Question 1

Solve the following rational equation.

Accepted Answer

A)    
B)    
C) 4 
D) 17 
E)    
A)    
B)    
C) 4 
D) 17 
E)

Question 2

Solve the following equation.

Accepted Answer

A) 10 
B)    
C)    
D)    
E)    
A) 10 
B)    
C)    
D)    
E)

Question 3

Use the power principle to solve the following radical equation.

Accepted Answer

A) 28 
B) 96 
C) 20 
D) 10 
E) 266 
A) 28 
B) 96 
C) 20 
D) 10 
E) 266

Question 4

Running at an average rate of 5 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 4 meters per second. The total time for the sprint and the jog back was 2 minutes 15 seconds. Find the length of the track.

Accepted Answer

A) 310 meters 
B) 315 meters 
C) 300 meters 
D) 290 meters 
E) 320 meters 
A) 310 meters 
B) 315 meters 
C) 300 meters 
D) 290 meters 
E) 320 meters

Question 5

Solve the equation below.

Accepted Answer

A) 8 
B) -1 
C) -6 
D) -10 
E) 6 
A) 8 
B) -1 
C) -6 
D) -10 
E) 6

Question 6

Write an equation that represents the relationship between the given variables below. Use k as the variation constant. d varies jointly as r as well as t

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

The Gunning-Fog Index is often used to estimate the reading grade level required by a person if he or she is to fully understand the written material being assessed. The formula is given by   where A is the average number of words per sentence and P is the percentage of words that have three or more syllables. The Gunning-Fog Index is defined as the minimum grade level required by a person if he or she is to easily understand the text on the first reading. In a large sample of sentences from a given novel, the average number of words per sentence is 12.7, and the percentage of words with three or more syllables is 18.2. Use the Gunning-Fog Index formula to estimate the reading grade level required to easily understand this novel. Round your answer to the nearest tenth.

Accepted Answer

A) 15.7 reading grade level 
B) 14.6 reading grade level 
C) 12.4 reading grade level 
D) 16.8 reading grade level 
E) 13.5 reading grade level 
A) 15.7 reading grade level 
B) 14.6 reading grade level 
C) 12.4 reading grade level 
D) 16.8 reading grade level 
E) 13.5 reading grade level

Question 8

Use interval notation to express the solution set of the inequality below.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

A mason can lay the bricks in a sidewalk in 14 hours. The mason's apprentice requires 20 hours to do the same job. After working together for 3 hours, the mason leaves for another job and the apprentice continues working. How long will it take the apprentice to complete the job?

Accepted Answer

A)    hour 
B)    hours 
C)    hours 
D)    hours 
E)    hours 
A)    hour 
B)    hours 
C)    hours 
D)    hours 
E)    hours

Question 10

The speed of a bicycle gear, in revolutions per minute, is inversely proportional to the number of teeth on the gear. If a gear with 50 teeth has a speed of 24 revolutions per minute, what will be the speed of a gear with 66 teeth? Round your answer to the nearest revolution per minute.

Accepted Answer

A) 19 revolutions per minute 
B) 18 revolutions per minute 
C) 23 revolutions per minute 
D) 22 revolutions per minute 
E) 17 revolutions per minute 
A) 19 revolutions per minute 
B) 18 revolutions per minute 
C) 23 revolutions per minute 
D) 22 revolutions per minute 
E) 17 revolutions per minute

Question 11

Use the power principle to solve the following radical equation.

Accepted Answer

A) 16 
B) -2 
C) 100 
D) -22 
E) 10 
A) 16 
B) -2 
C) 100 
D) -22 
E) 10

Question 12

Solve the absolute value equation below for x .

Accepted Answer

A)    and   
B)    
C)    and   
D)    and   
E)    and   
A)    and   
B)    
C)    and   
D)    and   
E)    and

Question 13

A company has determined that the profit P , in dollars, it can expect from the manufacture and sale of x tennis racquets is given by   . How many racquets should the company manufacture and sell to earn a profit of $425,000?

Accepted Answer

A) 4600 or 8400 racquets 
B) 4600 or 5000 racquets 
C) 5000 or 8400 racquets 
D) 5000 or 5900 racquets 
E) 4600 or 5900 racquets 
A) 4600 or 8400 racquets 
B) 4600 or 5000 racquets 
C) 5000 or 8400 racquets 
D) 5000 or 5900 racquets 
E) 4600 or 5900 racquets

Question 14

Jon went to his local electronics store and purchased an HDTV whose screen measured 64 inches diagonally, and whose aspect ratio was 16 to 9. Find the width and height of the screen. Round to the nearest tenth.

Accepted Answer

A) width: 57.9 in; height: 34.0 in 
B) width: 54.5 in; height: 32.9 in 
C) width: 55.8 in; height: 31.4 in 
D) width: 55.0 in; height: 30.2 in 
E) width: 54.0 in; height: 32.8 in 
A) width: 57.9 in; height: 34.0 in 
B) width: 54.5 in; height: 32.9 in 
C) width: 55.8 in; height: 31.4 in 
D) width: 55.0 in; height: 30.2 in 
E) width: 54.0 in; height: 32.8 in

Question 15

A model rocket is launched upward with an initial velocity of 170 feet per second. The height, in feet, of the rocket t seconds after the launch is given by   . How many seconds after the launch will the rocket be 450 feet above the ground? Round to the nearest tenth of a second.

