# Precalculus

**Course Code:**None

**Credits:**Noncredit

**Certificate Via Westcott**

Enroll Now (Noncredit)

View the Credit Option

**Credit Information**

Course Title: | Precalculus |

Course Code: | None |

Credits: | Noncredit |

Certificate Provider: | Westcott Courses |

Transfer: | No, but can be used at some colleges as a prerequisite. |

Grading Mode: | Standard letter grade |

**Course Requirements**

Enrollment Type: | Rolling | Sign up and start any day of the year. |

Requires Textbook? | No | All of the course materials are online. |

Proctored Final: | No | The noncredit version doesn't have a proctored final; but your college may require it. |

**Course Description**

This course was designed to emphasize topics which are fundamental to the study of calculus. 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 right triangle trigonometry, trigonometric identities and equations, vectors, complex numbers, Laws of sines and cosines, the binomial theorem, arithmetic, geometric sequences and series, systems, partial fractions, matrices and determinants, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students will be able to solve practical problems and use appropriate models for analysis.

Precalculus is an Omega Math

^{TM}Course.

**Prerequisite:**Intermediate Algebra with a grade of C or better.

**Course Pricing**

The full cost of the course is $150.00; however, you may use the payment plan to split the cost into two payments.

**Payment Plan:**

1st payment: $86.00 (Start your class immediately!)

2nd payment: $71.00 (Automatically charged 30 days later.)

Enroll Now - Noncredit - $150 View Credit Option - $498

**Helpful Links:**

Math Placement Test

View a free Demo Lesson from this course.

See the Certificate & Preapproval tab for more details on this topic.

The noncredit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. The noncredit courses can be used for remediation, personal enrichment, or students can learn the material and then receive credit at a home college using their college's Credit by Examination option.

**Enrollment Information**

Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 1 - 3 months. The upper level math courses, such as Calculus and above, usually take students 2 - 4 months.

**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.

**Proctored Final Requirement:**

A proctored final is not required for the noncredit courses. However, many colleges permit their students to use our noncredit certificate as a prerequisite for the next level course. These colleges require a proctored final for the course. If you are a student from one of these colleges, the final exam must be proctored at college testing center or a Sylvan Learning Center. A valid driver's license or State ID must be shown at the testing center. An expired license or State ID will not be accepted. Use this link to help you find a college testing center or Sylvan Learning center near your home: Proctored Final Instructions

Note: Cal State Maritime, San Francisco State University, and College of the Desert provide a testing center for their students on their campus.

**Student's Requirements:**

You must have internet access.

You must have access to email.

Omega Math

^{TM}Courses - you must be at or above a 7th grade reading level. Other courses require at least a 10th grade reading level.

**Payment Plan:**

The cost of each class can be divided into two payments by checking the payment plan box when you enroll. The first payment is 55% of the total amount, and the second payment is 45% of the total amount. Your first payment will be charged when you enroll, and the second payment will be charged in 30 days. Your course is activated once your first payment is made. There is a $3.50 additional fee for the credit card split for each of the two payments.

If paying by check, you can either send in a check for the two payments 30 days apart. Or you may send in both checks at the same time, with one post dated by 30 days for the 2nd payment. Just click on "Check by Mail" under Payment Information when you enroll. The form at the end of your enrollment will give you the address for mailing the checks.

**Certificate Information:**

A certificate of completion is issued from Westcott Courses, which includes a letter grade and an overall percentage earned in the class. This course under the noncredit option does not go through Brandman University; thus, it does not carry any units and an official transcript is not included with the course. Some colleges such as Cal State Maritime, San Francisco State University, College of the Desert, etc., accept the certificate of completion for this class as a prerequisite towards another course on their campus. Please see our Associated Schools page to see if your college will accept this class under noncredit. If your college is not on this list, then they most likely want you to take the class under the credit option, which will go through Brandman University.

If you would like preapproval from your school, please see the section below on "Preapproval from your School".

