Question 1

Solve and check the equation.
-$$( x + 11 ) ^ { 3 / 2 } = 125$$

Accepted Answer

A)  $\{ 14 \}$ 
B)  $\{ - 6 \}$ 
C)  $\{ \sqrt [ 3 ] { 5 } - 11 \}$ 
D)  $\{ 36 \}$ 
A)  $\{ 14 \}$ 
B)  $\{ - 6 \}$ 
C)  $\{ \sqrt [ 3 ] { 5 } - 11 \}$ 
D)  $\{ 36 \}$ A

Question 2

Express the interval in set-builder notation and graph the interval on a number line.
-$(-\infty, 5.5]$

Accepted Answer

A)  $\{ x \mid x \leq 5.5 \}$
  
B)  $\{ x \mid x  5.5 \}$
  
D)  $\{ x \mid x \geq 5.5 \}$
  
A)  $\{ x \mid x \leq 5.5 \}$
  
B)  $\{ x \mid x  5.5 \}$
  
D)  $\{ x \mid x \geq 5.5 \}$
  A

Question 3

Perform the indicated operations and write the result in standard form.
-$$( \sqrt { - 36 } ) ( \sqrt { - 49 } )$$

Accepted Answer

A)  $- 42$ 
B)  $42 \mathrm { i } ^ { 2 }$ 
C)  42 
D)  $- 42 \mathrm { i }$ 
A)  $- 42$ 
B)  $42 \mathrm { i } ^ { 2 }$ 
C)  42 
D)  $- 42 \mathrm { i }$ A

Question 4

Solve the problem using this formula.
-Find $E$, the voltage of a circuit, if $\mathrm { I } = ( 9 + 6 \mathrm { i } )$ amperes and $\mathrm { R } = ( 7 + 2 \mathrm { i } )$ ohms.

Accepted Answer

A)  $( 51 + 60 i )$ volts 
B)  $( 51 - 60 \mathrm { i } )$ volts 
C)  $( 60 + 51 i )$ volts 
D)  (60 - 51i) volts 
A)  $( 51 + 60 i )$ volts 
B)  $( 51 - 60 \mathrm { i } )$ volts 
C)  $( 60 + 51 i )$ volts 
D)  (60 - 51i) volts

Question 5

6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation
-

Accepted Answer

A)  x-intercepts: $- 2 \pm \sqrt { 11 }$
  
B)  $x$-intercepts: $- 4$ and 3
  
C)  $x$-intercepts: none
  
D)  $x$-intercept: 4
  
A)  x-intercepts: $- 2 \pm \sqrt { 11 }$
  
B)  $x$-intercepts: $- 4$ and 3
  
C)  $x$-intercepts: none
  
D)  $x$-intercept: 4

Question 6

Solve the problem.
-Suppose a cost-benefit model is given by $y = \frac { 2652 x } { 100 - x }$, where $y$ is the cost for removing $x$ percent of a given pollutant. What percent of pollutant can be removed for $\$ 22,000$ ? Round your answer to the nearest tenth of a percent.

Accepted Answer

A)  $89.2 \%$ 
B)  $113.7 \%$ 
C)  $8.9 \%$ 
D)  $453.4 \%$ 
A)  $89.2 \%$ 
B)  $113.7 \%$ 
C)  $8.9 \%$ 
D)  $453.4 \%$

Question 7

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } - 5 x$$

Accepted Answer

A)  $\frac { 25 } { 4 } ; x ^ { 2 } - 5 x + \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
B)  $- \frac { 25 } { 4 } ; x ^ { 2 } - 5 x - \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
C)  $\frac { 5 } { 2 } ; x ^ { 2 } - 5 x + \frac { 5 } { 2 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
D)  $25 ; x ^ { 2 } - 5 x + 25 = ( x - 5 ) ^ { 2 }$ 
A)  $\frac { 25 } { 4 } ; x ^ { 2 } - 5 x + \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
B)  $- \frac { 25 } { 4 } ; x ^ { 2 } - 5 x - \frac { 25 } { 4 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
C)  $\frac { 5 } { 2 } ; x ^ { 2 } - 5 x + \frac { 5 } { 2 } = \left( x - \frac { 5 } { 2 } \right) ^ { 2 }$ 
D)  $25 ; x ^ { 2 } - 5 x + 25 = ( x - 5 ) ^ { 2 }$

