Functions

MCR3U is a university-preparation math course that introduces students to key concepts in algebra and functions. It builds the foundation needed for Grade 12 Advanced Functions and Calculus.

Students will explore characteristics of:

• Polynomial
• Exponential Trigonometric functions
• Develop multiple representations of functions
• Apply algebraic techniques to solve equations.

Unit 1: Characteristics of Functions
Students begin by exploring different ways to represent and analyze functions.
Lessons include:

• Introduction to Functions
• Function Notation
• Domain and Range
• Rate of Change
• Transformations of Functions
• Piecewise Functions

Unit 2: Quadratic Functions
This unit focuses on quadratic functions and their properties.
Lessons include:

• Standard, Vertex, and Factored Forms
• Completing the Square
• Solving Quadratic Equations
• Applications in Context
• Transformations of Quadratic Graphs

Unit 3: Polynomial and Rational Functions
Students investigate polynomial and rational functions, including their graphs and end behaviour.
Lessons include:

• Exponents and Laws of Exponents
• Exponential Growth and Decay Models
• Transforming Exponential Functions
• Applications in Real-World Situations

Unit 4: Exponential Functions
This unit introduces growth and decay through exponential relationships.
Lessons include:

• Generating Ideas
• Art Criticism Techniques
• The Creative Process
• Elements and Principles of Art
• Artistic Methods and Production
• Presenting Artworks to an Audience

Unit 5: Trigonometric Functions
Students apply trigonometry in both geometric and functional contexts.
Lessons include:

• Introduction to Radian Measure
• Graphing Sine and Cosine Functions
• Amplitude, Period, and Phase Shift
• Trigonometric Equations
• Real-Life Applications of Periodic Phenomena

• 70% of the final grade is based on coursework, including:
  • Assignments on transformations, function analysis, and problem sets
  • Quizzes and unit tests focused on algebraic and graphical methods
• 30% of the final grade is based on final evaluations:
  • 10% Culminating project (e.g., function modeling or mathematical investigation)
  • 20% Final exam assessing skills across all units

All assessments follow Ontario curriculum standards, reinforcing analytical thinking, symbolic reasoning, and application in both academic and real-life settings.