Math Videos  

Number Sets:

• Introduction

• Natural Numbers

• Whole Numbers

• Integer Numbers

• Rational Numbers

• Irrational Numbers

• Real Numbers

• Undefined or Indeterminate

• Square root - rational or not?

• Examples of Number Sets

Simple - Weighted Averages:

• Simple vs Weighted Average

• Current Grade Average

• Grade 8 Exam Challenge

Basics:

• Brackets & Absolute Value

• Place Values

• Comparison Symbols

• Graphing a decimal

• Rounding

• Add & Subtract (no calculator)

• Multiply Integers (no calculator)

• Multiply Decimals (no calculator)

• Long Division (integers)

• Long Division (decimals)

• Order of Operations (BEDMAS)

• Order of Operations (Examples)

• Number Representation

• Significant Figures & Estimated Digit

• Rounding to Correct Sig Figs

• Metric Prefixes

Fractions:

• Primes, Composite, Divisibility, Prime Factorization

• Proper, Improper, Mixed Numbers

• Reducing Fractions

• Naming Fractions

• Graphing Fractions

• Multiply & Divide (fractions)

• Greatest Common Multiple (GCM)

• Lowest Common Multiple / Denominator (LCM or LCD)

• Add & Subtract (fractions)

• Adding Large Mixed Numbers

• Subtracting Mixed Numbers

• Challenge Example (fractions)

• Conversions: decimal, percent, fractions

Exponents and Radicals:

• Intro to Exponents

• Zero Exponents

• Exponent Laws

• Test on Exponents

• Like terms

• Polynomials

• Distributive Property

• Intro to Radicals

• Fractional Exponents

• Simplifying Radicals (Part 1)

• Simplifying Radicals (Part 2)

• Test: Radicals

• Radicals & Exponents

Scientific Notation (SN):

• Introduction

• Converting decimals to SN

• Converting SN to decimals

• Equivalence

• Add / Subtract of SN

• Multiply / Divide of SN

Solving for one unknown:

• Introduction

• Simple Equation

• Unknown in Denominator

• Collecting terms

• Bracket Equations

• Complex Denominator

• Ex 1: brackets

• Ex 2: brackets

• Ex 3: brackets

• Ex 4: fractions

• Ex 5: denominator

• Test:  solving for one unknown

Relations (Part #1)

• Intro to Relations

• Hypothesis, Data Sources

• Data Sampling

• 2D Coordinate System (xy-axis, origin, ordered pair)

• Experiment: dependent, independent variables

• Trends, outliers, interpolate, extrapolate

• Linear vs Non-linear; distance vs time

• Test: Relations (Part 1)

Relations (Part #2)

• Direct Variation (Proportion)

• Partial Variation 

• Slope of a line

• Slope & rate of change

• 1st & 2nd difference

• Test: Relations (Part 2)

Lines in 2-dimensions

• Line: y=mx+b form

• Finding y=mx+b from two points

• Line: Ax+By+C=0 (standard form)

• Parallel & perpendicular lines

• Linear systems in two variables

• Test: Lines in 2-dimensions

Angles & Polygons

• Parallel lines, Angles & Triangle Relationships

• Angles & Quadrilaterals

• Angles & Polygons (Concave & Convex)

• Midpoint, Median & Triangles + Area

• Congruent Triangles

• Midpoints, Diagonals & Quadrilaterals

• Test: Angles & Polygons

Measurement: Area & Volume

• Where does pi come from?

• Pythagorean Theorem

• Composite Shapes: Area & Perimeter

• Prisms, Pyramids: Surface Area, Volume

• Volume of Pyramid (why 1/3 in formula?)

• Surface Area of Cylinders & Cones

• Volume of Cylinders & Cones

• Sphere: Surface Area & Volume

• Test: Surface Area & Volume

Maximizing & Minimizing Shapes

• Maximizing Area of Rectangle

• Minimizing Surface Area of a Prism

• Maximizing Volume of a Prism

• Maximing Volume of a Cylinder

• Quiz: Minimizing Surface Area of a Cylinder

Bonus:

• General Proof of Volume of Pyramid Formula

• Why 1/3 in volume of Cone

• Why 1/3 in volume of Frustum

Linear Systems

• Table of Values, Domain, Range, Graphing

• Substitution Method

• Elimination (Integers) Method

• Elimination (Decimals) Method

• Elimination (Fractions) Method

• Words into Math

• Word Problems (Part 1)

• Word Problems (Part 2)

• Word Problems (Part 3)

• Test: Linear Systems

Line Segments & Circles:

• Equation of a Median

• Equation of a Right Bisector

• Midpoint of a Line Segment

• Length of a Line Segment

• Shortest distance from a point to a line

• Equation of a circle

• Challenge: points, lines, circles

• Identifying: triangles & quadrilaterals

• Identifying: triangles & quadrilaterals on x-y plane

• Challenge: Circles!