Question 8

Solve the absolute value equation or indicate that the equation has no solution.
-$\left| 2 x ^ { 2 } - x - 1 \right| = 3$

Accepted Answer

A)  $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
C)  $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
B)  $\left\{ - \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
C)  $\left\{ \frac { 1 - \sqrt { 33 } } { 4 } , - \frac { 1 + \sqrt { 33 } } { 4 } \right\}$ 
D)  $\varnothing$

Question 9

Solve the problem.
-A formula used to determine the velocity $v$ in feet per second of an object (neglecting air resistance) after it has fallen a certain height is $\mathrm { v } = \sqrt { 2 g h }$, where $g$ is the acceleration due to gravity and $h$ is the height the object has fallen. If the acceleration $g$ due to gravity on Earth is approximately 32 feet per second per second, find the velocity of a bowling ball after it has fallen 40 feet. (Round to the nearest tenth.)

Accepted Answer

A)  $50.6 \mathrm { ft }$ per $\mathrm { sec }$ 
B)  $35.8 \mathrm { ft }$ per sec 
C)  $8.9 \mathrm { ft }$ per sec 
D)  $2560 \mathrm { ft }$ per sec 
A)  $50.6 \mathrm { ft }$ per $\mathrm { sec }$ 
B)  $35.8 \mathrm { ft }$ per sec 
C)  $8.9 \mathrm { ft }$ per sec 
D)  $2560 \mathrm { ft }$ per sec

Question 10

Use graphs to find the set.
-$( - \infty , 8 ) \cap [ - 2,17 )$

Accepted Answer

A)  $[ - 2,8 )$ 
B)  $( - \infty , 17 )$ 
C)  $( 8,17 )$ 
D)  $( - \infty , - 2 ]$ 
A)  $[ - 2,8 )$ 
B)  $( - \infty , 17 )$ 
C)  $( 8,17 )$ 
D)  $( - \infty , - 2 ]$

Question 11

Solve the problem.
-A square sheet of paper measures 45 centimeters on each side. What is the length of the diagonal of this paper?

Accepted Answer

A)  $45 \sqrt { 2 } \mathrm {~cm}$ 
B)  $45 \mathrm {~cm}$ 
C)  $4050 \mathrm {~cm}$ 
D)  $90 \mathrm {~cm}$ 
A)  $45 \sqrt { 2 } \mathrm {~cm}$ 
B)  $45 \mathrm {~cm}$ 
C)  $4050 \mathrm {~cm}$ 
D)  $90 \mathrm {~cm}$

Question 12

Solve the compound inequality. Other than ∅, use interval notation to express the solution set and graph the
solution set on a number line.
-The formula for converting Fahrenheit temperature, $\mathrm { F }$, to Celsius temperature, $\mathrm { C }$, is
$$C = \frac { 5 } { 9 } ( F - 32 ) \text {. }$$
If Celsius temperature ranges from $- 20 ^ { \circ }$ to $50 ^ { \circ }$, inclusive, what is the range for the Fahrenheit temperature?

Accepted Answer

A)  $\left[ - 4 ^ { \circ } \mathrm { F } , 122 ^ { \circ } \mathrm { F } \right]$ 
B)  $\left( - 4 ^ { \circ } \mathrm { F } , 122 ^ { \circ } \mathrm { F } \right)$ 
C)  $\left[ - 20 ^ { \circ } \mathrm { F } , - 12 ^ { \circ } \mathrm { F } \right]$ 
D)  $\left( - 20 ^ { \circ } \mathrm { F } , - 12 ^ { \circ } \mathrm { F } \right)$ 
A)  $\left[ - 4 ^ { \circ } \mathrm { F } , 122 ^ { \circ } \mathrm { F } \right]$ 
B)  $\left( - 4 ^ { \circ } \mathrm { F } , 122 ^ { \circ } \mathrm { F } \right)$ 
C)  $\left[ - 20 ^ { \circ } \mathrm { F } , - 12 ^ { \circ } \mathrm { F } \right]$ 
D)  $\left( - 20 ^ { \circ } \mathrm { F } , - 12 ^ { \circ } \mathrm { F } \right)$

