study guide for ci 0832 algebra review table of...

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Study Guide for CI 0832 Algebra Review

Table of Contents

Revised 1 September 2016

Syllabus for CI 0832 Algebra Review, Distance Learning Section .................................. 1

The Three Steps of Each Lesson ....................................................................................... 6

Registering to Use the Software ........................................................................................ 7

Submission 1: Sec R.2 Order of Operations ................................................................... 11

Textbook Homework for Section R.2 Order of Operations ................................. 14

Checkpoint for Sec R.2 Order of Operations ....................................................... 15

Submission 1: Sec R.2 Order of Operations ........................................................ 16

Submission 2: Section R.3 Expressions ......................................................................... 17

Text Homework for Sec R.3 ................................................................................... 17

Checkpoint for Sec R.3 .......................................................................................... 17

Submission 2: Sec R.3 Expressions ..................................................................... 18

Submission 3: Section 1.1 Linear Equations .................................................................. 19

Text Homework for Sec 1.1 .................................................................................... 19

Checkpoint for Sec 1.1 ........................................................................................... 19

Submission 3: Sec 1.1 Linear Equations .............................................................. 20

Submission 4: Section 1.2 Linear Inequalities ............................................................... 21



Submission 4: Sec 1.2 Linear Inequalities ........................................................... 22

Submission 5: Section 1.4 Absolute Value Equations & Inequalities ........................... 23



Submission 5: Sec 1.4 Absolute Value Equations and Inequalities ................... 24

Submission 6: RE1-Review for Exam 1 ........................................................................... 25

Text Homework for RE1 ......................................................................................... 25

Submission 6: RE1-Review for Exam 1 ................................................................ 25

Exam 1 on Chapters R and 1 ............................................................................................ 26

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Submission 7: Section 2.1 X - Y Graphing ...................................................................... 27



Submission 7: Sec 2.1 X - Y Graphing .................................................................. 28

Submission 8: Section 2.2 Relations and Functions ..................................................... 29



Submission 8: Sec 2.2 Relations and Functions ................................................. 30

Submission 9: Section 2.3 Function Notation ................................................................ 31



Submission 9: Sec 2.3 Function Notation ............................................................ 32

Submission 10: Section 2.4 Graphs ................................................................................ 33



Submission 10: Sec 2.4 Graphs ............................................................................ 34

Submission 11: Section 2.5 Equations of Lines ............................................................. 35



Submission 11: Sec 2.5 Equations of Lines ......................................................... 36

Submission 12: Section 3.1 Systems of Linear Equations ............................................ 37



Submission 12: Sec 3.1 Systems of Linear Equations ........................................ 38

Submission 13: Section 4.1 Rules for Exponents .......................................................... 39



Submission 13: Sec 4.1 Rules for Exponents ...................................................... 40

Submission 14: Section 4.2 Polynomial Functions ........................................................ 41



Submission 14: Sec 4.2 Polynomial Functions .................................................... 42

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Submission 15: Section 4.3 Multiplying Polynomials .................................................... 43



Submission 15: Sec 4.3 Multiplying Polynominals .............................................. 44

Submission 16: Section 4.4 Dividing Polynomials ......................................................... 45



Submission 16: Sec 4.4 Dividing Polynomials ..................................................... 46

Submission 17: Section RE2 Review for Exam 2 ........................................................... 47


Submission 17: RE2-Review for Exam 2 .............................................................. 47

Exam 2 on Chapters 2, 3, and 4 ....................................................................................... 48

Submission 18: Section 5.1 GCF and Factoring by Grouping ...................................... 49



Submission 18: Sec 5.1 GCF and Factoring by Grouping .................................. 50

Submission 19: Section 5.2 Factoring Trinomials.......................................................... 51



Submission 19: Sec 5.2 Factoring Trinomials ..................................................... 52

Submission 20: Section 5.3 A General Factoring Strategy ........................................... 53



Submission 20: Sec 5.3 A General Factoring Strategy ....................................... 54

Submission 21: Section 5.4 Polynomial Equations........................................................ 55



Submission 21: Sec 5.4 Polynomial Equations ................................................... 56

Submission 22: Section 6.1 Rational Expressions......................................................... 57



Submission 22: Sec 6.1 Rational Expressions .................................................... 58

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Submission 23: Section 6.2 Multiply and Divide Rational Expressions ....................... 59



Submission 23: Sec 6.2 Multiply and Divide Rational Expressions ................... 60

Submission 24: Section 6.3 Add and Subtract Rational Expressions .......................... 61



Submission 24: Sec 6.3 Add and Subtract Rational Expressions ...................... 62

Submission 25: Section 6.5 Rational Equations ............................................................ 63



Submission 25: Sec 6.5 Rational Equations ........................................................ 64

Submission 26: Section RE3 Review for Exam 3 ........................................................... 65


Submission 26: RE3-Review for Exam 3 .............................................................. 65

Exam 3 on Chapters 5 and 6 ............................................................................................ 66

Submission 27: Section 7.1 Radical Expressions .......................................................... 67



Submission 27: Sec 7.1 Radical Expressions ...................................................... 68

Submission 28: Section 7.3 Rational Exponents & Simplify Radical Expressions ..... 69



Submission 28: Sec 7.3 Rational Exp & Simplify Radical Express .................... 70

Submission 29: RFin Final Exam Review ........................................................................ 71

Homework for RFin ................................................................................................ 71

Answers to Review for the Final Exam ................................................................. 73

Submission 30: Course Evaluation ................................................................................. 78

Final Exam on Chapters R, 1, 2, 3, 4, 5, 6, and 7 ............................................................. 79

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Syllabus for CI 0832 Algebra Review, Distance Learning Section

Instructor: Douglas Robertson, 270D Peik Hall, [email protected], 612-625-1075.

I am a professor in the Department of Curriculum and Instruction (CI), which is in the College of Education and Human Development.

My web site is http://www.z.umn.edu/robertson

My mailing addresses are:

Postal Mail: 125 Peik Hall, 159 Pillsbury Drive SE, Minneapolis, MN 55455-0208 Campus Mail: 125 Peik Hall (delivery code 4301)

Office hours: Check my web site for my current office hours. If you cannot make it during those times contact me and we can schedule something else.

CI Math Courses:

CI 0832 Algebra Review is designed to provide you with the algebra background needed in order for you to be successful in a college level mathematics course. If you scored low on the mathematics placement exam, or if you have been away from algebra for some time, or if you are anxious about starting a college level mathematics course you should consider taking CI 0832. It covers expressions, equations, systems, graphing, factoring, polynomials, rational expressions and equations, and radicals. If you earn a C or better you should be able to take as your next math course CI 1806 College Algebra Through Modeling, Math 1031 College Algebra and Probability, or Math 1051 Precalculus I (prepares you for the calculus sequence), all of which satisfy the Mathematical Thinking graduation requirement.

CI 0832 counts as four credits for the purposes of full-time status, athletic eligibility, and financial aid, but shows up as 0 credits on the transcript.

