Question 1

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$0.3 ( x - 8 ) - 0.5 ( x - 8 ) = - 0.2 x + 1.6$$

Accepted Answer

A)  Identity; {all real numbers} 
B)  Conditional; $\{ 0.8 \}$ 
C)  Conditional; $\{ - 8 \}$ 
D)  Contradiction; $\varnothing$ 
A)  Identity; {all real numbers} 
B)  Conditional; $\{ 0.8 \}$ 
C)  Conditional; $\{ - 8 \}$ 
D)  Contradiction; $\varnothing$

Question 2

Solve for y.
-$$4 x - 7 y = 5$$

Accepted Answer

A)  $y = 4 x - 12$ 
B)  $y = 4 x + 12$ 
C)  $\mathrm { y } = \frac { 4 \mathrm { x } + 5 } { 7 }$ 
D)  $y = \frac { 4 x - 5 } { 7 }$ 
A)  $y = 4 x - 12$ 
B)  $y = 4 x + 12$ 
C)  $\mathrm { y } = \frac { 4 \mathrm { x } + 5 } { 7 }$ 
D)  $y = \frac { 4 x - 5 } { 7 }$

Question 3

Indicate whether the statement is true always, sometimes, or never.
-The difference between two real numbers is a real number.

Accepted Answer

A)  Always 
B)  Never 
C)  Sometimes 
A)  Always 
B)  Never 
C)  Sometimes

Question 4

Determine whether or not the equation is linear.
-2x + 7(x - 9) = 11x

Accepted Answer

A)  Not linear 
B)  Linear 
A)  Not linear 
B)  Linear

Question 5

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 3 } } { \sqrt { - 12 } }$$

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 2 i }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 } i$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $\frac { 1 } { 2 i }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 2 } i$

Question 6

Solve the problem.
-Which one of the following equations is set up for direct use of the square root property?

Accepted Answer

A)  $4 x ^ { 2 } + 7 x - 8 = 0$ 
B)  $( 4 x + 7 ) ( x - 8 ) = 0$ 
C)  $x ^ { 2 } + x = 8$ 
D)  $( 4 x + 7 ) ^ { 2 } = 8$ (4x 
A)  $4 x ^ { 2 } + 7 x - 8 = 0$ 
B)  $( 4 x + 7 ) ( x - 8 ) = 0$ 
C)  $x ^ { 2 } + x = 8$ 
D)  $( 4 x + 7 ) ^ { 2 } = 8$ (4x

Question 7

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$4 x + 1 = 2 ( 2 x - 4 )$$

Accepted Answer

A)  Identity; $\{$ all real numbers $\}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 2 \}$ 
D)  Conditional; $\{ - 2 \}$ 
A)  Identity; $\{$ all real numbers $\}$ 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{ 2 \}$ 
D)  Conditional; $\{ - 2 \}$

Question 8

Solve the problem.
-On a recent trip, Sarahʹs car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarahʹs car on the first
Part of the trip.

Accepted Answer

A)  66 mph 
B)  11 mph 
C)  48 mph 
D)  46 mph 
A)  66 mph 
B)  11 mph 
C)  48 mph 
D)  46 mph

Question 9

Find the product. Write the answer in standard form.
-$$\mathrm { i } ( 6 - 2 \mathrm { i } ) ( 4 - 5 \mathrm { i } )$$

Accepted Answer

A)  $- 38 - 14 i$ 
B)  $38 + 14 \mathrm { i }$ 
C)  $34 + 22 i$ 
D)  $10 \mathrm { i } ^ { 3 } + 38 \mathrm { i } ^ { 2 } + 24 \mathrm { i }$ 
A)  $- 38 - 14 i$ 
B)  $38 + 14 \mathrm { i }$ 
C)  $34 + 22 i$ 
D)  $10 \mathrm { i } ^ { 3 } + 38 \mathrm { i } ^ { 2 } + 24 \mathrm { i }$

Question 10

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$- 8 x - 42 + 2 ( 4 x + 23 ) = 0$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 4 \}$ 
C)  Identity; $\{$ all real numbers $\}$ 
D)  Conditional; $\{ 1 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 4 \}$ 
C)  Identity; $\{$ all real numbers $\}$ 
D)  Conditional; $\{ 1 \}$

