AP® Calculus AB & BC - Challenging Concepts

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

  1. Limits - Pario-Lee Law
  2. Chain Rule - Monique Morton
  3. Implicit Differentiation - Monique Morton
  4. Rectilinear Motion - Vicki Carter
  5. Parametric Equations - Vicki Carter
  6. L'Hospital's Rule - Mark Howell
  7. Riemann Sums - Peter Atlas
  8. Functions Defined by Definite Integrals - Scott Pass
  9. Modeling with & Solving Differential Equations (1) - Jennifer Wexler
  10. Modeling with & Solving Differential Equations (2) - Jennifer Wexler
  11. Introduction to Series - Jane Wortman
  12. Series Convergence - Jane Wortman
  13. Series Manipulation - Jane Wortman

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.