Question 1

Factor the trinomial, if possible.
-$$12 z ^ { 2 } + 7 z - 12$$

Accepted Answer

A)  $( 12 z - 3 ) ( z - 12 )$ 
B)  $( 4 \mathrm { z } + 3 ) ( 3 \mathrm { z } - 4 )$ 
C)  $( 12 z - 3 ) ( z + 4 )$ 
D)  $( 4 z - 3 ) ( 3 z + 4 )$ 
A)  $( 12 z - 3 ) ( z - 12 )$ 
B)  $( 4 \mathrm { z } + 3 ) ( 3 \mathrm { z } - 4 )$ 
C)  $( 12 z - 3 ) ( z + 4 )$ 
D)  $( 4 z - 3 ) ( 3 z + 4 )$

Question 2

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x } { y } > 0$$

Accepted Answer

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

Question 3

Use the distributive property to rewrite a sum as a product or the product as a sum.
--(6 + 9x)

Accepted Answer

A)  6 + 9x 
B)  -6 - 9x 
C)  -6 + 9x 
D)  6 - 9x 
A)  6 + 9x 
B)  -6 - 9x 
C)  -6 + 9x 
D)  6 - 9x

Question 4

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$

Accepted Answer

A)  $x ^ { 22 / 7 }$ 
B)  $\frac { 1 } { x ^ { 22 / 7 } }$ 
C)  $\frac { 1 } { x ^ { 11 / 5 } }$ 
D)  $x ^ { 11 / 5 }$ 
A)  $x ^ { 22 / 7 }$ 
B)  $\frac { 1 } { x ^ { 22 / 7 } }$ 
C)  $\frac { 1 } { x ^ { 11 / 5 } }$ 
D)  $x ^ { 11 / 5 }$

Question 5

Provide an appropriate response.
-The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$, where $b$ is the length of the base, $a$ is the length of the top, and $h$ is the height. Visualize the figure if $a = b = h$. What would the figure be?

Accepted Answer

A)  A cylinder 
B)  A cube 
C)  A sphere 
D)  A cone 
A)  A cylinder 
B)  A cube 
C)  A sphere 
D)  A cone

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$\frac { 1 } { \sqrt { 3 } } + \frac { 5 } { \sqrt { 27 } } - \frac { 3 } { \sqrt { 12 } }$

Accepted Answer

A)  $- \frac { 1 } { 2 } \sqrt { 3 }$ 
B)  $\frac { 7 } { 18 } \sqrt { 21 }$ 
C)  $\frac { 1 } { 2 } \frac { 1 } { \sqrt { 3 } }$ 
D)  $\frac { 7 } { 18 } \sqrt { 3 }$ 
A)  $- \frac { 1 } { 2 } \sqrt { 3 }$ 
B)  $\frac { 7 } { 18 } \sqrt { 21 }$ 
C)  $\frac { 1 } { 2 } \frac { 1 } { \sqrt { 3 } }$ 
D)  $\frac { 7 } { 18 } \sqrt { 3 }$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$9 \sqrt { 3 } + 2 \sqrt { 3 }$

Accepted Answer

A)  $11 \sqrt { 3 }$ 
B)  33 
C)  $18 \sqrt { 3 }$ 
D)  $11 \sqrt { 6 }$ 
A)  $11 \sqrt { 3 }$ 
B)  33 
C)  $18 \sqrt { 3 }$ 
D)  $11 \sqrt { 6 }$

Question 8

Solve the problem.
-The length of the diagonal of a rectangle is given by $D = \sqrt { L ^ { 2 } + W ^ { 2 } }$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 83 inches long and 22 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Accepted Answer

A)  $80 \mathrm { in }$. 
B)  $10.2 \mathrm { in }$. 
C)  $42.7 \mathrm { in }$. 
D)  $85.9 \mathrm { in }$. 
A)  $80 \mathrm { in }$. 
B)  $10.2 \mathrm { in }$. 
C)  $42.7 \mathrm { in }$. 
D)  $85.9 \mathrm { in }$.

Question 9

Evaluate the expression.
-$$( - 8 ) ^ { 2 / 3 }$$

Accepted Answer

A)  not a real number 
B)  $- 2$ 
C)  4 
D)  $- 4$ 
A)  not a real number 
B)  $- 2$ 
C)  4 
D)  $- 4$

Question 10

Tell whether the statement is true or false.
-$$\{ 2,4,5,7 \} \cup \varnothing = \{ 2,4,5,7 \}$$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 11

Factor the trinomial, if possible.
-$$9 z ^ { 2 } + 6 z - 8$$

Accepted Answer

A)  $( 3 z + 4 ) ( 3 z - 2 )$ 
B)  $( 3 z - 4 ) ( 3 z + 2 )$ 
C)  $( 9 z + 1 ) ( z - 8 )$ 
D)  $( 9 z + 4 ) ( z - 2 )$ 
A)  $( 3 z + 4 ) ( 3 z - 2 )$ 
B)  $( 3 z - 4 ) ( 3 z + 2 )$ 
C)  $( 9 z + 1 ) ( z - 8 )$ 
D)  $( 9 z + 4 ) ( z - 2 )$

