Pre-Calculus 12

This course aligns with the learning outcomes for:


This course aligns with the learning outcomes for:


Are you searching for a Pre-Calculus 12 curriculum that will help your students master its topics so that if and when they hit Calculus they can not only survive but even thrive? And all the while still enjoying the course itself? Your search is over.

StudyForge proudly presents: Pre-Calculus 12.

Pre-Calculus 12 is the culmination of a students’ high school mathematical journey, as they learn the fundamentals of advanced functions, logarithms, trigonometric identities and more. The course thoroughly prepares students for the oncoming rigor of Calculus, yet does so in a manner that is compelling and rewarding, and fosters an appreciation for the real-life applications of each topic explored, as well as for math itself.

With auditory, visual, and hands-on components throughout, this is truly a course that suits all learning styles. The lessons are engaging, interactive and student-friendly, with interactive videos that allow students to pause and rewind at any point and go at their own speed, as well as fun, interactive applets and dynamic graphs scattered throughout that enhance student understanding.

Each video is accompanied by a student-friendly note package that allows students to take notes to whatever level of detail they like. There are also an abundance of practice questions for students to internalize the material, with full, detailed solutions for each, as well as a comprehensive review assignment and practice test. Furthermore, with randomized question banks, students can redo every quiz and test in the course to help them master the material and perform their very best.

This course is a prerequisite for students who might take Calculus in the future, whether in high school (Calculus 12 or AP Calculus) or in post-secondary.

Table of Contents

*Each lesson is designed to take 60 – 90 minutes to complete with the exception of major projects and assignments.
Lesson 1: Review of Functions
Lesson 2: Vertical and Horizontal Translations
Lesson 3: Reflections
Lesson 4: Vertical and Horizontal Compressions and Stretches
Lesson 5: Combinations of Transformations
Lesson 6: Transformation of Radical Functions and More
Lesson 1: Basic Function Operations
Lesson 2: Composition of Functions
Lesson 3: Inverse Functions
Lesson 4: Inverse Reflections
Lesson 5: Parabolas and Circles
Lesson 6: Ellipses and Hyperbolas
Lesson 1: Continuous Exponential Growth
Lesson 2: Transforming Exponential Equations
Lesson 3: Introduction to Logarithms
Lesson 4: Solving Equations Using Logarithms
Lesson 5: Product and Quotient Laws
Lesson 6: Graphing Exponential Functions
Lesson 7: Graphing Logarithmic Functions
Lesson 1: Geometric Sequences
Lesson 2: Sum of a Finite Geometric Series
Lesson 3: Infinite Geometric Series
Lesson 4: Sigma Notation
Lesson 1: Dividing Polynomials
Lesson 2: The Remainder Theorem
Lesson 3: Factor Theorem
Lesson 4: Solve Polynomials by Factoring
Lesson 5: Sketching Polynomials by Finding Zeros
Lesson 6: Graphing Rational Functions
Lesson 1: Angles and the Coordinate Plane – Degree
Lesson 2: Angular Measure – Radians
Lesson 3: Trigonometric Ratios of Any Angle
Lesson 4: Discovering Parameters of Sine and Cosine
Lesson 5: Graphing Sine and Cosine
Lesson 6: Graphing Tangent
Lesson 7: Graphing Inverse Trigonometric Functions
Lesson 8: Applications of Trigonometric Functions
Lesson 1: Solving Trigonometric Equations Graphically
Lesson 2: Solving Trigonometric Equations Algebraically
Lesson 3: Using Technology to Solve More Complex Equations
Lesson 4: Trigonometric Identities – An Introduction
Lesson 5: Sum, Difference and Double Angle Identities
Lesson 1: Absolute Value and Reciprocal Operations
Lesson 2: Radical Operations

Experience a lesson as your students would

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See What Others Have to Say:

StudyForge has been an effective instructional program for students who are learning math. There are many visual representations as well as audio explanations on all the topics. Most of the practice questions provide both an answer and a solution to help students understand the procedures. From the teacher’s perspective, the course instruction can be easily rearranged for students who need a review of concepts from a previous grade.


Online Teacher at EBUS Academy

I have been using the StudyForge math videos for a year now. The benefits were immediate as I was able to free up the time spent with my students to better track their progress and construct personalized learning goals. My students love the ease of use of the system and most of all, the increase in their test scores! I can’t ever imagine going back to a traditional classroom!


Blended Teacher at Brampton Christian School

I think the videos are excellent. Unlike lectures, I can actually rewind back and forth as much as I want. In class, students kind of miss important information because they are busy writing notes.

Alice P

StudyForge Student

I love the reporting tool. In my distributed learning context, seeing student’s work habits in a helpful format has become invaluable to me. I wouldn’t ever want to give one on one help to students again without the course overview report handy!

Ryan J.

Online Teacher

Course Features

  • Interactive applets which help foster a conceptual and intuitive understanding of fundamental topics.
  • Digital DESMOS Graphing Calculator within the course
  • Inquiry-Based Projects such as:
    • Comparing how acidic (or basic) household products are using logarithms
    • Analyzing financial investments using sequences and series. 
    • Exploring Conic Sections
    • Modeling real-life data using trigonometric functions