• Centroid of a triangle

• Circumcenter

• Altitudes & Orthocenter

• Chords & Intersecting Chords Theorem

• Test: Line Segments & Circles

Quadratics (Part 1)

• Introduction to quadratics

• Factoring & Polynomials

• Factoring Quadratics (x^2+bx+c)

• Factoring Quadratics (ax^2+bx+c)

• Factoring Quadratics by Example

• Factoring Perfect Squares

• Factoring Difference of Squares

• Quadratics, Factoring, and Graphing

• Quadratics, Parabolas, and Line of Symmetry

• Quadratics, Parabolas, and their Vertex

• Test: Introduction to Quadratics

Quadratics (Part 2):

• Relation y=ax^2

• Vertex Form

• Translating, Reflecting, Stretching, Compressing

• Graph to Quadratic Relation

• Quadratic Applications

• Solving Quadratic Equations (Intro)

• Solving Quadratic Equations (by graphing)

• Perfect Squares (with a=1)

• Perfect Squares (with a not 1)

• Vertex Form and Completing the Square

• Solving Quadratic Equations by Completing the Square

• Using the Quadratic Formula

• Derivation of the Quadratic Formula

• Test: Quadratics (Part 2)

Similar Triangles:

• Similar vs Congruent Triangles

• Congruent Triangles

• Similar & Congruent Applications

Trigonometry Introduction:

• Trigonometry Basics

• Defining: Sine, Cosine, Tangent

• Trigonometry Applications & Inverses

• Sine Law 

• Sine Law Proof for Obtuse Triangle

• Why does sin^2 + cos^2 = 1?

• Cosine Law

• Test: Trigonometry & Similar Triangles

Bonus: Linear Inequalities

• Solving Linear Inequalities

• Linear Inequalities Examples

Introduction to Functions:

• Function vs Relation

• Interval Notation

• Function Notation

• Asymptotes

• Parent Functions

• Set Notation, Domain, Range

• Inverses

• Examples (Part 1): Domain, Range, Inverses

• Examples (Part 2): Domain, Range, Inverses

• Transformations (Part 1)

• Transformations (Part 2)

• Test: Intro to Functions

Polynomial Expressions:

• Add, Subtract Polynomials

• Multiplication of Polynomials

• Factoring Review

• Intro to Rational Functions

• Rational Polynomials: Multiplication & Division

• Restrictions on Rational Polynomials

• Add, Subtract Rational Polynomials

• Test: Polynomial Expressions

Quadratic Functions:

• Properties Review

• Maximum, Minimum

• Inverses

• Quadratic & Linear Systems

• Test: Quadratic Functions

Bonus: Inequalities

• Solving Linear Inequalities

• Linear Inequalities Examples

• Linear vs Nonlinear Expressions

• Solving Nonlinear Inequalities

Polynomial Functions:

• Power Functions

• Order / Degree 

• Domain / Range

• Zeros / Roots

• Minimums / Maximums (local & absolute)

• nth Difference

• Factored Form

• Long Division

• Remainder Theorem (Factor Theorem)

• Difference / Sum of Cubes

• Test: Polynomial Functions

Exponents & Radicals (Review):

• Intro to Exponents

• Zero Exponents

• Exponent Laws

• Test on Exponents

• Like terms

• Polynomials

• Distributive Property

• Intro to Radicals

• Fractional Exponents

• Simplifying Radicals (Part 1)

• Simplifying Radicals (Part 2)

• Test: Radicals

• Radicals & Exponents

Exponential Functions:

• Exponential parent function

• Transformations of exponential functions

• Examples of Transformations

• Exponential Growth & Decay

• Exponential Growth & Decay Examples

• Half-life Exponential Decay

• Test: Exponential Functions

Logarithmic Introduction:

• What is log used for?

