Question 1

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$$

Accepted Answer

A)  True 
B)  False; $\left| ( - 5 ) ^ { 3 } \right| = 5 ^ { 3 }$

Question 2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 } { 5 } ( - 5 y + 15 x - 5 z )$$

Accepted Answer

A)  $- 4 y - 12 x - 4 z$ 
B)  $- 4 y - 12 x + 4 z$ 
C)  $- 4 y + 12 x + 4 z$ 
D)  $- 4 y + 12 x - 4 z$

Question 3

Factor the trinomial, if possible.
-$$x ^ { 2 } + 4 x y - 192 y ^ { 2 }$$

Accepted Answer

A)  $( x + 16 y ) ( x - 12 y )$ 
B)  prime 
C)  $( x - 16 y ) ( x + y )$ 
D)  $( x - 16 y ) ( x + 12 y )$

Question 4

Find the product or quotient.
-$$\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }$$

Accepted Answer

A)  $\frac { 8 ( x + 8 ) ^ { 2 } } { 15 x ^ { 2 } ( 9 x + 8 ) }$ 
B)  $\frac { 40 } { 3 x ^ { 4 } ( 9 x + 8 ) }$ 
C)  $\frac { 3 x ^ { 4 } } { 40 ( 9 x + 8 ) }$ 
D)  $\frac { 3 x ^ { 3 } } { 40 ( 9 x + 8 ) }$

Question 5

Factor by grouping.
-$$6 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 6$$

Accepted Answer

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

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 144 } + \sqrt { 16 }$

Accepted Answer

A)  4 
B)  $4 \sqrt { 10 }$ 
C)  16 
D)  8

Question 7

Find the domain of the expression.
-$$\frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }$$

Accepted Answer

A)  $\left\{ \left\{ x \mid x \neq \frac { 4 } { 3 } , - 2 \right\} \right.$ 
B)  $\left\{ \left\{ x \mid x \neq \frac { 3 } { 4 } , - 2 \right\} \right.$ 
C)  $\left\{ \left\{ x \mid x \neq - \frac { 3 } { 4 } , 2 \right\} \right.$ 
D)  all real numbers

Question 8

Evaluate the expression.
-Let $x = - 1 , y = 4$. Evaluate $\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }$

Accepted Answer

A)  $\frac { 24 } { 7 }$ 
B)  $- \frac { 16 } { 7 }$. 
C)  $- \frac { 16 } { 17 }$ 
D)  $- \frac { 16 } { 17 }$.

Question 9

Decide whether the expression has been simplified correctly.
-$4 ^ { 0 } x = 0$

Accepted Answer

A)  Simplified correctly 
B)  Not simplified correctly

Question 10

Determine the degree of the polynomial.
-$3 a ^ { 2 } + 16 a ^ { 5 } - 8 a$

Accepted Answer

A)  7 
B)  5 
C)  3 
D)  8

Question 11

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }$$

Accepted Answer

A)  $x ^ { 25 / 3 }$ 
B)  $\frac { 1 } { x ^ { 17 / 3 } }$ 
C)  $\frac { 1 } { x ^ { 25 / 3 } }$ 
D)  $x ^ { 17 / 3 }$

Question 12

Write the expression in lowest terms.
-$$\frac { 5 x + 20 } { 3 x + 12 }$$

Accepted Answer

A)  1 
B)  $\frac { x + 4 } { x + 12 }$ 
C)  $\frac { 5 } { 3 }$ 
D)  $x + 4$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }$$

Accepted Answer

A)  $- \frac { \sqrt { 210 } } { 7 }$ 
B)  $\frac { 5 \sqrt { 6 } } { 7 }$ 
C)  $\frac { 5 \sqrt { 6 } } { 49 }$ 
D)  $\frac { 7 \sqrt { 6 } } { 7 }$

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$- \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right)$$

