AP+Calculus+AB

What do we mean when we say a function is continuous? || Definition of a limit Taking limits graphically, numerically, and algebraically ||  || //Larson and Hostetler// //AP Calculus, 9th ed.// Ch 1 || Exploration: Limit Activity || Quizzes and Tests The Tests and quizzes will follow the AP Format: Multiple Choice and Free Response. The Free Response requires students to show their work and demonstrate clear understanding of the underlying concepts necessary to solve the problem. || How is a derivative defined? How do we interpret the derivative? How do we determine the derivative for various types of functions? || Definition of derivative Using the derivative as a rate of change. Power Rule for derivatives Product and Quotient Rules. Chain Rule for derivatives Derivatives of trigonometric functions Implicit differentiation Related Rates Derivatives of transcendental functions ||  || Ch 2
 * ~ Unit ||~ Start Date (duration) ||~ Essential Questions ||~ Content / Concepts ||~ Skills ||~ Texts ||~ Supporting / Supplementary Materials ||~ **Assessment** ||
 * 1 || 5 weeks || What is a limit?
 * 2 || 6 weeks || What is a derivative?

Ch 5.1,3,4,6 || Exploration: Module on Motion Exploration: Relationship between graphs of a function and its derivatives || Quizzes and Tests || How do we use the derivative in optimization problems? What do we mean by an infinite limit? || Curve sketching using the 1st and 2nd derivatives. Solving optimization problems.
 * 3 || 5 weeks || How do we use the derivative to graph functions?

Calculating limits at infinity. ||  || Ch 3 || Exploration: Relationship between Graphs of functions and derivatives (part 2) || Quizzes and Tests (group Test on Curve sketching) || What is an antiderivative? How do we find the average value of a functions? How are derivatives and integrals related? || Definition of antiderivative. Riemann Sums and Integrals Integration as an acumulation function Fundamental Theorems of Calculus Integration Techniques ||  || Ch 4 and Ch 5 ||   || Quizzes and Tests || What is a differential equation? What are some techniques we can use to solve differential equations? || Developing and Interpreting Slope Fields. Separable Differential equations Homogeneous Differential Equations Solving differential equations ||  || Ch 6 || Exploration: Slope Fields Class Activity || Quizzes and Tests || How can we use integration to determine the volumes of solids of revolution? || Calculating the area under a curve. Calculating the area between two curves. Using the Disc, Washer, and Shell Methods to calculate the volume of a solid of revolution ||  || Ch 7 ||   || Quizzes, Tests, and AP Exam ||
 * 4 || 6 Weeks || How do we calculate the area under a curve?
 * 5 || 5 Weeks || What is a slope field?
 * 6 || 5 Weeks || How do we calculate the area between 2 curves?