Question 1

Write the equation for line that passes through the given point and has the slope indicated. ​   with slope   ​

Accepted Answer

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

Question 2

The number (in millions) of U.S. cellular telephone subscribers can be described by   , where x is the number of years past 1990. For years beyond 2010, does this graph increase or decrease? (Look at this graph in a window that includes these years.) ​

Accepted Answer

A) increases 
B) decreases 
A) increases 
B) decreases

Question 3

The percent p of high school seniors who smoke cigarettes can be described by   , where t is the number of years past 1975. Choose the sentence that correctly interprets the meaning of the slope as a rate of change. ​

Accepted Answer

A) The slope represents the annual 33.58% increase of high school seniors who smoke. 
B) The slope represents the annual 6% decrease of high school seniors who smoke. 
C) The slope represents the annual 0.06% decrease of high school seniors who smoke. 
D) The slope represents the annual 0.06% increase of high school seniors who smoke. 
E) The slope represents the annual 33.58% decrease of high school seniors who smoke. 
A) The slope represents the annual 33.58% increase of high school seniors who smoke. 
B) The slope represents the annual 6% decrease of high school seniors who smoke. 
C) The slope represents the annual 0.06% decrease of high school seniors who smoke. 
D) The slope represents the annual 0.06% increase of high school seniors who smoke. 
E) The slope represents the annual 33.58% decrease of high school seniors who smoke.

Question 4

Solve the system by elimination, or by any convenient method. ​   ​

Accepted Answer

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

Question 5

A shipping crate has a square base with sides of length x feet, and it is half as tall as it is wide. If the material for the bottom and sides of the box costs $2.75 per square foot and the material for the top costs $1.00 per square foot, express the total cost (in dollars) of material for the box as a function of x. ​

Accepted Answer

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

Question 6

Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she will also change the lowest test score to match the final exam score if the final exam score is higher. If a student's four test scores are 82, 75, 55, and 92, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course? ​

Accepted Answer

A) 76 
B) 96 
C) 87 
D) 83 
E) 79 
A) 76 
B) 96 
C) 87 
D) 83 
E) 79

Question 7

If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by the function   , where x is the length of each side of the cross section (in inches). What restrictions must be placed on x (the domain) so that the volume makes physical sense? ​

Accepted Answer

A) 0 < x < 44 
B) -44 < x < 0 
C) 0 < x < 22 
D) 0 < x < 2 
E) -2 < x < 2 
A) 0 < x < 44 
B) -44 < x < 0 
C) 0 < x < 22 
D) 0 < x < 2 
E) -2 < x < 2

Question 8

Suppose a radio manufacturer has the total cost function   and the total revenue function   , where x represents the number of radios produced and sold. Write down the profit function   and then use this function to determine how many radios must be sold to avoid losing money. Round your answer to the nearest whole number. ​

Accepted Answer

A) 700 
B) 38 
C) 40 
D) 165 
E) 1,935 
A) 700 
B) 38 
C) 40 
D) 165 
E) 1,935

Question 9

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​     ​

Accepted Answer

A) parallel lines 
B) perpendicular lines 
C) neither 
A) parallel lines 
B) perpendicular lines 
C) neither

Question 10

A company charting its profits notices that the relationship between the number of units sold x and the profit   is linear. If 250 units sold results in $2,200 profit and 300 units sold results in $5,500 profit. Use these two points on the graph of   to find the marginal profit. ​

Accepted Answer

A) $8.80 
B) $66.00 
C) $18.33 
D) $7.33 
E) $22.00 
A) $8.80 
B) $66.00 
C) $18.33 
D) $7.33 
E) $22.00

Question 11

A woman has $445,000 invested in two rental properties. One yields an annual return of 10% of her investment, and the other returns 12% per year on her investment. Her total annual return from the two investments is $47,000. Let x represent the amount of the 10% investment and y represent the amount of the 12% investment. Find how much is invested in each property by solving the equations for the total amount invested and the return from each property. ​

Accepted Answer

A) $111,250 at 10% and $360,000 at 12% 
B) $320,000 at 10% and $125,000 at 12% 
C) $110,000 at 10% and $85,000 at 12%​ 
D) $360,000 at 10% and $125,000 at 12% 
E) $85,000 at 10% and $110,000 at 12% 
A) $111,250 at 10% and $360,000 at 12% 
B) $320,000 at 10% and $125,000 at 12% 
C) $110,000 at 10% and $85,000 at 12%​ 
D) $360,000 at 10% and $125,000 at 12% 
E) $85,000 at 10% and $110,000 at 12%

Question 12

Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 1,000 when the price is $1.00 each but that the demand is 2,000 when the price is $0.90 each. Assume the demand function is linear. Choose the correct equation for demand where p denotes price and q denotes quantity. ​

Accepted Answer

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

Question 13

For   , find   . ​

Accepted Answer

A) 1 
B) ​   
C)    
D) ​   
E) x 
A) 1 
B) ​   
C)    
D) ​   
E) x

Question 14

If   and   , find   and simplify. ​

Accepted Answer

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

Question 15

Complete the problem by using your calculator.​ ​
If   , find   and   ​

Accepted Answer

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

Question 16

The height above ground, S (in feet), of a ball thrown vertically into the air is given by   , where t is the time in seconds since the ball was thrown. Graph this equation with a graphing utility and the range   . Estimate the time at which the ball is at its highest point. Round your answer to two decimal places. ​

