MCV4U
Calculus and Vectors
This Grade 12 university preparation course builds on students’ experience with functions and rates of change. Students develop differential-calculus concepts, solve problems involving derivatives and optimization, and study geometric and Cartesian vectors, lines and planes in three-dimensional space. The course is intended for students pursuing university programs requiring calculus, linear algebra or physics.
Grade
12
Credit
1.0
Delivery
Online
Prerequisite
MHF4U
About This Course
This Grade 12 university preparation course builds on students’ experience with functions and rates of change. Students develop differential-calculus concepts, solve problems involving derivatives and optimization, and study geometric and Cartesian vectors, lines and planes in three-dimensional space. The course is intended for students pursuing university programs requiring calculus, linear algebra or physics.
What You'll Learn
- Analyze average and instantaneous rates of change and develop the concept of the derivative.
- Differentiate polynomial, sinusoidal, exponential, rational and radical functions as appropriate to the course.
- Use derivatives to analyze curve behaviour and solve optimization and modelling problems.
- Work with geometric vectors and operations in two and three dimensions.
- Use Cartesian vectors to solve problems involving vector equations and relationships.
- Represent and analyze lines and planes in three-dimensional space.
Skills You'll Develop
- Calculus and derivative techniques
- Rates of change and optimization
- Geometric and Cartesian vectors
- Three-dimensional analytic geometry
- Advanced problem solving, modelling and mathematical communication
Learning Outcomes
By the end of the course, students will be able to:
- Demonstrate understanding of rate of change and derivative concepts.
- Determine derivatives and use them to analyze functions and solve problems.
- Apply derivatives to curve sketching, optimization and real-world modelling.
- Perform operations with geometric and Cartesian vectors.
- Solve problems involving dot products, projections and vector relationships as addressed in the course.
- Represent and analyze lines and planes in three-dimensional space.
- Use mathematical processes to reason, justify, model and communicate solutions.
Course Units
The following reflects the school’s planned organization of the course. Approximate time allocations may be adjusted while all curriculum expectations and required planned learning are maintained.
| Unit | Title / Major Learning Focus | Approx. Time |
|---|---|---|
| 1 | Rates of Change | 12 hours |
| 2 | Derivatives | 14 hours |
| 3 | Curve Sketching | 14 hours |
| 4 | Derivatives of Sinusoidal Functions | 10 hours |
| 5 | Exponential and Logarithmic Functions | 13 hours |
| 6 | Geometric Vectors | 15 hours |
| 7 | Cartesian Vectors | 15 hours |
| 8 | Lines and Planes | 15 hours |
| Final | Mandatory Written Final Examination | 2 hours |
Assessment
Assessment uses evidence gathered over time from student work, conversations and observations. The final grade for 2026–2027 is determined as follows:
| Component | Weight | How It Is Determined |
|---|---|---|
| Coursework throughout the course | 65% | Evaluation evidence gathered throughout the course, reflecting the student's most consistent achievement with special consideration for more recent evidence. |
| Mandatory written final examination | 25% | Mandatory Grade 12 mathematics written final examination. |
| Attendance and participation | 10% | Based on meaningful attendance and participation; excused absences do not negatively affect this component. |
Examples of Assessment Evidence
Assessment may include problem sets, investigations, mathematical modelling, graphing and vector tasks, written solutions, tests, oral explanations, conferences and the mandatory written final examination.
Pathways
MCV4U prepares students for postsecondary pathways that use calculus, linear algebra or physics, including science, engineering, economics, mathematics, computer science and quantitative areas of business.
Students connect problem solving, reasoning, modelling, precision and mathematical communication to university study and career contexts.
Teacher Support
- Students learn through the school's secure online learning environment and receive ongoing support from qualified teachers.
- Teacher-supported conferencing, tutorials and scheduled live support are available as appropriate.
- Teachers activate prerequisite knowledge from functions, trigonometry, algebra and analytic geometry before extending ideas into calculus and vectors.
- Explicit modelling supports mathematical reasoning, notation, proof, algebraic manipulation and multi-step problem solving.
- Graphing technology and dynamic mathematics tools support derivative functions, curve behaviour, vectors, lines and planes.
- Worked examples, deliberate practice, error analysis, conferencing and differentiated supports help students progress toward independent problem solving.
Frequently Asked Questions
What is the course code?
MCV4U — Calculus and Vectors, Grade 12, University Preparation.
What is the prerequisite?
Advanced Functions, Grade 12, University Preparation (MHF4U), taken before or concurrently with MCV4U.
How many credits is MCV4U?
The course is worth 1.0 Ontario secondary school credit.
What topics are covered?
Rates of change, derivatives, curve sketching, derivatives of sinusoidal and exponential/logarithmic functions, geometric vectors, Cartesian vectors, lines and planes.
How is the final grade calculated?
65% coursework, 25% mandatory written final examination, and 10% attendance and participation.
Who is MCV4U intended for?
Students pursuing university programs requiring calculus, linear algebra or physics, including many science, engineering, economics, mathematics and computer-science pathways.
Can MHF4U be taken at the same time?
Yes. The course outline states that MHF4U must be taken prior to or concurrently with MCV4U.
Ready to Take This Course?
$549 / Credit
- Provided by CSW — Canadian School of the World
- Ontario Ministry of Education registered
- Delivered fully online
Need Help Deciding?
Not sure if this is the right course? Book a free 30-minute meeting with a CSW advisor.
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