2017 Raytheon MATHCOUNTS National Competition
2017 Raytheon MATHCOUNTS National CompetitionMonday May 15, 2017 - Orlando, StudentRobitaille, LukeCai, AndrewWang, WilliamAlbright, JackWu, GeoffreyChoi, ReaganXu, AlexZhou, JeremyLiu, BrianWatson, HoldenLi, KevinHuang, AndrewMui, HoldenTran, CobyChen, AlanEpstein, BenLi, DavidKrishna, ChinmayYu, AaronWhyte, JaedonHu, DavidCong, KevinThomas, RahulXia, DanielQian, TimothyHong, DanielXiao, JustinDeng, TimmyRank123456789101112TeamTexasNew tudentVerma, RishiAn, JoyGu, AndrewDong, DerekChalasani, VivekDing, JasonShi, AustinGoodman, SamYue, WilliamChheda, DevJiang, StephenFrazer, JakeGoel, GopalSharan, VismayWalsh, NoahXu, BrianLee, DavidYuan, DanielHuang, LucasZhang, JeffreyYang, EricGoel, Abhinav MihirZhou, LawrenceAkula, AdityaRajesh, KishoreFlorin, SamCamacho, JosephYang, hioColoradoArizonaMissouriNew YorkConnecticutNevadaIndianaIowaWritten Competition Champion - Luke Robitaille, TexasWritten Competition Runner-Up - Geoffrey Wu, IllinoisS - Semifinalist; Q - Quarterfinalist; P - Countdown Round 88878
National CompetitionStatistical Analysis05/15/2017Indiv. TotalSprint ScoreTarget ScoreTeam TotalTeam Maximum45291659.7520Std. 0668127180145U0000Total189350224
National CompetitionScore Distributions05/15/2017Number of Students per Individual 4446Individual Total ScoreNumber of Students per Sprint Score2015105001234567891011121314151617Individual Sprint Score18192021222324252627282930
National CompetitionScore Distributions05/15/2017Number of Students per Target Score504030201000246810121416Individual Target ScoreNumber of Teams per Team Score1086420051015202530354045Team Total Score (Rounded to the closest multiple of 5)50556065
National CompetitionScore Distributions05/15/2017Number of Teams per Team Round Score1210864200246810Team Round Score1214161820
National CompetitionQuestion Analysis05/15/2017Number of Correct 81920212223242526272829Sprint Round QuestionNumber of Correct Responses25020015010050012345Target Round Question67830
National CompetitionQuestion Analysis05/15/2017Number of Correct Responses50403020100123456Team Round Question78910
2017National 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 SponsorsRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3MgivesArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2017. All rights reserved.04-N17ANS
Sprint Round Answers1.5600 gallons11. 121. 222.7212. 8 gallons22. 220 ways3.44 percent13. 8 10 units23. 2 3 cm24.144 units214.5.–6.6596424.51615. 55025. 10 units672 terms16. 29 students26.7.–417. 12 3 cm27. 9 19 units28.16 base 818.28. 0.259.11 integers916519.1620. 35,28730. 2 – 3 units10. 72 squares52329. 90.8 inchesIMPORTANT NOTICE REGARDING SPRINT #25The intended interpretation for Sprint Round 25 is that side AB has length 9 units, side BC has length 10 units andside AC has length 13 units. The correct answer, given these assigned side lengths, is 10 units. Two alternate answersresult if side lengths are assigned differently. Due to this ambiguity, all three answers were accepted.Target Round Answers1.493.67,800,320 ways5.237.42 – 5 or – 5 2.61 percent4.72 degrees6. 178.288 cryptocodes42Team Round Answers1.4 prime numbers6.21 ways2.12 lines7.553.4448.214.149.165 meters5.40 mi/h10. 3420 waysCopyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Answer Key
2017National CompetitionSprint RoundProblems 1 30DO NOT BEGIN UNTIL YOU ARE INSTRUCTED TO DO SO.This section of the competition consists of 30 problems. You will have 40 minutes tocomplete all the problems. You are not allowed to use calculators, books or other aidsduring this round. If you are wearing a calculator wrist watch, please give it to yourproctor now. Calculations may be done on scratch paper. All answers must be complete,legible and simplified to lowest terms. Record only final answers in the blanks in theleft-hand column of the competition booklet. If you complete the problems before time iscalled, use the remaining time to check your answers.In each written round of the competition, the required unit for the answer is included inthe answer blank. The plural form of the unit is always used, even if the answer appearsto require the singular form of the unit. The unit provided in the answer blank is the onlyform of the answer that will be accepted.National SponsorsRaytheon CompanyNorthrop Grumman FoundationU.S. Department of DefenseNational Society of Professional EngineersCNA FoundationPhillips 66Texas Instruments Incorporated3MgivesArt of Problem SolvingNextThoughtFounding Sponsors: National Society of Professional Engineers, National Council of Teachers of Mathematics and CNA FoundationCopyright MATHCOUNTS, Inc. 2017. All rights reserved.04-N17SPR
