Course Information
| Course Title: | College Algebra |
| Course Code: | None |
| Credits: | 0 credits |
| Certificate Provider: | Westcott Courses |
| Grading Mode: | Standard letter grade |
| Proctored Final: |
No |
Textbook Requirement:
No outside textbook is needed. Our Omega Math
TM courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Our lessons start out with the easiest examples, and then move slowly to the more advanced problems. Between examples, there are interactive problems which make sure the student understands the concepts, as well as enables the student to store the information into long term memory.
Course Description
Presents a study of College Algebra and Analytic Geometry with an emphasis on mathematical modeling. The student will analyze functions in depth including transformations, inverses and compositions, while paying particular attention to quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Other topics include complex numbers, the binomial theorem, arithmetic and geometric sequences, series, systems of equations and inequalities, matrices and determinants, partial fractions, algebraic equations and inequalities, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students should be able to solve practical problems and use appropriate models for analysis. This course is designed to prepare students for Calculus.
College Algebra is an Omega Math
TM Course.
Prerequisite: Intermediate Algebra with a grade of C or better.
Learning Outcomes
At the conclusion of this course, students should be able to:
- Represent functions verbally, numerically, graphically and algebraically. Demonstrate a fundamental concept of the mathematical function and its properties such as inverse, domain, range, addition, subtraction, product, division, and composition.
- Sketch graphs, appropriate transformations and inverses for polynomial functions, rational functions, trigonometric functions, exponential and logarithmic functions, rational functions, piece-wise functions, and conic sections.
- Analyze the graph of a function and determine the intervals where the graph is increasing, decreasing and constant. Find the minimum and maximum values of the function and apply these concepts to applications in the physical world.
- Solve a variety of equations, including linear, polynomial, rational, radical, exponential and logarithmic.
- Solve a variety of systems including linear, nonlinear and inequalities using graphical and algebraic techniques. Solve real-world applications modeled by these systems.
- Use the Rational Root Theorem, Fundamental Theorem of Algebra and other techniques to find the zeros of a polynomial function. Be able to factor a polynomial into linear factors over the complex numbers.
- Perform operations with matrices, such as addition, subtraction, scalar multiplication and matrix multiplication, including applications with matrices. Use matrices to solve systems of linear equations including the Gauss-Jordan elimination method, and the inverse of a matrix.
- Identify and express conic sections in standard rectangular form, graph the conic, and solve applied problems.
- Express general terms of an arithmetic and geometric sequence. Write series in summation notation, find the sum of an arithmetic and geometric series, and use the Binomial Theorem to expand powers of binomials.
- Determine the sample space of an event and calculate the probability of an experiment.
- Recognize a language description, geometric and algebraic representation, and be able to transfer from one form to the other.
- Identify and express conic sections in standard rectangular form, graph the conics, and solve applied problems.
- Model situations from a variety of settings using functions. Apply a variety of problem-solving strategies, including algebraic, numerical and graphical techniques to solve these real world applications.
Methods Of Evaluation
Homework quizzes 15%
Chapter tests 60%
Final Exam 25%
(You must get at least 60% on this final in order to pass the class with a C or better.)
Homework Quizzes: 15%
Homework assignments are essential in a mathematics course. It is not possible to master the course without a considerable amount of time being devoted to studying the concepts and solving problems. Each lesson contains a set of homework problems, and you are required to do all the odd problems for each section. Work out each problem, and then check the solution manual for a detailed solution. Do not continue to the next problem until you understand your mistake. Once you feel comfortable with the homework set, take the homework quiz for that section. The homework quizzes are revised problems from the homework sets. You may take each quiz twice, and the higher of the two scores is used to calculate your quiz grade. Once you take a quiz, figure out what you did wrong on the problems that you missed and then try the quiz again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the test or the final. The struggle to figure out what you did wrong stores the mathematics into your long-term memory, and aids in building abstract thinking.
Chapter Tests: 60%
After you have completed a chapter, and understand everything in the lessons, homework sets and quizzes, take the chapter test. The chapter tests are revised problems from the quizzes. You may take each chapter test twice, and the higher of the two scores is used to calculate your chapter test grade. Once you take a chapter test, figure out what you did wrong on the problems that you missed and then try the chapter test again. It is important to figure what you did wrong before you push forward. If you figure out your errors at this step, you will be less likely to make the same error on the final.
