Calculus I & II Study Guide

Limits and Continuity

Foundation for calculus exploring limit evaluation, continuity analysis, and asymptotic behavior essential for derivative definitions.

Differentiation: Definition and Fundamental Rules

Master derivative definitions, basic rules, product, quotient, and chain rules for computing rates of change.

Advanced Differentiation Techniques and Applications

Apply implicit differentiation, related rates, and optimization to solve complex real-world modeling problems.

Analytical Applications of Differentiation

Use derivatives for curve sketching, Mean Value Theorem, L'Hôpital's Rule, and function behavior analysis.

Integration and the Fundamental Theorem of Calculus

Connect antiderivatives to definite integrals through FTC, enabling area calculations and accumulation functions.

Advanced Integration Techniques

Master integration by parts, partial fractions, and improper integrals—BC-specific techniques for complex antiderivatives.

Applications of Integration

Calculate areas, volumes, arc lengths, and solve differential equations including logistic growth models.

Parametric Equations and Vector-Valued Functions

Analyze motion using parametric derivatives, arc length, and vector functions for position, velocity, acceleration.

Polar Functions and Their Applications

Convert, differentiate, and integrate polar functions; calculate areas and analyze curves in polar coordinates.

Infinite Sequences and Series

Evaluate sequence convergence and apply divergence, integral, comparison, ratio, and alternating series tests.

Taylor and Maclaurin Series

Construct Taylor polynomials, determine intervals of convergence, and apply Lagrange error bounds for approximations.

AP Exam Problem-Solving Strategies

Integrate all concepts through practice FRQs, calculator techniques, and mathematical communication for maximum scoring.