Question 1

Tell whether the statement is true or false.
-$7 \notin \{ 0,5,6,8,10 \}$

Accepted Answer

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

Question 2

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( - 3 x ) ^ { 4 }$

Accepted Answer

A)  $- 12 x$ 
B)  $12 x$ 
C)  $- 81 x ^ { 4 }$ 
D)  $81 x ^ { 4 }$ 
A)  $- 12 x$ 
B)  $12 x$ 
C)  $- 81 x ^ { 4 }$ 
D)  $81 x ^ { 4 }$

Question 3

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { y + 5 x } { y - 4 a }$$

Accepted Answer

A)  $- \frac { 7 } { 23 }$ 
B)  $- \frac { 6 } { 19 }$ 
C)  $- \frac { 9 } { 19 }$ 
D)  $- \frac { 7 } { 19 }$ 
A)  $- \frac { 7 } { 23 }$ 
B)  $- \frac { 6 } { 19 }$ 
C)  $- \frac { 9 } { 19 }$ 
D)  $- \frac { 7 } { 19 }$

Question 4

Decide whether the expression has been simplified correctly.
-$$\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }$$

Accepted Answer

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

Question 5

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 $R = \{ 3,4,5,6 \}$.
$( N \cup R ) \cap Q$

Accepted Answer

A)  $\varnothing ; N$ and $R$ are disjoint sets. 
B)  $\{ 5 \}$ 
C)  $\{ 3,5 \}$ 
D)  $\{ 3 \}$ 
A)  $\varnothing ; N$ and $R$ are disjoint sets. 
B)  $\{ 5 \}$ 
C)  $\{ 3,5 \}$ 
D)  $\{ 3 \}$

Question 6

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

Accepted Answer

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

Question 7

Find the product.
-$- 11 x ^ { 5 } \left( 6 x ^ { 4 } - 12 x ^ { 3 } \right)$

Accepted Answer

A)  $66 x ^ { 9 } + 66 x ^ { 8 }$ 
B)  $66 x ^ { 5 }$ 
C)  $- 66 x ^ { 9 } + 132 x ^ { 8 }$ 
D)  $- 66 x ^ { 9 } - 12 x ^ { 3 }$ 
A)  $66 x ^ { 9 } + 66 x ^ { 8 }$ 
B)  $66 x ^ { 5 }$ 
C)  $- 66 x ^ { 9 } + 132 x ^ { 8 }$ 
D)  $- 66 x ^ { 9 } - 12 x ^ { 3 }$

Question 8

Perform the indicated operations.
-$\frac { 3 } { 5 x } - \frac { 1 } { 5 x }$

Accepted Answer

A)  $\frac { 2 } { 5 x }$ 
B)  1 
C)  $\frac { 1 } { 5 x }$ 
D)  $\frac { 5 } { 2 x }$ 
A)  $\frac { 2 } { 5 x }$ 
B)  1 
C)  $\frac { 1 } { 5 x }$ 
D)  $\frac { 5 } { 2 x }$

Question 9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-70

Accepted Answer

A)  $- 1$ 
B)  7 
C)  1 
D)  0 
A)  $- 1$ 
B)  7 
C)  1 
D)  0

Question 10

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( 8 \mathrm { t } ) ^ { 4 }$

Accepted Answer

A)  $8^4 t^{4}$ 
B)  $32 t ^ { 4 }$ 
C)  $8 ^ { 4 } \mathrm { t }$ 
D)  $8 \mathrm { t } ^ { 4 }$ 
A)  $8^4 t^{4}$ 
B)  $32 t ^ { 4 }$ 
C)  $8 ^ { 4 } \mathrm { t }$ 
D)  $8 \mathrm { t } ^ { 4 }$

