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34th Annual

American Mathematics Competitions

American InvitationalMathematics Examination

TEACHERS’MANUAL

Instructions and Reporting Forms

for School Contest Managers

dates to remember:

AIME - Thursday, March 3, 2016

AIME II - Wednesday, March 16, 2016

Please read this booklet thoroughly upon receipt.

CELEBRATING A CENTURY OF ADVANCING MATHEMATICS

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MAA American Mathematics Competitions9050 Junction Drive | Annapolis Junction, MD 20701

800.527.3690/phone | 240.396.5647/fax | [email protected] | maa.org/amc

o All AIME Managers:

Please read this manual regarding the AIME rules and regulations thoroughly. Note our policy or the official administration

o the AIME. Te AIME I can only be given officially on HURSDAY, March 3rd, and the AIME II can only be given officially

on WEDNESDAY, March 16, 2016. Te contest should be scheduled rom 9 to 12 noon i possible.

All students who are in the top 5% o all American Mathematics Contest 12 (AMC 12) participants or score at least 100 points

on the AMC 12 and those with a score in the top 2.5% o the American Mathematics Contest 10 (AMC 10) participants or

score at least 120 points, are invited to take the AIME. Te AIME is the second in the sequence o mathematics contests which

leads to participation in the USA Mathematical Olympiad and the designation o Winners o the USA(J)MO. Te AIME is

a 15-question, 3-hour examination. All answers are integers ranging rom 000 to 999, inclusive. Te score is the number o

correct answers. Tere is neither partial credit nor a penalty or wrong answers.

I call your attention to several items ound in this manual which answer inquiries I requently receive rom AIME Managers:

1. All administrations o the AIME must take place on the scheduled dates.

Te processing ee or the second AIME contest is as ollows: $25 or 1–10 students, and $50 or 11 or more students. Wemust have your payment beore we grade the answer orms. Te AIME II payment orm can be ound on page 13 o thismanual. All AIME II answer orms must be returned by trackable express mail service, so that they arrive in the AMC office

by March 21, 2016.

2. Email requests or the second AIME may be sent to: [email protected]

Email requests should include the school’s CEEB number and complete mailing address, teacher name, teacher email address,

number o students taking the AIME II, and method o payment. You may also register online using a credit card at

amc-reg.maa.org.

3. Under no circumstances can a student take both AIMEs.

4. In section V you will find a discussion o how and when you will receive results.

5. You will find all the inormation and orms relevant to the taking o the USA(J)MO on our website, maa.org/amc. I

you have had students qualiy or the USA(J)MO in the past, or you are anticipating this to be so this year, please go tomaa.org/amc to find the USA(J)MO eachers’ Manual.

6. Te second AIME on Wednesday, March 16, 2016 is a set o 15 questions, different rom, but comparable to the AIME I on

March 3, 2016.

7. Selection o USAMO & USAJMO participants will depend on the AMC 10/12 score, and AIME score.

We eel that the 2016 AIME will be interesting and challenging to your student(s). On behal o the Committee on the American

Mathematics Competitions, I send my appreciation to you or assisting with the implementation o this examination.

Sincerely,

Mark Saul

Director

MAA American Mathematics Competitions


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Contents

I. List o the Sponsors o the American Mathematics Competitions ............. ............ ............ ............. ............ ............ 3

Attention Contest Managers ........... ............. ............ ............. ............ ............ ............. ............ ............. ............ ............. . 4

II. Contents o Package ............. ............ ............. ............ ............. ............ ............ ............. ............ ............. ............ ............. . 5

III. Preparation Instructions ............ ............. ............ ............ ............. ............ ............. ............ ............. ............ ............. ..... 5

IV. Day o the AIME Instructions ............ ............. ............ ............. ............ ............. ............ ............ ............. ............ .......... 5

V. Report o the AIME Results.......................................................................................................................................... 6

VI. Eligibility ............ ............. ............ ............ ............. ............ ............. ............ ............. ............ ............. ............ ............ ........ 6

VII. Policy on AIME Administration ............. ............ ............ ............. ............ ............. ............ ............. ............ ............. ..... 6

VIII. Visually Impaired and Learning Disabled Students ............ ............ ............. ............ ............ ............. ............ ............ 7

IX. Request or Student Names ........... ............. ............ ............ ............. ............ ............. ............ ............. ............ ............. ... 7

X. Fascimile o the March 3, 2016 AIME Front Cover ............ ............ ............. ............ ............ ............. ............ ............ 8

FORM A – Examination Certiication 2016 AIME ............ ............ ............. ............ ............ ............. ............ ............ 9

FORM B – USAMO/USAJMO Inormation Form ............. ............ ............. ............ ............ ............. ............ ......... 10

FORM C – Publication Order Form ............ ............ ............. ............ ............. ............ ............ ............. ............ ......... 11FORM D – AIME II Payment .................................................................................................................................. 13

FORM E – Rescore Form ........................................................................................................................................... 14

FORM F – AMC Academic Integrity Form ............ ............. ............ ............. ............ ............ ............. ............ ......... 16

