Preparation for College Mathematics, 2nd Edition
0.1 How to Read a Math Textbook
0.2 Tips for Success in a Math Course
0.3 Tips for Improving Math Test Scores
0.4 Practice, Patience, and Persistence!
0.5 Note Taking
0.6 Do I Need a Math Tutor?
0.7 Tips for Improving Your Memory
0.8 Overcoming Anxiety
0.9 Online Resources
0.10 Preparing for a Final Math Exam
0.11 Managing Your Time Effectively
1.1 Introduction to Whole Numbers
1.2 Addition and Subtraction with Whole Numbers
- Examples
- Example 1: Adding Whole Numbers
- Example 2: Adding Whole Numbers When Carrying is Required
- Example 3: Adding Whole Numbers Using Sums of 10
- Example 4: Adding Whole Numbers
- Example 5: Recognizing the Properties of Addition
- Example 7: Application: Calculating the Perimeter of a Rectangle
- Example 8: Subtracting Whole Numbers
- Example 9: Subtracting Whole Numbers
- Example 10: Subtracting Whole Numbers by Borrowing
- Example 11: Subtracting Whole Numbers by Borrowing
- Example 12: Finding a Missing Addend
- Example 13: Application: Subtracting Whole Numbers
- Example 14: Application: Adding and Subtracting Numbers
1.3 Multiplication with Whole Numbers
- Examples
- Example 1: Recognizing the Properties of Multiplication
- Example 3: Using the Distributive Property
- Example 4: Multiplying Whole Numbers
- Example 5: Multiplying Whole Numbers
- Example 6: Multiplying Whole Numbers
- Example 7: Multiplying Whole Numbers that End with s
- Example 8: Application: Calculating the Area of a Rectangle
1.4 Division with Whole Numbers
1.5 Rounding and Estimating with Whole Numbers
- Examples
- Example 1: Rounding Whole Numbers
- Example 2: Rounding Whole Numbers
- Example 3: Application: Rounding Whole Numbers
- Example 4: Estimating a Sum of Whole Numbers
- Example 6: Estimating a Difference of Whole Numbers
- Example 7: Application: Estimating a Difference of Whole Numbers
- Example 8: Estimating Products of Whole Numbers
- Example 9: Estimating Products of Whole Numbers
- Example 10: Estimating Quotients of Whole Numbers
- Example 11: Estimating Quotients of Whole Numbers
- Example 13: Estimating Quotients of Whole Numbers
1.6 Problem Solving with Whole Numbers
- Examples
- Example 1: Application: Adding Whole Numbers
- Example 2: Application: Multiplying Whole Numbers
- Example 3: Application: Dividing Whole Numbers
- Example 4: Application: Calculating Loan Amounts
- Example 5: Application: Balancing a Checking Account
- Example 6: Application: Finding the Area of Rectangles
- Example 7: Calculating an Average
- Example 8: Application: Calculating an Average
- Example 9: Application: Calculating an Average
- Example 10: Application: Calculating an Average
1.7 Solving Equations with Whole Numbers (x + b = c and ax = c)
- Examples
- Example 1: Checking Solutions to an Equation
- Example 2: Solving Equations of the form x + b = c
- Example 3: Solving Equations of the Form x + b = c
- Example 4: Solving Equations of the Form x + b = c
- Example 5: Solving Equations of the form ax = c
- Example 6: Solving Equations of the Form ax = c
- Example 7: Solving Equations of the Form ax = c
1.8 Exponents and Order of Operations
- Examples
- Example 1: Identifying the Base and Exponent
- Example 3: Evaluating Exponential Expressions
- Example 4: Evaluating Exponential Expressions
- Example 5: Using the Order of Operations with Whole Numbers
- Example 6: Using the Order of Operations with Whole Numbers
- Example 7: Using the Order of Operations with Whole Numbers
- Example 8: Using the Order of Operations with Whole Numbers
- Example 9: Using the Order of Operations with Whole Numbers
1.9 Tests for Divisibility
1.10 Prime Numbers and Prime Factorizations
- Examples
- Example 1: Determining Prime Numbers
- Example 2: Determining Composite Numbers
- Example 3: Determining Whether a Number is Prime
- Example 4: Determining Whether a Number is Prime
- Example 5: Determining Whether a Number is Prime
- Example 7: Finding the Prime Factorization of a Number
- Example 8: Finding the Prime Factorization of a Number
- Example 10: Finding the Factors of a Composite Number
- Example 12: Using Factors of Counting Numbers
2.1 Introduction to Integers
- Examples
- Example 1: Finding the Opposite of an Integer
- Example 2: Graphing Integers
- Example 3: Verifying Inequalities
- Example 4: Finding Absolute Value
- Example 5: Finding Absolute Value
- Example 6: Simplifying Expressions Containing Absolute Value
- Example 7: Verifying Absolute Value Inequalities
- Example 8: Solving Absolute Value Equations
- Example 9: Solving Absolute Values Equations
