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