Table Of ContentThe MaTheMaTical associaTion of aMerica
aMerican MaTheMaTics coMpeTiTions
learning Mathematics Through Meaningful problem solving
57th Annual
examinations prepared by subcommittees
of the american Mathematics competitions
and administered by the aMc office
2007 aMc contest dates:
aMc 8 - TUesDaY, november 14, 2006
aMc 10 & aMc 12 - TUesDaY, february 6, 2007
&/or WeDnesDaY, february 21, 2007
aiMe - TUesDaY, March 13, 2007
or WeDnesDaY, March 28, 2007
UsaMo - april 24-25, 2007
copyright 2006
The Mathematical association of america
The
American Mathematics
Competitions
are sponsored by:
The Mathematical Association of America
Akamai Foundation
Contributors:
American Mathematical Association of Two Year Colleges
American Mathematical Society
American Society of Pension Actuaries
American Statistical Association
Art of Problem Solving
Awesome Math
Canada/USA Mathcamp
Canada/USA Mathpath
Casualty Actuarial Society
Clay Mathematics Institute
Institute for Operations Research and the Management Sciences
L. G. Balfour Company
Mu Alpha Theta
National Council of Teachers of Mathematics
National Assessment & Testing
Pedagoguery Software Inc.
Pi Mu Epsilon
Society of Actuaries
U.S.A. Math Talent Search
W. H. Freeman and Company
Wolfram Research
Table of ConTenTs
Miami Springs Senior High School, Miami Springs, Florida .....................................4
Report of the Director ......................................................................................5
I. Introduction ................................................................................................5
II. 2006 Enrollment Analysis and Statistical Results .......................................5
III. International Participation .......................................................................5
IV. 2007 Contest Dates, Registration and Fees ...............................................5
Table I: 2006 AMC 12 Enrollment Analysis and Statistical Results ..........................................6
Table II: 2006 AMC 10 Enrollment Analysis and Statistical Results.........................................7
V. NASSP’s Sanction ......................................................................................8
VI. The 2006 AIME .......................................................................................8
VII. The USAMO ..........................................................................................8
VIII. Acknowledgement .................................................................................9
IX. Contributions of the Lincoln Staff ...........................................................9
X. Sponsors / Contributors / AMC Committee Members ..............................9
XI. Contributions of the University of Nebraska ............................................9
XII. Additional Information – Inquiries .........................................................9
NCTM National Convention - St Louis ................................................................10
XIII. Examination Dates ..............................................................................0
Message from the CaMC Chair ......................................................................11
Message from the aMC 10 Chair ....................................................................12
St. Johnsbury Academy, St. Johnsbury, Vermont .......................................................13
Message from the aMC 12 Chair ....................................................................14
Quotations ......................................................................................................15
Pope Pius X High School, Lincoln Nebraska ...........................................................16
edyth May sliffe awards .................................................................................17
Distinguished High School Mathematics Teaching .......................................7
Peter Kasmar, Lower Merion High School, Ardmore, PA .........................................17
2006 High School Award Winners ...............................................................8
Sliffe Awards Reception ...............................................................................20
Current & Former Sliffe Winners Attending Reception ............................................20
2005 Sliffe Winners Attending Reception ..............................................................20
2006 Sliffe Awards Reception, Miscellaneous pictures ..............................................21
aMC's Volunteers ...........................................................................................22
Committee on the American Mathematics Competitions..............................22
CAMC Executive Committee ..........................................................................22
CAMC Advisory Board ....................................................................................22
USAMO at Loyola High School, Los Angles, CA ....................................................22
AMC 8 Contest Committee ............................................................................23
AMC 0/2 Contest Committee .....................................................................23
AIME Contest Committee...............................................................................23
USAMO Committee .......................................................................................23
Advisory Panel .................................................................................................24
Sponsors and Contributors ............................................................................26
Boxes of answer sheets waiting to be scanned ...........................................................26
Exam Directors by State and Province ...........................................................27
american Mathematics Competition 8 ...........................................................28
Table III: 2005 AMC 8 National Statistics .......................................................................................28
AMC 8 Student Award Recipients ................................................................29
United States ....................................................................................................29
Canada ............................................................................................................29
International ....................................................................................................30
Sorting envelopes for the AMC 10/12A ..................................................................30
Table of Contents, Continued
Historical listing of Perfect scores .................................................................31
AHSME .......................................................................................................3
AMC 2 ......................................................................................................34
AMC 0 ......................................................................................................36
AMC's Booth at the NCTM Spring Convention .....................................................39
2006 Perfect aMC 10/12 scorers, photos .......................................................40
United States ................................................................................................40
Canada ..........................................................................................................45
International .................................................................................................45
Regions for the aMC 10 & aMC 12 ..............................................................46
Loyola High School, Los Angeles, California ...........................................................46
national school awards ..................................................................................47
Committee and Donor Award Descriptions ..................................................47
