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Grade 12
1500+ Students

MHF4U – Grade 12 Advanced Functions Online Course (Ontario)

MHF4U is Ontario’s Grade 12 university-preparation math course that prepares students for calculus and is a required credit for most STEM, business and economics programs. It covers exponential and logarithmic functions, trigonometric functions, polynomial and rational functions, and characteristics of functions including rates of change. MHF4U is the direct prerequisite for Calculus and Vectors (MCV4U). Ontario eSecondary School (OES) offers MHF4U fully online and self-paced, with marking and support from Ontario Certified Teachers.

Credit: 1.0
Prerequisite: MCR3U or MCT4C
110 course hours
Registration open year-round

💻 Fulfills OSSD Online Graduation Requirement

The Advanced Functions Grade 12 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 in MHF4U 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.

110 course hours
Assignments
Final Exam
Interactive Submissions
Simulation Labs
Language: English
24/7 Tutoring
Developed by: M. Angjeli (OCT)
University
Prerequisite: MCR3U or MCT4C

MHF4U Course outline — 6 units, 110 hours

Full unit-by-unit breakdown.

Learning-skills self-assessment · goal setting · strategies for online math learning

Self-reflection, skill-building and strategy development to prepare for online math learning — students assess previous experience, identify areas for improvement, and set strategies for success.

Key topics

Learning-skills self-assessment · goal setting · strategies for online math learning

Assessed by

Preparation activities — not graded

Cubic, quartic and quintic functions · factoring · transformations · domain, range and intervals · polynomial inequalities

Video lessons and practice problems extend linear and quadratic knowledge to cubic, quartic and quintic functions — factoring to the 5th degree, transformations, key features of graphs, and solving polynomial equations and inequalities.

Key topics

Cubic, quartic and quintic functions · factoring · transformations · domain, range and intervals · polynomial inequalities

Assessed by

Assignments (incl. a Desmos rollercoaster design) · question-response interview · proctored unit test

Reciprocals of linear and quadratic functions · vertical and horizontal asymptotes · rational equations and inequalities

Investigate reciprocals of linear and quadratic functions: vertical and horizontal asymptotes, domain and range, intercepts and intervals — connecting algebraic and graphical representations to solve rational equations and inequalities.

Key topics

Reciprocals of linear and quadratic functions · vertical and horizontal asymptotes · rational equations and inequalities

Assessed by

Quiz and assignments · culminating assignment · question-response interview · proctored unit test

Laws of logarithms · evaluating logarithms · exponential and logarithmic equations · growth, decay and logarithmic scales

Connect exponential and logarithmic forms, verify and apply the laws of logarithms, and solve exponential and logarithmic equations algebraically — including problems from real-world applications.

Key topics

Laws of logarithms · evaluating logarithms · exponential and logarithmic equations · growth, decay and logarithmic scales

Assessed by

Equations assignment · culminating assignment · question-response interview · proctored unit test

Radian measure and the unit circle · sine and cosine graphs (period, amplitude) · reciprocal trig functions · trigonometric identities and equations

Radian measure from the unit circle, the graphs and properties of sine and cosine, sinusoidal modelling — then proving trigonometric identities through reasoning and verifying them with technology.

Key topics

Radian measure and the unit circle · sine and cosine graphs (period, amplitude) · reciprocal trig functions · trigonometric identities and equations

Assessed by

Quizzes (transformations, reciprocal functions, trig equations) · trig identities assignment · question-response interview · proctored unit test

Operations on functions · composition f(g(x)) · secant slope and average rate of change · tangent slope and instantaneous rate of change

Combine functions through addition, subtraction, multiplication, division and composition, then connect secant slopes to average rates of change and tangent slopes to instantaneous rates — the doorway into calculus.

