Question 1

Insert   in the blank to make the statement true.
-

Accepted Answer

A)  $\Phi$ 
B)  $\subseteq$ 
A)  $\Phi$ 
B)  $\subseteq$

Question 2

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( \frac { y ^ { - 3 / 8 } } { a ^ { - 3 / 2 } } \right) ^ { 3 } \left( \frac { a ^ { 1 / 3 } } { y ^ { 1 / 4 } } \right) ^ { - 3 }$$

Accepted Answer

A)  $\frac { a ^ { 11 / 2 } } { y ^ { 15 / 8 } }$ 
B)  $\frac { y ^ { 15 / 8 } } { a ^ { 11 / 2 } }$ 
C)  $\frac { y ^ { 3 / 8 } } { a ^ { 7 / 2 } }$ 
D)  $\frac { a ^ { 7 / 2 } } { y ^ { 3 / 8 } }$ 
A)  $\frac { a ^ { 11 / 2 } } { y ^ { 15 / 8 } }$ 
B)  $\frac { y ^ { 15 / 8 } } { a ^ { 11 / 2 } }$ 
C)  $\frac { y ^ { 3 / 8 } } { a ^ { 7 / 2 } }$ 
D)  $\frac { a ^ { 7 / 2 } } { y ^ { 3 / 8 } }$

Question 3

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( x ^ { 4 } \right) ^ { 6 }$

Accepted Answer

A)  $x ^ { 24 }$ 
B)  $6 x ^ { 4 }$ 
C)  $x ^ { 10 }$ 
D)  $24 x$ 
A)  $x ^ { 24 }$ 
B)  $6 x ^ { 4 }$ 
C)  $x ^ { 10 }$ 
D)  $24 x$

Question 4

Factor the trinomial, if possible.
-$$9 a ^ { 2 } + 18 a b + 9 b ^ { 2 }$$

Accepted Answer

A)  $9 ( a + b ) ^ { 2 }$ 
B)  $( 3 a + 3 b ) ^ { 2 }$ 
C)  $( 3 a - 3 b ) ^ { 2 }$ 
D)  $9 ( a - b ) ^ { 2 }$ 
A)  $9 ( a + b ) ^ { 2 }$ 
B)  $( 3 a + 3 b ) ^ { 2 }$ 
C)  $( 3 a - 3 b ) ^ { 2 }$ 
D)  $9 ( a - b ) ^ { 2 }$

Question 5

Find the sum or difference.
-$12 a ^ { 2 } x ^ { 8 } \left( - 4 a ^ { 7 } x ^ { 9 } - 3 x ^ { 5 } - 8 a \right)$

Accepted Answer

A)  $- 48 a ^ { 14 } x ^ { 72 } + 36 a ^ { 2 } x 40 + 96 a ^ { 2 } x$ 
B)  $48 a ^ { 9 } x ^ { 17 } + 36 a ^ { 2 } x 13 + 96 a ^ { 3 } x ^ { 8 }$ 
C)  $- 48 a ^ { 9 } x ^ { 17 } - 3 x ^ { 5 } - 8 a$ 
D)  $- 48 a ^ { 9 } x ^ { 17 } - 36 a ^ { 2 } x ^ { 13 } - 96 a ^ { 3 } x ^ { 8 }$ 
A)  $- 48 a ^ { 14 } x ^ { 72 } + 36 a ^ { 2 } x 40 + 96 a ^ { 2 } x$ 
B)  $48 a ^ { 9 } x ^ { 17 } + 36 a ^ { 2 } x 13 + 96 a ^ { 3 } x ^ { 8 }$ 
C)  $- 48 a ^ { 9 } x ^ { 17 } - 3 x ^ { 5 } - 8 a$ 
D)  $- 48 a ^ { 9 } x ^ { 17 } - 36 a ^ { 2 } x ^ { 13 } - 96 a ^ { 3 } x ^ { 8 }$