2.2 Addition with Integers
2.3 Subtraction with Integers
- Examples
- Example 1: Subtracting Integers
- Example 2: Subtracting Integers
- Example 3: Addition and Subtraction with Integers
- Example 4: Application: Calculating Change in Values
- Example 5: Application: Calculating Change in Value
- Example 6: Application: Calculating Net Change
- Example 7: Checking Solutions in Equations
2.4 Multiplication, Division, and Order of Operations with Integers
- Examples
- Example 1: Multiplying Integers
- Example 2: Multiplying Integers
- Example 3: Multiplying Integers
- Example 4: Dividing Integers
- Example 5: Division Involving 0
- Example 6: Using the Order of Operations with Integers
- Example 7: Using the Order of Operations with Integers
- Example 8: Using the Order of Operations with Integers
- Example 9: Using the Order of Operations with Integers
- Example 10: Order of Operations with Signed Integers
- Example 12: Application: Calculating an Average
- Example 13: Application: Calculating an Average
2.5 Simplifying and Evaluating Expressions
2.6 Translating English Phrases and Algebraic Expressions
2.7 Solving Equations With Integers (ax + b = c)
- Examples
- Example 1: Verifying the Solution to an Equation
- Example 2: Solving Equations of the Form x + b = c
- Example 3: Solving Equations of the Form ax = c
- Example 4: Solving Equations of the form ax + b = c
- Example 5: Solving Equations of the Form ax + b = c
- Example 6: Solving Equations of the Form ax + b = c
- Example 7: Solving Equations of the form ax + b = c
- Example 9: Application: Solving Equations of the Form
3.1 Introduction to Fractions and Mixed Numbers
- Examples
- Example 1: Understanding Fractions
- Example 2: Understanding Fractions
- Example 3: Understanding Proper Fractions
- Example 4: Understanding Improper Fractions
- Example 5: Evaluating Fractions Involving 0
- Example 6: Placing Negative Signs in Fractions
- Example 7: Graphing Proper Fractions
- Example 8: Graphing Improper Fractions
- Example 9: Identifying Types of Fractions and Mixed Numbers
- Example 10: Application: Understanding Mixed Numbers
- Example 11: Application: Understanding Mixed Numbers
- Example 12: Graphing Mixed Numbers
- Example 13: Changing Mixed Numbers to Improper Fractions
- Example 14: Changing Mixed Numbers to Improper Fractions
- Example 15: Changing Improper Fractions to Mixed Numbers
- Example 16: Changing Improper Fractions to Mixed Numbers
3.2 Multiplication with Fractions
- Examples
- Example 1: Multiplying Fractions
- Example 2: Multiplying Fractions
- Example 3: Application: Multiplying Fractions
- Example 4: Recognizing the Properties of Multiplication
- Example 5: Reducing Fractions to Lowest Terms
- Example 7: Reducing Fractions to Lowest Terms
- Example 9: Application: Reducing Fractions to Lowest Terms
- Example 10: Multiplying and Reducing Using Prime Factors
- Example 11: Multiplying and Reducing Using Prime Factors
- Example 12: Multiplying and Reducing Using Prime Factors
- Example 15: Application: Multiplying and Reducing Fractions
- Example 16: Multiplying and Reducing Using the Division Method
- Example 17: Multiplying and Reducing Using the Division Method
- Example 18: Multiplying and Reducing Using the Division Method
3.3 Division with Fractions
3.4 Multiplication and Division with Mixed Numbers
- Examples
- Example 1: Multiplying Mixed Numbers
- Example 2: Multiplying and Reducing Mixed Numbers
- Example 3: Multiplying and Reducing Mixed Numbers
- Example 4: Multiplying and Reducing Mixed Numbers
- Example 6: Finding Fractional Parts of Mixed Numbers
- Example 7: Finding Fractional Parts of Mixed Numbers
- Example 8: Application: Finding the Area of a Rectangle
- Example 9: Finding the Area of a Triangle
- Example 10: Dividing and Reducing Mixed Numbers
- Example 11: Dividing and Reducing Mixed Numbers
- Example 13: Application: Dividing Mixed Numbers
3.5 Least Common Multiple (LCM)
- Examples
- Example 1: Finding the Least Common Multiple (LCM)
- Example 2: Finding the Least Common Multiple (LCM)
- Example 4: Finding the Least Common Multiple (LCM)
- Example 5: Finding the Least Common Multiple (LCM)
- Example 6: Finding the Least Common Multiple (LCM)
- Example 7: Find the Least Common Multiple (LCM)
- Example 9: Application: Finding the LCM
- Example 10: Finding the LCM of a Set of Algebraic Terms
- Example 11: Finding the LCM of a Set of Algebraic Terms
- Example 13: Finding Equivalent Fractions
- Example 14: Finding Equivalent Fractions
3.6 Addition and Subtraction with Fractions
- Examples
- Example 1: Adding Fractions with the Same Denominator
