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AP Calculus BC Topics

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1. Limits & Continuity

1.1

Finding limits from graphs

1.2

Limit laws

1.3

Finding limits algebraically - direct substitution

1.4

Finding limits algebraically - when direct substitution is not possible

1.5

Squeeze theorem

1.6

l'Hospital's rule

1.7

Infinite limits - vertical asymptotes

1.8

Continuity

1.9

Intermediate value theorem

2. Derivatives

2.1

Definition of derivative

2.2

Estimating derivatives from a table

2.3

Power rule

2.4

Chain rule

2.5

Derivative of trigonometric functions

2.6

Derivative of exponential functions

2.7

Derivative of logarithmic functions

2.8

Product rule

2.9

Quotient rule

2.10

Derivative of inverse trigonometric functions

2.11

Implicit differentiation

2.12

Higher order derivatives

3. Derivative Applications

3.1

Slope and equation of tangent line

3.2

Critical number & maximum and minimum values

3.3

Tangents and concavity of parametric equations

3.4

Tangents of polar curves

3.5

Curve sketching

3.6

Mean value theorem

3.7

Rectilinear motion: Derivative

3.8

Related rates

3.9

Optimization

8. Sequence and Series

8.1

Introduction to sequences

8.2

Introduction to infinite series

8.3

Convergence and divergence of normal infinite series

8.4

Convergence and divergence of geometric series

8.5

Divergence of harmonic series

8.6

P Series

8.7

Alternating series test

8.8

Divergence test

8.9

Comparison and limit comparison test

8.10

Integral test

8.11

Ratio test

8.12

Absolute and conditional convergence

8.13

Radius and interval of convergence with power series

8.14

Functions expressed as power series

8.15

Taylor and maclaurin series

8.16

Approximating functions with Taylor polynomials and error bounds

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