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
• Find the absolute value of a real number
• 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
• 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
• Chapter Fifteen – Roots and Radicals, Part II

• 15.2 Rationalizing the Denominator
• Rationalize denominators containing square roots
• 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