IX. Exam Auxiliary Material ............................................................................................................................................ 16

Practice Worksheets ............. ............ ............. ............ ............. ............ ............ ............. ............ ............. ............ ........... 16

Press Release ................................................................................................................................................................ 21

Letter to Parents .......................................................................................................................................................... 22

I. List of Sponsors

TeMAA American Mathematics Competitions

are supported by

Patron’s CircleAkamai FoundationSimons Foundation

Innovator’s Circle

udor Investment Corporationwo Sigma

Winner’s Circle

American Mathematical Society Te D.E. Shaw Group

DropboxMathWorks

Susquehanna International Group

Achiever’s Circle

Art o Problem SolvingJane Street Capital

Sustainer’s Circle

Academy o Applied ScienceAmerican Statistical Association

Army Educational Outreach Program

Visit http://www.maa.org/about-maa/our-partners or a complete list o donors.

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ATTENTION CONTEST MANAGERS

IMPORTANT DATES – AIME I

February 26, 2016 Final day or AIME qualifier schools to change rom the AIME II date to the AIME I date.

Beore March 3, 2016 Have students fill in all name and demographic inormation on answer sheets — beore the dayo the contest.

March 3, 2016 Official contest administration date.March 4, 2016 Return answer sheets to the MAA AMC office the day afer contest administration — don’t or-

get to use a trackable method. All answer sheets must be received no later than March 21, 2016.

By March 21, 2016 Last date that AIME I contest answer sheets will be accepted by the AMC office.

IMPORTANT DATES – AIME II

March 4, 2016 Final day to register or the AIME II contest.

Beore March 15, 2016 Have students fill in all name and demographic inormation on answer sheets — beore the dayo the contest.

March 15, 2016 Contest managers will receive by email an electronic copy o the AIME II contest booklet whichshould be printed or contest administration.

March 16. 2016 Official contest administration date.

March 17, 2016 Return answer sheets to the MAA AMC office the day afer contest administration — don’t or-get to use a trackable method. All answer sheets must be received no later than March 21, 2016.

By March 21, 2016 Last date that AIME II contest answer sheets will be accepted by the AMC office.

• For domestic schools, that all students will take the AIME I contest, unless registered separately or AIME II.

• Veriy your contest materials immediately upon delivery. Tere should be enough answer sheets included to match the number ostudents invited to participate in the AIME contest. Tere should also be one AIME return envelope, one school ID orm, and enoughAIME I contest booklets and answer sheets or the students invited to participate in the AIME contest. I any materials are missingplease contact Customer Service immediately.

• Instruct students that they must use the same name on the AIME answer sheet that they used on the AMC10/12 contests. Use onicknames or other versions o their name may result in a student not being invited to take the USA(J)MO.

• All award packets or schools that have AIME qualified students will include AIME I contest booklets and answer sheets. I participat

ing in the AIME II contest, the AIME II contest booklets will be emailed to the contest manager by 12 ES on March 15, 2016. Teanswer sheets, school ID orm, certification orm, and return envelope provided in the award packet should be used or the AIME Icontest.

• Te AIME eacher’s Manual is online this year. Please download and print your copy atwww.maa.org/math-competitions under eacherResources.

• Do not use photocopied answer sheets. Photocopied answer sheets cannot be read by our scanners and cannot be scored. Contaccustomer service immediately i you did not receive enough official answer sheets.

• Check that all answer sheets are complete. Have students fill in the answer sheets, filling in the bubbles completely with their nameage, date o birth, grade, gender, and address prior to the contest date. Incomplete answer sheets could result in incorrect or delayedscoring. Afer the contest administration, please veriy that these portions o each answer sheet have been completed correctly.

• Complete and include the School Identification Form. Te correct CEEB (school) code, number o answer sheets returned, and datethe contest was given are crucial to the scoring process. I you are unsure o the correct code, please contact Customer Service prio

to returning your contest materials. Errors in completion o this orm can lead to inaccurate score reports.• Complete and include Form A (Examination Certification 2016 AIME), Form B (USAMO/USAJMO Inormation Form) and FormF (AMC Academic Integrity Form). Tese orms are included in your contest package, but can also be ound on pages 9, 10, and 15respectively, o the AIME eachers’ Manual. Please be sure to include all signatures, dates, and necessary exceptions.

• Please mail completed answer sheets the day afer the contest administration. Answer sheets must be returned within 10 days (othe AIME I) and 7 days (or the AIME II) o the contest date to receive your contest report and any awards earned. Answer sheetreceived afer this time will be subject to a delay in scoring and will receive only electronic scores.

• Late return o answer sheets may disqualiy students rom the USA(J)MO invitational contests.

• Returned answer sheets must be shipped via a trackable method. Te MAA AMC is not responsible or lost answer sheet packages. Iis recommended that overnight service be used.

