## Course Description

In this Pre-Calculus course, learners are given the chance to extend their knowledge and explore a variety of different functions, such as linear, polynomial, rational, exponential, and logarithmic. These functions will provide a mathematical foundation moving forward. This course also explores trigonometric functions, as well as more advanced Pre-Calculus topics such as systems of equations and inequalities, analytic geometry, sequences, probability, and counting theory. Materials There is no extra cost for textbooks or materials. All materials are included with this course. Transferability Ed4Credit’s courses have all either been recommended for credit through the American Council on Education’s Alternative Credit Project™ or their College Credit Recommendation Service (CREDIT®). This highly... Read More »

In this Pre-Calculus course, learners are given the chance to extend their knowledge and explore a variety of different functions, such as linear, polynomial, rational, exponential, and logarithmic. These functions will provide a mathematical foundation moving forward. This course also explores trigonometric functions, as well as more advanced Pre-Calculus topics such as systems of equations and inequalities, analytic geometry, sequences, probability, and counting theory.

**Materials**

There is no extra cost for textbooks or materials. All materials are included with this course.

**Transferability**

Ed4Credit’s courses have all either been recommended for credit through the American Council on Education’s Alternative Credit Project™ or their College Credit Recommendation Service (CREDIT®). This highly regarded recommendation means that your Ed4Credit classes will be considered for credit at almost 2,000 colleges and universities across the United States.

It’s important that you check with the college you are planning to transfer this course to in order to verify the transferability to your college. Also, every college individually determines if a course will count as a lower-level course or an upper-level course. Please contact your college and make sure you understand their policies regarding ACE credit transfers.

Ed4Credit courses go through an intensive quality review process by ACE CREDIT® prior to being available to students. ACE CREDIT has evaluated and recommended this Ed4Credit course for college credit. Once you have completed an Ed4Credit course, you are eligible to receive an ACE Transcript for credit transfer purposes. Upon completion of your Ed4Credit courses simply create an account with the American Council on Education (ACE). Once you’ve created your account select the courses you’ve completed and choose the appropriate educational institution and ACE will send them your transcript.

*The ACE CREDIT® logo is a registered trademark of the American Council on Education and cannot be used or reproduced without the express written consent of the American Council on Education. Used with permission.*

**More Information**

**Ed4Online has partnered with ProctorU!**

**ProctorU** is a live online proctoring service that allows exam takers to complete their certification exams at home. This partnership allows us to maintain the professionalism and integrity that we desire within the exam taking process. You can take your proctored exam online from anywhere using a webcam and a high speed internet connection. Here are some things to keep in mind as you prepare to take your exam…

- You will need to create a
**FREE PROCTORU ACCOUNT**and schedule an exam - Exams need to be scheduled 3 days in advance!
- You will need a webcam, speakers and a microphone for the exam.

- Recall the basic types of functions, such as linear, polynomial, rational, exponential, and logarithmic
- Recognize the fundamentals of trigonometric functions and how to solve them
- Identify trigonometric identities and equations, as well as more advanced properties
- List systems of equations and inequalities, as well as how to solve analytic geometry problems
- Define the basic principles of sequencing, probability, and counting theory

#### Access Timeframe

#### Prerequisites

#### Type of Certification

#### Format of Certification

#### Professional Association/Affiliation

#### Method of Obtaining Certification

#### Additional Details

## Course Outline

- Functions and Function Notation
- Domain and Range
- Rates of Change and Behavior of Graphs
- Composition of Functions
- Transformation of Functions
- Absolute Value Functions
- Inverse Functions

- Recall functions and function notation
- Define domain and range
- Identify rates of change and behavior of graphs
- Recognize the basic composition of functions
- Recall transformation of functions
- Define absolute value functions
- Identify types of inverse functions

- Read Chapter 1
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 1

- Linear Functions (Examples)
- Graphs of Linear Functions
- Modeling with Linear Functions
- Fitting Linear Models to Data

- Recall types of linear functions
- Identify graphs of linear functions
- Recognize how to model with linear functions
- Recall how to fit linear models to data

- Read Chapter 2
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 1

- Complex Numbers
- Quadratic Functions
- Power Functions and Polynomial Functions
- Graphs of Polynomial Functions
- Dividing Polynomials
- Zeros of Polynomials Functions
- Rational Functions
- Inverses and Radical Functions
- Modeling Using Variation

- Define complex numbers
- Define quadratic functions
- Identify power functions and polynomial functions
- Recall graphs of polynomial functions
- Recognize zeros of polynomials
- Identify how to solve rational functions
- Recall the basics of inverses and radical functions
- Recognize modeling using variation

- Read Chapter 3
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 1

- Graphs of Exponential Functions
- Graphs of Logarithmic Functions
- Logarithmic Prosperities
- Exponential and Logarithmic Equations
- Exponential and Logarithmic Models
- Fitting Exponential Models to Data

- Recall types of graphs of exponential functions
- Recognize graphs of logarithmic functions
- Identify logarithmic prosperities
- Recall the basics of exponential and logarithmic equations
- Recognize exponential and logarithmic models
- Identify how to fit exponential models to data

- Read Chapter 4
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 1

- Angles
- Unit Circle: Sine and Cosine Functions
- The Other Trigonometric Functions
- Right Triangle Trigonometry

