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.

Overall Provincial Curriculum Expectations

See Ontario math curriculum for grades 9 and 10 for details.

A: Quadratic Relations of the Form $y=ax^2+bx+c$

  1. determine the basic properties of quadratic relations;
  2. relate transformations of the graph of $y = x^2$ to the algebraic representation $y = a(x - h)^2 + k$;
  3. solve quadratic equations and interpret the solutions with respect to the corresponding relations;

B: Analytic Geometry

  1. model and solve problems involving the intersection of two straight lines;
  2. solve problems using analytic geometry involving properties of lines and line segments;
  3. verify geometric properties of triangles and quadrilaterals, using analytic geometry.

C: Trigonometry

  1. use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
  2. solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
  3. solve problems involving acute triangles, using the sine law and the cosine law.

Specific Provincial Curriculum Expectations

A1: Investigating the Basic Properties of Quadratic Relations

A2: Relating the Graph of $y=x^2$ And Its Transformations

A3: Solving Quadratic Equations

A4: Solving Problems Involving Quadratic Equations

B1: Using Linear Systems to Solve Problems

B2: Solving Problems Involving Properties of Line Segments

B3: Using Analytic Geometry to Verify Geometric Properties

C1: Investigating Similarity and Solving Problems Involving Similar Triangles

C2: Solving Problems Involving the Trigonometry of Right Triangles

C3: Solving Problems Involving the Trigonometry of Acute Triangles