Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 7 } + \sqrt { 6 } ) ( \sqrt { 7 } - \sqrt { 6 } )$

Accepted Answer

A)  $7 + 2 \sqrt { 42 }$ 
B)  $7 - 2 \sqrt { 42 }$ 
C)  13 
D)  1 
A)  $7 + 2 \sqrt { 42 }$ 
B)  $7 - 2 \sqrt { 42 }$ 
C)  13 
D)  1

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 11 } + 4 ) ( \sqrt { 11 } - 4 )$

Accepted Answer

A)  $11 - 2 \sqrt { 4 }$ 
B)  7 
C)  27 
D)  $- 5$ 
A)  $11 - 2 \sqrt { 4 }$ 
B)  7 
C)  27 
D)  $- 5$

Question 3

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \sqrt { 100 } }$

Accepted Answer

A)  10 
B)  $\sqrt [ 3 ] { 10 }$ 
C)  $\sqrt [ 5 ] { 100 }$ 
D)  $\sqrt { 10 }$ 
A)  10 
B)  $\sqrt [ 3 ] { 10 }$ 
C)  $\sqrt [ 5 ] { 100 }$ 
D)  $\sqrt { 10 }$

Question 4

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-3(π) is a real number.

Accepted Answer

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

Question 5

Factor by grouping.
-$8 x ^ { 4 } - 10 x ^ { 2 } - 12 x ^ { 2 } + 15$

Accepted Answer

A)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 5 \right)$ 
B)  $\left( 2 x ^ { 2 } + 3 \right) \left( 4 x ^ { 2 } + 5 \right)$ 
C)  $\left( 2 x ^ { 4 } - 3 \right) ( 4 x - 5 )$ 
D)  $\left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } - 5 \right)$ 
A)  $\left( 8 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 5 \right)$ 
B)  $\left( 2 x ^ { 2 } + 3 \right) \left( 4 x ^ { 2 } + 5 \right)$ 
C)  $\left( 2 x ^ { 4 } - 3 \right) ( 4 x - 5 )$ 
D)  $\left( 2 x ^ { 2 } - 3 \right) \left( 4 x ^ { 2 } - 5 \right)$

Question 6

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 4 } { 5 } }$$

Accepted Answer

A)  27 
B)  $\frac { 2 \sqrt { 5 } } { 5 }$ 
C)  $\frac { 4 \sqrt { 5 } } { 5 }$ 
D)  $2 \sqrt { 5 }$ 
A)  27 
B)  $\frac { 2 \sqrt { 5 } } { 5 }$ 
C)  $\frac { 4 \sqrt { 5 } } { 5 }$ 
D)  $2 \sqrt { 5 }$

Question 7

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 14 \mathrm {~m} ^ { 5 } } \cdot \sqrt { 7 \mathrm {~m} ^ { 9 } }$

Accepted Answer

A)  $7 m ^ { 7 } \sqrt { 2 }$ 
B)  $7 \mathrm {~m}^ 6 \sqrt { 2 }$ 
C)  $14 m ^ { 4 } \sqrt { 7 }$ 
D)  $7 \mathrm {~m} ^ { 8 }$ 
A)  $7 m ^ { 7 } \sqrt { 2 }$ 
B)  $7 \mathrm {~m}^ 6 \sqrt { 2 }$ 
C)  $14 m ^ { 4 } \sqrt { 7 }$ 
D)  $7 \mathrm {~m} ^ { 8 }$

Question 8

Evaluate the expression.
-$75 - 5 \cdot 4 + 76 \div ( - 19 )$

Accepted Answer

A)  $- 295$ 
B)  51 
C)  276 
D)  $- 8$ 
A)  $- 295$ 
B)  51 
C)  276 
D)  $- 8$

Question 9

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , \mathrm { M } = \{ 3,5,7,9 \} , \mathrm { N } = \{ 4,6,8,10,12 \} , \mathrm { Q } = \{ 3,5,7,9,11,13 \}$, and $R = \{ 3,4,5,6 \}$.
$\mathrm { M } \cap \mathrm { R }$

Accepted Answer

A)  $\varnothing ; M$ and $R$ are disjoint sets. 
B)  $\{ 3,4,5,6 \}$ 
C)  $\{ 3,4,5,6,7,9 \}$ 
D)  $\{ 3,5 \}$ 
A)  $\varnothing ; M$ and $R$ are disjoint sets. 
B)  $\{ 3,4,5,6 \}$ 
C)  $\{ 3,4,5,6,7,9 \}$ 
D)  $\{ 3,5 \}$