**Transfer Information:**No, but can be used at some colleges as a prerequisite.

Courses under noncredit are not transferable. If you would like to take this class for personal enrichment, the noncredit course is the exact same class as the credit course; it is just less expensive since it is not sent through our partner university for credit. If you want to transfer the course to your college, you will need to enroll under the semester credit option. If you would like preapproval from your school, please send your counselor or registrar's office the link to this page. The noncredit courses can also be used to learn the material and then receive credit at a home college using Credit by Examination.

(K-12 use)

**Preapproval from your School:**

Westcott Courses/Omega Math is the teacher of the course, and a certificate of completion is issued. A course under the noncredit option cannot be used towards college graduation; however, it may be able to be used as a prerequisite at some colleges, such as College of the Desert, and/or graduate programs. View the Associated Colleges page to see if your school is listed. If your school is not on our list, they will most likely want the official transcript and semester credits from our credit option. Click on the link above "View the Credit Option", and then view the Preapproval tab.

## Course Information

Course Title: | Precalculus |

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

This course was designed to emphasize topics which are fundamental to the study of calculus. 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 right triangle trigonometry, trigonometric identities and equations, vectors, complex numbers, Laws of sines and cosines, the binomial theorem, arithmetic, geometric sequences and series, systems, partial fractions, matrices and determinants, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students will be able to solve practical problems and use appropriate models for analysis.Precalculus 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, including quadratic, polynomial, rational, power, root/radical, exponential, logarithmic and piecewise-defined functions. Model a variety of real-world problems and applications involving functions.
- Determine if a graph is a function, find the domain and range and be able to perform transformations including translations, reflections, stretching and shrinking.
- Perform function operations such as addition, subtraction, multiplication, division and composition. Be able to find the inverse of a function and its graph.
- Find the vertex of a quadratic function, the zeros of a polynomial function, the end behavior of the graph, symmetry, intercepts, and asymptotes. Be able to sketch the graph.
- 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.
- Use the Rational Zeros Theorem and the Fundamental Theorem of Algebra to find the zeros of a polynomial function. Be able to factor a polynomial into linear factors over the complex numbers.
- Solve a variety of equations, including linear, polynomial, rational, radical, exponential and logarithmic. Solve a variety of linear and non-linear inequalities.
- Solve systems of linear and non-linear equations graphically and algebraically by substitution and elimination. Be able to solve applications modeled by these systems.
- Identify and express conic sections in standard rectangular form, graph the conics, and solve applied problems.
- Perform operations with matrices: 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, Cramer's Rule and using the inverse of a matrix.
- 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 the probability of an experiment.
- State the basic trigonometric definitions and apply them to the acute angles of a right triangle. Define signs of the trigonometric functions for each quadrant.
- Find the values of the six trigonometric functions using the unit circle and/or one of the special triangles.
- Graph trigonometric functions and their inverses.
- Analyze and interpret trigonometric functions using graphs, tables and equations.
- Describe the measure of an angle in both radians and degrees, convert angles measured in degrees to radian measure and vice versa.
- Apply the Law of Sines and the Law of Cosines for various types of situations.
- Verify and apply trigonometric identities.
- Demonstrate an understanding of vectors, their graphical representation and vector algebra.
- Model situations from a variety of settings using trigonometric functions. Apply a variety of problem-solving strategies, including algebraic, numerical and graphical techniques to solve multiple-step problems involving trigonometric equations and identities.
- Demonstrate real-world problem solving skills: analyze the problem and break it into parts, recognize the concepts applicable to the parts, recognize the relationship between the parts, write the concepts in proper algebraic representations, solve the problem in symbols, interpret the final results.