Question 6

Factor by any method.
-$$y ^ { 2 } - \frac { 49 } { 121 }$$

Accepted Answer

A)  $\left( y ^ { 2 } + \frac { 7 } { 11 } \right) \left( y ^ { 2 } - \frac { 7 } { 11 } \right)$ 
B)  $\left( y + \frac { 7 } { 11 } \right) \left( y - \frac { 7 } { 11 } \right)$ 
C)  $\left( y - \frac { 7 } { 11 } \right) \left( y - \frac { 7 } { 11 } \right)$ 
D)  $\left( y + \frac { 49 } { 11 } \left( y - \frac { 49 } { 11 } \right) \right.$ 
A)  $\left( y ^ { 2 } + \frac { 7 } { 11 } \right) \left( y ^ { 2 } - \frac { 7 } { 11 } \right)$ 
B)  $\left( y + \frac { 7 } { 11 } \right) \left( y - \frac { 7 } { 11 } \right)$ 
C)  $\left( y - \frac { 7 } { 11 } \right) \left( y - \frac { 7 } { 11 } \right)$ 
D)  $\left( y + \frac { 49 } { 11 } \left( y - \frac { 49 } { 11 } \right) \right.$

Question 7

Factor out the greatest common factor. Simplify the factors, if possible.
-$10 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }$

Accepted Answer

A)  $\left( 10 a ^ { 2 } + 5 b ^ { 2 } \right) ( a - 3 b )$ 
B)  $\left( 2 a ^ { 2 } + 5 b \right) ( 5 a - 3 b )$ 
C)  $\left( 2 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a + 3 b )$ 
D)  $\left( 2 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a - 3 b )$ 
A)  $\left( 10 a ^ { 2 } + 5 b ^ { 2 } \right) ( a - 3 b )$ 
B)  $\left( 2 a ^ { 2 } + 5 b \right) ( 5 a - 3 b )$ 
C)  $\left( 2 a ^ { 2 } - 5 b ^ { 2 } \right) ( 5 a + 3 b )$ 
D)  $\left( 2 a ^ { 2 } + 5 b ^ { 2 } \right) ( 5 a - 3 b )$

Question 8

Factor out the greatest common factor. Simplify the factors, if possible.
-$$6 x ( 3 x + 4 ) - 5 ( 3 x + 4 )$$

Accepted Answer

A)  $( 6 x + 5 ) ( 3 x - 4 )$ 
B)  $( 6 x - 5 ) ( 3 x + 4 )$ 
C)  $( 18 x + 5 ) ( x - 4 )$ 
D)  $( 18 x - 5 ) ( x + 4 )$ 
A)  $( 6 x + 5 ) ( 3 x - 4 )$ 
B)  $( 6 x - 5 ) ( 3 x + 4 )$ 
C)  $( 18 x + 5 ) ( x - 4 )$ 
D)  $( 18 x - 5 ) ( x + 4 )$

Question 9

Solve the problem. Round to two decimal places unless otherwise indicated.
-Suppose a cost-benefit model is given by y $= \frac { 5.9 x } { 100 - x }$ , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 75% to the nearest dollar.

Accepted Answer

A)  $4425 
B)  $3000 
C)  $17,700 
D)  $5900 
A)  $4425 
B)  $3000 
C)  $17,700 
D)  $5900

Question 10

Factor the trinomial, if possible.
-$15 y ^ { 2 } + 22 y + 8$

Accepted Answer

A)  $( 15 y + 2 ) ( y + 4 )$ 
B)  $( 15 y + 1 ) ( y - 8 )$ 
C)  $( 3 y + 2 ) ( 5 y + 4 )$ 
D)  $( 3 y - 2 ) ( 5 y - 4 )$ 
A)  $( 15 y + 2 ) ( y + 4 )$ 
B)  $( 15 y + 1 ) ( y - 8 )$ 
C)  $( 3 y + 2 ) ( 5 y + 4 )$ 
D)  $( 3 y - 2 ) ( 5 y - 4 )$

Question 11

Use set notation, and list all the elements of the set.
-$$\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots , \frac { 1 } { 243 } \right\}$$

Accepted Answer

A)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 5 } , \frac { 1 } { 6 } , \frac { 1 } { 7 } , \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 729 } , \frac { 1 } { 19,683 } \right\}$ 
C)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 243 } \right\}$ 
D)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \frac { 1 } { 243 } \right\}$ 
A)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 5 } , \frac { 1 } { 6 } , \frac { 1 } { 7 } , \frac { 1 } { 8 } \right\}$ 
B)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 729 } , \frac { 1 } { 19,683 } \right\}$ 
C)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 243 } \right\}$ 
D)  $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \frac { 1 } { 27 } , \frac { 1 } { 81 } , \frac { 1 } { 243 } \right\}$

Question 12

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 13

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-The length of the diagonal of a box is given by $\mathrm { D } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } }$ where $\mathrm { L } , \mathrm { W }$, and $\mathrm { H }$ are the length, width, and height of the box. Find the length of the diagonal, D, of a box that is $2 \mathrm { ft }$ long, $6 \mathrm { ft }$ high, and $4 \mathrm { ft }$ wide. Give the exact value.

