CALCULUS & VECTORS (MCV4U)
MCV4U (Calculus and Vectors) is the Ontario Grade 12 mathematics course that prepares students for university programs in science, engineering, mathematics, and economics. The course focuses on derivatives, curve sketching, optimization, vector operations, and three-dimensional geometry.
CHAPTERS
Click a chapter to access notes, videos, and practice problems.
Chapter 1 – Introduction to Calculus
Average and instantaneous rates of change
Tangent lines and slopes of curves
Understanding change using graphical and numerical methods
Chapter 2 – Derivatives
Derivative rules
Differentiating functions
Applications of derivatives
Chapter 4 – Curve Sketching
Increasing and decreasing intervals
Local maximum and minimum values
Concavity and inflection points
Chapter 3 – Applications of Derivatives
Optimization problems
Motion, velocity, and acceleration
Solving real-world problems using derivatives
Chapter 5 – Derivatives of Exponential and Trigonometric Functions
Derivatives of exponential functions
Derivatives of sine and cosine functions
Applying derivative rules to transcendental functions
Chapter 6 – Introduction to Vectors
Magnitude and direction of vectors
Vector addition and scalar multiplication
Vectors in two- and three-dimensional space
Chapter 7 – Applications of Vectors
Dot product of vectors
Vector projections
Cross product and geometric applications
Chapter 8 – Equations of Lines and Planes
Vector equations of lines in 3D space
Cartesian equations of planes
Intersections and relationships between lines and planes