5 Steps to a 5 AP Calculus AB 2019 - William Ma

(Marvins-Underground-K-12) #1

  • MA 3972-MA-Book May 24, 2018 14:

    • 1 What You Need to Know About the AP Calculus AB Exam STEP 1 Set Up Your Study Plan

      • 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





    • 3 Take a Diagnostic Exam STEP 2 Determine Your Test Readiness

      • 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





    • 4 How to Approach Each Question Type STEP 3 Develop Strategies for Success

      • 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







  • MA 3972-MA-Book May 24, 2018 14:

    • 5 Review of Precalculus STEP 4 Review the Knowledge You Need to Score High

      • 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



    • 6 Limits and Continuity Big Idea 1: Limits

      • 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 (asx→a)

        • Limits at Infinity (asx→±∞)

        • Horizontal and Vertical Asymptotes



      • 6.3 Continuity of a Function

        • Continuity of a Function at a Number







  • MA 3972-MA-Book May 24, 2018 14:

    • Continuity of a Function over an Interval Contents v

    • 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

    • 7 Differentiation Big Idea 2: Derivatives

      • 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

        • Exponential, and Logarithmic Functions 7.2 Derivatives of Trigonometric, Inverse Trigonometric,

        • 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’sRule 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







  • MA 3972-MA-Book May 24, 2018 14:

    • 8.4 Graphs of Derivatives vi Contents

    • 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

        • and Minimum Problems General Procedure for Solving Applied Maximum

        • 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 thenth 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



  • MA 3972-MA-Book May 24, 2018 14:

  • 11 Integration Big Idea 3: Integrals and the Fundamental Theorems of Calculus

    • 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

      • and Exponential Functions Definite Integrals Involving Trigonometric, Logarithmic,

      • 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

    • af(t)dt ∫x

    • 13.2 Approximating the Area Under a Curve

      • Rectangular Approximations

      • Trapezoidal Approximations





  • MA 3972-MA-Book May 24, 2018 14:

    • 13.3 Area and Definite Integrals viii Contents

      • 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

      • AP Calculus AB Practice Exam STEP 5 Build Your Test-Taking Confidence

      • AP Calculus AB Practice Exam

      • Appendix

      • Bibliography

      • Websites





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