MPM2D, Grade 10, Principles of Mathematics, Academic

Course Title/ Grade/ Course Type: Principles of Mathematics, Grade 10, Academic

Ministry Course Code: MPM2D

Curriculum Document: The Ontario Curriculum, Grades 9 and 10: Mathematics, 2005, Addendum to Principles of Mathematics (Issued Winter 2022); Growing Success Documents, 2010

Prerequisite: Grade 9 Mathematics, De-streamed (2021), or Grade 9 Principles of Mathematics, Academic (2005)
*If you are a current UMC High School student, please contact your advisor.

SKU: N/A Category: Tags: ,



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.


Outline of Course Content

Unit 1: Linear System

Linear relationships are not only important to understand for everyday use – understanding the interplay between distance and time for the calculation of speed, or rates of change in business, for example. Linear relationships are also fundamental to more complex forms of mathematics. This unit reviews the concepts of linear algebra that were developed in Grade 9, and expands upon important procedures such as rearranging equations and developing accurate graphs.


Unit 2: Analytic Geometry 

Expanding upon the foundation built in the last unit, the equations of lines and line segments will be examined. Developing logical and mathematical methods for determining line segment length and midpoint, based upon an equation or upon coordinates, will enable a deeper study of geometric shapes and properties.


Unit 3: Properties of Quadratic Relations

Until this point, all algebraic relations that have been considered have been linear. In this unit, second-order functions are introduced. The concept of the function will be studied; the domain, range, and simple transformations of quadratic functions will be explored; and students will learn how to complete the square.


Unit 4: Application of Quadratic Relations

Having explored quadratic functions graphically, the algebra of quadratic equations will be considered. The Quadratic Formula, which will be used extensively throughout all future math courses, will be derived and used.


Unit 5: Similar Triangles – Trigonometry

In this unit, students will learn to analyze and classify triangles as similar or congruent. Students will also investigate the relationship between sides and angles in both right and non-right triangles. Students will apply their understanding of trigonometric ratios to determine unknown sides and angles, as well as solve problems that are encountered in the real world.


Unit 6: Acute Triangle – Trigonometry 

Triangles have a particularly significant role to play in mathematics. This unit is all about triangles and how they can be used to describe many phenomena in the universe. A review of the Pythagorean Theorem will start the discussion, which will lead the student through sine, cosine, and tangent ratios, the sine law and cosine law, and the ability to solve problems using these tools.

Final Mark will be determined following percentages:

70% Determined by the evaluations conducted throughout the duration of the course:

Products – Assignments, Essays, Journals, Portfolio

Observations – Presentations

Conversations – Conferences with the Teacher

30% Final Exam and/or Final Culminating Activity