - 7 + 4 x ^ { 7 } \right) - \left( - 1 + 8 x ^ { 7 } + 8 x ^ { 8 } - 9 x ^ { 6 } \right)$$

Accepted Answer

A)  $14 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 6$ 
B)  $14 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
C)  $- 2 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
D)  $- 2 x ^ { 8 } - 4 x ^ { 7 } + 16 x ^ { 6 } - 6$ 
A)  $14 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 6$ 
B)  $14 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
C)  $- 2 x ^ { 8 } + 12 x ^ { 7 } - 2 x ^ { 6 } - 8$ 
D)  $- 2 x ^ { 8 } - 4 x ^ { 7 } + 16 x ^ { 6 } - 6$

Question 9

Find the sum or difference.
-$$\frac { 16 s t ^ { 6 } - 5 t ^ { 10 } + 64 s t ^ { 5 } } { 4 s t ^ { 5 } }$$

Accepted Answer

A)  $4 t - s t ^ { 5 } + 16$ 
B)  $4 t - \frac { 5 t ^ { 5 } } { 4 s } + 16$ 
C)  $4 t - \frac { t ^ { 5 } } { s } + 16$ 
D)  $4 \mathrm { st } - \frac { 5 \mathrm { t } ^ { 5 } } { 4 \mathrm {~s} } + 16$ 
A)  $4 t - s t ^ { 5 } + 16$ 
B)  $4 t - \frac { 5 t ^ { 5 } } { 4 s } + 16$ 
C)  $4 t - \frac { t ^ { 5 } } { s } + 16$ 
D)  $4 \mathrm { st } - \frac { 5 \mathrm { t } ^ { 5 } } { 4 \mathrm {~s} } + 16$

Question 10

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

Accepted Answer

A)  $4 s ^ { 4 } - 2 s ^ { 3 } - 6 s ^ { 2 } + 13 s + 6$ 
B)  $4 s ^ { 4 } - 20 s ^ { 3 } - 6 s ^ { 2 } + 13 s + 6$ 
C)  $4 s ^ { 4 } - 2 s ^ { 3 } - 6 s ^ { 2 } + 4 s + 6$ 
D)  $4 s ^ { 4 } - 2 s ^ { 3 } + 15 s ^ { 2 } + 13 s + 6$ 
A)  $4 s ^ { 4 } - 2 s ^ { 3 } - 6 s ^ { 2 } + 13 s + 6$ 
B)  $4 s ^ { 4 } - 20 s ^ { 3 } - 6 s ^ { 2 } + 13 s + 6$ 
C)  $4 s ^ { 4 } - 2 s ^ { 3 } - 6 s ^ { 2 } + 4 s + 6$ 
D)  $4 s ^ { 4 } - 2 s ^ { 3 } + 15 s ^ { 2 } + 13 s + 6$

Question 11

Write in radical form. Assume all variables represent positive real numbers.
-$( 7 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $- \sqrt [ 5 ] { 7 x }$ 
B)  $\frac { \sqrt { 7 x } } { 5 }$ 
C)  $\sqrt [ 1 / 5 ] { 7 x }$ 
D)  $\sqrt [ 5 ] { 7 x }$ 
A)  $- \sqrt [ 5 ] { 7 x }$ 
B)  $\frac { \sqrt { 7 x } } { 5 }$ 
C)  $\sqrt [ 1 / 5 ] { 7 x }$ 
D)  $\sqrt [ 5 ] { 7 x }$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$11 \sqrt [ 3 ] { 3 } + 9 \sqrt [ 3 ] { 3 }$$

Accepted Answer

A)  $20 \sqrt [ 3 ] { 3 }$ 
B)  $- 2 \sqrt [ 3 ] { 3 }$ 
C)  $20 \sqrt [ 3 ] { 9 }$ 
D)  $20 \sqrt [ 3 ] { 6 }$ 
A)  $20 \sqrt [ 3 ] { 3 }$ 
B)  $- 2 \sqrt [ 3 ] { 3 }$ 
C)  $20 \sqrt [ 3 ] { 9 }$ 
D)  $20 \sqrt [ 3 ] { 6 }$

Question 13

Find the domain of the expression.
-$$\frac { 7 x } { x - y }$$

Accepted Answer

A)  $\{ x \mid x \neq y \}$ 
B)  $\{ x \mid x \neq 0$ and $y \mid y \neq 0 \}$ 
C)  $\{ x \mid x \neq - y \}$ 
D)  $\{ x \mid x \neq 1$ and $y \mid y \neq 1 \}$ 
A)  $\{ x \mid x \neq y \}$ 
B)  $\{ x \mid x \neq 0$ and $y \mid y \neq 0 \}$ 
C)  $\{ x \mid x \neq - y \}$ 
D)  $\{ x \mid x \neq 1$ and $y \mid y \neq 1 \}$