CI 1806 College Algebra Through Modeling is a 3-credit course that focuses on using algebra to create, interpret, and apply mathematical models (equations and graphs) to real-world settings. This is basically a college algebra course (it is equivalent to Math 1031) but it is geared more toward applications of mathematics than theoretical mathematics. It covers applications of linear, polynomial, rational, exponential, logarithmic, and logistic equations and some counting and probability. This course satisfies the Mathematical Thinking graduation requirement.

Course Prerequisites: If you have questions or concerns as to which mathematics course you should take, check out the document Which Math Course to Take on my web site, or talk to me. For CI 0832 I will assume that you have had algebra in high school and so know some of the basics, such as operations on signed numbers and solving simple equations.

Course Materials: The following are available at the bookstore. The bookstore hours may be found at www.bookstore.umn.edu or by calling 612-625-6000.

• MyMathLab eCourse for Trigsted/Gallaher/Bodden Intermediate Algebra Access Card Plus eText Reference, 2/E. The ISBN for the bundle is 9780321990501. This bundle contains the access code you will need to log on to the software and a printed copy of the textbook.

• Calculator A $15 scientific calculator is sufficient for this course. If you already have a graphing calculator it will be fine to use that but a scientific calculator is all you need.

• Miscellaneous supplies including pens, pencils, stapler, scissors, paper, file folders. For graph paper, see http://www.z.umn.edu/robertson

http://campusmaps.umn.edu/peik-hall

http://news.cehd.umn.edu/category/departments/curriculum-and-instruction/

http://education.umn.edu/

http://www.z.umn.edu/robertson

http://www.bookstore.umn.edu/

http://www.z.umn.edu/robertson

SG2 COURSE OVERVIEW

Course Objectives: CI 0832 is designed to help you build the skills and understand the concepts of high school algebra so you can be successful in a college level mathematics course.

Pedagogy: To be successful you must take an active role in your own instruction. You will be responsible for learning the material and for getting help when you have questions. I will monitor your progress and, along with the free tutors (see below), will provide help as you need it.

The primary source of new material in this course will be multimedia software, which includes the eTextbook. They will explain mathematical concepts and theory and show you procedures typically used to solve algebra problems.

Pacing: In the packet I sent you that contains the lesson Submission Sheets, there is a SUGGESTED calendar for when you should do the assigned work. The course pacing is completely up to you but the best strategy is to work on math every day so you keep up the momentum and do not forget too much. But, you must finish all the work and exams by the last day of the course.

Course Difficulty: Although this course covers material typically found in high school algebra, the pace, difficulty, level of abstraction, and expectations are much higher. Instructors of other courses (higher math, science, economics, business, psychology, sociology) will expect you to be able to do algebra, especially those skills related to graphing, simplifying expressions, and solving equations.

Credits and Workload Expectations: One credit is designed to correspond to an average of 3 hours of learning effort per week necessary for an average student to achieve a C in the course. So, a student taking a 4 credit course that meets for 4 hours a week should expect to spend an additional 8 hours per week on coursework outside the classroom. This means that an average student can expect to spend about 12 hours per week on this course. If math is a difficult subject for you then you will have to spend more hours on it.

Extra Credit: There are no opportunities for earning extra credit in this course. Your grade will be based solely on your scores on the homework and exams.

Getting help: Here are some resources that you may find useful:

• Get help from me: You are welcome to come to my day school sections, which meet in 302 Appleby Hall. Check my web site for the days and times.

• Get help from free mathematics tutors: Free tutors are available through the SMART Learning Commons. To see their current hours of operation and to sign up to work with a tutor, check out their web site at https://www.lib.umn.edu/smart

Free tutors are available through the Multicultural Center for Academic Excellence. MCAE has an instructional center in 141 Appleby Hall. The Center is a place where students can take their time to learn and where students are not afraid to ask questions. For tutoring schedules go to http://www.mcae.umn.edu/acadsupport/index.html

• Get help from a private tutor: The School of Mathematics has information on hiring a private mathematics tutor at http://www.math.umn.edu/undergrad/

https://www.lib.umn.edu/smart

http://www.mcae.umn.edu/acadsupport/index.html

http://www.math.umn.edu/undergrad/

COURSE OVERVIEW SG3

• Get help on computer issues: Go to the Tech Stop in rooms 101 Coffman Union, 90 Blegen Hall (West Bank), and 4 Saint Paul Student Center. They generally are open Monday through Friday from 8 am to 6 pm and on Saturdays from Noon to 5 pm. A list of their free services is available at http://it.umn.edu/help Anyone at the U can schedule an appointment online to meet with a technician at Tech Stop. You can also phone them at 612-301-4357 or send an email to [email protected]

• Get help on academic issues: If you would like to get some help in areas such as how to read more efficiently, how to study better for tests, or how to manage time more effectively check out the Student Counseling Services at http://www.uccs.umn.edu/academic.htm

• Get help on navigating the U: Your academic adviser is there to help you in any way he or she can. Ask your adviser any questions you have on scheduling, requirements, child care, etc.

• Get help on conflict resolution: The Student Conflict Resolution Center works with students to resolve campus-based problems and concerns. The services are free and confidential. http://www.sos.umn.edu/

Homework Problems: Practicing the skills you learn is of utmost importance. In order to be able to use mathematics you must become automatic at doing symbolic manipulation, such as simplifying expressions and solving equations. Like learning to dance, to play the piano, or to read, learning mathematics involves lots of memorization of what people before you have discovered and then you practicing it until it becomes second nature to you. As the problems become more complex and difficult you will have to perform basic operations and manipulations without thinking about them — they must be automatic. Homework is designed to get you to practice the skills.

Homework is assigned according to the schedule listed for each lesson (see below). Be sure to do every assigned problem and to check every answer in the back of your textbook. Do more than the assigned problems if you are having difficulty with a particular topic. Doing mathematics is the only way you can learn it.

Homework ID Numbers: I will assign you a homework ID number (HWID) that will be used to identify your written work. Write this HWID on everything you turn in for grading.

Writing and Turning in Homework Assignments: A list of the problems you are to do and hand in for grading is listed for each submission (see below).

On lined notebook paper or graph paper, write out the solution to each assigned problem, and circle your answer. You will be graded on your written solution—not only your answer—so be sure to SHOW YOUR WORK. You may write on both sides of the paper. Be sure to write clearly and large enough so that I can read it. I must process thousands papers during the semester and so I cannot spend time trying to figure out messy or unclear papers.

http://it.umn.edu/help

mailto:[email protected]

http://www.uccs.umn.edu/academic.htm

http://www.sos.umn.edu/

SG4 COURSE OVERVIEW

Homework Grading: To receive full credit for homework and exam problems, you must show the mathematical steps necessary to solve the problems. Your written work is meant to “communicate” to me what you know about math, not just the answers, so your work must be neat, organized, and complete. For each problem, be sure to check the answer so you can see if your procedure is correct.

Exams: Exams are designed to help determine how much algebra you know and can do. They help pinpoint those areas where you need to do additional study and they are a significant part of your final course grade, which is used to certify your level of accomplishment in algebra. The exams will be open book and notes and you may use a calculator.

