Chabot College
Fall 2008
Course Outline for Mathematics 55
INTERMEDIATE ALGEBRA
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Catalog Description:
MTH 55 - Intermediate Algebra
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5.00 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.
Prerequisite: MTH 65 or , MTH 65B or , MTH 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 or Mathematics 55L have been completed.
Units
(Min)
Units
(Max)
Contact Hours
Week
(Min)
5.00
Lecture
Laboratory
Clinical
Total
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5.00
Week
(Max)
Term
(Min)
Term
(Max)
5.00
5.00
5.00
0.00
0.00
5.00
5.00
1.00
0.00
6.00
87.50
0.00
0.00
87.50
87.50
17.50
0.00
105.00
Prerequisite Skills:
Before entry into this course, the student should be able to:
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write using 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.
add, subtract, multiply, and divide polynomials;
apply the properties of integral exponents;
convert between scientific notation and standard notation;
apply the formula for squaring the binomial;
factor special products, general trinomials, and four terms;
add, subtract, multiply, divide and simplify rational expressions;
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solve rational equations;
apply algebraic methods to solve word problems;
solve quadratic equations by factoring;
solve quadratic equations by factoring, using the principle of square roots and using the quadratic
formula
Expected Outcomes for Students:
Upon completion of 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.
Course Content:
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Review rational expressions and equations
Absolute value equations and inequalities
Exponents
A. Review integral exponents
B. Review properties
C. Rational exponents
Factoring
A. Review strategy
B. Sum and differences of cubes
Radicals
A. Simplifying
B. Operations
Rational exponents
Solving equations with radicals
Complex numbers
Quadratic equations
A. Review Factoring
B. Completing the square
C. The quadratic formula
D. The discriminant
E. Complex roots
Solving equations involving quadratic forms
Review graphing linear equations and slope of a line
Graphing inequalities in two variables
Distance and midpoint formulas
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
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Methods of Presentation
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D. Composite
E. Inverse
Direct and inverse variation
Exponential and logarithmic functions
A. Definition
B. Properties of logarithms
C. Graphing
D. Applications
Graphing general circles
Systems of linear equations using elimination and substitution
A. Review two by two systems
B. Three by three systems
Optional topics (instructor’s choice)
A. Sequences and series
B. Conic sections
C. Simple counting principles
Lecture/Discussion
Class discussion of problems, solutions and student’s questions
Audio-visual materials
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
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B.
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?
Collaboratives- Perform an experiment with water and coffee filters and model with an
exponential function.
2. Methods of Evaluating Student Progress
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Textbook (Typical):
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Exams/Tests
Quizzes
Home Work
Final Examination
Blitzer (2006). Algebra for College Students Pearson-Prentice Hall.
Special Student Materials
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A graphing calculator may be required