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Grade 10 Academic Math (MPM2D) - Principles of Mathematics
1.1 - Graphing Lines and Translating English to Mathematics
PDF for Questions Below
1) Create Algebraic Expression from Phrase (video)
2) Create Algebraic Equation from Phrase (video)
3) Find Point of Intersection by Graphing Example 1 (video)
4) Find Point of Intersection by Graphing Example 2 (video)
5) Find Point of Intersection by Graphing Example 3 (video)
6) Comparing Costs of Two Companies Word Problem (video)
7) Comparing Two Earnings Systems Word Problem (video)
8) Comparing Two Investment Rates Word Problem (video)
1.2 - Solving Linear Systems with Substitution
PDF for Questions Below
1) Substitution Example 1 (video)
2) Substitution Example 2 (video)
3) Substitution Example 3 (video)
4) Substitution Example 4 (video)
5) Substitution Example 5 (video)
6) Substitution Example with Fractions 1 (video)
7) Substitution Example with Fractions 2 (video)
8) Substitution Word Problem 1 (video)
9) Substitution Word Problem 2 (video)
10) Substitution Word Problem 3 (video)
11) Substitution Word Problem 4 (video)
12) Substitution Word Problem 5 (video)
13) Find Constant if 3 Lines Intersecting at Same Point (video)
14) Solve for 3 Variables with Substitution 1 (video)
15) Solve for 3 Variables with Substitution 2 (video)
1.3 - Equivalent Linear Relations and Systems
PDF for Questions Below
1) Which of These Lines are Equivalent? (video)
2) Find a Constant to Make Lines Equivalent 1 (video)
3) Find a Constant to Make Lines Equivalent 2 (video)
4) Create a Linear System given Solution (video)
1.4 - Solving Linear Systems by Elimination
PDF for Questions Below
1) Elimination Example 1 (video)
2) Elimination Example 2 (video)
3) Elimination Example 3 (video)
4) Elimination Example 4 (video)
5) Elimination Example 5 (video)
6) Infinite vs No Solutions with Elimination (video)
7) Linear System Word Problem with Elimination 1 (video)
8) Linear System Word Problem with Elimination 2 (video)
9) Linear System Word Problem with Elimination 3 (video)
10) Linear System with Elimination + Extra Algebra (video)
11) Linear System with Elimination + Decimals (video)
12) Linear System with Elimination + Fractions 1 (video)
13) Linear System with Elimination + Fractions 2 (video)
14) Linear System with Elimination + No Numbers (video)
15) Solve for 3 Variables with Elimination (video)
1.5 - Solving Linear System Word Problems
PDF of Questions Below
Linear Systems Word Problem 1 (video)
Linear Systems Word Problem 2 (video)
Linear Systems Word Problem 3 (video)
Linear Systems Word Problem 4 (video)
Linear Systems Word Problem 5 (video)
Linear Systems Word Problem 6 (video)
Linear Systems Word Problem 7 (video)
Linear Systems Word Problem 8 (video)
Linear Systems Word Problem 9 (video)
Linear Systems Word Problem 10 (video)
Linear Systems Word Problem 11 (video)
Linear Systems Word Problem 12 (video)
Linear Systems Word Problem 13 (video)
Linear Systems Word Problem 14 (video)
Linear Systems Word Problem 15 (video)
Linear Systems Word Problem 16 (video)
Linear Systems Word Problem 17 (video)
Linear Systems Word Problem 18 (video)
Linear Systems Word Problem 19 (video)
Linear Systems Word Problem 20 (video)
Linear Systems Word Problem 21 (video)
Linear Systems Word Problem 22 (video)
Linear Systems Word Problem 23 (video)
Linear Systems Word Problem 24 (video)
2.1 - Midpoint of a Line Segment
PDF of Questions Below
1) Midpoint of a Line Segment Overview (video)
2) Find Equation of Median (video)
3) Find Other Endpoint given Endpoint & Midpoint (video)
4) Find Right/Perpendicular Bisector of a Line (video)