Questions? Contact Customer Service: 800-527-3690 (US), 301-617-7805 (outside the US), or [email protected]

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AIME 2016 Teachers’ Manual

II. Contents of PackageEnclosed with your AMC10/12 award packet you will find theollowing material:

• A list o your qualified AIME students.• A sealed envelope containing one AIME or each o your

qualified students and an extra copy or you. Te envelopemust NO be opened until just beore the examination is

given on the authorized date.• One AIME Answer Form or each participating student.• One AIME School Identification Form.• One AIME Report Envelope.• One AIME II Payment Form (page 13 in this Manual) and

return envelope.

We will mail the Solutions or the AIME with your AIME schoolreport.

III. Preparation Instructions1. Please study the contents o this eachers’ Manual.

2. Reserve a room or 3 1/2 hours rom 8:45 –12:15 in your

own (U.S.) time zone. Tis allows 15 minutes or pre- and post-examination activities and 3 hours or the examination itsel.For time zones outside the continental U.S., the AIME I mustbe given afer 9 , ED (UC-4) on March 3, 2016, at theearliest convenient time, with a similar scheduling requirementor the AIME II on March 16, 2016. In extreme cases when youcannot administer the AIME between 7:00 and 3:00 ,please complete the academic integrity pledge orm on page 15.

3. Inorm your students o the time and place well in advanceo the competition. Urge them to prepare or the AIME bystudying past AIME exams and solutions. For inormationabout ordering past AIME contest questions, see Form C

(Publication Order Form) on page 11 in this manual.4. Review the examination rules printed on the sealed envelope

containing the examination.

5. Obtain a supply o:

a. Number 2 lead pencils with good erasers;

b. Unmarked scratch paper;

c. Rulers, compasses, protractors, and graph paper.

6. Calculators, smart phones or watches, computers or computingdevices are NO permitted, nor is any device allowingcommunication with someone outside the contest venue.

7. Complete the AIME School Identification Form using the

instructions ound on that orm.

8. Please study the AIME Student Answer Form. Have each studentcomplete Side 1 o the Form using the instructions ound on theorm. Please ollow careully the marking instructions printedon both the identification orm and the student answer orm.Double check to see that all the items are filled out correctly.Students may not complete the personal inormation afer thetime allowed or the test. Only the inormation which has beenproperly blackened will be read by the scanning equipment.Be sure to note the student’s AMC 10 or AMC 12 score in theappropriate area, including decimal ractions i needed.

9. Afer completing step 8, the AIME answer orm will be readyor distribution to your participating students on TursdayMarch 3rd.

10. Make arrangements to mail your AIME Report Envelope bytrackable mail service. Please note that this is an oversizedenvelope, which may require special postage even i its weighis one ounce or less.

IV. Instructions for the Day of the AIME1. Sign the Certification Form (on page 9) to certiy that the

package was opened not more than one hour beore the contest

2. Seat participants in alternate seats.

3. Ensure that each participant has the supplies listed in Item 5under Section III.

4. Inorm the students that they are not to open the exam bookleuntil instructed to do so.

5. Pass out the contest booklets and have the students read theinstructions on the ront cover.

6. Distribute the AIME Answer Forms (which you or youstudents have previously prepared) to the students. Inorm themthat their answers should be marked with a pencil on SIDE 2o the answer orm and that each problem has only one correctanswer, which is an integer between 000 and 999 inclusive.

7. Read aloud the ollowing instructions or recording answers tothe problems:

a. For each question you answer, use a #2 pencil to write youanswer at the top o the problem’s answer column. Use 3digits. Ten, in each o these columns, blacken the one circlewhich is labeled with the digit you have written at the topPLEASE NOE: A single digit answer, such as 7, should be

written and blackened as 007 and a two digit answer, suchas 43, should be written and blackened as 043.

b. DO NO BLACKEN ANSWERS UNIL YOU ARECERAIN OF YOUR FINAL CHOICE. AVOID, IFPOSSIBLE, ERASURES IN HE CIRCLES.

c. Te results will be graded by computer. Only the blackenedcircles will be graded.

8. Ask the students i they have any questions about usingthe AIME Answer Form or about the instructions or theexamination.

9. Start the Examination.

10. Check to see that each student is marking his/her Answer Formproperly.

11. Allow exactly 3 hours working time.

12. I there is an urgent need to use a bathroom, only one studenmay leave at one time and the AIME answer orm and contesbooklet should be retained by you while the student is out othe room. I there is a health or medical emergency, a backupcontest manager should be available to assist.

13. At the end o 3 hours, instruct the students to:

a. SOP.

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b. Put aside the contest booklet and scratch paper and lookagain to be sure the AIME Answer Form has been filled outcorrectly.

c. Be sure the written answers on the top o the AIME AnswerForm are in agreement with the answers coded in theblackened circles.

d. Sign their name on Side 2 o the answer orm.

e. Hand in the AIME Answer Form.. Keep the contest booklet or their reerence in reviewing

the solutions.

Inorm the students that they may now leave the examinationroom.

14. Complete the Certification Form (Form A) and USA(J)MOInormation Form (Form B) ound on pages 9 and 10.

15. Te ollowing material should be sealed in the AIME ReportEnvelope, postmarked NO LAER HAN 24 hours afer theexamination is given, and sent to the AMC Customer Service:

a. the signed AIME Certification Form A and USA(J)MOInormation Form B;

b. the AIME School Identification Form;

c. one AIME Answer Form or each participating student.Please do not paper clip or staple the orms together. Pleasedo not old the orms.

