Algebra I Table of Contents

CD 1 - Real Numbers, Variables, and Algebraic Expressions

Chapter One – Introduction to Real Numbers and Variables

1.1 Variables and Algebraic Expressions

  • Write word phrases as algebraic expressions
  • Find values of algebraic expressions given values of the variables
  • 1.2 Order of Operations
  • Define and use order of operations to evaluate an expression
  • Use substitution to evaluate an expression
  • 1.3 Set of Real Numbers
  • Identify common sets of numbers
  • Construct a number line
  • 1.4 Comparing Real Numbers
  • Define the meaning of <, >, and =
  • Compare and order real numbers
  • 1.5 Exponents
  • Evaluate exponential expressions
  • Chapter Two – Operations With Real Numbers

2.1 Adding Real Numbers on the Number Line

  • Add real numbers on a number line
  • 2.2 Adding Real Numbers
  • Find the absolute value of a real number
  • Add real numbers
  • 2.3 Subtracting Real Numbers
  • Find the opposite of a real number
  • Subtract real numbers

2.4 Multiplying Real Numbers

  • Multiply real numbers
  • 2.5 Dividing Real Numbers
  • Divide real numbers
  • 2.6 Properties of Real Numbers
  • Understand and use the properties of real numbers
  • Chapter Three – Algebraic Expressions

3.1 Evaluating Algebraic Expressions

  • Use the order of operations to evaluate expressions.
  • Find values of algebraic expressions given replacement values.
  • 3.2 Combining Like Terms
  • Combine like terms
  • 3.3 Simplifying Algebraic Expressions
  • Simplify algebraic expressions by combining like terms.
  • CD 2 - Solving Equations and Problem Solving

Chapter Four – Solving Equations

4.1 Solution Sets

  • Find the solution set of an open sentence from a given replacement set
  • 4.2 Solving Equations Using Addition and Subtraction Properties
  • Use the addition and subtraction properties for equations to solve equations
  • 4.3 Solving Equations Using Multiplication and Division Properties
  • Solve equations using multiplication and division properties for equations
  • 4.4 Solving Equations Requiring More Than One Property
  • Solve equations using more than one property
  • 4.5 Solving Equations with Variables on Both Sides
  • Solve equations containing variables on both sides of the equal sign
  • 4.6 Solving Percent Equations
  • Use equations to solve percent problems
  • 4.7 Solving Literal Equations
  • Solve literal equations for a specified variable
  • 4.8 Solving Absolute Value Equations
  • Solve equations containing the absolute value of a variable expression
  • Chapter Five – Problem Solving

5.1 Problem Solving: Using Formulas to Solve Applications

  • Use formulas to solve word problems, and solve an equation for a specified variable
  • 5.2 Problem Solving: From Words to Symbols
  • Write equations to solve problems
  • 5.3 Problem Solving: Geometry Applications

Solve problems using geometric formulas

5.4 Problem Solving: Percent Applications

  • Solve problems involving percent (percent increase, or percent decrease)
  • 5.5 Problem Solving: Mixtures
  • Solve problems involving mixtures
  • 5.6 Problem Solving: Distance/Rate/Time
  • Use the formula d = r t to solve problems
  • CD 3 - Inequalities and Exponents

Chapter Six - Solving Inequalities

6.1 Graphing Inequalities

  • Graph inequalities on a number line
  • 6.2 Solving Inequalities Using Addition and Subtraction Properties
  • Solve inequalities using addition and subtraction properties for inequalities
  • 6.3 Solving Inequalities Using Multiplication and Division Properties
  • Solve inequalities using multiplication and division properties for inequalities
  • 6.4 Solving Inequalities Requiring More Than One Step
  • Solve inequalities using more than one property
  • 6.5 Solving Combined Inequalities
  • Solve combined inequalities and graph their solution sets
  • 6.6 Solving Absolute Value Inequalities
  • Solve inequalities containing the absolute value of a variable expression
  • Chapter Seven - Exponents

7.1 Multiplying Monomials

  • Define an exponent
  • Product rule for exponents
  • Identify and multiply monomials
  • 7.2 Powers of Monomials
  • Raise a monomial to a power
  • 7.3 Dividing Monomials
  • Divide monomials
  • 7.4 Negative Exponents
  • Simplify exponential expressions containing negative exponents
  • 7.5 Scientific Notation
  • Write numbers in Scientific Notation
  • Convert and find product or quotient in Scientific Notation.
  • CD 4 - Operations on Polynomials and Factoring

Chapter Eight – Operations With Polynomials

8.1 Polynomials

  • Identify the degree of a polynomial
  • Review combining like terms
  • 8.2 Adding and Subtracting Polynomials
  • Add polynomials
  • Subtract polynomials
  • 8.3 Multiplying Polynomials
  • Review multiplying monomials and multiply polynomials
  • 8.4 Multiplying Binomials
  • Use the FOIL order of multiplication to multiply binomials
  • 8.5 Special Products
  • Square binomials
  • Find product of the sum and difference of the same two terms
  • 8.6 Dividing Polynomials
  • Divide polynomials
  • Chapter Nine - Factoring Polynomials

