83
1260
1 = 9
-12
47
14/9
Answer
-5
1or0
1or0
& = − * − 4
)
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
8,191
200
3
997
30[diagonals]
Answer
386
1or0
1or0
960[ways]
60[3’s]
1,068
4327[m3]
2
486
65, −26 -3
or0.0768or7.68% !"
(5,-3)
!!;
:)
6 2
#$%
1,3 16-30TOTAL:
Total Correct:
KEY
1/48
10,816
937.5[L]
96, 94 [$]3.50
1716[ways]
Answer
61
1or0
1or0
11
[$]21,000
Room#: 31-40TOTAL:
2345
ALGEBRA2
31
32
33
34
35
36
37
38
39
40
Algebra2-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
33[°]
$
16[sides]
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
16
STUDENTNAME:
ProctorName: 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1-15TOTAL:
83
1260
1 = 9
-12
47
14/9
Answer
-5
1or0
1or0
& = − * − 4
)
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
8,191
200
3
997
30[diagonals]
Answer
386
1or0
1or0
960[ways]
60[3’s]
1,068
4327[m3]
2
486
65, −26 -3
or0.0768or7.68% !"
(5,-3)
!!;
:)
6 2
#$%
1,3 16-30TOTAL:
Total Correct:
1/48
10,816
937.5[L]
96, 94 [$]3.50
1716[ways]
Answer
61
1or0
1or0
11
[$]21,000
Room#: 31-40TOTAL:
2345
ALGEBRA2
31
32
33
34
35
36
37
38
39
40
Algebra2-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
33[°]
$
16[sides]
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
16
STUDENTNAME:
ProctorName: 1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1-15TOTAL:
STUDENTNAME:
ProctorName: & = − * − 4
)
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
Total Correct:
KEY
1or0
Room#: 1or0
Answer
61
1or0
1or0
Answer
386
1716[ways]
2345
!
$
or0.0768or7.68% 30[diagonals]
!"
#$%
96, 94 -3
937.5[L]
65, −26 10,816
486
or* >= ?
=
3
3
4327[m3]
<
;
5
31
32
33
34
35
36
37
38
11
[$]21,000
39
40
1,068
31-40TOTAL:
23[stamps]
960[ways]
(5,-3)
:)
!!;
16-30TOTAL:
PRE-CALCULUS
1,3 PRE-CALCULUS-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
1or0
1or0
1260
16
17
18
19
20
21
22
23
Answer
-5
-12
1 = 9
83
14/9
8,191
200
3
24
25
26
27
28
29
30
997
47
33[°]
$
1
2
3
4
5
6
7
8
5/9
16
9
10
11
12
13
14
15
1-15TOTAL:
STUDENTNAME:
ProctorName: & = − * − 4
)
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
Total Correct:
1or0
Room#: 1or0
Answer
61
1or0
1or0
Answer
386
1716[ways]
2345
!
$
or0.0768or7.68% 30[diagonals]
!"
#$%
96, 94 -3
937.5[L]
65, −26 10,816
486
or* >= ?
=
3
3
4327[m3]
<
;
5
31
32
33
34
35
36
37
38
11
[$]21,000
39
40
1,068
31-40TOTAL:
23[stamps]
960[ways]
(5,-3)
:)
!!;
16-30TOTAL:
PRE-CALCULUS
1,3 PRE-CALCULUS-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
1or0
1or0
1260
16
17
18
19
20
21
22
23
Answer
-5
-12
1 = 9
83
14/9
8,191
200
3
24
25
26
27
28
29
30
997
47
33[°]
$
1
2
3
4
5
6
7
8
5/9
16
9
10
11
12
13
14
15
1-15TOTAL:
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
1or0
1or0
3
200
8,191
1 = 9
-12
& = −8* − 2
Room#: Total Correct:
KEY
1or0
1or0
1or0
1or0
Answer
61
Answer
386
!
)B
!A
2345
$
1716[ways]
30[diagonals]
or0.0768or7.68% !"
)
or* >= #$%
96, 94 -3
937.5[L]
65, −26 !
;
or1 <
)
;
3
3
4327[m3]
=
?
