AIME Teacher's Manual

34th Annual

American Mathematics Competitions

American InvitationalMathematics Examination

TEACHERS’MANUALInstructions and Reporting Formsfor School Contest Managers

dates to remember:

AIME - Thursday, March 3, 2016AIME 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

To All AIME Managers:

Please read this manual regarding the AIME rules and regulations thoroughly. Note our policy for the official administration of the AIME. The AIME I can only be given officially on ThursdAy, March 3rd, and the AIME II can only be given officially on WEdNEsdAy, March 16, 2016. The contest should be scheduled from 9am to 12 noon if possible.

All students who are in the top 5% of 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% of the American Mathematics Contest 10 (AMC 10) participants or score at least 120 points, are invited to take the AIME. The AIME is the second in the sequence of mathematics contests which leads to participation in the usA Mathematical Olympiad and the designation of Winners of the usA(J)MO. The AIME is a 15-question, 3-hour examination. All answers are integers ranging from 000 to 999, inclusive. The score is the number of correct answers. There is neither partial credit nor a penalty for wrong answers.

I call your attention to several items found in this manual which answer inquiries I frequently receive from AIME Managers:

1. All administrations of the AIME must take place on the scheduled dates. The processing fee for the second AIME contest is as follows: $25 for 1–10 students, and $50 for 11 or more students. We must have your payment before we grade the answer forms. The AIME II payment form can be found on page 13 of this manual. All AIME II answer forms must be returned by trackable express mail service, so that they arrive in the AMC office by March 21, 2016.

2. Email requests for 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 of students taking the AIME II, and method of 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 of how and when you will receive results.

5. you will find all the information and forms relevant to the taking of the usA(J)MO on our website, maa.org/amc. If you have had students qualify for the usA(J)MO in the past, or you are anticipating this to be so this year, please go to maa.org/amc to find the usA(J)MO Teachers’ Manual.

6. The second AIME on Wednesday, March 16, 2016 is a set of 15 questions, different from, but comparable to the AIME I on March 3, 2016.

7. selection of usAMO & usAJMO participants will depend on the AMC 10/12 score, and AIME score.

We feel that the 2016 AIME will be interesting and challenging to your student(s). On behalf of the Committee on the American Mathematics Competitions, I send my appreciation to you for assisting with the implementation of this examination.

sincerely,

Mark saul director MAA American Mathematics Competitions

MAA American Mathematics Competitions

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ContentsI. List of the sponsors of the American Mathematics Competitions .......................................................................... 3 Attention Contest Managers ......................................................................................................................................... 4II. Contents of Package ....................................................................................................................................................... 5III. Preparation Instructions .............................................................................................................................................. 5IV. day of the AIME Instructions ...................................................................................................................................... 5V. report of the AIME results .......................................................................................................................................... 6VI. Eligibility ......................................................................................................................................................................... 6VII. Policy on AIME Administration .................................................................................................................................. 6VIII. Visually Impaired and Learning disabled students .................................................................................................. 7IX. request for student Names ........................................................................................................................................... 7X. Fascimile of the March 3, 2016 AIME Front Cover .................................................................................................. 8 FOrM A – Examination Certification 2016 AIME .................................................................................................. 9 FOrM B – usAMO/usAJMO Information Form ................................................................................................ 10 FOrM C – Publication Order Form ........................................................................................................................ 11 FOrM d – AIME II Payment .................................................................................................................................. 13 FOrM E – rescore Form ........................................................................................................................................... 14 FOrM F – AMC Academic Integrity Form ............................................................................................................ 16IX. Exam Auxiliary Material ............................................................................................................................................ 16 Practice Worksheets .................................................................................................................................................... 16 Press release ................................................................................................................................................................ 21 Letter to Parents .......................................................................................................................................................... 22

I. List of SponsorsThe

MAA American Mathematics Competitionsare supported byPatron’s Circle

Akamai Foundationsimons FoundationInnovator’s Circle

Tudor Investment Corporation Two sigma

Winner’s CircleAmerican Mathematical society

The d.E. shaw Groupdropbox

MathWorkssusquehanna International Group

Achiever’s CircleArt of Problem solving

Jane street CapitalSustainer’s Circle

Academy of Applied scienceAmerican statistical Association

Army Educational Outreach Program

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

ATTENTION CONTEST MANAGERS

IMPORTANT DATES – AIME I

February 26, 2016 Final day for AIME qualifier schools to change from the AIME II date to the AIME I date.Before March 3, 2016 Have students fill in all name and demographic information on answer sheets — before the day

