Precalculus 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.R.6 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
1.R.7 Addition with Real Numbers
1.R.8 Subtraction with Real Numbers
1.R.9 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
1.1 Real Numbers and Algebraic Expressions
- Examples
- Example 1: Types of Real Numbers
- Example 2: Drawing the Real Number Line
- Example 3: Working with Order
- Example 4: Set-Builder Notation
- Example 5: Intervals of Real Numbers
- Example 6: Union and Intersection of Intervals
- Example 7: Union and Intersection
- Example 8: Absolute Value
- Example 9: Using Absolute Value Properties
- Example 10: Terminology of Algebraic Expressions
- Example 11: Evaluating Algebraic Expressions
- Example 12: Using the Field Properties
- Example 14: Using the Cancellation and Zero-Factor Properties
1.2 Properties of Exponents and Radicals
- Examples
- Example 1: Using Natural Number Exponents
- Example 2: Simplifying Exponents
- Example 3: Using Properties of Exponents
- Example 4: Using Scientific Notation
- Example 5: Simplifying Expressions with Scientific Notation
- Example 6: Using Geometric Formulas
- Example 7: Using Radical Notation
- Example 8: Using Radical Notation
- Example 9: Simplifying Radical Expressions
- Example 11: Rationalizing the Numerator
- Example 12: Combining Radical Expressions
- Example 13: Simplifying Expressions
- Example 14: Simplifying Radical Expressions
1.3 Polynomials and Factoring
- Examples
- Example 1: Polynomial Expressions
- Example 2: Adding and Subtracting Polynomials
- Example 3: Multiplying Polynomials
- Example 4: The FOIL Method
- Example 8: Factoring Special Binomials
- Example 9: Factoring a Trinomial
- Example 10: Factoring a Trinomial by Grouping
- Example 11: Perfect Square Trinomials
- Example 12: Factoring Expressions with Noninteger Rational Exponents
1.4 Rational Expressions
1.5 Complex Numbers
1.6 Linear Equations in One Variable
1.7 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
1.8 Polynomial and Polynomial-Like Equations in One Variable
- Examples
- Example 2: Perfect Square Quadratic Equations
- Example 3: Completing the Square
- Example 4: Using the Quadratic Formula
- Example 5: The Discriminant
- Example 6: Methods of Solving Quadratic Equations
- Example 7: Gravity Problems
- Example 8: Quadratic-Like Equations
- Example 9: Solving Equations by Factoring
- Example 10: Solving Equations by Factoring
1.9 Rational and Radical Equations in One Variable
2.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
2.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
2.R.3 Evaluating Radicals
2.R.4 Simplifying Radicals
2.R.5 Introduction to the Cartesian Coordinate System
2.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
2.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
2.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
2.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
3.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
3.R.2 Translating English Phrases and Algebraic Expressions
3.R.3 Applications: Number Problems and Consecutive Integers
3.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
3.R.5 Factoring Trinomials: x^2 + bx + c
3.R.6 Factoring Trinomials: ax^2 + bx + c
3.R.7 Review of Factoring Techniques
3.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
3.R.9 Multiplication and Division with Complex Numbers
3.R.10 Quadratic Equations: The Quadratic Formula
4.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
4.R.2 Simplifying and Evaluating Algebraic Expressions
4.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
4.R.4 Division with Polynomials
4.R.5 Introduction to Rational Expressions
4.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
4.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
6.R.1 Rules for Exponents
6.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
6.R.3 Rational Exponents
6.R.4 Introduction to Logarithmic Functions
7.R.1 Angles
7.R.2 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
8.1 Fundamental Trigonometric Identities
8.2 Sum and Difference Identities
- Examples
- Example 1: Using the Sum and Difference Identities for Exact Evaluation
- Example 3: Using the Sum and Difference Identities for Exact Evaluation
- Example 4: Using the Sum and Difference Identities for Exact Evaluation
- Example 5: Using the Sum and Difference Identities
- Example 7: Using the Sum and Difference Identities
- Example 8: Using the Sum and Difference Identities
- Example 9: Using the Sum of Sines and Cosines Identity
8.3 Product-Sum Identities
- Examples
