Grade 12 Advanced Functions
Course and Tutoring

Google Rating

Welcome to Queen Elizabeth Academy, providing MHF4U Grade 12 Advanced Functions Course and Tutoring, for you to excel at grade 12 Advanced Functions. Our course instructors and tutors have deep experience in MHF4U Grade 12 Advanced Functions course / advanced functions, for you to understand the concepts and be able to tackle application / thinking problems, which many students lose their marks.

MHF4U Course - Advanced Functions Grade 12

MHF4U Grade 12 Advanced Functions is the key grade 12 course for students to enter a top university. Having a good foundation skill and understanding the concepts is critical to succeed in this course. Many students stumbled upon memorizing equations or losing marks on application / thinking problems. We teach our students with the proper approach for you to achieve in this course.

Functions. Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation.
12 (University)
Ministry of Education:
Curriculum Format:
A. In Person lesson 110 hours (credit granted)
B. Online live lesson 110 hours (credit granted)
C. Tutoring (non credit)

Queen Elizabeth Academy offers MHF4U Grade 12 Advanced Functions course as an online course or in person (subject to space availability). Our MHF4U Grade 12 Advanced Functions online course runs the same as in person, with a small class settings (maximum 9 students) where our students will have a full interactive experience with our teachers. This includes teaching the foundational skills, the concepts step by step in an easy to understand manner, and going over problems, especially the application and thinking problems.

to enrolMHF4U:

Private MHF4U Grade 12 Advanced Functions

In Person, Classroom Lectures (Credit Course)
Experience our Online Live Teaching (Credit Course)
Physics 11 online live
Experience our online live teaching that is fully interactive. Our students participate and clarify their understanding, rather than sitting passively watching a screen.
Calculus class online live
Experience our online live teaching where our teachers explain complicated concepts in an easy to understand, step by step manner. We facilitate understanding of the student, not memorizing.

Benefits to Students
in taking MHF4U Grade 12 Advanced Functions
Private Credit with QEA:

1. Small Class Sizes

To maintain the quality of our lessons, class size is limited to a max of 9 students, giving students the opportunity to ask questions throughout an on-going lecture.

2. Step by Step

Our focus is to build step by step on the students’ understanding of the materials. We turn complex concepts into simpler steps for our students to absorb and understand.

3. Building

For our students who are applying to universities, building a better foundational knowledge is key to success.

4. One on One Attention:

We structure a work period in each of our lessons that our teachers walk around and help each student one by one. In our online live class, each student will get a ‘slice’ of time, where our teacher will enter their virtual room, to work with them one by one. This will help clarify any misunderstanding immediately.

Success Stories
Congratulations to our students who were admitted to their top choice university (Queens, Wilfred Laurier, McGill etc.).  Our students obtained scholarships from $2,000 to $23,000
Jeff R. Queen’s Commerce
Paul M. Queen’s Engineering
Melissa W. Western Ivey
Taylor W. Western Medical Science
Josh M. OCAD
Miranda D. Wilfred Laurier BBA (Co-op)
Colin H. Queen’s Commerce
Stephanie L. Queen’s Commerce
Jeremy R. Western Ivey
Robbie M. Wilfrid Laurier BBA (Co-op)
Eric M. Wilfrid Laurier BBA (Co-op)
Jiv S. Wilfrid Laurier BBA (Coop)
Vivian T. U of T Rotman
Stacy L. Western Engineering
Laura P. Western Medical Science
David P. U of T Rotman
Britney R. Wilfred Laurier BBA (Co-op)
Monika S. Western Health Science
Lisa V. U of T Architecture
Katie F. McGill Arts
  And more...
to enrolMHF4U:

One on one private tutoring MHF4U Grade 12 Advanced Functions course

Queen Elizabeth Academy’s Private Tutoring Program provides our students with one on one, personalized tutoring lessons that are based on a step by step, easy to understand methodology.

