Question 1

Simplify the expression. Assume all variables represent positive real numbers.
-$$- \sqrt [ 3 ] { - 125 x ^ { 3 } }$$

Accepted Answer

A)  $5 x$ 
B)  $- 5 x$ 
C)  $5 x ^ { 3 }$ 
D)  not a real number 
A)  $5 x$ 
B)  $- 5 x$ 
C)  $5 x ^ { 3 }$ 
D)  not a real number

Question 2

Find the product.
-$$\left( - 4 x ^ { 2 } y ^ { 4 } \right) \left( - 4 x ^ { 2 } y ^ { 2 } \right)$$

Accepted Answer

A)  $16 x ^ { 4 } y ^ { 6 }$ 
B)  $16 x y ^ { 6 }$ 
C)  $16 x y ^ { 4 }$ 
D)  $16 x ^ { 6 } y ^4$ 
A)  $16 x ^ { 4 } y ^ { 6 }$ 
B)  $16 x y ^ { 6 }$ 
C)  $16 x y ^ { 4 }$ 
D)  $16 x ^ { 6 } y ^4$

Question 3

Determine the degree of the polynomial.
-$- 4 x ^ { 2 } + 4 x ^ { 3 } + 4 x ^ { 4 } + 3$

Accepted Answer

A)  4 
B)  10 
C)  9 
D)  2 
A)  4 
B)  10 
C)  9 
D)  2

Question 4

Solve the problem. Round to two decimal places unless otherwise indicated.
-Suppose the cost per ton, $y$, to build an oil platform of $x$ thousand tons is approximated by $y =$ $\frac { 162,500 } { x + 325 }$. What is the cost per ton for $x = 10$ ?

Accepted Answer

A)  $\$ 16250.00$ 
B)  $\$ 15925.00$ 
C)  $\$ 485.07$ 
D)  $\$ 50.00$ 
A)  $\$ 16250.00$ 
B)  $\$ 15925.00$ 
C)  $\$ 485.07$ 
D)  $\$ 50.00$

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$3 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }$

Accepted Answer

A)  $( 3 - 2 x ) \sqrt [ 5 ] { x y }$ 
B)  $2 x \sqrt [ 5 ] { x y }$ 
C)  $x \sqrt [ 5 ] { x y }$ 
D)  cannot be simplified 
A)  $( 3 - 2 x ) \sqrt [ 5 ] { x y }$ 
B)  $2 x \sqrt [ 5 ] { x y }$ 
C)  $x \sqrt [ 5 ] { x y }$ 
D)  cannot be simplified

Question 6

Factor the trinomial, if possible.
-$\mathrm { u } ^ { 2 } - 2 \mathrm { uv } - 48 \mathrm { v } ^ { 2 }$

Accepted Answer

A)  $( u + 6 v ) ( u - 8 v )$ 
B)  prime 
C)  $( u - 6 v ) ( u + 8 v )$ 
D)  $( u - 6 v ) ( u + v )$ 
A)  $( u + 6 v ) ( u - 8 v )$ 
B)  prime 
C)  $( u - 6 v ) ( u + 8 v )$ 
D)  $( u - 6 v ) ( u + v )$

Question 7

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 $R = \{ 5,6,7,8 \}$.
$\mathrm { M } \cap \mathrm { N }$

Accepted Answer

A)  $\{ 5,6,7,8,9,10,11,12,14 \}$ 
B)  $\{ 7,8,9,10,14 \}$ 
C)  $\{ 6,7,8,9,10,11,12,13,14 \}$ 
D)  $\varnothing ; M$ and $N$ are disjoint sets. 
A)  $\{ 5,6,7,8,9,10,11,12,14 \}$ 
B)  $\{ 7,8,9,10,14 \}$ 
C)  $\{ 6,7,8,9,10,11,12,13,14 \}$ 
D)  $\varnothing ; M$ and $N$ are disjoint sets.

