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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