AP微积分5分制胜

STEP 1 Set Up Your Study Plan

1 What You Need to Know About the AP Calculus AB/BC Exams

1.1 What Is Covered on the AP Calculus Exams?

1.2 What Is the Format of the AP Calculus AP/BC Exams?

1.3 What Are the Advanced Placement Exam Grades?

How Is the AP Calculus Exam Grade Calculated?

1.4 Which Graphing Calculators Are Allowed for the Exam?

Calculators and Other Devices Not Allowed for the AP Calculus

Exam

Other Restrictions on Calculators

2 How to Plan Your Time

2.1 Three Approaches to Preparing for the AP Calculus Exam

Overview of the Three Plans

2.2 Calendar for Each Plan

Summary of the Three Study Plans

STEP 2 Determine Your Test Readiness

STEP 1 Set Up Your Study Plan

1 What You Need to Know About the AP Calculus AB/BC Exams

1.1 What Is Covered on the AP Calculus Exams?

1.2 What Is the Format of the AP Calculus AP/BC Exams?

1.3 What Are the Advanced Placement Exam Grades?

How Is the AP Calculus Exam Grade Calculated?

1.4 Which Graphing Calculators Are Allowed for the Exam?

Calculators and Other Devices Not Allowed for the AP Calculus

Exam

Other Restrictions on Calculators

2 How to Plan Your Time

2.1 Three Approaches to Preparing for the AP Calculus 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/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

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 → ±∞)

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

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

6.7 Indeterminate Forms

L’H?opital’s Rule for Indeterminate Forms 97

6.8 Rapid Review

6.9 Practice Problems

6.10 Cumulative Review Problems

6.11 Solutions to Practice Problems

6.12 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 130

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

10 Integration

11 Definite Integrals

12 Areas and Volumes

13 More Applications of Definite Integrals

14 Series (For Calculus BC Students Only)

STEP 5 Build Your Test-Taking Confidence

Appendixes

本系列AP考试丛书引进自美国知名教育出版公司McGraw-Hill
Education，由AP考试相关领域专家编写，是美国本土大学课堂使用教材，可以帮助考生提前适应全英学习模式。此系列中，AP各学科分册紧扣考试命题特点，以“五步”方案为学习框架，囊括与考试相关的学科要点。同时，还精选针对性练习以及全真模拟试题，配以准确答案和详尽解析，利于考生巩固所学，紧抓重点，取得高分。

科学的“五步”学习方案
　　巧妙的解题方法和策略
　　详细的学科内容讲解
　　典型的针对性练习
　　高仿真模拟套题