MHF4U – Advanced Functions, Grade 12 (University)
Grade 12 Online Mathematics – Ontario Curriculum
Course Overview
MHF4U extends students’ understanding of advanced algebraic concepts, focusing on polynomial, rational, exponential, logarithmic, and trigonometric functions. Through both algebraic and graphical approaches, students learn to analyze functions, prove identities, and solve complex equations.
This course is required preparation for MCV4U (Calculus and Vectors) and is essential for university programs in engineering, sciences, mathematics, business, and computer science.
Units & Major Topics
Unit 1 – Algebraic Foundations & Function Characteristics
- Review of essential Grade 11 algebra
- Properties of functions and key features
- Transformations, reflections, stretches, and shifts
- Compositions of functions and inverse functions
Unit 2 – Polynomial & Rational Functions
- End behaviour, turning points, and multiplicity
- Polynomial division and synthetic division
- Asymptotes and discontinuities in rational functions
- Graphing and solving polynomial/rational equations
Unit 3 – Exponential & Logarithmic Functions
- Solving exponential and logarithmic equations
- Properties and laws of logarithms
- Applications in finance, science, and real-world modelling
- Function transformations and graph analysis
Unit 4 – Trigonometric Functions & Identities
- Radians and degree measure
- Graphing sine, cosine, and tangent functions
- Amplitude, period, and phase shift
- Proving trigonometric identities
- Solving trigonometric equations algebraically
Unit 5 – Trigonometric Applications
- Sinusoidal modelling of periodic phenomena
- Real-life applications in physics, engineering, and signal processing
- Inverse trigonometric functions
Unit 6 – Culminating Task & Final Review
- Multi-topic mixed problem-solving
- Function analysis, modelling, and algebraic reasoning
- Preparation for MCV4U and university programs
Assessment and Evaluation
The final grade for MHF4U 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)
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30% Final evaluation:
- Culminating Task – 10%
- Final Examination – 20%