2014 Raytheon MATHCOUNTS National Competition
2014 Raytheon MATHCOUNTS National CompetitionFriday May 9, 2014 - Washington, 28Rank123456789101112StudentSwapnil GargKevin LiuDaniel ZhuAlan PengNicholas SunHongyi ChenColin TangVinjai ValeFreddie ZhaoJun-Hee LeeGraham O’DonnellAkshaj KadaveruElbert DuAndy XuDaniel KimFranklyn WangKevin FengVincent HuangAlexander GuJason LeeBrian ReinhartDaniel LiuZack LeeRaymond FengJeffrey ChangChang YuAllen RyuJoseph FefferState niaMarylandVirginiaNew 1920212223StudentHarry WangRajiv MovvaWilliam SunHannah ZhangWilliam WangWalker KroubalkianChristopher LeePeter RowleyJeffery LiJae Hyun LimKaan DokmeciSrivats NarayananJoshua LeeDaniel ChuSpencer LiuRichard XuThomas LuoDavid MaMatthew DaiAllen ChenAlan TuJeremy ChenWanlin LiSamuel MersonMichelle ShenAnders OlsenRichard LiuPeter ZhuTeamKansasMichiganNevadaNew JerseyNorth CarolinaSouth CarolinaIowaWisconsinOregonOhioArizonaWritten Competition Champion - Kevin Liu, IndianaWritten Competition Runner-Up - Nicholas Sun, IllinoisS - Semifinalist; Q - Quarterfinalist; P - Countdown Round ParticipantState NY8MD7MA8NC8IL7NY7MA8PA8AZ8IN8OR8FL8OH8
2014 Raytheon MATHCOUNTSNational CompetitionOrlando, FLCompetition StatisticsFriday, May 9, 2014National CompetitionScoring Statistics---------------Team -------------------------------- Individual --------------------Indiv. TotalSprint ScoreTarget ScoreTeam TotalTeam 8.3235.2711.11Maximum43.0028.0016.0052.7518.00Std. Dev.9.375.644.239.972.88Grade / Gender 1Total5/9/2014 8:21:52 PMU0Total224Page 1 of 1
2014 Raytheon MATHCOUNTSNational CompetitionOrlando, FLScore DistributionsFriday, May 9, 2014Number of StudentsNational Competition161514131211109876543210135791113 151719 21 23 25 27 29Individual Total Score31 3335373941 43452018Number of Students1614121086420123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Individual Sprint Score5045Number of Students403530252015105005/9/2014 8:22:33 PM246810Individual Target Score121416Page 1 of 2
2014 Raytheon MATHCOUNTSNational CompetitionOrlando, FLScore DistributionsFriday, May 9, 2014National Competition16Number of Teams141210864205101520253035404550Team Total Score (Rounded to the closest m ultiple of 5)55606516Number of Teams1412108642025/9/2014 8:22:33 PM4681012Team Round Score14161820Page 2 of 2
2014 Raytheon MATHCOUNTSNational CompetitionOrlando, FLQuestion AnalysisFriday, May 9, 2014National Competition250212211201 208219217194Number 2978774136585554465135120123456789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Sprint Round Question250209Number Correct2001771671501229183100663950012345678Target Round Question6055555452Number Correct50402827301920101065012345678910Team Round Question5/9/2014 8:22:58 PMPage 1 of 1
2014National CompetitionAnswer KeyThe appropriate units (or their abbreviations) are providedin the answer blanks.Note to coordinators: Answers to the Tiebreaker Roundproblems appear in the Tiebreaker Round Booklet.National Sponsors2014 MATHCOUNTSNational Competition SponsorRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3M FoundationArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2014. All rights reserved.04-N14ANS
Sprint Round Answers141.5000.511. 9021.2.30 %12. 201322. 423.8 years13. 4 solutions23. 9 base 104. 6.5014. 9 pairs24. 225.2015.6.(1, 1)16. 11 m226. 3.757.2817. 1927.8.24 cm18.28. 09. 1135722619.920. 530. 810. 2 3 cmor 3 213102425. 2253529. 32 pagesTarget Round Answers1.53.655.56 in27.2. 3.834.13 travelers6.2328.19118710 inTeam Round Answers1.25 boxes6.32 units22. 1150 or 1150.007.46 in23.26858.2715, 6254.659.1020 ways5.15410. 80 degreesCopyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Answer Key
2014National CompetitionSprint RoundProblems 1 30HONOR PLEDGEI pledge to uphold the highest principles of honesty and integrity as a Mathlete . I will neither give noraccept unauthorized assistance of any kind. I will not copy another’s work and submit it as my own. Iunderstand that any competitor found to be in violation of this honor pledge is subject to disqualification.Signature DatePrinted NameStateDO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.This section of the competition consists of 30 problems. You will have 40 minutes to completeall the problems. You are not allowed to use calculators, books or other aids during this round.If you are wearing a calculator wrist watch, please give it to your proctor now. Calculationsmay be done on scratch paper. All answers must be complete, legible and simplified to lowestterms. Record only final answers in the blanks in the left-hand column of the competitionbooklet. If you complete the problems before time is called, use the remaining time to checkyour answers.In each written round of the competition, the required unit for the answer is included in theanswer blank. The plural form of the unit is always used, even if the answer appears to requirethe singular form of the unit. The unit provided in the answer blank is the only form of theanswer that will be accepted.Total CorrectScorer’s InitialsNational Sponsors2014 MATHCOUNTSNational Competition SponsorRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3M FoundationArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2014. All rights reserved.04-N14SPR
