# AMC 10 AMC 12

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```					       Sample Questions                                                                                                                                                                    On Thursday, May 11, 1950 the first Mathe-
The MAA AMericAn                                                                                               matical Contest, sponsored by the New York
2008 amC 10a
MATheMATics coMpeTiTions                                                                                        Metropolitan Section of the Mathematical
12. In a collection of red, blue, and green marbles,                                                                                                                                       Association of America (MAA) took place. It
there are 25% more red marbles than blue
marbles, and there are 60% more green marbles                                                                                                                                          was given in 238 schools to 6,000 students

of
The akamai Foundation
than red marbles. Suppose that there are r red                                                                                                                                         in the New York area only. Today the contest
marbles. What is the total number of marbles in                               with the following Contributors
is taken in every state and around the world.
the collection?

Excellence
American Mathematical Association of                                                                         It is translated into braille, French, Spanish
(A) 2.85r       (B) 3r        (C)3.4r                                      Two-Year Colleges
(D) 3.85r       (E) 4.25r
and Chinese, and has evolved into a series
American Mathematical Society                                                                                of five contests.
2008 amC 10a/12a                                                              American Society of Pension Actuaries
10A-4; 12A-3. Suppose that ⅔ of 10 bananas are
60 years of the
American Statistical Association
American Mathematics
1950-2009
worth as much as 8 oranges. How many oranges
are worth as much as ½ of 5 bananas?
(A) 2          (B) 5        (C) 3      (D) 7
Art of Problem Solving
Competitions
2                       2                               Awesome Math
(E) 4

The
10A-13; 12A-10. Doug can paint a room in 5 hours.                             Casualty Actuarial Society
Dave can paint the same room in 7 hours. Doug
and Dave paint the room together and take a                                Clay Mathematics Institute
one-hour break for lunch. Let t be the total time,
in hours, required for them to complete the job
working together, including lunch. Which of the
IDEA Math

Institute for Operations Research and
American
the Management Sciences
following equations is satisfied by t ?
(A) (5 + 7) (t + 1) = 1 (B) ( 5 + 7) t + 1 = 1
1 1                     1 1                                           L. G. Balfour Company                                                                                         Mathematics
Mu Alpha Theta
(C) (1 + 7) t = 1          (D) (1 + 7) (t – 1) = 1
Competitions
1                          1
5                          5                                          National Assessment & Testing
(E) (5 + 7)t = 1                                                           National Council of
Teachers of Mathematics
2008 amC 12a                                                                                                                                                                               Help us celebrate 60 years of the
AMC 10
Pedagoguery Software Inc.
14. What is the area of the region defined by the                                                                                                                                          American Mathematics Competi-
inequality |3x – 18| + |2y + 7| ≤ 3 ?                                     Pi Mu Epsilon

(A) 3           (B) 2
7
(C) 4               9
(D) 2                      Society of Actuaries