Schools located outside the U.S. must return materials by AIREXPRESS MAIL (DHL, Federal Express, etc.).

16. Please note that i you have requested the AIME II you mustsend your payment separately and in advance o the day o thecontest (Wednesday, March 16th).

V. Report of the AIME Results

Your students’ AIME scores, along with certificates o participationand an AIME Solutions Pamphlet, will be sent to you afer thecontest.

Please retain this report or uture reerence, either in your own filesor with your student counselor office. Many students cite their scoreson college applications, and want verification. Te AMC office willnot be able to retrieve or veriy student scores.

VI. EligibilityAny student who is officially enrolled in high school (or below), oris a actively working towards a high school diploma (and has notgraduated) is eligible to take the AIME (with qualiying score). US

and Canadian Citizens and students studying in the United States(with qualiying scores) are eligible to take the USA(J)MO.

Home schooled students age 19.5 and under are eligible or theAIME (with qualiying scores).

Students learning English as a second language (ESL) may use abook or dual-language nontechnical dictionary o English and theirnative language. A student may use the dictionary only the first timethat he/she takes the AIME contest. Te dictionary must be given tothe school contest manager to examine and retain or the 24-hourperiod preceding the contest. Te proctor must announce to otherstudents that this student has been given special permission to usethe dictionary during the contest.

VII. AIME Administration PolicyYou must administer the AIME on the official date (March 3rd and16th, 2016), to all your students, in the same place and at the sametime. Students invited to take the AIME who cannot be there wilmiss this opportunity. Students who miss the AIME I contest onTursday, March 3, may take the AIME II on Wednesday, March 16Te AIME II contest is a new set o 15 questions, different rombut comparable to the questions on the AIME I contest. Afer thedate o the AIME I contest, questions rom this contest may be usedor practice.

I you need to have a student sit or the AIME II on March 16 th, pleaseread the applicable details below. Contact the AMC office i youhave questions. Tere is a charge or the second contest. Tese twodates will be the only ones acceptable to qualiy or the USA(J)MO

Te processing ee or the second AIME contest is as ollows: $25 or1–10 students, and $50 or 11 or more students. We must have yourpayment beore we grade the answer orms. Te AIME II paymenorm can be ound on page 13 o this manual. All AIME II answerorms must be returned by trackable express mail service, so thatthey arrive in the AMC office by March 21, 2016.

Email requests or the second AIME may be sent to:

[email protected]

Email requests should include the school’s CEEB number andcomplete mailing address, teacher’s name, teacher’s email addressthe number o students taking the AIME II, and the method opayment. Alternatively, you may wish to register online, usinga credit card, at amc-reg.maa.org. he AMC oice will send aconfirmation o registration or the AIME II. Please note that youwill be billed or all AIME II orders unless you cancel your orderbeore March 10, 2016.

Under no circumstances can a student take both AIME contests

Procedures for the AIME II

Te AMC uses a different procedure or delivery o the AIME IIcontest. Recall that the date or the AIME II is Wednesday, March 162016.

1. Te AMC office will mail the 2016 AMC 10 and 2016 AMC 12reports back to schools starting in mid-February and continuinguntil early March. Your school’s AIME qualifiers are listed inthat report.

2. Te AIME I contest will be included with the AMC 10 and AMC12 school reports, in a sealed envelope. Tere will be one contesbooklet and one answer orm or each AIME qualifier.

3. I your AIME qualifiers will be taking the AIME I on TursdayMarch 3, 2016, you need only ollow the directions or the AIMEI in this eachers’ Manual and send back the AIME answer ormsor scoring.

4. I your AIME qualifiers will be taking the AIME II on WednesdayMarch 16, 2016 then you will still need to fill out the AIME IIregistration either on our web page at amc-reg.maa.org/home orby using the orm in this AIME eacher’s Manual. Be sure toinclude a valid email address.

5. SAVE the AIME Answer Forms you receive in the AMC 10/AMC12 Report. Te answer orms can be used either or the AIME

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or the AIME II contests, simply by filling in the correspondingcircle above the name portion on the ront o the answer orm.Also save the AIME Report Envelope, which can be used orsending back either contest.

6. Watch your email on uesday, March 15, 2016 (afer 12:00 noonED) or an email with an attachment containing the AIME IIexam. Te AIME II will come as a PDF document attached tothe email. Print the AIME II, and then make enough copies to

have one or each participating AIME qualifier.

7. Be sure to have students taking the AIME II fill in the AIMEII circle on the ront o the answer orm, near the space or thestudent’s name.

I you have any questions or concerns, email the AMC office [email protected].

Questionable Scores

I it is clear to the Contest Manager rom personal observationthat a student has cheated, then the Manager must disqualiy thestudent. I the Contest Manager receives an accusation o cheating,or obtains other indirect evidence o cheating, then the Manager

must hold back the student’s paper and immediately report all theacts o the situation to the AMC Director, who in conjunction withthe Chair o the CAMC, will determine what to do. UNDER NOCIRCUMSANCES may the school decide on its own to accept aquestionable score, nor should a school retest the student in ques-tion beore receiving instructions rom the AMC Office.