gallons1.The gauge on an oil tank indicated that the tank was two-sevenths full. After3200 gallons were added to the tank the gauge indicated that the tank wassix-sevenths full. How many gallons of oil will the tank hold when full?2.What is the maximum possible absolute difference between a two-digit integerand the two-digit integer resulting when the digits are reversed?percent3.At Salisbury Central School, 60% of the students are 7th graders, and therest are 8th graders. Half of the 7th graders ride a bus to school, 20% of theremaining 7th graders arrive by car, and the rest walk to school. A quarter ofthe 8th graders ride a bus to school, a third of the remaining 8th graders arriveby car, and the rest walk to school. What percent of Salisbury Central Schoolstudents walk to school?units4.25.XYWZRectangle WXYZ, shown here, consists of eightsquares. If the white square is a 1 1 unit square,what is the area of rectangle WXYZ?What is the slope of a line perpendicular to the line given by the equationx 8 6 ? Express your answer as a common fractiony 4 5Copyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
terms6.In the sequence 121, 1221, 12221, the nth number consists of n copies of thedigit 2, surrounded by two 1s. How many of the first 2017 terms in the sequenceare divisible by 3?7.For what value of x is x x 1 equal to 9?base 88.Computing in base 8, a certain two-digit base-8 number N is added to five timesthe sum of its digits. The sum has the same digits as N but in reverse order. Whatis N in base 8?integers9.The median of a list of positive integers is 3, and the mean of the list is lessthan 2.1. What is the fewest number of integers possible in the list?squares10.How many perfect squares are divisors of the product 1! 2! 3! 4! 5! 6! 7! ?Copyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
11.If x and y are nonzero real numbers such that mx ny u, nx my v andu 2 v 2 x 2 y 2, what is the value of m 2 n 2?gallons12.Zeno’s tank holds 24 gallons of water. Zeno starts filling the tank, but when it ishalfway full he decides to start draining water out. Once half of the water that headded is drained, he decides to add back half of the water that he just drained.He then drains half of the water that he just added, and continues alternatelyadding or draining half of the previous quantity of water. After 100 cycles ofadding and draining water, how many gallons of water are in the tank? Expressyour answer to the nearest whole number.units13.In right triangle ABC with right angle at vertex C, a semicircle is constructed,as shown, with center P on leg AC, so that the semicircle is tangent to leg BCat C, tangent to the hypotenuse AB, and intersects leg AC at Q betweenA and C. The ratio of AQ to QC is 2:3. If BC 12, then what is thevalue of AC? Express your answer in simplest radical form.A14.15.QPBCPhilippa stands on the shaded square of the 8-by-8 checkerboardshown. She moves to one of the four adjacent squares sharingan edge with her starting square, with each of the four squaresequally likely to be chosen. She then makes two more movesto adjacent squares in the same way. Given any square S, let P(S ) be theprobability that Philippa lands on that square after her third move. What is thegreatest possible value of P(S )? Express your answer as a common fraction.n 0.D75 , what is theIf n is a positive integer and D is a digit such that814value of n?Copyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
students16.A college dorm houses math majors and chemistry majors. There is at leastone student in each major and no students are majoring in both. Students livein single or double rooms. If four-fifths of the math majors are roommateswith six-sevenths of the chemistry majors, what is the least possible number ofstudents living in the dorm?cm17.The sum of twelve times the numerical value of the total length, in centimeters,of the edges of a cube and the numerical value of its volume, in cubiccentimeters, is equal to four times the numerical value of the total surface area,in square centimeters. What is the length of its space diagonal? Express youranswer in simplest radical form.18.The diagonals of parallelogram ABCD intersect at E. Point F is the midpoint ofsegment BE and H is the midpoint of segment CE. What is the ratio of the areaof quadrilateral AFHD to the area of the parallelogram? Express your answer asa common fraction.19.Sam creates a six-digit positive integer by writing the digit 7 in thehundred-thousands place, and then tossing a fair coin five times. If the coincomes up heads, he writes a 7 for the next digit; if the coin comes up tails,he writes a 0 for the next digit. What is the probability that Sam’s number isdivisible by 77? Express your answer as a common fraction.20.What is the sum of the positive integers less than 1000 that are multiples of 7but not multiples of 2?Copyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
