Question 1

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

Accepted Answer

A)  $\left\{ \frac { 5 } { 6 } \right\}$ 
B)  $\{ 30 \}$ 
C)  $\{ - 30 \}$ 
D)  $\left\{ - \frac { 5 } { 6 } \right\}$ 
A)  $\left\{ \frac { 5 } { 6 } \right\}$ 
B)  $\{ 30 \}$ 
C)  $\{ - 30 \}$ 
D)  $\left\{ - \frac { 5 } { 6 } \right\}$

Question 2

Decide what number must be added to the binomial to make a perfect square trinomial.
-$$x ^ { 2 } + \frac { 4 } { 5 } x$$

Accepted Answer

A)  $\frac { 4 } { 25 }$ 
B)  $\frac { 16 } { 25 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 8 } { 25 }$ 
A)  $\frac { 4 } { 25 }$ 
B)  $\frac { 16 } { 25 }$ 
C)  $\frac { 1 } { 5 }$ 
D)  $\frac { 8 } { 25 }$

Question 3

Solve the problem.
-Find the dimensions of a rectangle whose perimeter is 38 meters and whose area is 84 square meters.

Accepted Answer

A) 8 m by 11 m 
B) 6 m by 11 m 
C) 7 m by 12 m 
D) 6 m by 13 m 
A) 8 m by 11 m 
B) 6 m by 11 m 
C) 7 m by 12 m 
D) 6 m by 13 m

Question 4

Solve the equation after making an appropriate substitution.
-$$x ^ { 2 / 3 } + 2 x ^ { 1 / 3 } - 8 = 0$$

Accepted Answer

A)  $\{ - 8,64 \}$ 
B)  $\{ - 64,8 \}$ 
C)  $\{ - 2,4 \}$ 
D)  $\{ - 4,2 \}$ 
A)  $\{ - 8,64 \}$ 
B)  $\{ - 64,8 \}$ 
C)  $\{ - 2,4 \}$ 
D)  $\{ - 4,2 \}$

Question 5

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-2x + 3 < 11

Accepted Answer

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

Question 6

Perform the desired operation. Write the answer in the form a + bi.
-$$( 6 + 7 i ) ( 6 - 7 i )$$

Accepted Answer

A)  $- 13$ 
B)  $36 - 49 i ^ { 2 }$ 
C)  85 
D)  $36 - 49 \mathrm { i }$ 
A)  $- 13$ 
B)  $36 - 49 i ^ { 2 }$ 
C)  85 
D)  $36 - 49 \mathrm { i }$

Question 7

Solve the equation.
-$$| x + 6 | = 0$$

Accepted Answer

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

Question 8

Solve the equation.
-$$| x + 4 | = 2$$

Accepted Answer

A)  $\{ - 6 , - 2 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 6 , - 2 \}$ 
D)  no real solution 
A)  $\{ - 6 , - 2 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 6 , - 2 \}$ 
D)  no real solution

Question 9

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$x ^ { 2 } - 4 x + 5 = 0$$

Accepted Answer

A) two real solutions 
B) two nonreal solutions 
C) exactly one real solution 
A) two real solutions 
B) two nonreal solutions 
C) exactly one real solution

Question 10

Solve the radical equation.
-$$\sqrt { 8 x + 33 } = x$$

Accepted Answer

A)  $\left\{ - \frac { 33 } { 7 } \right\}$ 
B)  $\{ 11 \}$ 
C)  $\{ - 3,11 \}$ 
D)  no real solution 
A)  $\left\{ - \frac { 33 } { 7 } \right\}$ 
B)  $\{ 11 \}$ 
C)  $\{ - 3,11 \}$ 
D)  no real solution

Question 11

Write the expression in the standard form a + bi.
-$8 \mathrm { i } + ( - 6 - \mathrm { i } )$

Accepted Answer

A)  $- 6 + 7 i$ 
B)  $- 6 + 9 i$ 
C)  $6 - 9 i$ 
D)  $6 - 7 \mathrm { i }$ 
A)  $- 6 + 7 i$ 
B)  $- 6 + 9 i$ 
C)  $6 - 9 i$ 
D)  $6 - 7 \mathrm { i }$

