PatrickJMT: making FREE and hopefully useful math videos for the world!
ALGEBRA
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Arithmetic Basics: Long Division of Numbers
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Arithmetic Basics: Finding the Percent of a Number
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Arithmetic Basics: Multiplying Decimals
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Arithmetic Basics: Dividing Decimals
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Arithmetic Basics: Converting Decimals into Fractions
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Fractions – Adding and Subtracting
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Fractions: Adding and Subtracting – Numerical and Variable Examples
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Fractions: Adding and Subtracting Fractions with Different Denominators
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Fractions – Multiplying and Dividing
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Basic Math: Dividing Fractions
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Comparing Fractions using Inequalities – Ex 1
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Comparing Fractions using Inequalities – Ex 2
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Fractions: Multiplying, Reducing, Adding and Subtracting
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Simplifying Complex Fractions – Ex 1
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Simplifying Complex Fractions – Ex 2
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Simplifying Complex Fractions – Ex 3
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Partial Fraction Decomposition – Example 1
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Partial Fraction Decomposition – Example 2
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Partial Fraction Decomposition – Example 4
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Partial Fraction Decomposition – Example 5
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Partial Fraction Decomposition – Example 6
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Averages and Word Problems – Basic Example
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Averages: Finding an Average Grade You Need to Make to Bring Your Grade up to a Desired Amount
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Averages: What Grade do I Need on the Final to Pass the Class?!
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Radical Notation and Simplifying Radicals
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Radicals: Simplifying Radical Expressions Involving Variables – Ex 1
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Simplifying Numbers under Square Roots
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Rationalize the Denominator
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Rationalizing the Denominator – Ex 1
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Rationalize the Denominator – Harder Example
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Rationalizing the Denominator – Ex 3
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Factoring a Number
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Factoring a Number
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Greatest Common Factor, GCF
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Least Common Multiple
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An Intro to Solving Linear Equations: What Does it Mean to be a Solution?
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An Intro to Solving Linear Equations: Solving some Basic Linear Equations
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An Intro to Solving Linear Equations: Solving some Basic Linear Equations, Ex 2
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Solving Linear Equations
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Solving Linear Equations – Example 1
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Solving a Basic Linear Equation – Example 2
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Solving a Basic Linear Equation – Example 3
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Direct Variation / Direct Proportion – Ex 1
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Direct Variation / Direct Proportion – Ex 2
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Direct Variation / Direct Proportion – Ex 3
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Slope of a Line
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Equation of a Line: Point-Slope Form
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Graphing a Line Using a Point and Slope
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Linear Functions: Graphing by Finding X,Y Intercept
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An Introduction To Solving Inequalities – Ex 1
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An Introduction To Solving Inequalities – Ex 2
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An Introduction To Solving Inequalities – Ex 3
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Fundamental True/False Questions about Inequalities!
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Solving Word Problems Involving Inequalities – Ex 1
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Solving Word Problems Involving Inequalities – Ex 2
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Solving Word Problems Involving Inequalities – Ex 3
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Using Interval Notation to Express Inequalities – Ex 1
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Using Interval Notation to Express Inequalities – Ex 2
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Interval Notation – A basic question!
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Writing Compound Inequalities Using Interval Notation – Ex 1
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Writing Compound Inequalities Using Interval Notation – Ex 2
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Writing Compound Inequalities Using Interval Notation – Ex 3
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Absolute Value: Evaluating Numbers
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Absolute Value: Evaluating Expressions – Ex 1
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Absolute Value: Evaluating Expressions – Ex 2
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Absolute Value: Evaluating Expressions – Ex 3
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Matching Number Lines with Absolute Value Inequalities – Ex 1
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Solving Absolute Value Equations – Ex 1
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Solving Absolute Value Equations – Ex 2
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Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 1
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Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 2
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Solving Absolute Value Equations Containing TWO Absolute Value Expressions – Ex 3
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Solving Absolute Value Inequalities – Ex 1
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Solving Absolute Value Inequalities – Ex 2
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Solving Absolute Value Inequalities – Ex 3
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Solving Absolute Value Inequalities, MORE Ex 1
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Solving Absolute Value Inequalities, MORE Ex 2
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Solving Linear Absolute Value Equations and Inequalities
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Graphing Systems of Linear Inequalities – Ex 1
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Graphing Systems of Linear Inequalities – Ex 2
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Solving Linear Compound Inequalities – Ex 1
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Solving Linear Compound Inequalities – Ex 2
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Solving Linear Compound Inequalities – Ex 3
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Exponents: Basic Properties
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Exponents: Basic Problems – Ex 1
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Exponents: Basic Problems – Ex 2
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Exponents: A Few True/False Questions
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Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 1
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Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 2
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Exponents: Evaluating Expressions (Numbers Only, No Variables) – Ex 3
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Exponents: Applying the Rules of Exponents – Basic Ex 1
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Exponents: Applying the Rules of Exponents – Basic Ex 2
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Exponents: Applying the Rules of Exponents – Basic Ex 3
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Exponents: Applying the Rules of Exponents – Basic Ex 3
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Exponents: Negative Exponents
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Negative Exponents – Basic Rules and Examples
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Exponents: Simplifying Expressions with Negative Exponents – Ex 1
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Exponents: Simplifying Expressions with Negative Exponents – Ex 2
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Exponents: Simplifying Expressions with Negative Exponents – Ex 3
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Exponents: Numbers Raised to Fractional Exponents
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Exponents: Evaluating Numbers Raised to Fractional Exponents
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Exponents: Evaluating Numbers with Rational Exponents by using Radical Notation – Basic Ex 1
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Exponents: Multiplying Variables with Rational Exponents – Basic Ex 1
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Exponents: Multiplying Variables with Rational Exponents – Basic Ex 2
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Polynomial… or NOT?! Recognizing Polynomials, the degree and some Terminology
