Online Class: Precalculus 101

This course provides a bridge between algebra and calculus, guiding students through the underlying mathematical concepts needed to understand and appreciate calculus.

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19

Lessons
21

Exams &
Assignments
2,595

Students
have taken this course
35

Hours
average time
3.5

CEUs

Course Description

Calculus is a mathematical tool that is required in a variety of scientific, technical, and other professional fields. Because it is a higher-level area of math, many people think it is a subject that they can never understand. Unfortunately, such an attitude limits an individual's career choices, particularly in a technology-focused society.

This course provides a bridge between algebra and calculus, guiding students through the underlying mathematical concepts needed to understand and appreciate calculus. The course reviews real and complex numbers, functions, and equations and inequalities. It then goes into some detail on specific types of functions, such as polynomials, exponentials, and logarithms. It also provides a derivation of the principles of trigonometry on the basis of simple right-triangle and circle geometry. After reviewing vectors, polar coordinates, and conic sections, the material sets up calculus proper by examining limits as well as sequences and series.

The final lessons of the course use the basic principles of algebra to derive the two key tools of calculus: differentiation (the derivative) and integration (the integral). At the end of this course, students will be prepared to study calculus in greater depth, further investigating and applying derivatives and integrals to solve a variety of math, physics, and other problems.

Courses Frequently Bought Together:

Statistics 101

Algebra 101: Beginner to Intermediate Level

Pre-Algebra 101

Completely Online
Self-Paced
Printable Lessons
Full HD Video
6 Months to Complete
24/7 Availability
Start Anytime
PC & Mac Compatible
Android & iOS Friendly
Accredited CEUs

Universal Class is an IACET Accredited Provider

Course Lessons

Average Lesson Rating:

"Extraordinarily Helpful"

(1,072 votes)

Lesson 1 - Real and Complex Numbers

In this lesson, we begin the process of setting a foundation for understanding calculus by looking briefly at real and complex numbers. These are the sets of values that we will be studying at length in this course. Additional lesson topics: Basic Characteristics of Complex Numbers Video ; Definition of Absolute Value; Number sense 21 Total Points

Lesson 1 Video A
Lesson 1 Video B : How to Take an Exam
Lesson discussions: Reasons for Taking this Course
Complete Assignment: Introduction
Assessment: Lesson 1 Exam

Lesson 2 - Functions I

Having introduced the real and complex number sets in the previous lesson, we now begin to look in depth at series of operations on numbers, or more particularly, numbers and variables. Additional lesson topics: Characteristics of a Function Video ; Independent and Dependent Variables 20 Total Points

Lesson 2 Video
Assessment: Lesson 2 Exam

Lesson 3 - Functions II

Having defined functions in the previous lesson, we now look in more detail at the characteristics of functions. These concepts are critical and will underlie the remainder of this course. Additional lesson topics: Composition of two functions; How to find the Domain and Range of a Function Video 20 Total Points

Lesson 3 Video
Assessment: Lesson 3 Exam

Lesson 4 - Equations and Inequalities

Having looked in detail at functions, the course now turns to equations and inequalities: two mathematical expressions that relate different algebraic relations involving numbers, variables, or both. 20 Total Points

Lesson 4 Video
Assessment: Lesson 4 Exam

Lesson 5 - Polynomials and Rational Functions I

Having looked in general at characteristics of functions and their relationship to equations and inequalities, we now turn to a common class of functions, polynomials, and their close cousins, rational functions.x` Additional lesson topics: Graphing the Rational Function 20 Total Points

Lesson 5 Video
Assessment: Lesson 5 Exam

Lesson 6 - Polynomials and Rational Functions II

In the previous lesson, we defined and discussed some characteristics of polynomials and rational functions. In this lesson, we will look at these functions in slightly more depth. Additional lesson topics: How to Solve Higher Degree Polynomials; Rational Functions and Asymptotes 20 Total Points

Lesson 6 Video
Assessment: Lesson 6 Exam

Lesson 7 - Exponential and Logarithmic Functions

This lesson turns away from polynomials (and their close cousins, rational functions) and looks at another type of function: exponential and logarithmic functions. We consider the basic rules of exponents and logarithms and apply them to simple functions. Additional lesson topics: LOGARITHMIC AND EXPONENTIAL FUNCTIONS; Solving Equations Using Logarithms 20 Total Points

Lesson 7 Video
Assessment: Lesson 7 Exam

Lesson 8 - Trigonometric Functions I

We now consider another class of functions called trigonometric ("trig") functions. These functions are useful in a variety of contexts involving triangles and circles. This lesson considers the origin of these functions in right triangles and looks at so Additional lesson topics: Right Triangle Trig Calculator 20 Total Points

Lesson 8 Video
Assessment: Lesson 8 Exam

Lesson 9 - Trigonometric Functions II

In the previous lesson, we reviewed the origin of trigonometric functions in the context of right triangles. Interestingly, however, trig functions also have applicability to circles. The present lesson will focus on circles and the relationship of circle 20 Total Points

Lesson 9 Video
Assessment: Lesson 9 Exam

Lesson 10 - Trigonometric Functions III

In this lesson, we will look at a few more aspects of trigonometry, including trigonometric identities and inverse trigonometric functions. Additional lesson topics: Inverse Trigonometric Functions; Table of Trigonometric Identities 20 Total Points

Lesson 10 Video
Assessment: Lesson 10 Exam

Lesson 11 - Vectors I

In this lesson, we introduce a new quantity: the vector. Vectors-unlike simple numbers (scalars) that have only a magnitude-have both a magnitude (length) and direction. We will explore how to represent vector quantities, as well as how to add and subtr Additional lesson topics: Adding and Subtracting Vectors Video ; Introduction to Vectors Video 20 Total Points

