College Algebra
Topic outline
-
Welcome to College Algebra [CMAT 1213]!
Course Introduction
This College Algebra [CMAT 1213] course adheres to the scope and sequence of a one-semester College Algebra course. The course description provided is the from the statewide common course information.Course Description: In-depth treatment of solving equations and inequalities; function properties and graphs; inverse functions; linear, quadratic, polynomial, rational, exponential and logarithmic functions with applications; systems of equations.
Upon successful completion of this course, the student will be able to:
- Solve equations and inequalities.
- Graph and analyze mathematical functions.
-
- Model and solve application problems.
Adopting instructors can embed a welcome video or add additional text here.
Structure of the CourseThe course includes 6 content Modules which covers each of the 6 chapters in the textbook (provided link). Each module includes a brief introduction text with module learning objectives, links to the corresponding Pressbook sections, homework assignments in MyOpenMath, a Chapter Review with Exercises, a Chapter Practice Test, a Quiz in MyOpenMath, and a Q&A discussion forum for that Module. There are additional modules for smaller Exams, a Midterm Exam, and/or Final Exam.
Navigating the Course
This course is set up in Modules covering various topics which may be accessed from the course navigation menu on the left or by scrolling below. Modules may be collapsed in the menu and it the body of the course to minimize scrolling. Many items are required and may be marked as completed automatically when the activity has been submitted (the broken check box), but others will marked as done by the student (the solid check box).
Please move through the items below and continue through the Learner Support and Getting Started modules before moving on to Module 1. Be sure to check for announcements and due dates to stay on track.Adopting instructors can embed a navigation video or add additional text here.
This course and its contents are licensed under a Creative Commons Attribution 4.0 International License by LOUIS: The Louisiana Library Network, except where otherwise noted. Adopting instructors should edit the About Your Instructor and Office Hours Information pages in this Module.
-
Adopting instructors should edit all pages in this Module - as per their own Institution's policies.
-
This module contains all the items you should review and complete before you begin Module 1. Before moving on, be sure to:
- Check the News and Announcements Forum
- Read the Course Syllabus
- Introduce yourself to the class
- Read the instructions for the Q & A Forum
Good luck in the course!-
This forum contains general news and announcements. You can find all announcements listed in the "Latest News" block in Course Tools within this course or on your My Courses page.
-
Students mustMark as done
Use this forum to tell us a little about yourself and your interests. Some topic ideas:
- What is your field of study/research interest or concentration?
- What are you most interested in learning about in this class and why?
- Have you ever taken an online class before?
- Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.
-
Students mustMark as done
Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours M-F, next business day on weekends.]
Subscription should be set to Auto.
-
This forum contains general news and announcements. You can find all announcements listed in the "Latest News" block in Course Tools within this course or on your My Courses page.
-
Students mustMark as done
Use this forum to tell us a little about yourself and your interests. Some topic ideas:
- What is your field of study/research interest or concentration?
- What are you most interested in learning about in this class and why?
- Have you ever taken an online class before?
- Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.
-
Students mustMark as done
Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours M-F, next business day on weekends.]
Subscription should be set to Auto.
-
This forum contains general news and announcements. You can find all announcements listed in the "Latest News" block in Course Tools within this course or on your My Courses page.
-
Students mustMark as done
Use this forum to tell us a little about yourself and your interests. Some topic ideas:
- What is your field of study/research interest or concentration?
- What are you most interested in learning about in this class and why?
- Have you ever taken an online class before?
- Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.
-
Students mustMark as done
Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours M-F, next business day on weekends.]
Subscription should be set to Auto.
-
This forum contains general news and announcements. You can find all announcements listed in the "Latest News" block in Course Tools within this course or on your My Courses page.
-
Students mustMark as done
Use this forum to tell us a little about yourself and your interests. Some topic ideas:
- What is your field of study/research interest or concentration?
- What are you most interested in learning about in this class and why?
- Have you ever taken an online class before?
- Any other information you would like to share with your classmates, such as special interests or activities.
Post a picture! We look forward to meeting you.
-
Students mustMark as done
Use this forum to ask your instructor any questions you have about the course. You may post at any time, and your instructor will respond here. Be as specific as possible.
Please keep in mind that others can see your posts, so do not post any personal information. If you have questions about your grade, please email your instructor directly. You can expect a response to posts and emails within [X] hours. [Recommendation is 24 hours M-F, next business day on weekends.]
Subscription should be set to Auto.
- Check the News and Announcements Forum
-
It’s a cold day in Antarctica. In fact, it’s always a cold day in Antarctica. The coldest temperature ever recorded, over one hundred degrees below zero on the Celsius scale, was recorded by remote satellite. It is no surprise then, that no native human population can survive the harsh conditions. Only explorers and scientists brave the environment for any length of time.
Measuring and recording the characteristics of weather conditions in Antarctica requires a use of different kinds of numbers. For tens of thousands of years, humans have undertaken methods to tally, track, and record numerical information. While we don't know much about their usage, the Lebombo Bone (dated to about 35,000 BCE) and the Ishango Bone (dated to about 20,000 BCE) are among the earliest mathematical artifacts. Found in Africa, their clearly deliberate groupings of notches may have been used to track time, moon cycles, or other information. Performing calculations with them and using the results to make predictions requires an understanding of relationships among numbers. In this chapter, we will review sets of numbers and properties of operations used to manipulate numbers. This understanding will serve as prerequisite knowledge throughout our study of algebra.
