Good Advice for Students taking the AP Calculus Exam
“Get plenty of rest and have a good breakfast with quality protein.”
NCTM 2006 St.Louis
AP Calc: Lessons from 2005
Free-response Problems
Speaker: Craig Wright, Education Testing
Service, New Jersey
Typed by Sean Bird
Also included are “Global Tips” by Dan Kennedy, “Be Careful” by Dave Slomer,
Instructions for the AP Calc Exam, AP Calc course description, and more.
General Comments
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Show work. Answers w/o supporting work
may not receive credit.
Communicate reasoning clearly in a concise
way using proper notation. “Precise & Concise”
Graphical,
Justify conclusions using mathematical Numerical
(tabular), &
(CALCULUS) arguments
Analytical
There will be application problems (like we’ve
been doing all along). Real life math
TRY EACH part of EACH free-response
problem. It doesn’t go in increasing difficulty.
(no 2.34 people)
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10 Reminders about calculator
1.
2.
3.
Set the calculator to RADIAN mode
Report decimal approximation to [at least]
three decimal places after the decimal point.
E.g. 2.367 [truncate or round]
Be proficient with the 4 expected
capabilities.
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4.
Graph, zeros, numerically differentiate & integrate
SHOW set up but don’t try to do things by
hand on the calculator portion.
10 Reminders about calculator
5. Watch parenthesis
6. Store function in y1(x) (or something like that)
7. Be able to store important values (e.g. zero or
point of intersection) for a short cut! [“xc” on 89]
(trace won’t cut it for precision. Avoid TRACE)
Use the variable in subsequent calculations.
2005#1
Look at the graph provided.
Consider the period of the
sin curve. It looks like ½ a
cycle. Pi is ½ a cycle.
Perhaps x is around 1.
Assign xmin and xmax, then
ZoomFit. I picked xmin= -0.1
and xmax a bit more than 1.
In fact, clearly, algebraically you can
see that x = 1 is an intersection.
On 89,
2005#1
On 89,
On the TI 83/84
10 Reminders about calculator
5. Watch parenthesis
6. Store function in y1(x) (or something like that)
7. Be able to store important values (e.g. zero or
point of intersection) for a short cut! “xc” on 89
(trace won’t cut it for precision. Avoid TRACE)
Use the variable in subsequent calculators
8. If you round too much then your solution will
be wrong & unacceptable. E.g. Definite integral
9. “Because my calculator said so” will never get
you the justification point.
10. Use standard mathematical notion, not
calculator syntax, on the exam. Never us “it”!
Now you in the back can see #10, but you can’t see this. 
Wisdom from 2005 FR
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BC2 candidates test
AB/BC3 – never use a regression. Do the
problem they give; don’t make up your own. It
will be hard for you to get any points. #3 has
will likely be a problem that you can
reasonably come back to without the use of
your calculator.
BC4 “most common error was not doing
something that it told you to do” and then not
making a numerical answer even when you
can’t use your calculator.
Wisdom from 2005 FR
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BC6 check endpoints on interval of
convergence.
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Be careful of arithmetic errors
Most common error 2n! Instead of (2n)! …NO CREDIT
GIVEN.
You are scored on what you show on paper and NOT
ON WHAT YOU WERE THINKING
DON’T USE DECIMAL APPROXIMATION OF
pi!!! (Unless you use the decimal approximation out to 10 decimal places.)
Global Tips for Students
By Dan Kennedy, Chattanooga, TN – from apcentral.com
Do not round partial answers.
Store them in your calculator so that you can use them
unrounded in further calculations.
Do not let the points at the beginning keep you from
getting the points at the end.
If you can do part (c) without doing (a) and (b), do it. If
you need to import an answer from part (a), make a
credible attempt at part (a) so that you can import the
(possibly wrong) answer and get your part (c) points.
If it seems like this is repetitive, that probably
means it is REALLY important. We need reminded
again and again of some things (see 2 Peter 1).