5
31
32
33
34
35
36
37
38
2,5
[$]21,000
39
40
1,068
31-40TOTAL:
23[stamps]
960[ways]
(5,-3)
:)
!!;
16-30TOTAL:
CALCULUS
1,3 CALCULUS-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
Answer
-5
STUDENTNAME:
ProctorName: 14/9
997
15/16
33[°]
16
17
18
19
20
21
22
23
83
5/9
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
16
47
9
10
11
12
13
14
15
1-15TOTAL:
December10,2016
SchoolName:
Team#: “MathisCool”Masters–2016-17
1or0
1or0
3
200
8,191
1 = 9
-12
& = −8* − 2
Room#: Total Correct:
1or0
1or0
1or0
1or0
Answer
61
Answer
386
!
)B
!A
2345
$
1716[ways]
30[diagonals]
or0.0768or7.68% !"
)
or* >= #$%
96, 94 -3
937.5[L]
65, −26 !
;
or1 <
)
;
3
3
4327[m3]
=
?
5
31
32
33
34
35
36
37
38
2,5
[$]21,000
39
40
1,068
31-40TOTAL:
23[stamps]
960[ways]
(5,-3)
:)
!!;
16-30TOTAL:
CALCULUS
1,3 CALCULUS-IndividualContest–ScoreSheet
DONOTWRITEINSHADEDREGIONS
Answer
-5
STUDENTNAME:
ProctorName: 14/9
997
15/16
33[°]
16
17
18
19
20
21
22
23
83
5/9
24
25
26
27
28
29
30
1
2
3
4
5
6
7
8
16
47
9
10
11
12
13
14
15
1-15TOTAL:
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
HighSchoolMentalMathContest
Followalongasyourproctorreadstheseinstructionsto
you.YourMentalMathscoresheetisontheback.
GENERALINSTRUCTIONSapplyingtoalltests:
§
§
§
§
§
§
§
§
§
§
§
Goodsportsmanshipisexpectedthroughoutthecompetitionbyallinvolved,bothcompetitorsandobservers.Displayof
poorsportsmanshipmayresultindisqualification.
Calculatorsoranyotheraidsmaynotbeusedonanyportionofthiscontest.
Unlessstatedotherwise,allrational,non-integeranswersneedtobeexpressedasreducedcommonfractionsexceptincaseo
problemsdealingwithmoney.Inthecaseofproblemsrequiringdollaranswers,answerasadecimalroundedtothenearest
hundredth(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”Masters–2016-17
Sponsoredby:
HighSchool–December10,2016
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
WhatisthemodeoftheFibonacciSequence?
Thesumoffiveconsecutiveintegersisone-hundredsixty-five.Whatisthe
smallestofthefiveintegers?
Whatistheperimeter,inmeters,ofarectanglewithawidthofthirty-six
metersandanareaofseven-hundredfifty-sixsquaremeters?
Ifthere’saroomfullofelevenpeople,andtheyalldecidedtoexchange
phonenumberswitheachother,howmanyphonenumberexchanges
occur?Note:oneexchangeincludesbothpeoplegivingtheirphonenumber
totheother.
Howmanyverticesdoesadodecahedronhave?
Solvethefollowingequation:“four-factorialplusthree-Xequalsnine”
Whatisthesumoftheprimefactorsofone-hundredtwenty-seven?
Whatistheproductofthezeroesofthefunction“F-of-XequalsX-cubed
minusfour-X-squaredminussix-Xplusnine”?
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
PRE-CALCULUS-IndividualContest
Tearthiscoversheetandscratchpaperoffandfilloutthetopofthe
coloredanswersheetpriortothestartofthetest.Thegraphbelow
isforyouruse,ifneeded.
INDIVIDUALTEST–PRE-CALCULUS-35minutes
YoumayNOTbeseatednexttoanyonefromyourschool.IfyouareMOVENOWtoavoidbeingdisqualified!Whenyouare
promptedtobegin,tearoffthecoloredsheetandbegintesting.Makesureyournameandschoolarerecordedontheanswer
sheet.Therawscorewillbe2pointsforcorrectanswerstoproblems1-30and3pointsfor31-40.Recordyouranswersonthe
scoresheet.Notalkingduringthetest.Youwillbegivena5minutetimewarning.
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
ALGEBRA2-IndividualContest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Questions1-30:2pointseach
Evaluate:3 + 2 −
Evaluate:
)
+
+
+
,
%∗ '()
*
,
÷ *
Simplifyintermsof.,where. = −1:3. 1 + (3 − 4.)(6 + 8.)
