Kevin Quattrin, EdD
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The AP Calculus BC Exam


AP Calculus BC the SI Way
            
Chapter 1: Review of Derivatives 

1.1:   The Power and Exponential Rules 
Explanation    
Example A      Example B                    
1.1:   The Chain Rule
Explanation    
Example A      Example B     Example C      Example D          
1.2:   Trig, Trig Inverse, and Log Rules   
Explanation     Example A      Example B     Example C      Example D                
1.3:   The Product Rule

Explanation     Example A     Example B     Example C      Example D                                         
1.3:   The Quotient Rule

Explanation     Example A     Example B     Example C      Example D
1.4:   Local Linearity and Approximations

Explanation     Example A      Example B              
1.4:   Euler’s Method and Approximations
Explanation     Example A      Example B    Example C      Example D

1.5:    ​Intro to AP:  Basic Derivatives Numerically and Graphically
Explanation Part 1   Example A    Example B    Example C     Example D
Explanation Part 2  Example A    Example B  

1.6:   Higher Order Derivatives
Explanation
    Example A      Example B     Example C      Example D
1.7:   Implicit Differentiation

Explanation     Example A      Example B     Example C      Example D                                    
1.8:   Related Rates 

Explanation     Example A      Example B     Example C      Recap   
1.9:   Logarithmic Differentiation
Example A     Example B

Chapter 2: Anti-Derivatives  

2.1:   The Power and Transcendental Rules    

Explanation     Example A      Example B     Example C      Example D 
2.1:   Common Errors in Integration

Explanation

2.2:   Integration by Substitution--the Chain Rule
Explanation     Example A      Example B     Example C      Example D

2.3:   Separable Differential Equations

Explanation     Example A      Example B     Example C      Example D
2.4   Back Substitution

Explanation     Example A     Example B     Example C  
2.5:   Powers of Trig Functions:  Sine and Cosine

Explanation     Example A     Example B     Example C     Example D     Example E    
2.6:    Powers of Trig Functions:  Secant and Tangent

Explanation     Example A     Example B     Example C     Example D
2-7:   Creating Slope Fields   (general
Explanation)
Explanation    Example A      Example B     Example C
     Example D 
2-7:   Reading Slope Fields
Explanation    Examples A-C
     Examples D-F
                                                                                             

Chapter 3: Integrals   

3.0.  The Limit Definition of the Definite Integral
Explanation    Example A     Example B
3.1:   The Fundamental Theorem of Calculus

Explanation
    Example A      Example B     Example C      Example D
3.2:   Definite Integrals and Integration by Substitution
Explanation
    Example A      Example B     Example C      Example D
3.3:   Context:  Area, Displacement, and Net Change
Explanation     Example A      Example B     Example C      Example D

3.4:   Intro to AP:  Accumulation of Rates

Explanation     Example A      Example B     Example C      Example D
3.5:   Approximate Integration – Riemann Sums
Explanation
     Example A      Example B     Example C      Example D     Example E
3.5:   Approximate Integration – Trapezoidal Rule
Explanation
     Example A      Example B     Example C      Example D
3.6:  
Intro to AP:   Table Problems  
Explanation     Example A     Example B      Example C 


Chapter 4: Derivatives and Graphs    

4.1:   Extremes and the Derivative Tests

Explanation     Example A      Example B     Example C     Example D      Example E

4.1:   Optimization 
Explanation     Example A      Example B     Example C     

4.2:  The Mean Value Theorem
Explanation     Example A      Example B     Example C

4.3:    Accumulation of Rates Revisited
Explanation     Example A     Example B     Example C    
4.4:   The Second Derivative, Points of Inflection, and Concavity
Explanation     Example A     Example B     Example C     Example D  
4.5:   Graphing with Derivatives
Explanation     Example A      Example B     Example C      Example D       Example E

4.6:   Graphical Analysis I

Explanation    Example A      Example B      Example C     Example D        Example E   
4.7:   Graphical Analysis II 
Explanation    
Example A      Example B     Example C      Example D

4.8:   Intro to AP:   Rectilinear Motion 
Explanation     Example A      Example B     Example C      Example D/E      


Chapter 5: Applications of Integrals 

Chapter 5 OVERVIEW
5.1:   Area between Two Curves  
Explanation
Example A      Example B     Example C
     Example D
5.2:   Arc Length
Explanation   Example A      Example B     Example C      Example D
    
 

Intro To Volume

5.3:   Volume by Rotation about  the x-Axis
Explanation    Example A      Example B   
Example C 
5.4:   Volume by Rotation about the  y-Axis: 
Explanation    
Example A      Example B/C
5.5:   Volume by Rotation about a Line not an Axis
Explanation
     Example A      Example B     Example C     
6.6:   Volume by Cross-section Method 
Explanation     Example A  and B     Example C      Example D     Example E
5.7:   AP Volume FRQs
Explanation    Example A     Example B      Example C      
5.8:   Volume by Shell Method
Explanation      Example A     Example B     


Chapter 6: Limits, Continuity and Differentiability    

6.1:   Basic Limits

Explanation     Example A     Example B     Example C     Example D
6.1:   L’Hopital’s Rule
Explanation     Example A     Example B     Example C     Example D
6.1:   The Limit Definitions of a Derivative
Explanation     Example A     Example B     Example C     Example D
6.2:   Continuity and One-sided Limits
Explanation     Example A      Example B     Example C      Example D
6.3:   Differentiability and Smoothness
Explanation     Example A      Example B     Example C      Example D

