Ace Precalculus in 6 Hours (The Complete Course)

Learn the connections between numeric, graphical, and algebraic representations of relations and functions
(1) Ratings
884 students
Created by Gina Chou

What you'll learn

  • Identify whether a rule is a function
  • Find the domain and range of a function (algebraic and transcendental functions)
  • Identify whether a graph is a function by using the vertical line test
  • Identify whether a graph is a one-to-one function by using the horizontal line test
  • Understand and identify properties of a graph (x- and y-intercepts, roots, local extrema, concavity, increasing/decreasing, inflection point, and more)
  • Calculate the average rate of change of a function over an interval
  • Find the domain of a combination of functions
  • Understand transformations of functions (translations, expansion/compression, and reflection)
  • Sketch a function using transformations of functions
  • Determine whether a function is an even or odd function, or neither
  • Find the inverse of a function algebraically and graphically
  • Learn the algebraic and graphical properties of algebraic functions (power, polynomial, and rational functions)
  • Factor a polynomial function and sketch the function without a graphical calculator
  • Understand and evaluate absolute value functions
  • Learn the algebraic and graphical properties of transcendental functions (exponential, logarithmic, trigonometric, and inverse trigonometric functions)
  • Evaluate transcendental functions without using calculator
  • Convert angles from degrees to radians and from radians to degrees
  • Find the exact values of trigonometric and inverse trigonometric functions using the unit circle
This course includes:
6 total hours on-demand video
7 articles
7 downloadable resources
53 lessons
Full lifetime access
Access on mobile and TV
Certificate of completion

Course content


  • Familiarity with algebra
  • Some basic knowledge with the cartesian coordinates



This course, Ace Precalculus in 6 Hours (The Complete Course), is intended to introduce the student to advanced functions and prepare the student to take calculus courses in the future. The course includes videos, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:

  • Functions and Graphs

  • Operations, Transformations, and Inverses

  • Algebraic Functions

  • Factorization of Polynomials (NEWLY ADDED SECTION)

  • Transcendental Functions


Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.

Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don’t have internet access (but I encourage you to take your own notes while taking the course!).

Assignments: After you watch me doing some examples, now it’s your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.


  • An instructor who truly cares about your success

  • Lifetime access to Ace Precalculus in 6 Hours (The Complete Course)


#1: Downloadable lectures so you can watch the videos whenever and wherever you are.

#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.

#3: Five problem sets at the end of each section (with solutions!) for you to do more practice.

#4: Step-by-step guide to help you solve problems.

See you inside the course!

– Gina 🙂

Who this course is for:

  • Students about to start precalculus or calculus who are looking to get ahead
  • Current precalculus students who are looking for extra help on functions and graphs
  • Homeschool parents looking for extra support with precalculus
  • Homeschool parents whose child is interested in taking calculus courses in university
  • Anyone who is familiar with algebra and is interested in more advanced math and calculus
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