Contest Proctoring

Te proctoring o the AIME contest should be by:

1st preerence, a math teacher at the school

2nd preerence, a teacher or administrator at the school

3rd preerence, a college or university teacher o mathematics or a

responsible adult who is a math club or team coach, and notrelated to any o the participants

4th preerence, a responsible adult not related to any o the partici-pants such as librarian, clergy, etc.

• Te proctoring o the contest must take place in a public building,(i.e., school library, college or university, church, etc.).

• All students must take the contest at the same time, either in onegroup or in separate classrooms and be under the supervisiono a proctor.

• Te proctor should not be related to any o the participants

• I a parent wishes to help, they can arrange room reservationsand set-up, help with student sign-up, provide treats, etc. Par-

ents may not proctor the contest.

VIII. Visually Impaired and Learning Disabled StudentsI one o your AIME qualified students is visually impaired and/orlearning disabled please call the AMC office and we will discuss theoptions available to you. We do not have copies available in brailleTe time allowance or students with learning disabilities is 4.5hours. It is the responsibility o the school and the contest manageto make arrangements consistent with the student’s accommodation

plan. Please contact us at [email protected] or more inormation.

IX. Request for Student NamesTe ollowing statement appears on the student answer orms orthe AMC 10 and AMC 12:

1. Te American Mathematics Competitions (AMC) receivesrequests rom educational institutions and organizations orthe names, addresses and grade levels o high scoring studentsTis inormation is used or recruiting and academic purposes

2. Blacken this circle i you give the AMC permission to releasethis inormation to these organizations. (Your score will notbe affected i you do not blacken the circle.)

Receiving inormation is an “opt-in” decision or each individualstudent.

Te AMC handles requests rom institutions and organizationson a case-by-case basis and evaluates each individually orappropriateness. We provide legitimate educational institutions oall levels, both secondary and collegiate/university level, with onetime use o selected names and addresses or postal mailings. Wealso provide proessional and scholarly organizations such as thoselisted as contributors to the AMC with one-time use o names andaddresses or postal mailings, generally or proessional or careerinormation.

Te only inormation we provide is the name, address, city, state

and zip code necessary or a postal mailing.

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X. Fascimile of the March 3, 2016 AIME Front Cover

American Mathematics Competitions

34th Annual

AIME IAmerican Invitational Mathematics Examination I

Thursday, March 3, 2016

1. DO NO OPEN HIS BOOKLE UNIL YOUR PROCOR GIVES HESIGNAL O BEGIN.

2. Tis is a 15-question, 3-hour examination. All answers are integers ranging

rom 000 to 999, inclusive. Your score will be the number o correct answers.Tere is neither partial credit nor a penalty or wrong answers.

3. No aids other than scratch paper, graph paper, ruler, compass, and protractorare permitted. In particular, calculators, calculating devices, smart phones orwatches, and computers are not permitted.

4. A combination o the AIME and the American Mathematics Contest 12 areused to determine eligibility or participation in the USA Mathematical Olym-piad (USAMO). A combination o the AIME and the American MathematicsContest 10 are used to determine eligibility or participation in the USA JuniorMathematical Olympiad (USAJMO). Te USAMO and USAJMO will be givenon UESDAY and UESDAY, April 19 and 20, 2016.

5. Record all your answers, and identification inormation, on the AIME answerorm. Only the answer orm will be collected rom you.

Te publication, reproduction, or communication of the problems or solutions for thiscontest during the period when students are eligible to participate seriously jeopardizesthe integrity of the results. Dissemination at any time during this period, via copier,telephone, email, internet, or media of any type is a violation of the competition rules.

© 2016 Mathematical Association o America

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FORM A – Examination Certifcation 2016 AIMECertification by the Examination Manager:

I certify that the 2016 American Invitational Mathematics Examination was given today, Thursday, March 3, 2016 / Wednesday, March 16,2016 (circle appropriate date); that all students who took it did so at the same time and place; that only invited students took it; thatthe 3-hour time limit was strictly enforced; that the test envelope was sealed until the time of the test; that no student had access tothe test questions in advance; that the students were continually supervised by a proctor while they were taking the test; that I am

returning those materials as required in Section IV; and that all other rules for administering the test were followed.o YES o NO If no, describe the exceptions on a separate sheet of paper.I also certify that I understand and accept the following for our school. The Committee on the American Mathematics Competitionsreserves the right to:

1. Disqualify all scores from our school if it is determined that the required security procedures were not followed.

2. Re-examine students if, after an inquiry, there is a reasonable basis to believe that the scores do not validly represent the ability of the students(The procedures for disqualication, follow-up inquiries and re-examination are similar to those for the AMC 10 and AMC 12, as outlined in theAMC 10/12 Teachers’ Manual.)

