Question 1

Write the inequality in interval notation.
-

Accepted Answer

A)  $( - \infty , - 1 ]$ 
B)  $[ 2 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 1 , \infty )$ 
A)  $( - \infty , - 1 ]$ 
B)  $[ 2 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 1 , \infty )$

Question 2

Multiply or divide, as indicated. Simplify the answer.
-$\sqrt { - 17 } \cdot \sqrt { - 17 }$

Accepted Answer

A)  $17 \mathrm { i }$ 
B)  17 
C)  $- 17$ 
D)  $- 17 \mathrm { i }$ 
A)  $17 \mathrm { i }$ 
B)  17 
C)  $- 17$ 
D)  $- 17 \mathrm { i }$

Question 3

Solve the problem.
-The outside of a picture frame has a length which is 6 cm more than width. The area enclosed by the outside of the picture frame is 72 square cm. Find the width of the outside of the picture frame.

Accepted Answer

A)  $18 \mathrm {~cm}$ 
B)  $12 \mathrm {~cm}$ 
C)  $6 \mathrm {~cm}$ 
D)  $8 \mathrm {~cm}$ 
A)  $18 \mathrm {~cm}$ 
B)  $12 \mathrm {~cm}$ 
C)  $6 \mathrm {~cm}$ 
D)  $8 \mathrm {~cm}$

Question 4

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { - 5 } { - 5 x - 6 } > 0$$

Accepted Answer

A)  $( 0 , \infty )$ 
B)  $\left( - \frac { 6 } { 5 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 6 } { 5 } \right)$ 
D)  $\left( - \infty , - \frac { 5 } { 6 } \right)$ 
A)  $( 0 , \infty )$ 
B)  $\left( - \frac { 6 } { 5 } , \infty \right)$ 
C)  $\left( - \infty , \frac { 6 } { 5 } \right)$ 
D)  $\left( - \infty , - \frac { 5 } { 6 } \right)$

Question 5

Solve the problem.
-The sum of the squares of two consecutive integers is 365 . Find the integers.

Accepted Answer

A)  13,14 
B)  $- 13 , - 14$ 
C)  13,14 or $- 13 , - 14$ 
D)  $13 , - 14$ 
A)  13,14 
B)  $- 13 , - 14$ 
C)  13,14 or $- 13 , - 14$ 
D)  $13 , - 14$

Question 6

Solve the equation.
-$$| 9 x + 2 | = 3$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } , - \frac { 5 } { 9 } \right\}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ \frac { 5 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 9 } , - \frac { 1 } { 9 } \right\}$ 
B)  $\left\{ \frac { 1 } { 9 } , - \frac { 5 } { 9 } \right\}$ 
C)  $\left\{ \frac { 1 } { 9 } \right\}$ 
D)  $\left\{ \frac { 5 } { 9 } , - \frac { 1 } { 9 } \right\}$

Question 7

Find the quotient. Write the answer in standard form.
-$$\frac { 6 + 2 i } { 6 - 9 i }$$

Accepted Answer

A)  $- \frac { 2 } { 15 } + \frac { 22 } { 45 } \mathrm { i }$ 
B)  $- \frac { 6 } { 5 } + \frac { 22 } { 45 } \mathrm { i }$ 
C)  $\frac { 2 } { 13 } + \frac { 22 } { 39 } \mathrm { i }$ 
D)  $\frac { 18 } { 13 } + \frac { 14 } { 13 } \mathrm { i }$ 
A)  $- \frac { 2 } { 15 } + \frac { 22 } { 45 } \mathrm { i }$ 
B)  $- \frac { 6 } { 5 } + \frac { 22 } { 45 } \mathrm { i }$ 
C)  $\frac { 2 } { 13 } + \frac { 22 } { 39 } \mathrm { i }$ 
D)  $\frac { 18 } { 13 } + \frac { 14 } { 13 } \mathrm { i }$