- Example 2: Finding the Least Common Denominator (LCD)
- Example 3: Adding Fractions with Different Denominators
- Example 4: Adding Fractions with Different Denominators
- Example 5: Adding Three Fractions with Different Denominators
- Example 6: Application: Adding Fractions
- Example 7: Subtracting Fractions with the Same Denominator
- Example 8: Subtracting Fractions with Different Denominators
- Example 9: Subtracting Fractions with Different Denominators
- Example 10: Subtracting Fractions with Different Denominators
- Example 11: Application: Subtracting Fractions with Different Denominators
- Example 12: Adding and Subtracting Fractions Containing Variables
- Example 13: Adding Fractions Containing Variables
- Example 14: Adding Fractions Containing Variables
- Example 15: Subtracting Fractions Containing Variables
3.7 Addition and Subtraction with Mixed Numbers
- Examples
- Example 1: Adding Mixed Numbers with the Same Denominator
- Example 2: Adding Mixed Numbers with Different Denominators
- Example 3: Adding Mixed Numbers
- Example 4: Calculating Perimeter
- Example 5: Subtracting Mixed Numbers with the Same Denominator
- Example 6: Subtracting Mixed Numbers with Different Denominators
- Example 7: Subtracting Mixed Numbers with Borrowing
- Example 8: Subtracting Mixed Numbers with Borrowing
- Example 9: Subtracting Mixed Numbers by Borrowing
- Example 11: Application: Subtracting Mixed Numbers
- Example 12: Finding Sums of Negative Mixed Numbers
- Example 13: Finding Sums with Negative Mixed Numbers
- Example 14: Adding Mixed Numbers Using Improper Fractions
- Example 15: Adding Mixed Numbers Using Improper Fractions
- Example 16: Subtracting Mixed Numbers Using Improper Fractions
3.8 Comparisons and Order of Operations with Fractions
- Examples
- Example 1: Comparing Fractions
- Example 2: Comparing Fractions
- Example 3: Comparing Fractions
- Example 4: Using the Order of Operations with Fractions
- Example 5: Using the Order of Operations with Fractions
- Example 6: Using the Order of Operations with Fractions
- Example 8: Using the Order of Operations with Variables
- Example 9: Finding the Average
- Example 10: Simplifying Complex Fractions
- Example 11: Simplifying Complex Fractions
- Example 12: Simplifying Complex Fractions
3.9 Solving Equations with Fractions
3.10 Ratios and Unit Rates
- Examples
- Example 1: Application: Writing Ratios
- Example 2: Writing Ratios that Compare Mixed Numbers
- Example 3: Writing Ratios that Compare Numbers
- Example 4: Application: Writing Ratios from Graphs
- Example 5: Writing Ratios in Geometry
- Example 6: Writing Ratios that Compare Measurements
- Example 7: Writing a Rate
- Example 10: Application: Writing a Unit Rate
3.11 Proportions
- Examples
- Example 1: Verifying Proportions
- Example 3: Solving Proportions
- Example 4: Solving Proportions
- Example 5: Solving Proportions
- Example 6: Solving Proportions
- Example 8: Application: Solving Proportions
- Example 9: Application: Solving Proportions
- Example 10: Application: Solving Proportions
- Example 13: Application: Solving Proportions Written in Medical Notation
3.12 Probability
4.1 Introduction to Decimal Numbers
- Examples
- Example 1: Reading and Writing Decimal Numbers
- Example 2: Reading and Writing Decimal Numbers
- Example 3: Reading and Writing Decimal Numbers
- Example 4: Comparing Positive Decimal Numbers
- Example 5: Comparing Positive Decimal Numbers
- Example 6: Comparing Negative Decimal Numbers
- Example 7: Rounding Decimal Numbers
- Example 8: Rounding Decimal Numbers
4.2 Addition and Subtraction with Decimal Numbers
- Examples
- Example 1: Adding Decimal Numbers
- Example 2: Adding Decimal Numbers
- Example 3: Adding Decimal Numbers
- Example 4: Application: Adding Decimal Numbers
- Example 5: Subtracting Decimal Numbers
- Example 6: Subtracting Decimal Numbers
- Example 7: Adding Signed Decimal Numbers
- Example 8: Subtracting Signed Decimal Numbers
- Example 9: Application: Adding and Subtracting Decimal Numbers
- Example 10: Combining Like Terms with Decimal Coefficients
- Example 11: Combining Like Terms with Decimal Coefficients
4.3 Multiplication and Division with Decimal Numbers
- Examples
- Example 1: Multiplying Decimal Numbers
- Example 2: Multiplying Decimal Numbers
- Example 3: Multiplying Decimal Numbers
- Example 5: Application: Multiplying Decimal Numbers
- Example 6: Multiplying by Powers of 10
- Example 7: Dividing Decimal Numbers
- Example 8: Dividing Positive and Negative Decimal Numbers
- Example 9: Dividing Decimal Numbers