Our Approach of Tutoring for
MHF4U Grade 12 Advanced Functions

At QEA, we focus on tutoring the students and build his or her foundation and understanding. Our tutoring approach facilitates independent thinking, so that our students can analyze the questions properly. Our tutors go through math and science lessons step by step, and make sure that you have a firm foundation before they move onto more complex math and science concepts.

1. Step by step explanation

For our science and math tutoring programs, we focus on providing step by step explanations during the tutoring session, facilitating the student’s understanding of the math and science concepts.

2. Building Foundations

Math and science are cumulative. Therefore, building a good foundation is important for the student’s long-term success. In our math and science tutoring, we focus on clarifying the student’s knowledge gaps to help them build a good foundation in math and science.

3. Organize Knowledge

Our tutors will categorize types of problems and organize knowledge making it easier for students to retain.

QEA helps students succeed in Math, English and Science through our excellent tutoring. We have online tutoring services in Toronto, Ottawa, Calgary and Milton. We focus on building good foundations in the area of Mathematics, Science and English for student success.

The challenge for students for MHF4U Grade 12 Advanced Functions online or in person course, is to understand the concept and have a good foundation skills. On top of this, the student needs to understand how to dissect complex application questions and apply the concepts to the equations and steps. We provide good guidance and lessons, and want our students to work hard and practice to master this skills.

QEA Tutoring - in Action!

MHF4U Grade 12 Advanced Functions and other courses


Meet our 25+ Teachers and Tutors

Diana J.
English Teacher
PhD candidate, English literature. York University. 6+ teachers of teaching experience. Teaching university level tutorials at York University.
Nikki V.
Math Teacher
Certified Teacher. Master degree in Education. Nikki has been QEA math teacher for 6 years and have over 1,000+ hours of teaching experience.
Angela K.
Chemistry and Biology Teacher
Master graduate in Science, University of Toronto Angela explains how we take an extra step during Covid 19 period, to support our students and ensure that they get a good foundation.
Ben T.
English Teacher
Teaches:  English grade 5 to 12

PhD Candidate, English literature

Writing Course Director, Guelph-Humber University 

Laura C.
MD Candidate
Harvard University

Queen Elizabeth Advisor

Designed Learning Strategies for our courses. 

John C.
Math Tutor and Science Tutor
Teaches:  Calculus, Advanced Functions, Physics

PhD Candidate, University of Toronto

Taught university math tutoring classes for 2+ years

Renuka R.
Math Tutor
Teaches:  Advanced Functions

1200+ hours of tutoring experience.  Specialized in making complex concepts easy to understand

Candy C.
Math Teacher
Teaches:  Calculus, Grade 9-12 Math

Certified Teacher, Mathematics.

6 years of university teaching experience as a TA

Aditya S.
Science Tutor
Teaches:  Chemistry, Math 9-12

Recipient of E.A. Robinson Medal.  Rank#1 in Science, University of Toronto

TA teaching first year university tutorial

and 27+ tutors each specializing in a subject area, grade and student’s need

Math, Science, Chemistry and Physics tutors at QEA are specialized in their subject areas. QEA operates in cities such as Toronto, Ottawa, Calgary and Markham. Students who receive our programming walk away with the foundations and skills they need to be successful in the long run.

Google Rating
Thank you
Queen Elizabeth Academy!

Students from MHF4U Grade 12 Advanced Functions and other courses

Matt B.
a grade 12 student admitted to Laurier Business
Sebastian G.
a grade 12 student admitted to McGill University
Andrew G.
admitted to Western University

Paige M.
Admitted to Queen’s University student alumni of QEA enrolled in QEA English 12 private credit course

Kristen C.
Admitted to University of Waterloo student alumni of QEA enrolled in QEA English 12 private credit course
Yohan B.
Wilfrid Laurier BBA
Will O.
Queen’s Engineering
Mark J.
Western Ivey
Google Reviews
Queen Elizabeth Academy | Private Credit Courses
powered by Google

MHF4U Grade 12 Advanced Functions
Private Credit Course Overview

MHF4U Grade 12 Advanced Functions is one of the most important Math courses in grade 12 for university admission

What is MHF4U Grade 12 Advanced Functions?

