MPM2D Foundation of Mathematics
MPM2D Unit 1: Linear Systems
Note: Linear Regression is not in the MPM2D Curriculum
1.1 Modelling Linear Equations
Website Video Clips with Solutions:
Pages 46 #
Plotting Points
Graphing from an equation to table of values
Calculating the slope review
Graphing a line using Slope and Y-int
Graphing a line using x and y-intercepts
Introduction to Linear Systems
Watch concept video and practice videos 1-2
Khan Academy Practice
Graphing Points Practice
1.2 and 1.3 Table of Values and
Graphing by Hand
Pages 56 #
Website Video Clips with Solutions:
1.4-1.6 Graphing Lines using
Technology
Website Video Clips with Solutions:
Using a table of Values
Applying a Table of Values example
Graphing from a table of values example 2
Solve by Graphing example 3
Go to topic “Algebra” then click on “Linear systems” then click on “Solve by Graphing”
Pages 74 #
Application problem example 1
Solving Linear systems through graphing example
Graphing to find a point of intersection
Additional Support Tools:
Graphing Software: Geogebra
Graphing software that you can use at home: select “Applet start”. From here, you
can enter equations and get the graph. You also have the choice to download the
software for free.
Graphing Calculator Emulator
Download the free graphing calculator software.
1.7 Solving Linear Systems using
technology
Pages 76 #
Website Video Clips with Solutions:
1.8 Solving Linear Systems by
Substitution
Website Video Clips with Solutions:
Solving Linear System application problem
Watch concept video and practice problem #3
Application Problem: Mixture of two different prices
Watch concept video and practice problem 1-2
Application Problem: Rate of change (price, travel)
Watch concept video and practice problem 1-2
Application Problem: Sum of digits
Watch concept video and practice problem 1-2
Application Problem: Age of two people
Watch concept video and practice problem 1-2
Pages 86 #
Solving by substitution example 1
Solving by substitution example 2
Solving by Substitution multiple examples
Go to topic “Algebra” then click on “Linear systems” then click on “Substitution”
Solving by Substitution examples
Watch concept video and practice problems 1-3
1.9 Solving Linear Systems by
Elimination
Website Video Clips with Solutions:
Pages 96 #
Solving by elimination example 1
Solving by elimination example 2
Solving by elimination example 3
Solving by Elimination multiple examples
Go to topic “Algebra” then click on “Linear systems” then click on “Addition Method”
Solving by Elimination examples
Watch concept video and practice problems 1-3
Khan Academy Exercises:
Solving Linear System Practice
Review
Pages 118 #
MPM2D Unit 2: Geometry
2.3 Distance on the Plane Part 1
Website Video Clips with Solutions:
Additional Support Tools:
Pages 149 #
Distance Formula examples
Watch concept video and practice problems 1-2
Review these videos for essential Knowledge
Line Segments
Defining a line, plane and point
Graphing Software: Geogebra
Graphing software that you can use at home: select “Applet start”. From here, you can enter
equations and get the graph. You also have the choice to download the software for free.
Graphing Calculator Emulator
Download the free graphing calculator software.
