Question 1

Evaluate the expression.
-$$92 - 22 \cdot 4 + 224 \div ( - 16 )$$

Accepted Answer

A)  $- 997$ 
B)  $- 19$ 
C)  266 
D)  $- 10$ 
A)  $- 997$ 
B)  $- 19$ 
C)  266 
D)  $- 10$

Question 2

Write in radical form. Assume all variables represent positive real numbers.
-$$( 2 m + 7 n ) ^ { 4 / 5 }$$

Accepted Answer

A)  $\sqrt [ 5 ] { ( 2 m + 7 n ) ^ { 4 } }$ 
B)  $\sqrt [ 5 ] { 2 m + 7 n ^ { 4 } }$ 
C)  $\sqrt [ 4 ] { 2 m + 7 n ^ { 5 } }$ 
D)  $\sqrt [ 4 ] { ( 2 m + 7 n ) ^ { 5 } }$ 
A)  $\sqrt [ 5 ] { ( 2 m + 7 n ) ^ { 4 } }$ 
B)  $\sqrt [ 5 ] { 2 m + 7 n ^ { 4 } }$ 
C)  $\sqrt [ 4 ] { 2 m + 7 n ^ { 5 } }$ 
D)  $\sqrt [ 4 ] { ( 2 m + 7 n ) ^ { 5 } }$

Question 3

Perform the indicated operations.
-$$\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
A)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$ 
B)  $\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
C)  $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$ 
D)  $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question 4

Factor the polynomial by substitution.
-$$12 z ^ { 4 } - 7 z ^ { 2 } - 12$$

Accepted Answer

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

Question 5

Find the product. Assume variables represent positive real numbers.
-$\left( 7 p ^ { 3 / 5 } + 4 p ^ { 4 / 5 } \right) ^ { 2 }$

Accepted Answer

A)  $49 p ^ { 6 / 5 } + 28 p ^ { 7 / 5 } + 16 p ^ { 8 / 5 }$ 
B)  $ 49 p^{6 / 5}+56 p^{7 / 5}+16 p^{8 / 5} $ 
C)  $49 p ^ { 9 / 25 + 7 p }$ 
D)  $14 \mathrm { p } ^ { 6 / 5 } + 28 \mathrm { p } ^ { 8 / 5 } + 8 \mathrm { p } ^ { 8 / 5 }$ 
A)  $49 p ^ { 6 / 5 } + 28 p ^ { 7 / 5 } + 16 p ^ { 8 / 5 }$ 
B)  $ 49 p^{6 / 5}+56 p^{7 / 5}+16 p^{8 / 5} $ 
C)  $49 p ^ { 9 / 25 + 7 p }$ 
D)  $14 \mathrm { p } ^ { 6 / 5 } + 28 \mathrm { p } ^ { 8 / 5 } + 8 \mathrm { p } ^ { 8 / 5 }$

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

Accepted Answer

A)  $6 - 2 \sqrt { 4 }$ 
B)  $- 10$ 
C)  2 
D)  22 
A)  $6 - 2 \sqrt { 4 }$ 
B)  $- 10$ 
C)  2 
D)  22

Question 7

Find the sum or difference.
-$$( x - 8 ) ( x + 8 ) \left( x ^ { 2 } + 64 \right)$$

Accepted Answer

A)  $x ^ { 4 } - 64$ 
B)  $x ^ { 4 } - 16 x ^ { 2 } - 64$ 
C)  $x ^ { 4 } - 4096$ 
D)  $x ^ { 4 } - 256 x ^ { 2 } + 4096$ 
A)  $x ^ { 4 } - 64$ 
B)  $x ^ { 4 } - 16 x ^ { 2 } - 64$ 
C)  $x ^ { 4 } - 4096$ 
D)  $x ^ { 4 } - 256 x ^ { 2 } + 4096$

Question 8

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

Accepted Answer

A)  $x ^ { - 7 } \left( x - 4 x ^ { 6 } \right)$ 
B)  $x ^ { - 7 } \left( x - 4 x ^ { 5 } \right)$ 
C)  $x ^ { - 7 } \left( 1 - 4 x ^ { 5 } \right)$ 
D)  $x ^ { - 7 } \left( 1 + 4 x ^ { 7 } \right)$ 
A)  $x ^ { - 7 } \left( x - 4 x ^ { 6 } \right)$ 
B)  $x ^ { - 7 } \left( x - 4 x ^ { 5 } \right)$ 
C)  $x ^ { - 7 } \left( 1 - 4 x ^ { 5 } \right)$ 
D)  $x ^ { - 7 } \left( 1 + 4 x ^ { 7 } \right)$

Question 9

Factor the polynomial by substitution.
-$$8 x ^ { 4 } + 18 x ^ { 2 } + 9$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
B)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$ 
C)  $\left( 4 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } - 3 \right)$ 
D)  $\left( 4 x ^ { 2 } + 1 \right) \left( 2 x ^ { 2 } + 9 \right)$ 
A)  $\left( 4 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } + 3 \right)$ 
B)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 3 \right)$ 
C)  $\left( 4 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } - 3 \right)$ 
D)  $\left( 4 x ^ { 2 } + 1 \right) \left( 2 x ^ { 2 } + 9 \right)$