Signature of AIME School Manager ____________________________________________________________

Email ___________________________________________________________________________________

Date _________________________________ School Telephone # ________________________________

Name of School ____________________________________________________________________________

State _________________________ School Identication Number (CEEB) ___ ___ ___ ___ ___ ___

The AIME was administered on (circle correct date) March 3, 2016 March 16, 2016

Starting Time ________________________________ Ending Time _________________________________

(For time zones outside the continental U.S., the AIME must be given after 9 AM, EDT (UTC-4) on March 3, 2016, at the earliest

convenient time. Similarly for the AIME II on March 16, 2016.)

Student(s) who qualied for the AIME at other locations (than our school):

Student Name: ________________________________________________________

Reg.attended school: CEEB#:___ ___ ___ ___ ___ ___ Name:________________________________________ Other location: CEEB#:___ ___ ___ ___ ___ ___ Name:________________________________________

Student Name: ________________________________________________________

Reg.attended school: CEEB#:___ ___ ___ ___ ___ ___ Name:________________________________________

Other location: CEEB#:___ ___ ___ ___ ___ ___ Name:________________________________________

If there are more than 2 students, please attach a separate page with this information listed for each student.

The Examination Manager and the Principal, Assistant Principal, or Headmaster must sign this form. Return it with your student AnswerForms.

Certification by the Principal, Official or person with comparable title:

I agree that the contest manager followed all the rules and procedures listed above.

Signature _________________________________________________________________________ Time _____________________________________________

Title _________________________________________________________________________ Date ________________________________________

Please also complete the USAMO/USAJMO INFORMATION Form B, found on Page 10.

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FORM B – USAMO/USAJMO Information Form

When a student qualies for the United States of America Mathematical Olympiad (USA(J)MO), both the student and the USA(J)MOSchool Manager are notied at least one week before the USA(J)MO date. When a USA(J)MO invitation is extended, both the studentand the USA(J)MO School Manager must complete and return a USA(J)MO Response Form. If the Form is not returned, the situation isnoted and corrected.

Please provide the information requested below if you agree to administer the USA(J)MO. There is no fee for participating in the USA(J)MO

AGREEMENT STATEMENT:In the event that I have a qualifying student(s), I or my designee (indicated below) agree to:

1. Serve as the USA(J)MO School Manager.

2. Administer the USA(J)MO on Tuesday, April 19th, and Wednesday, April 20th, 2016 to the student(s) in my school who qualify and not to anyother students.

3. Arrange for the exclusive use of a room for four and a half hours (from 12:30 PM to 5:00 PM, eastern daylight time or your time zone equivalenton the designated days which will be used to administer the USA(J)MO.

4. Have a proctor present in the room to supervise the student(s) during the entire nine hours of the examination.

5. Have the ability to scan & email or fax the students’ answer sheets to the AMC email or fax number immediately, to be graded by the AMC

I understand that results of my participating USA(J)MO students can be voided if the rules and procedures associated with theadministration of the USA(J)MO are not followed.

Signature ___________________________________________________________________________________

Telephone Number ________________________________________________ Date ____________________

Name of USA(J)MO School Manager ______________________________________________________________

eMail _____________________________________________________________________________________

School _____________________________________________________CEEB#: ___ ___ ___ ___ ___ ___

City _____________________________________________________ State _________ Zip _______________

PLEASE NOTE THE 4.5 HOURS PER DAY TIME LENGTH AND 2 DAYS LENGTH FOR THE2016 USA(J)MO:

TUESDAY, April 19, 2016 WEDNESDAY, April 20, 2016

12:30–5:00 P.M., Eastern Daylight Time 12:30–5:00 P.M., Eastern Daylight Time

11:30–4:00P.M.

, Central Daylight Time 11:30–4:00P.M.

, Central Daylight Time 10:30–3:00 P.M., Mountain Daylight Time 10:30–3:00 P.M., Mountain Daylight Time

9:30–2:00 P.M., Pacic Daylight Time 9:30–2:00 P.M., Pacic Daylight Time

For other time zones, contact the AMC ofce at [email protected].

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FORM D – AIME II Payment Form2016 AIME II

Wednesday, March 16, 2016

The AIME II on Wednesday, March 16, 2016 is a set of 15 questions, different from but comparable to the AIME I on March 3, 2016. Pleasesend payment before March 10, 2016. If you are using a credit card, you may register online at

amc-reg.maa.org

PLEASE PRINT

School CEEB # __ __ __ __ __ __

Contest Manager: ___________________________________________________________________________________________

School Name: _______________________________________________________________________________________________

School Address: _____________________________________________________________________________________________

City: ____________________________________________State: _________________________ Zip: ________________________

School Phone #: ____________________________________________________________________________________________

Email: _______________________________________________________________________________________________________

The processing fee for the second AIME is as follows: 1–10 students = $25, 11+ students = $50. We must have your payment beforethe answer forms can be graded. All AIME II answer forms must be returned by trackable express mail service, so that they arrivein the AMC ofce by March 21, 2016.

