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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

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Presentation on theme: "Right and Wrong Ways to Use your calculator on the AP Calc Exam Notes taken by Sean Bird at Greg Hills"— Presentation transcript:

1 Right and Wrong Ways to Use your calculator on the AP Calc Exam Notes taken by Sean Bird at Greg Hills ghill@hinsdale86.org presentation at the T 3 International Conference in DC 2005.

2 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.

3 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.

4 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? Dont try to integrate that by hand. Dont graph the integral Speed up graphing by changing RES Graph f and look for zeros.

5 #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]

6 AB2003#1 Read the instructions (NOW)- set up! E.g. DO NOT round off till the end, i.e. store your answer On the calculator portion of the test will not have to show the integral 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. ŒfnInt(Y1-Y2,x,0,x)

7 #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 (ASIDE: Explain verbally a number line critical point beginning this year)

8 2003AB#83 v(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 For the 89

9 2003AB#84 Initial temp is 350 degrees Fahrenheit ( F). The temperature of the pizza is changing at a rate of T(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.

10 2001AB#2 Never use STAT PLOT on the AP Calc Exam

11 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 point for mc & 18 points on fr 67-108 = A

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