Principles of Mathematics, Grade 9, Academic (MPM1D)
This course enables students to develop an understanding of mathematical concepts related to
Algebra, analytic geometry, and measurement and geometry through investigation, the
effective use of technology, and abstract reasoning. Students will investigate relationships,
which they will then generalize as equations of lines, and will determine the connections
between different representations of a linear relation. They will also explore relationships that
emerge from the measurement of three-dimensional figures and two-dimensional shapes.
Students will reason mathematically and communicate their thinking as they solve multi-step
Principles of Mathematics, Grade 10, Academic (MPM2D)
This course enables students to broaden their understanding of relationships and extend their
problem-solving and algebraic skills through investigation, the effective use of technology, and
abstract reasoning. Students will explore quadratic relations and their applications; solve and
apply linear systems; verify properties of geometric figures using analytic geometry; and
investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Prerequisite: Grade 9 Mathematics, Academic, or Grade 9 Mathematics Transfer, Applied to
Functions, Grade 11, University (MCR3U)
This course introduces the mathematical concept of the function by extending students’
experiences with linear and quadratic relations. Students will investigate properties of discrete
and continuous functions, including trigonometric and exponential functions; represent
functions numerically, algebraically, and graphically; solve problems involving applications of
functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Prerequisite: Principles of Mathematics, Grade 10, Academic
Advanced Functions, Grade 12, University (MHF4U)
This course extends students’ experience with functions. Students will investigate the
properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques
for combining functions; broaden their understanding of rates of change; and develop facility in
applying these concepts and skills. Students will also refine their use of the mathematical
processes necessary for success in senior mathematics. This course is intended both for
students taking the Calculus and Vectors course as a prerequisite for a university program and
for those wishing to consolidate their understanding of mathematics before proceeding to any
one of a variety of university programs.
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College
Technology, Grade 12, College Preparation
Calculus & Vectors, Grade 12, University (MCV4U)
This course builds on students’ previous experience with functions and their developing
understanding of rates of change. Students will solve problems involving geometric and
algebraic representations of vectors and representations of lines and planes in three dimensional space; broaden their understanding of rates of change to include the derivatives
of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these
concepts and skills to the modelling of real-world relationships. Students will also refine their
use of the mathematical processes necessary for success in senior mathematics. This course
is intended for students who choose to pursue careers in fields such as science, engineering,
economics, and some areas of business, including those students who will be required to take
a university-level calculus, linear algebra, or physics course.
Prerequisite: Note: Advanced Functions, Grade 12, University Preparation, must be taken prior
to or concurrently with Calculus and Vectors.