# Algebra

**Sets**

Lesson 1: Introduction to Sets

Lesson 2: Examples of Sets

Lesson 3: Intersection of Sets

Lesson 4: Intersection of Sets Part 2

Lesson 5: Union of Sets

Lesson 6: Definition of Subset

Lesson 7: Definition of Universal Set

Note: Tutorials on Integers can be found in the **Basic Math** page.

**Algebraic Expressions**

Lesson 1: Introduction to Algebraic Expressions

Lesson 2: Representation with Algebraic Expressions

Lesson 3: Representing Multiplication Using Algebraic Expression

Lesson 4: Representing Exponentiation with Algebraic Expressions

Lesson 5: Representing Division with Algebraic Expressions

Lesson 6: Evaluating Algebraic Expressions

Lesson 7: Terms and Coefficients of Algebraic Expressions

Lesson 8: Addition of Algebraic Expressions Part 1

Lesson 9: Addition of Algebraic Expressions Part 2

Lesson 10: Subtraction of Algebraic Expressions

Lesson 11: Multiplication of Algebraic Expressions

Lesson 12: The Distributive Property

Lesson 13: Division of Algebraic Expressions

**Rational Expressions**

Lesson 1: Introduction to Rational Expression

Lesson 2: Evaluating Rational Expression

Lesson 3: Ruling Out Values of the Variable

Lesson 4: Domain and Range of Rational Functions

Lesson 5: Reducing Rational Expressions to Lowest Terms Part 1

Lesson 6: Reducing Rational Expressions to Lowest Terms Part 2

Lesson 7: Reducing Rational Expressions to Lowest Terms Part 3

Lesson 8: Simplifying Expression Containing m – n and n – m

Lesson 9: Multiplication of Rational Numbers

Lesson 10: Multiplication of Rational Expressions Part 1

Lesson 11: Multiplication of Rational Expressions Part 2

Lesson 12: Multiplication of Rational Expressions Part 3 (Cancellation)

Lesson 13: Multiplication of Rational Expressions Part 4 (Cancellation)

Lesson 14: Division of Rational Numbers

Lesson 15: Division of Rational Expressions Part 1

Lesson 16: Division of Rational Expressions Part 2

Lesson 17: Division of Rational Expressions Part 3

Lesson 18: Equivalent Fractions and Equivalent Rational Expressions

Lesson 19: How to Get the LCD of Rational Expressions

Lesson 20: Addition and Subtraction of Rational Expressions Part 1 (Same Denominator)

Lesson 21: Addition and Subtraction of Rational Expressions Part 2 (Same Denominator)

Lesson 22: Addition and Subtraction of Rational Expressions Part 1 (Different Denominators)

Lesson 23: Addition and Subtraction of Rational Expressions Part 2 (Different Denominator)

Lesson 24: Addition and Subtraction of Rational Expressions Part 3 (Different Denominator)

Lesson 25: Addition and Subtraction of Rational Expressions Part 4 (Different Denominator)

Lesson 26: Addition and Subtraction of Rational Expressions Part 5 (Different Denominator)

Lesson 27: Addition and Subtraction of Rational Expressions Part 6 (Different Denominator)

**Linear Equations**

Lesson 1 : Introduction to Equations

Lesson 2: Solutions to Equations

Lesson 3: Properties of Equality

Lesson 4: Solving Equations Part 1

Lesson 5: Solving Equations Part 2

Lesson 6: Solving Equations Part 3

Lesson 7: Solving Equations Part 4

How to Solve Equations (New!)

