Algebra 1 - Full Course

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Algebra 1 – Full Course

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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.

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Table of Contents

Chapter 1 – THE REAL NUMBER SYSTEM

  • 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

Chapter 2 – FUNDAMENTALS OF ALGEBRA

  • 2.1 Writing and Evaluating Algebraic Expressions
  • 2.2 Simplifying Algebraic Expressions
  • 2.3 Algebra and Problem Solving
  • 2.4 Introduction to Equations

Chapter 3 – LINEAR EQUATIONS AND PROBLEM SOLVING

  • 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

Chapter 4 – EQUATIONS AND INEQUALITIES IN TWO VARIABLES

  • 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

Chapter 5 – EXPONENTS AND POLYNOMIALS

  • 5.1 Negative Exponents and Scientific Notation
  • 5.2 Adding and Subtracting Polynomials
  • 5.3 Multiplying Polynomials: Special Products
  • 5.4 Dividing Polynomials

Chapter 5 – EXPONENTS AND POLYNOMIALS

  • 5.1 Negative Exponents and Scientific Notation
  • 5.2 Adding and Subtracting Polynomials
  • 5.3 Multiplying Polynomials: Special Products
  • 5.4 Dividing Polynomials

Chapter 6 – FACTORING AND SOLVING EQUATIONS

  • 6.1 Factoring Polynomials with Common Factors
  • 6.2 Factoring Trinomials
  • 6.3 More About Factoring Trinomials
  • 6.4 Factoring Polynomials with Special Forms
  • 6.5 Solving Quadratic Equations by Factoring

Chapter 7 – RATIONAL EXPRESSIONS AND EQUATIONS

  • 7.1 Simplifying Rational Expressions
  • 7.2 Multiplying and Dividing Rational Expressions
  • 7.3 Adding and Subtracting Rational Expressions
  • 7.4 Complex Fractions
  • 7.5 Rational Equations and Applications

Chapter 8 – SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES

  • 8.1 Solving Systems of Equations by Graphing
  • 8.2 Solving Systems of Equations by Substitution
  • 8.3 Solving Systems of Equations by Elimination
  • 8.4 Applications of Systems of Linear Equations
  • 8.5 Systems of Linear Inequalities

Chapter 9 – RADICAL EXPRESSIONS AND EQUATIONS

  • 9.1 Roots and Radicals
  • 9.2 Simplifying Radicals
  • 9.3 Operations with Radical Expressions
  • 9.4 Radical Equations and Applications

Chapter 10 – QUADRATIC EQUATIONS AND FUNCTIONS

  • 10.1 Solution by the Square Root Property
  • 10.2 Solution by Completing the Square
  • 10.3 Solution by the Quadratic Formula
  • 10.4 Graphing Quadratic Equations
  • 10.5 Applications of Quadratic Equations
  • 10.6 Complex Numbers
  • 10.7 Relations, Functions, and Graphs