College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 6th edit

INSTRUCTOR’S TESTING MANUAL JAMES LAPP

COLLEGE ALGEBRA IN CONTEXT WITH APPLICATIONS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES

SIXTH EDITION

Ronald Harshbarger University of South Carolina

Lisa S. Yocco East Georgia State College

Table of Contents Chapter 1: Functions, Graphs, and Models; Linear Functions Test Form A ....................................................................................................................................1-1 Test Form B ....................................................................................................................................1-5 Test Form C ....................................................................................................................................1-9 Chapter 2: Linear Models, Equations, and Inequalities Test Form A ....................................................................................................................................2-1 Test Form B ....................................................................................................................................2-3 Test Form C ....................................................................................................................................2-5 Chapter 3: Quadratic, Piecewise-Defined, and Power Functions Test Form A ....................................................................................................................................3-1 Test Form B ....................................................................................................................................3-3 Test Form C ....................................................................................................................................3-5 Chapter 4: Additional Topics with Functions Test Form A ....................................................................................................................................4-1 Test Form B ....................................................................................................................................4-3 Test Form C ....................................................................................................................................4-5 Chapter 5: Exponential and Logarithmic Functions Test Form A ....................................................................................................................................5-1 Test Form B ....................................................................................................................................5-3 Test Form C ....................................................................................................................................5-5 Chapter 6: Higher-Degree Polynomial and Rational Functions Test Form A ....................................................................................................................................6-1 Test Form B ....................................................................................................................................6-3 Test Form C ....................................................................................................................................6-5 Chapter 7: Systems of Equations and Matrices Test Form A ....................................................................................................................................7-1 Test Form B ....................................................................................................................................7-3 Test Form C ....................................................................................................................................7-5 Chapter 8: Special Topics in Algebra Test Form A ....................................................................................................................................8-1 Test Form B ....................................................................................................................................8-3 Test Form C ....................................................................................................................................8-5

Chapter 1 Answers Answers: Test Form A ................................................................................................................. A1-1 Answers: Test Form B ................................................................................................................. A1-2 Answers: Test Form C ................................................................................................................. A1-3 Chapter 2 Answers Answers: Test Form A ................................................................................................................. A2-1 Answers: Test Form B ................................................................................................................. A2-2 Answers: Test Form C ................................................................................................................. A2-3

Chapter 3 Answers Answers: Test Form A ................................................................................................................. A3-1 Answers: Test Form B ................................................................................................................. A3-2 Answers: Test Form C ................................................................................................................. A3-3 Chapter 4 Answers Answers: Test Form A ................................................................................................................. A4-1 Answers: Test Form B ................................................................................................................. A4-2 Answers: Test Form C ................................................................................................................. A4-3 Chapter 5 Answers Answers: Test Form A ................................................................................................................. A5-1 Answers: Test Form B ................................................................................................................. A5-2 Answers: Test Form C ................................................................................................................. A5-3 Chapter 6 Answers Answers: Test Form A ................................................................................................................. A6-1 Answers: Test Form B ................................................................................................................. A6-3 Answers: Test Form C ................................................................................................................. A6-5 Chapter 7 Answers Answers: Test Form A ................................................................................................................. A7-1 Answers: Test Form B ................................................................................................................. A7-2 Answers: Test Form C ................................................................................................................. A7-3 Chapter 8 Answers Answers: Test Form A ................................................................................................................. A8-1 Answers: Test Form B ................................................................................................................. A8-2 Answers: Test Form C ................................................................................................................. A8-3

Chapter 1 Test: Form A 1-1 1. Determine which of the following relations indicates that y is NOT a function of x. a.

Relationship 1: The number of minutes, y billed to a cell phone on a given day, x, in September.

Relationship 2: The pet, y (name of pet), of a child, x (name of child), at one school.

Table 1

b.

2 1 4 3

x y

0 2

Table 2 1 3

2 4

x y

4 3 2 1

2 0

3 1

c.

d.

Equation 1: 2 y 2  5 x  11

Equation 2: 2 x 2  5 y  11

2. Determine the domain and range for each function. a.

x f  x

4

2

0

1

3

5

8

6

3

7

3

0

3

2

b.

c.

f  x  5x  7

.

4 2

1-2

Chapter 1 Test: Form A

3. The number of cars sold by a dealership is given by N  x   56 x  78 cars, x years after the dealership was founded in 2010. a.

How many cars were sold by the dealership in 2013?

b.

Find and interpret the y-intercept of the function.

c.

Find the rate of change in the number of cars sold by the dealership.

4. Find the slope and y-intercept for each linear equation. a.

y  3x  7

b.

3x  5 y  10

c.

y

2 x 5

5. Graph each function using graphing technology and a standard viewing window of  10,10 and  10,10.

Determine the x-intercept(s) and y-intercept of each function, if they exist. a.

y  5 x  7

b.

y

c.

y  x 4  x3  2 x 2

3 x2

6. Write the equation of a line through the point 1, 2 for each of the given conditions. a.

parallel to 3 x  2 y  6

b.

perpendicular to y 

c.

perpendicular to the x-axis

1 x5 4

7. For each of the given conditions, write the equation of a line.

2 and y-intercept of 6 5

a.

slope of 

b.

slope of 4 and passing through the point 2, 5

c.

passing through the two points  7, 2 and 3, 6

8. The table shows the number of downloads of an author's eBook from 2015 to 2019.

Year eBooks downloaded (hundreds)

2015 55

2016 67

2017 79

2018 91

2019 103

a.

Find the linear model where x is the number of years after 2015, and y is the number of eBooks downloaded (in hundreds).

b.

Use the model to predict the number of downloads in 2024.

.

Chapter 1 Test: Form A 1-3 9. The price of gas, p (in dollars), for a gallon of gas in a region of the US is given by the function p( x)  0.000002 x3  0.0004 x 2  0.03 x  2.69, where x is the number of days after May 1, 2015.

a.

Determine p(25) . (Round your answer to the nearest hundredth.)

b.

On what day is the price of gas approximately $3.09? (Use graphing technology to graph the function p( x) for 0  x  20 .)

10. The points on the figure below give the water level, in feet, of a reservoir for a range of days of a month.

Water Level

Water Level (feet)

800 700 600 500 400 300

1

2

3 4 5 Day of the Month

6

7

a.

What is the domain of the function represented by the graph

b.

What was the approximate level of the reservoir on day 5 of the month?

c.

On what day of the month was the level of the reservoir approximately 600 feet?

11. A company produces and sells a toy with revenue given by R  x   19.99 x dollars and cost given by C  x   12.75 x  590 dollars, where x is the number of toys produced and sold.

a.

What is the marginal revenue for this toy, and what does it mean?

b.

Find the profit function.

c.

What is the marginal profit for this toy, and what does it mean?

.

1-4

Chapter 1 Test: Form A

12. Write the equation of the line for each of the following graphs. a.

c.

b.

d.

.

Chapter 1 Test: Form B 1-5 1. Determine which of the following relations indicates that y is NOT a function of x. a.

Relationship 1: The number of miles, y, on the meter of a taxi for one fare during the day, x.

Relationship 2: The book, y (title of book), read by a child, x (name of child), in one family.

Table 1

b.

Table 2

x

4

6

8

6

4

x

5 3

0

3

5

y

5 3

0

3

5

y

4

8

6

4

6

c.

d.

Equation 1: x 2  3 y  7

Equation 2: y 2  3 x  7

2. Determine the domain and range for each function. a.

x f  x

3

1

0

2

5

7

9

4

2

6

8

0

6

3

b.

c.

f  x   3 x  4

.

1-6

Chapter 1 Test: Form B

3. The number of houses in a new subdivision from 2010 and 2016 is given by N  x   8 x  11 houses, x years after the subdivision was started in 2010. a.

How many houses were in the subdivision in 2014?

b.

Find and interpret the y-intercept of the function.

c.

Find the rate of change in the number in the subdivision.

4. Find the slope and y-intercept for each linear equation. a.

y  5x  3

b.

4 x  3 y  18

c.

y

7 x 5

5. Graph each function using graphing technology and a standard viewing window of  10,10 and  10,10.

Determine the x-intercept(s) and y-intercept of each function, if they exist. a.

y  3x  8

b.

y

c.

y  x 4  x3  20 x 2

2 x  10

6. Write the equation of a line through the point  3, 7  for each of the given conditions. a.

parallel to 3 x  2 y  5

b.

perpendicular to y 

c.

perpendicular to the y-axis

1 x3 2

7. For each of the given conditions, write the equation of a line.

4 and y-intercept of 7 3

a.

slope of 

b.

slope of 5 and passing through the point 3, 2

c.

passing through the two points  5, 6 and  1, 2

8. The table shows the number of downloads of an author's eBook from 2015 to 2019.

Year eBooks downloaded (hundreds)

2015 47

2016 56

2017 65

2018 74

2019 83

a.

Find the linear model where x is the number of years after 2015, and y is the number of eBooks downloaded (in hundreds).

b.

Use the model to predict the number of downloads in 2024.

.

Chapter 1 Test: Form B 1-7 9. The time, t (in minutes), it takes to get to class from your room each day is given by the function t ( x)  0.0373x3  0.308 x 2  0.395 x  7.95, where x is the number of days since the start of the semester.

a.

Determine t (9) . (Round your answer to the nearest hundredth.)

b.

Approximately how many days have passed, if it takes you 7.48 minutes to get to class from your room?

(Use graphing technology to graph the function t ( x ) for 0  x  10 .)

10. The points on the figure below give the water level, in feet, of a reservoir for a range of days of a month.

Water Level

Water Level (feet)

900 800 700 600 500 400

23

24

25 26 27 Day of the Month

28

29

a.

What is the domain of the function represented by the graph?

b.

What was the approximate level of the reservoir on day 25 of the month?

c.

On what day of the month was the level of the reservoir approximately 700 feet?

11. A company produces and sells a wireless speaker with revenue given by R  x   79.99 x dollars and cost given

by C  x   52.68 x  3584 dollars, where x is the number of wireless speakers produced and sold. a.

What is the marginal revenue for this wireless speaker, and what does it mean?

b.

Find the profit function.

c.

What is the marginal profit for this wireless speaker, and what does it mean?

.

1-8

Chapter 1 Test: Form B

12. Write the equation of the line for each of the following graphs. a.

c.

b.

d.

.

Chapter 1 Test: Form C 1-9 1. Determine which of the following relations indicates that y is NOT a function of x. a.

Relationship 1: The salary of a person, y (in dollars), based on the number of years employed, x (in years).

Relationship 2: The uncle, y (name of uncle), of a child, x (name of child), in a family where the father has 3 brothers.

Table 1

b.

x y

2 1 7 8

0 9

Table 2 1 8

2 7

x y

7 8 2 1

9 0

8 1

c.

d.

