Answer
STUDENTNAME:
ProctorName: 1or0
1or0
October19,2016
SchoolName:
Team#: Total Correct:
KEY
5[deg]
0
2
4
3[units]
1
6
Answer
20
1or0
1or0
31-40TOTAL:
29[orderedpairs]
5[units]
4
84[terms]
1[solutions]
0[numbers]
18[days]
44
148
Answer
5[primes]
1or0
1or0
12
2[times]
Room#: 6
31
32
33
34
35
36
37
38
39
40
18[squares]
2
43
16-30TOTAL:
3[points]
HighSchoolIndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
“MathisCool”Championships–2016-17
1 11236
2 3
3 [x=]7
4 25[%]
5 2
6 3
7 13
8 36[sqcm]
9 48[ways]
10 21[instructors]
11 52[*+,-.]
12 49
13 26[cm]
14 92
15 20[vertices]
1-15TOTAL:
Answer
STUDENTNAME:
ProctorName: 1or0
1or0
October19,2016
SchoolName:
Team#: Total Correct:
5[deg]
0
2
4
3[units]
1
6
Answer
20
1or0
1or0
31-40TOTAL:
29[orderedpairs]
5[units]
4
84[terms]
1[solutions]
0[numbers]
18[days]
44
148
Answer
5[primes]
1or0
1or0
12
2[times]
Room#: 6
31
32
33
34
35
36
37
38
39
40
18[squares]
2
43
16-30TOTAL:
3[points]
HighSchoolIndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
“MathisCool”Championships–2016-17
1 11236
2 3
3 [x=]7
4 25[%]
5 2
6 3
7 13
8 36[sqcm]
9 48[ways]
10 21[instructors]
11 52[*+,-.]
12 49
13 26[cm]
14 92
15 20[vertices]
1-15TOTAL:
“MathisCool”Championships–2016-17
Sponsoredby:
October19,2016
HighSchoolMentalMathContest
Followalongasyourproctorreadstheseinstructionsto
you.YourMentalMathscoresheetisontheback.
GENERALINSTRUCTIONSapplyingtoalltests:
§
§
§
§
§
§
§
§
§
§
§
Goodsportsmanshipisexpectedthroughoutthecompetitionbyallinvolved,bothcompetitorsandobservers.Displayof
poorsportsmanshipmayresultindisqualification.
Calculatorsoranyotheraidsmaynotbeusedonanyportionofthiscontest.
Unlessstatedotherwise,allrational,non-integeranswersneedtobeexpressedasreducedcommonfractionsexceptin
caseofproblemsdealingwithmoney.Inthecaseofproblemsrequiringdollaranswers,answerasadecimalroundedto
thenearesthundredth(ie,tothenearestcent).
Allradicalsmustbesimplifiedandalldenominatorsmustberationalized.
Unitsarenotnecessaryaspartofyouranswerunlessitisaproblemthatdealswithtimeandinthat
case,a.m.orp.m.isrequired.However,ifyouchoosetouseunits,theymustbecorrect.
Leaveallanswersintermsofπwhereapplicable.
Donotroundanyanswersunlessstatedotherwise.
Recordallanswersonthecoloredcoversheetsintheanswercolumnonly.
Makesureallanswersheetshavealltheinformation(name,teamnumber,etc.)atthetopofthesheet
filledout.
Testswillbescoredasa0ifanswersarenotrecordedontheanswersheets.
Blankanswersheetsandanswersheetswithnonamewillbescoredasa0.
MentalMath–30secperquestion
8problemsreadorallytoeveryone-Approximately8%ofIndividualScore-25%ofteamscore
Whenitistimetobegin,theproctorwillreadthefirstquestiontwice.Youmaynotdoanywritingortalkingwhile
arrivingatasolution.Onceyouhaveasolution,recorditonthesheetinfrontofyou.Youmaynotchangeorcrossout
answersonceyouhavewrittenananswerdown.Ifthereareerasermarks,write-overs,orcrossed-outanswers,
theywillbemarkedwrong.Onceallstudentshavelaidtheirpencilsonthedesk,anotherquestionwillbeasked.Ifa
studentdoesn’tlayhis/herpencildown,themaximumwaittimeis30secondsaftercompletionofthesecondreadingof
thequestionbeforeanotherquestionisasked.Youmaycontinuetoworkonaproblemwhilethenextquestionisbeing
read.Thevalueofeachquestionisaoneorzero.Eachstudentwillbeaskedthesameeightquestions.Individualscores
usedtodetermineindividualplacingwillbedeterminedbythesumoftheMentalMathscoreandtheIndividualTest
scoreforeachindividual.Inaddition,thetopthreeMentalMathscoresfromoneteamwillbetotaledanddoubledand
willcontributeto25%oftheteamscore.
