Question 1

Solve the equation by factoring.
-$$x ^ { 2 } + 5 = 6 x$$

Accepted Answer

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

Question 2

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the
equation.
-$$x ^ { 2 } + 10 x + 25 = 0$$

Accepted Answer

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

Question 3

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-$$\frac { 1 } { 3 } x \geq 5 + \frac { 1 } { 18 } x$$

Accepted Answer

A)  $( 18 , \infty )$
  
B)  $[ - 18 , \infty )$
  
C) $( - \infty , 18 ]$
  
D)  $[ 18 , \infty )$
  
A)  $( 18 , \infty )$
  
B)  $[ - 18 , \infty )$
  
C) $( - \infty , 18 ]$
  
D)  $[ 18 , \infty )$

Question 4

Solve the problem.
-A bank loaned out $69,000, part of it at the rate of 15% per year and the rest at a rate of 8% per year. If the interest received was $7480, how much was loaned at 15%?

Accepted Answer

A) $40,000 
B) $28,000 
C) $29,000 
D) $41,000 
A) $40,000 
B) $28,000 
C) $29,000 
D) $41,000

Question 5

Write the sentence as an equation. Let the variable x represent the number.
-The product of 4 and a number increased by 3 is 20.

Accepted Answer

A) 4x + 3 = 20 
B) 12x = 20 
C) 4(x + 3)= 20 
D) 4x - 3 = 20 
A) 4x + 3 = 20 
B) 12x = 20 
C) 4(x + 3)= 20 
D) 4x - 3 = 20

Question 6

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
--4(6x + 1)< -28x + 12

Accepted Answer

A)  $( 4 , \infty )$
  
B) $( - \infty , 4 ]$
  
C) $( - \infty , - 2 ]$
  
D) $( - \infty , 4 )$
  
A)  $( 4 , \infty )$
  
B) $( - \infty , 4 ]$
  
C) $( - \infty , - 2 ]$
  
D) $( - \infty , 4 )$

Question 7

Solve the radical equation.
-$$\sqrt { \mathrm { x } + 1 } = 8$$

Accepted Answer

A)  $\{ 63 \}$ 
B)  $\{ 64 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 65 \}$ 
A)  $\{ 63 \}$ 
B)  $\{ 64 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 65 \}$

Question 8

Solve the problem.
-Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 83?

Accepted Answer

A) 78 or greater 
B) 81 or greater 
C) 80 or greater 
D) 79 or greater 
A) 78 or greater 
B) 81 or greater 
C) 80 or greater 
D) 79 or greater

Question 9

Solve the polynomial inequality. Express the solution in interval notation.
-$$2 x ^ { 2 } - 5 x \geq 7$$

Accepted Answer

A)  $( - \infty , - 1 ] \cup \left[ \frac { 7 } { 2 } , \infty \right)$ 
B)  $\left[ - 1 , \frac { 7 } { 2 } \right]$ 
C)  $\left( - 1 , \frac { 7 } { 2 } \right)$ 
D)  $( - \infty , - 1 ) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
A)  $( - \infty , - 1 ] \cup \left[ \frac { 7 } { 2 } , \infty \right)$ 
B)  $\left[ - 1 , \frac { 7 } { 2 } \right]$ 
C)  $\left( - 1 , \frac { 7 } { 2 } \right)$ 
D)  $( - \infty , - 1 ) \cup \left( \frac { 7 } { 2 } , \infty \right)$

Question 10

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
--4x - 5 > -5x - 11

Accepted Answer

A)  $[ - 6 , \infty )$
  
B)  $( - 6 , \infty )$
  
C) $( - 16 , \infty )$
  
D)  $( - \infty , - 6 ]$
  
A)  $[ - 6 , \infty )$
  
B)  $( - 6 , \infty )$
  
C) $( - 16 , \infty )$
  
D)  $( - \infty , - 6 ]$

Question 11

Solve the problem.
-Two trains leave a train station at the same time. One travels east at 12 miles per hour. The other train travels west at 7 miles per hour. In how many hours will the two trains be 114 miles apart?

Accepted Answer

A) 6.5 hr 
B) 12 hr 
C) 3 hr 
D) 6 hr 
A) 6.5 hr 
B) 12 hr 
C) 3 hr 
D) 6 hr

Question 12

Solve the equation.
-$0.10 ( 70 ) + 0.70 x = 0.40 ( 70 + x )$

Accepted Answer

A)  $\{ 80 \}$ 
B)  $\{ 35 \}$ 
C)  $\{ 60 \}$ 
D)  $\{ 70 \}$ 
A)  $\{ 80 \}$ 
B)  $\{ 35 \}$ 
C)  $\{ 60 \}$ 
D)  $\{ 70 \}$

Question 13

Solve the problem.
-An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long would it take the experienced auditor working alone?

Accepted Answer

A) 4 hr 
B) 6 hr 
C) 8 hr 
D) 12 hr 
A) 4 hr 
B) 6 hr 
C) 8 hr 
D) 12 hr

Question 14

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation.
-5x - 2 > 4x - 7

Accepted Answer

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

Question 15

Solve the problem.
-During the first five months of the year, Len earned commissions of $3810, $2330, $3380, $2310, and $3420. If Len must have average monthly earnings of at least $3130 in order to qualify for retirement benefits, what must he earn in the sixth month in order to qualify for benefits?