Question 8

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } ( x + 100 ) ^ { 2 } < 0$$

Accepted Answer

A)  $[ - 10,0 ] \cup [ 10 , \infty )$ 
B)  $( - \infty , - 10 ] \cup [ 0,10 ]$ 
C)  $( - \infty , \infty )$ 
D)  $\varnothing$ 
A)  $[ - 10,0 ] \cup [ 10 , \infty )$ 
B)  $( - \infty , - 10 ] \cup [ 0,10 ]$ 
C)  $( - \infty , \infty )$ 
D)  $\varnothing$

Question 9

Solve the equation by completing the square.
-$$x ^ { 2 } + 3 x - 9 = 0$$

Accepted Answer

A)  $\left\{ \frac { - 3 \pm 3 \sqrt { 5 } } { 2 } \right\}$ 
B)  $\{ - 3 \pm 3 \sqrt { 5 } \}$ 
C)  $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 3 + 3 \sqrt { 5 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 3 \pm 3 \sqrt { 5 } } { 2 } \right\}$ 
B)  $\{ - 3 \pm 3 \sqrt { 5 } \}$ 
C)  $\left\{ \frac { - 3 - 3 \sqrt { 5 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 3 + 3 \sqrt { 5 } } { 2 } \right\}$

Question 10

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-8

Accepted Answer

A)  Nonreal complex 
B)  Complex, pure imaginary, nonreal complex 
C)  Real, complex 
D)  Complex 
A)  Nonreal complex 
B)  Complex, pure imaginary, nonreal complex 
C)  Real, complex 
D)  Complex

Question 11

Solve the equation using the quadratic formula.
-$$2 x ^ { 2 } + 12 x = - 5$$

Accepted Answer

A)  $\left\{ \frac { - 6 \pm \sqrt { 26 } } { 4 } \right\}$ 
B)  $\left\{ \frac { - 6 \pm \sqrt { 26 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 12 \pm \sqrt { 26 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 46 } } { 2 } \right\}$ 
A)  $\left\{ \frac { - 6 \pm \sqrt { 26 } } { 4 } \right\}$ 
B)  $\left\{ \frac { - 6 \pm \sqrt { 26 } } { 2 } \right\}$ 
C)  $\left\{ \frac { - 12 \pm \sqrt { 26 } } { 2 } \right\}$ 
D)  $\left\{ \frac { - 6 \pm \sqrt { 46 } } { 2 } \right\}$

Question 12

Solve the problem.
-The number of non-text books read by college students ranges from 7 to 61 . Using B as the variable, write an absolute value inequality that corresponds to this range.

Accepted Answer

A)  $| B - 54 | \leq 7$ 
B)  $| B - 27 | \leq 34$ 
C)  $| B - 7 | \leq 54$ 
D)  $| B - 34 | \leq 27$ 
A)  $| B - 54 | \leq 7$ 
B)  $| B - 27 | \leq 34$ 
C)  $| B - 7 | \leq 54$ 
D)  $| B - 34 | \leq 27$

Question 13

Solve the problem.
-The height of a box is 10 inches. Its length is 4 inches more than its width. Find the length if the volume is 450.

Accepted Answer

A)  9 in. 
B)  5 in. 
C)  10 in. 
D)  45 in. 
A)  9 in. 
B)  5 in. 
C)  10 in. 
D)  45 in.

Question 14

Use these equations to convert between the two systems. $$C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$$ Round answer to the nearest tenth of a degree if necessary.
-$$\mathrm { F } = 10 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { C } = 2 ^ { \circ }$ 
B)  $C = - 39.6 ^ { \circ }$ 
C)  $\mathrm { C } = 23.3 ^ { \circ }$ 
D)  $C = - 12.2 ^ { \circ }$ 
A)  $\mathrm { C } = 2 ^ { \circ }$ 
B)  $C = - 39.6 ^ { \circ }$ 
C)  $\mathrm { C } = 23.3 ^ { \circ }$ 
D)  $C = - 12.2 ^ { \circ }$

Question 15

Solve the equation for the indicated variable. Assume no denominator is 0.
-$r m = t ^ { 2 } - m t$, for $t$

