Principles of Mathematics, grade 10, Academic (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.

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


  • 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