Quarter One Topic Review and Recommended Problems

AP Calculus AB

Please note that the topics and problems below are intended to prepare you for the exam. This review sheet is not intended to be all encompassing, i.e. the exam is limited only by covered material and not by topics and problems outlined here.

BRING THIS TO CLASS EVERYDAY UNTIL THE EXAM

Be able to:

· Use all the mathematics you have learned in previous courses and all of the mathematics you have learned in this course up to this point.

· Think.

· State, Explain, and Apply the verbal definition of a limit (p. 10)

· State, Explain, and Apply the definition of the existence of a Limit.

· State, Explain, and Apply the definition of Continuity at a point.

· State, Explain, and Apply the definition of Continuity on an interval.

· State, Explain, and Apply the Intermediate Value Theorem.

· Explain, Identify and demonstrate three types of discontinuities: Step, Infinite, and Point. (the only other type is called gap).

· Identify, from graphs, tables, and equations, vertical and horizontal asymptotes.

· Know the difference between indefinite, indeterminate, and infinite expressions.

· Use the limit theorems for limit proofs.

· Discuss one sided limits and infinity in limits.

· Tell me that a limit going off to infinity is a way of telling me that the limit DNE since it is going off to infinity.

· State, Explain, and Apply both definitions of the derivative.

· Explain the graphical interpretation of the derivative.

· Explain the physical interpretation of the derivative.

· Explain what is meant by a “Difference Quotient” and how limits and derivatives relate to this difference quotient.

· Sketch f’ when given f

· Explain the differences between position, distance, speed, velocity, and acceleration (and jerk if you want to be really good).

· Use all different types of notation and terminology for Derivatives.

· State (verbally and symbolically), Explain, and Apply the following differentiation “rules”: Power, Chain, Product, Quotient, Trigonometric, Exponential, Logarithmic, Constant.

· Tell me at least one thing about the squeeze theorem. (other than it’s also called the sandwich theorem and that it was invented/discovered by a man named neither squeeze, nor sandwich).

· Explain what the derivative and tangent to a function are doing when the function is at a max or min (relative or absolute).

· Find an average velocity when given a graph of position.

· State, Explain, and Apply the definition of differentiability.