Question 1

Solve the equation using the square root property.
-$$( x + 2 ) ^ { 2 } - 4 = 0$$

Accepted Answer

A)  $\{ - 4 \}$ 
B)  $\{ - 2,2 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ - 4,0 \}$ 
A)  $\{ - 4 \}$ 
B)  $\{ - 2,2 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ - 4,0 \}$

Question 2

Solve the problem.
-How much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

A) 4.5 gal 
B) 22.5 gal 
C) 36 gal 
D) 13.5 gal 
A) 4.5 gal 
B) 22.5 gal 
C) 36 gal 
D) 13.5 gal

Question 3

Solve the radical equation.
-$$\sqrt { 4 x + 5 } = 5$$

Accepted Answer

A)  $\left\{ \frac { 15 } { 2 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\{ 25 \}$ 
D)  $\left\{ \frac { 25 } { 4 } \right\}$ 
A)  $\left\{ \frac { 15 } { 2 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\{ 25 \}$ 
D)  $\left\{ \frac { 25 } { 4 } \right\}$

Question 4

Solve the rational inequality. Express the solution in interval notation.
-$$\frac { 3 x } { x + 5 } < x$$

Accepted Answer

A)  $( - \infty , - 5 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 5 ) \cup ( - 2,0 )$ 
D)  $( - 5 , - 2 ) \cup ( 0 , \infty )$ 
A)  $( - \infty , - 5 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 5 ) \cup ( - 2,0 )$ 
D)  $( - 5 , - 2 ) \cup ( 0 , \infty )$

Question 5

Solve the equation.
--5x - 2 - 2 = -4(x + 9)

Accepted Answer

A)  $\{ 32 \}$ 
B)  $\{ 13 \}$ 
C)  $\{ - 36 \}$ 
D)  $\{ - 32 \}$ 
A)  $\{ 32 \}$ 
B)  $\{ 13 \}$ 
C)  $\{ - 36 \}$ 
D)  $\{ - 32 \}$

Question 6

Decide what number must be added to the binomial to make a perfect square trinomial.
-$$x ^ { 2 } - \frac { 1 } { 2 } x$$

Accepted Answer

A)  $- \frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 16 }$ 
A)  $- \frac { 1 } { 8 }$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 16 }$

Question 7

Solve the radical equation.
-$$\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$$

Accepted Answer

A)  $\{ 3,8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 2,38 \}$ 
D)  $\{ - 2 \}$ 
A)  $\{ 3,8 \}$ 
B)  $\{ 2 \}$ 
C)  $\{ 2,38 \}$ 
D)  $\{ - 2 \}$

Question 8

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

Accepted Answer

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

Question 9

Solve the problem.
-The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound. They have a 40-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of raisins so that they hit their target value of $6 per pound for the mixture?

Accepted Answer

A) 52 lb 
B) 64 lb 
C) 56 lb 
D) 60 lb 
A) 52 lb 
B) 64 lb 
C) 56 lb 
D) 60 lb

Question 10

Solve the equation.
-5(x + 2)= 6(x - 3)

Accepted Answer

A)  $\{ - 8 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 28 \}$ 
D)  $\{ - 28 \}$ 
A)  $\{ - 8 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ 28 \}$ 
D)  $\{ - 28 \}$

Question 11

Solve the three-part linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-$$15 \leq \frac { 7 } { 2 } x + 8 < 29$$

Accepted Answer

A)  $( 2,3 ]$
  
B)  $[ 2,3 )$
  
C)  $( 2,6 ]$
  
D)  $[ 2,6 )$
  
A)  $( 2,3 ]$
  
B)  $[ 2,3 )$
  
C)  $( 2,6 ]$
  
D)  $[ 2,6 )$

Question 12

Solve the rational inequality. Express the solution in interval notation.
-$$\frac { ( x + 9 ) ( x - 7 ) } { x - 1 } \geq 0$$

Accepted Answer

A)  $( - \infty , - 9 ] \cup [ 7 , \infty )$ 
B)  $[ - 9,1 ) \cup [ 7 , \infty )$ 
C)  $[ - 9,1 ) \cup ( 1,7 ]$ 
D)  $( - \infty , - 9 ] \cup ( 1,7 ]$ 
A)  $( - \infty , - 9 ] \cup [ 7 , \infty )$ 
B)  $[ - 9,1 ) \cup [ 7 , \infty )$ 
C)  $[ - 9,1 ) \cup ( 1,7 ]$ 
D)  $( - \infty , - 9 ] \cup ( 1,7 ]$

Question 13

Solve the equation.
-$$\frac { 6 } { x + 4 } - \frac { 8 } { x - 4 } = \frac { 8 } { x ^ { 2 } - 16 }$$

Accepted Answer

A)  $\{ 2 \sqrt { 14 } \}$ 
B)  $\{ 64 \}$ 
C)  $\{ - 32 \}$ 
D)  $\{ 32 \}$ 
A)  $\{ 2 \sqrt { 14 } \}$ 
B)  $\{ 64 \}$ 
C)  $\{ - 32 \}$ 
D)  $\{ 32 \}$

Question 14

Solve the problem.
-During an intramural basketball game, Team A scored 19 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game?

