Right and Wrong Ways to Use your calculator on the AP Calc Exam

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Right and Wrong Ways to Use your calculator on
the AP Calc Exam

• Notes taken by Sean Bird at Greg Hills
  ghill_at_hinsdale86.org http//cstaff.hinsdale86.org
  /ghill
• presentation at the T3 International Conference
  in DC 2005.
• Updated April 26, 2008
• (partially for the TI-Nspire CAS)

seanbird_at_covenantchristian.org
http//covenantchristian.org/bird
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Things To Remember(Common Mistakes That Make
Readers Pull Their Hair Out.)

• Ben Cornelius from the Oregon Institute of
  Technology compiled this list several years
  ago.   It still works for me and my students.
  from AP Calc listserv April 27,2005    1.   
  There is no need to simplify arithmetic.  It
  wont make the answer any more correct (even in a
  long Riemann sum).
• 2.    Dont cross out your work unless you know
  you can do better.
• 3.    Be sure to label your answers and use
  correct units.
• 4.    If you are worried that your result in
  part (a) is incorrect, use it anyway to finish
  the problem.
• 5.    If you use your calculator, describe it
  clearly in mathematical terms, not in calculator
  speak.
• 6.    Dont write bad math.  (e.g.  Slope of
  the derivative. or 6.2368 6.237" or -17.21
  17.21")
• 7.    Remember 3 decimal places, rounded or
  truncated.  (More is ok.)
• 8.    Dont write f(x) 2(1.5) 3 when you
  really mean f(1.5) 2(1.5) 3.
• 9.    Every pronoun needs an antecedent.  Name
  the function you are referring to.  Do not say,
  The slope is ....  Say, The slope of g is
  ...., especially when more than one function is
  being discussed.
• 10.    When asked to write an integral, start
  with the limits and any constants of
  multiplication.  Then you can make a guess as to
  the integrand.

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• 11.    Know the difference between increasing and
  positive.  f is increasing when f is positive.
• 12.    Calculator work will be limited to the
  four required functionalities graphing, roots,
  numerical derivative, and numerical integration. 
  You will not be required to do anything else with
  your calculator and no question will be asked
  where using an additional feature would give an
  advantage. (e.g. curve fitting)
• 13.    Know the difference between local and
  global extrema.
• 14.    Know the difference between the extreme
  value (y-coordinate) and the location of the
  extreme value (x- and y-coordinate).
• 15.    When justifying local extrema or points of
  inflection, make sure your number line or chart
  is labeled.  Summarize the results in complete
  sentences.

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Calculator as learning tool vs. How to use it on
the exam

• The test is developed so that any extra
  calculator functionality will provide no
  significant advantage.
• 2003AB mc
• 81. Let f be the function with the derivative
• How many relative extrema does f have on the
  interval 2ltxlt4?

Graph f and look for zeros.
Do NOT try to integrate that by hand. Do NOT
graph the integral On 84 or 89, speed up graphing
by changing RES
5

• 81. Let f be the function with the derivative
• How many relative extrema does f have on the
  interval 2ltxlt4?

Graph f and look for zeros. Before graphing in
on your Nspire (or with any graphing calculator)
think about the window. What does sine do?
What is significant about these points?
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92. Where is g(x) decreasing between -1x3

• Graph Derivative (see where negative)
• Set your window to the domain so that your arent
  distracted by what occurs outside that area of
  interest set the x, then zoom Fit

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92. Where is g(x) decreasing between -1x3
Doing this on the TI-Nspire, finding the zeros is
quite easy. 1. Open up a GG (Graphs Geometry).
This can be done using /I to insert a new page,
or c2 2. Set up the window using the given
domain. b4x, v1e3 3. Graph the DERIVATIVE (to
consider where it is negative) 4. Optional Zoom
Fit b4A
(you could have already set the y-axis to be from
about -1 to 1 since sine oscillates between
that.) 5. On the TI-Nspire, the value of the
intersection points between two graph are
automatically given, so graph f2(x)0 and press
b63
/x to grab and move text to make it easy to see
(/G removes entry line)
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AB20031 Free Response find area between curves
volume about y1

• Read the instructions (NOW), e.g. show set up!
• E.g. DO NOT round off till the end, i.e. store
  your intersection answer
• On the calculator portion of the test you will
  not have to show the integration step unless
  specifically asked to do so.
• USE PROPER CALCULUS NOTATION not calculator
  notation. (But they dont count off for dx)

Especially with 83/84, decrease mess by using Y1
and Y2, e.g. fnInt(Y1-Y2,x,0,x)
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76 v(t) 3 4.1 cos(0.9t). What is a(4)?
Dont make the common mistake of putting in t4,
before you take the derivative!!

• On the 83/84 nDeriv(34.1cos(.9x),x,4)1.633
• For the 89
• With TI-NspireCAS you can use the shortcut SHIFT
  , g-, for the derivative template.

This is the such that or with bar.
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2003AB83 What is the average velocity of
the particle from time t 0 to time t 3?

• On the 83/84 fnInt(exxex,x,0,3)/3
• For the 89
• On the TI-NspireCAS, use SHIFT, g, as a
  shortcut for the integral template.

Gives the approximate answer when youre in AUTO
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2003AB84 Initial temp is 350 degrees Fahrenheit
(?F). The temperature of the pizza is changing
at a rate ofT(5)? (A) 112?F
(D) 238?F

• Dont need to remember Newtons Laws of Cooling.
• Area under a curve. Integrate from 0 5.
• Dont be so quick that you are careless.
• On the 83/84
• fnInt(-110e(-.4x),x,0,5) -237.783
• For the 89
• Dont forget to add the initial 350.

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2001AB2

• Never use
• STAT PLOT on the AP Calc Exam

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In summary clearly demonstrate that you know
calculus ?

• USE PROPER CALCULUS NOTATION not calculator
  notation.
• 84 users fnInt(Y1-Y2,x,0,x) is not an
  acceptable way to communicate to an AP grader
• Writing trap program will not get any credit
  where is the set up?
• For a verbal explanation, dont say, the
  function is going up, therefore it is
  increasing. Use calculus words, like the
  derivative is positive, so the function is
  increasing

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Note to teacherMAKE all your tests AP tests

• For 90 min block
• 7mc 1 fr NO calculator
• 7mc 1 fr with calculator
• 2/3 of test you get an A
• 18 pts for mc 18 pts fr
• 67 A
• 52 B
• 35 C
• 22 D
• The above is a guideline from the following data

year       5        4 3
2 88       83      68      48     
32     93     67      53      36     
24        97       72      56      39     
25     98       74      57      39     
24        2003    66      47      29     
16      average 72.4   56.2   38.2   24.2  half  
   36.2   28.1   19.1   12.1    grade   
5       4       3       2     
0.670  0.520  0.354  0.224 A
B C D Scores provided by Mike
Tamblyn 4/20/2008 on the AP Calc EDG