Lesson 11 Video
Assessment: Lesson 11 Exam

Lesson 12 - Vectors II

In the previous lesson, we introduced vectors as quantities with a magnitude and direction. In this lesson, we look more deeply into vectors to flesh out some of the concepts introduced previously. Additional lesson topics: Vector Addition and Scalar Multiplication; Unit Vector; Algebraic Representation of Vectors 20 Total Points

Lesson 12 Video
Assessment: Lesson 12 Exam

Lesson 13 - Polar Coordinates

In this lesson, we introduce a new type of coordinate system: polar coordinates. Polar coordinates are one example of the many alternative coordinate systems that can be devised; these alternatives can greatly simplify certain problems. Additional lesson topics: Video Demonstration of Polar Coordinates 20 Total Points

Lesson 13 Video
Assessment: Lesson 13 Exam

Lesson 14 - Conic Sections I

In this lesson, we introduce conic sections and show how they are related to cross sections of a cone (hence their name). The basic characteristics-algebraic and graphical-of two conic sections are discussed in detail: circles and parabolas. The next less Additional lesson topics: Introduction to Conic Sections Video 20 Total Points

Lesson 14 Video
Assessment: Lesson 14 Exam

Lesson 15 - Conic Sections II

This lesson continues our examination of conic sections, focusing specifically on ellipses and hyperbolas. The end of the lesson presents a practical way of relating all the conics we have studied thus far by way of the motion of celestial objects. Additional lesson topics: Conic Sections; Conic Sections, Hyperbola, Shifted: Sketch the Graph Video- 20 Total Points

Lesson 15 Video
Assessment: Lesson 15 Exam

Lesson 16 - Limits

In this lesson, we introduce limits, a topic fundamental to understanding differentiation and integration-two critical aspects of calculus. Limits are generally intuitive, but a solid ability to use them is important to the remainder of the course. Additional lesson topics: Basic Limit Laws; Introduction to Limits Video Demonstration 20 Total Points

Lesson 16 Video
Assessment: Lesson 16 Exam

Lesson 17 - Sequences and Series

The current lesson switches our focus slightly to look briefly at sequences and series. These mathematical constructs play an important role in calculus and other branches of mathematics. Additional lesson topics: Introduction to Sequences Video Demonstration ; Introduction to Series 20 Total Points

Lesson 17 Video
Assessment: Lesson 17 Exam

Lesson 18 - Introduction to Derivatives

Having covered all the necessary mathematical background, the final two lessons of the course turn to two fundamental concepts in calculus: the derivative and the integral. Although we will not go into great depth on these subjects, we will show how they Additional lesson topics: Introduction of Derivatives 20 Total Points

Lesson 18 Video
Assessment: Lesson 18 Exam

Lesson 19 - Introduction to Integrals

In the previous lesson, we covered one of two major aspects of calculus: the derivative. For this closing lesson to the course, we will look briefly at the other of these two concepts: the integral. Additional lesson topics: Introduction of Definite Integrals Video Demonstration 100 Total Points

Lesson 19 Video
Lesson discussions: Your Opinion Matters: Course Rating; Program Evaluation Follow-up Survey (End of Course); Course Comments
Assessment: Lesson 19 Exam
Assessment: The Final Exam

461

Total Course Points

Learning Outcomes

By successfully completing this course, students will be able to:

Define, identify and demonstrate use of real and complex numbers.
Define, identify and demonstrate use of functions.
Define, identify and demonstrate use of equations and inequalities.
Define, identify and demonstrate use of polynomials and rational functions.
Define, identify and demonstrate use of exponential and logarithmic functions.
Define, identify and demonstrate use of trigonometric functions.
Define, identify and demonstrate use of vectors.
Define, identify and demonstrate use of polar coordinates.
Define, identify and demonstrate use of conic sections.
Define, identify and demonstrate use of limits, sequences, and series.
Define, identify and demonstrate use of derivatives and integrals.
Demonstrate mastery of lesson content at levels of 70% or higher.

Additional Course Information

Document Your Lifelong Learning Achievements
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Course Title: Precalculus 101

Course Number: 9770456

Lessons Rating: 4.5 / 5 Stars (1,072 votes)

Languages: English - United States, Canada and other English speaking countries

Category:

UniversalClass.com > Mathematics > Algebra and Math Studies

Availability: This course is online and available in all 50 states including: California, Florida, Georgia, Illinois, New York, Pennsylvania, Ohio, and Texas.

Last Updated: October 2022

Course Type: Self-Paced, Online Class

CEU Value: 3.5 IACET CEUs (Continuing Education Units)

CE Accreditation: Universal Class, Inc. has been accredited as an Authorized Provider by the International Association for Continuing Education and Training (IACET).

Grading Policy: Earn a final grade of 70% or higher to receive an online/downloadable CEU Certification documenting CEUs earned.

Assessment Method: Lesson assignments and review exams

Course Author: Dr. Jeffrey Clark, Ph.D.

Instructor: April Cordry-Moore

Syllabus: View Syllabus

Course Fee: $110.00 U.S. dollars

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Student Testimonials

"Very helpful specially in the sense of improving the cognitive level of keywords and key concepts in order to gain more specific insight into details and concepts that are sometimes seemingly unimportant or easy to forget." -- Jorge E.
"My instructor was very prompt in grading all of my submitted tests and responded quickly when I had questions about the current lesson or the test." -- Stephen M.
"I want to stress that April Cordry Moore is an excellent instructor." -- Doug G.
"Great learning experience." -- Rafael J.