Question 1

Write in radical form. Assume all variables represent positive real numbers.
-$$( 9 m + n ) ^ { 8 / 9 }$$

Accepted Answer

A)  $\sqrt [ 9 ] { 9 m + n ^ { 8 } }$ 
B)  $\sqrt [ 8 ] { ( 9 m + n ) ^ { 9 } }$ 
C)  $\sqrt [ 8 ] { 9 m + n ^ { 9 } }$ 
D)  $\sqrt [ 9 ] { ( 9 m + n ) ^ { 8 } }$ 
A)  $\sqrt [ 9 ] { 9 m + n ^ { 8 } }$ 
B)  $\sqrt [ 8 ] { ( 9 m + n ) ^ { 9 } }$ 
C)  $\sqrt [ 8 ] { 9 m + n ^ { 9 } }$ 
D)  $\sqrt [ 9 ] { ( 9 m + n ) ^ { 8 } }$

Question 2

Factor the trinomial, if possible.
-$$49 m ^ { 2 } + 70 m + 25$$

Accepted Answer

A)  $( 7 m + 5 ) ^ { 2 }$ 
B)  $( 7 m - 6 ) ^ { 2 }$ 
C)  $( 7 m - 5 ) ^ { 2 }$ 
D)  $( 7 m + 5 ) ( 7 m - 5 )$ 
A)  $( 7 m + 5 ) ^ { 2 }$ 
B)  $( 7 m - 6 ) ^ { 2 }$ 
C)  $( 7 m - 5 ) ^ { 2 }$ 
D)  $( 7 m + 5 ) ( 7 m - 5 )$

Question 3

Find the sum or difference.
-$$\left( - 8 x ^ { 5 } + 2 x ^ { 7 } + 9 + 3 x ^ { 6 } \right) - \left( 8 + 8 x ^ { 6 } + 5 x ^ { 7 } + 5 x ^ { 5 } \right)$$

Accepted Answer

A)  $7 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 17$ 
B)  $- 3 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 17$ 
C)  $- 3 x ^ { 7 } - 5 x ^ { 6 } - 13 x ^ { 5 } + 1$ 
D)  $7 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 1$ 
A)  $7 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 17$ 
B)  $- 3 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 17$ 
C)  $- 3 x ^ { 7 } - 5 x ^ { 6 } - 13 x ^ { 5 } + 1$ 
D)  $7 x ^ { 7 } + 11 x ^ { 6 } - 3 x ^ { 5 } + 1$

Question 4

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\left( x ^ { - 6 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 6 } \right) ^ { - 1 }$$

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
--7 {7, 9, 11, 13}

Accepted Answer

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

Question 7

Find the domain of the expression.
-$$\frac { 3 } { m + 1 }$$

Accepted Answer

A)  $\{ \mathrm { m } \mid \mathrm { m } > 3 \}$ 
B)  $\{ m \mid m \neq 1 \}$ 
C)  $\{ \mathrm { m } \mid \mathrm { m } \neq - 1 \}$ 
D)  all real numbers 
A)  $\{ \mathrm { m } \mid \mathrm { m } > 3 \}$ 
B)  $\{ m \mid m \neq 1 \}$ 
C)  $\{ \mathrm { m } \mid \mathrm { m } \neq - 1 \}$ 
D)  all real numbers

Question 8

Simplify the expression. Assume all variables represent positive real numbers.
-$7 \sqrt { 5 } + 8 \sqrt { 5 }$

Accepted Answer

A)  75 
B)  $15 \sqrt { 10 }$ 
C)  $15 \sqrt { 5 }$ 
D)  $56 \sqrt { 5 }$ 
A)  75 
B)  $15 \sqrt { 10 }$ 
C)  $15 \sqrt { 5 }$ 
D)  $56 \sqrt { 5 }$

Question 9

Write in exponential form. Assume all variables are positive real numbers.
-$$\sqrt [ 2 ] { x ^ { 3 } }$$

Accepted Answer

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

Question 10

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 3 } { 6 - \sqrt { 2 } }$$

Accepted Answer

A)  $\frac { 18 + 3 \sqrt { 2 } } { 4 }$ 
B)  $\frac { 3 } { 6 } - \frac { 3 } { \sqrt { 2 } }$ 
C)  $\frac { 18 - 3 \sqrt { 2 } } { 34 }$ 
D)  $\frac { 18 + 3 \sqrt { 2 } } { 34 }$ 
A)  $\frac { 18 + 3 \sqrt { 2 } } { 4 }$ 
B)  $\frac { 3 } { 6 } - \frac { 3 } { \sqrt { 2 } }$ 
C)  $\frac { 18 - 3 \sqrt { 2 } } { 34 }$ 
D)  $\frac { 18 + 3 \sqrt { 2 } } { 34 }$

Question 11

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 1,2,3,4,5,6 \} , \mathrm { B } = \{ 3,5,7 \} , \mathrm { C } = \{ 1,2,4,6 \} , \mathrm { D } = \{ 1,6 \}$, and $\mathrm { U } = \{ 1,2,3,4,5,6,7 \}$.
$$\{ 0,2,6 \} \subseteq C$$