5) Find Median and Right Bisector on Same Triangle (video)
6) Find Diameter Point(s) given Points of Radius (video)
7) Dividing a Line Segment into 3 Equal Parts (video)
8) Tricky Thinking Problem Dealing with Midpoint (video)
9) Multiple Midpoints In A Line Segment (video)
10) Find Missing Coordinates using Midpoint (video)
2.2 - Length of a Line Segment
PDF of Questions Below
1) Length of a Line Segment Calculation (video)
2) Length of Radius in Circle (video)
3) Finding Missing Coordinate giving Length of Line Segment (video)
4) Show a Triangle is Isosceles with Length of Line Formula (video)
5) Show a Triangle is Equilateral with Length of Line Formula (video)
6) Find Two Other Coordinates on Equilateral Triangle (video)
7) Find Length of Median in Triangle (video)
8) Determine Area of Right Triangle (video)
9) Verify Midpoint of a Line Segment with Length Formula (video)
10) Triangle Midpoint Theorem (video)
11) List Coordinates that Are Certain Length from Other Point (video)
2.3 - Slope vs Midpoint vs Length of Line Segments
PDF of Questions Below
1) Verify a Right Triangle (video)
2) Verify a Point Lies on Right/Perpendicular Bisector (video)
3) Verify a Quadrilateral is a Parallelogram (video)
4) Find the 4th Point of a Parallelogram (video)
5) Shortest Distance of Point to Line Overview + Example 1 (video)
6) Shortest Distance of Point to Line Example 2 (video)
7) Shortest Distance of Point to Line Example 3 (video)
8) Shortest Distance of Point to Line Example 4 (video)
9) Find Equation of an Altitude (video)
10) Find the Area of a Triangle using Altitude (video)
2.4 - Circles
PDF of Questions Below
1) State the Radius of a Circle and Provide Coordinate (video)
2) Find Equation of Circle given Coordinate (video)
3) Find Whether Point Lies Within, On our Outside of Circle (video)
4) Find Equation of Circle given Endpoints of Diameter (video)
5) Perpendicular Bisector of Chord Example 1 (video)
6) Perpendicular Bisector of Chord Example 2 (video)
7) Perpendicular Bisector of Chord Example 3 (video)
8) Stone Drops in Water Word Problem (video)
9) Draw Regions Within, Outside, In Between Circles (video)
10) Tricky Problem Dealing with Circles (video)
11) Find Area of Region Bounded by Lines and Circle (video)
12) Find Equation of Circle Centred Other than Origin (video)
13) Finding the Circumcentre of a Circle (video)
3.1 and 3.2 Investigate and Verify Properties of Triangles
PDF of Questions Below
1) Median Bisects a Triangle's Area (Video)
2) Median and Altitude Coincide in an Isosceles Triangle (video)
3) Centroid vs Circumcentre vs Orthocentre (video)
4) Distance from Midpoint of Hypotenuse to 3 Vertices (video)
5) Centroid Splits Median into 2:1 Ratio (video)
6) Find Unknown Angles in Isosceles Triangle (video)
7) Three Cases of Circumcentre of Triangle (video)
8) Verify Circumcentre Lies on Hypotenuse of Right Triangle (video)
9) Pythagorean Inequality - Tool to Classify Triangles (video)
10) Classifying Triangles Example 1 (video)
11) Classifying Triangles Example 2 (video)
12) Classifying Triangles Example 3 (video)
13) Verifying Triangle and Medial Triangle are Similar (video)
14) Triangle Midpoint Theorem with No Numbers (video)
15) Circumcentre of Triangle = Orthocentre of Medial Triangle (video)
16) Centroid of Triangle vs Centroid of Medial Triangle (video)
3.3 - Investigate Properties of a Quadrilateral
PDF of Questions Below
1) The Diagonals of a Parallelogram (video)
2) The Midpoints of Any Quadrilateral Forms a Parallelogram (video)
3) Trapezoid Midsegment Theorem Overview (video)
4) Trapezoid Midsegment Theorem Example 1 (video)
5) Trapezoid Midsegment Theorem Example 2 (video)
6) Trapezoid Midsegment Theorem Example 3 (video)
