Pathways to College Mathematics
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
R.1 Exponents, Prime Numbers, and LCM
- Examples
- Example 1: Writing Expressions using Exponents
- Example 2: Evaluating Exponential Expressions
- Example 3: Determining Prime Numbers
- Example 4: Determining Composite Numbers
- Example 5: Finding the Prime Factorization of a Number
- Example 6: Find the Prime Factorization of Each Number
- Example 7: Finding the Least Common Multiple (LCM)
- Example 8: Finding the Least Common Multiple (LCM)
R.2 Fractions (Multiplication and Division)
- Examples
- Example 1: Understanding Fractions
- Example 2: Multiplying Fractions
- Example 3: Multiplying Fractions
- Example 4: Multiplying Fractions
- Example 5: Finding Equivalent Fractions
- Example 6: Finding Equivalent Fractions
- Example 7: Reducing Fractions to Lowest Terms
- Example 8: Reducing Fractions to Lowest Terms
- Example 9: Multiplying and Reducing Fractions
- Example 10: Multiplying and Reducing Fractions
- Example 11: Multiplying and Reducing Fractions
- Example 12: Dividing Fractions
- Example 13: Dividing and Reducing Fractions
- Example 14: Application: Writing and Reducing Fractions
- Example 15: Application: Dividing Fractions
R.3 Fractions (Addition and Subtraction)
- Examples
- Example 1: Adding Fractions with the Same Denominator
- Example 2: Adding Fractions with the Same Denominator
- Example 3: Adding Fractions with Different Denominators
- Example 4: Adding Fractions with Different Denominators
- Example 5: Application: Adding Fractions
- Example 8: Subtracting Fractions with the Same Denominator
- Example 7: Subtracting Fractions with Different Denominators
- Example 8: Subtracting Fractions with Different Denominators
R.4 Decimal Numbers
- Examples
- Example 1: Writing in Decimal Notation
- Example 2: Reading and Writing Decimal Numbers
- Example 3: Reading and Writing Decimal Numbers
- Example 4: Comparing Decimal Numbers
- Example 5: Comparing Decimal Numbers
- Example 6: Adding Decimal Numbers
- Example 7: Subtracting Decimal Numbers
- Example 8: Application: Adding and Subtracting Decimal Numbers
- Example 9: Multiplying Decimal Numbers
- Example 10: Dividing Decimal Numbers
- Example 11: Dividing Decimal Numbers and Rounding
- Example 12: Changing Decimal Numbers to Percents
- Example 13: Changing Percents to Decimal Numbers
R.5 Bar Graphs, Pictographs, Circle Graphs, and Line Graphs
1.1 The Real Number Line and Absolute Value
- Examples
- Example 1: Finding the Opposite of an Integer
- Example 2: Graphing Integers on a Number Line
- Example 3: Identifying Types of Numbers
- Example 5: Graphing Sets of Numbers
- Example 6: Verifying Inequalities
- Example 7: Finding Absolute Values
- Example 8: Verifying Absolute Value Inequalities
- Example 9: Solving Absolute Value Equations
- Example 10: Solving Absolute Value Equations
1.2 Operations with Real Numbers
- Examples
- Example 1: Addition with Like Signs
- Example 2: Addition with Unlike Signs
- Example 3: Application: Reading a Table
- Example 4: Application: Calculating the Perimeter of a Rectangle
- Example 5: Subtraction with Real Numbers
- Example 6: Application: Calculating Change in Value
- Example 7: Multiplication with Positive and Negative Real Numbers
- Example 8: Application: Calculating the Area of a Rectangle
- Example 9: Division with Positive and Negative Real Numbers
- Example 10: Division with 0
1.3 Problem Solving with Real Numbers
- Examples
- Example 1: Application: Adding Real Numbers
- Example 2: Application: Multiplying Real Numbers
- Example 3: Application: Dividing Real Numbers
- Example 4: Application: Calculating Loan Amounts
- Example 5: Application: Balancing a Checking Account
- Example 6: Calculating an Average
- Example 7: Application: Calculating an Average
- Example 8: Application: Calculating an Average
- Example 9: Application: Calculating an Average
1.4 Square Roots and Order of Operations with Real Numbers
- Examples
- Example 1: Finding Square Roots
- Example 2: Using the Order of Operations with Real Numbers
- Example 3: Using the Order of Operations with Real Numbers
- Example 4: Using the Order of Operations with Real Numbers
- Example 5: Using the Order of Operations with Real Numbers
- Example 7: Using the Order of Operations with Real Numbers
- Example 8: Using the Order of Operations with Real Numbers
1.5 Properties of Real Numbers