6.4:   Limits at Infinity and End Behavior  
Explanation     Example A      Example B     Example C      Example D & E
6.5:   Type I Improper Integrals 
Explanation     Example A      Example B     Example C      Example D
6.6:   Infinite Limits and Type II Improper Integrals 
Explanation    
Example A      Example B     Example C


Chapter 7: Sequences and Numerical Series    

7.1:    Intro to Sequences and series
Explanation
    
Sequence Examples    Example A      Example B     Example C      Example D

Series Examples:          Example A      Example B     Example C      Example D
7.2:   Convergence and Divergence: 
Explanation    
Sequence Examlples:     Example A      Example B    
Series Examples:              Example A      Example B     
7.3:   The Integral Test 
Explanation     Example A      Example B     Example C      Example D
7.4:   The Comparison Tests:  DCT
Explanation     Example A      Example B     Example C      Example D
7.4:   The Comparison Tests:  LCT
Explanation     Example A      Example B     Example C    

7.5:   Absolute Convergence    
Explanation     Example A and B     Example C    

7.6:   The Ratio Test  
Explanation     Example A      Example B     Example C      Example D
7.6:   The Nth Root Test
Explanation     Example A
7.7:   General Series Summary
Explanation/Example A      Example B     Example C      Example D



Chapter 8: Advanced Integration     

8.1:   Integrals of Rational Functions
Explanation   Example A/B     Example C      Example D
8.2:   Partial Fractions I -- Simple Linear Factors
Explanation   Example A      Example B     Example C      Example D

8.3:    Models of Growth and Decay
Explanation     Example A      Example B     Example C/D     
8.3:    Simple Bounded Growth
Explanation     Example A      Example B     Example C    
8.3:    Logistic Growth

Explanation   Example A      Example B     Example C       Example D  
8.4:   Integration by Parts 
Explanation   Example A      Example B     Example C      Example D   Example E
8.5:   Trig Substitution
Explanation   Example A      Example B     Example C      Example D
8.6:   Partial Fractions II -- Repeated Linear Factors     
Explanation
   Example A      Example B     Example C   
8.7:   Partial Fractions III -- Quadratic Factors   
Explanation
   Example A      Example B     Example C   
8.8:   General Integration
Explanation   Example A      Example B     Example C      Example D      Example E  

8.9:    AP Advanced Integration Problems
Explanation.    Example A    Example B     Example C 

Chapter 9: Parametric and Polar Coordinates     

9.1:   Parametrics
Motion
Explanation   Example A      Example B     Example C      Example D
9.2:   Parametrics and Graphing
Explanation   Example A      Example B     Example C      Example D
9.3.  Intro to AP:  Parametrics
Explanation     Example A    Example B    
9.4:   Polar and Cartesian Coordinates

Explanation   Example A      Example B     Example C      Example D
9.5:   Polar Coordinates and Simple Area
Explanation   Example A      Example B     Example C      Example D

9.5:   Polar Graphs and Arc Length
Explanation   Example A      Example B     Example C    
Example D
9.6:   Integrals and Polar Graphs-- Area Inside Two Curves
Explanation   Example A      Example B     Example C      Example D

9.6:   Integrals and Polar Graphs-- Area Inside one curve and Outside another
Explanation   Example A      Example B     Example C      Example D

9.7:   Derivatives and Polar Graphs
Explanation   Example A      Example B     Example C      Example D
9.7:   Tangent Lines and Polar Graphs
Explanation   Example A & B olar    Example C     Example D   

9.8.  Intro to AP:  Parametrics
Explanation.    Example A    Example B    


Chapter 10: Power Series     

10.1:   Taylor and Maclaurin Series

Explanation   Example A      Example B     Example C      Example D
10.2:   Series Approximations and Error   
Explanation   Example A      Example B     Example C      Example D
10.3:   Power Series    
Explanation/Example A        Example B     Example C     
10.4:   Review of Numerical Series 

Explanation/Example A        Example B     Example C      Example D 
10.5:   Radius and Intervals of Convergence 
Radius Explanation     Interval Explanation
Example A      Example B     Example C      Example D      Example E

10.6   Intro to AP:  Series
Explanation.    Example A    Example B    


Chapter 11: AP Calculus FRQ Topic Reviews

11.0:     The AP Exam
11.1:      Accumulation of Rates
  • Solution to the Tombstone Mine Problem
11.2:     Table Problems
  • Solution to Dr. Quattrin's Solar panels Problem
11.3:     Graphical Analysis
  • Solution to the Graphical Analysis Practice problem
11.4:      Power Series
  • Solution to the Series Practice Problem
11.5:     Separation of Variables
  • Solution to the Parachutist Problem
11.6:       Parametrics Review
  • Solution to the Parametric Practice Problem
11.7:      Polars Review
  • Solution to the Polar Practice Problem
11.8:     Area and Volume
  • Solution to the Wood Table and Practice Volume Problems
11.9:     Related Rates
  • Solution to the Two Train Problem
11.10:      Miscellaneous BC Topics (including Partial Fractions)
  • Solutions to the Miscellaneous BC Topics Problems
11.11:     Miscellaneous AB Topics
  • Solutions to the AB Miscellaneous Practice Problems
11.12:     Rectilinear Motion
  • Solution to the Two Particle Problem
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