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

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 for the AIME II contest.Before March 15, 2016 Have students fill in all name and demographic information on answer sheets — before the day

of the contest.March 15, 2016 Contest managers will receive by email an electronic copy of the AIME II contest booklet which

should be printed for contest administration.March 16. 2016 Official contest administration date.March 17, 2016 Return answer sheets to the MAA AMC office the day after contest administration — don’t for-

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 for AIME II.• Verify your contest materials immediately upon delivery. There should be enough answer sheets included to match the number of

students invited to participate in the AIME contest. There should also be one AIME return envelope, one school ID form, and enough AIME I contest booklets and answer sheets for the students invited to participate in the AIME contest. If any materials are missing, please 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 of nicknames or other versions of their name may result in a student not being invited to take the USA(J)MO.

• All award packets for schools that have AIME qualified students will include AIME I contest booklets and answer sheets. If participat-ing in the AIME II contest, the AIME II contest booklets will be emailed to the contest manager by 12 pm EST on March 15, 2016. The answer sheets, school ID form, certification form, and return envelope provided in the award packet should be used for the AIME II contest.

• The AIME Teacher’s Manual is online this year. Please download and print your copy at www.maa.org/math-competitions under Teacher Resources.

• Do not use photocopied answer sheets. Photocopied answer sheets cannot be read by our scanners and cannot be scored. Contact customer service immediately if 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 name, age, date of birth, grade, gender, and address prior to the contest date. Incomplete answer sheets could result in incorrect or delayed scoring. After the contest administration, please verify that these portions of each answer sheet have been completed correctly.

• Complete and include the School Identification Form. The correct CEEB (school) code, number of answer sheets returned, and date the contest was given are crucial to the scoring process. If you are unsure of the correct code, please contact Customer Service prior to returning your contest materials. Errors in completion of this form can lead to inaccurate score reports.

• Complete and include Form A (Examination Certification 2016 AIME), Form B (USAMO/USAJMO Information Form) and Form F (AMC Academic Integrity Form). These forms are included in your contest package, but can also be found on pages 9, 10, and 15 respectively, of the AIME Teachers’ Manual. Please be sure to include all signatures, dates, and necessary exceptions.

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

• Late return of answer sheets may disqualify students from the USA(J)MO invitational contests.• Returned answer sheets must be shipped via a trackable method. The MAA AMC is not responsible for lost answer sheet packages. It

is 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 the following material:

• A list of your qualified AIME students.• A sealed envelope containing one AIME for each of your

qualified students and an extra copy for you. The envelope must NOT be opened until just before the examination is given on the authorized date.

• One AIME Answer Form for 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 for the AIME with your AIME school report.

III. Preparation Instructions 1. Please study the contents of this Teachers’ Manual.2. reserve a room for 3 1/2 hours from 8:45 am–12:15 pm in your

own (u.s.) time zone. This allows 15 minutes for pre- and post-examination activities and 3 hours for the examination itself. For time zones outside the continental u.s., the AIME I must be given after 9 am, EdT (uTC-4) on March 3, 2016, at the earliest convenient time, with a similar scheduling requirement for the AIME II on March 16, 2016. In extreme cases when you cannot administer the AIME between 7:00 am and 3:00 pm, please complete the academic integrity pledge form on page 15.

3. Inform your students of the time and place well in advance of the competition. urge them to prepare for the AIME by studying past AIME exams and solutions. For information about 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 of: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 computing devices are NOT permitted, nor is any device allowing communication with someone outside the contest venue.

7. Complete the AIME school Identification Form using the instructions found on that form.

8. Please study the AIME student Answer Form. have each student complete side 1 of the Form using the instructions found on the form. Please follow carefully the marking instructions printed on both the identification form and the student answer form. double check to see that all the items are filled out correctly. students may not complete the personal information after the time allowed for the test. Only the information which has been properly blackened will be read by the scanning equipment. Be sure to note the student’s AMC 10 or AMC 12 score in the appropriate area, including decimal fractions if needed.

