Right and Wrong Ways to Use your calculator on the AP Calc Exam Notes taken by Sean Bird at Greg Hill’s ghill@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@covenantchristian.org http://covenantchristian.org/bird
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 won’t make the answer any more correct (even in a long Riemann sum). 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. Remember: 3 decimal places, rounded or truncated. (More is ok.) 8. 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 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 How many relative extrema does f have on the interval 2<x<4? 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
81. Let f be the function with the derivative How many relative extrema does f have on the interval 2<x<4? 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? From the graph we can see that f ‘ changes sign four times in the interval…. Answer is D What is significant about these points?
#92. Where is g(x) decreasing between -1≤x≤3 Graph Derivative (see where negative) 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]
#92. Where is g(x) decreasing between -1≤x≤3 Doing this on the TI-Nspire, finding the zeros is quite easy. 1. Open up a G&G (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)
AB2003#1 Free Response find area between curves & volume about y=1 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 don’t count off for dx) Especially with 83/84, decrease mess by using Y1 and Y2, e.g. fnInt(Y1-Y2,x,0,x)
#76 v(t) = 3 + 4.1 cos(0.9t). What is a(4)? Don’t make the common mistake of putting in t=4, before you take the derivative!! #76 v(t) = 3 + 4.1 cos(0.9t). What is a(4)? On the 83/84 nDeriv(3+4.1cos(.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.
2003AB#83 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 For the 89 On the TI-NspireCAS, use SHIFT+, g+, as a shortcut for the integral template. Gives the approximate answer when you’re in AUTO
2003AB#84 Initial temp is 350 degrees Fahrenheit (F) 2003AB#84 Initial temp is 350 degrees Fahrenheit (F). The temperature of the pizza is changing at a rate of T(5)=? (A) 112F (D) 238F Don’t need to remember Newton’s Laws of Cooling. Area under a curve. Integrate from 0 – 5. Don’t be so quick that you are careless. On the 83/84 fnInt(-110e(-.4x),x,0,5) = -237.783 For the 89 Don’t forget to add the initial 350.
2001AB#2 Never use STAT PLOT on the AP Calc Exam
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, 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
Note to teacher: MAKE 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