“MathisCool”Championships–2016-17
Sponsoredby:
HighSchool–October19,2016
MentalMathContest
MentalMath–30secperquestion
8problemsreadorallytoeveryone-Approximately8%ofIndividualScore-25%ofteamscore
Whenitistimetobegin,theproctorwillreadthefirstquestiontwice.Youmaynotdoanywritingortalkingwhile
arrivingatasolution.Onceyouhaveasolution,recorditonthesheetinfrontofyou.Youmaynotchangeorcrossout
answersonceyouhavewrittenananswerdown.Ifthereareerasermarks,write-overs,orcrossed-outanswers,
theywillbemarkedwrong.Onceallstudentshavelaidtheirpencilsonthedesk,anotherquestionwillbeasked.Ifa
studentdoesn’tlayhis/herpencildown,themaximumwaittimeis30secondsaftercompletionofthesecondreadingof
thequestionbeforeanotherquestionisasked.Youmaycontinuetoworkonaproblemwhilethenextquestionisbeing
read.Thevalueofeachquestionisaoneorzero.Eachstudentwillbeaskedthesameeightquestions.Individualscores
usedtodetermineindividualplacingwillbedeterminedbythesumoftheMentalMathscoreandtheIndividualTest
scoreforeachindividual.Inaddition,thetopthreeMentalMathscoresfromoneteamwillbetotaledanddoubledand
willcontributeto25%oftheteamscore.
#
1
2
3
4
5
6
7
8
Problem
Whatisthesumoftheevenintegersbetween1and11?
IfIflipafaircoin3times,inhowmanywayscanIgetexactly2heads?
Arectanglewithintegerwidthandlengthhasanareaequalto60.How
manydifferentperimetersarepossible?
Iffofxequalsthreexplusten;whatisf-inverseofthirty-seven?
Arectanglemeasuring12by6inchesisdividedinto4trianglesbydrawingits
twodiagonals.Whatisthesmallestareaofanyofthetrianglesinsquare
inches?
Whatisthesumoftheintegersfromnegativetentopositivefifteen
inclusive?
Inthegraphoftheparabola,12yequalsx-squaredminus4xplus7,
[PAUSE]whatisthedistancefromthevertextothefocus?
Iamdealttwocardsfromastandard52-carddeck.Inhowmanyways
canIgetapair,thatis,twocardsofthesamevalue;2-fours,2-kings,etc.?
“MathisCool”Championships–2016-17
Sponsoredby:
October19,2016
HighSchoolIndividualContest
Tearthiscoversheetandscratchpaperoffandfilloutthetopofthe
coloredanswersheetpriortothestartofthetest.Thegraphbelow
isforyouruse,ifneeded.
INDIVIDUALTEST–HighSchool-35minutes
YoumayNOTbeseatednexttoanyonefromyourschool.IfyouareMOVENOWtoavoidbeingdisqualified!Whenyouare
promptedtobegin,tearoffthecoloredsheetandbegintesting.Makesureyournameandschoolarerecordedontheanswer
sheet.Therawscorewillbe2pointsforcorrectanswerstoproblems1-30and3pointsfor31-40.Recordyouranswersonthe
scoresheet.Notalkingduringthetest.Youwillbegivena5minutetimewarning.
“MathisCool”Championships–2016-17
Sponsoredby:
October19,2016
HighSchoolIndividualContest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Questions1-30:2pointseach
Calculate:106$ .
Howmanyofthefollowingarerationalnumbers &, 4, 2, 4,
*
+
?
Solveforx:4 , + 5 − 6 = 2 3, − 1 + 2
Astoreownerhasasalethatreducesthepriceofacoatby20%.Bywhatpercentdoesshe
havetoraisethepricetogetbacktotheoriginalcost?
Evaluate:17 − 14 −
5−3
$
− 6 − 9/3.
Whatisthesumofthesolutionstotheequation:, $ − 1 = 3(, + 1)
Whatisthelargestprimefactorof2*$ − 1?
Asquareisinscribedinacircleofarea18&squarecentimeters.Whatistheareaofthesquare,
insquarecentimeters?
