Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$$- 3 \sqrt { 3 } - 9 \sqrt { 75 }$$

Accepted Answer

A)  $- 12 \sqrt { 3 }$ 
B)  $48 \sqrt { 3 }$ 
C)  $- 48 \sqrt { 3 }$ 
D)  $- 42 \sqrt { 3 }$ 
A)  $- 12 \sqrt { 3 }$ 
B)  $48 \sqrt { 3 }$ 
C)  $- 48 \sqrt { 3 }$ 
D)  $- 42 \sqrt { 3 }$

Question 2

Solve the problem.
-When determining appropriate doses of medication, it is sometimes important to estimate the body surface area (BSA) of a patient. This surface area (in $\mathrm { m } ^ { 2 }$ ) can be approximated using the Mosteller formula BSA $= \left( \frac { h \cdot w } { 3600 } \right) ^ { 1 / 2 }$, where $h$ is the patient's height in centimeters and $w$ is the weight in kilograms. Determine the BSA for a patient with height $172 \mathrm {~cm}$ and weight $80 \mathrm {~kg}$. Round your answer to two decimal places.

Accepted Answer

A)  $3.82 \mathrm {~m} ^ { 2 }$ 
B)  $0.03 \mathrm {~m} ^ { 2 }$ 
C)  $1.96 \mathrm {~m} ^ { 2 }$ 
D)  $14.61 \mathrm {~m} ^ { 2 }$ 
A)  $3.82 \mathrm {~m} ^ { 2 }$ 
B)  $0.03 \mathrm {~m} ^ { 2 }$ 
C)  $1.96 \mathrm {~m} ^ { 2 }$ 
D)  $14.61 \mathrm {~m} ^ { 2 }$

Question 3

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\{ 6,10 \}$ _____$\{ 3 , - 4,8 , - 6,10,5 \}$

Accepted Answer

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

Question 4

Solve the equation
-$$\frac { y ^ { 2 } + 12 y + 36 } { y + 6 }$$

Accepted Answer

A)  $y + 6$ 
B)  $y + \frac { 6 } { y + 6 }$ 
C)  $y - 6$ 
D)  $y ^ { 2 } + 6$ 
A)  $y + 6$ 
B)  $y + \frac { 6 } { y + 6 }$ 
C)  $y - 6$ 
D)  $y ^ { 2 } + 6$

Question 5

Find the product. Assume variables represent positive real numbers.
-$$\left( m ^ { 1 / 4 } + m ^ { - 1 / 4 } \right) \left( m ^ { - 1 / 4 } - m ^ { 1 / 4 } \right)$$

Accepted Answer

A)  $1 - m ^ { 1 / 2 } + m ^ { - 1 / 2 } - m$ 
B)  $- m ^ { 1 / 2 } + m ^ { - 1 / 2 }$ 
C)  $m ^ { 1 / 2 } - m ^ { - 1 / 2 }$ 
D)  $m - m ^ { 1 / 2 } + m - 1 / 2 - 1$ 
A)  $1 - m ^ { 1 / 2 } + m ^ { - 1 / 2 } - m$ 
B)  $- m ^ { 1 / 2 } + m ^ { - 1 / 2 }$ 
C)  $m ^ { 1 / 2 } - m ^ { - 1 / 2 }$ 
D)  $m - m ^ { 1 / 2 } + m - 1 / 2 - 1$

Question 6

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { x ^ { 1 / 2 } } { x ^ { 3 / 4 } \cdot x ^ { - 4 } }$$

Accepted Answer

A)  $\frac { 1 } { x ^ { 21 / 4 } }$ 
B)  $\frac { 1 } { x ^ { 15 / 4 } }$ 
C)  $x ^ { 21 / 4 }$ 
D)  $x ^ { 15 / 4 }$ 
A)  $\frac { 1 } { x ^ { 21 / 4 } }$ 
B)  $\frac { 1 } { x ^ { 15 / 4 } }$ 
C)  $x ^ { 21 / 4 }$ 
D)  $x ^ { 15 / 4 }$

Question 7

Perform the indicated operation and write your answer with positive integer exponents.
-$$\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } }$$

Accepted Answer

A)  $\frac { m n } { n + m }$ 
B)  $\frac { n } { n ^ { 2 } - m ^ { 2 } }$ 
C)  $\frac { m ^ { 2 } + n ^ { 2 } } { m n }$ 
D)  $\frac { m n } { n ^ { 2 } + m ^ { 2 } }$ 
A)  $\frac { m n } { n + m }$ 
B)  $\frac { n } { n ^ { 2 } - m ^ { 2 } }$ 
C)  $\frac { m ^ { 2 } + n ^ { 2 } } { m n }$ 
D)  $\frac { m n } { n ^ { 2 } + m ^ { 2 } }$