Assessment
A 90-100 A Clearly stands out as excellent performance and, exhibits mastery of learning outcomes.
B 80-89 B Grasps subject matter at a level considered to be good to very good, and exhibits partial mastery of learning outcomes.
C 70-79 C Demonstrates a satisfactory comprehension of the subject matter, and exhibits sufficient understanding and skills to progress in continued sequential learning.
D 60-69 D Quality and quantity of work is below average and exhibits only partial understanding and skills to progress in continued sequential learning.
F 0-59 F Quality and quantity of work is below average and not sufficient to progress.
Instructional Process
In this course we will explore mathematical concepts, methods and applications from life issues, business and finance, social and environmental issues. Civic and social issues will be used as problems to apply the subject principles. Using the civic, social, and life related examples will help students understand the subject at a deeper level. After an introduction in each section, problems will be solved that start with the easiest examples and move slowly to the more advanced problems with Student Interactive Problems (SIP) in between. The SIPs are important! They give you a chance to slow down and make sure you understand the material. If you get the problem correct, continue on with the next example. If you get the problem wrong, you will be taken to a page that works out the problem in detail. The SIPs play a large part in storing the topics along with their procedures into your long-term memory. Each homework set contains applications for that lesson. These real life applications create a better understanding of math in our world and how it applies to every day life.
Course Content Menu
| Lessons | Homework | Quiz |
| |
| 1.1 - Properties of Real & Complex Numbers | 1.1 | 1.1 |
| 1.2 - Polynomials | 1.2 | 1.2 |
| 1.3 - Factoring | 1.3 | 1.3 |
| 1.4 - Linear Equations | 1.4 | 1.4 |
| 1.5 - Linear Inequalities | 1.5 | 1.5 |
| 1.6 - Quadratic Equations | 1.6 | 1.6 |
| 1.7 - Rational & Other Non-linear Equations | 1.7 | 1.7 |
| 1.8 - Non-linear Inequalities | 1.8 | 1.8 |
| |
| Chapter 1 Test ( 28 questions ) |
| |
| Chapter 2 - Functions and their Graphs |
| Lessons | Homework | Quiz |
| |
| 2.1 - Relations & Functions | 2.1 | 2.1 |
| 2.2 - Domain and Range of a Function | 2.2 | 2.2 |
| 2.3 - Linear Equations and Functions | 2.3 | 2.3 |
| 2.4 - Combinations of Functions | 2.4 | 2.4 |
| 2.5 - Graphs of Functions | 2.5 | 2.5 |
| 2.6 - Transformation of Functions | 2.6 | 2.6 |
| 2.7 - Inverse Function | 2.7 | 2.7 |
| |
| Chapter 2 Test ( 37 questions ) |
| |
| Chapter 3 - Polynomial and Rational Functions |
| Lessons | Homework | Quiz |
| |
| 3.1 - Quadratic Functions | 3.1 | 3.1 |
| 3.2 - Graphs of Polynomial Functions | 3.2 | 3.2 |
| 3.3 - Division of Polynomials | 3.3 | 3.3 |
| 3.4 - Zeros of Polynomial Functions | 3.4 | 3.4 |
| 3.5 - More on Zeros of Polynomial Functions | 3.5 | 3.5 |
| 3.6 - Graphs of Rational Functions | 3.6 | 3.6 |
| |
| Chapter 3 Test ( 29 questions ) |
| |
| Chapter 4 - Exponential and Logarithmic Functions |
| Lessons | Homework | Quiz |
| |
| 4.1 - Exponential Functions | 4.1 | 4.1 |
| 4.2 - Logarithmic Functions | 4.2 | 4.2 |
| 4.3 - Properties of Logarithmic Functions | 4.3 | 4.3 |
| 4.4 - Exponential and Logarithmic Equations | 4.4 | 4.4 |
| 4.5 - Applications of Exponential & Logarithmic Functions | 4.5 | 4.5 |
| |
| Chapter 4 Test ( 28 questions ) |