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Symmetry – A Quick Discussion for Testing if a Polynomial is Even / Odd
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Polynomials: Adding and Subtracting
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Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 1
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Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 2
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Polynomials: Adding, Subtracting, Multiplying and Simplifying – Ex 3
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Polynomials: Multiplying – Slightly Harder Ex 1
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Polynomials: Multiplying – Slightly Harder Ex 2
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Polynomials: Multiplying – Slightly Harder Ex 3
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Polynomials: Multiplying – Slightly Harder Ex 4 – Cubing Binomials
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Polynomials: Multiplying – Slightly Harder Ex 5 – Cubing Binomials
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Polynomials: Multiplying – Slightly Harder Ex 6
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Long Division of Polynomials
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Long Division of Polynomials – A slightly harder example
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Synthetic Division
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Synthetic Division – Ex 2
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The Remainder Theorem – Example 1
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The Remainder Theorem – Example 2
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Factoring Trinomials (A quadratic Trinomial) by Trial and Error
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Factoring Trinomials by Trial and Error – Ex 2
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Factoring Trinomials: Factor by Grouping – Ex 1
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Factoring Trinomials: Factor by Grouping – Ex 2
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Factoring Trinomials: Factor by Grouping – Ex 3
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Factoring Perfect Square Trinomials – Ex1
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Factoring Perfect Square Trinomials – Ex 2
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Factoring Perfect Square Trinomials – Ex3
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Factoring the Difference of Two Squares – Ex 1
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Factoring the Difference of Two Squares – Ex 2
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Factoring the Difference of Two Squares – Ex 3
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Factoring Sums and Differences of Cubes
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Factoring Sums and Differences of Cubes – Ex 3
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Factoring Using the Great Common Factor, GCF – Ex 1
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Factoring Using the Great Common Factor, GCF – Ex 2 – Factoring Out Binomials
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Finding all the Zeros of a Polynomial – Example 1
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Finding all the Zeros of a Polynomial – Example 2
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Finding all the Zeros of a Polynomial – Example 3
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Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 1
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Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 2
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Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 3
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Rational Roots Test
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Descartes’ Rule of Signs
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The Conjugate Pair Theorem – Example 1
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The Conjugate Pair Theorem – Example 2
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Quadratic Equations – Factoring and Quadratic Formula
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Solving Quadratic Equations by Factoring – Basic Examples
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Solving Quadratic Equations by Factoring – Another Example
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Factoring by Grouping
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Factoring by Grouping – Ex 1
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Factoring By Grouping – Ex 2
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Quadratic Equations – Completing the Square
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Completing the Square – Solving Quadratic Equations
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Completing the Square: Solving Quadratic Equations – Ex 2
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Completing the Square to Solve Quadratic Equations: More Ex 1
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Completing the Square to Solve Quadratic Equations: More Ex 2
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Completing the Square to Solve Quadratic Equations: More Ex 3
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Completing the Square to Solve Quadratic Equations: More Ex 4
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Completing the Square to Solve Quadratic Equations: More Ex 5
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Completing the Square to Solve Quadratic Equations: More Ex 6
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Quadratic Formula
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Quadratic Formula: How to Derive
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Solving Quadratic Equations using the Quadratic Formula – Ex 1
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Solving Quadratic Equations using the Quadratic Formula – Ex 2
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Solving Quadratic Equations using the Quadratic Formula – Ex 3
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Quadratic Equations: Using the Discriminant
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Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 1
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Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 2
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Using the Discriminant to Predict the Types of Solutions to a Quadratic Equation – Ex 3
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Graphing Quadratic Functions – Ex 1
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Solving Fancy Quadratics – Ex 1
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Solving Fancy Quadratics – Ex 2
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Solving Fancy Quadratics – Ex 3
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Solving a Geometry Word Problem by Using Quadratic Equations – Ex 1
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Solving a Geometry Word Problem by Using Quadratic Equations – Ex 2
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Solving a Geometry Word Problem by Using Quadratic Equations – Ex 3
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Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 1
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Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 2
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Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 3
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Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 1
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Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 2
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Solving Word Problems in Distance, Rate, and Time Using Quadratics – Ex 3
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Solving a Projectile Problem Using Quadratics – Ex 1
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Solving a Projectile Problem Using Quadratics – Ex 2
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Solving a Projectile Problem Using Quadratics – Ex 3
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More Word Problems Using Quadratic Equations – Ex 1
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More Word Problems Using Quadratic Equations – Ex 2
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More Word Problems Using Quadratic Equations – Example 3
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Solving Quadratic Inequalities – The Basics
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Solving Quadratic Inequalities
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Solving Quadratic Inequalities – A Common Mistake
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Solving Quadratic Inequalities – Ex 1
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Solving Quadratic Inequalities – Ex 2
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Solving Quadratic Inequalities – Ex 3
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Solving Quadratic Inequalities, More Ex 1
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Solving Quadratic Inequalities, More Ex 2
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Solving Quadratic Inequalities, More Ex 3
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Solving Quadratic Inequalities, More Ex 4
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Solving Quadratic Inequalities – More Examples
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Rational Expressions and Domain
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Finding the Domain of an Expression Involving Fractions – Ex 1
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Finding the Domain of an Expression Involving Fractions – Ex 2
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Finding the Domain of an Expression Involving Fractions – Ex 3
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Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Example 1
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Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Ex 2
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Finding Domains of Functions Involving Radicals (Square Roots to be More Precise!) – Ex 3
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Finding the Domain of a Function Algebraically (No graph!)
