AP Calculus AB: Exam Review equips students with the essential skills and knowledge to excel on the AP Calculus AB exam, focusing on practical problem-solving and exam strategies. This intensive review course covers all major topics, reinforcing fundamental concepts and building confidence through targeted practice with AP-style multiple-choice questions. Students will develop a strong command of calculus principles and enhance their ability to apply these principles to diverse problems.

Limits and Continuity

• Evaluate limits using algebraic manipulation, including factoring and rationalization
• Apply the Squeeze Theorem to determine limits of complex functions
• Analyze continuity of functions at a point and over an interval—identifying removable and non-removable discontinuities

Derivatives

• Master differentiation techniques—power rule, product rule, quotient rule, and chain rule
• Calculate derivatives of trigonometric, inverse trigonometric (arcsin, arctan, arccos), exponential, and logarithmic functions
• Apply implicit differentiation to find derivatives of implicitly defined functions

Applications of Derivatives

• Solve related rates problems—analyzing how rates of change of different variables are related
• Apply L'Hôpital's Rule to evaluate indeterminate forms (0/0, ∞/∞)
• Use linearization to approximate function values near a specific point

Chain Rule and Inverse Functions

• Apply the chain rule in complex differentiation scenarios
• Calculate derivatives of inverse functions—understanding the relationship between a function and its inverse

Differential Equations

• Analyze slope fields to understand the behavior of solutions to differential equations
• Match slope fields to their corresponding differential equations
• Solve separable differential equations

Area and Volume

• Calculate area between curves using definite integrals
• Determine volumes of solids with known cross-sections
• Apply disk and washer methods to find volumes of solids of revolution
• Motion problems — determine when a particle is moving left or right and when it is speeding up or slowing down.

Exam Strategies and Practice

• Practice extensively with AP-style multiple-choice questions
• Identify common pitfalls and learn strategies to avoid them
• Simulate exam conditions to build pacing and time-management skills