Image Caption: Earth’s southernmost continent, Antarctica experiences the coldest, driest, and windiest conditions known. (Credit: Andreas Kambanls)
(Content & Image Source: Chapter 1 Introduction, Algebra and Trigonometry 2e, Jay Abramson, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:Section 1.1 Real Numbers: Algebra Essentials
- Classify a real number as a natural, whole, integer, rational, or irrational number. (CLO #)
- Perform calculations using order of operations.
- Use the following properties of real numbers: commutative, associative, distributive, inverse, and identity.
- Evaluate algebraic expressions.
- Simplify algebraic expressions.
Section 1.2 Exponents and Scientific Notation
- Use the product rule of exponents.
- Use the quotient rule of exponents.
- Use the power rule of exponents.
- Use the zero exponent rule of exponents.
- Use the negative rule of exponents.
- Find the power of a product and a quotient.
- Simplify exponential expressions.
- Use scientific notation.
Section 1.3 Radicals and Rational Exponents
- Evaluate square roots.
- Use the product rule to simplify square roots.
- Use the quotient rule to simplify square roots.
- Add and subtract square roots.
- Rationalize denominators.
- Use rational roots.
Section 1.4 Polynomials
- Identify the degree and leading coefficient of polynomials.
- Add and subtract polynomials.
- Multiply polynomials.
- Perform operations with polynomials of several variables.
Section 1.5 Factoring Polynomials
- Factor the greatest common factor of a polynomial.
- Factor a trinomial.
- Factor by grouping.
- Factor a perfect square trinomial.
- Factor a difference of squares.
- Factor the sum and difference of cubes.
- Factor expressions using fractional or negative exponents.
Section 1.6 Rational Expressions
- Simplify rational expressions.
- Multiply rational expressions.
- Divide rational expressions.
- Add and subtract rational expressions.
- Simplify complex rational expressions.
To achieve these objectives:- Read the Module 1 Introduction (see above).
- Read Sections 1.1 - 1.6 of Chapter 1: Prerequisites in College Algebra (links to each Section provided below)
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
- Practice the problems on the Chapter 1 Review Exercises, checking the solutions provided (link provided below)
- View the Chapter 1 Practice Test (link provided below)
- Complete the MyOpenMath Quiz for Chapter 1 (link provided below) - This is graded!
- Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 1 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.
-
For most people, the term territorial possession indicates restrictions, usually dealing with trespassing or rite of passage and takes place in some foreign location. What most Americans do not realize is that from September through December, territorial possession dominates our lifestyles while watching the NFL. In this area, territorial possession is governed by the referees who make their decisions based on what the chains reveal. If the ball is at point A (x1, y1) then it is up to the quarterback to decide which route to point B (x2, y2) the end zone, is most feasible.
Image Caption: A large orange circle with an arrow printed on it facing to the right atop a rectangular base, known as chains in football, is shown prominently in the foreground. In the background there is a game of football ongoing with fans in their seats. (Credit: Jeramey Jannene, Flickr)
(Content & Image Source: Chapter 2 Introduction, Algebra and Trigonometry, Jay Abramson, OpenStax, CC BY 4.0 License)
Upon completion of this module, you will be able to:Section 2.1 Linear Equations in One VariableSection 2.2 Models and Applications- Solve equations in one variable.
- Solve a rational equation.
Section 2.3 Complex Numbers- Set up a linear equation to solve a real-world application.
- Use a formula to solve a real-world application.
Section 2.4 Quadratic Equations- Add and subtract complex numbers.
- Multiply complex numbers.
- Divide complex numbers.
- Simplify powers of i
Section 2.5 Other Types of Equations- Solve quadratic equations by factoring.
- Solve quadratic equations by the square root property.
- Solve quadratic equations by completing the square.
- Solve quadratic equations by using the quadratic formula.
- Solve equations involving rational exponents.
- Solve equations using factoring.
- Solve radical equations.
- Solve absolute value equations.
- Solve other types of equations.
Section 2.6 Linear Inequalities and Absolute Value Inequalities- Write solutions using interval notation.
- Solve inequalities in one variable algebraically.
- Solve absolute value inequalities.
To achieve these objectives:- Read the Module 2 Introduction (see above).
- Read Sections 2.1 - 2.6 of Chapter 2: Equations and Inequalities in College Algebra (links to each Section provided below)
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- At the end of each Section there is a list of Key Concepts, Section Exercises, and a Glossary of terms
- Complete the MyOpenMath Homework Assignments for each Section (links provided below) - These are graded!
- Practice the problems on the Chapter 2 Review Exercises, checking the solutions provided (link provided below)
- View the Chapter 2 Practice Test (link provided below)
- Complete the MyOpenMath Quiz for Chapter 2 (link provided below) - This is graded!
- Once you complete the Quiz, upload your work in the Quiz Work Upload Assignment using the submission link below.
- Post in the Chapter 2 Q&A Discussion Forum - link provided below.
Note the check boxes to the right that help you track your progress: some are automatic, and some are manual.
Module Pressbooks Resources and Activities
You will find the following resources and activities in this module at the Pressbooks website. Click on the links below to access or complete each item.