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)
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