Question 10

Perform the indicated operations.
-$$\frac { - 4 x } { 5 ( 2 x + 1 ) } + \frac { 1 } { 5 x ( 2 x + 1 ) } - \frac { 1 } { x }$$

Accepted Answer

A)  $\frac { - 4 x ^ { 2 } - 10 x - 4 } { 5 x }$ 
B)  $- \frac { 2 ( x + 2 ) } { 10 x ^ { 2 } + 5 x }$ 
C)  $\frac { - 4 x ^ { 2 } - 10 x - 4 } { 10 x ^ { 2 } + 5 x }$ 
D)  $- \frac { 2 ( x + 2 ) } { 5 x }$ 
A)  $\frac { - 4 x ^ { 2 } - 10 x - 4 } { 5 x }$ 
B)  $- \frac { 2 ( x + 2 ) } { 10 x ^ { 2 } + 5 x }$ 
C)  $\frac { - 4 x ^ { 2 } - 10 x - 4 } { 10 x ^ { 2 } + 5 x }$ 
D)  $- \frac { 2 ( x + 2 ) } { 5 x }$

Question 11

Perform the indicated operations.
-$$\frac { 6 } { 7 x } + \frac { 4 } { 7 x }$$

Accepted Answer

A)  1 
B)  $\frac { 10 } { 7 x }$ 
C)  $\frac { 7 } { 10 x }$ 
D)  $\frac { 10 } { 14 x }$ 
A)  1 
B)  $\frac { 10 } { 7 x }$ 
C)  $\frac { 7 } { 10 x }$ 
D)  $\frac { 10 } { 14 x }$

Question 12

Use the distributive property to rewrite a sum as a product or the product as a sum.
-$$- 11 y + 3 y$$

Accepted Answer

A)  $8 \mathrm { y }$ 
B)  $- 8 \mathrm { y }$ 
C)  $14 y$ 
D)  $- 14 y$ 
A)  $8 \mathrm { y }$ 
B)  $- 8 \mathrm { y }$ 
C)  $14 y$ 
D)  $- 14 y$

Question 13

Write in exponential form. Assume all variables are positive real numbers.
-$- 6 \sqrt { 2 m ^ { 9 } }$

Accepted Answer

A)  $- 6 \cdot 2 ^ { 1 / 2 } \mathrm {~m} ^ { 9 / 2 }$ 
B)  $- 72 \mathrm {~m} ^ { 9 / 2 }$ 
C)  $( - 6 \cdot 2 ) ^ { 1 / 2 } m ^ { 9 / 2 }$ 
D)  $72 \mathrm {~m} ^ { 2 / 9 }$ 
A)  $- 6 \cdot 2 ^ { 1 / 2 } \mathrm {~m} ^ { 9 / 2 }$ 
B)  $- 72 \mathrm {~m} ^ { 9 / 2 }$ 
C)  $( - 6 \cdot 2 ) ^ { 1 / 2 } m ^ { 9 / 2 }$ 
D)  $72 \mathrm {~m} ^ { 2 / 9 }$

Question 14

Use set notation, and list all the elements of the set.
-{82, 77, 72, . . ., 32}

Accepted Answer

A)  {82, 77, 72, 67, 62, 57, 52, 47, 42, 37, 32} 
B)  {82, 77, 72, 66, 61, 56, 51, 46, 41, 36, 31} 
C)  {82, 77, 72, 62, 52, 42, 32} 
D)  {82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132} 
A)  {82, 77, 72, 67, 62, 57, 52, 47, 42, 37, 32} 
B)  {82, 77, 72, 66, 61, 56, 51, 46, 41, 36, 31} 
C)  {82, 77, 72, 62, 52, 42, 32} 
D)  {82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132}

Question 15

Factor the trinomial, if possible.
-$64 m ^ { 2 } - 144 m + 81$

Accepted Answer

A)  $( 8 m - 10 ) ^ { 2 }$ 
B)  $( 8 m - 9 ) ^ { 2 }$ 
C)  $( 8 m + 9 ) ^ { 2 }$ 
D)  $( 8 m + 9 ) ( 8 m - 9 )$ 
A)  $( 8 m - 10 ) ^ { 2 }$ 
B)  $( 8 m - 9 ) ^ { 2 }$ 
C)  $( 8 m + 9 ) ^ { 2 }$ 
D)  $( 8 m + 9 ) ( 8 m - 9 )$

Question 16

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

Accepted Answer

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

Question 17

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$3 x ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { 81 x ^ { 4 } }$ 
B)  $\frac { 3 } { x ^ { 4 } }$ 
C)  $- \frac { 1 } { 12 x }$ 
D)  $- 12 x$ 
A)  $\frac { 1 } { 81 x ^ { 4 } }$ 
B)  $\frac { 3 } { x ^ { 4 } }$ 
C)  $- \frac { 1 } { 12 x }$ 
D)  $- 12 x$