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Rational Expressions: Writing in Lowest Terms – Ex 1
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Rational Expressions: Writing in Lowest Terms – Ex 2
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Rational Expressions: Adding and Subtracting
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Rational Expressions: Adding and Subtracting. Ex 1
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Rational Expressions: Adding and Subtracting. Ex 2
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Rational Expressions: Multiplying and Dividing. Ex 1
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Rational Expressions: Multiplying and Dividing. Ex 2
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Rational Expressions: Multiplying and Dividing. Ex 3
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Rational Equations: Solving
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Solving a Basic Rational Equation – Ex 1
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Solving a Basic Rational Equation – Ex 2
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Solving a Basic Rational Equation – Ex 3
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Solving a Basic Rational Equation – Ex 4
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Solving a Basic Rational Equation – Ex 5
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Graphing Some Basic Rational Functions – Example 1
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Graphing a Rational Function – Example 1
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Graphing a Rational Function – Example 2
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Graphing a Rational Function – Example 3
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Graphing a Rational Function – Example 4
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Rational Functions: Shortcut to Find Horizontal Asymptotes
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Rational Functions: Vertical Asymptotes
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Rational Functions: Slant Asymptotes
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Find Asymptotes of a Rational Function (Vertical and Oblique/Slant)
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Find Asymptotes of a Rational Function (Vertical and Oblique/Slant), Ex 2
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Graphing a Rational Function that has an Oblique/Slant Asymptote and a Vertical Asymptote
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Rational Inequalities: Solving
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Solving a Rational Inequality – Ex 1
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Solving a Rational Inequality – Ex 2
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Solving a Rational Inequality – Ex 3
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Solving a Rational Inequality, More Examples – Ex 1
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Solving a Rational Inequality, More Examples – Example 2
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Solving a Rational Inequality, More Examples – Example 3
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Piecewise Defined Functions: Graphing
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Graphing a Piece-Wise Defined Function – Another Example
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Piecewise Functions: Find the Formula from a Graph – Ex 1
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Piecewise Functions: Find the Formula from a Graph – Ex 2
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Evaluating Piecewise Defined Functions
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Functions: Adding and Subtracting
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Functions: Multiplying and Dividing
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Composition of Functions
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Finding Functions that Form a Particular Composite Function
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The Vertical Line Test
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X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 1
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X-Intercepts and Y-Intercepts of a Functions and Finding Them! Example 2
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The Difference Quotient – Example 1
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The Difference Quotient – Example 2
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Graphing the Greatest Integer or Floor Function
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Solving an Equation for a Specified Variable
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Solving Equations Involving Square Roots
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Solving an Equation Involving a Single Radical (Square Root) – Ex 1
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Solving an Equation Involving a Single Radical (Square Root) – Ex 2
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Solving an Equation Involving a Single Radical (Square Root) – Ex 3
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Solving an Equation Containing Two Radicals – Ex 1
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Solving an Equation Containing Two Radicals – Ex 2
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Solving an Equation Containing Two Radicals – Ex 3
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Solving Equations Involving Rational Exponents
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Solving an Equation Involving Rational Exponents – Ex 1
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Solving an Equation Involving Rational Exponents – Ex 2
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Solving an Equation Involving Rational Exponents – Ex 3
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The Cartesian Coordinate System – A few basic questions
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Basic Graphs that Every Algebra Student Should Know!!
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Graphing Equations by Plotting Points – Example 1
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Graphing Equations by Plotting Points – Example 2
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Graphing Equations by Plotting Points – Example 3
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Finding Domain and Range of a Function using a Graph
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Domain and Range From a Graph
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Local Max/Min, Inc/Dec: On a Graph
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Finding Limits From a Graph
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Horizontal and Vertical Graph Transformations
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Horizontal And Vertical Graph Stretches and Compressions Part 1 of 3
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Horizontal And Vertical Graph Stretches and Compressions Part 2 of 3
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Graph Transformations about the X-axis and Y-axis
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Graphing Using Graph Transformations – Ex 1
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Graphing Using Graph Transformations – Ex 2
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Inverse Functions – The Basics!
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Inverse of a Function
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Finding the Inverse of a Function or Showing One Does not Exist, Ex 2
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Finding the Inverse of a Function or Showing One Does not Exist, Ex 3
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Finding the Inverse of a Function or Showing One Does not Exist, Ex 4
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Solving a Linear System of Equations by Graphing
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Linear System of Equations: Row Reducing – Part 1
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Linear System of Equations: Row Reducing – Part 2
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Linear System of Equations: Solving using Substitution
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Linear System of Equations: Solving using Elimination by Addition
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 1
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 2
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Solving a System of Equations Involving 3 Variables Using Elimination by Addition – Example 3
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Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 1
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Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 2
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Systems of Linear Equations – Inconsistent Systems Using Elimination by Addition – Example 3
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Solving a Dependent System of Linear Equations involving 3 Variables
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Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 1
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Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 2
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Cramer’s Rule to Solve a System of 3 Linear Equations – Example 1
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Cramer’s Rule to Solve a System of 3 Linear Equations – Example 2
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The Distance Formula
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The Distance Formula and Finding the Distance Between Two Points – Example 1
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The Distance Formula and Finding the Distance Between Two Points – Example 2
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The Midpoint Formula
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The Midpoint Formula – Finding the Midpoint
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Collinearity and Distance: Determining if Three Points are Collinear, Example 1
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Collinearity and Distance: Determining if Three Points are Collinear, Example 2
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Collinearity and Distance: Determining if Three Points are Collinear, Example 3
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Word Problem: Distance, Rate, and Time
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Pythagorean Theorem
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Word Problems Using the Pythagorean Theorem – Ex 1
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Word Problems Using the Pythagorean Theorem – Ex 2
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Word Problems Using the Pythagorean Theorem – Ex 3
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Word Problem Involving Perimeter of a Triangle – Ex 1
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Word Problem Involving Perimeter of a Triangle – Ex 2
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Word Problem Involving the Perimeter of a Rectangle – Ex 1
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Word Problem Involving the Perimeter of a Rectangle – Ex 2
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Coterminal Angles – Example 1
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Coterminal Angles – Example 2
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Coterminal Angles – Example 3
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Finding the Quadrant in Which an Angle Lies – Example 1
