Question 1

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( \frac { 5 } { x } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 25 } { x ^ { 2 } }$ 
B)  $\frac { 25 } { x }$ 
C)  $25 x ^ { 2 }$ 
D)  $\frac { 5 } { x ^ { 2 } }$ 
A)  $\frac { 25 } { x ^ { 2 } }$ 
B)  $\frac { 25 } { x }$ 
C)  $25 x ^ { 2 }$ 
D)  $\frac { 5 } { x ^ { 2 } }$

Question 2

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-(0 _____{ 1,3,0,5,4 }

Accepted Answer

A)  $\mathrm {  }  \notin$ 
B)  $\in$ 
A)  $\mathrm {  }  \notin$ 
B)  $\in$

Question 3

Factor by any method.
-$$y ^ { 6 } + 1$$

Accepted Answer

A)  $\left( \mathrm { y } ^ { 3 } + 1 \right) \left( \mathrm { y } ^ { 3 } - 1 \right)$ 
B)  $( y + 1 ) ( y - 1 ) \left( y ^ { 2 } + y + 1 \right) \left( y ^ { 2 } - y + 1 \right)$ 
C)  $( y + 1 ) ( y - 1 ) \left( y ^ { 4 } - y ^ { 2 } + 1 \right)$ 
D)  $\left( \mathrm { y } ^ { 2 } + 1 \right) \left( \mathrm { y } ^ { 4 } - \mathrm { y } ^ { 2 } + 1 \right)$ 
A)  $\left( \mathrm { y } ^ { 3 } + 1 \right) \left( \mathrm { y } ^ { 3 } - 1 \right)$ 
B)  $( y + 1 ) ( y - 1 ) \left( y ^ { 2 } + y + 1 \right) \left( y ^ { 2 } - y + 1 \right)$ 
C)  $( y + 1 ) ( y - 1 ) \left( y ^ { 4 } - y ^ { 2 } + 1 \right)$ 
D)  $\left( \mathrm { y } ^ { 2 } + 1 \right) \left( \mathrm { y } ^ { 4 } - \mathrm { y } ^ { 2 } + 1 \right)$

Question 4

Write the expression in lowest terms.
-$\frac { 8 x ^ { 3 } + 4 x } { 16 x ^ { 2 } }$

Accepted Answer

A)  $\frac { 2 x ^ { 2 } + 1 } { 4 x }$ 
B)  $2 x ^ { 2 } + 1$ 
C)  $\frac { 2 x ^ { 2 } } { 4 x + 1 }$ 
D)  $\frac { 2 x + 1 } { 16 }$ 
A)  $\frac { 2 x ^ { 2 } + 1 } { 4 x }$ 
B)  $2 x ^ { 2 } + 1$ 
C)  $\frac { 2 x ^ { 2 } } { 4 x + 1 }$ 
D)  $\frac { 2 x + 1 } { 16 }$

Question 5

Factor by grouping.
-$$12 x ^ { 2 } - 20 x y + 15 x y - 25 y ^ { 2 }$$

Accepted Answer

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

Question 6

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

Accepted Answer

A)  81 
B)  $- 81$ 
C)  $- \frac { 1 } { 81 }$ 
D)  $\frac { 1 } { 81 }$ 
A)  81 
B)  $- 81$ 
C)  $- \frac { 1 } { 81 }$ 
D)  $\frac { 1 } { 81 }$

Question 7

Find the distance between two points given their coordinates.
-Find the distance between points $P$ and $Q$ on a number line, with coordinates 6 and $- 11$, respectively.

Accepted Answer

A)  $d ( P , Q ) = - 17$ 
B)  $d ( P , Q ) = - 5$ 
C)  $d ( P , Q ) = 17$ 
D)  $d ( P , Q ) = 5$ 
A)  $d ( P , Q ) = - 17$ 
B)  $d ( P , Q ) = - 5$ 
C)  $d ( P , Q ) = 17$ 
D)  $d ( P , Q ) = 5$

Question 8

Find the product.
-$$( r - 8 ) ^ { 2 }$$

Accepted Answer

A)  $64 r ^ { 2 } - 16 r + 64$ 
B)  $r ^ { 2 } + 64$ 
C)  $r + 64$ 
D)  $r ^ { 2 } - 16 r + 64$ 
A)  $64 r ^ { 2 } - 16 r + 64$ 
B)  $r ^ { 2 } + 64$ 
C)  $r + 64$ 
D)  $r ^ { 2 } - 16 r + 64$

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$$( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$$

Accepted Answer

A)  13 
B)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } - 8 \sqrt [ 3 ] { 5 } + 13$ 
C)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } + 8 \sqrt [ 3 ] { 5 } - 3$ 
D)  $- 3$ 
A)  13 
B)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } - 8 \sqrt [ 3 ] { 5 } + 13$ 
C)  $4 \sqrt [ 3 ] { 5 ^ { 2 } } + 8 \sqrt [ 3 ] { 5 } - 3$ 
D)  $- 3$

Question 10

Factor by any method.
-$12 x ^ { 2 } - 8 x y + 9 x y - 6 y ^ { 2 }$

Accepted Answer

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

Question 11

Insert ⊆ or ⊈ in the blank to make the statement true.
-{-15,10,-16,0,14\} ___________$\varnothing$

