AP Calculus

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Course Syllabus and Standards

Important Files + Links for Videos

AB: Quarter Schedules and Gateway Exams

Quarter 1 Schedule · Quarter 2 Schedule · Quarter 3 Schedule · Quarter 4 Schedule

Gateway Exam #1 (Differentiation) with Kahoot! · Gateway Exam #2 (Chapters 1-3)

Gateway Exam #3 (Integration) with Kahoot! · Gateway Exam #4 (Chapters 4-7)

BC: Quarter Schedules and Gateway Exams

Quarter 1 Schedule · Quarter 2 Schedule · Quarter 3 Schedule · Quarter 4 Schedule

Gateway Exam #1 (Differentiation) with Kahoot! · Gateway Exam #2 (Integration) with Kahoot!

Gateway Exam #3 (Chapters 1-4) · Gateway Exam #4 (Chapters 5-9)

AP Night Resources

AP Calculus

Course Syllabus and Standards

Important Files + Links for Videos

AB: Quarter Schedules and Gateway Exams

BC: Quarter Schedules and Gateway Exams

AP Night Resources

Summer Homework

Chapter 1: Limits and Their Properties

§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 2: Differentiation

§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 3: Applications of Differentiation

§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 4: Integration

§4.1: Antiderivatives and Indefinite Integration

§4.3a: Riemann Sums and Trapezoidal Approximations

§4.3b: Properties of 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 5: Differential Equations

§5.1a: Slope Fields

§5.1b: Euler’s Method (BC only)

§5.3: Separation of Variables

§5.4: The Logistic Equation (BC only)

Chapter 6: Applications of Integration

§6.1: Area of a Region Between Two Curves

§6.2a: Volume: The Disk and Washer Methods

§6.2b: Volume: Solid with Known Cross Sections

§6.4: Arc Length (BC only)

Chapter 7: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals

§7.1: Basic Integration Rules

§7.2: Integration by Parts (BC only)

§7.5: Partial Fractions (BC only)

§7.7: Indeterminate Forms and L’Hôpital’s Rule

§7.8: Improper Integrals (BC only)

Chapter 8: Taylor Polynomials and Infinite Series (BC only)

§8.1: Review of Sequences and Series (BC only)

§8.2: An Introduction to Taylor Polynomials (BC only)

§8.3: A Systematic Approach to Taylor Polynomials (BC only)

§8.4: Lagrange Remainder (BC only)

§8.6: Power Series and the Ratio Test (BC only)

§8.7a: The Integral Test and p-Series (BC only)

§8.7b: The Direct and Limit Comparison Tests (BC only)

§8.8a: Alternating Series (BC only)

§8.8b: Varying-Sign Series (BC only)

§8.10a: Taylor Series (BC only)

§8.10b: Manipulation of Known Taylor Series (BC only)

Taylor Polynomials and Infinite Series by Benjamin Goldstein (BC only)

Chapter 9: Parametric Equations, Polar Coordinates, and Vectors (BC only)

§9.2: Plane Curves and Parametric Equations (BC only)

§9.3: Parametric Equations and Calculus (BC only)

§9.4a: Polar Coordinates and Polar Graphs (BC only)

§9.4b: Polar Coordinates and Differentiation (BC only)

§9.5: Area in Polar Coordinates (BC only)

§9.7: Vector-Valued Functions (BC only)

§9.8: Velocity and Acceleration (BC only)