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Finding the Quadrant in Which an Angle Lies – Example 2
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Finding the Quadrant in Which an Angle Lies – Example 3
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Adding and Subtracting Complex (Imaginary) Numbers
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Rewriting Radicals using Complex Numbers
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Rewriting Powers of ‘ i ‘ – Ex 1
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Rewriting Powers of ‘ i ‘ – Ex 2
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Complex Numbers: Graphing, Adding, Subtracting
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Complex Numbers: Multiplying and Dividing
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Complex Numbers: Multiplying – Ex 1
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Complex Numbers: Multiplying – Ex 2
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Complex Numbers: Dividing – Ex 1
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Complex Numbers: Dividing – Ex 2
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Complex Numbers: Dividing – Ex 3
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Conic Sections: Parabolas, Part 1
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Conic Sections: Parabolas, Part 2 (Directrix and Focus)
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Conic Sections: Parabolas, Part 3 (Focus and Directrix)
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Conic Sections: Parabolas, Part 4 (Focus and Directrix)
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Conic Sections: Parabolas, Part 5 (Focus and Directrix)
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Graphing a Parabola
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Conic Sections: Hyperbolas, An Introduction
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Conic Sections: Hyperbolas, An Introduction – Graphing Example
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Finding the Equation for a Hyperbola Given the Graph – Example 1
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Conic Sections: Graphing Ellipses – Part 1
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The Center-Radius Form for a Circle – A few Basic Questions, Example 1
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The Center-Radius Form for a Circle – A few Basic Questions, Example 2
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Finding the Center-Radius Form of a Circle by Completing the Square – Example 1
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Finding the Center-Radius Form of a Circle by Completing the Square – Example 2
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Finding the Center-Radius Form of a Circle by Completing the Square – Example 3
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Identifying a Conic from an Equation by Completing the Square, Ex 1
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Identifying a Conic from an Equation by Completing the Square, Ex 2
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Identifying a Conic from an Equation by Completing the Square, Ex 3
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Matrices: Basic Matrix Operations (add, subtract, multiply by constant)
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Matrices: Multiplying a Matrix by another Matrix
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 1
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 2
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Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 3
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Logarithms: Properties of Logarithms – Part 1
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Logarithms: Properties of Logarithms – Part 2
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Properties of Logarithms
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Solving Logarithmic Equations – Example 1
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Solving Logarithmic Equations – Example 2
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Change of Base Formula for Logarithms
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Solving Exponential Equations
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Exponential Function From a Graph
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Word Problem: Exponential Growth
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Factoring Trigonometric Expressions, Example 1
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Factoring and Simplifying Trigonometric Expressions – Example 2
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Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2
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Binomial Theorem – Ex 1
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Binomial Theorem – Ex 2
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Arithmetic Sequences: A Quick Intro
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Arithmetic Sequences: Finding a General Formula Given Two Terms
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Finding the Sum of a Finite Arithmetic Series
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Proof by Induction – Example 1
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Proof by Induction – Example 2
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Proof by Induction – Example 3
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Understanding Simple Interest and Compound Interest
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Deriving the Annual Compound Interest Formula
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Compound Interest – More than Once Per Year
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Compound Interest – More than Once Per Year – Part 2
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Finding an Interest Rate to Match Certain Financial Goals, Ex 1
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Finding an Interest Rate to Match Certain Financial Goals, Ex 2
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Finding an Interest Rate to Match Certain Financial Goals, Ex 3
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Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement – Ex 2
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Word Problem: Finding Consecutive Numbers That Satisfy a Given Requirement – Ex 3
ARITHMETIC
CALCULUS
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What is a Limit? Basic Idea of Limits
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Calculating a Limit by Factoring and Cancelling
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Calculating a Limit by Getting a Common Denominator
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Calculating a Limit by Expanding and Simplifying
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Calculating a Limit by Multiplying by a Conjugate
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Calculating a Limit Involving Absolute Value
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sin(x)/x Limit as x Approaches Zero
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Squeeze Theorem for Limits
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Infinite Limits
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Infinite Limits – Basic Idea and Shortcuts for Rational Functions
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Infinite Limits with a Radical in the Expression
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Continuity – Part 1 of 2
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Continuity – Part 2 of 2
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Intermediate Value Theorem
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Partial Fraction Decomposition – Example 1
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What is a Derivative? Understanding the Definition
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Sketching the Derivative of a Function
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Derivatives – Basic Examples
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Derivatives: Product Rule
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Derivatives: Quotient Rule
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Derivatives: Chain Rule
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Tangent Line: Finding the Equation
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Chain Rule: Basic Problems
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Chain Rule + Product Rule + Factoring
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Chain Rule + Product Rule + Simplifying – Ex 1
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Chain Rule + Product Rule + Simplifying – Ex 2
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Chain Rule +Quotient Rule + Simplifying
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Chain Rule – Harder Ex 1
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Chain Rule – Harder Ex 2
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Chain Rule – Harder Ex 3
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Derivatives – More Complicated Examples
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Derivatives – More Complicated Examples
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Critical Numbers – Ex 1
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Critical Numbers – Ex 2
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Local Max/Min, Inc/Dec: From a Function
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Local Maximums/Minimums – Second Derivative Test
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Mean Value Theorem
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Proof By Contradiction – Calculus Based Example
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The Closed Interval Method to Find Absolute Maximums and Minimums
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Implicit Differentiation – Basic Idea and Examples
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Implicit Differentiation – Extra Examples
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Implicit Differentiation – More Examples
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Implicit Differentiation and Second Derivatives
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Concavity and Second Derivatives
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Related Rates – A Point on a Graph
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Related Rates Involving Baseball!
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Related Rates Problem Using Implicit Differentiation
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Related Rates Involving Trigonometry
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Related Rates Using Cones
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Linearization at a Point
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Sketching the Curve Using Calculus – Part 1 of 2
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Sketching the Curve Using Calculus – Part 2 of 2
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Sketching the Curve Summary – Graphing Ex 2 – Part 1 of 4
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Sketching the Curve Summary – Graphing Ex 2 – Part 2 of 4
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Sketching the Curve Summary – Graphing Ex 2 – Part 3 of 4
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Sketching the Curve Summary – Graphing Ex 2 – Part 4 of 4
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Optimization Problem #1
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Optimization Problem #3 – Making a Rain Gutter!
