Question 1

Perform the indicated operations.
-$$\frac { - 81 x } { 7 ( 9 x + 1 ) } + \frac { 1 } { 7 x ( 9 x + 1 ) } - \frac { 4 } { x }$$

Accepted Answer

A)  $\frac { - 81 x ^ { 2 } - 252 x - 27 } { 7 x }$ 
B)  $- \frac { 9 ( x + 3 ) } { 63 x ^ { 2 } + 7 x }$ 
C)  $- \frac { 9 ( x + 3 ) } { 7 x }$ 
D)  $\frac { - 81 x ^ { 2 } - 252 x - 27 } { 63 x ^ { 2 } + 7 x }$ 
A)  $\frac { - 81 x ^ { 2 } - 252 x - 27 } { 7 x }$ 
B)  $- \frac { 9 ( x + 3 ) } { 63 x ^ { 2 } + 7 x }$ 
C)  $- \frac { 9 ( x + 3 ) } { 7 x }$ 
D)  $\frac { - 81 x ^ { 2 } - 252 x - 27 } { 63 x ^ { 2 } + 7 x }$

Question 2

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \}$, $Q = \{ 5,7,9,11,13,15 \}$, and $R = \{ 5,6,7,8 \}$.

$\mathrm { Q } ^ { \prime } \cap \left( \mathrm { N } ^ { \prime } \cap \mathrm { U } \right)$

Accepted Answer

A)  $\{ 6,8,10,12,14 \}$ 
B)  $\{ 5,7,9,11,13,15 \}$ 
C)  $\{ 6,7,8,9,10,11 \}$ 
D)  $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets. 
A)  $\{ 6,8,10,12,14 \}$ 
B)  $\{ 5,7,9,11,13,15 \}$ 
C)  $\{ 6,7,8,9,10,11 \}$ 
D)  $\varnothing ; Q ^ { \prime }$ and $\left( N ^ { \prime } \cap U \right)$ are disjoint sets.

Question 3

Solve the equation
-$$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 7 x + 2 } { 2 x + 1 }$$

Accepted Answer

A)  $x ^ { 2 } - 3 x - 2$ 
B)  $2 x ^ { 2 } + 2$ 
C)  $x ^ { 2 } + 3 x + 2$ 
D)  $2 x ^ { 2 } + 3 x + 2$ 
A)  $x ^ { 2 } - 3 x - 2$ 
B)  $2 x ^ { 2 } + 2$ 
C)  $x ^ { 2 } + 3 x + 2$ 
D)  $2 x ^ { 2 } + 3 x + 2$

Question 4

Factor by any method.
-$$t ^ { 3 } + 512$$

Accepted Answer

A)  $( t + 8 ) \left( t ^ { 2 } + 64 \right)$ 
B)  $( t + 8 ) \left( t ^ { 2 } - 8 t + 64 \right)$ 
C)  $( t - 512 ) \left( t ^ { 2 } - 1 \right)$ 
D)  $( t - 8 ) \left( t ^ { 2 } + 8 t + 64 \right)$ 
A)  $( t + 8 ) \left( t ^ { 2 } + 64 \right)$ 
B)  $( t + 8 ) \left( t ^ { 2 } - 8 t + 64 \right)$ 
C)  $( t - 512 ) \left( t ^ { 2 } - 1 \right)$ 
D)  $( t - 8 ) \left( t ^ { 2 } + 8 t + 64 \right)$

Question 5

Factor the trinomial, if possible.
-$36 m ^ { 2 } - 84 m + 49$

Accepted Answer

A)  $( 6 m - 7 ) ^ { 2 }$ 
B)  $( 6 m + 7 ) ^ { 2 }$ 
C)  $( 6 m - 8 ) ^ { 2 }$ 
D)  $( 6 m + 7 ) ( 6 m - 7 )$ 
A)  $( 6 m - 7 ) ^ { 2 }$ 
B)  $( 6 m + 7 ) ^ { 2 }$ 
C)  $( 6 m - 8 ) ^ { 2 }$ 
D)  $( 6 m + 7 ) ( 6 m - 7 )$

Question 6

Evaluate the expression.
-$$- \left| \frac { 4 } { 9 } \right|$$

Accepted Answer

A)  0 
B)  $\pm \frac { 4 } { 9 }$ 
C)  $- \frac { 4 } { 9 }$ 
D)  $\frac { 4 } { 9 }$ 
A)  0 
B)  $\pm \frac { 4 } { 9 }$ 
C)  $- \frac { 4 } { 9 }$ 
D)  $\frac { 4 } { 9 }$

Question 7

Evaluate the expression.
-Let $x = - 4 , y = 5$. Evaluate $| x + y |$.

