by James
You’ve decided to take the AP Calc exam, either AB or
BC depending on your skill level or the course selections at
your local high school. As always, I cannot stress the importance
of having adequate training for the exam by taking a calculus
course in school. The subject matter and topics discussed in
such a class are almost elementary after you’ve learned
them, but are horribly opaque if you are trying to learn it
by yourself. If your school does not offer AP-level calculus
or has a poor teacher, I suggest a summer course or night-school
course to supplement that knowledge.
Now that you’ve had your preparation squared away, here
are some the things to expect on the exam itself. You will be
presented with a lengthy multiple-choice section and a free-response
section with six questions. The multiple-choice section is further
split between problems that may be solved with the help of a
calculator, and those that may not. Don’t let this intimidate
you, as the non-calculator problems are often simpler with rounder
numbers (but not always). Since this is a math exam, equivalent
answers are fine; if you seem to get a nasty improper fraction
for an answer and you know it’s correct, then just leave
it as it is.
Hopefully your calculus preparation course in school is fairly
quick on its schedule, and you will have been doing or plan
to do many practice tests months before the actual test date.
If this is not the case, I strongly suggest you take as many
practice tests as possible on your own; they’re easy to
find online, or you can ask your teacher to access the materials
and then ask questions about the answers when you’re finished
with them. This is really the only way to train yourself on
the multiple-choice section: exposing yourself to a wide variety
of potential questions that could be asked, since there are
only so many things the exam writers can ask of students at
this level. Also, watch out when you’re choosing your
answer choices. Often, on the non-calculator section, you will
have to find a ballpark answer and be presented with choices
like 4, 4.17, 4.75, and 5: folks with good logical reasoning
will find this simple, but only exposure to questions like these
will help the rest of us. Also, don’t be taken by the
obvious-looking but totally wrong (on further inspection) answer.
These choices exist to deceive, so if a question looks a little
bit too easy, it probably is.
The free response section generally gives the test writers
more opportunity to exploit the weaknesses of potential test-takers,
but the way to prevent this from happening to you is the same
as above: expose yourself to a lot of sample questions beforehand,
and look at the example solutions for sample answers. I also
strongly recommend preparing for the test, and the free-response
section especially, in groups of 3 or 4. Doing the problems
together engenders discussion of what to write down on the questions,
and the different ways your group members will try to solve
the same problem will familiarize you with how to operate on
the test. Plus, your group interaction will help you discover
your own weaknesses, so you can reinforce those areas in time.
When you are actually taking the test and writing the free-response,
remember to write down everything you know about a particular
question: formulae, rules, etc. and if you’re pressed
for time, cross things out instead of erasing. Pace yourself,
and look over all 6 questions before starting even one, so you
know what to expect and can choose a question you’re most
comfortable with to begin solving. The free-response section
was devilishly hard my year, with questions on parametric notation
and graphs with cusps, and from what I hear was even more annoying
this past May. Don’t let yourself fall into the traps
that the test writers have set for you.
The difference between the two tests, AB and BC, are small
but substantial: the BC test covers additional topics like sequences
and series, with wonderful things like ratio testing and Taylor
polynomials. These really should also be covered in class, but
if you took Calc AB as a class and want to take the BC test,
a little independent preparation should suffice. You will not
have to get every question correct because the curve is very
generous; even the scoring on the free-response section is optimistically
in your favor, as you will earn credit for things that you demonstrate
you know. This seems at odds with my previous advice, but that
is simply because the calculus tests have a considerably larger
margin for error than tests like US History. If you do follow
this advice, your framework for scoring high on the AP Calculus
tests will be laid.