Accepted Answer

A)  $\frac { 5 } { 2 } y + \frac { 1 } { 5 } x + \frac { 1 } { 2 }$ 
B)  $\frac { 5 } { 2 } y + \frac { 1 } { 5 } x - \frac { 1 } { 2 }$ 
C)  $\frac { 5 } { 2 } y - \frac { 1 } { 5 } x - \frac { 1 } { 2 }$ 
D)  $\frac { 5 } { 2 } y - \frac { 1 } { 5 } x + \frac { 1 } { 2 }$

Question 15

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the
-In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $\mathrm { x } : \mathrm { y } = \frac { 0.37 \mathrm { x } } { 100.5 - \mathrm { x } }$. How many hours of study are needed to score $82 ?$

Accepted Answer

A)  $1.64 \mathrm { hr }$ 
B)  $16.40 \mathrm { hr }$ 
C)  $4.22 \mathrm { hr }$ 
D)  $101.04 \mathrm { hr }$

Question 16

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }$$

Accepted Answer

A)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 3 }$ 
B)  $\frac { \sqrt { 21 } - 2 \sqrt { 3 } } { 9 }$ 
C)  $\frac { \sqrt { 21 } + 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 3 \sqrt { 21 } + 73 } { 14 }$

Question 17

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 4,5,6,7,8,9,10,11,12,13,14 \} , \mathrm { M } = \{ 4,6,8,10 \} , \mathrm { N } = \{ 5,7,9,11,13 \} , \mathrm { Q } = \{ 4,6,8,10,12,14 \}$, and $\mathrm { R } = \{ 4,5,6,7 \}$.

$( \mathrm { N } \cup \mathrm { R } ) \cap \mathrm { Q }$

Accepted Answer

A)  $\{ 4 \}$ 
B)  $\varnothing ; \mathrm { N }$ and $\mathrm { R }$ are disjoint sets. 
C)  $\{ 4,6 \}$ 
D)  $\{ 6 \}$

Question 18

Factor the trinomial, if possible.
-$$16 x ^ { 2 } - 56 x - 32$$

Accepted Answer

A)  $( 2 x - 1 ) ( 8 x + 32 )$ 
B)  $8 ( 2 x + 1 ) ( x - 4 )$ 
C)  $( 16 x - 8 ) ( x + 4 )$ 
D)  $8 ( 2 x - 1 ) ( x + 4 )$

Question 19

Factor by any method.
-$24 k ^ { 3 } m - 375 m ^ { 4 }$

Accepted Answer

A)  $\left( 6 \mathrm {~km} - 15 \mathrm {~m} ^ { 2 } \right) \left( 4 \mathrm { k } ^ { 2 } + 25 \mathrm {~m} ^ { 2 } \right)$ 
B)  $3 m ( 8 k - 5 m ) \left( k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
C)  $3 m ( 2 k - 5 m ) \left( 4 k ^ { 2 } + 10 k m + 25 m ^ { 2 } \right)$ 
D)  $3 m \left( 2 k + 5 m ^ { 2 } \right) \left( 4 k ^ { 2 } - 10 k m + 25 m ^ { 2 } \right)$

Question 20

Factor the trinomial, if possible.
-$$9 x ^ { 2 } - 39 x - 30$$

Accepted Answer

A)  $( 3 x + 2 ) ( 3 x - 15 )$ 
B)  $3 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 9 x + 6 ) ( x - 5 )$ 
D)  $3 ( 3 x - 2 ) ( x + 5 )$

Exam 1: Review of Basic Concepts

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 4 } { 5 } ( - 5 y + 15 x - 5 z )$

Factor the trinomial, if possible. - $x ^ { 2 } + 4 x y - 192 y ^ { 2 }$

Find the product or quotient. - $\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }$

Factor by grouping. - $6 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 6$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 144 } + \sqrt { 16 }$

Find the domain of the expression. - $\frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }$

Evaluate the expression. -Let $x = - 1 , y = 4$ . Evaluate $\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }$

Decide whether the expression has been simplified correctly. - $4 ^ { 0 } x = 0$

Determine the degree of the polynomial. - $3 a ^ { 2 } + 16 a ^ { 5 } - 8 a$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }$