Types of Exam Questions: Exams will contain 10 to 20 questions that ask you to apply what you have learned by carrying out mathematical operations in order to solve problems. I will not ask you to define specific terms or properties or to list specific procedures but you will need to know definitions, properties, and procedures in order to do the problems. For example, I might ask you to “Solve 2(x – 7) = –3x + 1.” You will have to know what the word “Solve” means in relation to an algebraic equation, and you will have to know the steps needed to solve an equation, and you will have to do it without making any errors. I will grade you mostly on how you solved the problem rather than on the answer. This means you must show all your work. If you simply write down the answer you will get 0 points for the problem, even if your answer is correct. If you show your work and make a simple arithmetic error (like 2 2 5 ) you will get almost all of the points for the problem. Your

written solution to the above example should look like that shown on the right.

If you were to simply write down 3 for the answer and show little work you would get 0 points.

How to Study for and Write an Exam: An exam is intended to demonstrate what you have learned so I can give you a grade and so you can re-study those parts of the curriculum you have not yet mastered. To really find out what you know I would have to ask you at least two questions covering every topic and subtopic you studied. This is not possible because the exam would have hundreds of questions. So, I select a representative sample of what was covered and ask you to solve those problems. I select problems that are similar to the ones you did for homework. You will do well on the exams if you understand the concepts behind the homework problem solutions.

Here are some steps you should follow when preparing for an exam:

1. Faithfully go through the software. Carefully go through the worked examples so you understand them. Take written notes on what you do. Remember, the computer software takes the place of me lecturing so this is where you will learn the concepts and procedures you will need to solve homework and exam problems. It has plenty of videos and extra instruction that you can use as you see fit.

2. Complete and hand in every homework problem assigned. These are designed to give you practice at the skills and procedures I think are important. If particular problems give you difficulty, work on them again and again until you can find their solutions quickly and accurately and you understand why you are doing what you are doing.

Writing formulas, properties, and procedures on 3 by 5 note cards is a great way to help you memorize them.

3. Pay particular attention to the exam review problems. I make up exams by choosing questions that are similar to those on the review. If you understand and can do the exam review questions you will be well prepared for the real exam.

2 7 3 1

2 14 3 1

3 3

5 14 1

14 14

5 15

5 15

5 5

3

x x

x x

x x

x

x

x

x

COURSE OVERVIEW SG5

4. Read the exam questions carefully and be sure you understand what they are asking. Write out complete solutions and show all the steps needed to solve each problem. The more you do in your head the more likely you are to make mistakes and the less partial credit you will earn.

Remember, I grade your entire solution and not just your final answer. The correct answer earns 0 points if it is not supported by the proper algebraic steps. I am not trying to measure how smart you are; I am trying to measure how much algebra you know and can do.

5. When you get the graded exam back go over the problems you missed and get help if you need it. You will need to know the material covered on the exam for later work and you will see similar problems on the final exam. Figuring out what you did wrong right after the exam is a good strategy for future success.

Final Course Grades: The weights for the items that count in your final grade are as follows: Homework counts 10%; Midterm Exams count 60%; Final counts 30%

Letter Grades: Letter grades are assigned as follows:

Grade Total Points needed A = 4.00 95 Represents achievement that is outstanding relative A– = 3.67 90 to the level necessary to meet course requirements.

B+ = 3.33 87 B = 3.00 83 Represents achievement that is significantly above B– = 2.67 80 the level necessary to meet course requirements.

C+ = 2.33 77 C = 2.00 73 Represents achievement that meets the course C– = 1.67 70 requirements in every respect.

D+ = 1.33 67 Represents achievement that is worthy of credit even D = 1.00 65 though it fails to meet fully the course requirements.

S none 70 Represents achievement that meets or exceeds the course requirements in every respect.

F = 0.0 under 65 Represents a failure to meet course requirements. N = 0.0 under 70

Grades of Incomplete: Incompletes are normally not given in math courses but are possible. Talk to me if your situation warrants consideration of this.

Next Math Course: When registration for next semester rolls around, feel free to call or email me to talk about which math course you should take next. This will be my best guess based on your work in the course to date, and it assumes that your performance for the rest of the course will be at least as good as your performance during the first two-thirds of the course.

Reports: Several times during the semester, progress reports will be emailed to your U of M Gmail account. If you use a different account, be sure to forward email from your U of M account to your preferred account. To do that log on to your U of M Gmail account, click the down arrow next to the gear (on the upper right) and select Settings. Click Forwarding and POP/IMAP. Click Add a forwarding address and follow the directions after that.

SG6 COURSE OVERVIEW

Disability Accommodations: Reasonable accommodations will be provided for students with disabilities. The staff at Disability Services will determine appropriate accommodations through consultation with the student. More information is available at https://diversity.umn.edu/disability/

Complaints Regarding Teaching/Grading: Students with complaints about teaching or grading should first try to resolve the problem with the instructor. If no resolution can be reached, students may then discuss the matter with the Chair of the Department of Curriculum and Instruction who will attempt to mediate. Failing an informal resolution, the Department Chair will facilitate filing a formal complaint.

Mental Health Issues: If you or a friend are having mental health issues that you cannot handle, you might want to take advantage of the services offered by the University through its mental health web site, http://www.mentalhealth.umn.edu/ This site is designed for students, parents, faculty, and staff who are looking for student mental health information and related resources at the University of Minnesota, Twin Cities campus.

Boynton Health Service http://www.bhs.umn.edu/east-bank-clinic/index.htm offers counseling, urgent consultation, group therapies, medication assessment/management, social work assistance, and chemical health assessment/treatment. Hours are Monday 8 am to 6 pm, and Tuesday through Friday 8 am to 4:30 pm. Consultation about student situations is available by phone at 612-624-1444.

Crisis/Urgent Consultation/After Hours Consultation is available 24 hours a day at 612-379-6363 or 1-866-379-6363 (toll free). If there is a life-threatening emergency, by all means call 911.

The Three Steps of Each Lesson

To learn the material in the most efficient way, follow the steps given below:

Step 1 Computer

The computer software will take the place of the lectures I normally give in a math class. It will present the ideas, concepts, and procedures for each topic, show you examples, ask you questions, give you hints if you need them, evaluate your answers, and show you the correct solutions to each problem. The advantage of a computer-mediated system is that you can go as fast or as slow as you wish, you can go back to interact with parts of the computer lecture as often as you wish, and you can do the work at any time and in any location that has a computer and internet connection.

The disadvantage of a computer-mediated approach is that you don’t have a live human to describe the mathematics to you. If you need a human to lecture you, you will have to take a high school algebra review course at some other college. Be honest with yourself. Some people do not interact well with computers.

Step 2 Homework

After you complete a computer lesson you will use paper and pencil to work out the solutions to the assigned textbook homework problems. These problems will help you practice what you have learned so that it sticks with you and so that you can perform well on the exams. You will turn in this work for grading.

https://diversity.umn.edu/disability/

http://www.mentalhealth.umn.edu/

http://www.bhs.umn.edu/east-bank-clinic/index.htm

COURSE OVERVIEW SG7

After completing the textbook homework problems, you will work out the solutions to 4 "Checkpoint" problems in this Study Guide. These problems are like open book and notes mini-quizzes to see if you have mastered the material. The answers to the Checkpoints are not provided so you have to be very careful as you work the solutions.