Accepted Answer

A)  $48 \mathrm { ft }$ 
B)  $2 \sqrt { 14 } \mathrm { ft }$ 
C)  $12 \mathrm { ft }$ 
D)  $4 \sqrt { 3 } \mathrm { ft }$ 
A)  $48 \mathrm { ft }$ 
B)  $2 \sqrt { 14 } \mathrm { ft }$ 
C)  $12 \mathrm { ft }$ 
D)  $4 \sqrt { 3 } \mathrm { ft }$

Question 14

Write in radical form. Assume all variables represent positive real numbers.
-$$m ^ { 8 / 3 }$$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 8 ] { m } }$ 
B)  $( \sqrt [ 3 ] { \mathrm { m } } ) ^ { 8 }$ 
C)  $( \sqrt [ 8 ] { \mathrm { m } } ) ^ { 3 }$ 
D)  $\sqrt [ 8 ] { \mathrm { m } ^ { 3 } }$ 
A)  $\frac { 1 } { \sqrt [ 8 ] { m } }$ 
B)  $( \sqrt [ 3 ] { \mathrm { m } } ) ^ { 8 }$ 
C)  $( \sqrt [ 8 ] { \mathrm { m } } ) ^ { 3 }$ 
D)  $\sqrt [ 8 ] { \mathrm { m } ^ { 3 } }$

Question 15

Use the distributive property to rewrite a sum as a product or the product as a sum.
-$2 - 10 b$

Accepted Answer

A)  $2 ( 1 - 5 b )$ 
B)  $2 ( 1 - 6 b )$ 
C)  $12 b$ 
D)  $- 8 b$ 
A)  $2 ( 1 - 5 b )$ 
B)  $2 ( 1 - 6 b )$ 
C)  $12 b$ 
D)  $- 8 b$

Question 16

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$x ^ { 1 / 8 } \cdot x ^ { 7 / 8 }$$

Accepted Answer

A)  $x ^ { 7 / 64 }$ 
B)  $x$ 
C)  $\frac { 1 } { x }$ 
D)  $x ^ { 7 / 8 }$ 
A)  $x ^ { 7 / 64 }$ 
B)  $x$ 
C)  $\frac { 1 } { x }$ 
D)  $x ^ { 7 / 8 }$

Question 17

Simplify the expression. Assume all variables represent nonzero real numbers.
-$4 ^ { 8 } \cdot 4 ^ { 5 }$

Accepted Answer

A)  413 
B)  1640 
C)  440 
D)  $8 ^ { 13 }$ 
A)  413 
B)  1640 
C)  440 
D)  $8 ^ { 13 }$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 5 } + 3 ) ( \sqrt { 3 } + 5 )$

Accepted Answer

A)  $\sqrt { 15 } + 15$ 
B)  $\sqrt { 15 } + 8 \sqrt { 3 } + 15$ 
C)  $9 \sqrt { 15 } + 15$ 
D)  $\sqrt { 15 } + 5 \sqrt { 5 } + 3 \sqrt { 3 } + 15$ 
A)  $\sqrt { 15 } + 15$ 
B)  $\sqrt { 15 } + 8 \sqrt { 3 } + 15$ 
C)  $9 \sqrt { 15 } + 15$ 
D)  $\sqrt { 15 } + 5 \sqrt { 5 } + 3 \sqrt { 3 } + 15$

Question 19

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$, and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$.
$$\{ 6,8 \} \subseteq B$$

Accepted Answer

A) True 
 B)False

Question 20

Factor by any method.
-$343 p ^ { 3 } - 1$

Accepted Answer

A)  $( 343 p - 1 ) \left( p ^ { 2 } + 7 p + 1 \right)$ 
B)  $( 7 p - 1 ) \left( 49 p ^ { 2 } + 1 \right)$ 
C)  $( 7 p + 1 ) \left( 49 p ^ { 2 } - 7 p + 1 \right)$ 
D)  $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$ 
A)  $( 343 p - 1 ) \left( p ^ { 2 } + 7 p + 1 \right)$ 
B)  $( 7 p - 1 ) \left( 49 p ^ { 2 } + 1 \right)$ 
C)  $( 7 p + 1 ) \left( 49 p ^ { 2 } - 7 p + 1 \right)$ 
D)  $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$