National School Award Recipients ................................................................48
United States ....................................................................................................48
Canada ............................................................................................................49
Hon. Vincent Massey Secondary School, Windsor, Ontario, Canada .........................49
School Pedagoguery Award Recipients ..........................................................50
United States ....................................................................................................50
Canada ............................................................................................................52
School Honor Roll, AMC 2 A&B ...............................................................53
United States ....................................................................................................53
Canada ............................................................................................................54
International. ..............................................................................................54
School Merit Roll, AMC 2 A&B .................................................................55
United States ....................................................................................................55
Ben Lippen School, Columbia, ,South Carolina ......................................................68
Canada ............................................................................................................69
International ....................................................................................................70
Late - AMC 2A&B ........................................................................................7
Lincoln Southeast High School, Lincoln, Nebraska ..................................................71
national student awards ................................................................................72
Committee and Donor Awards Descriptions .................................................72
Student Award Recipients ............................................................................73
United States ....................................................................................................73
Canada ............................................................................................................75
student Distinguished Honor Roll .................................................................76
United States .................................................................................................76
AMC 2 A&B .................................................................................................76
Saint Augustine Academy, Tulsa, Oklahoma ...........................................................86
AMC 0 A&B ................................................................................................87
Canada ..........................................................................................................92
AMC 2A&B ..................................................................................................92
AMC 0 A&B .................................................................................................93
Lincoln Southwest High School, Lincoln, NE .........................................................93
International .................................................................................................94
AMC 2 A&B .................................................................................................94
AMC 0 A&B .................................................................................................97
Late - AMC 0/2 A&B .............................................................................0
Lincoln Northeast High School, Lincoln, NE ........................................................101
student Honor Roll ......................................................................................102
United States ...............................................................................................02
2
Table of Contents, Continued
AMC 2 A&B ...............................................................................................02
AMC 0 A&B ...............................................................................................95
Lincoln High School, Lincoln, NE ......................................................................231
Canada ........................................................................................................232
AMC 2 A&B ...............................................................................................232
Lincoln East High School, Lincoln, Nebraska .......................................................236
AMC 0 A&B ...............................................................................................237
International .............................................................................................239
AMC 2 A&B ...............................................................................................239
AMC 10/12 Committee ......................................................................................252
AMC 0 A&B ...............................................................................................253
Late, AMC 0/2 A&B ..............................................................................265
FACE Homeschool Group, Columbia, South Carolina ..........................................265
student achievement Roll ............................................................................266
United States ...............................................................................................266
Canada ........................................................................................................289
International ...............................................................................................290
Gold Medal Recipients ..................................................................................292
Tables & Graphs ...........................................................................................293
Distribution of Team Scores .......................................................................293
Table IV-AMC 12A ....................................................................................................................................293
Table IV-AMC 12B ....................................................................................................................................293
Table IV-AMC 12: Historical Mean - AMC 12 Team Scores .....................................................293
Distribution of School Winner Scores .........................................................294
Table V-AMC 12A .....................................................................................................................................294
Table V-AMC 12B .....................................................................................................................................294
Table V-AMC 12: Historical Mean - AMC 12 ...............................................................................294
Table V-AMC 10A .....................................................................................................................................295
Table V-AMC 10B .....................................................................................................................................295
Table V-AMC 10: Historical Mean - AMC 10 ...............................................................................295
U. S. National Statistics ..............................................................................296
Table VI-AMC 12 A&B .............................................................................................................................296