Question 13

Solve and check the linear equation.
-$$0.40 x - 0.20 ( 80 + x ) = - 0.10 ( 80 )$$

Accepted Answer

A)  $\{ 40 \}$ 
B)  $\{ 30 \}$ 
C)  $\{ 50 \}$ 
D)  $\{ 20 \}$ Find all values of x satisfying the given conditions. 
A)  $\{ 40 \}$ 
B)  $\{ 30 \}$ 
C)  $\{ 50 \}$ 
D)  $\{ 20 \}$ Find all values of x satisfying the given conditions.

Question 14

Solve the formula for the specified variable.
-$P = 2 L + 2 W \quad$ for $L$

Accepted Answer

A)  $L = \frac { P - 2 W } { 2 }$ 
B)  $L = P - W$ 
C)  $L = \frac { P - W } { 2 }$ 
D)  $\mathrm { L } = \mathrm { P } - 2 \mathrm {~W}$ 
A)  $L = \frac { P - 2 W } { 2 }$ 
B)  $L = P - W$ 
C)  $L = \frac { P - W } { 2 }$ 
D)  $\mathrm { L } = \mathrm { P } - 2 \mathrm {~W}$

Question 15

Solve the equation by factoring.
-$$9 x ^ { 2 } + 18 x + 8 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ \frac { 2 } { 3 } , \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 9 } , - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$ 
A)  $\left\{ - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$ 
B)  $\left\{ \frac { 2 } { 3 } , \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 9 } , - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$

Question 16

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set
on a number line.
-$$2 x + 8 < 16$$

Accepted Answer

A)  $( - \infty , 4 )$
  
B)  $( 4 , \infty )$
  
C)  $[ 4 , \infty )$
  
D)  $( - \infty , 4 ]$
  
A)  $( - \infty , 4 )$
  
B)  $( 4 , \infty )$
  
C)  $[ 4 , \infty )$
  
D)  $( - \infty , 4 ]$

Question 17

Find the product and write the result in standard form.
-$$( - 9 - 6 i ) ( 5 + i )$$

Accepted Answer

A)  $- 39 - 39 \mathrm { i }$ 
B)  $- 51 - 39 \mathrm { i }$ 
C)  $- 39 + 21 \mathrm { i }$ 
D)  $- 51 + 21 \mathrm { i }$ 
A)  $- 39 - 39 \mathrm { i }$ 
B)  $- 51 - 39 \mathrm { i }$ 
C)  $- 39 + 21 \mathrm { i }$ 
D)  $- 51 + 21 \mathrm { i }$

Question 18

Match the story with the correct figure.
-Mark started out by walking up a hill for 5 minutes. For the next 5 minutes he walked down a steep hill to an elevation lower than his starting point. For the next 10 minutes he walked on level ground. For the next 10 minutes he walked uphill. Determine which graph of elevation above sea level versus time illustrates the story.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$8 x ^ { 2 } - 3 x + 1 = 0$$

Accepted Answer

A)  $\left\{ \frac { 3 \pm \mathrm { i } \sqrt { 23 } } { 16 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm i \sqrt { 23 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 3 - \mathrm { i } \sqrt { 23 } } { 16 } , \frac { - 3 + \mathrm { i } \sqrt { 23 } } { 16 } \right\}$ 
D)  $\left\{ \frac { 3 \pm \sqrt { 23 } } { 16 } \right\}$ 
A)  $\left\{ \frac { 3 \pm \mathrm { i } \sqrt { 23 } } { 16 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm i \sqrt { 23 } } { 16 } \right\}$ 
C)  $\left\{ \frac { 3 - \mathrm { i } \sqrt { 23 } } { 16 } , \frac { - 3 + \mathrm { i } \sqrt { 23 } } { 16 } \right\}$ 
D)  $\left\{ \frac { 3 \pm \sqrt { 23 } } { 16 } \right\}$

Question 20

Solve the problem.
-When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the ground is given by the equation $t = \sqrt { \frac { h } { 4.9 } }$, where $t$ is measured in seconds. Solve the equation for h.
Use the result to determine the height from which an object was dropped if it hits the ground after falling for 3 seconds.

