Principles of Mathematics, Grade 10 (Academic)
Ontario · Grade 10 · Mathematics — the complete curriculum-aligned outline, taught skill by skill by MapleMind's AI tutor.
3Units
11Lessons
45Skills
Unit 1: Quadratic Relations of the Form y = ax² + bx + c
Investigating quadratic relations from data and graphs, transforming the graph of y = x², factoring and solving quadratic equations, and solving real problems that involve quadratic relations.
Investigating the Basic Properties of Quadratic Relations
- Collecting and graphing quadratic data
- Recognizing a parabola from a table of second differences
- Identifying the key features of a parabola
- Comparing y = x² with y = 2ˣ and meaning zero and negative exponents
Relating the Graph of y = x² and Its Transformations
- Effect of a, h, and k on the graph of y = x²
- Roles of a, h, and k in vertex form
- Sketching y = a(x − h)² + k by hand
- Finding the vertex-form equation from a graph
Solving Quadratic Equations
- Expanding and simplifying second-degree polynomials
- Factoring common factors and simple trinomials
- Factoring complex trinomials (a ≠ 1)
- Factoring differences of squares
- Connecting factors of a quadratic to its x-intercepts
- Interpreting real and non-real roots
- Completing the square
- Sketching or graphing from standard form
- Exploring the algebraic development of the quadratic formula
- Solving quadratic equations by factoring
- Solving quadratic equations with the quadratic formula
Solving Problems Involving Quadratic Relations
- Finding the zeros and the maximum or minimum value
- Solving realistic problems with a quadratic graph or equation
Unit 2: Analytic Geometry
The slope-and-line toolkit bridging from Grade 9 (parallel/perpendicular slopes, the slope formula, line-equation forms), solving linear systems, and using coordinates to verify properties of line segments and geometric figures.
The Slope-and-Line Toolkit (2022 Addendum)
- Slopes of parallel and perpendicular lines
- Developing and using the slope formula
- Determining a line's equation from a graph, table, or two points
- Translating between forms of a line's equation
Solving Systems of Linear Equations
- Solving linear systems by substitution or elimination
- Solving realistic problems with linear systems
Solving Problems Involving Properties of Line Segments
- Developing and using the midpoint formula
- Developing and using the length-of-a-segment formula
- Developing the equation of a circle centred at the origin
- Finding a circle's radius, equation, and sketch
- Solving problems with slope, length, and midpoint together
Using Analytic Geometry to Verify Geometric Properties
- Investigating properties of geometric figures
- Verifying geometric properties using algebra and analytic geometry
- Planning a multi-step proof of a geometric property
Unit 3: Trigonometry
Similar triangles, the primary trigonometric ratios in right triangles, and the sine law and cosine law for solving acute triangles.
Solving Problems Involving the Trigonometry of Right Triangles
- Verifying properties of similar triangles
- Comparing similarity and congruence
- Solving real problems with similar triangles
Right-Triangle Trigonometry
- Defining the sine, cosine, and tangent ratios
- Finding sides and angles in right triangles
- Solving real-life right-triangle problems
Solving Problems Involving the Trigonometry of Acute Triangles
- Exploring the development of the sine law
- Exploring the development of the cosine law
- Using the sine law and cosine law to find sides and angles
- Solving real problems with acute triangles
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