- Example 1: Using the Double-Angle Identities
- Example 2: Using Trigonometric Identities
- Example 3: Using the Power-Reducing Identities
- Example 4: Using the Half-Angle Identities
- Example 5: Using the Half-Angle Identities for Exact Evaluation
- Example 6: Using the Product-to-Sum Identities
- Example 7: Using the Sum-to-Product Identities
8.4 Trigonometric Equations
- Examples
- Example 1: Solving Equations by Isolating the Trigonometric Function
- Example 2: Solving Equations by Isolating the Trigonometric Function
- Example 3: Solving Trigonometric Equations by Factoring
- Example 4: Solving Equations Using Trigonometric Identities
- Example 5: Solving Trigonometric Equations by Graphing
- Example 6: Solving Equations Using Trigonometric Identities
- Example 7: Solving Equations by Isolating the Trigonometric Function
- Example 8: Solving Equations Using Inverse Trigonometric Functions
- Example 9: Solving Equations Using Inverse Trigonometric Functions
9.1 The Law of Sines
- Examples
- Example 1: Using the Law of Sines in an AAS Situation
- Example 2: Using the Law of Sines in an ASA Situation
- Example 3: Using the Law of Sines in an SSA Situation with Two Solutions
- Example 4: Using the Law of Sines in an SSA Situation with No Solution
- Example 5: Using the Sine Formula to Find the Area of a Triangle
9.2 The Law of Cosines
9.3 Polar Coordinates and Polar Equations
- Examples
- Example 1: Plotting in Polar Coordinates
- Example 2: Converting from Polar to Cartesian Coordinates
- Example 4: Rewriting an Equation in Polar Form
- Example 5: Rewriting an Equation in Rectangular Form
- Example 6: Graphing Polar Equations
- Example 7: Graphing Polar Equations
- Example 8: Graphing Common Polar Equations Using Symmetry
- Example 9: Graphing Common Polar Equations Using Symmetry
9.4 Parametric Equations
9.5 Trigonometric Form of Complex Numbers
- Examples
- Example 1: Finding the Magnitude
- Example 2: Graphing Regions in the Complex Plane
- Example 3: Writing Complex Numbers in Trigonometric Form
- Example 4: Writing Complex Numbers in Standard Form
- Example 5: Multiplying Complex Numbers
- Example 6: Dividing Complex Numbers
- Example 7: Graphing Complex Numbers and Their Product
- Example 8: Using De Moivre's Theorem
- Example 9: Finding Roots of Complex Numbers
- Example 10: Finding Roots of Complex Numbers
9.6 Vectors in the Cartesian Plane
- Examples
- Example 1: Graphing the Sum of Two Vectors
- Example 2: Graphing Vectors
- Example 3: Using Vector Operations
- Example 4: Finding the Unit Vector and Linear Combination of a Vector
- Example 5: Finding the Vector Form of the Velocity
- Example 6: Applying Vector Operations
- Example 7: Applying Vector Operations
9.7 The Dot Product
9.8 Hyperbolic Functions
10.1 Ellipses
10.2 Parabolas
10.3 Hyperbolas
10.4 Rotation of Conic Sections
10.5 Polar Equations of Conic Sections
11.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
11.R.2 Systems of Linear Equations: Solutions by Substitution
11.R.3 Systems of Linear Equations: Solutions by Addition
11.R.4 Systems of Linear Inequalities
11.1 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
11.2 Matrix Notation and Gauss-Jordan Elimination
11.3 Determinants and Cramer's Rule
11.4 Basic Matrix Operations
11.5 Inverses of Matrices
11.6 Partial Fraction Decomposition
- Examples
- Example 1: Finding the Partial Fraction Decomposition of a Function
- Example 2: Finding the Partial Fraction Decomposition of a Function
- Example 3: Finding the Partial Fraction Decomposition of a Function
- Example 4: Finding the Partial Fraction Decomposition of a Function
- Example 5: Finding the Partial Fraction Decomposition of a Function
11.7 Systems of Linear Inequalities and Linear Programming
11.8 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
12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
12.4 Mathematical Induction
12.5 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
12.6 Probability
13.1 Rates of Change and Tangents
13.2 Limits in the Plane
13.3 The Mathematical Definition of Limit
13.4 Determining Limits of Functions
13.5 Continuity
- Examples
- Example 1: Finding Points of Continuity and Discontinuity
- Example 2: Finding Points of Discontinuity
- Example 5: Using the ε-δ Definition of Continuity
- Example 6: Understanding Rational Functions and Continuity
- Example 7: Using Theorems to Determine Continuity of Functions
- Example 8: Using Alternate Formulations to Prove Functions Are Continuous
- Example 10: Defining Continuous Extensions of Functions
- Example 11: Using the Intermediate Value Theorem