Course Details
Course Code


Course Type

University Preparation

OSSD Credit Value



MCR3U Functions, Grade 11, University Preparation
MCT4C Mathematics for College Technology, Grade 12, College Preparation

Course Outline



This is a credit course for University-bound students. 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.

High quality video lectures

All lessons in this course are video-based lectures that gently guide you through important concepts. Our expert teachers will help you succeed in this course and give you a good head start to your post secondary education.
Watch sample

Overall Course Expectations

Throughout this course, students will learn the following:

A. Rate of Change
A1 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;
A2 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;
A3 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.
B. Derivatives and their Applications
B1 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;
B2 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.
C. Geometry and Algebra of Vectors
C1 demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;
C2 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;
C3 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;
C4 represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

Read more of course description

Ministry of Education Curriculum

This is an OSSD credit course that has been developed based on the following Ontario Ministry of Education documents

  • The Ontario Curriculum, Grades 11 and 12 Mathematics, Revised 2007
  • Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools (2010)

Major Units and Corresponding Hours

Unit 1

Characteristics of Functions

The basic characteristics of functions and the transformations of functions will be examined. The characteristics of polynomial, rational, logarithmic, and trigonometric functions will be compared. Average and instantaneous rates of change of a function will be determined.

24 Hours

Unit 2

Polynomial and Rational Functions

The key features of polynomial and rational functions will be examined, as well as relationships between the numeric, graphical, and algebraic representations of these functions.

28 Hours

Unit 3

Trigonometric Functions

The meaning and application of the radian measure will be demonstrated. Trigonometric ratios will be connected to graphical and algebraic representations of their corresponding functions and their reciprocal functions. Related trigonometric equations of one variable will be solved and trigonometric identities of one and two variables will be proven.

28 Hours

Unit 4


Exponential and Logarithmic Functions

The relationship between exponential and logarithmic expressions will be examined, as well as that of the corresponding functions. The laws of logarithms and exponents will be applied to solving exponential and logarithmic equations of one variable.

24 Hours




Culminating Activity


4 Hours

Final Exam


2 Hours

Total Hours


110 Hours

Read more of course content

All course content is accessed online.

Resources required by the student

  • A non-programmable, non-graphing, scientific calculator
  • A scanner, smart phone camera, or similar device to upload handwritten or hand-drawn work
  • A front-facing camera on a desktop, laptop, or mobile device to allow for proctoring over the internet
  • Internet access and a modern standards-compliant web browser

Teaching and Learning Strategies

The course will include instruction using PowerPoint and screen recordings. There will be ample opportunities for students and the teacher to engage in 1 to 1 correspondence and discussion. Independent, self-regulated learning will also be required along with teacher facilitation.
Example exercises and problems will be included in worksheet format, also requiring individual research from external sources.

Assessment & Evaluation

The assessment and evaluation strategies of our school follows the Ministry of Education's Growing Success document. Growing Success articulates the vision the Ministry has for the purpose and structure of assessment and evaluation techniques.
Assessments help to monitor student progression and provide reflection and feedback. Evaluation is the process of judging the quality of student work in relation to the achievement chart categories and criteria, and assigning a percentage grade to represent that quality. Evaluation is based on gathering evidence of student achievement through:

  • Products
  • Observations
  • Conversations

Weighting of the Categories of Achievement

Knowledge & Understanding Thinking Communication Application
30% 20% 20% 30%

The Final Grade

  • The evaluation for this course is based on the student's achievement of curriculum expectations and the demonstrated skills required for effective learning. The final percentage grade represents the quality of the student's overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline.


  • The tests are typically a paper-pen evaluation written at a mutually agreed time, date, and location. The tests will be proctored, meaning a suitable adult with a dedicated identifiable and authentic email address will supervise you writing the tests. This process ensures the security and integrity of the test. Any person related or affiliated to the student in a personal way cannot serve as a test supervisor.

Course withdrawal and repeats

Since this is a Grade 11/12 course, please read the following carefully. We have the following safety features in place.

You can safely enroll and try this course. We do not notify your day school in any way when you register and enroll in our courses. Only when you explicity instruct us to share your grades will we send your registration information and your grades to your day school.

In addition, you can safely drop this course without any academic penalty at any time before the first report card. Once you have received the first report card, you will still have five (5) days to drop this course without any academic penalty. The first report card is issued right after the midterm point of this course.

The midterm point of this course is based on work completed rather than time elapsed, since this is a self-paced course. It is roughly after the first half of the assessments in the course, at which point you will have a fairly good idea of how well you are doing.

At this point, you will have to manually indicate, by pressing an acknowledgement button, that you would like to continue in the course and that you would like us to send your registration information and your marks to your day school.

As a courtesy to our students, our system requires you to manually indicate that you would like to progress beyond the midterm point and receive the first report card. This safety feature is designed to ensure that you do not accidentally pass the deadline to drop the course without academic penalty.

After receiving your first report card, we will also send you notifications via email regarding the 5 day deadline to drop the course.

Read more about ministry guidelines regarding course withdrawals and retakes.
Ministry guidelines regarding course withdrawals and retakes

According to Ministry policies, grade 9 and grade 10 courses can be withdrawn at any time without any academic penalty. The grade 9 and 10 courses can also be repeated an unlimited number of times without any academic penalty. Grade 9 or 10 courses withdrawn are simply not recorded on the OST (it is as if you have never registered for the course). When students retake grade 9 or 10 courses, the highest mark is recorded on their OST, replacing the lower mark.

However, withdrawing from grade 11 or grade 12 courses without academic penalty must be done within 5 days of receiving the first report card. In this case, the mark will not be recorded on the OST. On the other hand, withdrawal from a grade 11 or grade 12 course after 5 days of receiving the first report card results in the following permanent record on the student’s OST: a "W" being entered in the "Credit" column of the OST along with the mark at the time of the withdrawal. If there are extraordinary circumstances relating to a student's withdrawal from a course, an "S" may be entered in the "Note" column on the OST.

Retaking grade 11 and grade 12 courses leads to permanent records of all repeats on the student’s OST, along with the marks of each attempt. Only one credit is earned if a course is retaken. An “R” is entered in the “Credit” column of the OST for the repeats with the lower mark.

It is therefore advised that students taking grade 11 and grade 12 courses be mindful of withdrawal deadlines pertaining to their enrollment, and do their best in the course if they have passed the withdrawal deadline.