Question 1

Write the number in standard form a + bi.
-$$\frac { - 4 - \sqrt { - 108 } } { 2 }$$

Accepted Answer

A)  $- 2 + 6 i \sqrt { 6 }$ 
B)  $- 2 + 6 i \sqrt { 3 }$ 
C)  $- 2 - 3 i \sqrt { 3 }$ 
D)  $- 2 - 3 i \sqrt { 6 }$ 
A)  $- 2 + 6 i \sqrt { 6 }$ 
B)  $- 2 + 6 i \sqrt { 3 }$ 
C)  $- 2 - 3 i \sqrt { 3 }$ 
D)  $- 2 - 3 i \sqrt { 6 }$

Question 2

Solve the problem.
-A boat is 40 feet from the base of cliff. If the distance from the top of the cliff to the boat is 10 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest
Tenth of a foot if necessary.

Accepted Answer

A)  50 ft 
B)  30 ft 
C)  23.3 ft 
D)  16.7 ft 
A)  50 ft 
B)  30 ft 
C)  23.3 ft 
D)  16.7 ft

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$- 10 x - 5 \leq - 11 x - 14$$

Accepted Answer

A)  $( - \infty , - 9 ]$
  
B)  $( - 10 , \infty )$
  
C)  $( - \infty , - 10 )$
  
D)  $[ - 9 , \infty )$
  
A)  $( - \infty , - 9 ]$
  
B)  $( - 10 , \infty )$
  
C)  $( - \infty , - 10 )$
  
D)  $[ - 9 , \infty )$

Question 4

Solve the inequality. Write the solution set in interval notation.
-$$| x + 5 | < 0$$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\{ - 5 \}$ 
C)  $\varnothing$ 
D)  $( - \infty , - 5 )$ 
A)  $\{ 5 \}$ 
B)  $\{ - 5 \}$ 
C)  $\varnothing$ 
D)  $( - \infty , - 5 )$

Question 5

Solve and graph the inequality. Give answer in interval notation.
-$$9 < - 3 x + 3 \leq 21$$

Accepted Answer

A)  $( 2,6 ]$
  
B)  $[ 2,6 )$
  
C)  $( - 6 , - 2 ]$
  
D)  $[ - 6 , - 2 )$
  
A)  $( 2,6 ]$
  
B)  $[ 2,6 )$
  
C)  $( - 6 , - 2 ]$
  
D)  $[ - 6 , - 2 )$

Question 6

Solve the formula for the indicated variable.
-$$F = \frac { 9 } { 5 } C + 32 , \text { for } C$$

Accepted Answer

A)  $C = \frac { F - 32 } { 9 }$ 
B)  $C = \frac { 9 } { 5 } ( F - 32 )$ 
C)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
D)  $C = \frac { 5 } { F - 32 }$ 
A)  $C = \frac { F - 32 } { 9 }$ 
B)  $C = \frac { 9 } { 5 } ( F - 32 )$ 
C)  $C = \frac { 5 } { 9 } ( F - 32 )$ 
D)  $C = \frac { 5 } { F - 32 }$

Question 7

Decide whether the statement is true or false.
-14 is a solution of -2x = -32.

Accepted Answer

A) True 
 B)False

Question 8

Solve the equation using the quadratic formula.
-$$3 x ^ { 2 } = - 8 x - 1$$

Accepted Answer

A)  $\left\{ \frac { - 4 \pm \sqrt { 13 } } { 3 } \right\}$ 
B)  $\left\{ \frac { - 4 \pm \sqrt { 19 } } { 3 } \right\}$ 
C)  $\left\{ \frac { - 4 \pm \sqrt { 13 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 8 \pm \sqrt { 13 } } { 3 } \right\}$ 
A)  $\left\{ \frac { - 4 \pm \sqrt { 13 } } { 3 } \right\}$ 
B)  $\left\{ \frac { - 4 \pm \sqrt { 19 } } { 3 } \right\}$ 
C)  $\left\{ \frac { - 4 \pm \sqrt { 13 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 8 \pm \sqrt { 13 } } { 3 } \right\}$

Question 9

Solve and graph the inequality. Give answer in interval notation.
-$$15 x - 20 > 5 ( 2 x + 2 )$$