Equation 1: y  2 x  8

Equation 2: x  2 y  8

2. Determine the domain and range for each function. a.

x f  x

5 8

1 4

0 7

3 5

5 2

6 0

9 4

b.

c.

f  x  2x  1

.

7 2

1-10

Chapter 1 Test: Form C

3. The number of appliances sold by a retailer is given by N  x   72 x  125 appliances, x years after the retailer opened for business in 2010. a.

How many appliances were sold by the dealership in 2014?

b.

Find and interpret the y-intercept of the function.

c.

Find the rate of change in the number of appliances sold by the retailer.

4. Find the slope and y-intercept for each linear equation. a.

y  2x  6

b.

3x  5 y  20

c.

y

4 x 3

5. Graph each function with a graphing calculator using the standard viewing window of  10,10 and  10,10.

Determine the x-intercept(s) and y-intercept of each function, if they exist.

a.

y  2 x  3

b.

y

c.

y   x 4  3 x3  4 x 2

2 3x  4

6. Write the equation of a line through the point  3, 2 for each of the given conditions. a.

parallel to 3 x  2 y  7

b.

perpendicular to y 

c.

perpendicular to the x-axis

1 x6 5

7. For each of the given conditions, write the equation of a line.

3 and y-intercept of 8 7

a.

slope of 

b.

slope of 6 and passing through the point 5,3

c.

passing through the two points  4,3 and  2, 1

8. The table shows the number of downloads of an author's eBook from 2015 to 2019.

Year eBooks downloaded (hundreds)

2015 29

2016 42

2017 55

2018 68

2019 81

a.

Find the linear model where x is the number of years after 2015, and y is the number of eBooks downloaded (in hundreds).

b.

Use the model to predict the number of downloads in 2024.

.

Chapter 1 Test: Form C 1-11 9. The price for a gallon of 2% milk, p (in dollars), for a six-year period is given by the function p( x)  0.0325 x3  0.1975 x 2  0.453 x  2.95, where x is the number of years since 2003.

a.

Determine p(2) . (Round your answer to the nearest hundredth.)

b.

In what year did a gallon of milk cost approximately $3.68? (Use graphing technology to graph the function p( x) for 0  x  5 .)

10. The points on the figure below give the water level, in feet, of a reservoir for a range of days of a month.

Water Level

Water Level (feet)

700 600 500 400 300 200

14

15

16 17 18 Day of the Month

19

20

a.

What is the domain of the function represented by the graph?

b.

What was the approximate level of the reservoir on day 16 of the month?

c.

On what day of the month was the level of the reservoir approximately 300 feet?

11. A company produces and sells a small drone with revenue given by R  x   119.99 x dollars and cost given by C  x   87.35 x  9731 dollars, where x is the number of small drones produced and sold.

a.

What is the marginal revenue for this wireless speaker, and what does it mean?

b.

Find the profit function.

c.

What is the marginal profit for this small drone, and what does it mean?

.

1-12

Chapter 1 Test: Form C

12. Write the equation of the line for each of the following graphs. a.

c.

b.

d.

.

Chapter 2 Test: Form A 2-1 1. Given the literal equation A  P (1  rt ), a.

solve the equation for P.

b.

solve the equation for t.

2. For the function f  x   8 

3 x, 4

a.

find the solution to f  x   0.

b.

find the x-intercept of f  x  .

c.

find the zero of the function f  x  .

3. Given the equation 3x  7  5( x  2)  x, a.

solve the equation algebraically.

b.

solve the equation graphically.

c.

use your graph from (b) and the intersection method to solve the linear inequality 3x  7  5( x  2)  x.

State the solution in interval notation.

4. A band wants to make shirts to sell at their concerts. The cost to make x shirts is given by C  x   6.5 x  140 dollars. The band plans to sell them for $10. Find the number of units that gives break-even for the shirts.

5. An office manager is choosing between two options for a new printing service. Plan A has a monthly fee of $40 and charges $0.08 per page printed. Plan B has a monthly fee of $32 and charges $0.10 per page printed. How many pages must the office print in a month for Plan A to be less expensive?

6. Denise is saving money to buy a new 3D printer that costs $1560 for her company. Denise models her savings by the equation y  65 x  585 dollars, where x is the number of consecutive months, and y is her total savings.

If Denise began saving in January 2020 and continues saving each month thereafter, in what month and year will she be able to buy her 3D printer?

7. The price of an electronics item is influenced by the number of years since 2015. Use the data in the table to answer the given questions.

Number of Years after 2015 0 Price (in dollars) 1199.95

3 1113.28

6 1026.61

9 939.94

11 882.16

a.

Can a linear function exactly model the points from the data? Explain.

b.

Find a linear model that fits the data; round to two decimal places.

c.

Should the data be interpreted as discrete or continuous?

d.

If you use the linear model to find the price after the year 2020, is this considered interpolation or extrapolation of the data?

.

2-2

Chapter 2 Test: Form A

8. The gasoline mileage of a certain automobile is influenced by its horsepower. Use the data in the table to answer the given questions.

Speed 49 Horsepower 65.2

52 56.3

55 46.7

58 48.9

61 39.7

64 38.2

67 36.4

a.

Find a linear model that fits the data; round to four decimal places.

b.

Graph the model found in (a) and the scatter plot of the data on the same axes. Discuss how well the model fits the data.

c.

Using the model, find the miles per gallon of the automobile when the horsepower is 60.

d.

Interpret, in words, what the slope of the model in part a. represents.

9. Solve each system of linear equations using (i) elimination and (ii) substitution. Label each. a.

 5 x  6 y  29  2 x  3 y  10

b.

 y  4 x  13  2 y  3 x  1

10. Use the algebraic method to solve the linear inequality 3(2 x  4)  7  4 x  5.

11. A vocational training center claims that the number of bricks a starting mason can correctly set in place during one workday is determined by the number of hours spent training beforehand. This relationship is given by the function y  12 x  30, where y is the number of bricks correctly set in place during one workday, and x is the number of hours spent training beforehand. Use a linear double inequality and algebraic methods to determine how many hours a starting mason must train beforehand to correctly set between 57 and 81 bricks, inclusive, correctly in place in a workday. Use interval notation to state the solution; round to the nearest hundredth.

12. Match the three systems (A, B, and C) to the correct graphical solution and type of system (I, II, and III). 2 x  3 y  6 A.  4 x  6 y  12

2 x  3 y  6 B.  4 x  6 y  12

2 x  3 y  6 C.  4 x  6 y  12

I

II

III

.

Chapter 2 Test: Form B 2-3 1. Given the literal equation A  a.

solve the equation for h.

b.

solve the equation for a.

2. For the function f  x   9 

( a  b) h , 2

5 x, 2

a.

find the solution to f  x   0.

b.

find the x-intercept of f  x  .

c.

find the zero of the function f  x  .

3. Given the equation 5 x  9  3( x  2)  x, a.

solve the equation algebraically.

b.

solve the equation graphically.

c.

use your graph from (b) and the intersection method to solve the linear inequality 5 x  9  3( x  2)  x.

State the solution in interval notation.

4. A band wants to make posters to sell at their concerts. The cost to make x posters is given by C  x   3.25 x  63 dollars. The band plans to sell them for $5. Find the number of units that gives break-even for the posters.

5. An office manager is choosing between two options for a new coffee service. Plan A has a weekly fee of $12 and charges $1.32 for each cup of coffee. Plan B has a weekly fee of $15 and charges $1.26 for each cup of coffee. How many cups of coffee must the office consume each week to make Plan B less expensive?

6. Jasmine is saving money to buy a new 3D printer that costs $1220 for her company. Jasmine models her savings by the equation y  95 x  365 dollars, where x is the number of consecutive months, and y is her total savings.

If Jasmine began saving in January 2020 and continues saving each month thereafter, in what month and year will she be able to buy her 3D printer?

7. The average price of a certain car built in 2016 is based on its age. Use the data in the table to answer the given questions.

Number of years after 2016 Average price (in dollars)

0 35,000

2 28,700

4 22,400

6 16,100

8 9800

a.

Can a linear function exactly model the data? Explain.

b.

Find a linear model that fits the data; round to two decimal places.

c.

Should the data be interpreted as discrete or continuous?

d.

Suppose the linear model is used to find the estimated car value for some input between 3 and 7. Is this considered interpolation or extrapolation of the data?

.

2-4

Chapter 2 Test: Form B

8. Average hourly wages are influenced by the number of grades completed in public school. Use the data in the table to answer the given questions.

Average Highest Grade of School 7.6 Completed Average Hourly Wage 1.531

8.1

8.4

8.8

9.1

1.927

2.458

2.802

3.146

a.

Find a linear model that fits the data; round to four decimal places.

b.

Graph the model found in part a. and the scatter plot of the data on the same axes. Discuss how well the model fits the data.

c.

Using the model, find the average hourly wage when the average highest grade of school completed is 9.5.

d.

Interpret, in words, what the slope of the model in part a. represents.

9. Solve each system of linear equations using (i) elimination and (ii) substitution. Label each. a.

 3x  8 y  18  5 x  4 y  22

b.

 y  2 x  5  6 y  7 x  10

10. Use the algebraic method to solve the linear inequality 2(4  2 x)  7  5 x  12.

11. A vocational training center claims that the number of bricks a starting mason can correctly set in place during one workday is determined by the number of hours spent training beforehand. This relationship is given by the function y  16 x  32, where y is the number of correctly bricks set in place during one workday, and x is the number of hours spent training beforehand. Use a linear double inequality and algebraic methods to determine how many hours a starting mason must train beforehand to correctly set between 72 and 116 bricks, inclusive, correctly in place in a workday. Use interval notation to state the solution; round to the nearest hundredth.

12. Match the three systems (A, B, and C) to the correct graphical solution and type of system (I, II, and III).  5 x  3 y  15 A.  15 x  9 y  45

 5 x  3 y  15 B.  15 x  9 y  45

 5 x  3 y  15 C.  15 x  9 y  45

I

II

III

.

Chapter 2 Test: Form C 2-5 1. Given the literal equation h( R  r 2 )  RH , a.

solve the equation for h.

b.

solve the equation for R.

2. For the function f  x   7 

3 x, 4

a.

find the solution to f  x   0.

b.

find the x-intercept of f  x  .

c.

find the zero of the function f  x  .

3. Given the equation 4 x  3  2( x  1)  x, a.

solve the equation algebraically.

b.

solve the equation graphically.

c.

use your graph from (b) and the intersection method to solve the linear inequality 4 x  3  2( x  1)  x.

State the solution in interval notation.

4. A band wants to make bandanas to sell at their concerts. The cost to make x bandanas is given by C  x   4.75 x  72 dollars. The band plans to sell them for $7. Find the number of units that gives break-even for the bandanas.

