Question 1

Evaluate the expression.
-$$- \left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }$$

Accepted Answer

A)  $\frac { 6 } { 5 }$ 
B)  $- \frac { 5 } { 6 }$ 
C)  not a real number 
D)  $- \frac { 25 } { 72 }$ 
A)  $\frac { 6 } { 5 }$ 
B)  $- \frac { 5 } { 6 }$ 
C)  not a real number 
D)  $- \frac { 25 } { 72 }$

Question 2

Factor the polynomial by substitution.
-$$a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$$

Accepted Answer

A)  $( a - 9 b ) ( a + 8 b ) ( a + b )$ 
B)  $( a + b ) ^ { 2 } ( a - 9 ) ( a + 8 )$ 
C)  $( a + b ) ^ { 2 } ( a - 8 b ) ( a + 9 b )$ 
D)  $( a + b ) ^ { 2 } ( a - 9 b ) ( a + 8 b )$ 
A)  $( a - 9 b ) ( a + 8 b ) ( a + b )$ 
B)  $( a + b ) ^ { 2 } ( a - 9 ) ( a + 8 )$ 
C)  $( a + b ) ^ { 2 } ( a - 8 b ) ( a + 9 b )$ 
D)  $( a + b ) ^ { 2 } ( a - 9 b ) ( a + 8 b )$

Question 3

Determine which property of absolute value justifies the statement.
-$$| - x | = | x |$$

Accepted Answer

A)  Property 5: the triangle inequality 
B)  Property 1: the opposite of a number is equal to the absolute value of the number . 
C)  Property 2: the absolute value of a number and its opposite are equal. 
D)  Property 2: the opposite of the absolute value of a number is equal to the absolute value of the number. 
A)  Property 5: the triangle inequality 
B)  Property 1: the opposite of a number is equal to the absolute value of the number . 
C)  Property 2: the absolute value of a number and its opposite are equal. 
D)  Property 2: the opposite of the absolute value of a number is equal to the absolute value of the number.

Question 4

Solve the problem. Round to two decimal places unless otherwise indicated.
-If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 1500 } { x + 50 }$, what do 200 units cost?

Accepted Answer

A)  $\$ 1200.00$ 
B)  $\$ 1499.75$ 
C)  $\$ 6000.00$ 
D)  $\$ 60.00$ 
A)  $\$ 1200.00$ 
B)  $\$ 1499.75$ 
C)  $\$ 6000.00$ 
D)  $\$ 60.00$

Question 5

Find the sum or difference.
-$$\left( - 7 + 7 x ^ { 4 } + 7 x ^ { 6 } + 9 x ^ { 5 } \right) + \left( - 3 x ^ { 5 } + 7 x ^ { 4 } + 8 + 9 x ^ { 6 } \right)$$

Accepted Answer

A)  $16 x ^ { 12 } + 6 x ^ { 10 } + 14 x ^ { 8 } + 1$ 
B)  $16 x ^ { 6 } + 6 x ^ { 5 } + 14 x ^ { 4 } + 1$ 
C)  $36 x ^ { 30 } + 1$ 
D)  $- 10 x ^ { 6 } - 10 x ^ { 5 } + 15 x ^ { 4 } + 18$ 
A)  $16 x ^ { 12 } + 6 x ^ { 10 } + 14 x ^ { 8 } + 1$ 
B)  $16 x ^ { 6 } + 6 x ^ { 5 } + 14 x ^ { 4 } + 1$ 
C)  $36 x ^ { 30 } + 1$ 
D)  $- 10 x ^ { 6 } - 10 x ^ { 5 } + 15 x ^ { 4 } + 18$

Question 6

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 8,9,10,11,12,13,14,15,16,17,18 \} , \mathrm { M } = \{ 8,10,12,14 \} , \mathrm { N } = \{ 9,11,13,15,17 \}$, $Q = \{ 8,10,12,14,16,18 \}$, and $R = \{ 8,9,10,11 \}$.
$\varnothing \cup N$