Question 8

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$\frac { 1 } { ( a + 7 ) } \cdot ( a + 7 ) = 1$, if $a + 7 \neq 0$

Accepted Answer

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

Question 9

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$\left( - 2 t ^ { 4 } \right) \left( 5 t ^ { 3 } \right) \left( - 2 t ^ { 7 } \right)$$

Accepted Answer

A)  $1 t ^ { 12 }$ 
B)  $20 t ^ { 15 }$ 
C)  $1 t ^ { 14 }$ 
D)  $20 \mathrm { t } ^ { 14 }$ 
A)  $1 t ^ { 12 }$ 
B)  $20 t ^ { 15 }$ 
C)  $1 t ^ { 14 }$ 
D)  $20 \mathrm { t } ^ { 14 }$

Question 10

Simplify the expression. Assume all variables represent positive real numbers.
-$- 16 \sqrt { 5 } - 6 \sqrt { 5 }$

Accepted Answer

A)  $- 22 \sqrt { 5 }$ 
B)  $21 \sqrt { 5 }$ 
C)  $11 \sqrt { 5 }$ 
D)  $- 10 \sqrt { 5 }$ 
A)  $- 22 \sqrt { 5 }$ 
B)  $21 \sqrt { 5 }$ 
C)  $11 \sqrt { 5 }$ 
D)  $- 10 \sqrt { 5 }$

Question 11

Simplify the expression. Assume all variables represent nonzero real numbers.
-$x ^ { 3 } \cdot x ^ { 2 }$

Accepted Answer

A)  $x ^ { 5 }$ 
B)  $( 2 x ) ^ { 5 }$ 
C)  $( 2 x ) ^ { 6 }$ 
D)  $x ^ { 6 }$ 
A)  $x ^ { 5 }$ 
B)  $( 2 x ) ^ { 5 }$ 
C)  $( 2 x ) ^ { 6 }$ 
D)  $x ^ { 6 }$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { - 343 }$

Accepted Answer

A)  $- 7$ 
B)  49 
C)  $\pm 7$ 
D)  not a real number 
A)  $- 7$ 
B)  49 
C)  $\pm 7$ 
D)  not a real number

Question 13

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$

Accepted Answer

A)  $x ^ { 22 / 5 }$ 
B)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
C)  $x ^ { 34 / 5 }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$ 
A)  $x ^ { 22 / 5 }$ 
B)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
C)  $x ^ { 34 / 5 }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$

Question 14

Evaluate the expression.
-$- 5 ( - 2 ) ^ { 3 }$

Accepted Answer

A)  40 
B)  1,000 
C)  $- 1,000$ 
D)  $- 40$ 
A)  40 
B)  1,000 
C)  $- 1,000$ 
D)  $- 40$

Question 15

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 2 x ^ { 2 }$

Accepted Answer

A)  Monomial 
B)  Binomial 
C)  None of these 
D)  Trinomial 
A)  Monomial 
B)  Binomial 
C)  None of these 
D)  Trinomial

Question 16

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
$$\mathrm { BSA } = \left( \frac { \mathrm { h } \cdot \mathrm { w } } { 3600 } \right) ^ { 1 / 2 } ,$$
where $h$ is the patient's height in centimeters and $w$ is the weight in kilograms. Determine the BSA for a patient with height $181 \mathrm {~cm}$ and weight $60 \mathrm {~kg}$. Round your answer to two decimal places.

Accepted Answer

A)  $0.03 \mathrm {~m} ^ { 2 }$ 
B)  $1.74 \mathrm {~m} ^ { 2 }$ 
C)  $3.02 \mathrm {~m} ^ { 2 }$ 
D)  $9.10 \mathrm {~m} ^ { 2 }$ 
A)  $0.03 \mathrm {~m} ^ { 2 }$ 
B)  $1.74 \mathrm {~m} ^ { 2 }$ 
C)  $3.02 \mathrm {~m} ^ { 2 }$ 
D)  $9.10 \mathrm {~m} ^ { 2 }$

Question 17

Evaluate the expression.
-Let $x = 1 , y = 5$. Evaluate $\frac { | x + 4 | - | - 5 y | } { | 2 y - 4 x | }$.