- Example 10: Dividing Decimal Numbers
- Example 11: Application: Calculating Average Amount per Unit
- Example 12: Application: Calculating Total Distance Traveled
- Example 13: Dividing by Powers of 10
4.4 Estimating and Order of Operations with Decimal Numbers
- Examples
- Example 1: Estimating Sums of Decimal Numbers
- Example 3: Estimating Products of Decimal Numbers
- Example 4: Estimating Quotients of Decimal Numbers
- Example 5: Application: Estimating with Decimal Numbers
- Example 6: Using the Order of Operations with Decimal Numbers
- Example 7: Using the Order of Operations with Decimal Numbers
- Example 8: Using the Order of Operations with Decimal Numbers
4.5 Statistics: Mean, Median, Mode, and Range
4.6 Decimal Numbers and Fractions
- Examples
- Example 1: Changing Decimal Numbers to Fractions
- Example 3: Changing Decimal Numbers to Fractions
- Example 4: Changing Fractions to Decimal Numbers
- Example 5: Changing Fractions to Decimal Numbers
- Example 6: Changing Fractions to Decimal Numbers
- Example 7: Changing Fractions to Decimal Numbers
- Example 8: Simplifying Expressions with Decimals and Fractions
- Example 9: Comparing Decimals Numbers and Fractions
- Example 10: Simplifying Expressions with Decimals and Fractions
- Example 11: Evaluating Expressions with Decimals and Fractions
- Example 12: Application: Decimal and Fraction Expressions
4.7 Solving Equations with Decimal Numbers
- Examples
- Example 1: Solve Equations of the Form ax + b = c
- Example 2: Solve Equations of the Form ax + b = cx + d
- Example 3: Solve Equations of the Form ax + b = cx + d
- Example 4: Solve Equations of the Form ax + b = cx + d
- Example 6: Application: Solving Equations
- Example 7: Application: Solving Equations
5.1 Basics of Percent
- Examples
- Example 1: Changing Fractions with Denominators of to Percents
- Example 2: Changing Decimal Numbers to Percents
- Example 3: Changing Percents to Decimal Numbers
- Example 4: Changing Fractions to Percents
- Example 5: Changing Fractions to Percents
- Example 6: Changing Mixed Numbers to Percents
- Example 8: Changing Fractions to Percents
- Example 9: Application: Changing Fractions to Percents
- Example 10: Changing Percents to Fractions
- Example 11: Changing Percents to Mixed Numbers
5.2 Solving Percent Problems Using Proportions
5.3 Solving Percent Problems Using Equations
5.4 Applications of Percent
- Examples
- Example 1: Application: Solving Discount Problems
- Example 2: Application: Solving Discount Problems
- Example 3: Application: Solving Sales Tax Problems
- Example 4: Application: Solving Commission Problems
- Example 5: Finding the Percent Increase
- Example 6: Finding the Percent Decrease
- Example 7: Application: Calculating Percent of Profit
5.5 Simple and Compound Interest
- Examples
- Example 1: Application: Calculating Simple Interest
- Example 3: Application: Calculating Total Amount Due
- Example 4: Application: Calculating Principal using Simple Interest
- Example 5: Application: Calculating Time using Simple Interest
- Example 6: Application: Calculating Compound Interest
- Example 7: Application: Calculating Compound Interest
- Example 8: Application: Using the Compound Interest Formula
- Example 9: Application: Calculating Total Interest Earned
- Example 11: Application: Calculating Inflation
- Example 12: Application: Calculating the Current Value Due to Depreciation
5.6 Reading Graphs
6.1 US Measurements
- Examples
- Example 1: Basic Conversions in the US Customary System
- Example 2: Converting US Units of Measure Using Multiplication/Division
- Example 3: Application: Converting US Units of Measure
- Example 4: Using Unit Fractions to Convert US Units of Measure
- Example 5: Application: Converting US Units of Measure
- Example 6: Application: Converting US Units of Measure
6.2 The Metric System: Length and Area
- Examples
- Example 1: Converting Metric Units of Length
- Example 2: Application: Converting Metric Units of Length
- Example 3: Converting Metric Units of Length
- Example 4: Converting Metric Units of Length
- Example 5: The Prefixes Mega-, Giga-, and Tera-
- Example 6: Converting Metric Units of Area
- Example 7: Converting Metric Units of Area
- Example 8: Converting Metric Units of Area
- Example 9: Converting Metric Units of Land Area
6.3 The Metric System: Capacity and Weight
- Examples
- Example 1: Common Metric Units of Capacity
- Example 2: Converting Metric Units of Capacity
- Example 3: Converting Metric Units of Capacity
- Example 4: Converting Metric Units of Capacity
- Example 5: Application: Converting Metric Units of Capacity