9. After completing step 8, the AIME answer form will be ready for distribution to your participating students on Thursday, March 3rd.

10. Make arrangements to mail your AIME report Envelope by trackable mail service. Please note that this is an oversized envelope, which may require special postage even if its weight is one ounce or less.

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

package was opened not more than one hour before the contest.2. seat participants in alternate seats.3. Ensure that each participant has the supplies listed in Item 5

under section III.4. Inform the students that they are not to open the exam booklet

until instructed to do so.5. Pass out the contest booklets and have the students read the

instructions on the front cover. 6. distribute the AIME Answer Forms (which you or your

students have previously prepared) to the students. Inform them that their answers should be marked with a pencil on sIdE 2 of the answer form and that each problem has only one correct answer, which is an integer between 000 and 999 inclusive.

7. read aloud the following instructions for recording answers to the problems:a. For each question you answer, use a #2 pencil to write your

answer at the top of the problem’s answer column. use 3 digits. Then, in each of these columns, blacken the one circle which is labeled with the digit you have written at the top. PLEAsE NOTE: A single digit answer, such as 7, should be written and blackened as 007 and a two digit answer, such as 43, should be written and blackened as 043.

b. dO NOT BLACKEN ANsWErs uNTIL yOu ArE CErTAIN OF yOur FINAL ChOICE. AVOId, IF POssIBLE, ErAsurEs IN ThE CIrCLEs.

c. The results will be graded by computer. Only the blackened circles will be graded.

8. Ask the students if they have any questions about using the AIME Answer Form or about the instructions for the examination.

9. start the Examination.10. Check to see that each student is marking his/her Answer Form

properly.11. Allow exactly 3 hours working time.12. If there is an urgent need to use a bathroom, only one student

may leave at one time and the AIME answer form and contest booklet should be retained by you while the student is out of the room. If there is a health or medical emergency, a backup contest manager should be available to assist.

13. At the end of 3 hours, instruct the students to:a. sTOP.

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b. Put aside the contest booklet and scratch paper and look again to be sure the AIME Answer Form has been filled out correctly.

c. Be sure the written answers on the top of the AIME Answer Form are in agreement with the answers coded in the blackened circles.

d. sign their name on side 2 of the answer form.e. hand in the AIME Answer Form.f. Keep the contest booklet for their reference in reviewing

the solutions. Inform the students that they may now leave the examination room.

14. Complete the Certification Form (Form A) and usA(J)MO Information Form (Form B) found on pages 9 and 10.

15. The following material should be sealed in the AIME report Envelope, postmarked NO LATEr ThAN 24 hours after the examination is given, and sent to the AMC Customer service:a. the signed AIME Certification Form A and usA(J)MO

Information Form B;b. the AIME school Identification Form; c. one AIME Answer Form for each participating student.

Please do not paper clip or staple the forms together. Please do not fold the forms.

schools located outside the u.s. must return materials by AIr EXPrEss MAIL (dhL, Federal Express, etc.).

16. Please note that if you have requested the AIME II you must send your payment separately and in advance of the day of the contest (Wednesday, March 16th).

V. Report of the AIME Resultsyour students’ AIME scores, along with certificates of participation and an AIME solutions Pamphlet, will be sent to you after the contest. Please retain this report for future reference, either in your own files or with your student counselor office. Many students cite their scores on college applications, and want verification. The AMC office will not be able to retrieve or verify student scores.

VI. EligibilityAny student who is officially enrolled in high school (or below), or is a actively working towards a high school diploma (and has not graduated) is eligible to take the AIME (with qualifying score). us and Canadian Citizens and students studying in the united states (with qualifying scores) are eligible to take the usA(J)MO.home schooled students age 19.5 and under are eligible for the AIME (with qualifying scores). students learning English as a second language (EsL) may use a book or dual-language nontechnical dictionary of English and their native language. A student may use the dictionary only the first time that he/she takes the AIME contest. The dictionary must be given to the school contest manager to examine and retain for the 24-hour period preceding the contest. The proctor must announce to other students that this student has been given special permission to use the dictionary during the contest.