5. An office manager is choosing between two options for a new printing service. Plan A has a monthly fee of $31 and charges $0.09 per page. Plan B has a monthly fee of $38 and charges $0.07 per page. How many pages 4must the office print in a month for Plan B to be less expensive?

6. Kim is saving money to buy a new 3D printer that costs $1640 for her company. Kim models her savings by the equation y  85 x  280 dollars, where x is the number of consecutive months, and y is her total savings. If Kim began saving in January 2020 and continues saving each month thereafter, in what month and year will she be able to buy her 3D printer?

7. The price of a certain item made in 1920 is based on its age. Use the data in the table to answer the given questions.

Years since 1920 Price of item (in dollars)

25 35.00

40 57.50

55 80.00

70 102.50

85 125.00

95 140.00

a.

Can a linear function exactly model the data? Explain.

b.

Find a linear model that fits the data; round to two decimal places.

c.

Should the data be interpreted as discrete or continuous?

d.

Suppose the linear model is used to find the price of the item in 2020. Is this considered interpolation or extrapolation of the data?

.

2-6

Chapter 2 Test: Form C

8. The price of beef in cents per pound at a certain grocery store is influenced by the number of years since 1925.

Use the data in the table to answer the given questions.

Years since 1925 Price of Beef (cents/lb)

0 56

2 60

4 69

6 74

8 78

a.

Find a linear model that fits the data; round to two decimal places.

b.

Graph the model found in (a) and the scatter plot of the data on the same axes. Discuss how well the model fits the data.

c.

Using the model, find the price of beef in 1938.

d.

Interpret, in words, what the y-intercept of the model in (a) represents.

9. Solve each system of linear equations using (i) elimination and (ii) substitution. Label each a.

2 x  5 y  16   4 x  3 y  6

b.

 y  3x  7  3 y  4 x  47

10. Use the algebraic method to solve the linear inequality 4( x  5)  3  3x  11 .

11. A vocational training center claims that the number of bricks a starting mason can correctly set in place during one workday is determined by the number of hours spent training beforehand. This relationship is given by the function y  20 x  28, where y is the number of correctly bricks set in place during one workday, and x is the number of hours spent training beforehand. Use a linear double inequality and algebraic methods to determine how many hours a starting mason must train beforehand to correctly set between 103 and 133 bricks, inclusive, correctly in place in a workday. Use interval notation to state the solution; round to the nearest hundredth.

12. Match the three systems (A, B, and C) to the correct graphical solution and type of system (I, II, and III). 3 x  4 y  12 A.  6 x  8 y  24

3 x  4 y  12 B.  6 x  8 y  24

3 x  4 y  12 C.  6 x  8 y  24

I

II

III

.

Chapter 3 Test: Form A 3-1 1. For each quadratic function: (i) give the coordinates of the vertex; (ii) state whether the vertex is a maximum or minimum; (iii) state whether the parabola is concave up or down. a.

f  x   3  x  4  7 2

b.

f  x  x2  x  3

2. The revenue from making and selling x units of a product is given by f  x   3x 2  126 x  960 dollars. a.

What is the domain of this function?

b.

Over what interval of x is the profit decreasing?

c.

To maximize profit, how many units must be sold?

d.

What is the maximum possible profit?

e.

How many units should be produced and sold in order to make a profit of $120?

3. Using the following graph of a quadratic function: a.

write the equation of the quadratic function.

b.

what is the axis of symmetry of this function?

c.

what is the range of this function?

d.

on what interval of the domain is the function decreasing?

4. A science club is using a model trebuchet to launch basketballs off the roof of a building that is 38 meters high.

In one test, the basketball has an initial velocity of 22 m/s, and the height, in meters, of the basketball can be modeled by s t   4.9t 2  22t  38, where t is the number of seconds after the basketball is launched. (Round

answers to three decimal places.) a.

When does the basketball hit the ground?

b.

What is the maximum height of the basketball?

c.

When does the basketball reach its maximum height?

d.

What is the domain of this function?

5. If the graph of a quadratic function/parabola intersects the x-axis once, a.

is the discriminant of the function positive, negative, or zero?

b.

f ( x)  0 has how many real solutions?

6. Solve the following quadratic equations. a.

x2  7 x  5  0

b.

3x 2  11x  4

.

c.

5 x 2  20  0

3-2 Chapter 3 Test: Form A 7. For each of the given functions, find the interval(s) of the domain for which the function is increasing: a.

f ( x)  x 2  5

b.

f ( x)  2 x3  6

8. Solve x 2  5 x  3  3.

9. Find the equation of a quadratic function whose graph is a parabola passing through the points  1, 17  ,

0, 9 , and 2, 11 .  x  1, x  4 , 10. Given the piecewise function f ( x)   2 x  10, x  4

a.

sketch the graph of the piecewise function on the grid provided.

b.

find the value of f (4) and f (12).

c.

what is the range of this function?

200, 0  x  40  11. The cost, in dollars, to cater a breakfast meeting is given by C  x    , where x is the 200  10  x  40 , x  40 total number of meals served.

a.

Find C  40 .

b.

Find C 55 and express in words what this represents.

12. The table below shows the number of fruit flies with a specific genetic mutation.

Generation Number of flies with mutation

2

5

8

11

14

17

20

11

22

40

69

107

154

209

a.

Find a quadratic model for the data. Round to six decimal places.

b.

Find a power model for the data. Round to six decimal places.

c.

Which is the better model? Use that model to estimate the number of fruit flies with mutations in the 27th generation?

.

Chapter 3 Test: Form B 3-3 1. For each quadratic function: (i) give the coordinates of the vertex; (ii) state whether the vertex is a maximum or minimum; (iii) state whether the parabola is concave up or down. a.

f  x   2  x  5  9 2

b.

f  x    x 2  3x  5

2. The revenue from making and selling x units of a product is given by f  x   2 x 2  88 x  576 dollars. a.

What is the domain of this function?

b.

Over what interval of x is the profit decreasing?

c.

To maximize profit, how many units must be sold?

d.

What is the maximum possible profit?

e.

How many units should be produced and sold in order to make a profit of $294?

3. Using the following graph of a quadratic function: a.

write the equation of the quadratic function.

b.

what is the axis of symmetry of this function?

c.

what is the range of this function?

d.

on what interval of the domain is the function decreasing?

4. A science club is using a model trebuchet to launch basketballs off the roof of a building that is 42 meters high.

In one test, the basketball has an initial velocity of 15 m/s, and the height, in meters, of the basketball can be modeled by s t   4.9t 2  15t  42, where t is the number of seconds after the basketball is launched. (Round answers to three decimal places.) a.

When does the basketball hit the ground?

b.

What is the maximum height of the basketball?

c.

When does the basketball reach its maximum height?

d.

What is the domain of this function?

5. If the graph of a quadratic function/parabola intersects the x-axis twice, a.

is the discriminant of the function positive, negative, or zero?

b.

f ( x)  0 has how many real solutions?

6. Solve the following quadratic equations. a.

2 x 2  7 x  15

b.

x2  3x  1  0

.

c.

7 x 2  63  0

3-4 Chapter 3 Test: Form B 7. For each of the given functions, find the interval(s) of the domain for which the function is

increasing: a.

f ( x)   x 2  7

b.

f ( x) 

1 3 x

8. Solve x 2  7 x  5  5.

9. Find the equation of a quadratic function whose graph is a parabola passing through the points 2, 19 ,

0,3 , and 1,8 . 2 x  12, x  4 10. Given the piecewise function f ( x )   ,  x  5, x  4

a.

sketch the graph of the piecewise function on the grid provided.

b.

find the value of f (4) and f (7).

c.

what is the range of this function?

 150, 0  x  20 11. The cost, in dollars, to cater a lunch meeting is given by C  x    , where x is the total 150  9  x  20 , x  20 number of meals served.

a.

Find C 20 .

b.

Find C 30 and express in words what this represents.

12. The table below shows the number of fruit flies with a specific genetic mutation.

Generation Number of flies with mutation

3

6

9

12

15

18

21

11

27

47

76

110

152

200

a.

Find a quadratic model for the data. Round to six decimal places.

b.

Find a power model for the data. Round to six decimal places.

c.

Which is the better model? Use that model to estimate the number of fruit flies with mutations in the 36th generation.

.

Chapter 3 Test: Form C 3-5 1. For each quadratic function: (i) give the coordinates of the vertex; (ii) state whether the vertex is a maximum or minimum; (iii) state whether the parabola is concave up or down. a.

f  x   4  x  7   11 2

b.

f  x   x2  3x  2

2. The revenue from making and selling x units of a product is given by f  x   4 x 2  152 x  1300 dollars. a.

What is the domain of this function?

b.

Over what interval of x is the profit decreasing?

c.

To maximize profit, how many units must be sold?

d.

What is the maximum possible profit?

e.

How many units should be produced and sold in order to make a profit of $108?

3. Using the following graph of a quadratic function: a.

write the equation of the quadratic function.

b.

what is the axis of symmetry of this function?

c.

what is the range of this function?

d.

on what interval of the domain is the function decreasing?

4. A science club is using a model trebuchet to launch basketballs off the roof of a building that is 32 meters high.

In one test, the basketball has an initial velocity of 16 m/s, and the height, in meters, of the basketball can be modeled by s t   4.9t 2  16t  32, where t is the number of seconds after the basketball is launched. (Round answers to three decimal places.) a.

When does the basketball hit the ground?

b.

What is the maximum height of the basketball?

c.

When does the basketball reach its maximum height?

d.

What is the domain of this function?

5. If the graph of a quadratic function/parabola does not intersect the x-axis, a.

is the discriminant of the function positive, negative, or zero?

b.

f ( x)  0 has how many real solutions?

6. Solve the following quadratic equations. a.

2 x 2  3 x  20

b.

4 x 2  64  0

.

c.

x2  5x  3  0

3-6 Chapter 3 Test: Form C 7. For each of the given functions, find the interval(s) of the domain for which the function is increasing: a.

1

f ( x)  2 x 2  3

b.

g ( x)  x 3

8. Solve x 2  6 x  4  4.

9. Find the equation of a quadratic function whose graph is a parabola passing through the points  1, 3 ,

0, 7 , and 3, 11. 2 x  6, x  1 , 10. Given the piecewise function f ( x)    x  8, x  1

a.

sketch the graph of the piecewise function on the grid provided.

b.

find the value of f (1) and f (6).

c.

What is the range of this function?

300, 0  x  30  , where x is the total 11. The cost, in dollars, to cater a dinner meeting is given by C  x    300  12  x  30 , x  30 number of meals served.

a.

Find C 30 .

b.

Find C  45 and express in words what this represents.

12. The table below shows the number of fruit flies with a specific genetic mutation.

Generation Number of flies with mutation

4

6

8

10

12

14

16

18

30

43

61

82

105

133

a.