Accepted Answer

A)  $\subseteq$ 
B)   
A)  $\subseteq$ 
B)

Question 12

Factor the trinomial, if possible.
-$$x ^ { 2 } - x - 72$$

Accepted Answer

A)  $( x + 9 ) ( x - 8 )$ 
B)  $( x + 1 ) ( x - 17 )$ 
C)  $( x + 8 ) ( x - 9 )$ 
D)  $( x - 9 ) ( x + 9 )$ 
A)  $( x + 9 ) ( x - 8 )$ 
B)  $( x + 1 ) ( x - 17 )$ 
C)  $( x + 8 ) ( x - 9 )$ 
D)  $( x - 9 ) ( x + 9 )$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt [ 3 ] { x ^ { 2 } y } \cdot \sqrt [ 3 ] { x } } { \sqrt [ 3 ] { y ^ { 2 } } }$$

Accepted Answer

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

Question 14

Find the domain of the expression.
-$$\frac { 1 } { p + 9 }$$

Accepted Answer

A)  all real numbers 
B)  $\{ p \mid p > 1 \}$ 
C)  $\{ p \mid p \neq - 9 \}$ 
D)  $\{ p \mid p \neq 9 \}$ 
A)  all real numbers 
B)  $\{ p \mid p > 1 \}$ 
C)  $\{ p \mid p \neq - 9 \}$ 
D)  $\{ p \mid p \neq 9 \}$

Question 15

Factor by any method.
-$12 x ^ { 2 } + 10 x - 30 x - 25$

Accepted Answer

A)  $( 12 x + 5 ) ( x - 5 )$ 
B)  $( 12 x - 5 ) ( x + 5 )$ 
C)  $( 2 x - 5 ) ( 6 x + 5 )$ 
D)  $( 2 x + 5 ) ( 6 x - 5 )$ 
A)  $( 12 x + 5 ) ( x - 5 )$ 
B)  $( 12 x - 5 ) ( x + 5 )$ 
C)  $( 2 x - 5 ) ( 6 x + 5 )$ 
D)  $( 2 x + 5 ) ( 6 x - 5 )$

Question 16

Evaluate the expression.
-$( - 125 ) ^ { 1 / 3 }$

Accepted Answer

A)  5 
B)  $- 5$ 
C)  $- 125$ 
D)  not a real number 
A)  5 
B)  $- 5$ 
C)  $- 125$ 
D)  not a real number

Question 17

Factor by any method.
-$$64 s ^ { 3 } + 1$$

Accepted Answer

A)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 1 \right)$ 
B)  $( 4 \mathrm {~s} - 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 4 \mathrm {~s} + 1 \right)$ 
C)  $( 64 \mathrm {~s} + 1 ) \left( \mathrm { s } ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
D)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
A)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 1 \right)$ 
B)  $( 4 \mathrm {~s} - 1 ) \left( 16 \mathrm {~s} ^ { 2 } + 4 \mathrm {~s} + 1 \right)$ 
C)  $( 64 \mathrm {~s} + 1 ) \left( \mathrm { s } ^ { 2 } - 4 \mathrm {~s} + 1 \right)$ 
D)  $( 4 \mathrm {~s} + 1 ) \left( 16 \mathrm {~s} ^ { 2 } - 4 \mathrm {~s} + 1 \right)$

Question 18

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

Accepted Answer

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

Question 19

Find the product.
-$$( 6 x - 4 y + 5 ) ( 6 x - 4 y - 5 )$$

Accepted Answer

A)  $- 48 x y - 30 x + - 20 y - 25$ 
B)  $12 x ^ { 2 } - 8 y ^ { 2 } - 50$ 
C)  $36 x ^ { 2 } + 48 x y - 16 y ^ { 2 } - 50$ 
D)  $36 x ^ { 2 } - 48 x y + 16 y ^ { 2 } - 25$ 
A)  $- 48 x y - 30 x + - 20 y - 25$ 
B)  $12 x ^ { 2 } - 8 y ^ { 2 } - 50$ 
C)  $36 x ^ { 2 } + 48 x y - 16 y ^ { 2 } - 50$ 
D)  $36 x ^ { 2 } - 48 x y + 16 y ^ { 2 } - 25$

Question 20

Find the product.
-$8 a x ^ { 3 } \left( 7 a x ^ { 7 } - 8 x ^ { 3 } + 6 a \right)$