• Solving for an unknown exponent

• Solving for unknown using log (examples)

• Log and exponential growth example

• Log and exponential decay example

• Log and half-life

Logarithmic Functions:

• Logarithm - inverse of exponential

• Log Transformations

• Log Properties (Part 1)

• Log Properties (Part 2)

• Log Properties Examples

• Solving Log Equations

• Euler's Number

• Natural Logarithm (Ln)

• Test: Logs

Trigonometric Ratios:

• Ratios defined

• Ratios for 30, 45, 60 degrees

• Ratios for angles greater than 90

• Ratio Practice

• Degrees and Radians

• Unit Circle

• Trig Identities

• Sine Law (Revisit from Grade 10)

• Cosine Law (Revisit from Grade 10)

• Ambiguous Case: Sine Law

• Ambiguous Case: Cosine Law

• Summary of Sine and Cosine Law

• Test: Trigonometry Challenge

Sinusoidal Functions:

• Intro to Periodic Functions

• Intro to Sine and Cosine Functions

• Transforming Sine and Cosine (Part 1)

• Transforming Sine and Cosine (Part 2)

• Test: Sinusoidal Functions

Discrete Functions: 

Sequence & Series

• Arithmetic Sequence

• Geometric Sequence

• (Bonus) How to plot a sequence in Desmos

• Fibonacci Sequence

• Arithmetic Series

• Geometric Series

• Pascal's Triangle and Binomial Expansion

• Test: Sequence & Series 

Application: Interest

• Arithmetic Sequence & Simple Interest

• Geometric Sequence & Compound Interest

Bonus: Compound Interest

• Compound Interest Basics

• Number of Terms

• Term Rate

• Compounding Factor

• Compounding Factor derivation

• Future Value

• Present Value

• Finding number of terms

• Finding the term rate

• BA II Plus Calculator

• Playlist on Compound Interest

Function Review:

• Introduction

• Absolute Value Function

• Odd, Even, Continuous, Discontinuous Functions

• Parent Functions Extended

• Transformations Review

• Inverse Functions Review

• Piecewise Functions

• Operations on Functions

Rates of Change:

• Introduction to Rates of Change

• Instantaneous Rates

• Tangent Lines

• Speed as a Rate

• Max, Min, and Rates

• Test: Rates of Change

Polynomial Functions:

• Power Functions

• Power Functions Transformations

• Order / Degree 

• Domain / Range

• Zeros / Roots

• Minimums / Maximums (local & absolute)

• nth Difference

• Factored Form

• Long Division

• Remainder Theorem (Factor Theorem)

• Difference / Sum of Cubes

• Test: Polynomial Functions

Inequalities:

• Solving Polynomial Equations

• Solving Linear Inequalities

• Linear Inequalities Examples

• Linear vs Nonlinear Expressions

• Solving Nonlinear Inequalities

• Rates of Change in Polynomial Functions

Rational Functions:

• Reciprocal Functions

• Holes and Asymptotes

• Special Case: (ax+b)/(cx+d)

• Solving Rational Equations

• Solving Rational Inequalities

• Rational Functions & Rates

• Test: Rational Functions

Review of Trigonometric Ratios:

• Ratios defined

• Ratios for 30, 45, 60 degrees

• Ratios for angles greater than 90

• Ratio Practice

• Degrees and Radians

• Unit Circle

• Trig Identities

• Sine Law (Revisit from Grade 10)

• Cosine Law (Revisit from Grade 10)

• Ambiguous Case: Sine Law

• Ambiguous Case: Cosine Law

• Summary of Sine and Cosine Law

• Test: Trigonometry Challenge

Trigonometric Functions:

• Intro to Sine and Cosine Functions

• Transforming Sine and Cosine (Part 1)

• Transforming Sine and Cosine (Part 2)

• Test: Sinusoidal Functions

• Trig Reciprocal Functions

• Transforming cosecant and secant

• Trig Rates of Change

Trigonometric Identities & Equations

• Equivalent Trig Functions (Part 1)

• Equivalent Trig Functions (Part 2)

• Compound Angle Formulas

• Double Angle Formulas

• Trig Identity Examples

• Solving Linear & Quadratic Trigonometric Equations

Review of Exponential Functions:

• Exponential parent function

• Transformations of exponential functions

• Examples of Transformations

• Exponential Growth & Decay

• Exponential Growth & Decay Examples

• Half-life Exponential Decay

• Test: Exponential Functions

Logarithmic Introduction:

• What is log used for?

• Solving for an unknown exponent

• Solving for unknown using log (examples)

• Log and exponential growth example

• Log and exponential decay example

• Log and half-life

Logarithmic Functions:

• Logarithm - inverse of exponential

• Log Transformations

• Log Properties (Part 1)

• Log Properties (Part 2)

• Log Properties Examples

• Solving Log Equations

• Euler's Number

• Natural Logarithm (Ln)

• Test: Logs

Note: Grade 12 Advanced Functions overlaps with Grade 11 Math.

