AP Calculus AB 2025 Cheat Sheet

Unit 1: Limits & Continuity

• Understanding limits as x approaches c from both sides.
• Techniques to simplify limits: completing the square, rationalization, factoring.
• Growth rates: f(x)/g(x) comparison for determining limits.
• Continuity and types of discontinuities: removable, asymptote, jump.
• Intermediate Value Theorem (IVT) applications for continuous functions.
• Average Rate of Change (AROC) estimation from tables and graphs.
• Differentiable functions are continuous; not all continuous functions are differentiable.

Unit 2: Fundamentals of Differentiation

• Power, product, quotient, and chain rules for differentiation.
• Chain Rule: Differentiate outer function and multiply by the derivative of the inner function.
• Implicit Differentiation: Differentiate each term, multiply by dy/dx when differentiating y.
• Inverse functions and inverse trig cofunctions derivatives.
• Higher order derivatives: continue differentiating.

Unit 3: Composite, Implicit, & Inverse Functions

• Differentiation techniques for composite, implicit, and inverse functions.

Unit 4: Contextual Applications of Differentiation

• Derivative as the rate of change.
• Related Rates: draw a picture, list knowns/unknowns, write and solve the equation.
• Linearization and L'Hopital's Rule (LHR) for indeterminate forms.
• Mean Value Theorem (MVT) and Rolle's Theorem for function properties.
• Extreme Value Theorem (EVT) for determining local/global maxima and minima.
• Understanding critical points, local and global extrema, and inflection points.
• Steps for Optimization: drawing, writing equations, solving for extrema.

Unit 5: Analytical Applications of Differentiation

• Analysis of function behavior: inc/dec, concavity, inflection points.
• Determining extrema using first and second derivatives.

Unit 6: Integration of Accumulation of Change

• Integration as accumulation or area between graph and x-axis.
• Use geometry for integrals: circles, triangles, squares.
• Riemann Sum and Fundamental Theorem of Calculus (FTOC) applications.
• U-substitution for integration.

Unit 7: Differential Equations

• Slope Fields for visualizing solutions.
• Separation of Variables technique.
• Initial value problems and particular solutions.
• Exponential growth/decay models.

Unit 8: Applications of Integration

• Average Value Theorem (AVT) for determining average function values.
• Relationship between displacement and distance traveled.
• Area under curves: disk/washer method, sectional integration.
• Strategy for tackling Free Response Questions (FRQs): work on known parts, show all work, use shorthand for theorems.

Exam Tips

• Use abbreviations for theorems (IVT, MVT, FTOC).
• Don’t simplify answers unnecessarily to avoid losing points.