Threecouplesgotoamovieandsitinthesamerowinsixconsecutiveseats.Inhowmany
wayscantheysitifthecouplesstaynexttoeachother?
Thereare463studentsinthetenthgradeatKingHighSchool.Eachstudenttakesaclass
duringeachofthe6periodsinadayandclasssizeisrestrictedto28students.Eachinstructor
teachesatmost5classes;whatistheminimalnumberofinstructorsrequiredtoteachthe
tenthgraders?
Twocongruentcirclesofradius6havecentersthatare20unitsapart.Thelengthofastring
stretchedaroundtheexteriorofthecircleshaslength8 + 9&,whatis8 + 9?
Arighttrianglewithintegersidelengthshasonesideoflength7.Whatisthesumoflengthsof
theothertwosides?
Whatisthelargestperimeterofarectangleofareaof12squarecentimetersthatcanbe
constructedusingintegersidelengths?
Myscoresonthefirstfourtestsare:87,84,94and91.Thelasttestisworthdouble.WhatdoI
havetoscoretohaveanoverallaverageof90?
Adodecahedronhas12regularpentagonsasfaces.Howmanyverticesdoesithave?
Howmanypositivethree-digitnumbersareoddanddivisibleby23?
Howmany4-digitbinarynumbersare2-digitbase10numbers?
Theequationofthelinethatgoesthroughthepoint(2,4)andisparalleltotheline3, − 2; =
1iswrittenintheform:<, + =; = >whereAispositiveandA,B,andChavenocommon
factors.Whatis < + = + > ?
Thesurfacearea,greaterthan0,ofasphereisequaltoitsvolumeinmagnitude.Whatisits
radius?
20
21
22
Mymomhas4billsinherpurse;a$1bill,two$5billsanda$10bill.Formybirthday,I
randomlyselecttwobills.WhatistheprobabilitythatIget$15total?Multiplyyouranswerby
12.
If? = −1,whatis
29
30
A
?
IfC > E > F > 0thenhowmanyofthesestatementsareguaranteedtobetrue:
*
G
23
24
25
26
27
28
*@A B
*
*
H
H
> ,
G
J
G
J
G
H
< , – < − Howmanydegreeslargeristhemeasureofeachinteriorangleofaregularnonagonthana
regularoctagon?
Findtheminimumvalueof:, $ + 4, + 16
Howmanytimesdoesthegraphof
MB
N
−
OB
P
= 1crossthex-axis?
Findthegeometricmeanof3,9,8.
A7x4gridisdrawnonapieceofpaper.Ifthetwodiagonalsaredrawn,howmanysquareson
thegridhavealinethroughthem?
Let(,, ;)bethepointthatis60%ofthewayfromthepoint(2, 3)tothepoint(7, −7).What
is, + ;?
Ofthesepointswhatisthemaximumnumberofpointsthatarecollinear?
{ 0, −1 , 1,2 , 3,0 , 1,1 , −3, −2 }
If , + ; = 7and,; = 9,whatis, + ;?
ChallengeQuestions:3ptseach
31
32
33
34
35
36
37
38
39
40
Howmanyprimenumberslessthan200canbeexpressedasthedifferenceoftwopositive
perfectcubes?
1 3 6
Whatisthedeterminantofthematrix 8 0 4 ?
0 5 3
Whatistheaverageofall2-digitnumberswhosedigitsconsistonlyofthenumbers1,3,4and
8?
Acontractorbidsaremodelquoting3daystocompletethejobwithhercurrentcrewof
workers.Ifshehad3moreworkers,thecrewcouldfinishin2days.Ifallworkersdothesame
amountofworkeachday,howlongwouldittakeforoneworkertocompletethejob?
Howmanyprimenumbersaregreaterthan10! + 1andlessthan10! + 10?
Howmanyrealsolutionsaretheretotheequation:3, T + , U + 5, $ + 6 = 0?
Theexpression C + E + F + V W isexpandedandliketermscombined.Howmanytermsare
intheresultingexpression?
AnangleischosenrandomlyfromtheintervalX ∈ [0, 2&).Letpbetheprobabilitythat
cos 2X > cos X .Whatis12timesp?
Atrianglehassidesoflength10,14,and16.Thealtitudeisdrawnfromthevertextotheside
oflength16anddividesitintotwosmallersegments.Whatisthelengthoftheshorter
segment?
Let,and;denotenonzerointegers.Howmanyorderedpairs(,, ;)aretherethatsatisfythe
followingequation?