- Example 7: Converting Metric Units of Weight
- Example 8: Application: Converting Metric Units of Weight
6.4 US and Metric Equivalents
- Examples
- Example 1: Equivalent Measures of Temperature
- Example 2: Converting Units of Temperature
- Example 3: Converting Units of Temperature
- Example 4: Converting Units of Length
- Example 5: Converting Units of Area
- Example 6: Converting Units of Capacity (Liquid Volume)
- Example 7: Converting Units of Weight (Mass)
6.5 Angles and Triangles
- Examples
- Example 1: Measuring Angles
- Example 2: Classifying Angles by Their Measure
- Example 3: Identifying Complementary and Supplementary Angles
- Example 4: Calculating Measures of Angles
- Example 5: Identifying Congruent Angles
- Example 6: Calculating Measures of Angles
- Example 7: Finding Adjacent Angles
- Example 8: Calculating Measures of Angles
- Example 9: Classifying a Triangle by Its Sides
- Example 10: Determining Whether a Triangle Exists
- Example 11: Analyzing Triangles
6.6 Perimeter
- Examples
- Example 1: Calculating the Perimeter of a Square
- Example 2: Calculating the Perimeter of a Triangle
- Example 3: Calculating the Perimeter of a Rectangle
- Example 4: Calculating the Perimeter of a Polygon
- Example 5: Calculating the Perimeter of a Polygon
- Example 6: Application: Calculating the Perimeter of a Polygon
6.7 Area
- Examples
- Example 1: Calculating the Area of a Triangle Using a Formula
- Example 2: Calculating the Area of a Trapezoid Using a Formula
- Example 3: Calculating the Area of a Circle
- Example 4: Calculating the Area of a Composite Figure
- Example 5: Calculating Area
- Example 6: Calculating Area
- Example 7: Calculating Area
- Example 8: Application: Calculating the Perimeter and Area
6.8 Volume and Surface Area
- Examples
- Example 1: Calculating the Volume of a Rectangular Solid
- Example 2: Calculating the Volume of a Sphere
- Example 3: Calculating the Volume of a Cone
- Example 4: Calculating the Volume of a Solid
- Example 5: Finding the Volume of a Cube
- Example 6: Calculating the Surface Area of a Rectangular Solid
- Example 7: Calculating the Surface Area of a Cylinder
6.9 Similar and Congruent Triangles
6.10 Square Roots and the Pythagorean Theorem
- Examples
- Example 1: Evaluating Perfect Squares
- Example 2: Evaluating Square Roots
- Example 3: Evaluating Expressions Containing Square Roots
- Example 5: Verifying Right Triangles
- Example 6: Finding the Length of the Hypotenuse
- Example 7: Finding the Length of a Leg
- Example 8: Application: Finding the Length of the Hypotenuse
7.1 Properties of Real Numbers
7.2 Solving Linear Equations: x + b = c and ax = c
- Examples
- Example 1: Checking Given Solutions in Equations
- Example 2: Solving Linear Equations of the Form x + b = c
- Example 3: Solving Linear Equations of the Form x + b = c
- Example 4: Solving Linear Equations of the Form x + b = c
- Example 5: Solving Linear Equations of the Form x + b = c
- Example 6: Simplifying and Solving Linear Equations
- Example 8: Solving Linear Equations of the Form ax = c
- Example 9: Solving Linear Equations of the Form ax=c
- Example 10: Solving Linear Equations of the Form ax = c
- Example 12: Application: Solving Linear Equations
7.3 Solving Linear Equations: ax + b = c
- Examples
- Example 1: Solving Linear Equations of the Form ax + b = c
- Example 2: Solving Linear Equations of the Form ax + b = c
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations Involving Decimals
- Example 5: Solving Linear Equations Involving Fractions
- Example 6: Solving Linear Equations Involving Fractions
7.4 Solving Linear Equations: ax + b = cx + d
- Examples
- Example 1: Solving Equations of the Form ax + b = cx + d
- Example 2: Solving Equations of the Form ax + b = cx + d
- Example 3: Solving Linear Equations Involving Decimals
- Example 4: Solving Linear Equations Involving Fractions
- Example 5: Solving Equations Involving Parentheses
- Example 6: Solving Equations Involving Parentheses
- Example 8: Determining Types of Equations
- Example 9: Determining Types of Equations
- Example 10: Determining Types of Equations
7.5 Working with Formulas
- Examples
- Example 1: Application: Evaluating Formulas
- Example 2: Evaluating Formulas
- Example 3: Application: Evaluating Formulas
- Example 4: Evaluating Formulas
- Example 5: Solving for Different Variables
- Example 6: Solving for Different Variables
- Example 7: Solving for Different Variables
- Example 8: Solving for Different Variables
7.6 Applications: Number Problems and Consecutive Integers