AMC 12
(E) 5                                                                      U.S.A. Math Talent Search
to participate in the 60 th annual
American Mathematics Contest 12
18. Triangle ABC, with sides of length 5, 6, and 7,                           W. H. Freeman and Company
has one vertex on the positive x-axis, one on                             Wolfram Research Inc.
and the 10th annual American Math-
the positive y-axis, and one on the positive z-                                                                                                                                        ematics Contest 10. The AMC 10 is
axis. Let O be the origin. What is the volume of
tetrahedron OABC?
___           ___           ___                                                                                                 2008-2009 ConteSt DateS                           designed for 9th and 10th grade stu-
(A) √ 85       (B) √ 90      (C) √ 95
For 2008-2009 the National Association of Second-
ary School Principals (NASSP) has again placed the
amC 8 - November 18, 2008
amC 10 - February 10 and/or February 25, 2009
dents, and the AMC 12 is designed
___
(D) 10         (E) √105
AMC 8, AMC 10, and AMC 12 on the NASSP Na-
tional Advisory List of Contests and Activities.                             amC 12 - February 10 and/or February 25, 2009   for 11th and 12th grade students. The
aime - March 17 or April 1, 2009
Mathematical Association of America                            uSamo - April 28-29, 2009                       Contests will be held on two dates:
moSp - June 2009                                TUESDAY, February 10, 2009 and/or
12A-14.(A); 12A-18. (C)
American Mathematics Competitions
10A-12. (C); 10A-4 + 12A-3. (C); 10A-13 + 12A-10. (D);                                                                                imo - July 2009, Germany
amcinfo@maa.org      http://www.unl.edu/amc/   800-527-3690
WEDNESDAY, February 25, 2009.
American Mathematics Contest 10                      The AMC 10A and AMC 12A date is TUESDAY, February 10, 2009, and the AMC 10B and AMC 12B date is WEDNESDAY, February 25, 2009. The contests are
given at the same time to all participating students in a convenient 75-minute interval, preferably in the morning. The contests should be proctored by a faculty/staff
amC 12 & amC 10                                      member of the participating school.
To offer more opportunities for students to participate, the AMC is encouraging colleges and universities to offer the AMC 10B/12B on their campuses. Contact local
math departments to see if they will be offering the B-date contests in your area. In the fall we will post the names of participating institutions on our website as they
partiCipation & eligibility                           become available.
Both AMC 10 and AMC 12 are 25-question,
75-minute multiple-choice contests administered       regiStration anD feeS                                                           reSultS & StuDent awarDS                                    purpoSe
in your school by you or a designated teacher.        Register by returning the enclosed registration form                            Each participating school receives a copy of the contest    The Mathematical Association of America
The AMC 12 covers the high school mathemat-           or on the web at www.unl.edu/amc.                                               and solutions, individual school results, school awards     wants to increase interest in mathematics and
ics curriculum, excluding calculus. The AMC 10        Standard fees are as follows:                                                   and the National Summary of Results and Awards              to develop problem solving through a friendly,
covers subject matter normally associated with        - Registration & Std Shipping (to Dec 15, Contest A only)......\$40
booklet.                                                    and fun, competition. We believe that one way
grades 9 and 10. To challenge students at all         - Registration & 2-day Shipping (Dec 16-Jan 26)....................\$50          Schools with at least three participants on a contest       to meet this goal is to identify, recognize, and
grade levels, and with varying mathematical skills,   - registration & 1-day Shipping 12A (Jan 27-Feb 3) .....\$60                     date will be eligible for team, state and national          reward excellence in mathematics through a
the problems range from fairly easy to extremely      - registration & 1 day Shipping 12B (Jan 27-Feb 18) ...\$60                      awards. The USA and Canada are divided into                 series of national contests.
difficult. Approximately 12 questions are com-        - AMC 10 - One bundle of 10 Contests .....................................\$15   eleven contest regions, and National Awards are
mon to both contests. Students may not use            - AMC 12 - One bundle of 10 Contests .....................................\$16   given in each region to the top five schools and top
calculators on the contests.                          Schools using a credit card or purchase order                                   ten students who officially participate in the contests.
AMC 12 Eligibility – A student in a program           may register at www.unl.edu/amc or fax to us at                                 There are a variety of other national and student
leading to a high school diploma, and under 19.5      402-472-6087. We accept Visa and Mastercard.                                    awards; they can be seen on our website.
years of age on the day of the contest.               When paying by check, please mail your registration                             AMC 12 students who rank in the top 5% nationally (or
aMC 10 eligibility – A student in a program           form with payment well in advance of the deadline                               score at least 100) will qualify for the American Invita-
leading to a high school diploma, under 17.5          dates.                                                                          tional Mathematics Exam (AIME). AMC 10 students
years of age on the day of the contest, and not       6 poSter Set - When you register for the                                        who rank in the top 1% nationally (or score at least 120)
enrolled in grades 11 or 12 or equivalent.            AMC 10 &/or AMC 12 we will include a free gift – a                              will also qualify for the AIME. The USA Mathematical
Home schools must indicate the site of the            set of six posters celebrating the sixty years of the                           Olympiad (USAMO) qualifiers are picked from the top
exam (not the student’s home) and the name            American Mathematics Competitions.                                              students on the AIME.
eDyth may Sliffe awarD
of the proctor (not a parent) and attach this                                                                                                                                                     The Edyth May Sliffe Award for Distinguished
information to the registration form. Please call                                                                                                                                                 High School Teaching is given each year to at
the AMC office for details.                                                                                                                                                                       least twenty teachers, based on students who
do well on the AMC 12 and the nominations of
the student team members. The winners receive
a cash prize, a certificate, and a one-year com-
plimentary membership in the Mathematical As-
sociation of America (MAA) and in the National
Council of Teachers of Mathematics.

math Club paCkage
For an additional \$25.00 you can order a Math Club
Package, which includes a Club Advisor’s Handbook
Spanish and French editions of the 2009 AMC 10 and AMC12 are available on request. Braille and large print
archives) plus a CD with all the contests given from
editions are also available. All requests must be made at least three weeks before the contest.
2001 through Spring 2008, including the AMC 8, 10,
Early registration will reduce your cost and provide you extra time to fully utilize the study guide found in the                           and 12, the AIME, and the USAMO.
Teachers’ Manual and the Math Club package, if you have ordered the 2008-2009 edition.

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