Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 14 \mathrm {~m} ^ { 5 } } \cdot \sqrt { 7 \mathrm {~m} ^ { 5 } }$

Accepted Answer

A)  $7 \mathrm {~m} ^ { 5 } \sqrt { 2 }$ 
B)  $7 \mathrm {~m} ^ { 4 } \sqrt { 2 }$ 
C)  $14 m ^ { 2 } \sqrt { 7 }$ 
D)  $7 \mathrm {~m} ^ { 6 }$ 
A)  $7 \mathrm {~m} ^ { 5 } \sqrt { 2 }$ 
B)  $7 \mathrm {~m} ^ { 4 } \sqrt { 2 }$ 
C)  $14 m ^ { 2 } \sqrt { 7 }$ 
D)  $7 \mathrm {~m} ^ { 6 }$

Question 2

Factor by any method.
-Find all values of a that will make the polynomial a perfect square trinomial. $$4 x ^ { 2 } + a x + 16$$

Accepted Answer

A)  $16 , - 16$ 
B)  16 
C)  8 
D)  $8 , - 8$ 
A)  $16 , - 16$ 
B)  16 
C)  8 
D)  $8 , - 8$

Question 3

Evaluate the expression.
-$\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }$

Accepted Answer

A)  $\frac { 3 } { 4 }$ 
B)  not a real number 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 9 } { 4 }$ 
A)  $\frac { 3 } { 4 }$ 
B)  not a real number 
C)  $\frac { 3 } { 16 }$ 
D)  $\frac { 9 } { 4 }$

Question 4

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. Calculate the volume if $a = 283$ feet, $b = 680$ feet, and $\mathrm { h } = 222$ feet.

Accepted Answer

A)  54,385,746 cubic feet 
B)  54,384,746 cubic feet 
C)  163,154,238 cubic feet 
D)  54,394,746 cubic feet 
A)  54,385,746 cubic feet 
B)  54,384,746 cubic feet 
C)  163,154,238 cubic feet 
D)  54,394,746 cubic feet

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 28 a ^ { 2 } b } { c ^ { 2 } } }$

Accepted Answer

A)  $\frac { 2 \sqrt { 7 a ^ { 2 } b } } { c }$ 
B)  $\frac { 4 a \sqrt { 7 b } } { c }$ 
C)  $\frac { 2 a \sqrt { 7 b } } { c }$ 
D)  $\frac { a \sqrt { 28 b } } { c }$ 
A)  $\frac { 2 \sqrt { 7 a ^ { 2 } b } } { c }$ 
B)  $\frac { 4 a \sqrt { 7 b } } { c }$ 
C)  $\frac { 2 a \sqrt { 7 b } } { c }$ 
D)  $\frac { a \sqrt { 28 b } } { c }$

Question 6

Evaluate the expression.
-$$\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }$$

Accepted Answer

A)  $\frac { 7 } { 6 }$ 
B)  $- \frac { 6 } { 7 }$ 
C)  $\frac { 49 } { 72 }$ 
D)  not a real number 
A)  $\frac { 7 } { 6 }$ 
B)  $- \frac { 6 } { 7 }$ 
C)  $\frac { 49 } { 72 }$ 
D)  not a real number

Question 7

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$6 \cdot 1 = 6$

Accepted Answer

A)  Distributive 
B)  Inverse 
C)  Identity 
D)  Closure 
A)  Distributive 
B)  Inverse 
C)  Identity 
D)  Closure

Question 8

Use the distributive property to rewrite a sum as a product or the product as a sum.
-$$- 4 ( x + k )$$

Accepted Answer

A)  $- 4 \times k$ 
B)  $- 4 x + k$ 
C)  $- 4 x + 4 k$ 
D)  $- 4 x - 4 k$ 
A)  $- 4 \times k$ 
B)  $- 4 x + k$ 
C)  $- 4 x + 4 k$ 
D)  $- 4 x - 4 k$

Question 9

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$$\frac { x ^ { 2 } } { y } < 0$$

Accepted Answer

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

Question 10

Identify the set as finite or infinite.
-$\{ \mathrm { x } \mid \mathrm { x } \text { is an even natural number } \}$

Accepted Answer

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

Question 11

Calculate the value mentally.
-$$\frac { 500 ^ { 1 / 2 } } { 5 ^ { 1 / 2 } }$$

Accepted Answer

A)  1,000 
B)  none of these 
C)  100 
D)  10 
A)  1,000 
B)  none of these 
C)  100 
D)  10