Accepted Answer

A)  $56 a ^ { 2 } x ^ { 21 } - 64 a x ^ { 9 } + 48 a ^ { 2 } x ^ { 3 }$ 
B)  $56 a x ^ { 10 } - 64 a x ^ { 6 } + 48 a x ^ { 3 }$ 
C)  $56 a ^ { 2 } x ^ { 10 } - 64 a x ^ { 6 } + 48 a ^ { 2 } x ^ { 3 }$ 
D)  $56 a ^ { 2 } x ^ { 10 } + 64 a x ^ { 6 } - 48 a ^ { 2 } x ^ { 3 }$ 
A)  $56 a ^ { 2 } x ^ { 21 } - 64 a x ^ { 9 } + 48 a ^ { 2 } x ^ { 3 }$ 
B)  $56 a x ^ { 10 } - 64 a x ^ { 6 } + 48 a x ^ { 3 }$ 
C)  $56 a ^ { 2 } x ^ { 10 } - 64 a x ^ { 6 } + 48 a ^ { 2 } x ^ { 3 }$ 
D)  $56 a ^ { 2 } x ^ { 10 } + 64 a x ^ { 6 } - 48 a ^ { 2 } x ^ { 3 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( \frac { 5 } { x } \right) ^ { 2 }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -(0 _____{ 1,3,0,5,4 }

Factor by any method. - $y ^ { 6 } + 1$

Write the expression in lowest terms. - $\frac { 8 x ^ { 3 } + 4 x } { 16 x ^ { 2 } }$

Factor by grouping. - $12 x ^ { 2 } - 20 x y + 15 x y - 25 y ^ { 2 }$

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

Find the distance between two points given their coordinates. -Find the distance between points $P$ and $Q$ on a number line, with coordinates 6 and $- 11$ , respectively.

Find the product. - $( r - 8 ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)$

Factor by any method. - $12 x ^ { 2 } - 8 x y + 9 x y - 6 y ^ { 2 }$

Insert ⊆ or ⊈ in the blank to make the statement true. -{-15,10,-16,0,14\} ___________ $\varnothing$

Factor the trinomial, if possible. - $x ^ { 2 } - x - 72$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { x ^ { 2 } y } \cdot \sqrt [ 3 ] { x } } { \sqrt [ 3 ] { y ^ { 2 } } }$

Find the domain of the expression. - $\frac { 1 } { p + 9 }$

Factor by any method. - $12 x ^ { 2 } + 10 x - 30 x - 25$

Evaluate the expression. - $( - 125 ) ^ { 1 / 3 }$

Factor by any method. - $64 s ^ { 3 } + 1$

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

Find the product. - $( 6 x - 4 y + 5 ) ( 6 x - 4 y - 5 )$

Find the product. - $8 a x ^ { 3 } \left( 7 a x ^ { 7 } - 8 x ^ { 3 } + 6 a \right)$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

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Trigonometric Identities and Equations

Applications of Trigonometry

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Exam 12: Review of Basic Concepts

Simplify the expression. Assume all variables represent nonzero real numbers. - (5x)2\left( \frac { 5 } { x } \right) ^ { 2 }(x5​)2

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -(0 _____{ 1,3,0,5,4 }

Factor by any method. - y6+1y ^ { 6 } + 1y6+1

Write the expression in lowest terms. - 8x3+4x16x2\frac { 8 x ^ { 3 } + 4 x } { 16 x ^ { 2 } }16x28x3+4x​

Factor by grouping. - 12x2−20xy+15xy−25y212 x ^ { 2 } - 20 x y + 15 x y - 25 y ^ { 2 }12x2−20xy+15xy−25y2

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

Find the distance between two points given their coordinates. -Find the distance between points PPP and QQQ on a number line, with coordinates 6 and −11- 11−11 , respectively.

Find the product. - (r−8)2( r - 8 ) ^ { 2 }(r−8)2

Simplify the expression. Assume all variables represent positive real numbers. - (53−2)(523+253+4)( \sqrt [ 3 ] { 5 } - 2 ) \left( \sqrt [ 3 ] { 5 ^ { 2 } } + 2 \sqrt [ 3 ] { 5 } + 4 \right)(35​−2)(352​+235​+4)

Factor by any method. - 12x2−8xy+9xy−6y212 x ^ { 2 } - 8 x y + 9 x y - 6 y ^ { 2 }12x2−8xy+9xy−6y2

Insert ⊆ or ⊈ in the blank to make the statement true. -{-15,10,-16,0,14\} ___________ ∅\varnothing∅

Factor the trinomial, if possible. - x2−x−72x ^ { 2 } - x - 72x2−x−72

Simplify the expression. Assume all variables represent positive real numbers. - x2y3⋅x3y23\frac { \sqrt [ 3 ] { x ^ { 2 } y } \cdot \sqrt [ 3 ] { x } } { \sqrt [ 3 ] { y ^ { 2 } } }3y2​3x2y​⋅3x​​

Find the domain of the expression. - 1p+9\frac { 1 } { p + 9 }p+91​

Factor by any method. - 12x2+10x−30x−2512 x ^ { 2 } + 10 x - 30 x - 2512x2+10x−30x−25

Evaluate the expression. - (−125)1/3( - 125 ) ^ { 1 / 3 }(−125)1/3

Factor by any method. - 64s3+164 s ^ { 3 } + 164s3+1

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

Find the product. - (6x−4y+5)(6x−4y−5)( 6 x - 4 y + 5 ) ( 6 x - 4 y - 5 )(6x−4y+5)(6x−4y−5)

Find the product. - 8ax3(7ax7−8x3+6a)8 a x ^ { 3 } \left( 7 a x ^ { 7 } - 8 x ^ { 3 } + 6 a \right)8ax3(7ax7−8x3+6a)