|
M
2/2/09
|
HW due: Write review problems on pp. 429-433 #4-7
all, 9, 11-17 all, 20, 21, 23-31 all. It is assumed that you will finish most
of these. If there are any you cannot finish for today, be sure to finish
them as part of your review for tomorrow’s test.
In class: Review.
|
|
|
T
2/3/09
|
Test (100
pts.) on all of Chapter 9 except for Trigonometry. There will be at least one coordinate geometry
proof, and you will be required to sketch a rectangular solid and its
diagonal in 3-D.
|
|
|
W
2/4/09
|
HW due: Correct your old HW problems by checking hwstore.org, and do both of the following coordinate
geometry proofs that were featured on yesterday’s test.
21. Using a coordinate geometry proof, show that the figure formed by joining
the midpoints of any rectangle is a rhombus. Important: Your rectangle must be wlog.
22.(a) Plot the points A(0, a), B(b, 0), C(0, –a), and
D(–b, 0) on a coordinate plane. For
full credit, label the points with both their letter names and their
coordinates.
(b) Write
a sentence (or at most, two sentences) to explain why the points you plotted
in (a) form the vertices of a rhombus. A proof is not expected.
(c) Is the
rhombus defined in (a) wlog? ______ Explain briefly.
(d) Write
a coordinate geometry proof to show that the midpoints of the sides of
rhombus ABCD, if joined in order, form a rectangle. Two-column format is not
expected.
|
|
|
Th
2/5/09
|
HW due:
1. Read §10.1; write §10.1 #2.
2. Make sure that all old HW is corrected by checking hwstore.org. A few problems may be
spot-checked for accuracy.
3. Unless you know for certain that yesterday’s version was correct, use your
in-class notes to re-do #22 from yesterday’s assignment. (Use a clean sheet
of paper.)
|
|
|
F
2/6/09
|
Make-Up
Test for All Seven Students Who Were Absent Tuesday (100 pts.) will be held at 7:00 a.m. in our regular classroom.
If you cannot make this date and time, or if you think you are still going to
be sick, please e-mail me immediately or leave a message on 24-hour voice
mail, 703-599-6624.
HW due: Read §10.2; write §10.2 #6, 8, 11-15 all. You should have this
assignment (and be able to show good progress), but because of the vast
number of people absent, the assignment will not be collected until Monday.
|
|
|
M
2/9/09
|
Make-Up Test
for the Four Students Who Were Absent Tuesday and Also Absent Friday Morning
(100 pts.) will be held at 7:00
a.m. in our regular classroom. If you cannot make this date and time, or if
you think you are still going to be sick, please e-mail me immediately or
leave a message on 24-hour voice mail, 703-599-6624.
HW due: Read §10.3; write §10.3 #1-4 all, 11, 12, 15, 25. The assignment due
last Friday will also be collected.
If you are unable to complete both assignments, then you should have the
following words and headings copied (yes, copied) into your notes:
Everything I need to know from §10.1:
- Let l
be a line, C the center of a circle, p
a proper chord. (A “proper chord” is a chord that is not a diameter.)
- (l contains C)
 (l  C)  (l contains C) (l bis. p)
- (l p) (l bis. p)
 (l contains
C)
Everything I need to know from §10.2:
- chords
 chords equid. from ctr.
Everything I need to know from §10.3:
Note that §10.2 and §10.3 can be linked together to
form a “theorem ring” of 8 theorems yielding a bonanza of interlocking
definitions: chords arcs central
 s chords
equid. from ctr.
|
|
|
T
2/10/09
|
HW due: Read §10.4; use the remaining time to patch
up your previously assigned problems from recent days.
Problems covered in class (even if in a sketchy format, as were some of the
proofs) should now be in final form. Also, note that the assignments that
have been posted on hwstore.org should be fully
corrected, in perfect shape, ready for a spot-check of any problem. If the
only way you can get a problem is by emulating what is posted in hwstore.org,
then that is what you will have to do, though of course you should first make
a solid try. Without making the solid try first, you are cheating yourself of
the chance to grow and develop fully.
|
|
|
W
2/11/09
|
HW due: Read the 33
Numb3rs handout (students in “A” period, please note corrections on second
page: 4,000 miles is the approximate radius
of the earth, and 400,000 miles is the approximate radius of the sun); read §10.5; write §10.4 #2, 4, 6, 9, 10, 16,
plus your choice of 22 or the “HUGH” Theorem below.
“HUGH” Theorem: Given lines l and m tangent to circle C at points G and
T, respectively, prove that HU = GH. (Note that line n is a secant passing through S and T.)
|
|
|
Th
2/12/09
|
HW due: Read the Angle
Equals Half SAD summary; write §10.5 #5-14 all, 18. There is no textbook
reading assignment, since we need to consolidate our knowledge before we
proceed. Please glance at the angle-arc
puzzles and more angle-arc
puzzles written by previous classes, and see if you can write even better
ones!
|
|
|
F
2/13/09
|
No school (teacher professional day).
|
|
|
M
2/16/09
|
No school (holiday).
|
|
|
T
2/17/09
|
HW due: There are two things everyone needs to do. The
third and fourth items are optional.
1. (Required.) Write a 2-column proof of the “HUGH” Theorem shown in the 2/11
calendar entry. Neatness counts. If your handwriting is poor, get a parent to
serve as your scribe, or use a word processor. You may follow one of the two
versions that were given in class last Thursday, or you may devise a
different proof on your own. Whatever path you choose, it is a safe bet that
you will find it helpful to add at least one auxiliary radius, from C to T.
If you wish, you may use a printed copy of the diagram instead of redrawing
it by hand.