Question 11

Factor the trinomial, if possible.
-$49 m ^ { 2 } - 126 m + 81$

Accepted Answer

A)  $( 7 m + 9 ) ( 7 m - 9 )$ 
B)  $( 7 m - 9 ) ^ { 2 }$ 
C)  $( 7 m + 9 ) ^ { 2 }$ 
D)  $( 7 m - 10 ) ^ { 2 }$ 
A)  $( 7 m + 9 ) ( 7 m - 9 )$ 
B)  $( 7 m - 9 ) ^ { 2 }$ 
C)  $( 7 m + 9 ) ^ { 2 }$ 
D)  $( 7 m - 10 ) ^ { 2 }$

Question 12

Write in radical form. Assume all variables represent positive real numbers.
-$$( 4 \mathrm {~m} + 3 \mathrm { n } ) ^ { 2 / 5 }$$

Accepted Answer

A)  $\sqrt [ 2 ] { ( 4 m + 3 n ) ^ { 5 } }$ 
B)  $\sqrt [ 5 ] { ( 4 m + 3 n ) ^ { 2 } }$ 
C)  $\sqrt [ 5 ] { 4 m + 3 n ^ { 2 } }$ 
D)  $\sqrt [ 2 ] { 4 m + 3 n ^ { 5 } }$ 
A)  $\sqrt [ 2 ] { ( 4 m + 3 n ) ^ { 5 } }$ 
B)  $\sqrt [ 5 ] { ( 4 m + 3 n ) ^ { 2 } }$ 
C)  $\sqrt [ 5 ] { 4 m + 3 n ^ { 2 } }$ 
D)  $\sqrt [ 2 ] { 4 m + 3 n ^ { 5 } }$

Question 13

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

Accepted Answer

A)  $( 3 x + 2 ) ( 4 x - 5 )$ 
B)  $( 3 x - 2 ) ( 4 x + 5 )$ 
C)  $( 12 x - 2 ) ( x + 5 )$ 
D)  $( 12 x + 2 ) ( x - 5 )$ 
A)  $( 3 x + 2 ) ( 4 x - 5 )$ 
B)  $( 3 x - 2 ) ( 4 x + 5 )$ 
C)  $( 12 x - 2 ) ( x + 5 )$ 
D)  $( 12 x + 2 ) ( x - 5 )$

Question 14

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$( 8 x ) ^ { 0 }$

Accepted Answer

A)  1 
B)  8x 
C)  8 
D)  0 
A)  1 
B)  8x 
C)  8 
D)  0

Question 15

Find the product or quotient.
-$\frac { 6 p - 6 } { p } \div \frac { 8 p - 8 } { 4 p ^ { 2 } }$

Accepted Answer

A)  $\frac { 48 p ^ { 2 } + 96 p + 48 } { 4 p ^ { 3 } }$ 
B)  $\frac { 24 p ^ { 3 } - 24 p ^ { 2 } } { 8 p ^ { 2 } - 8 p }$ 
C)  $3 p$ 
D)  $\frac { 1 } { 3 } p$ 
A)  $\frac { 48 p ^ { 2 } + 96 p + 48 } { 4 p ^ { 3 } }$ 
B)  $\frac { 24 p ^ { 3 } - 24 p ^ { 2 } } { 8 p ^ { 2 } - 8 p }$ 
C)  $3 p$ 
D)  $\frac { 1 } { 3 } p$

Question 16

Factor by any method.
-$$( 3 x - 5 ) ^ { 2 } - y ^ { 2 }$$

Accepted Answer

A)  $( 3 x - 5 + y ) ( 3 x + 5 - y )$ 
B)  $( 3 x + 5 + y ) ( 3 x + 5 - y )$ 
C)  $( 3 x - 5 + y ) ( 3 x - 5 - y )$ 
D)  prime 
A)  $( 3 x - 5 + y ) ( 3 x + 5 - y )$ 
B)  $( 3 x + 5 + y ) ( 3 x + 5 - y )$ 
C)  $( 3 x - 5 + y ) ( 3 x - 5 - y )$ 
D)  prime