Accepted Answer

A)  $\{ 10,12,14,16,18 \}$ 
B)  $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
C)  $\varnothing ; N$ and $\varnothing$ are disjoint sets. 
D)  $\mathrm { N }$, or $\{ 9,11,13,15,17 \} ; \mathrm { N }$ and $\varnothing$ are disjoint sets. 
A)  $\{ 10,12,14,16,18 \}$ 
B)  $\{ 8,9,10,11,12,13,14,15,16,17,18 \}$ 
C)  $\varnothing ; N$ and $\varnothing$ are disjoint sets. 
D)  $\mathrm { N }$, or $\{ 9,11,13,15,17 \} ; \mathrm { N }$ and $\varnothing$ are disjoint sets.

Question 7

Evaluate the expression.
-$( - 4 ) ^ { 2 }$

Accepted Answer

A)  64 
B)  $- 8$ 
C)  16 
D)  $- 16$ 
A)  64 
B)  $- 8$ 
C)  16 
D)  $- 16$

Question 8

Find the product.
-$$- 6 x ^ { 4 } \left( 4 x ^ { 7 } + 7 x ^ { 2 } \right)$$

Accepted Answer

A)  $- 24 x ^{11} + 7 x ^ { 2 }$ 
B)  $- 24 x ^ { 11 } + 42 x ^ { 6 }$ 
C)  $- 24 x ^ { 28 } - 42 x ^ { 8 }$ 
D)  $- 24 x ^ { 11 } - 42 x ^ { 6 }$ 
A)  $- 24 x ^{11} + 7 x ^ { 2 }$ 
B)  $- 24 x ^ { 11 } + 42 x ^ { 6 }$ 
C)  $- 24 x ^ { 28 } - 42 x ^ { 8 }$ 
D)  $- 24 x ^ { 11 } - 42 x ^ { 6 }$

Question 9

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { x ^ { 9 } } { x ^ { 19 } }$

Accepted Answer

A)  $- x ^ { 10 }$ 
B)  $\frac { 1 } { x ^ { 10 } }$ 
C)  $x ^ { 10 }$ 
D)  $\frac { 1 } { x ^ { 28 } }$ 
A)  $- x ^ { 10 }$ 
B)  $\frac { 1 } { x ^ { 10 } }$ 
C)  $x ^ { 10 }$ 
D)  $\frac { 1 } { x ^ { 28 } }$

Question 10

Find the domain of the expression.
-$\frac { 3 } { a - 8 }$

Accepted Answer

A)  $\{ a \mid a \neq 3 \}$ 
B)  $\{ a \mid a \neq 8 \}$ 
C)  all real numbers 
D)  $\{ a \mid a \neq - 8 \}$ 
A)  $\{ a \mid a \neq 3 \}$ 
B)  $\{ a \mid a \neq 8 \}$ 
C)  all real numbers 
D)  $\{ a \mid a \neq - 8 \}$

Question 11

Tell whether the statement is true or false.
-$$\{ 0,1,4,9 \} = \{ 4,1,9,0 \}$$

Accepted Answer

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

Question 12

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$$20 z ^ { 5 } - 4 z ^ { 4 } - 7 z ^ { 3 } + 12$$

Accepted Answer

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

Question 13

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { y } { 2 } } { \frac { 7 } { y + 9 } }$$

Accepted Answer

A)  $\frac { 7 y } { 2 ( y + 9 ) }$ 
B)  $\frac { y + 9 } { 14 y }$ 
C)  $14 y ( y + 9 )$ 
D)  $\frac { \mathrm { y } ( \mathrm { y } + 9 ) } { 14 }$ 
A)  $\frac { 7 y } { 2 ( y + 9 ) }$ 
B)  $\frac { y + 9 } { 14 y }$ 
C)  $14 y ( y + 9 )$ 
D)  $\frac { \mathrm { y } ( \mathrm { y } + 9 ) } { 14 }$

Question 14

Evaluate the expression.
-Let $x = - 2 , y = - 18$.
Evaluate $| - 6 y - 10 x | - | 2 y |$.

