Ace Precalculus in 5 Hours - The Complete Course
Learn the connections between numeric, graphical, and algebraic representations of relations and functions
Updated on Jun, 2025
Language - English
Teaching and Academics ,Math,Calculus
Lectures -58
Resources -17
Duration -5.5 hours
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Course Description
HOW THIS COURSE WORK:
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
CONTENT YOU WILL GET INSIDE EACH SECTION:
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.
THINGS THAT ARE INCLUDED IN THE COURSE:
An instructor who truly cares about your success
Lifetime access to Ace Precalculus in 6 Hours (The Complete Course)
HIGHLIGHTS:
#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 :)
Goals
- 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
Prerequisites
- Familiarity with algebra
- Some basic knowledge with the cartesian coordinates
Curriculum
Check out the detailed breakdown of what’s inside the course
Introduction
3 Lectures
-
Overview
02:17
02:17
-
Welcome and How It Works
02:32
02:32
-
Tips to Maximize Your Learning
Functions and Graphs
13 Lectures
Operations, Transformations, and Inverses
11 Lectures
Algebraic Functions
11 Lectures
Factorization of Polynomials (NEWLY ADDED SECTION)
7 Lectures
Transcendental Functions
11 Lectures
Conclusion
2 Lectures
Instructor Details
Gina Chou
During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!
A bit about me:
I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.
Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.
I look forward to seeing you in class!
Gina C.
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