Question 14

Evaluate the expression.
-$$\left( \frac { 1 } { 16 } \right) ^ { 7 / 2 }$$

Accepted Answer

A)  $\frac { 1 } { 16,384 }$ 
B)  $- 16,384$ 
C)  not a real number 
D)  $- 56$ 
A)  $\frac { 1 } { 16,384 }$ 
B)  $- 16,384$ 
C)  not a real number 
D)  $- 56$

Question 15

Factor, using the given factor. Assume all variables represent positive real numbers.
-$$( \mathrm { q } + 2 ) ^ { - 3 / 11 } + ( \mathrm { q } + 2 ) ^ { - 1 / 11 } + ( \mathrm { q } + 2 ) ^ { 1 / 11 } ; \quad ( \mathrm { q } + 2 ) ^ { - 3 / 11 }$$

Accepted Answer

A)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { 4 / 11 } + ( q + 2 ) ^ { 6 / 11 } \right]$ 
B)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { 2 / 11 } + ( q + 2 ) ^ { 4 / 11 } \right]$ 
C)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { - 2 / 11 } + ( q + 2 ) ^ { - 4 / 11 } \right]$ 
D)  $( \mathrm { q } + 2 ) ^ { - 3 / 11 } \left[ 1 + ( \mathrm { q } + 2 ) ^ { 1 / 11 } + ( \mathrm { q } + 2 ) ^ { 3 / 11 } \right]$ 
A)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { 4 / 11 } + ( q + 2 ) ^ { 6 / 11 } \right]$ 
B)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { 2 / 11 } + ( q + 2 ) ^ { 4 / 11 } \right]$ 
C)  $( q + 2 ) ^ { - 3 / 11 } \left[ 1 + ( q + 2 ) ^ { - 2 / 11 } + ( q + 2 ) ^ { - 4 / 11 } \right]$ 
D)  $( \mathrm { q } + 2 ) ^ { - 3 / 11 } \left[ 1 + ( \mathrm { q } + 2 ) ^ { 1 / 11 } + ( \mathrm { q } + 2 ) ^ { 3 / 11 } \right]$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$8 \sqrt { 11 } + 2 \sqrt { 11 }$

Accepted Answer

A)  110 
B)  $16 \sqrt { 11 }$ 
C)  $10 \sqrt { 22 }$ 
D)  $10 \sqrt { 11 }$ 
A)  110 
B)  $16 \sqrt { 11 }$ 
C)  $10 \sqrt { 22 }$ 
D)  $10 \sqrt { 11 }$

Question 17

Use set notation, and list all the elements of the set.
-The first four natural numbers.

Accepted Answer

A)  {0, 2, 4, 6} 
B)  {1, 2, 3, 4} 
C)  {0, 1, 2, 3} 
D)  {0, 1, 2, 3, 4} 
A)  {0, 2, 4, 6} 
B)  {1, 2, 3, 4} 
C)  {0, 1, 2, 3} 
D)  {0, 1, 2, 3, 4}

Question 18

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

Accepted Answer

A)  $14 a x ^ { 21 } - 14 a x ^ { 14 } - 21 a x ^ { 7 }$ 
B)  $14 a ^ { 2 } x ^ { 10 } - 14 a x ^ { 9 } - 21 a x ^ { 7 }$ 
C)  $- 14 a ^ { 2 } x ^ { 21 } + 14 a x ^ { 14 } + 21 a x ^ { 7 }$ 
D)  $- 14 a ^ { 2 } x ^ { 10 } + 14 a x ^ { 9 } + 21 a x ^ { 7 }$ 
A)  $14 a x ^ { 21 } - 14 a x ^ { 14 } - 21 a x ^ { 7 }$ 
B)  $14 a ^ { 2 } x ^ { 10 } - 14 a x ^ { 9 } - 21 a x ^ { 7 }$ 
C)  $- 14 a ^ { 2 } x ^ { 21 } + 14 a x ^ { 14 } + 21 a x ^ { 7 }$ 
D)  $- 14 a ^ { 2 } x ^ { 10 } + 14 a x ^ { 9 } + 21 a x ^ { 7 }$

Question 19

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-The cost of manufacturing clocks is given by c $c = 25 ( n + 64 ) ^ { 1 / 2 }$ , where c is the cost in dollars and n is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $1600 
B)  $25 
C)  $200 
D)  $40 
A)  $1600 
B)  $25 
C)  $200 
D)  $40

Question 20

Provide an appropriate response.
-Consider the following figure, which is a square divided into two squares and two rectangles. 
 
The length of each side of the large square is $x + 4$. Find a formula for the area of the largest square as a binomia raised to a power. Write the expansion of this binomial.

