Grade 10 Principles of Mathematics

Ontario High School

Course Overview

Lessons & Practice

I. Welcome

1. Review: Linear Relations

1.4hr

1.1.1. Relations5 min

1.1.2. Linear Relations6 min

1.1.3. Example8 min

1.1.4. Practice Level 14 min

1.1.5. Practice Level 27 min

1.2.1. Linear Equations4 min

1.2.2. Practice Level 113 min

1.2.3. Practice Level 27 min

1.2.4. Parallel & Perpendicular Lines7 min

1.2.5. Practice Level 35 min

1.3.1. Graphing Linear Equations - Table of Values3 min

1.3.2. Graphing Linear Equations - Slope y-Intercept Form5 min

1.3.3. Graphing Linear Equations - Using Intercepts4 min

1.3.4. Practice4 min

2. Systems of Linear Equations

2hr

2.1.1. Intro to Systems of Linear Equations (Simultaneous Equations)3 min

2.2.1. Solving Graphically7 min

2.2.2. Example2 min

2.2.3. Practice Level 12 min

2.2.4. Practice Level 22 min

2.2.5. Practice Level 22 min

2.3.1. Solving by Substitution12 min

2.3.2. Example5 min

2.3.3. Practice Level 12 min

2.3.4. Practice Level 25 min

2.3.5. Practice Level 37 min

2.4.1. Solving by Simple Elimination12 min

2.4.2. Example3 min

2.4.3. Practice Level 13 min

2.4.4. Practice Level 22 min

2.4.5. Practice Level 24 min

2.5.1. Solving by Multiplication before Elimination8 min

2.5.2. Example4 min

2.5.3. Example4 min

2.5.4. Practice Level 14 min

2.5.5. Practice Level 24 min

2.5.6. Practice5 min

2.6.1. No Solution or Many Solutions5 min

2.6.2. Example 1 7 min

2.6.3. Example 2 4 min

2.6.4. Practice4 min

3. Analytic Geometry

1.1hr

3.1.1. Pythagorean Theorem5 min

3.1.2. Example5 min

3.1.3. Practice6 min

3.2.1. Midpoint of a Line Segment2 min

3.2.2. Example2 min

3.2.3. Practice Level 12 min

3.2.4. Practice Level 24 min

3.2.5. Practice Level 37 min

3.3.1. Length of a Line Segment2 min

3.3.2. Example3 min

3.3.3. Practice Level 12 min

3.3.4. Practice Level 39 min

3.3.5. Practice Level 23 min

3.4.1. Equation of a Circle around the Centre (Origin)2 min

3.4.2. Example3 min

3.4.3. Practice Level 13 min

3.4.4. Practice Level 23 min

4. Analytic Geometry: Geometric Properties

2.3hr

4.1.1. Classifying Triangles3 min

4.1.2. Practice Level 13 min

4.1.3. Example7 min

4.1.4. Practice Level 26 min

4.1.5. Practice Level 37 min

4.2.1. Line Segments & Centers of Triangles8 min

4.2.2. Example9 min

4.2.3. Practice Level 210 min

4.2.4. Practice Level 310 min

4.3.1. Classifying Quadrilaterals 4 min

4.3.2. Practice Level 14 min

4.3.3. Example5 min

4.3.4. Practice Level 28 min

4.3.5. Practice Level 37 min

4.4.1. Example11 min

4.4.2. Practice Level 28 min

4.4.3. Practice Level 39 min

4.5.1. Example11 min

4.5.2. Practice Level 39 min

5. Expanding Polynomials

1.1hr

5.1.1. Terminology Review5 min

5.1.2. Practice

5.1.3. Practice2 min

5.1.4. Multiplying by a Monomial7 min

5.1.5. Example3 min

5.2.1. Binomial

\times

5.2.2. Using Algebra Tiles3 min

5.2.3. Example7 min

5.2.4. Practice Level 15 min

5.2.5. Practice Level 29 min

5.2.6. Practice Level 38 min

5.3.1. Binomial

\times

5.3.2. Example3 min

5.3.3. Practice Level 13 min

5.3.4. Practice Level 1

5.3.5. Practice Level 2

5.3.6. Practice Level 3

6. Quadratic Relations

1.6hr

6.1.1. Quadratic Relations13 min

6.1.2. Example7 min

6.1.3. Practice Level 15 min

6.1.4. Practice Level 25 min

6.1.5. Practice Level 37 min

6.2.1. Properties of Quadratic Graphs5 min

6.2.2. Example9 min

6.2.3. Practice Level 13 min

6.2.4. Practice Level 13 min

6.2.5. Practice Level 23 min

6.2.6. Practice Level 37 min

6.2.7. Practice Level 38 min