3.4 - Verify Properties of Quadrilateral
PDF of Questions Below
1) Verify a Quadrilateral is a Trapezoid (video)
2) Verify a Quadrilateral is a Rhombus (video)
3) Verify a Quadrilateral is a Kite + One Diagonal Bisects (video)
4) Verify a Rectangle + Diagonals Bisect (video)
5) Verify a Quadrilateral is a Square + Diagonals Bisect at Right Angles (video)
6) Midpoints of a Quadrilateral Example 1 (video)
7) Midpoints of a Quadrilateral Example 2 (video)
3.5 - Properties of Circles
PDF of Questions Below
1) Dealing with Diameters + Thale's Theorem (video)
2) Verify Points Lie on a Circle Example 1 (video)
3) Verify Points Lie on a Circle Example 2 (video)
4) Verify Right Bisectors of Chords Pass Through Centre of Circle (video)
5) Find The Equation of a Circle given 3 Points (video)
4.1 - Non Linear Relationships
PDF of Questions Below
1) Drawing Curve of Best Fit from Table of Values (video)
2) Length vs Width vs Area Quadratic Word Problem (video)
4.2 - Quadratic Relations
PDF of Questions Below
1) Quadratic Modelling Problem 1 (video)
2) Quadratic Modelling Problem 2 (video)
3) Quadratic Modelling Problem 3 (video)
4) Use Finite Differences to Figure out Linear vs Quadratic (video)
5) Find Quadratic Relation given Table of Values (video)
6) Deriving Sum of Natural Numbers Formula (video)
4.3 - Transformations of Quadratics
PDF of Questions Below
1) Transformations of Quadratics Overview (video)
2) Vertical Stretch/Compression of Quadratics (video)
3) Horizontal Translation of Quadratics (video)
4) Vertical Translation of Quadratics (video)
5) Describe Transformations given Quadratic (video)
6) Write an Equation for Quadratic given Transformations (video)
7) Word Problem with Quadratic Transformations (video)
8) Create a Transformed Quadratic from Visual Pattern (video)
9) Describe Transformations on Unique Form Quadratics (video)
10) Find Constants given Points on Quadratic (video)
11) Comparing Transformed Quadratics (video)
4.4 - Graphing Vertex Form Quadratics
PDF of Questions Below
1) Vertex Form Overview (video)
2) Find Characteristics of Parabola and Sketch (video)
3) Write an Equation for Quadratic given Vertex and Direction (video)
4) Write Equation of Parabola given Graph 1 (video)
5) Write Equation of Parabola given Graph 2 (video)
6) Write Equation of Parabola given Graph 3 (video)
7) Find Equation of Parabola given Transformations (video)
8) Find Equation of Parabola given Vertex and Coordinate (video)
9) Vertex Form Word Problem 1 (video)
10) Vertex Form Word Problem 2 (video)
11) Vertex Form Word Problem 3 (video)
12) Transformations given on Transformed Quadratic (video)
4.5 - Factored Form of Quadratic Relations
PDF of Questions Below
1) Factored Form of Quadratics Overview (video)
2) Sketch a Factored Form Quadratic 1 (video)
3) Sketch a Factored Form Quadratic 2 (video)
4) Sketch a Factored Form Quadratic 3 (video)
5) Find the Equation of a Sketched Parabola (video)
6) Factored Form Word Problem 1 (video)
7) Factored Form Word Problem 2 (video)
8) Factored Form Word Problem 3 (video)
9) Factored Form & Distance of Line Problem (video)
4.6 - Negative and Zero Exponents
PDF of Questions Below
1) Rewrite Expressions with Positive Exponents (video)
2) Evaluate Expressions with Negative Exponents (video)
3) Solve Equations with Negative Exponents (video)
4) Negative Exponents Word Problem 1 (video)
5) Negative Exponents Word Problem 2 (video)
6) Negative Exponents Word Problem 3 (video)
5.1 - Multiplying Polynomials
PDF of Questions Below
1) Grade 9 Review - Algebraic Tiles 1 (video)
2) Grade 9 Review - Algebraic Tiles 2 (video)
3) Model Product using Algebraic Tiles (video)