1 1
1
+ = , ; 12
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
IndividualMultipleChoiceContest
1
2
3
Whichofthefollowingisequivalentto
3M + 3M + 3M + 3M + 3M + 3M ?
A)6M B)2 ∗ 3M@* C)2 ∗ 3M D)6 ∗ 3M@* ListJ,KandLfromsmallesttolargest:
b = 11UP , c = 169*+ , d = 3We A)cbd
B)bcd
C)dbcD)dcb
FindfgFX.
U
A) $h
4
5
6
A)
U
$
8
9
10
B)−
U
$
Wh
W*
**
**
C) D) N
IfX = 15°,whatisthevalueof
sinP X − cos P X − 2 sin$ X?
*
C) D)−1
$
E)_`a<
E)_`a<
E)_`a<
Findtheunitsdigitof3487PN ∗ 31728*h$ .
A)2
B)4
C)6D)8
E)NOTA
Writethebase12repeatingdecimal0.24*$ asafractioninbase10.
A)
$P
*PU
7
W*
B) E)_`a<
*
B) T
**
*U
PT
WW
C) D) E)_`a<
Givena3x3x3gridofpointsformingacube.Inhowmanyways,canwechoose3ofthepoints
sothattheyareinaline?
A)32
B)43
C)64D)67
E)_`a<
Whatistheareaoftheellipsedefinedby:4, $ + 9; $ − 16, + 18; = 11?
A)&
B)6&
C)12&D)24&
E)_`a<
Atapicnic,5identicalpiesaregivenoutto5peopleatrandom,whereanyonecouldhave0-5
pies.Howmanywayscanthepiesbegivenout?
A)120
B)126
C)180D)625
E)NOTA
Evaluate:
m
9
2l
A)1
U
B) $
ln*
C)2D)4
E)_`a<
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
TeamContest
1
2
3
4
Howmanypositiveintegerslessthan30arerelativelyprimeto30?
o
Whatisthesquareofthedistancefromtheorigintothepoint 5, , 5 3 givenincylindrical
U
coordinates.
Whatisthepositivedifferencebetween2016andthesumofitsproperfactors?
Findtheaverageoftherootsofthepolynomialequation:
, U − 21, $ − 2016 = 0
Evaluate:
5
6
7
8
−1
−1
−1
− 2+ 2+ 2+⋯
…
− 2+ 2+ 2+⋯
Whatistheaveragevalueoftheslopeofthetangentlineofthefunction
; = 3, P − 3, U − 3, $ + 3, − 3
between, = −3and, = 4?
Definevectors
r = 4s + t − 2u,
v = 2s − 3t + u,
w = s − u.
Thevectorx =< 4,5, −3 >isexpressibleasauniquelinearcombinationofx,y,andz.Find
C − E + Fgiventhaty = Cr + Ev + Fw.
Apairofcirclesthatshareacommonpointhavecommonoutertangentsthatmeetinanangle
o
of .Whatistheratioofthelargecircle’sradiustothesmallercircle’sradius?
U
Thesumofthegeometricseries:
9
10
13 26 52 104
+
−
−
+ ⋯
3
9? 27 81?
canbewrittenasC + E?, where? = −1.WhatisC − E?
Onadenseplanetoid,lightislensedbyintensegravitytofollowaparabolicpathgivenby
−, $ + E,.AflagpostFfeettallonthisplanetoidcastsaneight-footshadowwhenlightpasses
Uo
thetopofthepostatanangleof
P
fromthehorizon.FindF + E.
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
PressureRoundContest
1
2
3
4
5
SixdistinctintegersC* , C$ , CU , CP , CT , CW arechosenrandomly.Letpbethe
probabilitythatatleasttwoofthemdifferbyamultipleof5.Whatis30timesp?
Letr,s,andtbethesolutionstothefollowingequation:, U − 3, $ + 5, − 8 = 0.
Whatis~ $ + f $ +  $ ?
Mikechoosesa5-digitpositiveinteger,rearrangesitsdigitsyieldingasmaller
numberandsubtractsthenewintegerhegetsfromtheoriginalinteger.Hethen
multipliesthatdifferencebyanunknown3-digitintegertogetthenumberS.Six
ofthesevendigitsofS,inrandomorder,are8,1,2,9,9and4.Whatisthe7th
digitofS?
Labelthethreesidesofanacutetrianglea,bandc.Supposethefollowing
relationshipholds: C + E + F C + E − F = 3CE.Whatisthemeasure,in
degrees,oftheangleoppositethesideoflengthc?
