Question 1

Factor by any method.
-$$25 x ^ { 2 } + 20 x + 4 - y ^ { 2 }$$

Accepted Answer

A)  $( 5 x - 2 + y ) ( 5 x - 2 - y )$ 
B)  $( 5 x + 2 + y ) ( 5 x + 2 - y )$ 
C)  prime 
D)  $( 5 x + 2 + y ) ( 5 x - 2 - y )$ 
A)  $( 5 x - 2 + y ) ( 5 x - 2 - y )$ 
B)  $( 5 x + 2 + y ) ( 5 x + 2 - y )$ 
C)  prime 
D)  $( 5 x + 2 + y ) ( 5 x - 2 - y )$

Question 2

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$$- 6 x ^ { 2 } \left( 10 x ^ { 6 } - 11 x ^ { 3 } \right)$$

Accepted Answer

A)  $6 x ^ { 2 }$ 
B)  $- 60 x ^ { 8 } + 66 x ^ { 5 }$ 
C)  $6 x ^ { 8 } + 6 x ^ { 5 }$ 
D)  $- 60 x ^ { 8 } - 11 x ^ { 3 }$ 
A)  $6 x ^ { 2 }$ 
B)  $- 60 x ^ { 8 } + 66 x ^ { 5 }$ 
C)  $6 x ^ { 8 } + 6 x ^ { 5 }$ 
D)  $- 60 x ^ { 8 } - 11 x ^ { 3 }$

Question 3

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$\frac { | - 2 | } { | 3 | } = \left| \frac { - 2 } { 3 } \right|$$

Accepted Answer

A)  True 
B)  False; $\frac { | - 2 | } { | 3 | } = \left| \frac { 2 } { - 3 } \right|$ 
A)  True 
B)  False; $\frac { | - 2 | } { | 3 | } = \left| \frac { 2 } { - 3 } \right|$

Question 4

Factor, using the given factor. Assume all variables represent positive real numbers.
-$$24 y ^ { 4 } ( 2 y + 1 ) ^ { - 2 / 5 } + 32 y ^ { 3 } ( 2 y + 1 ) ^ { 3 / 5 } - 64 y ^ { 2 } ( 2 y + 1 ) ^ { 8 / 5 } ; \quad 8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 }$$

Accepted Answer

A)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 21 y ^ { 2 } - 28 y + 8 \right)$ 
B)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 19 y ^ { 2 } - 28 y - 8 \right)$ 
C)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 19 y ^ { 2 } - 28 y + 8 \right)$ 
D)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 21 y ^ { 2 } - 28 y - 8 \right)$ 
A)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 21 y ^ { 2 } - 28 y + 8 \right)$ 
B)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 19 y ^ { 2 } - 28 y - 8 \right)$ 
C)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 19 y ^ { 2 } - 28 y + 8 \right)$ 
D)  $8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 21 y ^ { 2 } - 28 y - 8 \right)$

Question 5

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

Accepted Answer

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

Question 6

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 $R = \{ 5,6,7,8 \}$.

$\mathrm { N } ^ { \prime }$

Accepted Answer

A)  $\mathrm { M }$, or $\{ 5,7,9,11 \}$ 
B)  $\{ 6,8,10,12,14 \}$ 
C)  $\{ 7,9,11,13,15 \}$ 
D)  $Q$, or $\{ 5,7,9,11,13,15 \}$ 
A)  $\mathrm { M }$, or $\{ 5,7,9,11 \}$ 
B)  $\{ 6,8,10,12,14 \}$ 
C)  $\{ 7,9,11,13,15 \}$ 
D)  $Q$, or $\{ 5,7,9,11,13,15 \}$

Question 7

Factor the polynomial by substitution.
-$$15 z ^ { 4 } + 2 z ^ { 2 } - 8$$

Accepted Answer

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

Question 8

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 9,10,11,12,13,14,15,16,17,18,19 \} , \mathrm { M } = \{ 9,11,13,15 \} , \mathrm { N } = \{ 10,12,14,16,18 \}$, $Q = \{ 9,11,13,15,17,19 \}$, and $R = \{ 9,10,11,12 \}$.
$\mathrm { M } \cup \mathrm { N }$

