Question 1

Solve the polynomial inequality. Express the solution in interval notation.
-$( x - 1 ) ( x + 8 ) > 0$

Accepted Answer

A) $ (- 8 ,  \infty $) 
B)  $( - 8,1 )$ 
C)  $( - \infty , - 1 ) \cup ( 8 , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( 1 , \infty )$ 
A) $ (- 8 ,  \infty $) 
B)  $( - 8,1 )$ 
C)  $( - \infty , - 1 ) \cup ( 8 , \infty )$ 
D)  $( - \infty , - 8 ) \cup ( 1 , \infty )$

Question 2

Write the power of i as i, -1, -i, or 1.
-$$\mathrm { i } 8$$

Accepted Answer

A) 1 
B) i 
C) -i 
D) -1 
A) 1 
B) i 
C) -i 
D) -1

Question 3

Perform the indicated operations and write the result in standard form.
-$$\sqrt { - 4 } \cdot \sqrt { - 36 }$$

Accepted Answer

A)  $- 12 \mathrm { i }$ 
B)  $- 12$ 
C)  12 
D)  $12 \mathrm { i } ^ { 2 }$ 
A)  $- 12 \mathrm { i }$ 
B)  $- 12$ 
C)  12 
D)  $12 \mathrm { i } ^ { 2 }$

Question 4

Perform the indicated operations and write the result in standard form.
-$\sqrt { - 49 } + \sqrt { - 81 }$

Accepted Answer

A)  $- 16$ 
B)  $16 \mathrm { i }$ 
C)  $- 16 \mathrm { i }$ 
D)  $63 \mathrm { i }$ 
A)  $- 16$ 
B)  $16 \mathrm { i }$ 
C)  $- 16 \mathrm { i }$ 
D)  $63 \mathrm { i }$

Question 5

Solve the equation.
-$$\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }$$

Accepted Answer

A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 3 } { 10 } \right\}$ 
C)  $\left\{ \frac { 3 } { 2 } \right\}$ 
D)  no solution 
A)  $\{ 3 \}$ 
B)  $\left\{ \frac { 3 } { 10 } \right\}$ 
C)  $\left\{ \frac { 3 } { 2 } \right\}$ 
D)  no solution

Question 6

Solve the equation.
-$\left| x ^ { 2 } - 6 x \right| = 0$

Accepted Answer

A)  $\{ - 6,0 \}$ 
B)  $\{ 0,6 \}$ 
C)  $\{ - 6,0,6 \}$ 
D)  no real solution 
A)  $\{ - 6,0 \}$ 
B)  $\{ 0,6 \}$ 
C)  $\{ - 6,0,6 \}$ 
D)  no real solution

Question 7

Perform the desired operation. Write the answer in the form a + bi.
-$$( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )$$

Accepted Answer

A)  $60 - 36 \mathrm { i }$ 
B)  $- 12 i ^ { 2 } - 36 i + 48$ 
C)  $60 + 36 i$ 
D)  $36 + 60 \mathrm { i }$ 
A)  $60 - 36 \mathrm { i }$ 
B)  $- 12 i ^ { 2 } - 36 i + 48$ 
C)  $60 + 36 i$ 
D)  $36 + 60 \mathrm { i }$

Question 8

Solve the equation.
-$$\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x$$

Accepted Answer

A)  $\{ - 45 \}$ 
B)  $\{ 45 \}$ 
C)  $\{ 90 \}$ 
D)  $\{ - 90 \}$ 
A)  $\{ - 45 \}$ 
B)  $\{ 45 \}$ 
C)  $\{ 90 \}$ 
D)  $\{ - 90 \}$

Question 9

Solve the rational inequality. Express the solution in interval notation.
-$$\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }$$

Accepted Answer

A)  $( - 43 , - 1 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , - 43 ) \cup ( - 1,6 )$ 
C)  $( - 43 , - 1 ) \cup ( - 1,6 )$ 
D)  $( - \infty , - 43 ) \cup ( 6 , \infty )$ 
A)  $( - 43 , - 1 ) \cup ( 6 , \infty )$ 
B)  $( - \infty , - 43 ) \cup ( - 1,6 )$ 
C)  $( - 43 , - 1 ) \cup ( - 1,6 )$ 
D)  $( - \infty , - 43 ) \cup ( 6 , \infty )$

Question 10

Solve the equation by factoring.
-$$x ^ { 2 } + x - 20 = 0$$

Accepted Answer

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

Question 11

Find all solutions.
-$$x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0$$

Accepted Answer

A)  $\{ - 3,3,2 \}$ 
B)  $\{ - 3,3 , - 2 \}$ 
C)  $\{ 9 , - 2 \}$ 
D)  $\{ 3 , - 2 \}$ 
A)  $\{ - 3,3,2 \}$ 
B)  $\{ - 3,3 , - 2 \}$ 
C)  $\{ 9 , - 2 \}$ 
D)  $\{ 3 , - 2 \}$

Question 12

Solve the equation using the square root property.
-$$( 2 x - 3 ) ^ { 2 } - 49 = 0$$

Accepted Answer

A)  $\{ 10 , - 4 \}$ 
B)  $\{ 4 , - 10 \}$ 
C)  $\{ 5 , - 2 \}$ 
D)  $\{ 2 , - 5 \}$ 
A)  $\{ 10 , - 4 \}$ 
B)  $\{ 4 , - 10 \}$ 
C)  $\{ 5 , - 2 \}$ 
D)  $\{ 2 , - 5 \}$