## 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

Chapter 1 - Functions and their Graphs |

Lessons | Homework | Quiz |

1.1 - Relations & Functions | 1.1 | 1.1 |

1.2 - Domain and Range of a Function | 1.2 | 1.2 |

1.3 - Linear Equations and Functions | 1.3 | 1.3 |

1.4 - Combinations of Functions | 1.4 | 1.4 |

1.5 - Graphs of Functions | 1.5 | 1.5 |

1.6 - Transformation of Functions | 1.6 | 1.6 |

1.7 - Inverse Function | 1.7 | 1.7 |

1.8 - Complex Numbers | 1.8 | 1.8 |

Chapter 2 - Polynomial and Rational Functions |

Lessons | Homework | Quiz |

2.1 - Quadratic Functions | 2.1 | 2.1 |

2.2 - Graphs of Polynomial Functions | 2.2 | 2.2 |

2.3 - Division of Polynomials | 2.3 | 2.3 |

2.4 - Zeros of Polynomial Functions | 2.4 | 2.4 |

2.5 - More on Zeros of Polynomial Functions | 2.5 | 2.5 |

2.6 - Graphs of Rational Functions | 2.6 | 2.6 |

Chapter 3 - Exponential and Logarithmic Functions |

Lessons | Homework | Quiz |

3.1 - Exponential Functions | 3.1 | 3.1 |

3.2 - Logarithmic Functions | 3.2 | 3.2 |

3.3 - Properties of Logarithmic Functions | 3.3 | 3.3 |

3.4 - Exponential and Logarithmic Equations | 3.4 | 3.4 |

3.5 - Applications of Exponential & Logarithmic Functions | 3.5 | 3.5 |

Chapter 4 - Trigonometric Functions |

Lessons | Homework | Quiz |

4.1 - Geometry Review | 4.1 | 4.1 |

4.2 - Angles, Degrees and Special Triangles | 4.2 | 4.2 |

4.3 - Trigonometric Functions | 4.3 | 4.3 |

4.4 - Introduction to the Unit Circle | 4.4 | 4.4 |

4.5 - Right Triangle Trigonometry | 4.5 | 4.5 |

4.6 - Other Angles and Trigonometric Functions | 4.6 | 4.6 |

4.7 - Solving Right Triangles | 4.7 | 4.7 |

4.8 - Applications | 4.8 | 4.8 |

Chapter 5 - Radian Measure & Trigonometric Identities |

Lessons | Homework | Quiz |

5.1 - Reference Angle | 5.1 | 5.1 |

5.2 - Radians and Degrees | 5.2 | 5.2 |

5.3 - Circular Functions | 5.3 | 5.3 |

5.4 - Proving Identities | 5.4 | 5.4 |

5.5 - Sum and Difference Formulas | 5.5 | 5.5 |

5.6 - Double-Angle Formulas | 5.6 | 5.6 |

5.7 - Half-Angle Formulas | 5.7 | 5.7 |

Chapter 6 - Additional Trigonometry Topics |

Lessons | Homework | Quiz |

6.1 - Graphs of Basic Trigonometric Functions | 6.1 | 6.1 |

6.2 - Inverse Trigonometric Functions | 6.2 | 6.2 |

6.3 - Trigonometric Equations | 6.3 | 6.3 |

6.4 - Law of Cosines | 6.4 | 6.4 |

6.5 - Law of Sines | 6.5 | 6.5 |

6.6 - Vectors | 6.6 | 6.6 |

6.7 - Trigonometric Form of a Complex Number | 6.7 | 6.7 |

Chapter 7 - Systems of Equations |

Lessons | Homework | Quiz |

7.1 - Linear Systems in Two Variables | 7.1 | 7.1 |

7.2 - Linear Systems in Three Variables | 7.2 | 7.2 |

7.3 - Partial Fractions | 7.3 | 7.3 |

7.4 - Nonlinear Systems in Two Variables | 7.4 | 7.4 |

Chapter 8 - Matrices |

Lessons | Homework | Quiz |

8.1 - Introduction to Matrices | 8.1 | 8.1 |

8.2 - Matrix Multiplication | 8.2 | 8.2 |

8.3 - Solving Systems using Matrices | 8.3 | 8.3 |

8.4 - Systems without a Unique Solution | 8.4 | 8.4 |

8.5 - Applications of Linear Systems using Matrices | 8.5 | 8.5 |

8.6 - Determinants | 8.6 | 8.6 |

8.7 - Inverse of a Matrix | 8.7 | 8.7 |

Chapter 9 - Sequence, Series, Counting and Probability |

Lessons | Homework | Quiz |

9.1 - Sequences and Series | 9.1 | 9.1 |

9.2 - Arithmetic Sequences | 9.2 | 9.2 |

9.3 - Geometric Sequences | 9.3 | 9.3 |

9.4 - Binomial Theorem | 9.4 | 9.4 |

9.5 - Counting | 9.5 | 9.5 |

9.6 - Permutations and Combinations | 9.6 | 9.6 |

9.7 - Finite Basic Probabilities | 9.7 | 9.7 |

9.8 - Basic Laws of Probability | 9.8 | 9.8 |

Chapter 10 - Conic Sections |

Lessons | Homework | Quiz |

10.1 - The Circle | 10.1 | 10.1 |

10.2 - The Parabola | 10.2 | 10.2 |

10.3 - The Ellipse | 10.3 | 10.3 |

10.4 - The Hyperbola | 10.4 | 10.4 |

10.5 - Systems of Inequalities | 10.5 | 10.5 |

## 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.Week | Complete Sections |

1 | 1.1 - 1.4 |

2 | 1.5 - 2.1 |

3 | 2.2 - 2.5 |

4 | 2.6 - 2.6 |

5 | 3.1 - 3.4 |

6 | 3.5 - 4.3 |

7 | 4.4 - 4.8 |

8 | 5.1 - 5.4 |

