KCS Online Learning

Name of School:
Department: Department of Mathematics
Course Development Date: 2017
Revision Date:
Course Title: Principles of Mathematics
Ministry Course Code: MPM2D
Credit Value: 1.0
Developed from: The Ontario Curriculum, Grades 9 and 10: Mathematics, 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.

### Curriculum Overall Expectations:

#### A. Quadratic Relations of the Form y=ax2+bx+c

• Determine the basic properties of quadratic relations;

• Relate transformations of the graph of y = x2 to the algebraic representation y = a(x - h)2 + k;

• Solve quadratic equations and interpret the solutions with respect to the corresponding relations;

• Solve problems involving quadratic relations.

#### Analytic Geometry

• model and solve problems involving the intersection of two straight lines;

• solve problems using analytic geometry involving properties of lines and line segments;

• verify geometric properties of triangles and quadrilaterals, using analytic geometry.

#### C. Trigonometry

• use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;

• solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;

• solve problems involving acute triangles, using the sine law and the cosine law.