Find a quadratic model for the data. Round to six decimal places.

b.

Find a power model for the data. Round to six decimal places.

c.

Which is the better model? Use that model to estimate the number of fruit flies with mutations in the 36th generation.

.

Chapter 4 Test: Form A 4-1 1. Write the equation of the function g  x  , shown below, that is transformed from the given function f  x   x .

2. Given the function, g  x  

1 4  x  5, which is transformed from the base function, f  x   x , 3

a.

what is the horizontal shift of the function?

b.

what is the vertical shift of the function?

c.

what is the reflection of the function?

d.

what is the stretch or compression of the function?

3. Suppose that f  x  is an even function and 4 f 3  12. What is 6 f  3 ?

4. Given f  x    x  4 and g  x   3

a.

9 , find each of the following. x

 f  g 3

b.

 g  f  x 

5. Given f  x   x 2  3x  1 and g  x   5 x  4, find each of the following. a.

 f  g 2

c.

 fg 5

b.

 f  g 3

d.

f  g   2

6. A company is ordering custom mugs as thank you gifts for their customers. For each order, there is a one-time processing fee of $30 and an additional cost of $3.50 per mug. a.

Find the cost function for an order of x mugs.

b.

Find the average cost function for an order of x mugs.

c.

Find the average cost for an order of 200 mugs. (Round to the nearest cent.)

.

4-2

Chapter 4 Test: Form A

7. Sketch the graph of f 1  x  on the same axes below with the graph of f ( x).

8. Find the inverse of f  x   7 x  3.

9. Solve 5 x  2  8  3.

10. Solve

2 x  5  7.

3

11. Solve 2 x 4  58 x 2  200.

12. The height of a drone during a given flight is described by h t   8t 2  480t , t  0, where h t  is the height in feet, and t is the time in minutes. During what time interval(s) will the height of the drone exceed 5000 feet?

Round to two decimal places.

.

Chapter 4 Test: Form B 4-3 1. Write the equation of the function g  x  , shown below, that is transformed from the given function f  x   x .

2. Given the function, g  x   2 3  x  4, which is transformed from the base function, f  x   x , a.

what is the horizontal shift of the function?

b.

what is the vertical shift of the function?

c.

what is the reflection of the function?

d.

what is the stretch or compression of the function?

3. Suppose that f  x  is an odd function and 3 f  4  15. What is 7 f  4 ?

4. Given f  x    x  2 and g  x   3

a.

4 , find each of the following. x 1

 f  g 3

b.

 g  f  x 

5. Given f  x   x 2  3 x  4 and g  x   2 x  7, find each of the following. a.

 f  g 2

c.

 fg 3

b.

 f  g 2

d.

f  g   2

6. A company is ordering custom pens as thank you gifts for their customers. For each order, there is a one-time processing fee of $20 and an additional cost of $1.50 per pen. a.

Find the cost function for an order of x pens.

b.

Find the average cost function for an order of x pens.

c.

Find the average cost for an order of 300 pens. (Round to the nearest cent.)

.

4-4 Chapter 4 Test: Form B 7.

Sketch the graph of f 1  x  on the same axes below with the graph of f ( x).

8. Find the inverse of f  x    x  5 .

3

9. Solve 2 x  7  7  1.

10. Solve

2 x  4  10.

5

11. Solve 2 x 4  68 x 2  450.

12. The height of a drone during a given flight is described by h t   9t 2  522t , t  0, where h t  is the height in feet, and t is the time in minutes. During what time interval(s) will the height of the drone exceed 5000 feet?

Round to two decimal places.

.

Chapter 4 Test: Form C 4-5 1. Write the equation of the function g  x  , shown below, that is transformed from the given function f  x   x .

2. Given the function, g  x   5 x  3  4, which is transformed from the base function, f  x   x , a.

what is the horizontal shift of the function?

b.

what is the vertical shift of the function?

c.

what is the reflection of the function?

d.

what is the stretch or compression of the function?

3. Suppose that f  x  is an even function and 2 f  3  6. What is 5 f 3 ?

4. Given f  x   2  x  1 and g  x   x 2 , find each of the following.

3

a.

 f  g 3

b.

 g  f  x 

5. Given f  x   x 2  7 x  3 and g  x   2 x  5, find each of the following. a.

 f  g 2

c.

 fg 3

b.

 f  g 2

d.

f  g   2

6. A company is ordering custom water bottles as thank you gifts for their customers. For each order, there is a one-time processing fee of $40 and an additional cost of $6.50 per mug. a.

Find the cost function for an order of x water bottles.

b.

Find the average cost function for an order of x water bottles.

c.

Find the average cost for an order of 150 water bottles. (Round to the nearest cent.)

.

4-6 Chapter 4 Test: Form C 7. Sketch the graph of f 1  x  on the same axes below with the graph of f ( x).

8. Find the inverse of f  x   3 x  7.

9. Solve 3 x  1  2  4.

10. Solve

3 x  6  12.

4

11. Solve 2 x 4  50 x 2  288.

12. The height of a drone during a given flight is described by h t   4t 2  368t , t  0, where h t  is the height

in feet, and t is the time in minutes. During what time interval(s) will the height of the drone exceed 5000 feet?

Round to two decimal places.

.

Chapter 5 Test: Form A 5-1 Round all monetary answers to the nearest cent.

1. Use the properties of logarithms to evaluate each expression. a.

 1  log3    27 

c.

1 ln  4  e 

b.

eln 3

d.

log 6 1

x

1 2. Given the function g  x      4, 2

a. what is the horizontal asymptote of the function? b. what is the y-intercept of the function? c. sketch the graph of the function on the grid provided.

3. Solve the equation

3 ln  2 x  3  1  5. Round to three decimal places.

4

4. The population of a certain city was 42,600 in 2018, and it increases at 2.3% each year. a.

Write the equation of the exponential function that models the population of the city t years after 2018.

b.

Use the model to predict the population of the city in 2025.

c.

In what year will the population of the city reach 50,000?

 

5. Solve the equation 3 23 x  14. Round to four decimal places.

6. Solve the equation 95 x3  27.

7. Solve the equation log5 4 x  9  2.

8. The table shows the sales for a manufacturer since 1995.

Year Sales (in millions)

1996 19.3

1997 23.8

2002 74.9

2005 158.6

2006 204.7

2010 746.5

2015 1634.3

2016 2758.6

Round answers to three decimal places. a.

Find an exponential function that models these data, with x as the number of years after 1995.

b.

Find a logarithmic function that models these data, with x as the number of years after 1995.

c.

Which is the better model? Use the better model to estimate the sales for 2020.

.

5-2 Chapter 5 Test: Form A 9. $5000 is deposited in a bank account earning 2 34 % per year. If no money is withdrawn from the account, what will the account balance be after 5 years if the interest is compounded: a.

quarterly.

b.

daily.

c.

How much more is earned by compounding monthly?

10. Use properties of logarithms to simplify. a.

Rewrite each expression as the sum, difference, or product of logarithms in simplest form. ii. ln  e3 e  4

 x i. log  4  y 

b.

Rewrite each expression as a single logarithm.

1 i. 2 ln x  ln y   ln z 3

ii. ln

1 x3

11. The expected revenue, in thousands of dollars, from a new advertising campaign is given by 500 R , where x is the amount invested in the campaign, in thousands of dollars.

1  9.16e 0.023 x a.

What would be the expected revenue for an investment of $100,000?

b.

What is the limit on revenue, if this model is accurate?

12. A furniture company wants to buy a new delivery van costing $64,000 amortized with monthly payments over 10 years. The interest on the loan is 4.2%, and a 10% down payment is required. a.

What is the monthly payment?

b.

What would be the total cost of the van ?

c.

How much would the company save, if the van could be purchased without a loan?

.

Chapter 5 Test: Form B 5-3 Round all monetary answers to the nearest cent.

1. Use the properties of logarithms to evaluate each expression. a.

log 4 64

c.

10log 8

b.

log5 1

d.

1 ln  5  e 

2. Given the function g  x   4 x  3, a.

what is the horizontal asymptote of the function?

b.

what is the y-intercept of the function?

c.

sketch the graph of the function on the grid provided.

3. Solve the equation

3 ln 3 x  2  4  10. Round to three decimal places.

2

4. The population of a certain city was 56,700 in 2018, and it increases at 3.5% each year. a.

Write the equation of the exponential function that models the population of the city t years after 2018.

b.

Use the model to predict the population of the city in 2028.

c.

In what year will the population of the city reach 90,000?

 

5. Solve the equation 4 35 x  17. Round to four decimal places.

6. Solve the equation 492 x 5  343.

7. Solve the equation log3 3 x  7   3.

8. The table shows sales for a manufacturer since 1995.

Year Sales (in millions)

1996 44.3

1997 67.6

2002 1225.6

2005 1554.2

2006 1643.3

2010 1989.7

2015 2148.5

2016 2241.2

Round answers to three decimal places. a.

Find an exponential function that models these data with x as the number of years after 1995.

b.

Find a logarithmic function that models these data with x as the number of years after 1995.

c.

Which is the better model? Use the better model to estimate the sales for 2020.

.

5-4 Chapter 5 Test: Form B 9. $4500 is deposited in a bank account earning 3 14 % per year. If no money is withdrawn from the account, what will the account balance be after 6 years if the interest is compounded: a.

quarterly.

b.

daily.

c.

How much more is earned by compounding monthly?

10. Use properties of logarithms to simplify. a.

Rewrite each expression as the sum, difference, or product of logarithms in simplest form. i.

b.

ii. ln e2 e  1

log x5

log 3 y Rewrite each expression as a single logarithm.

1 i. 3 ln x  ln y   ln z 2

 1  ii. ln  5  y 

11. The expected revenue, in thousands of dollars, from a new advertising campaign is given by 600 R , where x is the amount invested in the campaign, in thousands of dollars.

1  8.29e 0.015 x a.

What would be the expected revenue for an investment of $80,000?

b.

What is the limit on revenue, if this model is accurate?

12. A florist wants to buy a new delivery van costing $68,000 amortized with monthly payments over 10 years. The interest on the loan is 4.8%, and a 10% down payment is required. a.

What is the monthly payment?

b.

What would be the total cost of the van ?

c.

How much would the florist save, if the van could be purchased without a loan?

.

Chapter 5 Test: Form C 5-5 Round all monetary answers to the nearest cent.

1. Use the properties of logarithms to evaluate each expression. a.

10log 2

c.

log8 1

b.

1 ln  3  e 

d.

log10, 000

2. Given the function g  x   5 x  3, a.

what is the horizontal asymptote of the function?

b.

what is the y-intercept of the function?

c.

sketch the graph of the function on the grid provided.

3. Solve the equation

5 ln  2 x  5  7  8. Round to three decimal places.

