Principles of Mathematics, Grade 10, Academic
Curriculum Policy
Mathematics, The Ontario Curriculum, Grades 9 and 10, 2005 (Revised)

Course Description:

This course helps students deepen their understanding of relationships and enhance their problem-solving and algebraic skills through investigation, technology use, 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 study the trigonometry of right and acute triangles. Throughout the course, students will engage in mathematical reasoning and effectively communicate their thought processes while tackling multi-step problems.

Chapters and Descriptions:

• Understanding Linear Systems
  This unit emphasizes the importance of linear relationships in everyday life, such as the connection between distance and time or rates of change in business. Building on Grade 9 concepts, students will review linear algebra and expand their skills in rearranging equations and creating accurate graphs.
• Exploring Analytical Geometry
  Continuing from the previous unit, students will examine the equations of lines and line segments. They will develop logical and mathematical methods to determine the length and midpoint of line segments based on equations or coordinates, enabling a deeper understanding of geometric shapes and their properties.
• Mastering Algebraic Skills
  To advance in mathematics, students must master essential algebraic skills. This unit focuses on operations with monomials, binomials, and polynomials, with particular attention to factoring binomials and trinomials.
• Introducing Quadratic Functions.
  In this unit, students will transition from linear to quadratic relations by exploring second-order functions. They will study the concept of functions, examine the domain and range, and learn about simple transformations of quadratic functions, including how to complete the square.
• Diving into Quadratic Equations
  After graphically exploring quadratic functions, this unit focuses on the algebra of quadratic equations. Students will derive and apply the Quadratic Formula, which will be instrumental in their future math studies.
• Exploring Trigonometry
  Triangles play a vital role in mathematics and the understanding of various phenomena in the universe. This unit begins with a review of the Pythagorean Theorem and progresses to sine, cosine, and tangent ratios, as well as the sine law and cosine law, equipping students with the tools to solve related problems.