1.What is the mean of the 10,000 integers from 1 to 10,000, inclusive? Expressyour answer as a decimal to the nearest tenth.%2.What percent of the integers from 3 to 12, inclusive, are neither primes normultiples of 4?years3.On the next full moon, Bob will celebrate being alive for 100 full moons. Onaverage, the cycle of the moon has lasted 29.53 days since he was born. In years,how old will Bob be on his 100-moons birthday? Express your answer to thenearest whole number. 4.Samantha bought 6 total pounds of red and green candies to share with herfriends. The red candies cost 1.00 per pound and the green candies cost 1.25per pound. She bought twice as many pounds of red candies as greencandies. How much did Samantha pay for the 6 pounds of candies?5.The sum of nine consecutive integers is 216. What is the smallest of the nineintegers?(,)6.A kite is a quadrilateral in which two pairs of adjacent sides are congruent.Points A ( 2, 1), B (1, 5), C (4, 1) and D (x, y) are vertices of a convex kite withan area of 18 units2. If x and y are integers, what are the coordinates of point D?Express your answer as an ordered pair.Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Sprint Round
7.What is the smallest value of x such that 3(x 21) 8 and x is a multiple of 7?acm8.Two squares, with integer side lengths a and b, are arranged sothat one entire side of the smaller square overlaps a part of aside of the larger square, and the two squares share a vertex, asshown. The perimeter of the entire figure is 86 cm, and the sumof the areas of the two squares is 386 cm2. In centimeters, whatis the value of a b?b9.The mean of 10, 4, 1, x and 1 is equal to the median. What is the smallestpossible value of x?cm10.Lothario wants to cut out five circles, each 2 cm in diameter, from a rectangularpiece of cardboard that is 6 cm long. What must be the minimum width ofthe rectangular cardboard? Express your answer in simplest radical form.j11.If j k, what is the value of x, in the figure shown?k12.20 140 x 30 20133 2 · 20132 · 2014 3· 2013· 20142 20143 1What is the value of?2013· 2014Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Sprint Round
solutions13.pairs14.15.The integers 1 through 6 are to be used, each exactly once to fill the sixcircles in the figure so that the sums of three integers along each side ofthe triangle are the same. How many different solutions are possible?(Note that two solutions are considered the same if one can be rotatedor reflected to obtain the other.)How many pairs of consecutive, positive three-digit multiples of 9 contain thesame three digits?7531553133311111A square dartboard is divided into 16 congruent regions, witha point value assigned to each region as shown. Assumingeach dart thrown hits the dartboard in a region, what is theprobability that the sum of the points earned from threerandomly thrown darts will be greater than 15? Express youranswer as a common fraction.m216.A right triangle has a hypotenuse of 10 m and a perimeter of 22 m. In squaremeters, what is the area of the triangle?17.For the following system of equations, what is the value of c?a b c d 88a b c e 84a b d e 82a c d e 78b c d e 7218.Alexi rolled four standard dice and lined them up to create a 4-digit number. Heremoved two dice from the line and rolled them again. Alexi then returned eachre-rolled die to its original position in the line, thereby creating a new4-digit number. What is the probability that the new 4-digitnumber is greater than the original 4-digit number?Express your answer as a common fraction.Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Sprint Round
19.In circle P with radius 2 units, m NPR 100 . If the shadedregion has area k π units2, what is the value of k? ExpressNyour answer as a common fraction.R11P20.For integers a, b, c and d, (x 2 a x b)(x 2 c x d ) x 4 x 3 – 2x 2 17x – 5.What is the value of a b c d?21.Two random integers, a and b, are independently chosen, with replacement,from 1 to 1000, inclusive. What is the probability that both 2a 2b and 3a 3bare multiples of 5? Express your answer as a common fraction.22.What is the smallest integer greater than 38 that cannot be the length of thehypotenuse of a right triangle with integer side lengths?base 1023.In base b, 441b is equal to n2 in base 10, and 351b is equal to (n – 2)2 in base 10.What is the value of b, expressed in base 10?24.Larry tells Mary and Jerry that he is thinking of two consecutive integers from1 to 10. He tells Mary one of the numbers, and he tells Jerry the other number.Then the following conversation occurs between Mary and Jerry:Mary: I don’t know your number.Jerry: I don’t know your number, either.Mary: Ah, now I know your number.Assuming both Mary and Jerry used correct logic, whatis the sum of the possible numbers Mary could have?Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Sprint Round
