Mathematics

MATHEMATICS

Mathematics is a quantitative language that combines discovered truths, abstract
reasoning, and creativity to describe numerical, algebraic, and geometric patterns.
Mathematics major importance lies in its ability to be applied to real life problems and in
developing logic and reasoning. The emphases in the mathematics program is on
reasoning; problem solving; understanding ideas, processes, and result; communicating;
and the use of appropriate technology.

Principles of Mathematics: Grade 9, Academic Level 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 problems.

Foundations of Mathematics: Grade 9, Applied Level MFM1P

This course enables students to develop an understanding of mathematical concepts related to
introductory algebra, proportional reasoning, and measurement and geometry through
investigation, the effective use of technology, and hands-on activities. Students will investigate
real-life examples to develop various representations of linear relations, and will determine the
connections between the representations. They will also explore certain relationships that emerge
from the measurement of three-dimensional figures and two-dimensional shapes. Students will
consolidate their mathematical skills as they solve problems and communicate their thinking.

Principles of Mathematics: Grade 10, Academic Level 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: MPM1D or MFM1P

Foundations of Mathematics: Grade 10, Applied Level MFM2P

This course enables students to consolidate their understanding of linear relations and extend their
problem-solving and algebraic skills through investigation, the effective use of technology, and
hands-on activities. Students will develop and graph equations in analytic geometry; solve and
apply linear systems, using real-life examples; and explore and interpret graphs of quadratic
relations. Students will investigate similar triangles, the trigonometry of right triangles, and the
measurement of three-dimensional figures. Students will consolidate their mathematical skills as
they solve problems and communicate their thinking.
Prerequisite: MPM1D or MFM1P

Functions: Grade 11, University Preparation 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

Foundations for College Mathematics, Grade 11, College Preparation MBF3C

NOTE: This course is offered on an alternate year basis.
This course enables students to broaden their understanding of mathematics as a problem-solving
tool in the real world. Students will extend their understanding of quadratic relations; investigate
situations involving exponential growth; solve problems involving compound interest; solve
financial problems connected with vehicle ownership; develop their ability to reason by
collecting, analysing, and evaluating data involving one variable; connect probability and
statistics; and solve problems in geometry and trigonometry. Students will consolidate their
mathematical skills as they solve problems and communicate their thinking.
Prerequisite: Foundations of Mathematics, Grade 10, Applied

Advanced Functions, Grade 12, University Preparation 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: MCR3U

Calculus and Vectors, Grade 12, University Preparation 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: MHF4U

Foundations for College Mathematics: Grade 12 College Preparation MAP4C

NOTE: This course is offered on an alternate year basis.
This course enables students to broaden their understanding of real-world applications of
mathematics. Students will analyse data using statistical methods; solve problems involving
applications of geometry and trigonometry; solve financial problems connected with annuities,
budgets, and renting or owning accommodation; simplify expressions; and solve equations.
Students will reason mathematically and communicate their thinking as they solve multi-step
problems. This course prepares students for college programs in areas such as business, health
sciences, and human services, and for certain skilled trades.
Prerequisite: Foundations for College Mathematics, Grade 11, College Preparation, or Functions
and Applications, Grade 11, University/College Preparation

Data Management: Grade 12 University Preparation MDM4U

Note: Available Online Only
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