MCV4U – Calculus and Vectors, Grade 12, University Preparation
Course Description
This course builds on students’ previous knowledge of advanced functions and introduces the fundamental concepts of calculus and vector mathematics. Students explore limits and derivatives, and apply differentiation techniques to solve problems involving rates of change, optimization, and curve sketching.
The course also introduces vectors in two and three-dimensional space, including vector operations, lines and planes, and applications to geometry and motion.
Emphasis is placed on mathematical reasoning, problem-solving, and real-world applications, preparing students for university programs in mathematics, science, engineering, business, and related fields.
Course Content
| Unit | Course Content | Time Allocation | |
|---|---|---|---|
|
1 |
Introduction to Calculus |
13.5 |
|
|
2 |
Derivatives |
11.5 |
|
|
3 |
Derivatives and Their Applications |
13.5 |
|
|
4 |
Increasing and Decreasing Functions |
11.5 |
|
|
5 |
The Derivatives of Exponential Functions |
8.5 |
|
|
6 |
Introduction to Vectors |
12.5 |
|
|
7 |
Vectors as Forces Velocity |
12.5 |
|
|
8 |
Equations in R^2 and R^3 |
17.5 |
|
|
|
Final Assignment: Final Exam (30% of final mark) |
9 |
|
|
Total Hours |
|
110 |
Assessment & Evaluation
Purpose
The primary purpose of assessment is to improve student learning. Assessment relates directly to the expectations for the course.
A variety of assessments for and as learning are conducted on a regular basis to allow ample opportunities for students to improve and ultimately demonstrate their full range of learning and in order for the teacher to gather information to provide feedback. Assessment tasks relate to the success criteria set out in lesson plans. Success criteria allow students to see what quality looks like.
Evaluation is the process of judging the quality of student work in relation to the achievement chart categories and criteria, and assigning a percentage grade to represent that quality. Evaluation is based on gathering evidence of student achievement through:
- Products
- Observations
- Conversations
Weighting of Categories
| Knowledge & Understanding | Thinking | Communication | Application |
|---|---|---|---|
|
30% |
20% |
20% |
30% |
Grading
- The final grade is based on performance in 3 areas: products, observations, conversations.
- 70% of the grade is based on evaluations conducted throughout the course.
- 30% is based on a final evaluation.