Question 1

Factor the trinomial, if possible.
-$60 x ^ { 2 } + 35 x y + 5 y ^ { 2 }$

Accepted Answer

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

Question 2

Evaluate the expression.
-$11 + 6 ^ { 2 } - ( - 3 ) \cdot 7$

Accepted Answer

A)  308 
B)  26 
C)  182 
D)  68 
A)  308 
B)  26 
C)  182 
D)  68

Question 3

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$\left| ( - 4 ) ^ { 3 } \right| = - \left| ( 4 ) ^ { 3 } \right|$

Accepted Answer

A) True 
 B)False

Question 4

Tell whether the statement is true or false.
-$\{ x \mid x \text { is a natural number greater than } 1 \} = \{ 1,2,3 , \ldots \}$

Accepted Answer

A) True 
 B)False

Question 5

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 1 } { a } + 1 } { \frac { 1 } { a } - 1 }$$

Accepted Answer

A)  $\frac { a } { 1 - a ^ { 2 } }$ 
B)  1 
C)  $1 - a ^ { 2 }$ 
D)  $\frac { 1 + a } { 1 - a }$ 
A)  $\frac { a } { 1 - a ^ { 2 } }$ 
B)  1 
C)  $1 - a ^ { 2 }$ 
D)  $\frac { 1 + a } { 1 - a }$

Question 6

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { y } { 8 } } { \frac { 9 } { y + 6 } }$

Accepted Answer

A)  $\frac { y ( y + 6 ) } { 72 }$ 
B)  $\frac { 9 y } { 8 ( y + 6 ) }$ 
C)  $\frac { y + 6 } { 72 y }$ 
D)  $72 y ( y + 6 )$ 
A)  $\frac { y ( y + 6 ) } { 72 }$ 
B)  $\frac { 9 y } { 8 ( y + 6 ) }$ 
C)  $\frac { y + 6 } { 72 y }$ 
D)  $72 y ( y + 6 )$

Question 7

Factor the trinomial, if possible.
-$$3 x ^ { 2 } + 4 x y + y ^ { 2 }$$

Accepted Answer

A)  prime 
B)  $( 3 x + y ) ( x + y )$ 
C)  $( 3 x + y ) ( x + 3 y )$ 
D)  $( 3 x - y ) ( x - y )$ 
A)  prime 
B)  $( 3 x + y ) ( x + y )$ 
C)  $( 3 x + y ) ( x + 3 y )$ 
D)  $( 3 x - y ) ( x - y )$

Question 8

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

Accepted Answer

A)  26 
B)  22 
C)  25 
D)  28 
A)  26 
B)  22 
C)  25 
D)  28

Question 9

Factor, using the given factor. Assume all variables represent positive real numbers.
-$8 s ^ { 2 / 7 } - 3 s ^ { - 4 / 7 } ; \quad s ^ { - 4 / 7 }$

Accepted Answer

A)  $s ^ { - 4 / 7 } \left( 8 s ^ { 6 / 7 } - 3 s \right)$ 
B)  $s ^ { 1 / 3 } \left( 8 - 3 s ^ { 2 / 1 } \right)$ 
C)  $s ^ { 2 / 7 } \left( 8 s ^ { 6 / 7 } - 3 ^ { 2 / 1 } \right)$ 
D)  $s ^ { - 4 / 7 } \left( 8 s ^ { 6 / 7 } - 3 \right)$ 
A)  $s ^ { - 4 / 7 } \left( 8 s ^ { 6 / 7 } - 3 s \right)$ 
B)  $s ^ { 1 / 3 } \left( 8 - 3 s ^ { 2 / 1 } \right)$ 
C)  $s ^ { 2 / 7 } \left( 8 s ^ { 6 / 7 } - 3 ^ { 2 / 1 } \right)$ 
D)  $s ^ { - 4 / 7 } \left( 8 s ^ { 6 / 7 } - 3 \right)$

Question 10

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 8 ] { ( - 4 ) ^ { 8 } }$

Accepted Answer

A)  not a real number 
B)  16 
C)  $- 4$ 
D)  4 
A)  not a real number 
B)  16 
C)  $- 4$ 
D)  4

Question 11

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 5 / 3 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 13 / 3 } }$ 
B)  $x ^ { 13 / 3 }$ 
C)  $\frac { 1 } { \mathrm { x } ^ { 17 / 3 } }$ 
D)  $x ^ { 17 / 3 }$ 
A)  $\frac { 1 } { x ^ { 13 / 3 } }$ 
B)  $x ^ { 13 / 3 }$ 
C)  $\frac { 1 } { \mathrm { x } ^ { 17 / 3 } }$ 
D)  $x ^ { 17 / 3 }$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }$$

Accepted Answer

A)  not a real number 
B)  $- 3 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
C)  $3 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$ 
D)  $3 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
A)  not a real number 
B)  $- 3 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$ 
C)  $3 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 3 } }$ 
D)  $3 a b \sqrt [ 3 ] { a ^ { 2 } b ^ { 2 } }$

Question 13

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-Use the formula Passing Rating $\approx 85.68 \left( \frac { \mathrm { C } } { \mathrm { A } } \right) + 4.31 \left( \frac { \mathrm { Y } } { \mathrm { A } } \right) + 326.42 \left( \frac { \mathrm { T } } { \mathrm { A } } \right) - 419.07 \left( \frac { \mathrm { T } } { \mathrm { A } } \right)$, where $\mathrm { A } =$ number of passes attempted, $\mathrm { C } =$ number of passes completed, $\mathrm { Y } =$ total number of yards gained passing, $T =$ number of touchdown passes, and I = number of interceptions, to approximate the passing rating for $\mathrm { C }$. Felix. Round to the nearest tenth.