Accepted Answer

A) 9.25 
B) 0.22 
C) 0.05 
D) 18.50 
E) 4.63 
A) 9.25 
B) 0.22 
C) 0.05 
D) 18.50 
E) 4.63

Question 17

Use the x-intercept method to find the solution of the equation below where   . Round your answer to five decimal places. ​   ​

Accepted Answer

A) x = 0.74431 
B) x = -2.91098 
C) x = 3.99431 
D) x = -2.07986 
E) x = 0.08681 
A) x = 0.74431 
B) x = -2.91098 
C) x = 3.99431 
D) x = -2.07986 
E) x = 0.08681

Question 18

Solve the system of equations by substitution. ​   ​

Accepted Answer

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

Question 19

A manufacturer of DVD players has monthly fixed costs of $9,800 and variable costs of $65 unit for one particular model. The company sells this model to dealers for $100 each. Find the manufacturer's profit function   where x denotes the number of DVD players produced and sold. ​

Accepted Answer

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

Question 20

The percent p of high school seniors who smoke cigarettes can be modeled by the equation   , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year. ​

Accepted Answer

A) 2981 
B) 2035 
C) 2005 
D) 3763 
E) 2034 
A) 2981 
B) 2035 
C) 2005 
D) 3763 
E) 2034

Write the equation for line that passes through the given point and has the slope indicated. with slope

The number (in millions) of U.S. cellular telephone subscribers can be described by , where x is the number of years past 1990. For years beyond 2010, does this graph increase or decrease? (Look at this graph in a window that includes these years.)

The percent p of high school seniors who smoke cigarettes can be described by , where t is the number of years past 1975. Choose the sentence that correctly interprets the meaning of the slope as a rate of change.

Solve the system by elimination, or by any convenient method.

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these.

A company charting its profits notices that the relationship between the number of units sold x and the profit is linear. If 250 units sold results in $2,200 profit and 300 units sold results in $5,500 profit. Use these two points on the graph of to find the marginal profit.

For , find .

If and , find and simplify.

Complete the problem by using your calculator. If , find and

Use the x-intercept method to find the solution of the equation below where . Round your answer to five decimal places.

Solve the system of equations by substitution.

A manufacturer of DVD players has monthly fixed costs of $9,800 and variable costs of $65 unit for one particular model. The company sells this model to dealers for $100 each. Find the manufacturer's profit function where x denotes the number of DVD players produced and sold.

The percent p of high school seniors who smoke cigarettes can be modeled by the equation , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year.

Algebraic Concepts

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 2: Linear Equations and Functions

Write the equation for line that passes through the given point and has the slope indicated. ​ with slope ​

The number (in millions) of U.S. cellular telephone subscribers can be described by , where x is the number of years past 1990. For years beyond 2010, does this graph increase or decrease? (Look at this graph in a window that includes these years.) ​

The percent p of high school seniors who smoke cigarettes can be described by , where t is the number of years past 1975. Choose the sentence that correctly interprets the meaning of the slope as a rate of change. ​

Solve the system by elimination, or by any convenient method. ​ ​

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. ​ ​

A company charting its profits notices that the relationship between the number of units sold x and the profit is linear. If 250 units sold results in $2,200 profit and 300 units sold results in $5,500 profit. Use these two points on the graph of to find the marginal profit. ​

For , find . ​

If and , find and simplify. ​

Complete the problem by using your calculator.​ ​ If , find and ​

Use the x-intercept method to find the solution of the equation below where . Round your answer to five decimal places. ​ ​

Solve the system of equations by substitution. ​ ​

A manufacturer of DVD players has monthly fixed costs of $9,800 and variable costs of $65 unit for one particular model. The company sells this model to dealers for $100 each. Find the manufacturer's profit function where x denotes the number of DVD players produced and sold. ​

The percent p of high school seniors who smoke cigarettes can be modeled by the equation , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year. ​

Algebraic Concepts

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Write the equation for line that passes through the given point and has the slope indicated. with slope

The number (in millions) of U.S. cellular telephone subscribers can be described by , where x is the number of years past 1990. For years beyond 2010, does this graph increase or decrease? (Look at this graph in a window that includes these years.)

The percent p of high school seniors who smoke cigarettes can be described by , where t is the number of years past 1975. Choose the sentence that correctly interprets the meaning of the slope as a rate of change.

Solve the system by elimination, or by any convenient method.

Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these.

A company charting its profits notices that the relationship between the number of units sold x and the profit is linear. If 250 units sold results in $2,200 profit and 300 units sold results in $5,500 profit. Use these two points on the graph of to find the marginal profit.

For , find .

If and , find and simplify.

Complete the problem by using your calculator. If , find and

Use the x-intercept method to find the solution of the equation below where . Round your answer to five decimal places.

Solve the system of equations by substitution.

A manufacturer of DVD players has monthly fixed costs of $9,800 and variable costs of $65 unit for one particular model. The company sells this model to dealers for $100 each. Find the manufacturer's profit function where x denotes the number of DVD players produced and sold.

The percent p of high school seniors who smoke cigarettes can be modeled by the equation , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year.