Accepted Answer

A)  $\mathrm { h } = 4.9 \mathrm { t } ^ { 2 } ; 44.1 \mathrm {~m}$ 
B)  $\mathrm { h } = 24.01 \mathrm { t } ; 72 \mathrm {~m}$ 
C)  $h = 24.01 t ^ { 2 } ; 216.1 \mathrm {~m}$ 
D)  $\mathrm { h } = 4.9 \mathrm { t } ; 14.7 \mathrm {~m}$ 
A)  $\mathrm { h } = 4.9 \mathrm { t } ^ { 2 } ; 44.1 \mathrm {~m}$ 
B)  $\mathrm { h } = 24.01 \mathrm { t } ; 72 \mathrm {~m}$ 
C)  $h = 24.01 t ^ { 2 } ; 216.1 \mathrm {~m}$ 
D)  $\mathrm { h } = 4.9 \mathrm { t } ; 14.7 \mathrm {~m}$

Solve and check the equation. - $( x + 11 ) ^ { 3 / 2 } = 125$

Express the interval in set-builder notation and graph the interval on a number line. - $(-\infty, 5.5]$ $Express the interval in set-builder notation and graph the interval on a number line. - (-\infty, 5.5]$

Perform the indicated operations and write the result in standard form. - $( \sqrt { - 36 } ) ( \sqrt { - 49 } )$

Solve the problem using this formula. -Find $E$ , the voltage of a circuit, if $\mathrm { I } = ( 9 + 6 \mathrm { i } )$ amperes and $\mathrm { R } = ( 7 + 2 \mathrm { i } )$ ohms.

6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation -

Solve the problem. -Suppose a cost-benefit model is given by $y = \frac { 2652 x } { 100 - x }$ , where $y$ is the cost for removing $x$ percent of a given pollutant. What percent of pollutant can be removed for $\$ 22,000$ ? Round your answer to the nearest tenth of a percent.

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $x ^ { 2 } - 5 x$

Solve the absolute value equation or indicate that the equation has no solution. - $\left| 2 x ^ { 2 } - x - 1 \right| = 3$

Use graphs to find the set. - $( - \infty , 8 ) \cap [ - 2,17 )$

Solve the problem. -A square sheet of paper measures 45 centimeters on each side. What is the length of the diagonal of this paper?

Solve and check the linear equation. - $0.40 x - 0.20 ( 80 + x ) = - 0.10 ( 80 )$

Solve the formula for the specified variable. - $P = 2 L + 2 W \quad$ for $L$

Solve the equation by factoring. - $9 x ^ { 2 } + 18 x + 8 = 0$

Solve the linear inequality. Other than ∅, use interval notation to express the solution set and graph the solution set on a number line. - $2 x + 8 < 16$

Find the product and write the result in standard form. - $( - 9 - 6 i ) ( 5 + i )$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. - $8 x ^ { 2 } - 3 x + 1 = 0$

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 1: Equations and Inequalities

Solve and check the equation. - (x+11)3/2=125( x + 11 ) ^ { 3 / 2 } = 125(x+11)3/2=125

Express the interval in set-builder notation and graph the interval on a number line. - (−∞,5.5](-\infty, 5.5](−∞,5.5]

Perform the indicated operations and write the result in standard form. - (−36)(−49)( \sqrt { - 36 } ) ( \sqrt { - 49 } )(−36​)(−49​)

Solve the problem using this formula. -Find EEE , the voltage of a circuit, if I=(9+6i)\mathrm { I } = ( 9 + 6 \mathrm { i } )I=(9+6i) amperes and R=(7+2i)\mathrm { R } = ( 7 + 2 \mathrm { i } )R=(7+2i) ohms.