Kevin Quattrin, EdD
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  • Project Manager/Lead Writer: Kevin Quattrin
  • Associate Writers: Najla (nee Fawal) Abrao and Paul Maychrowitz
  • Chief Editor: Elizabeth Regalia
Download the book section by section below.

Solution Manual

Table of Contents and Introduction: General Overview of Calculus


Chapter 1: Review of Derivatives   [Chapter 1 pdf]
  • 1.1:   The Power and Exponential Rules with the Chain Rule                
  • 1.2:   Trig, Trig Inverse, and Log Rules                                               
  • 1.3:   Product and Quotient Rules     
  • 1.4:   Local Linearity, Euler’s Method, and Approximations                                               
  • 1.5:   Intro to AP:  Basic Derivatives Numerically and Graphically
  • 1.6:   Higher Order Derivatives                                                  
  • 1.7:   Implicit Differentiation
  • 1.8:   Related Rates
  • 1.9:   Logarithmic Differentiation                      
  • Chapter 1 Test
  • Chapter 1 Answer Key

Chapter 2: Anti-Derivatives    [Chapter 2 pdf]
  • 2.1:   The Power and Transcendental Rules    
  • 2.2:   Integration by Substitution--the Chain Rule    
  • 2.3:   Separable Differential Equations  
  • 2.4:   Integration by Substitution--Back Substitution
  • 2.5:   Powers of Trig Functions:  Sine and Cosine     
  • 2.6:    Powers of Trig Functions:  Secant and Tangent 
  • 2.7:   Slope Fields               
  • Chapter 2 Test
  • Chapter 2 Answer Key                                                                                               

Chapter 3: Integrals       [Chapter 4 pdf]
  • 3.0:    Limit Definition of the Definite Integral                                
  • 3.1:    The Fundamental Theorem of Calculus                                 
  • 3.2:    Definite Integrals and Integration by 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:    Approximate Integration – Table Problems and MVT (rewrite)
  • Chapter 4 Test  
  • Chapter 4 Answer Key
Chapter 4: Derivatives and Graphs       [Chapter 3 pdf]
  • 4.1:   Extremes and the Derivative Tests  
  • 4.2:  Accumulation of Rates Revisited
  • 4.3:   The Second Derivative, Points of Inflection, and Concavity
  • 4.4:   Graphing with Derivatives         
  • 4.5:   Graphical Analysis I 
  • 4.6:    Graphical Analysis II      
  • 4.t:    Intro to AP:  Rectilinear Motion
  • Chapter 4 Test
  • Chapter 4 Answer Key                                                                                                 

Chapter 5: Applications of Integrals    [Chapter 5 pdf]     
  • 5.1:   Area between Two Curves   
  • 5.2:   Arc Length 
  • 5.3:   Volume by Rotation about the x-Axis    
  • 5.4:   Volume by Rotation about the y-Axis     
  • 5.5:   Volume by Rotation about a Line not an Axis  
  • 5.6:   Volume by Cross-section Method   
  • 5.7:   AP Area and Volume Problems
  • 5.8:   Volume by Shell Method                         
  • Chapter 5 Test  
  • Chapter 5 Answer Key 

Chapter 6: Limits, Continuity and Differentiability    [Chapter 6 pdf]     
  • 6.1:   Limits, L’Hopital’s Rule, and The Limit Definitions of a Derivative
  • 6.2:   Continuity and One-sided Limits
  • 6.3   Differentiability and Smoothness    
  • 6.4:   Limits at Infinity and End Behavior    
  • 6.5:   Type I Improper Integrals     
  • 6.6:   Infinite Limits and Type II Improper Integrals   
  • Chapter 6 Test 
  • Chapter 6 Answer Key         

Chapter 7: Sequences and Numerical Series    [Chapter 7 pdf]     
  • 7.1:   Sequences and series—Preliminary Algebra
  • 7.2:   Convergence and Divergence     
  • 7.3:   The Integral Test                  
  • 7.4:   The Comparison Tests   
  • 7.5:   The Ratio Test and Nth Root Tests 
  • 7.6:   Alternating Series    
  • 7.7:   General Series Summary   
  • Chapter 7 Test
  • Chapter 7 Answer Key

Chapter 8: Advanced Integration      [Chapter 8 pdf]
  • 8.1:   Integrals of Rational Functions  
  • 8.2:   Partial Fractions I  
  • 8.3:   Models of Growth
  • 8.4:   Integration by Parts 
  • 8.5:   Trig Substitution (optional)   
  • 8.6:   Partial Fractions II (optional)        
  • 8.7:   Partial Fractions III (optional)     
  • 8.8:   General Integration 
  • Chapter 8 Test
  • Chapter 8 Answer Key 

Chapter 9: Parametric and Polar Coordinates     [Chapter 9 pdf]
  • 9.1:   Parametric Motion   
  • 9.2:   Parametric Graphing   
  • 9.3:   AP Parametric Problems
  • 9.4:   Polar  and Cartesian Graphs   
  • 9.5:   Polar Coordinates, Arc Length, and Simple Area  
  • 9.6:   Area Involving Two Polar Graphs
  • 9.7:   Derivatives and Polar Graphs   
  • 9.8:   AP Polar Problems
  • Chapter 9 Test
  • Chapter 9 Answer Key        

Chapter 10: Power Series       [Chapter 10 pdf]
  • 10.1:   Taylor and Maclaurin Series     
  • 10.2:  Error Bound Problems
  • 10.3:   Power Series    
  • 10.4:   Review of Numerical Series  
  • 10.5:   Radius and Intervals of Convergence 
  • 10.6:   AP Power Series Problems
  • Chapter 10 Test
  • Chapter 10 Answer Key
 
Chapter 11:  AP Calculus BC FRQ Review [Chapter 11 pdf]
Overview:   The last 10 years
  • 11.1   Accumulation of Rates (AB1)
  • 11.2   Reasoning from Tabular Data (AB2)
  • 11.3   Graphical Analysis (AB3)
  • 11.4   Power Series  
  • 11.5   Differential Equations (AB5)
  • 11.6   Parametric Motion
  • 11.7   Polar Coordinates
  • 11.8   Area and Volume (AB6)
  • 11.9   Related Rates (AB7)
  • 11.10 Advanced Integration.
  • 11.11 Miscellaneous AB Topics


Appendix B: Synthesis of PreCalculus      [Chapter B pdf]
  • Overview: Functions and Traits
  • 0.1:   Recognizing and Identifying Graphs, Graphing from Traits
  • 0.2:   Factoring Review and Zeroes of Functions
  • 0.3:   Sign Patterns and Domains
  • 0.4:   Calculator Review
  • 0.5:   Important Facts for Calculus



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