Math 098
Intermediate Algebra

Course Introduction

Overview

Welcome to Intermediate Algebra! This online course is designed to cover the same subject areas currently presented in the Math 098 courses on campus at the University of Washington. It covers chapters 1 through 11 of the required text, as well as some additional materials that do not appear in the text. The online course materials provide materials that equate to the lectures you would receive for a course on campus.

Math 098 will provide you with the background needed to continue on in mathematics. The skills you will learn apply to various aspects of your lives. At least half of the assigned problems will demonstrate directly how the concepts presented apply to "real-life" situations. You will learn methods to present data graphically. This will be useful in providing results of your work to your clients or managers. You also will learn how to take data and translate it into a solvable problem statement. This course will help you develop your sense of logic and your problem-solving skills whatever your goals are in mathematics.

For each lesson, you will be required to complete a reading assignment from the textbook, and to read the information presented in the online course materials. Please be sure to read these online course materials and text before beginning each homework assignment. It may seem to save time to just begin the assignment and check the text when you run into trouble, but without the benefit of a lecture, you will find the assignments much easier if you have read the information first. The homework problems will be similar to the examples presented in the lesson.

Problems to be sent in and graded are assigned for each lesson. There are three exams, which will give you an opportunity to verify that you are learning the material.

To succeed in this course, you should have completed "Beginning Algebra" with a grade of 2.0 or better. If it has been a long time since you took a math course, you may wish to review basic algebra before proceeding. However, even if it has been some time since your last course, if you understood the material, you should be able to succeed in this course.

The amount of time required for this course will vary depending on your background and capabilities. An average estimate of time allotment is to spend one hour on the lecture notes, two hours on the text reading assignment, and three to four hours on the assignments. Additional time may be required if the practice assignments or self-tests are used. An estimate for on-campus courses is upwards of two hours of study time for each hour in class, or about three hours per course credit and one hour per assignment. That equals to about 15 hours per assignment, or 150 hours total for this course.

This course consists of 13 lessons. You need to complete the 13 lessons within three months, so you should start on the assignments as soon as you receive the course materials. Then set a goal of completing one assignment every week, and try to stick to that. Please use the "Assignment Due Dates" tool included in the course syllabus to help you plan your schedule. Extensions can be granted under various circumstances, but you should be able to finish the course without an extension if you follow the study schedule that you set.

About the Online Environment

Your online course offers several advantages to the traditional classroom, including the comprehensive Online Student Handbook, the ability to communicate electronically with students and with your instructor, and links to a rich array of online resources.

Online Student Handbook

This handbook answers questions about your online learning course, such as how to purchase your text, schedule an exam, obtain a transcript, and get technical help if you need it. The handbook also provides additional resources, such as how to order books or journals from the library and how to study for an online course.

Communication with Your Instructor and Student Peers

• Online Discussion Forums, designed by the University of Washington award winning Catalyst team, allow you to communicate with other currently enrolled students and with your instructor. We encourage you to use the forum to exchange ideas, resources, and comments about your course work with other students in this course. This unstructured forum is monitored by your instructor.
• You can use e-mail to ask me a question or preferably post your question on the discussion forum. I will reply there.

Online Resources

As an online student, you have access to a wealth of Web resources compiled to provide fast, easy access to information that supports your online learning experience. Organized by subjects, Online Resources link you to sites with help for writing and research, study skills, language learning, and library reference materials. All links have been assessed for credibility and reliability, and they are regularly monitored to ensure their usability.

Course Objectives

This course provides you with a background in algebra. The applications presented are designed to help you develop educated approaches to problem solving.

The objectives for this course are to

• review algebraic principles that are applicable to future courses (particularly precalculus and calculus) and careers in business, economics, the sciences, or engineering;
• solve problems involving linear and quadratic algebraic functions, exponentials, logarithms, and conics;
• learn how to interpret "word" problems and to translate the data into mathematical models so that they can be solved;
• recognize logical solutions in terms of each problem; and
• interpret your solutions.

This course is designed to help you learn basic concepts and rules for working with numbers and equations. You will learn the process for using data points and a problem statement to develop an equation or a set of equations to solve a problem. You'll be presented with methods for solving the equations for a unique solution, as well as tools to help you graphically interpret the results, if appropriate; the combination of these steps represents mathematical modeling of a problem. Finally, you will be encouraged to interpret the mathematical solution back into a verbal description of the results.

The process previously mentioned is critical to developing the ability to solve real-life problems. A client, or your supervisor, will not likely provide you with the equations necessary to solve a problem; if they could get to that point, they could solve the problem themselves. Rather, they will present the problem, and expect that you will know how to solve correctly. What they will need is a person who can take the information provided, determine what the question is, identify and set up appropriate methods to answer the question, and provide an interpretation of the solution. Having the ability to display the data (such as in a graph) will enhance your ability to present your results.