Step 3 Submit

When you complete the computer work, assigned textbook homework, and Checkpoint problems for a lesson, arrange your papers as follows:

Homework Submission Sheet on top. Completed textbook problems next. Completed Checkpoint problems at the end.

Staple the packet in the upper left corner. Mail or bring the packet to the address on the Homework Submission Sheet. I will grade your work and send it back to you. Don’t hand in an incomplete packet; keep the packet until you have completed all the assigned work for that submission.

Registering to Use the Software

In order to use the software you must purchase an access code at the bookstore (it comes bundled with the textbook). Do NOT buy the code online from someone else since their code most likely will not work for our course. If you have not bought the access code by the time you wish to start your work you can still get set up to use the software for free for 14 days. Be sure to buy and enter your access code before the end of the two-week period or you will be locked out.

Follow these steps to register:

1. Open your web browser. I used Internet Explorer but FireFox or Chrome will also work.

2. In the address box, type mymathlab.com

Tap Enter to get:

3. To register, on the right under Register Now, click STUDENT.

The following screen will appear:

SG8 COURSE OVERVIEW

4. Click OK! Register now and then type our course ID, which is robertson16906

Click Continue. You will see this:

5. Click Create. Fill in the requested information and check I accept license agreement.

Click Create Account. You will see the following:

Makeup any name you wish or use your email

COURSE OVERVIEW SG9

If you have an Access Code from the Bookstore, click Access Code and enter it.

If you want to buy an Access Code, click Use a Credit Card or PayPal.

If you do not have an Access Code or Credit Card right now, click Get temporary access without payment for 14 days. That gives you two weeks to use the software before having to buy a code.

6. I clicked Get temporary access without payment for 14 days. When asked if I was sure, I clicked Yes.

7. To start working, click Go to My Courses.

8. To open our course click CI 0832 Algebra Review

The next time you go to type mymathlab.com you will click and enter your username and password. Then, click on our course and begin your work.

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Submission 1: Sec R.2 Order of Operations

After you sign in and click our course icon you will see a screen like this:

1. On the left, click Read eText and then click multimedia eText.

You will see the electronic version of the textbook.

You can access any part of the eText by clicking its name under Table of Contents.

2. You will begin with the review so click Review Chapter

You will see the names of the three sections in the review chapter.

I assume that you know the material in R.1 Sets of Numbers so I did not assign any problems from that section. However, you might want to skim it as a refresher.

SG12 SUBMISSION 1: SECTION R.2 ORDER OF OPERATIONS

3. Click R.2 Order of Operations and Properties of Real Numbers.

This is basically page R-12 of the printed textbook.

Each section begins with a THINGS TO KNOW part that tells you what you should have already mastered before attempting the new lesson.

4. Click You Try It next to 1. Compute the Absolute Value for a sample problem that you can work on. Work out the solution, type it in the answer box, and then click Check Answer (lower right corner of the screen). You will be given feedback on your answer. After three tries the answer will be given to you. When you are done you can close the You Try It window and the R.2 window will appear again.

5. If you want to go to where Absolute Value was explained in detail in the book, click

To get back to page R.2-1, click Last Page Visited (upper left corner of screen)

6. To see a video on how to compute absolute value, click

SUBMISSION 1: SECTION R.2 ORDER OF OPERATIONS SG13

7. When you are ready to begin lesson R.2, click Next page (upper left corner).

This shows the four objectives of this lesson. Most of the time you will do all of the objectives. However, for this first lesson, you will do only Objective 4. If you think you need a review of the other three objectives click on the ones you want. In any case, you might want to skim those pages just to be sure you know that material, but there are no homework problems associated with those objectives.

8. Click Use Order of Operations This takes you to page R.2-28 (page R-23 in the printed text).

If you have a large screen, you might want to display two pages at a time. If so, click

If you want to show the entire page on the screen, click

9. Read the text and study the worked examples. Click words in red to see their definitions.

Here, I clicked and got this popup box:

To dismiss the box, click the X in the upper right corner.


When you are finished with this page, click the Next Page button to move on to page R.2-29.

When you see this icon, you can click it to see a video that explains the problem.

When you see this icon, you can click it to get a practice problem that you can use to see if you understand the problem being explained.

When you see something like this you can either start doing the assigned problems in the range 73 to 82 or continue with instruction.

10. When you get to the end of instruction, you will see the Exercises page (R.2-33 in the eText and R-26 in the printed text). Now, you can start the assigned homework problems that you will turn in for grading.

11. When you have completed your computer work, click Sign Out in the upper right corner.

Textbook Homework for Section R.2 Order of Operations

On lined notebook paper or graph paper, work out the solutions to the following problems in the textbook. Show your work, check your answers in the back of the textbook, and circle your answers.

Sec Num Page in eText

Page in Print text Problems with solutions to be handed in for grading

R.2 1 R.2-35 R-27 73,75,77,79,81,83,85,87,89,91,93

After you have completed the textbook problems do the Checkpoint problems listed on the next two pages. I do not provide the answers to these so be sure to do them very carefully.

SUBMISSION 1: SECTION R.2 ORDER OF OPERATIONS SG15

Checkpoint for Sec R.2 Order of Operations

After you have completed the computer work and the textbook homework for this section, tear out this page (or photocopy both sides), work out the solutions to the following problems in the spaces provided, and write your answers in the spaces provided. These problems will act as a final check on your understanding and help as you review for the exams.

1. Simplify:

23 2

72 (6 8)5 6

Answer: ________________________

2. Simplify: 28 12 3 • 4 2 3 ( 2) Answer: ________________________


3. Simplify: 2 23 12 4 3 2 3 3 2 Answer: ________________________

4. Simplify: 8 2 8 2 8 2 Answer: ________________________

Submission 1: Sec R.2 Order of Operations

Put your papers in the following order, staple them in the upper left corner, and submit them for grading.

Homework Submission Sheet 1

Textbook problem solutions

Checkpoint for Sec R.2

Due to problems with formatting, viruses, and incompatible systems

do not email lessons to me—you must submit paper copy.

— 17 —

Submission 2: Section R.3 Expressions

Log on to the web site and complete the instruction for this section.

Text Homework for Sec R.3



Page in Print text Problem solutions to be handed in for grading

R.3 2 R.3-11 R-32 1,9,17,25,27,31,33,35,37,41,43,45

After you have completed the textbook problems do the following Checkpoint problems.


1. Simplify: 2 3 5 3 2x x Answer: ________________________

2. Simplify: 8 4 3x Answer: ________________________

SG18 SUBMISSION 2: SEC R.3 EXPRESSIONS

3. 2Simplify: 3 2 4 3 2 1x x x Answer: ________________________

4. 2Evaluate 3 2 3 for 2 and 3xy x y x y Answer: ________________________

Submission 2: Sec R.3 Expressions

Put papers in the following order, staple in the upper left corner, and submit for grading.




