College Board
AP Calculus AB
Advanced Placement Calculus AB Exam
The College Board's first-semester-college-calculus exam for high-school students. A score of 3+ earns college credit or placement at most US universities, making it a standard accelerator for STEM-bound students.
What's on the exam
AP Calculus AB Course and Exam Description (College Board)
Limits and Continuity
10–12%Estimating and evaluating limits · Limit laws and algebraic manipulation · Squeeze theorem · Continuity and discontinuities · Asymptotes and limits at infinity · Intermediate Value Theorem
Differentiation: Definition and Fundamental Properties
10–12%Definition of the derivative · Differentiability and continuity · Power, product, and quotient rules · Derivatives of trigonometric functions · Derivatives of exponential and logarithmic functions
Differentiation: Composite, Implicit, and Inverse Functions
9–13%Chain rule · Implicit differentiation · Derivatives of inverse functions · Derivatives of inverse trigonometric functions · Higher-order derivatives
Contextual Applications of Differentiation
10–15%Rates of change in context · Straight-line motion · Related rates · Local linearity and approximation · L'Hospital's Rule
Analytical Applications of Differentiation
15–18%Mean Value Theorem · Extreme values and critical points · Increasing/decreasing behavior and concavity · Curve sketching · Optimization · Behavior of implicit relations
Integration and Accumulation of Change
17–20%Riemann sums and the definite integral · Accumulation functions · Fundamental Theorem of Calculus · Antiderivatives and basic rules · Integration by substitution
Differential Equations
6–12%Modeling with differential equations · Slope fields · Separation of variables · Exponential growth and decay
Applications of Integration
10–15%Average value of a function · Motion and accumulation problems · Area between curves · Volumes by cross sections · Volumes of revolution (disc and washer)
Frequently asked questions
How much does the AP Calculus AB cost?
The AP Calculus AB costs $99. US/Canada exam fee; international fee is higher and late-order fees apply.
How long is the AP Calculus AB and how many questions does it have?
45 multiple-choice + 6 free-response — 3 hours 15 minutes.
What do you need to pass the AP Calculus AB?
Scored 1–5; most colleges grant credit or placement for 3 and above.
Can you retake the AP Calculus AB?
Offered once per year; the exam may be retaken in a subsequent year.
What is the best way to study for the AP Calculus AB?
Study the official blueprint, not random material: the exam is weighted by domain (Limits and Continuity 10–12%, Differentiation: Definition and Fundamental Properties 10–12%, Differentiation: Composite, Implicit, and Inverse Functions 9–13%, Contextual Applications of Differentiation 10–15%, Analytical Applications of Differentiation 15–18%, Integration and Accumulation of Change 17–20%, Differential Equations 6–12%, Applications of Integration 10–15%). Spaced-repetition flashcards built domain-by-domain against that blueprint are the most time-efficient way to cover everything the exam tests.
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