Table Vi-AMC 10 A&B .............................................................................................................................296
Distribution of Scores - Gender ..................................................................297
Table VII-AMC 12 A&B ............................................................................................................................297
Chart VII-AMC 12A ..................................................................................................................................299
Chart VII-AMC 12B .................................................................................................................................300
Table VII-AMC 10 A&B ............................................................................................................................301
Chart VII-AMC 10A .................................................................................................................................303
Chart VII-AMC 10B .................................................................................................................................304
School & Student Enrollment by State or Province .....................................305
Table VIII .....................................................................................................................................................305
Item Difficulty - Aime Qualifying Students .................................................306
Table IX-AMC 12A ....................................................................................................................................306
Table IX-AMC 12B ...................................................................................................................................307
Table IX-AMC 10A ....................................................................................................................................308
Table IX-AMC 10B ....................................................................................................................................309
Item Difficulty - All Official Students .........................................................30
Table X-AMC 12A .....................................................................................................................................310
Chart X-AMC 12A ....................................................................................................................................311
Table X-AMC 12B .....................................................................................................................................312
Chart X-AMC 12B ....................................................................................................................................313
Table X-AMC 10A .....................................................................................................................................314
Chart X-AMC 10A ....................................................................................................................................315
Table X-AMC 10B .....................................................................................................................................316
3
Table of Contents, Continued
Chart X-AMC 10B ....................................................................................................................................317
aIMe - american Invitational Mathematics examination ............................318
Message from the AIME Chair ....................................................................38
AIME Grand Statistics ................................................................................39
AIME – Scores of 6+ ..................................................................................32
U.s.a. Mathematical olympiad ....................................................................346
Qualifiers for 2006 ......................................................................................346
2006 USAMO Results ................................................................................356
Balles Awards .................................................................................................356
USAMO Ceremonies ..................................................................................357
2005 Winners in Washington, D.C. .....................................................................357
2006 Winners in Washington, D.C. .....................................................................357
2005 International Mathematical olympiad ................................................358
U.S.A. International Mathematical Olympiad Team ............................................358
appendix - school abbreviations ..................................................................359
Convent of the Sacred Heart, New York, NY ........................................................359
Index .............................................................................................................360
Miami Springs Senior High School, Miami Springs, Florida
Sam Koski, teacher. Students being creative after the Contest by spelling out the letters
A - M - C.
4
RePoRT of THe DIReCToR
sTeVen DUnbaR
I. InTRoDUCTIon
I am extremely pleased to announce that this year approximately
230,000 students enrolled in the AMC 0/2 contests and a mul-
titude of positive comments received from teachers once again con-
firmed that the Committee created examinations which were both
exciting and challenging. Congratulations to all of you for continuing
to recognize the fact the AMC 0 and 2 play a complementary role
in supporting the mathematics curriculum at the high school level.
This summary includes a listing of results and awards associated with
this year’s AMC 0 and 2.
II. 2006 enRollMenT analysIs anD sTaTIsTICal
ResUlTs
Our outstanding AMC Lincoln office staffers were once again able to process and mail
the results and awards in a timely and efficient manner. The results for schools with
American Invitational Mathematics Examination qualifiers were mailed in less than
two weeks following the exam, and all other results were mailed during the following
week. This is rather remarkable when one considers the extensive checks which are
necessary to ensure the accuracy of the results.
We continue to send an ever increasing pool of contest managers their schools’ results
by email. If you are able to communicate via email and wish to be added to our data
base, please send a message to “[email protected]” as soon as possible.
In addition to the results and awards of the AMC 0/2, this summary contains an
analysis of the results of the 2005 American Mathematics Contest 8 (AMC 8) as well
as the 2006 American Invitational Mathematics Examination and the 2006 USA
Mathematical Olympiad.
Once again, the AMC 0 and AMC 2 was available in French, Spanish, Braille and
Large Print.
III. InTeRnaTIonal PaRTICIPaTIon
I am pleased to report that the exam was administered in Puerto Rico, Guam, Virgin
Islands, the Marianna Islands, many USA embassy and military schools, and indi-
vidual International schools. A list of these schools is found in this summary. Special
recognition is given to the teachers abroad who provide an opportunity for students
at US military bases and embassies to participate in the AMC 0/2.
The CAMC extends its appreciation to Professor Paul Charlebois who translates the
exams into French for students in Canada. We are also grateful to Professor Maria de
Losada and Mario Cruz from Bogota, Colombia for translating the AMC 0 and AMC
2 into Spanish for use in Puerto Rico as well as in the USA and Colombia. Special
thanks to Professor Peter Shiue for translating the exams into Chinese for more than
300 schools in Taiwan that participated in the AMC 0/2 this year.
IV. 2007 ConTesT DaTes, ReGIsTRaTIon anD
fees
There will again be two official dates for the AMC 0 & AMC 2. Please note that
the contests are being held a week later than the two dates they were given in 2006.
