Mathematics Guide - Grade 12 Canada

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Grade 12 Mathematics (MHF4U / MCV4U) 📐

Ontario Curriculum · TDSB · Curated Video Lessons

Grade 12 Mathematics in Ontario offers two primary university-preparation courses: Advanced Functions (MHF4U) and Calculus and Vectors (MCV4U). MHF4U is a prerequisite for MCV4U. Together they form the mathematical foundation for university programs in STEM, economics, and business. This guide covers key concepts from both courses.

MHF4U – Advanced Functions

📈 Advanced Functions: Comparing Function Types

MHF4U builds on MCR3U to study polynomial, rational, exponential, logarithmic, and trigonometric functions in depth. This lesson compares the characteristics of different function types — zeros, asymptotes, end behaviour, symmetry — a foundational skill in MHF4U and essential preparation for understanding calculus in MCV4U and university-level mathematics.

  • Polynomial Functions
  • Rational Functions
  • Logarithmic Functions
  • Trig Functions

Source: MHF4U Ontario

MHF4U – Function Properties

🔁 Odd vs Even Functions

Understanding symmetry in functions — odd functions (symmetric about the origin, satisfying f(-x) = -f(x)) and even functions (symmetric about the y-axis, satisfying f(-x) = f(x)) — is a key MHF4U concept with direct applications in calculus, Fourier analysis, and physics. This Ontario-specific lesson explains how to identify function symmetry both algebraically and graphically.

  • Even Functions
  • Odd Functions
  • Symmetry
  • Algebraic Tests

Source: MHF4U Advanced Functions

MCV4U – Calculus

∫ Calculus: Limits & Derivatives

MCV4U introduces differential calculus — limits, derivatives using first principles and derivative rules (power, product, quotient, chain), and their applications in curve sketching, optimization problems, and related rates. This lesson on one-sided limits builds the foundational understanding of what a limit is — the essential concept before derivatives are introduced.

  • Limits
  • One-Sided Limits
  • Derivatives
  • Calculus Foundations

Source: MCV4U Ontario

MCV4U – Vectors

➡️ Vectors in 2D and 3D (MCV4U)

The Vectors unit of MCV4U covers geometric and algebraic representations of vectors in two and three dimensions — vector addition, subtraction, scalar multiplication, dot products, cross products, and applications to equations of lines and planes. This lesson introduces how to find resultant vectors from unit vectors, a core skill in the MCV4U Vectors strand.

  • Vectors in 3D
  • Dot Product
  • Cross Product
  • Lines & Planes

Source: MCV4U Calculus & Vectors

Built for TDSB students · Ontario Curriculum (MHF4U / MCV4U) · Grade 12 Mathematics

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