Algebra/Geometry

The OAC Algebra and Geometry course helps students' abstract reasonning ability. Covering areas such as matrices and vectors, complex numbers and mathematical induction, it helps students combine the knowledge gained in pre-OAC math courses and apply it. It also gives the student a basic idea of how to apply the knowledge and skills learned in math courses to "real life situations. Algebra and Geometry is probably the most important of the math OAC courses taken by students looking to go on to the sciences in post-secondary education.

Units Covered

Conics and Translations

In this unit the class looks at the three different types of conic sections, the ellipse, parabola, and hyperbola, using a double cone. This unit identifies conics in standard position as well as conics that have been translated (moved from standard position)

Circle and Parabola
Ellipse
Hyperbola
Translations
Classification & Applications

Matrices and Linear Transformations

A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are tools used for solutions of systems of equations and geometric transformations.

Matrix Multiplication
Linear Transformations
Reflections
Inverse Matrices
Rotations
Stretches and Shears
Other Transformations and Composite Transformations
Transpose of a Matrix

Matrices and Conic Sections

This unit combines what has been learned in the frist two units. It introduces important operations involving the moving, rotating and changing the general form of a conic section using matrices.

Quadradic Forms
Matrix Equations
Matrix Equations of a Rotated Conic
Identifying Graphs by Rotations
Identifying Graphs by Rotations and Turns
Identifying Conics by Invariants

Mathematical Induction

Mathematical induction looks at how to use thinking and imagination to solve problems. Inductive reasoning is looking for patterns and predicting answers for complicated problems by analysing facts of individual cases.

Inductive and Deductive Reasoning
Principal of Mathematical Induction
Multiples
Inequalities

Vectors

Vectors play a role in a variety of studies which include physical chemistry, electromagnetic theory, economics, psychology, and electrocardiography. This unit illustrates simple vector proofs.

Vectors as Directed Line Segments and Addition of Vectors
Multiplication of Vectors by Scalars
Components and Projections
The Dot Product
The Cross Product

Vector Applications

Vector Applications looks at the principle of adding forces. It looks at the properties of forces and how to represent them mathematically. The unit teaches the principles for solving problems involving forces which are useful in physics and engineering.

Forces as Vectors
Resolution of Forces
Applications of Forces as Vectors
Tension & Thrust
Momentum of a Force - Torque
Work

Linear Combinations and Vectors

This unit show students how to represent vectors as geometric entities. It also treats the general theory of dimensionality and understanding of operations in three space. This unit in mainly the study of dimensions.

Linear Combination
Linear Dependence and Independence
Division of a Line Segment

Analytic Vectors

An analytic vector is the expression of a vector in ordered pair form. It treats vectors located in coordinate space.

Ordered Pairs as Vectors, Vector Addition, Scalar Multiplication
Basis Vectors, Vectors in 3 Space
Vector Addition in 3 Space
Dot product in component Form
Direction of a Vector in 3 Space
Cross product in Component Form
Applications of Vector Products

Equations of Lines and Planes

This unit studies the application of analytic vectors to create the equations of lines and planes in two and three dimensions.

Vector Equation of a Line in 2 Space
Cartesian Equation of a Line
Cartesian Equation of a Plane
Vector Equation of a Line in 3 Space
Symmetric Equations of a Line
Vector Equations of a Line
Vector Equations of a Plane

Systems of Equations

This is the study of systems in motion. This unit demonstrates methods by which solutions for these problems can be easily obtained. At the end of this unit a student should be able solve the system regardless of the magnitude.

Linear Systems in 2 Space
Linear Systems in 3 Space
Solving Using Matrices
Analysis Using Normals

Complex Numbers

Complex numbers were invented for entirely algebraic reasons. They are connected with the geometry of the plane. Complex numbers are the square roots of negative numbers.

Definition of Complex Numbers
Division of a Complex Numbers
Complex Numbers in Polar Form
De Moivre's Theorem
Roots of Complex Numbers
Complex Numbers in Exponent Form
Solution of Polynomial Equations

Main Page

Finite Home Page

Calculus Home Page

University Page

Math Contest

Comics

Calulator page