Online Class: Precalculus 101

'Precalculus 101' bridges basic algebra and the intricate world of calculus, nurturing a profound understanding of mathematical principles that unlock the potential of modern, tech-driven fields. Explore essential topics like functions, vectors, and limits, ensuring a seamless transition to calculus, fostering both knowledge and boldness.
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  • 19
    Lessons
  • 21
    Exams &
    Assignments
  • 3,010
    Students
    have taken this course
  • 35
    Hours
    average time
  • 3.5
    CEUs
 
 
 

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.

Courses Frequently Bought Together:
  • 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:
4.44 / 5 Stars (Average Rating)
"Extraordinarily Helpful"
(1,144 votes)

Lesson 1. Real and Complex Numbers: A Pre-Calculus Introduction

Complex numbers extend the real number system by incorporating imaginary numbers, represented by the symbol i, where i squared equals -1. The lesson explores their representation in the form a + bi and describes basic arithmetic rules and properties like the complex conjugate. Additional lesson topics: Definition of Absolute Value; Basic Characteristics of Complex Numbers Video ; 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. Exploring the Foundations of Functions: A Pre-Calculus Journey

The lesson highlights the critical role of functions in mathematics by distinguishing unique output-producing relations and illustrates the plotting of these functions on coordinate axes to track continuity and changes. A practical exercise on graph plotting solidifies these theoretical underpinnings with hands-on problem-solving. Additional lesson topics: Characteristics of a Function Video ; Independent and Dependent Variables 20 Total Points
  • Lesson 2 Video
  • Assessment: Lesson 2 Exam

Lesson 3. Understanding Domain and Range in Functions: Key Insights and Applications

The lesson delves into domain and range, illustrating limitations within real-valued functions and utilizing different tests to identify one-to-one functions. Students learn to construct composite functions and compute inverses, fundamental for understanding function interactions. 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. Understanding Mathematical Relationships: Equations and Inequalities

This lesson explores how equations and inequalities relate algebraic expressions, with solutions verified either as distinct points or continuous intervals. Mastery involves both algebraic manipulation and the graphical portrayal of solution sets. 20 Total Points
  • Lesson 4 Video
  • Assessment: Lesson 4 Exam

Lesson 5. The Intricacies of Polynomials and Rational Functions

Polynomials are fundamental in calculus, representing expressions with constant coefficients and variable powers, whereas rational functions focus on polynomial-based fractions acknowledging domain limitations. The domain, roots, and intercepts of these functions help in graphing and solving them, with tools like the quadratic formula applied for quadratic functions. Additional lesson topics: Graphing the Rational Function 20 Total Points
  • Lesson 5 Video
  • Assessment: Lesson 5 Exam

Lesson 6. Roots and Asymptotes: Uncovering Mathematical Patterns

Synthetic division offers a streamlined method to determine the roots of higher-degree polynomials, shedding light on their underlying structure and factors. Rational functions' asymptotic behavior, whether approaching infinity or shifting diagonally, is critical to understanding their limits and domain. 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. Understanding Logarithmic Functions

Exponential and logarithmic functions are the lesson's protagonists, with their rules showcased through applications in continuous compounding and decay modeling. The session underscores the functionality of the constant e and natural logarithms as tools for solving complex equations in these contexts. Additional lesson topics: LOGARITHMIC AND EXPONENTIAL FUNCTIONS; Solving Equations Using Logarithms 20 Total Points
  • Lesson 7 Video
  • Assessment: Lesson 7 Exam

Lesson 8. Sine, Cosine, and Tangent: A Pre-Calculus Journey

Trigonometric functions stem from right triangle geometry, assisting in determining unknown measurements in triangles via sine, cosine, and tangent. Calculators serve as valuable tools for generating function values required in both theoretical and practical problem-solving. Additional lesson topics: Right Triangle Trig Calculator 20 Total Points
  • Lesson 8 Video
  • Assessment: Lesson 8 Exam

Lesson 9. Angles in Radians: A New Perspective

By examining the unit circle, this lesson interrelates trigonometry with circular motion, transitioning from traditional angle measurements in degrees to radians. Students are equipped to tackle complex problems involving trigonometric functions and circular geometry. 20 Total Points
  • Lesson 9 Video
  • Assessment: Lesson 9 Exam

Lesson 10. Mastering Trig Identities and Inverse Functions

A focus on graphical analysis and the properties of trigonometric functions emphasizes their symmetries and inverse relationships, illustrating the impact on their algebraic and geometric applications. Key exercises provided train students in identifying the correct function manipulations and solutions specific to the characteristics of triangles. Additional lesson topics: Inverse Trigonometric Functions; Table of Trigonometric Identities 20 Total Points
  • Lesson 10 Video
  • Assessment: Lesson 10 Exam