Organized Counting:

• Multiplicative Counting Principle

• Additive Counting Principle

• n! (Factorial)

• Permutations of Distinct Objects

• Permutations under repetition (Part 1)

• Permutations under repetition (Part 2)

• Pascal's Triangle Introduction

• Pascal's Triangle Application

Organized Counting:

• Test: Organized Counting

• Factorial Example

• Arrangement Example 1

• Arrangement Example 2

• Arrangement Example 3

• Permutations with Repetition Example 

• Pascal's Triangle and Pathways Example

Combinations:

• Introduction to Venn Diagrams

  • • Venn Diagram with 3 subsets

    • Venn Diagram with 4 subsets

• Combination formula derivation

  • • Simple Combination Examples

    • Combination under repetition

• Combinations, Pascal's Triangle, Binomial Theorem

• All Possible Combinations

• Test: Combinations

Combinations: Challenge:

• Poker Introduction

• Royal Flush & Straight Flush

• Flush & Straight

• Four of a Kind & Full House

• Three of a Kind & Two Pairs

• One Pair & High Card

• Full Poker Playlist

Probability Introduction:

• Introduction to Probability

• Tree Diagrams

• Subjective, Empirical, Theoretical Examples

• Calculating Odds

• Examples:

  • • Part #1

    • Part #2

    • Part #3

    • Part #4 (coins)

    • Part #5 (cards)

    • 3 cards with at least a king

    • A coin and a die

    • A coin and a die (part 2)

    • 15 basic examples

Probability Continued:

• Independent Events

• Conditional Probability

• Mutually Exclusive Events

• Contingency Tables

• Examples:

  • • Conditional Example #1

    • Conditional Example #2

    • Monty Hall Example

    • False Negative / False Positive 

• Test: Probability

Probability Distributions

• Introduction

• Binomial Distribution

  • Proof: Expected Value for Binomial Distribution

  • Example: Binomial Distribution

• Geometric Distribution

  • Proof: Expected Value for Geometric Distribution

• Hypergeometric Distribution

  • Proof: Expected Value for Hypergeometric Distribution

  • Example: Hypergeometric Distribution

Statistics Introduction

• Introduction 

• Sampling Techniques

• Quantitative vs Qualitative Variable

• Variable vs Data Set

• Descriptive vs Inferential 

• Survey Bias

• Bar Graph vs Pie Chart

• Stem and Leaf Plots

• Pareto Chart

• Frequency Histograms (Grouped, Class Weight, Ungrouped)

• Frequency Histograms (relative, cumulative, ogive)

• Mean, Median, Mode, Midrange

• Deviation, Variance, Standard Deviation

  • • Quartiles

    • Percentiles

    • Z-Scores

• Introduction to an Index (Indices)

  • Bonus: Index Fund

Statistics of Two Variables

• Linear Correlation & Covariance

• Linear Regression

  • • Linear Regression on DESMOS

• Causation vs Correlation

Normal Distribution

• Intro to Continuous Distribution

  • Exponential Distribution

• Normal Distribution - Bell Curve Intro

  • • Examples

    • Sampling and Modelling

    • Approximating the Binomial Distribution

    • Repeated Sampling

    • Hypothesis Testing

    • Confidence Intervals

    • Proportion of a Population, Confidence Intervals 

    • Margin of Error, Finding Sample Size

Getting Ready (review):

• Introduction to Rates of Change

• Instantaneous Rates

• Tangent Lines

• Speed as a Rate

• Max, Min, and Rates

• Test Practice: Rates of Change

• Polynomial Functions & Rates of Change

• Rational Functions & Rates of Change

• Trig Functions & Rates of Change

• Odd, Even Functions and Discontinuity

• Piecewise Functions

Limits and Continuity:

• Getting Ready for Calculus!

• Intro to Limits

• Limits and Continuity

  • Limits and Continuity summary

• Limit Properties

• Limits and Discontinuity

• Intro to Derivatives

• Non-differentiability

• Test Challenge:

  • Question 1: Limits

  • Question 2-4: Limits, Discontinuity

  • Question 5: Derivatives by First Principles Definition

Derivatives:

• Power & Radical Functions

  • Difference of nth degree

  • Proof for x^n and x^-n

  • Proof for x^(1/m)

  • Proof for x^(n/m) 

• Polynomial Functions

• Product Rule

  • Proof of the Product Rule

• Chain Rule: Composite Functions 

  • Proof of Chain Rule for Power Functions

  • Proof of Chain Rule General 

• Quotient Rule

  • Proof of Quotient Rule

• Summary of All Derivative Rules

Derivative Applications:

• Displacement, velocity, and acceleration (Introduction)

• Examples of position, velocity, and acceleration

• Examples of kinetic and potential energy

• Challenge Example: Cost, Revenue, Profit (and their derivatives)

Sketching Functions:

• Increasing, decreasing functions

• Critical Points: min/ max (local & absolute)

• Inflection Points: concave up/down

• Max/Min Optimization: Rectangle, Prism

• Max/Min Optimization: Cylinder

• Accurate Sketching:

  • • Simple Polynomial Function

    • Complex Polynomial Function

    • Challenge: Piecewise Rational Function

Sinusoidal Derivatives:

• What to review?

