5 Steps to a 5: AP Calculus AB 2024 (2024)

Name: 5 Steps to a 5: AP Calculus AB 2024 (2024)
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Author: Elizabeth Chen

Reinforce your learning with 5 Steps to a 5: AP Calculus AB 2024 (2024), a set of structured practice exams tailored for success.

Elizabeth Chen

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CONTENTS
Preface
Acknowledgments
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 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!

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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

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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

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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

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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

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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

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5 Steps to a 5: AP Calculus AB 2024 (2024)

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