5 Steps to a 5: AP Calculus BC 2019
1st Edition
Published on 6. August 2018
464 pages
978-1-260-12273-2 (ISBN)
Available for download
Description
A PERFECT PLAN FOR THE PERFECT SCORE Score-Raising Features Include:*3 full-length practice exams with thorough answer explanations*Comprehensive overview of the AP Calculus BC exam format*Cumulative review sections at the end of each chapter provide continuous practice that builds on previously-covered material*An appendix of common formulas and theorems frequently tested in the AP Calculus BC exam*AP-style scoring guidelines for free-response practice questionsFREE AP Planner app that delivers a customizable study schedule for tests in the book, and extra practice questions to your mobile devices (see the last page of the books for details)The 5-Step Plan:Step 1: Set up your study plan with three model schedulesStep 2: Determine your readiness with an AP-style Diagnostic ExamStep 3: Develop the strategies that will give you the edge on test dayStep 4: Review the terms and concepts you need to achieve your highest scoreStep 5: Build your confidence with full-length practice exams
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William Ma
5 Steps to a 5: AP Calculus BC 2019
Book
08/2018
McGraw-Hill Education
€16.08
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Content
- Cover
- Title Page
- Copyright Page
- Contents
- Dedication and Acknowledgments
- Preface
- About the Authors
- Introduction: The Five-Step Program
- STEP 1 Set Up Your Study Plan
- 1 What You Need to Know About the AP Calculus BC Exam
- 1.1 What Is Covered on the AP Calculus BC Exam?
- 1.2 What Is the Format of the AP Calculus BC Exam?
- 1.3 What Are the Advanced Placement Exam Grades?
- How Is the AP Calculus BC Exam Grade Calculated?
- 1.4 Which Graphing Calculators Are Allowed for the Exam?
- Calculators and Other Devices Not Allowed for the AP Calculus BC Exam
- Other Restrictions on Calculators
- 2 How to Plan Your Time
- 2.1 Three Approaches to Preparing for the AP Calculus BC 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 BC Diagnostic Exam
- 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
- Big Idea 1: Limits
- 5 Limits and Continuity
- 5.1 The Limit of a Function
- Definition and Properties of Limits
- Evaluating Limits
- One-Sided Limits
- Squeeze Theorem
- 5.2 Limits Involving Infinities
- Infinite Limits (as x a)
- Limits at Infinity (as x ±8)
- Horizontal and Vertical Asymptotes
- 5.3 Continuity of a Function
- Continuity of a Function at a Number
- Continuity of a Function over an Interval
- Theorems on Continuity
- 5.4 Rapid Review
- 5.5 Practice Problems
- 5.6 Cumulative Review Problems
- 5.7 Solutions to Practice Problems
- 5.8 Solutions to Cumulative Review Problems
- Big Idea 2: Derivatives
- 6 Differentiation
- 6.1 Derivatives of Algebraic Functions
- Definition of the Derivative of a Function
- Power Rule
- The Sum, Difference, Product, and Quotient Rules
- The Chain Rule
- 6.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions
- Derivatives of Trigonometric Functions
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Exponential and Logarithmic Functions
- 6.3 Implicit Differentiation
- Procedure for Implicit Differentiation
- 6.4 Approximating a Derivative
- 6.5 Derivatives of Inverse Functions
- 6.6 Higher Order Derivatives
- L'Hôpital's Rule for Indeterminate Forms
- 6.7 Rapid Review
- 6.8 Practice Problems
- 6.9 Cumulative Review Problems
- 6.10 Solutions to Practice Problems
- 6.11 Solutions to Cumulative Review Problems
- 7 Graphs of Functions and Derivatives
- 7.1 Rolle's Theorem, Mean Value Theorem, and Extreme Value Theorem
- Rolle's Theorem
- Mean Value Theorem
- Extreme Value Theorem
- 7.2 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
- 7.3 Sketching the Graphs of Functions
- Graphing without Calculators
- Graphing with Calculators
- 7.4 Graphs of Derivatives
- 7.5 Parametric, Polar, and Vector Representations
- Parametric Curves
- Polar Equations
- Types of Polar Graphs
- Symmetry of Polar Graphs
- Vectors
- Vector Arithmetic
- 7.6 Rapid Review
- 7.7 Practice Problems
- 7.8 Cumulative Review Problems
- 7.9 Solutions to Practice Problems
- 7.10 Solutions to Cumulative Review Problems
- 8 Applications of Derivatives
- 8.1 Related Rate
- General Procedure for Solving Related Rate Problems
- Common Related Rate Problems
- Inverted Cone (Water Tank) Problem
- Shadow Problem