4) Expand and Simplify Expressions Part 1 (video)
5) Expand and Simplify Expressions Part 2 (video)
6) Expand and Simplify Expressions Part 3 (video)
7) Expand and Simplify + Verify (video)
8) Multiply Polynomials Word Problem 1 (video)
9) Multiply Polynomials Word Problem 2 (video)
10) Multiply Polynomials Word Problem 3 (video)
11) Multiply Polynomials Word Problem 4 (video)
12) Multiply Polynomials Word Problem 5 (video)
13) Multiply Polynomials Word Problem 6 (video)
14) Multiply Polynomials Word Problem 7 (video)
15) Multiply Polynomials Word Problem 8 (video)
5.2 - Special Products
PDF of Questions Below
1) Special Products with Diagrams (video)
2) Expand and Simplify Special Products 1 (video)
3) Expand and Simplify Special Products 2 (video)
4) Special Products Word Problem 1 (video)
5) Special Products Word Problem 2 (video)
6) Special Products Word Problem 3 (video)
7) Special Products Word Problem 4 (video)
8) Special Products Word Problem 5 (video)
9) Special Products Word Problem 6 (video)
10) Extra Cases for Special Products (video)
5.3 - Greatest Common Factors
1) Factoring Overview (video)
2) Find the Greatest Common Factor (video)
3) Factoring by GCF Part 1 (video)
4) Factoring by GCF Part 2 (video)
5) Binomial Common Factors (video)
6) Factoring by Grouping (video)
7) Write Initial Expression given GCF (video)
8) Factoring Surface Area Formulas (video)
9) Find Possibilities for Length and Width (video)
10) Binomial Common Factors with Extra Algebra (video)
11) Find Factored Expression for Diagram Patterns (video)
12) Find Factored Expression for Shaded Regions (video)
13) Find x-intercepts of Quadratic by Factoring (video)
14) Greatest Common Factor with Fractions (video)
15) Equating Expressions with GCF (video)
16) Show Sum of 4 Consecutive Integers is Even (video)
5.4 - Factoring Quadratics (a = 1)
1) Factoring by Decomposition Overview (video)
2) Factoring Quadratics Part 1 (video)
3) Factoring Quadratics Part 2 (video)
4) Factoring Quadratics Part 3 (video)
5) Factor Area of Rectangle Problem (video)
6) Greatest Common Factor + Decomposition (video)
7) Find Value(s) of b so that Quadratic can Factor (video)
8) Find Value(s) of c so that Quadratic can Factor (video)
9) Multi-Variable Factoring with Decomposition (video)
10) Graphing Quadratic with Characteristics (video)
11) A Ball Thrown off Roof Word Problem (video)
12) Factoring by Decomposition with Higher Exponents (video)
5.5 - Factoring Quadratics (a doesn't equal 1)
Factoring by Decomposition with a Not Equal to 1 (video)
Factoring by Decomposition Practice 1 (video)
Factoring by Decomposition Practice 2 (video)
Factoring by Decomposition Practice 3 (video)
Multi-Variable Factoring (video)
Factoring + Greatest Common Factor (video)
Find Constants so Trinomials can be Factored 1 (video)
Find Constants so Trinomials can be Factored 2 (video)
Why Is It Easy to Factor if A and C are Prime Numbers (video)
Factoring Rectangle Area (video)
A Ball Thrown off Roof Word Problem (video)
Factoring with Higher Degrees (video)
Factoring with Fraction Coefficients (video)
Special Cases of Factoring (video)
Factoring + Area of Certain Shape (video)
Factoring the Volume of a Solid (video)
5.6 - Factoring Difference of Squares & Perfect Square Trinomials
1) Difference of Squares Overview (video)
2) Difference of Squares Practice 1 (video)
3) Difference of Squares Practice 2 (video)
4) Perfect Square Trinomial Overview (video)
5) Verify and Factor Perfect Square Trinomials 1 (video)
6) Verify and Factor Perfect Square Trinomials 2 (video)
7) Why Trinomial isn't a Perfect Square or Diff of Squares (video)
8) Multi-Variable Diff of Squares & Perfect Squares (video)
9) Special Case Factoring 1 (video)
