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