Required Text

There is one required textbook:

Marvin L. Bittinger and David J. Ellenbogen; Intermediate Algebra: Concepts and Applications, 7th ed. Addison Wesley, Publisher: 2006. ISBN 0321233867

This text provides a thorough understanding of the processes needed to solve algebraic problems. The authors' goal is to provide the background necessary to advance from understanding the skills needed to solve problems, to working with mathematics concepts, and solving real problems. Each chapter or section begins with a statement of goals. Concepts are presented in mathematical terms and then described in simple English. Definitions are given for each math phrase.

For each section, problems are presented to enhance your understanding of the subject. Basic concept problems first let you practice the subjects; these are usually given as algebraic expressions with instructions on what you must do (factor, solve for x, and so on). These are followed with "word" problems that let you demonstrate your ability to apply what you have just learned to "real-life" issues.

There seems to be no mathematics text that all students can relate to. A common complaint is that solution examples don't include intermediate steps. This text includes most of those intermediate steps and explains each of one. The explanations, examples, and exercises use situations that you should easily relate to. Graphics are included to help you visualize the data. Alternate or additional explanations of materials and/or solution techniques are provided in these online course materials.

Materials

You will need a calculator, preferably a scientific calculator, for this course; you'll be using at least the following functions: 1/x; y^x; ln x; log x; 10^x, and e^x. A graphing calculator may help you visualize the functions, but it is not required. You can decide whether or not to purchase a graphing calculator; subsequent courses may require it, so it may benefit you financially to purchase one now so that you don't need to purchase a second calculator later.

You should use graphing paper for problems requiring graphic interpretation or display of the data. It is nearly impossible to accurately represent data without using a scaled coordinate system. However, there is no need for expensive graphing paper. Quadrille paper (1/4-inch squares) should work fine. A straight edge, such as a ruler, will be useful for some problems.

Optional Materials

No additional materials are required. If you have difficulty with any of the explanations in this text, it may be useful to read an alternate description in another text. If you'd like recommendations on alternate texts, please contact your instructor.

The authors have enlisted another person, Judith A. Penna, to prepare a "Student Solutions Manual" as a companion to the text for this course. It contains detailed solutions to the odd-numbered problems in the text. You may find it useful to refer to the solutions as a guide to help identify the approach that should be taken to the assigned problems. However, note that this is not a required text, and it will not be referred to in the course; purchase is completely optional. You may wish to check the examples in the text first, and purchase this supplement only if you feel you need additional instruction.

In addition to the solutions manual, students who have computers with the Windows operating system may wish to purchase the MathXL tutorials on CD-ROM. This software provides practice problems, examples, and guided solutions. Some video clips are provided for visualization of the concepts. Note that this software is not a requirement for this course and will not be used by the instructor. Additionally, the publisher provides a Math Tutor Center, which for an additional cost, provides you with toll-free telephone, fax, or e-mail access to help you understand any math concepts.

Lessons

Lesson One provides a review of the mathematic basics required for solving problems in the following lessons. Lessons Two through Four cover the subjects that will be on the first exam, including graphing, linear equations, systems of linear equations, and inequalities. The second portion of the course includes Lessons Six through Eight, covering polynomials, rational functions, exponents, and radicals. The final portion of the course includes Lessons Ten through Twelve and covers quadratic equations, exponential and logarithmic functions, conics, and mathematical sequences. Applications of the concepts are presented throughout the course.

• Lesson One: Algebra and Problem Solving
  Algebra Basics; Properties of Real Numbers; Solving Equations; Formulas; Basic Properties of Exponents; Practice Assignment; Written Assignment.
• Lesson Two: Graphs, Functions, and Linear Equations
  Graphs; Functions; Linear Functions; Line Equations; Practice Assignment; Written Assignment.
• Lesson Three: Systems of Linear Equations
  Systems of Equations in Two Variables; Methods for Solving (Substitution, Elimination); Systems in Three Variables; Matrices; Determinants; Kramer's Rule; Practice Assignment; Written Assignment.
• Lesson Four: Inequalities
  Inequalities; Intersections, Unions, and Compound Inequalities; Absolute Value Equations and Inequalities; Inequalities in Two Variables; Linear Programming; Practice Assignment; Written Assignment
• Lesson Five: Preparing for the Midterm
  Subjects to Review; Practice Problems.
• Lesson Six: Polynomials and Polynomial Functions
  Multiplication; Factoring Methods; Practice Assignment; Written Assignment.
• Lesson Seven: Rational Expressions, Equations, and Functions
  Operations with Rationals; Complex Rational Expressions; Rational Equations; Division; Synthetic Division; Practice Assignment; Written Assignment.
• Lesson Eight: Exponents and Radicals
  Radical Expressions; Rational Numbers as Exponents; Multiplying, Dividing, and Combining Radicals; Geometric Applications; Complex Numbers; Practice Assignment; Written Assignment.
• Lesson Nine: Preparing for the Midterm
  Subjects to Review; Practice Problems.
• Lesson Ten: Quadratic Functions and Equations
  Solution Methods; Quadratic Formula; Graphs; Problem Solving; Polynomial and Rational Inequalities; Practice Assignment; Written Assignment
• Lesson Eleven: Exponential and Logarithmic Functions
  Composite and Inverse Functions; Exponential and Logarithmic Functions; Properties or of Logarithms; Solutions of Equations; Applications; Practice Assignment; Written Assignment.
• Lesson Twelve: Conic Sections and Sequences, Series, and the Binomial Theorem
  Parabolas, Circles, Ellipses, and Hyperbolas; Arithmetic and Geometric Sequences and Series; Binomial Theorem; Practice Assignment; Written Assignment.
• Lesson Thirteen: Preparing for the Final Exam
  Subjects to Review; Practice Problems.