Question 12

Solve the linear inequality. Express the solution in set-builder notation.
-$24 x - 24 > 6 ( 3 x - 6 )$

Accepted Answer

A) $\{ x \mid x > 24 \}$ B) $\{ x \mid x > - 2 \}$ C) $\{ x \mid x < - 2 \}$ D) $\{ x \mid x < 24 \}$ A) $\{ x \mid x > 24 \}$ B) $\{ x \mid x > - 2 \}$ C) $\{ x \mid x < - 2 \}$ D) $\{ x \mid x < 24 \}$

Question 13

Solve the equation.
--4x - 20 = -2x - 4

Accepted Answer

A)  $\{ 10 \}$ 
B)  $\{ - 10 \}$ 
C)  $\{ - 8 \}$ 
D)  $\{ 8 \}$ 
A)  $\{ 10 \}$ 
B)  $\{ - 10 \}$ 
C)  $\{ - 8 \}$ 
D)  $\{ 8 \}$

Question 14

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-$$9 \leq 2 x + 3 \leq 13$$

Accepted Answer

A)  $[ - 5 , = 3 ]$
  
B)  $( - 5 , - 3 )$
  
C) $[ 3,5 ]$
  
D)  $( 3,5 )$
  
A)  $[ - 5 , = 3 ]$
  
B)  $( - 5 , - 3 )$
  
C) $[ 3,5 ]$
  
D)  $( 3,5 )$

Question 15

Find the real solutions, if any, of the equation. Use the quadratic formula.
-$3 x ^ { 2 } + x - 7 = 0$

Accepted Answer

A)  $\left\{ \frac { 1 - \sqrt { 85 } } { 6 } , \frac { 1 + \sqrt { 85 } } { 6 } \right\}$ 
B)  no real solution 
C)  $\left\{ \frac { - 1 - \sqrt { 85 } } { 6 } , \frac { - 1 + \sqrt { 85 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 1 - \sqrt { 85 } } { 2 } , \frac { - 1 + \sqrt { 85 } } { 2 } \right\}$ 
A)  $\left\{ \frac { 1 - \sqrt { 85 } } { 6 } , \frac { 1 + \sqrt { 85 } } { 6 } \right\}$ 
B)  no real solution 
C)  $\left\{ \frac { - 1 - \sqrt { 85 } } { 6 } , \frac { - 1 + \sqrt { 85 } } { 6 } \right\}$ 
D)  $\left\{ \frac { - 1 - \sqrt { 85 } } { 2 } , \frac { - 1 + \sqrt { 85 } } { 2 } \right\}$

Question 16

Solve the equation after making an appropriate substitution.
-$$x ^ { 6 } - 26 x ^ { 3 } - 27 = 0$$

Accepted Answer

A)  $\{ 27 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3,1 \}$ 
D)  $\{ 3 , - 1 \}$ 
A)  $\{ 27 \}$ 
B)  $\{ 3 \}$ 
C)  $\{ - 3,1 \}$ 
D)  $\{ 3 , - 1 \}$

Question 17

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-$$- 1 < x - 2 \leq 1$$

Accepted Answer

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

Question 18

Solve the linear inequality. Express the solution in set-builder notation.
-$x - 3 \leq 1$ and $x - 3 > - 4$

Accepted Answer

A)  $[ - 7 , - 2 )$ 
B)  $( - 7 , - 2 ]$ 
C)  $( - 1,4 ]$ 
D)  $[ - 1,4 )$ 
A)  $[ - 7 , - 2 )$ 
B)  $( - 7 , - 2 ]$ 
C)  $( - 1,4 ]$ 
D)  $[ - 1,4 )$

Question 19

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
--3x - 7 ≥-4x - 2

Accepted Answer

A)  $[ 5 , \infty )$
  
B)  $( - \infty , 5 ]$
  
C) $( - 9 , \infty )$
  
D)  $( - \infty , 5 )$
  
A)  $[ 5 , \infty )$
  
B)  $( - \infty , 5 ]$
  
C) $( - 9 , \infty )$
  
D)  $( - \infty , 5 )$

Question 20

Solve the problem.
-Two cars start from the same point and travel in the same direction. If one car is traveling 59 miles per hour and the other car is traveling at 52 miles per hour, how far apart will they be after 2.1 hours?