Write the expression in lowest terms. - $\frac { 5 x + 20 } { 3 x + 12 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right)$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }$

Factor the trinomial, if possible. - $16 x ^ { 2 } - 56 x - 32$

Factor by any method. - $24 k ^ { 3 } m - 375 m ^ { 4 }$

Factor the trinomial, if possible. - $9 x ^ { 2 } - 39 x - 30$

Exam 1: Review of Basic Concepts

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣(−5) 3∣=−∣(5) 3∣\left| ( - 5 ) ^ { 3 } \right| = - \left| ( 5 ) ^ { 3 } \right|​(−5) 3​=−​(5) 3​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 45(−5y+15x−5z) \frac { 4 } { 5 } ( - 5 y + 15 x - 5 z ) 54​(−5y+15x−5z)

Factor the trinomial, if possible. - x2+4xy−192y2x ^ { 2 } + 4 x y - 192 y ^ { 2 }x2+4xy−192y2

Find the product or quotient. - 9x2+64x−645x−20⋅x2−4x81x2−64÷8x+643x3\frac { 9 x ^ { 2 } + 64 x - 64 } { 5 x - 20 } \cdot \frac { x ^ { 2 } - 4 x } { 81 x ^ { 2 } - 64 } \div \frac { 8 x + 64 } { 3 x ^ { 3 } }5x−209x2+64x−64​⋅81x2−64x2−4x​÷3x38x+64​

Factor by grouping. - 6x4−4x2−9x2+66 x ^ { 4 } - 4 x ^ { 2 } - 9 x ^ { 2 } + 66x4−4x2−9x2+6

Simplify the expression. Assume all variables represent positive real numbers. - 144+16\sqrt { 144 } + \sqrt { 16 }144​+16​

Find the domain of the expression. - 6x−7(4x−3) (x+2) \frac { 6 x - 7 } { ( 4 x - 3 ) ( x + 2 ) }(4x−3) (x+2) 6x−7​

Evaluate the expression. -Let x=−1,y=4x = - 1 , y = 4x=−1,y=4 . Evaluate ∣x−3∣−∣5y∣∣3y+5x∣\frac { | x - 3 | - | 5 y | } { | 3 y + 5 x | }∣3y+5x∣∣x−3∣−∣5y∣​

Decide whether the expression has been simplified correctly. - 40x=04 ^ { 0 } x = 040x=0

Determine the degree of the polynomial. - 3a2+16a5−8a3 a ^ { 2 } + 16 a ^ { 5 } - 8 a3a2+16a5−8a

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (x2/3) 2(x3) 7/3\frac { \left( x ^ { 2 / 3 } \right) ^ { 2 } } { \left( x ^ { 3 } \right) ^ { 7 / 3 } }(x3) 7/3(x2/3) 2​

Write the expression in lowest terms. - 5x+203x+12\frac { 5 x + 20 } { 3 x + 12 }3x+125x+20​

Simplify the expression. Assume all variables represent positive real numbers. - 2167−267+649\frac { \sqrt { 216 } } { 7 } - \frac { 2 \sqrt { 6 } } { 7 } + \frac { \sqrt { 6 } } { \sqrt { 49 } }7216​​−726​​+49​6​​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −23(−154y−310x+34) - \frac { 2 } { 3 } \left( - \frac { 15 } { 4 } y - \frac { 3 } { 10 } x + \frac { 3 } { 4 } \right) −32​(−415​y−103​x+43​)

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 37+2\frac { \sqrt { 3 } } { \sqrt { 7 } + 2 }7​+23​​

Factor the trinomial, if possible. - 16x2−56x−3216 x ^ { 2 } - 56 x - 3216x2−56x−32

Factor by any method. - 24k3m−375m424 k ^ { 3 } m - 375 m ^ { 4 }24k3m−375m4

Factor the trinomial, if possible. - 9x2−39x−309 x ^ { 2 } - 39 x - 309x2−39x−30