Warning:
When you write your name on your paper, you are saying that you did the work
yourself. (Since a parent who transcribes your work is not adding
intellectual value, assistance of that sort is acceptable.) There is no such
thing as two people “working together” to produce what is essentially the
same proof if both are to earn full credit. I feel I must say this as a
result of a recent incident in one of my classes in which students claimed
that they were “pooling their efforts” and producing a single product.
Nonsense. If you produce a single product, even if it is on two different
pieces of paper and has superficial differences, then I conclude that either
(a) one person did the bulk of the work, and the other copied, or (b) neither
person did a full effort. Either one of those situations is an honor
violation. After all, if I hired you and a friend to carry a heavy garbage
can across the Close, and two people were required to carry it, would you
come to me and say, “I carried the garbage can by myself and deserve the full
payment”? Of course not. Yes, you did some work, and yes, you deserve some
payment (I would say 50%), but if you write your name at the top of your
paper, you are stating that you yourself deserve full credit for the work.
Ideas can be shared and exchanged freely before you start to write, but WHEN IT COMES DOWN TO WRITING OUT THE
PROOF, THE WORK MUST BE YOURS AND YOURS ALONE. OTHERWISE, YOU RUN THE RISK OF
FACING THE HONOR COUNCIL.
Incidentally, there is one
intellectually honest way to “pool your work” that would not place you in
danger of facing the Honor Council, and that would be to write in the upper
right corner of the paper the names of everyone who worked on the proof. Of
course, the credit would also be divided accordingly.
2. (Required.) Sometime after noon on Saturday, 2/14, compare all of your
second semester HW with the contents to be posted at hwstore.org. Make corrections or additions
as necessary. If you check too soon, you will not see everything that will be
posted there. Homework checks will consist of problems randomly chosen from
the second semester posted answers.
3. (Optional.) Try your hand at writing an angle-arc puzzle of your own that
contains some original cleverness not already seen in the student-written angle-arc puzzles and more angle-arc puzzles. If you do
this, you must provide a thorough description of your solution.
4. (Optional.) Work on the student-written
brainteasers from November 2004. A total of five problems are posed here,
and you should be able to answer three or four of them. The fourth part of #2
would require you to read §§9.9 and 9.10 on your own and teach yourself
trigonometry, but who knows? You might enjoy that.
Because the Feb. 3 test was somewhat more difficult than usual, I will
provide extra credit for anyone who does either or both of the optional
assignments listed above. I will not specify the number of points, except to
say that I will make it worth your while. As you know, my tests usually have
a mean of 77 or 78 and a standard deviation of 10 points. The Feb. 3 test had
a mean and median of 66 and a standard deviation of 12.
You can also earn 3 points of extra credit for visiting me after school
during the week of Feb. 16 to discuss the problems that you missed on your
test. Be sure to bring your test with you when you come.
|
|
|
W
2/18/09
|
HW due: Read the entire Common Tangent Procedure handout; write
#3abc, 5abcd found on the handout.
|
|
|
Th
2/19/09
|
HW due: Read §10-6; write §10-6 #2, 4, 7, 8, and the
two problems below.
Problem A: Given two congruent circles, A and B, each with radius of 10, and
given that the common internal tangent has length 7, find AB.
Problem B. Given two externally tangent circles whose radii are in a 3:2
ratio, find the radii if the length of a common external tangent is 9.
|
|
|
F
2/20/09
|
Test (100
pts.), cumulative through §10-6, emphasizing angle-arc techniques and
common tangent procedure. If you have worked and carefully checked the solutions to Problems A and B,
have read and worked through the Common
Tangent Procedure handout, and have solved the Angle-Arc Puzzle Collection for Review, you
should be in good shape. Other facts to be tested may include the 33 Numb3rs handout, the terms tautology
and algorithm, and various other concepts discussed since September.
Solutions to the Angle-Arc Puzzle Collection for Review are available! Choose
desired page: Page 1, Page 2, or Page 3. These solutions are also
posted at hwstore.org.
|
|
|
M
2/23/09
|
Thanks to everyone who helped me in my long,
exhaustive search for the red gradebook. I turned the campus upside down,
looking in every sensible place I could think of (and quite a few nonsensical
places as well). I went through garbage cans, took my office apart
systematically—you get the idea. Finally, at about 6:10 p.m. Friday, I gave
up and left campus, heading for Politics & Prose to buy a new gradebook.
On my way to the car, I walked past the Little Sanctuary, which Isaac W. and
I had already searched thoroughly, three times altogether. I walked straight
to one of the numerous pews where I had been sitting during the sports
assembly Friday morning, took a few hymnals and prayer books out of the pew .
. . and there it was.
Therefore, in celebration of this providential event, I am declaring a No
Homework Weekend. No additional homework is due today. Whew!
|
|
|
T
2/24/09
|
HW due: Read §10.7; write §10-7 #1-7.
|
|
|
W
2/25/09
|
HW due: Read §10-8; write §10-8 #1-12 all, 14.
|
|
|
Th
2/26/09
|
HW due: Read §10-9; write §10-9 #2-7 all, 9bc, 11,
14. Solutions to these problems (thanks to Mac!) are now posted at hwstore.org.
|
|
|
F
2/27/09
|
HW due: Review problems on pp. 505-509 #1-5 all, 7,
8, 12, 14, 17, 18, 19, 20, 23, 24, 25, 26a. After you have tried most of the
problems, check the answer key at hwstore.org,
and bring any remaining questions to class.
Over the weekend, you should finish all the review problems on your own, as
well as the additional practice
test problems (which has a detailed solution key with it). As was
strongly (hint, hint) suggested in class Friday, you should also attempt #16
on p. 507, since it is a good problem that exercises the skill of breaking a
problem into separate cases. A solution to #16 is available at hwstore.org.
|
|