AnarithmeticsequencehasCU = 12andC+ = 15.WhatisthesumC+ + Ce +
⋯ + C*T ?
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#1–
#1
#
1
2
3
4
5
6
7
8
9
10
SET1
Problem
Answer
Whatisthenumberthatis4timesthecubedrootof512?
32
Howmanypositivefactorsdoes68have?
6[factors]
Whatistheareaboundedbytheequationthirty-twoxsquaredplus
twoysquaredequalssixtyfour?
8pi[squn]
Ifacityof100peopleincreasesby25inthefirstyear,then60percent
moreinthesecondyear.Howmanypeopleareinthecityafterthe
200[people]
secondyear?
1101P Expressthebasetwonumber:one-zero-zero-one[pause]squaredin
orone-one-zerobasefour.
onebase4.
Whatisthesumofthefirst10Fibonaccinumbersifthefirstnumber
isone?
143
Howmanywaysarethereforahaberdashertosellonehateachto4
peopleoutofastockof8distincthats?
1680[ways]
Whatisthedifferencebetweenthesumofthefirst5primenumbers
andthenext5primenumbers?
73
Howmanypointswithintegervaluecoordinatesareexactlythirty-six
unitsawayfromtheorigin?
4[points]
Polygonsaremadebyconnectingverticesofaregulardodecagon.
Howmanyregularpolygonscanbemade?
10[polygons]
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#2–
SET2
#2
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer
Anoctopus,with8legs,isinclasswith5crabsand3dogs.Ifcrabs
have6legshowmanylegsareintheclassroom?
50[legs]
Whatisthesumofthefactorsof78?
168
Thegraphofthefunctionyequalsxandthegraphofthefunctiony
equalscosineofxintersectinhowmanypoints?
1[point]
120hasnfactors,howmanypositivefactorsdoesnhave?
5[factors]
Whatisthevolumeofatetrahedronwithedgelengththree?
9 2
4
nineroot2over4.
[cuunits]
Howmanywaysaretheretoreorderthelettersintheword‘C-A-L-CU-L-U-S’?
5040[ways]
Theaveragetestscoreinacalculusclassof20studentsis75%.What
istheminimumnumberofadditionalstudentsat100%wouldneedto 14[students]
jointheclasstomakeanaverageclasstestscoreatleast85%?
Thereisafarmwithcowsandchickens.Betweenthecowsand
chickens,thereare46legsand18heads.Howmanychickensare
13[chickens]
there?
Thegraphofthepolarequation,sineofthetaequals5overriswhat
shape?
line
Anisoscelestrapezoidhasbaseanglesof60degrees.Thelengthsof
thebasesare5and21units.Whatisthelengthofoneofits
diagonals?
19[units]
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#3–
#
#3
1
2
3
4
5
6
7
8
9
10
SET3
Problem
Answer
Whatisthesumoftherootsofthepolynomialfourx-cubedminus
3xplus9?
0
Whatistheunitsdigitof24tothepowerof16?
6
Whatisthelimitasxapproachesinfinity,ofthefunctiononehundred
0
overthequantityxsquaredplusfive?
Acubeisinscribedinaspherewithasurfaceareaofonehundred
forty-fourpi.Whatisthesurfaceareaofthecube?
288[squnits]
Whatisthequantitylogbasesixteenoftwothirdspluslogbase
sixteenofninety-six?Answerasafraction.
3/2
Whatistheproductoffiveplusfourianditsconjugate?
41
Whatis5factorialtimes6factorialdividedby7factorialrepresented
asamixednumber?
17and1/7
Thesumofxsquaredandysquaredis58,thequantityxplusy
squaredisequalto16.Whatisthevalueofthequantityxtimesy.
−21
Whatisthevolumeoftheparallelepipedformedbythevectors:4j
plus3k[pause]3jplus4k[pause]and5iplus5jplus5k?
35[cuunits]
Whatisthecotangentoftheangleinthefirstquadrantifthesineof
theangleistwentyoneovertwentynine?
20/21
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#4–
SET4
#4
#
1
2
3
4
5
6
7
Problem
Answer
Whatistheleastcommonmultipleofthenumbers4,6and7?
84
Howmuchlargeristhemeanofthesmallest50positiveintegersthan
51
themeanofthelargest50negativeintegers?
Whatwouldyouaddtoboththenumeratoranddenominatortoturn
thefraction7/9into10/11?
