Mathematics

“We can only see a short distance ahead, but we can see plenty there that needs to be done.”

― Alan Turing

Functions: Grade 11

Our Functions Program follows Ontario's Academic Curriculum (MCR3U) with the goal of fostering knowledge for university and beyond. Your child will develop an indepth understanding of rates of change and vector representations of functions. Our programs will explore geometric and algebraic representations of vectors, representations of lines and planes in three- dimensional space, derivatives of polynomial, sinusoidal, exponential, rational, and radical functions. Emphasis will be placed on modelling of real-world relationships and refining mathematical reasoning and proofs. necessary for success in careers in fields such as science, engineering, economics and academia.

 

Introduction to Functions

Relations and Functions

Function Notation

Properties of Parent Functions

Domain and Range of a Function

The Inverse Function

Transformation of Parent Functions

Algebraic Expressions

Adding and Subtracting Polynomials

Multiplying and Factoring Polynomials

Simplifying Rational Functions

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions

Quadratic Functions

Quadratic Functions

Maximum and Minimum Values of a Quadratic Function

The Inverse of a Quadratic Function

Quadratic Function Models

Zeros of a Quadratic Function

Families of Quadratic Functions

Linear-Quadratic Systems

Exponential Functions

Growth and Decay

Integer Exponents and Rational Exponents

Algebraic Expressions Involving Exponents

Properties of Exponential Functions

Transformations and Applications of Exponential Functions

Trigonometric Ratios

Trigonometric Ratios of Acute Angles

Trigonometric Ratios for Special Angles

Exploring Trigonometric Ratios for Angles Greater than 90°

Evaluating Trigonometric Ratios for Any Angle Between 0° and 360°

Trigonometric Identities

The Sine and Cosine Law

Trigonometry in Three-Dimensions

Sinusoidal Functions

Periodic Functions

Properties of Sinusoidal Functions

Interpreting Sinusoidal Functions

Transformations of Sinusoidal Functions

Models of Sinusoidal Functions

Discrete Functions

Arithmetic Sequences and Geomeric Sequences

Defining Sequences

Recursive Sequences

Arithmetic Series

Geometric Series

Pascal's Triangle and Binomial Expansions

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