Monthly Schedule

(Geometry, Periods E and F)

T 2/1/05

HW due: Write §9.1 #1-9 all, 13.

 

W 2/2/05

HW due: Read §9.2; write §9.2 #1, 2, 4, 5.

In class: Geometry, plus the importance of definitions, the IRS, parabolic mirrors for flashlights, ellipsoidal whispering chambers, sidereal time, the amazing wealth of Bill Gates, tort reform, abusive tax shelters, and the American political process.

 

Th 2/3/05

HW due: Read §9.3; write §9.3 #1, 2, 3.

In class, do the following:

 

1.   Go over the answers to §9.1 #5-9 plus 13, either individually or as a class, whichever seems to work better. These problems were previously assigned. Here are the answers:
5a-f. ±5, ±12, ±13, ±½, ±2Ö3, ±3Ö2
6a-f. ±3, ±8, ±5, ±3, ±4, ±4Ö5
7a. x Î {–1, 6}
7b. x Î {–6, 2}
7c. x Î {3, 5}
7d. x Î {–3, 6}
7e. x Î {–3, 12}
7f. x Î {–4, 9}
8a. x Î {0, 4}
8b. x Î {0, 10}
8c. x Î {0, 13}
8d. x Î {0, 8}
9a. x = 20 (reject –20 since x is a length)
9b. x = 2Ö3
9c. x » 8.2 (leave answer as Ö(4.12 + 7.12) if you have no calculator)
13a-d. –h, 3 – x, pq, –x1.5y
Note for #13a: |h| is also acceptable, since |h| = –h if h < 0

 

2.   Do §9.2 #4, 5, 6, 10. Two of these were previously assigned. Hint: If you did not read the bottom of p. 372, you’d better read it now.

 

3.   If possible, use Dr. Bennett’s visual aid (the colored triangles with pushpins) to see why Theorem 68 on p. 378 follows immediately from similar triangles. We did not really get to this yesterday. If Dr. Bennett’s visual aid is not available, then look at a reasonable facsimile.

 

4.   Work on tomorrow’s HW.

 

F 2/4/05

HW due: Read §9.4; write §9.3 #4, 14, plus any of the problems you did not finish from yesterday’s in-class work and before.

 

M 2/7/05

HW due: Read §9.5; write §9.4 #7-13 all, 17.

 

T 2/8/05

No additional HW due. However, make sure all previously assigned HW and class notes are up to date. If you ran out of time previously (by hitting the 35-minute mark), you need to log another 35 minutes of work.

 

W 2/9/05

HW due: Write §9.5 #1, 3, 4, 5, 14.

 

Th 2/10/05

HW due: Write §9.5 #16, §9.6 #1-5 all (no work required; just jot down the answers), 10, 11, 16, 18. Do show work for the last four problems.

 

F 2/11/05

HW due: Write §9.6 #1-4 all (no work required), 5, 14, 20, 21. Optional reading assignment: §9.7.

 

M 2/14/05

HW due: Review problems: pp. 429-433 #1, 3, 5, 6, 7, 11, 12, 16, 17, 23, 24, 27, 28, 31.

In class: Review for test.

 

T 2/15/05

HW due: Please finish your review problems if you have not already done so.

In class: Write §9.8 #1, 2, 3. As you study for tomorrow’s quiz, be sure to check out the answer key below.

 

W 2/16/05

HW due: Read §9.8; write §9.8 #1-7 all. If you did #1, 2, and 3 in your notebook during class, you do not need to write them out a second time. However, all 7 problems are subject to being scanned, and since we went over #1, 2, and 3, those should all be complete and correct.

Quiz (50 points) on Chapter 8. This will be essentially a rehash of the other Chapter 8 quiz, on which many students scored poorly. Those scores will stand. However, today’s quiz gives you an opportunity to dilute those scores by (let us hope) acing the quiz this time. The test on §§9.1–9.7, which was originally scheduled for today, is now postponed until “Twosday” (2/22).

Answers and some brief explanations for the original Chapter 8 quiz (n = 23, sample mean = 71.6%/C, standard deviation = 15.7%):

1. 20:75, or 4:15 (Note: This ratio has no units. It is incorrect to say “cents” after giving the ratio.)
2. 120:30, or 4:1
3. (12.6 + 7.4)/2 = 10
4. Ö(12.6 · 7.4)
5. CW/OW
6.  (We did problems of this type in class on Monday, 1/3.)


7. 29:2
8. DO/ON
9-13. True, False, True, False, True
14. 13.2 (use Angle Bisector Theorem to get RS, then use TR + RS to get TS)
15. 35
16. 4.5 by Side-Splitter Theorem
17. 15 by similar triangles (Note: You cannot use Side-Splitter here, since y and 22.5 are not split.)

18. Let sides of unknown rectangle be 7x and 12x, so that the perimeter is 7x + 12x + 7x + 12x = 38x. Since 38x = 95, x = 95/38, and the smaller side is 7x, namely 7(95)/38, or 17.5 if you simplified.

19. Many people assumed DAEB ~ DDEC to get 9/6 = 12/CE Þ CE = 8. However, this is completely wrong. The actual pair of similar triangles (using alt. int. Ðs and AA~) should be DAEB ~ DCED. Therefore, 8/9 = CE/12, which gives 9CE = 96 Þ CE = 96/9 = 32/3.

20. 6.5 feet (Note: Because we had covered this exact type of problem multiple times in class, no partial credit was awarded for the incorrect solution based on the improper use of Side-Splitter. You cannot use Side-Splitter here; you must instead use the proportion 15/(13 + x) = 5/x, which is based on similar triangles.)

21. m = rise/run = Dy/Dx = 6/8 or 3/4

22. Since m = Dy/Dx, we can use the given information (namely, Dx = 4) to solve very quickly for Dy. By algebra, Dy = m Dx = (3/4) (4) = 3. This is the same technique that we were using in class to find the change in elevation for a highway. For example, if you drive for 4 miles on a highway that has a 10% grade, your change in elevation equals Dy = m Dx = (.10) (4) = .4 miles, or approximately 2000 feet. That’s quite a change in elevation!

 

Th 2/17/05

HW due: §9.8 #14, 19. Most of you finished these during class yesterday.

In class: Review. Over the weekend, please check all the answers to the review problems.

 

F 2/18/05

No school.

 

M 2/21/05

No school.

 

T 2/22/05

Test on §§9.1–9.7. As you prepare for your test, please check all of your review problems against the answer key.

 

W 2/23/05

HW due: Read §9.9 (reading notes required, as always) and the SOHCAHTOA Details. Then perform the following exercises:

Sketch a right triangle (wlog) with right angle at point C. Place point A to the left of point C (along a horizontal line), and place point B above C (i.e., on a vertical line). Label the hypotenuse as c, the side opposite ÐA as a, and the side opposite ÐB as b. Prove the following extremely useful facts:

1. a = b tan ÐA (In English: We can find a by multiplying b by the tangent of angle A.)
2. b = c cos ÐA
3. c = a / (sin ÐA)

 

Th 2/24/05

No school (snow).

 

F 2/25/05

HW due: §9.9 #1, 2, 3, 4, 10, 13.

In class: Trigonometry factory.

 

M 2/28/05

No school (snow).

 

 

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Last updated: 02 Mar 2004