Principles of Mathematics

MPM2D deepens students' understanding of mathematical concepts by exploring algebra, linear and quadratic relations, geometry, and trigonometry

This course emphasizes

• Abstract reasoning
• Problem solving
• Real-world application

Students develop mathematical models, analyze data, and strengthen their ability to communicate mathematical ideas clearly and effectively. MPM2D prepares learners for advanced math courses and future STEM pathways.

Unit 1: Systems of Linear Equations
Students analyze linear relationships and learn multiple methods of solving systems.
Lessons include:

• Representing Linear Relations
• Graphical and Algebraic Solutions
• Substitution and Elimination Methods
• Translating Verbal Problems to Equations
• Application of Systems in Real Life

Unit 2: Analytical Geometry
This unit develops spatial reasoning and coordinate geometry skills.
Lessons include:

• Midpoint and Length Formulas
• Circles in Standard Form
• Triangle Properties and Geometric Verification
• Applications of Slope and Coordinate Proofs

Unit 3: Quadratic Relations
Students explore the characteristics of quadratic functions and their graphical representations
Lessons include:

• Identifying and Exploring Quadratics
• Properties of Parabolas
• Quadratic Transformations and Vertex Form
• Expanding and Factoring Quadratic Expressions
• Solving Quadratic Equations (Various Methods)

Unit 4: Trigonometry
Students apply trigonometric concepts to right and non-right triangles
Lessons include:

• Congruence and Similarity
• Similar Triangles in Applications
• Right-Angle Trigonometry (SOH-CAH-TOA)
• Law of Sines and Law of Cosines
• Solving Acute Triangle Problems

MPM2D assessment balances procedural fluency with conceptual understanding and problem solving:

• 70% of the final grade is based on coursework, and assignments
• 30% of the final grade is based on final evaluations:
  • 10% Culminating math portfolio or real-world modelling task
  • 20% Final written exam covering all strands.

All assessments align with the Ontario mathematics curriculum and aim to build both technical skills and confidence in mathematical thinking.