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Master limits, derivatives, integrals, and their applications for the AP Calculus AB exam.
This AP Calculus AB course on Study Mondo covers 72 topics organized across 11 categories. Each topic includes detailed written explanations, worked examples, practice problems with step-by-step solutions, flashcards for review, and interactive lessons to help you master the material.
All content is completely free. Start with any category below, or jump to a specific topic that you need help with.
Take a diagnostic test covering all 7 AP Calculus AB units. Get a personalized study plan with 3-5 modules to focus on.
Pick the plan that matches your timeline — from a 1-month build-up to a night-before review.
Jump into high-impact topics and keep your study momentum moving.
Evaluating limits, squeeze theorem, continuity, and the Intermediate Value Theorem
Limit definition, evaluation, one-sided limits, squeeze theorem, and IVT
An intuitive introduction to the concept of limits in calculus
Learn to estimate limit values by examining tables of function values
Visualize limit behavior by reading and interpreting function graphs
A structured 4-week plan that builds mastery without burning out.
~60 hours total over 4 weeks
Understand left-hand and right-hand limits and when to use them
Definition of the derivative, basic rules, chain rule, and implicit differentiation
Derivative as a limit, differentiability, graphical interpretation, and tangent lines
Power rule, product rule, quotient rule, trig derivatives, and higher-order derivatives
Chain rule, implicit differentiation, and related rates
Derivatives of inverse functions, inverse trig derivatives, and logarithmic differentiation
Differentiation rules, techniques, and applications
Understanding the fundamental concept of derivatives
Master the fundamental rule for differentiating polynomial functions
Understanding the different ways to write derivatives
Understanding derivatives through tangent lines and slope
Understanding derivatives through real-world rates of change
The most fundamental differentiation rule for polynomials
Essential rules for differentiating linear combinations of functions
Differentiating the product of two functions
Differentiating fractions and rational functions
Finding derivatives of composite functions
Finding derivatives of sine, cosine, tangent, and other trig functions
Finding derivatives involving e^x and other exponential functions
Finding derivatives involving ln(x) and other logarithmic functions
Finding derivatives when y is not isolated
Finding how rates of change are related to each other
Second derivatives, third derivatives, and beyond
Using logarithms to simplify difficult differentiation problems
Critical points, curve sketching, optimization, and linearization
Critical points, first/second derivative tests, concavity, and curve sketching
Setting up and solving optimization problems in business and geometry
Linear approximation, differentials, error estimation, and tangent line approximation
Mean Value Theorem, Rolle's Theorem, Extreme Value Theorem, and IVT applications
Position, velocity, acceleration, speed, displacement, and distance
Using derivatives to solve real-world problems
Finding maximum and minimum values of functions
Using the derivative to classify critical points as maxima, minima, or neither
Using the second derivative to classify critical points
Using calculus to find maximum and minimum values in real-world situations
Using derivatives to sketch accurate graphs of functions
Understanding the theoretical foundation connecting average and instantaneous rates
Evaluating indeterminate forms using derivatives
Using tangent lines to approximate function values
Using derivatives to find numerical solutions to equations
Finding absolute maximum and minimum values on closed intervals
Antiderivatives and the reverse process of differentiation
Understanding the reverse process of differentiation
Understanding integral notation and basic integration rules
The chain rule in reverse - substitution technique for integration
The product rule in reverse for integrating products of functions
Approximating area under curves using rectangles
The connection between derivatives and integrals
Finding area enclosed by two functions
Finding volumes by rotating regions around an axis
Finding volumes of solids with holes using washers
Finding volumes using cylindrical shells
Riemann sums, definite integrals, FTC, antiderivatives, and u-substitution
Riemann sums, definite integral definition, properties, and the Fundamental Theorem of Calculus
Antiderivative basics, power rule for integration, trig antiderivatives, and initial value problems
Basic u-substitution, definite integrals with u-sub, and complex substitutions
Accumulation concept, interpreting integrals, FTC connections, and rate in vs rate out
Area, volumes, average value, and real-world integration applications
Advanced integration techniques for Calculus BC
Slope fields, separation of variables, and exponential models
FRQ strategies, tables/data analysis, and full exam review