MATH 110: College Algebra
MC 406, MWF 1:10-2:00, R 1:00-1:50
Office Hours:MWF 9-10, T 2-3, R 12-1
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:Larson, Hostetler, Hodgkins, College Algebra, Concepts and Models, 2nd Edition, D.C. Heath, 1996.
CORE SKILL OBJECTIVES
A. Using reasoned standards in solving problems and presenting arguments.
A. Reading with comprehension and the ability to analyze and evaluate.
B. Listening with an open mind and responding with respect.
A. Analyzing, evaluating and responding to ethical issues from an informed personal value system.
A. Demonstrating knowledge of the signs and symbols of another culture.
B. Participating in activity that broadens the student’s customary way of thinking.
A. Developing an aesthetic sensitivity.
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
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
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.
A. Developing an appreciation for the austere intellectual beauty of deductive reasoning.
B. Developing an appreciation for mathematical elegance.
Most simply put, 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). By “tools” here I mean 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, etc.) 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.
I have come to think 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). I will try to stress this repeatedly during the course.
In general, 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.
Homework: There will be a daily homework assignment. While these 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 generally 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: I believe that various people have various learning styles; some of us learn best by working alone in silence, others learn best by talking about the material with colleagues. I will try to build into the course some amount of group work, not because I think it is the best way for all of you to learn but because I know that some of you learn best by talking about things; what I am trying to do is provide an environment in which you can all latch onto some activities.
Use of Technology: It is important to make use of technology, specifically computers and calculators, in doing mathematics. While we do 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, probably a TI-83. I will use an overhead display frequently in class and it will be to your advantage if you can “play along”. I will also give you an introduction to DERIVE, a computer algebra system package created by Texas Instrument.
Grading Procedure: In general I use the following scale: 90% for an “A”, 80% for a “B”, 70% for a “C”, and 60% for a “D”. There will be nearly 1,000 points during the semester: 6 Labs (about 20 points each), 3 Exams (100 points each), 3 Quizzes (50 points each), 7 Chapter Reviews (about 300 points in all), and a Final Exam (150 points).I am trying to create a situation in which you have adequate opportunity 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.
15 Jan <P.1> Real numbers, Order, Absolute value p 9 #3-63 odd
17 Jan <P.2> Basic rules of Algebra p 20 #11-69 odd, 75-79 odd
18 Jan <P.3> Integer exponents p 30 #1-61 odd, 73-89 odd
19 Jan <P.4> Radicals, Rational exponents p 41 #1-71 odd, 83-91 odd
22 Jan <P.5> Polynomials p 51 #1-25 odd, 33-55 odd, 67-73 odd
24 Jan <P.6> Factoring p 59 #1-67 odd, 77-80
25 Jan <P.7> Rational expressions p 70 #5-57 odd, 63-67 odd
26 Jan Lab #1 Chapter Review: p 75 #2-90 even [45 points]
29 Jan QUIZ #1 [50 points]
31 Jan <1.1> Linear equations p 86 #1-55 odd, 67, 69
1 Feb <1.2> Linear equations and modeling p 97 #1-19 odd, 25-53 odd
2 Feb <1.3> Quadratic equations p 103 #1-51 odd, 59-71 odd, 77
5 Feb <1.4> Quadratic formula p 120 #5-33 odd, 39, 45, 47, 51, 55-61 odd, 67, 69
7 Feb <1.5> Other types of equations p 133 #1-65 odd
8 Feb <1.6> Linear inequalities p 144 #1-63 odd, 67, 75
9 Feb <1.7> Other types of inequalities p 155 #1-4 odd, 49, 51
12 Feb Lab #2 Chapter Review: p 160 #2-90 even [45 points]
14 Feb GROUP PRACTICE EXAM #1 [25 points]
15 Feb EXAM #1 [75 points]
16 Feb <2.1> The Cartesian Plane p 174 #1-51 odd
19 Feb <2.2> Graphs of equations p 184 #1-35 odd, 43-55 odd, 61, 65, 69, 75
21 Feb <2.3> Graphing calculators, DERIVE Take-home problem set
22 Feb <2.4> Lines in the plane p 205 #1-55 odd, 59, 63, 67
23 Feb <2.5> Linear modeling p 216 #1-33 odd
26 Feb QUIZ #2 [50 points] Chapter Review: p 223 #2-88 even [44 points]
28 Feb <3.1> Functions p 238 #1-47 odd, 55, 59, 61, 67
1 Mar <3.2> Graphs of functions p 250 #1-33 odd, 45-61 odd, 65
2 Mar <3.3> Translating and combining functions p 263 #1-19 odd, 23-65 odd
- S P R I N G BR E A K -
12 Mar <3.4> Inverse functions p 274 #3-49 odd, 57
14 Mar <3.5> Quadratic functions p 285 #1-45 odd, 49, 51
15 Mar <3.6> Polynomial functions of higher degree p 298 #1-13 odd, 19-39 odd, 47-55 odd, 61
16 Mar <3.7> Rational functions p 308 #1-47 odd, 53, 55
19 Mar Lab #3 Chapter Review: p 314 #2-94 even [47 points]
21 Mar GROUP PRACTICE EXAM #2 [25 points]
22 Mar EXAM #2 [75 points]
23 Mar <4.1> Polynomial division, Synthetic division p 328 #1-53 odd
26 Mar <4.2> Real zeros of polynomial functions p 337 #1-39 odd, 49, 57, 59
28 Mar <4.3> Approximating zeros of polynomial functions p 346 #17-21 odd
29 Mar <4.4> Complex numbers p 356 #1-67 odd
30 Mar <4.5> Fundamental Theorem of Algebra p 364 #1-45 odd
2 Apr Lab #4 Chapter Review: p 368 #2-70 even [35 points]
4 Apr QUIZ #3 [50 points]
5 Apr <5.1> Exponential functions p 380 #1-41 odd, 49, 51, 54
6 Apr <5.2> Logarithmic functions p 391 #1-53 odd, 59, 63, 65
9 Apr <5.3> Properties of logarithms p 398 #9-79 odd
11 Apr <5.4> Solving exponential and logarithmic equations p 410 #1-61 odd, 67, 71
- E A S T E R B R E A K -
18 Apr <5.5> Exponential and logarithmic modeling p 420 #1-31 odd, 35, 39, 43, 47, 49
19 Apr Lab #5 Chapter Review: p 427 #2-86 even [43 points]
20 Apr GROUP PRACTICE EXAM #3 [25 points]
23 Apr EXAM #3 [75 points]
25 Apr <6.1> Systems of equations p 441 #1-5 odd, 13-35 odd, 41, 45, 47, 53
26 Apr <6.2> Systems of linear equations in two variables p 452 #1, 5, 7, 11, 15-35 odd, 39, 41
27 Apr <6.3> Systems of linear equations in three variables p 464 #1-29 odd, 37
30 Apr <6.4> Systems of inequalities p 477 #1-41 odd, 47 57
2 May <6.5> Linear programming p 487 #1-15 odd, 33-37 odd
3 May Lab #6 Chapter Review: p 493 #2-66 even [33 points]
4 May GROUP PRACTICE FINAL EXAM [25 points]
Final Exam: Friday, 11 May 2001, 7:40-9:40 am [125 points]