AP Calculus AB — Free Practice Questions, Study Guides & Mock Exams
Master limits, derivatives, integrals, and the Fundamental Theorem of Calculus
Topics covered
- Limits and Continuity
- Derivatives
- Derivative Applications
- Integration
- Fundamental Theorem of Calculus
- Differential Equations
- Applications of Integration
- 1.1.a
- 1.1.b
- 1.1.c
- True/False
- MCQ
- Word Bank
- Trap Classification
Free AP Calculus AB study guides
- Limits from Notation, Graphs, and Tables — Interpret limiting behavior across analytic, graphical, numerical, and verbal representations before selecting a computation.
- Limit Laws and Evaluation Strategies — Move deliberately from direct substitution to algebraic rewriting, squeeze arguments, and cross-representation verification.
- Continuity, Asymptotes, and the IVT — Classify discontinuities, connect infinite behavior to asymptotes, and write theorem-based existence arguments with every hypothesis visible.
- Derivative Definition, Estimation, and Differentiability — Build the derivative from difference quotients and interpret it as tangent slope and instantaneous rate across representations.
- Foundational Derivative Rules — Differentiate powers, sums, products, quotients, and the standard trigonometric, exponential, and logarithmic functions efficiently.
- Composite, Implicit, Inverse, and Higher Derivatives — Combine the chain rule with implicit and inverse-function reasoning, then select and repeat procedures for higher derivatives.
- Contextual Derivatives and Motion — Translate derivatives into rates with units and connect position, velocity, acceleration, speed, and direction of motion.
- Related Rates, Linearization, and L'Hospital's Rule — Differentiate linked quantities with respect to time, approximate locally with tangent lines, and evaluate eligible indeterminate limits.
- Mean Value Theorem, Extrema, and First-Derivative Analysis — Use existence theorems and derivative signs to locate and justify critical behavior on open and closed intervals.
- Concavity, Graph Relationships, and Optimization — Connect f, f', and f''; construct derivative-supported sketches; and turn constraints into optimized one-variable models.
- Accumulation, Riemann Sums, and Integral Notation — Model accumulated change, construct left/right/midpoint sums, and pass from sigma notation to definite integrals.
- The FTC, Accumulation Functions, and Definite Integrals — Differentiate accumulation functions, interpret their behavior, and evaluate definite integrals through the Fundamental Theorem of Calculus.
- Antiderivatives and Core Integration Techniques — Use basic antiderivative rules, substitution, long division, and completing the square while preserving constants and bounds.
- Differential Equations, Slope Fields, and Models — Model rates with differential equations, verify solutions, read slope fields, separate variables, and solve exponential initial-value problems.
- Applied Integrals, Motion, and Area — Use definite integrals for average value, displacement, distance, accumulated change, and areas bounded in x or y.
- Volume by Cross Sections, Discs, and Washers — Build volume integrals from geometric slices, with radii measured from the stated axis and bounds matched to the integration variable.
Units
- Unit 1
- Unit 2
- Unit 3
- Unit 4
- Unit 5
- Unit 6
- Unit 7
- Unit 8