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 9 } - \sqrt { 100 }$

Accepted Answer

A)  $- \sqrt { 7 }$ 
B)  $- 3.5$ 
C)  $- \sqrt { 91 }$ 
D)  $- 7$ 
A)  $- \sqrt { 7 }$ 
B)  $- 3.5$ 
C)  $- \sqrt { 91 }$ 
D)  $- 7$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$13 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$$

Accepted Answer

A)  $- 12 \sqrt [ 3 ] { 2 }$ 
B)  $12 \sqrt [ 3 ] { 2 }$ 
C)  $13 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$ 
D)  $8 \sqrt [ 3 ] { 2 }$ 
A)  $- 12 \sqrt [ 3 ] { 2 }$ 
B)  $12 \sqrt [ 3 ] { 2 }$ 
C)  $13 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$ 
D)  $8 \sqrt [ 3 ] { 2 }$

Question 14

Find the sum or difference.
-$$n ^ { 2 } \left( 3 n - \frac { 1 } { 4 } \right) \left( 11 n + \frac { 1 } { 2 } \right)$$

Accepted Answer

A)  $33 n ^ { 4 } - \frac { 17 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
B)  $33 n ^ { 4 } - \frac { 5 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
C)  $33 n ^ { 4 } + \frac { 5 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
D)  $33 n ^ { 4 } - \frac { 5 } { 4 } n ^ { 3 } + \frac { 1 } { 8 } n ^ { 2 }$ 
A)  $33 n ^ { 4 } - \frac { 17 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
B)  $33 n ^ { 4 } - \frac { 5 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
C)  $33 n ^ { 4 } + \frac { 5 } { 4 } n ^ { 3 } - \frac { 1 } { 8 } n ^ { 2 }$ 
D)  $33 n ^ { 4 } - \frac { 5 } { 4 } n ^ { 3 } + \frac { 1 } { 8 } n ^ { 2 }$

Question 15

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$- ( - 4 ) ^ { - 1 }$$

Accepted Answer

A)  $- 4$ 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $- \frac { 1 } { 4 }$ 
A)  $- 4$ 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $- \frac { 1 } { 4 }$

Question 16

Find the sum or difference.
-$$( 12 y + x ) ( 12 y - x )$$

Accepted Answer

A)  $24 y ^ { 2 } - x ^ { 2 }$ 
B)  $144 y ^ { 2 } - 24 x y - x ^ { 2 }$ 
C)  $144 y ^ { 2 } - x ^ { 2 }$ 
D)  $144 y ^ { 2 } + 24 x y - x ^ { 2 }$ 
A)  $24 y ^ { 2 } - x ^ { 2 }$ 
B)  $144 y ^ { 2 } - 24 x y - x ^ { 2 }$ 
C)  $144 y ^ { 2 } - x ^ { 2 }$ 
D)  $144 y ^ { 2 } + 24 x y - x ^ { 2 }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt [ 4 ] { 625 }$$

Accepted Answer

A)  $- 5$ 
B)  $- 4$ 
C)  $- 25$ 
D)  not a real number 
A)  $- 5$ 
B)  $- 4$ 
C)  $- 25$ 
D)  not a real number

Question 18

Factor by any method.
-$30 x ^ { 2 } + 25 x - 18 x - 15$

Accepted Answer

A)  $( 5 x + 3 ) ( 6 x - 5 )$ 
B)  $( 5 x - 3 ) ( 6 x + 5 )$ 
C)  $( 30 x - 3 ) ( x + 5 )$ 
D)  $( 30 x + 3 ) ( x - 5 )$ 
A)  $( 5 x + 3 ) ( 6 x - 5 )$ 
B)  $( 5 x - 3 ) ( 6 x + 5 )$ 
C)  $( 30 x - 3 ) ( x + 5 )$ 
D)  $( 30 x + 3 ) ( x - 5 )$

Question 19

Evaluate the expression.
-$$( - 64 ) ^ { 1 / 3 }$$

Accepted Answer

A)  $- 4$ 
B)  $- 64$ 
C)  4 
D)  not a real number 
A)  $- 4$ 
B)  $- 64$ 
C)  4 
D)  not a real number

Question 20

Find the sum or difference.
-$\left( - 2 x ^ { 2 } y ^ { 4 } \right) \left( - 2 x ^ { 2 } y ^ { 2 } \right)$

Accepted Answer

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

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 14 \mathrm {~m} ^ { 5 } } \cdot \sqrt { 7 \mathrm {~m} ^ { 5 } }$