VII. AIME Administration Policyyou must administer the AIME on the official date (March 3rd and 16th, 2016), to all your students, in the same place and at the same time. students invited to take the AIME who cannot be there will miss this opportunity. students who miss the AIME I contest on Thursday, March 3, may take the AIME II on Wednesday, March 16. The AIME II contest is a new set of 15 questions, different from, but comparable to the questions on the AIME I contest. After the date of the AIME I contest, questions from this contest may be used for practice.If you need to have a student sit for the AIME II on March 16th, please read the applicable details below. Contact the AMC office if you have questions. There is a charge for the second contest. These two dates will be the only ones acceptable to qualify for the usA(J)MO. The processing fee for the second AIME contest is as follows: $25 for 1–10 students, and $50 for 11 or more students. We must have your payment before we grade the answer forms. The AIME II payment form can be found on page 13 of this manual. All AIME II answer forms must be returned by trackable express mail service, so that they arrive in the AMC office by March 21, 2016. Email requests for the second AIME may be sent to:

[email protected]

Email requests should include the school’s CEEB number and complete mailing address, teacher’s name, teacher’s email address, the number of students taking the AIME II, and the method of payment. Alternatively, you may wish to register online, using a credit card, at amc-reg.maa.org. The AMC office will send a confirmation of registration for the AIME II. Please note that you will be billed for all AIME II orders unless you cancel your order before March 10, 2016.

Under no circumstances can a student take both AIME contests.

Procedures for the AIME IIThe AMC uses a different procedure for delivery of the AIME II contest. recall that the date for the AIME II is Wednesday, March 16, 2016.1. The AMC office will mail the 2016 AMC 10 and 2016 AMC 12

reports back to schools starting in mid-February and continuing until early March. your school’s AIME qualifiers are listed in that report.

2. The AIME I contest will be included with the AMC 10 and AMC 12 school reports, in a sealed envelope. There will be one contest booklet and one answer form for each AIME qualifier.

3. If your AIME qualifiers will be taking the AIME I on Thursday, March 3, 2016, you need only follow the directions for the AIME I in this Teachers’ Manual and send back the AIME answer forms for scoring.

4. If your AIME qualifiers will be taking the AIME II on Wednesday, March 16, 2016 then you will still need to fill out the AIME II registration either on our web page at amc-reg.maa.org/home or by using the form in this AIME Teacher’s Manual. Be sure to include a valid email address.

5. sAVE the AIME Answer Forms you receive in the AMC 10/AMC 12 report. The answer forms can be used either for the AIME I

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or the AIME II contests, simply by filling in the corresponding circle above the name portion on the front of the answer form. Also save the AIME report Envelope, which can be used for sending back either contest.

6. Watch your email on Tuesday, March 15, 2016 (after 12:00 noon EdT) for an email with an attachment containing the AIME II exam. The AIME II will come as a PdF document attached to the email. Print the AIME II, and then make enough copies to have one for each participating AIME qualifier.

7. Be sure to have students taking the AIME II fill in the AIME II circle on the front of the answer form, near the space for the student’s name.

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

Questionable ScoresIf it is clear to the Contest Manager from personal observation that a student has cheated, then the Manager must disqualify the student. If the Contest Manager receives an accusation of cheating, or obtains other indirect evidence of cheating, then the Manager must hold back the student’s paper and immediately report all the facts of the situation to the AMC director, who in conjunction with the Chair of the CAMC, will determine what to do. uNdEr NO CIrCuMsTANCEs may the school decide on its own to accept a questionable score, nor should a school retest the student in ques-tion before receiving instructions from the AMC Office.

Contest Proctoring

The proctoring of the AIME contest should be by:1st preference, a math teacher at the school2nd preference, a teacher or administrator at the school3rd preference, a college or university teacher of mathematics or a

responsible adult who is a math club or team coach, and not related to any of the participants

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

• The proctoring of 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 one group or in separate classrooms and be under the supervision of a proctor.

• The proctor should not be related to any of the participants• If a parent wishes to help, they can arrange room reservations

and set-up, help with student sign-up, provide treats, etc. Par-ents may not proctor the contest.

