AP Calculus

* * * Updated for 2020-2021 school year * * *
Course Syllabus and Standards Important Files Important Links for Videos

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Course Schedules        
Gateway Exams
 
BC Files Qtr 1 Qtr 2 Qtr 3 Qtr 4
Course Schedules        
Gateway Exams
 

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

Summer Homework HW Sol        
Summer Homework (Letter and Instructions)
       
Prerequisite Content (Problems and Solutions)
       
Precalculus Review (Problems and Solutions)
       
 
Chapter 1: Limits and Their Properties Notes Vids HW Sol CW Sol
§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 Notes Vids HW Sol CW Sol
§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 Notes Vids HW Sol CW Sol
§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 Notes Vids HW Sol CW Sol
§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 Notes Vids HW Sol CW Sol
§5.1a Slope Fields
§5.1b Euler's Method
§5.3 Separation of Variables
§5.4 The Logistic Equation
 
Chapter 6: Applications of Integration Notes Vids HW Sol CW Sol
§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 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals Notes Vids HW Sol CW Sol
§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 8: Taylor Polynomials and Infinite Series Notes Vids HW Sol CW Sol
§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 The Integral Test and p-Series
§8.7b The Direct and Limit Comparison Tests
§8.8a Alternating Series
§8.8b Varying-Sign Series
§8.10a Taylor Series
§8.10b Manipulation of Known Taylor Series
Chapter Text and Solutions by B. Goldstein
       
 
Chapter 9a: Polar Coordinates Notes Vids HW Sol CW Sol
§9.4a Polar Coordinates and Polar Graphs
   
§9.4b Polar Coordinates and Differentiation
§9.5 Area in Polar Coordinates
 
Chapter 9b: Parametric Equations and Vectors Notes Vids HW Sol CW Sol
§9.2 Plane Curves and Parametric Equations
   
§9.3 Parametric Equations and Calculus
§9.7 Vector-Valued Functions
   
§9.8 Velocity and Acceleration

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