Contest A will be held on the first Tuesday in February (February 6, 2007), Contest
B will be given 5 days later, Wednesday, February 2, 2007 All rules and awards
5
Table I: 2006 aMC 12 enrollMenT analysIs and sTaTIsTICal resulTs
(Four year comparison of the AMC 12 Contest)
Year 2006 2005 2004 2003
Version 12A 12B 12A 12B 12A 12B 12A 12B
Registered schools 2,417 1,827 2,596 1,687 3,139 1,320 3,272 1,264
Answer forms received 76,806 50,201 84,402 44,511 103,739 31,366 99,322 39,633
Official registered students 76,439 50,147 83,728 44,303 103,237 31,299 98,608 38,599
Unofficial registered students 367 54 674 208 502 67 714 1,034
National student average 85.7 85.5 78.7 83.4 73.9 84.5 77.8 76.6
Number female participants 31,426 20,646 34,822 18,138 43,287 12,767 41,015 15,851
Number male participants 41,746 26,697 44,744 24,160 56,293 17,114 54,266 21,145
Number unspecified gender 3,267 2,804 4,162 2,005 3,657 1,418 3,291 1,603
Average female score 82.1 81.0 74.8 80.2 69.5 80.2 73.5 71.9
Average male score 88.6 88.8 81.9 85.9 77.4 87.8 81.2 80.2
Average “no gender” score 83.5 87.6 77.5 81.3 72 81.4 76.2 74.5
Number students - grade 13 88 129 87 178 105 161 348 209
Number students - grade 12 31,879 19,720 34,272 17,593 42,597 12,650 40,357 15,928
Number students - grade 11 35,722 23,123 39,471 20,735 48,470 14,284 47,034 17,538
Number students - grade 10 5,367 4,210 6,080 3,721 8,050 2,436 7,233 3,069
Number students - grade 9 1,848 1,373 1,701 1,158 2,188 782 1,971 842
Number students - grade 8 137 228 161 185 133 182 115 188
Number students - unknown 1,398 1,364 1,956 733 1,694 804 1,550 825
Average score - grade 13 88.7 94.9 82.7 88.4 80 91.9 83.2 84.6
Average score - grade 12 87.3 86.9 80.5 84.6 75.9 86 79.6 78.4
Average score - grade 11 84.3 83.5 77.1 82.1 72.1 83 76.2 74.9
Average score - grade 10 87.0 87.5 80.3 84.2 74.7 85.6 77.6 76.5
Average score - grade 9 83.1 88.6 76.4 85.1 72.6 86.2 75.5 76.4
Average score - grade 8 93.8 95.4 82.8 89.5 83.2 91.8 87.5 82.8
Average score - Unknown 82.3 89.1 76.8 80.8 71.9 77.5 79.5 73.9
AIME qualifying score 100 100 100 100 100 100 100 100
Number of AIME Qualifiers 17,118 10,654 9,441 5,692 8,401 6,036 12,089 3,812
Schools sending in results 2,365 1,692 2,577 1.541 3,108 1,199 3,017 1,386
Average school winner score 111.5 111.9 106.68 107.73 103.13 109.1 107.6 107.16
Average School Team Score 314.0 311.1 295.75 298.93 285.24 299.35 298.56 290.19
Perfect papers 14 2 1 6 12 5 19 13
6
Table II: 2006 aMC 10 enrollMenT analysIs and sTaTIsTICal resulTs
(Four year comparison of the AMC 10/12 Contest)
Year 2006 2005 2004 2003
Version 10A 10B 10A 10B 10A 10B 10A 10B
Answer forms received 62,033 38,519 67,738 34,204 81,596 23,624 77,421 28,652
Official registered students 61,743 38,420 67,074 34,070 81,122 23,528 76,805 27,895
Unofficial registered 290 99 664 134 474 96 616 757
students
National student average 79.0 68.5 74.7 77.9 69.1 80.4 74.4 79.6
Number female participants 27,229 17,140 30,379 15,062 36,217 10,614 34,107 12,450
Number male participants 30,803 18,149 32,731 16,772 40,248 11,589 38,598 13,717
Number unspecified gender 3,711 3,131 3,964 2,241 4,657 1,325 4,100 1,728
Average female score 75.6 64.1 71.6 75.1 66.3 77.1 71.3 76.4
Average male score 82.3 71.6 77.8 80.7 71.7 83.7 77.4 82.8
Average “no gender” score 76.7 75.4 72.6 75.8 67.3 78.4 72.4 77.9
Number students - grade 10 32,930 20,013 36,012 18,193 42,960 12,128 40,998 14,321
Number students - grade 9 24,211 15,158 26,452 13,699 33,095 9,450 30,844 11,300
Number students - grade 8 2,873 1,600 2,723 1,160 2,793 1,334 3,138 1,293
Number students - unknown 1,729 1,649 1,887 1,018 2,274 616 1,825 981
Average score - grade 10 80.8 69.8 76.2 79.8 70.4 82.3 76 81.4
Average score - grade 9 75.8 64.8 72.2 75.6 67 78.3 72 77.6
Average score - grade 8 86.4 74.5 80.3 80.4 75.7 81.4 78.9 79.2
Average score - Unknown 75.9 82.2 71.3 73.8 65.5 74.6 72.3 77.4
AIME qualifying score 120 120 120 120 110 120 119 121
Number of AIME Qualifiers 1,680 870 1,258 555 1,118 487 1,534 350
Schools sending in results 2,092 1,282 2,362 1,196 2,829 910 2,735 1,046
Average school winner 108.7 103.6 104.36 106.65 97.02 108.66 104.77 108.64
score
Perfect papers 33 48 18 15 6 2 36 3
7
Report of the Director, Continued
apply to both tests for all schools and students. Students will be allowed to take the
exam booklets home with them the day of the contest.