Question 10

Find the product.
-$$[ ( 4 x - y ) + 5 z ] [ ( 4 x - y ) - 5 z ]$$

Accepted Answer

A)  $16 x ^ { 2 } + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$ 
B)  $16 x ^ { 2 } - 8 x y + y ^ { 2 } - 25 z ^ { 2 }$ 
C)  $16 x ^ { 2 } - 8 x y + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$ 
D)  $16 x ^ { 2 } + y ^ { 2 } - 25 z ^ { 2 }$ 
A)  $16 x ^ { 2 } + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$ 
B)  $16 x ^ { 2 } - 8 x y + y ^ { 2 } - 25 z ^ { 2 }$ 
C)  $16 x ^ { 2 } - 8 x y + y ^ { 2 } + 40 x z + 10 y z - 25 z ^ { 2 }$ 
D)  $16 x ^ { 2 } + y ^ { 2 } - 25 z ^ { 2 }$

Question 11

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$, and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$. $D \nsubseteq C$

Accepted Answer

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

Question 12

Perform the indicated operations.
-$$\frac { 2 } { 15 x } + \frac { 4 } { 21 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 6 } { 15 x + 21 x ^ { 2 } }$ 
B)  $\frac { 6 } { 315 x ^ { 2 } }$ 
C)  $\frac { 2 ( 7 x + 10 ) } { 105 x }$ 
D)  $\frac { 2 ( 7 x + 10 ) } { 105 x ^ { 2 } }$ 
A)  $\frac { 6 } { 15 x + 21 x ^ { 2 } }$ 
B)  $\frac { 6 } { 315 x ^ { 2 } }$ 
C)  $\frac { 2 ( 7 x + 10 ) } { 105 x }$ 
D)  $\frac { 2 ( 7 x + 10 ) } { 105 x ^ { 2 } }$

Question 13

Find the product or quotient.
-$$\frac { 4 x ^ { 2 } + 9 x - 9 } { 7 x - 21 } \cdot \frac { x ^ { 2 } - 3 x } { 16 x ^ { 2 } - 9 } \div \frac { 5 x + 15 } { 8 x ^ { 3 } }$$

Accepted Answer

A)  $\frac { 8 x ^ { 3 } } { 35 ( 4 x + 3 ) }$ 
B)  $\frac { 8 x ^ { 4 } } { 35 ( 4 x + 3 ) }$ 
C)  $\frac { 35 } { 8 x ^ { 4 } ( 4 x + 3 ) }$ 
D)  $\frac { 5 ( x + 3 ) ^ { 2 } } { 56 x ^ { 2 } ( 4 x + 3 ) }$ 
A)  $\frac { 8 x ^ { 3 } } { 35 ( 4 x + 3 ) }$ 
B)  $\frac { 8 x ^ { 4 } } { 35 ( 4 x + 3 ) }$ 
C)  $\frac { 35 } { 8 x ^ { 4 } ( 4 x + 3 ) }$ 
D)  $\frac { 5 ( x + 3 ) ^ { 2 } } { 56 x ^ { 2 } ( 4 x + 3 ) }$

Question 14

Identify the set as finite or infinite.
-$\{ x \mid x$ is an animal alive now $\}$

Accepted Answer

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

Question 15

Factor out the greatest common factor. Simplify the factors, if possible.
-$5 t ^ { 2 } - 10 t - 25$

Accepted Answer

A)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$ 
B)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
D)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$ 
A)  $5 \left( t ^ { 2 } - 5 t - 20 \right)$ 
B)  $5 t \left( t ^ { 2 } - 2 t - 5 \right)$ 
C)  $5 \left( t ^ { 2 } - 2 t - 5 \right)$ 
D)  $5 \left( t ^ { 2 } - 10 t - 25 \right)$

Question 16

Evaluate the expression for x = -2, y = 3, and a = -4.
-(-4x - 6y)(4a)

Accepted Answer

A)  -160 
B)  0 
C)  -416 
D)  160 
A)  -160 
B)  0 
C)  -416 
D)  160

Question 17

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$$- 7 y ^ { 4 } + 6 y ^ { 3 } + 2$$

Accepted Answer

A)  Trinomial 
B)  Binomial 
C)  Monomial 
D)  None of these 
A)  Trinomial 
B)  Binomial 
C)  Monomial 
D)  None of these

Question 18

Solve the problem.
-The radius of a sphere is given by the formula $r = \sqrt { \frac { S } { 4 \pi } }$, where $S$ is the surface area. If the surface area is 9598 square inches, what is the radius? Use $3.14$ for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  $49 \mathrm { in }$. 
B)  0 in. 
C)  $86.8$ in. 
D)  $27.6 \mathrm { in }$. 
A)  $49 \mathrm { in }$. 
B)  0 in. 
C)  $86.8$ in. 
D)  $27.6 \mathrm { in }$.