Question 12

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

Accepted Answer

A)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } - 9 } { a ^ { 2 } x + 9 }$ 
B)  $\frac { a ^ { 2 } x + 6 a \sqrt { x } - 9 } { a ^ { 2 } x - 9 }$ 
C)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x - 9 }$ 
D)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x + 9 }$ 
A)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } - 9 } { a ^ { 2 } x + 9 }$ 
B)  $\frac { a ^ { 2 } x + 6 a \sqrt { x } - 9 } { a ^ { 2 } x - 9 }$ 
C)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x - 9 }$ 
D)  $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x + 9 }$

Question 13

Factor the trinomial, if possible.
-$$2 x ^ { 3 } + 4 x ^ { 2 } y - 30 x y ^ { 2 }$$

Accepted Answer

A)  $\left( 2 x ^ { 2 } + 6 x y \right) ( x - 5 y )$ 
B)  $2 x ( x - 3 y ) ( x + 5 y )$ 
C)  $( x - 3 y ) \left( 2 x ^ { 2 } + 10 x y \right)$ 
D)  $2 x ( x + 3 y ) ( x - 5 y )$ 
A)  $\left( 2 x ^ { 2 } + 6 x y \right) ( x - 5 y )$ 
B)  $2 x ( x - 3 y ) ( x + 5 y )$ 
C)  $( x - 3 y ) \left( 2 x ^ { 2 } + 10 x y \right)$ 
D)  $2 x ( x + 3 y ) ( x - 5 y )$

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { 6 } { y } } { \frac { 4 } { y + 6 } }$

Accepted Answer

A)  $\frac { 2 y } { 3 ( y + 6 ) }$ 
B)  $\frac { 3 ( y + 6 ) } { 2 y }$ 
C)  $\frac { y + 6 } { 24 y }$ 
D)  $24 y ( y + 6 )$ 
A)  $\frac { 2 y } { 3 ( y + 6 ) }$ 
B)  $\frac { 3 ( y + 6 ) } { 2 y }$ 
C)  $\frac { y + 6 } { 24 y }$ 
D)  $24 y ( y + 6 )$

Question 15

Solve the problem.
-The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss).

The absolute value of the profit or loss was smallest in

Accepted Answer

A)  December 
B)  February 
C)  June 
D)  January 
A)  December 
B)  February 
C)  June 
D)  January

Question 16

Factor out the greatest common factor. Simplify the factors, if possible.
-$48 x ^ { 8 } y ^ { 9 } - 36 x ^ { 3 } y ^ { 6 } - 42 x ^ { 6 } y ^ { 4 }$

Accepted Answer

A)  $x ^ { 3 } y ^ { 4 } \left( 48 x ^ { 5 } y ^ { 5 } - 36 y ^ { 2 } - 42 x ^ { 3 } \right)$ 
B)  $6 x ^ { 3 } \left( 8 x ^ { 5 } y ^ { 9 } - 6 y ^ { 6 } - 7 x ^ { 3 } y ^ { 4 } \right)$ 
C)  $6 \left( 8 x ^ { 8 } y ^ { 9 } - 6 x ^ { 3 } y ^ { 6 } - 7 x ^ { 6 } y ^ { 4 } \right)$ 
D)  $6 x ^ { 3 } y ^ { 4 } \left( 8 x ^ { 5 } y ^ { 5 } - 6 y ^ { 2 } - 7 x ^ { 3 } \right)$ 
A)  $x ^ { 3 } y ^ { 4 } \left( 48 x ^ { 5 } y ^ { 5 } - 36 y ^ { 2 } - 42 x ^ { 3 } \right)$ 
B)  $6 x ^ { 3 } \left( 8 x ^ { 5 } y ^ { 9 } - 6 y ^ { 6 } - 7 x ^ { 3 } y ^ { 4 } \right)$ 
C)  $6 \left( 8 x ^ { 8 } y ^ { 9 } - 6 x ^ { 3 } y ^ { 6 } - 7 x ^ { 6 } y ^ { 4 } \right)$ 
D)  $6 x ^ { 3 } y ^ { 4 } \left( 8 x ^ { 5 } y ^ { 5 } - 6 y ^ { 2 } - 7 x ^ { 3 } \right)$

Question 17

Find the domain of the expression.
-$\frac { 8 p } { p - m }$

Accepted Answer

A)  $\{ p \mid p \neq 0$ and $m \mid m \neq 0 \}$ 
B)  $\{ p \mid p \neq m \}$ 
C)  $\{ p \mid p \neq - m \}$ 
D)  $\{ p \mid p \neq 1$ and $m \mid m \neq 1 \}$ 
A)  $\{ p \mid p \neq 0$ and $m \mid m \neq 0 \}$ 
B)  $\{ p \mid p \neq m \}$ 
C)  $\{ p \mid p \neq - m \}$ 
D)  $\{ p \mid p \neq 1$ and $m \mid m \neq 1 \}$

Question 18

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 4 x ^ { - 4 } } { 8 x ^ { - 8 } }$