Accepted Answer

A)  $t = \sqrt { m r - m }$ 
B)  $t = \frac { m \pm \sqrt { m ^ { 2 } - 4 m r } } { 4 }$ 
C)  $ t = \frac { m \pm \sqrt { m ^ { 2 } + 4 r m } } { 2 }$ 
D)  $t = \frac { m \pm \sqrt { m ^ { 2 } + 4 m r } } { 2 m }$ 
A)  $t = \sqrt { m r - m }$ 
B)  $t = \frac { m \pm \sqrt { m ^ { 2 } - 4 m r } } { 4 }$ 
C)  $ t = \frac { m \pm \sqrt { m ^ { 2 } + 4 r m } } { 2 }$ 
D)  $t = \frac { m \pm \sqrt { m ^ { 2 } + 4 m r } } { 2 m }$

Question 16

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 8 x + 7 > 0$$

Accepted Answer

A)  $( - 1 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 1 , \infty )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - 7 , - 1 )$ 
A)  $( - 1 , \infty )$ 
B)  $( - \infty , - 7 ) \cup ( - 1 , \infty )$ 
C)  $( - \infty , - 7 )$ 
D)  $( - 7 , - 1 )$

Question 17

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

Accepted Answer

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

Question 18

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 4 x - 12 < 0$$

Accepted Answer

A)  $( - \infty , - 2 )$ 
B)  $( - \infty , - 2 ) \cup ( 6 , \infty )$ 
C)  $( 6 , \infty )$ 
D)  $( - 2,6 )$ 
A)  $( - \infty , - 2 )$ 
B)  $( - \infty , - 2 ) \cup ( 6 , \infty )$ 
C)  $( 6 , \infty )$ 
D)  $( - 2,6 )$

Question 19

Solve the equation by completing the square.
-$5 x ^ { 2 } - 7 x = 1$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 7 \pm \sqrt { 69 } } { 10 } \right\}$ 
C)  $\left\{ \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i } \right\}$ 
D)  $\left\{ \frac { 7 \pm \sqrt { 69 } } { 10 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { - 7 \pm \sqrt { 69 } } { 10 } \right\}$ 
C)  $\left\{ \frac { 7 } { 10 } \pm \frac { \sqrt { 69 } } { 10 } \mathrm { i } \right\}$ 
D)  $\left\{ \frac { 7 \pm \sqrt { 69 } } { 10 } \right\}$

Question 20

Write the number in standard form a + bi.
-$$\frac { - 6 + \sqrt { - 108 } } { 2 }$$

Accepted Answer

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

Write the inequality in interval notation. -

Multiply or divide, as indicated. Simplify the answer. - $\sqrt { - 17 } \cdot \sqrt { - 17 }$

Solve the problem. -The outside of a picture frame has a length which is 6 cm more than width. The area enclosed by the outside of the picture frame is 72 square cm. Find the width of the outside of the picture frame.

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 5 } { - 5 x - 6 } > 0$

Solve the problem. -The sum of the squares of two consecutive integers is 365 . Find the integers.

Solve the equation. - $| 9 x + 2 | = 3$

Find the quotient. Write the answer in standard form. - $\frac { 6 + 2 i } { 6 - 9 i }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 100 ) ^ { 2 } < 0$

Solve the equation by completing the square. - $x ^ { 2 } + 3 x - 9 = 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -8

Solve the equation using the quadratic formula. - $2 x ^ { 2 } + 12 x = - 5$

Solve the problem. -The number of non-text books read by college students ranges from 7 to 61 . Using B as the variable, write an absolute value inequality that corresponds to this range.

Solve the problem. -The height of a box is 10 inches. Its length is 4 inches more than its width. Find the length if the volume is 450.

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $\mathrm { F } = 10 ^ { \circ }$

Solve the equation for the indicated variable. Assume no denominator is 0. - $r m = t ^ { 2 } - m t$ , for $t$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 8 x + 7 > 0$

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

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 4 x - 12 < 0$

Solve the equation by completing the square. - $5 x ^ { 2 } - 7 x = 1$

Write the number in standard form a + bi. - $\frac { - 6 + \sqrt { - 108 } } { 2 }$

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

Write the inequality in interval notation. -

Multiply or divide, as indicated. Simplify the answer. - −17⋅−17\sqrt { - 17 } \cdot \sqrt { - 17 }−17​⋅−17​