5 Steps to a 5: AP Calculus AB 2022
1st Edition
Published on 4. August 2021
448 pages
978-1-264-26782-8 (ISBN)
Available for download
Description
MATCHES THE LATEST EXAM!Let us supplement your AP classroom experience with this multi-platform study guide. The immensely popular 5 Steps to a 5: AP Calculus AB guide has been updated for the 2021-22 school year and now contains:3 full-length practice exams (available in the book and online) that reflect the latest examAccess to a robust online platformComprehensive overview of the AP Calculus AB exam formatStep-by-step explanations for nearly 800 AP Calculus AB problemsHundreds of practice exercises with thorough answer explanationsAn appendix of common formulas and theorems frequently tested on the examProven strategies specific to each section of the testA self-guided study plan including flashcards, games, and more online
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William Ma
5 Steps to a 5: AP Calculus AB 2022
Book
09/2021
McGraw-Hill Education
€37.32
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Content
- Cover
- Ad Page
- Title Page
- Copyright Page
- Contents
- Preface
- Acknowledgments
- About the Author
- Introduction: The Five-Step Program
- STEP 1 Set Up Your Study Plan
- 1 What You Need to Know About the AP Calculus AB Exam
- 1.1 What Is Covered on the AP Calculus AB Exam?
- 1.2 What Is the Format of the AP Calculus AB Exam?
- 1.3 What Are the Advanced Placement Exam Grades?
- How Is the AP Calculus AB Exam Grade Calculated?
- 1.4 Which Graphing Calculators Are Allowed for the Exam?
- Calculators and Other Devices Not Allowed for the AP Calculus AB Exam
- Other Restrictions on Calculators
- 2 How to Plan Your Time
- 2.1 Three Approaches to Preparing for the AP Calculus AB Exam
- Overview of the Three Plans
- 2.2 Calendar for Each Plan
- Summary of the Three Study Plans
- STEP 2 Determine Your Test Readiness
- 3 Take a Diagnostic Exam
- 3.1 Getting Started!
- 3.2 Diagnostic Test
- 3.3 Answers to Diagnostic Test
- 3.4 Solutions to Diagnostic Test
- 3.5 Calculate Your Score
- Short-Answer Questions
- AP Calculus AB Diagnostic Test
- STEP 3 Develop Strategies for Success
- 4 How to Approach Each Question Type
- 4.1 The Multiple-Choice Questions
- 4.2 The Free-Response Questions
- 4.3 Using a Graphing Calculator
- 4.4 Taking the Exam
- What Do I Need to Bring to the Exam?
- Tips for Taking the Exam
- STEP 4 Review the Knowledge You Need to Score High
- 5 Review of Precalculus
- 5.1 Lines
- Slope of a Line
- Equations of a Line
- Parallel and Perpendicular Lines
- 5.2 Absolute Values and Inequalities
- Absolute Values
- Inequalities and the Real Number Line
- Solving Absolute Value Inequalities
- Solving Polynomial Inequalities
- Solving Rational Inequalities
- 5.3 Functions
- Definition of a Function
- Operations on Functions
- Inverse Functions
- Trigonometric and Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- 5.4 Graphs of Functions
- Increasing and Decreasing Functions
- Intercepts and Zeros
- Odd and Even Functions
- Shifting, Reflecting, and Stretching Graphs
- 5.5 Rapid Review
- 5.6 Practice Problems
- 5.7 Cumulative Review Problems
- 5.8 Solutions to Practice Problems
- 5.9 Solutions to Cumulative Review Problems
- Big Idea 1: Limits
- 6 Limits and Continuity
- 6.1 The Limit of a Function
- Definition and Properties of Limits
- Evaluating Limits
- One-Sided Limits
- Squeeze Theorem
- 6.2 Limits Involving Infinities
- Infinite Limits (as x a)
- Limits at Infinity (as x ±8)
- Horizontal and Vertical Asymptotes
- 6.3 Continuity of a Function
- Continuity of a Function at a Number
- Continuity of a Function over an Interval
- Theorems on Continuity
- 6.4 Rapid Review
- 6.5 Practice Problems
- 6.6 Cumulative Review Problems
- 6.7 Solutions to Practice Problems
- 6.8 Solutions to Cumulative Review Problems
- Big Idea 2: Derivatives
- 7 Differentiation
- 7.1 Derivatives of Algebraic Functions
- Definition of the Derivative of a Function
- Power Rule
- The Sum, Difference, Product, and Quotient Rules
- The Chain Rule
- 7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
- Derivatives of Trigonometric Functions
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Exponential and Logarithmic Functions
- 7.3 Implicit Differentiation
- Procedure for Implicit Differentiation
- 7.4 Approximating a Derivative
- 7.5 Derivatives of Inverse Functions
- 7.6 Higher Order Derivatives
- 7.7 L'Hôpital's Rule for Indeterminate Forms
- 7.8 Rapid Review
