About Advanced Functions Grade 12 Course:-
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.
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College
Technology, Grade 12, College Preparation
In this unit, students will learn to calculate the average and instantaneous rate of change of a function given a table of values, a graph, or an equation. They will learn to interpret the average rate of change of a function over a given interval, interpret the instantaneous rate of change of a function at a given point, and solve problems that involve the rate of change.Â
In this unit, students will learn to identify and describe key characteristics of polynomial functions, divide one polynomial by another polynomial, factor polynomial expressions, and solve problems that involve polynomial equations and inequalities graphically and algebraically.
In this unit, students will learn to determine the roots of polynomial equations, with and without technology. They will solve polynomial inequalities, with and without technology, and solve problems involving polynomial function models.
This unit will introduce students to the radian measurements of the angles. Students will investigate trigonometric functions, their reciprocals, and inverse functions and will learn to develop compound angle formulas, prove trigonometric identities, and solve trigonometric equations algebraically and graphically. Â
In this unit, students will learn to recognize equivalent trigonometric relationships and use compound angle formulas to determine the exact values of trigonometric ratios that involve sums, differences, and products of different angles. They will practice proving trigonometric identities and solving trigonometric equations using a variety of strategies.Â
In this unit, students will investigate the logarithmic function and its connection to the exponential function. They will learn to solve exponential and logarithmic equations and explore some of their applications to the real world. Further, students will relate logarithmic functions to exponential functions, and describe the characteristics of logarithmic functions and their graphs. They will also learn to evaluate logarithms and simplify logarithm equations, use exponential and logarithmic functions to solve problems involving exponential growth and decay, and applications of logarithmic scales.   Â
This unit will help students consolidate their understanding of the characteristics of functions, creating new functions by adding, subtracting, multiplying, and dividing functions. Students will explore the creation of composite functions numerically, graphically, and algebraically, and determine key characteristics of these new functions. They will also solve problems using a variety of function models.Â
