Course Description

"AP® Calculus AB & BC - Challenging Concepts" is an advanced mathematics course designed to help students master the most demanding concepts in the AP® Calculus AB & BC curriculum. Led by well-respected AP instructors from across the United States, this course offers a comprehensive and engaging learning experience through video instruction, exam-style questions, and interactive activities. The course breaks down complex topics into manageable segments, allowing students to build a strong foundation in calculus principles and develop the skills necessary to excel in their AP® exams.

What Students Will Learn

• Mastery of challenging concepts from the AP® Calculus AB & BC curricula
• Increased confidence in understanding and applying complex calculus principles
• Enhanced graphical intuition through interactive graphing exercises
• Improved exam performance through practice with graded exam-style questions
• In-depth knowledge of topics such as limits, derivatives, integrals, differential equations, and series

Prerequisites

Students should have foundational knowledge in Calculus AB and/or BC before attempting these units. A strong background in pre-calculus and algebra is also recommended.

Course Contents

• Limits and continuity
• Definition of derivatives and the chain rule
• Implicit differentiation and the Mean Value Theorem
• L'Hospital's Rule and its applications
• Riemann sums and definite integrals
• Functions defined by definite integrals
• Modeling and solving differential equations
• Rectilinear motion and parametric equations
• Introduction to series, convergence, and manipulation

Who This Course Is For

• AP® Calculus AB and BC students seeking additional support and exam preparation
• High school students aiming to excel in their AP® Calculus exams
• Teachers looking for supplementary materials to enhance their AP® Calculus instruction
• Students who want to strengthen their understanding of challenging calculus concepts

Real-World Applications

• Engineering and physics: Analyzing motion, forces, and complex systems
• Economics and finance: Modeling economic trends and financial forecasting
• Computer science: Developing algorithms and solving optimization problems
• Data science: Analyzing trends and patterns in large datasets
• Medicine: Understanding drug interactions and modeling disease spread

Syllabus

This course offers a unique opportunity to learn from experienced AP® Calculus instructors and gain a deeper understanding of the most challenging concepts in the curriculum. By combining video instruction, interactive activities, and exam-style practice questions, students will be well-prepared to tackle their AP® Calculus exams with confidence and achieve success in their mathematical endeavors.