| |
| Chapter 5 - Linear and Nonlinear Systems |
| Lessons | Homework | Quiz |
| |
| 5.1 - Linear Systems in Two Variables | 5.1 | 5.1 |
| 5.2 - Linear Systems in Three Variables | 5.2 | 5.2 |
| 5.3 - Partial Fractions | 5.3 | 5.3 |
| 5.4 - Nonlinear Systems in Two Variables | 5.4 | 5.4 |
| |
| Chapter 5 Test ( 22 questions ) |
| |
| Chapter 6 - Matrices and Determinants |
| Lessons | Homework | Quiz |
| |
| 6.1 - Introduction to Matrices | 6.1 | 6.1 |
| 6.2 - Matrix Multiplication | 6.2 | 6.2 |
| 6.3 - Solving Systems using Matrices | 6.3 | 6.3 |
| 6.4 - Systems without a Unique Solution | 6.4 | 6.4 |
| 6.5 - Applications of Linear Systems using Matrices | 6.5 | 6.5 |
| 6.6 - Determinants | 6.6 | 6.6 |
| 6.7 - The Inverse of a Matrix | 6.7 | 6.7 |
| |
| Chapter 6 Test ( 27 questions ) |
| |
| Chapter 7 - Sequences and Series |
| Lessons | Homework | Quiz |
| |
| 7.1 - Sequences and Series | 7.1 | 7.1 |
| 7.2 - Arithmetic Sequences | 7.2 | 7.2 |
| 7.3 - Geometric Sequences | 7.3 | 7.3 |
| 7.4 - Binomial Theorem | 7.4 | 7.4 |
| |
| Chapter 7 Test ( 23 questions ) |
| |
| Chapter 8 - Conic Sections |
| Lessons | Homework | Quiz |
| |
| 8.1 - The Circle | 8.1 | 8.1 |
| 8.2 - The Parbola | 8.2 | 8.2 |
| 8.3 - The Ellipse | 8.3 | 8.3 |
| 8.4 - The Hyperbola | 8.4 | 8.4 |
| 8.5 - Systems of Inequalities | 8.5 | 8.5 |
| |
| Chapter 8 Test ( 28 questions ) |
| |
| Lessons | Homework | Quiz |
| |
| 9.1 - Counting | 9.1 | 9.1 |
| 9.2 - Permutations and Combinations | 9.2 | 9.2 |
| 9.3 - Finite Basic Probabilities | 9.3 | 9.3 |
| 9.4 - Basic Laws of Probability | 9.4 | 9.4 |
| 9.5 - Conditional Probability | 9.5 | 9.5 |
| 9.6 - Independent Events | 9.6 | 9.6 |
| |
| Chapter 9 Test ( 22 questions ) |
| |
| College Algebra Final Exam |
Time on Task
This course is online and your participation at home is imperative. A minimum of 8 - 10 hours per week of study time is required for covering all of the online material to achieve a passing grade. You must set up a regular study schedule. You have five months of access to your online account with a thirty-day extension at the end if needed. If you do not complete the course within this time line, you will need to enroll in a second term.
Schedule
Below is the suggested time table to follow to stay on a 17 week schedule for the course. The following schedule is the minimum number of sections that need to be completed each week if you would like to finish in a regular semester time frame. You do not have to adhere to this schedule. You have five months of access plus a 30 day extension at the end if needed. You can finish the course as soon as you are able, with a minimum coursework time of at least four weeks.
| Week |
Complete Sections |
| 1 |
1.1 - 1.3 |
| 2 |
1.4 - 1.7 |
| 3 |
2.1 - 2.3 |
| 4 |
2.4 - 2.6 |
| 5 |
2.7 - 3.2 |
| 6 |
3.3 - 3.5 |
| 7 |
3.6 - 4.2 |
| 8 |
4.3 - 4.5 |
| 9 |
5.1 - 5.3 |
| 10 |
5.4 - 6.2 |
| 11 |
6.3 - 6.5 |
| 12 |
6.6 - 6.8 |
| 13 |
7.1 - 7.3 |
| 14 |
7.4 - 8.2 |
| 15 |
8.3 - 8.5 |
| 16 |
9.1 - 9.3 |
| 17 |
9.4 - 9.6 |
| Final Exam |
|
Code of Conduct:
It is the student's responsibility and duty to read the information below and become acquainted with all provisions of what constitutes academic misconduct involving the topics below. Students are required to read each statement below, and the given repercussions. There are no exceptions to these policies, and the pretext of not reading each part will not be deemed as a reasonable excuse to contest the policies.
