Course and Tutoring
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Welcome to Queen Elizabeth Academy, providing MCV4U Course and Tutoring, for you to excel at grade 12 Calculus and Vectors. Our course instructors and tutors have deep experience in MCV4U course / calculus and vectors, for you to understand the concepts and be able to tackle application / thinking problems, which many students lose their marks.

MCV4U Course - Grade 12 Calculus and Vectors

MCV4U Course / Grade 12 Calculus is a key grade 12 course for students going into business, science and engineering. This course contains two parts, one with derivative and the other with vectors. If you want to do well in this course, your foundation skill must be improved with a deep understanding of the concept. We teach both in our tutoring / course program.

The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)
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 MCV4U course as an online course or in person (subject to space availability). Our MCV4U 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 enrolMCV4U:

Private MCV4U course | Calculus and Vectors

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 MCV4U
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 enrolMCV4U:

One on one private tutoring MCV4U 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
MCV4U Calculus and Vectors

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 prepares students to succeed in subject areas such as Math, English and Science. We have excellent online tutors in Canadian cities such as Toronto, Ottawa, Calgary and Milton. Students who have worked with us have developed good foundations in the area of Mathematics, Science and English.

The challenge for students for MCV4U 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!

MCV4U Calculus and Vectors 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

QEA tutors are qualified in subjects including Math, Science, Chemistry and Physics. They teach students across Canada in cities such as Toronto, Ottawa, Calgary and Markham by helping them develop skills and build a foundation of learning to help them in the long run.

Google Rating
Thank you
Queen Elizabeth Academy!

Students from Calculus and Vectors MCV4U 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
mcv4u calculus vectors 25

MCV4U Calculus and Vectors
Private Credit Course Overview

MCV4U / Calculus and Vectors is one of the most important Math courses in grade 12 for university admission

MCV4U Calculus and Vectors - Course Description

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.

What is taking MCV4U Calculus and Vectors like?

There are two different sections in this course; the first is derivative or extends from work in Advanced Functions; the second other is Vectors, which, unlike the first, is totally new. Vectors are essentially similar to Physics when it comes to problem-solving.

The derivative section takes root in work done in Advanced Functions and will typically include algebra, graphing, trigonometry, and logarithms.

The vector aspect of the course includes 3D equations of lines and planes. Because of the similarity of vector problem-solving to physics, many students find this course component more complicated than the first one.

Tips to succeed in MCV4U Calculus and Vectors

For students to succeed in Vector Calculus, they must be proficient in exponents, factoring, combining rational expressions such as fractions with algebra, and solving equations.

You want to pay special attention to the Optimization Unit, which usually includes many word problems. However, if you have trouble dealing with word problems, be sure to prepare for this unit in particular. Do not forget to keep your notes organized while you identify the different kinds of problems. This will significantly help you to clarify the concepts in the course, and to keep track of your progress.

The concepts of vectors are very complex. So when approaching vector problems, be sure to layout and write down all of the steps clearly. Also, write down why such steps are necessary. For instance, what variable are you attempting to achieve with each step? This approach will undoubtedly simplify even more complicated questions and allow you to easily identify areas where you need additional help.

FAQ for MCV4U course

How can MCV4U 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.

How is QE MCV4U different from others?

QE provides quality education. What does this mean? To achieve high grade, it is important to have a systematic approach to build your child's foundation: Lessons, Homework Practice and coaching. For lessons, we actively teach the material, organizing knowledge in a step by step fashion. This way we facilitate understanding, without forcing memorization equations or steps. We provide packages of homework practic so that our students can learn a variety of problems and prepare well for tests. We also provide past tests and mock exams, such that we teach test writing techniques to optimize their performance.

How can my child achieve higher grade in MCV4U?

Academic excellence comes with understanding and hardwork. We take care of the understanding part in our lessons, where we teach the concepts in a easy-to-understand manner. To achieve high grade, the students need to practice and establish a good routine for working through homework. Making their own study notes will be preferred. We also teach test writing strategies, such as tackling multiple choice and complex application questions.

What are QE's credentials?

QE is Ministry accredited, which means we offer high school courses. We know the curriculum of each subject inside-out. We know what foundation building block is important leading to the next grade. As we have worked with 5,000+ students over the past 9 years, we are familiar with the common weakness and challenge they face on each subject. Therefore, we focus on what matters most to achieve success. Our students were admitted to top universities: Waterloo, Laurier, Queen's, Western, McGill with scholarship from $2,000 to $50,000.

What is MCV4U?

MCV4U is a Grade 12 University preparation level course for Calculus and Vectors.

What course is MCV4U?

Course description: This course builds on your previous experience with functions and your developing understanding of rates of change.


Admission Requirements Summary
Admission Requirements Summary. Major university programs. (Grade cut off, Admission essay etc.)
mcv4u calculus vectors 26
How to Get into the
Top Universities?
How I got into my top choice universities?
by QEA student alumni
mcv4u calculus vectors 27
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]

mcv4u calculus vectors 28
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
mcv4u calculus vectors 27
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]

mcv4u calculus vectors 28
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

RATE OF CHANGE for Math grade 12

1. demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit;

1.1 describe examples of real-world applications of rates of change, represented in a variety of ways (e.g., in words, numerically, graphically, algebraically)

2. graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative;

2.2determine numerically and graphically the intervals over which the instantaneous rate of change is positive, negative, or zero for a function that is smooth over these intervals (e.g., by using graphing technology to exam- ine the table of values and the slopes of tan- gents for a function whose equation is given; by examining a given graph), and describe the behaviour of the instantaneous rate of change at and between local maxima and minima

3.verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.

3.1 determine algebraically the derivatives of polynomial functions, and use these deriva- tives to determine the instantaneous rate of change at a point and to determine point(s) at which a given rate of change occurs


1. make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching;

1.1recognize the second derivative as the rate of change of the rate of change (i.e., the rate of change of the slope of the tangent), and sketch the graphs of the first and second derivatives, given the graph of a smooth function

2. solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.

2.1 make connections between the concept of motion (i.e., displacement, velocity, accelera- tion) and the concept of the derivative in a variety of ways (e.g., verbally, numerically, graphically, algebraically)


1.demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;

1.4 recognize that points and vectors in three-space can both be represented using Cartesian coor- dinates, and determine the distance between two points and the magnitude of a vector using their Cartesian representations

2. perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications;

2.3 perform the operations of addition, subtrac- tion, and scalar multiplication on vectors represented as directed line segments in two- space, and on vectors represented in Cartesian form in two-space and three-space

3. distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space;

3.2 recognize that the solution points (x, y) in two-space of a single linear equation in two variables form a line and that the solution points (x, y) in two-space of a system of two linear equations in two variables determine the point of intersection of two lines, if the lines are not coincident or parallel

4. represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

4.2 recognize that a line in three-space cannot be represented by a scalar equation, and rep- resent a line in three-space using the scalar equations of two intersecting planes and using vector and parametric equations (e.g., given a direction vector and a point on the line, or given two points on the line)

Sources: Ministry of Education Ontario:

Course organization for Math grade 12

UnitUnit Title (Description)Time
Unit 1Limits14 hours – 5 classes
Unit 2Derivatives20 hours – 7 classes
Unit 3Derivatives and Applications15 hours – 5 classes
Unit 4Geometric & Cartesian Vectors20 hours – 7 classes
Unit 5Vectors in Three Dimensions13 hours – 4 classes
Unit 6Equations of Lines and Planes23 hours – 7 classes
Review and Exam5 hours – 2 classes

Total Hours 110 hours


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 (15-20%)

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.

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*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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