Algebra I Course Outline

Algebra is a gateway to all higher mathematics. Students will learnthe skills and concepts that will help them think logically, problem-solve, recognize relationships and patterns, and represent verbal situations as equations.

Chapter 1: Basic Concepts of Algebra

  • Identify, classify, graph, compare real numbers 
  • Absolute Values 
  • Add, subtract, multiply, divide signed numbers 
  • Powers and Exponents 
  • Order of Operations 
  • Scientific Notation 
  • Evaluate algebraic expressions 

Chapter 2: Linear Equations

  • Solve and check 
  • Distributive Property 
  • Absolute Value Equations 
  • Formulas and Literal Equations 

Chapter 3: Linear Inequalities

  • Write, graph, solve inequalities 
  • Compound Inequalities 
  • Inequalities involving absolute value expressions 

Chapter 4: Relations and Functions

  • Represent relations 
  • Relations and Functions  
  • Domain and Range 
  • Function Notation 
  • Vertical Line Test 

Chapter 5: Linear Functions

  • Linear functions and their graphs 
  • Slope 
  • Direct Variation 
  • Slope-Intercept Form 
  • Parallel and Perpendicular Lines 
  • Linear inequality in Two Variables 

Chapter 6: Systems of Linear Equations and Inequalities

  • Graph systems of linear equations 
  • Solve systems of linear equations by substitution and elimination 
  • Equivalent Systems of Linear Equations 
  • Applications 
  • Graph and solve systems of linear inequalities in two variables 

Chapter 7: Operations with Polynomials

  • identify and classify polynomials 
  • Standard Form 
  • Add, subtract, multiply, divide polynomials 
  • Binomial Multiplication  
  • Polynomial Long Division 

Chapter 8: Factoring Polynomials

  • GCMF 
  • Square a binomial 
  • Factor quadratic trinomials (leading coefficient 1, leading coefficient other than 1, perfect-square trinomial, difference of two squares, factor by grouping) 
  • Factor completely 

Chapter 9: Radical Expressions and Equations

  • Simple Radical Form 
  • Add, subtract, multiply, divide radical expressions 
  • Solve radical equations 

Chapter 10: Quadratic Functions and Equations

  • Quadratic functions and their graphs (direction of opening, vertex, axis of symmetry, intercepts, maximum/minimum, domain & range) 
  • Solve quadratic equations (by factoring, completing the square, using the QF) 
  • Discriminant 
  • Verbal problems involving quadratic equations 

Chapter 12: Rational Expressions and Equations

  • Excluded Values 
  • Simplify, multiply, divide rational expressions 
  • Combine rational expressions with like & unlike denominators 
  • Solve rational equations 

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