Accepted Answer

A)  228 
B)  132 
C)  204 
D)  92 
A)  228 
B)  132 
C)  204 
D)  92

Question 15

Simplify the expression. Assume all variables represent positive real numbers.
-$- \sqrt [ 3 ] { \frac { 7 x } { y } }$

Accepted Answer

A)  $- \frac { \sqrt [ 3 ] { 7 x ^ { 2 } y ^ { 2 } } } { y }$ 
B)  $- \frac { \sqrt [ 3 ] { 7 x y ^ { 2 } } } { y }$ 
C)  $- \frac { \sqrt [ 3 ] { 7 x ^ { 2 } y } } { y }$ 
D)  $- \frac { \sqrt [ 3 ] { 7 x y } } { y }$ 
A)  $- \frac { \sqrt [ 3 ] { 7 x ^ { 2 } y ^ { 2 } } } { y }$ 
B)  $- \frac { \sqrt [ 3 ] { 7 x y ^ { 2 } } } { y }$ 
C)  $- \frac { \sqrt [ 3 ] { 7 x ^ { 2 } y } } { y }$ 
D)  $- \frac { \sqrt [ 3 ] { 7 x y } } { y }$

Question 16

Decide whether the expression has been simplified correctly.
-$( a b ) ^ { 3 } = a b ^ { 3 }$

Accepted Answer

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

Question 17

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-9 + 0 = 9

Accepted Answer

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

Question 18

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 7,8,9,10,11,12 \} , \mathrm { B } = \{ 9,11,13 \} , \mathrm { C } = \{ 7,8,10,12 \} , \mathrm { D } = \{ 7,12 \}$, and $\mathrm { U } = \{ 7,8,9,10,11,12,13 \}$.
$\mathrm { A } \subseteq \mathrm { B }$

Accepted Answer

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

Question 19

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

Accepted Answer

A)  $\frac { 1 } { x ^ { 26 / 3 } }$ 
B)  $x^{ 26 / 3}$ 
C)  $x ^ { 22 / 3 }$ 
D)  $\frac { 1 } { x ^ { 22 / 3 } }$ 
A)  $\frac { 1 } { x ^ { 26 / 3 } }$ 
B)  $x^{ 26 / 3}$ 
C)  $x ^ { 22 / 3 }$ 
D)  $\frac { 1 } { x ^ { 22 / 3 } }$

Question 20

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( 10 x y ) ^ { 2 }$

Accepted Answer

A)  $100 x ^ { 2 } y ^ { 2 }$ 
B)  $100 x y$ 
C)  $20 x ^ { 2 } y ^ { 2 }$ 
D)  $20 x y$ 
A)  $100 x ^ { 2 } y ^ { 2 }$ 
B)  $100 x y$ 
C)  $20 x ^ { 2 } y ^ { 2 }$ 
D)  $20 x y$

Evaluate the expression. - $- \left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }$

Factor the polynomial by substitution. - $a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }$

Determine which property of absolute value justifies the statement. - $| - x | = | x |$

Solve the problem. Round to two decimal places unless otherwise indicated. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 1500 } { x + 50 }$ , what do 200 units cost?

Find the sum or difference. - $\left( - 7 + 7 x ^ { 4 } + 7 x ^ { 6 } + 9 x ^ { 5 } \right) + \left( - 3 x ^ { 5 } + 7 x ^ { 4 } + 8 + 9 x ^ { 6 } \right)$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 8,9,10,11,12,13,14,15,16,17,18 \} , \mathrm { M } = \{ 8,10,12,14 \} , \mathrm { N } = \{ 9,11,13,15,17 \}$ , $Q = \{ 8,10,12,14,16,18 \}$ , and $R = \{ 8,9,10,11 \}$ . $\varnothing \cup N$

Evaluate the expression. - $( - 4 ) ^ { 2 }$

Find the product. - $- 6 x ^ { 4 } \left( 4 x ^ { 7 } + 7 x ^ { 2 } \right)$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { 9 } } { x ^ { 19 } }$

Find the domain of the expression. - $\frac { 3 } { a - 8 }$

Tell whether the statement is true or false. - $\{ 0,1,4,9 \} = \{ 4,1,9,0 \}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $20 z ^ { 5 } - 4 z ^ { 4 } - 7 z ^ { 3 } + 12$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { y } { 2 } } { \frac { 7 } { y + 9 } }$

Evaluate the expression. -Let $x = - 2 , y = - 18$ . Evaluate $| - 6 y - 10 x | - | 2 y |$ .