Accepted Answer

A)  $x ^ { 2 } - 8 x + 16$ 
B)  $x ^ { 2 } - 16$ 
C)  $x ^ { 2 } + 8 x + 16$ 
D)  $x ^ { 2 } + 16$ 
A)  $x ^ { 2 } - 8 x + 16$ 
B)  $x ^ { 2 } - 16$ 
C)  $x ^ { 2 } + 8 x + 16$ 
D)  $x ^ { 2 } + 16$

Find the sum or difference. - $( 4 x + 3 ) ^ { 3 }$

Write the expression in lowest terms. - $\frac { 19 \mathrm { k } ^ { 2 } } { 13 \mathrm { k } }$

Write in exponential form. Assume all variables are positive real numbers. - $\sqrt [ 7 ] { x ^ { 4 } }$

Identify the expression as a polynomial or not a polynomial. - $0.6 x ^ { 9 } - 8.2$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 12 | = - | 12 |$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 9 } { y } }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $\frac { 1 } { ( a + 2 ) } \cdot ( a + 2 ) = 1 , \text { if } a + 2 \neq 0$

Find the sum or difference. - $\left( 7 x ^ { 6 } + 6 x ^ { 8 } - 7 + 4 x ^ { 7 } \right) - \left( - 1 + 8 x ^ { 7 } + 8 x ^ { 8 } - 9 x ^ { 6 } \right)$

Find the sum or difference. - $\frac { 16 s t ^ { 6 } - 5 t ^ { 10 } + 64 s t ^ { 5 } } { 4 s t ^ { 5 } }$

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

Write in radical form. Assume all variables represent positive real numbers. - $( 7 x ) ^ { 1 / 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $11 \sqrt [ 3 ] { 3 } + 9 \sqrt [ 3 ] { 3 }$

Find the domain of the expression. - $\frac { 7 x } { x - y }$

Evaluate the expression. - $\left( \frac { 1 } { 16 } \right) ^ { 7 / 2 }$

Factor, using the given factor. Assume all variables represent positive real numbers. - $( \mathrm { q } + 2 ) ^ { - 3 / 11 } + ( \mathrm { q } + 2 ) ^ { - 1 / 11 } + ( \mathrm { q } + 2 ) ^ { 1 / 11 } ; \quad ( \mathrm { q } + 2 ) ^ { - 3 / 11 }$

Simplify the expression. Assume all variables represent positive real numbers. - $8 \sqrt { 11 } + 2 \sqrt { 11 }$

Use set notation, and list all the elements of the set. -The first four natural numbers.

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

Equations and Inequalities

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Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Arithmetic Sequence: Common Difference and First n Terms

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Exam 1: Review of Basic Concepts

Find the sum or difference. - (4x+3)3( 4 x + 3 ) ^ { 3 }(4x+3)3

Write the expression in lowest terms. - 19k213k\frac { 19 \mathrm { k } ^ { 2 } } { 13 \mathrm { k } }13k19k2​

Write in exponential form. Assume all variables are positive real numbers. - x47\sqrt [ 7 ] { x ^ { 4 } }7x4​

Identify the expression as a polynomial or not a polynomial. - 0.6x9−8.20.6 x ^ { 9 } - 8.20.6x9−8.2

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−12∣=−∣12∣| - 12 | = - | 12 |∣−12∣=−∣12∣

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 - 6y−a2x2+9y\frac { \frac { 6 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 9 } { y } }2x​+y9​y6​−2a​​

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 1(a+2)⋅(a+2)=1, if a+2≠0\frac { 1 } { ( a + 2 ) } \cdot ( a + 2 ) = 1 , \text { if } a + 2 \neq 0(a+2)1​⋅(a+2)=1, if a+2=0

Find the sum or difference. - (7x6+6x8−7+4x7)−(−1+8x7+8x8−9x6)\left( 7 x ^ { 6 } + 6 x ^ { 8 } - 7 + 4 x ^ { 7 } \right) - \left( - 1 + 8 x ^ { 7 } + 8 x ^ { 8 } - 9 x ^ { 6 } \right)(7x6+6x8−7+4x7)−(−1+8x7+8x8−9x6)

Find the sum or difference. - 16st6−5t10+64st54st5\frac { 16 s t ^ { 6 } - 5 t ^ { 10 } + 64 s t ^ { 5 } } { 4 s t ^ { 5 } }4st516st6−5t10+64st5​

Find the sum or difference. - (2s+3)(2s3−4s2+3s+2)( 2 s + 3 ) \left( 2 s ^ { 3 } - 4 s ^ { 2 } + 3 s + 2 \right)(2s+3)(2s3−4s2+3s+2)

Write in radical form. Assume all variables represent positive real numbers. - (7x)1/5( 7 x ) ^ { 1 / 5 }(7x)1/5

Simplify the expression. Assume all variables represent positive real numbers. - 1133+93311 \sqrt [ 3 ] { 3 } + 9 \sqrt [ 3 ] { 3 }1133​+933​

Find the domain of the expression. - 7xx−y\frac { 7 x } { x - y }x−y7x​

Evaluate the expression. - (116)7/2\left( \frac { 1 } { 16 } \right) ^ { 7 / 2 }(161​)7/2

Simplify the expression. Assume all variables represent positive real numbers. - 811+2118 \sqrt { 11 } + 2 \sqrt { 11 }811​+211​