- Recall how to solve angles
- Define sine and cosine functions
- Recognize other trigonometric functions
- Identify right triangle trigonometry

- Read Chapter 5
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 2

- Graphs of the Sine and Cosine Functions
- Graphs of the Other Trigonometric Functions
- Inverse Trigonometric Functions

- Recall graphs of sine and cosine functions
- Identify graphs of other trigonometric functions
- Recognize inverse trigonometric functions

- Read Chapter 6
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 2

- Solving Trigonometric Equations with Identities
- Sum and Difference Identities
- Double-Angle, Half- Angle, and Reduction Formulas
- Sum-to-Product and Product-to-Sum Formulas
- Solving Trigonometric Equations
- Modeling with Trigonometric Equations

- Recall how to solve trigonometric equations with identities
- Recognize sum and difference identities
- Differentiate between double-angle, half-angle, and reduction formulas
- Recall sum-to-product and product-to-sum formulas
- Recognize how to solve trigonometric equations
- Identify how to model for trigonometric equations

- Read Chapter 7
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 3

- Non-right Triangles: Law of Sines
- Non-right Triangles: Law of Cosines
- Polar Coordinates
- Polar Coordinates: Graphs
- Polar Form of Complex Numbers
- Parametric Equations: Graphs
- Vectors

- Recall the law of sines
- Identify the law of cosines
- Define polar coordinates
- Recognize types of polar coordinates: graphs
- Identify the polar form of complex numbers
- Define parametric equations
- Identify types of vectors

- Read Chapter 8
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 3

- Systems of Linear Equations: Two Variables
- Systems of Linear Equations: Three Variables
- Systems of Nonlinear Equations and Inequalities: Two Variables
- Partial Fractions
- Matrices and Matrix Operations
- Solving Systems of Gaussian Elimination
- Solving Systems with Inverses
- Solving Systems with Cramer’s Rule

- Recall how to solve systems of linear equations: two variables
- Recognize how to solve systems of linear equations: three variables
- Identify systems of nonlinear equations and inequalities: two variables
- Recall partial fractions
- Recognize matrices and matrix operations
- Identify how to solve systems of Gaussian elimination
- Recall how to solve systems with inverses
- Identify how to solve systems with cramer’s rule

- Read Chapter 9
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 4

- The Ellipse
- The Hyperbola
- The Parabola
- Rotation of Axes
- Conic Sections in Polar Coordinates

- Define the ellipse
- Define the hyperbola
- Define the parabola
- Define rotation of axes
- Identify conic sections in polar coordinates

- Read Chapter 10
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 4

- Sequences and Their Notations
- Arithmetic Sequences
- Geometric Sequences
- Series and Their Notations
- Counting Principles
- Binomial Theorem
- Probability

- Recall sequences and their notations
- Identify types of arithmetic sequences
- Recognize geometric sequences
- Recall series and their notations
- Define counting principles
- Define binomial theorem
- Define probability

- Read Chapter 11
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 5

- Finding Limits: Numerical and Graphical Approaches
- Finding Limits: Prosperities of Limits
- Continuity
- Derivatives

- Recall how to find limits: numerical and graphical approaches
- Identify how to find limits: prosperities of limits
- Define continuity
- Define derivatives

- Read Chapter 12
- Practice the Learning Activities
- Watch the Videos
- Review the Webliography (Web Links)
- Take the Exam

- 5

- Final Exam
- Course Survey
- Certificate of Completion

- N/A

- Take the Optional Cumulative Practice Final Exam
- Review the Proctored Exam Information
- Create an Account with Proctor U
- Schedule an Exam Time
- Take the Cumulative Proctored Final Exam
- Submit the Course Survey
- Print Your Certificate of Completion

- 1, 2, 3, 4, 5

## Technical Requirements

**Internet Connection**

- Broadband or High-Speed - DSL, Cable, and Wireless Connections

*****Dial-Up internet connections will result in a diminished online experience. Classroom pages may load slowly and viewing large audio and video files may not be possible.

**Hardware Requirements**

- Processor - 2GHz Processor or Higher
- Memory - 1 GB RAM Minimum Recommended

**PC Software Requirements**

- Operating Systems - Windows 7 or higher
- Microsoft Office 2007 or higher. Also, you could use a general Word Processing application to save and open Microsoft Office formats (.doc, .docx, .xls, .xlsx, .ppt, .pptx)
- Internet Browsers - Google Chrome is highly recommended
- Cookies MUST be enabled
- Pop-ups MUST be allowed (Pop-up Blocker disabled)

- Kindle Reader App is needed for many of our courses (No special equipment needed. This can be downloaded for FREE onto your computer.)
- PowerPoint Viewer (if you do not have PowerPoint)
- Adobe PDF Reader
- QuickTime, Windows Media Player &/or Real Player

**MAC Software Requirements**

- Operating Systems - Mac OS x 10 or higher with Windows
- Mac office programs or a Word Processing application to save and open Microsoft Office formats (.doc, .docx, .xls, .xlsx, .ppt, .pptx)
- Internet Browsers- Google Chrome is highly recommended
- Cookies MUST be enabled
- Pop-ups MUST be allowed (Pop-up Blocker disabled)

- PowerPoint Viewer (if you do not have PowerPoint)
- Adobe PDF Reader
- Apple QuickTime Media Player