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Optimization Problem #2
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Newton’s Method
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Definite Integral – Understanding the Definition
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Approximating a Definite Integral Using Rectangles
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Riemann Sums: Calculating a Definite Integral – Part 1
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Riemann Sums: Calculating a Definite Integral – Part 2
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Integration by U-Substitution: Antiderivatives
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Integration by U-Substitution, Definite Integral
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Integration by U-Substitution – Indefinite Integral, Another 2 Examples
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Integration by U-substitution, More Complicated Examples
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Areas Between Curves
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Fundamental Theorem of Calculus Part 1
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Area Between Curves – Integrating with Respect to y
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Area Between Curves – Integrating with Respect to y – Part 2
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Volumes of Revolution: Disk/Washers about Vertical Lines
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Volumes of Revolution: Disk/Washers – Ex 1
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Volumes of Revolution: Disk/Washers – Ex 2
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Volumes of Revolution: Cylindrical Shells
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Volumes of Revolution: Cylindrical Shells – Longer Version
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Volumes of Revolution: Disk/Washers – Ex 3
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Work and Hooke’s Law – Ex 1
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Work and Hooke’s Law – Ex 2
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Work Required to Drain a Tank
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Work: The Cable/Rope Problem Part 1
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Work: The Cable/Rope Problem – Part 2
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Derivatives of Exponential Functions
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Exponents: Negative Exponents
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Integrals: Exponential Functions – Ex 1 and 2
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Integrals: Exponential Functions – Ex 3 and 4
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Derivatives of Logarithmic Functions
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Derivatives of Logarithmic Functions – More Examples
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Logarithmic Differentiation – Ex 1
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Logarithmic Differentiation – Ex 2
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Logarithmic Differentiation – Ex 3
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Inverse Trigonometric Functions: Derivatives – Ex 2
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Inverse Trigonometric Functions: Derivatives – Ex 3
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Integrals: Inverse Trigonometric Functions – Ex 1
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Integrals: Inverse Trigonometric Functions – Ex 2
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Hyperbolic Functions – The Basics
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Derivatives of Hyperbolic Functions
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Derivatives of Inverse Hyperbolic Functions
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Integrals: Hyberbolic Functions
-
L’Hospital’s Rule – Indeterminate Quotients
-
L’Hospital’s Rule – Indeterminate Products
-
L’Hospital’s Rule – Indeterminate Differences
-
L’Hospital’s Rule – Indeterminate Powers
-
Integration by Parts – Ex 1
-
Integration by Parts – Definite Integral
-
Integration By Parts – Using IBP’s Twice
-
Integration by Parts – A Loopy Example!
-
Trigonometric Integrals – Part 1 of 6
-
Trigonometric Integrals – Part 2 of 6
-
Trigonometric Integrals – Part 3 of 6
-
Trigonometric Integrals – Part 4 of 6
-
Trigonometric Integrals – Part 5 of 6
-
Trigonometric Integrals – Part 6 of 6
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Trigonometric Substitution – Ex 2
-
Trigonometric Substitution – Ex 3/ Part 1
-
Trigonometric Substitution – Ex 3 / Part 2
-
Integration by Partial Fractions: Long Division
-
Integration by Partial Fractions: Determining Coefficients
-
Integration by Partial Fractions: A Complete Problem
-
Integration by Partial Fractions and a Rationalizing Substitution
-
Approximating Integrals: Simpsons Rule
-
Approximating Integrals: Simpsons Rule Error Bound
-
Improper Integral – Infinity in Upper and Lower Limits
-
Improper Integral with Infinite Discontinuity at Endpoint
-
Approximating Integrals: Trapezoid Rule
-
Arc Length
-
Arc Length Formula – Example 1
-
Arc Length Formula – Example 2
-
Centroids / Centers of Mass – Part 1 of 2
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Centroids / Centers of Mass – Part 2 of 2
-
First Order Linear Differential Equations
-
Solving Separable First Order Differential Equations – Ex 1
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Separable Differential Equations: Mixing Problems
-
Exponential Decay / Finding Half Life
-
Laplace Transform
-
Polar Coordinates – The Basics
-
Polar Coordinates – Basic Graphing
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Parametric Curves – Basic Graphing
-
Arc Length Using Parametric Curves – Ex 1
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Arc Length Using Parametric Curves – Ex 2
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Derivatives of Parametric Functions
-
Parametric Curves: Finding Second Derivatives
-
Parametric Curves – Calculating Area
-
Graphing a Polar Curve – Part 1
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Graphing a Polar Curve – Part 2
-
Polar Coordinates: Finding Areas
-
Conic Sections: Graphing Ellipses – Part 2
-
Factorials – Evaluating Factorials! Basic Info
-
What is a Sequence? Basic Sequence Info
-
Geometric Sequences: A Quick Intro
-
Geometric Sequences: A Formula for the’ n – th ‘ Term.
-
Sequences – Examples Showing Convergence or Divergence
-
Summation Notation
-
What is a Series?
