AP Calculus AB

• Estimating Limits from Graphs and Tables
• Limits from Both Sides
• One-Sided Limits
• Limit Laws
• Limits by Factoring and Canceling
• Limits by Rationalizing
• The Squeeze Theorem
• Special Trigonometric Limits
• Infinite Limits and Vertical Asymptotes
• Limits at Infinity and Horizontal Asymptotes
• Continuity
• The Intermediate Value Theorem

• From Average to Instantaneous Rate
• The Derivative at a Point
• Tangent Lines
• The Derivative as a Function
• Where Derivatives Fail to Exist
• Constant, Power and Sum Rules
• The Product Rule
• The Quotient Rule
• Derivatives of Trig Functions
• Derivatives of Exponential and Log Functions

• The Chain Rule
• Chain Rule with Several Layers
• Implicit Differentiation
• Derivatives of Inverse Functions and Inverse Trig
• Higher Derivatives

• Leibniz Notation and Units
• Position, Velocity and Acceleration
• Related Rates
• Linear Approximation and Differentials
• L'Hôpital's Rule

• The Mean Value Theorem
• Critical Points and Absolute Extrema
• Increasing, Decreasing and the First Derivative Test
• Concavity and the Second Derivative Test
• Curve Sketching
• Optimization

The course's last topic here, the behavior of implicit relations, is practiced only through Implicit Differentiation for now.

• Approximating Area with Rectangles
• Riemann Sums
• The Definite Integral
• Properties of Definite Integrals
• Accumulation Functions and FTC Part 1
• Evaluating Integrals with FTC Part 2
• Antiderivatives
• Integration by Substitution
• Substitution in Definite Integrals
• Integrals Giving Exponentials and Logarithms
• Integrals Giving Inverse Trig Functions

Rewriting with long division or by completing the square before integrating has no topic of its own yet; it shows up inside the substitution and inverse-trig integral topics.

• What a Differential Equation Is
• Direction Fields and Euler's Method
• Separable Equations
• Antiderivatives with Initial Conditions
• Growth, Decay and Newton's Law of Cooling

Euler's method appears in our slope-field topic but is only on the BC exam. Exponential growth and decay models come from the Differential Equations course, which goes further than AP.

• Average Value of a Function
• Net Change and Total Distance
• Area Between Curves
• Volume by Slicing
• Disks and Washers