Question 8

Insert $\subseteq$ or  $\nsubseteq$ in the blank to make the statement true.
-$\varnothing$_____$\{ 1,4,8,0,5,9 \}$

Accepted Answer

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

Question 9

Factor by any method.
-$x ^ { 3 } - 216$

Accepted Answer

A)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right)$ 
C)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
D)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$ 
A)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right)$ 
C)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
D)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$

Question 10

Evaluate the expression.
-$$\left( \frac { 4 } { 49 } \right) ^ { - 1 / 2 }$$

Accepted Answer

A)  not a real number 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 7 } { 2 }$ 
D)  $\frac { 2 } { 49 }$ 
A)  not a real number 
B)  $\frac { 2 } { 7 }$ 
C)  $\frac { 7 } { 2 }$ 
D)  $\frac { 2 } { 49 }$

Question 11

Tell whether the statement is true or false.
-$4 \in \{ 2,32,4,5 \}$

Accepted Answer

A) True 
 B)False

Question 12

Factor the trinomial, if possible.
-$$8 y ^ { 2 } + 18 y + 9$$

Accepted Answer

A)  $( 8 y + 1 ) ( y - 9 )$ 
B)  $( 2 y - 3 ) ( 4 y - 3 )$ 
C)  $( 8 y + 3 ) ( y + 3 )$ 
D)  $( 2 y + 3 ) ( 4 y + 3 )$ 
A)  $( 8 y + 1 ) ( y - 9 )$ 
B)  $( 2 y - 3 ) ( 4 y - 3 )$ 
C)  $( 8 y + 3 ) ( y + 3 )$ 
D)  $( 2 y + 3 ) ( 4 y + 3 )$

Question 13

Provide an appropriate response.
-Consider the following figure, which is a square divided into two squares and two rectangles.  
The length of each side of the large square is $x + 5$. Find a formula for the area of the largest square a binomial raised to a power. Write the expansion of this binomial.

Accepted Answer

A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } + 10 x + 25$ 
C)  $x ^ { 2 } - 25$ 
D)  $x ^ { 2 } - 10 x + 25$ 
A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } + 10 x + 25$ 
C)  $x ^ { 2 } - 25$ 
D)  $x ^ { 2 } - 10 x + 25$

Question 14

Use the distributive property to rewrite a sum as a product or the product as a sum.
--(-7r + 4a)

Accepted Answer

A)  -7r - 4a 
B)  7r - 4a 
C)  7r + 4a 
D)  -7r + 4a 
A)  -7r - 4a 
B)  7r - 4a 
C)  7r + 4a 
D)  -7r + 4a

Question 15

Decide whether the expression has been simplified correctly.
-$6 ^ { 0 } x = 1$

Accepted Answer

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

Question 16

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\frac { x ^ { - 3 } } { x ^ { - 17 } }$$

Accepted Answer

A)  $x ^ { 14 }$ 
B)  $- x ^ { 14 }$ 
C)  $\frac { 1 } { x ^ { 14 } }$ 
D)  $\frac { 1 } { x ^ { 20 } }$ 
A)  $x ^ { 14 }$ 
B)  $- x ^ { 14 }$ 
C)  $\frac { 1 } { x ^ { 14 } }$ 
D)  $\frac { 1 } { x ^ { 20 } }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt [ 3 ] { \frac { 6 x } { y } }$$

Accepted Answer

A)  $- \frac { \sqrt [ 3 ] { 6 x ^ { 2 } y } } { y }$ 
B)  $- \frac { \sqrt [ 3 ] { 6 x y ^ { 2 } } } { y }$ 
C)  $- \frac { \sqrt [ 3 ] { 6 x y } } { y }$ 
D)  $- \frac { \sqrt [ 3 ] { 6 x ^ { 2 } y ^ { 2 } } } { y }$ 
A)  $- \frac { \sqrt [ 3 ] { 6 x ^ { 2 } y } } { y }$ 
B)  $- \frac { \sqrt [ 3 ] { 6 x y ^ { 2 } } } { y }$ 
C)  $- \frac { \sqrt [ 3 ] { 6 x y } } { y }$ 
D)  $- \frac { \sqrt [ 3 ] { 6 x ^ { 2 } y ^ { 2 } } } { y }$

Question 18

Insert $$\in$$ or $\notin$ in the blank to make the statement is true.
-{8} {6, 8, 10, 12}

