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Master Exponents: Solve Math Problems with Confidence

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

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Intro

- Hi and welcome to this question right here. So trying to write...well not trying to write. We're going to write the volume of this cube below as a power. Once you see the word cube right away we know that each side is going to be the same length. So this is 8 and this is also 8 and this is 8 as well, okay? So we've got length times the height times the width which is the volume of the cube, okay? But they want it in terms of power. Before we must do that let's just do it regularly. If I wanted to figure the volume for this one because it's a cube it will be the side times the side times the side, right? And I know it's going to be 8 times 8 times 8. Now if I want to write that as a power it would just be the base of the 8 raised to the power of 3 times, okay? And once you're done with that you just have to use a calculator, punch it in, you get yourself 512 and please don't forget about a unit. It's cubit. So centimeter cubed, alright?

Finding the volume of a cube using exponent notation

Writing a general expression for bacteria growth after n hours

Calculating bacteria count after 7 hours of doubling

Doubling bacteria problem using exponential growth formula

Understanding the difference between powers, bases, and exponents

In this section, you will try to apply what we learn about exponents in the previous sections to solve word problems such as, calculating the volume of a cube, and more.

Applying exponent rules to solve math problems

Mastering Exponents for Effective Problem-Solving

What You'll Learn

Calculate the volume of a cube using exponents and express it as a power

Apply exponential notation to represent repeated multiplication in word problems

Use the exponential growth formula to model bacteria doubling over time

Create general expressions with exponents for real-world scenarios involving growth

Distinguish between base, exponent, and power in mathematical expressions

What You'll Practice

Finding cube volumes and writing them in exponential form

Calculating bacteria population after a given number of hours

Creating algebraic expressions with exponents for n hours of growth

Converting repeated multiplication into power notation

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

5 Video lessons

Learning resources

Skills

Exponents

Volume

Exponential Growth

Word Problems

Powers

Base and Exponent

Real-World Applications