Question 11

Solve and graph the inequality. Give answer in interval notation.
-$$- 3 < 2 x + 3 \leq 5$$

Accepted Answer

A)  $( - 3,1 )$
  
B)  $[ - 3,1 ]$
  
C)  $[ - 3,1 )$
  
D)  $( - 3,1 ]$
  
A)  $( - 3,1 )$
  
B)  $[ - 3,1 ]$
  
C)  $[ - 3,1 )$
  
D)  $( - 3,1 ]$

Question 12

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.
-$25 x ^ { 2 } - 10 x + 1 = 0$

Accepted Answer

A)  Two distinct rational solutions 
B)  Two distinct nonreal complex solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions 
A)  Two distinct rational solutions 
B)  Two distinct nonreal complex solutions 
C)  One rational solution (a double solution) 
D)  Two distinct irrational solutions

Question 13

Find the sum or difference. Write the answer in standard form.
-$$( 1 + 3 i ) - ( - 3 - 8 i ) + ( 9 - 9 i )$$

Accepted Answer

A)  $- 13 + 20 \mathrm { i }$ 
B)  $13 + 2 \mathrm { i }$ 
C)  $7 - 14 \mathrm { i }$ 
D)  $13 - 14 \mathrm { i }$ 
A)  $- 13 + 20 \mathrm { i }$ 
B)  $13 + 2 \mathrm { i }$ 
C)  $7 - 14 \mathrm { i }$ 
D)  $13 - 14 \mathrm { i }$

Question 14

Solve the equation using the quadratic formula.
-$$6 x ^ { 2 } + 12 x + 1 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 6 \pm \sqrt { 42 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 30 } } { 6 } \right\}$ 
C)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 12 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 6 } \right\}$ 
A)  $\left\{ \frac { - 6 \pm \sqrt { 42 } } { 6 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 30 } } { 6 } \right\}$ 
C)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 12 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 30 } } { 6 } \right\}$

Question 15

Solve the problem.
-A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $160 \mathrm { ft } / \mathrm { sec }$, and the gorge is $384 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 \mathrm { t } ^ { 2 } + \mathrm { v } _ { 0 } \mathrm { t } + \mathrm { h } _ { 0 } \right.$.)

Accepted Answer

A)  $4 < \mathrm { t } < 6$ 
B)  $12 < t < 14$ 
C)  $8 < t < 10$ 
D)  $0 < \mathrm { t } < 4$ 
A)  $4 < \mathrm { t } < 6$ 
B)  $12 < t < 14$ 
C)  $8 < t < 10$ 
D)  $0 < \mathrm { t } < 4$

Question 16

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.
-$$w ^ { 2 } - 2 w + 6 = 0$$

Accepted Answer

A)  One rational solution (a double solution) 
B)  Two distinct rational solutions 
C)  Two distinct irrational solutions 
D)  Two distinct nonreal complex solutions 
A)  One rational solution (a double solution) 
B)  Two distinct rational solutions 
C)  Two distinct irrational solutions 
D)  Two distinct nonreal complex solutions

Question 17

Solve the equation.
-$$3 x ^ { - 2 / 5 } + 11 x ^ { - 1 / 5 } + 6 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 243 } , \frac { 243 } { 32 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 243 } , - \frac { 243 } { 32 } \right\}$ 
C)  $\{ 3,2 \}$ 
D)  $\left\{ - \frac { 1 } { 3 } , - \frac { 3 } { 2 } \right\}$ 
A)  $\left\{ \frac { 1 } { 243 } , \frac { 243 } { 32 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 243 } , - \frac { 243 } { 32 } \right\}$ 
C)  $\{ 3,2 \}$ 
D)  $\left\{ - \frac { 1 } { 3 } , - \frac { 3 } { 2 } \right\}$

Question 18

Find the quotient. Write the answer in standard form.
-$$\frac { 9 + 2 i } { 3 - 5 i }$$

