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AP Calculus AB

College-level calculus covering limits, derivatives, integrals, and differential equations. Aligned to the College Board AP Calculus AB Course and Exam Description. Equivalent to a first-semester college calculus course.

14 Units

45-60 minutes per unit

What You Will Learn

College Board Aligned

All eight AP Calculus AB CED units — from limits and continuity through differential equations.

Calculator & No-Calculator

Practice with both calculator-active and no-calculator problem types, mirroring the AP exam format.

College Credit Potential

A qualifying AP exam score can earn 3-4 college credits (Calculus I equivalent) at most universities.

All Units

Introduction to Limits

Explore the foundational concept of limits — what it means for a function to approach a value — using graphical, numerical, and intuitive methods.

•Describe the concept of a limit informally and formally using limit notation
•Estimate limits from graphs by analyzing function behavior near a point
•Estimate limits numerically using tables of values
+2 more objectives

Algebraic Techniques for Limits

Master algebraic strategies for evaluating limits exactly — including factoring, rationalization, the squeeze theorem, and limits involving infinity.

•Apply direct substitution as the first strategy for evaluating limits
•Resolve indeterminate forms using factoring, rationalization, and algebraic manipulation
•State and apply the Squeeze Theorem to evaluate limits of oscillating or bounded functions
+2 more objectives

Continuity, Discontinuities, and Asymptotes

Formalize the concept of continuity using limits, classify types of discontinuities, explore the Intermediate Value Theorem, and connect limits to asymptotic behavior.

•State the three conditions for continuity at a point and verify them for given functions
•Classify discontinuities as removable, jump, or infinite and identify them from graphs and formulas
•Determine intervals of continuity for polynomial, rational, trigonometric, and piecewise functions
+2 more objectives

The Derivative: Definition and Interpretation

Build the derivative from first principles — as a limit of average rates of change — and develop deep intuition for what a derivative means geometrically and physically.

•Calculate average rate of change over an interval and interpret it as slope of a secant line
•Define the derivative as the limit of the difference quotient and compute derivatives from the definition
•Interpret the derivative as instantaneous rate of change and as slope of the tangent line
+2 more objectives

Derivative Rules: Power, Product, Quotient, and Trig

Master the fundamental differentiation rules that make calculus computationally tractable — from the power rule to derivatives of all six trigonometric functions.

•Apply the power rule, constant rule, and constant multiple rule to differentiate polynomial functions
•Use the sum and difference rules to differentiate combinations of functions
•Apply the product rule to differentiate products of two functions
+3 more objectives

Chain Rule, Implicit Differentiation, and Related Rates

Master the chain rule for differentiating composite functions, extend it to implicit differentiation for relations, and apply both to solve related rates problems.

•State and apply the chain rule to differentiate composite functions
•Differentiate exponential and logarithmic functions using the chain rule
•Use implicit differentiation to find dy/dx for implicitly defined relations
+2 more objectives

Derivative Applications: MVT, Extreme Values, and Monotonicity

Deploy the derivative to analyze function behavior — proving results with the Mean Value Theorem, locating extreme values with the First Derivative Test, and characterizing where functions increase or decrease.

•State and apply Rolle's Theorem and the Mean Value Theorem, including verifying hypotheses
•Define absolute and relative (local) extrema and distinguish between them
•Apply the First Derivative Test to classify critical points as local maxima, minima, or neither
+2 more objectives

Derivative Applications: Concavity, Optimization, and L'Hôpital's Rule

Use the second derivative to analyze concavity and inflection points, build a complete curve sketch, solve real-world optimization problems, and resolve indeterminate limits with L'Hôpital's Rule.

•Use the second derivative to determine concavity on intervals and locate inflection points
•Apply the Second Derivative Test to classify critical points as local maxima or minima
•Produce a complete sketch of a function using derivatives, critical points, and asymptotes
+2 more objectives

Antiderivatives and Indefinite Integrals

Reverse the differentiation process — find functions whose derivatives equal a given function — and use initial conditions to specify unique antiderivatives for applied problems.

•Define the antiderivative and explain why it is not unique without additional conditions
•Evaluate indefinite integrals using the power rule for integration and basic integral formulas
•Apply linearity rules (sum, difference, constant multiple) to integrate combinations of functions
+2 more objectives

Definite Integrals and Riemann Sums

Build the definite integral from Riemann sums, interpret it as signed area and net accumulation, and connect it to the Fundamental Theorem of Calculus Part 1.

•Approximate definite integrals using left, right, and midpoint Riemann sums
•Understand the definite integral as the limit of a Riemann sum
•Interpret the definite integral as signed area under a curve and as net accumulation
+2 more objectives

FTC Part 2, U-Substitution, and Integral Properties

Apply the Fundamental Theorem of Calculus Part 2 to evaluate definite integrals exactly, master u-substitution as the chain rule in reverse, and use integral properties for strategic computation.

•State and apply FTC Part 2 to evaluate definite integrals using antiderivatives
•Perform u-substitution on indefinite integrals by identifying an appropriate inner function
•Apply u-substitution to definite integrals using the method of changing limits
+2 more objectives

Integral Applications: Area Between Curves and Volumes

Apply definite integrals to compute areas of regions bounded by two curves and volumes of solids generated by revolving regions around an axis using the disk and washer methods.

•Set up and evaluate definite integrals for area between two curves with respect to x
•Set up area integrals using horizontal slices (with respect to y) when appropriate
•Apply the disk method to find volumes of solids of revolution about the x-axis or y-axis
+2 more objectives

Integral Applications: Accumulation, Net Change, and Average Value

Interpret the definite integral as total accumulation and net change, compute the average value of a function over an interval, and solve problems involving particle motion and contextual rates.

•Interpret the definite integral as the net change of a quantity when given its rate of change
•Distinguish between net displacement and total distance traveled for a particle moving along a line
•Compute the average value of a function over an interval using the mean value theorem for integrals
+2 more objectives

Differential Equations: Slope Fields, Separation, and Exponential Models

Solve separable differential equations analytically, visualize solution families with slope fields, and model exponential growth and decay using calculus's most powerful applied framework.

•Sketch and interpret slope fields as visual representations of differential equations
•Identify which solution curve passes through a given point by reading a slope field
•Solve separable differential equations by separating variables and integrating both sides
+2 more objectives

AP Calculus AB. College-level course aligned to College Board CED. Replaces Precalculus pathway.