Anna测速器在线测网速

2016StanfordInternationalMathTournament(HighSchool)August,2016StanfordUniversity"SpeedTest60"QuestionsTimeLimit45minutes(2pointseach)—CalculatorsarePROHIBITEDDirectionsThisisatestofspeedandaccuracy.
ThequestionsareNOTarrangedinorderofdifficulty.
Answersexactlyequivalenttotheofficialanswerswillbegivencredit.
Nooneisexpectedtosolveall60questionsinthetimegiven.
Donotspendtoomuchtimeonanyonequestion.
Writeyouranswertoeachquestionintheanswerboxtotherightofeachquestion.
Eachquestionisworth2points.
Youwillhave45minutesinwhichtoanswer60questions.
2016StanfordInternationalMathTournament(HighSchool)"SpeedTest60"QuestionsTimeLimit45minutes—CalculatorsarePROHIBITED—PAGE1of3Writeyouranswerintheanswerboxtotherightofeachquestion.
(2pointseach)Name:NumberCorrect:1.
Whatisthevalueof(1+)21.
2.
74+7+9+1926=2000+2.
3.
Whenwritteninstandardform,howmanyzerosdoes(1010)10have3.
4.
Apenandapenciltogethercost$1.
30.
Ifthepencosts$1morethanthepencil,howmuchdoesthepencilcostindollars4.
5.
Whatistheleastvalueofxthatsatisfiesx2+x=22+2.
5.
6.
Whatisthereciprocalof(+)6.
7.
Howmanyofthefirst100positiveintegershaveexactly3positiveintegraldivisors7.
8.
Forwhatrealnumbercarebothrootsof10x2+20x+c=0equal8.
9.
IfthecircumferenceofcircleCisthesameastheperimeterofasquareofareaπ,whatistheareaofcircleC9.
10.
Anna'sbrotherhas1morebrotherthanhehassisters.
HowmanymorebrothersthansistersdoesAnnahave10.
11.
Twointegersbetween10and99havethesamedigitsbutindifferentorder.
Whatisthegreatestpossiblevalueofthedifferencebetweentheseintegers11.
12.
True/False:Lines4x+y=7andy=4x–9areparallel.
12.
13.
Howmanyrealnumbershavetheirreciprocalsequaltotheiropposites13.
14.
Whatisthegreatestintegerthatislessthanorequalto-π14.
15.
True/False:Itispossibleforatrapezoidtohaveexactly3congruentangles.
15.
16.
Whatvalueofxsatisfies3336*9336*27336=3x16.
17.
Iboughtapaintingfor$1andthensolditforaprofitof10000%onmycost.
ForwhatpriceindollarsdidIsellthispainting17.
18.
Whatisthelengthofasideofarhombuswhosediagonalshavelengths3and418.
19.
Acomputercandownload2%ofafilein10seconds.
Howmanysecondsdoesittaketodownload100%ofthefile19.
20.
Whatisthelengthofthealtitudetotheshortestsideofatrianglewithside-lengthsof3,4,and520.
2016StanfordInternationalMathTournament(HighSchool)"SpeedTest60"QuestionsTimeLimit45minutes—CalculatorsarePROHIBITED—PAGE2of3Writeyouranswerintheanswerboxtotherightofeachquestion.
(2pointseach)Name:NumberCorrect:21.
Whatistheperimeterofarighttrianglewithonelegoflength51andhypotenuseoflength8521.
22.
True/False:Theproductof2differentprimenumbersisalwaysodd.
22.
23.
True/False:Thesumof2differentcompositenumberscanbeaprime.
23.
24.
True/False:Thesumof2differentprimescanbeacompositenumber.
24.
25.
Whatisthesmallestintegergreaterthan999whichusesonlythedigit9andisdivisibleby99925.
26.
Ifthelastthreedigitsofanintegernare625,thenwhatisthelargestintegerthatmustbeadivisorofn26.
27.
Rotatinganimage2016°clockwiseisthesameasrotatingitd°counterclockwise,where06n232.
33.
Whatisthesmallestnforwhicharegularn-gonhaseachinteriorangle≥162°33.
34.
Whatisthesumoftheremainderswheneachofthefirst100positiveintegersisdividedby634.
35.
Whatisthesumoftheremainderswhen20isdividedbyeachofthepositiveintegersgreaterthan1andlessthan2035.
36.
Ifab=2anda2+b2=24,whatis|a–b|36.
37.
Ifab=2anda2+b2=24,whatis||37.
38.
Ifab=2anda2+b2=24,whatis|a3+b3|38.
39.
Ifforallx,2f(x)+3g(x)=12x–1and4f(x)+8g(x)=28x–8,whatisg(0)39.
40.
TrueorFalse:>940.
2016StanfordInternationalMathTournament(HighSchool)"SpeedTest60"QuestionsTimeLimit45minutes—CalculatorsarePROHIBITED—PAGE3of3Writeyouranswerintheanswerboxtotherightofeachquestion.
(2pointseach)Name:NumberCorrect:41.
Ifthesurfaceareaofacubeis150cm2,whatisthecube'svolumeincm341.
42.
TrueorFalse:Ifa,b,andcarethelengthsofthesidesofatriangle,thenthereisalwaysatrianglewithsidesoflengtha2,b2,andc242.
43.
Plant1isnow5cmtallandgrowsuniformlyatarateof1cm/week.
Plant2isnow7cmtallandgrowsuniformlyatarateof2cmevery3weeks.
Inhowmanyweekswillthetwoplantsbethesameheight43.
44.
Whenmyspinnerstopsspinning,itlandson1of3numbers.
Itlandsoneachnumberwithequalprobability.
Ifmyspinnerisspun3times,whatistheprobabilitythatitdoesnotlandonadifferentnumbereachtime44.
45.
Whatistheareaofacirclewhosecircumferenceis2π245.
46.
Itraveled1kmat2km/hrand2kmat1km/hr.
Whatismyaveragespeedinkm/hrfortheentire3kmtrip46.
47.
Iftheareabetweenasquareanditsinscribedcircleis16–π2,whatistheareaofthesquare47.
48.
True/False:Thesumof2017oddintegerscanneverequal2016.
48.
49.
Whatistheleastintegerxthatsatisfiesx5>x49.
50.
Howmanyrealnumberssatisfyx+x3+x5=050.
51.
Arectangularboxhasdimensions1,4,and5.
Whatisthegreatestpossibledistancebetweenany2pointsinoronthebox51.
52.
True/False:>.
52.
53.
Whatisthegreatestprimefactorofthesumofthefirst200positiveintegers53.
54.
Ifa+b=2,b+c=4,a+c=2016,whatisthevalueofa+b+c54.
55.
Ifthelengthofthemediantothehypotenuseofarighttriangleis5andonelegofthetrianglehaslength8,whatistheareaofthetriangle55.
56.
True/False:Ifabc=1.
2016,thena2+b2+c2>1.
56.
57.
True/False:Givenany4integers,thereisalwaysanonemptysubsetoftheintegerswhosesumisdivisibleby4.
57.
58.
IfP(x)isa3rddegreepolynomialwithroots1,2,and3,whatisthesumoftherootsofP(2x+1)58.
59.
True/False:Ifa,b,andcarepositivenumbersanda2+b2+c2>3,abc>1.
59.
60.
Whatisthelargestevenintegerlessthan200withexactly4positivedivisors60.