Course Code:     MPM2D

Prerequisite:      MPM1D

### 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 & 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 Expectations

Please refer to the Ontario Ministry of Education curriculum document for details of Overall and Specific Expectations HERE.

Quadratic Relations in the Form y = ax2 + bx + c

1. 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
2. Solve quadratic equations and interpret the solutions with respect to the corresponding relations;
3. Solve problems involving quadratic relations.

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.

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.