Lesson 1: Solving Equations – Worked Examples 1

Lesson 2: Solving Equations – Worked Examples 2

Lesson 3: Solving Equations – Worked Examples 3

Lesson 4: Solving Equations – Worked Examples 4

Lesson 5: Solving Equations – Worked Examples 5

Lesson 6: Solving Equations – Worked Examples 6

Lesson 7: Solving Equations – Worked Examples 7

Lesson 8: Solving Equations with Parentheses Part 1

Lesson 9: Solving Equations with Parentheses Part 2

Lesson 10: Solving Equations with Parentheses Part 3

Lesson 11: Solving Equations with Fractions Part 1

Lesson 12: Solving Equations with Fractions Part 2

Lesson 13: Solving Equations with Fractions Part 3

Lesson 14: Solving Equations with Fractions Part 4

**Quadratic Equations**

Lesson 1: Introduction to Quadratic Equations

Lesson 2: Solving Quadratic Equation – Extracting the Square Root Part 1

Lesson 3: Solving Quadratic Equation – Extracting the Square Root Part 2

Lesson 4: Solving Quadratic Equations – Factoring Part 1

Lesson 5: Solving Quadratic Equations – Factoring Part 2

Lesson 6: Solving Quadratic Equations – Completing the Square Part 1

Lesson 7: Solving Quadratic Equations – Completing the Square Part 2

Lesson 8: Solving Quadratic Equations – Completing the Square Part 3

Lesson 9: Derivation of the Quadratic Formula

Lesson 10: Quadratic Equations – Quadratic Formula Part 1

Lesson 11: Quadratic Equations – Quadratic Formula Part 2

Lesson 12: Nature of the Roots of Quadratic Equations

Lesson 13: Quadratic Equations – Equal Roots

Lesson 14:Quadratic Equations -Distinct Roots

Lesson 15: Quadratic Equations – Complex Roots

Lesson 16: Getting the Quadratic Equation Given its Roots Part 1

Lesson 17: Getting the Quadratic Equation Given its Roots Part 2

Lesson 18: Quadratic Word Problems Part 1

Lesson 19: Quadratic Word Problems Part 2

Lesson 20: Quadratic Word Problems Part 3

Lesson 21: Quadratic Word Problems Part 4

**Systems of Linear Equations**

Lesson 1: Introduction to Systems of Equations

Lesson 2: Systems of Linear Equation – Substitution Part 1

Lesson 3: Systems of Linear Equations – Substitution Part 2

Lesson 4: Systems of Linear Equations – Elimination Part 1

Lesson 5: Systems of Linear Equations – Elimination Part 2

Lesson 6: Systems of Equations – Graphing

**Arithmetic Sequence**

Lesson 1: Introduction to Arithmetic Sequence

Lesson 2: Derivation of the Formula for Arithmetic Sequence

Lesson 3: Arithmetic Sequence Sample Problems 1 and 2

Lesson 4: Arithmetic Sequence Sample Problem 3

Lesson 5: Arithmetic Sequence Sample Problem 4

Lesson 6: Arithmetic Sequence Sample Problem 5

Lesson 7: Arithmetic Sequence Sample Problem 6

**Geometric Sequence**

Lesson 1 : Introduction to Geometric Sequence

Lesson 2: Definition of Geometric Sequence

Lesson 3: Deriving the Formula for the General Term of a Geometric Sequence

Lesson 4: Geometric Sequence Sample Problem 1

Lesson 5: Geometric Sequence Sample Problem 2

Lesson 6: Geometric Sequence Sample Problem 3

Lesson 7: Geometric Sequence Sample Problem 4

Lesson 8: Geometric Sequence Sample Problem 5

Lesson 9: Geometric Sequence Sample Problem 6

Lesson 10: Geometric Sequence Sample Problem 7

**Ratio and Proportion**

Lesson 1: Ratio and Proportion: Definition and Representation of Ratio

Lesson 2: Ratio Sample Problem 1

Lesson 3: Ratio Sample Problem 2

Lesson 4: Ratio Sample Problem 3

Lesson 5: Understanding the Meaning of Proportion

Lesson 6: Proportion and Equivalent Fractions

Lesson 7: Ratio and Proportion Sample Problem 1

Lesson 8: Ratio and Proportion Sample Problem 2

Lesson 9: Ratio and Proportion Sample Problem 3

Lesson 10: Ratio and Proportion Sample Problem 4

**Direct and Inverse Proportion**

Lesson 1: Introduction to Direct Proportion

Lesson 2: Direct Proportion Sample Problem 1

Lesson 3: Direct Proportion Sample Problem 2

Lesson 4: Direct Proportion Sample Problem 3

Lesson 5: Constant of Proportionality Part 1

Lesson 6: Constant of Proportionality Part 2

Lesson 7: Introduction to Inverse Proportion

Lesson 8: Inverse Proportion Sample Problem 1

Lesson 9: Inverse Proportion Sample Problem 2

Lesson 10: Constant of Proportionality Part 3

Lesson 11: Direct and Inverse Proportion (Summary)

**Direct Linear Variation**

Lesson 1: Introduction to Direct Linear Variation

Lesson 2: Direct Linear Variation Sample Problems Part 1

Lesson 3: Direct Linear Variation Sample Problems Part 2

Lesson 4: Direct Linear Variation Sample Problems Part 3

Lesson 5: Direct Linear Variation Sample Problems Part 4

Lesson 6: Links among Direct Variation, Direct Proportion, and Linear Function

**Direct Square Variation**

Lesson 1: Introduction to Direct Square Variation

Lesson 2: Direct Square Variation Sample Problem Part 1

Lesson 3: Direct Square Variation Sample Problem Part 2

Lesson 4: Direct Square Variation Sample Problem Part 3

Lesson 5: Graphs of Direct Square Variation

**Inverse Variation**

Lesson 1: Introduction to Inverse Variation

Lesson 2: Inverse Variation Sample Problems Part 1

Lesson 3: Inverse Variation Sample Problems Part 2

Lesson 4: Inverse Variation Sample Problems Part 3

**Joint Variation**

Lesson 1: Introduction to Joint Variation Part 1

Lesson 2: Introduction to Joint Variation Part 2

Lesson 3: Joint Variation Sample Problem Part 1

Lesson 4: Joint Variation Sample Problem Part 2

**Combined Variation**

Lesson 1: Introduction to Combined Variation

Lesson 2: Combined Variation Tutorial Part 2

Lesson 3: Combined Variation Tutorial Part 3

**Factoring**

Lesson 1: Basic Concepts of Factoring

Lesson 2: Factoring Polynomials with Common Monomial Factor

Lesson 3: Factoring Polynomials by Grouping Part 1

Lesson 4: Factoring Polynomials by Grouping Part 2

Lesson 5: Factoring Perfect Square Trinomials

Lesson 6: Factoring General Trinomials Part 1

Lesson 7: Factoring General Trinomials Part 2

Lesson 8: Factoring General Trinomials Part 3

Lesson 9: Factoring Difference of Two Squares

Lesson 10: Factoring Sum and Difference of Two Cubes

Lesson 11: Factoring Polynomials with More than 2 Factors