AP Calculus

Important Files Gateway Exams and Projects AB Quarter Schedules BC Quarter Schedules

Note: Topics that are BC-only are highlighted in yellow.

Summer Homework Prob Sol  
Prerequisite Content (Problems and Solutions)
Precalculus Review (Problems and Solutions)
Chapter 1: Limits and Their Properties Notes Video ?s
§1.2 Finding Limits Graphically and Numerically
§1.3 Evaluating Limits Analytically
§1.4 Continuity and One-Sided Limits
§1.5 Infinite Limits
§1.6 Limits at Infinity
Chapter 1 Homework (Problems and Solutions)
Chapter 2: Differentiation Notes Video ?s
§2.1 The Derivative and the Tangent Line Problem
§2.2 Basic Differentiation Rules and Rates of Change
§2.3 Product and Quotient Rules and Higher-Order Derivatives
§2.4a The Chain Rule
§2.4b The Chain Rule
§2.5 Implicit Differentiation
§2.6 Derivatives of Inverse Functions
§2.7 Related Rates
Chapter 2 Homework (Problems and Solutions)
Chapter 3: Applications of Differentiation Notes Video ?s
§3.1 Extrema on an Interval
§3.2 Rolle's Theorem and the Mean Value Theorem
§3.3a Increasing and Decreasing Functions
§3.3b The First Derivative Test
§3.4a Concavity
§3.4b The Second Derivative Test
§3.5 A Summary of Curve Sketching
§3.6 Optimization Problems
Chapter 3 Homework (Problems and Solutions)
Chapter 4: Integration Notes Video ?s
§4.1 Antiderivatives and Indefinite Integration
§4.3 Riemann Sums and Definite Integrals
§4.4a The First Fundamental Theorem of Calculus
§4.4b The Second Fundamental Theorem of Calculus
§4.4c The Net Change Theorem
§4.5 Integration by Substitution
§4.6 The Natural Logarithmic Function: Integration
§4.7 Inverse Trigonometric Functions: Integration
Chapter 4 Homework (Problems and Solutions)
Chapter 5: Differential Equations Notes Video ?s
§5.1a Slope Fields
§5.1b Euler's Method
§5.3 Separation of Variables
§5.4 The Logistic Equation
Chapter 5 Homework (Problems and Solutions)
Chapter 6: Applications of Integration Notes Video ?s
§6.1 Area of a Region Between Two Curves
§6.2a Volume: The Disk and Washer Methods
§6.2b Volume: Solids with Known Cross Sections
§6.4 Arc Length
Chapter 6 Homework (Problems and Solutions)
Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals Notes Video ?s
§7.1 Basic Integration Rules
§7.2 Integration by Parts
§7.5 Partial Fractions
§7.7 Indeterminate Forms and L'Hôpital's Rule
§7.8 Improper Integrals
Chapter 7 Homework (Problems and Solutions)
Chapter 8: Taylor Polynomials and Infinite Series Notes Video ?s
§8.1 Review of Sequences and Series
§8.2 An Introduction to Taylor Polynomials
§8.3 A Systematic Approach to Taylor Polynomials
§8.4 Lagrange Remainder
§8.6 Power Series and the Ratio Test
§8.7a Positive-Term Series
§8.7b Positive-Term Series
§8.8a Varying-Sign Series
§8.8b Varying-Sign Series
§8.10a Taylor Series
§8.10b Taylor Series
Chapter 8 Homework (Textbook, Problems, and Solutions)
Chapter 9a: Polar Coordinates Notes Video ?s
§9.4a Polar Coordinates and Polar Graphs (Desmos Activity)
§9.4b Polar Coordinates and Differentiation
§9.5 Area in Polar Coordinates
Chapter 9a Homework (Problems and Solutions)
Chapter 9b: Parametric Equations and Vectors Notes Video ?s
§9.2 Plane Curves and Parametric Equations
§9.3 Parametric Equations and Calculus
§9.7 Vector-Valued Functions
§9.8 Velocity and Acceleration
Chapter 9b Homework (Problems and Solutions)

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