Accepted Answer

A) True 
 B)False

Question 12

Evaluate the expression.
-$27 ^ { 4 / 3 }$

Accepted Answer

A)  243 
B)  81 
C)  729 
D)  2187 
A)  243 
B)  81 
C)  729 
D)  2187

Question 13

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( - 2 t ^ { 5 } \right) \left( 4 t ^ { 2 } \right) \left( - 2 t ^ { 7 } \right)$

Accepted Answer

A)  $0 \mathrm { t } ^ { 14 }$ 
B)  $16 t ^ { 14 }$ 
C)  $0 \mathrm { t } ^ { 12 }$ 
D)  $16 \mathrm { t } ^{15}$ 
A)  $0 \mathrm { t } ^ { 14 }$ 
B)  $16 t ^ { 14 }$ 
C)  $0 \mathrm { t } ^ { 12 }$ 
D)  $16 \mathrm { t } ^{15}$

Question 14

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { 96 x ^ { 2 } y }$$

Accepted Answer

A)  $4 x y \sqrt { 6 }$ 
B)  $4 x ^ { 2 } \sqrt { 6 y }$ 
C)  $4 x \sqrt { 6 y }$ 
D)  $4 x y ^ { 2 } \sqrt { 6 }$ 
A)  $4 x y \sqrt { 6 }$ 
B)  $4 x ^ { 2 } \sqrt { 6 y }$ 
C)  $4 x \sqrt { 6 y }$ 
D)  $4 x y ^ { 2 } \sqrt { 6 }$

Question 15

Solve the problem.
-The radius of a right circular cone is given by the formula $\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } }$, where $\mathrm { V }$ is the volume and $\mathrm { h }$ is the height. If the volume is 946 cubic inches and the height is 4 inches, what is the radius? Use $3.14$ for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  $15 \mathrm { in }$. 
B)  $8.7 \mathrm { in }$. 
C)  $0.1$ in. 
D)  $15.7 \mathrm { in }$. 
A)  $15 \mathrm { in }$. 
B)  $8.7 \mathrm { in }$. 
C)  $0.1$ in. 
D)  $15.7 \mathrm { in }$.

Question 16

Determine which property of absolute value justifies the statement.
-$| x | \geq 0$

Accepted Answer

A)  Property 1: the absolute value of a number is greater than 0. 
B)  Property 1: the absolute value of a number is positive or 0. 
C)  Property 5: the triangle inequality 
D)  Property 1: the absolute value of a number is positive. 
A)  Property 1: the absolute value of a number is greater than 0. 
B)  Property 1: the absolute value of a number is positive or 0. 
C)  Property 5: the triangle inequality 
D)  Property 1: the absolute value of a number is positive.

Question 17

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.
-$$( x - 1 ) ( 3 x - 11 )$$

Accepted Answer

A)  $3 x ^ { 2 } + 11 x - 14$ 
B)  $x ^ { 2 } - 14 x - 14$ 
C)  $3 x ^ { 2 } - 15 x + 11$ 
D)  $3 x ^ { 2 } - 14 x + 11$ 
A)  $3 x ^ { 2 } + 11 x - 14$ 
B)  $x ^ { 2 } - 14 x - 14$ 
C)  $3 x ^ { 2 } - 15 x + 11$ 
D)  $3 x ^ { 2 } - 14 x + 11$

Question 18

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-During a certain football game, a player gained 91 yards rushing and -45 yards returning fumbles. 155) Find his total yardage. Is this the same as the sum of the absolute values of the two categories? Why
Or why not?

Accepted Answer

A)  -46; yards; No, it is not the same because the sum of the absolute values is -136. 
B)  46 yards; Yes, it is the same. 
C)  136 yards; No, it is not the same because the sum of the absolute values is 46 . 
D)  46 yards; No, it is not the same because the sum of the absolute values is 136. 
A)  -46; yards; No, it is not the same because the sum of the absolute values is -136. 
B)  46 yards; Yes, it is the same. 
C)  136 yards; No, it is not the same because the sum of the absolute values is 46 . 
D)  46 yards; No, it is not the same because the sum of the absolute values is 136.