13
Whatisthesumofthefirst5decimalplacesofthequantity584
dividedby999?
30
Considerthesequencexsubnequalsthesquarerootofn.After
eliminatingalltherationalnumbersfromthesequence,whatisthe
Squarerootof110
th
100 number?
Aglassisthreefourthsfullandoneeighthofglasscapacityisemptied
tofillaglassthatcanhold15ounces.Howmuchliquidwasoriginally 90[ounces]
inthefirstglass?
Ihaveaspinnerseparatedinto7equalsectionsnumberedoneto
seven.Whatistheprobabilityofspinningasumofsevenwithtwo
6/49
spins?
8
9
10
AmyandBertgotothestorewiththesameamountofmoney,Amy
spends$435andBertspends$324andhastwo-fifthsofhismoney
left.HowmanydollarsdidAmyhaveleft?
[$]105
Whatisthelargestvalueofxlessthan2pisuchthatthesineofx
timesthecosineofxequalsone-fourth?
17piover12
Ifthelogbasebof32isfive-thirds,whatisthebaseb?
8
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#5–
#5
#
1
2
3
4
5
6
7
8
9
10
SET5
Problem
Answer
Whatisfourplusfiveminustentimesfiveplusthree?
−38
Expressedasadecimal,howmanytimesgreateris50times55than
thequantity20times25?
5.5
Findtheminimumpointofthegraph,yequalsthreexsquaredplus
eighteenxminusthirty?
Negative3comma
negative57
Ifthesumoftwonumbersistwenty,andtheproductisfive,whatis
thesumofthereciprocalsofthetwonumbers?
4
AtrainleavespointAat4amandreachespointBat8am.Another
trainleavespointBat6amandreachespointAat12:00pm.How
manyminutesafterthetrainleavesstationBwillthetwomeet?
72[minutes]
Onehundredeighty-sixplusxisequaltosixtypercentoffour
hundredsixtyfive.Findx.
93
Iffofxiseighteenminusfourx,whatisf-inverseofnegativeten?
7
Apyramidhasabaseof50andaheightof8,ifthebaseareais
doubledandtheheightishalved,Whatistheratioofthenewvolume 1OR1to1.
totheoldvolume?
Whatisthelogbase2ofthequantitycosinesquaredof30degrees
minussinesquaredof30degrees?
−1
Whatisthevolumeoftheshapewithequationxsquaredoverfour,
plusysquaredoversixteen,equalsoneminuszsquaredovernine?
32pi[cuunits]
“MathisCool”Championships–2016-17
Sponsoredby:
11th&12thGrade–October19,2016
COLLEGEKNOWLEDGEBOWLROUND#6–
SET6
#6
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer
Theunitsdigitandthehundredsdigitareinterchangedinthenumber
13049
6574.Whatisthesumoftheoriginalnumberandthenewnumber?
Evaluatetheareabetweenthexaxisandthelineyequals4xplus6
fromxequals1to4.
48[squnits]
Whatisthesquareofthelengthofthelongestmedianinatriangle
withsidelengthsof8,15,and17?
241
Evaluate7tothe4thpower.
2401
Whatisthelateralsurfaceareaofaconewithradiusfiveandheight
twelve?
65pi[squn]
Whatistheareaoftheshapewithverticesatthepointthreecomma
one,thepointonecommanegativeone,thepointnegativethree
commaoneandthepointnegativetwocommanegativeone?
9[squnits]
Inthebinomialexpansionof2xplus3yquantitytothe6thpower.
Whatisthecoefficientinfrontofthex-cubed,y-cubedterm?
4320
Fullyfactor6xsquaredplus5xminus6.
3xminus2times
2xplus3OR
reversed
Ardenissolvingaparabolawithequationxsquaredminus4xplus
12yplus40equals0.Whatarethecoordinatesofthefocus?
Twocomma
negative6.
Whatisthemaximumvalueofthefunctionfofxequalsxcubed
minus6xsquaredplus9xminus6ontheclosedintervalfrom0to3?
−2
“MathisCool”Championships–2016-17
Sponsoredby:
HighSchool–October19,2016
COLLEGEKNOWLEDGEBOWLROUND–
#
1
2
3
4
5
6
7
EXTRA
Problem
Answer
Whatisthemeasureindegreesofthesmalleranglebetweenthehour
andminutehandsofaanalogclockatfourforty-four?