Whatistheequation,inslope-intercept 7 = 89 + : form,ofthelinethroughthepoints
(−15, 6)and 6, −8 ?
If= > =
? @ A+? B (*?(,
?A%
,evaluate= 3 .
WhatvalueofCwillmakethesystemofequations2= + 3> = 4and6= + C> = 8haveno
solution?
Youhave5(indistinguishable)redhatsand1blackhat.Inhowmany(distinguishable)wayscan
youdistributethesehatstoyourtenbestfriends?(Notethat6friendswillhaveahatand4
friendswillbehatless).
Giventhefollowingfunctions:
g(x)=2x+1
f(x)=2x–1
h(x)=2x+2
a(x)=2x–2
Whatisthevalueofg(f(g(h(a(g(1))))))?
Evaluate:2D + 2) + 2+ + 2, + ⋯ + 2)+ .
Acirclewithradius5isinscribedinasquare,whichisinscribedinacircle,whichisinscribedin
anothersquare.Whatistheareaoftheoutermostsquare?
Whatvalue(s)ofFsatisfy3 ⋅ 2H() + 16 = 2+H ?
Adamchoosesathree-digitnumberandshowsittohisthreefriendsBilly,Cate,andDina.Billy
noticesthatAdam’snumberhasaremainderof1whendividedby2.Cate,ontheotherhand,
noticesthatithasaremainderof1whendividedby3.Dinanoticesthatthenumberhasa
remainderof1whendividedby4.WhatisthelargestpossiblevalueofAdam’snumber?
Whatisthecomplementofthesupplementoftheanglethatis34°smallerthanthe
supplementofthecomplementof67°?
Anexteriorangleofaregularpolygonmeasures22.5degrees.Howmanysidesdoesthis
polygonhave?
Ulrichwon’tsitbyVal,Wallywon’tsitbyXena,andYveswon’tsitbyZach.Valmustsitby
Zach,XenamustsitbyUlrich,andYvesmustsitbyVal.Whentheysitinarowofsixchairs,
howmanyseatingarrangementsarepossible?
Whatisthefifteenthterminthesequence5,4,8,7,14,13,26….
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Aregular12-gonhassidesmeasuring10m.Howmanydiagonalscanbedrawnthatarelonger
than30m?
Carlosisattemptingtowinateddybearatacarnival.However,thebearismerelythesecond
prize,andhehastohit4outof5targetstowinabear.Ifhisshootingskillsgivehima40%
probabilitytohitthetargetonanygivenshot,whatisthechanceofhimgettingabear?
Ms.Takesaccidentallytaughther1stgradestudentsalessonincorrectly!Shetoldthemthat
the“+”signmeansdivision,the“-“signmeansaddition,the“x”signmeanssubtraction,and
thatthe“/”signmeansmultiplication!Ohmy!ShegaveherstudentEinsteintheproblem
“Evaluate(4+2)–1x(2/3).”AssumingthatEinsteinnevermakesamistakeandthathe
solvedtheproblemusingtheincorrectsignsfromMs.Takes’lesson,whatdidEinsteingetasan
answerfortheproblem?
Whatpointisthree-fourthsofthewayfrompointA −7, −68 topointB(89, −12)along
segmentLM?
Asequenceofnumbersstartswiththenumber5.Afterthefirstterm,eachtermis3morethan
twicethepreviousterm.Findthesumofthefirst6termsofthissequence.
Nickisstandingonthexaxis.Hethrowsafootballaccordingtothegraph7 = −9 + − 69 + 9.
Thefootballlandsonthexaxis.Howfarhorizontallydidittravel?
NancyandOliverstartatthesamepointonaquarter-miletrack,runninginthesamedirection.
Iftheirspeedsare6milesperhour(mph)and7mph,andtheyrunfor20minutes,howmany
timeswilltheybeatthesomepointonthetrack,includingthestartingmomentandperhaps
theendingmoment?
Whatisthevolume,incubicmeters,ofarightcircularcylinderwithaheightof12manda
surfaceareaof216Nm2?
Whatisthesmallestnumbergreaterthan1000thatleavesaremainderof4whenitisdivided
by56andaremainderof12whenitisdividedby48?
Onhisdrivehome,Jackpasseshousesnumbered200-400,andcountsthenumberoftimeshe
seesa3ontheevensideofthestreet(i.e.Jackseesthehousesnumbered200,202,204,etc).