Accepted Answer

A)  $- \frac { 10 } { 7 }$ 
B)  $- \frac { 10 } { 9 }$ 
C)  5 
D)  $- \frac { 10 } { 3 }$ 
A)  $- \frac { 10 } { 7 }$ 
B)  $- \frac { 10 } { 9 }$ 
C)  5 
D)  $- \frac { 10 } { 3 }$

Question 18

Solve the problem.
-The Blood Alcohol Concentration (BAC) of a person who has been drinking is given by the expression
number of $\mathrm { oz } \times \%$ alcohol $\times .075 \div$ body weight in $\mathrm { lb }$ - hours of drinking $\times .015$.
Find the BAC to the nearest thousandth for a $170 - \mathrm { lb }$ woman, who, in 5 hours, has drunk $410 - \mathrm { oz }$ beers ( $40 \mathrm { oz } )$, each having a $3.2 \%$ alcohol content.

Accepted Answer

A)  $- 0.364$ 
B)  $- 0.061$ 
C)  $- 0.019$ 
D)  $- 333.277$ 
A)  $- 0.364$ 
B)  $- 0.061$ 
C)  $- 0.019$ 
D)  $- 333.277$

Question 19

Find the sum or difference.
-$$2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)$$

Accepted Answer

A)  $- 28 r ^ { 4 } - 9 r ^ { 3 } + 18 r ^ { 2 } - 12 r$ 
B)  $- 28 r ^ { 4 } + 6 r ^ { 2 } - 5 r$ 
C)  $- 28 r ^ { 4 } + 18 r ^ { 3 } - 6 r ^ { 2 } - r$ 
D)  $- 28 r ^ { 4 } + 45 r ^ { 3 } - 18 r ^ { 2 }$ 
A)  $- 28 r ^ { 4 } - 9 r ^ { 3 } + 18 r ^ { 2 } - 12 r$ 
B)  $- 28 r ^ { 4 } + 6 r ^ { 2 } - 5 r$ 
C)  $- 28 r ^ { 4 } + 18 r ^ { 3 } - 6 r ^ { 2 } - r$ 
D)  $- 28 r ^ { 4 } + 45 r ^ { 3 } - 18 r ^ { 2 }$

Question 20

Determine the degree of the polynomial.
-$- a + 9 a ^ { 3 } - 4 a ^ { 7 } + 4 a ^ { 2 }$

Accepted Answer

A)  12 
B)  7 
C)  4 
D)  13 
A)  12 
B)  7 
C)  4 
D)  13

Simplify the expression. Assume all variables represent positive real numbers. - $- \sqrt [ 3 ] { - 125 x ^ { 3 } }$

Find the product. - $\left( - 4 x ^ { 2 } y ^ { 4 } \right) \left( - 4 x ^ { 2 } y ^ { 2 } \right)$

Determine the degree of the polynomial. - $- 4 x ^ { 2 } + 4 x ^ { 3 } + 4 x ^ { 4 } + 3$

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, $y$ , to build an oil platform of $x$ thousand tons is approximated by $y =$ $\frac { 162,500 } { x + 325 }$ . What is the cost per ton for $x = 10$ ?

Simplify the expression. Assume all variables represent positive real numbers. - $3 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }$

Factor the trinomial, if possible. - $\mathrm { u } ^ { 2 } - 2 \mathrm { uv } - 48 \mathrm { v } ^ { 2 }$

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 $R = \{ 5,6,7,8 \}$ . $\mathrm { M } \cap \mathrm { N }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $\frac { 1 } { ( a + 7 ) } \cdot ( a + 7 ) = 1$ , if $a + 7 \neq 0$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 2 t ^ { 4 } \right) \left( 5 t ^ { 3 } \right) \left( - 2 t ^ { 7 } \right)$

Simplify the expression. Assume all variables represent positive real numbers. - $- 16 \sqrt { 5 } - 6 \sqrt { 5 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $x ^ { 3 } \cdot x ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 343 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$

Evaluate the expression. - $- 5 ( - 2 ) ^ { 3 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 2 x ^ { 2 }$

Evaluate the expression. -Let $x = 1 , y = 5$ . Evaluate $\frac { | x + 4 | - | - 5 y | } { | 2 y - 4 x | }$ .

