AP Calculus BC: Exam Mastery Through Comprehensive Review

This intensive AP Calculus BC review course provides students with the tools and strategies needed to excel on the AP exam. Participants will reinforce their understanding of calculus fundamentals while mastering advanced techniques for problem-solving and application, ensuring confidence and readiness for exam day. By the end of this course, students will have a robust understanding of calculus concepts and be able to apply them to solve complex problems.

Limits and Continuity

• Graphical and analytical evaluation of limits — including indeterminate forms
• Application of limit laws and squeeze theorem
• Understanding and applying the concept of continuity

Derivatives: Fundamentals and Advanced Techniques

• Mastery of the limit definition of the derivative
• Application of power, product, quotient, and chain rules — for differentiating algebraic and transcendental functions
• Implicit differentiation — to find derivatives of implicitly defined functions
• Derivatives of trigonometric functions — including sine, cosine, tangent, and their inverses

Applications of Derivatives

• Related rates problems — involving rates of change in various contexts
• Optimization — finding maximum and minimum values of functions
• Linearization — using tangent lines to approximate function values
• L'Hôpital's Rule — for evaluating indeterminate limits

Integration Techniques

• Mastery of u-substitution
• Integration by parts — for integrating products of functions

Differential Equations

• Solving differential equations — using separation of variables
• Slope fields — creating and interpreting graphical solutions
• Euler's method — for numerical approximation of solutions
• Exponential growth and decay models
• Logistic growth models

Sequences and Series

• Convergence and divergence tests — including the n-th term test, geometric series test, alternating series test, integral test, p-series test, ratio test, and comparison tests
• Maclaurin and Taylor series — representations of functions
• Lagrange error bound and alternating series error bound — for estimating the error in series approximations
• Interval of convergence — determining the values for which a series converges
• Memorization of key Maclaurin series — including e^x, sin(x), cos(x), and geometric series