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Submission 3: Section 1.1 Linear Equations

Log on to the web site and complete the instruction for this section. SKIP Objective 5.

Text Homework for Sec 1.1




1.1 3 1.1-30 1-14 7,25,27,29,31,35,39,43,47,55,57,59,61,63,65,67


Checkpoint for Sec 1.1

1. Solve: 5 6 2 3 2x x x Answer: ________________________

2. Solve: 3 2 1 4 2 1x x Answer: ________________________

SG20 SUBMISSION 3: SEC 1.1 LINEAR EQUATIONS

3. Solve: 3 3 4 4 7x x x Answer: ________________________

4. 2 1

Solve: 2 3 13 2

x x Answer: ________________________

Submission 3: Sec 1.1 Linear Equations





— 21 —

Submission 4: Section 1.2 Linear Inequalities






1.2 4 1.2-30 1-28 9,11,17,21,23,29,35,41,45,53,55,57,59



1. Solve: 3 3 2x Answer: ________________________

2. Solve:8( 2) 2x x Answer: ________________________

SG22 SUBMISSION 4: SEC 1.2 LINEAR INEQUALITIES

3. Solve: 5 2 3 7x Answer: ________________________

4. Solve:8 4 2 0x Answer: ________________________

Submission 4: Sec 1.2 Linear Inequalities





— 23 —

Submission 5: Section 1.4 Absolute Value Equations &

Inequalities

Log on to the web site and complete the instruction for this section. Note that we SKIP Sec 1.3.





1.4 5 R.2-36 1-44 1,5,11,15,17,23,27,29,33



1. Solve: 2 5 3x Answer: ________________________

2. Solve: 3 2 1 13x Answer: ________________________

SG24 SUBMISSION 5: SEC 1.4 ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

3. Solve: 5 11x Answer: ________________________

4. Solve: 7 3 5 10 38x Answer: ________________________

Submission 5: Sec 1.4 Absolute Value Equations and Inequalities





— 25 —

Submission 6: RE1-Review for Exam 1

Study for Exam 1, which will cover the Review Chapter and Chapter 1. Note that we SKIP Sec 1.5.

Text Homework for RE1

On lined notebook paper or graph paper, work out the solutions to the following problems in the textbook. Show your work, check your answers in the back of the textbook, and circle your answers. Remember that the answers to the even numbered problems are at the back of the online eText but not the printed eText.

HW Num Page in eText


RE1 6 R.2-36 R-27 86,94

R.3-11 R-33 12,14,32,38,42,44

1.1-31 1-15 42,46,62,68

1.2-27 1-29 22,36,44,56,60

1.4-19 1-44 16,31,34

There are no Checkpoint problems.





There are no Checkpoint problems for RE1

— 26 —

Exam 1 on Chapters R and 1

When you are ready to take the exam, send me an email. I will email the exam to you as a pdf file.

Print the exam. If you have difficulty opening attachments, let me know and I will send a paper copy via the US Postal Service.

Write your solutions to the problems on the exam paper. The exam is open book and notes and you may use a calculator but you may not get help from anyone.

Return the completed exam to me in the usual way (US mail, campus mail, or hand deliver). Be sure to attach Submission Form for Exam 1 to the front.

You should complete the exam within 48 hours so be sure you are ready to take it and have set aside an appropriate amount of time (2 hours should do it) before you request it.

I will grade the exam and send it back to you. Let me know if you would like to go over the exam with me and we can set up a time.

— 27 —

Submission 7: Section 2.1 X - Y Graphing






2.1 7 2.1-21 2-9 1,5,11,13,15,17,19,21,23,25



1. Graphby plottingpoints: 2 3y x

2. Graphby plottingpoints: 2 4x y

SG28 SUBMISSION 7: SEC 2.1 X - Y GRAPHING

3. Graphby plotting points: 2 3y x

4. Find the x- and y-intercepts of this graph: Answer: x-intercepts are __________________

Answer: y-intercept is ____________________

Submission 7: Sec 2.1 X - Y Graphing





— 29 —

Submission 8: Section 2.2 Relations and Functions






2.2 8 2.2-16 2-17 1,3,5,7,9,13,15,21,23,25,31



1. Find the domain and range of this function: Answer: Domain: _________________

2,1 , 5,4 , 8,0 , 0,3 Answer: Range: __________________

2. Find the domain and range of this function: Answer: Domain: _________________

Answer: Range: __________________

SG30 SUBMISSION 8: SEC 2.2 RELATIONS AND FUNCTIONS

3. Is this the graph of a function? Answer: ________________________

4. 2Is this a function? 3y x Answer: ________________________

Submission 8: Sec 2.2 Relations and Functions





— 31 —

Submission 9: Section 2.3 Function Notation






2.3 9 2.3-20 2-29 3,5,7,13,17,19,23,25



1.

2 1

Write using function notation.3

yx Answer: f x __________________

Name the function and assumef is the independent variable and is the dependant variable.x y

2. 2Given 3, find 2f x x f Answer: ________________________

SG32 SUBMISSION 9: SEC 2.3 FUNCTION NOTATION

3. Given 4, findf x x f x h Answer: ________________________

4. Plot points to graph 2 1g x x

Submission 9: Sec 2.3 Function Notation





— 33 —

Submission 10: Section 2.4 Graphs






2.4 10 2.4-15 2-40 7,11,13,19,23,25,27,29



1. Graphusing intercepts: 2 8f x x

2. Graph: 5f x

SG34 SUBMISSION 10: SEC 2.4 GRAPHS

3. Graph: 5x

4. Graph: 3 2 6x y

Submission 10: Sec 2.4 Graphs





— 35 —

Submission 11: Section 2.5 Equations of Lines






2.5 11 2.5-33 2-55 1,7,9,11,15,19,21,23,25,29,33,35,37,49,51,53,57,59



1. Find the x-intercept and the y-intercept of 1

62

y x Answer: x-intercept: _______________

Answer: y-intercept: _______________

2. Find the slope of the line that passes through. Answer: ________________________ the points (6, –2) and (–5, 8).

SG36 SUBMISSION 11: SEC 2.5 EQUATIONS OF LINES

3. Find the equation of the line that passes Answer: ________________________ through the point (5,2) and has slope 3.

4. Find the equation of the line that passes Answer: ________________________

through the points (–2,3) and (2,–5).

Write your answer in slope-intercept form ( y mx b ).

Submission 11: Sec 2.5 Equations of Lines





— 37 —

Submission 12: Section 3.1 Systems of Linear Equations

Log on to the web site and complete the instruction for this section. SKIP Objective 6. Note that we skip Sec 2.6.