1.6 Simplifying and Evaluating Algebraic Expressions
1.7 Translating English Phrases and Algebraic Expressions
2.1 Solving One-Step Linear Equations
- 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
2.2 Solving Multi-Step Linear Equations
- 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 Fractions
- Example 5: Solving Equations of the Form ax + b = cx + d
- Example 6: Solving Equations of the Form ax + b = cx + d
- Example 7: Solving Linear Equations Involving Decimals
- Example 8: Solving Linear Equations Involving Fractions
- Example 9: Solving Equations Involving Parentheses
- Example 11: Determining Types of Equations
- Example 12: Determining Types of Equations
- Example 13: Determining Types of Equations
2.3 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
2.4 Applications of Linear Equations
- Examples
- Example 1: Solving Number Problems
- Example 2: Solving Number Problems
- Example 3: Application: Calculating Living Expenses
- Example 4: Application: Calculating Costs of Purchases
- Example 5: Application: Solving Distance-Rate-Time Problems
- Example 6: Application: Solving Distance-Rate-Time Problems
- Example 7: Application: Finding the Average (or Mean)
- Example 8: Application: Calculating Selling Price
2.5 Ratios, Rates, and Proportions
- Examples
- Example 1: Application: Writing Ratios
- Example 2: Application: Writing Ratios from Graphs
- Example 3: Writing Ratios in Geometry
- Example 4: Writing a Rate
- Example 5: Application: Writing a Unit Rate
- Example 6: Application: Comparing Unit Prices
- Example 7: Verifying Proportions
- Example 8: Solving Proportions
- Example 9: Solving Proportions
- Example 10: Application: Solving Proportions
- Example 11: Application: Solving Proportions
2.6 Modeling using Variation
2.7 Solving Linear Inequalities in One Variable
- 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 12: Solving Compound Inequalities
- Example 13: Solving Compound Inequalities
- Example 14: Application: Using Inequalities
- Example 15: Application: Using Inequalities
3.1 The Cartesian Coordinate System, Scatter Plots, and Linear Equations
- Examples
- Example 1: Graphing Ordered Pairs
- Example 2: Reading Points on a Graph
- Example 3: Creating a Scatter Plot
- Example 4: Graphing a Linear Equation in Two Variables
- Example 5: Graphing a Linear Equation in Two Variables
- Example 6: Graphing a Linear Equation in Two Variables
- Example 7: Using Intercepts to Graph Linear Equations
- Example 8: Using Intercepts to Graph Linear Equations
3.2 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
3.3 Point-Slope Form
- Examples
- Example 1: Graphing a Line Given a Point and the Slope
- Example 2: Finding Equations of Lines Using a Point and the Slope
- Example 3: Finding Equations of Lines Given Two Points
- Example 4: Finding Equations of Lines Using a Graph
- Example 5: Finding Equations of Parallel Lines
- Example 6: Finding Equations of Perpendicular Lines
3.4 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 Whether 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
3.5 Linear Correlation and Regression
3.6 Systems of Linear Equations in Two Variables
- Examples
- Example 1: Solving a Consistent System by Graphing
- Example 2: Solving a Consistent System by Graphing
- Example 4: Solving an Inconsistent System by Substitution
- Example 5: Solving a Consistent System by Addition
- Example 6: Solving a Consistent System by Addition
- Example 7: Application: Mixture
- Example 8: Application: Interest
- Example 9: Application: Work
3.7 Graphing Linear Inequalities in Two Variables
4.1 Exponents
- Examples
- Example 2: Evaluating the Exponent 0
- Example 3: Using the Quotient Rule for Exponents
- Example 4: Simplifying Expressions with Negative Exponents
- Example 5: Using Combinations of the Rules for Exponents
- Example 6: Using Two Approaches with Fractional Expressions and Negative Exponents
- Example 7: Simplifying a More Complex Example
4.2 Scientific Notation
4.3 Modeling with Exponential Functions
4.4 Addition and Subtraction with Polynomials
4.5 Multiplication with Polynomials
- Examples
- Example 1: Multiplying Polynomials
- Example 2: Multiplying Polynomials
- Example 4: Multiplying Polynomials
- Example 5: Multiplication with Polynomials
- Example 6: Using the FOIL Method to Multiply Binomials
- Example 7: Using the FOIL Method to Multiply Binomials
