Monthly Schedule

(AP Calculus AB, Period D)

M 1/3/05	HW due: Read §6.1 and make written notes. Practice using the SLOPES and EULER (pronounced “Oiler”) programs that were distributed in class. However, no other written work is due.
T 1/4/05	HW due: Practice using SLOPES and EULER (pronounced “Oiler”) so that we don’t have to spend any time today talking about what button to push next. Keep a time log. Try exploring the behavior of the non-separable differential equation y′ = x + 2y as described below. 1. First, use the WINDOW key to set the graphing window to be [–5, 5] ´ [–5, 5], and store the slope information (namely x + 2y) into your Y1 function. 2. Then run SLOPES to see the slope field. Press 2nd QUIT to return to the command mode. 3. Run EULER, using (–2.5, 1.01) as your initial condition and a step size (i.e., Dx) of 0.1. Observe how the solution trajectory bends upward and to the right. 4. Run EULER again, using (–2.5, 0.99) as your initial condition and Dx = 0.1. Observe how this time the solution trajectory is completely different. 5. Challenge problem if you have time: Prove that of all the trajectories (i.e., solutions) possible for y, the only one that follows a straight line has a slope of –½ and a y-intercept of –¼. You can more or less tell this from the slope field. The challenge, of course, is proving it.
W 1/5/05	HW due: §6.1 #1-42 all. Technically, since this posting was made at 2:43 p.m., you are not required to do this assignment. However, we will go over it in class, and I would ask that you work a reasonable subset of the problems. Thank you.
Th 1/6/05	HW due: If time permits, please do §6.1 #43, 44, 53, 54 (your choice of any 3 of the 4 problems). Otherwise, please focus on finishing up the problems from Tuesday and Wednesday. In class: Midterm exam review.
F 1/7/05	No additional HW due. However, bring all previously assigned HW to class for a general spot check covering the second quarter. In class: Midterm exam review (continued).
M 1/10/05	Midterm Exam, 11:00 a.m.–1:00 p.m., Room S. Bring several sharpened pencils, your calculator, and spare batteries. Paper will be provided; do not bring any paper or notes. Just as on the AP exam, you will not be allowed to swap calculators during the exam, and if your batteries die, they die. A sample exam is available. Note that this exam was designed for BC students and is therefore somewhat harder than the one you can expect to see. You should be able to do all of the problems except for 9(b) and 13(e). Helpful references: A blank copy of the Chapter 5 test (standard version) and the answer key are now available. Also, in case you did not obtain a copy of the EULER2 program in class last Friday, here is a revised and improved version of EULER2. Format of the real exam will be as follows: 1. The first half will be multiple choice, with calculator. Budget 2 to 3 minutes per question (3 to 4½ minutes each if you have extended time). Here are some multiple-choice practice questions with an answer key. When you have finished those, here are more multiple-choice practice questions with an answer key. Consult the Barron’s, Princeton, or similar AP review books for additional examples of questions you may expect to see. 2. The second half will include essay questions, fill-in-the-blank questions, and free-response questions requiring algebraic computation. No calculator will be permitted on the second half. Also, please read the fairly complete midterm study guide. I will take questions up until 6:30 p.m. on the day before the exam.
W 1/19/05	Classes resume. In class: Group work to answer the multiple-choice exam questions 100% correctly.
Th 1/20/05	HW due: Reading is optional, since we have already covered “u substitutions” and separable diff. eqs. in class. Write §6.1 #53, 54, §6.2 #2-28 even, 5, 11, 39-44 all.
F 1/21/05	No additional HW due. However, finish all the problems that were previously assigned.
M 1/24/05	HW due: Read §6.4 (reading notes for 2 pts. extra credit). No additional written work. Send e-mail or voice mail if you are stuck on #39-44 of the previous HW set. Please note that we are mostly skipping §6.3, since it is on the syllabus for AP Calculus BC, not AB.
T 1/25/05	HW due: Read §6.4 if you have not already done so. Extra credit (2 pts.) for your choice of one (1) of the following: Make good-quality §6.4 reading notes (far beyond the mere copying of the highlighted boxes that so many people did for yesterday), or write §6.3 #2, 4, 8, 10. What constitutes “good-quality” reading notes? For starters, when the book contains a marginal comment such as the one in the middle of p. 331, you should at a minimum see whether the statement is reasonable, either by using algebra or by performing a calculator investigation and tabulating your results. When a yellow box, such as the one on p. 332, is closely related to a fact that we have already investigated in class (“Rule of 72”), you should not simply parrot the yellow box in your notes; you should actually prove it. Finally, if you choose to include an equation such as equation (1) on p. 333 in your notes, you should define all of the symbols clearly and write a plain-English description of what the equation means. Otherwise, you are simply wasting your time. I would also expect that for any worked example in the text, you choose a similar problem from the exercises and practice making the “switch-and-compare” substitutions in your reading notes. Moral of the story: Reading notes, if done correctly, require a fair amount of time and effort.
W 1/26/05	HW due: Read §6.4 and write good-quality notes. (See yesterday’s entry for what constitutes good-quality notes.) The other part of your assignment is to answer the midterm multiple-choice questions to the best of your ability. The majority votes for the first 11 questions were EDBBA CBBBA E. Normally, I would not allow you to compare answers. However, since nobody has come up with a completely correct set of answers yet, and since not even the “majority answers” listed above are completely correct, I feel that it is safe to allow you to compare answers. We will score this as a 16-point homework. I will go around the room and ask you to list your answers. At the end, we will see who has a perfect score of 16/16, or if nobody does, we will see if we can correct (as a group) the paper that is the closest to perfect. Please remember that there is a penalty of 25% for each wrong guess. Therefore, it is not to your advantage to guess unless you can positively rule out one or more of the choices, and then you should make a random choice from among those that remain. If you are absent today for any reason, e-mail your set of 16 answers to me before the start of class. If you do not wish to make a big effort, you may use your group’s choices. Most of the groups had managed to achieve a score of at least 11/16 (12 right, 4 wrong) when time ran out yesterday.
Th 1/27/05	No additional HW due today. Make sure your reading notes are up to date, through §6.4.
F 1/28/05	HW due: §6.3 #2, 4, 8, 10, 12, 14.
M 1/31/05	HW due: §6.4 #1-10 all, 12, 14-18 all, 22, 24. For #5-10, also report the doubling time based on the Rule of 72. In class: Review.

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Last updated: 02 Feb 2005