Question 19

Factor the trinomial, if possible.
-$64 m ^ { 2 } + 288 m n + 324 n ^ { 2 }$

Accepted Answer

A)  $4 ( 4 m + 9 n ) ^ { 2 }$ 
B)  $( 16 m - 4 n ) ^ { 2 }$ 
C)  $( 16 m + 36 n ) ^ { 2 }$ 
D)  $4 ( 4 m - 9 n ) ^ { 2 }$ 
A)  $4 ( 4 m + 9 n ) ^ { 2 }$ 
B)  $( 16 m - 4 n ) ^ { 2 }$ 
C)  $( 16 m + 36 n ) ^ { 2 }$ 
D)  $4 ( 4 m - 9 n ) ^ { 2 }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- ( - 4 ) ^ { 0 }$

Accepted Answer

A)  -1 
B) 4 
C) 0 
D) 1 
A)  -1 
B) 4 
C) 0 
D) 1

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 7 } + \sqrt { 6 } ) ( \sqrt { 7 } - \sqrt { 6 } )$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 11 } + 4 ) ( \sqrt { 11 } - 4 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \sqrt { 100 } }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -3(π) is a real number.

Factor by grouping. - $8 x ^ { 4 } - 10 x ^ { 2 } - 12 x ^ { 2 } + 15$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 4 } { 5 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 14 \mathrm {~m} ^ { 5 } } \cdot \sqrt { 7 \mathrm {~m} ^ { 9 } }$

Evaluate the expression. - $75 - 5 \cdot 4 + 76 \div ( - 19 )$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , \mathrm { M } = \{ 3,5,7,9 \} , \mathrm { N } = \{ 4,6,8,10,12 \} , \mathrm { Q } = \{ 3,5,7,9,11,13 \}$ , and $R = \{ 3,4,5,6 \}$ . $\mathrm { M } \cap \mathrm { R }$

Find the product. - $[ ( 4 x - y ) + 5 z ] [ ( 4 x - y ) - 5 z ]$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 6,7,8,9,10,11 \} , \mathrm { B } = \{ 8,10,12 \} , \mathrm { C } = \{ 6,7,9,11 \} , \mathrm { D } = \{ 6,11 \}$ , and $\mathrm { U } = \{ 6,7,8,9,10,11,12 \}$ . $D \nsubseteq C$

Perform the indicated operations. - $\frac { 2 } { 15 x } + \frac { 4 } { 21 x ^ { 2 } }$

Find the product or quotient. - $\frac { 4 x ^ { 2 } + 9 x - 9 } { 7 x - 21 } \cdot \frac { x ^ { 2 } - 3 x } { 16 x ^ { 2 } - 9 } \div \frac { 5 x + 15 } { 8 x ^ { 3 } }$

Identify the set as finite or infinite. - $\{ x \mid x$ is an animal alive now $\}$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 t ^ { 2 } - 10 t - 25$

Evaluate the expression for x = -2, y = 3, and a = -4. -(-4x - 6y)(4a)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 7 y ^ { 4 } + 6 y ^ { 3 } + 2$

Solve the problem. -The radius of a sphere is given by the formula $r = \sqrt { \frac { S } { 4 \pi } }$ , where $S$ is the surface area. If the surface area is 9598 square inches, what is the radius? Use $3.14$ for $\pi$ , and round your answer to the nearest tenth of an inch.

Factor the trinomial, if possible. - $64 m ^ { 2 } + 288 m n + 324 n ^ { 2 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- ( - 4 ) ^ { 0 }$

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Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Exam 12: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - (7+6)(7−6)( \sqrt { 7 } + \sqrt { 6 } ) ( \sqrt { 7 } - \sqrt { 6 } )(7​+6​)(7​−6​)

Simplify the expression. Assume all variables represent positive real numbers. - (11+4)(11−4)( \sqrt { 11 } + 4 ) ( \sqrt { 11 } - 4 )(11​+4)(11​−4)

Simplify the expression. Assume all variables represent positive real numbers. - 1003\sqrt [ 3 ] { \sqrt { 100 } }3100​​