• Derivatives of sin, cos, tan!

• Derivatives of csc, sec, cot!

• Tougher Derivative Examples

• Sketching Sinusoidal Functions

• Optimization Challenge Question

Exponential Derivatives

• What to review?

• e^x - expressed as power functions

• Derivative of e^x (with proof)

• Derivative of b^x (with proof)

• Exponential Derivative Examples

Logarithmic Derivatives

• Implicit Differentiation

  • • Example of Implicit Differentiation

• Derivative of ln(x) - with proof

• Derivative of log_b (x) - with proof

• One Example - All Derivative Rules

• Summary:

  • • All Parent Derivatives

    • All Rules (Review)

Geometric Vectors:

• Introduction to Vectors

• Direction: True Bearing, Quadrant Bearing, Horizontal Reference

• Adding & Subtracting Vectors

  • • Part 1

    • Part 2

    • Challenge Example

• Multiplying by a Scalar

• Equilibrium of Vectors

• Tension Example

• Heading, Bearing, and Velocities

Cartesian Vectors 2D

• Introduction 

• Dot Product and Properties

• Angle between Vectors

• Vector Projection

• Work and the Dot Product

• Work and Vectors Example

Cartesian Vectors 3D

• Introduction to 3D vectors

• Add, Subtract, Scalar Multiplication, Dot Product

• Properties of 3D Vectors

• Example: distributive property

• Vector projection with dot product

• Cross Product

• Cross Product Properties

• Triple Scalar Product

• Torque & Cross Product

Lines & Planes in 3D

• Vector & Parametric Equations of Lines 2D

• Equation of Lines 3D

• Introduction to Planes

• Normal Vectors & Planes

• Vector & Parametric Equations of Planes 3D

• Dot Product, Cross Product, and Planes

• Intersection of Lines in 3D

• Intersection of lines and planes

• Distance from a point to a plane

  • Proof: Formula for distance from a point to a plane

• Intersection of 2 Planes

• Intersection of 3 Planes 

  • 3 Equations 3 Unknowns (Part 1)

  • 3 Equations 3 Unknowns (Part 2)

  • Row Reduction (Part 3)

Break-Even Analysis

• Introduction to Break-Even Part #1

• Introduction to Break-Even Part #2

• Break-Even Models

• Unknown Variable Cost & Selling Price

• Graphing Break-Even Charts

• BA II Plus - Break-Even

• Examples:

  • • Example 1

    • Example 2

    • Example 3

    • Example 4

Trade and Cash Discounts

• Introduction to Trade Discounts

• Single Equivalent Rate of Discount

• Trade Discount Examples:

  • Trade Discount 

  • Net Price Factor, Single Equivalent Rate

• Introduction to Cash Discounts

• Ordinary Dating, End of Month (EOM), Receipt of Goods (ROG)

• Cash Discounts and Partial Payment

• Trade & Cash Discounts Example #1

• Trade & Cash Discounts Example #2

Markup and Markdown

• Understanding Markup

• Markdown and Operating Profit

• Markup and Markdown Example

Simple Interest

• Introduction

• Conversion of time to years

• BA II Plus, finding days and date

  • Finding days time manually

• Future Value

• Present Value

• Example: finding time

• Equivalent Values

  • Equivalent Values & Equal Payments

• Promissory Note Example #1

• Promissory Note Example #2

• T-Bill Example

• Loan Repayment

• On Demand Loan

• Line of Credit

Compound Interest

• Basics of Compounding

• Number of terms

• Term Rate

• Compounding factor

  • Derivation of compounding factor

• Future Value

• Present Value

• Finding number of terms

• Finding the term rate

• BA II Plus and Compound Interest

• Compound vs Simple Review

• Equivalent Values 

• Equivalent Values, Loan Repayment

• Example: number of terms

• Example: Doubling money

• Example: Making $1M 

• Example: Equivalent values

Introduction to Annuities

• Introduction: Ordinary, Due, Simple, General Annuity

• Ordinary Simple Annuities 

  • • Future Value

    • Derivation of Future Value formula

    • BA II Plus and Future Value 

    • Present Value

    • BA II Plus and Present Value

    • Finding the Payment

    • BA II Plus and Finding Payment

    • Finding number of payments

    • Solving for the interest

    • Isolating for the interest

• Bonus: Index Fund