AP Calculus AB & BC

Getting Ready:

Appendix: Precalculus stuff to know cold  (Notes)

Appendix: Parent Function Catalog  (Notes)

Appendix: The Unit Circle  (Notes)

Spleen: Prerequisite Algebra Skills (WS/KEY)

Chapter P: Calculus Prerequisites 

P.1  What is AP Calculus? (Notes)

P.2  Parent Functions  (Notes, WS/KEY)

P.3  Simplifying Expressions  (Notes, WS/KEY)

P.4  Equations of Lines  (Notes, WS)

P.5  Domain, Range, and Symmetry  (Notes, WS)

P.6  Fun with Functions  (Notes, WS)

P.7  Trigonometry  (Notes, WS)

Chapter 1: Limits

1.1  Limits & Continuity (Notes, WS/KEY)

1.2  Properties of Limits (Notes, WS/KEY)

1.3  Limits at Infinity (Notes, WS/KEY)

1.4  Algebraic Limits (Notes, WS/KEY)

       1.4 Xtra Practice (WS/KEY)

1.5  Continuity on Intervals & IVT (Notes, WS/KEY)

Chapter 2: Differentiation

2.1  Tangent Line & Differentiability (Notes, WS/KEY)

2.2  Derivatives on the Calculator (Notes, WS/KEY)

2.3  Basic Differentiation Rules (Notes, WS/KEY)

2.4  Product & Quotient Rules (Notes, WS/KEY)

2.5  Rates of Change and Particle Motion I (Notes, WS/KEY) 

2.6  The Chain Rule (Notes/, WS/KEY)

2.7  Implicit Differentiation (Notes, WS/KEY)

2.8  Derivatives of Inverse & Inverse Trig Functions (Notes, WS/KEY)

2.9  Derivatives of Exponential Functions (Notes, WS/KEY)

2.10 Derivatives of Log Functions & LOG DIFF (Notes, WS/KEY)

Chapter 3: Applications of Differentiation

3.1   Extrema on an interval (Notes, WS/KEY)

3.2   Rolle’s Theorem and the MVT (Notes, WS/KEY)

3.3   Increasing, Decreasing, and 1st Derivative Test (Notes, WS/KEY)

3.4   Concavity and the Second Derivative Test (Notes, WS/KEY) 

3.5   f,  f ‘, and f ” (Notes, WS/KEY) 

3.5B Summary Sheet (Notes)

3.6   Optimization (Notes, WS/KEY)                    

3.7   Linearization and Differentials (Notes, WS/KEY)

3.8   Related Rates (Notes, WS/KEY) 

Chatper 4: Integration

4.1  Antiderivatives and Indefinite Integration (Notes, WS/KEY)

4.1B Basic Differentiation Practice (WS/KEY)

4.1C Mixed AP MC Review (WS)

4.2  Numeric Definite Integrals (Notes, WS/KEY)

4.3  The FTOC I & II and MVT II (Notes, WS/KEY)

4.4  Integration by u-Substitution (Notes, WS/KEY)

Chapter 5: Differential Equations & Modeling

5.1  Separable Differential Equations (Notes, WS/KEY)

5.2  Slope Fields (Notes, WS/KEY)

5.2B Mega Integration Practice (AB methods) (WS)

5.3  *Euler’s Method (Notes, WS/KEY)

5.4  *Integration by Parts (Notes, WS/KEY)

5.5  *Partial Fractions & Logistic Growth (Notes, WS/KEY)

Chapter 6: Applications of Integration

6.1  Integral as Net Change (Notes, WS/KEY)

6.2  Area between Curves (Notes, WS/KEY)

6.3  Volumes (Notes, WS/KEY)

6.4  *Arc Length (Notes, WS/KEY)

6.5  L’Hôpital’s Rule and Indeterminate Forms (Notes, WS/KEY)

6.6  *Improper Integrals (Notes, WS/KEY) 

Chatper 7: Vector Calculus

7.1  *Intro to Parametric & Vector Calculus (Notes, WS/KEY)

7.2  *Parametric & Vector Accumulation (Notes, WS/KEY) Worksheet II/KEY

Chapter 8: Polar Calculus

8.1 *Polar Intro & Derivatives (Notes, WS/KEY)

8.2 *Polar Area (Notes, WS/KEY)

Chapter 9: Sequences & Series

9.1 *Infinite Sequences & Series (Notes, WS/KEY)

        Summary of Tests for Convergence and Series Flow Chart with practice problems

9.2 *Taylor Polynomials (Notes, WS/KEY)

9.3 *Power Series I: Taylor & Maclaurin Series (Notes, WS/KEY)

9.4 *Power Series II: Geometric Series (Notes, WS/KEY)

9.5 *Lagrange Error Bound (Notes, WS/KEY)

Chapter 10: After the AP Exam

10.1 Trig Substitution Integration (Notes/KEY, WS/KEY)

10.2 Partial Fraction Decomposition (Notes/KEY, WS/KEY)

10.3 Epsilon-Delta Proofs (Notes/KEY, WS/KEY)

10.4 Newton’s Method (Notes/KEY, WS/KEY)

10.5 Surface Area (Notes/KEY, WS/KEY)

10.6 Hyperbolic Trig Functions (Notes/KEY, WS/KEY)