Howmany3’sdoesJacksee?
TheInncontainsfiveFighters,threeWizards,fourRogues,andtwoClerics.Inhowmanyways
canaPatronhireapartyofsixadventurersthatincludesatleasttwoFightersandatleastone
ofeachofthefourclasses?
Ifaparabolaoftheform7 = O9 + + :9 + Fpassesthroughthepoints(1,1),(9,1),and(13,13),
whatisthevertexoftheparabola?
Whatistherange,inintervalnotation,ofthefunctionP Q =
R B (,
R B ()
?
Youhavetwoidenticalunfairdice.Foreachdie,theprobabilityofrollinganumberis
proportionaltothenumber(e.g.,theprobabilityofrollinga6istwotimestheprobabilityof
rollinga3).Supposethatyourollthesetwodice.Findtheprobabilitythatthesumofthetwo
numbersshowingisa10.
ChallengeQuestions:3ptseach
31
32
33
34
35
36
37
38
39
40
Inadatasetofsevenintegertestscoresfrom0to100inclusive,themeanis41,themodeis
67,andtherangeis89.Whatisthelargestpossiblevalueofthemedian?
IftheBLUNICORNisdealta5cardhand,howmanywayscantheBLUNICORNbedealttwopair
(2ofonerankand2ofanotherrank(and1ofathirdrank))?RememberthatBLUNICORNSuse
onlytheredcardsfromastandard52-carddeck.
Fredbought3notebooksand7erasers,spendingatotalof$14.50.Georgebought5notebooks
and4erasers,spendingatotalof$16.50.Howmuchwoulditcosttobuy1notebookand1
eraser?
Whenthepoint −36, −8 isrotated90°clockwiseaboutthepoint 81, −23 ,whatarethe
coordinates,intheform 9, 7 ,ofthenewpoint?
JackandJillpourapailofwaterintoawatertrough.Thewatertroughisarighttrapezoidal
prism,withabase1meterby3meters,anopeningatthetop3metersby3meters,anda
depthwhenfullof1meter.Ifthewateriscurrently0.25metersdeep,howmanywater
LITERSofwaterareinthetrough(asadecimal)?Note:aliterisacubicdecimeter.
Evaluate:32, − 28, ArrangethevariablesA-Dindescendingorder(e.g.,youranswermightbeABCD):
L = 8!
M = 8U V = 8* W = 3U Ifadodecahedraldie(12faces)isrolledthreetimes,whatistheprobabilitythatthesumofthe
rollswillequalten?
3 0 5
Evaluatethedeterminant: 6 −1 8 ?
4 0 3
ThemembersoftheCoopevilleCarshareCooperativeeachcontributeequallytothepurchase
ofaMini-Coopercar,whichtheyagreetoshare.Iftherehadbeenonefewermemberofthe
group,eachmemberwouldhavehadtopay$100morethantheydid.Iftherehadbeentwo
fewermembersthanthat,eachmemberwouldhavehadtopay$350morethantheyactually
did.HowmanydollarsdidtheypayfortheirMini-Cooper?
ALGEBRA2
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
PRE-CALCULUS-IndividualContest
Tearthiscoversheetandscratchpaperoffandfilloutthetopofthe
coloredanswersheetpriortothestartofthetest.Thegraphbelow
isforyouruse,ifneeded.
INDIVIDUALTEST–PRE-CALCULUS-35minutes
YoumayNOTbeseatednexttoanyonefromyourschool.IfyouareMOVENOWtoavoidbeingdisqualified!Whenyouare
promptedtobegin,tearoffthecoloredsheetandbegintesting.Makesureyournameandschoolarerecordedontheanswer
sheet.Therawscorewillbe2pointsforcorrectanswerstoproblems1-30and3pointsfor31-40.Recordyouranswersonthe
scoresheet.Notalkingduringthetest.Youwillbegivena5minutetimewarning.
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
PRE-CALCULUS-IndividualContest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Questions1-30:2pointseach
Evaluate:3 + 2 −
Evaluate:
)
+
+
+
,
%∗ '()
*
,
÷ *
Simplifyintermsof.,where. = −1:3. 1 + (3 − 4.)(6 + 8.)
Whatistheequation,inslope-intercept 7 = 89 + : form,ofthelinethroughthepoints
(−15, 6)and 6, −8 ?