- Example 8: Using the FOIL Method to Multiply Binomials
- Example 10: Difference of Two Squares
- Example 11: Squares of Binomials (Perfect Square Trinomials)
5.1 GCF and an Introduction to Factoring Polynomials
- Examples
- Example 1: Finding the GCF
- Example 2: Dividing by a Monomial
- 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 Polynomial
- Example 6: Factoring Out the GCF of a Multi-Variable Polynomial
- Example 7: Factoring Out a Common Binomial Factor
- Example 8: Factoring Polynomials by Grouping
- Example 9: Factoring Polynomials by Grouping
- Example 10: Factoring Polynomials by Grouping
- Example 11: Factoring Polynomials by Grouping
- Example 12: Factoring Polynomials by Grouping
5.2 Factoring Trinomials
5.3 Special Factoring Techniques and General Guidelines for Factoring
5.4 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
5.5 Operations with Radicals
5.6 Solving Quadratic Equations by the Square Root Property and the Quadratic Formula
- Examples
- Example 1: Using the Square Root Property
- Example 2: Using the Square Root Property
- Example 3: Using the Square Root Property
- Example 4: Using the Square Root Property
- Example 5: Using the Square Root Property
- Example 7: The Quadratic Formula
- Example 8: The Quadratic Formula
- Example 9: The Quadratic Formula
- Example 11: The Quadratic Formula
- Example 12: The Quadratic Formula and a Double Solution
- Example 13: The Quadratic Formula and Nonreal Solutions
5.7 Applications of Quadratic Equations
- Examples
- Example 1: Solving Quadratic Number Problems
- Example 2: Application: Solving Quadratic Equations
- Example 3: Finding the Dimensions of a Rectangle
- Example 4: Application: Finding the Dimensions of a Rectangle
- Example 5: Application: Finding the Dimensions of a Box
- Example 6: Application: The Pythagorean Theorem
- Example 7: Application: The Pythagorean Theorem
- Example 8: Using The Pythagorean Theorem
5.8 Graphing Quadratic Functions
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
- 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
6.6 Triangles
- Examples
- Example 1: Classifying a Triangle by Its Sides
- Example 2: Determining Whether a Triangle Exists
- Example 3: Analyzing Triangles
- Example 4: Determining Whether Triangles are Similar
- Example 5: Finding Unknown Values Using Similar Triangles
- Example 6: Application: Finding Unknown Values Using Similar Triangles
- Example 7: Determining Whether Triangles are Congruent
- Example 8: Verifying Right Triangles
- Example 9: Finding the Length of the Hypotenuse
- Example 10: Finding the Length of a Leg
- Example 11: Finding the Length of the Hypotenuse
6.7 Perimeter and Area
- Examples
- Example 1: Calculating the Perimeter of a Square
- Example 2: Calculating the Perimeter of a Triangle
- Example 3: Calculating the Perimeter of a Polygon
- Example 4: Application: Calculating the Perimeter of a Polygon
- Example 5: Calculating the Circumference of a Circle
- Example 6: Calculating the Perimeter
- Example 7: Calculating Perimeter
- Example 8: Calculating the Area of a Triangle
- Example 9: Calculating the Area of a Trapezoid
- Example 10: Calculating the Area of a Circle
- Example 11: Calculating the Area of a Composite Figure
- Example 12: Calculating Area
- Example 13: Calculating 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 Right Triangle Trigonometry
7.1 Percents
- Examples
- Example 1: Changing between Percents and Decimal Numbers
- Example 2: Changing between Percents and Fractions
- Example 3: Finding the Amount
- Example 4: Finding the Base
- Example 5: Finding the Percent
- Example 6: Application: Finding a Discount
- Example 7: Application: Calculating Sales Tax
- Example 8: Application: Determining Commission
- Example 9: Application: Finding the Percent Increase
- Example 10: Application: Finding the Percent Decrease
- Example 11: Application: Calculating Percent of Profit
7.2 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
7.3 Buying a Car
7.4 Buying a House
8.1 Introduction to Sets
- Examples
- Example 1: Writing Sets Using Roster Notation
- Example 2: Writing Sets Using Roster Notation
- Example 3: Writing Sets Using Set-Builder Notation
- Example 4: Writing Sets
- Example 5: Using the Symbols ∈ and ∉
- Example 6: Using the Symbols ∈ and ∉
- Example 7: Recognizing the Empty Set
- Example 8: Finding All Proper Subsets of a Given Set
- Example 9: Using the symbols ⊆ and ⊂.