Show all work.
Remember that the grader is not really interested in
finding out the answer to the problem. The grader is
interested in seeing if you know how to solve the
problem.
Global Tips for Students continued
By Dan Kennedy, Chattanooga, TN – from apcentral.com
If it seems like this is repetitive, that probably
means it is REALLY important. We need reminded
again and again of some things (see 2 Peter 1).
If you use your calculator to find a definite integral, write the
integral first.
An answer without an integral will not get full credit, even if
it is correct. [Always at least write the limits of
integration and constant]
Do not waste time erasing bad solutions.
If you change your mind, simply cross out the bad solution
after you have written the good one. Crossed-out work will
not be graded. If you have no better solution, leave the old
one there. It might be worth a point or two.
Do not use your calculator for anything except:
(a) graph functions, (b) compute numerical derivatives,
(c) compute definite integrals, and (d) solve equations. In
particular, do not use it to determine max/min points,
concavity, inflection points, increasing/decreasing, domain,
and range. (You can explore all these with your calculator,
but your solution must stand alone.)
Global Tips for Students continued
By Dan Kennedy, Chattanooga, TN – from apcentral.com
If you can eliminate some incorrect answers in the multiple-choice
section, it is advantageous to guess.
Otherwise it is not. Wrong answers can often be eliminated by
estimation, or by thinking graphically. [Don’t be fooled by distractors]
If they ask you to justify your answer, think about what needs justification.
They are asking you to say more. If you can figure out why, your
chances are better of telling them what they want to hear. For
example, if they ask you to justify a point of inflection, they are looking
to see if you realize that a sign change of the second derivative must
occur.
If it seems like this is repetitive, that probably
means it is REALLY important. We need reminded
again and again of some things (see 2 Peter 1).
Be sure you have answered the problem.
For example, if it asks for the maximum value of a function, do not
stop after finding the x at which the maximum value occurs. Be sure to
express your answer in correct units if units are given.
Top Ten Student Errors
Not unless f ’’ changes
Not
fromunless
+ to –,f ’orchanges
– to +
from + to –, or – to +
Avoid “it”
Show set up
“Be Careful”
by Dave Slomer posted Saturday 4/29/2006
FWIW, here're my booboos.
1. Find the min value of x ln x.
At x = 1/e, the function has a min. Since 1/e was not an alternative and since "none"
was, I selected 'none' because of the ln approaching -inf.. While explaining to
the class why this was correct [and while Julie was frowning], I took the limit as x
-> 0 and got ... AWK! ZERO instead of -inf. D'OH!! THEN I realized that I hadn't
even FOUND the FUNCTION VALUE, which was -1/e. Dumb. Dumb.
2. Find the derivative of y = cuberoot(x^2+8) DIVIDED BY fourthroot(2x+1). Since it
was calculator legal, I did Nderiv but omitted the division sign, essentially
omitting the negative exponent. CARELESS!!! [It's a wonder I got one of the
alternatives.]
3. Particle's position is -4 cos t - (t^2/2) + 10. Find velocity when acceleration is first
zero. The acceleration was first zero when t = 1.32, alternative C. End of
problem. D'OH!! We want the VELOCITY. CARELESS!! DUMB.
4. The top of a 25-foot ladder is sliding down a wall at 3 feet per minute yadda
yadda yadda. Needless to say, I didn't make this rate NEGATIVE. How dumb
can ya get? Of course, if I had only thought about NEGATIVE 7/8 ft/min not
being logical since the distance was increasing... GAH!
… But my point is maybe to share these common easy to make errors with your kids Mon or Tue. It's never too late to emphasize being careful.
Final IMPORTANT advice
Read the instructions before test day
http://apcentral.collegeboard.com/repository/ap
05_calc_rev_comment_22817.pdf
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And the course description, especially pg “5”ff
(pdf page 11ff)
http://apcentral.collegeboard.com/repository/05
836apcoursdesccalc0_4313.pdf