Accepted Answer

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

Question 19

Factor by any method.
-$$12 x ^ { 2 } + 9 x y + 20 x y + 15 y ^ { 2 }$$

Accepted Answer

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

Question 20

Solve the problem.
-$$( m + 7 ) ( m - 7 )$$

Accepted Answer

A)  $m ^ { 2 } - 14 m - 49$ 
B)  $m ^ { 2 } - 49$ 
C)  $m ^ { 2 } - 14$ 
D)  $m ^ { 2 } - 14 m + 49$ 
A)  $m ^ { 2 } - 14 m - 49$ 
B)  $m ^ { 2 } - 49$ 
C)  $m ^ { 2 } - 14$ 
D)  $m ^ { 2 } - 14 m + 49$

Simplify the expression. Assume all variables represent positive real numbers. - $- 3 \sqrt { 3 } - 9 \sqrt { 75 }$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{ 6,10 \}$ _____ $\{ 3 , - 4,8 , - 6,10,5 \}$

Solve the equation - $\frac { y ^ { 2 } + 12 y + 36 } { y + 6 }$

Find the product. Assume variables represent positive real numbers. - $\left( m ^ { 1 / 4 } + m ^ { - 1 / 4 } \right) \left( m ^ { - 1 / 4 } - m ^ { 1 / 4 } \right)$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { x ^ { 3 / 4 } \cdot x ^ { - 4 } }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } }$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\varnothing$ _____ $\{ 1,4,8,0,5,9 \}$

Factor by any method. - $x ^ { 3 } - 216$

Evaluate the expression. - $\left( \frac { 4 } { 49 } \right) ^ { - 1 / 2 }$

Tell whether the statement is true or false. - $4 \in \{ 2,32,4,5 \}$

Factor the trinomial, if possible. - $8 y ^ { 2 } + 18 y + 9$

Use the distributive property to rewrite a sum as a product or the product as a sum. --(-7r + 4a)

Decide whether the expression has been simplified correctly. - $6 ^ { 0 } x = 1$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 3 } } { x ^ { - 17 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 3 ] { \frac { 6 x } { y } }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -{8} {6, 8, 10, 12}

Factor by any method. - $12 x ^ { 2 } + 9 x y + 20 x y + 15 y ^ { 2 }$

Solve the problem. - $( m + 7 ) ( m - 7 )$

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

Simplify the expression. Assume all variables represent positive real numbers. - −33−975- 3 \sqrt { 3 } - 9 \sqrt { 75 }−33​−975​

Insert ⊆\subseteq⊆ or ⊈\nsubseteq⊈ in the blank to make the statement true. - {6,10}\{ 6,10 \}{6,10} _____ {3,−4,8,−6,10,5}\{ 3 , - 4,8 , - 6,10,5 \}{3,−4,8,−6,10,5}

Solve the equation - y2+12y+36y+6\frac { y ^ { 2 } + 12 y + 36 } { y + 6 }y+6y2+12y+36​

Find the product. Assume variables represent positive real numbers. - (m1/4+m−1/4)(m−1/4−m1/4)\left( m ^ { 1 / 4 } + m ^ { - 1 / 4 } \right) \left( m ^ { - 1 / 4 } - m ^ { 1 / 4 } \right)(m1/4+m−1/4)(m−1/4−m1/4)

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x1/2x3/4⋅x−4\frac { x ^ { 1 / 2 } } { x ^ { 3 / 4 } \cdot x ^ { - 4 } }x3/4⋅x−4x1/2​

Perform the indicated operation and write your answer with positive integer exponents. - (mn)−1 m−2+n−2\frac { ( \mathrm { mn } ) ^ { - 1 } } { \mathrm {~m} ^ { - 2 } + \mathrm { n } ^ { - 2 } } m−2+n−2(mn)−1​

Insert ⊆\subseteq⊆ or ⊈\nsubseteq⊈ in the blank to make the statement true. - ∅\varnothing∅ _____ {1,4,8,0,5,9}\{ 1,4,8,0,5,9 \}{1,4,8,0,5,9}

Factor by any method. - x3−216x ^ { 3 } - 216x3−216

Evaluate the expression. - (449)−1/2\left( \frac { 4 } { 49 } \right) ^ { - 1 / 2 }(494​)−1/2

Tell whether the statement is true or false. - 4∈{2,32,4,5}4 \in \{ 2,32,4,5 \}4∈{2,32,4,5}

Factor the trinomial, if possible. - 8y2+18y+98 y ^ { 2 } + 18 y + 98y2+18y+9