Accepted Answer

A)  $- 9$ 
B)  9 
C)  1 
D)  $- 1$ 
A)  $- 9$ 
B)  9 
C)  1 
D)  $- 1$

Question 8

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-{2} {2, 3, 4, 5, 6, 7}

Accepted Answer

A)  $\notin$ 
B)  $\in$ 
A)  $\notin$ 
B)  $\in$

Question 9

Evaluate the expression.
-$- | - 20 |$

Accepted Answer

A)  20 
B)  0 
C)  $- 20$ 
D)  $\pm 20$ 
A)  20 
B)  0 
C)  $- 20$ 
D)  $\pm 20$

Question 10

Factor the trinomial, if possible.
-$$8 z ^ { 2 } + 6 z - 9$$

Accepted Answer

A)  $( 4 z + 3 ) ( 2 z - 3 )$ 
B)  $( 8 z - 3 ) ( z + 3 )$ 
C)  $( 8 z - 3 ) ( z - 9 )$ 
D)  $( 4 z - 3 ) ( 2 z + 3 )$ 
A)  $( 4 z + 3 ) ( 2 z - 3 )$ 
B)  $( 8 z - 3 ) ( z + 3 )$ 
C)  $( 8 z - 3 ) ( z - 9 )$ 
D)  $( 4 z - 3 ) ( 2 z + 3 )$

Question 11

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

Question 12

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-In an economics study, three quantities m, p, and q have been found to be related by the equation $$\mathrm { m } = \mathrm { p } ^ { 1 / 2 } \cdot \mathrm { q } ^ { 1 / 2 } \text {. Find } \mathrm { m } \text {, if } \mathrm { p } = 4 \text { and } \mathrm { q } = 25 \text {. }$$

Accepted Answer

A)  50 
B)  100 
C)  7 
D)  10 
A)  50 
B)  100 
C)  7 
D)  10

Question 13

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$9 ( \pi ) \text { is a real number. }$

Accepted Answer

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

Question 14

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( 8 a ^ { 5 } \right) \cdot \left( 2 a ^ { 8 } \right)$

Accepted Answer

A)  $16 a ^{40}$ 
B)  $16 a ^ { 13 }$ 
C)  $10 ^ { 13 }$ 
D) $ 10^{40}$ 
A)  $16 a ^{40}$ 
B)  $16 a ^ { 13 }$ 
C)  $10 ^ { 13 }$ 
D) $ 10^{40}$

Question 15

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-The cost of manufacturing clocks is given by c $$c = 64 ( n + 4 ) ^ { 1 / 2 }$$ , where c is the cost in dollars and n is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $64 
B)  $16 
C)  $256 
D)  $128 
A)  $64 
B)  $16 
C)  $256 
D)  $128

Question 16

Factor the trinomial, if possible.
-$$5 x ^ { 3 } + 10 x ^ { 2 } - 40 x$$

Accepted Answer

A)  $\left( 5 x ^ { 2 } + 10 x \right) ( x - 4 )$ 
B)  $5 x ( x - 2 ) ( x + 4 )$ 
C)  $( x - 2 ) \left( 5 x ^ { 2 } + 20 \right)$ 
D)  $5 x ( x + 2 ) ( x - 4 )$ 
A)  $\left( 5 x ^ { 2 } + 10 x \right) ( x - 4 )$ 
B)  $5 x ( x - 2 ) ( x + 4 )$ 
C)  $( x - 2 ) \left( 5 x ^ { 2 } + 20 \right)$ 
D)  $5 x ( x + 2 ) ( x - 4 )$

Question 17

Factor by any method.
-$$( p - q ) ^ { 2 } + 20 ( p - q ) + 100$$

Accepted Answer

A)  $( p - q + 10 ) ^ { 2 }$ 
B)  $( p - q + 10 ) ( p - q - 10 )$ 
C)  prime 
D)  $( p - q + 100 ) ( p - q )$ 
A)  $( p - q + 10 ) ^ { 2 }$ 
B)  $( p - q + 10 ) ( p - q - 10 )$ 
C)  prime 
D)  $( p - q + 100 ) ( p - q )$

Question 18

Solve the problem.
-$$( 2 x + 3 ) ^ { 4 }$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 6 x + 9 \right) ^ { 4 }$ 
B)  $16 x ^ { 3 } + 96 x ^ { 2 } + 216 x + 216$ 
C)  $48 x ^ { 4 } + 288 x ^ { 3 } + 216 x ^ { 2 } + 648 x + 81$ 
D)  $16 x ^ { 4 } + 96 x ^ { 3 } + 216 x ^ { 2 } + 216 x + 81$ 
A)  $\left( 4 x ^ { 2 } + 6 x + 9 \right) ^ { 4 }$ 
B)  $16 x ^ { 3 } + 96 x ^ { 2 } + 216 x + 216$ 
C)  $48 x ^ { 4 } + 288 x ^ { 3 } + 216 x ^ { 2 } + 648 x + 81$ 
D)  $16 x ^ { 4 } + 96 x ^ { 3 } + 216 x ^ { 2 } + 216 x + 81$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt { \frac { 25 } { 12 } }$$

