Transcript Slide 1
Right and Wrong Ways to Use your calculator on the AP Calc Exam
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.
a long Riemann sum).
It won’t make the answer any more correct (even in 2.
Don’t 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.
Don’t write bad math. (e.g. “Slope of the derivative.” or “6.2368 = 6.237" or “-17.21 = 17.21") 7.
8.
Remember: 3 decimal places, rounded or truncated. (More is ok.) Don’t 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.
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.
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 sin(
x
2 1) How many relative extrema does
f
have Do
NOT
try to integrate that by hand.
Do
NOT
graph the integral On 84 or 89, speed up graphing by changing RES
81. Let
f
be the function with the derivative sin(
x
2 1) How many relative extrema does
f
have on the interval 2 What is significant about these points? g ( x ) 0 x Graph Derivative (see where negative) 2 t dt Set your window to the domain so that your aren’t distracted by what occurs outside that area of interest [set the x , then zoom Fit] Free Response find area between curves & volume about y=1 Read the instructions, NOW show set up! DO NOT round off till the end, i.e. store your intersection answer (be sure to write them on the integral) 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*. Especially with 83/84, decrease mess by using Y1 and Y2, e.g. fnInt(Y1-Y2,x,0,x) Don’t make the common mistake of putting in t=4, before you take the derivative!! #76 v ( t ) = 3 + 4.1 cos(0.9 t ). What is a (4)? On the 83/84 nDeriv(3+4.1cos(.9x),x,4)=1.633, or put in Y1 and use the Calc menu For the 89 e te t What is the average velocity of the particle from time t = 0 to time t = 3? On the 83/84 fnInt(e^x+x*e^x,x,0,3)/3, or under Y1=(e^x+x*e^x)/3, go to Calc menu and integrate from 0 to 3 For the 89 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 “INTEGRAL program” will not get any credit – where is the set up? For a verbal explanation, don’t say, “the function is going up, therefore it is increasing.” Use calculus words, like the “derivative is positive, so the function is increasing#92. Where is
between -1 ≤x≤3 decreasing
AB2003#1
2003AB#83
In summary – clearly demonstrate that you know calculus