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MCV4U Grade 12 Calculus And Vectors (University)

Course Details

  • 4. Grade 12

PREREQUISITE: Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)

GRADE: 12 (University)

AVAILABILITY: Full-time – All Campuses, Part-time – All campuses, Private – All campuses, Summer School – Accelerated, Blyth Academy Online


Course Overview

MCV4U online builds on student’s 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, rational, exponential, and sinusoidal functions; and apply these concepts and skills to modelling of real-world relationships. MCV4U online is intended for students who plan to study mathematics in university and who may choose to pursue careers in fields such as physics and engineering. Whether you take MCV4U online or on campus, the course will prepare you for the next steps in your university education and future career. The course will allow you to refine the use of mathematical processes needed for success in senior mathematics and beyond.

Course Outline

Below is a course outline for the MCV4U course. The curriculum and outcomes remain the same whether you take this course in person or online. The curriculum is set by the Ministry of Education in Ontario, ensuring that all students follow the same requirements and gain the same skills, regardless of whether they complete the course in person or online.

MCV4U is intended for students interested in pursuing careers in fields such as economics, engineering, and science as well as some areas of business, including students who will need to take a university-level course in subjects such as algebra, calculus, or physics.


Essential Question: How can mathematics be used to explain orientation in space?

In this unit, students will be studying a quantity known as a vector. It is simply your typical line segment with a direction, but what is surprising is the number of applications that make use of it. For example, in the field of physics there is position, displacement, velocity, acceleration, forces, momentum, fields and so on. Students will look at some vector applications and solve related problems both geometrically and algebraically by performing operations on vectors.

Lines and Planes

Essential Question: How can two and three-dimensional models be used to imagine solutions to complex problems?

In this unit, students will be required to combine the understandings from the previous unit with new concepts such as three-dimensional vectors and planes.

Rates of Change

Essential Question: How can rates of change found in the real world be modeled using mathematics?

In this unit, students will notice a shift in content as we move from the vectors portion of the course to the calculus portion. Students will be introduced to the idea of a rate of change. This is one of the most important concepts needed to understand calculus and will be used often throughout the course.


Essential Question: How can mathematical concepts be used to make sense of real-world problems?

In this unit, students will be introduced to one of the most fundamental operations in the study of calculus – the derivative! Understanding the derivative will require the use of the understandings students developed throughout the first unit. A concrete understanding of the derivative is necessary to understand the remaining units in this course.

Curve Sketching

Essential Question: How can problem solving tools be used to represent functions visually?

In this unit, students will develop the skills needed to sketch any given function. This unit will require students to connect algebraic concepts with graphical concepts in order to deepen their understanding of what the graph of a given function looks like.

Derivatives of Exponential and Sinusoidal Functions

Essential Question: How can derivatives be used to analyze specific functions?

In this unit, students will be required to apply their understanding of derivatives to analyze both exponential and sinusoidal functions.


Overall evaluation for the course is based on a student’s achievement of curriculum expectations. Students will demonstrate skills required for effective learning throughout the duration of the course. A final percentage grade will represent the quality of a student’s overall achievement of course expectations, reflecting their level of achievement as described in the grading rubric.

Final grades will be calculated as follows:

70% of the grade: Based on evaluations throughout the duration of the course. This component of a student’s grade will reflect the most consistent achievement level attained throughout the course.

30% of the grade: Based on final evaluations a student completes at the conclusion of the course. The final evaluation for this course is a final exam (30% of the final grade).

Please consult our Frequently Asked Questions Page or the Exam section within your course for more details on final exams and the exam fee. More information can also be found in our Student Handbook
Ready to get started? Register today

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