# Mathematics

## MATH 110: College Algebra

Fall Semester, 2005

MC 404, MWF 2:10-3:00, R 2:00-2:50

Terry R. Witzke, Instructor, 788-4875 (Home), trwitzke@yahoo.com.

CATALOG COURSE DESCRIPTION

Review of basic algebra, second-degree equations and inequalities, roots of polynomials, exponential and logarithmic functions, and systems of equations. Not applicable toward mathematics major or minor sequence. Prerequisite: acceptable score on placement exam, grade of B-minus or better in one year of high school algebra, or grade of C or higher in MATH 001.

TEXTBOOK

College Algebra, by Beecher, Penna, Bittinger, Second Edition, 2005.

### CORE SKILL OBJECTIVES

1. Thinking Skills:

A. Using reasoned standards in solving problems and presenting arguments.

2. Communication Skills:

A. Reading with comprehension and the ability to analyze and evaluate.

B. Listening with an open mind and responding with respect.

3. Life Values:

A. Analyzing, evaluating and responding to ethical issues from an informed      personal value system.

4. Cultural Skills:

A. Demonstrating knowledge of the signs and symbols of another culture.

B. Participating in activity that broadens the student’s customary way of thinking.

5. Aesthetic Skills:

A. Developing an aesthetic sensitivity.

### COURSE OBJECTIVES

1. Thinking Skills:

A. Studying briefly the basic ideas of a first algebra course.

B. Learning to solve quadratic equations by factoring, completing the square, and by use of the quadratic formula.

C. Improving one’s ability to read and solve application problems by means of constructing appropriate algebraic models and then applying algebraic techniques to find a solution.

D. Exploring exponential and logarithmic functions, including application problems, and the efficient and appropriate use of logarithms and their properties.

E. Learning the techniques of solving systems of equations and appropriately applying these processes to word problems.

2. Communication Skills:

A. Producing both written and oral communication throughout the course; particular attention is paid to the accurate and appropriate use of the language of algebra.

B. Using technology - calculators, in some cases graphing calculators - to solve problems and to be able to communication solutions and explore options.

3. Life Value Skills:

A. Developing an appreciation for the intellectual honesty of deductive reasoning; a mathematician’s work must stand up to the scrutiny of logic, and it is unethical to try to pass off invalid work.

B. Understanding the need to do one’s own work, to honestly challenge yourself to master the material.

4. Cultural Skills:

A. Learning to read, write and manipulate mathematical notation

B. Experiencing mathematics as a culture of its own, with its own language and modes of thinking.

5. Aesthetic Skills:

A. Developing an appreciation for the austere intellectual beauty of deductive reasoning.

B. Developing an appreciation for mathematical elegance.

This course is designed to give students the algebraic tools required in subsequent courses, specifically MATH 180 (Elementary Functions), MATH 230 (Elements of Statistics), or MATH 270 (Managerial Mathematics). “Tools” here means both symbol manipulation and the logical and problem-solving skills - in short, how to “do” algebra and “what to do with it”.

In a sense, College Algebra is a remedial or review course, since it is essentially the same course as high school’s Algebra II. It is nevertheless a college course, which means we will cover the material at about three times the pace of the typical high school version, and much more will be expected of you outside the classroom. I do think the rule of thumb, “2 hours outside of class for each hour in class”, is appropriate here. You need to see yourself as an active learner, to take responsibility for your own learning, to avail yourself of the aids in place (tutors, the teacher, study groups, computer software, web sites) but to make sure that you honestly learn how to do what is required of you – you can only rely on others up to a point!

You should be capable of success, as long as you apply yourself sufficiently. You are here because your ACT score, your placement exam, or your grades in previous courses, or some combination of these, indicate that this is the appropriate level for you – you are ready for this material, but not yet ready to move on to the course beyond this one. This does not mean this course will be “easy” for you, but that you should be able to handle it.

Mr. Maresh, math department chair believes that, although it is an oversimplification to think that there is one principle leading to success in algebra, the primary cause of error is a misunderstanding regarding “order of operations”. It makes all the difference in the world whether you interpret “3 x 4 + 2” as “12 + 2” (correct) or as “3 x 6” (incorrect). This idea will be stressed repeatedly during the course.

You must believe that “Mathematics is not a spectator sport”. You are the LEARNER and you must engage in the learning process. The purpose of the course is not for me to convince you that I know algebra, but for you to learn it. Again, it comes down to your accepting responsibility for your learning.

COURSE PROCEDURES

Homework:

There will be a daily homework assignment. While most of the assignments will not be collected or graded it is essential that you do at least enough of the indicated problems that you master the material in that section. I cannot stress this strongly enough – it is utterly ESSENTIAL that you work problems on a daily basis. I assign odd numbered problems since the book provides the answers to these problems in the back of the book, so that you can check your work. I also expect to spend some time in class on a regular basis exploring questions related to the homework assignments.

Learning Styles:

People have various learning styles; some of us learn best by working alone in silence, others learn best by talking about the material with peers. Therefore, there will be some group work in class, not because it is the best way for all of you to learn but because some of you learn best by talking about ideas with others.  You are strongly encouraged to find at least one other person to work with on the assignments if that is a good way for you to learn the ideas in this course.

Use of Technology:

It is important to make use of technology, specifically computers and calculators, in doing mathematics. While it is not require the purchase of a specific calculator, you will find it very helpful to acquire and learn to use a graphing calculator of some sort, such as a TI-83, TI-83 Plus, TI 84 Plus or a TI 85.  This is especially important for those of you who will be taking additional math courses.  While some class time will be used to talk about the use of a calculator you will need to spend out of class time to become proficient in the use of a calculator to solve problems.