25.If the 4014th term of a geometric sequence of non-negative numbers is 135, andthe 14th term is 375, what is the 2014th term? 26.A certain car drives 40 mi per gallon of gas at a rate of 60 mi/h. The same cardrives 35 mi per gallon of gas at a rate of 75 mi/h. Thus, traveling at the higherspeed saves time, but uses more gas. Gasoline costs 3.50 per gallon. What isthe expense for each hour of time saved when traveling at the higher speed?27.An unfair coin has the property that when flipped four times, the probabilityof it landing twice heads up and twice tails up (in any order) is the same as theprobability of it landing three times heads up and once tails up (in any order).What is the probability of this coin landing heads up in one flip? Express youranswer as a common fraction.28.If f (x) ax b, abcd 0 and f (f (x)) x for all x in the domain of f, what is thecx dvalue of a d ?pages29.Sam and Delilah are reading different books. Today, Sam and Delilah readone chapter in their respective books, and they each read more than one page.Interestingly, they read the same number of pages, but the sum of the pagenumbers for the chapter Sam read was 880, and the sum of the page numbers forthe chapter Delilah read was 1008. How many pages did Sam read today?30.The area of the largest equilateral triangle that can be inscribed in a square ofside length 1 unit can be expressed in the form a b c units2, where a, b and care integers. What is the value of a b c?Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Sprint Round
2014National CompetitionTarget RoundNameStateDO NOT BEGIN UNTIL YOU ARE INSTRUCTED TODO SO.Total CorrectScorer’s InitialsNational Sponsors2014 MATHCOUNTSNational Competition SponsorRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3M FoundationArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2014. All rights reserved.
1.If f (x) ax2 bx c, f (1) 0, f (2) 1 and f (3) 8, what is the value of c? 2.Ezra spent 60 on gas each week for a period of three weeks. The first week gaswas 3 per gallon, the second week it was 4 per gallon, and the third week itwas 5 per gallon. What was the average amount Ezra paid per gallon of gasover this three-week period? Express youranswer as a decimal to the nearest hundredth.204060Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Target Round
3.A two-digit, positive integer, b, is formed by reversing the digits of anothertwo-digit, positive integer, a. If both a b and a – b are perfect squares, what isthe value of a?travelers4.At a New York airport 135 international travelers were polled to see whatlanguage or languages each spoke. Of those polled, 87 spoke English;86 spoke Spanish; 39 spoke French; 31 spoke English and Spanish, but notFrench; and 19 spoke English and French, but not Spanish. Only oneperson polled spoke Spanish and French but not English. If everyonespoke at least one of these three languages, how many travelers spokeall three languages?Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Target Round
in25.A 1-inch by 35-inch piece of wood was divided into six pieces by making five45 cuts, as shown. The four trapezoidal pieces were kept, and the two triangularpieces were discarded. All four trapezoidal pieces were then used to form a1rectangular picture frame. A picture measuring 17 2 inches by 20 inches wasreduced proportionally so it could fit in the interior of the frame. If the cuts weremade so that the re-sized picture fit exactly within the frame, what was the areaof the interior of the frame?35 in1 in6.What is the sum of all real values of x that are solutions to the equation22 (x – 9x 20)2 2x –x– 1? Express your answer as a common fraction.33()Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Target Round
7.If 1% of the planets in the universe contain water, and astronomers develop atest that is 95% accurate for determining whether or not a planet contains water,then what is the probability that a planet identified by the test as containingwater really does contain water? Express your answer as a common fraction.in8.A circle passes through two diagonally opposite vertices of a 3-inch by 4-inchrectangle. What is the least possible distance between the center of the circle anda vertex of the rectangle? Express your answer as a common fraction.Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Target Round
