Chabot College
Fall 2002
Course Outline for Mathematics 31
COLLEGE ALGEBRA
Catalog Description:
31 – College Algebra
3 units
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. Preparation for Calculus for Business and Social Science
students. Prerequisite: Mathematics 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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perform basic operations on complex numbers;
solve quadratic equations by factoring, completing the square, and quadratic formula;
find complex roots of a quadratic equation;
sketch the graphs of functions and relations:
a. algebraic, including polynomial and rational
b. logarithmic
c. exponential
d. circles;
find and sketch inverse functions;
perform function composition;
solve exponential and logarithmic equations;
apply the concepts of logarithmic and exponential functions;
solve systems of linear equations in three unknowns using elimination and substitution;
apply the properties of and perform operations with radicals;
apply the properties of and perform operations with rational exponents;
solve equations and inequalities involving absolute values;
solve equations involving radicals;
graph linear inequalities in two variables;
find the distance between two points;
find the midpoint of a line segment.
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.
Chabot College
Course Outline for Mathematics 31
College Algebra
Fall Semester 2002
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
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
Problem solving with student participation
Class discussion
Audio-visual materials
Page 2
Chabot College
Course Outline for Mathematics 31
College Algebra
Fall Semester 2002
Page 3
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
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, 2000
Special Student Materials:
A scientific or graphing calculator may be required.
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Revised: 05/03/01