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 3 ] { \frac { 7 x } { y } }$

Decide whether the expression has been simplified correctly. - $( a b ) ^ { 3 } = a b ^ { 3 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -9 + 0 = 9

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 7,8,9,10,11,12 \} , \mathrm { B } = \{ 9,11,13 \} , \mathrm { C } = \{ 7,8,10,12 \} , \mathrm { D } = \{ 7,12 \}$ , and $\mathrm { U } = \{ 7,8,9,10,11,12,13 \}$ . $\mathrm { A } \subseteq \mathrm { B }$

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

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 10 x y ) ^ { 2 }$

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Exam 12: Review of Basic Concepts

Evaluate the expression. - −(2536)1/2- \left( \frac { 25 } { 36 } \right) ^ { 1 / 2 }−(3625​)1/2

Factor the polynomial by substitution. - a2(a+b)2−ab(a+b)2−72b2(a+b)2a ^ { 2 } ( a + b ) ^ { 2 } - a b ( a + b ) ^ { 2 } - 72 b ^ { 2 } ( a + b ) ^ { 2 }a2(a+b)2−ab(a+b)2−72b2(a+b)2

Determine which property of absolute value justifies the statement. - ∣−x∣=∣x∣| - x | = | x |∣−x∣=∣x∣

Solve the problem. Round to two decimal places unless otherwise indicated. -If the average cost per unit C(x)C ( x )C(x) to produce xxx units of plywood is given by C(x)=1500x+50C ( x ) = \frac { 1500 } { x + 50 }C(x)=x+501500​ , what do 200 units cost?

Find the sum or difference. - (−7+7x4+7x6+9x5)+(−3x5+7x4+8+9x6)\left( - 7 + 7 x ^ { 4 } + 7 x ^ { 6 } + 9 x ^ { 5 } \right) + \left( - 3 x ^ { 5 } + 7 x ^ { 4 } + 8 + 9 x ^ { 6 } \right)(−7+7x4+7x6+9x5)+(−3x5+7x4+8+9x6)

Evaluate the expression. - (−4)2( - 4 ) ^ { 2 }(−4)2

Find the product. - −6x4(4x7+7x2)- 6 x ^ { 4 } \left( 4 x ^ { 7 } + 7 x ^ { 2 } \right)−6x4(4x7+7x2)

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - x9x19\frac { x ^ { 9 } } { x ^ { 19 } }x19x9​

Find the domain of the expression. - 3a−8\frac { 3 } { a - 8 }a−83​

Tell whether the statement is true or false. - {0,1,4,9}={4,1,9,0}\{ 0,1,4,9 \} = \{ 4,1,9,0 \}{0,1,4,9}={4,1,9,0}

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - 20z5−4z4−7z3+1220 z ^ { 5 } - 4 z ^ { 4 } - 7 z ^ { 3 } + 1220z5−4z4−7z3+12

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - y27y+9\frac { \frac { y } { 2 } } { \frac { 7 } { y + 9 } }y+97​2y​​

Evaluate the expression. -Let x=−2,y=−18x = - 2 , y = - 18x=−2,y=−18 . Evaluate ∣−6y−10x∣−∣2y∣| - 6 y - 10 x | - | 2 y |∣−6y−10x∣−∣2y∣ .

Simplify the expression. Assume all variables represent positive real numbers. - −7xy3- \sqrt [ 3 ] { \frac { 7 x } { y } }−3y7x​​

Decide whether the expression has been simplified correctly. - (ab)3=ab3( a b ) ^ { 3 } = a b ^ { 3 }(ab)3=ab3