MHF4U Grade 12 Advanced Functions is a key math course in grade 12, pre-calculus. It explores important concepts in trigonometry, graphing, polynomials and rational functions.

What does MHF4U Grade 12 Advanced Functions stand for?

MHF4U Grade 12 Advanced Functions is a course code designed by the Ministry of Education. MHF stands for Advanced Functions, 4 stands for 4th year in high school (grade 12) and U stands for a course preparing for university

What is Advanced Functions?

Advanced Functions is one of the 3 math courses in grade 12, besides calculus and data management. It’s a pre-calculus course, therefore many concepts you learn in this course will serve as a foundation for calculus, whether you are taking it in grade 12 or first year.

Is Advanced Functions harder than Calculus?

Some units in Advanced Functions are very difficult, such as trigonometry (double angle formulas). We will say that in general Calculus is harder.

MHF4U Grade 12 Advanced Functions - Course Description

MHF4U Grade 12 Advanced Functions 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.

MHF4U 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.

What is taking MHF4U Grade 12 Advanced Functions like?

MHF4U Grade 12 Advanced Functions is a very important course for many students because most university programs require this course as a pre-requisite. The skills learned in the Grade 11 course are built upon in this course, including factoring, graphing, trigonometry and exponents.

Students will likely have varying levels of proficiency when taking this course, as some units, such as polynomial functions, are quite simple, while others, such as trigonometry and proofs. Some students have thus described it as a roller coaster ride of a course, with all the thrills (and challenges) that that entails.

Tips to succeed in MHF4U Grade 12 Advanced Functions

It would be a good idea, before the beginning of this course, to brush up on the foundations of mathematics, such as factoring (especially trinomial factoring), domain and range, graphing, adding rational expression, and trigonometry ratios. If you wait until the course beings, it may be difficult to keep pace with the new material which is being taught. Foundations are always important, and as with all mathematics courses, this one builds upon your past knowledge, so be sure to review.

Also, make sure to keep good, organized notes to stay on top of the course units. Do not be afraid to practice problems beyond those assigned in the homework, as MHF4U Advanced Functions is known for containing a very wide variety of questions and problems, and therefore the more you expose yourself to such problems, the better prepared you will be. Because of this, the Queen Elizabeth Academy provides all of our students with extra worksheets and practice tests to hone their skills and succeed.

FAQ for MHF4U Grade 12 Advanced Functions course

What is a reasonable price for MHF4U Grade 12 Advanced Functions?

QEA charges a very competitive price for tutoring. You are not just paying for a tutor, you have the whole support of our program and system. For example, we will provide foundation skills packages to begin, and we provide weekly homework packages with application and thinking problems that mimic tests for better practice. Towards the final exam, we also provide a mock exam.

What MHF4U Grade 12 Advanced Functions tutor will be assigned to my child?

The average tenure of our tutors at QE is at least 3 years. Many of our tutors stay with QE for 5-6 years. In this way, they are experienced and have worked with hundreds of students. Many of them have taught our 110 hours credit courses. New tutors need to go through a rigorous audition process in order to join QE. This includes showing in depth knowledge on our tests while also being able to explain concepts in a way that students can understand.

How much does MHF4U Grade 12 Advanced Functions tutoring cost?

We charge per month (4 or 8 lessons a month). Depending on the program, we offer very competitive and fair rate. We provide much more value than the average tutoring centers or go-to-home agencies: successful experience, coaching, homework package, mock tests and exams, test writing strategies and lesson based tutoring.

How can MHF4U Grade 12 Advanced Functions tutor help my child?

QE has a strong track record on supporting our students to academic excellence and long term success. Our tutoring program is private one on one, tailored towards the strengths and weaknesses of your child. Our tutoring program is lesson based, which means we don't sit back and wait for questions, because oftentimes they don't know what to ask. We actively teach lessons and provide weekly homework for practice.

What is math MHF4U Grade 12 Advanced Functions?

