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

Course description:
This course allows students to deepen their understanding of relationships while enhancing their problem-solving and algebraic skills through investigation, technology use, and hands-on activities. Students will learn to develop and graph equations in analytic geometry, solve and apply linear systems with real-life applications, and explore graphs of quadratic relationships. Additionally, they will study similar triangles, the trigonometry of right-angled triangles, and the measurement of three-dimensional objects. Throughout the course, students will solidify their mathematical skills by solving problems and effectively communicating their thought processes.
Chapters and Descriptions:

• Similar Triangles
  Triangles play a significant role in mathematics. In this unit, the concept of similarity will be explored in a mathematical context, and tools to check for similarity will be learned. A review of the Pythagorean Theorem will precede a more advanced discussion of triangles.
• Trigonometry
  This unit focuses on triangles and their applications in describing various phenomena in the universe. Students will examine sine, cosine, and tangent ratios and learn how to solve problems using these tools.
  Formulas and Equations
  To progress in mathematics, mastering fundamental skills is essential. In this unit, strategies for performing measurement conversions will introduce the larger topic of solving equations. By the end of the unit, students will be able to solve multi-step equations and equations with more than one variable.
• Linear Functions
  Understanding linear relationships is crucial for everyday applications, such as calculating speed and rates of change in business. This unit reviews the concepts of linear algebra developed in Grade 9 and expands on important procedures such as rearranging equations and developing accurate graphs.
  Systems of Linear Equations
  Knowing where two lines intersect on a graph is often important for practical reasons. This unit focuses on determining this intersection point, both graphically and mathematically.
• Algebraic Expressions
  In this unit, students will explore various operations on monomials, binomials, and polynomials. They will also manipulate differences of squares and factor trinomials, applying these skills to different situations.
• Quadratic Functions
  Up to this point, all algebraic relations studied have been linear. In this unit, second-order functions are introduced. Students will investigate vertices, axes of symmetry, intercepts, and the direction of opening in parabolas. They will discover the links between parameters in equations and the features of their curves, using this knowledge to sketch parabolas.