Accepted Answer

A)  $( 6 , \infty )$
  
B)  $( - \infty , 6 )$
  
C)  $( 15 , \infty )$
  
D)  $( - \infty , 15 )$
  
A)  $( 6 , \infty )$
  
B)  $( - \infty , 6 )$
  
C)  $( 15 , \infty )$
  
D)  $( - \infty , 15 )$

Question 10

Solve the equation using the quadratic formula.
-$$6 x ^ { 2 } + 12 x + 3 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 2 \pm \sqrt { 6 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 2 \pm \sqrt { 2 } } { 12 } \right\}$ 
C)  $\left\{ \frac { - 12 \pm \sqrt { 2 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 2 \pm \sqrt { 2 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 2 \pm \sqrt { 6 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 2 \pm \sqrt { 2 } } { 12 } \right\}$ 
C)  $\left\{ \frac { - 12 \pm \sqrt { 2 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 2 \pm \sqrt { 2 } } { 2 } \right\}$

Question 11

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 3 x ^ { 2 } - 9 x \leq 27$$

Accepted Answer

A)  $[ 3 , \infty )$ 
B)  $[ - 3,3 ]$ 
C)  $( - \infty , - 3 ] \cup [ 3 , \infty )$ 
D)  $( - \infty , 3 ]$ 
A)  $[ 3 , \infty )$ 
B)  $[ - 3,3 ]$ 
C)  $( - \infty , - 3 ] \cup [ 3 , \infty )$ 
D)  $( - \infty , 3 ]$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 8 } - \frac { 1 } { 9 } x \right| < \frac { 2 } { 11 }$$

Accepted Answer

A)  $\left( - \infty , - \frac { 639 } { 88 } \right) \cup \left( \frac { 351 } { 88 } , \infty \right)$ 
B)  $\left( \frac { 351 } { 88 } , \frac { 639 } { 88 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , \frac { 351 } { 88 } \right) \cup \left( \frac { 639 } { 88 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 639 } { 88 } \right) \cup \left( \frac { 351 } { 88 } , \infty \right)$ 
B)  $\left( \frac { 351 } { 88 } , \frac { 639 } { 88 } \right)$ 
C)  $( - \infty , \infty )$ 
D)  $\left( - \infty , \frac { 351 } { 88 } \right) \cup \left( \frac { 639 } { 88 } , \infty \right)$

Question 13

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 8 = 0$$

Accepted Answer

A)  $\{ - 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ - 2,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 2 , \pm 2 i \}$ 
D)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$ 
A)  $\{ - 2,1 \pm i \sqrt { 6 } \}$ 
B)  $\{ - 2,1 \pm \mathrm { i } \sqrt { 3 } \}$ 
C)  $\{ - 2 , \pm 2 i \}$ 
D)  $\{ - 2 , - 1 \pm \sqrt { 5 } \}$

Question 14

Solve the equation using the quadratic formula.
-$$\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 1$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ \frac { 3 \pm 2 \sqrt { 2 } } { 2 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } \right\}$ 
D)  $\left\{ \frac { 3 \pm 2 \sqrt { 2 } } { 2 } \right\}$

Question 15

Solve the rational inequality. Write the solution set in interval notation.
-The cost of producing t units i $C = 2 t ^ { 2 } + 7 t$ t, and the revenue generated from sales is $\mathrm { R } = 3 \mathrm { t } ^ { 2 } + \mathrm { t }$ Determine the number of units to be sold in order to generate a profit.

Accepted Answer

A)  t > 0 
B)  t > 6 
C)  t > 8 
D)  t > 7 
A)  t > 0 
B)  t > 6 
C)  t > 8 
D)  t > 7

Question 16

Solve the problem.
-Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 6 mi, the distance between the cars was 2 mi more than the distance traveled by the car
Heading east. How far had the east bound car traveled?

Accepted Answer

A)  10 mi 
B)  6 mi 
C)  8 mi 
D)  12 mi 
A)  10 mi 
B)  6 mi 
C)  8 mi 
D)  12 mi

Question 17

Solve the equation.
-$$\left| \frac { 7 } { x - 9 } \right| = 9$$

Accepted Answer

A)  $\left\{ \frac { 88 } { 9 } , \frac { 74 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 74 } { 9 } , - \frac { 88 } { 9 } \right\}$ 
C)  $\{ 9 \}$ 
D)  $\left\{ - \frac { 88 } { 9 } , - \frac { 74 } { 9 } \right\}$ 
A)  $\left\{ \frac { 88 } { 9 } , \frac { 74 } { 9 } \right\}$ 
B)  $\left\{ - \frac { 74 } { 9 } , - \frac { 88 } { 9 } \right\}$ 
C)  $\{ 9 \}$ 
D)  $\left\{ - \frac { 88 } { 9 } , - \frac { 74 } { 9 } \right\}$

