AP Calculus AB review

Calculator policy: Graphing calculator required for the calculator parts.

1. Unit 1

   Limits and Continuity

   Estimating and computing limits, one-sided limits, asymptotes, continuity and the Intermediate Value Theorem.

   Topics: Limits from graphs and tables, Algebraic limits, Continuity and IVT.

   Unit 1 notes and practice

   Calculus AB Unit 1 Practice: Limits and Continuity (timed)

2. Unit 2

   Differentiation: Definition and Basic Rules

   The derivative as a limit, differentiability, power, product and quotient rules and trig derivatives.

   Topics: Definition of the derivative, Basic rules.

   Unit 2 notes and practice

3. Unit 3

   Differentiation: Composite, Implicit and Inverse Functions

   Chain rule, implicit differentiation, inverse function and inverse trig derivatives, higher derivatives.

   Topics: Chain rule, Implicit differentiation.

   Unit 3 notes and practice

4. Unit 4

   Contextual Applications of Differentiation

   Rates of change in context, motion, related rates, linearization and L'Hospital's rule.

   Topics: Related rates, Linearization.

   Unit 4 notes and practice

   Particle Motion on a Line (free response)

5. Unit 5

   Analytical Applications of Differentiation

   Mean Value Theorem, extrema, increasing and decreasing intervals, concavity and optimization.

   Topics: Mean Value Theorem, Optimization.

   Unit 5 notes and practice

6. Unit 6

   Integration and Accumulation of Change

   Riemann sums, definite integrals, the Fundamental Theorem, antiderivatives and substitution.

   Topics: Riemann sums, Fundamental Theorem, u-substitution.

   Unit 6 notes and practice

7. Unit 7

   Differential Equations

   Modeling with differential equations, slope fields and separable equations including exponential models.

   Topics: Slope fields, Separation of variables.

   Unit 7 notes and practice

8. Unit 8

   Applications of Integration

   Average value, motion, accumulation, area between curves and volumes by cross sections and revolution.

   Topics: Area between curves, Volumes of revolution.

   Unit 8 notes and practice

   Water in a Tank (free response)

Original practice questions in the free-response style. You score them with a point-by-point rubric; AI grading appears only when this site has it configured.

• Limits Study Guide (study guide)
• Derivative Rules cheat sheet (one-page formulas)
• Derivative Basics Quiz (quick quiz)
• Derivatives Practice Test (25-minute timed test)
• Derivative Rules (9 flashcards)
• Calculus practice problems (with worked solutions)