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt [ 3 ] { - 8 x ^ { 3 } }$$

Accepted Answer

A)  $2 x ^ { 3 }$ 
B)  $2 x$ 
C)  not a real number 
D)  $- 2 x$ 
A)  $2 x ^ { 3 }$ 
B)  $2 x$ 
C)  not a real number 
D)  $- 2 x$

Question 20

Evaluate the expression.
-$$\frac { - 7 \cdot 6 - 4 - ( - 7 - 5 ) } { - 7 \cdot 4 + 7 }$$

Accepted Answer

A)  0 
B)  $\frac { 34 } { 77 }$ 
C)  $\frac { 2 } { 77 }$ 
D)  $\frac { 34 } { 21 }$ 
A)  0 
B)  $\frac { 34 } { 77 }$ 
C)  $\frac { 2 } { 77 }$ 
D)  $\frac { 34 } { 21 }$

Write in radical form. Assume all variables represent positive real numbers. - $( 9 m + n ) ^ { 8 / 9 }$

Factor the trinomial, if possible. - $49 m ^ { 2 } + 70 m + 25$

Find the sum or difference. - $\left( - 8 x ^ { 5 } + 2 x ^ { 7 } + 9 + 3 x ^ { 6 } \right) - \left( 8 + 8 x ^ { 6 } + 5 x ^ { 7 } + 5 x ^ { 5 } \right)$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\left( x ^ { - 6 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 6 } \right) ^ { - 1 }$

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

Insert $\in$ or $\notin$ in the blank to make the statement is true. --7 {7, 9, 11, 13}

Find the domain of the expression. - $\frac { 3 } { m + 1 }$

Simplify the expression. Assume all variables represent positive real numbers. - $7 \sqrt { 5 } + 8 \sqrt { 5 }$

Write in exponential form. Assume all variables are positive real numbers. - $\sqrt [ 2 ] { x ^ { 3 } }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 3 } { 6 - \sqrt { 2 } }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 1,2,3,4,5,6 \} , \mathrm { B } = \{ 3,5,7 \} , \mathrm { C } = \{ 1,2,4,6 \} , \mathrm { D } = \{ 1,6 \}$ , and $\mathrm { U } = \{ 1,2,3,4,5,6,7 \}$ . $\{ 0,2,6 \} \subseteq C$

Evaluate the expression. - $27 ^ { 4 / 3 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 2 t ^ { 5 } \right) \left( 4 t ^ { 2 } \right) \left( - 2 t ^ { 7 } \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 96 x ^ { 2 } y }$

Determine which property of absolute value justifies the statement. - $| x | \geq 0$

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. - $( x - 1 ) ( 3 x - 11 )$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 3 ] { - 8 x ^ { 3 } }$

Evaluate the expression. - $\frac { - 7 \cdot 6 - 4 - ( - 7 - 5 ) } { - 7 \cdot 4 + 7 }$

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

Write in radical form. Assume all variables represent positive real numbers. - (9m+n)8/9( 9 m + n ) ^ { 8 / 9 }(9m+n)8/9

Factor the trinomial, if possible. - 49m2+70m+2549 m ^ { 2 } + 70 m + 2549m2+70m+25

Find the sum or difference. - (−8x5+2x7+9+3x6)−(8+8x6+5x7+5x5)\left( - 8 x ^ { 5 } + 2 x ^ { 7 } + 9 + 3 x ^ { 6 } \right) - \left( 8 + 8 x ^ { 6 } + 5 x ^ { 7 } + 5 x ^ { 5 } \right)(−8x5+2x7+9+3x6)−(8+8x6+5x7+5x5)

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (x−6y8)(x−2y6)−1\left( x ^ { - 6 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 6 } \right) ^ { - 1 }(x−6y8)(x−2y6)−1

Simplify the expression. Assume all variables represent nonzero real numbers. - (4x)2\left( \frac { 4 } { x } \right) ^ { 2 }(x4​)2

Insert ∈\in∈ or ∉\notin∈/ in the blank to make the statement is true. --7 {7, 9, 11, 13}

Find the domain of the expression. - 3m+1\frac { 3 } { m + 1 }m+13​

Simplify the expression. Assume all variables represent positive real numbers. - 75+857 \sqrt { 5 } + 8 \sqrt { 5 }75​+85​

Write in exponential form. Assume all variables are positive real numbers. - x32\sqrt [ 2 ] { x ^ { 3 } }2x3​

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 36−2\frac { 3 } { 6 - \sqrt { 2 } }6−2​3​

Evaluate the expression. - 274/327 ^ { 4 / 3 }274/3

Simplify the expression. Assume all variables represent nonzero real numbers. - (−2t5)(4t2)(−2t7)\left( - 2 t ^ { 5 } \right) \left( 4 t ^ { 2 } \right) \left( - 2 t ^ { 7 } \right)(−2t5)(4t2)(−2t7)

Simplify the expression. Assume all variables represent positive real numbers. - 96x2y\sqrt { 96 x ^ { 2 } y }96x2y​

Determine which property of absolute value justifies the statement. - ∣x∣≥0| x | \geq 0∣x∣≥0

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. - (x−1)(3x−11)( x - 1 ) ( 3 x - 11 )(x−1)(3x−11)

Simplify the expression. Assume all variables represent positive real numbers. - −−8x33- \sqrt [ 3 ] { - 8 x ^ { 3 } }−3−8x3​

Evaluate the expression. - −7⋅6−4−(−7−5)−7⋅4+7\frac { - 7 \cdot 6 - 4 - ( - 7 - 5 ) } { - 7 \cdot 4 + 7 }−7⋅4+7−7⋅6−4−(−7−5)​