AP Calculus AB Monthly Review

This comprehensive review course prepares students for the AP Calculus AB exam by thoroughly covering the curriculum's core concepts and problem-solving techniques. Through targeted monthly sessions, students will reinforce their understanding of limits, derivatives, and integrals, building a strong foundation for success on the exam and in future STEM endeavors. By the end of this course, students will have a robust understanding of the fundamental principles of calculus and the ability to apply them to solve a wide range of problems.

Limits and Continuity

• Evaluate limits graphically, numerically, and analytically — including one-sided limits and limits at infinity
• Apply limit laws and properties to determine the existence and value of limits
• Understand continuity and its implications — including the Intermediate Value Theorem

Derivatives

• Calculate derivatives using the power rule, product rule, quotient rule, and chain rule
• Understand implicit differentiation — find the derivatives of implicitly defined functions
• Apply derivatives to solve related rates problems — understand how the rates of change of different variables relate to each other

Applications of Derivatives

• Determine intervals where a function is increasing or decreasing — use the first derivative test
• Find local and global extrema — apply the extreme value theorem
• Analyze concavity and inflection points — use the second derivative test

Integrals

• Evaluate definite and indefinite integrals using the power rule, u-substitution, and integration by parts
• Apply the Fundamental Theorem of Calculus — connect differentiation and integration
• Calculate the area between curves — use definite integrals to find the area bounded by two or more functions

Differential Equations

• Solve separable differential equations — find general and particular solutions
• Interpret slope fields — visualize the solutions to differential equations
• Model real-world phenomena with differential equations — applications in physics, biology, and engineering

Review and Exam Preparation

• Practice a wide range of multiple-choice and free-response questions — simulate the AP exam experience
• Review key concepts and formulas — reinforce understanding and retention
• Develop effective test-taking strategies — manage time effectively and avoid common errors