Question 1

Solve the equation.
-$$\frac { 3 } { x - 7 } + \frac { 7 } { x + 2 } = \frac { 5 } { x ^ { 2 } - 5 x - 14 }$$

Accepted Answer

A)  $\left\{ \frac { 51 } { 7 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
D)  $\left\{ \frac { 24 } { 5 } \right\}$ 
A)  $\left\{ \frac { 51 } { 7 } \right\}$ 
B)  $\varnothing$ 
C)  $\left\{ - \frac { 4 } { 3 } \right\}$ 
D)  $\left\{ \frac { 24 } { 5 } \right\}$

Question 2

Solve the problem.
-A retailer knows that $\mathrm { n }$ games can be sold in a month if the price is $30 - 0.2 \mathrm { n }$ dollars per game. If he buys each game for $\$ 14$, and if he wishes to make a profit of at least $\$ 300$ per month on sales of this game, how many games must he sell each month?

Accepted Answer

A)  $30 \leq n \leq 80$ 
B)  $30 \leq \mathrm { n } \leq 50$ 
C)  $25 \leq \mathrm { n } \leq 40$ 
D)  $25 \leq \mathrm { n } \leq 30$ 
A)  $30 \leq n \leq 80$ 
B)  $30 \leq \mathrm { n } \leq 50$ 
C)  $25 \leq \mathrm { n } \leq 40$ 
D)  $25 \leq \mathrm { n } \leq 30$

Question 3

Solve the problem.
-A bank loaned out $57,000, part of it at the rate of 2.5% per year and the rest at a rate of 3.5% per year. If the interest received was $1705.00, how much was loaned at 2.5%?

Accepted Answer

A)  $27,000 
B)  $29,000 
C)  $28,000 
D)  $30,000 
A)  $27,000 
B)  $29,000 
C)  $28,000 
D)  $30,000

Question 4

Find the quotient. Write the answer in standard form.
-$$\frac { 1 + 3 i } { 5 + 6 i }$$

Accepted Answer

A)  $- \frac { 13 } { 61 } - \frac { 21 } { 61 } \mathrm { i }$ 
B)  $\frac { 23 } { 61 } + \frac { 9 } { 61 } \mathrm { i }$ 
C)  $- \frac { 23 } { 11 } + \frac { 9 } { 11 } \mathrm { i }$ 
D)  $\frac { 13 } { 11 } + \frac { 9 } { 11 } \mathrm { i }$ 
A)  $- \frac { 13 } { 61 } - \frac { 21 } { 61 } \mathrm { i }$ 
B)  $\frac { 23 } { 61 } + \frac { 9 } { 61 } \mathrm { i }$ 
C)  $- \frac { 23 } { 11 } + \frac { 9 } { 11 } \mathrm { i }$ 
D)  $\frac { 13 } { 11 } + \frac { 9 } { 11 } \mathrm { i }$

Question 5

Solve the equation.
-$$4 \sqrt { x } = \sqrt { 9 x + 9 }$$

Accepted Answer

A)  $\left\{ - \frac { 9 } { 5 } \right\}$ 
B)  $\left\{ \frac { 9 } { 7 } \right\}$ 
C)  $\left\{ \frac { 9 } { 25 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 8 } \right\}$ 
A)  $\left\{ - \frac { 9 } { 5 } \right\}$ 
B)  $\left\{ \frac { 9 } { 7 } \right\}$ 
C)  $\left\{ \frac { 9 } { 25 } \right\}$ 
D)  $\left\{ - \frac { 9 } { 8 } \right\}$

Question 6

Find the product. Write the answer in standard form.
-$( 3 - 5 \mathrm { i } ) ( 4 - 4 \mathrm { i } )$

