This list is drawn from the topical outline for AP Calculus furnished by the College Board. You might find
that your teacher covers some additional topics, or omits some, in your course. Some of the topics are
very broad, so we cannot guarantee that this book covers these topics exhaustively.
I.Functions, Graphs, and Limits
A.Analysis of Graphs- You should be able to analyze a graph based on “the interplay between geometric and analytic
information.” The preceding phrase comes directly from the College Board. Don’t let it scare
you. What the College Board really means is that you should have covered graphing in
precalculus, and you should know (a) how to graph and (b) how to read a graph. This is a
precalculus topic and we won’t cover it in this book.
B.Limits- You should be able to calculate limits algebraically or to estimate them from a graph or from a
table of data. - You do not need to find limits using the Delta-Epsilon definition of a limit.
- You need to know how to use L’Hôpital’s Rule to evaluate a limit of indeterminate form.
C.Asymptotes- You should understand asymptotes graphically and be able to compare the growth rates of
different types of functions (namely polynomial functions, logarithmic functions, and
exponential functions). This is a topic that should have been covered in precalculus, and we
won’t cover it in this book. - You should understand asymptotes in terms of limits involving infinity.
D.Continuity- You should be able to test the continuity of a function in terms of limits, and you should
understand continuous functions graphically. - You should understand the intermediate value theorem and the extreme value theorem.
II.Differential Calculus
A.The Definition of the Derivative- You should be able to find a derivative by finding the limit of the difference quotient.