AP Calculus AB

Turns out, adding up infinite tiny things and finding the slope of a curve are somehow the exact same idea.

24 days — make them count.

Monday, May 11, 2026

Start Unit 1 — it's free →Explore the course ↓

31%Multiple ChoicePart A30q · 60 min

23%Multiple ChoicePart B15q · 45 min · calculator required

15%Free ResponsePart A2q · 30 min · calculator required

31%Free ResponsePart B4q · 60 min

of students scored 4 or higher in 2025

285,891 test-takers

2,851 colleges grant credit

5 · 20%

4 · 29%

3 · 15%

2 · 23%

1 · 13%

3.2 avg

543 (passing)21

Every technique in AP Calculus AB is either a limit, or a consequence of one.

Derivatives measure instantaneous change by taking limits of difference quotients. Definite integrals measure exact accumulation by taking limits of Riemann sums. The Fundamental Theorem of Calculus is the course's central revelation: those two operations, which look completely unrelated, are inverses of each other.

Units 5 and 6 carry the heaviest exam weight — students who can't apply derivatives and integrals analytically lose points they can't recover elsewhere.

The AP exam places significant emphasis on Units 5 and 6, as they cover critical applications of differentiation and integration, which are central to the course's thesis.

How the course builds

Change · Limits · Analysis of Functions

Limits and ContinuityEstablishes the foundational concept of limits, which underpins all subsequent calculus concepts.

10–12% of exam

Differentiation: Definition and Fundamental PropertiesIntroduces the derivative as a limit, connecting limits to the concept of instantaneous rate of change.

10–12% of exam

Differentiation: Composite, Implicit, and Inverse FunctionsExpands differentiation techniques to more complex functions, deepening understanding of derivatives.

9–13% of exam

Contextual Applications of DifferentiationApplies differentiation to real-world contexts, demonstrating its utility in modeling change.

10–15% of exam

Analytical Applications of DifferentiationDevelops analytical skills for solving problems using derivatives, reinforcing their mathematical power.

15–18% of exam

Integration and Accumulation of ChangeIntroduces integration as the inverse process of differentiation, linking it to accumulation.

17–20% of exam

Differential EquationsExplores simple differential equations, showing how integration and differentiation can model dynamic systems.

6–12% of exam

★ Hardest unitApplications of IntegrationApplies integration techniques to solve practical problems, cementing the concept's real-world relevance.“Requires synthesis of multiple differentiation techniques and application to complex problems.”

10–15% of exam

Unit 5: Analytical Applications of Differentiation is where most students hit a wall.

Requires synthesis of multiple differentiation techniques and application to complex problems.

Students often struggle with the algebraic manipulation required for optimization problems.

What You Need

Interpreting motion quantitiesBasic sequence notation awarenessExponential and logarithmic function fluencyCore trigonometric fluencyFunction notation and evaluation fluencyFunction transformations and graph interpretationAverage rate of changeLinear equation and inequality fluencyFunction composition and inverse functionsUnit-circle understandingMulti-representation reasoning with functionsArea and geometric measurement fluencyAlgebraic manipulation and simplificationPolynomial and rational function fluency

Start this course free. Upgrade anytime.

Unit 1 free · Course Pass $15 · All-Access $45 through May 31 —

See pricing