10) Special Case Factoring 2 (video)
11) Find Area of Shaded Region (video)
12) Find Constants so Trinomial is a Perfect Square (video)
13) Factoring the Area of Square (video)
14) Factoring the Volume of Cylinder (video)
15) Finding Change in Cylinder with Factoring (video)
16) Find a Pattern in Factored Form (video)
17) Find Values of Expressions (video)
18) Factoring a Rectangular Prism Volume (video)
6.1 - Maxima vs Minima
PDF of Questions Below
1) Completing the Square Overview (video)
2) Completing the Square Practice 1 (video)
3) Completing the Square Practice 2 (video)
4) Completing the Square with Fractions and Decimals (video)
5) Finding the Max Height of a Soccer Ball Kicked (video)
6) Max Revenue vs Profit Word Problem (video)
7) Finding Depth of Half Pipe Word Problem (video)
8) Finding Constants in Vertex vs Standard Form (video)
9) Finding Max Area of Rectangle Made from String (video)
10) Determine Max Area of Triangle (video)
11) Find Dimensions of Fencing that Maximize Area (video)
12) Find the Vertex of Parabola given 3 Coordinates (video)
13) Finding Coordinates of Vertex in terms of a,b, and c (video)
6.2 - Solve Quadratic Equations
PDF of Questions Below
1) Quadratic Equations Overview (video)
2) Solve Quadratic Equations Practice 1 (video)
3) Solve Quadratic Equations Practice 2 (video)
4) Solve Quadratic Equations Practice 3 (video)
5) A Ball Thrown Off Roof Word Problem (video)
6) Find Dimensions of Rectangle given Area (video)
7) Quadratic Equations with Fractions vs Decimals (video)
8) Write a Quadratic Equations given Roots (video)
9) Finding Dimensions of Right Triangles Problem (video)
10) Formula of First n Even Natural Numbers (video)
11) Finding Product Price given Specific Revenue (video)
12) Find Dimensions of Rectangular Prism (video)
13) Find Perimeter of Rectangle given Length, Width and Diagonals (video)
14) Profit of Store Word Problem (video)
15) Solve Multi-Variable Quadratic Equations (video)
6.3 - Graph Quadratics using X-Intercepts
1) Graph Quadratics using X Intercepts Part 1 (video)
2) Graph Quadratics using X Intercepts Part 2 (video)
3) Find Equation of Quadratic given Graph Part 1 (video)
4) Find Equation of Quadratic given Graph Part 2 (video)
5) Find Equation of Quadratic given Graph Part 3 (video)
6) Cross Section of a Tunnel Word Problem (video)
7) Ball Thrown off Roof Quadratic Word Problem (video)
8) Parabolic Tunnel Quadratic Word Problem (video)
9) Finding Characteristics of Quadratic given Other Characteristics (video)
10) Goalie kicks Soccer Ball Quadratic Word Problem (video)
11) Create Examples of Quadratics Given # Of Intercepts (video)
12) Find Coefficients if Quadratic has One Zero (video)
13) Compare Number of Intercepts Between Different Quadratics (video)
14) Find Coefficient and Intercept of Quadratic (video)
6.4 - The Quadratic Formula
1) Quadratic Formula Overview (video)
2) Solve Quadratic Equations with Quadratic Formula 1 (video)
3) Solve Quadratic Equations with Quadratic Formula 2 (video)
4) Find X-Intercepts of Quadratic and Sketch (video)
5) Verify Number of X-Intercepts with Quadratic Formula (video)
6) Create Quadratics given Characteristics (video)
7) Cross Section of a Tunnel Problem with Quadratic Formula (video)
8) Half Pipe Quadratic Word Problem with Quadratic Formula (video)
9) Ball Thrown Off Roof with Quadratic Formula (video)
10) Find a Quadratic Equation given Exact Value Roots (video)
11) Solve for Width of Deck Word Problem (video)
12) Find Point(s) of Intersection with Circle and Quadratic (video)
13) Show Roots are Negative Reciprocals of Eachother (video)
14) Find Roots of Unique Formatted Equation (video)
