MCV4U – Calculus and Vectors, Grade 12 (University)
Grade 12 Online Mathematics – Ontario Curriculum
Course Overview
MCV4U introduces students to the fundamental concepts of differential calculus and vector analysis. Students learn to reason mathematically, analyze functions, solve limits, and apply calculus to real-world optimization and motion problems.
This course is a required prerequisite for many university programs in mathematics, engineering, computer science, business, health sciences, and physical sciences.
Units & Major Topics
Unit 1 – Functions & Rates of Change
- Review of advanced algebraic and trigonometric functions
- Average rate of change vs. instantaneous rate of change
- Exploring slopes of secant and tangent lines
- Connecting change in functions to real-world motion
Unit 2 – Limits & Introduction to Derivatives
- Understanding limits formally and graphically
- Continuity and one-sided limits
- Definition of the derivative
- The power rule and basic derivative rules
Unit 3 – Differentiation Techniques
- Product, quotient, and chain rules
- Derivatives of exponential and logarithmic functions
- Implicit differentiation
- Applications to motion, economics, and optimization
Unit 4 – Curve Sketching & Optimization
- Analyzing derivatives to identify key features
- Increasing/decreasing intervals and concavity
- Finding maxima and minima
- Solving optimization problems in real-life contexts
Unit 5 – Vector Geometry
- Representing vectors algebraically and geometrically
- Vector operations (addition, subtraction, scalar multiples)
- Dot product and projection
- Applications to physics, navigation, and motion
Unit 6 – Lines & Planes in 3D Space
- Parametric and symmetric equations of lines
- Vector and Cartesian equations of planes
- Intersections of lines and planes
- Distances between points, lines, and planes
Unit 7 – Culminating Task & Final Review
- Mixed problems linking calculus and vectors
- Comprehensive review for the final evaluation
- Preparation for university-level calculus
Assessment and Evaluation
The final grade for MCV4U follows the Ontario Ministry evaluation policy: Assessment and evaluation practices are aligned with Growing Success.
- Final grades are based on 70% Term work (assignments, quizzes, tests)
-
30% Final evaluation:
- Culminating Task – 10%
- Final Examination – 20%