VIII. Visually Impaired and Learning Disabled StudentsIf one of your AIME qualified students is visually impaired and/or learning disabled please call the AMC office and we will discuss the options available to you. We do not have copies available in braille. The time allowance for students with learning disabilities is 4.5 hours. It is the responsibility of the school and the contest manager to make arrangements consistent with the student’s accommodation plan. Please contact us at [email protected] for more information.

IX. Request for Student NamesThe following statement appears on the student answer forms for the AMC 10 and AMC 12:1. The American Mathematics Competitions (AMC) receives

requests from educational institutions and organizations for the names, addresses and grade levels of high scoring students. This information is used for recruiting and academic purposes.

2. Blacken this circle if you give the AMC permission to release this information to these organizations. (your score will not be affected if you do not blacken the circle.)

receiving information is an “opt-in” decision for each individual student. The AMC handles requests from institutions and organizations on a case-by-case basis and evaluates each individually for appropriateness. We provide legitimate educational institutions of all levels, both secondary and collegiate/university level, with one-time use of selected names and addresses for postal mailings. We also provide professional and scholarly organizations such as those listed as contributors to the AMC with one-time use of names and addresses for postal mailings, generally for professional or career information. The only information we provide is the name, address, city, state, and zip code necessary for 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 NOT OPEN ThIs BOOKLET uNTIL yOur PrOCTOr GIVEs ThE sIGNAL TO BEGIN.

2. This is a 15-question, 3-hour examination. All answers are integers ranging from 000 to 999, inclusive. your score will be the number of correct answers. There is neither partial credit nor a penalty for wrong answers.

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

4. A combination of the AIME and the American Mathematics Contest 12 are used to determine eligibility for participation in the usA Mathematical Olym-piad (usAMO). A combination of the AIME and the American Mathematics Contest 10 are used to determine eligibility for participation in the usA Junior Mathematical Olympiad (usAJMO). The usAMO and usAJMO will be given on TuEsdAy and TuEsdAy, April 19 and 20, 2016.

5. record all your answers, and identification information, on the AIME answer form. Only the answer form will be collected from you.

The publication, reproduction, or communication of the problems or solutions for this contest during the period when students are eligible to participate seriously jeopardizes the 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 of America

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FORM A – Examination Certification 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; that the 3-hour time limit was strictly enforced; that the test envelope was sealed until the time of the test; that no student had access to the 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 Competitions reserves 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 disqualification, follow-up inquiries and re-examination are similar to those for the AMC 10 and AMC 12, as outlined in the AMC 10/12 Teachers’ Manual.)

Signature of AIME School Manager ____________________________________________________________

Email ___________________________________________________________________________________

Date _________________________________ School Telephone # ________________________________

Name of School ____________________________________________________________________________

State _________________________ School Identification 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 qualified 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 Answer Forms.

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 FormWhen a student qualifies for the United States of America Mathematical Olympiad (USA(J)MO), both the student and the USA(J)MO School Manager are notified at least one week before the USA(J)MO date. When a USA(J)MO invitation is extended, both the student and the USA(J)MO School Manager must complete and return a USA(J)MO Response Form. If the Form is not returned, the situation is noted 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 any other 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 equivalent) on 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 the administration 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 THE 2016 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 11:30–4:00 p.m., Central Daylight Time 11:30–4:00 p.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., Pacific Daylight Time 9:30–2:00 p.m., Pacific Daylight Time

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

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13


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. Please send 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 before the answer forms can be graded. All AIME II answer forms must be returned by trackable express mail service, so that they arrive in the AMC office by March 21, 2016.

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

Number of AIME II Exams Requested: #_______

1–10 student qualifiers @ $25.00 = $_______

OR

11+ student qualifiers @ $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

14


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 answer form 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 ___________________________________________________________________________________________________ $ ___________________

15


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 at a later time from the other students, due to the requirement of attendance at an official academic function, which conflicted with the regularly scheduled time of the administration of the AIME. Reexamination may be requested if, after an inquiry, there is a reasonable basis 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 had absolutely 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 / Wednesday, March 16, 2016 (please circle correct date), but at a time different from the regularly scheduled time.

This student (these students) participated in an officially 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 any previous 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.

