# 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