3.1 12 3.1-33 3-16 1,5,17,19,25,31,35,41,47,49



1. Use substitution to solve:

4

3 4

x y

x y Answer: ________________________

2. Use elimination to solve:

4 5 12

6 10 18

x y

x y Answer: ________________________

SG38 SUBMISSION 12: SEC 3.1 SYSTEMS OF LINEAR EQUATIONS

3. Solve by any method: Answer: ________________________

3 4 2

32

4

x y

y x

4. Solve by any method: Answer: ________________________

5

3 15 3

x y

x y

Submission 12: Sec 3.1 Systems of Linear Equations





— 39 —

Submission 13: Section 4.1 Rules for Exponents






4.1 13 4.1-32 4-14 7,21,25,35,40,67,69,71,73,75,77,79,81,87,88,97



1. 3 8

2Simplify:

x x

x Answer: ________________________

2.

412 3

9 4Simplify:

x x

x x Answer: ________________________

SG40 SUBMISSION 13: SEC 4.1 RULES FOR EXPONENTS

3. 5 2 0

2Simplify:

x y z

xy Answer: ________________________

4. 3

2 02 3 5 2

5Simplify:

xx x x x

x Answer: ________________________

Submission 13: Sec 4.1 Rules for Exponents





— 41 —

Submission 14: Section 4.2 Polynomial Functions






4.2 14 4.2-18 4-23 1,7,9,11,13,17,19,25,29,35,37,41,49



1. 2 4Evaluate 6 4 5 for when -3 and 2x xy y x y Answer: ________________________

2. 3 2 2Simplify: 2 5 5 3 1x x x x Answer: ________________________

SG42 SUBMISSION 14: SEC 4.2 POLYNOMIAL FUNCTIONS

3. 6 2What is the degree of this polynomial? 2 5 6f x x x Answer: ___________________

4. 2 3 2Given: 4 2 1and 5P x x x Q x x x Answer: ________________________

find P Q x

Submission 14: Sec 4.2 Polynomial Functions





— 43 —

Submission 15: Section 4.3 Multiplying Polynomials






4.3 15 4.3-21 4-33 1,2,7,19,23,27,31,37,39,61



1. Mulifply and simplify: 2 3 5 1x x Answer: ________________________

2. Mulifply and simplify: 3 3x x Answer: ________________________

SG44 SUBMISSION 15: SEC 4.3 MULTIPLYING POLYNOMINALS

3. 2

Simplify: 3 2x Answer: ________________________

4. Given 5 2 and 1 findP x x Q x x P Q x Answer: ________________________

Submission 15: Sec 4.3 Multiplying Polynominals





— 45 —

Submission 16: Section 4.4 Dividing Polynomials

Log on to the web site and complete the instruction for this section. SKIP Objectives 4, 5, and 6.





4.4 16 4.4-28 4-45 1,5,7,13,15,19,25



1. 6 10

4

15Divide:

10

m n

m n Answer: ________________________

2. 12 9

4 12

24 5Divide:

15

x y

x y Answer: ________________________

SG46 SUBMISSION 16: SEC 4.4 DIVIDING POLYNOMIALS

3.

3 23 2 5Divide using long division:

1

x x x

x Answer: ________________________

4. 3Divide using long division: 2 3 4 2x x x Answer: ________________________

Submission 16: Sec 4.4 Dividing Polynomials





— 47 —

Submission 17: Section RE2 Review for Exam 2

Study for Exam 2, which will cover Chapters 2, 3, and 4.





RE2 17 2.1-22 2-10 18,20,24

2.2-18 2-19 24,26

2.3-21 2-29 24,26

2.4-15 2-40 18,24,26,28

2.5-35 2-56 18,22,24,34,50,54,58

3.1-34 3-16 20,36,52

4.1-34 4-15 72,76,82

4.2-19 4-24 28,36,40,46

4.3-21 4-33 6,8,28,40

4.4-28 4-45 10,26







— 48 —

Exam 2 on Chapters 2, 3, and 4







— 49 —

Submission 18: Section 5.1 GCF and Factoring by Grouping






5.1 18 5.1-18 5-8 15,17,23,25,27,29,35



1. 4 8 10Find the GCF of 24 , 18 and 36x x x Answer: ________________________

2. 4 3 2 5 2Factor out the GCF: 20 2 4x y x y x y Answer: ________________________

SG50 SUBMISSION 18: SEC 5.1 GCF AND FACTORING BY GROUPING

3. 3Factor: 2 3 4 3 3 4x x x Answer: ________________________

4. 2Factor by grouping:10 5 4 2x xy x y Answer: ________________________

Submission 18: Sec 5.1 GCF and Factoring by Grouping





— 51 —

Submission 19: Section 5.2 Factoring Trinomials






5.2 19 5.2-31 5-23 1,3,5,11,15,19,21,23,25,51,55,59,65,67,71,75,77



1. 2Factor: 5 6x x Answer: ________________________

2. 3 2Factor: 3 15 18x x x Answer: ________________________

SG52 SUBMISSION 19: SEC 5.2 FACTORING TRINOMIALS

3. 2Factor: 2 28x x Answer: ________________________

4. 6 3Factor: 8 6x x Answer: ________________________

Submission 19: Sec 5.2 Factoring Trinomials





— 53 —

Submission 20: Section 5.3 A General Factoring Strategy






5.3 20 5.3-23 5-35 1,7,13,19,23,31,35,41,43,61,67,71,73,77



1. 2Factor:16 24 9x x Answer: ________________________

2. 2Factor: 4 25x Answer: ________________________

SG54 SUBMISSION 20: SEC 5.3 A GENERAL FACTORING STRATEGY

3. 3Factor: 8 125x Answer: ________________________

4. 3 2Factor: 5 20x xy Answer: ________________________

Submission 20: Sec 5.3 A General Factoring Strategy





— 55 —

Submission 21: Section 5.4 Polynomial Equations

Log on to the web site and complete the instruction for this section. Do Examples 1, 2, and 3 ONLY.





5.4 21 5.4-25 5-47 1,2,7,11,17,19,23,25



1. Solve: 2 0x x Answer: ________________________

2. 2Solve: 7 10 0x x Answer: ________________________

SG56 SUBMISSION 21: SEC 5.4 POLYNOMIAL EQUATIONS

3. 2Solve: 6 5x x Answer: ________________________

4. 2Solve:11 6 3x x Answer: ________________________

Submission 21: Sec 5.4 Polynomial Equations





— 57 —

Submission 22: Section 6.1 Rational Expressions






6.1 22 6.1-20 6-9 1,5,7,11,17,19,21,23,37,47



1.

2

2Find the domain:

2 3

x

x x Answer: ________________________

2.

2

2

2 1Reduce:

1

x x

x Answer: ________________________

SG58 SUBMISSION 22: SEC 6.1 RATIONAL EXPRESSIONS

3.

2

2

5 6Reduce:

9

x x

x Answer: ________________________

4.

2

2

2 3 2Reduce:

6 5 1

x x

x x Answer: ________________________

Submission 22: Sec 6.1 Rational Expressions





— 59 —

Submission 23: Section 6.2 Multiply and Divide Rational

Expressions






6.2 23 6.2-17 6-17 1,5,11,15,29,41,45,53,61



1. 2

3

5Simplify:

12 4

x y xy

z w zw Answer: ________________________

2.

6

4

3

5

8

Simplify:12

x

y

x

y

Answer: ________________________

SG60 SUBMISSION 23: SEC 6.2 MULTIPLY AND DIVIDE RATIONAL EXPRESSIONS

3.

