MCR3U – Functions, Grade 11 (University)
Grade 11 Online Mathematics – Ontario Curriculum
Course Overview
MCR3U introduces students to the fundamental concept of a function, exploring algebraic, graphical, and numerical representations. Students study quadratic, polynomial, radical, rational, and trigonometric functions, developing strong algebraic skills and mathematical reasoning.
This course prepares students for Grade 12 Advanced Functions (MHF4U) and is required for many postsecondary programs in science, mathematics, business, health, and technology.
Units & Major Topics
Unit 1 – Algebra, Functions & Graphs
- Review of algebraic operations
- Understanding functions, domain, and range
- Function notation and evaluating functions
- Relations vs. functions
- Graph transformations (shift, stretch, reflection)
Unit 2 – Quadratic Functions
- Standard, factored, and vertex forms
- Completing the square
- Graphing parabolas using key features
- Solving quadratic equations
- Word problems involving quadratics
Unit 3 – Polynomial Functions
- Characteristics of polynomial graphs
- End behaviour and turning points
- Factoring polynomial expressions
- Solving higher-degree polynomial equations
- Using polynomials in modelling
Unit 4 – Rational & Radical Functions
- Square root functions and transformations
- Reciprocal functions (1/x and 1/x²)
- Asymptotes and restrictions
- Simplifying rational expressions
- Solving rational equations
Unit 5 – Trigonometric Functions
- Sine, cosine, and tangent as functions
- Graphing sinusoidal functions
- Amplitude, period, and phase shift
- Solving trigonometric equations
- Applications: periodic motion, waves, real-life contexts
Unit 6 – Culminating Task & Final Review
- Mixed problems involving multiple function types
- Function analysis and modelling
- Preparing for the final evaluation
Assessment and Evaluation
The final grade for MCR3U 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%