3

4. The population of a certain city was 48,900 in 2018, and it increases at 2.7% each year. a.

Write the equation of the exponential function that models the population of the city t years after 2018.

b.

Use the model to predict the population of the city in 2026.

c.

In what year will the population of the city reach 75,000?

 

5. Solve the equation 5 42 x  12. Round to four decimal places.

6. Solve the equation 1252 x  4  25.

7. Solve the equation log 4 7 x  11  3.

8. The table shows the sales for a manufacturer since 1995.

Year Sales (in millions)

1996 33.2

1997 60.7

2002 87.7

2005 98.5

2006 150.3

2010 233.2

2015 320.2

2016 478.1

Round answers to three decimal places. a.

Find an exponential function that models these data with x as the number of years after 1995.

b.

Find a logarithmic function that models these data with x as the number of years after 1995.

c.

Which is the better model? Use the better model to estimate the sales for 2020.

.

5-6 Chapter 5 Test: Form C 9. $5500 is deposited in a bank account earning 1 34 % per year. If no money is withdrawn from the account, what will the account balance be after 8 years if the interest is compounded: a. quarterly. b. daily. c. How much more is earned by compounding monthly?

10. Use properties of logarithms to simplify. a.

Rewrite each expression as the sum, difference, or product of logarithms in simplest form. i.

b.

ii. ln  e 4 e  3

log y 3 4

log x Rewrite each expression as a single logarithm.

i.

1 ln x  ln y   4 ln z 2

ii. ln

1 y

11. The expected revenue, in thousands of dollars, from a new advertising campaign is given by 550 , where x is the amount invested in the campaign, in thousands of dollars.

R 1  7.34e 0.031x a. What would be the expected revenue for an investment of $120,000? b. What is the limit on revenue, if this model is accurate?

12. An electrician wants to buy a new service van costing $66,000 amortized with monthly payments over 10 years.

The interest on the loan is 4.5%, and a 10% down payment is required. a. What is the monthly payment? b. What would be the total cost of the van ? c. How much would the graduate save, if the van could be purchased without a loan?

.

Chapter 6 Test: Form A 6-1 1. Use the given graph of the polynomial function to: a.

estimate the x-intercept(s).

b.

state whether the lead coefficient is positive or negative.

c.

determine whether the polynomial is cubic or quartic.

2. Find the cubic function that models the given data. 3

2

1

0

1

2

3

y 125

52

19

8

1

20

73

x

3. Find the quartic function that models the given data. 4

3

2

1

0

1

2

y 229

68

13

4

5

4

13

x

4. Solve x3  3x 2  10 x  0.

5. Solve x 4  14 x 2  49  0.

6. If 2 is a root of f  x   0 for f  x   2 x3  11x 2  x  30, find the factorization of f  x  .

7. Given f  x   2 x3  x 2  13x  6, a.

determine all possible rational solutions of f  x   0.

b.

solve exactly in the complex number system. [Hint: use synthetic division.]

8. Solve

5x  6 2

x  2x

9. For f  x  



x4 . x2

x2  9 , give: x2

a.

the x-intercept(s).

d.

any horizontal asymptotes.

b.

the y-intercept(s).

e.

any slant asymptotes.

c.

any vertical asymptotes.

.

6-2 Chapter 6 Test: Form A 10. Use the information from your answers to question #9 to help you graph the rational function.

11. Solve

x8  3. x2

12. Solve 4 x 4  100 x 2  0.

.

Chapter 6 Test: Form B 6-3 1. Use the given graph of the polynomial function to: a.

estimate the x-intercept(s).

b.

state whether the lead coefficient is positive or negative.

c.

determine whether the polynomial is cubic or quartic.

2. Find the cubic function that models the given data. x 3 2 1 y 24 28 18

0 6

1 2 4 24

3 78

3. Find the quartic function that models the given data. x y

2 19

1 13

0 11

1 7

2 29

3 4 151 437

4. Solve x3  x 2  12 x  0.

5. Solve x 4  22 x 2  121  0.

6. If 3 is a root of f  x   0 for f  x   5 x3  7 x 2  58 x  24 , find the factorization of f  x  .

7. Given f  x   2 x3  3x 2  5 x  6 , a.

determine all possible rational solutions of f  x   0.

b.

solve exactly in the complex number system. [Hint: use synthetic division.]

8. Solve

x  7 4 x  10  . x  2 x2  2 x

9. For f  x  

x2  2 , give: x 1

a.

the x-intercept(s).

d.

any horizontal asymptotes.

b.

the y-intercept(s).

e.

any slant asymptotes.

c.

any vertical asymptotes.

.

6-4 Chapter 6 Test: Form B 10. Use the information from your answers to question #9 to help you graph the rational function.

11. Solve

3x  7  1. x3

12. Solve 5 x 4  45 x 2  0.

.

Chapter 6 Test: Form C 6-5 1. Use the given graph of the polynomial function to: a.

estimate the x-intercept(s).

b.

state whether the lead coefficient is positive or negative.

c.

determine whether the polynomial is cubic or quartic.

2. Find the cubic function that models the given data. 3

2

1

0

1

2

3

y 153

45

1

9

3

7

45

x

3. Find the quartic function that models the given data. 4

3

2

1

0

1

2

y 201

54

9

6

9

6

9

x

4. Solve x3  3x 2  18 x  0.

5. Solve x 4  6 x 2  9  0.

6. If 4 is a root of f  x   0 for f  x   2 x3  3x 2  32 x  48, find the factorization of f  x  .

7. Given f  x   2 x3  x 2  13x  6, a.

determine all possible rational solutions of f  x   0.

b.

solve exactly in the complex number system. [Hint: use synthetic division.]

8. Solve

6x  6 2

x  3x

9. For f  x  



x5 . x3

x2  4 , give: x 1

a. the x-intercept(s).

d. any horizontal asymptotes.

b. the y-intercept(s).

e. any slant asymptotes.

c. any vertical asymptotes.

.

6-6 Chapter 6 Test: Form C 10. Use the information from your answers to question #9 to help you graph the rational function.

11. Solve

5x  7  2. x4

12. Solve 2 x 4  32 x 2  0.

.

Chapter 7 Test: Form A 7-1 2 x  3 y  z  11  1. Solve the system 5 x  7 y  2 z  5 . x  y  z  3  x  y  z  6  2. Solve the system  x  2 y  3 z  14 .  x  4 y  7 z  30 

3x  5 y  7 using Cramer’s rule. Show the determinate fractions.

3. Solve the system  2 x  4 y  5 4. Each of the following matrices is associated with the solution to a system of linear equations in x, y, and z.

Write the solution to each system, if it exists. State if it is an inconsistent system. a.

5  1 0 7  0 1 3 2   0 1  0 0

b.

5 3 1 0  0 1 4 7     0 0 0 0

c.

3 1 0 0  0 1 0 0    0 0 1 5

 7 1 5  5. Given A   ,  2 0 6

a.

state the dimensions of matrix A.

b.

determine  A.

c.

find A    A .

1  3  1 7  6. Given A   2 0 and B   3 5 , find each of the following, if possible.      5 2  6 4

a.

4 A  3B

b.

A  2B

 2 3 1   6 8  7. Given A   and B     , find each of the following, if possible. 0 4 5  9 7

a.

b.

AB

BA

8. A package contains x round stickers and y rectangular stickers. Each round sticker has six colored stars and 5 colored dots. Each rectangular sticker has five colored stars and 4 colored dots. If there are a total of 43 stars and 35 dots, how many round and rectangular stickers are in the package? a.

Write the matrix equation, AX  B, that represents this scenario.

b.

Find A1.

c.

Use your answer to (b) to solve the system.

4 7  5 7  9. Show that   and  3 4 are inverse matrices.

3 5    

.

7-2 Chapter 7 Test: Form A  x 2  y 2  20 .

10. Solve the system  x y  6 

11. A concert promoter needs to make $247,500 from the sale of 500 tickets. Tickets in sections A, B, and C cost $1250, $750, and $400, respectively. If the number of tickets in section C is four times the sum of the remaining tickets, how many of each type should be sold?

12. An artist bought brass, steel, and aluminum rods for a scupture. The rods have a total length of 17 meters and a total weight of 16 kilograms. If the artist spent $36 on the purchase, how many of each type of rod were there?

The following table describes the washers.

Rod Type Length (m) Weight (kg) Cost

Brass 2 4 $8

Steel 3 3 $5

.

Aluminum 2 1 $3

Chapter 7 Test: Form B 7-3  x  3 y  z  16  1. Solve the system 7 x  5 y  2 z  25. 2 x  3 y  z  7  x  y  z  7  2. Solve the system 4 x  y  11z  18 . 3 x  2 y  12 z  11 

4 x  7 y  2 using Cramer’s rule. Show the determinate fractions.

3. Solve the system   3x  6 y  5 4. Each of the following matrices is associated with the solution to a system of linear equations in x, y, and z.

Write the solution to each system, if it exists. State if it is an inconsistent system. a.

 1 0 0 0  0 1 0 2   0 0 1 7 

b.

 1 0 2 8 0 1 5 6   0 0 0 2

c.

 1 0 3 5 0 1 6 2   0 0 0 0

 2 3  5. Given A   4 0  ,    5 1

a.

state the dimensions of matrix A.

b.

determine  A.

c.

find A    A .

 1 2  6 4 6. Given A   3 5 and B   4 2 , find each of the following, if possible.      0 6  1 5

a.

4 A  3B

b.

A  2B

8 9 5 4    7. Given A   and B  2 7 , find each of the following, if possible.    0 3   1 6  a.

b.

AB

BA

8. A package contains x round stickers and y rectangular stickers. Each round sticker has six colored stars and 5 colored dots. Each rectangular sticker has five colored stars and 4 colored dots. If there are a total of 39 stars and 54 dots, how many round and rectangular stickers are in the package? a.

Write the matrix equation, AX  B, that represents this scenario.

b.

Find A1.

c.

Use your answer to (b) to solve the equation.

 9 4  5 4 9. Show that   and  11 9  are inverse matrices.

11 5    

.

7-4 Chapter 7 Test: Form B  x 2  y 2  29 10. Solve the system  . x y 3 

11. A concert promoter needs to make $97,500 from the sale of 800 tickets. Tickets in sections A, B, and C cost $200, $150, and $75, respectively. If the number of tickets in section C is equal to the sum of the remaining tickets, how many of each type should be sold?

12. An artist bought brass, steel, and aluminum rods for a scupture. The rods have a total length of 20 meters and a total weight of 17 kilograms. If the artist spent $38, how many of each type of rod were in the purchase? The following table describes the washers.

Rod Type Length (m) Weight (kg) Cost

Brass 3 4 $2

Steel 2 1 $6

.