9.1 Factoring Integers

  • Write a number as a product of prime numbers
  • Find the Greatest Common Factor of a list of integers
  • 9.2 The Greatest Common Factor
  • Find the GCF of a list of monomials
  • Factor the GCF from a polynomial
  • Factor polynomials by factoring out common binomials
  • Factor polynomials by grouping the terms
  • 9.4 Factoring the Difference of Two Squares
  • Factor the difference of two squares
  • 9.5 Factoring x 2 + bx + c
  • Factor a trinomial of the form x 2 + bx + c
  • 9.6 Factoring ax 2 + bx + c
  • Factor a trinomial of the form ax 2 + bx + c
  • 9.7 Factoring Completely
  • Factor a polynomial completely
  • 9.8 Solving Equations by Factoring
  • Solve equations by factoring
  • CD 5 - Rational Expressions

Chapter Ten – Rational Expressions

10.1 Simplifying Rational Expressions

  • Define rational expressions and identify values for which one is undefined
  • Write a rational expression in lowest terms
  • 10.2 Multiplying Rational Expressions
  • Multiply rational expressions
  • 10.3 Dividing Rational Expressions
  • Divide rational expressions
  • 10.4 Least Common Denominator
  • Find the least common denominator of a list of rational expressions.
  • Write a rational expression as an equivalent rational expression whose denominator is given.
  • 10.5 Adding and Subtracting Rational Expressions with Like Denominators
  • Add and subtract rational expressions with the same denominators
  • 10.6 Adding and Subtracting Rational Expressions with Unlike Denominators
  • Add and subtract rational expressions with different denominators
  • 10.7 Operations on Rational Expressions
  • Add, subtract, multiply, and divide rational expressions
  • 10.8 Complex Fractions
  • Define and simplify complex fractions
  • 10.9 Solving Equations with Rational Expressions
  • Solve equations containing rational expressions
  • CD 6 - Graphs and Systems of Equations

Chapter Eleven – Graphing Linear Equations and Inequalities

11.1 Graphing Ordered Pairs

  • Graph ordered pairs
  • Identify solutions of linear equations in two variables
  • 11.2 Graphing Linear Equations in Two Variables
  • Graph a linear equation in two variables
  • 11.3 Graphing Using x- and y- Intercepts
  • Graph linear equations from their x- and y-intercepts
  • 11.4 Relations
  • Understand a relation and identify the domain and range of a relation
  • 11.5 Functions
  • Understand a function and identify the domain and range of a function
  • Use the vertical line test.
  • Use function notation.
  • 11.6 Graphing Linear Inequalities in Two Variables
  • Graph linear inequalities in two variables
  • Chapter Twelve – Slope and Forms of Equations of Lines

12.1 Slope

  • Find the slope of a line given two points of the line
  • 12.2 Slope-Intercept Form of a Linear Equation
  • Use the Slope-Intercept form to graph a linear equation
  • Write an equation of a line given its slope and y-intercept
  • Determine whether two lines are parallel
  • 12.3 Point-Slope Form of a Linear Equation
  • Write an equation of a line, given its slope and coordinates of one point
  • 12.4 Using Two Points to Write Equations of Lines
  • Write an equation of a line, given the coordinates of 2 points of the line
  • Write an equation of a line parallel to a given line and through a given point
  • Chapter Thirteen – Systems of Linear Equations

13.1 Graphing Systems of Linear Equations

  • Solve a system of linear equations by graphing
  • 13.2 Using the Substitution Method
  • Use substitution to solve a system of linear equations
  • 13.3 Using the Addition Method
  • Use the addition method to solve a system of linear equations
  • 13.4 Using Multiplication with the Addition Method
  • Use multiplication with the addition method to solve a system of linear equations
  • CD 7 - Roots and Radicals

Chapter Fourteen – Roots and Radicals, Part I

14.1 Square Roots

  • Find the square roots of perfect squares
  • Identify rational and irrational numbers
  • 14.2 Simplifying Square Roots
  • Use the product rule and the quotient rule to simplify radicals
  • 14.3 Simplifying Square Roots Containing Variables
  • Simplify square roots containing variables
  • 14.4 Addition and Subtraction of Radicals
  • Add and subtract like radicals
  • Simplify radical expressions, and then add or subtract any like radicals
  • 14.5 Multiplication of Radicals
  • Multiply and simplify radicals
  • Chapter Fifteen – Roots and Radicals, Part II

15.1 Division of Radicals

  • Divide and simplify radicals
  • 15.2 Rationalizing the Denominator
  • Rationalize denominators containing square roots
  • 15.3 Solving Radical Equations
  • Solve equations containing square roots of variable expressions
  • 15.4 The Pythagorean Theorem
  • Use the Pythagorean Formula to solve triangles
  • 15.5 The Distance Formula
  • Use the Distance Formula to find the distance between two points on the coordinate plane
  • CD 8 - Solving Quadratic Equations

Chapter Sixteen – Solving Quadratic Equations

16.1 Solving Quadratic Equations with the Square Root Property

  • Review the factoring method for solving equations
  • Use the square root property to solve equations
  • 16.2 Solving Quadratic Equations by Completing the Square
  • Find perfect square trinomials
  • Solve a quadratic equation by completing the square
  • 16.3 Solving Quadratic Equations Using the Quadratic Formula
  • Solve quadratic equations using the Quadratic Formula