Number of AIME qualiers who will be taking the AIME II on Wednesday, March 16, 2016:

Number of AIME II Exams Requested: #_______

1–10 student qualiers @ $25.00 = $_______ OR

11+ student qualiers @ $50.00 = $_______

Method of Payment:

Check enclosed (US funds only) made payable and mailed with this form

MAA AMERICAN MATHEMATICS COMPETITIONS9050 Junction Drive

Annapolis Junction, MD 20701

Charge to Visa/Mastercard #: _________________________________________ Name on card (print): ________________________________________________________________________

Signed: _______________________________________________________________________________________

Expiration Date: ___________________ Telephone: ______________________________________________

Email: _______________________________________________________________________________________

1-800-527-3690 Email: [email protected] Fax: 240-396-5647

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Form E – Rescoring Request FormI would like to have the following student’s answer form rescored. I understand that there is a $10.00 charge for each student answerform rescored.

$ 10.00/each

School Name_____________________________________________CEEB # _______________________________________________________________

Name: _______________________________________________________________________________________________________________

Email: _______________________________________________________________________________________________________________

Address: _______________________________________________________________________________________________________________

City ___________________________________________________________________________________ State: ____________ Zip ______________

Method of Payment: Check (US funds only) made payable and mailed with this form to:

MAA AMERICAN MATHEMATICS COMPETITIONS

9050 Junction Drive

Annapolis Junction, MD 20701

Charge to Visa/Mastercard#: _______________________________________________________________________________________________

Name on card (print): __________________________________________________________________________________________________

Signed _______________________________________________________________________________________________________________

Expiration Date: _______________________________________Telephone: ____________________________________________________

FAX to: 240-396-5647

Student Name _________________________________________________________________________________________________ $ ___________________

Contest taken: AMC 10-A AMC 10-B AMC12-A AMC12-B AIME AIME II

Student Name _________________________________________________________________________________________________ $ ___________________


Student Name _________________________________________________________________________________________________ $ ___________________


Grand Total ___________________________________________________________________________________________________ $ ___________________

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FORM F – AMC Academic Integrity FormETS/CEEB #_______

American Invitational Mathematics Examination (AIME)

On-site Official

Section 1 – Student

This disclaimer statement is to be completed by all students taking the AIME in their school on the scheduled date of the contest, but aa later time from the other students, due to the requirement of attendance at an ofcial academic function, which conicted with the

regularly scheduled time of the administration of the AIME. Reexamination may be requested if, after an inquiry, there is a reasonablebasis to believe that a high score is well beyond a student’s ability.

I certify that prior to my taking of the 2016 AIME on Thursday, March 3, 2016 / Wednesday, March 16, 2016 (please circle correct date), I haabsolutely no contact or communication with any student who participated in the contest, nor had I seen any of this year’s contest questions

Signed: ___________________________________________ Date: __________________________________

Name of School: __________________________________________________

Section 2 – Contest Administrator

This section is to be completed by the teacher who administered the AIME on the day of the contest, Thursday, March 3, 2016 / WednesdayMarch 16, 2016 (please circle correct date), but at a time different from the regularly scheduled time.

This student (these students) participated in an ofcially sanctioned academic function. The student(s) had no contact or communication

with any student who participated in the contest, nor had they seen any of this year’s AIME. All contest papers were collected after anprevious administrations, and students were instructed not to discuss the questions.

I administered the AIME to the student(s) indicated in Section 1 on (DATE): _________________________

Contest time period: From ______________ to _______________

Name (please print): ____________________________________________________________

Title (please print): _____________________________________________________________

Signature: ______________________________________________________________________

School name and address: ______________________________________________________

______________________________________________________

Date this form completed: ________________________

PLEASE INCLUDE THIS FORM WITH THE ANSWER FORMS OF THE STUDENTS.

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IX. EXAM AUXILIARY MATERIAL

Practice Worksheets

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Problem Worksheets, continued

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Press ReleaseTe sample Contest Announcement news release below should be prepared and distributed to the newspapers, radio and television stationin your region. o make preparation o the news release easier, visit our web site, and download the text rom the online copy o the AIMEeachers’ Manual. See the AMC website or statistics and figures rom the 2015 contest. Statistics and figures or the 2016 Contest will beavailable on our website in late March and early April 2016. Printing this on a sheet o school stationery gives an official look to the page

(School or School District)FOR IMMEDIATE RELEASE

(School) STUDENTS PARTICIPATE IN NATIONAL MATHEMATICS COMPETITION

( # ) students at (School) participated in the 34th annual American Invitational Mathematics Examination (AIME). (Student names)

qualified or the AIME by scoring in the top 2.5% o the American Mathematics Contest 10 (AMC 10, 10th grade and below). (Student

names) qualified or the AIME by scoring in the top 5% (approximately) on the American Mathematics Contest 12 (AMC 12, 12th grade

and below).

Te AIME was held on Tursday, March 3, 2016, (or Wednesday, March 16, 2016). Tis contest was established in 1973 as an

intermediate step between the high school (AMC 10 and AMC 12) contests and the U. S. A. Mathematical Olympiad (USA(J)MO).Te AIME is a 15 question, 3 hour examination in which each answer is an integer rom 0 to 999. Students are very unlikely to obtain

the correct answer by guessing. Te questions on the AIME require only high school mathematics, and are much more difficult than

those on the AMC 10 and AMC 12. All problems on the AIME can be solved without calculus. Te use o calculators is not allowed.

