Precalculus plus Integrated Review, 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.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 Reducing Fractions to Lowest Terms
- Examples
- Example 1: Reducing Fractions to Lowest Terms
- Example 2: Reducing Fractions to Lowest Terms
- Example 4: Application: Reducing Fractions to Lowest Terms
- Example 5: Multiplying and Reducing Using Prime Factors
- Example 6: Multiplying and Reducing Using Prime Factors
- Example 7: Multiplying and Reducing Using Prime Factors
- Example 9: Application: Multiplying and Reducing Fractions
- Example 10: Multiplying and Reducing Using the Division Method
- Example 11: Multiplying and Reducing Using the Division Method
- Example 12: Multiplying and Reducing Using the Division Method
- Example 13: Multiplying and Reducing Using the Division Method
1.R.3 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.4 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.5 Decimals 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 8: Application: Changing Fractions to Percents
- Example 10: Changing Percents to Fractions
- Example 11: Changing Percents to Mixed Numbers
1.R.6 Applications: Number Problems and Consecutive Integers
1.R.7 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.8 Simplifying Radicals
1.1a The Real Number System
1.1b The Arithmetic of Algebraic Expressions
- Examples
- Example 1: Terminology of Algebraic Expressions
- Example 2: Evaluating Algebraic Expressions
- Example 3: Applying the Field Properties
- Example 4: Visualizing the Distributive Property
- Example 5: Properties of Real Numbers
- Example 6: Order of Operations
- Example 7: Union and Intersection of Intervals
- Example 8: Union and Intersection
1.2a Properties of Exponents
1.2b Scientific Notation and Geometric Problems Using Exponents
1.2c Properties of Radicals
1.2d Rational Number Exponents
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 5: The Greatest Common Factor Method
- Example 6: Factoring by Grouping
- Example 7: Factoring Special Binomials
- Example 8: Factoring a Trinomial
- Example 9: Factoring a Trinomial by Grouping
- Example 10: Perfect Square Trinomials
- Example 11: Factoring Expressions with Fractional Exponents
1.4 The Complex Number System
1.5a Linear Equations in One Variable
1.5b Applications of Linear Equations in One Variable
1.6 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: Compound Linear Inequalities
- Example 6: Absolute Value Inequalities
- Example 7: Translating Inequality Phrases
- Example 8: Applications of Inequalities
1.7a Quadratic Equations in One Variable
1.7b Higher Degree Polynomial Equations
1.8a Rational Expressions and Equations
1.8b Radical Equations
2.R.1 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.2 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.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
3.R.2 Identifying Like Terms
3.R.3 Simplifying Expressions
- Examples
- Example 1: Combining Like Terms
3.R.4 Translating English Phrases and Algebraic Expression
5.R.1 Rules for Exponents
5.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
5.R.3 Rational Exponents
6.R.1 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.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
6.1 Radian and Degree Measure of Angles
6.2 Trigonometric Functions of Acute Angles
6.3 Trigonometric Functions of Any Angle
- Examples
- Example 1: Finding the Values of the Six Trigonometric Functions
- Example 2: Finding the Values of the Six Trigonometric Functions
- Example 3: Finding the Reference Angle
- Example 4: Evaluating Trigonometric Functions
- Example 5: Using Cofunction Identities
- Example 6: Using the Relationships Between Trigonometric Functions
- Example 7: Using the Relationships Between Trigonometric Functions
6.4 Graphs of Trigonometric Functions
- Examples
- Example 1: Graphing the Cosecant Function
- Example 2: Finding the Period of Trigonometric Functions
- Example 3: Graphing the Tangent Function
- Example 4: Using Simple Harmonic Motion
- Example 5: Graphing Transformed Trigonometric Functions
- Example 6: Graphing Transformed Trigonometric Functions
- Example 7: Graphing Transformed Trigonometric Functions
- Example 8: Modeling Damped Harmonic Motion
6.5 Inverse Trigonometric Functions
- Examples
- Example 1: Defining and Plotting the Arccosine Function
- Example 2: Evaluating Inverse Trigonometric Functions
- Example 3: Evaluating Compositions of Trigonometric Functions
- Example 4: Evaluating Compositions of Trigonometric Functions
- Example 5: Using Inverse Trigonometric Functions
- Example 6: Using Inverse Trigonometric Functions
7.1 Fundamental Identities and their Uses
7.2 Sum and Difference Identities
- Examples
- Example 1: Using the Sum and Difference Identities for Exact Evaluation
- Example 2: 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 6: Using the Sum and Difference Identities
- Example 7: Using the Sum and Difference Identities
- Example 8: Using the Sum of Sines and Cosines Identity
7.3 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
7.4 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
8.1a The Law of Sines and the Law of Cosines
- 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: Determining If a Triangle Exists
- Example 4: Determining If a Triangle Exists
- Example 5: Using the Law of Cosines in a SSS Situation
- Example 6: Using the Law of Cosines in an SAS Situation
8.1b Area of Triangles
8.2 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 Coordinates
- Example 5: Rewriting an Equation in Rectangular Coordinates
- 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
8.3a Parametric Equations - Graphing and Applications
8.3b Parametric Equations - Eliminating the Parameter
8.3c Parametric Equations - Constructing Equations
8.4a Trigonometric Form of Complex Numbers
8.4b Operations with Complex Numbers
8.5 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
8.6 The Dot Product and Its Uses
10.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
10.R.2 Systems of Linear Inequalities
10.1 Solving Systems by Substitution and Elimination
- Examples
- Example 1: Solving a System of Equations by Substitution
- Example 2: Solving a System of Equations by Substitution
- Example 3: Solving a System of Equations by Elimination
- Example 4: Solving a System of Equations by Elimination
- Example 5: Solving a System of Equations by Elimination
- Example 6: Solving a System of Equations by Elimination
- Example 7: Mixing Alloys
- Example 8: Determining Ages
10.2 Matrix Notation and Gaussian Elimination
10.3 Determinants and Cramer's Rule
10.4 The Algebra of Matrices
10.5 Inverses of Matrices
10.6 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
10.7 Linear Programming
10.8 Nonlinear Systems of Equations
- Examples
- Example 1: Solving Nonlinear Systems by Graphing
- Example 2: Solving Nonlinear Systems by Graphing
- Example 3: Solving Nonlinear Systems Algebraically
- Example 4: Solving Nonlinear Systems Algebraically
- Example 5: Solving Nonlinear Systems Algebraically
- Example 6: Solving Nonlinear Systems of Inequalities by Graphing