College Algebra plus Integrated Review, 3rd 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.R.1 Exponents, Prime Numbers, and LCM
- 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: Divisibility by 2
- Example 8: Divisibility by 3
- Example 9: Divisibility by 4
- Example 10: Divisibility by 5
- Example 11: Divisibility by 6
- Example 12: Divisibility by 9
- Example 13: Divisibility by 10
- Example 15: Determining Prime Numbers
- Example 16: Determining Composite Numbers
- Example 17: Determining Whether a Number is Prime
- Example 18: Determining Whether a Number is Prime
- Example 20: Finding the Prime Factorization of a Number
- Example 22: Finding the Factors of a Composite Number
- Example 24: Finding the Least Common Multiple (LCM)
- Example 25: Finding the Least Common Multiple (LCM)
- Example 27: Finding the Least Common Multiple (LCM)
- Example 28: Finding the Least Common Multiple (LCM)
- Example 30: Application: Finding the LCM
- Example 31: Finding Equivalent Fractions
- Example 32: Finding Equivalent Fractions
1.R.2 Multiplication and Division 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 6: Reducing Fractions to Lowest Terms
- Example 8: Application: Reducing Fractions to Lowest Terms
- Example 9: Multiplying and Reducing Using Prime Factors
- Example 10: Multiplying and Reducing Using Prime Factors
- Example 11: Multiplying and Reducing Using Prime Factors
- Example 13: Application: Multiplying and Reducing Fractions
- Example 14: Multiplying and Reducing Using the Division Method
- Example 15: Multiplying and Reducing Using the Division Method
- Example 16: Multiplying and Reducing Using the Division Method
- Example 17: Multiplying and Reducing Using the Division Method
- Example 18: Finding Reciprocals
- Example 19: Finding Reciprocals
- Example 20: Dividing Fractions
- Example 21: Dividing Fractions
- Example 22: Dividing and Reducing Fractions
- Example 23: Dividing and Reducing Fractions
- Example 26: Finding a Missing Number
- Example 27: Application: Dividing Fractions
- Example 28: Application: Multiplying and Dividing Fractions
1.R.3 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: Application: Adding Fractions
- Example 8: Subtracting Fractions with the Same Denominator
- Example 9: Subtracting Fractions with Different Denominators
- Example 10: Subtracting Fractions with Different Denominators
- Example 11: Subtracting Fractions with Different Denominators
- Example 12: Application: Subtracting Fractions with Different Denominators
1.R.4 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
1.R.5 Decimals, Fractions, and Percents
- 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
1.1 Real Numbers
1.2 The Arithmetic of Algebraic Expressions
- Examples
- Example 1: Terminology of Algebraic Expressions
- Example 2: Evaluating Algebraic Expressions
- Example 3: Using the Field Properties
- Example 5: Using the Cancellation and Zero-Factor Properties
- Example 6: Order of Operations
- Example 7: Union and Intersection of Intervals
- Example 8: Union and Intersection
1.3 Properties of Exponents
1.4 Properties of Radicals
- Examples
- Example 1: Using Radical Notation
- Example 2: Using Radical Notation
- Example 3: Simplifying Radical Expressions
- Example 5: Rationalizing the Numerator
- Example 6: Combining Radical Expressions
- Example 7: Simplifying Expressions
- Example 8: Simplifying Radical Expressions
- Example 9: Using Radical Notation
1.5 Polynomials
1.6 Factoring Polynomials
1.7 Rational Expressions
1.8 Complex Numbers
2.R.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 4: Graphing Sets 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
- Example 11: Application: Solving Absolute Value Equations
2.R.2 Addition with Real Numbers
2.R.3 Subtraction with Real Numbers
2.R.4 Multiplication and Division with Real Numbers
- Examples
- Example 1: Multiplying Positive and Negative Real Numbers
- Example 2: Multiplying Two Negative Real Numbers
- Example 3: Multiplication by
- Example 4: Dividing Real Numbers
- Example 5: Dividing Fractions and Decimals
- Example 6: Application: Calculating an Average
- Example 7: Application: Calculating an Average
- Example 8: Application: Calculating an Average
2.1 Linear Equations in One Variable
2.2 Linear Inequalities in One Variable
- Examples
- Example 1: Multiplying Inequalities by Negative Numbers
- Example 2: Solving Linear Inequalities
- Example 3: Graphing Intervals of Real Numbers
- Example 4: Calculating Final Grades
- Example 5: Solving Double Linear Inequalities
- Example 6: Solving Linear Absolute Value Inequalities
- Example 7: Translating Inequality Phrases
- Example 8: Applications of Inequalities
2.3 Quadratic Equations in One Variable
2.4 Polynomial and Polynomial-Like Equations in One Variable
2.5 Rational Equations in One Variable
2.6 Radical Equations in One Variable
3.R.1 Formulas in Geometry
- 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
