Chabot College
Fall 2003
Course Outline for Mathematics 55
INTERMEDIATE ALGEBRA
Catalog Description:
55 - Intermediate Algebra
5 units
Concepts involving complex numbers, quadratic equations, parabolas and circles, functions and their
graphs, systems of equations, rational exponents, radical equations, absolute value equations and
inequalities, exponential and logarithmic functions and equations. Prerequisites: Mathematics 65 or
Mathematics 65B or Mathematics 65L (completed with a grade of C or higher) or an appropriate skill
level demonstrated through the Mathematics Assessment process. May not receive credit if
Mathematics 55A and Mathematics 55B have been completed. May be offered in Distance Education
delivery format. 5 hours lecture, 0-1 hour laboratory.
Prerequisite Skills:
Before entering the course the student should be able to:
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write set theory notation;
apply order of operations to simplify algebraic expressions;
solve linear equations in one variable;
solve and graph linear inequalities in one variable;
graph linear equations in two variables by various methods;
add, subtract, multiply, and divide polynomials;
apply the formula for squaring a binomial;
factor special products, general trinomials, and polynomials with four terms;
add, subtract, multiply, divide and simplify rational expressions;
apply algebraic methods to solve word problems;
solve quadratic equations by factoring, using the principle of square roots, and using the quadratic
formula;
solve systems of equations by graphing, substitution and elimination;
apply the properties of integral exponents;
solve formulas for any given variable;
solve rational equations;
find the slope of a line from the graph, from the definition and from the slope-intercept equation of
the line;
find the equation of a line using the point-slope equation;
convert between scientific notation and standard notation.
Expected Outcomes for Students:
Upon the completion of the 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;
Chabot College
Course Outline for Mathematics 55, Page 2
Fall 2003
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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.
Course Content:
1. Review rational expressions and equations
2. Absolute value equations and inequalities
3. Exponents
a. Review integral exponents
b. Review properties
c. Rational exponents
4. Factoring
a. Review strategy
b. Sum and differences of cubes
5. Radicals
a. Simplifying
b. Operations
6. Rational exponents
7. Solving equations with radicals
8. Complex numbers
9. Quadratic equations
a. Review Factoring
b. Completing the square
c. The quadratic formula
d. The discriminant
e. Complex roots
10. Solving equations involving quadratic forms
11. Review graphing linear equations and slope of a line
12. Graphing inequalities in two variables
13. Distance and midpoint formulas
14. Introduction to functions
a. Basic function types and their graphs (linear, quadratic, square root, absolute value, simple
rational functions to introduce asymptotes)
b. Basic reflection and translation
c. Operations
d. Composite
e. Inverse
15. Direct and inverse variation
16. Exponential and logarithmic functions
a. Definition
b. Properties of logarithms
c. Graphing
d. Applications
17. Graphing general circles
18. Systems of linear equations using elimination and substitution
a. Review two by two systems
b. Three by three systems
19. Optional topics (instructor’s choice)
a. Sequences and series
b. Conic sections
c. Simple counting principles
Chabot College
Course Outline for Mathematics 55, Page 3
Fall 2003
Methods of Presentation:
1. Informal lectures
2. Class discussion of problems, solutions and student’s questions
3. Audio-visual materials
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. Exercises from the text book
The half-life of tritium is 12.4 years. How long will it take for 25% of a sample of tritium to
decompose?
b. Collaboratives
Perform an experiment with water and coffee filters and model with an exponential function.
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Midterms
d. Final Examination
Textbook(s) (Typical):
Intermediate Algebra, Gustafson/Frisk, Brooks/Cole Publishing Co., 2002
Special Student Materials:
A graphing calculator may be required
989curriculum/math/55/9810.05 hps
css Revised: 09/20/00
css Revised: 09-06-01