MHF4U Course Grade 12 Advanced FunctionsCourse and Tutoring

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Welcome to Queen Elizabeth Academy, providing MHF4U Course - 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.

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

Thank you QE - for the Foundation

Emily H.

admitted to

Queen's Commerce

Jivan K.

admitted to

Waterloo Engineering

Stephanie L.

admitted to

Queen's Commerce

Andrew G.

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Western Engineering

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Private MHF4U Course - Grade 12 Advanced Functions

In Person, Classroom Lectures (Credit Course)
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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.

Benefit to Students - MHF4U Course

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 ongoing lecture.

MHF4U
2. Step by Step Explanations

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

 
 
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3. Building Foundations:

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...

Success Stories

Success Stories

Congratulations to Stephanie L., who ranked Top 15 in Canada selected by University Hub.

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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)
  And more...
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Jerry T.
Admitted to Queen’s Commerce
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Taylor W.
Admitted to Western Medical Science
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Sam A.
Admitted to Queen’s Science Honours

Our Math tutor can help you to achieve success in your Math courses

Success of QEA alumni

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Investment banking analyst
Canaccord Genuity
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Graduate of Western University
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Microsoft Manager
Graduate of Queen’s Commerce
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Graduate Queen's Law School
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Business Dev. associate
Fidelity Investments
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Master degree candidate
UC Berkeley
Data analyst, Citigroup
Graduate of Boston University
QEA student alumni
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Sam A.
MD Candidate
University of Queensland
Graduate of Queen’s University
QEA student alumni

Meet our Advanced Functions Teachers MHF4U Course

Meet our Teachers for Summer MHF4U Course

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.
Kosal C.
Master candidate, Mathematics York University QEA Math Tutor
Dev D.
QEA Biology and Chemistry Teacher
Dev is graduated with a science degree at York University, currently enrolled in dental school. Dev has been working with QEA for 4 years.
Chris L.
QEA Physics Teacher
Chris is our physics tutor, explaining his approach in teaching physics. Chris is going to John Hopkins University this fall studying PhD in Physics
Amjad M.
Calculus Teacher
Graduate with Master degree of Mathematics University of Toronto. Employed by U of T to teach calculus tutorial as TA.

QEA Summer School - MHF4U Course - In Action!

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Students from MHF4U Grade 12 Advanced Functions and other courses

Yohan B.
Wilfrid Laurier BBA
Emily H.
Queen's Commerce
Mark J.
Western Ivey
Stephanie L.
Queen’s Commerce
Jivan K.
Waterloo Engineering
Andrew G.
Western Engineering
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
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Course Description

Summer MHF4U Course

Summer MHF4U Course | 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 Course 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 Course 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 Course 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 Course 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 prerequisite. 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 Course 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 begins, 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.

MHF4U Course FAQ

What is the MHF4U course?

The MHF4U course is a Grade 12 Advanced Functions course in the Ontario curriculum, focusing on advanced topics in algebra and functions.

What are the prerequisites for taking MHF4U?

Prerequisites for the MHF4U course typically include successful completion of Grade 11 Mathematics courses, such as MCR3U.

What topics are covered in the MHF4U curriculum?

The MHF4U curriculum covers a variety of topics, including polynomial, rational, exponential, logarithmic, and trigonometric functions, as well as sequences and series.

Is MHF4U a mandatory course for graduation?

In many educational jurisdictions, MHF4U (or its equivalent) is a mandatory course for high school graduation, fulfilling mathematics requirements.

University Admission Tips

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. [...to 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 [...to be continued]

email to: vlee@QETutoring.com

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MHF4U
by Sam A.BSc. graduate, Queen’s University QEA student alumni
MHF4U
by Jessica K.Master in English literatureQueen’s University QEA English teacher
Summer mhf4u 32

MHF4U Course - Syllabus

Topics and Syllabus

Overall Expectation of MHF4U Course

EXPONENTIAL AND LOGARITHMIC FUNCTIONS - MHF4U Course

MHF4U 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;

MHF4U 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

MHF4U 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;

MHF4U 2.2 recognize the relationship between an exponential function and the corresponding logarithmic function to be that of a function and its inverse, deduce that the graph of a logarithmic function is the reflection of the graph of the corresponding exponential function in the line y = x, and verify the deduction using technology

MHF4U 3. solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.

MHF4U 3.1 recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types

TRIGONOMETRIC FUNCTIONS for MHF4U Course

MHF4U 1. demonstrate an understanding of the meaning and application of radian measure;

MHF4U 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 center of a unit circle, and develop and apply the relationship between radian and degree measure

MHF4U 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;

MHF4U 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

MHF4U 3. solve problems involving trigonometric equations and prove trigonometric identities.

MHF4U 3.4 solve linear and quadratic trigonometric equations, with and without graphing technology, for the domain of real values from 0 to 2π, and solve related problems

POLYNOMIAL AND RATIONAL FUNCTIONS for MHF4U Course

MHF4U 1. identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;

MHF4U 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

MHF4U 2. identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;

MHF4U 2.3 sketch the graph of a simple rational function using its key features, given the algebraic representation of the function

MHF4U 3. solve problems involving polynomial and simple rational equations graphically and algebraically;

MHF4U 3.2 factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies (i.e., common factoring, difference of squares, trinomial factoring, factoring by grouping, remainder theorem, factor theorem)

MHF4U 4. demonstrate an understanding of solving polynomial and simple rational inequalities.

MHF4U 4.2 determine solutions to polynomial inequalities 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 technology, and identifying intervals for which x satisfies the inequalities

CHARACTERISTICS OF FUNCTIONS for MHF4U Course

MHF4U 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;

MHF4U 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)

MHF4U 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;

MHF4U 2.2 recognize real-world applications of combinations 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 frequencies of tones associated with the numbers on a telephone involve the addition of two trigonometric functions), and solve related problems graphically

MHF4U 3. compare the characteristics of functions, and solve problems by modeling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

MHF4U 3.1 compare, through investigation using a variety 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, trigonometric, exponential, logarithmic)

Sources: Ministry of Education Ontario:http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Course organization for MHF4U Course

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

ASSESSMENT AND EVALUATION POLICY for MHF4U Course

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

MHF4U Course Advanced Functions grade 12 math course description

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. Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation

TEACHING/LEARNING STRATEGIES for MHF4U Course

  • 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.

CONSIDERATIONS ON PROGRAM PLANNING

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

Queen Elizabeth Academy - Find MHF4U Course at your neighborhood

*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.

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