Accepted Answer

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

Question 9

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( 4 x y ) ^ { 2 }$

Accepted Answer

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

Question 10

Factor by grouping.
-$10 x ^ { 2 } + 25 x y - 12 x y - 30 y ^ { 2 }$

Accepted Answer

A)  $( 5 x - 6 y ) ( 2 x + 5 y )$ 
B)  $( 10 x - 6 y ) ( x + 5 y )$ 
C)  $( 5 x - 6 ) ( 2 x + 5 )$ 
D)  $( 5 x + 6 y ) ( 2 x + 5 y )$ 
A)  $( 5 x - 6 y ) ( 2 x + 5 y )$ 
B)  $( 10 x - 6 y ) ( x + 5 y )$ 
C)  $( 5 x - 6 ) ( 2 x + 5 )$ 
D)  $( 5 x + 6 y ) ( 2 x + 5 y )$

Question 11

Solve the problem.
-$$\frac { - 10 x ^ { 5 } + 10 x ^ { 4 } - 15 x ^ { 3 } } { - 5 x ^ { 4 } }$$

Accepted Answer

A)  $2 x - 2$ 
B)  $2 x + 10 x ^ { 4 } + \frac { 3 } { x }$ 
C)  $2 x - 2 + \frac { 3 } { x }$ 
D)  $5 x - 2$ 
A)  $2 x - 2$ 
B)  $2 x + 10 x ^ { 4 } + \frac { 3 } { x }$ 
C)  $2 x - 2 + \frac { 3 } { x }$ 
D)  $5 x - 2$

Question 12

Factor the trinomial, if possible.
-$5 x ^ { 2 } - 31 x y - 28 y ^ { 2 }$

Accepted Answer

A)  $y ( 5 x + 4 ) ( x - 7 )$ 
B)  $( 5 x + 4 y ) ( x - 7 y )$ 
C)  prime 
D)  $( 5 x + 7 y ) ( x - 4 y )$ 
A)  $y ( 5 x + 4 ) ( x - 7 )$ 
B)  $( 5 x + 4 y ) ( x - 7 y )$ 
C)  prime 
D)  $( 5 x + 7 y ) ( x - 4 y )$

Question 13

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-If the radius of a sphere is doubled, by what factor will the volume change?

Accepted Answer

A)  2 
B)  8 
C)  6 
D)  4 
A)  2 
B)  8 
C)  6 
D)  4

Question 14

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\{ 1,3,6,8 \}$ _____$\{ 1,1,3,4,5,6 \}$

Accepted Answer

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

Question 15

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-$- \frac { x } { y } > 0$

Accepted Answer

A)  x and y have the same sign. 
B)  x and y must be negative. 
C)  x and y have different signs. 
D)  x and y must be positive. 
A)  x and y have the same sign. 
B)  x and y must be negative. 
C)  x and y have different signs. 
D)  x and y must be positive.

Question 16

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$$

Accepted Answer

A)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$ 
B)  $\frac { 4 \sqrt { h } } { h }$ 
C)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
D)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$ 
A)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$ 
B)  $\frac { 4 \sqrt { h } } { h }$ 
C)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
D)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$

Question 17

Factor the trinomial, if possible.
-$$x ^ { 2 } - x - 56$$

Accepted Answer

A)  $( x + 8 ) ( x - 7 )$ 
B)  $( x - 8 ) ( x + 8 )$ 
C)  $( x + 7 ) ( x - 8 )$ 
D)  $( x + 1 ) ( x - 15 )$ 
A)  $( x + 8 ) ( x - 7 )$ 
B)  $( x - 8 ) ( x + 8 )$ 
C)  $( x + 7 ) ( x - 8 )$ 
D)  $( x + 1 ) ( x - 15 )$

Question 18

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$, and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$.
$\mathrm { D } \nsubseteq \mathrm { C }$

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

A)  $27 x ^ { 3 } + 108 x ^ { 2 } + 144 x + 64$ 
B)  $9 x ^ { 2 } + 24 x + 16$ 
C)  $27 x ^ { 3 } + 108 x ^ { 2 } + 108 x + 64$ 
D)  $9 x ^ { 6 } + 12 x ^ { 3 } + 4096$ 
A)  $27 x ^ { 3 } + 108 x ^ { 2 } + 144 x + 64$ 
B)  $9 x ^ { 2 } + 24 x + 16$ 
C)  $27 x ^ { 3 } + 108 x ^ { 2 } + 108 x + 64$ 
D)  $9 x ^ { 6 } + 12 x ^ { 3 } + 4096$

Question 20

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-xy < 0

Accepted Answer

A)  x and y must be negative. 
B)  x and y have different signs. 
C)  x and y must be positive. 
D)  x and y have the same sign. 
A)  x and y must be negative. 
B)  x and y have different signs. 
C)  x and y must be positive. 
D)  x and y have the same sign.