- 7.9 Practice Problems
- 7.10 Cumulative Review Problems
- 7.11 Solutions to Practice Problems
- 7.12 Solutions to Cumulative Review Problems
- 8 Graphs of Functions and Derivatives
- 8.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
- Rolle's Theorem
- Mean Value Theorem
- Extreme Value Theorem
- 8.2 Determining the Behavior of Functions
- Test for Increasing and Decreasing Functions
- First Derivative Test and Second Derivative Test for Relative Extrema
- Test for Concavity and Points of Inflection
- 8.3 Sketching the Graphs of Functions
- Graphing without Calculators
- Graphing with Calculators
- 8.4 Graphs of Derivatives
- 8.5 Rapid Review
- 8.6 Practice Problems
- 8.7 Cumulative Review Problems
- 8.8 Solutions to Practice Problems
- 8.9 Solutions to Cumulative Review Problems
- 9 Applications of Derivatives
- 9.1 Related Rate
- General Procedure for Solving Related Rate Problems
- Common Related Rate Problems
- Inverted Cone (Water Tank) Problem
- Shadow Problem
- Angle of Elevation Problem
- 9.2 Applied Maximum and Minimum Problems
- General Procedure for Solving Applied Maximum and Minimum Problems
- Distance Problem
- Area and Volume Problems
- Business Problems
- 9.3 Rapid Review
- 9.4 Practice Problems
- 9.5 Cumulative Review Problems
- 9.6 Solutions to Practice Problems
- 9.7 Solutions to Cumulative Review Problems
- 10 More Applications of Derivatives
- 10.1 Tangent and Normal Lines
- Tangent Lines
- Normal Lines
- 10.2 Linear Approximations
- Tangent Line Approximation (or Linear Approximation)
- Estimating the nth Root of a Number
- Estimating the Value of a Trigonometric Function of an Angle
- 10.3 Motion Along a Line
- Instantaneous Velocity and Acceleration
- Vertical Motion
- Horizontal Motion
- 10.4 Rapid Review
- 10.5 Practice Problems
- 10.6 Cumulative Review Problems
- 10.7 Solutions to Practice Problems
- 10.8 Solutions to Cumulative Review Problems
- Big Idea 3: Integrals and the Fundamental Theorems of Calculus
- 11 Integration
- 11.1 Evaluating Basic Integrals
- Antiderivatives and Integration Formulas
- Evaluating Integrals
- 11.2 Integration by U-Substitution
- The U-Substitution Method
- U-Substitution and Algebraic Functions
- U-Substitution and Trigonometric Functions
- U-Substitution and Inverse Trigonometric Functions
- U-Substitution and Logarithmic and Exponential Functions
- 11.3 Rapid Review
- 11.4 Practice Problems
- 11.5 Cumulative Review Problems
- 11.6 Solutions to Practice Problems
- 11.7 Solutions to Cumulative Review Problems
- 12 Definite Integrals
- 12.1 Riemann Sums and Definite Integrals
- Sigma Notation or Summation Notation
- Definition of a Riemann Sum
- Definition of a Definite Integral
- Properties of Definite Integrals
- 12.2 Fundamental Theorems of Calculus
- First Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus
- 12.3 Evaluating Definite Integrals
- Definite Integrals Involving Algebraic Functions
- Definite Integrals Involving Absolute Value
- Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions
- Definite Integrals Involving Odd and Even Functions
- 12.4 Rapid Review
- 12.5 Practice Problems
- 12.6 Cumulative Review Problems
- 12.7 Solutions to Practice Problems
- 12.8 Solutions to Cumulative Review Problems
- 13 Areas and Volumes
- 13.1 The Function F(x) = ?xa f(t)dt
- 13.2 Approximating the Area Under a Curve
- Rectangular Approximations
- Trapezoidal Approximations
- 13.3 Area and Definite Integrals
- Area Under a Curve
- Area Between Two Curves
- 13.4 Volumes and Definite Integrals
- Solids with Known Cross Sections
- The Disc Method
- The Washer Method
- 13.5 Rapid Review
- 13.6 Practice Problems
- 13.7 Cumulative Review Problems
- 13.8 Solutions to Practice Problems
- 13.9 Solutions to Cumulative Review Problems
- 14 More Applications of Definite Integrals
- 14.1 Average Value of a Function
- Mean Value Theorem for Integrals
- Average Value of a Function on [a, b]
- 14.2 Distance Traveled Problems
- 14.3 Definite Integral as Accumulated Change
- Business Problems
- Temperature Problem
- Leakage Problem
- Growth Problem
- 14.4 Differential Equations
- Exponential Growth/Decay Problems
- Separable Differential Equations
- 14.5 Slope Fields
- 14.6 Rapid Review
- 14.7 Practice Problems
- 14.8 Cumulative Review Problems
- 14.9 Solutions to Practice Problems
- 14.10 Solutions to Cumulative Review Problems
- STEP 5 Build Your Test-Taking Confidence
- AP Calculus AB Practice Exam 1
- AP Calculus AB Practice Exam 2
- Appendix
- Bibliography
- Websites
