Departmental Syllabus for Algebra

UPG Catalog Description: A college-level algebra course that covers topics
such as operations with polynomials and rational expressions, linear equations
and inequalities in one variable , linear equations in two variables and their
graphs, factoring , roots, and radicals. Additional topics such as complex fractions,
functions and their graphs , logarithms, and exponential functions are
covered in less depth.

Prerequisite : Placement or Math 6000 with a grade of C or better.
Current Text: Intermediate Algebra by D. Franklin Wright, 5th Edition.

Topics to covered:
1. Review of Real Numbers , Solving Equations , and Exponents:
• Properties of Real Numbers
• Operations with Real Numbers
• Linear equations and absolute value equations
• Evaluating and solving formulas
• Applications
• Linear inequalities and absolute value inequalities
• Properties of exponents

2. Straight Lines and Functions:
• Cartesian coordinate system and straight lines
• Slope intercept form
• Point intercept form
• Introduction to functions
• Graphing linear inequalities

3. Systems of Linear Equations :
• Systems of linear equations in two variables and applications
• Systems of linear equations in three variables*
• Graphing systems of linear inequalities*

4. Polynomials :
• Addition and subtraction of polynomials
• Multiplication of polynomials
• Division of polynomials and synthetic division
• Introduction to factoring
• Special factoring techniques
• Polynomial equations and applications

5. Rational Expressions :
• Multiplication and division of rational expressions
• Addition and subtraction of rational expressions
• Complex fractions
• Equations and inequalities with rational expressions
• Applications (Variation*)

6. Roots , Radicals , and Complex Numbers:
• Roots and Radicals
• Rational Exponents
• Arithmetic with Radicals
• Functions with Radicals
• Introduction to Complex Numbers*
• Multiplication and division with Complex Numbers*

7. Quadratic Equations :
• Completing the square
• The Quadratic Formula
• Applications
• Equations with Radicals
• Equations in quadratic form

8. Quadratic Functions:
• Quadratic functions (Parabolas)

9. Exponential and Logarithmic Functions :
• Operations of functions
• Inverse functions
• Exponential functions
• Logarithmic functions
• Properties of Logarithms
• Logarithmic and exponential equations
• Applications*

NOTE:  means if times allows .
NOTE: The order of presentation of the contents of this syllabus, exams, and
grading policies are entirely at the discretion of the individual instructor.