Getting Ready for Grade 10 Math

Eight tutor-led lessons that turn Grade 9's linear relations into the slope, distance, and system-solving skills Grade 10 academic math assumes.

Who it's for: Students finishing Grade 9 destreamed math (MTH1W) and heading into Grade 10 academic (MPM2D) in September, in small tutor-led groups of four, opening MPM2D already fluent. Drills radicals, binomials, and equation-solving, then previews distance, midpoint, line equations, and linear systems.

✓ Simplifies square-root radicals to exact simplest form by pulling out the largest perfect-square factor, and applies the Pythagorean theorem exactly.✓ Expands and multiplies binomials fluently by the distributive method, including perfect-square and difference-of-squares patterns, and rearranges any formula.✓ Calculates the exact length and midpoint of a segment from two coordinates, computes slope from two points instantly, and writes a line's equation in any form.✓ Recognizes parallel lines from equal slopes and perpendicular lines from negative reciprocal slopes, and writes a line's equation through a given point.✓ Solves a system of two linear equations by substitution and elimination, sets one up from a word problem, and checks every solution in both original equations.

The 8-lesson plan

Slides are what your tutor works from in the live lesson. The practice module is homework: do it before the next lesson.

1

Exact Answers: Simplifying Radicals and the Pythagorean Theorem

Move from Grade 9's decimal estimate of a square root to the exact simplified radical MPM2D expects, then apply the Pythagorean theorem with exact radical answers.

Slides Practice module
2

Expanding and Multiplying Polynomials: FOIL, Perfect Squares, and Difference of Squares

Push binomial multiplication from MTH1W's introduced skill to instant fluency, adding the perfect-square and difference-of-squares patterns MPM2D uses constantly.

Slides Practice module
3

Equation Fluency and Rearranging Formulas: Isolating Any Variable

Push multi-step equation-solving to automatic fluency and rearrange formulas with several variables - especially Ax + By + C = 0 - to isolate any given variable.

Slides Practice module
4

Slope, Parallel Lines, and Perpendicular Lines

Consolidate slope from two points using the formal slope formula, then learn the parallel and perpendicular slope relationship MPM2D's opening unit assumes.

Slides Practice module
5

The Distance Formula and the Midpoint Formula

Derive the distance formula from the Pythagorean theorem with exact radical answers, then find the midpoint of a segment - MPM2D's first two analytic geometry skills.

Slides Practice module
6

Writing the Equation of a Line: Point-Slope Form and Converting Between Forms

Write the equation of a line from a slope and a point, or from two bare points, using point-slope form, then convert fluently to slope-intercept and standard form.

Slides Practice module
7

Solving Systems of Linear Equations: Substitution and Elimination

Solve a system of two linear equations using substitution when a variable is easy to isolate, and elimination when it is not, verifying each solution in both equations.

Slides Practice module
8

Applications of Linear Systems and the Analytic Geometry Toolkit

Set up and solve a system of equations from a real word problem, then combine slope, distance, and midpoint into a shape-verification capstone problem.

Slides Practice module
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