Monthly Schedule

(AP Calculus AB, Period D)

M 2/2/04	Groundhog Day. If for some reason there is no class today, the Form V students and anyone who is having difficulty should still check in for extra help. Your HW on slope fields and Euler’s Method was posted at 6:15 p.m. Sunday.
T 2/3/04	HW due (70 minutes): Read §7-4 and §7-5 (reading notes required); write §7-2 #6a-e, §7-4 #2, 4. For the two problems in §7-4, do not use a photocopy, and do not write directly in your textbook; instead, sketch the slope field and the requested solutions on your HW paper. Remember, for the AP exam you need to be able to sketch slope fields. You will find that the calculator programs described below make everything except for #4(c) quite easy. The following calculator programs are required as part of your Homework and a Half: SLOPES and EULER. You may either key these in manually, following the instructions provided, or get them via link cable from a classmate. There are several slight typos in the instructions that you can report for bonus points if you are the first to find them. Please note: SLOPES and EULER, or programs similar to them, will be required for the work we do in the days ahead. If you cannot figure out how to key in or download SLOPES and EULER, then you must use the resources of the Internet to locate comparable programs on your own. (You are also welcome to write your own programs if they provide similar functionality.) Both SLOPES and EULER work correctly on any of the following calculators: TI-82, TI-83, TI-83 Plus. For the calculator portion of your HW scan, you will be required to demonstrate (on your calculator) the slope field for y ¢ = –.8y/x with the Euler’s Method solution overlaid, using initial condition of (1, 3.5) and step size of .05. Set your graphing window for [–5, 5] ´ [–5, 5]. You will have to read the instructions for the programs in order to figure out how to do this. The notation f (X, Y) used in the instructions for both programs means that you should put the dy/dx information, which is a function of x and y, into your calculator’s Y1 function. For example, to plot the slope field and Euler’s Method solution for y ¢ = –.8y/x, you would press the “Y=” button on your calculator and key in the expression –.8Y/X for Y1. That’s all it means.
W 2/4/04	HW due: First and most important, patch up your homework that was supposed to be finished yesterday. Then, for the diffeq. y ¢ = –.8y/x, use the keystrokes we discussed in class (reproduced below) to fill in an Euler’s Method table for 5 steps, using Dx = h = –.03 and initial condition (–2, –4.7). In other words, your final answer should give an estimate for the point where x = –2.15. Then solve the diffeq. using pencil and paper and compare the Euler estimate with the true value. Is the Euler estimate too high or too low? Does this make sense in view of the local concavity that the solution has? Keystrokes: [step size]®H    [For example, if the step size is –.03, you would key in –.03®H ENTER.] [initial x value]®X [initial y value]®Y [diffeq., for example, –.8Y/X]®Z Y+ZH®Y X+H®X 2nd ENTRY [repeat as necessary to iterate the last 3 commands] In case you took incomplete class notes, remember that your table should contain the following columns: i, xi, yi, dy/dx, and yi + 1 = yi + Dx · (dy/dx).
Th 2/5/04	CFU (ungraded quiz) on Chapter 7. Closed book, open notes. Please note that I revised yesterday’s calendar entry to make the keystrokes somewhat more informative. (Of course, those who took careful class notes probably already understood what was meant.) The remainder of class will be spent on review.
F 2/6/04	HW due: Read §8-2; write §8-1 #1-5 all, plus the following exercise: Trace the curve found in Fig. 8-2n on p. 360, and mark the 8 solid points and 1 open circle found there. Then close your book and practice identifying the points according to their characteristics (point of inflection, cusp, minimum, etc.) and the concavity for the intervals between points. Write your answers down, and then check them against the textbook.
Weekend	You should work review problems from the ends of Chapter 6 and 7. You should also work problems from your AP review book, and it would be a good idea to re-take a blank copy of Thursday’s CFU to make sure you can do it quickly and with facility.
M 2/9/04	Test on Chapters 6 and 7, omitting §7-6.
T 2/10/04	HW due: Read §8-3 and read §8-2 #39; then write §8-2 #3-36 mo3.