7.7 Applications: Distance-Rate-Time, Interest, Average, and Cost
- Examples
- Example 1: Application: Solving Distance-Rate-Time Problems
- Example 2: Application: Solving Distance-Rate-Time Problems
- Example 3: Application: Solving Interest Problems
- Example 4: Application: Finding the Average (or Mean)
- Example 5: Application: Using Bar Graphs
- Example 6: Application: Calculating Cost
7.8 Solving Linear Inequalities
- Examples
- Example 1: Graphing Intervals
- Example 2: Graphing Intervals
- Example 3: Graphing Intervals
- Example 4: Graphing Intervals
- Example 5: Solving an Inequality and Graphing the Solution Set
- Example 6: Solving an Inequality and Graphing the Solution Set
- Example 7: Solving an Inequality and Graphing the Solution Set
- Example 8: Solving an Inequality and Graphing the Solution Set
- Example 9: Solving Linear Inequalities
- Example 10: Solving Linear Inequalities
- Example 11: Solving Linear Inequalities
- Example 13: Application: Using Inequalities
7.9 Compound Inequalities
- Examples
- Example 1: Finding the Union and Intersection of Two Sets
- Example 2: Finding the Union and Intersection of Two Sets
- Example 3: Finding the Union and Intersection of Two Sets
- Example 4: Graphing Compound Inequalities
- Example 5: Graphing Compound Inequalities
- Example 6: Solving Compound Inequalities Containing AND
- Example 7: Solving Compound Inequalities Containing AND
- Example 8: Solving Compound Inequalities Containing AND
- Example 9: Solving Compound Inequalities Containing OR
- Example 10: Solving Compound Inequalities Containing OR
7.10 Absolute Value Equations
7.11 Absolute Value Inequalities
- Examples
- Example 1: Solving Absolute Value Inequalities
- Example 2: Solving Absolute Value Inequalities
- Example 3: Solving Absolute Value Inequalities
- Example 4: Solving Absolute Value Inequalities
- Example 5: Solving Absolute Value Inequalities
- Example 6: Solving Absolute Value Inequalities
- Example 7: Solving Absolute Value Inequalities
- Example 8: Solving Absolute Value Inequalities
- Example 9: Solving Absolute Value Inequalities
8.1 The Cartesian Coordinate System
8.2 Graphing Linear Equations in Two Variables
- Examples
- Example 1: Graphing a Linear Equation in Two Variables
- Example 2: Graphing a Linear Equation in Two Variables
- Example 3: Graphing a Linear Equation in Two Variables
- Example 4: Using Intercepts to Graph Linear Equations
- Example 5: Using Intercepts to Graph Linear Equations
- Example 7: Graphing Horizontal Lines
- Example 8: Graphing Vertical Lines
8.3 Slope-Intercept Form
- Examples
- Example 1: Finding the Slope of a Line
- Example 2: Finding the Slope of a Line
- Example 3: Finding the Slope of a Horizontal Line
- Example 4: Finding the Slope of a Vertical Line
- Example 5: Using Slope and the y‑Intercept to Graph a Line
- Example 6: Using Slope and the y-Intercept to Graph a Line
- Example 7: Finding Equations Given the Slope and the y‑Intercept
8.4 Point-Slope Form
- Examples
- Example 1: Graphing a Line Given a Point and the Slope
- Example 2: Finding Equations of Lines Using the Slope and a Point
- Example 3: Finding Equations of Lines Using Two Points
- Example 4: Finding Equations of Lines Using a Graph
- Example 5: Finding the Equations of Parallel Lines
- Example 6: Finding the Equations of Perpendicular Lines
8.5 Introduction to Functions and Function Notation
- Examples
- Example 1: Finding the Domain and Range
- Example 2: Reading the Domain and Range from the Graph of a Relation
- Example 3: Determining if a Relation is a Function
- Example 4: Using the Vertical Line Test
- Example 5: Finding the Domain of a Function
- Example 6: Evaluating Functions
- Example 7: Evaluating Nonlinear Functions
- Example 8: Evaluating Functions From a Graph
8.6 Graphing Linear Inequalities in Two Variables
9.1 Systems of Linear Equations: Solutions by Graphing
- Examples
- Example 1: Checking Solutions to Systems (Solution)
- Example 2: Checking Solutions to Systems (Not a Solution)
- Example 3: Solving Systems (One Solution/A Consistent System)
- Example 4: Solving Systems (No Solution/An Inconsistent System)
- Example 5: Solving Systems (Infinite Solutions/A Dependent System)
- Example 6: Solving a System that Requires Estimation
9.2 Systems of Linear Equations: Solutions by Substitution
- Examples
- Example 1: Solving Systems by Substitution (One Solution)
- Example 2: Solving Systems by Substitution (One Solution)
- Example 3: Solving Systems by Substitution (No Solution)
- Example 4: Solving Systems by Substitution (Infinite Solutions)
