πŸ“

AP Calculus AB 2025 Comprehensive Overview

May 11, 2025

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.