In general the following minimum levels are required for the grades indicated: 90% for an “A”, 85% for an AB, 80% for a “B”, 75% for a BC, 70% for a “C”, 65% for a CD and 60% for a “D”.  Quizzes, tests, attendance, homework collected, extra credit and class participation will be factors in determining points earned in this course.  There should be adequate opportunities to practice and to demonstrate your mastery of the material.

Americans with Disability Act: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs.

### Course Schedule:

29 Aug <R.1> Real Number System,                                                                     p6, #1-77 odd

31 Aug <R.2> Integer Exponents, Scientific Notation and Order of Operations   p13, #1-85 odd

01 Sept <R.3> Addition, Subtraction and Multiplication of Polynomials,           p 19, #1-41 odd

02 Sept <R.4> Factoring,                                                                                       p28, #1-85 odd

07 Sept <R.5> Rational Expressions,                                                                     p35, #1-61 odd

08 Sept <R.6> Radical Notation and Rational Exponents,                                    p44, #1-123 odd

09 Sept Lab #1, Review Exercises,                                                                      p. 48, #2-60 even (30 points)

12 Sept Exam #1, Chapter R

14 Sept <1.1> Introduction to Graphing,                                                               p65, #1-91 odd

15 Sept <1.2> Functions and Graphs,                                                                   p79, #1-73 odd

16 Sept <1.3> Linear Functions, Slope and Applications,                                    p92, #1-47 odd

19 Sept <1.4> Equations of Lines and Modeling,                                                  p108, #1-71 odd

21 Sept <1.5> More on Functions,                                                                        p119, #1-61 odd

22 Sept <1.6> The Algebra of Functions,                                                              p133, #1-91 odd

23 Sept Lab #2, Review Exercises,                                                                      p 159, #2-60 even (30 points)

26 Sept Exam #2, Chapter 1

28 Sept <2.1> Linear Equations, Functions and Models,                                      p178, #1-89 odd

29 Sept <2.2> The Complex Numbers,                                                                  p189, #1-75 odd

30 Sept <2.3> Quadratic Equations, Functions and Models,                                p204, #1-99 odd

3 Oct <2.4> Analyzing Graphs of Quadratic Equations,                                       p217, #1-47 odd

5 Oct <2.5> More Equation Solving,                                                                     p.227, #1-79 odd

6 Oct <2.6> Solving Linear Inequalities,                                                                p234, #1-63 odd

7 Oct Lab #3, Review Exercises,                                                                          p238, #6-64 even (30 points)

10 Oct Exam #3, Chapter 2

12 Oct <3.1> Polynomial Functions and Models,                                                 p.263, #7-77 odd

13 Oct <3.2> Polynomial Division; The Remainder and the Factor Theorem,      p.273, #1-51 odd

14 Oct <3.3> Theorems About Zeros of Polynomial Functions,                          p283, #1-57 odd, #71-75 odd, #79-83 odd, #95

17 Oct <3.4> Rational Functions,                                                                          p301, #1-73 odd

19 Oct <3.5> Polynomial and Rational Inequalities,                                              p311, #1-67 odd

20 Oct <3.6> Variation and Application,                                                               p319, #1-39 odd

24 Oct Lab #4,  Review Exercises,                                                                       p 324, #6-64 even (30 points)

26 Oct Exam #4, Chapter 3

27 Oct <4,1> Inverse Functions,                                                                            p338, #1-87 odd

28 Oct <4.2>  Exponential Functions and Graphs,                                                p352, #1-57 odd

31 Oct <4.3> Logarithmic Functions and Graphs,                                                 p369, #1-91 odd

2 Nov <4.4> Properties of Logarithmic Functions,                                               p378, #1-75 odd

3 Nov <4.5>  Solving Exponential and Logarithmic Equations,                             p389, #1-47 odd

4 Nov Lab #5, Review Exercises,                                                                         p 407, #2-60 even (30 points)

7 Nov Exam #5, Chapter 4

9 Nov <5.1> Systems of Equations in Two Variables,                                          p423, #1-45 odd

10 Nov <5.2> Systems of Equations in Three Variables,                                      p434, #1-25 odd

11 Nov  <5.3> Matrices and Systems of Equations,                                             p444, #1-39 odd

14 Nov <5.4>  Matrix Operations,                                                                        p455, #1-31 odd, 39-43 odd

16 Nov <5.6> Determinants and Cramer’s Rule,                                                   p472, #1-37 odd

17 Nov <5.7>  Systems of Inequalities and Linear Programming,                         p482, #1-59 odd

18 Nov Lab #6, Review Exercises,                                                                       p 495, #2-50 even (25 points)

21 Nov Exam #6, Chapter 5

28 Nov <6.1> The Parabola,                                                                                  p509, #1-33 odd

30 Nov <6.2> The Circle and the Ellipse,                                                              p519, #1-45 odd, 51, 53.

01 Dec <6.3> The Hyperbola,                                                                               p530, #1-39 odd

02 Dec <6.4>  Non-Linear Systems of Equations,                                                 p.541, #1-45 odd, , 55, 57.

05 Dec Lab #7, Review Exercises, 2-30 even (15 points)

07 Dec Exam #7, Chapter 6

08 Dec Final Review (Chapters 1-3)

09 Dec Final Review (Chapters 4-6)

12 Dec Final Exam, 3 to 5 PM