Grade 10 Mathematics (MPM2D) 📐
Ontario Curriculum · Toronto District School Board · Curated Video Lessons
This guide covers the core units of Ontario's Grade 10 Principles of Mathematics course (MPM2D), aligned to the TDSB curriculum. Each section pairs a key concept with a high-quality video lesson — from linear systems and analytic geometry to quadratic relations and trigonometry.
⚖️ Solving Linear Systems by Elimination
A linear system is a pair of equations with two unknowns that share a common solution point. This lesson demonstrates the elimination method — adding or subtracting equations to cancel one variable, making it straightforward to solve for the other. Elimination is especially efficient when coefficients can be matched quickly, and it's one of the two main algebraic methods tested in MPM2D alongside substitution.
Source: MPM2D Academic Math
📏 Midpoint & Length of a Line Segment
Analytic geometry uses algebra and coordinates to study geometric shapes. This lesson covers two of the foundational tools of the unit: the midpoint formula — which finds the exact centre point between two coordinates — and the length formula derived from the Pythagorean Theorem. These are essential for working with medians, perpendicular bisectors, and the properties of triangles in MPM2D.
Source: MPM2D Ontario Curriculum
📈 Introduction to Quadratic Relations
Quadratic relations are the defining feature of MPM2D — they produce parabolas rather than straight lines. This lesson introduces the three forms of a quadratic equation: standard form (y = ax² + bx + c), vertex form (y = a(x – h)² + k), and factored form (y = a(x – r)(x – s)). Understanding how each form reveals different properties of the parabola — vertex, axis of symmetry, direction of opening, and x-intercepts — is the core skill of this unit.
Source: Grade 10 Math Ontario MPM2D
🔢 Solving Quadratic Equations by Factoring
Factoring is the most accessible algebraic technique for solving quadratic equations — when a quadratic expression can be written as a product of two binomials, the zero-product property immediately gives the solutions. This lesson walks through common factoring strategies including common factors, simple trinomials, and difference of squares, with clear examples from the MPM2D curriculum.
Source: Grade 10 Math Ontario MPM2D
📐 Introduction to Trigonometry (SOH CAH TOA)
Grade 10 trigonometry focuses on right triangles — using the three primary trig ratios (sine, cosine, tangent) to find unknown side lengths and angles. The acronym SOH CAH TOA (Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent) is the foundation. This lesson introduces how to set up and solve trig equations, including real-world applications such as angles of elevation and depression that appear regularly in MPM2D assessments.
Source: MPM2D Introduction to Trigonometry
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