Accepted Answer

A)  $- 8 + 32 \mathrm { i }$ 
B)  $- 8 - 32 \mathrm { i }$ 
C)  $20 \mathrm { i } ^ { 2 } - 32 \mathrm { i } + 12$ 
D)  $32 - 8 \mathrm { i }$ 
A)  $- 8 + 32 \mathrm { i }$ 
B)  $- 8 - 32 \mathrm { i }$ 
C)  $20 \mathrm { i } ^ { 2 } - 32 \mathrm { i } + 12$ 
D)  $32 - 8 \mathrm { i }$

Question 7

Solve the equation.
-$$x ^ { 2 } = 9$$

Accepted Answer

A)  $\pm \mathrm { i } \sqrt { 3 }$ 
B)  $\pm \sqrt { 3 }$ 
C)  $\pm 3 \mathrm { i }$ 
D)  $\pm 3$ 
A)  $\pm \mathrm { i } \sqrt { 3 }$ 
B)  $\pm \sqrt { 3 }$ 
C)  $\pm 3 \mathrm { i }$ 
D)  $\pm 3$

Question 8

Solve the equation.
-$$x ^ { 1 / 2 } = - 5 x ^ { 1 / 4 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 0,25 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 0 , - 5 \}$ 
A)  $\varnothing$ 
B)  $\{ 0,25 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 0 , - 5 \}$

Question 9

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.
-$$\mathrm { F } = 102 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { C } = 126 ^ { \circ }$ 
B)  $\mathrm { C } = 53.1 ^ { \circ }$ 
C)  $\mathrm { C } = 215.6 ^ { \circ }$ 
D)  $C = 38.9 ^ { \circ }$ 
A)  $\mathrm { C } = 126 ^ { \circ }$ 
B)  $\mathrm { C } = 53.1 ^ { \circ }$ 
C)  $\mathrm { C } = 215.6 ^ { \circ }$ 
D)  $C = 38.9 ^ { \circ }$

Question 10

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 7 miles per hour, and Delvis is traveling at a speed of 15 miles per hour. In 5 hours what is the distance
Between them (assuming that they began at the same point and time)?

Accepted Answer

A)  49 mi 
B)  41 mi 
C)  37 mi 
D)  40 mi 
A)  49 mi 
B)  41 mi 
C)  37 mi 
D)  40 mi

Question 11

Solve the equation.
-$$( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\{ - 3 \}$ 
A)  $\varnothing$ 
B)  $\{ 3 \}$ 
C)  $\left\{ 3 , \frac { 11 } { 9 } \right\}$ 
D)  $\{ - 3 \}$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$| 4 x + 7 | + 8 < 16$$

Accepted Answer

A)  $\left( - \infty , - \frac { 15 } { 4 } \right)$ 
B)  $\left( - \frac { 15 } { 4 } , \frac { 1 } { 4 } \right)$ 
C)  $\varnothing$ 
D)  $\left( - \infty , - \frac { 15 } { 4 } \right) \cup \left( \frac { 1 } { 4 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 15 } { 4 } \right)$ 
B)  $\left( - \frac { 15 } { 4 } , \frac { 1 } { 4 } \right)$ 
C)  $\varnothing$ 
D)  $\left( - \infty , - \frac { 15 } { 4 } \right) \cup \left( \frac { 1 } { 4 } , \infty \right)$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$| - 5 x + 6 | \geq - 5$$

Accepted Answer

A)  $\left( \frac { 1 } { 5 } , \frac { 11 } { 5 } \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - \infty , \frac { 11 } { 5 } \right)$ 
A)  $\left( \frac { 1 } { 5 } , \frac { 11 } { 5 } \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\varnothing$ 
D)  $\left( - \infty , \frac { 11 } { 5 } \right)$

Question 14

Solve the inequality. Write the solution set in interval notation.
-$$| - 9 x + 1 | < 8$$