Lesson 11. Mastering Vectors in Pre-Calculus

While scalars embody pure magnitude, vectors integrate direction, offering a richer toolkit for problem-solving. This lesson guides through representing vectors in a coordinate system, adding, and subtracting them, with practical exercises to reinforce learning. 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 Unleashed: Exploring Unit Vectors and Scalar Products

Lesson Summary 4: This lesson extends basic vector theory by introducing unit vectors in algebraic form and discusses the influence of scalar multiplication on vectors. Learners also explore the scalar product computation as a means to determine vector magnitude, enhancing their mathematical toolkit. 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. Understanding Polar Coordinates through Trigonometry

Polar coordinates offer an alternative to the traditional Euclidean system, simplifying various mathematical problems by expressing a point's location as a distance and an angle from the origin. This lesson covers the relationship between polar and rectangular coordinates, conversion techniques, and the benefits of using polar coordinates in certain algebraic expressions. Additional lesson topics: Video Demonstration of Polar Coordinates 20 Total Points
  • Lesson 13 Video
  • Assessment: Lesson 13 Exam

Lesson 14. Circles and Parabolas: A First Look

Conic sections are derived from slicing a cone at various angles, resulting in shapes like circles and parabolas, which are explored in this lesson. The algebraic and graphical properties of these shapes demonstrate their underlying mathematical principles while highlighting their unique characteristics. Additional lesson topics: Introduction to Conic Sections Video 20 Total Points
  • Lesson 14 Video
  • Assessment: Lesson 14 Exam

Lesson 15. Exploring the Intricacies of Ellipses and Hyperbolas

Ellipses, described as flattened circles, accommodate the Sun in their focus, portraying celestial orbits, while hyperbolas, akin to parabolas, demonstrate more open loops. Conic sections dictate planetary paths, emphasizing varying speeds and distances that result in hyperbolic or elliptical motions. 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: The Gateway to Calculus

Limits enable us to predict how functions behave near specific points, playing a critical role in calculus concepts like differentiation and integration. By examining both one-sided and two-sided limits, we delve into the nuances of function behavior and their continuity. Additional lesson topics: Basic Limit Laws; Introduction to Limits Video Demonstration 20 Total Points
  • Lesson 16 Video
  • Assessment: Lesson 16 Exam

Lesson 17. Diving into Sequences and Series

Exploring sequences and series, the lesson offers a holistic overview of these comprehensive topics, detailing how sequences are ordered number sets, while series unite sequence terms into sums. Essential concepts like convergence and divergence provide a sneak peek into the world of limits, paving the way for calculus applications. Additional lesson topics: Introduction to Sequences Video Demonstration ; Introduction to Series 20 Total Points
  • Lesson 17 Video
  • Assessment: Lesson 17 Exam

Lesson 18. Derivatives Simplified

Lesson Summary 1: This pre-calculus lesson introduces the concept of derivatives, connecting it to algebra and limits by exploring how they quantify the rate of change in a function. Through examining the slope of both linear and nonlinear functions, the lesson demonstrates how differentiation offers insights into varying rates of change. Additional lesson topics: Introduction of Derivatives 20 Total Points
  • Lesson 18 Video
  • Assessment: Lesson 18 Exam

Lesson 19. Integrals and Antiderivatives: A Prelude

This lesson delves into integrals, complementing derivatives, and uses rectangles through Riemann sums to approximate curve-under areas. The resultant calculated areas reflect a fundamental calculus concept foundational for physics and advanced math studies. 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

Online CEU Certificate
  • Document Your Lifelong Learning Achievements
  • Earn an Official Certificate Documenting Course Hours and CEUs
  • Verify Your Certificate with a Unique Serial Number Online
  • View and Share Your Certificate Online or Download/Print as PDF
  • Display Your Certificate on Your Resume and Promote Your Achievements Using Social Media
Document Your CEUs on Your Resume
 
Course Title: Precalculus 101
Course Number: 9770456
Lessons Rating: 4.44 / 5 Stars (1,144 votes)
Languages: English - United States, Canada and other English speaking countries
Availability: You can take this course online in every U.S. state including California, Texas, Florida, New York, Pennsylvania, Illinois, Ohio, and Georgia. International availability includes English-speaking countries like Canada, Australia, the UK, and South Africa.
Last Updated: April 2024
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.
Course Type: Self-Paced, Online Classes
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.

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