Key topics

Operations on functions · composition f(g(x)) · secant slope and average rate of change · tangent slope and instantaneous rate of change

Assessed by

Quizzes (operations, composition of functions) · question-response interview · proctored unit test

MHF4U Advanced Functions
Grade 12 · University

How the final mark is calculated from September 2026

65% Coursework
25% Final written exam
5% Attendance
5% Participation
Domestic Student Fee

$595.00

International Student Fee

$895.00

ALL STUDENTS RECEIVE
24/7 Tutoring
Proctored Final Exam
Fast Track
Includes Priority Exam Scheduling

Fully online and self-paced

MHF4U

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FAQ About %course-code%.

Supported by Ontario Certified Teachers

MHF4U is the Grade 12 University-preparation math course extending the study of functions: polynomial, rational, exponential, logarithmic, and trigonometric functions, plus rates of change. It’s required by most university STEM, business, and many health-science programs, and it’s the prerequisite for Calculus and Vectors (MCV4U). This course has been developed based on the following Ministry of Ontario Curriculum for Grade 12 Mathematics.

MHF4U is one of the more challenging Grade 12 courses — it moves quickly through advanced algebra, trigonometric identities, and rational functions. The trigonometry unit (compound- and double-angle identities) is typically the hardest. Steady practice is the difference-maker, and OES includes free 24/7 math tutoring for exactly those moments.

The prerequisite for MHF4U is MCR3U (Grade 11 Functions) or MCT4C (Grade 12 Mathematics for College Technology). The MCT4C route matters: it gives students who took MCF3M in Grade 11 a path into Advanced Functions.

MHF4U is required or strongly recommended by most business/commerce, computer science, engineering (with MCV4U), mathematics, and many health-science and economics programs. It’s the most broadly required Grade 12 math. If your program list isn’t final, taking MHF4U keeps the most options open.

MHF4U (Advanced Functions) deepens function skills — polynomial, logarithmic, trigonometric — while MCV4U (Calculus and Vectors) introduces derivatives and 2D/3D vectors. MHF4U comes first and is required by more programs; MCV4U is required mainly for engineering, physical sciences, and some CS and math programs.

Most programs requiring MHF4U expect at least 70%, and competitive STEM, business, and health-science programs often look for mid-70s to high-80s. Since MHF4U usually counts in your admission average, a strong mark helps twice — meeting the requirement and lifting the average.

Yes. OES offers a dedicated Upgrade: MHF4U course built specifically for retaking MHF4U to raise your mark — Ontario universities and colleges use your highest grade. It’s self-paced and open year-round, so you can upgrade alongside your day school, a job, or a gap year and finish in as little as 4 weeks. See the Upgrade: MHF4U page for details.

Yes. Ontario students who started Grade 9 in the 2020–21 school year or later must earn at least two online learning credits to graduate, and MHF4U at OES — a Ministry-inspected online school (BSID #667186) — counts toward that requirement. An opt-out process exists through school boards, and specific provisions apply to students affected by the 2021 school closures.

MHF4U meets the Ministry of Education’s attendance and participation expectations through activities blended directly into the course. OES requires students to log in at least once per week for attendance, and participation activities appear throughout the course and are reflected in the grade book — preserving self-paced flexibility while satisfying the requirements for online courses.

Yes — mathematics is one of Ontario’s STEM-related course groups (business studies, computer studies, cooperative education, mathematics, science, and technological education), from which students entering Grade 9 in 2024 or later must complete one credit. For math and science, the credit counts when earned in addition to your compulsory math and science credits, so MHF4U can double as your STEM-group credit.

Ontario’s Growing Success policy pre-determines the evaluation structure for every credit. Beginning in the 2026–27 school year, MHF4U is graded on classroom work completed throughout the course (65%) plus a Ministry-mandated final evaluation worth 25% for Grades 11–12, with attendance and participation also reflected in the final grade. A credit is granted at 50% or higher — and as an inspected private school, OES may administer final evaluations online, while school-board online courses generally require in-person exam sittings.

Book a Free 15-Min Guidance Call
Domestic Student Fee

$595.00

International Student Fee

$895.00

ALL STUDENTS RECEIVE
24/7 Tutoring
Proctored Final Exam
Fast Track
Includes Priority Exam Scheduling