Principles of Mathematics, Grade 10, Academic

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 Expectations

- determine the basic properties of quadratic relations;
- relate transformations of the graph of the parent quadratic to the algebraic equation in vertex form
- solve quadratic equations and interpret the solutions with respect to the corresponding relations.

- 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

- 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

Copious Exercises

- In progress: Similar triangles
- In progress: Applications of similar triangles
- In progress: Right triangles and trig ratios
- In progress: Applications of right triangles
- In progress: Oblique triangles (sine law)
- In progress: Oblique triangles (cosine law)
- In progress: Applications of oblique triangles