Question 13

Solve the problem.
-A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

Accepted Answer

A) $3100 
B) $983 
C) $2800 
D) $2950 
A) $3100 
B) $983 
C) $2800 
D) $2950

Question 14

Solve the equation.
--4x + 1 - 4(x + 1)= -6x + 1

Accepted Answer

A)  $\left\{ - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ - 6 \}$ 
D)  $\{ - 2 \}$ 
A)  $\left\{ - \frac { 7 } { 4 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } \right\}$ 
C)  $\{ - 6 \}$ 
D)  $\{ - 2 \}$

Question 15

Solve the problem.
-Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

Accepted Answer

A) 35 hr 
B) 50 hr 
C) 70 hr 
D) 15 hr 
A) 35 hr 
B) 50 hr 
C) 70 hr 
D) 15 hr

Question 16

Solve the polynomial inequality. Express the solution in interval notation.
-$$x ^ { 3 } - 4 x ^ { 2 } > 0$$

Accepted Answer

A)  $( 4 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 4 )$ 
A)  $( 4 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 4 )$

Question 17

Solve the polynomial inequality. Express the solution in interval notation.
-$$( x + 5 ) ( x - 5 ) \leq 0$$

Accepted Answer

A)  $( - 5,5 )$ 
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 5 ] \cup [ 5 , \infty )$ 
D)  $[ - 5,5 ]$ 
A)  $( - 5,5 )$ 
B)  $( - \infty , - 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 5 ] \cup [ 5 , \infty )$ 
D)  $[ - 5,5 ]$

Question 18

Solve the equation.
--35 - 3x = -10 + 2x

Accepted Answer

A)  $\{ - 7 \}$ 
B)  $\{ - 5 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ 7 \}$ 
A)  $\{ - 7 \}$ 
B)  $\{ - 5 \}$ 
C)  $\{ 5 \}$ 
D)  $\{ 7 \}$

Question 19

Solve the equation after making an appropriate substitution.
-$$x + \sqrt { x } = 72$$

Accepted Answer

A)  $\{ 8 \}$ 
B)  $\{ 9 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 64 \}$ 
A)  $\{ 8 \}$ 
B)  $\{ 9 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 64 \}$

Question 20

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-$$11 - 3 ( 3 - x ) \leq 14$$

Accepted Answer

A)  $( - \infty , 5 ]$
  
B)  $( - \infty , 4 )$
  
C) $[ 4 , \infty )$
  
D)  $( - \infty , 4 ]$
  
A)  $( - \infty , 5 ]$
  
B)  $( - \infty , 4 )$
  
C) $[ 4 , \infty )$
  
D)  $( - \infty , 4 ]$

Solve the polynomial inequality. Express the solution in interval notation. - $( x - 1 ) ( x + 8 ) > 0$

Write the power of i as i, -1, -i, or 1. - $\mathrm { i } 8$

Perform the indicated operations and write the result in standard form. - $\sqrt { - 4 } \cdot \sqrt { - 36 }$

Perform the indicated operations and write the result in standard form. - $\sqrt { - 49 } + \sqrt { - 81 }$

Solve the equation. - $\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }$

Solve the equation. - $\left| x ^ { 2 } - 6 x \right| = 0$

Perform the desired operation. Write the answer in the form a + bi. - $( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )$

Solve the equation. - $\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x$

Solve the rational inequality. Express the solution in interval notation. - $\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }$

Solve the equation by factoring. - $x ^ { 2 } + x - 20 = 0$

Find all solutions. - $x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0$

Solve the equation using the square root property. - $( 2 x - 3 ) ^ { 2 } - 49 = 0$

Solve the problem. -A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

Solve the equation. --4x + 1 - 4(x + 1)= -6x + 1

Solve the problem. -Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 3 } - 4 x ^ { 2 } > 0$

Solve the polynomial inequality. Express the solution in interval notation. - $( x + 5 ) ( x - 5 ) \leq 0$

Solve the equation. --35 - 3x = -10 + 2x

Solve the equation after making an appropriate substitution. - $x + \sqrt { x } = 72$

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - $11 - 3 ( 3 - x ) \leq 14$ $Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - 11 - 3 ( 3 - x ) \leq 14$

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 1: Equations, Inequalities, and Applications

Solve the polynomial inequality. Express the solution in interval notation. - (x−1)(x+8)>0( x - 1 ) ( x + 8 ) > 0(x−1)(x+8)>0

Write the power of i as i, -1, -i, or 1. - i8\mathrm { i } 8i8

Perform the indicated operations and write the result in standard form. - −4⋅−36\sqrt { - 4 } \cdot \sqrt { - 36 }−4​⋅−36​

Perform the indicated operations and write the result in standard form. - −49+−81\sqrt { - 49 } + \sqrt { - 81 }−49​+−81​

Solve the equation. - 65x−1x+1=3x(2x+2)\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }5x6​−x+11​=x(2x+2)3​

Solve the equation. - ∣x2−6x∣=0\left| x ^ { 2 } - 6 x \right| = 0​x2−6x​=0

Perform the desired operation. Write the answer in the form a + bi. - (8+2i)(6−6i)( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )(8+2i)(6−6i)

Solve the equation. - 25x=3+13x\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x52​x=3+31​x

Solve the rational inequality. Express the solution in interval notation. - 14x−6>12x+1\frac { 14 } { x - 6 } > \frac { 12 } { x + 1 }x−614​>x+112​

Solve the equation by factoring. - x2+x−20=0x ^ { 2 } + x - 20 = 0x2+x−20=0

Find all solutions. - x3+2x2−9x−18=0x ^ { 3 } + 2 x ^ { 2 } - 9 x - 18 = 0x3+2x2−9x−18=0

Solve the equation using the square root property. - (2x−3)2−49=0( 2 x - 3 ) ^ { 2 } - 49 = 0(2x−3)2−49=0