Factor by any method. -Find all values of a that will make the polynomial a perfect square trinomial. $4 x ^ { 2 } + a x + 16$

Evaluate the expression. - $\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 28 a ^ { 2 } b } { c ^ { 2 } } }$

Evaluate the expression. - $\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $6 \cdot 1 = 6$

Use the distributive property to rewrite a sum as a product or the product as a sum. - $- 4 ( x + k )$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $\frac { x ^ { 2 } } { y } < 0$

Identify the set as finite or infinite. - $\{ \mathrm { x } \mid \mathrm { x } \text { is an even natural number } \}$

Calculate the value mentally. - $\frac { 500 ^ { 1 / 2 } } { 5 ^ { 1 / 2 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 9 } - \sqrt { 100 }$

Simplify the expression. Assume all variables represent positive real numbers. - $13 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }$

Find the sum or difference. - $n ^ { 2 } \left( 3 n - \frac { 1 } { 4 } \right) \left( 11 n + \frac { 1 } { 2 } \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- ( - 4 ) ^ { - 1 }$

Find the sum or difference. - $( 12 y + x ) ( 12 y - x )$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 4 ] { 625 }$

Factor by any method. - $30 x ^ { 2 } + 25 x - 18 x - 15$

Evaluate the expression. - $( - 64 ) ^ { 1 / 3 }$

Find the sum or difference. - $\left( - 2 x ^ { 2 } y ^ { 4 } \right) \left( - 2 x ^ { 2 } y ^ { 2 } \right)$

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Exam 1: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - 14 m5⋅7 m5\sqrt { 14 \mathrm {~m} ^ { 5 } } \cdot \sqrt { 7 \mathrm {~m} ^ { 5 } }14 m5​⋅7 m5​

Factor by any method. -Find all values of a that will make the polynomial a perfect square trinomial. 4x2+ax+164 x ^ { 2 } + a x + 164x2+ax+16

Evaluate the expression. - (916)1/2\left( \frac { 9 } { 16 } \right) ^ { 1 / 2 }(169​)1/2

Simplify the expression. Assume all variables represent positive real numbers. - 28a2bc2\sqrt { \frac { 28 a ^ { 2 } b } { c ^ { 2 } } }c228a2b​​

Evaluate the expression. - (−4936)−1/2\left( - \frac { 49 } { 36 } \right) ^ { - 1 / 2 }(−3649​)−1/2

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 6⋅1=66 \cdot 1 = 66⋅1=6

Use the distributive property to rewrite a sum as a product or the product as a sum. - −4(x+k)- 4 ( x + k )−4(x+k)

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - x2y<0\frac { x ^ { 2 } } { y } < 0yx2​<0

Identify the set as finite or infinite. - {x∣x is an even natural number }\{ \mathrm { x } \mid \mathrm { x } \text { is an even natural number } \}{x∣x is an even natural number }

Calculate the value mentally. - 5001/251/2\frac { 500 ^ { 1 / 2 } } { 5 ^ { 1 / 2 } }51/25001/2​

Simplify the expression. Assume all variables represent positive real numbers. - 9−100\sqrt { 9 } - \sqrt { 100 }9​−100​

Simplify the expression. Assume all variables represent positive real numbers. - 1323−5250313 \sqrt [ 3 ] { 2 } - 5 \sqrt [ 3 ] { 250 }1332​−53250​

Find the sum or difference. - n2(3n−14)(11n+12)n ^ { 2 } \left( 3 n - \frac { 1 } { 4 } \right) \left( 11 n + \frac { 1 } { 2 } \right)n2(3n−41​)(11n+21​)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −(−4)−1- ( - 4 ) ^ { - 1 }−(−4)−1

Find the sum or difference. - (12y+x)(12y−x)( 12 y + x ) ( 12 y - x )(12y+x)(12y−x)

Simplify the expression. Assume all variables represent positive real numbers. - −6254- \sqrt [ 4 ] { 625 }−4625​

Factor by any method. - 30x2+25x−18x−1530 x ^ { 2 } + 25 x - 18 x - 1530x2+25x−18x−15

Evaluate the expression. - (−64)1/3( - 64 ) ^ { 1 / 3 }(−64)1/3

Find the sum or difference. - (−2x2y4)(−2x2y2)\left( - 2 x ^ { 2 } y ^ { 4 } \right) \left( - 2 x ^ { 2 } y ^ { 2 } \right)(−2x2y4)(−2x2y2)