Ace Precalculus in 5 Hours (The Complete Course)

person icon Gina Chou

Ace Precalculus in 5 Hours (The Complete Course)

Learn the connections between numeric, graphical, and algebraic representations of relations and functions

updated on icon Updated on Oct, 2023

language icon Language - English

person icon Gina Chou

architecture icon Math,Calculus

Lectures -50

Resources -14

Duration -4.5 hours


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Course Description


This course, Ace Precalculus in 5 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

  • 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 5 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: Four 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 :)


What will you learn in this course:

  • 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)
  • 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


What are the prerequisites for this course?

  • Familiarity with algebra
  • Some basic knowledge with the cartesian coordinates
Ace Precalculus in 5 Hours (The Complete Course)


Check out the detailed breakdown of what’s inside the course

3 Lectures
  • play icon Overview 02:17 02:17
  • play icon Welcome and How It Works 02:32 02:32
  • play icon Tips to Maximize Your Learning
Functions and Graphs
13 Lectures
Operations, Transformations, and Inverses
11 Lectures
Algebraic Functions
11 Lectures
Transcendental Functions
11 Lectures
2 Lectures

Instructor Details

Gina Chou

Gina Chou

Physics PhD candidate

While I was in undergrad, I was always excited to take exams because I was always well prepared and I felt accomplished after finishing each exam. I know that it is not the case for most of the students. So here, I will share my knowledge and help you to make your university life easier! :D

More about my background

I received my BSc in Atmospheric Science and Physics with a minor in Mathematics from the McGill University in 2018 and my MSc in Physics at the University of Toronto in 2019. I am currently a Ph.D. candidate in the Physics Department and I am interested in the impact of wind observation on the global predictability, Arctic climate, and weather processes.

Since my second year of undergraduate studies, I have had extensive tutoring experiences, teaching at Liberty Tutoring, as well as high school and university students through SUS Peer Tutoring and Saturday Programs. Additionally, I have been/currently am a TA for math and physics undergraduate and graduate courses.

I hope to see you in class!

- Gina C.

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