122[degrees]
Howmanytwodigitnumbersdonotcontainaprimenumberasoneof
thedigits?
30[numbers]
38iswhatpercentof95?
40[%]
Youtakeoutaloanof$3500andyoupaytheprincipleand60%interest.
[$]5600
Howmuchwillyoupaybackintotal?
Whatis75times750?
56250
Howmanysecondsaretherein3hours?
10800
Findtheharmonicmeanof3and27.
Twentysevenover
five.
27
5
Extra
Final Score:
“MathisCool”Championships--2016-17 KEY
School:
Room#
Name:
Team#
Proctor:
(Out of8)
HighSchool MentalMath–30secperquestion
8problemsreadorallytoeveryone-Approximately8%ofIndividualScore-25%ofteamscore
Whenitistimetobegin,theproctorwillreadthefirstquestiontwice.Youmaynotdoanywritingortalkingwhile
arrivingatasolution.Onceyouhaveasolution,recorditonthesheetinfrontofyou.Youmaynotchangeorcrossout
answersonceyouhavewrittenananswerdown.Ifthereareerasermarks,write-overs,orcrossed-outanswers,
theywillbemarkedwrong.Onceallstudentshavelaidtheirpencilsonthedesk,anotherquestionwillbeasked.Ifa
studentdoesn’tlayhis/herpencildown,themaximumwaittimeis30secondsaftercompletionofthesecondreadingof
thequestionbeforeanotherquestionisasked.Youmaycontinuetoworkonaproblemwhilethenextquestionisbeing
read.Thevalueofeachquestionisaoneorzero.Eachstudentwillbeaskedthesameeightquestions.Individualscores
usedtodetermineindividualplacingwillbedeterminedbythesumoftheMentalMathscoreandtheIndividualTestscore
foreachindividual.Inaddition,thetopthreeMentalMathscoresfromoneteamwillbetotaledanddoubledandwill
contributeto25%oftheteamscore.
Answer
1or0
1or0
1
2
3
4
5
6
7
8
30
3[ways]
6
9
18[sqin]
65
3
78[ways]
Final Score:
MathisCool”Championships–2016-17
KEY
11th&12thGrade–October19,2016
StudentName
ProctorName
SCHOOLNAME Room#
Team#
First Score
(out of 20)
INDIVIDUALMULTIPLECHOICE-15minutes–10problems–20%ofteamscore
Thistestistheonlytestwhereyouwillbepenalizedforincorrectresponses.Youwillreceive2pointsforacorrectletter
response,0pointsforleavingitblankand-1pointforanincorrectresponse.Itisnotnecessarytowriteyourpersonal
nameonthetest,butyoumayputitatthebottomofthetestsoyourcoachwillbeabletogiveyoubackthecorrect
test.Thistestistakenindividually,butitispartofyourteamscore,includingzerosformissingteammembers.Your
teamscorewillbecalculatedbytakingthemeanofyourfourteammembers’scores.Whenyouarepromptedtobegin,
tearoffthecoloredsheetandbegintesting.Sincethisisamultiplechoicetest,ONLYaletterresponseshouldbe
indicatedasananswerontheanswersheet.Notalkingduringthetest.
DONOTWRITEINSHADEDREGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
-1,0or2
-1,0or2
B
C
D
D
D
D
B
B
B
C
Final Score:
“MathisCool”Championships–2016-17
KEY
11th&12thGrade–October19,2016
SCHOOLNAME ProctorName
Team#
First Score
Room#
(out of 10)
TeamContest–ScoreSheet
TEAMTEST-15minutes–30%ofteamscore
Whenyouarepromptedtobegin,tearoffthecoloredsheetandgiveacopyofthetesttoeachofyourteammembers
andbegintesting.Eachproblemisscoredas1or0.Recordallanswersonthecoloredanswersheet.
DONOTWRITEINSHADEDREGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
8[integers]
100
4536
7
1
36
1
3
5
71
1or0
1or0
Final Score:
“MathisCool”Championships–2016-17
KEY
11th&12thGrade–October19,2016
ProctorName
Room#
Team#
First Score
SCHOOLNAME PRESSUREROUND-10minutes–5problems-5rounds–15%ofteamscore
Whenitistimetobegin,youwillbehandedapacketoffiveproblems.Thereisacopyoftheproblemsforeachteam
member.Twominutesafterthestartofthetestyouareexpectedtosubmitananswerforoneoftheproblems(itcan
simplybeaguess).Themaximumvalueofthisansweris1point.Inanothertwominutesyouareexpectedtosubmit
anotheranswertooneofthefourremainingproblems;itsmaximumvalueistwopoints.Thisprocesswillcontinue
untilalltheproblemsareansweredandeachconsecutiveproblem’sworthwillgoupbyonepoint.Youmustsubmit
youranswersonthecoloredsheetsgiventoyou.Ifyoudonothaveananswerattheendofatwominuteperiod,you
muststillsubmitananswersheetwithanidentifiedproblemnumberonit.Failuretodosowillresultinlossofpoints.
