Calculus and Vectors, Grade 12 (MCV4U) Online Course
Curriculum Coordinator and Learning Strategist
Cheryl Richardson
B.Sc., OCT
MCV4U
Grade 12
University Preparation

Mathematics (Calculus and Vectors)

Find additional course details below, including delivery format, course availability, course duration, prerequisite, tuition fee, hardware/software requirements, etc.

MCV4U
Grade 12
University Preparation

Mathematics (Calculus and Vectors)

Find additional course details below, including delivery format, course availability, course duration, prerequisite, tuition fee, hardware/software requirements, etc.

Course Code

MCV4U

Course Name

Mathematics (Calculus and Vectors)

Grade

Grade 12

Course Type

University Preparation

Format

Asynchronous Delivery

Prerequisite

MHF4U – Advanced Functions, Grade 12, University Preparation

Tuition Fee

$500.00

Course Duration

At Your Own Pace (4 weeks to 6 months)

Credit Value

1.0

Availability

Start Anytime

Course Reviser/Developer

Natasha Pomeroy

Latest Revision Date

July 2026
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.

Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U).
Outlined below is a description of each unit, including what students will learn and the recommended hours for completion.
Unit Title & Description
Time Allocated
Unit 1: Motion and Change

Explore how rates of change shape real-world scenarios such as vehicle dynamics, cyclist speed, population growth, and supply and demand. Key topics include secant and tangent slopes, limits, and instantaneous rates of change. Engage in interactive activities like analyzing traffic flow through H5P graphing, using Desmos to explore cyclist motion, CloudLabs simulations on reaction rates, and an economics-based supply and demand equilibrium simulation.
14 Hours
Unit 2: Climate Change and Environmental Monitoring

Apply derivatives to model environmental and financial trends, biomedical growth, sound waves, and motion in physics. Topics include polynomial, sinusoidal, and exponential derivatives. Activities feature carbon emissions modeling in Desmos, CloudLabs simulations on biological decay, spreadsheet-based stock market analysis, and interactive sound wave explorations.
14 Hours
Unit 3: Optimization in Business and Economics

Use calculus to optimize business profits, minimize costs, and design efficient structures. Explore the power rule, product and chain rules, and maximizing and minimizing functions. Activities include business profit modeling in Desmos, bridge design optimization, interactive sustainable home energy planning, and a problem-based learning task on cost reduction.
14 Hours
Unit 4: The Math Behind Sports and Athletics

Analyze real-world motion in sports science, autonomous vehicles, and engineering. Concepts include displacement, velocity, acceleration, and derivatives in motion. Engage with H5P interactive video analysis of athletes, model autonomous vehicle paths in GeoGebra, and explore PhET physics-based motion simulations.
14 Hours
Unit 5: Vectors and Navigation

Explore vector applications in robotics, autonomous navigation, video game development, and sports science. Topics include vector representation, trigonometric relationships, and Cartesian coordinates. Use Desmos for vector operations, simulate drone navigation, and track player movement in sports analytics.
15 Hours
Unit 6: 3D Design & Architecture

Apply calculus and vectors to engineering, urban planning, and architecture, focusing on intersections of planes and three-space geometry. Activities include 3D graphing with GeoGebra, CloudLabs visualizations, interactive CAD exploration, and urban planning simulations to analyze structural intersections and design optimizations.
13 Hours
Unit 7: 3D Computer Graphics and Animation

Explore mathematics in animation, computer graphics, and physics-based game design. Key topics include scalar, vector, and parametric equations, as well as normal vectors to planes. Engage with 3D game development using GeoGebra, model light reflection with vector normals, and investigate graphic rendering through shader programming basics.
14 Hours
Unit 8: Integration & Practice

Apply concepts from calculus and vectors to real-world consulting projects. Solve real-life problems such as optimizing environmental models, sports analytics, or business strategies. Activities include an H5P auto-graded practice exam, peer reviews, and mathematical modeling to support final projects.
10 Hours

Final Exam/Culminating Task

A comprehensive assessment covering all topics in the course. The final exam consists of multiple-choice questions and applied problem-solving scenarios.
2 Hours
Total Hours
110 Hours
A wide variety of assessment and evaluation tools will be used to earn credits towards the Ontario Secondary School Diploma at Royal Ontario Academy, including quizzes, tests, projects, essays, journals, and final assessments. The final exam is a closed-book, online test that is proctored and has a time limit. Students may also be required to appear on video for other assessments in certain courses.

At Royal Ontario Academy, the final mark in every course is made up of three parts:
  • 65% is based on coursework completed throughout the online course.
  • 25% is based on a final evaluation.
  • 10% is based on attendance and participation, reflecting consistent weekly engagement with the course.
Depending on the course, the final evaluation may be a proctored written exam, a culminating task such as a project, essay, or presentation, or a combination of both. Attendance and participation reflects how consistently a student engages with their learning each week, and excused absences approved by the Principal do not lower this part of the mark.

Students will receive two reports per course:
  • First Report (Midterm): Issued when the student reaches the halfway point of the course. It reflects achievement and development to that point, including attendance and participation.
  • Final Report: Reflects overall achievement and development for the entire course, including attendance and participation.
This course follows the current Growing Success requirements, including the mandatory assessment and evaluation updates that take effect in the 2026-2027 school year. According to Growing Success: Assessment, Evaluation, and Reporting in Ontario Schools, the primary purpose of assessment and evaluation is to improve student learning. To ensure that assessment, evaluation, and reporting are valid and reliable, and that they lead to the improvement of learning for all students, Royal Ontario Academy teachers use practices and procedures that:
  • 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, Metis, 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 appropriate points throughout the 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.
General Resources Students Should Be Equipped With
  1. Scanner or Smartphone Camera: To digitize handwritten or hand-drawn work for submission.
  2. Basic Scientific Calculator: A non-programmable, non-graphing calculator for essential calculations.
  3. Spreadsheet Application:
    • Options: Google Sheets, Microsoft Excel.
  4. Word Processing Application:
    • Options: Google Docs, Microsoft Word.
  5. Presentation Application:
    • Options: Google Slides, Microsoft PowerPoint.
Canadian Course Pricing

$500

/ 1 course

$900

 / 2 courses

$1275

 / 3 courses

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