Find the sum or difference. - $2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)$

Determine the degree of the polynomial. - $- a + 9 a ^ { 3 } - 4 a ^ { 7 } + 4 a ^ { 2 }$

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 12: Review of Basic Concepts

Simplify the expression. Assume all variables represent positive real numbers. - −−125x33- \sqrt [ 3 ] { - 125 x ^ { 3 } }−3−125x3​

Find the product. - (−4x2y4)(−4x2y2)\left( - 4 x ^ { 2 } y ^ { 4 } \right) \left( - 4 x ^ { 2 } y ^ { 2 } \right)(−4x2y4)(−4x2y2)

Determine the degree of the polynomial. - −4x2+4x3+4x4+3- 4 x ^ { 2 } + 4 x ^ { 3 } + 4 x ^ { 4 } + 3−4x2+4x3+4x4+3

Solve the problem. Round to two decimal places unless otherwise indicated. -Suppose the cost per ton, yyy , to build an oil platform of xxx thousand tons is approximated by y=y =y= 162,500x+325\frac { 162,500 } { x + 325 }x+325162,500​ . What is the cost per ton for x=10x = 10x=10 ?

Simplify the expression. Assume all variables represent positive real numbers. - 3x6y5−2xxy53 \sqrt [ 5 ] { x ^ { 6 } y } - 2 x \sqrt [ 5 ] { x y }35x6y​−2x5xy​

Factor the trinomial, if possible. - u2−2uv−48v2\mathrm { u } ^ { 2 } - 2 \mathrm { uv } - 48 \mathrm { v } ^ { 2 }u2−2uv−48v2

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 1(a+7)⋅(a+7)=1\frac { 1 } { ( a + 7 ) } \cdot ( a + 7 ) = 1(a+7)1​⋅(a+7)=1 , if a+7≠0a + 7 \neq 0a+7=0

Simplify the expression. Assume all variables represent nonzero real numbers. - (−2t4)(5t3)(−2t7)\left( - 2 t ^ { 4 } \right) \left( 5 t ^ { 3 } \right) \left( - 2 t ^ { 7 } \right)(−2t4)(5t3)(−2t7)

Simplify the expression. Assume all variables represent positive real numbers. - −165−65- 16 \sqrt { 5 } - 6 \sqrt { 5 }−165​−65​

Simplify the expression. Assume all variables represent nonzero real numbers. - x3⋅x2x ^ { 3 } \cdot x ^ { 2 }x3⋅x2

Simplify the expression. Assume all variables represent positive real numbers. - −3433\sqrt [ 3 ] { - 343 }3−343​

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x3/5x6/5⋅x−5\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }x6/5⋅x−5x3/5​

Evaluate the expression. - −5(−2)3- 5 ( - 2 ) ^ { 3 }−5(−2)3

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −2x2- 2 x ^ { 2 }−2x2

Evaluate the expression. -Let x=1,y=5x = 1 , y = 5x=1,y=5 . Evaluate ∣x+4∣−∣−5y∣∣2y−4x∣\frac { | x + 4 | - | - 5 y | } { | 2 y - 4 x | }∣2y−4x∣∣x+4∣−∣−5y∣​ .

Find the sum or difference. - 2(−2r4+9r3−3r)−3(8r4−9r3+6r2−2r)2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)2(−2r4+9r3−3r)−3(8r4−9r3+6r2−2r)

Determine the degree of the polynomial. - −a+9a3−4a7+4a2- a + 9 a ^ { 3 } - 4 a ^ { 7 } + 4 a ^ { 2 }−a+9a3−4a7+4a2