Accepted Answer

A)  82.3 
B)  83.6 
C)  82 
D)  83 
A)  82.3 
B)  83.6 
C)  82 
D)  83

Question 14

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { 4 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 8 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$$

Accepted Answer

A)  $\frac { 1 + 2 x ^ { 3 } + 6 x } { 4 }$ 
B)  $\frac { 1 - 2 x ^ { 3 } + 6 x } { 8 }$ 
C)  $\frac { 1 + 2 x ^ { 3 } - 6 x } { 4 }$ 
D)  $\frac { 1 - 2 x ^ { 3 } - 6 x } { 8 }$ 
A)  $\frac { 1 + 2 x ^ { 3 } + 6 x } { 4 }$ 
B)  $\frac { 1 - 2 x ^ { 3 } + 6 x } { 8 }$ 
C)  $\frac { 1 + 2 x ^ { 3 } - 6 x } { 4 }$ 
D)  $\frac { 1 - 2 x ^ { 3 } - 6 x } { 8 }$

Question 15

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$x y < 0$

Accepted Answer

A)  $x$ and $y$ must be negative. 
B)  $x$ and $y$ must be positive. 
C)  $x$ and $y$ have different signs. 
D)  $x$ and $y$ have the same sign. 
A)  $x$ and $y$ must be negative. 
B)  $x$ and $y$ must be positive. 
C)  $x$ and $y$ have different signs. 
D)  $x$ and $y$ have the same sign.

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Accepted Answer

A)  $10 \sqrt [ 3 ] { 35 }$ 
B)  $10 \sqrt [ 3 ] { 15 }$ 
C)  $5 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$ 
A)  $10 \sqrt [ 3 ] { 35 }$ 
B)  $10 \sqrt [ 3 ] { 15 }$ 
C)  $5 \sqrt [ 3 ] { 35 }$ 
D)  $5 \sqrt [ 3 ] { 25 }$

Question 17

Solve the problem. Round to two decimal places unless otherwise indicated.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 62,500 } { x + 125 }$. What is the cost per ton for $x = 20$ ?

Accepted Answer

A)  $\$ 3000.00$ 
B)  $\$ 431.03$ 
C)  $\$ 3125.00$ 
D)  $\$ 25.00$ 
A)  $\$ 3000.00$ 
B)  $\$ 431.03$ 
C)  $\$ 3125.00$ 
D)  $\$ 25.00$

Question 18

Find the distance between two points given their coordinates.
-Find the distance between points $R$ and $S$ on a number line, with coordinates 8 and $- 7$, respectively.

Accepted Answer

A)  $d ( R , S ) = 1$ 
B)  $d ( R , S ) = - 1$ 
C)  $d ( R , S ) = - 15$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 15$ 
A)  $d ( R , S ) = 1$ 
B)  $d ( R , S ) = - 1$ 
C)  $d ( R , S ) = - 15$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = 15$

Question 19

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$\frac { 2 ( 2 x - 3 ) ^ { 1 / 3 } - ( x - 1 ) ( 2 x - 3 ) ^ { - 2 / 3 } } { ( 2 x - 3 ) ^ { 2 / 3 } }$

Accepted Answer

A)  $\frac { 3 x + 5 } { ( 2 x + 3 ) ^ { 5 / 3 } }$ 
B)  $\frac { 3 x - 5 } { ( 2 x + 3 ) ^ { 4 / 3 } }$ 
C)  $\frac { 5 x - 5 } { ( 2 x + 3 ) ^ { 5 / 3 } }$ 
D)  $\frac { 5 x + 5 } { ( 2 x + 3 ) ^ { 4 / 3 } }$ 
A)  $\frac { 3 x + 5 } { ( 2 x + 3 ) ^ { 5 / 3 } }$ 
B)  $\frac { 3 x - 5 } { ( 2 x + 3 ) ^ { 4 / 3 } }$ 
C)  $\frac { 5 x - 5 } { ( 2 x + 3 ) ^ { 5 / 3 } }$ 
D)  $\frac { 5 x + 5 } { ( 2 x + 3 ) ^ { 4 / 3 } }$

Question 20

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 3 x ^ { - 3 } } { 9 x ^ { - 9 } }$