Accepted Answer

A)  $\left( - \frac { 7 } { 9 } , - 1 \right)$ 
B)  $\left( - \infty , - \frac { 11 } { 9 } \right) \cup \left( \frac { 5 } { 9 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 9 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \frac { 7 } { 9 } , 1 \right)$ 
A)  $\left( - \frac { 7 } { 9 } , - 1 \right)$ 
B)  $\left( - \infty , - \frac { 11 } { 9 } \right) \cup \left( \frac { 5 } { 9 } , \infty \right)$ 
C)  $\left( - \infty , - \frac { 7 } { 9 } \right) \cup ( 1 , \infty )$ 
D)  $\left( - \frac { 7 } { 9 } , 1 \right)$

Question 15

Solve the inequality. Write the solution set in interval notation.
-$$| 8 x + 2 | + 6 < 14$$

Accepted Answer

A)  $\left( - \infty , - \frac { 5 } { 4 } \right)$ 
B)  $\left( - \frac { 5 } { 4 } , \frac { 3 } { 4 } \right)$ 
C)  $\left( - \infty , - \frac { 5 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
D)  $\varnothing$ 
A)  $\left( - \infty , - \frac { 5 } { 4 } \right)$ 
B)  $\left( - \frac { 5 } { 4 } , \frac { 3 } { 4 } \right)$ 
C)  $\left( - \infty , - \frac { 5 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
D)  $\varnothing$

Question 16

Solve and graph the inequality. Give answer in interval notation.
-$$12 x - 27 > 3 ( 3 x - 11 )$$

Accepted Answer

A)  $( - \infty , - 2 )$
  
B)  $( - \infty , 12 )$
  
C)  $( - 2 , \infty )$
  
D)  $( 12 , \infty )$
  
A)  $( - \infty , - 2 )$
  
B)  $( - \infty , 12 )$
  
C)  $( - 2 , \infty )$
  
D)  $( 12 , \infty )$

Question 17

Solve the equation.
-$( x - 3 ) ^ { 4 } - 5 ( x - 3 ) ^ { 2 } + 4 = 0$

Accepted Answer

A)  $\{ - 2 , - 1,1,2 \}$ 
B)  $\{ 1,2,4,5 \}$ 
C)  $\{ 1,4 \}$ 
D)  $\{ - 1 , - 4 \}$ 
A)  $\{ - 2 , - 1,1,2 \}$ 
B)  $\{ 1,2,4,5 \}$ 
C)  $\{ 1,4 \}$ 
D)  $\{ - 1 , - 4 \}$

Question 18

Write the number in standard form a + bi.
-$$\frac { - 5 + \sqrt { - 75 } } { 25 }$$

Accepted Answer

A)  $- \frac { 1 } { 5 } + \frac { 3 \sqrt { 5 } } { 5 } \mathrm { i }$ 
B)  $- \frac { 1 } { 5 } + \frac { 5 \sqrt { 3 } } { 5 } \mathrm { i }$ 
C)  $- \frac { 1 } { 5 } + \frac { \sqrt { 3 } } { 5 } \mathrm { i }$ 
D)  $- \frac { 1 } { 5 } + \frac { \sqrt { 3 } } { 25 } \mathrm { i }$ 
A)  $- \frac { 1 } { 5 } + \frac { 3 \sqrt { 5 } } { 5 } \mathrm { i }$ 
B)  $- \frac { 1 } { 5 } + \frac { 5 \sqrt { 3 } } { 5 } \mathrm { i }$ 
C)  $- \frac { 1 } { 5 } + \frac { \sqrt { 3 } } { 5 } \mathrm { i }$ 
D)  $- \frac { 1 } { 5 } + \frac { \sqrt { 3 } } { 25 } \mathrm { i }$

Question 19

Decide whether or not the equations are equivalent.
-4x - 3 = 6 -4x + 6 = -3

Accepted Answer

A)  Not equivalent 
B)  Equivalent 
A)  Not equivalent 
B)  Equivalent

Question 20

Solve the problem.
-Hannah borrowed $45,338 at 4.5% simple interest for 22 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 22 months?
Round answers to the nearest cent if necessary.