Accepted Answer

A)  $\frac { 37 } { 2 } + \frac { 39 } { 2 } \mathrm { i }$ 
B)  $- \frac { 1 } { 16 } + \frac { 3 } { 16 } \mathrm { i }$ 
C)  $- \frac { 37 } { 16 } + \frac { 3 } { 16 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i }$ 
A)  $\frac { 37 } { 2 } + \frac { 39 } { 2 } \mathrm { i }$ 
B)  $- \frac { 1 } { 16 } + \frac { 3 } { 16 } \mathrm { i }$ 
C)  $- \frac { 37 } { 16 } + \frac { 3 } { 16 } \mathrm { i }$ 
D)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i }$

Question 19

Solve the problem.
-A chemist needs 120 milliliters of a 40% solution but has only 30% and 54% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  80 mL of 30%; 40 mL of 54% 
B)  50 mL of 30%; 70 mL of 54% 
C)  40 mL of 30%; 80 mL of 54% 
D)  70 mL of 30%; 50 mL of 54% 
A)  80 mL of 30%; 40 mL of 54% 
B)  50 mL of 30%; 70 mL of 54% 
C)  40 mL of 30%; 80 mL of 54% 
D)  70 mL of 30%; 50 mL of 54%

Question 20

Solve the equation.
-$$x ^ { 4 } + 1125 = 134 x ^ { 2 }$$

Accepted Answer

A)  $\{ 9,125 \}$ 
B)  $\{ 3,5 \sqrt { 5 } \}$ 
C)  $\{ - 125 , - 9,9,125 \}$ 
D)  $\{ - 5 \sqrt { 5 } , - 3,3,5 \sqrt { 5 } \}$ 
A)  $\{ 9,125 \}$ 
B)  $\{ 3,5 \sqrt { 5 } \}$ 
C)  $\{ - 125 , - 9,9,125 \}$ 
D)  $\{ - 5 \sqrt { 5 } , - 3,3,5 \sqrt { 5 } \}$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $0.3 ( x - 8 ) - 0.5 ( x - 8 ) = - 0.2 x + 1.6$

Solve for y. - $4 x - 7 y = 5$

Indicate whether the statement is true always, sometimes, or never. -The difference between two real numbers is a real number.

Determine whether or not the equation is linear. -2x + 7(x - 9) = 11x

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 3 } } { \sqrt { - 12 } }$

Solve the problem. -Which one of the following equations is set up for direct use of the square root property?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $4 x + 1 = 2 ( 2 x - 4 )$

Solve the problem. -On a recent trip, Sarahʹs car traveled 20 mph faster on the first 150 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarahʹs car on the first Part of the trip.

Find the product. Write the answer in standard form. - $\mathrm { i } ( 6 - 2 \mathrm { i } ) ( 4 - 5 \mathrm { i } )$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $- 8 x - 42 + 2 ( 4 x + 23 ) = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 3 < 2 x + 3 \leq 5$ $Solve and graph the inequality. Give answer in interval notation. - - 3 < 2 x + 3 \leq 5$

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. - $25 x ^ { 2 } - 10 x + 1 = 0$

Find the sum or difference. Write the answer in standard form. - $( 1 + 3 i ) - ( - 3 - 8 i ) + ( 9 - 9 i )$

Solve the equation using the quadratic formula. - $6 x ^ { 2 } + 12 x + 1 = 0$

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. - $w ^ { 2 } - 2 w + 6 = 0$

Solve the equation. - $3 x ^ { - 2 / 5 } + 11 x ^ { - 1 / 5 } + 6 = 0$

Find the quotient. Write the answer in standard form. - $\frac { 9 + 2 i } { 3 - 5 i }$

Solve the problem. -A chemist needs 120 milliliters of a 40% solution but has only 30% and 54% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Solve the equation. - $x ^ { 4 } + 1125 = 134 x ^ { 2 }$

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

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 0.3(x−8)−0.5(x−8)=−0.2x+1.60.3 ( x - 8 ) - 0.5 ( x - 8 ) = - 0.2 x + 1.60.3(x−8)−0.5(x−8)=−0.2x+1.6

Solve for y. - 4x−7y=54 x - 7 y = 54x−7y=5