If= > =
? @ A+? B (*?(,
?A%
,evaluate= 3 .
WhatvalueofCwillmakethesystemofequations2= + 3> = 4and6= + C> = 8haveno
solution?
Youhave5(indistinguishable)redhatsand1blackhat.Inhowmany(distinguishable)wayscan
youdistributethesehatstoyourtenbestfriends?(Notethat6friendswillhaveahatand4
friendswillbehatless).
Giventhefollowingfunctions:
g(x)=2x+1
f(x)=2x–1
h(x)=2x+2
a(x)=2x–2
Whatisthevalueofg(f(g(h(a(g(1))))))?
Evaluate:2D + 2) + 2+ + 2, + ⋯ + 2)+ .
Acirclewithradius5isinscribedinasquare,whichisinscribedinacircle,whichisinscribedin
anothersquare.Whatistheareaoftheoutermostsquare?
Whatvalue(s)ofFsatisfy3 ⋅ 2H() + 16 = 2+H ?
Adamchoosesathree-digitnumberandshowsittohisthreefriendsBilly,Cate,andDina.Billy
noticesthatAdam’snumberhasaremainderof1whendividedby2.Cate,ontheotherhand,
noticesthatithasaremainderof1whendividedby3.Dinanoticesthatthenumberhasa
remainderof1whendividedby4.WhatisthelargestpossiblevalueofAdam’snumber?
Whatisthecomplementofthesupplementoftheanglethatis34°smallerthanthe
supplementofthecomplementof67°?
ForanangleinQuadrantII,ifcos(α)=-2/3,thenwhatissin+ [?
Ulrichwon’tsitbyVal,Wallywon’tsitbyXena,andYveswon’tsitbyZach.Valmustsitby
Zach,XenamustsitbyUlrich,andYvesmustsitbyVal.Whentheysitinarowofsixchairs,
howmanyseatingarrangementsarepossible?
Whatisthefifteenthterminthesequence5,4,8,7,14,13,26….
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Aregular12-gonhassidesmeasuring10m.Howmanydiagonalscanbedrawnthatarelonger
than30m?
Carlosisattemptingtowinateddybearatacarnival.However,thebearismerelythesecond
prize,andhehastohit4outof5targetstowinabear.Ifhisshootingskillsgivehima40%
probabilitytohitthetargetonanygivenshot,whatisthechanceofhimgettingabear?
Ms.Takesaccidentallytaughther1stgradestudentsalessonincorrectly!Shetoldthemthat
the“+”signmeansdivision,the“-“signmeansaddition,the“x”signmeanssubtraction,and
thatthe“/”signmeansmultiplication!Ohmy!ShegaveherstudentEinsteintheproblem
“Evaluate(4+2)–1x(2/3).”AssumingthatEinsteinnevermakesamistakeandthathe
solvedtheproblemusingtheincorrectsignsfromMs.Takes’lesson,whatdidEinsteingetasan
answerfortheproblem?
Whatpointisthree-fourthsofthewayfrompointA −7, −68 topointB(89, −12)along
segmentLM?
Asequenceofnumbersstartswiththenumber5.Afterthefirstterm,eachtermis3morethan
twicethepreviousterm.Findthesumofthefirst6termsofthissequence.
)
IfP 9 = 9 , and\ 9 = ,whatis(P ∘ \)A) ?
]
)
If9 = ,whatisthevalueoftan(arcsin 9 )?
+
Whatisthevolume,incubicmeters,ofarightcircularcylinderwithaheightof12manda
surfaceareaof216Nm2?
Whatisthesmallestnumbergreaterthan1000thatleavesaremainderof4whenitisdivided
by56andaremainderof12whenitisdividedby48?
Youhaveasetof5¢stampsandasetof7¢stamps.Usingthesestamps,youcouldpayanexact
postageof48¢(withfour5¢stampsandfour7¢stamps),butyoucouldnotpayanexact
postageof8¢.Whatisthelargestintegeramountofpostageyoucouldnotpayexactlywith
yourstamps?
TheInncontainsfiveFighters,threeWizards,fourRogues,andtwoClerics.Inhowmanyways
canaPatronhireapartyofsixadventurersthatincludesatleasttwoFightersandatleastone
ofeachofthefourclasses?