MHF4U is a Grade 12 level University preparation course in Advanced Functions. Mathematical processes are integrated into student learning in all facets of the course. Students will learn a broad range of material, including making conceptual connections, mathematical procedures, and advanced math skills.

What does MHF4U Grade 12 Advanced Functions mean?

Advanced Functions, Grade 12, University Preparation. You will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combing functions; broaden your understanding of rates of change; and develop facility in applying these concepts and skills.


Admission Requirements Summary
Admission Requirements Summary. Major university programs. (Grade cut off, Admission essay etc.)
How to Get into the
Top Universities?
How I got into my top choice universities?
by QEA student alumni
Jeremy R.
Admitted to Western Ivey School of Business
former QEA student

Early on in high school, I knew I wanted to apply to the top business schools in Canada, which led me to focus my attention on getting accepted to both the Western and Queen’s business programs. QE has given me significant support in my academic well-being as well as giving advice on ... [to be continued]

Colin H.
Admitted to
Queen’s Commerce
former QEA student

In Grade 12, managing your time is critical. You need to allocate your limited resources (i.e. your time) on what matters most. This principle applies to various tasks from focusing your energy on the most important subjects, to scoring the test questions you know first, to focusing on one or two job experiences or extracurricular activities that make you stand out....
[to be continued]

Tips on University
Application Essays
Western Ivey School of Business (AEO) application essay
by Jeremy R.
admitted to Western Ivey School of Business (AEO)
QEA student alumni

Attaining AEO status to the Western Ivey School of Business is not an easy task. However, with the right approach and execution, getting into this competitive program can certainly be done.

Aside from having strong academics, the main aspect the staff evaluating your application will look for is extra-curricular involvement. Simply put, they want to see. [ be continued]

by Colin H.
admitted to Queen’s Commerce
QEA student alumni

While applying to universities, many students will focus on their grades, but have often neglected the importance of the application essay. You should start early (one to two months before the deadline) and compose at least 4-5 drafts on each essay.

The words on your essay are very limited, often times you have to deliver your points in about 300-400 words. Therefore you must go [ be continued]

email to:

to receive a FREE University Admission Support Package


by Sam A.
BSc. graduate,
Queen’s University
QEA student
by Jessica K.
Master in English
Queen’s University
QEA English teacher

Overall Expectation for Math grade 12


1. demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions;

1.1 recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation (i.e., the undoing or reversing) of exponentiation, and evaluate simple logarithmic expressions

2. identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;

2.2 recognize the relationship between an expo- nential function and the corresponding loga- rithmic function to be that of a function and its inverse, deduce that the graph of a loga- rithmic function is the reflection of the graph of the corresponding exponential function in the line y = x, and verify the deduction using technology

3. solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

3.1 recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types


1. demonstrate an understanding of the meaning and application of radian measure;

1.1 recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure

2. make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems;

2.1 sketch the graphs of f(x) = sin x and f(x) = cos x for angle measures expressed in radians, and determine and describe some key properties (e.g., period of 2π, amplitude of 1) in terms of radians

3. solve problems involving trigonometric equations and prove trigonometric identities.

3.4 solve linear and quadratic trigonometric equa- tions, with and without graphing technology, for the domain of real values from 0 to 2π, and solve related problems


1. identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;

1.4 distinguish polynomial functions from sinusoidal and exponential functions [e.g., f(x) = sin x, g(x) = 2x], and compare and contrast the graphs of various polynomial functions with the graphs of other types of functions

2. identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;

2.3 sketch the graph of a simple rational function using its key features, given the algebraic rep- resentation of the function

3. solve problems involving polynomial and simple rational equations graphically and algebraically;

3.2 factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factor- ing, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem)

4. demonstrate an understanding of solving polynomial and simple rational inequalities.