Code of Ethics:
Regulations and rules are necessary to implement for classroom as well as online course behavior. Students are expected to practice honesty, integrity and respect at all times.
The definition of academic cheating is an act of dishonesty in order to obtain a higher grade in the course, and to gain an advantage over other students in the course.
Each of the infractions below represents a result of performing an act of dishonesty in order to obtain a higher grade in the course. The result of any of the offenses may result in an F in the course, and possible expulsion from Westcott. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct.
Examples of academic misconduct:
(A) Payments:
Student's who engage in fraudulent chargebacks for payments, will have their course(s) deactivated. Students who initiate chargebacks will not be able to take finals in their other courses until the courses with the chargebacks have been paid in full.
Westcott reserves the right to permanently expel a student from Westcott Courses for chargebacks.
(B) Cheating:
Any form of cheating is forbidden during exams and will result in an F in the class. By signing up for a course, you are legally signing a contract that states that the person who is named taking this course is the actual individual doing the course work and all examinations. You also agree that for courses that require proctored testing, that your final will be taken at a college testing center, a Sylvan Learning center or our one approved online proctor, and the individual signed up for this course will be the one taking the test. Thumb prints will be taken at the testing center and verified with the Department of Justice that the student taking the final, is the named student. Conspiracy to commit fraud is a federal crime, and any person attempting to take the final for another will be charged along with the student. Information about the federal charges will forever be available to other colleges and universities.
Unauthorized collaboration
By enrolling in a course offered through Westcott Courses, all students agree that they will do all of their own work. Students that engage in questionable behavior or suspicious activities will be deactivated and blocked from enrolling in future courses. This includes but is not limited to hiring a company whose business it is to do some or all the course work for the student and/or helping them remotely cheat on the final exam by using remote access. We collect the IP address for these test cheaters and record when they take a test for one of our students. A lot of these IP address come from countries outside the US. If a student's account shows they have tests/quizzes taken by one of these companies, their work will not be accepted and will receive an F for cheating. If students have tests taken with IP addresses outside the US, they may be asked to show proof that they have traveled outside the US to these destinations. This includes showing a stamped password over a zoom meeting for full verification of the location. If the student cannot show they have traveled to these international locations, they will receive an F for having someone else complete their tests and quizzes.
While taking the final with the online proctor, the final will be shut down if it is found that the student is using or most likely using a third party to take their final. Depending on the evidence, the student will either be told they need to take the final at a physical testing center or if there is substantial evidence a third party was indeed involved, then an F for cheating will be posted. If digital cheating is suspected and/or confirmed, all other finals will need to be taken at a physical testing center.
Other forms of cheating that will result in receiving an F:
Other forms of cheating include receiving or providing un-permitted assistance on an exam; taking an exam for another student; using unauthorized materials during an exam; altering an exam and submitting it for re-grading; failing to stop working on the exam when the time is up; providing false excuses to postpone due dates; fabricating data or references. Working with others on graded course work without specific permission of the instructor, including homework assignments, quizzes and tests, is considered a form of cheating.
Fabricating false information to Westcott to conceal cheating in order to gain a grade that was not earned.
Fabricating false information in the context of an academic assignment.
Fabricating or altering information or data and presenting it as legitimate.
Providing false or misleading information to Westcott, an instructor or other staff member.
Fabricating false information to gain access to a higher grade.
Claiming that Westcott Courses lost their test and/or quiz scores.
Copying Westcott Courses content and posting it on the internet. This includes assignments, quizzes, and tests.
Final exams are secure tests and the intellectual property of Westcott Courses. Taking screen shots of a digital final or copying a paper test is stealing our intellectual property and cheating. It is equivalent to stealing a copy of the final exam off an instructor's desk.
Plagiarism: All of the following are considered plagiarism, and will result in a zero on the plagiarized assignment, and there are no opportunities to redo the assignment.