Accepted Answer

A)  $- \frac { 5 \sqrt { 3 } } { 3 }$ 
B)  $- 5 \sqrt { 3 }$ 
C)  $- 12$ 
D)  $- \frac { 5 \sqrt { 3 } } { 6 }$ 
A)  $- \frac { 5 \sqrt { 3 } } { 3 }$ 
B)  $- 5 \sqrt { 3 }$ 
C)  $- 12$ 
D)  $- \frac { 5 \sqrt { 3 } } { 6 }$

Question 20

Solve the problem.
-$( 4 y + x ) ( 4 y - x )$

Accepted Answer

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

Perform the indicated operations. - $\frac { - 81 x } { 7 ( 9 x + 1 ) } + \frac { 1 } { 7 x ( 9 x + 1 ) } - \frac { 4 } { x }$

Solve the equation - $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 7 x + 2 } { 2 x + 1 }$

Factor by any method. - $t ^ { 3 } + 512$

Factor the trinomial, if possible. - $36 m ^ { 2 } - 84 m + 49$

Evaluate the expression. - $- \left| \frac { 4 } { 9 } \right|$

Evaluate the expression. -Let $x = - 4 , y = 5$ . Evaluate $| x + y |$ .

Insert $\in$ or $\notin$ in the blank to make the statement is true. -{2} {2, 3, 4, 5, 6, 7}

Evaluate the expression. - $- | - 20 |$

Factor the trinomial, if possible. - $8 z ^ { 2 } + 6 z - 9$

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

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $9 ( \pi ) \text { is a real number. }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 8 a ^ { 5 } \right) \cdot \left( 2 a ^ { 8 } \right)$

Factor the trinomial, if possible. - $5 x ^ { 3 } + 10 x ^ { 2 } - 40 x$

Factor by any method. - $( p - q ) ^ { 2 } + 20 ( p - q ) + 100$

Solve the problem. - $( 2 x + 3 ) ^ { 4 }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt { \frac { 25 } { 12 } }$

Solve the problem. - $( 4 y + x ) ( 4 y - x )$

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

Filters

Exam 1: Review of Basic Concepts

Perform the indicated operations. - −81x7(9x+1)+17x(9x+1)−4x\frac { - 81 x } { 7 ( 9 x + 1 ) } + \frac { 1 } { 7 x ( 9 x + 1 ) } - \frac { 4 } { x }7(9x+1)−81x​+7x(9x+1)1​−x4​

Solve the equation - 4x3+8x2+7x+22x+1\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 7 x + 2 } { 2 x + 1 }2x+14x3+8x2+7x+2​

Factor by any method. - t3+512t ^ { 3 } + 512t3+512

Factor the trinomial, if possible. - 36m2−84m+4936 m ^ { 2 } - 84 m + 4936m2−84m+49

Evaluate the expression. - −∣49∣- \left| \frac { 4 } { 9 } \right|−​94​​

Evaluate the expression. -Let x=−4,y=5x = - 4 , y = 5x=−4,y=5 . Evaluate ∣x+y∣| x + y |∣x+y∣ .

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. -{2} {2, 3, 4, 5, 6, 7}

Evaluate the expression. - −∣−20∣- | - 20 |−∣−20∣

Factor the trinomial, if possible. - 8z2+6z−98 z ^ { 2 } + 6 z - 98z2+6z−9

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

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 9(π) is a real number. 9 ( \pi ) \text { is a real number. }9(π) is a real number.

Simplify the expression. Assume all variables represent nonzero real numbers. - (8a5)⋅(2a8)\left( 8 a ^ { 5 } \right) \cdot \left( 2 a ^ { 8 } \right)(8a5)⋅(2a8)

Factor the trinomial, if possible. - 5x3+10x2−40x5 x ^ { 3 } + 10 x ^ { 2 } - 40 x5x3+10x2−40x

Factor by any method. - (p−q)2+20(p−q)+100( p - q ) ^ { 2 } + 20 ( p - q ) + 100(p−q)2+20(p−q)+100

Solve the problem. - (2x+3)4( 2 x + 3 ) ^ { 4 }(2x+3)4

Simplify the expression. Assume all variables represent positive real numbers. - −2512- \sqrt { \frac { 25 } { 12 } }−1225​​

Solve the problem. - (4y+x)(4y−x)( 4 y + x ) ( 4 y - x )(4y+x)(4y−x)