8.2 Venn Diagrams and Operations with Sets
- Examples
- Example 1: Interpreting Venn Diagrams
- Example 2: Interpreting a Venn Diagram with Disjoint Sets
- Example 3: Finding the Intersection of Two Sets
- Example 4: Finding the Intersection of Two Sets
- Example 5: Finding the Intersection of Two Sets
- Example 6: Drawing Venn Diagrams with Intersecting Sets
- Example 7: Drawing Venn Diagrams with Disjoint Sets
- Example 8: Finding the Union of Two Sets
- Example 9: Finding the Union of Two Sets
- Example 10: Using Venn Diagrams to Describe the Relationship Between Two Sets
- Example 11: Finding the Complement of a Set
- Example 12: Finding the Complement of a Set
8.3 Inductive and Deductive Reasoning
8.4 Logic Statements, Negations, and Quantified Statements
8.5 Compound Statements and Connectives
- Examples
- Example 1: Identifying Compound Statements
- Example 2: Writing Compound Statements with Conjunctions
- Example 3: Writing Compound Statements with Disjunctions
- Example 4: Writing Conditional Statements
- Example 5: Analyzing Conditional Statements
- Example 6: Writing Biconditional Statements
- Example 7: Working with Biconditional Statements
- Example 8: Working with Symbolic Logical Connectives
- Example 9: Expressing Logical Connectives Symbolically
8.6 Truth Tables
9.1 Introduction to Probability
- Examples
- Example 1: Tossing a Coin
- Example 2: Tossing a Coin Three Times
- Example 3: Rolling a Die
- Example 4: Choosing One Card from a Deck of Cards
- Example 5: Calculating Empirical Probability
- Example 6: Calculating Empirical Probability
- Example 7: Calculating Empirical Probability
- Example 8: Calculating Classical Probability
- Example 9: Calculating Classical Probability
- Example 10: Calculating Classical Probability
- Example 11: Using a Tree Diagram to Calculate Classical Probability
9.2 The Addition Rules of Probability and Odds
9.3 The Multiplication Rules of Probability and Conditional Probability
- Examples
- Example 1: Calculating Conditional Probability
- Example 2: Calculating Conditional Probability
- Example 3: Determining the Independence of Events
- Example 4: Using the Multiplication Rule for Independent Events
- Example 5: Using the Multiplication Rule for Independent Events
- Example 6: Using the Multiplication Rule for Independent Events
- Example 7: Using the Multiplication Rule for Independent Events
- Example 8: Using the Multiplication Rule for Dependent Events
- Example 9: Using the Multiplication Rule for Dependent Events
9.4 The Fundamental Counting Principle and Permutations
9.5 Combinations
9.6 Using Counting Methods to Find Probability
10.1 Collecting Data
10.2 Organizing and Displaying Data
10.3 Measures of Center
- Examples
- Example 1: Finding the Mean
- Example 2: Application: Finding the Mean
- Example 3: Finding the Median
- Example 4: Finding the Median
- Example 5: Finding the Mode
- Example 6: Finding the Mode
- Example 7: Finding the Mode
- Example 8: Finding Measures of Central Tendency from a Frequency Distribution
- Example 9: Finding the Weighted Mean