Question 18

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

Question 19

Find the sum or difference.
-$$( n - 1 ) ( n + 1 )$$

Accepted Answer

A)  $n ^ { 2 } - 2 n + 1$ 
B)  $n ^ { 2 } - 1$ 
C)  $n ^ { 2 } - 2 n - 1$ 
D)  $n ^ { 2 } - 2$ 
A)  $n ^ { 2 } - 2 n + 1$ 
B)  $n ^ { 2 } - 1$ 
C)  $n ^ { 2 } - 2 n - 1$ 
D)  $n ^ { 2 } - 2$

Question 20

Tell whether the statement is true or false.
-Let $A = \{ 1,2,3,4,5,6 \} , B = \{ 3,5,7 \} , C = \{ 1,2,4,6 \} , D = \{ 2,6 \}$, and $U = \{ 1,2,3,4,5,6,7 \}$.
$$\mathrm { U } \subseteq \mathrm { C }$$

Accepted Answer

A) True 
 B)False

Evaluate the expression. - $92 - 22 \cdot 4 + 224 \div ( - 16 )$

Write in radical form. Assume all variables represent positive real numbers. - $( 2 m + 7 n ) ^ { 4 / 5 }$

Perform the indicated operations. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$

Factor the polynomial by substitution. - $12 z ^ { 4 } - 7 z ^ { 2 } - 12$

Find the product. Assume variables represent positive real numbers. - $\left( 7 p ^ { 3 / 5 } + 4 p ^ { 4 / 5 } \right) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )$

Find the sum or difference. - $( x - 8 ) ( x + 8 ) \left( x ^ { 2 } + 64 \right)$

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

Factor the polynomial by substitution. - $8 x ^ { 4 } + 18 x ^ { 2 } + 9$

Perform the indicated operations. - $\frac { - 4 x } { 5 ( 2 x + 1 ) } + \frac { 1 } { 5 x ( 2 x + 1 ) } - \frac { 1 } { x }$

Perform the indicated operations. - $\frac { 6 } { 7 x } + \frac { 4 } { 7 x }$

Use the distributive property to rewrite a sum as a product or the product as a sum. - $- 11 y + 3 y$

Write in exponential form. Assume all variables are positive real numbers. - $- 6 \sqrt { 2 m ^ { 9 } }$

Use set notation, and list all the elements of the set. -{82, 77, 72, . . ., 32}

Factor the trinomial, if possible. - $64 m ^ { 2 } - 144 m + 81$

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

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $3 x ^ { - 4 }$

Find the sum or difference. - $( n - 1 ) ( n + 1 )$

Tell whether the statement is true or false. -Let $A = \{ 1,2,3,4,5,6 \} , B = \{ 3,5,7 \} , C = \{ 1,2,4,6 \} , D = \{ 2,6 \}$ , and $U = \{ 1,2,3,4,5,6,7 \}$ . $\mathrm { U } \subseteq \mathrm { C }$

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Exam 1: Review of Basic Concepts

Evaluate the expression. - 92−22⋅4+224÷(−16)92 - 22 \cdot 4 + 224 \div ( - 16 )92−22⋅4+224÷(−16)

Write in radical form. Assume all variables represent positive real numbers. - (2m+7n)4/5( 2 m + 7 n ) ^ { 4 / 5 }(2m+7n)4/5

Perform the indicated operations. - xx2−16−6x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+46​

Factor the polynomial by substitution. - 12z4−7z2−1212 z ^ { 4 } - 7 z ^ { 2 } - 1212z4−7z2−12

Find the product. Assume variables represent positive real numbers. - (7p3/5+4p4/5)2\left( 7 p ^ { 3 / 5 } + 4 p ^ { 4 / 5 } \right) ^ { 2 }(7p3/5+4p4/5)2

Simplify the expression. Assume all variables represent positive real numbers. - (6+4)(6−4)( \sqrt { 6 } + 4 ) ( \sqrt { 6 } - 4 )(6​+4)(6​−4)

Find the sum or difference. - (x−8)(x+8)(x2+64)( x - 8 ) ( x + 8 ) \left( x ^ { 2 } + 64 \right)(x−8)(x+8)(x2+64)

Factor, using the given factor. Assume all variables represent positive real numbers. - x−7−4x−2;x−7x ^ { - 7 } - 4 x ^ { - 2 } ; \quad x ^ { - 7 }x−7−4x−2;x−7

Factor the polynomial by substitution. - 8x4+18x2+98 x ^ { 4 } + 18 x ^ { 2 } + 98x4+18x2+9

Perform the indicated operations. - −4x5(2x+1)+15x(2x+1)−1x\frac { - 4 x } { 5 ( 2 x + 1 ) } + \frac { 1 } { 5 x ( 2 x + 1 ) } - \frac { 1 } { x }5(2x+1)−4x​+5x(2x+1)1​−x1​

Perform the indicated operations. - 67x+47x\frac { 6 } { 7 x } + \frac { 4 } { 7 x }7x6​+7x4​

Use the distributive property to rewrite a sum as a product or the product as a sum. - −11y+3y- 11 y + 3 y−11y+3y

Write in exponential form. Assume all variables are positive real numbers. - −62m9- 6 \sqrt { 2 m ^ { 9 } }−62m9​