MHF4U Grade 12 - University (Advanced Functions)

Authors: Chris, Heather, Steven (2010); Melissa and Rahim (2012); Lukasz and Inga (2013)

Ministry Guidelines

The Ontario Curriculum: Grades 11-12 Mathematics, Revised 2007
Advanced Functions, Grade 12 found on page 87 out of 160

Key Topics

Advanced Functions 12 Table of Contents
  1. Polynomial Functions
  2. Polynomial Equations and Inequalities
  3. Rational Functions
  4. Trigonometry
  5. Trigonometric Functions
  6. Exponential and Logarithmic Functions
  7. Tools and Strategies for Solving Exponential and Logarithmic Equations
  8. Combining Functions

Sample Course Outlines

OAME webpage
  • Sample lesson plans, unit plans and example problems
Sample Class Handout Outline
  • Sample course outline from Jarvis Collegiate Institute
  • Sample course outline with detailed unit plans
Virtual High School
  • Course outline summary
Ontario Online Academy
  • Course outline summary

Video Podcasts

Asymptotes of Rational Functions
  • This website graphs the function y = (x2)/(x2-16). The video shows the audience how to approximate functions (at infinity, and -ve infinity), and how to find asymptotes.
Composition of Functions
  • This video is a great explanation of the composition of functions. The author of this video has a bunch of great math tutorials! The only downside to these videos is the introduction music. Once you get past that, the material is great :)
Exponential Growth Functions
  • This is a great video on graphing exponential functions. The author gives a great visual on how quickly the values grow in these functions, and then graphs the function. A great start!
Khan Academy
  • The Khan Academy is a non-profit educational organization and a website created in 2006 by Bangladeshi-American educator Salman Khan, a graduate of MIT and Harvard Business School
Unit Circle Trick
  • A cool way to teach students the points on the unit circle for special angles
Graphing Reciprocal Functions
  • A video showing how to the asymptotes, holes, domain and range for reciprocal functions.


  • Grade 12 Math help videos with step-by-step solutions.
Gizmo Lessons
  • The world's largest library of interactive online simulations for math and science education in grades 3-12.
Leading Math Success
  • Leading Math Success includes lesson plans, videos, posters and other teaching resources for Grade 7 to 12 math classes.
National Council of Teachers of Mathematics
  • The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
Smartboard Resources
  • A directory of lessons for the SMART Board
Grade 12 Advanced Functions
  • A website that lists free resources for MHF4U.

Selected Teacher Webpages

Lesson Ideas