- Example 5: Solving Systems by Substitution (Decimal Numbers)
9.3 Systems of Linear Equations: Solutions by Addition
9.4 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
9.5 Applications: Interest and Mixture
9.6 Systems of Linear Equations: Three Variables
9.7 Matrices and Gaussian Elimination
9.8 Systems of Linear Inequalities
10.1 Rules for Exponents
10.2 Power Rules for Exponents
- Examples
- Example 1: Using the Power Rule for Exponents
- Example 2: Using the Rule for Power of a Product
- Example 3: Using the Rule for Power of a Quotient
- Example 4: Using Combinations of Rules for Exponents
- Example 5: Using Two Approaches with Fractional Expressions and Negative Exponents
- Example 6: Simplifying a More Complex Example
10.3 Applications: Scientific Notation
10.4 Introduction to Polynomials
10.5 Addition and Subtraction with Polynomials
10.6 Multiplication with Polynomials
- Examples
- Example 1: Multiplying Polynomials and Monomials
- Example 3: Multiplying Two Binomials
- Example 5: Multiplying Polynomials
- Example 6: Multiplying Polynomials
- Example 7: Multiplying Polynomials
- Example 8: Multiplying Polynomials
- Example 9: Using the FOIL Method to Multiply Binomials
- Example 10: Using the FOIL Method to Multiply Binomials
10.7 Special Products of Binomials
10.8 Division with Polynomials
10.9 Synthetic Division and the Remainder Theorem
11.1 Greatest Common Factor (GCF) and Factoring by Grouping
- Examples
- Example 1: Finding the GCF
- Example 2: Factoring Out the GCF of a Polynomial
- Example 3: Factoring Out the GCF of a Polynomial
- Example 4: Factoring Out the GCF of a Polynomial
- Example 5: Factoring Out the GCF of a Multi-Variable Polynomial
- Example 6: Factoring Out a Common Binomial Factor
- Example 7: Factoring Polynomials by Grouping
- Example 8: Factoring Polynomials by Grouping
- Example 9: Factoring Polynomials by Grouping
- Example 10: Factoring Polynomials by Grouping
- Example 11: Factoring Polynomials by Grouping
11.2 Factoring Trinomials: x^2+bx+c
11.3 Factoring Trinomials: ax^2+bx+c
11.4 Special Factoring Techniques
11.5 Review of Factoring Techniques
11.6 Solving Quadratic Equations by Factoring
- Examples
- Example 1: Solving Factored Quadratic Equations
- Example 2: Solving Quadratic Equations by Factoring
- Example 3: Solving Quadratic Equations by Factoring
- Example 4: Solving Quadratic Equations by Factoring
- Example 5: Solving Quadratic Equations by Factoring
- Example 6: Solving Quadratic Equations by Factoring
- Example 7: Solving Quadratic Equations by Factoring
- Example 9: Solving Higher Degree Equations
- Example 10: Finding Equations with Given Roots
11.7 Applications: Quadratic Equations
- Examples
- Example 1: Solving Quadratic Number Problems
- Example 2: Application: Solving Quadratic Equations
- Example 3: Application: Solving Quadratic Number Problems
- Example 4: Application: Solving Quadratic Equations
- Example 5: Consecutive Integers
- Example 6: Consecutive Integers
- Example 7: Application: The Pythagorean Theorem
12.1 Introduction to Rational Expressions
12.2 Multiplication and Division with Rational Expressions
- Examples
- Example 1: Multiplication with Rational Expressions
- Example 2: Multiplying with Rational Expressions
- Example 3: Multiplying with Rational Expressions
- Example 4: Multiplying with Rational Expressions
- Example 6: Dividing with Rational Expressions
- Example 7: Dividing with Rational Expressions
- Example 8: Dividing with Rational Expressions
12.3 Least Common Multiple of Polynomials
- Examples
- Example 1: Finding the LCM of a Set of Counting Numbers
- Example 2: Adding Fractions with the Same Denominator
- Example 3: Adding Fractions with Different Denominators
- Example 4: Finding the LCM of Polynomials
- Example 5: Finding the LCM of Polynomials
- Example 6: Writing Equivalent Rational Expressions
- Example 7: Writing Equivalent Rational Expressions
12.4 Addition and Subtraction with Rational Expressions
- Examples
- Example 1: Adding Rational Expressions with a Common Denominator
- Example 2: Adding Rational Expressions with Different Denominators
- Example 4: Subtracting Rational Expressions with a Common Denominator
- Example 5: Subtracting Rational Expressions with Different Denominators
- Example 7: Adding and Subtracting Rational Expressions
12.5 Simplifying Complex Fractions
- Examples
- Example 1: First Method for Simplifying Complex Fractions
- Example 2: First Method for Simplifying Complex Fractions
- Example 3: First Method for Simplifying Complex Fractions
- Example 4: Second Method for Simplifying Complex Fractions
