Geometry / Mr. Hansen 5/30/2010

Name: _________________________

Final Exam Format and Information Sheet

When and where: Wednesday, June 2, 11:00 a.m., Trapier Theater.

No calculator is allowed. Leave your phone, Blackberry, etc. outside the exam room or on the table at the front of the room.

What to bring:

• Several sharpened pencils
• Several erasers
• Straightedge
• (Optional) formula card with up to six (6) formulas of your choice. No other notes or scratch paper of any kind may be brought in. Approved scratch paper will be provided with your exam booklet.

Problems on the exam will focus on Chapters 8 through 14. However, you cannot forget the basic concepts from the first semester: complementary angles, supplementary angles, degrees/minutes/seconds, SSS, SAS, ASA, HL, PBT, “iff,” converse, inverse, contrapositive, etc. In the second semester we added AAS, altitude-on-hypotenuse theorems, angle-arc theorems (“Half SAD” and “near chunk–whole chunk”), the Pythagorean Theorem and its converse, families of triangles, trigonometry, coordinate geometry, locus, and many other concepts. Specific techniques that we learned included the distance formula, the midpoint formula, the slope formula, the point-slope equation of a line, the equation of a circle (including completing the square), walk-around problems, the external common tangent procedure, and the internal common tangent procedure.

All area and volume formulas that we studied are fair game for the exam. Since there are quite a few, you can use your formula card to reduce the load on your memory somewhat. See the 4/14 and 4/27 calendar entries for some long though not exhaustive lists. The entry for 4/27 even includes an answer key that you can look at.

You may wish to add the following to the second list: area of a regular polygon (), area of a sector (prorating factor times ), area of a circular segment, and, maybe, LSA of a right prism (ph). That last one is probably a waste of ink, since you can always use common sense in a situation like that.

Your numeric semester grade is computed as follows: 0.4(Q1 average) + 0.4(Q2 average) + 0.2(exam).

This year, there are no always/sometimes/never questions on the final exam, and there are no clock problems.

Trigonometry is tested in several places on the exam, but the numbers have been chosen to be super-easy to work with, even without a calculator. For example, can you multiply 40 by 0.75 in your head? I certainly hope so. Three-quarters of 40 is 30. And even if you need pencil and paper to do that, you should need only a few seconds longer than the students in other classes that are allowed to use calculators.

A trig table is provided on the second page of the exam booklet.

Because multiple-choice questions are always harder than students think they are, you will be allowed to omit several questions in Part I without penalty. (If you wish to answer them anyway, you can earn a few bonus points.) You should pace yourself and should allocate about an hour and 20 minutes to Part I. If you rush through it or guess too much, your score will suffer. DO NOT GUESS UNLESS YOU HAVE TO. If the answer choices are numbers, then always work the problem first, before looking at the possible answers.

In Part II, the first free-response question is a compound locus problem. Watch the compound locus video again if you need more practice.

The second free-response question is a 2-part coordinate geometry proof. Watch the coordinate geometry proof video again if you need more practice.

The third and final free-response question is a proof based on regular polygons. Make sure you know all your terminology: radius of a polygon, apothem, circumscribed circle, inscribed circle, external angle, central angle, etc. Although a 2-column proof format is permitted, it is not required. You may use any clear, coherent proof technique that you wish. It would be desirable if you put “Q.E.D.” or the Halmos sign at the end of your proof, but if you forget, there will be no point penalty. It is a long, comprehensive exam, and summer beckons.

The point penalties you do need to be concerned about are the penalties for unnecessary interruptions and unnecessary questions. Read the instructions on the cover page, and ask questions in the time provided before the silent part of the exam begins. After the exam starts, points will be deducted for talking, calling out (please raise your hand and wait quietly instead), making a disruption, or asking questions that have already been answered. No hints will be provided. If you find a typographical error that you think makes it impossible for you to continue, mark the error, explain your reasoning, and move on. In fact, the only reasons I can think of for raising your hand would be if you have a medical emergency or see someone else trying to cheat.

Below are presented the first 2 pages and a fragment of page 3 from the actual exam. If you read these now, you will be bored and will have nothing to do during the first few minutes (while everyone else reads the instructions, before we start the exam). However, I am providing this information to you in case you find it comforting to see it in advance. Much of what is on the cover page repeats information given above.

Ms. Dunn, Mr. Carozza, Mr. Hansen 6/2/2010

Name: _____________________________ Initial here after reading instructions below: ____

Geometry Final Examination, Chapters 8-14

Exam Rules (failure to comply may result in point penalties or Honor Council action):

• Wait! Read over this cover page until you are instructed to open your test booklet.
• Mark multiple-choice answers using capital letters only. Make your letters medium-sized, so that they are not visible from a distance.
• No notes other than your formula card are allowed. A trigonometry table is provided.
• No calculators, electronic devices, or unapproved scratch paper of any kind are allowed.
• Unless you have permission from a proctor, do not stand up until you have finished.
• If you finish early, please walk quietly to the front. Scratch paper must also be turned in.

Exam Manners (1 point may be deducted for each infraction):

• Be quiet during the exam and during the announcements at the beginning. No talking.
• Raise your hand if you have an important question. A proctor will assist you within a short time. Do not ask minor questions or questions that have already been answered.
• If you have a medical emergency or need to use the restroom, raise your hand.
• If you find the wording unclear, please make your best effort. (It will cost you 1 point to have a proctor come over to you and say, “Sorry, you’re supposed to know that word.”)
• If you find a serious typographical error that you feel makes it impossible to continue, then mark the problem and explain your reasoning. Then, go on to the next problem.
• Please do not ask for hints. No oral hints will be given. However, you may omit up to 6 multiple-choice problems without penalty, as described below.