6.3.1. Review: Exponent Rules (Laws of Exponents)2 min

6.3.2. Quadratic VS Exponential Graphs9 min

6.3.3. Practice Level 11 min

6.3.4. Practice Level 14 min

6.3.5. Practice Level 23 min

7. Factored Form of a Quadratic Equation

1.2hr

7.1.1. Factored Form of a Quadratic Equation9 min

7.1.2. Example8 min

7.1.3. Practice Level 14 min

7.1.4. Practice Level 27 min

7.1.5. Practice Level 35 min

7.1.6. Summary - Factored Form of a Quadratic Equation

7.2.1. Example7 min

7.2.2. Practice Level 16 min

7.2.3. Example5 min

7.2.4. Practice Level 211 min

7.2.5. Practice Level 34 min

7.2.6. Practice Level 3 🔥3 min

8. Factoring Polynomials

3hr

8.1.1. What is Factoring?3 min

8.2.1. Warm Up6 min

8.2.2. Common Factoring9 min

8.2.3. Practice Level 13 min

8.2.4. Example11 min

8.2.5. Practice Level 26 min

8.2.6. Example (Grouping)6 min

8.2.7. Practice Level 33 min

8.2.8. Practice Level 25 min

8.2.9. Extra Common Factoring Drills 💪

8.3.1. Factoring Simple Trinomials

y=x^2+bx+c

8.3.2. Practice Level 16 min

8.3.3. Example11 min

8.3.4. Practice Level 25 min

8.3.5. Practice Level 37 min

8.3.6. Practice Level 35 min

8.3.7. Extra Simple Trinomial Factoring Drills 💪

8.4.1. Factoring Harder Trinomials

y=ax^2+bx+c

8.4.2. Example5 min

8.4.3. Practice Level 14 min

8.4.4. Practice Level 22 min

8.4.5. Decompose Strategy (Easier but Longer Method❗)5 min

8.4.6. Practice Level 34 min

8.4.7. Practice Level 38 min

8.4.8. Extra Trinomial Factoring Drills 💪

8.5.1. Factoring a Difference of Squares3 min

8.5.2. Example2 min

8.5.3. Practice Level 11 min

8.5.4. Practice Level 22 min

8.5.5. Practice Level 34 min

8.5.6. Extra Difference of Squares Drills 💪

8.6.1. Factoring Perfect Square Trinomials4 min

8.6.2. Example3 min

8.6.3. Practice Level 12 min

8.6.4. Practice Level 21 min

8.6.5. Practice Level 34 min

8.6.6. Extra Perfect Square Trinomial Factoring Drills 💪8 min

8.7.1. Factoring Summary3 min

8.7.2. Factoring Drills 💪 Level 210 min

8.7.3. Practice Level 33 min

8.7.4. Practice Level 35 min

8.7.5. Practice Level 34 min

8.7.6. Practice Level 34 min

10. Completing the Square

59min

10.I. Chapter Intro

10.1.1. Exploring Perfect Squares

\left(x+\dfrac{b}{2}\right)^2

10.1.2. Practice Level 13 min

10.1.3. Example4 min

10.1.4. Practice Level 21 min

10.1.5. Practice Level 31 min

10.2.1. Completing the Square (

x^2+bx+c

10.2.2. Example4 min

10.2.3. Practice Level 15 min

10.2.4. Practice Level 25 min

10.2.5. Practice Level 34 min

10.2.6. Extra Completing the Square Practice Drill 💪

10.3.1. Completing the Square (

ax^2+bx+c

10.3.2. Example4 min

10.3.3. Practice Level 14 min

10.3.4. Practice Level 25 min

10.3.5. Practice Level 37 min

10.3.6. Extra Completing the Square Practice Drill 💪

11. Solving Quadratic Equations

2.1hr

11.I. Chapter Intro

11.1.1. Solving Quadratic Equations by Factoring2 min

11.1.2. Example5 min

11.1.3. Practice Level 14 min

11.1.4. Example3 min

11.1.5. Example4 min

11.1.6. Practice Level 27 min

11.1.7. Practice Level 311 min

11.1.8. Practice Level 37 min

11.2.1. Solving Quadratic Equations by Completing the Square4 min

11.2.2. Example4 min

11.2.3. Practice Level 14 min

11.2.4. Practice Level 25 min

11.2.5. Practice Level 38 min

11.2.6. Practice Level 34 min

11.3.1. Quadratic Formula7 min

11.3.2. Example6 min

11.3.3. Practice Level 14 min

11.3.4. Practice Level 23 min

11.3.5. Practice Level 25 min

11.3.6. Practice Level 33 min

11.4.1. Solutions From the Quadratic Formula3 min

11.4.2. Practice Level 14 min

