Calculus covers all content required for the AP Calculus Test - both AB and BC. The course starts with five major problems that introduce the following big ideas of calculus: optimization, limits, differential equations, exponential functions, the relationship between distance and velocity, piecewise functions, volumes of revolution, volumes by slicing, and the Fundamental Theorem of Calculus. Each of these five major problems is revisited again later in the course for students to solve using new calculus knowledge.
Each chapter reviews the concepts developed previously and builds on them. The curriculum contains several key labs and hands-on activities throughout the course to introduce concepts, such as when students recognize that the rate of a walker relates to the slope of a graph in the "Slope Walk." Labs also develop conceptual understanding, such as when the students discover instantaneous velocity in the "Ramp Lab." Students learn about derivatives and integrals simultaneously during the first four chapters and both are presented geometrically and in context. Read More...
The first four chapters cover:
The fifth chapter connects derivatives and integrals together with the Fundamental Theorem.
Chapters six through nine cover:
Some material required for the BC Calculus Exam is introduced throughout the course in optional extensions of Chapters 5 - 9. These topics include:
Chapters ten through thirteen cover additional BC Calculus content, including: