Course Title: College Algebra
Institution: Rogue Community College
Type of Program: Transfer
Length of Course: Forty-four (44) lecture hours for one term .
Prerequisites: MTH95 Intermediate Algebra or
equivalent, or appropriate
scores on RCC placement test.
Typical Required and Recommended Text(s):
Robert Blitzer, Pre-calculus, 3rd edition, Prentice
Hall Publishing, 2007.
Department Assignment: Mathematics
Department Mission Relationship: MTH111 reinforces traditional
mathematics
concepts and learning techniques with current graphic calculator
technology
emphasizing technical reading/writing and creative thinking skills.
Course Description: First course in the transfer mathematics sequence for
science, mathematics, engineering students, and for general ed math credit.
Course topics include; polynomial and rational functions , exponential and
logarithmic function, systems of equations and inequalities , and other
selected
topics.
Course Objectives and SCANS* (Secretary's Commission on Achieving Necessary
Skills) Competencies: On successful completion of this course, students will
be
able to perform the following skills:
| Expected Outcomes: |
Assessment Methods: |
1. Use mathematical problem solving
techniques
involving polynomial
and rational functions, and
systems of equations.
These
techniques include data fitting
and the use of graphical,
symbolic, narrative, and tabular
methods of analysis . |
1. Criterion referenced tests and
quizzes for
specific vocabulary,
skills, concepts, and daily
problem assignments. |
|
Expected Outcomes: (con't) |
Assessment Methods: (con't) |
2. Communicate mathematical
thoughts and ideas
using verbal
and written skills by creating
mathematical models of real
world situations. |
2. Criterion referenced tests and
quizzes for
specific vocabulary,
skills, concepts, daily problem
assignments,
in-class
observations, and project
completion and presentations. |
3. Use inductive and deductive
reasoning to
develop and verify
mathematical arguments. |
3. Criterion referenced tests and
quizzes for
specific vocabulary,
skills, concepts, and daily
problem assignments. |
4. Participate in problem solving
exercises and
teach others as a
team member. |
4. Daily problem assignments, in-
class
observations, and project
completion and presentations. |
5. Use appropriate technology to
enhance their
mathematical
thinking and understanding and
to solve mathematical
problems
and judge the reasonableness of
their results. |
5. Daily problem assignments, in-
class
observations, and project
completion and presentations. |
6. Do projects that encourage
independent,
nontrivial
exploration of situations best
modeled by polynomial,
rational, or systems of equations
concepts. |
6. In-class observation, and
project completion
and
presentations. |
Typical Required and Recommended Equipment and Materials:
Graphing
calculator (TI-83/84, TI-83/84 Plus or TI-84 Silver are recommended),
graph
paper, pencil, paper, and notebook.
COURSE CONTENT
Functions and Graphs (approx. 20% of course)
Graphs and Graphing Utilities (review)
Basics of Functions and Their Graphs (review)
Domain, Range; identify, evaluate, determine intercepts of functions ;
difference
quotient; piecewise functions; increasing/decreasing;
relative maximum and
minimums; step functions
Linear Functions and Slope (review)
Transformations of Functions
Vertical shifts
Horizontal shifts
Reflections
Vertical stretching and shrinking
Combinations of functions
Sum and difference
Product and quotient; specify domain
Composition; specify domain
Inverse Functions
Verifying inverse functions
Finding inverse functions
One to One functions
Graphing inverse functions
Distance and Midpoint Formulas; Circles
Find the distance between two points
Find the midpoint of a line segment
Write the standard form of the equation of a circle
Find center and radius of a circle in standard form and general form
Modeling with Functions
Functions from verbal descriptions
Functions from formulas (geometric, economic, banking, distance)
Polynomial and Rational Functions (approx. 20% of course)
Complex Numbers
Imaginary unit
Standard form a+bi
Properties of complex numbers
Operations with complex numbers
Quadratic equations with complex solutions
Quadratic Functions
Graphs of quadratic functions
Standard form of a quadratic function
Applications of quadratic functions
Maximum and minimum of quadratic functions
Polynomial Functions and Their Graphs
Continuity
Behavior of polynomials
Leading coefficient test
Zeros of polynomial functions
Multiplicity of roots
Intermediate value theorem
Turning points
Graphing polynomials
Cubic and quartic curve fitting using data points
Dividing Polynomials
Remainder Theorem
Factor Theorem
Long division of polynomials
Synthetic division
Zeros of Polynomial Functions
Rational Root Theorem
Properties of polynomial equations
The Fundamental Theorem of Algebra
Linear factorization theorem
Descartes’s Rule of Signs
Rational Functions and Their Graphs
Domain and range
Vertical asymptotes
Horizontal asymptotes
Graphing rational functions
Slant asymptotes
Average cost functions
Motion problems
Polynomial and Rational Inequalities (minor importance)
Solving polynomial inequalities
Solving rational inequalities
2004-05
Position function of a free falling body
Modeling Using Variation
Direct variation
Inverse variation
Combined variation
Joint variation
Exponential and Logarithmic Functions (approx. 20% of course)
Exponential Functions
Evaluate exponential functions including base e
Graph exponential functions
Use compound interest formulas
Logarithmic Functions
Change fro logarithmic to exponential form and vice-versa
Evaluate logarithms
Graph logarithmic functions
Determine domain and range of logarithmic functions
Use common and natural logarithms in applications
Properties of logarithms
Use the product, quotient, and power rules
Expand and condense logarithmic expressions
Use the change of base formula
Exponential and Logarithmic Equations
Use like bases to solve exponential equations
Use logarithms to solve exponential equations
Use the definition of a logarithm to solve logarithmic equations
Use 1-1 property of logarithms to solve logarithmic equations
Solve applied exponential and logarithmic problems including
exponential growth
and decay and model exponential data
Systems of Equations and Inequalities (approx. 20% of course)
Systems of Linear Equations in Two Variables
Substitution method
Addition method
Dependent systems
Inconsistent systems
Applications of systems of equations
Systems of Linear Equations in Three Variables
Addition method
Applications
Systems of Nonlinear Equations in Two Variables
Substitution method
Addition method
Systems of Inequalities
Linear inequalities in two variables
Nonlinear inequalities in two variables
Graphing systems of inequalities
Solving applied problems
Linear Programming
Objective function
Constraints
Solving problems with linear programming
Matrices and Determinants (approx. 20% of course)
Matrix Solutions to Linear Systems
Augmented matrix
Solving a system using a matrix
Matrix row operations
Row echelon form
Gaussian elimination with back-substitution
Gauss – Jordan elimination
Inconsistent and Dependent Systems and Their Applications
Inconsistent systems with three unknowns
Dependent systems with three unknowns
Non- square systems
Networking applications
Multiplicative Inverses of Matrices and Matrix Equations
Multiplicative identity matrix
Multiplicative inverse of a matrix
Solving systems of equations using multiplicative inverses
Applications of matrices - coding
