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