6.5 - Solve Word Problems with Quadratic Equations
1) Projectile Quadratic Problem (video)
2) Find Dimensions of Rectangle (video)
3) Solving for Integers Part 1 (video)
4) Solving for Integers Part 2 (video)
5) Solving for Integers Part 3 (video)
6) Solving for Integers Part 4 (video)
7) Solve for Triangle Part 1 (video)
8) Solve for Triangle Part 2 (video)
9) Solve for Triangle Part 3 (video)
10) Solve for Triangle Part 4 (video)
11) Ladder Word Problem (video)
12) Revenue and Profit Word Problem (video)
13) Picture with Uniform Width Problem (video)
14) Find Uniform Deck Width of Pool (video)
15) Open Top Box Word Problem Part 1 (video)
16) Open Top Box Word Problem Part 2 (video)
17) Find Point of Intersection between Parabolas (video)
18) Ball Thrown off Roof Problem (video)
7.2 - Solving Problems with Similar Triangles
1) Find Scale Factor of Similar Triangles (video)
2) Solve for Unknown Sides of Similar Triangles Part 1 (video)
3) Solve for Unknown Sides of Similar Triangles Part 2 (video)
4) Solve for Unknown Sides of Similar Triangles Part 3 (video)
5) Solve for Unknown Sides of Similar Triangles Part 4 (video)
6) Solve for Unknown Sides of Similar Triangles Part 5 (video)
7) Area of Similar Triangles Problem Part 1 (video)
8) Area of Similar Triangles Problem Part 2 (video)
9) Area of Similar Triangles Problem Part 3 (video)
10) Similar Triangles Word Problem Part 1 (video)
11) Similar Triangles Word Problem Part 2 (video)
12) Similar Triangles Word Problem Part 3 (video)
7.3 and 7.4 - The Sin, Cos and Tan Ratios
1) Find the 3 Primary Trig Ratios (video)
2) Find the Length using Trig Ratios (video)
3) Solve for Variable using Trig Ratios Part 1 (video)
4) Solve for Variable using Trig Ratios Part 2 (video)
5) Trig Ratios Word Problem 1 (video)
6) Trig Ratios Word Problem 2 (video)
7) Trig Ratios Word Problem 3 (video)
8) Trig Ratios Word Problem 4 (video)
9) Trig Ratios Word Problem 5 (video)
10) Trig Ratios Word Problem 6 (video)
7.5 - Right Triangle Word Problems
1) Right Triangle Word Problem 1 (video)
2) Right Triangle Word Problem 2 (video)
3) Right Triangle Word Problem 3 (video)
4) Right Triangle Word Problem 4 (video)
5) Right Triangle Word Problem 5 (video)
6) Right Triangle Word Problem 6 (video)
7) Right Triangle Word Problem 7 (video)
8) Right Triangle Word Problem 8 (video)
9) Right Triangle Word Problem 9 (video)
10) Right Triangle Word Problem 10 (video)
11) Right Triangle Word Problem 11 (video)
12) Right Triangle Word Problem 12 (video)
13) Right Triangle Word Problem 13 (video)
8.1 - The Sine Law
1) Solve for Sides using Sine Law (video)
2) Solve for Angle using Sine Law (video)
3) Sine Law Word Problem 1 (video)
4) Sine Law Word Problem 2 (video)
5) Sine Law Word Problem 3 (video)
8.2 - The Cosine Law
1) Solve for Side using Cosine Law (video)
2) Solve for Triangle using Cosine Law Part 1 (video)
3) Solve for Triangle using Cosine Law Part 2 (video)
4) Solve for Triangle using Cosine Law Part 3 (video)
5) Word Problem using Cosine Law (video)
8.3 - Find Angles with Cosine Law
1) Find Angle with Cosine Law (video)
2) Solve Triangle with Cosine Law (video)
3) Cosine Law Word Problem 1 (video)
4) Cosine Law Word Problem 2 (video)
8.4 - Word Problems with Triangles
1) Acute Triangles Word Problem 1 (video)
2) Acute Triangles Word Problem 2 (video)
3) Acute Triangles Word Problem 3 (video)
4) Acute Triangles Word Problem 4 (video)
5) Acute Triangles Word Problem 5 (video)
6) Acute Triangles Word Problem 6 (video)
7) Acute Triangles Word Problem 7 (video)
8) Acute Triangles Word Problem 8 (video)
7) Substitution Example with Fractions 2 (video)
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