-
Showing a Series Diverges using Partial Sums
-
Geometric Series and the Test for Divergence
-
Geometric Series and the Test for Divergence – Part 2
-
Geometric Series: Expressing a Decimal as a Rational Number
-
Telescoping Series Example
-
Integral Test for Series
-
Limit Comparison Test and Direct Comparison Test – 1
-
Limit Comparison Test and Direct Comparison Test – 2
-
Remainder Estimate for the Integral Test
-
Alternating Series
-
Alternating Series: More Examples
-
Alternating Series Estimation Theorem
-
Ratio Test for Series – Ex 1
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Ratio Test for Series – Ex 2
-
Absolute Convergence, Conditional Convergence and Divergence
-
Strategy for Testing Series – Practice Problems
-
Power Series: Finding the Interval of Convergence
-
Radius of Convergence for a Power Series
-
Power Series Representation of a Function
-
Power Series: Differentiating and Integrating
-
Power Series: Multiplying and Dividing
-
Taylor and Maclaurin Series – Ex 1
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Taylor and Maclaurin Series – Ex 2
-
Taylor / Maclaurin Series for Sin (x)
-
Taylor’s Inequality
-
Maclaurin/Taylor Series: Approximate a Definite Integral to a Desired Accuracy
-
Binomial Series – Ex 1
-
Binomial Series – Ex 2
-
Using Series to Evaluate Limits
-
An Introduction to Vectors, Part 1
-
Vector Basics: Drawing Vectors/Vector Addition
-
Finding the Components of a Vector, Ex 1
-
Finding the Components of a Vector, Ex 2
-
Vector Basics: Algebraic Representations – Part 1
-
Vector Basics: Algebraic Representations – Part 2
-
Vector Addition and Scalar Multiplication, Example 1
-
Vector Addition and Scalar Multiplication, Example 2
-
Magnitude and Direction of a Vector, Example 1
-
Magnitude and Direction of a Vector, Example 2
-
Magnitude and Direction of a Vector, Example 3
-
When Are Two Vectors Considered to Be the Same?
-
Finding a Unit Vector, Ex 1
-
Finding a Unit Vector, Ex 2
-
Word Problems Involving Velocity or Other Forces (Vectors), Ex 1
-
Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.
-
Finding the Vector Equation of a Line
-
Vectors: The Dot Product
-
Cross Product
-
Torque: An application of the cross product
-
Finding and Sketching the Domain of a Multivariable Function
-
Partial Derivatives: Higher Order
-
Showing a Limit Does NOT Exist
-
Partial Derivatives
-
Generalized Chain Rule – Part 1
-
Generalized Chain Rule – Part 2
-
Implicit Function Theorem
-
Implicit Differentiation, Multivariable Function – Ex 1
-
Implicit Differentiation, Multivariable Function – Ex 2
-
Double Integrals – Basic Idea and Examples
-
Finding the Scalar Equation of a Plane
-
Rational Functions: Shortcut to Find Horizontal Asymptotes
-
Finding the Point Where a Line Intersects a Plane
-
Evaluating a Line Integral Along a Straight Line Segment
-
Double Integrals over General Regions
-
Tangent Plane Approximations
-
Double Integral Using Polar Coordinates – Part 1 of 3
-
Double Integral Using Polar Coordinates – Part 2 of 3
-
Double Integral Using Polar Coordinates – Part 3 of 3
-
Double Integrals – Changing Order of Integration
-
Local Maximum and Minimum Values/ Function of Two Variables
-
Local Maximum and Minimum Values/ Function of Two Variables part 2
-
Absolute Maximum/Minimum Values of Multivariable Functions – Part 1 of 2
-
Absolute Maximum/Minimum Values of Multivariable Functions – Part 2 of 2
-
Change of Variables in Multiple Integrals – A Double Integral Example, Part 1 of 2
-
Change of Variables in Multiple Integrals – A Double Integral Example, Part 2 of 2
-
Double Integrals: Changing Order of Integration – Full Example
-
Triple Integrals
-
Triple Integral in Spherical Coordinates
-
LaGrange Multipliers
-
Lagrange Multipliers: Two Constraints – Part 1
-
Lagrange Multipliers: Two Constraints – Part 2
-
Finding the Domain of a Vector Function
-
Vector Fields – Sketching
-
Conservative Vector Fields – The Definition and a Few Remarks
-
Gradient Vector – Notation and Definition
-
Finding the Directional Derivative – Ex 1
-
The Difference Quotient – Example 1
-
The Difference Quotient – Example 2
-
Fundamental Theorem for Line Integrals
-
Potential of a Conservative Vector Field – Ex 2
-
Potential for a Conservative Vector Field – Ex 1
-
Conservative Vector Fields – Showing a Vector Field on R_2 is Conservative
-
Jacobian
-
Curl and Showing a Vector Field is Conservative on R_3 – Ex 1
-
Arc Length of a Vector Function
-
Line Integrals – Evaluating a Line Integral
-
Curl and Showing a Vector Field is Conservative on R_3 – Ex 2
-
Green’s Theorem
-
Surface Area – Part 1
-
Surface Integral – Basic Example
-
Local Max/Min, Inc/Dec: On a Graph
-
Finding Limits From a Graph
-
Inverse Functions – The Basics!
-
Inverse of a Function
-
Finding the Inverse of a Function or Showing One Does not Exist, Ex 2
-
Finding the Inverse of a Function or Showing One Does not Exist, Ex 3
-
Finding the Inverse of a Function or Showing One Does not Exist, Ex 4
-
Conic Sections: Graphing Ellipses – Part 1
-
Properties of Logarithms
-
Word Problem: Exponential Growth
-
Finding the Sum of a Finite Arithmetic Series
DIFFERENTIAL EQUATIONS
DISCRETE MATH
LINEAR ALGEBRA
-
Solving a System of Linear Equations Using Inverses
-
Vectors: Finding Magnitude or Length
-
Linear Programming
-
Finding the Determinant of a 3 x 3 matrix
-
The Law of Cosines
-
Markov Chains – Intro Part 1
-
Markov Chains – Intro Part 2
-
The Simplex Method – Finding a Maximum / Word Problem Example, Part 1 of 5
-
The Simplex Method – Finding a Maximum / Word Problem Example, Part 2 of 5
-
The Simplex Method – Finding a Maximum / Word Problem Example, Part 3 of 5
-
The Simplex Method – Finding a Maximum / Word Problem Example, Part 4 of 5
-
The Simplex Method – Finding a Maximum / Word Problem Example, Part 5 of 5
-
Multiplying Matrices – Example 2
-
Multiplying Matrices – Example 3
-
Determinant of a 2 x 2 Matrix – A Few Basic Questions
-
Solving a 3 x 3 System of Equations Using the Inverse
-
Determinants to Find the Area of a Triangle
-
Determinants to Find the Area of a Polygon
-
An Introduction to Vectors, Part 1
-
Vector Basics: Drawing Vectors/Vector Addition
-
Finding the Components of a Vector, Ex 1
-
Finding the Components of a Vector, Ex 2
-
Vector Basics: Algebraic Representations – Part 1
-
Vector Basics: Algebraic Representations – Part 2
-
Vector Addition and Scalar Multiplication, Example 1
-
Vector Addition and Scalar Multiplication, Example 2
-
Magnitude and Direction of a Vector, Example 1
-
Magnitude and Direction of a Vector, Example 2
-
Magnitude and Direction of a Vector, Example 3
-
When Are Two Vectors Considered to Be the Same?
