Algebra I Course Outline

The Algebra I course is designed for students who have demonstrated mastery of arithmetic and prealgebra and have shown an ability to engage in abstract mathematical reasoning. Algebra I will cover basic Algebraic operations through quadratic equations, rational expressions, and radical expressions. This course uses Algebra I: Expressions, Equations, and Applications by P. Foerster.

Semester I

Chapter 2: Operations with Negative Numbers

  • calculations with negative and signed numbers
  • commuting and associating
  • equations with two transformations

Chapter 3: Distributing Axioms and Other Properties

  • distribution multiplication over addition and subtraction
  • like terms and common factors
  • more distributive properties
  • axioms for adding and multiplying
  • properties of equality

Chapter 4: Harder Equations

  • equations with like terms and distributing
  • equations with variable in both members
  • equations that involve decimals
  • literal equations and formulas

Chapter 13: Inequalities

  • number-line graphs
  • solving inequalities
  • inequalities involving absolute values

Chapter 5: Some Operations with Polynomials and Radicals

  • polynomials
  • product of two binomials
  • factoring quadratic trinomials

Semester II

Chapter 5: Some Operations with Polynomials and Radicals

  • Squaring a binomial
  • factoring trinomial squares
  • radical and irrational numbers

Chapter 6: Quadratic Equations

  • Evaluating radical expressions
  • Equations with absolute values
  • Equations with squares and trinomial squares
  • completing the square
  • the Quadratic Formula
  • quadratic word problems
  • the Discriminant

Chapter 7: Expressions and Equations Containing Two Variables

  • Evaluating 2-variable expressions
  • the Cartesian Coordinate System
  • Graphs of equations with two variables
  • intercepts and slopes
  • graphing
  • solving systems of equations by substitution and combination
  • word problems with two variables

Chapter 9: Properties of Exponents

  • Prime number and prime factors
  • Exponentiation, products, and powers
  • Negative and Zero Exponents
  • Powers of 10 and Scientific Notation

Chapter 10: More Operations with Polynomials

  • Greatest common factors
  • factoring polynomials that have common factors
  • common binomial factors
  • factoring by grouping
  • solving quadratic equations by factoring

Chapter 11: Rational Algebraic Expressions

  • simplifying rational expressions
  • multiplying and dividing rational expressions
  • least common multiples
  • operations with rational expressions
  • long division of polynomials
  • extraneous solutions

Chapter 12: Radical Algebraic Expressions (as time allows)

  • operations with radicals
  • binomials with radicals
  • square roots
  • radical equations
  • higher-order radicals

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