MHF4U
Advanced Functions
This Grade 12 university preparation course extends students’ experience with functions. Students investigate polynomial, rational, logarithmic and trigonometric functions, combine functions, broaden their understanding of rates of change and refine the mathematical processes needed for senior mathematics. The course prepares students for Calculus and Vectors and a range of university programs requiring advanced mathematics.
Grade
12
Credit
1.0
Delivery
Online
Prerequisite
MCR3U or MCT4C
About This Course
This Grade 12 university preparation course extends students’ experience with functions. Students investigate polynomial, rational, logarithmic and trigonometric functions, combine functions, broaden their understanding of rates of change and refine the mathematical processes needed for senior mathematics. The course prepares students for Calculus and Vectors and a range of university programs requiring advanced mathematics.
What You'll Learn
- Analyze polynomial functions, equations and inequalities.
- Investigate rational functions and their algebraic and graphical properties.
- Apply trigonometry and analyze trigonometric functions.
- Investigate exponential and logarithmic functions and solve related equations.
- Combine functions and analyze resulting relationships.
- Use multiple representations, technology, reasoning and modelling to solve advanced multi-step problems.
Skills You'll Develop
- Advanced function analysis
- Algebraic manipulation and equation solving
- Trigonometric, exponential and logarithmic reasoning
- Graphing, transformations and modelling
- Mathematical proof, problem solving and communication
Learning Outcomes
By the end of the course, students will be able to:
- Analyze polynomial functions and solve polynomial equations and inequalities.
- Analyze rational functions and their representations.
- Use trigonometric concepts and analyze trigonometric functions.
- Analyze exponential and logarithmic functions and solve related equations.
- Combine functions and describe their properties and representations.
- Apply rates of change, modelling and mathematical processes to advanced problems.
- Communicate precise mathematical reasoning using appropriate notation, representations and technology.
Course Units
The following reflects the school’s planned organization of the course. Approximate time allocations may be adjusted while all curriculum expectations and required planned learning are maintained.
| Unit | Title / Major Learning Focus | Approx. Time |
|---|---|---|
| 1 | Polynomial Functions | 15 hours |
| 2 | Polynomial Equations and Inequalities | 15 hours |
| 3 | Rational Functions | 13 hours |
| 4 | Trigonometry | 13 hours |
| 5 | Trigonometric Functions | 13 hours |
| 6 | Exponential and Logarithmic Functions | 13 hours |
| 7 | Solving Exponential and Logarithmic Equations | 13 hours |
| 8 | Combining Functions | 13 hours |
| Final | Mandatory Written Final Examination | 2 hours |
Assessment
Assessment uses evidence gathered over time from student work, conversations and observations. The final grade for 2026–2027 is determined as follows:
| Component | Weight | How It Is Determined |
|---|---|---|
| Coursework throughout the course | 65% | Evaluation evidence gathered throughout the course, reflecting the student's most consistent achievement with special consideration for more recent evidence. |
| Mandatory written final examination | 25% | Mandatory Grade 12 mathematics written final examination. |
| Attendance and participation | 10% | Based on meaningful attendance and participation; excused absences do not negatively affect this component. |
Examples of Assessment Evidence
Assessment may include problem sets, investigations, function-analysis tasks, graphing and technology work, modelling applications, written solutions, tests, conferences and the mandatory written final examination.
Pathways
MHF4U prepares students for Calculus and Vectors and for university pathways that require or benefit from advanced mathematics, including science, engineering, economics, mathematics, computer science, health sciences and quantitative areas of business.
MHF4U is also a co-requisite or prerequisite for MCV4U and a gateway to many Ontario university STEM programs.
Teacher Support
- Students learn through the school's secure online learning environment and receive ongoing support from qualified teachers.
- Teacher-supported conferencing, tutorials and scheduled live support are available as appropriate.
- Teachers activate prerequisite knowledge from functions, algebra and trigonometry before extending ideas to advanced functions.
- Explicit modelling supports reasoning, notation, algebraic manipulation, transformations and multi-step strategies.
- Graphing technology and dynamic mathematics software support investigations of polynomial, rational, logarithmic and trigonometric functions.
- Worked examples, deliberate practice, error analysis, mathematical discussion and differentiated supports build independence.
Frequently Asked Questions
What is the course code?
MHF4U — Advanced Functions, Grade 12, University Preparation.
What is the prerequisite?
Functions, Grade 11, University Preparation (MCR3U), or Mathematics for College Technology, Grade 12, College Preparation.
How many credits is MHF4U?
The course is worth 1.0 Ontario secondary school credit.
What functions are studied?
Polynomial, rational, trigonometric, exponential and logarithmic functions, as well as combinations of functions.
How is the final grade calculated?
65% coursework, 25% mandatory written final examination, and 10% attendance and participation.
Does MHF4U prepare students for Calculus and Vectors?
Yes. The outline identifies MHF4U as preparation for MCV4U and for university programs requiring advanced mathematics.
Is MHF4U required for university admission?
Many Ontario university STEM and science programs require or strongly recommend MHF4U — students should check specific admission requirements.
Ready to Take This Course?
$549 / Credit
- Provided by CSW — Canadian School of the World
- Ontario Ministry of Education registered
- Delivered fully online
Need Help Deciding?
Not sure if this is the right course? Book a free 30-minute meeting with a CSW advisor.
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