- Example 5: Second Method for Simplifying Complex Fractions
- Example 6: Simplifying Complex Algebraic Expressions
12.6 Solving Rational Equations
12.7 Applications: Rational Expressions
12.8 Applications: Variation
13.1 Evaluating Radicals
13.2 Simplifying Radicals
13.3 Rational Exponents
13.4 Addition, Subtraction, and Multiplication with Radicals
13.5 Rationalizing Denominators
13.6 Solving Radical Equations
- Examples
- Example 1: Solving Equations with One Radical
- Example 2: Solving Equations with One Radical
- Example 3: Solving Equations with One Radical
- Example 4: Solving Equations with One Radical
- Example 6: Solving Equations with Two Radicals
- Example 7: Solving Equations with Two Radicals
- Example 8: Solving Equations containing a Cube Root
13.7 Functions with Radicals
13.8 Introduction to Complex Numbers
13.9 Multiplication and Division with Complex Numbers
14.1 Quadratic Equations: The Square Root Method
- Examples
- Example 1: Solving Quadratic Equations by Factoring
- Example 2: Solving Quadratic Equations by Factoring
- Example 3: Quadratic Equations Involving the Sum of Two Squares
- Example 4: Using the Square Root Property
- Example 5: Using the Square Root Property
- Example 7: The Pythagorean Theorem
- Example 8: The Pythagorean Theorem
14.2 Quadratic Equations: Completing the Square
- Examples
- Example 1: Completing the Square
- Example 2: Solving Quadratic Equations by Completing the Square
- Example 3: Solving Quadratic Equations by Completing the Square
- Example 4: Solving Quadratic Equations by Completing the Square
- Example 5: Solving Quadratic Equations by Completing the Square
- Example 7: Quadratic Equations with Known Roots
- Example 8: Quadratic Equations with Known Roots
- Example 9: Quadratic Equations with Known Roots
14.3 Quadratic Equations: The Quadratic Formula
14.4 More Applications of Quadratic Equations
14.5 Equations in Quadratic Form
- Examples
- Example 1: Using Substitution to Solve Equations in Quadratic Form
- Example 2: Using Substitution to Solve Equations in Quadratic Form
- Example 3: Using Substitution to Solve Equations in Quadratic Form
- Example 4: Using Substitution to Solve Equations in Quadratic Form
- Example 5: Solving Rational Equations that Simplify to Quadratic Equations
- Example 6: Solving Higher-Degree Equations
- Example 7: Solving Higher-Degree Equations
14.6 Graphing Quadratic Functions
14.7 More on Graphing Functions and Applications
- Examples
- Example 1: Graphing Quadratic Functions of the Form y = ax2 + bx + c
- Example 2: Graphing Quadratic Functions of the Form y = ax2 + bx + c
- Example 3: Graphing Quadratic Functions of the Form y = ax2 + bx + c
- Example 4: Graphing Quadratic Functions of the Form y = ax2 + bx + c
- Example 5: Application: Minimum and Maximum Values
- Example 6: Application: Minimum and Maximum Values
14.8 Solving Polynomial and Rational Inequalities
- Examples
- Example 1: Solving Polynomial Inequalities by Factoring
- Example 2: Solving Polynomial Inequalities by Factoring
- Example 3: Solving Polynomial Inequalities by Factoring
- Example 4: Solving Polynomial Inequalities Using the Quadratic Formula
- Example 5: Solving Polynomial Inequalities Using the Quadratic Formula
- Example 6: Solving Rational Inequalities
- Example 7: Solving Rational Inequalities
- Example 8: Solving Rational Inequalities
15.1 Algebra of Functions
15.2 Composition of Functions and Inverse Functions
- Examples
- Example 1: Evaluating a Function at an Algebraic Expression
- Example 2: Compositions
- Example 3: Compositions
- Example 4: Compositions
- Example 5: One-to-One Functions
- Example 6: Inverse Functions
- Example 7: Inverse Functions
- Example 8: Evaluating Compositions of Inverses
- Example 9: Finding the Inverse
- Example 10: Finding the Inverse
15.3 Exponential Functions
15.4 Logarithmic Functions
15.5 Properties of Logarithms
15.6 Common Logarithms and Natural Logarithms
15.7 Logarithmic and Exponential Equations and Change-of-Base
15.8 Applications: Exponential and Logarithmic Functions
16.1 Translations and Reflections
- Examples
- Example 1: Using Notation
- Example 2: Finding the Difference Quotient
- Example 3: Finding the Difference Quotient
- Example 4: Horizontal and Vertical Translations of y = |x|
- Example 5: Horizontal and Vertical Translations of y = |x|
- Example 6: Horizontal and Vertical Translations of y = |x|
- Example 7: Reflections and Translations of y = |x|
- Example 8: Graphing Translations of a Function Given its Graph
- Example 9: Graphing Translations of a Function Given Its Graph