5 Steps to a 5 Calculus AB 2020 1st Edition by William Ma 1260454940 9781260454949

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ISBN 10: 1260454940

ISBN 13: 9781260454949

Author: William Ma

Get ready to ace your AP Calculus Exam with this easy-to-follow, multi-platform study guide The immensely popular test prep guide has been updated and revised with new material and is now accessible in print, online and mobile formats. 5 Steps to a 5: AP Calculus 2020 introduces an easy to follow, effective 5-step study plan to help you build the skills, knowledge, and test-taking confidence you need to reach your full potential. The book includes hundreds of practice exercises with thorough answer explanations and sample responses. You’ll learn how to master the multiple-choice questions and achieve a higher score on this demanding exam. Because this guide is accessible in print and digital formats, you can study online, via your mobile device, straight from the book, or any combination of the three. This essential guide reflects the latest course syllabus and includes 4 full-length practice exams (2 in the book and 2 online), plus proven strategies specific to each section of the test. 5 Steps to a 5: AP Calculus AB 2020 features: 4 Practice Exams (2 in the book + 2 online) Access to the entire Cross-Platform Prep Course in Calculus AB 2020 Step-by-step explanations for nearly 800 AP Calculus AB problems An appendix of common formulas and theorems frequently tested on the exam Powerful analytics you can use to assess your test readiness Flashcards, games

5 Steps to a 5 Calculus AB 2020 1st Table of contents:

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 → ±∞)

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

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

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