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 Course Title : Principles of Mathematics, Grade 10, Academic (MPM2D) Course Name : Principles of Mathematics Course Code : MPM2D Grade : 10 Course Type : Academic Credit Value : 1.0 Prerequisite : None Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 9 and 10, 2005 (Revised)

### Course Description

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 Titles and Descriptions Time and Sequence
Unit 1: Linear Systems

Linear relationships are not only important to understand for everyday used – understanding the interplay between distance in time for the calculation of speed, or rates of change in business, for example – but they are also foundational 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.

20 hours
Unit 2: Analytical 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 & properties.

16 hours
Unit 3: Algebraic Skills

To progress beyond a certain point in any mathematics, some rather advanced algebraic skills must first be mastered. In this unit, students will consider various operations on monomials, binomials and polynomials. Factoring of binomials and trinomials will be studied.

16 hours

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”.

16 hours

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

19 hours
Unit 6: 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 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.

20 hours
Final Evaluation

The final assessment task is a three hour exam worth 30% of the student’s final mark.

3 hours
Total 110 hours