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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