Question 1

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

Accepted Answer

A) ( -6, 4) 
B) ( 3, 6) 
C) ( 0, -6) 
D) ( -6, 3) 
E) There is no solution to the equations. 
A) ( -6, 4) 
B) ( 3, 6) 
C) ( 0, -6) 
D) ( -6, 3) 
E) There is no solution to the equations.

Question 2

The figure below is the graph of both the demand function D and the supply function S for the same product, where P is the price per unit and Q is the number of units produced. Will there be a market surplus or shortage when the price P is $250? ​   ​

Accepted Answer

A) There will be a market shortage. 
B) There will be a market surplus. 
A) There will be a market shortage. 
B) There will be a market surplus.

Question 3

Suppose a mining company will supply 80,000 tons of ore per month if the price is $25 per ton but will supply only 60,000 tons per month if the price is $20 per ton. Assume the demand function is linear. Choose the correct equation for demand in the form p for price in terms of q for quantity. Round your coefficients to five decimal places. ​

Accepted Answer

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

Question 4

For the given graph, determine whether the line has a slope that is positive, negative, zero, or undefined. ​   ​

Accepted Answer

A) zero 
B) positive 
C) negative 
D) undefined 
A) zero 
B) positive 
C) negative 
D) undefined

Question 5

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 6

When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7%, and the current debt is $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan t in years. If we represent this function by   , then the following table defines the function. ​   ​
Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of   .
​

Accepted Answer

A) From the table,  
The value of  
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
B) From the table,  
The value of  
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%. 
C) From the table,  
The value of  
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
D) From the table,  
The value of  
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
E) From the table,  
The value of  
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
A) From the table,  
The value of  
Is the yearly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
B) From the table,  
The value of  
Is the monthly payment to repay half of a $100,000 loan in 10 years when the interest rate is 7%. 
C) From the table,  
The value of  
Is the weekly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
D) From the table,  
The value of  
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%. 
E) From the table,  
The value of  
Is the monthly payment to repay a $100,000 loan in 10 years when the interest rate is 7%.

Question 7

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

Accepted Answer

A) (2,-4) 
B) (4,2) 
C) (11,2) 
D) (4,-17) 
E) (8,2) 
A) (2,-4) 
B) (4,2) 
C) (11,2) 
D) (4,-17) 
E) (8,2)

Question 8

Solve the equation. ​   ​

Accepted Answer

A) ​-2 
B) 36 
C) -12 
D) 12 
E) -6 
A) ​-2 
B) 36 
C) -12 
D) 12 
E) -6

Question 9

Find the slope of the line passing through the given pair of points. ​   and   ​

Accepted Answer

A) -10 
B) 7 
C) 2 
D) -3 
E) The slope is undefined. 
A) -10 
B) 7 
C) 2 
D) -3 
E) The slope is undefined.

Question 10

Find the slope of the line passing through the given pair of points. ​   and   ​

Accepted Answer

A)    
B)    
C)    
D) 0 
E) The slope is undefined. 
A)    
B)    
C)    
D) 0 
E) The slope is undefined.

Question 11

Choose the equation of the line with the given slope and y-intercept. ​
Slope: 5 y-intercept: 3
​

Accepted Answer

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

Question 12

Graph the equation with a standard window   and   on a graphing utility. Does the graph appear to be a linear function? ​   ​

Accepted Answer

A) yes 
B) no 
A) yes 
B) no

Question 13

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by   . Find the domain of this function. Recall that p represents the percent pollution that is removed. ​

Accepted Answer

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

Question 14

​Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation? ​     ​
​​   ​

Accepted Answer

A) ​Yes 
B) ​No 
A) ​Yes 
B) ​No

Question 15

Find the slope m and y-intercept b of the line whose equation is given below. ​
Y = 5
​

Accepted Answer

A) m = 5, b = 0 
B) m = 0, b = 0 
C) m = 5, b = -5 
D) m = 0, b = 5 
E) Both m and b are undefined. 
A) m = 5, b = 0 
B) m = 0, b = 0 
C) m = 5, b = -5 
D) m = 0, b = 5 
E) Both m and b are undefined.

Question 16

Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget? ​

Accepted Answer

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

Question 17

The graph of   is shown in the figure below. ​   ​
If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
​

Accepted Answer

A) ​   
B)    
C)    
D)    
E) There is no relation. 
A) ​   
B)    
C)    
D)    
E) There is no relation.

