- You should be able to integrate using the power rule and u-Substitution.
E.Applications of Antidifferentiation- You should be able to find specific antiderivatives using initial conditions.
- You should be able to solve separable differential equations and logistic differential equations.
- You should be able to interpret differential equations via slope fields. Don’t be intimidated.
These look harder than they are.
GENERAL OVERVIEW OF THIS BOOK
The key to doing well on the exam is to memorize a variety of techniques for solving calculus problems
and to recognize when to use them. There’s so much to learn in AP Calculus that it’s difficult to remember
everything. Instead, you should be able to derive or figure out how to do certain things based on your
mastery of a few essential techniques. In addition, you’ll be expected to remember a lot of the math that
you did before calculus—particularly trigonometry. You should be able to graph functions, find zeros,
derivatives, and integrals with the calculator.
Furthermore, if you can’t derive certain formulas, you should memorize them! A lot of students don’t
bother to memorize the trigonometry special angles and formulas because they can do them on their
calculators. This is a big mistake. You’ll be expected to be very good with these in calculus, and if you
can’t recall them easily, you’ll be slowed down and the problems will seem much harder. Make sure that
you’re also comfortable with analytic geometry. If you rely on your calculator to graph for you, you’ll get
a lot of questions wrong because you won’t recognize the curves when you see them.
This advice is going to seem backward compared with what your teachers are telling you. In school
you’re often yelled at for memorizing things. Teachers tell you to understand the concepts, not just
memorize the answers. Well, things are different here. The understanding will come later, after you’re
comfortable with the mechanics. In the meantime, you should learn techniques and practice them, and,
through repetition, you will ingrain them in your memory.
Each chapter is divided into three types of problems: examples, solved problems, and practice problems.
The first type is contained in the explanatory portion of the unit. The examples are designed to further your
understanding of the subject and to show you how to get the problems right. Each step of the solution to
the example is worked out, except for some simple algebraic and arithmetic steps that should come easily
to you at this point.
The second type of problems is solved problems. The solutions are worked out in approximately the same
detail as the examples. Before you start work on each of these, cover the solution with an index card, then
check the solution afterward. And you should read through the solution, not just assume that you knew
what you were doing because your answer was correct.