Aluminum 3 3 $4

Chapter 7 Test: Form C 7-5 2 x  3 y  7 z  14  1. Solve the system 3x  4 y  z  12. x  y  z  7   x  2 y  3 z  2  2. Solve the system  x  y  2 z  5 . 2 x  3 y  z  3 

 5x  4 y  3 using Cramer’s rule. Show the determinate fractions.

3. Solve the system  8 x  7 y  1 4. Each of the following matrices is associated with the solution to a system of linear equations in x, y, and z.

Write the solution to each system, if it exists. State if it is an inconsistent system. a.

 1 0 2 7  0 1 5 8   0 0 0 0

b.

 1 0 0 3  0 1 0 0   0 0 1 5

c.

 1 0 3 4 0 1 2 7    3 0 0 0

 3 4 1 5. Given A   ,  6 0 2

a.

state the dimensions of matrix A.

b.

determine  A.

c.

find A    A .

1  6 5  2 6. Given A   4 1 and B   0 6 , find each of the following, if possible.      3 2  5 3

a.

4 A  3B

b.

A  2B

 8 6   4 7  7. Given A   3 0  and B   , find each of the following, if possible.   5 9    1 2

a.

b.

AB

BA

8. A package contains x round stickers and y rectangular stickers. Each round sticker has six colored stars and 5 colored dots. Each rectangular sticker has five colored stars and 4 colored dots. If there are a total of 53 stars and 43 dots, how many round and rectangular stickers are in the package? a.

Write the matrix equation, AX  B, that represents this scenario.

b.

Find A1.

c.

Use your answer to (b) to solve the equation.

 8 5  3 5 9. Show that   and  5 8 are inverse matrices.

5 3    

.

7-6 Chapter 7 Test: Form C  x 2  y 2  58 10. Solve the system  .  y  x  10

11. A concert promoter needs to make $131,500 from the sale of 1650 tickets. Tickets in sections A, B, and C cost $150, $90, and $65, respectively. If the number of tickets in section C is twice the sum of the remaining tickets, how many of each type should be sold?

12. An artist bought brass, steel, and aluminum rods for a scupture. The rods have a total length of 24 meters and a total weight of 17 kilograms. If the artist spent $31 how many of each type of rod were in the purchase? The following table describes the washers.

Rod Type Length (m) Weight (kg) Cost

Brass 4 1 6

Steel 2 3 2

.

Aluminum 4 2 5

Chapter 8 Test: Form A 8-1 x  y  1  1. Graph the solution of  x  2 y  10 . Identify/label the corners of the solution region.  x  0; y  0 

2. The corner points of a feasible region are 0, 0 , 2, 5 , 3, 4 , and 8,1 . Which corner point maximizes P  5 x  4 y, and what is the maximum value?

3. Find the first five terms of each defined sequence. a.

f n   4n  11

b.

f n    1 (3n) n

4. A landscaper is building a decorative fence. The first fence board will be 48 inches in length and each subsequent fence board will be 2 inches longer than the previous fence board. a.

What are the lengths of the first five fence boards?

b.

Write a formula for the length, Ln , of the nth fence board.

c.

What is the combined length of the first 11 boards?

5. A geometric sequence has a first term of 6 and a common ratio of a.

Write the first three terms of the sequence.

b.

Write a formula for the nth term of the sequence.

c.

What is the 8th term of the sequence?

3 .

4

6. Given f  x   2 x 2  3x  10,

a.

find f  x  h  .

b.

find

c.

what does

f  x  h  f  x h

, h  0.

f  x  h  f  x approach as h approaches 0? h

7. Expand 2 x  y  .

5

8. Use the distance formula to show A  2, 6 , B 1, 6 , and C 3,14 are all on the same line.

.

8-2

Chapter 8 Test: Form A

9. For the equation f  x   x 2  y 2  2 x  4 y  4  0, give the radius and the center.

10. Graph the equation y  x 2  2 x  8, and label the vertex and all intercepts with their coordinates.

11. For the equation 4 x 2  9 y 2  16 x  72 y  124  0, a.

give the center.

b.

give the endpoints of the major axis.

c.

give the endpoints of the minor axis.

12. Determine whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. a.

x 2  y 2  10 x  16 y  40  0

b.

9 x 2  16 y 2  36 x  160 y  292  0

c.

9 x 2  4 y 2  72 x  16 y  92  0

d.

x 2  10 x  13  y  0

.

Chapter 8 Test: Form B 8-3  x  6 y  48  1. Graph the solution of 7 x  y  49 . Identify/label the corners of the solution region.  x  0; y  0 

2. The corner points of a feasible region are 0, 0 ,  5,3 , 2, 4 , and 7, 6 . Which corner point maximizes P  6 x  2 y, and what is the maximum value?

3. Find the first five terms of each defined sequence. a.

f  n   3n  8

b.

f  n    1 (4n) n

4. A landscaper is building a decorative fence. The first fence board will be 36 inches in length and each subsequent fence board will be 3 inches longer than the previous fence board. a.

What are the lengths of the first five fence boards?

b.

Write a formula for the length, Ln , of the nth fence board.

c.

What is the combined length of the first 9 boards?

5. A geometric sequence has a first term of 10 and a common ratio of a.

Write the first three terms of the sequence.

b.

Write a formula for the nth term of the sequence.

c.

What is the 8th term of the sequence?

2 .

3

6. Given f  x   4 x 2  2 x  5, a.

find f  x  h  .

b.

find

c.

what does

f  x  h  f  x h

, h  0.

f  x  h  f  x approach as h approaches 0? h

7. Expand  x  3 y  .

5

8. Use the distance formula to show A  2, 11 , B 1, 2 , and C 3, 4 are all on the same line.

.

8-4

Chapter 8 Test: Form B

9. For the equation f  x   x 2  y 2  6 x  4 y  3  0, give the radius and the center.

10. Graph the equation y  x 2  x  6, and label the vertex and all intercepts with their coordinates.

11. For the equation 9 x 2  18 x  4 y 2  16 y  11  0, a.

give the center.

b.

give the endpoints of the major axis.

c.

give the endpoints of the minor axis.

12. Determine whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. a.

y2  6 y  x  3  0

b.

4 y 2  9 x 2  18 x  16 y  29  0

c.

x 2  y 2  6 x  4 y  12  0

d.

4 x 2  9 y 2  24 x  18 y  9  0

.

Chapter 8 Test: Form C 8-5 4 x  3 y  3  1. Graph the solution of 5 x  2 y  25. Identify/label the corners of the solution region.  x  0; y  0 

2. The corner points of a feasible region are 0, 0 , 2, 7  , 5, 1 , and 9, 2 . Which corner point maximizes P  3 x  5 y, and what is the maximum value?

3. Find the first five terms of each defined sequence. a.

f n   5n  12

b.

f n    1 (5n) n

4. A landscaper is building a decorative fence. The first fence board will be 42 inches in length and each subsequent fence board will be 2 inches longer than the previous fence board. a.

What are the lengths of the first five fence boards?

b.

Write a formula for the length, Ln , of the nth fence board.

c.

What is the combined length of the first 10 boards?

5. A geometric sequence has a first term of 5 and a common ratio of a.

Write the first three terms of the sequence.

b.

Write a formula for the nth term of the sequence.

c.

What is the 10th term of the sequence?

3 .

2

6. Given f  x   3x 2  2 x  7, a.

find f  x  h  .

b.

find

c.

what does

f  x  h  f  x h

, h  0.

f  x  h  f  x approach as h approaches 0? h

7. Expand 3 x  y  .

5

8. Use the distance formula to show A  2, 7  , B 1,8 , and C 3,18 are all on the same line.

.

8-6

Chapter 8 Test: Form C

9. For the equation f  x   x 2  y 2  8 x  6 y  21  0, give the radius and the center.

10. Graph the equation y  x 2  3 x  4, and label the vertex and all intercepts with their coordinates.

11. For the equation 4 x 2  16 y 2  24 x  32 y  12  0, a.

give the center.

b.

give the endpoints of the major axis.

c.

give the endpoints of the minor axis.

12. Determine whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. a.

4 x 2  9 y 2  16 x  54 y  61  0

b.

x2  2 x  y  8  0

c.

4 x 2  16 y 2  24 x  32 y  44  0

d.

x 2  y 2  8 x  10 y  5  0

.

Chapter 1 Answers: Form A A1-1 2. a. Domain: 4, 2, 0,1,3,5,8

1. a. Relationship 2

Range: 7, 3, 0, 2,3, 6

b. Table 2 c. Graph 1

b. Domain: ,   ; Range:  3,  

d. Equation 1 3. a.

c. Domain: ,   ; Range:  ,  

246 cars were sold by the dealership in 2013.

b. The y-intercept is 78. 78 cars were sold by the dealership in 2010. c. The rate of change is 56 cars sold by the dealership per year.

4. a. The slope is 3; the y-intercept is 0, 7  . b. The slope is

3 ; the y-intercept is 0, 2 .

5

c. The slope is

2 ; the y-intercept is 0, 0 .

5

 7  5. a. x:   , 0  ; y: 0, 7   5 

c. x: 2, 0 , 0, 0 , 1, 0

3  b. x: none; y:  0,    2

y: 0, 0

6. a.

3 1 y   x 2 2

7. a.

2 y   x6 5

b.

y  4 x  2

b.

y  4 x  3

c.

x 1

c.

y  2 x  12

8. a.

y  12 x  55 hundred downloads, x years after 2015.

b. 16,300 eBooks will be downloaded in 2024.

9. a.

p  25  $3.22

10. a.

b. 17 days; May 18

b.

1, 7  450 feet

c. Day 6 11. a. The marginal revenue is $19.99 per unit sold. The sale of each additional toy will result in additional revenue of $19.99. b.

P  x   7.24 x  590

c. The marginal profit is $7.24 per unit sold. The production and sale of each additional toy will result in an additional profit of $7.24.

12. a. b.

y  2 x  1

c.

x  3

5 8 x 7 7

d.

y2

y

.

A1-2 Chapter 1 Answers: Form B 2. a. Domain: 3, 1, 0, 2,5, 7,9

1. a. Relationship 2

Range: 3, 2, 0, 4, 6,8

b. Table 1 c. Graph 2

b. Domain: ,   ; Range:  5,  

d. Equation 2

c. Domain: ,   ; Range:  ,  

3. a. There were 43 houses in the subdivision in 2014. b. The y-intercept is 11. There were 11 houses in the subdivision in 2010. c. The rate of change is 8 houses in the subdivision per year.

4. a. The slope is 5; the y-intercept is 0, 3 . b. The slope is

4 ; the y-intercept is 0, 6 .

3

c. The slope is

7 ; the y-intercept is 0, 0 .

5

8  5. a. x:  , 0  ; y 0, 8 3 

c. x: 5, 0 , 0, 0 ,  4, 0

1  b. x: none; y:  0,    5

y: 0, 0

3 23 x 2 2

7. a.