16


IX. EXam auXIlIary matErIal

Practice Worksheets

17


Problem Worksheets, continued

18



19



20



21


Press ReleaseThe sample Contest Announcement news release below should be prepared and distributed to the newspapers, radio and television stations in your region. To make preparation of the news release easier, visit our web site, and download the text from the online copy of the AIME Teachers’ Manual. see the AMC website for statistics and figures from the 2015 contest. statistics and figures for the 2016 Contest will be available on our website in late March and early April 2016. Printing this on a sheet of 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 for the AIME by scoring in the top 2.5% of the American Mathematics Contest 10 (AMC 10, 10th grade and below). (student names) qualified for the AIME by scoring in the top 5% (approximately) on the American Mathematics Contest 12 (AMC 12, 12th grade and below).

The AIME was held on Thursday, March 3, 2016, (or Wednesday, March 16, 2016). This 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). The AIME is a 15 question, 3 hour examination in which each answer is an integer from 0 to 999. students are very unlikely to obtain the correct answer by guessing. The 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. The use of calculators is not allowed. This contest leads to the usA(J)MO, MOsP (Mathematical Olympiad summer Program) and the selection of the usA team sent to the International Mathematical Olympiad (IMO), the premier international high school level problem solving contest. This year the IMO will be held in hong Kong, July 6–16, 2016.

According to Mark saul, who serves as director of the MAA American Mathematics Competitions, the AIME is one of a series of contests sponsored each year by The Mathematical Association of America, through their program, the American Mathematics Competitions (AMC). The AMC offers the only math competition series in the country leading to the usA(J)MO and the Mathematical Olympiad summer Program (MOsP). The 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 qualify 2 dates in March usA Mathematical Olympiad (usAMO) All who qualify mid- to late-April usA Junior Mathematical Olympiad (usAJMO) All who qualify mid- to late-April Mathematical Olympiad summer Program (MOsP) Qualify thru usA(J)MO June International Mathematical Olympiad (IMO) Top six from usA(J)MO, MOsP July The MAA American Mathematics Competitions program is administered from the headquarters of the Mathematical Association of America. The MAA gratefully acknowledges the support of the following major organizational donors to the MAA competitions and Olympiads: Akamai Foundation and the simons Foundation at the Patron’s Circle level; Tudor Investment Corporation and Two sigma at the Innovator’s Circle level; American Mathematical society, The d.E. shaw Group, dropbox, MathWorks, and susquehanna International Group at the Winner’s Circle level; Art of Problem solving and Jane street Capital at the Achiever’s Circle level; and the Academy of 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 for a complete list of donors. The Contests are given across the u.s.A, Canada, and in many schools abroad.

details concerning the 2016 AIME contests for high school, as well as the rest of AMC’s programs are available on the AMC web site: maa.org/amc.

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


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). This contest was established in 1973 as an intermediate step between the high school (AhsME) contest and the usA Mathematical Olympiad (usA(J)MO). The AIME is taken by students who achieved a score in the top 5% (approximately) on the AMC 12, and students who achieve a score of 120 or more (approximately the top 2.5%) on the AMC 10 .

The AIME is a 15 question, 3 hour examination in which each answer is an integer number from 0 to 999. The 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. The use of calculators is not allowed.

This contest leads to the usAJMO, usAMO, MOsP (Mathematical Olympiad summer Program) and the selection of the usA team sent to the International Mathematical Olympiad (IMO), the premier international high school level problem solving contest. This year the IMO will be held in hong Kong, July 6–16, 2016.

The 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 furthering mathematical development and interest. The real value of the examination is in the learning that can come from the preparation beforehand and from further thought and discussion of the solutions.

Our organization regularly receives requests from well-known colleges and universities for the names of high scoring students. A few colleges offer scholarships to students in their region with high scores on the contests. But the real rewards come from challenging each student with mathematics that is new, different, and “outside of the box.” The problems on the contest are hard, but designed to be within reach. Even so, if your son or daughter managed to solve only one or two problems, one should still feel 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. Taking enough mathematics in high school is the gateway to jobs and careers of 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 sauldirectorMAA American Mathematics Competitions

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


MAA American Mathematics Competitions

AIME Teacher's Manual

Documents

Transcript of AIME Teacher's Manual