Ifaparabolaoftheform7 = O9 + + :9 + Fpassesthroughthepoints(1,1),(9,1),and(13,13),
whatisthevertexoftheparabola?
Whatistherange,inintervalnotation,ofthefunctionP Q =
R B (,
R B ()
?
Youhavetwoidenticalunfairdice.Foreachdie,theprobabilityofrollinganumberis
proportionaltothenumber(e.g.,theprobabilityofrollinga6istwotimestheprobabilityof
rollinga3).Supposethatyourollthesetwodice.Findtheprobabilitythatthesumofthetwo
numbersshowingisa10.
ChallengeQuestions:3ptseach
31
32
Inadatasetofsevenintegertestscoresfrom0to100inclusive,themeanis41,themodeis
67,andtherangeis89.Whatisthelargestpossiblevalueofthemedian?
IftheBLUNICORNisdealta5cardhand,howmanywayscantheBLUNICORNbedealttwopair
(2ofonerankand2ofanotherrank(and1ofathirdrank))?RememberthatBLUNICORNSuse
onlytheredcardsfromastandard52-carddeck.
33
34
35
Ifcos O = forN < O < 2N,evaluatesin
36
37
38
Evaluate:32, − 28, 39
40
,
f
*
+
.
Whenthepoint −36, −8 isrotated90°clockwiseaboutthepoint 81, −23 ,whatarethe
coordinates,intheform 9, 7 ,ofthenewpoint?
JackandJillpourapailofwaterintoawatertrough.Thewatertroughisarighttrapezoidal
prism,withabase1meterby3meters,anopeningatthetop3metersby3meters,anda
depthwhenfullof1meter.Ifthewateriscurrently0.25metersdeep,howmanywater
LITERSofwaterareinthetrough(asadecimal)?Note:aliterisacubicdecimeter.
ArrangethevariablesA-Dindescendingorder(e.g.,youranswermightbeABCD):
L = 8!
M = 8U V = 8* W = 3U JackandJillwalkupthehill(tofetchapailofwater).Whentheydo,theycantakeoneofa1
literpail,a3literpail,ora5literpail.Theyfillwhicheverpailtheytookandtakeitdownthe
hill.Iftheyneedto,theygobackup(perhapswithadifferentbucket),getsomemore,and
repeatuntiltheyhavebroughtexactly5Ldown.Howmanywayscouldtheycarry5litersof
waterdownthehill,iftheorderoftheirtripsmatters,andtheycanemptyabucketatthe
bottomofthehillandreuseitonanothertrip?
3 0 5
Evaluatethedeterminant: 6 −1 8 ?
4 0 3
ThemembersoftheCoopevilleCarshareCooperativeeachcontributeequallytothepurchase
ofaMini-Coopercar,whichtheyagreetoshare.Iftherehadbeenonefewermemberofthe
group,eachmemberwouldhavehadtopay$100morethantheydid.Iftherehadbeentwo
fewermembersthanthat,eachmemberwouldhavehadtopay$350morethantheyactually
did.HowmanydollarsdidtheypayfortheirMini-Cooper?
PRE-CALCULUS
“MathisCool”Masters–2016-17
Sponsoredby:
December10,2016
CALCULUS-IndividualContest
Tearthiscoversheetandscratchpaperoffandfilloutthetopofthe
coloredanswersheetpriortothestartofthetest.Thegraphbelow
isforyouruse,ifneeded.
INDIVIDUALTEST–PRE-CALCULUS-35minutes
YoumayNOTbeseatednexttoanyonefromyourschool.IfyouareMOVENOWtoavoidbeingdisqualified!Whenyouare
promptedtobegin,tearoffthecoloredsheetandbegintesting.Makesureyournameandschoolarerecordedontheanswer
sheet.Therawscorewillbe2pointsforcorrectanswerstoproblems1-30and3pointsfor31-40.Recordyouranswersonthe
scoresheet.Notalkingduringthetest.Youwillbegivena5minutetimewarning.
“MathisCool”Masters–2016-17
Sponsoredby:
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CALCULUS-IndividualContest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Questions1-30:2pointseach
Evaluate:3 + 2 −
Evaluate:
)
+
+
+
,
%∗ '()
*
,
÷ *
Simplifyintermsof.,where. = −1:3. 1 + (3 − 4.)(6 + 8.)