Assignments

A written assignment is due with each lesson except Lessons Five, Nine, and Thirteen, (a total of ten assignments). Each assignment consists of approximately 20 problems; all will be graded. The first assignment includes more problems than the others but these are less involved than those later on in the course, so the first assignment should not take longer than the others. Be sure to show your work on all problems. You will receive partial credit for using the correct method; in fact, you'll receive most of the possible credit for any problem in which your method is correct but you have a minor arithmetic error. Another reason for asking you to show work is that your instructor can help with your approach to the problem, pointing out where an error occurred, and sometimes showing an easier or more direct approach.

When doing "word problems," try to approach them in the following manner:

1. Write down all the facts and numbers you are given.
2. Write down all the relationships among the pieces of information.
3. Identify the "unknown" from the question part of the problem. What is it that you are asked to find?
4. Draw a picture and label the known and unknown components, if that is appropriate.
5. Write an equation based on the above information.
6. Solve the equation.
7. Check your work.

Note that checking your work is really a useful step. If the value you just found as the solution for your problem does not work when put it back into the original formula, then an error was made along the way. Particularly in exams, students can avoid turning in an incorrect solution to a problem if the answer is checked first.

Because we have calculators available, students have a tendency to rely on them whole-heartedly. However, some problems may be easier solved without a calculator. For example, 1/3 * 0.09 can be quickly converted to the correct and exact value of 0.03, but a calculator converts the fraction 1/3 to a decimal (0.333), and gives an inexact value. Try to examine the information before reaching for your calculator. The book's author describes "standard" rounding and/or truncating policies. These are not necessarily used globally, particularly in the science and engineering fields. Please try to remember to carry as many decimal places through to the end as possible, and "round" or "truncate" as the last step of the solution process, rather than at each step of the way. This will provide the most exact answer at the end, and will help assure that you match the answer in the back of the book (for the odd-numbered problems or self-tests).

Feel free to ask as many questions as needed with regards to your homework. Or preferably, ask questions before submitting your homework so you can obtain guidance to be sure your approach is correct.

Exams

There will be three examinations for this course. You are allowed two hours for each exam; this amount of time should allow you to complete the questions comfortably and to go back over your work to verify methods and answers, if necessary.

The problems on the exams will be of the same type and difficulty level as given in the assignments. Each exam will cover only the material from the assignments immediately preceding (since the previous exam). Specific information on content of the exams is given in Lessons Five, Nine, and Thirteen.

For the exams, you will be allowed to bring one page of notes (using both sides). Write down the basic principles and any formulas that you think you may need for the problems. Notes are a useful way to help you organize your thoughts during your study for the exam. But they do not help if you have not learned the material beforehand.

You will also need to bring a calculator and some graph paper to the exams. Remember that you will need to show all your work on the exams.

Grading Criteria

This is a non-credit course.  Your final grade will be "SC" or "USC" ("Successful Completion" or "Unsuccessful Completion").  An SC/USC grade is not numeric and is not computed in the UW grade point average.

In order to receive an "SC" for the course, you must complete all required assignments and examinations at an acceptable level (2.5 or above) as described in the table below. For example, upon completing all assignments and examinations and demonstrating acceptable work, your final grade would be reported as "SC."

Assessment	Interpretive Statement
4.0	Excellent and exceptional work. Unusually thorough, well reasoned, sophisticated, insightful, and professional.
3.5	Strong work. Is thorough and well-reasoned, and demonstrates clear recognition and good understanding of the course material.
2.5	Competent work. Adequate, though some weaknesses are evident. Shows understanding of the course material. Shows neither unusual strengths nor exceptional weaknesses.
2.0	Substandard performance. Understanding of course material is incomplete.
1.0	Lowest assessment. While learning may have occurred, the minimum requirements for the course were not met. Work is not adequately developed and/or has flaws or omissions.

Suggestions

Try to get started as early as possible. And as stated earlier, be sure to read the course materials and assigned text first, before beginning the homework assignment. You will find the problems much easier and more logical if approached in this way.

If you have questions, contact a tutor or your instructor. Don't sit and struggle until a problem becomes a frustration. Usually the problem is minor and requires just a change in how you are approaching it.

Please complete the Student Information Sheet and return it to your instructor as soon as possible.

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