Thiseventistimed,andyouwillbegivenaverbal5secondwarningandtoldtoholdyouranswersheetupintheair.
Youmaykeepworkingasthesheetsarecollected.Ifateamanswersthesamequestionmorethanonce,onlythefirst
answerwillbescoredandtheotherattemptswillbeignored.
PressureRoundAnswers
Answer
1
2
3
4
5
10
30
−1
3
60[degrees]
162
Final Score:
“MathisCool”Championships--2016-17
School:
Room#
Name:
Team#
Proctor:
(Out of8)
HighSchool MentalMath–30secperquestion
8problemsreadorallytoeveryone-Approximately8%ofIndividualScore-25%ofteamscore
Whenitistimetobegin,theproctorwillreadthefirstquestiontwice.Youmaynotdoanywritingortalkingwhile
arrivingatasolution.Onceyouhaveasolution,recorditonthesheetinfrontofyou.Youmaynotchangeorcrossout
answersonceyouhavewrittenananswerdown.Ifthereareerasermarks,write-overs,orcrossed-outanswers,
theywillbemarkedwrong.Onceallstudentshavelaidtheirpencilsonthedesk,anotherquestionwillbeasked.Ifa
studentdoesn’tlayhis/herpencildown,themaximumwaittimeis30secondsaftercompletionofthesecondreadingof
thequestionbeforeanotherquestionisasked.Youmaycontinuetoworkonaproblemwhilethenextquestionisbeing
read.Thevalueofeachquestionisaoneorzero.Eachstudentwillbeaskedthesameeightquestions.Individualscores
usedtodetermineindividualplacingwillbedeterminedbythesumoftheMentalMathscoreandtheIndividualTestscore
foreachindividual.Inaddition,thetopthreeMentalMathscoresfromoneteamwillbetotaledanddoubledandwill
contributeto25%oftheteamscore.
Answer
1or0
1or0
1
2
3
4
5
6
7
8
30
3[ways]
6
9
18[sqin]
65
3
78[ways]
Final Score:
MathisCool”Championships–2016-17
11th&12thGrade–October19,2016
StudentName
ProctorName
SCHOOLNAME Room#
Team#
First Score
(out of 20)
INDIVIDUALMULTIPLECHOICE-15minutes–10problems–20%ofteamscore
Thistestistheonlytestwhereyouwillbepenalizedforincorrectresponses.Youwillreceive2pointsforacorrectletter
response,0pointsforleavingitblankand-1pointforanincorrectresponse.Itisnotnecessarytowriteyourpersonal
nameonthetest,butyoumayputitatthebottomofthetestsoyourcoachwillbeabletogiveyoubackthecorrect
test.Thistestistakenindividually,butitispartofyourteamscore,includingzerosformissingteammembers.Your
teamscorewillbecalculatedbytakingthemeanofyourfourteammembers’scores.Whenyouarepromptedtobegin,
tearoffthecoloredsheetandbegintesting.Sincethisisamultiplechoicetest,ONLYaletterresponseshouldbe
indicatedasananswerontheanswersheet.Notalkingduringthetest.
DONOTWRITEINSHADEDREGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
-1,0or2
-1,0or2
B
C
D
D
D
D
B
B
B
C
Final Score:
“MathisCool”Championships–2016-17
11th&12thGrade–October19,2016
SCHOOLNAME ProctorName
Team#
First Score
Room#
(out of 10)
TeamContest–ScoreSheet
TEAMTEST-15minutes–30%ofteamscore
Whenyouarepromptedtobegin,tearoffthecoloredsheetandgiveacopyofthetesttoeachofyourteammembers
andbegintesting.Eachproblemisscoredas1or0.Recordallanswersonthecoloredanswersheet.
DONOTWRITEINSHADEDREGIONS
Answer
1
2
3
4
5
6
7
8
9
10
10
8[integers]
100
4536
7
1
36
1
3
5
71
1or0
1or0