4 y   x7 3

b.

y  2 x  1

b.

y  5 x  17

c.

y7

c.

y  2 x  4

6. a.

8. a.

y

y  9 x  47 hundred downloads, x years after 2015.

b. 12,800 eBooks will be downloaded in 2024.

9. a. t (9)  2.15

10. a.

b. 7 days

 23, 29

b. 650 feet c. Day 24

11. a. The marginal revenue is $79.99 per unit sold. The sale of each additional wireless speaker will result in additional revenue of $79.99. b.

P  x   27.31x  3584

c. The marginal profit is $27.31 per unit sold. The production and sale of each additional wireless speaker will result in an additional profit of $27.31.

12. a. b.

6 8 y   x 5 5

y  2x  2

.

c.

y  2

d.

x4

Chapter 1 Answers: Form C A1-3 2. a. Domain: 5, 1, 0,3,5, 6,9

1. a. Relationship 2

Range: 7, 5, 2, 0, 4,8

b. Table 2 c. Graph 1

b. Domain: ,   ; Range:  , 7 

d. Equation 1 3. a.

c. Domain: ,   ; Range:  ,  

413 appliances were sold by the retailer in 2014.

b. The y-intercept is 125. 125 appliances were sold by the retailer in 2010. c. The rate of change is 72 appliances sold by the retailer per year.

4. a. The slope is 2; the y-intercept is 0, 6 . b. The slope is

3 ; the y-intercept is 0, 4 .

5

c. The slope is

4 ; the y-intercept is 0, 0 .

3

3  5. a. x:  , 0  ; y: 0,3 2 

c. x: 4, 0 , 0, 0 , 1, 0

 1 b. x: none; y:  0,   2

y: 0, 0

3 13 x 2 2

7. a.

3 y   x8 7

b.

y  5 x  13

b.

y  6 x  27

c.

x  3

c.

y  2 x  5

6. a.

8. a.

y

y  13 x  29 hundred downloads, x years after 2015.

b. 14,600 eBooks will be downloaded in 2024.

9. a.

p(2)  $3.33

10. a.

b. year 4; 2007

14, 20

b. 550 feet c. Day 18

11. a. The marginal revenue is $79.99 per unit sold. The sale of each additional small drone will result in additional revenue of $79.99. b.

P  x   32.64 x  9731

c. The marginal profit is $32.64 per unit sold. The production and sale of each additional small drone will result in an additional profit of $32.64.

12. a. b.

y  2x  2

c.

x  1

3 5 y   x 7 7

d.

y4

.

A2-1 Chapter 2 Answers: Form A P

A 1  rt

b. t 

A P rP

1. a.

2. a.

x

3. a.

x  3

b.

x  3

c.

, 3

32 3

b.

 32    , 0  3

c.

x

32 3

4.

In order to break even, the band will have to sell 40 shirts.

5.

The office will have to print more than 400 pages in a month for Plan A to be less expensive.

6.

Denise will have saved enough in 15 months, which is April 2021.

7. a. Yes, the first differences are constant at $86.67. b.

y  28.89 x  1199.95 dollars

c. Continuous d. Extrapolation 8. a.

y  1.5429 x  136.8286

b. The scatter plot appears somewhat linear with first differences ranging from 9.6 to 2.2. c. 44.255 mpg (44.257 using technology with unrounded coefficients.) d. For every 1 unit increase in engine horsepower, MPG decreases by 1.5429.

9. a. Both methods give the same solution of 1, 4 . b. Both methods give the same solution of  5, 7  .

10.

x  1 or 1,  

11.

[2.25, 4.25]

12.

A→I; B→III; C→II

.

Chapter 2 Answers: Form B A2-2 1. a.

h

2A ab

b.

a

2 A  bh 2 A  b h h

2. a.

x

18 5

b.

 18   , 0  5

c.

x

18 5

3. a.

x3

b.

x3

c.

3,  

4.

In order to break even, the band will have to sell 36 posters.

5.

The office will have to consume more than 50 cups of coffee in a week for Plan B to be less expensive.

6.

Jasmine will have saved enough in 9 months, which is October 2020.

7. a. Yes, the first differences are constant at $6300. b.

y  3150 x  35, 000 dollars

c. Continuous d. Interpolation 8. a.

y  1.1015 x  6.8700

b. The scatter plot appears very linear with first differences ranging from 0.344 to 0.531. c. $3.59 d. For every 1 grade completed in school, the hourly wage increases by $1.10.

9. a. Both methods give the same solution of  2,3 .

b. Both methods give the same solution of  4,3 .

10.

x  3 or 3,  

11.

 2.50,5.25

12.

A→II; B→I; C→III

.

A2-3 Chapter 2 Answers: Form C Rh

1. a.

h

b.

R

2. a.

x

Rr

2

3. a.

x  1

b.

x  1

c.

, 1

hr 2 H h

28 3

b.

 28    , 0  3

c.

x

28 3

4.

In order to break even, the band will have to sell 32 bandanas.

5.

The office will have to print more than 350 pages in a month for Plan B to be less expensive.

6.

Kim will have saved enough in 16 months, which is May 2021.

7. a. Yes, the first differences are constant at $22.5. b.

y  1.5 x  2.5 dollars

c. Continuous d. Extrapolation 8. a.

y  2.90 x  55.80

b. The scatter plot appears close to linear with first differences ranging from 4 to 9. c. 93.5 cents per pound d. In 1925, beef cost 55.8 cents per pound.

9. a. Both methods give the same solution of  3, 2 . b. Both methods give the same solution of 2,13 .

10.

x  4 or  4,  

11.

3.75,5.25

12.

A→III; B→II; C→I

.

Chapter 3 Answers: Form A A3-1 1. a. i.

Vertex 4, 7 

7. a.

b. ,  

ii. Maximum iii. Concave down b. i.

 1 11  Vertex   ,   2 4

ii. Minimum

0,  

b.

21,  

8.

x  0, 2, 3, 5

9.

f  x   3 x 2  5 x  9

10. a.

iii. Concave up 2. a.

0,  

c. 21 units d. $363 e. 12 or 30 units 3. a.

f  x    x  5  7 2

b. x  5

b.

f  4  5; f  12  11

 7,  

c. ,5

d. , 5

11. a. C  40  200

c.

4. a. 5.822 seconds

b. C 55  $350; The cost to cater a breakfast

b. 62.694 meters

with 55 served meals is $350

c. 2.245 seconds d.

12. a.

0,5.822

b. y  3.438075 x1.299827

5. a. Zero

c. Quadratic; 375 flies.

b. One 6. a.

x

y  0.506614 x 2  0.133598 x  9.359788

7  29 2 1 3

b. x   , 4 c. x  2

.

A3-2 Chapter 3 Answers: Form B 1 a. i.

Vertex 5,9

7. a. (, 0) b. The function never increases.

ii. Minimum iii. Concave up b. i.

 3 11  Vertex  ,   2 4 

ii. Maximum

8.

x  7, 5, 2, 0

9.

f  x   2 x 2  7 x  3

10. a.

iii. Concave down 2. a.

0,  

b. 22,   c. 22 units d. $392 e. 15 or 29 units 3. a.

f ( x)  ( x  4) 2  7

b. x  4

b.

f 4  4; f 7   12

c. , 7 

c.

 4,  

11. a. C 20  150

d. 4,   4. a.

b. C 30  240; The cost to cater a lunch with

4.834 seconds

30 served meals is $240.

b. 53.480 meters

12. a.

c. 1.531 seconds d.

0, 4.834

b. y  1.953183x1.493087

5. a. Positive

c. Quadratic; 540 flies.

b. Two 6. a.

3 x   ,5 2

b. x 

y  0.370370 x 2  1.587302 x  3.285714

3  13 2

c. x  3

.

Chapter 3 Answers: Form C A3-3 1. a. i.

Vertex 7,11

7. a.

b. (, )

ii. Maximum iii. Concave down b. i.

 3 17  Vertex   ,    2 4

ii. Minimum

8.

x  0, 2, 4, 6

9.

f  x   4 x 2  6 x  7

10. a.

iii. Concave up 2. a.

0,  

0,  

b. 19,   c. 19 units d. $144 e. 16 or 22 units 3. a.

f  x    x  2  3 2

b.

b. x  2 c.

 3,  

f 1  7; f (6)  12

c. , 7 

d. , 2

11. a. C 30  300

b. C 45  480; The cost to cater a dinner

4. a. 4.665 seconds

with 45 meals served is $480.

b. 45.061 meters c. 1.633 seconds

12. a.

y  0.404762 x 2  1.440476 x  6.071429

0, 4.665

b. y  2.295003 x1.442716

5. a. Negative

c. Quadratic; 583 flies.

d.

b. Zero 6. a.

x  4,

5 2

b. x  4 c. x 

5  37 2

.

A4-1 Chapter 4 Answers: Form A g  x   x  2  3

1.

7.

2. a. shifted right 4 units b. shifted up 5 units c. reflection across the y-axis d. compressed by a factor of

1 3

6 f  3  18

3.

4. a. 1 b.

9

 x  4

3



9 3

2

x  12 x  48 x  64

x3 7

8.

f 1 ( x) 

9.

x3

c. 231

10.

 18,3

1 6

11.

x  2, 5

12.

13.42, 46.58

5. a. 5 b. 38

d.



6. a. C  x   3.50 x  30 b. C  x   c

3.50 x  30 x

$3.63 per mug

.

Chapter 4 Answers: Form B A4-2 g  x   x  2  1

1.

7.

2. a. shifted left 3 units b. shifted up 4 units c. reflection across both x- and y-axes d. stretched by a factor of 2 3.

7 f 4  35

4. a.

64

b.

4

 x  2  1 3



4 3

2

x  6 x  12 x  7

5. a. 17

8.

f 1 ( x)  3 x  5

b.

9

9.

x9

c.

4

10.

 15, 35

d.

2

11.

x  3, 5

12.

12.10, 45.90

6. a. C  x   1.50 x  20 b. C  x  

1.50 x  20 x

c. $1.57 per pen

.

A4-3 Chapter 4 Answers: Form C g  x   x  3  2

1.

7.

2. a. shifted left 3 units b. shifted up 4 units c. reflection across the x-axis d. stretched by a factor of 5 5 f 3  15

3.

4. a. 2000 b.

2

 2  x  13   4  x  16  

5. a. 2 b. 20 c.

33

d. 21 6. a. C  x   6.50 x  40 6.50 x  40 b. C  x   x

c. $6.77 per water bottle

.

8.

f 1 ( x)  x3  7

9.

x5

10.

 8, 24

11.

x  3, 4

12.

16.57, 75.43

Chapter 5 Answers: Form A A5-1 1. a.

3

b. 3 c.

4

d. 0 2. a.

y4

b.

