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

1. Relations and Functions
2. Function Notation
3. Properties of Parent Functions
4. Domain and Range of a Function
5. The Inverse Function
6. Transformation of Parent Functions

Algebraic Expressions

1. Adding and Subtracting Polynomials
2. Multiplying and Factoring Polynomials
3. Simplifying Rational Functions
4. Multiplying and Dividing Rational Expressions
5. Adding and Subtracting Rational Expressions

Quadratic Functions

1. Quadratic Functions
2. Maximum and Minimum Values of a Quadratic Function
3. The Inverse of a Quadratic Function
4. Quadratic Function Models
5. Zeros of a Quadratic Function
6. Families of Quadratic Functions
7. Linear-Quadratic Systems

Exponential Functions

1. Growth and Decay
2. Integer Exponents and Rational Exponents
3. Algebraic Expressions Involving Exponents
4. Properties of Exponential Functions
5. Transformations and Applications of Exponential Functions

Trigonometric Ratios

1. Trigonometric Ratios of Acute Angles
2. Trigonometric Ratios for Special Angles
3. Exploring Trigonometric Ratios for Angles Greater than 90°
4. Evaluating Trigonometric Ratios for Any Angle Between 0° and 360°
5. Trigonometric Identities
6. The Sine and Cosine Law
7. Trigonometry in Three-Dimensions

Sinusoidal Functions

1. Periodic Functions
2. Properties of Sinusoidal Functions
3. Interpreting Sinusoidal Functions
4. Transformations of Sinusoidal Functions
5. Models of Sinusoidal Functions

Discrete Functions

1. Arithmetic Sequences and Geomeric Sequences
2. Defining Sequences
3. Recursive Sequences
4. Arithmetic Series
5. Geometric Series
6. Pascal's Triangle and Binomial Expansions