Monthly Schedule

(Geometry, Periods E and F)

M 1/3/05

HW due: Read in Chapter 8 and the remaining portions of Chapter 7, as you are able. No reading notes are required at this time. More importantly, though, you should be working on the study guide and practice midterm exam for at least half an hour per day for most of the days during the break. That is more effective than working for an entire day all at the very end.

Answer keys for odd-numbered problems, even-numbered problems, and the fill-in-the-blank study guide at the beginning of the practice exam are available by e-mail request. In your request, please state which portion(s) you have completed and which answer keys you would like. Please send your request from the same e-mail address you placed on file with me at the beginning of the school year.

 

T 1/4/05

HW due: Read §§7.3 and 7.4 (reading notes required, as usual). If you did not follow the lightning-fast coverage of §8.1 that we did in class yesterday, you should also write out a few of the exercises in §8.1.

 

W 1/5/05

Quiz (10 pts.) on §8.1 and the easier aspects of §§7.3 and 7.4. You may use a formula card for the formulas that are new, such as each exterior Ð of a regular polygon = 360°/n. Diagonal counting will not be quizzed, since we have not discussed that formula in class yet.

HW due: §7.3 #1, 2, 6, 8, 10; §7.4 #2, 5, 7, 13.

 

Th 1/6/05

Review for midterm exam. If you have not already done so, please work on the study guide and practice midterm exam and bring your questions to class.

Prepare good questions. Here are some examples to help you focus your thinking.

#24 (example of a bad question to ask): “Mr. Hansen, I don’t understand this one at all.”
#24 (somewhat better): “Mr. Hansen, I have written the equation 3x + 4x + 5x + 6x = 360, but I don’t know what to do next.”
#24 (good): “Mr. Hansen, I have made a diagram, and after doing some algebra, I was able to show that the consecutive angles have measures 60, 80, 100, and 120. I know that I can rule out choices B and E—B is false since a kite must have at least 2 congruent angles, and E is false since all the angles have measure less than 180. However, I am having trouble deciding among choices A, C, and D.”

As you may have noticed by now, here are some of the things that make the midterm exam difficult:

1. The exam is cumulative since the beginning of the year.
2. Cramming/memorizing is of little value. You actually have to think.
3. There will be no constructions on the exam, unfortunately.
4. The exam is long. Concentrating for 2 hours requires patience and endurance. Eat a meal before you start!

 

F 1/7/05

Same as yesterday.

 

M 1/10/05

Optional review session, 2:30 p.m., Room R. Because this session was not confirmed until just this morning, it may not have been possible for you to find out in time. Therefore, you may wish to come to tomorrow’s session instead.

 

T 1/11/05

Optional review session: 2:30 p.m., Room S. (Nobody came.)

Links for exam preparation:


Answer keys to the midterm study guide, midterm odd-numbered problems, and midterm even-numbered problems are available by e-mail request. In your request, be sure to specify which section(s) you have already completed. Blanket requests, or requests based on hoped-for future completion of problems, will not be honored. Of course, there may be a few copies of answer keys floating around by now among your classmates, but I would recommend that you work the problems first, under time pressure, as a way of preparing yourself for the stress of the real exam.

 

W 1/12/05

I will be on campus beginning at about 10:30 a.m. in case anyone wishes to meet with me.

Midterm Exam, 2:00 p.m.–4:00 p.m., Trapier Theater. Bring several sharpened pencils with erasers. Optional equipment: straightedge and compass. Paper will be provided; do not bring any paper or notes.

Be sure to get a good night’s sleep the night before. The hardest thing about this exam is that you actually have to think. Merely cramming or memorizing a bunch of formulas will not help you very much.

 

W 1/19/05

Classes resume.

 

Th 1/20/05

HW due: The ABT problem posed in class was overdetermined (actually impossible, as Alex W. pointed out—for a typo point). Please correct the version of the ABT problem in your notes so that it reads as follows. (Most F period students already have the corrected version. If you do not wish to write all these words out, you may simply redraw the diagram appropriately.)

Two tall rectangular buildings, each 1200 ft. tall, are separated by a gap across level ground. A woman, in a prone position atop one building, aims a laser rangefinder from the top corner of her building to the ground corner of the other building. The rangefinder reports a corner-to-corner distance of 1500 ft. between the two buildings. If the angle of depression from the horizontal is bisected, the laser hits the other building at a point h ft. above the ground. Determine the width of the gap (using the Pythagorean Theorem) and then the value of h.

Solution: Let w = gap width. By the Pythagorean Theorem, w2 + 12002 = 15002. The arithmetic is super-easy if you write the length of each side in terms of football fields: w2 + 42 = 52. By inspection, w = 3 football fields. Then, if h = height of bisector above ground, then 1200 – h = remaining height of building. Mark the diagram, write a proportion, and solve for h. (Finish this up.)

Additional Problems: Write §7.3 #13, §8.5 #14, 16, 19a. Also find the typographical error on p.308 (not for a bonus, since it was found several years ago, but as part of your homework assignment).

 

F 1/21/05

HW due: §8.2 #1, 2, 3, 6, 7, 14; §8.3 #4, 8, 9, 10, 16. No reading notes are required this time.

Also due: Bring your Pentagon information slip if you have not already done so.

 

M 1/24/05

HW due: §8.4 #15, 18, 19, 20. No reading notes are required. This assignment is shorter than usual, so that you will have time to finish up any missing problems from Friday’s assignment.

 

T 1/25/05

HW due: Read §8.5 (reading notes required, as usual); write §8.5 #2, 3, 4, 6, 7, 8, 11.

 

W 1/26/05

Quest (50 points) on Chapter 6. This should be fairly straightforward, since you have already had an exam on this material, and there is only one significant theorem in Chapter 6 (namely, the one we discussed in class Monday). You need to know the four ways we have of determining a plane.

Before the quest, we will have some time for review.

 

Th 1/27/05

Quest on Chapter 7 (50 points). There will be a brief time before the test for questions.

 

F 1/28/05

Quest on Chapter 8 (50 points). Because today is a short period, there will be no time for questions beforehand.

 

M 1/31/05

HW due: Read §9.1 (reading notes required) and answer questions 1-4 below. The questions are based on “calculator-style” digits as depicted.

 

:

 

1.                    How many years between 1500 and 2099 have rotational symmetry? (Rotational symmetry, in this context, means that the object looks the same when turned upside down, i.e., rotated 180° about its center.) For example, 1551 has rotational symmetry, since the number looks like 1551 even when viewed upside down.

2.                    How many years between 1500 and 2099 have bilateral symmetry? (Bilateral symmetry, sometimes called “left-right symmetry,” means that the left half of the object is a mirror image of the right half. Human beings do not have bilateral symmetry (since our internal organs are asymmetric), but we appear to have bilateral symmetry when viewed externally. For example, our left hand looks like a mirror image of our right hand. One year that has bilateral symmetry is 1521.

3.                    How many years between 1500 and 2099 have “up-down” symmetry (i.e., can be divided by a horizontal line into two mirror images)? An example would be 1808.

4.                    How many years between 1500 and 2099 are on both list #1 and list #2?

 

For each question, make a list.

 

 

Return to the Geometry Zone

Return to Mr. Hansen’s home page

Return to Mathematics Department home page

Return to St. Albans home page

Last updated: 02 Feb 2004