MHF4U University Preparation
Advanced Functions

Course Summary

Grade 12

Prerequisites:
MCR3U or MCT4C

1 Credit

4 Units, 41 learning activities

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.

Course outline

Learning Activity 1 Recognizing applications of polynomial expressions

Learning Activity 2 Describing polynomial expressions

Preview

Learning Activity 3 Identifying polynomial functions

Learning Activity 4 Classifying polynomial functions

Learning Activity 5 Exploring the effect of degree on polynomial functions

Learning Activity 6 Determining the end behaviours of polynomial functions

Learning Activity 7 Describing polynomials in factored form

Learning Activity 8 Developing the factor theorem and remainder theorem

Learning Activity 9 Applying long division to polynomial functions

Learning Activity 10 Investigating transformations of polynomial functions

Learning Activity 11 Using symmetry to characterize odd and even polynomial functions

Learning Activity 12 Exploring the graphs of reciprocal functions

Learning Activity 13 Connecting algebraic and graphical representations of rational functions

Learning Activity 14 Solving rational equations

Learning Activity 15 Solving inequalities

Quick Links

Mathematics (Grades 11-12), Official Curriculum 2007

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MHF4U University Preparation Advanced Functions

Course Summary

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Course outline

Unit 1: Polynomial and rational functions

Learning Activity 1 Recognizing applications of polynomial expressions

Learning Activity 2 Describing polynomial expressions

Learning Activity 3 Identifying polynomial functions

Learning Activity 4 Classifying polynomial functions

Learning Activity 5 Exploring the effect of degree on polynomial functions

Learning Activity 6 Determining the end behaviours of polynomial functions

Learning Activity 7 Describing polynomials in factored form

Learning Activity 8 Developing the factor theorem and remainder theorem

Learning Activity 9 Applying long division to polynomial functions

Learning Activity 10 Investigating transformations of polynomial functions

Learning Activity 11 Using symmetry to characterize odd and even polynomial functions

Learning Activity 12 Exploring the graphs of reciprocal functions

Learning Activity 13 Connecting algebraic and graphical representations of rational functions

Learning Activity 14 Solving rational equations

Learning Activity 15 Solving inequalities

Unit 2: Exponential and logarithmic functions

Learning Activity 1 Defining logarithmic functions

Learning Activity 2 Exploring the characteristics of logarithmic functions

Learning Activity 3 Connecting exponential and logarithmic functions

Learning Activity 4 Solving logarithmic and exponential equations: part 1

Learning Activity 5 Solving logarithmic and exponential equations: part 2

Learning Activity 6 Exploring transformations of logarithmic functions

Unit 3: Trigonometric functions

Learning Activity 1 Introducing trigonometric functions

Learning Activity 2 Introducing radian measure

Learning Activity 3 Exploring angles expressed in radian measure

Learning Activity 4 Exploring characteristics of the sine, cosine, and tangent functions

Learning Activity 5 Graphing the reciprocal trigonometric functions

Learning Activity 6 Investigating transformations of sinusoidal functions

Learning Activity 7 Connecting algebraic and graphical representations of sinusoidal functions

Learning Activity 8 Solving trigonometric equations

Learning Activity 9 Verifying and applying the compound angle formulas

Learning Activity 10 Exploring equivalent trigonometric expressions

Learning Activity 11 Deriving and applying the double angle and Pythagorean formulas

Learning Activity 12 Solving trigonometric equations

Unit 4: Characteristics of functions

Learning Activity 1 Expressing a function as the combination of other functions

Learning Activity 2 Combining functions by adding, subtracting or multiplying

Learning Activity 3 Combining functions by dividing or applying one function to another

Learning Activity 4 Determining the domain and range of combined functions

Learning Activity 5 Exploring the average rate of change of a function

Learning Activity 6 Determining the instantaneous rate of change of a function

Learning Activity 7 Describing composite functions using symmetry

Learning Activity 8 Solving the equations of composite functions arising from real world applications

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MHF4U University Preparation
Advanced Functions