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Algebra 1 – Full Course

Core topics include solving linear equations and inequalities, graphing equations and inequalities with some use of the graphing calculator, exponents, polynomials, factoring, rational expressions and equations, systems of linear equations and inequalities, radical expressions and equations, and solving quadratic equations. Algebra I follows Prealgebra in the sequence of math courses and is often used as a developmental course at the college level under the name Elementary Algebra.

Table of Contents

  • 1.1 Real Numbers: Order and Absolute Value
  • 1.2 Adding and Subtracting Integers
  • 1.3 Multiplying and Dividing Integers
  • 1.4 Operations with Rational Numbers
  • 1.5 Exponents, Order of Operations, and Properties of Real Numbers
  • 2.1 Writing and Evaluating Algebraic Expressions
  • 2.2 Simplifying Algebraic Expressions
  • 2.3 Algebra and Problem Solving
  • 2.4 Introduction to Equations
  • 3.1 Solving Linear Equations
  • 3.2 Equations that Reduce to Linear Form
  • 3.3 Problem Solving with Percents
  • 3.4 Ratios and Proportions
  • 3.5 Geometric and Scientific Applications
  • 3.6 Linear Inequalities
  • 4.1 Ordered Pairs and Graphs
  • 4.2 Graphs of Equations in Two Variables
  • 4.3 Slope and Graphs of Linear Equations
  • 4.4 Equations of Lines
  • 4.5 Graphs of Linear Inequalities
  • 5.1 Negative Exponents and Scientific Notation
  • 5.2 Adding and Subtracting Polynomials
  • 5.3 Multiplying Polynomials: Special Products
  • 5.4 Dividing Polynomials

  • 6.1  Factoring Polynomials with Common Factors 17 min.

    • Greatest Common Factor
    • Common Monomial Factors
    • Factoring by Grouping

    6.2  Factoring Trinomials 23 min.

    • Factoring Trinomials of the Form x2 + bx + c
    • Factoring Trinomials in Two Variables
    • Factoring Completely

    6.3  More About Factoring Trinomials 17 min.

    • Factoring Trinomials of the form ax2 + bx + c
    • Factoring Completely

    6.4  Factoring Polynomials with Special Forms 29 min.

    • Difference of Two Squares
    • Repeated Factorization
    • Perfect Square Trinomials
    • Sum or Difference of Two Cubes

    6.5  Solving Quadratic Equations by Factoring24 min.

    • The Zero-Factor Property
    • Solving Quadratic Equations by Factoring

  • 7.1  Simplifying Rational Expressions 18 min.

    • Rational Expressions and Their Domains
    • Simplifying Rational Expressions

    7.2  Multiplying and Dividing Rational Expressions 15 min.

    • Multiplying Rational Expressions
    • Dividing Rational Expressions

    7.3  Adding and Subtracting Rational Expressions 25 min.

    • Rational Expressions with Like Denominators
    • Least Common Multiple
    • Rational Expressions with Unlike Denominators

    7.4  Complex Fractions 16 min.

    • Complex Fractions
    • Complex Fractions with Sums or Differences

    7.5  Rational Equations and Applications 25 min.

    • Equations Containing Constant Denominators
    • Equations Containing Variable Denominators
    • Applications

  • 8.1  Solving Systems of Equations by Graphing 11 min.

    • Systems of Linear Equations
    • Solving a System of Linear Equations by Graphing
    • The No-Solution and Many-Solution Cases

    8.2  Solving Systems of Equations by Substitution 15 min.

    • The Method of Substitution
    • The No-Solution and Many-Solution Cases

    8.3  Solving Systems of Equations by Elimination 25 min.

    • The Method of Elimination
    • The No-Solution and Many-Solution Cases

    8.4  Applications of Systems of Linear Equations 14 min.

    • Constructing Systems of Equations
    • Applications of Systems of Linear Equations

    8.5  Systems of Linear Inequalities 16 min.

    • Systems of Linear Inequalities in Two Variables
    • Finding Boundaries and Identifying the Solution Region

  • 9.1  Roots and Radicals 22 min.

    • Equal Factors and Roots
    • Radicals
    • Radicals and Calculators

    9.2  Simplifying Radicals 37 min.

    • Simplifying Radicals with Constant Factors
    • Simplifying Radicals with Variable Factors
    • Rationalizing Denominators

    9.3  Operations with Radical Expressions 26 min.

    • Adding and Subtracting Radical Expressions
    • Multiplying Radical Expressions
    • Conjugates
    • Simplifying Quotients Involving Radicals

    9.4  Radical Equations and Applications 29 min.

    • Solving Equations Involving One Radical
    • Solving Equations Involving Two Radicals
    • Applications Involving Radicals

  • 10.1  Solution by the Square Root Property 11 min.

    • Solving Quadratic Equations by Factoring
    • Solving Quadratic Equations by the Square Root Property

    10.2  Solution by Completing the Square 24 min.

    • Constructing Perfect Square Trinomials
    • Completing the Square

    10.3  Solution by the Quadratic Formula 23 min.

    • Deriving the Quadratic Formula
    • Solving Equations by the Quadratic Formula

    10.4  Graphing Quadratic Equations 36 min.

    • Quadratic Equations in Two Variables
    • Sketching the Graph of a Quadratic Equation

    10.5  Applications of Quadratic Equations 23 min.

    • Applications of Quadratic Equations

    10.6  Complex Numbers 28 min.

    • The Imaginary Unit i
    • Complex Numbers
    • Operations with Complex Numbers
    • Complex Conjugates
    • Quadratic Equations with Complex Solutions

    10.7  Relations, Functions, and Graphs 32 min.

    • Relations
    • Functions
    • Function Notation
    • Finding the Domain of a Function

Sample Videos from this Course

Section 3.1 - Solving Linear Equations
Section 4.3 - Slope and Graphs of Linear Equations
Section 6.2 - Factoring Trinomials
Section 9.2 - Simplifying Radicals
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