- Angle of Elevation Problem
- 8.2 Applied Maximum and Minimum Problems
- General Procedure for Solving Applied Maximum and Minimum Problems
- Distance Problem
- Area and Volume Problem
- Business Problems
- 8.3 Rapid Review
- 8.4 Practice Problems
- 8.5 Cumulative Review Problems
- 8.6 Solutions to Practice Problems
- 8.7 Solutions to Cumulative Review Problems
- 9 More Applications of Derivatives
- 9.1 Tangent and Normal Lines
- Tangent Lines
- Normal Lines
- 9.2 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
- 9.3 Motion Along a Line
- Instantaneous Velocity and Acceleration
- Vertical Motion
- Horizontal Motion
- 9.4 Parametric, Polar, and Vector Derivatives
- Derivatives of Parametric Equations
- Position, Speed, and Acceleration
- Derivatives of Polar Equations
- Velocity and Acceleration of Vector Functions
- 9.5 Rapid Review
- 9.6 Practice Problems
- 9.7 Cumulative Review Problems
- 9.8 Solutions to Practice Problems
- 9.9 Solutions to Cumulative Review Problems
- Big Idea 3: Integrals and the Fundamental Theorems of Calculus
- 10 Integration
- 10.1 Evaluating Basic Integrals
- Antiderivatives and Integration Formulas
- Evaluating Integrals
- 10.2 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
- 10.3 Techniques of Integration
- Integration by Parts
- Integration by Partial Fractions
- 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
- 11 Definite Integrals
- 11.1 Riemann Sums and Definite Integrals
- Sigma Notation or Summation Notation
- Definition of a Riemann Sum
- Definition of a Definite Integral
- Properties of Definite Integrals
- 11.2 Fundamental Theorems of Calculus
- First Fundamental Theorem of Calculus
- Second Fundamental Theorem of Calculus
- 11.3 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
- 11.4 Improper Integrals
- Infinite Intervals of Integration
- Infinite Discontinuities
- 11.5 Rapid Review
- 11.6 Practice Problems
- 11.7 Cumulative Review Problems
- 11.8 Solutions to Practice Problems
- 11.9 Solutions to Cumulative Review Problems
- 12 Areas, Volumes, and Arc Lengths
- 12.1 The Function F(x) = f (t)dt
- 12.2 Approximating the Area Under a Curve
- Rectangular Approximations
- Trapezoidal Approximations
- 12.3 Area and Definite Integrals
- Area Under a Curve
- Area Between Two Curves
- 12.4 Volumes and Definite Integrals
- Solids with Known Cross Sections
- The Disc Method
- The Washer Method
- 12.5 Integration of Parametric, Polar, and Vector Curves
- Area, Arc Length, and Surface Area for Parametric Curves
- Area and Arc Length for Polar Curves
- Integration of a Vector-Valued Function
- 12.6 Rapid Review
- 12.7 Practice Problems
- 12.8 Cumulative Review Problems
- 12.9 Solutions to Practice Problems
- 12.10 Solutions to Cumulative Review Problems
- 13 More Applications of Definite Integrals
- 13.1 Average Value of a Function
- Mean Value Theorem for Integrals
- Average Value of a Function on [a, b]
- 13.2 Distance Traveled Problems
- 13.3 Definite Integral as Accumulated Change
- Business Problems
- Temperature Problem
- Leakage Problem
- Growth Problem
- 13.4 Differential Equations
- Exponential Growth/Decay Problems
- Separable Differential Equations
- 13.5 Slope Fields
- 13.6 Logistic Differential Equations
- 13.7 Euler's Method
- Approximating Solutions of Differential Equations by Euler's Method
- 13.8 Rapid Review
- 13.9 Practice Problems
- 13.10 Cumulative Review Problems
- 13.11 Solutions to Practice Problems
- 13.12 Solutions to Cumulative Review Problems
- Big Idea 4: Series
- 14 Series
- 14.1 Sequences and Series
- Convergence
- 14.2 Types of Series
- p-Series
- Harmonic Series
- Geometric Series
- Decimal Expansion
- 14.3 Convergence Tests
- Divergence Test
- Integral Test
- Ratio Test
- Comparison Test
- Limit Comparison Test
- Informal Principle
- 14.4 Alternating Series
- Error Bound
- Absolute and Conditional Convergence
- 14.5 Power Series
- Radius and Interval of Convergence
- 14.6 Taylor Series
- Taylor Series and MacLaurin Series
- Common MacLaurin Series
- 14.7 Operations on Series
- Substitution
- Differentiation and Integration
- Error Bounds
- 14.8 Rapid Review
- 14.9 Practice Problems
- 14.10 Cumulative Review Problems
- 14.11 Solutions to Practice Problems
- 14.12 Solutions to Cumulative Review Problems
- STEP 5 Build Your Test-Taking Confidence
- AP Calculus BC Practice Exam 1
- AP Calculus BC Practice Exam 2
- Formulas and Theorems
- Bibliography
- Websites
