Mathematics
“Sir, an equation has no meaning for me unless it expresses a thought of GOD.”
― Srinivasa Ramanujan
Advanced Functions: Grade 12
Our Advanced Functions Program follows Ontario's Academic Curriculum (MHF4U) with the goal of fostering knowledge for university and beyond. Your child will develop an in-depth understanding of the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change. Emphasis will be placed on modelling of real-world relationships and refining your child's use of the mathematical processes necessary for success in careers in fields such as science, engineering, economics and academia.
Functions
Functions
Exploring Absolute Value
Sketching Graphs of Functions
Inverse Relations and Piecewise Functions
Determining Average Rate of Change
Instantaneous Rates
Rates of Change to Create a Graphical Model
Polynomial Functions
Exploring Polynomial Functions
Polynomial Functions
Transformations of Cubic and Quartic Functions
Dividing Polynomials and Factoring Polynomials
Factoring a Sum or Difference of Cubes
Polynomial Equations and Inequalities
Solving Polynomial Equations
Linear Inequalities and Polynomial Inequalities
Rates of Change in Polynomial Functions
Rational Functions, Equations, and Inequalities
Graphs of Reciprocal Functions
Exploring Quotients of Polynomial Functions
Solving Rational Equations and Rational Inequalities
Rates of Change in Rational Functions
Trigonometric Functions
Radian Measure and Angles on the Cartesian Plane
Primary Trigonometric Functions and Transformation of Trigonometric Functions
Reciprocal Trigonometric Functions
Modelling with Trigonometric Functions
Rates of Change in Trigonometric Functions
Trigonometric Identities and Equations
Exploring Equivalent Trigonometric Functions
Compound Angle Formulas and Double Angle Formulas
Proving Trigonometric Identities
Linear Trigonometric Equations and Quadratic Trigonometric Equations
Exponential and Logarithmic Functions
Exploring the Logarithmic Functions
Transformations of Logarithmic Functions and Evaluating Logarithms
Laws of Logarithms
Rates of Change in Exponential and Logarithmic Functions
Combinations of Functions
Sum and Differences of Two Functions
Product of Two Functions
Quotients of Functions
Composition of Functions
Solving Equations and Inequalities
Calculus and Vectors: Grade 12
Our Calculus and Vectors Program follows Ontario's Academic Curriculum (MCV4U) with the goal of fostering knowledge for university and beyond. Your child will develop an in-depth 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 your child's use of the mathematical processes necessary for success in careers in fields such as science, engineering, economics and academia.
Radical Expressions
The Slope of a Tangent and Rates of Change
Limit of a Function
Properties of Limits and Continuity
Derivatives
The Derivative Function
The Derivatives of Polynomial Functions
The Product Rule and The Quotient Rule
The Derivatives of Composite Functions
Derivatives and their Applications
Higher Order Derivaties, Velocity and Accerleration
Minimum and Maximum on an Interval
Optimization Problems and Applications
Curve Sketching
Increasing, Decreasing Functions, Critical Points, Local Maxima, and Local Minima
Vertical and Horizontal Asymptotes
Concavity and Points of Inflection
Derivatives of Exponential and Trigonometric Functions
Derivaties of Exponential Functions and The Derivatives of the General Exponential Function
Optimization Problems Involving Exponential Functions
The Derivatives of the cosine, sine and tangent fuctions
Vectors
Introduction to Vectors
Vector Addition and Multiplication of a Vector by a Scalar
Properties of Vectors in Vectors in R2
Properties of Vectors in Vectors in R3
Operations with Algebraic Vectors in R2 and in R3
Linear Combinations and Spanning Sets
Applications of Vectors
Vectors as Forces and Velocities
The Dot Product, Scalar and Vector Projections
The Cross Product of Two Vectors
Applications of the Dot Product and Cross Product
Equations of Lines and Planes
Vector and Parametric Equations of a Line in R2 and R3
Cartesian Equation of a Line
Vector and Parametric Equations of a Plane
The Cartesian Equation of a Plane
Applications of the Dot Product and Cross Product
Relationships between Points, Lines and Planes
The Intersection of a Line with a Plane and the Intersection of Two Lines
Systems of Equations
The Intersection of Planes
The Distance from a Point to a Line in R2 and R3
The Distance from a Point to a Plane
Mathematics of Data Management: Grade 12
Our Mathematics of Data Management Program follows Ontario's Academic Curriculum (MDM4U) with the goal of fostering knowledge for university and beyond. Your child will develop an in-depth understanding of methods for organizing and analysing large amounts of information; solve problems involving probability and statistics. Emphasis will be placed on use of the mathematical processes necessary for success in university and beyond
Counting and Probability
Discrete Sample Spaces
Counting Principles
Probability Distributions
Probability Distributions for Discrete Random Variables
Understanding Probability Distributions for Continuous Random Variables
Organization of Data for Analysis
Data Concepts
Collecting and Organizing Data
Statistical Analysis
Analysing One-Variable Data
Analysing Two-Variable Data
Evaluating Validity