Insert in the blank to make the statement true. -

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { y ^ { - 3 / 8 } } { a ^ { - 3 / 2 } } \right) ^ { 3 } \left( \frac { a ^ { 1 / 3 } } { y ^ { 1 / 4 } } \right) ^ { - 3 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( x ^ { 4 } \right) ^ { 6 }$

Factor the trinomial, if possible. - $9 a ^ { 2 } + 18 a b + 9 b ^ { 2 }$

Find the sum or difference. - $12 a ^ { 2 } x ^ { 8 } \left( - 4 a ^ { 7 } x ^ { 9 } - 3 x ^ { 5 } - 8 a \right)$

Factor by any method. - $y ^ { 2 } - \frac { 49 } { 121 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $10 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $6 x ( 3 x + 4 ) - 5 ( 3 x + 4 )$

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose a cost-benefit model is given by y $= \frac { 5.9 x } { 100 - x }$ , where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 75% to the nearest dollar.

Factor the trinomial, if possible. - $15 y ^ { 2 } + 22 y + 8$

Use set notation, and list all the elements of the set. - $\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots , \frac { 1 } { 243 } \right\}$

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

Write in radical form. Assume all variables represent positive real numbers. - $m ^ { 8 / 3 }$

Use the distributive property to rewrite a sum as a product or the product as a sum. - $2 - 10 b$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $x ^ { 1 / 8 } \cdot x ^ { 7 / 8 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $4 ^ { 8 } \cdot 4 ^ { 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 5 } + 3 ) ( \sqrt { 3 } + 5 )$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$ , and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$ . $\{ 6,8 \} \subseteq B$

Factor by any method. - $343 p ^ { 3 } - 1$

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Insert in the blank to make the statement true. -

Simplify the expression. Assume all variables represent nonzero real numbers. - (x4)6\left( x ^ { 4 } \right) ^ { 6 }(x4)6

Factor the trinomial, if possible. - 9a2+18ab+9b29 a ^ { 2 } + 18 a b + 9 b ^ { 2 }9a2+18ab+9b2

Find the sum or difference. - 12a2x8(−4a7x9−3x5−8a)12 a ^ { 2 } x ^ { 8 } \left( - 4 a ^ { 7 } x ^ { 9 } - 3 x ^ { 5 } - 8 a \right)12a2x8(−4a7x9−3x5−8a)

Factor by any method. - y2−49121y ^ { 2 } - \frac { 49 } { 121 }y2−12149​

Factor out the greatest common factor. Simplify the factors, if possible. - 10a3−6a2b+25ab2−15b310 a ^ { 3 } - 6 a ^ { 2 } b + 25 a b ^ { 2 } - 15 b ^ { 3 }10a3−6a2b+25ab2−15b3

Factor out the greatest common factor. Simplify the factors, if possible. - 6x(3x+4)−5(3x+4)6 x ( 3 x + 4 ) - 5 ( 3 x + 4 )6x(3x+4)−5(3x+4)

Factor the trinomial, if possible. - 15y2+22y+815 y ^ { 2 } + 22 y + 815y2+22y+8

Use set notation, and list all the elements of the set. - {1,13,19,…,1243}\left\{ 1 , \frac { 1 } { 3 } , \frac { 1 } { 9 } , \ldots , \frac { 1 } { 243 } \right\}{1,31​,91​,…,2431​}

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

Write in radical form. Assume all variables represent positive real numbers. - m8/3m ^ { 8 / 3 }m8/3

Use the distributive property to rewrite a sum as a product or the product as a sum. - 2−10b2 - 10 b2−10b

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x1/8⋅x7/8x ^ { 1 / 8 } \cdot x ^ { 7 / 8 }x1/8⋅x7/8

Simplify the expression. Assume all variables represent nonzero real numbers. - 48⋅454 ^ { 8 } \cdot 4 ^ { 5 }48⋅45

Simplify the expression. Assume all variables represent positive real numbers. - (5+3)(3+5)( \sqrt { 5 } + 3 ) ( \sqrt { 3 } + 5 )(5​+3)(3​+5)

Factor by any method. - 343p3−1343 p ^ { 3 } - 1343p3−1