W 2/11/04	HW due: Write §8-3 #1, 3, 9, 11, 13, 18, 19-23 all. Do as many as you can, and save the rest for the next day. Leave placeholders if you must, or call a friend, but at least make a diagram and algebraic setup for each one. Leave lots of space for later markups.
Th 2/12/04	HW due: Read §8-4 and finish the HW problems previously assigned in §8-3. In class: Pop quiz (10 pts.) with instant grading.
F 2/13/04	No school (faculty professional day).
M 2/16/04	No school (holiday).
T 2/17/04	HW due: Read §8-5; write §8-4 #3-15 mo3, 16, 19. In class: Pop quiz (10 pts.) with instant grading.
W 2/18/04	HW due: Write §8-5 #Q1-Q10 all. Although we have not yet discussed §8-5, you may use your remaining time to start working on Thursday’s problems. However, I would rather that you devote your time to patching up your problems in §8-4 from yesterday. Tonight, please set aside extra time to work on the calculus. The problems in §8-5 are quite challenging.
Th 2/19/04	HW due: §8-5 #2, 3, 5, 6, 13, 19. Also finish the proof (approx. 2 lines of straightforward algebra) to show that Vsquare pyramid = s^2h/3. We were almost finished with this when time ran out. Many students will find this assignment to be the hardest material of the entire year. A Math Lab visit may be appropriate. In class: Pop quiz (10 pts.) with instant grading.
F 2/20/04	Review day. No additional written HW due, but a minimum of 35 minutes of additional work on §§8-3 and 8-5 will be expected. In class: Pop quiz (10 pts.) with instant grading.
M 2/23/04	HW due: No reading assignment. The green boxes on pp. 492-493 are somewhat useful but include many techniques that are not required in the Calculus AB curriculum. Write §9-11 #1, 5-9 all, 13-18 all, 21, 22, 25, 26, 37, 38, 41, 42, 45, 46, 49-52 all, 57-59 all, 61-66 all, 69-78 all. If this assignment takes you longer than 45 minutes (i.e., 1 minute per problem), then you definitely need to do some heavy-duty review before the AP examination in May. Circle the troublesome problems and resolve to find out where your areas of uncertainty lie. If you do not have 45 minutes to spend, then spend 35 minutes patching your §8-3 and §8-5 problems, which are more critical for tomorrow’s test. (Keep a time log.) Or, if you prefer, you may split your time 20 + 20 between both tasks.
T 2/24/04	CFU Test on Chapter 8 (§§8-1 through 8-5 only). This is a required item, although it will not be graded. You should grade your own paper so that you can tell exactly how well you are doing. Answer key Multiple choice, Part A (no calculator): 3 C, 5 E, 11 E, 13 A, 15 B, 16 D, 22 D, 23 A. Multiple choice, Part B (with calculator): 77 D, 78 D, 82 B, 83 C, 84 C. Free response: Scoring key was distributed. If you forgot to pick yours up, see me or a classmate.
W 2/25/04	HW due (everyone): Finish your problems from Monday. If you already finished them (hopefully this is the case), then spend at least 35 minutes rewriting most of them on a fresh sheet of paper. Practice to build your speed and proficiency. Additional HW due (extra-time students only): Finish the free response portion from yesterday’s test. In class: Answers to most of the §9-11 problems.
Th 2/26/04	HW due: Score your CFU test. Use the answer key that was posted Tuesday, the free response key that was distributed Tuesday, and the instructions below. Some of you also have some older problems to make up. As I mentioned in class Wednesday, it has been a while since I have re-scanned any old problems, and I am itching to do some of that. Multiple choice: 4 points for each correct answer, –1 for each error, 0 for each omission. Maximum possible: 52 points. Free response: Use the AP scoring rubric that was distributed Tuesday. Note that there are no half points. Multiply your score (0-9) by 4 in order to get a number from 0 to 36. Then, after doing that multiplication, add 1 point for each situation in which you were robbed by the AP rubric. (Example: You wrote the limits of integration backwards, or you rounded incorrectly.) Remember, this is the sort of adjustment which I sometimes make but which the AP does not make. Add your two scores and convert to a letter grade: 81–88 = A+ 75–80 = A 69–74 = B+ 62–68 = B 56–61 = C+ 50–55 = C 44–49 = D+ 37–43 = D 36 or below = F Circle your letter grade and place it prominently on your test paper where I can see it when I scan your homework. The grade will not be scored; only the fact that you computed the grade will be scored.
F 2/27/04	HW due: Read §9-10; write §9-10 #1-16 all, 18-21 all.

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Last updated: 02 Mar 2004