Findtheequation,inslope-intercept 7 = 89 + : form,ofthelinethatpassesthroughthe
centeroftheellipse49 + + 7 + − 89 + 207 + 40 = 0andthevertexoftheparabola7 = 29 + −
89 − 10.
If= > =
? @ A+? B (*?(,
?A%
,evaluate= 3 .
WhatvalueofCwillmakethesystemofequations2= + 3> = 4and6= + C> = 8haveno
solution?
Pennywantstoplayacoin-flippinggamewithNicoleinwhichacoinisrepeatedlyflipped.
Whenheadscomesup4timesinarow,Nicolewins.IfaTailsisfollowedby3Headsinarow,
Pennywins.WhatistheprobabilitythatPennywinsundertheseconditions?
Giventhefollowingfunctions:
g(x)=2x+1
f(x)=2x–1
h(x)=2x+2
a(x)=2x–2
Whatisthevalueofg(f(g(h(a(g(1))))))?
Evaluate:2D + 2) + 2+ + 2, + ⋯ + 2)+ .
Acirclewithradius5isinscribedinasquare,whichisinscribedinacircle,whichisinscribedin
anothersquare.Whatistheareaoftheoutermostsquare?
Whatvalue(s)ofFsatisfy3 ⋅ 2H() + 16 = 2+H ?
Adamchoosesathree-digitnumberandshowsittohisthreefriendsBilly,Cate,andDina.Billy
noticesthatAdam’snumberhasaremainderof1whendividedby2.Cate,ontheotherhand,
noticesthatithasaremainderof1whendividedby3.Dinanoticesthatthenumberhasa
remainderof1whendividedby4.WhatisthelargestpossiblevalueofAdam’snumber?
Whatisthecomplementofthesupplementoftheanglethatis34°smallerthanthe
supplementofthecomplementof67°?
ForanangleinQuadrantII,ifcos(α)=-2/3,thenwhatissin+ [?
Ulrichwon’tsitbyVal,Wallywon’tsitbyXena,andYveswon’tsitbyZach.Valmustsitby
Zach,XenamustsitbyUlrich,andYvesmustsitbyVal.Whentheysitinarowofsixchairs,
howmanyseatingarrangementsarepossible?
Whatisthefifteenthterminthesequence5,4,8,7,14,13,26….
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Aregular12-gonhassidesmeasuring10m.Howmanydiagonalscanbedrawnthatarelonger
than30m?
Carlosisattemptingtowinateddybearatacarnival.However,thebearismerelythesecond
prize,andhehastohit4outof5targetstowinabear.Ifhisshootingskillsgivehima40%
probabilitytohitthetargetonanygivenshot,whatisthechanceofhimgettingabear?
Ms.Takesaccidentallytaughther1stgradestudentsalessonincorrectly!Shetoldthemthat
the“+”signmeansdivision,the“-“signmeansaddition,the“x”signmeanssubtraction,and
thatthe“/”signmeansmultiplication!Ohmy!ShegaveherstudentEinsteintheproblem
“Evaluate(4+2)–1x(2/3).”AssumingthatEinsteinnevermakesamistakeandthathe
solvedtheproblemusingtheincorrectsignsfromMs.Takes’lesson,whatdidEinsteingetasan
answerfortheproblem?
Whatpointisthree-fourthsofthewayfrompointA −7, −68 topointB(89, −12)along
segmentLM?
Evaluatethelimitlim 8 → ∞
) k
l
kmD * )
IfP 9 = 9 , and\ 9 = ,whatis(P ∘ \)A) ?
]
)
If9 = ,whatisthevalueoftan(arcsin 9 )?
+
Whatisthevolume,incubicmeters,ofarightcircularcylinderwithaheightof12manda
surfaceareaof216Nm2?
Whatisthesmallestnumbergreaterthan1000thatleavesaremainderof4whenitisdivided
by56andaremainderof12whenitisdividedby48?
Youhaveasetof5¢stampsandasetof7¢stamps.Usingthesestamps,youcouldpayanexact
postageof48¢(withfour5¢stampsandfour7¢stamps),butyoucouldnotpayanexact
postageof8¢.Whatisthelargestintegeramountofpostageyoucouldnotpayexactlywith
yourstamps?
TheInncontainsfiveFighters,threeWizards,fourRogues,andtwoClerics.Inhowmanyways
canaPatronhireapartyofsixadventurersthatincludesatleasttwoFightersandatleastone
ofeachofthefourclasses?
