Advanced Functions – MHF4U

Description

This Grade 12 university preparation course extends students’ experience with functions. Students investigate polynomial, rational, logarithmic and trigonometric functions, combine functions, broaden their understanding of rates of change and refine the mathematical processes needed for senior mathematics. The course prepares students for Calculus and Vectors and a range of university programs requiring advanced mathematics.

What You’ll Learn

• Analyze polynomial functions, equations and inequalities.
• Investigate rational functions and their algebraic and graphical properties.
• Apply trigonometry and analyze trigonometric functions.
• Investigate exponential and logarithmic functions and solve related equations.
• Combine functions and analyze resulting relationships.
• Use multiple representations, technology, reasoning and modelling to solve advanced multi-step problems.

Skills You’ll Develop

• Advanced function analysis
• Algebraic manipulation and equation solving
• Trigonometric, exponential and logarithmic reasoning
• Graphing, transformations and modelling
• Mathematical proof, problem solving and communication

Learning Outcomes

• Analyze polynomial functions and solve polynomial equations and inequalities.
• Analyze rational functions and their representations.
• Use trigonometric concepts and analyze trigonometric functions.
• Analyze exponential and logarithmic functions and solve related equations.
• Combine functions and describe their properties and representations.
• Apply rates of change, modelling and mathematical processes to advanced problems.
• Communicate precise mathematical reasoning using appropriate notation, representations and technology.