11.4.3. Practice Level 24 min

11.4.4. Practice Level 33 min

11.5.1. Solving Quadratic Equations4 min

11.5.2. Practice Level 25 min

11.5.3. Practice Level 33 min

11.5.4. Practice Level 33 min

12. Congruent & Similar Polygons/Triangles

58min

12.1.1. Congruent Triangles3 min

12.1.2. Practice59 sec

12.1.3. Practice2 min

12.2.1. Enlargements & Reductions4 min

12.2.2. Practice Level 14 min

12.2.3. Practice Level 2

12.2.4. Scale Diagrams3 min

12.2.5. Practice Level 14 min

12.2.6. Example8 min

12.2.7. Practice Level 22 min

12.2.8. Practice Level 34 min

12.3.1. Similar Triangles5 min

12.3.2. Example6 min

12.3.3. Practice Level 13 min

12.3.4. Practice Level 25 min

12.3.5. Practice Level 33 min

13. Trigonometry of Right Triangles

1.8hr

13.1.1. Pythagorean Theorem5 min

13.1.2. Example5 min

13.1.3. Practice Level 14 min

13.1.4. Practice Level 26 min

13.1.5. Practice Level 34 min

13.2.1. How to Label a Right-Angle Triangle?6 min

13.2.2. Practice Level 11 min

13.2.3. The Story of the 3 Primary Trig Ratios3 min

13.2.4. Primary Trig Ratios--

\sin

\cos

\tan

13.2.5. Practice Level 22 min

13.2.6. Practice Level 22 min

13.2.7. Example2 min

13.2.8. Practice Level 1

13.2.9. Example3 min

13.2.10. Practice Level 22 min

13.2.11. Practice Level 32 min

13.3.1. Example6 min

13.3.2. Practice Level 1

13.3.3. Practice Level 22 min

13.3.4. Practice Level 23 min

13.3.5. Practice Level 35 min

13.4.1. Finding Angles Using Primary Trig Ratios6 min

13.4.2. Practice Level 1

13.4.3. Practice Level 12 min

13.4.4. Example4 min

13.4.5. Practice Level 2

13.5.1. Solving a Right Triangle2 min

13.5.2. Practice Level 23 min

13.5.3. Practice Level 33 min

13.6.1. How can we Use Trigonometry in Real Life?2 min

13.6.2. Right Angle Triangle Problems1 min

13.6.3. Practice Level 36 min

13.6.4. Practice Level 32 min

13.6.5. Practice Level 33 min

13.6.6. Practice Level 33 min

14. Trigonometry of Acute Triangles

1.5hr

I Welcome

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Answered

N

Nasri Y

why do we need math?

J

Jessica Y

Instructor

Honestly, you don't NEED math to survive in this world that we've already built, but math will make your adult life a lot easier because it will give you a lot more options.

For example, you'll be able to pick from more jobs, have more options when it comes to saving and investing money (to make more money), building your dream house, figuring out the perfect meal plan for a healthy body, etc. 😊

Answered

A

Antneh K

Y=1/2x

J

Jessica Y

Instructor

Let me know if you have any specific math questions that I can help with :)

Answered

H

Halimat B

If a^2+b^2=18 and ab=5, evaluate (a-b)^2

J

Jessica Y

Instructor

Great question!

Let's start by expanding (a−b)2\left(a-b\right)^2(a−b)2:
(a−b)2=(a−b)(a−b)=(a)(a)+(a)(−b)+(−b)(a)+(−b)(−b)=a2−ab−ab+b2=a2+b2−2ab\begin{array}{ll}
&(a-b)^2\\
=&\left(a-b\right)(a-b)\\
=&(a)(a)+(a)(-b)+(-b)(a)+(-b)(-b)\\
=&a^2-ab-ab+b^2\\
=&a^2+b^2-2ab

\end{array}====​(a−b)2(a−b)(a−b)(a)(a)+(a)(−b)+(−b)(a)+(−b)(−b)a2−ab−ab+b2a2+b2−2ab​

The question gave us some information: a2+b2=18\colorThree{a^2+b^2=18}a2+b2=18 and ab=5\colorFour{ab=5}ab=5.

Now, try to substitute these values into our expanded expression: a2+b2−2ab\colorThree{a^2+b^2}-2\colorFour{ab}a2+b2−2ab.

Give this a try and let me know if you have any questions. Hope this helps 😄

Welcome to Grade 10 Math!
My name is Jess and I'm the instructor for this course.

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