Accepted Answer

A)  $\frac { x ^ { 3 } } { 3 }$ 
B)  $\frac { x ^ { 6 } } { 6 }$ 
C)  $\frac { x ^ { 6 } } { 3 }$ 
D)  $\frac { x ^ { 12 } } { 3 }$ 
A)  $\frac { x ^ { 3 } } { 3 }$ 
B)  $\frac { x ^ { 6 } } { 6 }$ 
C)  $\frac { x ^ { 6 } } { 3 }$ 
D)  $\frac { x ^ { 12 } } { 3 }$

Factor the trinomial, if possible. - $60 x ^ { 2 } + 35 x y + 5 y ^ { 2 }$

Evaluate the expression. - $11 + 6 ^ { 2 } - ( - 3 ) \cdot 7$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\left| ( - 4 ) ^ { 3 } \right| = - \left| ( 4 ) ^ { 3 } \right|$

Tell whether the statement is true or false. - $\{ x \mid x \text { is a natural number greater than } 1 \} = \{ 1,2,3 , \ldots \}$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 1 } { a } + 1 } { \frac { 1 } { a } - 1 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { y } { 8 } } { \frac { 9 } { y + 6 } }$

Factor the trinomial, if possible. - $3 x ^ { 2 } + 4 x y + y ^ { 2 }$

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

Factor, using the given factor. Assume all variables represent positive real numbers. - $8 s ^ { 2 / 7 } - 3 s ^ { - 4 / 7 } ; \quad s ^ { - 4 / 7 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 8 ] { ( - 4 ) ^ { 8 } }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 5 / 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 4 \left( x ^ { 2 } - 3 \right) ^ { 3 } + 8 x \left( x ^ { 2 } - 3 \right) ^ { 4 } } { 16 \left( x ^ { 2 } - 3 \right) ^ { 3 } }$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $x y < 0$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }$

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $y = \frac { 62,500 } { x + 125 }$ . What is the cost per ton for $x = 20$ ?

Find the distance between two points given their coordinates. -Find the distance between points $R$ and $S$ on a number line, with coordinates 8 and $- 7$ , respectively.

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { 2 ( 2 x - 3 ) ^ { 1 / 3 } - ( x - 1 ) ( 2 x - 3 ) ^ { - 2 / 3 } } { ( 2 x - 3 ) ^ { 2 / 3 } }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 3 x ^ { - 3 } } { 9 x ^ { - 9 } }$

Equations and Inequalities

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Exam 1: Review of Basic Concepts

Factor the trinomial, if possible. - 60x2+35xy+5y260 x ^ { 2 } + 35 x y + 5 y ^ { 2 }60x2+35xy+5y2

Evaluate the expression. - 11+62−(−3)⋅711 + 6 ^ { 2 } - ( - 3 ) \cdot 711+62−(−3)⋅7

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣(−4)3∣=−∣(4)3∣\left| ( - 4 ) ^ { 3 } \right| = - \left| ( 4 ) ^ { 3 } \right|​(−4)3​=−​(4)3​

Tell whether the statement is true or false. - {x∣x is a natural number greater than 1}={1,2,3,…}\{ x \mid x \text { is a natural number greater than } 1 \} = \{ 1,2,3 , \ldots \}{x∣x is a natural number greater than 1}={1,2,3,…}

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1a+11a−1\frac { \frac { 1 } { a } + 1 } { \frac { 1 } { a } - 1 }a1​−1a1​+1​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - y89y+6\frac { \frac { y } { 8 } } { \frac { 9 } { y + 6 } }y+69​8y​​

Factor the trinomial, if possible. - 3x2+4xy+y23 x ^ { 2 } + 4 x y + y ^ { 2 }3x2+4xy+y2

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 - 9x2−4y−a9 x ^ { 2 } - 4 y - a9x2−4y−a

Factor, using the given factor. Assume all variables represent positive real numbers. - 8s2/7−3s−4/7;s−4/78 s ^ { 2 / 7 } - 3 s ^ { - 4 / 7 } ; \quad s ^ { - 4 / 7 }8s2/7−3s−4/7;s−4/7

Simplify the expression. Assume all variables represent positive real numbers. - (−4)88\sqrt [ 8 ] { ( - 4 ) ^ { 8 } }8(−4)8​

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (x1/3)2(x3)5/3\frac { \left( x ^ { 1 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 5 / 3 } }(x3)5/3(x1/3)2​

Simplify the expression. Assume all variables represent positive real numbers. - −27a8b53\sqrt [ 3 ] { - 27 a ^ { 8 } b ^ { 5 } }3−27a8b5​

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - xy<0x y < 0xy<0

Simplify the expression. Assume all variables represent positive real numbers. - 1753⋅253\sqrt [ 3 ] { 175 } \cdot \sqrt [ 3 ] { 25 }3175​⋅325​

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by y=62,500x+125y = \frac { 62,500 } { x + 125 }y=x+12562,500​ . What is the cost per ton for x=20x = 20x=20 ?

Find the distance between two points given their coordinates. -Find the distance between points RRR and SSS on a number line, with coordinates 8 and −7- 7−7 , respectively.

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 3x−39x−9\frac { 3 x ^ { - 3 } } { 9 x ^ { - 9 } }9x−93x−3​