## 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.

**Prerequisite **: MPM1D

**Grade **: 10

**Credit value **: 1

## Unit One

#### Quadratic Relations

- Determine the basic properties of quadratic relations
- Relate transformations of the graph of y = x 2 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

## Unit Two

#### 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

## Unit Three

#### 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