Accepted Answer

A) 66 points 
B) 67 points 
C) 85 points 
D) 75 points 
A) 66 points 
B) 67 points 
C) 85 points 
D) 75 points

Question 15

Write the sentence as an equation. Let the variable x represent the number.
-The product of 6 and a number, increased by 3, is 21.

Accepted Answer

A) 6x + 3 = 21 
B) 18x = 21 
C) 6(x + 3)= 21 
D) 6x - 3 = 21 
A) 6x + 3 = 21 
B) 18x = 21 
C) 6(x + 3)= 21 
D) 6x - 3 = 21

Question 16

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

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 1,1 )$ 
B)  $( - 1,1 ) \cup ( 3 , \infty )$ 
C)  $( - 3 , - 1 ) \cup ( 1 , \infty )$ 
D)  $( - \infty , - 1 ) \cup ( 1,3 )$ 
A)  $( - \infty , - 3 ) \cup ( - 1,1 )$ 
B)  $( - 1,1 ) \cup ( 3 , \infty )$ 
C)  $( - 3 , - 1 ) \cup ( 1 , \infty )$ 
D)  $( - \infty , - 1 ) \cup ( 1,3 )$

Question 17

Solve the equation by completing the square.
-$$x ^ { 2 } - 12 x - 5 = 0$$

Accepted Answer

A)  $\{ 12 - \sqrt { 149 } , 12 + \sqrt { 149 } \}$ 
B)  $\{ 6 - \sqrt { 41 } , 6 + \sqrt { 41 } \}$ 
C)  $\{ - 6 - \sqrt { 41 } , - 6 + \sqrt { 41 } \}$ 
D)  $\{ 6 - \sqrt { 5 } , 6 + \sqrt { 5 } \}$ 
A)  $\{ 12 - \sqrt { 149 } , 12 + \sqrt { 149 } \}$ 
B)  $\{ 6 - \sqrt { 41 } , 6 + \sqrt { 41 } \}$ 
C)  $\{ - 6 - \sqrt { 41 } , - 6 + \sqrt { 41 } \}$ 
D)  $\{ 6 - \sqrt { 5 } , 6 + \sqrt { 5 } \}$

Question 18

Write the sentence as an equation. Let the variable x represent the number.
-Three less than 4 times a number equals 17.

Accepted Answer

A) x - 12 = 17 
B) 3 - 4x = 17 
C) 4x 17 
D) 4x - 3 = 17 3 = 
A) x - 12 = 17 
B) 3 - 4x = 17 
C) 4x 17 
D) 4x - 3 = 17 3 =

Question 19

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$5 x ^ { 2 } - 3 x - 1 = 0$$

Accepted Answer

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

Question 20

Solve the problem.
-Don James wants to invest $59,000 to earn $6170 per year. He can invest in B-rated bonds paying 13% per year or in a Certificate of Deposit (CD)paying 7% per year. How much money should be invested in each to realize exactly $6170 in interest per year?

Accepted Answer

A) $25,000 in B-rated bonds and $34,000 in a CD 
B) $35,000 in B-rated bonds and $24,000 in a CD 
C) $24,000 in B-rated bonds and $35,000 in a CD 
D) $34,000 in B-rated bonds and $25,000 in a CD 
A) $25,000 in B-rated bonds and $34,000 in a CD 
B) $35,000 in B-rated bonds and $24,000 in a CD 
C) $24,000 in B-rated bonds and $35,000 in a CD 
D) $34,000 in B-rated bonds and $25,000 in a CD

Solve the equation using the square root property. - $( x + 2 ) ^ { 2 } - 4 = 0$

Solve the problem. -How much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution?

Solve the radical equation. - $\sqrt { 4 x + 5 } = 5$

Solve the rational inequality. Express the solution in interval notation. - $\frac { 3 x } { x + 5 } < x$

Solve the equation. --5x - 2 - 2 = -4(x + 9)

Decide what number must be added to the binomial to make a perfect square trinomial. - $x ^ { 2 } - \frac { 1 } { 2 } x$

Solve the radical equation. - $\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 3$

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

Solve the equation. -5(x + 2)= 6(x - 3)

Solve the rational inequality. Express the solution in interval notation. - $\frac { ( x + 9 ) ( x - 7 ) } { x - 1 } \geq 0$

Solve the equation. - $\frac { 6 } { x + 4 } - \frac { 8 } { x - 4 } = \frac { 8 } { x ^ { 2 } - 16 }$

Solve the problem. -During an intramural basketball game, Team A scored 19 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game?

Write the sentence as an equation. Let the variable x represent the number. -The product of 6 and a number, increased by 3, is 21.

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

Solve the equation by completing the square. - $x ^ { 2 } - 12 x - 5 = 0$

Write the sentence as an equation. Let the variable x represent the number. -Three less than 4 times a number equals 17.

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - $5 x ^ { 2 } - 3 x - 1 = 0$

Solve the problem. -Don James wants to invest $59,000 to earn $6170 per year. He can invest in B-rated bonds paying 13% per year or in a Certificate of Deposit (CD)paying 7% per year. How much money should be invested in each to realize exactly $6170 in interest per year?

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 using the square root property. - (x+2)2−4=0( x + 2 ) ^ { 2 } - 4 = 0(x+2)2−4=0