NCTM 2006 St.Louis

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NCTM 2006 St.Louis
Good Advice for Students taking the AP Calculus
Exam Get plenty of rest and have a good
breakfast with quality protein.
Take practice tests grade them yourself
Study Stuff You MUST Know Cold (printable)

• 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.
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General Comments

• Show work. Answers w/o supporting work may not
  receive credit.
• Communicate reasoning clearly in a concise way
  using proper notation. Precise Concise
• Justify conclusions using mathematical (CALCULUS)
  arguments
• There will be application problems (like weve
  been doing all along). Real life math (no 2.34
  people)
• TRY EACH part of EACH free-response problem. It
  doesnt go in increasing difficulty.

Graphical,Numerical (tabular), Analytical
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10 Reminders about calculator

• 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.
• Graph, zeros, numerically differentiate
  integrate
• SHOW set up but dont try to do things by hand on
  the calculator portion.

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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 wont cut it for precision. Avoid
  TRACE) Use the variable in subsequent
  calculations.

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20051
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,
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20051
On 89,
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On the TI 83/84
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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 wont 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!
  Tell them what equation are you solving, or what
  are you differentiating.

Now you in the back can see 10, but you cant
see this. ?
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Wisdom from 2005 FR

• BC2 candidates test
• AB/BC3 never use a regression. Do the problem
  they give dont 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 cant use your
  calculator.

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Wisdom from 2005 FR

• BC6 check endpoints on interval of convergence.
• 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
• DONT USE DECIMAL APPROXIMATION OF pi!!! (Unless
  you use the decimal approximation out to 10
  decimal places.)

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Global Tips for Students
By Dan Kennedy, Chattanooga, TN from
apcentral.com

• 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.
• 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).
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Global Tips for Students continued
By Dan Kennedy, Chattanooga, TN from
apcentral.com

• 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.)

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).
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Global Tips for Students continued
By Dan Kennedy, Chattanooga, TN from
apcentral.com

• 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.
• 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. Dont 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).
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Top Ten Student Errors
Not unless f changes from to , or to
Not unless f changes from to , or to
Avoid it
Show set up
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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(x28)
  DIVIDED BY fourthroot(2x1). 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 - (t2/2)
  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.
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Final IMPORTANT advice

• Read the instructions before test day
• http//apcentral.collegeboard.com/repository/ap05_
  calc_rev_comment_22817.pdf
• And the course description, especially pg 5ff
  (pdf page 11ff)
• http//apcentral.collegeboard.com/repository/05836
  apcoursdesccalc0_4313.pdf

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