Credit: 1

Course Hours:110

Grade: Grade 10

Principles of Mathematics
MPM2D

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.

Topics include:

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

By the end of this course, students will:

• 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.

2. Analytic Geometry

By the end of this course, students will:

• 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

3. Trigonometry

By the end of this course, students will:

• 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.

Topics include:

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

By the end of this course, students will:

• 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.

2. Analytic Geometry

By the end of this course, students will:

• 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

3. Trigonometry

By the end of this course, students will:

• 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.

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