Question 1

Factor by any method.
-$$t ^ { 3 } + 8$$

Accepted Answer

A)  $( t - 2 ) \left( t ^ { 2 } + 2 t + 4 \right)$ 
B)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
C)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$ 
D)  $( \mathrm { t } - 8 ) \left( \mathrm { t } ^ { 2 } - 1 \right)$ 
A)  $( t - 2 ) \left( t ^ { 2 } + 2 t + 4 \right)$ 
B)  $( t + 2 ) \left( t ^ { 2 } - 2 t + 4 \right)$ 
C)  $( t + 2 ) \left( t ^ { 2 } + 4 \right)$ 
D)  $( \mathrm { t } - 8 ) \left( \mathrm { t } ^ { 2 } - 1 \right)$

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 250 }$

Accepted Answer

A)  15 
B)  $2 \sqrt [ 3 ] { 5 }$ 
C)  $5 \sqrt [ 3 ] { 2 }$ 
D)  6 
A)  15 
B)  $2 \sqrt [ 3 ] { 5 }$ 
C)  $5 \sqrt [ 3 ] { 2 }$ 
D)  6

Question 3

Write in radical form. Assume all variables represent positive real numbers.
-$( 7 x ) ^ { 1 / 3 }$

Accepted Answer

A)  $\frac { \sqrt { 7 x } } { 3 }$ 
B)  $\sqrt [ 1 / 3 ] { 7 x }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 7 x } }$ 
D)  $\sqrt [ 3 ] { 7 x }$ 
A)  $\frac { \sqrt { 7 x } } { 3 }$ 
B)  $\sqrt [ 1 / 3 ] { 7 x }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 7 x } }$ 
D)  $\sqrt [ 3 ] { 7 x }$

Question 4

Find the product.
-$$( 10 + x ) ( 4 x + 2 )$$

Accepted Answer

A)  $4 x ^ { 2 } + 41 x + 20$ 
B)  $4 x ^ { 2 } + 20 x + 42$ 
C)  $4 x ^ { 2 } + 42 x + 20$ 
D)  $x ^ { 2 } + 42 x + 42$ 
A)  $4 x ^ { 2 } + 41 x + 20$ 
B)  $4 x ^ { 2 } + 20 x + 42$ 
C)  $4 x ^ { 2 } + 42 x + 20$ 
D)  $x ^ { 2 } + 42 x + 42$

Question 5

Evaluate the expression.
-$27^{4 / 3}$

Accepted Answer

A)  243 
B)  2187 
C)  81 
D)  729 
A)  243 
B)  2187 
C)  81 
D)  729

Question 6

Solve the problem. Round to two decimal places unless otherwise indicated.
-In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x : y = \frac { 0.37 x } { 100.5 - x }$. How many hours of study are needed to score 98 ?

Accepted Answer

A)  $39.35 \mathrm { hr }$ 
B)  $100.12 \mathrm { hr }$ 
C)  $145.00 \mathrm { hr }$ 
D)  $14.50 \mathrm { hr }$ 
A)  $39.35 \mathrm { hr }$ 
B)  $100.12 \mathrm { hr }$ 
C)  $145.00 \mathrm { hr }$ 
D)  $14.50 \mathrm { hr }$

Question 7

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 + 5. Find a formula for the area of the largest square as a binomial raised to a power. Write the expansion of this binomial.

Accepted Answer

A)  $x ^ { 2 } - 10 x + 25$ 
B)  $x ^ { 2 } - 25$ 
C)  $x ^ { 2 } + 10 x + 25$ 
D)  $x ^ { 2 } + 25$ 
A)  $x ^ { 2 } - 10 x + 25$ 
B)  $x ^ { 2 } - 25$ 
C)  $x ^ { 2 } + 10 x + 25$ 
D)  $x ^ { 2 } + 25$

Question 8

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 } \left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }$$

Accepted Answer

A)  $\frac { \mathrm { y } ^ { 59 / 10 } } { \mathrm {~b} ^ { 28 / 5 } }$ 
B)  $\frac { b ^ { 28 / 5 } } { y ^ { 59 / 10 } }$ 
C)  $\frac { y ^ { 69 / 10 } } { b ^ { 32 / 5 } }$ 
D)  $\frac { b ^ { 32 / 5 } } { y ^ { 69 / 10 } }$ 
A)  $\frac { \mathrm { y } ^ { 59 / 10 } } { \mathrm {~b} ^ { 28 / 5 } }$ 
B)  $\frac { b ^ { 28 / 5 } } { y ^ { 59 / 10 } }$ 
C)  $\frac { y ^ { 69 / 10 } } { b ^ { 32 / 5 } }$ 
D)  $\frac { b ^ { 32 / 5 } } { y ^ { 69 / 10 } }$

Question 9

Factor by any method.
-$$y ^ { 2 } - 36$$

Accepted Answer

A)  $( y + 36 ) ( y - 36 )$ 
B)  $( y - 6 ) ( y - 6 )$ 
C)  $\left( y ^ { 2 } + 6 \right) \left( y ^ { 2 } - 6 \right)$ 
D)  $( y + 6 ) ( y - 6 )$ 
A)  $( y + 36 ) ( y - 36 )$ 
B)  $( y - 6 ) ( y - 6 )$ 
C)  $\left( y ^ { 2 } + 6 \right) \left( y ^ { 2 } - 6 \right)$ 
D)  $( y + 6 ) ( y - 6 )$

