Kevin Quattrin, EdD
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The Readable Calculus Project (AB version)
  • Project Manager/Lead Writer: Kevin Quattrin
  • Associate Writer: Paul Maychrowitz
  • Associate Writer: Najla (nee Fawal) Abrao
  • Chief Editor: Elizabeth Regalia

Table of Contents

Introduction: General Overview of Calculus [Intro pdf]
                                                          

Chapter 0:  Reminders from PreCalculus [2025-26 Chapter 0]
0.1:    PreCalculus Basics
0.2:   Important Facts for Calculus
0.3:   Factoring Review
0.4:   Sign Patterns         


Chapter 1: Derivatives  [2025-26 Chapter 1 pdf]
Overview:  Review of Derivatives Rules      
1.1:    The Power and Exponential Rules       
1.2:    Composite Functions and the Chain Rule 
1.3:    Trig, Trig Inverse, and Log Rules   
1.4:    Derivatives in Context:  Local Linearity and Motion   
1.5:    The Product Rule                 
1.6:    The Quotient Rule                                                             
1.7:    Higher Order Derivatives                                                     
1.8:    ​Intro to AP:  Basic Derivatives Numerically and Graphically     
Chapter 1 Practice Test 
Chapter 1 Answer Key   

Chapter 2:  Indefinite Integrals  [2025-26 Chapter 2 pdf]                                                         
Overview: The Operations of Calculus   
2.1:    The Power and Transcendental Rules
2.2:    Initial Conditions
2.3:    Rectilinear Motion
2.4:    Integration by Substitution:  Reversing the Chain Rule
2.5:    Integration by Substitution: Transcendental Functions 
2.6:    Separable Differential Equations     
2.7:    Intro to AP:  Slope Fields
Chapter 2 Practice Test     
Chapter 2 Answer Key    

 

Chapter 3:    Definite Integrals  [2025-26 Chapter 3 pdf]     
Overview:                                                                                   
3.1:    Definite Integrals and the Fundamental Theorem of Calculus    
3.2:    Integration by U-Substitution                                                                 
3.3:    Context:  Area, Displacement, and Net Change                                                            
3.4:    Intro to AP:   Accumulation of Rates                            
3.5:    Approximate Integration – Riemann Sums     
3.6:    Intro to AP:   Table Problems                                                       
Chapter 3Practice Test                                                                            
Chapter 3 Answer Key      
                                                                       

Chapter 4 Applications of the Derivative I--Graphing  [2025-26  Chapter 4 pdf]     
Overview:                                                                                   
4.1:    Extremes and the Derivative Tests   
4.2:    Optimization      
4.3     The Mean Value Theorem   
4.4     Intro to AP:  Input-Output Problems
4.5:    The Second Derivative, Points of Inflection, and Concavity 
4.6:    Graphing with Derivatives 
4.7:    Graphical Analysis I       
4.8:    Intro to AP:  Graphical Analysis II                                                
Chapter 4 Practice Test                                                                            
Chapter 4 Answer Key                                                                
 
Chapter 5:    Applications of the Derivative II—Rates of Change   [2025-26  Chapter 5 pdf]  
Overview:                                                                                   
5.1:    Motion                                                                               
5.2:    Implicit Differentiation                                                        
5.3:    Related Rates                                                                      
5.4:    Logistic Growth                                                                  
Chapter 5 Practice Test                                                                            
Chapter 5 Answer Key                                                                
                                                           
Chapter 6:    Applications of Integrals  [2025-26 Chapter 6 pdf]     
Overview:                                                                                   
6.1:    Area between Two Curves            
6.2:    Arc Length  
6.3:    Volume by Rotation about the x-axis 
6.3:    Volume by Rotation about the y-axis 
6.5:    Volume by Rotation about a Line not an Axis 
6.6:    Volume by Cross-section Method 
6.7:    AP Volume FRQs   
6.8:    Volume by Shell Method                                                
Chapter 6 Practice Test 

Chapter 6 Answer Key   

Chapter 7:  Limits, Continuity and Differentiability  [2025-26 Chapter 7 pdf]   
Overview:  Introduction to Limits                                                        
7.1:    Limits and L’Hopital’s Rule                                                 
7.2:    The Limit Definitions of a Derivative                                     
7.3:    One-sided Limits        
7.4:    Continuity                                 
7.5:    Differentiability and Smoothness                                           
7.6:    Limits at Infinity and End Behavior                                      
Chapter 7 Practice Test    
Chapter 7 Answer Key   

Chapter 8:    AP Calculus AB Review [2025-26  Chapter 8 pdf]
Overview:                                                                                   
8.1:    Accumulation of Rates               
8.2:    Reasoning from Tabular Data       
8.3:    Graphical Analysis               
8.4:    Rectilinear Motion              
8.5:    Differential Equations          
8.6:    Area & Volume          
8.7:    Related Rates                        
8.8:    Implicit Differentiation
8.9:    Miscellaneous Topics    
 
       
Finally, this book was funded, in part with money from a government grant allocated during the COVID pandemic.  It was written particularly to address learning loss due to COVID – since much material was cut from curricula due to shutdowns of schools, we revised this text to help students transition to an AP level course while teaching skills that were lost during school shutdowns.  The text has accompanying screencast designed so that a student can learn and study the material independently to make up for any deficits and .                                                        

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