Accepted Answer

A)  $3570.37; $48,908.37 
B)  $3771.82; $49,109.82 
C)  $3740.39; $49,078.39 
D)  $3910.40; $49,248.40 
A)  $3570.37; $48,908.37 
B)  $3771.82; $49,109.82 
C)  $3740.39; $49,078.39 
D)  $3910.40; $49,248.40

Solve the equation. - $\frac { 3 } { x - 7 } + \frac { 7 } { x + 2 } = \frac { 5 } { x ^ { 2 } - 5 x - 14 }$

Solve the problem. -A bank loaned out $57,000, part of it at the rate of 2.5% per year and the rest at a rate of 3.5% per year. If the interest received was $1705.00, how much was loaned at 2.5%?

Find the quotient. Write the answer in standard form. - $\frac { 1 + 3 i } { 5 + 6 i }$

Solve the equation. - $4 \sqrt { x } = \sqrt { 9 x + 9 }$

Find the product. Write the answer in standard form. - $( 3 - 5 \mathrm { i } ) ( 4 - 4 \mathrm { i } )$

Solve the equation. - $x ^ { 2 } = 9$

Solve the equation. - $x ^ { 1 / 2 } = - 5 x ^ { 1 / 4 }$

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. - $\mathrm { F } = 102 ^ { \circ }$

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 7 miles per hour, and Delvis is traveling at a speed of 15 miles per hour. In 5 hours what is the distance Between them (assuming that they began at the same point and time)?

Solve the equation. - $( 2 x + 3 ) ^ { 1 / 2 } + ( 4 - x ) ^ { 1 / 2 } = 4$

Solve the inequality. Write the solution set in interval notation. - $| 4 x + 7 | + 8 < 16$

Solve the inequality. Write the solution set in interval notation. - $| - 5 x + 6 | \geq - 5$

Solve the inequality. Write the solution set in interval notation. - $| - 9 x + 1 | < 8$

Solve the inequality. Write the solution set in interval notation. - $| 8 x + 2 | + 6 < 14$

Solve and graph the inequality. Give answer in interval notation. - $12 x - 27 > 3 ( 3 x - 11 )$

Solve the equation. - $( x - 3 ) ^ { 4 } - 5 ( x - 3 ) ^ { 2 } + 4 = 0$

Write the number in standard form a + bi. - $\frac { - 5 + \sqrt { - 75 } } { 25 }$

Decide whether or not the equations are equivalent. -4x - 3 = 6 -4x + 6 = -3

Solve the problem. -Hannah borrowed $45,338 at 4.5% simple interest for 22 months. How much will the interest amount to? What is the total amount that she will have to pay back at the end of 22 months? Round answers to the nearest cent if necessary.

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

Solve the equation. - 3x−7+7x+2=5x2−5x−14\frac { 3 } { x - 7 } + \frac { 7 } { x + 2 } = \frac { 5 } { x ^ { 2 } - 5 x - 14 }x−73​+x+27​=x2−5x−145​

Solve the problem. -A bank loaned out $57,000, part of it at the rate of 2.5% per year and the rest at a rate of 3.5% per year. If the interest received was $1705.00, how much was loaned at 2.5%?

Find the quotient. Write the answer in standard form. - 1+3i5+6i\frac { 1 + 3 i } { 5 + 6 i }5+6i1+3i​

Solve the equation. - 4x=9x+94 \sqrt { x } = \sqrt { 9 x + 9 }4x​=9x+9​

Find the product. Write the answer in standard form. - (3−5i)(4−4i)( 3 - 5 \mathrm { i } ) ( 4 - 4 \mathrm { i } )(3−5i)(4−4i)

Solve the equation. - x2=9x ^ { 2 } = 9x2=9

Solve the equation. - x1/2=−5x1/4x ^ { 1 / 2 } = - 5 x ^ { 1 / 4 }x1/2=−5x1/4

Use these equations to convert between the two systems. C=59(F−32)F=95C+32C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32C=95​(F−32)F=59​C+32 Round answer to the nearest tenth of a degree if necessary. - F=102∘\mathrm { F } = 102 ^ { \circ }F=102∘