0,5

17 2

7.

x

8. a.

y  14.446 1.279

b.

x

y  481.673  588.897 ln x

c. Exponential; 6784.397 million 9. a. $5734.31

c.

b. $5736.98 c. $2.67 10. a. i.

x

4. a.

P t   42, 600 1.023 people

ii.

3  ln e  4

b. i.

 x2  ln  2 3  y z

ii.

e8  3  1491.979 2

3.

1 log x  4 log y 2

3ln x

11. a. $260.638 thousand, or $260, 638

t

b. $500 thousand, or $500, 000

b.

49,950 people

c.

2025

b. $77,039.20

5.

x  0.7408

c. $13,039.20

6.

x

12. a. $588.66

9 10

.

A5-2 Chapter 5 Answers: Form B 1. a. 3 b. 0 c. 8 d.

2. a.

5

x

8. a.

y  103.090 1.199

b.

y3

20 3

7.

x

y  201.020  778.386 ln x

c. Logarithmic; 2304.508 million

b. (0, 2)

9. a. $5464.59

c.

b. $5468.85 c. $4.26 10. a. i. ii.

2  ln e  1

b. i.

ln x3 y 3 z

ii.

9

e 5  4054.042 2

3.

x

4. a.

P t   56, 700 1.035 people

6.

x

5ln y

12. a. $643.15 b. $83,978

2031 x  0.2634



b. $600 thousand, or $600, 000

t

5.



11. a. $171.581 thousand, or $171,581

b. 79,981 people c.

1 5log x  log y 3

c. $15,978

7 4

.

Chapter 5 Answers: Form C A5-3 1. a. 2 b.

3

c. 0 d. 4 2. a.

y  3

b.

0, 2

75 7

7.

x

8. a.

y  37.407 1.123

b.

x

y  30.606  106.094 ln x

c. Exponential; 679.903 million 9. a. $6324.57

c.

b. $6326.48 c. $1.91 10. a. i.

e9  1  4051.042 2

3.

x

4. a.

P t   48,900 1.027  people

ii.

4  ln e  3

b. i.

 z4 x  ln    y 

ii.

 ln y

11. a. $466.942 thousand, or $466,942

t

b. $550 thousand, or $550, 000

b. 60,516 people c.

1 3log y  log x 4

12. a. $615.61

2034

5.

x  0.3158

b. $80, 473.2

6.

x

7 3

c. $14, 473.20

.

A6-1 Chapter 6 Answers: Form A 1. a.

3, 0 , 1, 0 , 5, 0

9. a.

b. Negative c. Cubic 2.

y  3 x3  2 x 2  6 x  8

3.

y   x4  2x2  5

4.

x  5, 0, 2

5.

x 7

6.

f  x    x  2 2 x  3 x  5

7. a.

1, 2, 3, 6 1, 2

b.

1 x  3, , 2 2

8.

3.0 , 3, 0

b.

9   0,   2

c.

x  2

d. None e.

y  x2

10.

x3

.

11.

2  x  1

12.

5  x  0 or 0  x  5

Chapter 6 Answers: Form B A6-2 1. a.

2, 0 , 2, 0 , 3, 0

b. Positive

b.

0, 2

c. Quartic

c.

x 1

2.

y  2 x3  5 x 2  9 x  6

3.

y   x 4  3 x3  11

4.

x  3, 0, 4

5.

x   11

6.

f  x    x  35 x  2 x  4

7. a.

1, 2, 3, 6 1, 2

b.

8.

9. a. None

x  2, 1,

d. None e.

y  x 1

10.

3 2

x  5

.

11.

2 x3

12.

x  3 or x  3

A6-3 Chapter 6 Answers: Form C

5, 0

9. a.

b. Positive

b.

0, 4

c.

x  1

1. a.

c. Cubic 3

2

2, 0 , 2, 0

2.

y  4 x  7 x  3x  9

d. None

3.

y   x4  4x2  9

e.

4.

x  6, 3, 0

5.

x 3

6.

f  x    x  4 2 x  3 x  4

7. a.

1, 2, 3, 6 1, 2

b.

1 x  2,  ,3 2

8.

y  x 1

10.

x  2

.

11.

4  x  5

12.

4  x  0 or 0  x  4

Chapter 7 Answers: Form A A7-1 1.

2,1, 4

2.

 z  2,8  2 z, z 

3.

 7 5 3 7  5 4 2 5  53 1     ,  ,  3  5 3  5 22 22    2 4 2 4  

5 z  3, 4 z  7, z 

c.

3, 0, 5

5. a.

b.

 1 13  8 10    7 10

7. a. Not possible

4. a. Inconsistent; no solution b.

6. a.

 15 25  1 15   4  38

23

b.

 12 50 46  18 1 26  

8. a.

6 5  x   43 5 4  y   35     

b.

 7 1 5  2 0 6  

b.

c.

 0 0 0  0 0 0  

c.

9.

 4 7   5 7   1 0   5 7   4 7  1 0  3 5  3 4  0 1  and  3 4  3 5  0 1           

10.

4, 2 , 2, 4

11.

25, 75, and 400 tickets in sections A, B, and C, respectively

12.

2 brass rods, 1 steel rod, 5 aluminum rods

.

6 5 A1     5 4

1

 4 5     5 6

 4 5   43 3 X  A1 B         5 6 35 5 3 round stickers and 5 rectangular stickers.

A7-2 Chapter 7 Answers: Form B 1.

3, 2, 7

2.

2 z  5,3z  2, z 

3.

 2 7 4 2   5 6 3 5  47 26      ,   ,  4 7 4 7   3 3    3 6 3 6   

4. a.

0, 2, 7 

6. a.

7. a. Not possible

c.

 40 5  10 29    5 22 

b.

3z  5, 6 z  2, z 

5. a. 3  2 b.

 13 6   11 1     2 16

b.

b. Inconsistent; no solution c.

 14 20  0 26    9   3

 3 5  x  39  4 7   y   54     

8. a.

 2 3  4 0     5 1 

 3 5 A 1    4 7

b.

 0 0  0 0   0 0

c.

 7 5    4 3 

 7 5 39  3 X  A1 B         4 3  54 6 3 round stickers and six rectangular stickers.

9.

 9 4  5 4 1 0  5 4  9 4 1 0 11 5  11 9   0 1 and  11 9  11 5  0 1           

10.

2,5 , 5, 2

11.

150, 250, and 400 tickets in sections A, B, and C, respectively

12.

1 brass rod, 4 steel rods, 3 aluminum rods

.

1

Chapter 7 Answers: Form C A7-3 1.

3,5, 1

2.

7 z  12,5 z  7, z 

3.

 3 4 5 3   1 7 8 1  25 29     ,  ,  5 4 5 4   3 3    8 7 8 7   

4. a.

2 z  7,5 z  8, z 

b.

b.

10 3   4 11     7 4

7. a.

 2 110  12 21    14 11

b. Not possible 6 5  x  53 5 4  y    43     

8. a.

3, 0,5

c. Inconsistent; no solution 5. a.

23

b.

 3 4 1  6 0 2  

c.

 0 0 0  0 0 0  

6 5  5 4  

b.

c

 4 5     5 6

 4 5  53  3 X  A1 B         5 6  43 7  3 round stickers and 7 rectangular stickers

6. a.

23   18  16 22    27 17 

9.

8 5  3 5 1 0  3 5 8 5 1 0 5 3  5 8  0 1  and  5 8 5 3  0 1           

10.

3, 7  , 7,3

11.

175, 375, and 1100 tickets in sections A, B, and C, respectively

12.

3 brass rods, 4 steel rods, 1 aluminum rod

.

1

A8-1 Chapter 8 Answers: Form A 4. a. 48 inches, 50 inches, 52 inches, 54 inches, and 56 inches

1.

b.

Ln  48  2  n  1

c. 638 inches 5. a. 6,

2.

Maximum of 36 at 3, 4

3. a.

7, 3, 1, 5, 9

b.

3 an  6   4

c.

6561 8192

6. a.

b. 3, 6, 9, 12, 15

9 27 , 2 8 n 1

2  x  h   3  x  h   10 2

 2 x 2  2h 2  4hx  3x  3h  10

7.

32 x5  80 x 4 y  80 x3 y 2  40 x 2 y 3  10 xy 4  y 5

8.

AB  3 17, BC  2 17, AC  5 17; AB  BC  AC

9.

Radius: r  3; Center: C 1, 2

b.

4 x  2h  3

c.

4x  3

11. a. Center: C  2, 4 b. Endpoints (major axis): 1, 4 , 5, 4

10.

c. Endpoints (minor axis): 2, 6 , 2, 2 12. a. Circle b. Ellipse c. Hyperbola d. Parabola

.

Chapter 8 Answers: Form B A8-2 4. a. 36 inches, 39 in, 42 inches, 45 inches, and 48 inches

1.

b.

Ln  36  3  n  1

c. 432 inches 5. a. 10,

2.

Maximum of 30 at 7, 6

3. a.

5, 2, 1, 4, 7

b.

b.

2 an  10   3

c.

1280 2187

6. a.

4, 8, 12, 16, 20

20 40 , 3 9 n 1

4  x  h  2  x  h  5 2

 4 x 2  4h 2  8hx  2 x  2h  5

b. 8 x  4h  2 c. 8 x  2 7.

x5  15 x 4 y  90 x3 y 2  270 x 2 y 3  405 xy 4  243 y 5

8.

AB  3 10, BC  2 10, AC  5 10; AB  BC  AC

9.

Radius: r  4; Center: C 3, 2

11. a. Center: C  1, 2 b. Endpoints (major axis): 1,  1 ,  1,5

10.

c. Endpoints (minor axis): 3, 2 , 1, 2 12. a. Parabola b. Hyperbola c. Circle d. Ellipse

.

A8-3 Chapter 8 Answers: Form C 4. a. 42 inches, 44 inches, 46 inches, 48 inches, 50 inches

1.

b.

Ln  48  2  n  1

c. 510 inches 5. a.

2.

Maximum of 20 at 5, 6  1

3. a.

7, 2, 3, 8, 13

4,

15 45 , 2 4

b.

3 an  5   2

c.

98, 415 512

n 1

6. a. 3  x  h   2  x  h   7 2

b. 5, 10, 15, 20, 25

 3x 2  3h 2  6hx  2 x  2h  7

b. 6 x  3h  2 c. 6 x  2 7.

243 x5  405 x 4 y  270 x3 y 2  90 x 2 y 3  15 xy 4  y 5

8.

AB  3 26, BC  2 26, AC  5 26; AB  BC  AC

9.

Radius: r  2; Center: C  4,3

11. a. Center: C  3,1 b. Endpoints (major axis):  7,1 , 1,1

10.

c. Endpoints (minor axis):  3, 1 ,  3,3 12. a. Ellipse b. Parabola c. Hyperbola d. Circle

.