Question 18

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by   and   , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal? ​

Accepted Answer

A) 1982 
B) 1978 
C) 1983 
D) 1984 
E) 1981 
A) 1982 
B) 1978 
C) 1983 
D) 1984 
E) 1981

Question 19

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts? ​   ​

Accepted Answer

A) x-min = -100 x-max = 100 y-min = -10,000 y-max = 10,000 
B) x-min = -100 x-max = 100 y-min = -10,000 y-max = 30,000 
C) x-min = -100 x-max = 300 y-min = -10,000 y-max = 10,000 
D) x-min = -100 x-max = 300 y-min = -10,000 y-max = 30,000 
E) ​x-min = 100 x-max = 100 y-min = 10,000 y-max = 10,000 
A) x-min = -100 x-max = 100 y-min = -10,000 y-max = 10,000 
B) x-min = -100 x-max = 100 y-min = -10,000 y-max = 30,000 
C) x-min = -100 x-max = 300 y-min = -10,000 y-max = 10,000 
D) x-min = -100 x-max = 300 y-min = -10,000 y-max = 30,000 
E) ​x-min = 100 x-max = 100 y-min = 10,000 y-max = 10,000

Question 20

According to the U.S. Bureau of the Census, the relation between the average annual earnings of males and females with various levels of educational attainment can be modeled by the function F = 0.521M + 6.368 , where M and F represent the average annual earnings (in thousands of dollars) of males and females, respectively. Choose the correct interpretation of the slope.​ ​

Accepted Answer

A) For each $1 increase in the males' earnings, the females' earning increases by $0.521. 
B) For each $1000 increase in the males' earnings, the females' earning increases by $52.1. 
C) For each $1000 increase in the males' earnings, the females' earning decreases by $52.1. 
D) For each $1 increase in the males' earnings, the females' earning decreases by $0.521. 
E) For each $100 increase in the males' earnings, the females' earning increases by $5.21. 
A) For each $1 increase in the males' earnings, the females' earning increases by $0.521. 
B) For each $1000 increase in the males' earnings, the females' earning increases by $52.1. 
C) For each $1000 increase in the males' earnings, the females' earning decreases by $52.1. 
D) For each $1 increase in the males' earnings, the females' earning decreases by $0.521. 
E) For each $100 increase in the males' earnings, the females' earning increases by $5.21.

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

The figure below is the graph of both the demand function D and the supply function S for the same product, where P is the price per unit and Q is the number of units produced. Will there be a market surplus or shortage when the price P is $250?

For the given graph, determine whether the line has a slope that is positive, negative, zero, or undefined.

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

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

Solve the equation.

Find the slope of the line passing through the given pair of points. and

Find the slope of the line passing through the given pair of points. and

Choose the equation of the line with the given slope and y-intercept. Slope: 5 y-intercept: 3

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function?

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by . Find the domain of this function. Recall that p represents the percent pollution that is removed.

Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation?

Find the slope m and y-intercept b of the line whose equation is given below. Y = 5

Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget?

The graph of is shown in the figure below. If the point P (with coordinates (a, b)) is on the graph, how are a and b related?

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal?

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts?

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

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

The figure below is the graph of both the demand function D and the supply function S for the same product, where P is the price per unit and Q is the number of units produced. Will there be a market surplus or shortage when the price P is $250? ​ ​

For the given graph, determine whether the line has a slope that is positive, negative, zero, or undefined. ​ ​

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

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

Solve the equation. ​ ​

Find the slope of the line passing through the given pair of points. ​ and ​

Find the slope of the line passing through the given pair of points. ​ and ​

Choose the equation of the line with the given slope and y-intercept. ​ Slope: 5 y-intercept: 3 ​

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function? ​ ​

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by . Find the domain of this function. Recall that p represents the percent pollution that is removed. ​

​Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation? ​ ​ ​​ ​

Find the slope m and y-intercept b of the line whose equation is given below. ​ Y = 5 ​

Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget? ​

The graph of is shown in the figure below. ​ ​ If the point P (with coordinates (a, b)) is on the graph, how are a and b related? ​

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal? ​

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts? ​ ​

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

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

The figure below is the graph of both the demand function D and the supply function S for the same product, where P is the price per unit and Q is the number of units produced. Will there be a market surplus or shortage when the price P is $250?

For the given graph, determine whether the line has a slope that is positive, negative, zero, or undefined.

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

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

Solve the equation.

Find the slope of the line passing through the given pair of points. and

Find the slope of the line passing through the given pair of points. and

Choose the equation of the line with the given slope and y-intercept. Slope: 5 y-intercept: 3

Graph the equation with a standard window and on a graphing utility. Does the graph appear to be a linear function?

Suppose that the cost C (in dollars) of removing p percent of the particulate pollution from the smokestacks of an industrial plant is given by . Find the domain of this function. Recall that p represents the percent pollution that is removed.

Use a graphing utility with the specified range to graph the equation. Is the graph below the graph of the given equation?

Find the slope m and y-intercept b of the line whose equation is given below. Y = 5

Thrifty rents a compact car for $35 per day, and Budget rents a similar car for $20 per day plus an initial fee of $120. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget?

The graph of is shown in the figure below. If the point P (with coordinates (a, b)) is on the graph, how are a and b related?

In the United States between 1970 and 2002, the number (in millions) of black children B(x) and Hispanic children H(x) can be described by and , where x is the number of years after December 31st, 1970. In what year were the numbers of children equal?

Graph the equation with a graphing utility; use a window that includes the intercepts. Which range shows both the intercepts?