Khan Academy Exercises:
2.4 The equation of a Circle
Website Video Clips with Solutions:
Distance Formula Practice Problem
Pages 153 #
The equation of a Circle examples
Watch concept video and practice problems 1-3’
Introduction to circles
Only watch the first half of the video
2.5 Distance on the Plane Part 2
Pages 158 #
Website Video Clips with Solutions:
Distance Formula example
2.6-2.7 Finding the Mid-point of a
Line Segment
Pages 168 #
Website Video Clips with Solutions:
Khan Academy Exercises:
Midpoint Formula
Finding the midpoint of an algebraic line
Midpoint formula explained and examples
Watch concept video and practice problems 1-4
Midpoint Practice Problems
2.8 Classifying Shapes on a
Coordinate Plane
Website Video Clips with Solutions:
Pages 176#
Classifying Triangles Video examples
Go to topic “Geometry” then click on “Classification of Triangles”
Types of Triangles
Classifying Polygons
Watch concept video and practice problems 1-2
Khan Academy Exercises:
Geometry Practice #1
2.9-2.10 Using the Point of
Intersection to Solve Problems
Pages 194 #
Website Video Clips with Solutions:
See videos above
2.11 Verifying Geometric Properties
Pages 202#
Website Video Clips with Solutions:
Review
Finding the midpoint of an algebraic line
Distance Formula examples
Classifying Polygons
Watch concept video and practice problems 1-2
Pages 205 #
MPM2D Unit 3: Introduction to Quadratic Relations
3.1 Quadratic Relations
p. 254 #1, 2, 5, 6, 14, 16 Challenge: 18
Website Video Clips with Solutions:
Quadratic Functions
Click on “Quadratic Functions”- Classifying Relations: #8,9
Click on “Quadratic Functions” - Interpreting Quadratic Graphs: #10, 11
Khan Academy Exercises:
3.2 Properties of Quadratic
Relations
p. 267 #1, 2, 3, 4, 6, 7, 11 Challenger: 14
Website Video Clips with Solutions:
Quadratic Relations
Click on “Quadratic Relations” and watch examples 1 to 5: (Graphing Quadratic Functions,
Features of Parabolas, Interpreting parabolas 1, Interpreting parabolas 2, Interpreting
parabolas 3)
3.4 The Role of Zeros in a Quadratic
Relation
p. 280 #1, 2, 3, 5, 7, 9, 14, 19
Challenge: 22
Quadratic Functions
Click on “Quadratic Functions” - Solving by Factoring: #26-33 (Number and Type of
roots, Min/Max value, Sketching Quadratic relations)
Website Video Clips with Solutions:
3.7 Standard form of a Quadratic
Relation (Expanding)
Website Video Clips with Solutions:
p. 295 #1, 2, 3, 4, 5, 8, 10, 14
Challenge: 16
Quadratic Functions
Click on “Quadratic Functions” - Solving by Factoring: #26-33 (Number and Type of roots,
Min/Max value, Sketching Quadratic relations)
Adding and Subtracting Polynomials
Go to topic “Polynomials” and click on “Adding and Subtracting Polynomials”
Multiplying Polynomials
Go to topic “Polynomials” and click on “Multiplying Polynomials”
3.8 Factoring
Website Video Clips with Solutions:
Khan Academy Exercises:
p. 307 #2, 3, 4, 5, 6, 7, 11, 12
Challenge: 18
Quadratic Functions
Click on Quadratic Functions: Factoring: #13-19 (Common Factoring, Trinomials,
Differences of Squares)
Solving Quadratics by Factoring
Factoring Quadratic Expressions
Factoring Quadratics using the zero property
Go to topic “Quadratic” and click on “Factoring”
Solving Quadratics By Factoring
MPM2D Unit 4: Quadratic Relations Part 2
4.2 Vertex Form of a Quadratic
Relation
Website Video Clips with Solutions:
page 351 #1, 2, 3, 4, 5, 10, 11 Challenge: 21
Graphing in Vertex Form
Graphing quadratics in Vertex form video
Vertex to standard form
Click on “Quadratic Functions” – Quadratic Relations: J: 34 (Vertex to standard form)
Khan Academy Exercises:
4.3 Transformations of Quadratics
page 363 #1, 2, 3, 4, 6, 10 Challenge: 21 a, b, c
Website Video Clips with Solutions:
Types of Sketches and Transformations
Click on “Quadratic Functions” – Sketches and Transformations: M: 43 to 48 (Vertical
stretch, Compression, vertical translation, horizontal translation, combining translations)
4.4 Relating Vertex Form, Factored
Form, and Standard Form
Website Video Clips with Solutions:
page 377 #1, 2, 3, 6, 11
Challenge:22
Vertex to Standard Form
Click on “Quadratic Functions” – Completing the Square: N: 49 – Analyzing vertex/standard
form
Analyzing Vertex and Standard form
Click on “Quadratic Functions” – Quadratics Relations: J: 34 - Vertex to Standard form
4.5 Finding the Maximum and Minimum of
Quadratics using technology
Website Video Clips with Solutions:
page 383: practice #4.5 a-f
Using TI Graphing Calculator to find maximum and minimum values
Video shows step by step instructions to find the maximum and minimum
values using a TI calculator.
