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MHF4U Advanced Functions
University Prep.
Ministry of Education Course Title: Advanced Functions, Grade12, University preparation
Course Code: MHF4U
Grade Level: 12
Prerequisite: MCR3U
Department: Mathematics
Course Description:
This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university program.
Overall Curriculum Expectation - all units are interrelated
Unit 1 Polynomial and Rational Functions
- Connecting Graphs and Equations of Polynomial Functions
• describe key features of the graphs of polynomial functions - Connecting Graphs and Equations of Rational Functions
• sketch the graph of a simple rational function using its key features, given the algebraic representation of the function - Solving Polynomial and Rational Equations
• factor polynomial expressions in one variable, of degree no higher than four, by selecting and applying strategies - Solving Inequalities
• explain, for polynomial and simple rational functions, the difference between the solution to an equation in one variable and the solution to an inequality in one variable, and solve linear inequalities and factorable polynomial inequalities in one variable
Unit 2 Trigonometric Functions
- Understanding and Applying Radian Measure
• recognize the radian as an alternative unit to the degree for angle measurement, define the radian measure of an angle as the length of the arc that subtends this angle at the centre of a unit circle, and develop and apply the relationship between radian and degree measure - Connecting Graphs and Equations of Trigonometric Functions
• sketch the graphs of and for angle measures expressed in radians, and determine and describe some key properties in terms of radians - Solving Trigonometric Equations
• recognize equivalent trigonometric expressions by using transformations and verify equivalence using graphing technology
Unit 3 Exponential and Logarithmic Functions
- Evaluating Logarithmic Expressions
• recognize the logarithm of a number to a given base as the exponent to which the base must be raised to get the number, recognize the operation of finding the logarithm to be the inverse operation - Connecting Graphs and Equations of Logarithmic Functions
• determine, through investigation key features of the graphs of logarithmic functions of the form and make connections between the algebraic and graphical representations of these logarithmic functions - Solving Exponential and Logarithmic Equations
• recognize equivalent algebraic expressions involving logarithms and exponents, and simplify expressions of these types
Unit 4 Characteristics of Functions
- Understanding Rates of Change
• gather, interpret, and describe information about real-world applications of rates of change, and recognize different ways of representing rates of change - Combining Functions
• solve problems involving the composition of two functions, including problems arising from real-world applications - Using Function Models to Solve Problems
• solve problems, using a variety of tools and strategies, including problems arising from real-world applications, by reasoning with functions and by applying concepts and procedures involving functions