Accepted Answer

A) at least $3130 
B) at least $3050 
C) at least $3063 
D) at least $3530 
A) at least $3130 
B) at least $3050 
C) at least $3063 
D) at least $3530

Question 16

Solve the equation.
-$$| 5 x + 9 | = 3$$

Accepted Answer

A)  $\left\{ \frac { 6 } { 5 } , \frac { 12 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , - \frac { 12 } { 5 } \right\}$ 
D)  no real solution 
A)  $\left\{ \frac { 6 } { 5 } , \frac { 12 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 2 } { 3 } , - \frac { 4 } { 3 } \right\}$ 
C)  $\left\{ - \frac { 6 } { 5 } , - \frac { 12 } { 5 } \right\}$ 
D)  no real solution

Question 17

Solve the equation using the square root property.
-$$\mathrm { x } ^ { 2 } - 81 = 0$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  $\{ 9 , - 9 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 9 \}$ 
A)  $\{ - 9 \}$ 
B)  $\{ 9 , - 9 \}$ 
C)  $\{ 81 \}$ 
D)  $\{ 9 \}$

Question 18

Perform the desired operation. Write the answer in the form a + bi.
-$$( 2 - 3 i ) ^ { 2 }$$

Accepted Answer

A)  $- 5 - 12 \mathrm { i }$ 
B)  $4 - 12 \mathrm { i } + 9 \mathrm { i } ^ { 2 }$ 
C)  $13 - 12 \mathrm { i }$ 
D)  $- 5$ 
A)  $- 5 - 12 \mathrm { i }$ 
B)  $4 - 12 \mathrm { i } + 9 \mathrm { i } ^ { 2 }$ 
C)  $13 - 12 \mathrm { i }$ 
D)  $- 5$

Question 19

Solve the polynomial inequality. Express the solution in interval notation.
-$$x ^ { 2 } + 5 x + 6 > 0$$

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 2 , \infty )$ 
B)  $( - 3 , - 2 )$ 
C)  $( - 2 , \infty )$ 
D)  $( - \infty , - 3 )$ 
A)  $( - \infty , - 3 ) \cup ( - 2 , \infty )$ 
B)  $( - 3 , - 2 )$ 
C)  $( - 2 , \infty )$ 
D)  $( - \infty , - 3 )$

Question 20

Perform the desired operation. Write the answer in the form a + bi.
-$$4 ( 8 - 5 i )$$

Accepted Answer

A)  $32 i - 5 i$ 
B)  $8 - 20 \mathrm { i }$ 
C)  $32 - 20 \mathrm { i }$ 
D)  $32 + 20 \mathrm { i }$ 
A)  $32 i - 5 i$ 
B)  $8 - 20 \mathrm { i }$ 
C)  $32 - 20 \mathrm { i }$ 
D)  $32 + 20 \mathrm { i }$

Solve the equation by factoring. - $x ^ { 2 } + 5 = 6 x$

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - $x ^ { 2 } + 10 x + 25 = 0$

Solve the problem. -A bank loaned out $69,000, part of it at the rate of 15% per year and the rest at a rate of 8% per year. If the interest received was $7480, how much was loaned at 15%?

Write the sentence as an equation. Let the variable x represent the number. -The product of 4 and a number increased by 3 is 20.

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. --4(6x + 1)< -28x + 12

Solve the radical equation. - $\sqrt { \mathrm { x } + 1 } = 8$

Solve the problem. -Claire has received scores of 85, 88, 87, and 75 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 83?

Solve the polynomial inequality. Express the solution in interval notation. - $2 x ^ { 2 } - 5 x \geq 7$

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. --4x - 5 > -5x - 11

Solve the problem. -Two trains leave a train station at the same time. One travels east at 12 miles per hour. The other train travels west at 7 miles per hour. In how many hours will the two trains be 114 miles apart?

Solve the equation. - $0.10 ( 70 ) + 0.70 x = 0.40 ( 70 + x )$

Solve the problem. -An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long would it take the experienced auditor working alone?

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. -5x - 2 > 4x - 7

Solve the equation. - $| 5 x + 9 | = 3$

Solve the equation using the square root property. - $\mathrm { x } ^ { 2 } - 81 = 0$

Perform the desired operation. Write the answer in the form a + bi. - $( 2 - 3 i ) ^ { 2 }$

Solve the polynomial inequality. Express the solution in interval notation. - $x ^ { 2 } + 5 x + 6 > 0$

Perform the desired operation. Write the answer in the form a + bi. - $4 ( 8 - 5 i )$

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 by factoring. - x2+5=6xx ^ { 2 } + 5 = 6 xx2+5=6x

Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. - x2+10x+25=0x ^ { 2 } + 10 x + 25 = 0x2+10x+25=0

Solve the linear inequality. Graph the solution set on a number line, and express the solution using interval notation. - 13x≥5+118x\frac { 1 } { 3 } x \geq 5 + \frac { 1 } { 18 } x31​x≥5+181​x