Chabot College
Fall 2005
Course Outline for Mathematics 31
COLLEGE ALGEBRA
Catalog Description:
31 – College Algebra
3 units
Preparation for Calculus for Business and Social Science students. Functions and graphs:
polynomials, rational functions, exponential and logarithmic functions, circles, parabolas, binomial
theorem, sequences and series. Solving rational, radical, quadratic in form, exponential and
logarithmic equations. Prerequisite: Mathematics 54 or 54L or 55 or Mathematics 55B (completed
with a grade of C or higher) or an appropriate skill level demonstrated through the Mathematics
Assessment process. 3 hours.
Prerequisite Skills:
Before entering this course the student should be able to:
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solve systems of linear equations and interpret the solutions;
graph polynomial, rational, exponential, and logarithmic functions;
solve exponential equations;
find inverse functions and apply their properties;
perform function composition;
solve quadratic equations;
apply the properties and perform operations with radicals;
apply the properties and perform operations with rational exponents;
apply the properties and perform operations with logarithms;
apply the concepts of exponential functions.
Expected Outcomes for Students:
Upon completion of the course the student should be able to:
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graph given algebraic functions and relations;
sketch the graphs of circles and parabola;
find the equation of circles and parabolas;
sketch the graphs of logarithmic and exponential functions involving translations of basic graphs;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions to other fields;
find specified terms and sums of arithmetic and geometric progressions;
expand a power of a binomial and find a specified term in a binomial expansion:
solve nonlinear inequalities.
Course Content:
1. Review of functions and graphs
a. Definition
b. Operations
c. Inverse functions
d. Linear functions
e. Quadratic functions
2. Graphing factorable polynomial functions of degree three or higher
a. Intercepts
b. Signed charts
Chabot College
Course Outline for Math 31, page 2
Fall 2005
Course Content – continued:
3. Graphing rational functions
a. Intercepts
b. Sign charts
c. Vertical and horizontal asymptotes
4. Solving equations
a. Review linear
b. Review quadratic and quadratic in form
c. Polynomial
d. Rational
e. Radical
f. Exponential and logarithmic
5. Solving inequalities
a. Review linear
b. Polynomial
c. Rational
d. Absolute value
6. Exponential and logarithmic functions
a. Definition
b. Graphing, including translations of basic graph
c. Applications
7. Circles and parabolas
a. Find equations
b. Graphing, including translations
8. Sequences and series
a. Summation notation (sigma)
b. Arithmetic
c. Geometric
9. Binomial theorem
10. Systems of equations
Methods of Presentations:
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Lectures
Collaborative small groups
Class discussion
Audio-visual materials
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. Homework
1) Section 3.7: Read the definitions of rational function, asymptotes. Work out problems 1,
5, 9, 10, 11, 13, 15, 21, 23: submit detailed graphs of # 45, 65. The graphs should be on
graph paper.
2) Read 8.1. Learn all the definitions. Work out problems 1 – 27 every other odd, 29 – 33
odds, 35 – 45 all, and 47 – 57 odds.
b. Collaborative Assignments using a small mirror and a yard stick, work with your group to find
the height of a tree or a building.
Chabot College
Course Outline for Math. 31, page 3
Fall 2005
Assignments and Methods of Evaluating Student Progress – continued:
2. Methods of Evaluating Student Progress
a. Homework
b. Collaboratives
c. Quizzes
d. Midterms
e. Final Exams
Textbook(s) (Typical):
College Algebra, Stewart/Redlin/Watson, Brooks Cole, 2004
Special Student Materials:
None
AW
Revised: 10/05/04