Grade 12 : Advanced Functions
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 programs.
Unit Content and Courses of Delivery
Functions: Characteristics and Properties (10 hours)
Many situations can be modelled graphically. Interpreting those graphs is something that requires you to become familiar with all of the aspects of these graphs. Students will recall a few basic facts of a distance time graph. In previous math courses, students saw some transformations and studied their effects on a given graph. These will also be reviewed. The concepts of function notation, relation, range, domain, and function notation will all be reviewed.
Polynomial Functions (10 hours)
In this unit students learn to identify and describe some key features of polynomial functions and to make connections between the numeric, graphical, and algebraic representations of polynomial functions. Transformations of Cubic and Quartic functions. Dividing and Factoring Polynomials.
Polynomial Equations and Inequalities (13 hours)
Solving polynomial equations. Solving linear and polynomial equations by using factoring and graphing.
Rational Functions, Equations and Inequalities (13 hours)
The concepts of identifying and describing some key features of the graphs of rational functions are also presented. Students will represent rational functions graphically; solve problems involving polynomial and simple rational equations graphically and algebraically so they can demonstrate an understanding of how to solve rational inequalities.
Trigonometric Functions (15 hours)
This unit examines the meaning and application of radian measure. Students will make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals. Transformations of Trigonometric Functions
Trigonometric Identities and Equations (13 hours)
Exploring equivalent trigonometric functions. Compound and Double angle formulas. Proving Trigonometric Identities. Solving linear and quadratic trigonometric equations.
Exponential and Logarithmic Functions (15 hours)
This unit begins with a review of the rules associated with exponents. Exponential functions, examples and applications of them are the first new topic in this unit followed by logarithmic functions, identities and applications. Solving Exponential and Logarithmic equations.
Functions: Understanding Rates of Change (11 hours)
Determining Average rate of change, estimating Instantaneous rate of change from tables of values and equations. Exploring Instantaneous rate of change using graphs. Using rates of change to create a graphical model. Solving Problems involving rates of change.
Combinations of Functions (10 hours)
Focuses on the theory and practice of performing arithmetic operations on entire functions, including but not limited to the algebraic, graphical and practical implications of performing those operations. Sums, Differences, Products and Quotients of Functions. Composition of Functions.
Final Evaluation
30% of your grade will be determined at the end of the course.
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