2 2

2 2

2 3 3 7 6Simplify:

2 1 6 2

x x x x

x x x x Answer: ________________________

4. 2

2 3 8

7 9 3Simplify:

y x y x

x x x Answer: ________________________

Submission 23: Sec 6.2 Multiply and Divide Rational Expressions





— 61 —

Submission 24: Section 6.3 Add and Subtract Rational

Expressions






6.3 24 6.3-31 6-32 5,9,11,15,47,53,63,67,69,79



1.

1 1Simplify:

2 2x x Answer: ________________________

2.

1 1Simplify:

2 2x x Answer: ________________________

SG62 SUBMISSION 24: SEC 6.3 ADD AND SUBTRACT RATIONAL EXPRESSIONS

3.

2 2

3 12 2 3Simplify:

2 3 2 3

x x

x x x x Answer: ________________________

4. 2

2 3Simplify:

2 35 7

x

x x x Answer: ________________________

Submission 24: Sec 6.3 Add and Subtract Rational Expressions





— 63 —

Submission 25: Section 6.5 Rational Equations

Log on to the web site and complete the instruction for this section. SKIP Objective 5. Note that we SKIP sec 6.4.





6.5 25 6.5-35 6-58 5,7,9,15,17,19,21,23,25



1.

2

Solve: 56 2

x x Answer: ________________________

2. 15 6

Solve: 3x x

Answer: ________________________

SG64 SUBMISSION 25: SEC 6.5 RATIONAL EQUATIONS

3.

3 2 1

Solve:3 2

x x

x x Answer: ________________________

4. 2

4 1 12Solve:

3 3x x x x Answer: ________________________

Submission 25: Sec 6.5 Rational Equations





— 65 —

Submission 26: Section RE3 Review for Exam 3

Study for Exam 3, which will cover Chapters 5 and 6.





RE3 26 5.1-18 5-8 16,36

5.2-31 5-23 12,58,66,76

5.3-24 5-35 40,62,76

5.4-25 5-47 14,16,24

6.1-21 6-9 18,26

6.2-17 6-17 12,30,44

6.3-34 6-33 72,74

6.5-35 6-58 14,22







— 66 —

Exam 3 on Chapters 5 and 6







— 67 —

Submission 27: Section 7.1 Radical Expressions

Log on to the web site and complete the instruction for this section. SKIP Objectives 4 and 5.





7.1 27 7.1-15 7-8 5,7,17,21



1. Evaluate: 64 Answer: ________________________

2. 3Evaluate: 125 Answer: ________________________

SG68 SUBMISSION 27: SEC 7.1 RADICAL EXPRESSIONS

3. 2

Simplify: 8x Answer: ________________________

4. 2Simplify: 16 64x x Answer: ________________________

Submission 27: Sec 7.1 Radical Expressions





— 69 —

Submission 28: Section 7.3 Rational Exponents & Simplify

Radical Expressions

Log on to the web site and complete the instruction for this section. Note that we SKIP sec 7.2.



Sec Num

Page in

eText

Page in

Print text Problem solutions to be handed in for grading

7.3 28 7.3-28 7-28 1,3,11,17,21,23,29,31,35,37,39,41,49,51,53,55,57,59,61,65,71,75



1. 2/3Write as a radical expression: x Answer: ________________________

2. 1/2 1/6 1/10Simplify and write as a radical expression: x x x Answer: ________________________

SG70 SUBMISSION 28: SEC 7.3 RATIONAL EXP & SIMPLIFY RADICAL EXPRESS

3. 53Simplify: 250x Answer: ________________________

4. 3 8Simplify: 54a b Answer: ________________________

Submission 28: Sec 7.3 Rational Exp & Simplify Radical Express





— 71 —

Submission 29: RFin Final Exam Review

Study for the Final Exam, which will cover the Review Chapter and Chapters 1 through 7. The final

exam will have 14 problems that are similar to the Checkpoint problems you did throughout the semester. A good study strategy is to go through those problems again and review things you have forgotten and also to carefully work out the solutions to the following homework problems.

There are no Checkpoint problems for RFin.

Homework for RFin

On lined notebook paper or graph paper, work out the solutions to the following problems.

1.

2

5 15 ( 5)Simplify: 2

10 3 2 2. Simplify: 5(4 3) 2( 1)x x x

3. 2Evaluate 4 3 5 ( 1) for 2, 4x y xy x x y 4. Solve: 5(4 3) 2( 1) 7 9x x x

5. Solve: 1 1

2 ( 6) 12 6

y y 6. Solve: 14 2 4 0x

7. Graph 2 6 12x y 8.

22 3

3 5

2 3Simplify:

12

x x y

x y

9. Find the equation of the line that passes through the points (2, 3) and (–4, 5).

Write your answer in slope-intercept y mx b form.

10. Find the slope of a line that is perpendicular to the line 7 4 3x y

11. Solve this system: 12. Solve this system:

0.5 2

6 3 12

x y

x y

2 4 6

3 5 13

x y

x y

13. Multiply and simplify: 5 4 2x x 14. Factor 2 5 6x x

15. Factor 2 29 16x y 16. Factor 26 7 20x x

17. Solve 2 8 15 0x x 18. Simplify: 5 12

8 6

18

24

x y

x y

19. Simplify:

2

2

5 6

4

x x

x 20. Multiply:

2 5 4

8

2 25

15 10

x y x

xy y

21. Divide: 2 4 3 2

3

12 8

9 6

x y x y

xy xy 22. Reduce:

2

2

5 6

9

x x

x

23. Multiply:

2 2

2 2

4 45 4 45

81 7 10

x x x x

x x x 24. Divide:

2 2

2 2

2 3 10 21

4 5 9

x x x x

x x x

25. Add: 3 5

10 6

x x 26. Subtract:

2 2

2 2

2 1 1

x

x x x

SG72 SUBMISSION 29: SEC RFIN FINAL EXAM REVIEW

27. Solve: 3 8

5 7

x 28. Solve:

1 2 1

3 4 12

x x

29. Divide: 2 8 2 3x x x 30. Simplify: 6 518x y

31. Simplify: 3128

2 32. Simplify: 3 11 63 54x y z

33. Simplify: 9 53 16x y 34. Simplify: 1/3 3/4x x

35. Write as a radical: 5/6x 36. Write using rational exponents: 34 x

37. Simplify: 12 94

24

486

3

x y

x y 38. Simplify:

9 16

53

64

2

x y

x y

39. Find - and -intercepts of 3 5 15.x y x y

40. 2

Find the equation of the line that passes through 1,2 and which is perpendicular to 10.3

y x

41. Find the equation of the line that passes through 3, 3 and 5,1 .

42. Given 3 6 find a 2 b 0 c 10f x x f f f

43. Simplify:

2 2

5 9 2•

3 3 10 2

x xy y

x y x x x 44. Simplify:

2 2

2 3

12 35 49

x

x x x

45. Solve: 2 4

53x x

46. Solve: 3 2 2 1x

47. Solve: 4 5 2 4 36x 48. Solve: 10 4 2 7 50x

SUBMISSION 29: SEC RFIN FINAL EXAM REVIEW SG73

Answers to Review for the Final Exam

1. 2.