- Example 7: Calculating the Area of a Triangle Using a Formula
- Example 8: Calculating the Area of a Trapezoid Using a Formula
- Example 9: Calculating the Area of a Composite Figure
- Example 10: Calculating Area
- Example 11: Calculating Area
- Example 12: Application: Calculating Perimeter and Area
- Example 13: Calculating the Circumference and Area of a Circle
- Example 14: Calculating the Circumference and Area of a Circle
- Example 15: Calculating the Perimeter
- Example 16: Calculating the Area of a Washer
- Example 17: Calculating Perimeter and Area
- Example 18: Calculating the Perimeter and Area
- Example 19: Calculating the Volume of a Rectangular Solid
- Example 20: Calculating the Volume of a Sphere
- Example 21: Calculating the Volume of a Cone
- Example 22: Calculating the Volume of a Solid
- Example 23: Finding the Volume of a Cube
- Example 24: Calculating the Surface Area of a Rectangular Solid
- Example 25: Calculating the Surface Area of a Cylinder
3.R.2 Square Roots and the Pythagorean Theorem
- Examples
- Example 1: Evaluating Perfect Squares
- Example 2: Evaluating Square Roots
- Example 3: Calculating Square Roots Using a Calculator
- Example 4: Verifying Right Triangles
- Example 5: Finding the Length of the Hypotenuse
- Example 6: Finding the Length of the Hypotenuse
- Example 7: Finding the Length of the Hypotenuse
3.R.3 Evaluating Radicals
3.R.4 Simplifying Radicals
3.R.5 Introduction to the Cartesian Coordinate System
3.R.6 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
3.R.7 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
3.R.8 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 11: Solving Linear Inequalities
- Example 13: Application: Using Inequalities
3.R.9 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
4.R.1 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
4.R.2 Translating English Phrases and Algebraic Expressions
4.R.3 Applications: Number Problems and Consecutive Integers
4.R.4 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
4.R.5 Factoring Trinomials: x^2 + bx + c
4.R.6 Factoring Trinomials: ax^2 + bx + c
4.R.7 Review of Factoring Techniques
4.R.8 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
4.R.9 Multiplication and Division with Complex Numbers
4.R.10 Quadratic Equations: The Quadratic Formula
5.R.1 Order of Operations with Real Numbers
- Examples
- Example 1: Using the Order of Operations with Real Numbers
- 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 6: Using the Order of Operations with Real Numbers
- Example 7: Using the Order of Operations with Real Numbers
5.R.2 Simplifying and Evaluating Algebraic Expressions
5.R.3 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
5.R.4 Division with Polynomials
5.R.5 Introduction to Rational Expressions
5.R.6 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
5.R.7 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
7.R.1 Rules for Exponents
7.R.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
7.R.3 Rational Exponents
7.R.4 Introduction to Logarithmic Functions
9.R.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.R.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.R.3 Systems of Linear Equations: Solutions by Addition
9.R.4 Systems of Linear Inequalities
9.1 Solving Systems of Linear Equations by Substitution and Elimination
- Examples
- Example 1: Solving an Independent System by Substitution
- Example 2: Solving a Dependent System by Substitution
- Example 3: Solving an Independent System by Elimination
- Example 4: Solving an Inconsistent System by Elimination
- Example 5: Solving an Independent System by Elimination
- Example 6: Solving a Dependent System by Elimination
- Example 7: Mixing Alloys
- Example 8: Determining Ages
9.2 Matrix Notation and Gauss-Jordan Elimination
9.3 Determinants and Cramer's Rule
9.4 Basic Matrix Operations
9.5 Inverses of Matrices
9.6 Systems of Linear Inequalities and Linear Programming
9.7 Systems of Nonlinear Equations and Inequalities
- Examples
- Example 1: Solving Systems of Nonlinear Equations by Graphing
- Example 2: Solving Systems of Nonlinear Equations by Graphing
- Example 3: Solving Systems of Nonlinear Equations Algebraically
- Example 4: Solving Systems of Nonlinear Equations Algebraically
- Example 5: Solving Systems of Nonlinear Equations Algebraically
- Example 6: Solving Systems of Nonlinear Inequalities by Graphing
10.1 Sequences and Series
10.2 Arithmetic Sequences and Series
10.3 Geometric Sequences and Series
10.4 Mathematical Induction
10.5 Combinatorics
- Examples
- Example 2: Using the Multiplication Principle of Counting
- Example 3: Calculating Permutations
- Example 4: Calculating Permutations
- Example 5: Using the Permutation Formula
- Example 6: Calculating Permutations and Combinations
- Example 7: The Combination Formula and Forming Committees
- Example 8: Counting Rules and Forming "Words"
- Example 11: Using the Multinomial Theorem