Accepted Answer

A) 5.0 seconds and 5.6 seconds 
B) 5.0 seconds and 11.3 seconds 
C) 5.1 seconds and 11.3 seconds 
D) 5.1 seconds and 5.6 seconds 
E) 5.0 seconds and 5.1 seconds 
A) 5.0 seconds and 5.6 seconds 
B) 5.0 seconds and 11.3 seconds 
C) 5.1 seconds and 11.3 seconds 
D) 5.1 seconds and 5.6 seconds 
E) 5.0 seconds and 5.1 seconds

Question 16

Solve the compound inequality below. Write the solution set using set-builder notation.   or

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Use the critical value method to solve each rational inequality. Write each solution set in interval notation.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

The frequency of vibration of a guitar string under constant tension varies inversely as the length of the string. A guitar string with a length of 20 inches has a frequency of 270 vibrations per second. Find the frequency of a guitar string with a length of 16 inches. Assume the tension is the same for both strings. Round answer to nearest whole vibration.

Accepted Answer

A) 360 vibrations/s 
B) 277 vibrations/s 
C) 338 vibrations/s 
D) 216 vibrations/s 
E) 349 vibrations/s 
A) 360 vibrations/s 
B) 277 vibrations/s 
C) 338 vibrations/s 
D) 216 vibrations/s 
E) 349 vibrations/s

Question 19

The length of a rectangle is 12 feet less than 4 times the width of a rectangle. If the perimeter of the rectangle is 466 feet, find the width and the length.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?

Accepted Answer

A)    hours 
B)    hours 
C)    hour 
D)    hour 
E)    hours 
A)    hours 
B)    hours 
C)    hour 
D)    hour 
E)    hours

Solve the following rational equation.

Solve the following equation.

Use the power principle to solve the following radical equation.

Running at an average rate of 5 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 4 meters per second. The total time for the sprint and the jog back was 2 minutes 15 seconds. Find the length of the track.

Solve the equation below.

Write an equation that represents the relationship between the given variables below. Use k as the variation constant. d varies jointly as r as well as t

Use interval notation to express the solution set of the inequality below.

A mason can lay the bricks in a sidewalk in 14 hours. The mason's apprentice requires 20 hours to do the same job. After working together for 3 hours, the mason leaves for another job and the apprentice continues working. How long will it take the apprentice to complete the job?

The speed of a bicycle gear, in revolutions per minute, is inversely proportional to the number of teeth on the gear. If a gear with 50 teeth has a speed of 24 revolutions per minute, what will be the speed of a gear with 66 teeth? Round your answer to the nearest revolution per minute.

Use the power principle to solve the following radical equation.

Solve the absolute value equation below for x .

A company has determined that the profit P , in dollars, it can expect from the manufacture and sale of x tennis racquets is given by . How many racquets should the company manufacture and sell to earn a profit of $425,000?

Jon went to his local electronics store and purchased an HDTV whose screen measured 64 inches diagonally, and whose aspect ratio was 16 to 9. Find the width and height of the screen. Round to the nearest tenth.

A model rocket is launched upward with an initial velocity of 170 feet per second. The height, in feet, of the rocket t seconds after the launch is given by . How many seconds after the launch will the rocket be 450 feet above the ground? Round to the nearest tenth of a second.

Solve the compound inequality below. Write the solution set using set-builder notation. or

Use the critical value method to solve each rational inequality. Write each solution set in interval notation.

The length of a rectangle is 12 feet less than 4 times the width of a rectangle. If the perimeter of the rectangle is 466 feet, find the width and the length.

A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters

Exam 1: Equations and Inequalities

Solve the following rational equation.

Solve the following equation.

Use the power principle to solve the following radical equation.

Running at an average rate of 5 meters per second, a sprinter ran to the end of a track. The sprinter then jogged back to the starting point at an average rate of 4 meters per second. The total time for the sprint and the jog back was 2 minutes 15 seconds. Find the length of the track.

Solve the equation below.

Write an equation that represents the relationship between the given variables below. Use k as the variation constant. d varies jointly as r as well as t

Use interval notation to express the solution set of the inequality below.

A mason can lay the bricks in a sidewalk in 14 hours. The mason's apprentice requires 20 hours to do the same job. After working together for 3 hours, the mason leaves for another job and the apprentice continues working. How long will it take the apprentice to complete the job?

The speed of a bicycle gear, in revolutions per minute, is inversely proportional to the number of teeth on the gear. If a gear with 50 teeth has a speed of 24 revolutions per minute, what will be the speed of a gear with 66 teeth? Round your answer to the nearest revolution per minute.

Use the power principle to solve the following radical equation.

Solve the absolute value equation below for x .

A company has determined that the profit P , in dollars, it can expect from the manufacture and sale of x tennis racquets is given by . How many racquets should the company manufacture and sell to earn a profit of $425,000?

Jon went to his local electronics store and purchased an HDTV whose screen measured 64 inches diagonally, and whose aspect ratio was 16 to 9. Find the width and height of the screen. Round to the nearest tenth.

A model rocket is launched upward with an initial velocity of 170 feet per second. The height, in feet, of the rocket t seconds after the launch is given by . How many seconds after the launch will the rocket be 450 feet above the ground? Round to the nearest tenth of a second.

Solve the compound inequality below. Write the solution set using set-builder notation. or

Use the critical value method to solve each rational inequality. Write each solution set in interval notation.

The length of a rectangle is 12 feet less than 4 times the width of a rectangle. If the perimeter of the rectangle is 466 feet, find the width and the length.

A worker can build a fence in 8 hours. With the help of an assistant, the fence can be built in 5 hours. How long should it take the assistant, working alone, to build the fence?

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Topics in Analytic Geometry

Systems of Equations and Inequalities

Matrices

Sequences, Series, and Probability

Preliminary Concepts

Filters