Review Topics Final Exam Bc | Fall 2009

iLearnMath.net | AP Calculus | Final Exam Review  2009   

Chapter 1: ¾ ¾ ¾ ¾ ¾

Four ways of describing functions; New functions from old ones. Review library of functions: trigonometric, rational, polynomial, logarithmic, exponential Review unit circle Review formulae (inside cover) Understand transformations geometrically / domains of new functions

Chapter 2: ¾ ¾ ¾ ¾

Limits: Numerically, Graphically, Algebraically, Verbally. One sided limits / overall limit at a point Laws of Limits Continuity / One-sided continuity

Chapter 3: ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾ ¾

Derivatives and rates of change: The secant line’s slope approximates true slope. Definitions of the derivative at a point The Derivative as a function Differentiation shortcuts Chain Rule Implicit Differentiation Rates in the Natural Sciences Social Sciences (Applications to Economics) Related rates problems Linear Approximation Taylor Polynomials (BC ONLY)

Chapter 4: ¾ ¾ ¾ ¾ ¾ ¾ ¾

Max and Min Values The Mean Value Theorem How derivatives affect the shape of a graph Limits at infinity: Horizontal Asymptotes Sketching Guidelines Optimization problems Newton’s Method (BC ONLY)

Chapter 7: ¾ Inverses, Property of Inverse Functions for Derivatives ¾ Exponential Growth and Decay ¾ Inverse Trig Derivatives