2024-2025: College Algebra

Course Overview/Description

This course is a detailed study of functions and their graphs. Graphing calculators are used extensively. Topics covered include linear and quadratic equations, inequalities, polynomial and rational functions, exponential and logarithmic equations, and systems of equations. All PowerPoint lessons, fill-in note sheets, homework calendars, and test review materials will be available on my website. 

Course Learning Goals

Students will do the following in this course.

• Understand the real number system and classify numbers as natural numbers, whole numbers, integers, rational numbers and irrational numbers.
• Describe the rectangular coordinate system and find the distance between two points.
• Graph functions, determine their domain and range.
• Use graphs of functions to solve equations and optimize functions.
• Graph equations by hand and by using the graphing calculator.
• Solve linear, quadratic and radical functions.
• Graph the equations of a straight line and state the equations under several conditions.
• Understand when a relation is a function and find the inverse of a function.
• Use quadratic and linear functions to solve applied problems.
• Locate maxima and minima of functions.
• Identify, characterize, graph, apply, optimize polynomial, rational, radical, exponential and logarithmic functions.
• Solve polynomial, rational, radical, exponential and logarithmic equations.
• Sketch graphs of polynomial functions; apply factor theorem and remainder theorem; manipulate complex numbers.
• Find the value of exponential functions, convert from an exponential to a logarithmic and vice-versa, along with finding unknowns in logarithmic equations.
• Solve linear systems of equations with two or three variables.
• Find the equation for each conic section.
• To think logically and mathematically.

Course Outline:

• Polynomials Review
• Unit 1: Lines
• Unit 2: Functions
• Unit 3: Systems
• Unit 4: Matrices
• Unit 5: Quadratics
• Unit 6: Polynomials
• Midterm Exam 
• Unit 7: Rational Expressions and Equations
• Unit 8: Radical Expressions and Equations
• Unit 9: Exponentials and Logarithms
• Unit 10: Conics
• Final Exam

Methodology / Instructional Practices:

Instruction in this course emphasizes conceptual understanding, procedural skill development, problem-solving proficiency, critical thinking abilities, and situational analysis. Students will engage in a rich learning experience designed to strengthen their mathematical foundation and prepare them for future mathematical challenges. This is a fully web-based course with no face-to-face class meetings, allowing you to work at your own pace within set deadlines. It's important to note that this is not a self-paced class, and regular interaction with both fellow students and your instructor is essential for success. You will have assigned deadlines, and work must be submitted on time.

Course Materials

Required Texts:

Lial, Margaret L., John Hornsby, David I. Schneider, and Daniels J. Callie. College Algebra. 11th ed. Boston: Pearson, 2013.

The course uses Google Drive, Canvas, Discord, and Zoom. The live course meetings are hosted on Zoom. We will use DeltaMath, Desmos, and Kahoot. Scanner, cell phone, or camera to submit handwritten test and homework material as a good quality PDF.

Additional Course Resources:

TI-83 plus or TI-84 (or plus) calculator will be used regularly to reinforce and extend each concept. They will also be used to investigate topics and assist in interpreting results. Concepts will be taught in unifying the themes of the course.

A variety of printed and digital content may be provided during the course. Digital content will be found within the Canvas course site. There may be additional reading assignments as student interests dictate.

Technology/Software Requirements

1. Computer with an updated operating system (e.g. Windows, Mac, Linux) 
2. Updated Internet browsers (Google Chrome or Mozilla Firefox)
3. Ability to use Google Workspace for Education 
4. Minimum Processor Speed of 1 GHz or higher recommended. 
5. Reliable and stable internet connection.
6. Adobe Reader or alternative PDF reader (free)
7. A webcam and/or microphone is highly recommended.