-
Finding a Unit Vector, Ex 1
-
Finding a Unit Vector, Ex 2
-
Vectors: The Dot Product
-
Cross Product
-
Torque: An application of the cross product
-
The Cartesian Coordinate System – A few basic questions
-
Linear System of Equations: Row Reducing – Part 1
-
Linear System of Equations: Row Reducing – Part 2
-
Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 1
-
Using Gauss-Jordan to Solve a System of Three Linear Equations – Example 2
-
Cramer’s Rule to Solve a System of 3 Linear Equations – Example 1
-
Cramer’s Rule to Solve a System of 3 Linear Equations – Example 2
-
Matrices: Basic Matrix Operations (add, subtract, multiply by constant)
-
Matrices: Multiplying a Matrix by another Matrix
-
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 1
-
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 2
-
Finding the Inverse of a 3 x 3 Matrix using Determinants and Cofactors – Example 3
-
Proof by Induction – Example 1
-
Proof by Induction – Example 2
-
Proof by Induction – Example 3
PROBABILITY AND STATISTICS
TRIGONOMETRY
-
Solving Trigonometric Equations
-
Right Triangles and Trigonometry
-
A Way to Remember the Unit Circle
-
A Trick to Remember Values on The Unit Circle
-
Deriving Trigonometric Identities from Known Identities
-
Proving some Random Trigonometric Identities
-
A way to remember the Entire Unit Circle for Trigonometry
-
Inverse Trigonometric Functions: Derivatives – Ex 1
-
Graphing the Trigonometric Functions
-
Graphing Trigonometric Functions, Graph Transformations – Part 1
-
The Law of Cosines
-
Special Right Triangles in Trigonometry: 45-45-90 and 30-60-90
-
Complementary and Supplementary Angles – Example 1
-
Complementary and Supplementary Angles – Example 2
-
Degrees and Radians and Converting Between Them! Example 1
-
Degrees and Radians and Converting Between Them! Example 2
-
The Trigonometric Functions: The Basics! Example 1
-
The Trigonometric Functions: The Basics! Example 2
-
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 1
-
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 2
-
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 3
-
Finding an Angle Given the Value of a Trigonometric Function – Example 1
-
Finding an Angle Given the Value of a Trigonometric Function – Example 2
-
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 1
-
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 2
-
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 3
-
Finding the Height of an Object Using Trigonometry, Example 1
-
Finding the Height of an Object Using Trigonometry, Example 2
-
Finding the Height of an Object Using Trigonometry, Example 3
-
Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1
-
Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 2
-
Reference Angle for an Angle, Ex 1 (Using Degrees)
-
Reference Angle for an Angle, Ex 2 (Using Radians)
-
Evaluating Trigonometric Functions Using the Reference Angle, Example 1
-
Evaluating Trigonometric Functions Using the Reference Angle, Example 2
-
Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 1
-
Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 2
-
Evaluating Trigonometric Functions at Important Angles, Ex 1
-
Evaluating Trigonometric Functions at Important Angles, Ex 2
-
The Graph of Cosine, y = cos (x)
-
Graphing Sine and Cosine With Different Coefficients (Amplitude and Period), Ex 1
-
Graphing y = -2 cos(2x)
-
Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 1
-
Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 2
-
Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts, Ex 2
-
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 1
-
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 2
-
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 3
-
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4
-
Finding a Formula for a Trigonometric Graph, Ex 1
-
Finding a Formula for a Trigonometric Graph, Ex 2
-
Trigonometry Word Problem, Finding The Height of a Building, Example 1
-
Trigonometry Word Problem, Example 2
-
Trigonometry Word Problem, Determining the Speed of a Boat, Example 3
-
Simplifying Trigonometric Expressions Using Identities, Example 1
-
Simplifying Trigonometric Expressions Using Identities, Example 2
-
Simplifying Trigonometric Expressions Using Identities, Example 3
-
Simplifying Trigonometric Expressions Involving Fractions, Ex 1
-
Simplifying Trigonometric Expressions Involving Fractions, Example 2
-
Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1
-
Examples with Trigonometric Functions: Even, Odd or Neither, Example 1
-
Examples with Trigonometric Functions: Even, Odd or Neither, Example 2
-
Examples with Trigonometric Functions: Even, Odd or Neither, Example 3
-
Examples with Trigonometric Functions: Even, Odd or Neither, Example 4
-
Proving an Identity, Example 1
-
Proving an Identity, Example 2
-
Proving an Identity – Other Examples, Example 1
-
Proving an Identity – Other Examples, Example 2
-
Solving a Basic Trigonometric Equation, Example 1
-
Solving a Basic Trigonometric Equation, Example 2
-
Solving a Basic Trigonometric Equation, Example 3
-
Solving a Trigonometric Equation by Factoring, Example 1
-
Solving a Trigonometric Equation by Factoring, Example 2
-
Solving a Trigonometric Equation by Factoring, Example 3
-
Solving Trigonometric Equations with Coefficients in the Argument – Example 1
-
