AP Calculus
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Course Syllabus and Standards
Optional Google Forms
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This OPTIONAL form is for AP Calculus and AP Statistics students who wish to borrow a TI-Nspire CX CAS graphing calculator for the 2023-24 school year. These are available on a first-come, first-served basis.
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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
Chapter 1: Limits and Their Properties
§1.2: Finding Limits Graphically and Numerically
Notes · Videos · Problems · Answers · Solutions
§1.3: Evaluating Limits Analytically
Notes · Videos · Problems · Answers · Solutions
§1.4: Continuity and One-Sided Limits
Notes · Videos · Problems · Answers · Solutions
§1.5: Infinite Limits
Notes · Videos · Problems · Answers · Solutions
§1.6: Limits at Infinity
Chapter 2: Differentiation
§2.1: The Derivative and the Tangent Line Problem
Notes · Videos · Problems · Answers · Solutions
§2.2: Basic Differentiation Rules and Rates of Change
Notes · Videos · Problems · Answers · Solutions
§2.3: Product and Quotient Rules and Higher-Order Derivatives
Notes · Videos · Problems · Answers · Solutions
§2.4a: The Chain Rule
Notes · Videos · Problems · Answers · Solutions
§2.4b: The Chain Rule
Notes · Videos · Problems · Answers · Solutions
§2.5: Implicit Differentiation
Notes · Videos · Problems · Answers · Solutions
§2.6: Derivatives of Inverse Functions
Notes · Videos · Problems · Answers · Solutions
§2.7: Related Rates
Chapter 3: Applications of Differentiation
§3.1: Extrema on an Interval
Notes · Videos · Problems · Answers · Solutions
§3.2: Rolle’s Theorem and the Mean Value Theorem
Notes · Videos · Problems · Answers · Solutions
§3.3a: Increasing and Decreasing Functions
Notes · Videos · Problems · Answers · Solutions
§3.3b: The First Derivative Test
Notes · Videos · Problems · Answers · Solutions
§3.4a: Concavity
Notes · Videos · Problems · Answers · Solutions
§3.4b: The Second Derivative Test
Notes · Videos · Problems · Answers · Solutions
§3.5: A Summary of Curve Sketching
Notes · Videos · Problems · Answers · Solutions
§3.6: Optimization Problems
Chapter 4: Integration
§4.1: Antiderivatives and Indefinite Integration
Notes · Videos · Problems · Answers · Solutions
§4.3a: Riemann Sums and Trapezoidal Approximations
Notes · Videos · Problems · Answers · Solutions
§4.3b: Properties of Definite Integrals
Notes · Videos · Problems · Answers · Solutions
§4.4a: The First Fundamental Theorem of Calculus
Notes · Videos · Problems · Answers · Solutions
§4.4b: The Second Fundamental Theorem of Calculus
Notes · Videos · Problems · Answers · Solutions
§4.4c: The Net Change Theorem
Notes · Videos · Problems · Answers · Solutions
§4.5: Integration by Substitution
Notes · Videos · Problems · Answers · Solutions
§4.6: The Natural Logarithmic Function: Integration
Notes · Videos · Problems · Answers · Solutions
§4.7: Inverse Trigonometric Functions: Integration
Chapter 6: Applications of Integration
Chapter 7: Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
§7.1: Basic Integration Rules
Notes · Videos · Problems · Answers · Solutions
§7.2: Integration by Parts (BC only)
Notes · Videos · Problems · Answers · Solutions
§7.5: Partial Fractions (BC only)
Notes · Videos · Problems · Answers · Solutions
§7.7: Indeterminate Forms and L’Hôpital’s Rule
Notes · Videos · Problems · Answers · Solutions
§7.8: Improper Integrals (BC only)
Chapter 8: Taylor Polynomials and Infinite Series (BC only)
§8.1: Review of Sequences and Series (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.2: An Introduction to Taylor Polynomials (BC only)
§8.3: A Systematic Approach to Taylor Polynomials (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.4: Lagrange Remainder (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.6: Power Series and the Ratio Test (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.7a: The Integral Test and p-Series (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.7b: The Direct and Limit Comparison Tests (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.8a: Alternating Series (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.8b: Varying-Sign Series (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.10a: Taylor Series (BC only)
Notes · Videos · Problems · Answers · Solutions
§8.10b: Manipulation of Known Taylor Series (BC only)
Notes · Videos · Problems · Answers · Solutions
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)
Notes · Videos · Problems · Answers · Solutions
§9.3: Parametric Equations and Calculus (BC only)
Notes · Videos · Problems · Answers · Solutions
§9.4a: Polar Coordinates and Polar Graphs (BC only)
Notes · Videos · Problems · Answers · Solutions
§9.4b: Polar Coordinates and Differentiation (BC only)
Notes · Videos · Problems · Answers · Solutions
§9.5: Area in Polar Coordinates (BC only)
Notes · Videos · Problems · Answers · Solutions
§9.7: Vector-Valued Functions (BC only)
Notes · Videos · Problems · Answers · Solutions