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.

Course Code

MCV4U

Course Name

Mathematics (Calculus and Vectors)

Grade

Grade 12

Course Type

University Preparation

Format

Asynchronous Delivery

Prerequisite

Tuition Fee

$500.00

Course Duration

Credit Value

Availability

Course Reviser/Developer

Latest Revision Date

Feburary, 2025

Curriculum

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
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
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.

Price Detail

$500

/ 1 Course

$800

/ 2 Course

$1050

/ 3 Course

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