Factor by any method. - $25 x ^ { 2 } + 20 x + 4 - y ^ { 2 }$

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $- 6 x ^ { 2 } \left( 10 x ^ { 6 } - 11 x ^ { 3 } \right)$

Decide whether the statement is true or false. If false, correct the statement so it is true. - $\frac { | - 2 | } { | 3 | } = \left| \frac { - 2 } { 3 } \right|$

Factor, using the given factor. Assume all variables represent positive real numbers. - $24 y ^ { 4 } ( 2 y + 1 ) ^ { - 2 / 5 } + 32 y ^ { 3 } ( 2 y + 1 ) ^ { 3 / 5 } - 64 y ^ { 2 } ( 2 y + 1 ) ^ { 8 / 5 } ; \quad 8 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 }$

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

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 $R = \{ 5,6,7,8 \}$ . $\mathrm { N } ^ { \prime }$

Factor the polynomial by substitution. - $15 z ^ { 4 } + 2 z ^ { 2 } - 8$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 9,10,11,12,13,14,15,16,17,18,19 \} , \mathrm { M } = \{ 9,11,13,15 \} , \mathrm { N } = \{ 10,12,14,16,18 \}$ , $Q = \{ 9,11,13,15,17,19 \}$ , and $R = \{ 9,10,11,12 \}$ . $\mathrm { M } \cup \mathrm { N }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( 4 x y ) ^ { 2 }$

Factor by grouping. - $10 x ^ { 2 } + 25 x y - 12 x y - 30 y ^ { 2 }$

Solve the problem. - $\frac { - 10 x ^ { 5 } + 10 x ^ { 4 } - 15 x ^ { 3 } } { - 5 x ^ { 4 } }$

Factor the trinomial, if possible. - $5 x ^ { 2 } - 31 x y - 28 y ^ { 2 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -If the radius of a sphere is doubled, by what factor will the volume change?

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{ 1,3,6,8 \}$ _____ $\{ 1,1,3,4,5,6 \}$

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. - $- \frac { x } { y } > 0$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$

Factor the trinomial, if possible. - $x ^ { 2 } - x - 56$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$ , and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$ . $\mathrm { D } \nsubseteq \mathrm { C }$

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

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -xy < 0

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

Factor by any method. - 25x2+20x+4−y225 x ^ { 2 } + 20 x + 4 - y ^ { 2 }25x2+20x+4−y2

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - −6x2(10x6−11x3)- 6 x ^ { 2 } \left( 10 x ^ { 6 } - 11 x ^ { 3 } \right)−6x2(10x6−11x3)

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−2∣∣3∣=∣−23∣\frac { | - 2 | } { | 3 | } = \left| \frac { - 2 } { 3 } \right|∣3∣∣−2∣​=​3−2​​

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

Factor the polynomial by substitution. - 15z4+2z2−815 z ^ { 4 } + 2 z ^ { 2 } - 815z4+2z2−8

Simplify the expression. Assume all variables represent nonzero real numbers. - (4xy)2( 4 x y ) ^ { 2 }(4xy)2

Factor by grouping. - 10x2+25xy−12xy−30y210 x ^ { 2 } + 25 x y - 12 x y - 30 y ^ { 2 }10x2+25xy−12xy−30y2

Solve the problem. - −10x5+10x4−15x3−5x4\frac { - 10 x ^ { 5 } + 10 x ^ { 4 } - 15 x ^ { 3 } } { - 5 x ^ { 4 } }−5x4−10x5+10x4−15x3​

Factor the trinomial, if possible. - 5x2−31xy−28y25 x ^ { 2 } - 31 x y - 28 y ^ { 2 }5x2−31xy−28y2