2014National CompetitionTeam RoundProblems 1 10StateTeamMembers, CaptainDO NOT BEGIN UNTIL YOU ARE INSTRUCTED TODO SO.This section of the competition consists of 10 problems which the teamhas 20 minutes to complete. Team members may work together in anyway to solve the problems. Team members may talk to each other duringthis section of the competition. This round assumes the use of calculators,and calculations also may be done on scratch paper, but no other aids areallowed. All answers must be complete, legible and simplified to lowestterms. The team captain must record the team’s official answers on his/herown competition booklet, which is the only booklet that will be scored. If theteam completes the problems before time is called, use the remaining time tocheck your answers.Total CorrectScorer’s InitialsNational Sponsors2014 MATHCOUNTSNational Competition SponsorRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3M FoundationArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2014. All rights reserved.04-N14TEA
boxes1.The figure shows some identical boxes in a room stacked flushagainst a wall and each other. How many boxes, includingthose not visible, are in this arrangement? 2.At a health food store, income from trail mix is 4.95 per pound. Theexpense, in dollars, of preparing n pounds of the trail mix is represented by 0.005n2 5n 620. If the store prepares and sells 600 pounds of trail mix,after expenses, what is the total profit?3.The prime factorization of 1995, which is 3 5 7 19, uses each odd digitexactly once and 1995 is the smallest positive integer with this property. What isthe next smallest?4.A sequence is defined by a1 0, a2 4 and an 4(an 1 an 2) for n 2. What isthe greatest value of n such that n 100 and an is a power of 2?5.If three standard six-sided dice are rolled, what is the probability that the sumof the numbers on the top faces is 17 or 18? Express your answer as a commonfraction.units26.What is the area of the region defined by x y 4?Copyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Team Round
in27. has its center at C, AED has its center at B,In the figure, AFDAD DB 20 inches and m ACD 2(m ABD). What is thearea of the shaded region between the two arcs? Express youranswer to the nearest whole number.B8.AEFCDUsing a standard six-sided die and the directions shown, a string of six lettersis written in order. What is the probability that once ‘END’ is reached, the sixletters that have been written are B, A, N, A, N and A, in that order? Expressyour answer as a common fraction.NOSTARTRoll die.Result even?YESSix letterswritten?Write “A”.YESNORoll again.Result even?YESResult prime?ENDYESNOResult prime?NONOWrite “N”.YESWrite “B”.ways9.How many ways are there to color the walls of a pentagonal room using fivedifferent colors, so that no two non-adjacent walls have the same color?degrees10.In the triangle shown, what is the degree measure of ADB?E20 CD60 B50 30 ACopyright MATHCOUNTS, Inc. 2014. All rights reserved. 2014 National Team Round
Competition Statistics Friday, May 9, 2014 Orlando, FL 2014 Raytheon MATHCOUNTS National Competition National Competition 4.00 24.16 43.00 9.37 Indiv. Total Minimum Average
2017 Raytheon MATHCOUNTS National Competition Monday May 15, 2017 - Orlando, FL Written Competition Champion - Luke Robitaille, Texas Written Competition Runner-Up - Geoffrey Wu, Illinois S - Semifinalist; Q - Quarterfinalist; P - Countdown Round Participant Robitaille, Luke Cai, Andrew Wang, William Albright, Jack Wu, Geoffrey Choi, Reagan Xu .
The Raytheon DB-110 Sensor: Four Cameras in One Package November 1999 Ken Riehl, Lawrence A. Maver, Richard G. Sementelli Raytheon Systems Company 4 Hartwell Place, Lexington, MA 02421-3122 ABSTRACT Raytheon has designed, manufactured, and flight-tested a new reconnaissance system. The Raytheon DB-110 reconnaissance system is effectively four .
National MATHCOUNTS Competition. Rithvik Ganesh. Rice Middle School, 8. th. Grade Texas State MATHCOUNTS team member. 2018 Raytheon National MATHCOUNTS Champions. FINE ARTS Recognitions State of Texas Visual Arts Scholastic Event and Junior State of Texas Visual Ar
2005 MathCounts National Competition in Detroit, be it known that Detroit will host the 2005 Major League Baseball All-Star Game, the 2006 Super Bowl, and the 2009 NCAA Men’s Basketball Final Four. Obviously, the National MathCounts Competition fits right in with these other world-class c
2014 MATHCOUNTS Foundation 1420 King Street, Alexandria, VA 22314 703-299-9006 www.mathcounts.org info@mathcounts.org Unauthorized reproduction of the contents of this publication is a violation of applicable laws.
The MATHCOUNTS Competition Program is designed to excite and challenge middle school students. With four levels of competition - school, chapter (local), state and national - the Competition Program provides students with the incentive to prepare throughout the school year to represent their schools at these MATHCOUNTS-hosted* events. MATHCOUNTS
2018 AMC 8 Problem 2 exactly the same as 2012 3 is MathCounts State Sprint Problem 3, and very similar to the following 4 problems: 2017 MathCounts Chapter Countdown #49 2016 MathCounts National Sprint #11 2016 - 2017 MathCounts School
APM Group Limited 2014. AgilePgM is a trade mark of the DSDM Consortium. Dynamic Systems Development Method Limited 2014. The APMG International Swirl .
