Summer School

Grade 12 Advanced Functions | MHF4U

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4.9
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Private Summer School | Advanced Functions | MHF4U Course

The Queen Elizabeth Standard on Academic Excellence
Summer High School Credits that builds foundation and enable students to achieve higher

Queen Elizabeth Academy is a premier education facility providing high-quality academics for our students. We focus on building a sound foundation for our students preparing for successful entry to top universities.

Over the past 9 years, we worked with thousands of students, many of whom were admitted to top universities: Waterloo, Queen’s, Western, Laurier, and McGill, with scholarships from $2,000 to $23,000.

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.
MHF4U Course - Grade 12 Advanced Functions

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.

Pre-Requisite:
Functions. Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation.
Grade:
12 (University)

Table of Contents

to enrollMHF4U:
Summer School
How our lessons are conducted?

Summer MHF4U Course | Advanced Functions - In Person, Classroom Lectures

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Summer MHF4U Course | Advanced Functions - Experience our Online Live Teaching

Benefits to Students - Summer MHF4U Course | Advanced Functions

1. Small Class Sizes

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

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2. Step by Step

Explanations

students’ understanding of the materials. We turn complex concepts into simpler steps for our students to absorb and understand.

3. Building

Foundations:

For our students who are applying to universities, building a better foundational knowledge is key to success. This is achievable given the focus in our summer school, with only one single subject for the student.

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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. Our summer school students can clarify any misunderstanding.

to enroll
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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Mark J.
Investment banking analyst
Canaccord Genuity
Graduate of Western Ivey
QEA student alumni
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Dr. T. Ward-able
Family Physician
Graduate of Western University
QEA student alumni
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Julia S.
Business Dev. associate
Fidelity Investments
Graduate of Western University
QEA student alumni
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Justin C.
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

Find Queen Elizabeth Academy
- Summer School at your neighborhood

*Note that Queen Elizabeth premise are currently located in Vancouver, Oakville and Etobicoke. For the other locations, we offer online live tutoring over zoom.

to enroll
Meet our

Teachers

Meet our Teachers for Summer MHF4U Course

Nikki V.
QEA Math Teacher
Nikki is a certified teacher with a Master degree in Education from University of Toronto. She has been working with QEA for over 6 years, and many of QEA top students came out of her class
Chris L.
QEA SPH4U Physics 12 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
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.
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Ben T.
English Teacher
Teaches:  English grade 5 to 12

PhD Candidate, English literature

Writing Course Director, Guelph-Humber University 

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Laura C.
MD Candidate

Harvard University

Queen Elizabeth Advisor

Designed Learning Strategies for our courses. 

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

PhD Candidate, University of Toronto

Taught university mathematics tutoring classes for 2+ years

Summer MHF4U Course | Advanced Functions - in Action!

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If you want to do well in math, a step by step approach to building academic success is also important.
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How to achieve higher grade in Summer MHF4U Course | Advanced Functions

Stay on top

Since summer school runs rather quickly, it is important to organize your time well, so that you don't fall behind In summer school, you will expect to have a test every 3 days. There is no gap between the last day of class and the exam. Therefore, it is imperative for you to stay on top daily.

Organize your time

Dedicate 1 to 1.5 hour each day after class, to review your notes. This will help you to stay on top. In addition, practice as if you will get a test tomorrow on the new materials. Do your reading (if you are taking English) ahead of time, such as Shakespeare or the novel.

Maximize your learning during class

It is important to listen attentively, take notes, so that you will learn most of the materials in class. Since summer school runs quickly and your duration of the day is 5 hours. It is important to utilize that time effectively. Try to understand the concepts in class, do practice and ask questions.

Preparing for tests

Keeping on top is important, so that you are always ready for tests. Practice daily. On the day before the test, you need to review your own study notes / notes taken in class, and practice a variety of questions. Label questions under type 1, type 2, type 3 etc., and this will help you organize your knowledge and avoid getting confused. On concepts, try to write out the concepts in your own words, and this will facilitate your understanding of the materials.

to enroll
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Google Rating
4.9
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
Stephanie L.
Queen’s Commerce
Mark J.
Western Ivey
Google Reviews
Queen Elizabeth Academy | Private Credit Courses
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4.9

Find Queen Elizabeth Academy
- Summer School at your neighborhood

*Note that Queen Elizabeth premise are currently located in Vancouver, Oakville and Etobicoke. For the other locations, we offer online live tutoring over zoom.

Course

Description

Summer MHF4U Course | Grade 12 Advanced Functions

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 Summer 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 Summer 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.

Course Description - Summer MHF4U Course

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 Summer 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 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.

FAQ for MHF4U Grade 12 Advanced Functions course

Can you take advanced functions in summer school?

Yes, QEA offer grade 11 and grade 12 credit courses in summer.

What is Grade 11 advanced functions?

The course MCR3U, which is meant for Grade 11 students, builds upon students' knowledge of linear and quadratic relations and introduces them to the mathematical concept of the function.

Is Grade 12 functions harder than Grade 11?

From a student's perspective, Grade 11 can be more challenging than Grade 12. When students transition to Grade 11, they may feel overwhelmed by the extensive syllabus compared to the previous year in Grade 10.

Is advanced functions or calculus harder?

It's commonly believed that Calculus is a more challenging subject since it delves deeper into some of the concepts covered in Advanced Functions. However, the difficulty level may vary depending on the instructor.

What is covered in advanced functions?

As part of their studies, students will explore the characteristics of polynomial, rational, logarithmic, and trigonometric functions. They will also learn how to combine functions and expand their knowledge of rates of change, in order to effectively apply these concepts and skills.

How hard is advanced functions?

Both Advanced Functions and Data Management are considered relatively easy, while Calculus and Vectors are slightly more challenging. To summarize, Advanced Functions and Data Management should be manageable for students who have completed their Grade 10 math course. Completing the Advanced Functions course will make Calculus and Vectors easier to handle.

University

Admission

Tips

Admission Requirements Summary
Admission Requirements Summary. Major university programs. (Grade cut off, Admission essay etc.)
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How to Get into the

Top Universities?

How I got into my top choice universities?
by QEA student alumni
summer mhf4u course 39
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]

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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
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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]

summer mhf4u course 42
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

to receive a FREE University Admission Support Package

Study

Tips

summer mhf4u course 44
by Sam A.

BSc. graduate,

Queen’s University

QEA student

alumni

summer mhf4u course 45
by Jessica K.

Master in English

literature

Queen’s University

QEA English teacher

to enroll
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Syllabus for summer MHF4U course

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

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 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

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

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 centre 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

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 factor- ing, 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 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 technology, and identifying intervals for which x satisfies the inequalities

CHARACTERISTICS OF FUNCTIONS for MHF4U

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 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 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 modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

MHF4U 3.1 compare, through investigation using a vari- ety of tools and strategies (e.g., graphing with technology; comparing algebraic representations; 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:http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Course organization for Summer MHF4U Course

Unit Unit Title (Description) Time
Unit 1 Basic Functions and Transformation 12 hours
Unit 2 Polynomial Functions 15 hours
Unit 3 Rational Functions 15 hours
Unit 4 Trigonometry I 25 hours
Unit 5 Trigonometry II 15 hours
Unit 6 Logarithm 12 hours
Unit 7 Combination of Functions 16 hours

Total Hours 110 hours

ASSESSMENT AND EVALUATION POLICY for Summer 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

Summer MHF4U Course | Advanced Functions - 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 Summer 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.

Find Queen Elizabeth

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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