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

1. Functions
2. Exploring Absolute Value
3. Sketching Graphs of Functions
4. Inverse Relations and Piecewise Functions
5. Determining Average Rate of Change
6. Instantaneous Rates
7. Rates of Change to Create a Graphical Model

Polynomial Functions

1. Exploring Polynomial Functions
2. Polynomial Functions
3. Transformations of Cubic and Quartic Functions
4. Dividing Polynomials and Factoring Polynomials
5. Factoring a Sum or Difference of Cubes

Polynomial Equations and Inequalities

1. Solving Polynomial Equations
2. Linear Inequalities and Polynomial Inequalities
3. Rates of Change in Polynomial Functions

Rational Functions, Equations, and Inequalities

1. Graphs of Reciprocal Functions
2. Exploring Quotients of Polynomial Functions
3. Solving Rational Equations and Rational Inequalities
4. Rates of Change in Rational Functions

Trigonometric Ratios

1. Radian Measure and Angles on the Cartesian Plane
2. Primary Trigonometric Functions and Transformation of Trigonometric Functions
3. Reciprocal Trigonometric Functions
4. Modelling with Trigonometric Functions
5. Rates of Change in Trigonometric Functions

Trigonometric Identities and Equations

1. Exploring Equivalent Trigonometric Functions
2. Compound Angle Formulas and Double Angle Formulas
3. Proving Trigonometric Identities
4. Linear Trigonometric Equations and Quadratic Trigonometric Equations

Exponential and Logarithmic Functions

1. Exploring the Logarithmic Functions
2. Transformations of Logarithmic Functions and Evaluating Logarithms
3. Laws of Logarithms
4. Rates of Change in Exponential and Logarithmic Functions

Combinations of Functions

1. Sum and Differences of Two Functions
2. Product of Two Functions
3. Quotients of Functions
4. Composition of Functions
5. 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

1. The Slope of a Tangent and Rates of Change
2. Limit of a Function
3. Properties of Limits and Continuity

Derivatives

1. The Derivative Function
2. The Derivatives of Polynomial Functions
3. The Product Rule and The Quotient Rule
4. The Derivatives of Composite Functions

Derivatives and their Applications

1. Higher Order Derivaties, Velocity and Accerleration
2. Minimum and Maximum on an Interval
3. Optimization Problems and Applications

Curve Sketching

1. Increasing, Decreasing Functions, Critical Points, Local Maxima, and Local Minima
2. Vertical and Horizontal Asymptotes
3. Concavity and Points of Inflection

Derivatives of Exponential and Trigonometric Functions

1. Derivaties of Exponential Functions and The Derivatives of the General Exponential Function
2. Optimization Problems Involving Exponential Functions
3. The Derivatives of the cosine, sine and tangent fuctions

Vectors

1. Introduction to Vectors
2. Vector Addition and Multiplication of a Vector by a Scalar
3. Properties of Vectors in Vectors in R2
4. Properties of Vectors in Vectors in R3
5. Operations with Algebraic Vectors in R2 and in R3
6. Linear Combinations and Spanning Sets

Applications of Vectors

1. Vectors as Forces and Velocities
2. The Dot Product, Scalar and Vector Projections
3. The Cross Product of Two Vectors
4. Applications of the Dot Product and Cross Product

Equations of Lines and Planes

1. Vector and Parametric Equations of a Line in R2 and R3
2. Cartesian Equation of a Line
3. Vector and Parametric Equations of a Plane
4. The Cartesian Equation of a Plane
5. Applications of the Dot Product and Cross Product

Relationships between Points, Lines and Planes

1. The Intersection of a Line with a Plane and the Intersection of Two Lines
2. Systems of Equations
3. The Intersection of Planes
4. The Distance from a Point to a Line in R2 and R3
5. 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

1. Discrete Sample Spaces
2. Counting Principles

Probability Distributions

1. Probability Distributions for Discrete Random Variables
2. Understanding Probability Distributions for Continuous Random Variables

Organization of Data for Analysis

1. Data Concepts
2. Collecting and Organizing Data

Statistical Analysis

1. Analysing One-Variable Data
2. Analysing Two-Variable Data
3. Evaluating Validity