Merriam-Webster defines plagiarism as “the act of using another person's words or ideas without giving credit to that person”
Plagiarism includes, but is not limited to:
- having somebody else write your assignment for you
- turning in an assignment that contains work that is not your own
- changing words in phrases, sentences and/or blocks of text without giving credit to the source (paraphrase)
- copying ideas, phrases, sentences or entire blocks of text without giving credit to the source
- not crediting the correct source by providing incorrect information
Plagiarism is an act of fraud, and can usually be avoided by using quotation marks and citing the source of the material. Instructors apply plagiarism software to find assignments that contain plagiarized material. Again, assignments that contain one of the above infractions will receive a zero on the assignment and the student will not have the opportunity to redo the assignment.
Westcott Courses takes cheating very seriously and will pursue all means available to make sure student's caught cheating face the full consequences for their actions. Westcott reserves the right to permanently expel a student from Westcott courses for cheating and/or fraudulent chargebacks.
(C) Respectful Communication & Anti-Bully Policy
When contacting Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, belittling, harassing, threatening or bullying via telephone, email, or otherwise will be considered a disrespectful communication and/or bullying and will result in a formal warning. Further disrespectful communications will result in a second and final violation of the policy, and the student will immediately and permanently be expelled from Westcott. These students will not under any circumstances, be permitted to continue with their course(s). Westcott Courses has zero tolerance for this type of behavior towards instructors and staff.
A third disrespectful communication will result in a legal cease and desist order, the halting of further communication between our staff and the person(s) speaking on behalf of the student or the student themselves. Further disrespectful communications and/or bullying after a cease and desist order will result in legal action.
Bullying is defined by the CDC and DOE define as:
-Unwanted aggressive behavior
-Observed or perceived power imbalance
-Repetition or high likelihood of repetition of bullying behaviors
Additional unacceptable behaviors that fall under bullying policy, but are not limited to:
-Informing the instructor not to apply the regular grading system to their assignments, but to mark all their assignments with A’s.
-Discrediting the instructor’s authority and educational ability to set up the course content correctly. (Note: All our instructors hold a graduate degree in their field of study and teach at a California Community College and/or a California State University. They all have 20+ years teaching experience.)
-Playing the victim while concurrently bullying staff and/or instructors, and insist this justifies the behavior. This includes calling Westcott's staff or instructors racist, even though we don't know the student's race and they don't know ours. Or playing the victim after being issued the first violation of the Respectful Communications & Bullying Policy, and blaming others instead of taking responsibility for their unacceptable behavior.
-Threatening lawsuits because they are angry that we will not permit their violations of our policies. All threats of this kind will result in no further communication with the student.
We reserve the right to refuse service to anyone who violates our polices. If Westcott Courses receives disrespectful communications or bully tactics from person(s) representing the student, or the student themselves, the student will be expelled from Westcott Courses.
(D) Grading information and proctored final policies:
The grading rules are put in place to protect the integrity of online education by stopping grade inflation, which is done by demanding a display of competency in exchange for a grade.
By agreeing to the terms of service agreement, you agree to read the 'Grading and Course Directions' page within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first log-in to notify Westcott Courses if you do not agree to the grading policy and proctored final policy ( if applicable ) outlined in the pages inside of your account, otherwise it is assumed that you agree with the policies.
There are no exceptions to these policies, and the pretext of not reading the pages will not be deemed as a reasonable excuse to contest the policies.
Before students take the final, they sign a grade disclaimer, which gives them the exact grades on the final and the overall course grade that those grades produce. Depending on the course discipline, students either have to get a 50% or 60% on the final to get a C or better in the course.
Student's who contest this grading policy after they have signed their grade disclaimer and taken the final, will be considered trying to cheat in order to obtain a higher grade and will receive an F. The grade disclaimer is a legal and binding contract and should be read carefully before signing. The pretext of not reading this document is not an excuse for contesting the policies.
If you have questions, please read more information about plagiarism at plagiarism.org, or ask your instructor.
Important Notes:
This syllabus is subject to change and / or revision during the academic year. Students with documented learning disabilities should notify our office upon enrollment, as well as make sure we let the testing center know extended time is permitted. Valid documentation involves educational testing and a diagnosis from a college, licensed clinical psychologist or psychiatrist.