Suggestions for scoring higher:

• For scratch work, use the margins, the blank areas of your sheets, or the approved scratch paper provided. You will score higher if you work each problem in Part I carefully, even though the work is not graded in Part I.
• Do not rush through Part I (the multiple-choice problems). Always pick the best choice.
• If you cannot solve a multiple-choice problem, then make a guess, circle it, and move on. However, take your time. You have the skills to solve all the problems, though admittedly some of the problems require you combine skills in new or unusual ways.
• For any multiple-choice problem involving computation, it is usually better to solve the problem first, before looking at any of the choices. Be sure to answer the question posed!
• The last three problems (worth 10 points each) are free-response and require you to explain your reasoning. Write in the space provided, or write “BACK PAGE” if you need to continue on the back of the last page. If for some unforeseen reason you need even more room, write “SEE SCRATCH” and continue on the approved scratch sheets.

Allocation of points (109 total points, scored out of 100 possible with up to 9 bonus points):

• Multiple-choice (52 problems, 1½ points each, 78 points total). You are not expected to answer all 52 correctly. You can omit 6 problems and still earn a perfect score. However, since there is no penalty for guessing, you might as well try all 52.
• Free-response (3 problems, 10 points each). Problem #53 involves compound locus, #54 is a coordinate geometry proof, and #55 is a proof involving regular polygons. You are expected to do all of these.
• Initials at top of exam booklet (1 point).

Table of Trigonometric Ratios

	sin	cos	tan		sin	cos	tan
1°	.0175	.9998	.0175	46°	.7193	.6947	1.0355
2°	.0349	.9994	.0349	47°	.7314	.6820	1.0724
3°	.0523	.9986	.0524	48°	.7431	.6691	1.1106
4°	.0698	.9976	.0699	49°	.7547	.6561	1.1504
5°	.0872	.9962	.0875	50°	.7660	.6428	1.1918
6°	.1045	.9945	.1051	51°	.7771	.6293	1.2349
7°	.1219	.9925	.1228	52°	.7880	.6157	1.2799
8°	.1392	.9903	.1405	53°	.7986	.6018	1.3270
9°	.1564	.9877	.1584	54°	.8090	.5878	1.3764
10°	.1736	.9848	.1763	55°	.8192	.5736	1.4281
11°	.1908	.9816	.1944	56°	.8290	.5592	1.4826
12°	.2079	.9781	.2126	57°	.8387	.5446	1.5399
13°	.2250	.9744	.2309	58°	.8480	.5299	1.6003
14°	.2419	.9703	.2493	59°	.8572	.5150	1.6643
15°	.2588	.9659	.2679	60°	.8660	.5000	1.7321
16°	.2756	.9613	.2867	61°	.8746	.4848	1.8040
17°	.2924	.9563	.3057	62°	.8829	.4695	1.8807
18°	.3090	.9511	.3249	63°	.8910	.4540	1.9626
19°	.3256	.9455	.3443	64°	.8988	.4384	2.0503
20°	.3420	.9397	.3640	65°	.9063	.4226	2.1445
21°	.3584	.9336	.3839	66°	.9135	.4067	2.2460
22°	.3746	.9272	.4040	67°	.9205	.3907	2.3559
23°	.3907	.9205	.4245	68°	.9272	.3746	2.4751
24°	.4067	.9135	.4452	69°	.9336	.3584	2.6051
25°	.4226	.9063	.4663	70°	.9397	.3420	2.7475
26°	.4384	.8988	.4877	71°	.9455	.3256	2.9042
27°	.4540	.8910	.5095	72°	.9511	.3090	3.0777
28°	.4695	.8829	.5317	73°	.9563	.2924	3.2709
29°	.4848	.8746	.5543	74°	.9613	.2756	3.4874
30°	.5000	.8660	.5774	75°	.9659	.2588	3.7321
31°	.5150	.8572	.6009	76°	.9703	.2419	4.0108
32°	.5299	.8480	.6249	77°	.9744	.2250	4.3315
33°	.5446	.8387	.6494	78°	.9781	.2079	4.7046
34°	.5592	.8290	.6745	79°	.9816	.1908	5.1446
35°	.5736	.8192	.7002	80°	.9848	.1736	5.6713
36°	.5878	.8090	.7265	81°	.9877	.1564	6.3138
37°	.6018	.7986	.7536	82°	.9903	.1392	7.1154
38°	.6157	.7880	.7813	83°	.9925	.1219	8.1443
39°	.6293	.7771	.8098	84°	.9945	.1045	9.5144
40°	.6428	.7660	.8391	85°	.9962	.0872	11.4301
41°	.6561	.7547	.8693	86°	.9976	.0698	14.3007
42°	.6691	.7431	.9004	87°	.9986	.0523	19.0811
43°	.6820	.7314	.9325	88°	.9994	.0349	28.6363
44°	.6947	.7193	.9657	89°	.9998	.0175	57.2900
45°	.7071	.7071	1.0000

Part I. Multiple choice, 1½ points each.

In the blank provided, write the capital letter of the best answer. Read all choices, since sometimes there is more than one partially correct answer. There is no partial credit in Part I.