College Algebra with Applications
COURSE DESCRIPTION:
This course is a survey of mathematical applications of
functions. Topics that will be covered
include: Fundamental concepts of algebra, algebraic equations and inequalities ;
functions and
graphs, zeros of polynomial functions ; exponential and logarithmic functions,
systems of
equations and inequalities. The mathematics of finance will also be covered.
Three semester
credits.
COURSE OBJECTIVES:
1. Demonstrate an understanding of mathematical concepts
and terminology as evidenced
by the ability to utilize this information to solve both computational and
application
problems. Expectations apply, but are not limited to, the major skills of this
course as
listed below:
• Solve linear equations in one variable .
• Add , subtract , multiply and divide polynomials and utilize this skill in
solving
equations.
• Simplify expressions with rationale and negative exponents, as well as
associated
radicals.
• Graph equations that are linear, quadratic and other various types.
• Identify equations of linear functions by using the slope-intercept and
points-slope
formulas.
• Solve systems of equations via graphing, substitution, and elimination
methods .
These skills will be used to find equilibrium in supply-demand problems and
break even analysis.
• Solve linear inequalities and related practical problems.
• Demonstrate knowledge of domain, range and graphing functions.
• Graph quadratic functions and find maximums and minimums.
• Use logarithmic functions to solve practical problems.
2. Apply mathematical concepts and terminology to analyze
numerical data, interpret
results, compare options , propose solutions and make effective decisions in
situations
requiring quantitative thinking skills.
3. Utilize logic, reasoning, critical thinking skills and
problems solving strategies in the
fields of mathematics, sciences, social sciences and business.
4. Acquire fundamental knowledge and skills which are
needed for success in related
courses and careers that require quantitative analysis.
COURSE TOPICS:
Assignment 1 and Terms Tests 1: Review of algebra and
computation skills necessary for
the course
Chapter 0 - The following concepts and their applications
will be covered: exponents, root ,
scientific notation, polynomial operations , factoring polynomials, rational
expressions, solving
linear equations, solving absolute value equations , graphing calculator basics.
Assignment 2 and Terms Test 2: Functions, how to plot them, and how to use them
Chapter 0 - The following concepts and their applications
will be covered: graphing with your
Chapter 1 – The following concepts and their applications
will be covered: relations and
functions, maximums and minimums, combining functions , applications of functions
Assignment 3 and Terms Test 3: Polynomial functions of 1st, 2nd and higher degree.
Chapter 5 - The following concepts and their applications
will be covered: linear models,
systems of equations
Chapter 2 - The following concepts and their applications
will be covered: complex numbers,
solving quadratic equations, solving rational equations , solving inequalities.
Chapter 3 - The following concepts and their applications
will be covered: polynomials and their
characteristics
Assignment 4: Introduction to exponential and logarithmic functions
Chapter 1.6: The following concepts and their applications will be covered: Inverse functions
Chapter 4: The following concepts and their applications
will be covered: exponential functions
and their graphical characteristics, logarithmic functions and their properties
and graphical
characteristics, solving equations with exponentials and logarithms
Assignment 5: Applications of exponential and logarithmic functions, and data fitting
Chapter 4: The following concepts and their applications
will be covered: compound and
continuous interest, annuities and amortization, applications of growth and
decay and logarithms.
Chapter 5: The following concepts and their applications
will be covered: modeling with your
graphing calculator using functions discussed in course.
Final Exam: All material covered, with emphasis on material since terms test 3.
REQUIRED COURSE MATERIALS:
1. Textbook:Essentials of College Algebra, First Edition,
2006, Authors: M. Holtfrerich
and J. Haughn, Publishers: Thomson- Brooks/Cole, ISBN: 0-534-99801-1
2. Scientific Graphing Calculator, use one of the
following two models ONLY –
TI-83 or TI-84
3. Syllabus
OPTIONAL COURSE MATERIAL:
Student Solution Manual – while the manual is not required
you may find it very useful for this
course.
You may purchase your textbook through MBS Direct by
calling their toll free number at :
800-325-3252 or through the UIU homepage: www.uiu.edu. Click on the option for
current
students, then the link on the left side titled - order textbooks. Follow the
link and select External
Degree for your location.
COURSE OVERVIEW:
The course will proceed as follows:
Unit One – Assignment 1: Chapters 0.1-0.6
Exam One - Terms Test 1: First proctored test over material from chapters 0.1-0.6
Unit Two – Assignment 2: Chapters 0.7-0.8, Chapters 1.1-1.5
Exam Two – Terms Test 2:
Second proctored test over all material in previous
assignments, with emphasis on material in assignment 2.
Unit Three – Assignment 3: Chapters 5.1, 5.2, 2.1, 2.2, 2.4, 2.5, 3.1, 3.2
Exam Three - Terms Test 3:
Third proctored test over all material in previous
assignments, with emphasis on material in assignment 3.
Unit Four – Assignment 4: Chapters 1.6, 4.1-4.4
Unit Five – Assignment 5: Chapters 4.5-4.8, 5.2-5.4
Final exam:
Final proctored exam over all material in course with
emphasis on material in assignments 4 and 5.
Read each section and work the illustrated examples.
Complete the assigned problems as
stated for each section, following the directions provided by the text. In order
to receive
a grade, assignments must be submitted in Unit form with the appropriate cover
sheet.
ASSIGNMENT INFORMATION
The assignment sheets list the category or type of
problems within each section of a chapter, and
the corresponding problem numbers of that category at the end of the section. It
is advisable to
do as many of the problems in each category you can until you have mastered
those types of
problems. The odd problems have answers in the back of the book for your
guidance. Only a
selection of those problems will be graded, they are indicated in the right hand
column. Most of
the assigned problems are multiple choice with possible answers given in this
workbook. To
choose an answer circle the correct letter at the appropriate position on the
answer sheet
provided. In the last assignment there are some tables for you to fill out,
please do so in the
appropriate place on the answer sheet. Each assignment is worth 5% of your final
grade. Because
most of the questions are free response questions on the tests and exam, you
should always
calculate your answer first, and then see which option it corresponds to, rather
than just seeing
which of the options works.
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