9 | 5.5 - 5.7 |

10 | 6.1 - 6.4 |

11 | 6.5 - 6.7 |

12 | 7.1 - 7.4 |

13 | 8.1 - 8.4 |

14 | 8.5 - 9.1 |

15 | 9.2 - 9.5 |

16 | 9.6 - 10.1 |

17 | 10.2 - 10.5 |

Final Exam |

## Code of Conduct:

**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. It is the student's responsibility and duty to become acquainted with all provisions of the code below and what constitutes misconduct. Cheating is forbidden of any form will result in an F in the class.

**Respectful communications:**

When contacting Omega Math or Westcott Courses, you agree to be considerate and respectful. Communications from a student which are considered by our staff to be rude, insulting, disrespectful, harassing, or bullying via telephone, email, or otherwise will be considered a disrespectful communication and will result in a formal warning.

We reserve the right to refuse service. If we receive multiple disrespectful communications from person(s) representing the student, or the student themselves, the student will be excluded from taking future courses at Westcott Courses/Omega Math.

**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' Policy from within your account, and the 'Proctored Final Information' page, if applicable. You have 24 hours after your first log-in to notify us 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.

**Examples of academic misconduct:**

Cheating: Any form of cheating will result in an F in the class. If there is an associated college attached to the course, that college will be notified of the F due to cheating and they will determine any disciplinary action.

Any form of collaboration or use of unauthorized materials during a quiz or an exam is forbidden.

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, and the individual signed up for this course will be the one taking the test. Failure to do so will be considered a breach of contract.

Other forms of cheating include receiving or providing un-permitted assistance on an exam or quiz; 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, claiming that Westcott Courses/Omega Math lost your test and or quiz scores. This includes hiring someone to take the tests and quizzes for you.

**Unauthorized collaboration:**

Working with others on graded course work without specific permission of the instructor, including homework assignments, programs, quizzes and tests, is considered a form of cheating.

**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.

#### Related Information:

#### How it Works

These individual courses are available to anyone in the public who'd like to enroll. Unlike traditional colleges where one must enroll in a degree program, Westcott Courses offers individual courses that are available instantly. Westcott Courses is the teacher of the course, and the official transcript with academic semester credits comes from our partner university, Brandman University who is regionally accredited by WASC. Westcott Courses does not appear on the transcript; the transcript shows our courses the same way it would show a traditional class taken at the university's campus.Read more about transferring the credits.

#### Teachers for the course:

The classes are self-paced; however, a teacher is attached to each course who holds at least a master's degree in their field of study (or related). Most of our teachers are teachers who teach the exact same course on either a California State University or California Community college campus.#### Omega Math^{TM} Courses:

Courses that have the trademark of "Omega Math^{TM}Courses", are courses that have been written by our Omega Math team, and have a format that students love! These courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Students can take each test and quiz twice, and only the higher of the two scores counts towards their grade. This feature enables students to figure out what they did wrong before pushing forward, providing them with a deeper understanding of the course material.