The Registration cost for the 2006-2007 year has been raised one dollar from the fee
in the 2005-2006 season. We have again included the shipping cost in with the Reg-
istration Fee. Registration plus shipping for one AMC A Contest is $40 per school,
if you register by December 5, 2006. One bundle of ten AMC 2 exams will also
go up $, to $6 and one bundle of ten AMC 0 exams go up to $4. There will
be an extra $0.00 charge included with the Registration for the second contest (B)
to cover 2-day shipping. Contest B will be shipped on February 7, 2007, the day
after Contest A.
Materials for Contest A will be mailed in January of 2007. Please register by December
5, 2006 if possible. Completion of your registration as early as possible will be greatly
appreciated by our office staff.
If you do not receive one of our many fall mailings, a current registration form will be
available on our Web site. Please post our address: http://www.unl.edu/amc
V. nassP’s sanCTIon
The National Association of Secondary School Principals has placed this program on
the NASSP National Advisory List of Contests and Activities for 2006-2007.
VI. THe 2006 aIMe
A total of 22,636 students officially participated in the 24th American Invitational
Mathematics Examination (AIME) which was held on Tuesday, March 7, 2006 or
the “alternate” date, Wednesday, March 22, 2006. The comparable figure in 2005 is
2,476 students. The mean score on the AIME I was 2.7, and on the AIME II was
2.825, versus the 2.75 on the AIME I, and 2.43, on the AIME II, in 2005. A list of
the students with a score of at least 6 on the 2006 AIME is found in this summary.
The 2007 aIMe is scheduled for Tuesday, March 13, 2007 and the alternate date
is Wednesday, March 28, 2007. Please note that the AIME II has been changed from
a Tuesday to a Wednesday, to provide more flexibility in scheduling. To qualify for the
AIME in the year 2007 a student must score 00 or more or be in the top 5% on the
AMC 2 or score 20 or more or be in the top % of the AMC 0 participants. The
AIME consists of 5 questions with integer answers. A student’s score is the number
of correct answers. There is no partial credit. The time allowed is 3 hours.
VII. THe UsaMo
The USA Mathematical Olympiad (USAMO) was held on April 8-9, 2006 in each
respective student’s school. 430 students were invited to particpate this year. This is
70 more than the 260 who were invited to participate in 2005, because we received
a grant from the Art of Problem Solving to cover the costs associated with the addi-
tional number of students. All of the participants were chosen based on the selection
criteria published in the AMC 0/2 and AIME Teachers’ Manual. This summary
contains a list of those participants as well as names of the USAMO Winners, and
Honorable Mention.
The USAMO was once again administered over two days (4.5 hours each day). All
papers were graded by the USAMO Committee, and by Mathematical Olympiad
Summer Program staff members on April 2st, 22nd and 23rd. We are grateful to these
mathematicians for their excellent work associated with this important task.
The top twelve USAMO students were honored in Washington, DC May 2st and
22nd, 2006 with elaborate ceremonies held at the headquarters of the Mathematical
8
Description:of the american Mathematics competitions and administered by the aMc office. 2007 aMc contest dates: aMc 8 - TUesDaY, november 14, 2006.
