MPM2D

Course features
Principles of Mathematics, Grade 10, Academic
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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.

  • Unit 1: Linear Systems

    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. 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: 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 and properties.

  • 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.

  • Unit 4: Quadratic Functions

    Until this point, all algebraic relations that have been considered have been linear. In this unit, secondorder 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 5: Quadratic Equations

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 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.

Unit 7: Course Review and Final Exam

Students will be given time near the end of the course to review all the concepts they have learned throughout the course in preparation for the final exam that covers all overall expectations.

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