4.6 Completing the Square
page 390 #1, 2, 3, 4, 8, 12 Challenge: 17
Website Video Clips with Solutions:
Completing the Square Examples
Click on “Quadratic Functions”- watch Quadratics: M: 50 – 53:
Completing the Square Explanation
Completing the square example
Select topic “Algebra” then click on “quadratics” and then on “completing the square”
4.7 Solving Quadratics using the
Quadratic Formula
page 403 #1, 2, 4, 5, 6, 7, 12 (use geoalgebra)
Challenge: 31
Website Video Clips with Solutions:
Khan Academy Exercises:
Solving using the Quadratic Formula
Click on “Quadratic Functions”- watch Quadratics: K: 37-40 (examples of the quadratic
formula)
Proof of the Quadratic Formula
Quadratic Formula Example
Select topic “Algebra” then click on “quadratics” and then on “quadratic formula”
Quadratic Equation Exercise
MPM2D Unit 5: Trigonometry Part 1
5.2 Comparing Triangles
PAGE 460 #1, 3, 5, 7, 9
Website Video Clips with Solutions:
Similar Triangle Example problems
Click on topic “Geometry” – Similar Figures and Proportions – Examples #1 to 5
Khan Academy Exercises:
Practice finding angles
5.4 Modeling with Similar Triangles
PAGE 474 #2, 5, 6, 7, 8, 12
Website Video Clips with Solutions:
Similar Triangle example
Click on topic “Similar Triangles” – watch and work through examples #1 to 5
Khan Academy Exercises:
Pythagorean Theorem video
Pythagoras theorem practice
Review the Pythagoras theorem by watching the video
Practice your Pythagoras theorem skills
5.6 Slope and Angle
PAGE 485 #1, 2, 3, 13, 18
Website Video Clips with Solutions:
5.7 The Primary Trigonometric
Ratios
Website Video Clips with Solutions:
PAGE 496 #1-9, 14, 27
Challenge: 33
Problem Solving Questions
Click on topic “Trig Functions” – Solving Triangles A: 1 to 3 – watch and work through the
examples
Introduction to Trigonometry
Watch and work through the examples on the video
5.8 Problem Solving with
Trigonometry
Website Video Clips with Solutions:
PAGE 509 #1, 3, 5, 17, 19
Challenge: 20
Trigonometry Problems
Click on topic “Trigonometry” – Examples watch and work through the application examples
#68 and #71
Trigonometry Word Problems with solutions
Work through the questions and check your answers
MPM2D Unit 6: Trigonometry Part 2
6.2 Similar Triangles
Website Video Clips with Solutions:
Khan Academy Exercises:
6.3 Sine Law
Website Video Clips with Solutions:
Page 538
#1, 2, 3, 7, 11, 13
Similar Triangle Example problems
Click on topic “Geometry” – Similar Figures and Proportions – Examples #1 to 5
Similar Triangle example 2
Click on topic “Similar Triangles” – watch and work through examples #1 to 5
Similar Triangle Example 3
Watch the video and work through the examples
Practice finding angles
Page 549 #1, 2, 3, 4, 12
Challenge: 21
Sine Law examples
Click on topic “Trig Functions” – Sine Law B: 4 to 7 – watch and work through the examples
Sine Law example 2
Click on topic “Trigonometry” then click on “Triangles” - Law of Sines examples #1-2
6.4 Proving and Using Sine Law
Page 555 #1, 2, 3, 4, 9, 10
Website Video Clips with Solutions:
Sine Law Proof
6.6 Cosine Law
Page 567 #2, 4, 8, 10
Challenge: #25
Cosine Law Examples
Click on topic “Trig Functions” – Cosine Law C: 8 to 10 – watch and work through the
examples
Website Video Clips with Solutions:
Cosine Law example 2
Click on topic “Trigonometry” then click on “Triangles” - Law of Cosine example #1
6.7 Solving Measurement Problems
modelled by triangles
Website Video Clips with Solutions:
Khan Academy Exercises:
Page 574 #3, 4, 9, 16, 17
Challenge: #20
Problem Solving Questions
Click on topic “Trig Functions” – Solving Triangles A: 1 to 3 – watch and work through the
examples
Trigonometry Practice
Practice your trigonometric skills on Khan academy