Canada · Ontario Curriculum Expectations
Grade 10 Mathematics
This course bridges foundational arithmetic with abstract algebraic reasoning and geometric proof. Students explore the relationships between linear and non-linear functions while developing spatial reasoning through trigonometry and coordinate geometry.
Algebraic Expressions and Polynomials
Students master the manipulation of polynomial expressions through expansion and factoring. This unit focuses on recognizing patterns in algebraic structures to simplify complex problems.
Moving beyond distributive properties to multiply binomials and trinomials systematically.
Identifying common factors and using decomposition or special product patterns to reverse polynomial multiplication.
Linear Systems and Modeling
An investigation into the intersection of multiple linear relationships and their applications in real world decision making.
Solving pairs of equations using graphing, substitution, and elimination methods.
Applying system of equations logic to solve mixture, distance, and rate problems.
Analytic Geometry
Connecting algebra and geometry by using coordinates to prove properties of geometric figures and find distances.
Developing formulas for finding the center and length of line segments on a Cartesian plane.
Developing and applying the equation of a circle centered at the origin.
Quadratic Functions and Relations
Exploring the properties of parabolas and the transformation of the parent function y equals x squared.
Identifying vertex, axis of symmetry, direction of opening, and intercepts from graphs and equations.
Applying horizontal and vertical shifts and stretches to the parent quadratic function.
Solving Quadratic Equations
Moving from graphing to algebraic methods for finding the roots of quadratic equations.
Deriving and using the quadratic formula to solve equations that cannot be easily factored.
Solving real world problems involving area, physics, and revenue optimization.
Trigonometry of Right and Oblique Triangles
Extending geometric ratios to solve for unknown sides and angles in various types of triangles.
Applying Sine, Cosine, and Tangent ratios to solve for missing components in right triangles.
Using advanced laws to solve for sides and angles in non-right (oblique) triangles.