Question 17

Divide.
-$$\frac { 9 y ^ { 4 } + 12 y ^ { 3 } + 4 y - 1 } { 3 y ^ { 2 } + 1 }$$

Accepted Answer

A)  $3 y ^ { 2 } + 4 y$ 
B)  $3 y ^ { 2 } + 4 y - 1$ 
C)  $3 y ^ { 2 } - 4 y + 1$ 
D)  $3 y ^ { 2 } - 1$ 
A)  $3 y ^ { 2 } + 4 y$ 
B)  $3 y ^ { 2 } + 4 y - 1$ 
C)  $3 y ^ { 2 } - 4 y + 1$ 
D)  $3 y ^ { 2 } - 1$

Question 18

Evaluate the expression for x = -2, y = 3, and a = -4.
-5x + 7y - 3a

Accepted Answer

A)  23 
B)  13 
C)  -47 
D)  7 
A)  23 
B)  13 
C)  -47 
D)  7

Question 19

Decide whether the expression has been simplified correctly.
-$$3 ^ { 0 } x = 0$$

Accepted Answer

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

Question 20

Factor the trinomial, if possible.
-$$x ^ { 2 } + 5 x y - 14 y ^ { 2 }$$

Accepted Answer

A)  $( x + 7 y ) ( x - 2 y )$ 
B)  $( x - 7 y ) ( x + y )$ 
C)  $( x - y ) ( x + 2 y )$ 
D)  $( x - 7 y ) ( x + 2 y )$ 
A)  $( x + 7 y ) ( x - 2 y )$ 
B)  $( x - 7 y ) ( x + y )$ 
C)  $( x - y ) ( x + 2 y )$ 
D)  $( x - 7 y ) ( x + 2 y )$

Tell whether the statement is true or false. - $7 \notin \{ 0,5,6,8,10 \}$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( - 3 x ) ^ { 4 }$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { y + 5 x } { y - 4 a }$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }$

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 $R = \{ 3,4,5,6 \}$ . $( N \cup R ) \cap Q$

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

Find the product. - $- 11 x ^ { 5 } \left( 6 x ^ { 4 } - 12 x ^ { 3 } \right)$

Perform the indicated operations. - $\frac { 3 } { 5 x } - \frac { 1 } { 5 x }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. -70

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 8 \mathrm { t } ) ^ { 4 }$

Factor the trinomial, if possible. - $49 m ^ { 2 } - 126 m + 81$

Write in radical form. Assume all variables represent positive real numbers. - $( 4 \mathrm {~m} + 3 \mathrm { n } ) ^ { 2 / 5 }$

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

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( 8 x ) ^ { 0 }$

Find the product or quotient. - $\frac { 6 p - 6 } { p } \div \frac { 8 p - 8 } { 4 p ^ { 2 } }$

Factor by any method. - $( 3 x - 5 ) ^ { 2 } - y ^ { 2 }$

Divide. - $\frac { 9 y ^ { 4 } + 12 y ^ { 3 } + 4 y - 1 } { 3 y ^ { 2 } + 1 }$

Evaluate the expression for x = -2, y = 3, and a = -4. -5x + 7y - 3a

Decide whether the expression has been simplified correctly. - $3 ^ { 0 } x = 0$

Factor the trinomial, if possible. - $x ^ { 2 } + 5 x y - 14 y ^ { 2 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

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Exam 12: Review of Basic Concepts

Tell whether the statement is true or false. - 7∉{0,5,6,8,10}7 \notin \{ 0,5,6,8,10 \}7∈/{0,5,6,8,10}

Simplify the expression. Assume all variables represent nonzero real numbers. - (−3x)4( - 3 x ) ^ { 4 }(−3x)4

Evaluate the expression for x = -2, y = 3, and a = -4. - y+5xy−4a\frac { y + 5 x } { y - 4 a }y−4ay+5x​

Decide whether the expression has been simplified correctly. - (x4)2=x6\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 6 }(x4)2=x6

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

Find the product. - −11x5(6x4−12x3)- 11 x ^ { 5 } \left( 6 x ^ { 4 } - 12 x ^ { 3 } \right)−11x5(6x4−12x3)

Perform the indicated operations. - 35x−15x\frac { 3 } { 5 x } - \frac { 1 } { 5 x }5x3​−5x1​