MHF4U, Grade 12, Advanced Functions, University Preparation

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 programs.

Outline of Course Content

Unit 1: Polynomial & Rational Functions

Within this unit, you will investigate polynomial and rational functions and their corresponding graphical representations. You will also investigate the transformation of these functions; characteristics of rational functions; a process for graphing rational functions, applications of polynomials, and rational functions in the real world.

Unit 2: Trigonometric Functions

In this unit you will be introduced to the radian measurements of angles. You will investigate trigonometric functions, their reciprocal and inverse functions. You will develop the compound angle formulas, prove trigonometric identities and solve trigonometric equations algebraically and graphically.

Unit 3: Exponential & Logarithmic Functions

In this unit, you will investigate the logarithmic function and its connection to the exponential function. You will solve exponential and logarithmic equations and explore some of their applications to the real world.

Unit 4: Characteristics of Functions

In this unit you will investigate both the average & instantaneous rates of change of a function from a given interval or at a point. You will examine the properties of compound functions created through addition, subtraction, multiplication & division as well as composite functions.

Final Mark will be determined following percentages:

70% Determined by the evaluations conducted throughout the duration of the course:

Products – Assignments, Essays, Journals, Portfolio

Observations – Presentations

Conversations – Conferences with the Teacher

30% Final Exam and/or Final Culminating Activity

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