AP Calculus AB: 8-Week Exam Review equips students with the essential calculus skills and strategies needed to excel on the AP exam. This intensive review focuses on mastering derivative and integral calculus, emphasizing problem-solving techniques for both multiple-choice and free-response questions. By the end of this course, students will confidently apply calculus principles to solve real-world problems.

Limits and Continuity

• Average rate of change — connecting to slope concepts from algebra
• Instantaneous rate of change — understanding the derivative as a limit
• Limit definition of the derivative — both at a point and as a general expression

Differentiation Techniques

• Product rule, quotient rule, and chain rule — mastering the fundamental rules
• Implicit differentiation — for complex equations
• Derivatives of trigonometric and inverse trigonometric functions — with a focus on arcsine and arctan
• Related rates problems — applying derivatives to real-world scenarios

Applications of Derivatives

• L'Hôpital's Rule — simplifying limits
• Linearization — approximating function values using tangent lines
• Optimization problems — finding maximum and minimum values
• Motion problems — analyzing velocity, acceleration, and displacement
• Curve sketching — using first and second derivatives to analyze concavity and extrema
• Mean Value Theorem — understanding the relationship between average and instantaneous rates of change

Integration Techniques

• Riemann sums — approximating areas under curves
• Integration by long division — handling rational functions
• u-Substitution — reversing the chain rule
• Integration of trigonometric functions — mastering key integrals
• Fundamental Theorem of Calculus — connecting derivatives and integrals

Applications of Integration

• Start plus accumulation method — applying the Fundamental Theorem of Calculus
• Calculating area between curves — using definite integrals
• Volume calculations — using disks, washers, and shells
• Free-response question strategies — mastering the format and scoring rubrics

Exam Strategies and Practice

• Multiple-choice question strategies — time management and process of elimination
• Free-response question drills — practicing common question types
• Review of key theorems and formulas — ensuring comprehensive knowledge
• Full-length practice exams — simulating the AP Calculus AB exam experience