Download Math 1428 - College of DuPage

College of DuPage
FY Fall/17
ACTIVE COURSE FILE
Curricular Area: Mathematics
Course Number: 1428
Title: College Algebra with Applications
Semester Credit Hours: 3 Lecture Hours: 3
Lab Hours: 0 Clinical Hours: 0
This course is not an IAI approved general education course.
Changes from the present course must be accompanied by a yellow
Course Revision or Deletion Form.
Course description to appear in catalog:
The study of algebra with emphasis on applications. This course should not
be taken by students planning to enroll in calculus. Topics include, but are
not limited to, matrices, functions, conic sections, polynomials, exponential
and logarithmic functions, and sequences and series.
Prerequisite:
Demonstrated geometry competency (level 2), and Math 0482 (or college
equivalent) with a grade of C or better or a qualifying score on the
mathematics placement test or a qualifying A.C.T math sub-score
A.
General Course Objectives:
Upon successful completion of this course, students should be able to
do the following:
1. Determine the domain and range of relations and functions
2. Use function notation
3. Analyze graphs to determine the maximum and minimum
values of a variety of relations and functions
4. Analyze graphs to determine when a variety of relations and
functions are increasing and/or decreasing
5. Analyze graphs to determine the zeros of a variety of relations
and functions
6. Determine the composite of two functions and the inverse of a
one-to-one function
7. Construct the graphs of conic sections
8. Solve systems of linear equations
9. Perform matrix arithmetic
10. Determine the inverse of a nonsingular matrix
11. Solve exponential and logarithmic equations
12. Apply properties of logarithms
13. Determine terms of a sequence
14. Determine specific and general terms in arithmetic and
geometric sequences
15. Determine sums of arithmetic and geometric series
16. Solve a variety of application problems relating to topics
covered
B.
Topical Outline:
This topical outline is not necessarily sequential.
Applications are a major emphasis of this course.
1.
Relations and functions
a. Definition
b. Determining domain and range
c. Using tables of values
d. Using function notation
e. Forming the composite of two functions
f.
Graphing functions
i.
Determining if a graph is the graph of a
function
ii.
Determining if a relation is symmetric to the x-axis,
y-axis or origin.
iii.
Graphing using symmetry
iv.
Translating functions (horizontally and vertically)
g. Analyzing functions (maximum/minimum, increasing/decreasing,
zeros)
i.
Functions involving absolute value
ii.
Square root function
iii.
Functions defined by more than one formula
depending on the value of the independent
variable
iv.
Polynomial functions
v.
Rational functions
h.
Investigating the inverse of a function
i.
Determining a formula for f-l given f in
ii.
iii.
function notation
Determining the domain and range of f-l
Graphing a function and its inverse
2.
Analytic Geometry
a. Parabolas
i.
Graphing quadratic functions and quadratic
relations whose graphs are parabolas
ii.
Determining the coordinates of the vertex
and the equation of the axis of a parabola
b. Circles
i.
Determining the center-radius form of the
equation of a circle
ii.
Determining the center and radius of a
circle whose equation is given in general form
iii.
Graphing relations whose graphs are circles
c. Ellipses
d. Hyperbolas
e. Systems of non-linear equations
3.
Matrices
a. Definition and dimension
b. Operations with matrices
i.
Addition and subtraction
ii.
Scalar multiplication
iii.
Matrix multiplication
c. Gaussian elimination to solve linear systems
d. Gaussian elimination to find the inverse of a
nonsingular matrix
e. Use of the inverse of the coefficient matrix to
solve a linear system
4.
Exponential and logarithmic functions
a. Exponential functions
i.
Definition
ii.
Analysis of the graphs of exponential functions
iii.
Exponential equations involving the same base
iv.
Applications
b. Logarithmic functions
i.
Definition using the concept of function
inversion on the exponential function
ii.
Analysis of the graphs of logarithmic functions
iii.
Properties of logarithms
iv.
Logarithmic equations
v.
Solution of exponential equations with different
bases, using logarithms
vi.
The change of base formula
vii.
Applications
5.
Binomial Expansion Theorem
6.
Sequences and series
a. Definitions
b. Determination of the terms of a sequence given a
c.
d.
C.
formula for an or given a recursive definition
Arithmetic sequences and series
i.
Determining if a given sequence is arithmetic
ii.
Determining any term of an arithmetic sequence
iii.
Determining a formula for an
iv.
Determining the sum of an arithmetic series
Geometric sequences and series
i.
Determining if a given sequence is geometric
ii.
Determining any term of a geometric sequence
iii.
Determining a formula for an
iv.
Determining the sum of a geometric series
v.
Determining the sum (if it exists) of an infinite
geometric series
Methods of Evaluating Students:
Unit tests at appropriate intervals; quizzes, homework, projects, and a
comprehensive final examination, all at the discretion of the instructor.
_______________________________
Initiator
Date
_______________________________
Sponsor
Date
_______________________________
Division Dean
Date
Textbook for Math 1428
Title:
College Algebra, Graphs and Models, 6th edition
Author:
Bittinger, Beecher, Ellenbogen, Penna
Publisher:
Pearson
Copyright:
2017
The following chapters and sections of the textbook should be covered.
Chapter 1:
All Sections 1.1 – 1.6
Chapter 2:
Sections 2.1 (greatest integer function is optional), 2.2, 2.3,
2.4, 2.5 (cover basic functions, horizontal and vertical
translations)
Chapter 3:
All Section 3.1 – 3.5
Chapter 4:
Sections 4.1, 4.2, 4.5, 4.6 (Sections 4.3 and 4.4 Finding or
approximating zeros for polynomial functions is optional)
Chapter 5:
All Sections 5.1 – 5.6
Chapter 6:
Sections 6.1, 6.2, 6.3, 6.4, 6.5
Chapter 7:
Sections 7.1 (determine coordinates of vertex, equation of
axis, and graph), 7.2 (graph), 7.3 (graph), 7.4
Chapter 8:
Sections 8.1 (omit sigma notation), 8.2, 8.3, 8.7
Applications are a major emphasis of this course. Please cover as many as
time permits.
Use of Technology in Math 1428
The mathematics faculty recommends to all mathematics instructors that
any technology be allowed and encouraged in any level mathematics
course when it can be used by a student to either
1.
simplify calculations where the mechanics of the problem have
already been mastered or
2.
explore and experiment with concepts and problems that
enrich the understanding of the material that is being taught.
The use of either the TI-83 graphics calculator, TI-84 graphics calculator, or
computer software is required in this course. This technology should be
used to improve the speed and accuracy of complicated calculations and
graphing in realistic modeling once the concepts of the problem have
been developed.
Videos for Math 1428
Instructional videos for Math 1428 are available within Student’s
MyMathLab course.
In all Mathematics courses, students with a documented learning disability
that specifically requires a calculator as determined by Health Services, will
be allowed to use a basic calculator for all test/quiz questions where
arithmetic calculations are not the main objective. The specific disability
must be verified with Health Services before the accommodation can be
made.