4.2 determine solutions to polynomial inequali- ties in one variable [e.g., solve f(x) ≥ 0, where f(x) = x3 – x2 + 3x – 9] and to simple rational inequalities in one variable by graphing the corresponding functions, using graphing tech- nology, and identifying intervals for which x satisfies the inequalities


1. demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;

1.1 gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change (e.g., in words, numerically, graphically, algebraically)

2. determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;

2.2 recognize real-world applications of combi- nations of functions (e.g., the motion of a damped pendulum can be represented by a function that is the product of a trigonometric function and an exponential function; the fre- quencies of tones associated with the numbers on a telephone involve the addition of two trigonometric functions), and solve related problems graphically

3. compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

3.1 compare, through investigation using a vari- ety of tools and strategies (e.g., graphing with technology; comparing algebraic representa- tions; comparing finite differences in tables of values) the characteristics (e.g., key features of the graphs, forms of the equations) of various functions (i.e., polynomial, rational, trigono- metric, exponential, logarithmic)

Sources: Ministry of Education Ontario:

Course organization for Math grade 12

UnitUnit Title (Description)Time
Unit 1Basic Functions and Transformation12 hours
Unit 2Polynomial Functions15 hours
Unit 3Rational Functions15 hours
Unit 4Trigonometry I25 hours
Unit 5Trigonometry II15 hours
Unit 6Logarithm12 hours
Unit 7Combination of Functions16 hours

Total Hours 110 hours


The student’s final grade for this course will be determined as outlined in Growing Success (pg. 28)

Seventy per cent (70%) of the grade will be based on evaluations conducted throughout this course. This portion of the grade should reflect the students’ most consistent level of achievement throughout the course, although special consideration should be given to the more recent evidence of achievement.

Thirty per cent (30%) of the grade will be based on a final evaluation in the form of an examination, performance, essay and/or other method of evaluation suitable to the course content and administered towards the end of the course.

Assessment is the process of gathering information from a variety of sources (including assignments, demonstrations, projects, performances and tests) that accurately reflects how well students are achieving the curriculum expectations.

Evaluation is the process of judging the quality of a student’s work on the basis of established achievement criteria, and assigning a value to represent that quality.

The term score will be divided into 4 categories:

  • Knowledge (30 – 35%)
  • Applications (20 – 25%)
  • Thinking / Inquiry (15-20%)
  • Communications (10-15%)

There are four levels of achievement for students who are passing this course:

  • Level 1 (50-59%)
  • Level 2 (60-69%)
  • Level 3 (70-79%)
  • Level 4 (80-100%)

Level 3 is the provincial standard for student achievement.

A wide range of assessment strategies (tests, portfolios, journals, essays, presentations, observation, conferencing and projects), combined with an array of instrument tools (including detailed marking schemes, checklists, rubrics and exemplars), is used in order to measure student achievement of overall course expectations


  • Whole-class, small group, and individual instruction;
  • Electronic technology – use of dynamic software, calculators, the Internet, spreadsheets and multi-media in activities, demonstrations and investigations;
  • Encourage maximum student participation in classroom activities;
  • Share the rubrics for culminating activities at the beginning of the unit, so expectations are clear
  • Encourage inquiry – questioning, investigating, communicating in a variety of ways;
  • Provide opportunities to acquire knowledge and apply that knowledge in a variety of contexts;
  • Identify & address different learning styles throughout the course;
  • Use self- and peer assessments;
  • Encourage brainstorming, exchange of ideas, debating;
  • Encourage students to take responsibility for learning;
  • Encourage students to apply individual/group learning skills;
  • Respect cultural differences of international students.


Teachers who are planning a program in mathematics must take into account considerations in a number of important areas, including those discussed below.

Find Queen Elizabeth
at your neighbourhood

*Note that Queen Elizabeth Academy offers in class learning at our Mississauga location, at Unit 5, 1020 Johnson’s Lane. The rest of the locations we offer credits online via Zoom (TM) with live teaching.

Tutoring in Etobicoke near me
Tutoring in Georgetown near me
Tutoring in Caledon near me
Tutoring in Newmarket & Aurora near me
Tutoring in Vaughan near me
Tutoring in Whitby near me
Tutoring in Cambridge near me
Queen Elizabeth