21.Suppose f is a quadratic function defined by f (x) ax 2 bx c for somenumbers a, b and c. If g(x) x 2 and f (g(x)) 2x 2 5x 19 for all values of x,what is the value of a b c?ways22.How many ways are there to fill in each empty square in the diagram below witha positive integer so that no integer appears more than once in the diagram, andevery integer in the diagram is less than each integer to its right?12cm223.What is the total surface area of the largest regular tetrahedron that can beinscribed inside of a cube of edge length 1 cm? Express your answer in simplestradical form.24.Penny flips three fair coins into a box with two compartments. Eachcompartment is equally likely to receive each of the coins. What is theprobability that either of the compartments has at least two coins that landedheads? Express your answer as a common fraction.units25.Triangle ABC has side lengths 9, 10 and 13, with D the midpoint of side BC.What is the length of segment AD?Copyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
26.In a pile of 25 tiles, each tile has one of the letters A through E and one of theintegers from 1 through 5. Each possible combination of a letter and a numberappears on exactly one of the tiles. Jessica selects three tiles at random, withoutreplacement, from the pile. What is the probability that each of the three tilesJessica chooses has a letter or a number in common with at least one of the otherchosen tiles? Express your answer as a common fraction.units227.In isosceles trapezoid ABCD, shown here, sides AB and DC are parallel,AB 10 and CD 8. Trapezoids APQR and BCQP are both similar totrapezoid ABCD. What is the area of trapezoid ABCD? Express your answerin simplest radical form.DRACQPB28.What is the value of 2 1.75 3 – (1.75 decimal to the nearest hundredth.inches29.A 36-inch rope is cut into three pieces. One piece is five inches longer thananother, and one piece is twice as long as another. What is the sum of thepossible lengths of the longest piece? Express your answer as a decimal to thenearest tenth.units30.In the figure shown, two lines intersect at a right angle, and twosemicircles are drawn so that each semicircle has its diameter onone line and is tangent to the other line. The larger semicircle hasradius 1. The smaller semicircle intersects the larger semicircle,dividing the larger semicircular arc in the ratio 1:5. What is theradius of the smaller semicircle? Express your answer in simplestradical form.3)? Express your answer as aCopyright MATHCOUNTS, Inc. 2017. All rights reserved. 2017 National Sprint Round
2017National CompetitionTarget RoundProblems 1 8NameStateDO NOT BEGIN UNTIL YOU ARE INSTRUCTED TODO SO.This section of the competition consists of eight problems, which will bepresented in pairs. Work on one pair of problems will be completed andanswers will be collected before the next pair is distributed. The time limitfor each pair of problems is six minutes. The first pair of problems is on theother side of this sheet. When told to do so, turn the page over and beginworking. This r
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 .
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
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
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
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
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
math team placed fifth out of 32 middle schools competing in the MATHCOUNTS 2006 Oahu Chapter Competition, and are two of the six Oahu math teams that will represent Oahu in the Hawaii State MATHCOUNTS Competition on March 11, 2006. Other public . The first is the Sprint Round with its 30 problems, and then comes the Target
Gauge Field Theory Dr. Ben Gripaios CavendishLaboratory, JJThomsonAvenue, Cambridge,CB30HE,UnitedKingdom. January4,2016 E-mail: gripaios@hep.phy.cam.ac.uk. Contents 1 Avantpropos1 2 BedtimeReading2 3 Notationandconventions3 4 Relativisticquantummechanics5 4.1 WhyQMdoesanddoesn’twork5 4.2 TheKlein-Gordonequation7 4.3 TheDiracequation7 4.4 Maxwell’sequations10 4.5 .