Accepted Answer

A)  $\frac { x ^ { 12 } } { 2 }$ 
B)  $\frac { x ^ { 4 } } { 4 }$ 
C)  $\frac { x ^ { 2 } } { 2 }$ 
D)  $\frac { x ^ { 4 } } { 2 }$ 
A)  $\frac { x ^ { 12 } } { 2 }$ 
B)  $\frac { x ^ { 4 } } { 4 }$ 
C)  $\frac { x ^ { 2 } } { 2 }$ 
D)  $\frac { x ^ { 4 } } { 2 }$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$$

Accepted Answer

A)  $2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$ 
B)  $- 14 \sqrt [ 3 ] { 2 }$ 
C)  $14 \sqrt [ 3 ] { 2 }$ 
D)  $- 2 \sqrt [ 3 ] { 2 }$ 
A)  $2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$ 
B)  $- 14 \sqrt [ 3 ] { 2 }$ 
C)  $14 \sqrt [ 3 ] { 2 }$ 
D)  $- 2 \sqrt [ 3 ] { 2 }$

Question 20

Simplify the expression. Assume all variables represent positive real numbers.
-$4 \sqrt [ 3 ] { 64 x } + 4 \sqrt [ 3 ] { 8 x }$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 72 x }$ 
B)  $24 x$ 
C)  $6 \sqrt [ 3 ] { x }$ 
D)  $24 \sqrt [ 3 ] { x }$ 
A)  $4 \sqrt [ 3 ] { 72 x }$ 
B)  $24 x$ 
C)  $6 \sqrt [ 3 ] { x }$ 
D)  $24 \sqrt [ 3 ] { x }$

Factor the trinomial, if possible. - $12 z ^ { 2 } + 7 z - 12$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x } { y } > 0$

Use the distributive property to rewrite a sum as a product or the product as a sum. --(6 + 9x)

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { 1 } { \sqrt { 3 } } + \frac { 5 } { \sqrt { 27 } } - \frac { 3 } { \sqrt { 12 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $9 \sqrt { 3 } + 2 \sqrt { 3 }$

Evaluate the expression. - $( - 8 ) ^ { 2 / 3 }$

Tell whether the statement is true or false. - $\{ 2,4,5,7 \} \cup \varnothing = \{ 2,4,5,7 \}$

Factor the trinomial, if possible. - $9 z ^ { 2 } + 6 z - 8$

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

Factor the trinomial, if possible. - $2 x ^ { 3 } + 4 x ^ { 2 } y - 30 x y ^ { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 6 } { y } } { \frac { 4 } { y + 6 } }$

Solve the problem. -The NSC Corporation has just completed its first year of business. The following chart shows its monthly profit (or loss). The absolute value of the profit or loss was smallest in

Factor out the greatest common factor. Simplify the factors, if possible. - $48 x ^ { 8 } y ^ { 9 } - 36 x ^ { 3 } y ^ { 6 } - 42 x ^ { 6 } y ^ { 4 }$

Find the domain of the expression. - $\frac { 8 p } { p - m }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 4 x ^ { - 4 } } { 8 x ^ { - 8 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $2 \sqrt [ 3 ] { 2 } - 4 \sqrt [ 3 ] { 128 }$

Simplify the expression. Assume all variables represent positive real numbers. - $4 \sqrt [ 3 ] { 64 x } + 4 \sqrt [ 3 ] { 8 x }$

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Exam 12: Review of Basic Concepts

Factor the trinomial, if possible. - 12z2+7z−1212 z ^ { 2 } + 7 z - 1212z2+7z−12

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - xy>0\frac { x } { y } > 0yx​>0

Use the distributive property to rewrite a sum as a product or the product as a sum. --(6 + 9x)

Simplify the expression. Assume all variables represent positive real numbers. - 13+527−312\frac { 1 } { \sqrt { 3 } } + \frac { 5 } { \sqrt { 27 } } - \frac { 3 } { \sqrt { 12 } }3​1​+27​5​−12​3​

Simplify the expression. Assume all variables represent positive real numbers. - 93+239 \sqrt { 3 } + 2 \sqrt { 3 }93​+23​

Evaluate the expression. - (−8)2/3( - 8 ) ^ { 2 / 3 }(−8)2/3

Tell whether the statement is true or false. - {2,4,5,7}∪∅={2,4,5,7}\{ 2,4,5,7 \} \cup \varnothing = \{ 2,4,5,7 \}{2,4,5,7}∪∅={2,4,5,7}

Factor the trinomial, if possible. - 9z2+6z−89 z ^ { 2 } + 6 z - 89z2+6z−8

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - ax−3ax+3\frac { a \sqrt { x } - 3 } { a \sqrt { x } + 3 }ax​+3ax​−3​

Factor the trinomial, if possible. - 2x3+4x2y−30xy22 x ^ { 3 } + 4 x ^ { 2 } y - 30 x y ^ { 2 }2x3+4x2y−30xy2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 6y4y+6\frac { \frac { 6 } { y } } { \frac { 4 } { y + 6 } }y+64​y6​​