Solving Trigonometric Equations with Coefficients in the Argument – Example 2
-
Solving Trigonometric Equations with Coefficients in the Argument – Example 3
-
Solving Trigonometric Equations Using the Quadratic Formula – Example 1
-
Solving Trigonometric Equations Using the Quadratic Formula – Example 2
-
Solving Trigonometric Equations Using the Quadratic Formula – Example 3
-
Solving Word Problems Involving Trigonometric Equations, Example 2
-
Identities for Sum and Differences of Sine and Cosine, Example 1
-
Identities for Sum and Differences of Sine and Cosine, Example 2
-
Solving Word Problems Involving Trigonometric Equations, Example 1
-
Sum and Difference Identities to Simplify an Expression, Example 3
-
Identities for Sum and Differences of Sine and Cosine, Example 3
-
Sum and Difference Identities for Sine and Cosine, More Examples #1
-
Sum and Difference Identities for Sine and Cosine, More Examples #2
-
Sum and Difference Identities for Sine and Cosine, More Examples #3
-
Sum and Difference Identities to Simplify an Expression, Example 1
-
Sum and Difference Identities to Simplify an Expression, Example 2
-
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 1
-
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2
-
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 3
-
Using Double Angle Identities to Solve Equations, Example 1
-
Using Double Angle Identities to Solve Equations, Example 2
-
Half Angle Identities to Evaluate Trigonometric Expressions, Example 3
-
Using Double Angle Identities to Solve Equations, Example 3
-
Word Problems Involving Multiple Angle Identities, Example 1
-
Word Problems Involving Multiple Angle Identities, Example 2
-
Word Problems Involving Multiple Angle Identities, Example 3
-
Cofunction Identities, Example 2
-
Cofunction Identities, Example 3
-
Power Reducing Formulas for Sine and Cosine, Example 1
-
Power Reducing Formulas for Sine and Cosine, Example 2
-
Half Angle Identities to Evaluate Trigonometric Expressions, Example 1
-
Half Angle Identities to Evaluate Trigonometric Expressions, Example 2
-
Law of Cosines, Example 2
-
The Law of Sines, Example 1
-
The Law of Sines, Example 2
-
Law of Sines, Example 3
-
Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 1
-
Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 2
-
Solving a Triangle, SAS, Example 1
-
Solving a Triangle, SAS, Example 2
-
Law of Sines – Application/Word Problem, Ex 1
-
Law of Sines – Application / Word Problem, Ex 2
-
Heron’s Formula, Example 1
-
Heron’s Formula, Example 3
-
Law of Cosines, Example 1
-
Heron’s Formula, Ex 2
-
Law of Cosines, Example 3
-
Law of Cosines, Example 4
-
Law of Cosines, Example 5
-
Law of Cosines, Example 6
-
Law of Cosines, Word Problem #1
-
DeMoivre’s Theorem: Raising a Complex Number to a Power, Ex 1
-
DeMoivre’s Theorem: Raising a Complex Number to a Power, Ex 2
-
Degrees and Radians
-
Maximum and Minimum Values of Sine and Cosine Functions, Ex 1
-
Maximum and Minimum Values of Sine and Cosine Functions, Ex 2
-
Inverse Trigonometric Functions: Derivatives – Ex 2
-
Inverse Trigonometric Functions: Derivatives – Ex 3
-
Integrals: Inverse Trigonometric Functions – Ex 1
-
Integrals: Inverse Trigonometric Functions – Ex 2
-
Arc Length Formula – Example 1
-
Arc Length Formula – Example 2
-
Polar Coordinates – The Basics
-
Graphing a Polar Curve – Part 1
-
Graphing a Polar Curve – Part 2
-
Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 1
-
Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 2
-
Solving for ‘X’ ; Quadratic Equations Involving the Pythagorean Theorem – Ex 3
-
The Distance Formula and Finding the Distance Between Two Points – Example 1
-
Pythagorean Theorem
-
Word Problems Using the Pythagorean Theorem – Ex 1
-
Word Problems Using the Pythagorean Theorem – Ex 2
-
Word Problems Using the Pythagorean Theorem – Ex 3
-
Coterminal Angles – Example 1
-
Coterminal Angles – Example 2
-
Coterminal Angles – Example 3
-
Finding the Quadrant in Which an Angle Lies – Example 1
-
Finding the Quadrant in Which an Angle Lies – Example 2
-
Finding the Quadrant in Which an Angle Lies – Example 3
-
The Center-Radius Form for a Circle – A few Basic Questions, Example 1
-
The Center-Radius Form for a Circle – A few Basic Questions, Example 2
-
Factoring Trigonometric Expressions, Example 1
-
Factoring and Simplifying Trigonometric Expressions – Example 2
-
Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2
Misc
-
Venn Diagrams – An Introduction
-
Recursive Sequences
-
Graph Theory – An Introduction!
-
Euler Circuits and Euler Paths
-
Complex Numbers: Graphing and Finding the Modulus, Ex 1
-
Complex Numbers: Graphing and Finding the Modulus, Ex 2
-
Expressing a Complex Number in Trigonometric or Polar Form, Ex 1
-
Expressing a Complex Number in Trigonometric or Polar Form, Ex 2
-
Expressing a Complex Number in Trigonometric or Polar Form, Ex 3
-
Complex Numbers: Convert From Polar to Complex Form, Ex 1
-
Complex Numbers: Multiplying and Dividing in Polar Form, Ex 1
-
Complex Numbers: Multiplying and Dividing in Polar Form, Ex 2
-
DeMoivre’s Theorem: Raising a Complex Number to a Power, Ex 1
-
DeMoivre’s Theorem: Raising a Complex Number to a Power, Ex 2
-
Fractions – Adding and Subtracting
-
Fractions – Multiplying and Dividing
-
Proof By Contradiction – Calculus Based Example
-
Absolute Value: Evaluating Numbers
-
Negative Exponents – Basic Rules and Examples
