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
  • 21
    Exams &
  • 2,887
    have taken this course
  • 35
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  • 3.5

Course Description

Online Class: "Precalculus 101: Your Gateway to Advanced Mathematics"

In the intricate tapestry of mathematics, calculus stands as a pivotal thread, intricately weaving through a multitude of scientific, engineering, and professional domains. For many, calculus looms as a daunting peak, a challenging summit seemingly out of reach. Such apprehensions can inadvertently curtail the vast array of opportunities our modern, technology-centric world offers.

Enter "Precalculus 101," your bridge from foundational algebra to the captivating realm of calculus. Designed meticulously for learners, this course illuminates the path, breaking down complex concepts into digestible, relatable pieces, thereby transitioning you smoothly from algebraic foundations to the doors of calculus.

Course Takeaways:

  1. Reconnecting with the Basics: Dive deep into the foundational realms of real and complex numbers, cementing the core upon which advanced topics are built.

  2. The Symphony of Functions: Navigate through the nuanced world of functions — from the rhythmic patterns of polynomials to the exponential crescendos and logarithmic decrescendos.

  3. Trigonometry Demystified: Rediscover trigonometry through the lens of simple geometries like right triangles and circles, making it relatable and intuitive.

  4. Venturing into Pre-Calculus: Engage with foundational pre-calculus topics like vectors, polar coordinates, and the elegance of conic sections, setting the tone for advanced calculus principles.

  5. The Prelude to Calculus: Delve into the crux of calculus preparation by unraveling the mysteries of limits, sequences, and series, offering a sneak peek into what lies ahead.

  6. Unleashing Calculus: By utilizing algebraic fundamentals, embark on an enlightening journey as you're introduced to the cornerstone of calculus: differentiation and integration. These tools, once mastered, open the gates to a myriad of problem-solving techniques across diverse fields.

On completion of "Precalculus 101," students won't just be equipped with knowledge; they'll be imbued with confidence. A newfound understanding will empower learners to delve deeper into calculus, unearthing its potential to decode challenges across mathematics, physics, and beyond.

Join us on this transformative journey, and let "Precalculus 101" be your compass, guiding you from familiar shores to uncharted territories, all while making the journey exhilarating and enlightening.

  • 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:
4.5 / 5 Stars (Average Rating)
"Extraordinarily Helpful"
(1,123 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: Definition of Absolute Value; Number sense; Basic Characteristics of Complex Numbers Video 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: Algebraic Representation of Vectors; Unit Vector; Vector Addition and Scalar Multiplication 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
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

Online CEU Certificate
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Document Your CEUs on Your Resume
Course Title: Precalculus 101
Course Number: 9770456
Lessons Rating: 4.5 / 5 Stars (1,123 votes)
Languages: English - United States, Canada and other English speaking countries
Availability: This course is online and available in all 50 states including: California, Florida, Georgia, Illinois, New York, Pennsylvania, Ohio, and Texas.
Last Updated: September 2023
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
Instructor: April Cordry-Moore
Syllabus: View Syllabus
Course Fee: $120.00 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.