Tis contest leads to the USA(J)MO, MOSP (Mathematical Olympiad Summer Program) and the selection o the USA team sent to the

International Mathematical Olympiad (IMO), the premier international high school level problem solving contest. Tis year the IMO

will be held in Hong Kong, July 6–16, 2016.

According to Mark Saul, who serves as Director o the MAA American Mathematics Competitions, the AIME is one o a series o

contests sponsored each year by Te Mathematical Association o America, through their program, the American Mathematics

Competitions (AMC). Te AMC offers the only math competition series in the country leading to the USA(J)MO and the

Mathematical Olympiad Summer Program (MOSP). Te AMC program includes:

American Mathematics Contest 8 (AMC8) Grades 6–8 November American Mathematics Contest 10 (AMC 10) Grades 10 & below 2 dates in January/February

American Mathematics Contest 12 (AMC 12) Grades 12 & below 2 dates in January/February

American Invitational Mathematics Examination (AIME) All who qualiy 2 dates in March

USA Mathematical Olympiad (USAMO) All who qualiy mid- to late-April

USA Junior Mathematical Olympiad (USAJMO) All who qualiy mid- to late-April

Mathematical Olympiad Summer Program (MOSP) Qualiy thru USA(J)MO June

International Mathematical Olympiad (IMO) op six rom USA(J)MO, MOSP July

Te MAA American Mathematics Competitions program is administered rom the headquarters o the Mathematical Associationo America. Te MAA grateully acknowledges the support o the ollowing major organizational donors to the MAA competitionsand Olympiads: Akamai Foundation and the Simons Foundation at the Patron’s Circle level; udor Investment Corporation and woSigma at the Innovator’s Circle level; American Mathematical Society, Te D.E. Shaw Group, Dropbox, MathWorks, and Susquehanna

International Group at the Winner’s Circle level; Art o Problem Solving and Jane Street Capital at the Achiever’s Circle level; and theAcademy o Applied Science, American Statistical Association and Army Educational Outreach Program at the Sustainer’s Circle level.

Visit http://www.maa.org/about-maa/our-partners or a complete list o donors. Te Contests are given across the U.S.A, Canada, and

in many schools abroad.

Details concerning the 2016 AIME contests or High School, as well as the rest o AMC’s programs are available on the AMC web site:

maa.org/amc.

American Mathematics Competitions 9050 Junction Drive | Annapolis Junction, MD 20701

800.527.3690/phone | 240.396.5647/fax | [email protected] | maa.org/amc

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March 2016

Dear Parent or Guardian:

On March 3, 2016 or March 16, 2016 your son or daughter participated in the 34th annual American Invitational Mathematics

Examination (AIME). Tis contest was established in 1973 as an intermediate step between the high school (AHSME) contes

and the USA Mathematical Olympiad (USA(J)MO). Te AIME is taken by students who achieved a score in the top 5%

(approximately) on the AMC 12, and students who achieve a score o 120 or more (approximately the top 2.5%) on the AMC 10

Te AIME is a 15 question, 3 hour examination in which each answer is an integer number rom 0 to 999. Te questions

on the AIME are much more difficult than those on the AMC 10 and AMC 12, and students are very unlikely to obtain the

correct answer by guessing. All problems on the AIME can be solved without calculus. Te use o calculators is not allowed

Tis contest leads to the USAJMO, USAMO, MOSP (Mathematical Olympiad Summer Program) and the selection o the USAteam sent to the International Mathematical Olympiad (IMO), the premier international high school level problem solving

contest. Tis year the IMO will be held in Hong Kong, July 6–16, 2016.

Te AIME provides the exceptional students who are invited to take it with yet another opportunity to challenge their

mathematical abilities. Like all examinations, it is a means towards urthering mathematical development and interest. Te

real value o the examination is in the learning that can come rom the preparation beorehand and rom urther thought

and discussion o the solutions.

Our organization regularly receives requests rom well-known colleges and universities or the names o high scoring students

A ew colleges offer scholarships to students in their region with high scores on the contests. But the real rewards come rom

challenging each student with mathematics that is new, different, and “outside o the box.” Te problems on the contest are

hard, but designed to be within reach. Even so, i your son or daughter managed to solve only one or two problems, oneshould still eel that they accomplished something, because these problems are meant to be more challenging than those they

routinely encounter in their mathematics courses.

Mathematics is increasingly important in our technological and scientific age. aking enough mathematics in high school is

the gateway to jobs and careers o all kinds, even those that are not explicitly mathematical, scientific, or technological. We

hope that by offering these contests, we can challenge and inspire students to want to learn more mathematics. We hope that

your son or daughter enjoyed the contests, and will continue to take mathematics courses and competitions in high school

and beyond.

Sincerely,

Mark Saul

Director


American Mathematics Competitions9050 Junction Drive | Annapolis Junction MD 20701


Documents

TM-AIME