## 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

## Semester II

Chapter 5: Some Operations with Polynomials and Radicals

• Squaring a binomial
• factoring trinomial squares

• Equations with absolute values
• Equations with squares and trinomial squares
• completing the square
• 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)