Question 18

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

Accepted Answer

A)  $\pm 2$ 
B)  $\pm i \sqrt { 2 }$ 
C)  $\pm \sqrt { 2 }$ 
D)  $\pm 2 \mathrm { i }$ 
A)  $\pm 2$ 
B)  $\pm i \sqrt { 2 }$ 
C)  $\pm \sqrt { 2 }$ 
D)  $\pm 2 \mathrm { i }$

Question 19

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.
-$s ^ { 2 } + 4 s + 3 = 0$

Accepted Answer

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

Question 20

Solve the equation.
-$$\left| \frac { 7 x - 3 } { 6 } \right| = 6$$

Accepted Answer

A)  $\left\{ \frac { 9 } { 4 } , - \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 33 } { 4 } , - \frac { 39 } { 4 } \right\}$ 
C)  $\left\{ \frac { 39 } { 7 } \right\}$ 
D)  $\left\{ \frac { 39 } { 7 } , - \frac { 33 } { 7 } \right\}$ 
A)  $\left\{ \frac { 9 } { 4 } , - \frac { 3 } { 4 } \right\}$ 
B)  $\left\{ \frac { 33 } { 4 } , - \frac { 39 } { 4 } \right\}$ 
C)  $\left\{ \frac { 39 } { 7 } \right\}$ 
D)  $\left\{ \frac { 39 } { 7 } , - \frac { 33 } { 7 } \right\}$

Write the number in standard form a + bi. - $\frac { - 4 - \sqrt { - 108 } } { 2 }$

Solve the problem. -A boat is 40 feet from the base of cliff. If the distance from the top of the cliff to the boat is 10 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest Tenth of a foot if necessary.

Solve and graph the inequality. Give answer in interval notation. - $- 10 x - 5 \leq - 11 x - 14$ $Solve and graph the inequality. Give answer in interval notation. - - 10 x - 5 \leq - 11 x - 14$

Solve the inequality. Write the solution set in interval notation. - $| x + 5 | < 0$

Solve and graph the inequality. Give answer in interval notation. - $9 < - 3 x + 3 \leq 21$ $Solve and graph the inequality. Give answer in interval notation. - 9 < - 3 x + 3 \leq 21$

Solve the formula for the indicated variable. - $F = \frac { 9 } { 5 } C + 32 , \text { for } C$

Decide whether the statement is true or false. -14 is a solution of -2x = -32.

Solve the equation using the quadratic formula. - $3 x ^ { 2 } = - 8 x - 1$

Solve and graph the inequality. Give answer in interval notation. - $15 x - 20 > 5 ( 2 x + 2 )$

Solve the equation using the quadratic formula. - $6 x ^ { 2 } + 12 x + 3 = 0$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 3 x ^ { 2 } - 9 x \leq 27$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 8 } - \frac { 1 } { 9 } x \right| < \frac { 2 } { 11 }$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 8 = 0$

Solve the equation using the quadratic formula. - $\frac { 4 } { 9 } x ^ { 2 } - \frac { 4 } { 3 } x = - 1$

Solve the problem. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 6 mi, the distance between the cars was 2 mi more than the distance traveled by the car Heading east. How far had the east bound car traveled?

Solve the equation. - $\left| \frac { 7 } { x - 9 } \right| = 9$

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

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. - $s ^ { 2 } + 4 s + 3 = 0$

Solve the equation. - $\left| \frac { 7 x - 3 } { 6 } \right| = 6$

Review of Basic Concepts

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 2: Equations and Inequalities

Write the number in standard form a + bi. - −4−−1082\frac { - 4 - \sqrt { - 108 } } { 2 }2−4−−108​​

Solve the problem. -A boat is 40 feet from the base of cliff. If the distance from the top of the cliff to the boat is 10 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest Tenth of a foot if necessary.

Solve and graph the inequality. Give answer in interval notation. - −10x−5≤−11x−14- 10 x - 5 \leq - 11 x - 14−10x−5≤−11x−14

Solve the inequality. Write the solution set in interval notation. - ∣x+5∣<0| x + 5 | < 0∣x+5∣<0

Solve and graph the inequality. Give answer in interval notation. - 9<−3x+3≤219 < - 3 x + 3 \leq 219<−3x+3≤21

Solve the formula for the indicated variable. - F=95C+32, for CF = \frac { 9 } { 5 } C + 32 , \text { for } CF=59​C+32, for C