Question 10

Factor by grouping.
-$20 x ^ { 2 } + 12 x y - 25 x y - 15 y ^ { 2 }$

Accepted Answer

A)  $( 20 x - 5 y ) ( x + 3 y )$ 
B)  $( 4 x - 5 y ) ( 5 x + 3 y )$ 
C)  $( 4 x + 5 y ) ( 5 x + 3 y )$ 
D)  $( 4 x - 5 ) ( 5 x + 3 )$ 
A)  $( 20 x - 5 y ) ( x + 3 y )$ 
B)  $( 4 x - 5 y ) ( 5 x + 3 y )$ 
C)  $( 4 x + 5 y ) ( 5 x + 3 y )$ 
D)  $( 4 x - 5 ) ( 5 x + 3 )$

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 98 } } { 7 } - \frac { 3 \sqrt { 2 } } { 7 } + \frac { \sqrt { 2 } } { \sqrt { 49 } }$

Accepted Answer

A)  $\frac { 7 \sqrt { 2 } } { 7 }$ 
B)  $- \frac { \sqrt { 96 } } { 7 }$ 
C)  $\frac { 5 \sqrt { 2 } } { 49 }$ 
D)  $\frac { 5 \sqrt { 2 } } { 7 }$ 
A)  $\frac { 7 \sqrt { 2 } } { 7 }$ 
B)  $- \frac { \sqrt { 96 } } { 7 }$ 
C)  $\frac { 5 \sqrt { 2 } } { 49 }$ 
D)  $\frac { 5 \sqrt { 2 } } { 7 }$

Question 12

Find the product. Assume variables represent positive real numbers.
-$$6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 3 x \right)$$

Accepted Answer

A)  $6 x ^ { 17 / 5 } - \frac { 18 } { x ^ { 11 / 5 } }$ 
B)  $6 x ^ { 17 / 5 } - 18 x ^ { 11 / 5 }$ 
C)  $\frac { 6 } { x ^ { 17 / 5 } } - 18 x ^ { 11 / 5 }$ 
D)  $\frac { 6 } { x ^ { 17 / 5 } } - \frac { 18 } { x ^ { 11 / 5 } }$ 
A)  $6 x ^ { 17 / 5 } - \frac { 18 } { x ^ { 11 / 5 } }$ 
B)  $6 x ^ { 17 / 5 } - 18 x ^ { 11 / 5 }$ 
C)  $\frac { 6 } { x ^ { 17 / 5 } } - 18 x ^ { 11 / 5 }$ 
D)  $\frac { 6 } { x ^ { 17 / 5 } } - \frac { 18 } { x ^ { 11 / 5 } }$

Question 13

Write the expression in lowest terms.
-$\frac { x ^ { 3 } + 125 } { x + 5 }$

Accepted Answer

A)  $x ^ { 2 } - 5 x + 25$ 
B)  $x ^ { 2 } + 25$ 
C)  $x ^ { 2 } - 25 x + 5$ 
D)  $x ^ { 2 } - 5$ 
A)  $x ^ { 2 } - 5 x + 25$ 
B)  $x ^ { 2 } + 25$ 
C)  $x ^ { 2 } - 25 x + 5$ 
D)  $x ^ { 2 } - 5$

Question 14

Identify the set as finite or infinite.
-$\{ x \mid x$ is a fraction between 0 and $1 \}$

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-(2 ∙ 5) ∙ 8 = 2 ∙ (5 ∙ 8)

Accepted Answer

A)  Distributive 
B)  Commutative 
C)  Identity 
D)  Associative 
A)  Distributive 
B)  Commutative 
C)  Identity 
D)  Associative

Question 17

Evaluate the expression.
-$$\left( - \frac { 8 } { 125 } \right) ^ { - 2 / 3 }$$

Accepted Answer

A)  $- \frac { 4 } { 25 }$ 
B)  $\frac { 25 } { 4 }$ 
C)  $\frac { 4 } { 25 }$ 
D)  not a real number 
A)  $- \frac { 4 } { 25 }$ 
B)  $\frac { 25 } { 4 }$ 
C)  $\frac { 4 } { 25 }$ 
D)  not a real number

Question 18

Find the product.
-$$( p + 7 q ) ( p - 7 q )$$

Accepted Answer

A)  $p ^ { 2 } - 14 q ^ { 2 }$ 
B)  $p ^ { 2 } - 14 p q - 49 q ^ { 2 }$ 
C)  $p ^ { 2 } + 14 p q - 49 q ^ { 2 }$ 
D)  $p ^ { 2 } - 49 q ^ { 2 }$ 
A)  $p ^ { 2 } - 14 q ^ { 2 }$ 
B)  $p ^ { 2 } - 14 p q - 49 q ^ { 2 }$ 
C)  $p ^ { 2 } + 14 p q - 49 q ^ { 2 }$ 
D)  $p ^ { 2 } - 49 q ^ { 2 }$