Accepted Answer

A) 109.2 mi 
B) 233.1 mi 
C) 14.7 mi 
D) 123.9 mi 
A) 109.2 mi 
B) 233.1 mi 
C) 14.7 mi 
D) 123.9 mi

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

Decide what number must be added to the binomial to make a perfect square trinomial. - $x ^ { 2 } + \frac { 4 } { 5 } x$

Solve the problem. -Find the dimensions of a rectangle whose perimeter is 38 meters and whose area is 84 square meters.

Solve the equation after making an appropriate substitution. - $x ^ { 2 / 3 } + 2 x ^ { 1 / 3 } - 8 = 0$

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. -2x + 3 < 11

Perform the desired operation. Write the answer in the form a + bi. - $( 6 + 7 i ) ( 6 - 7 i )$

Solve the equation. - $| x + 6 | = 0$

Solve the equation. - $| x + 4 | = 2$

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - $x ^ { 2 } - 4 x + 5 = 0$

Solve the radical equation. - $\sqrt { 8 x + 33 } = x$

Write the expression in the standard form a + bi. - $8 \mathrm { i } + ( - 6 - \mathrm { i } )$

Solve the linear inequality. Express the solution in set-builder notation. - $24 x - 24 > 6 ( 3 x - 6 )$

Solve the equation. --4x - 20 = -2x - 4

Find the real solutions, if any, of the equation. Use the quadratic formula. - $3 x ^ { 2 } + x - 7 = 0$

Solve the equation after making an appropriate substitution. - $x ^ { 6 } - 26 x ^ { 3 } - 27 = 0$

Solve the linear inequality. Express the solution in set-builder notation. - $x - 3 \leq 1$ and $x - 3 > - 4$

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. --3x - 7 ≥-4x - 2

Solve the problem. -Two cars start from the same point and travel in the same direction. If one car is traveling 59 miles per hour and the other car is traveling at 52 miles per hour, how far apart will they be after 2.1 hours?

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 equation. - 12x−1=13x−6\frac { 1 } { 2 } x - 1 = \frac { 1 } { 3 } x - 621​x−1=31​x−6

Decide what number must be added to the binomial to make a perfect square trinomial. - x2+45xx ^ { 2 } + \frac { 4 } { 5 } xx2+54​x

Solve the problem. -Find the dimensions of a rectangle whose perimeter is 38 meters and whose area is 84 square meters.

Solve the equation after making an appropriate substitution. - x2/3+2x1/3−8=0x ^ { 2 / 3 } + 2 x ^ { 1 / 3 } - 8 = 0x2/3+2x1/3−8=0

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. -2x + 3 < 11

Perform the desired operation. Write the answer in the form a + bi. - (6+7i)(6−7i)( 6 + 7 i ) ( 6 - 7 i )(6+7i)(6−7i)

Solve the equation. - ∣x+6∣=0| x + 6 | = 0∣x+6∣=0

Solve the equation. - ∣x+4∣=2| x + 4 | = 2∣x+4∣=2

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - x2−4x+5=0x ^ { 2 } - 4 x + 5 = 0x2−4x+5=0

Solve the radical equation. - 8x+33=x\sqrt { 8 x + 33 } = x8x+33​=x

Write the expression in the standard form a + bi. - 8i+(−6−i)8 \mathrm { i } + ( - 6 - \mathrm { i } )8i+(−6−i)

Solve the linear inequality. Express the solution in set-builder notation. - 24x−24>6(3x−6)24 x - 24 > 6 ( 3 x - 6 )24x−24>6(3x−6)