Course Title: Calculus and Vectors, Grade 12, University Preparation (MCV4U)

Course Name: Calculus and Vectors

Course Code: MCV4U

Grade: 12

Course Type: University Preparation

Credit Value: 1.0

Prerequisite: MHF4U, Advanced Functions, Grade 12, University Preparation (may be taken concurrently)

Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)

Course Developer: Virtual High School

Department: Mathematics

Department Head: André Bergeron, B.Sc., B.Ed., OCT

Development Date: 2008

Most Recent Revision Date: 2021

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.

Teaching and Learning Strategies:

The over-riding aim of this course is to help students use the language of mathematics skillfully, confidently, and flexibly. A wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented:

  • Problem solving: This course scaffolds learning by introducing concepts and relating them back to concepts that were taught in prior units and mathematics courses. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve real-world problems.
  • Selecting Tools and Computational Strategies: This course models the use of 3D graphing software to help solve problems and to familiarize students with technologies that can help make solving problems faster and more accurately.
  • Connecting: Students will connect concepts learned in this course to real-world applications of Vectors and Calculus through assignments, examples, and practice problems.
  • Reflecting: This course models the reflective process. Through the use of examples and practice exercises, the course demonstrates proper communication to explain intermediate steps and reflect on solutions to determine if they make sense in the given context.
  • Representing: Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.

Assessment, Evaluation and Reporting Strategies of Student Performance:

Our theory of assessment and evaluation follows the Ministry of Education's Growing Success document, and it is our firm belief that doing so is in the best interests of students. We seek to design assessment in such a way as to make it possible to gather and show evidence of learning in a variety of ways to gradually release responsibility to the students, and to give multiple and varied opportunities to reflect on learning and receive detailed feedback.

Growing Success articulates the vision the Ministry has for the purpose and structure of assessment and evaluation techniques. There are seven fundamental principles that ensure best practices and procedures of assessment and evaluation by Virtual High School teachers. VHS assessments and evaluations,

  • are fair, transparent, and equitable for all students;
  • support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
  • are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
  • are communicated clearly to students and parents at the beginning of the course and at other points throughout the school year or course;
  • are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
  • provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
  • develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.

For a full explanation, please refer to Growing Success.


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. A credit is granted and recorded for this course if the student's grade is 50% or higher. The final grade will be determined as follows:

  • 70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will reflect the student's most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement.
  • 30% of the grade will be based on final evaluations administered at the end of the course. The final assessment may be a final exam, a final project, or a combination of both an exam and a project.

The Report Card:

Student achievement will be communicated formally to students via an official report card. Report cards are issued at the midterm point in the course, as well as upon completion of the course. Each report card will focus on two distinct, but related aspects of student achievement. First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student's strengths, areas for improvement, and next steps. Second, the learning skills are reported as a letter grade, representing one of four levels of accomplishment. The report card also indicates whether an OSSD credit has been earned. Upon completion of a course, VHS will send a copy of the report card back to the student's home school (if in Ontario) where the course will be added to the ongoing list of courses on the student's Ontario Student Transcript. The report card will also be sent to the student's home address.


Program Planning Considerations:

Teachers who are planning a program in this subject will make an effort to take into account considerations for program planning that align with the Ontario Ministry of Education policy and initiatives in a number of important areas.



This course is closed for enrollment.