Question 19

Find the product.
-$$\left( 4 m ^ { 3 } z ^ { 4 } \right) \left( 2 m ^ { 2 } z ^ { 2 } \right)$$

Accepted Answer

A)  $8 m ^ { 5 } z$ 
B)  $8 m ^ { 5 } z ^ { 6 }$ 
C)  $8 \mathrm { mz } ^ { 6 }$ 
D)  $8 \mathrm { mz } ^ { 5 }$ 
A)  $8 m ^ { 5 } z$ 
B)  $8 m ^ { 5 } z ^ { 6 }$ 
C)  $8 \mathrm { mz } ^ { 6 }$ 
D)  $8 \mathrm { mz } ^ { 5 }$

Question 20

Divide.
-$\frac { - 20 x ^ { 4 } - 16 x ^ { 3 } - 16 x ^ { 2 } } { - 4 x ^ { 3 } }$

Accepted Answer

A)  $5 x - 16 x ^ { 3 } + \frac { 4 } { x }$ 
B)  $5 x + 4 + \frac { 4 } { x }$ 
C)  $5 x + 4$ 
D)  $9 x + 4$ 
A)  $5 x - 16 x ^ { 3 } + \frac { 4 } { x }$ 
B)  $5 x + 4 + \frac { 4 } { x }$ 
C)  $5 x + 4$ 
D)  $9 x + 4$

Factor by any method. - $t ^ { 3 } + 8$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 250 }$

Write in radical form. Assume all variables represent positive real numbers. - $( 7 x ) ^ { 1 / 3 }$

Find the product. - $( 10 + x ) ( 4 x + 2 )$

Evaluate the expression. - $27^{4 / 3}$

Solve the problem. Round to two decimal places unless otherwise indicated. -In the following formula, $y$ is the minimum number of hours of studying required to attain a test score of $x : y = \frac { 0.37 x } { 100.5 - x }$ . How many hours of study are needed to score 98 ?

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 } \left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }$

Factor by any method. - $y ^ { 2 } - 36$

Factor by grouping. - $20 x ^ { 2 } + 12 x y - 25 x y - 15 y ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 98 } } { 7 } - \frac { 3 \sqrt { 2 } } { 7 } + \frac { \sqrt { 2 } } { \sqrt { 49 } }$

Find the product. Assume variables represent positive real numbers. - $6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 3 x \right)$

Write the expression in lowest terms. - $\frac { x ^ { 3 } + 125 } { x + 5 }$

Identify the set as finite or infinite. - $\{ x \mid x$ is a fraction between 0 and $1 \}$

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

Identify the property illustrated by the statement. Assume all variables represent real numbers. -(2 ∙ 5) ∙ 8 = 2 ∙ (5 ∙ 8)

Evaluate the expression. - $\left( - \frac { 8 } { 125 } \right) ^ { - 2 / 3 }$

Find the product. - $( p + 7 q ) ( p - 7 q )$

Find the product. - $\left( 4 m ^ { 3 } z ^ { 4 } \right) \left( 2 m ^ { 2 } z ^ { 2 } \right)$

Divide. - $\frac { - 20 x ^ { 4 } - 16 x ^ { 3 } - 16 x ^ { 2 } } { - 4 x ^ { 3 } }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Trigonometric Identities and Equations

Applications of Trigonometry

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Exam 12: Review of Basic Concepts

Factor by any method. - t3+8t ^ { 3 } + 8t3+8

Simplify the expression. Assume all variables represent positive real numbers. - 2503\sqrt [ 3 ] { 250 }3250​

Write in radical form. Assume all variables represent positive real numbers. - (7x)1/3( 7 x ) ^ { 1 / 3 }(7x)1/3

Find the product. - (10+x)(4x+2)( 10 + x ) ( 4 x + 2 )(10+x)(4x+2)

Evaluate the expression. - 274/327^{4 / 3}274/3

Factor by any method. - y2−36y ^ { 2 } - 36y2−36

Factor by grouping. - 20x2+12xy−25xy−15y220 x ^ { 2 } + 12 x y - 25 x y - 15 y ^ { 2 }20x2+12xy−25xy−15y2

Simplify the expression. Assume all variables represent positive real numbers. - 987−327+249\frac { \sqrt { 98 } } { 7 } - \frac { 3 \sqrt { 2 } } { 7 } + \frac { \sqrt { 2 } } { \sqrt { 49 } }798​​−732​​+49​2​​

Find the product. Assume variables represent positive real numbers. - 6x6/5(x11/5−3x)6 x ^ { 6 / 5 } \left( x ^ { 11 / 5 } - 3 x \right)6x6/5(x11/5−3x)

Write the expression in lowest terms. - x3+125x+5\frac { x ^ { 3 } + 125 } { x + 5 }x+5x3+125​

Identify the set as finite or infinite. - {x∣x\{ x \mid x{x∣x is a fraction between 0 and 1}1 \}1}

Decide whether the expression has been simplified correctly. - 40x=4x4 ^ { 0 } \mathrm { x } = 4 \mathrm { x }40x=4x