# Principles of Mathematics, grade 10, Academic (MPM2D)

\$399.00

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## 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