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Advanced Functions, Grade 12, University (MHF4U)
Course Code: MHF4U
Course Type: University Preparation
Delivery Options Available: Online / In Class ( You can only choose one )
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
$499.00
All course prices are in CAD – Canadian Dollars
Course Description For Advanced Functions, Grade 12, University (MHF4U)
This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Summary Of Units And Timelines For Advanced Functions, Grade 12, University (MHF4U)
Below is the suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview found in the MHF4U course profile.
| Unit | Title | Expectations Summary | Time |
|---|---|---|---|
| 1 | Exponential and Logarithmic Functions | Understand exponential-log relationships, laws of logs, graphs, and equations for real-world problems. | 26 Hours |
| 2 | Trigonometric Functions | Explore radian measure, graphs, identities, reciprocal functions, and trigonometric equations. | 30 Hours |
| 3 | Polynomial and Rational Functions | Connect numeric, algebraic, graphical models, solve equations and inequalities. | 26 Hours |
| 4 | Characteristics of Functions | Compare functions, calculate rate of change, perform operations and compositions. | 26 Hours |
| Final | Exam and Summative | Evaluation of all learning | 3 Hours |
What You Will Learn – Curriculum Expectations
- Understand relationships between exponential and logarithmic expressions
- Apply logarithmic laws to simplify and evaluate expressions
- Graph and interpret logarithmic functions
- Solve exponential and logarithmic equations including real-life applications
- Use radian measure to describe angles and arcs
- Graph primary and reciprocal trigonometric functions
- Prove trigonometric identities
- Solve trigonometric equations with real applications
- Analyze and graph polynomial functions of various degrees
- Understand rational functions and asymptotic behavior
- Solve rational equations and inequalities algebraically and graphically
- Determine average and instantaneous rate of change
- Perform operations and compositions of functions
- Compare properties of different types of functions
- Model and solve complex problems with function behavior
- 70% – Term Work (assignments, quizzes, unit tests, projects)
- 30% – Final Evaluation (summative + exam)
- 🧠 Knowledge & Understanding – 20%
- 💡 Thinking & Inquiry – 20%
- 🛠 Application – 40%
- 🗣 Communication – 20%
- Direct instruction and teacher-led discussions
- Worksheets, brainstorming, and problem-solving activities
- A mix of independent and group-based learning
- Real-world applications enhanced through technology and visual tools
- 📘 Advanced Functions – McGraw-Hill Ryerson (2008)
- 📘 Advanced Functions – Nelson Education Ltd (2008)
- 🌐 Online platforms: YouTube, Wikipedia, GeoGebra, Desmos
Ontario Ministry Guidelines: 110-Hour Course Requirement
Please be aware that, as per Ministry guidelines, CanSTEM Education has a mandatory minimum requirement of 2 weeks enrolment for students to be eligible for a midterm report card and 4 weeks enrolment to be eligible for a final report card. This 110-hour requirement ensures that students receive a standardized amount of learning time for each credit they earn. The 110 hours typically include planned learning activities, excluding homework, designed to achieve the course’s curriculum expectations, according to the Ontario Ministry of Education.
Frequently Asked Questions
MHF4U is a Grade 12 Advanced Functions course at a University preparation level.
4U refers to the Grade level of the courses and the pathway. 4 means it is a grade 12 course and U means it is a university preparation course.
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
At CanSTEM Education you can complete a high school credit courses as quickly as 4 weeks, or take as long as 6 months.
Yes, we can send the marks for your courses directly to OUAC, OCAS, your guidance counsellor and to you.