2

5 15 ( 5) 5 ( 3)2 2

10 3 2 10 9 2

82

10 18

82

8

2 1 3

5(4 3) 2( 1) 20 15 2 2

19 13

x x x x x x

x

3. 4.

2

2

4 3 5 ( 1)

4 3 5 1

4 4 4 3 40 3

64 3 40 3

4

64 3

2

1

4

20

187

2 2

x x xy y

5(4 3) 2( 1) 7 9

20 15 2 2 7 9

18 13 7 9

11 22

2

x x x

x x x

x x

x

x

5. 6.

1 12 ( 6) 1

2 6

1 16 6 2 6 ( 6) 6 1

2 6

3 12 1 6 6

3 12 6 6

2 24

12

y y

y y

y y

y y

y

y

14 2 4 0

2 2 2

16 4 2

14

2

1or 4

2

1or in interval notation ,4

2

x

x

x

x

7. Find the intercepts and then plot those points.

-intercept:

2 6 0 12

6

So, one point is 6,0 .

x

x

x

y-intercept:

2 0 6 12

2

So, one point is 0, 2 .

y

y


8. 9.

2 22 3 2 2 3 2

3 5 3 5

2 2 6 2

3 5

8 2

3 5

8 3

5 2

5

3

2 3 2 3

12 12

2 3

12

18

12

3

2

3

2

x x y x x y

x y x y

x x y

x y

x y

x y

x

y

x

y

rise 3 5 2 1

run 2 4 6 3

1

3

Use either point to find . I used 2,3 :

13 2

3

9 2

3 3

11

3

1 11

3 3

y mx b

m

y x b

b

b

b

b

y x

10. 11. No solution (parallel lines)

7 4 3

4 7 3

7 3

4 4

7 4so

4 7perp

x y

y x

y x

m m

Solve 0.5 2 for

and use substitution

0.5 2

6 0.5 2 3 12

3 12 3 12

12 12

This is a contradiction so no solution

x y x

x y

y y

y y

12. 1, 2 13. 25 14 8x x

14. 6 1x x 15. 3 4 3 4x y x y

16. 2 5 3 4x x 17. 5 or 3x x

18. 6

3

3

4

y

x 19.

3

2

x

x

20. 5

43

x

y 21.

1

x

22.

2

3

x

x 23.

5

2

x

x

24.

2

2

3 3 9or

5 7 12 35

x x x

x x x x 25.

17

15

x


26.

5

1 1 1

x x

x x x 27.

40

21

28. 29.

Multiply by the 12

1 2 112 12 12

3 4 12

4 3 2 1

2 4

2

LCD

x x

x x

x

x

2

2

5

3 8 2

3

5 2

5 15

13

13We can write this as 5

3

or 5 with remainder 13

x

x x x

x x

x

x

xx

x

30. 6 5 3 218 2 3 3 3 2x y xx xx xx yy yy y x y y

31. 333

12864 2 2 2 2 2 2 2 2 4

2

32. 3 11 6 3 2 23 3354 2 3 3 3 3 2x y z xxx yyy yyy yyy yy zzzzzz xy z y

33. 9 5 4/3 9/3 5/3 1 1/3 9/3 1 2/3 1 1 3 1 2 3 23 3 3 316 2 2 2 2 2 2 2x y x y x y y x y y x y y

34. 1/3 3/4 4/12 9/12 13/12x x x x 35. 56 x 36. 3/4x

37.

12 94 12 910 8 4 10 84 44

224

1/4 4/4 10/4 8/4 1/4 1 2 2/4 2 2 2 24

486 486162 2 3

33

2 3 2 3 3 2

x y x yx y x y

x yx y

x y x x y x y x

38. 9 16

15 5 15 5/5 6/5 15/5 1 1/5 15/5 35 5 553

6432 2 2 2 2

2

x yx y x y x y x x y xy x

x y

39. -intercept is 5,0 ; -intercept is 0,3x y

40. Since lines are perpendicular, their slopes are negative reciprocals.

Slope of given line is 2

3 so slope of perpendicular line is

3

2. Now, find b:

3 3 4 3 7

; ; 2 1 ; ;2 2 2 2 2

y mx b y x b b b b So, the equation is 3 7

2 2y x .


41. 2 9y x

42. a 2 0 b 0 6 c 10 6f f f

43.

2 2 2

5 9 2 5 3 • 3xy 2 3• • •

3 3 10 2 3 x + 5 2 2 2xy

x xy y x x

x y x x x x y x y

44.

2

2

2 2

2

2

2 35 7 5

49 7 7

7 5 7

2 3 2 7 3 5• •

12 35 49 7 5 7 7 7 5

2 14 3 15

7 5 7

2 11 15

7 5 7

x x x x

x x x

LCD x x x

x x x x

x x x x x x x x x

x x x

x x x

x x

x x x

45. Multiply by the LCD, which is 3x :

2 45

3

2 43 • 3 • 5 3 •

3

6 15 4

10 15

10

15

2

3

x x

x x xx x

x

x

x

x

46. Isolate the absolute value and then use its definition:

3 2 2 1

2 2 2

2 1

Now, break up this equation into two simple equations:

2 1 or 2 1

1 or 3

x

x

x

x x

x x


47. Isolate the absolute value and then use the fact that u a means a u a .

4 5 2 4 36

5 2 4 40

2 4 8

8 2 4 8

4 2 12

2 6

In interval notation this is 2,6

x

x

x

x

x

x

48. Isolate the absolute value and then use the fact that u a means u a or u a

10 4 2 7 50

4 2 7 60

2 7 15

2 7 15 or 2 7 15

2 8 or 2 22

4 or 11

In interval notation this is , 4 11,

x

x

x

x x

x x

x x

— 78 —

Submission 30: Course Evaluation

During the last two weeks of the semester you will be sent an email telling you that the web-based evaluation for this course is available. To access the evaluation, go to https://moodle.umn.edu/ and scroll down to the section labeled

A link to the evaluations for your courses should be there. The evaluations are only available through the last day of the semester so you must complete them by then. If you do not want to fill out the evaluation, log into the site anyway so the system knows you were there and then exit without answering any of the questions.

We use the Student Ratings of Teaching to help us improve the course for future students. Your candid comments, both positive and negative, are greatly appreciated.

There is nothing to turn in - just access the system.

https://moodle.umn.edu/

— 79 —

Final Exam on Chapters R, 1, 2, 3, 4, 5, 6, and 7


Print the exam.

If you have difficulty opening attachments, let me know and I will send a paper copy via the US Postal Service.


Return the completed exam to me in the usual way (US mail, campus mail, or hand deliver). Be sure to attach Submission Form for Final Exam to the front.


I will grade the exam and let you know your score. I am required to keep it on file for a year. Let me know if you would like to go over the exam with me and we can set up a time.

You're done!

If you would like to talk to me about which mathematics course

you should take next give me a call.

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