Canada · Ontario Curriculum Expectations
Grade 12 Mathematics
This course prepares students for university level mathematics by exploring the properties of polynomial, rational, exponential, and logarithmic functions. Students develop a deep understanding of rates of change and the geometric relationships within the Cartesian plane.
Polynomial and Rational Functions
Students explore the behavior of higher degree functions and the implications of vertical and horizontal asymptotes in rational expressions.
Analyzing end behavior, turning points, and zeros to determine the nature of polynomial functions.
Investigating how the ratio of two polynomials creates complex graphical features like holes and asymptotes.
Exponential and Logarithmic Relations
An investigation into inverse relationships and the modeling of rapid growth and decay phenomena.
Defining the logarithm as the inverse of an exponent and exploring its operational laws.
Applying exponential functions to financial, biological, and chemical scenarios.
Trigonometric Functions and Identities
Extending trigonometry beyond right triangles to periodic functions and analytical proofs.
Transitioning from degree based measurement to the more natural unit of radians for circular motion.
Using algebraic manipulation to prove equivalence between different trigonometric expressions.
Introduction to Calculus and Rates of Change
Bridging the gap between average slopes and instantaneous rates of change using the concept of limits.
Exploring the behavior of functions as they approach a specific value from both sides.
Defining the derivative as the limit of the difference quotient and the slope of a tangent line.
Vectors and Lines in Space
Developing geometric intuition through the study of magnitude, direction, and intersections in three dimensions.
Mastering the dot product and cross product to solve geometric problems.
Representing linear paths and flat surfaces using vector, parametric, and Cartesian forms.
Data Management and Probability
Applying statistical methods to analyze large datasets and calculate probabilities of complex events.
Counting techniques for determining the number of outcomes in structured scenarios.
Analyzing discrete and continuous variables using binomial and normal distributions.