Ifaparabolaoftheform7 = O9 + + :9 + Fpassesthroughthepoints(1,1),(9,1),and(13,13),
whatisthevertexoftheparabola?
Whatistherange,inintervalnotation,ofthefunctionP Q =
R B (,
R B ()
?
Youhavetwoidenticalunfairdice.Foreachdie,theprobabilityofrollinganumberis
proportionaltothenumber(e.g.,theprobabilityofrollinga6istwotimestheprobabilityof
rollinga3).Supposethatyourollthesetwodice.Findtheprobabilitythatthesumofthetwo
numbersshowingisa10.
ChallengeQuestions:3ptseach
31
32
Inadatasetofsevenintegertestscoresfrom0to100inclusive,themeanis41,themodeis
67,andtherangeis89.Whatisthelargestpossiblevalueofthemedian?
IftheBLUNICORNisdealta5cardhand,howmanywayscantheBLUNICORNbedealttwopair
(2ofonerankand2ofanotherrank(and1ofathirdrank))?RememberthatBLUNICORNSuse
onlytheredcardsfromastandard52-carddeck.
33
34
35
Ifcos O = forN < O < 2N,evaluatesin
36
37
38
39
40
,
f
*
+
.
Whenthepoint −36, −8 isrotated90°clockwiseaboutthepoint 81, −23 ,whatarethe
coordinates,intheform 9, 7 ,ofthenewpoint?
JackandJillpourapailofwaterintoawatertrough.Thewatertroughisarighttrapezoidal
prism,withabase1meterby3meters,anopeningatthetop3metersby3meters,anda
depthwhenfullof1meter.Ifthewateriscurrently0.25metersdeep,howmanywater
LITERSofwaterareinthetrough(asadecimal)?Note:aliterisacubicdecimeter.
*
Whatisthesumofthefirsttentermsofthesequencenl = B
?Assumethatn) isthe
l (%l(1
firsttermofthesequence.
ArrangethevariablesA-Dindescendingorder(e.g.,youranswermightbeABCD):
L = 8!
M = 8U V = 8* W = 3U JackandJillwalkupthehill(tofetchapailofwater).Whentheydo,theycantakeoneofa1
literpail,a3literpail,ora5literpail.Theyfillwhicheverpailtheytookandtakeitdownthe
hill.Iftheyneedto,theygobackup(perhapswithadifferentbucket),getsomemore,and
repeatuntiltheyhavebroughtexactly5Ldown.Howmanywayscouldtheycarry5litersof
waterdownthehill,iftheorderoftheirtripsmatters,andtheycanemptyabucketatthe
bottomofthehillandreuseitonanothertrip?
4 2
.
1 3
ThemembersoftheCoopevilleCarshareCooperativeeachcontributeequallytothepurchase
ofaMini-Coopercar,whichtheyagreetoshare.Iftherehadbeenonefewermemberofthe
group,eachmemberwouldhavehadtopay$100morethantheydid.Iftherehadbeentwo
fewermembersthanthat,eachmemberwouldhavehadtopay$350morethantheyactually
did.HowmanydollarsdidtheypayfortheirMini-Cooper?
Findalleigenvaluesofthematrix
CALCULUS
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
IndividualMultipleChoiceContest
1
2
Howmanypositiveintegerslessthan108arerelativelyprimetoit?
A)30
B)36
C)42
D)48
E)Answernotgiven.
Jimmyhasabudgetof30dollarsandcanpurchaseapplesfor4dollarseachandorangesfor6
dollarseach(thisisveryhighqualityfruit!).IfJimmyspendsallofhismoneyandmaximizesthe
numberofpiecesoffruithegets,howmanyapplesdoeshebuy?
3
4
5
6
A)4
B)5
C)6
D)7
E)Answernotgiven.
Howmanytimeswillthehourhandandminutehandmakearightangleina24hourperiod
startingatmidnight?
A)40 B)42 C)44 D)46 E)Answernotgiven.
Whatistheremainderwhen39 , − 99 + + 69 + 19isdividedby9 − 2?
A)19
B)20
C)21
WhatisSin(x)Sec(x)equalto?
D)22
E)Answernotgiven.
A)cos 9 B)csc 9 C)tan 9 D)1
E)Answernotgiven.
Threeburglarsarearrestedforacrimethatonlyonepersoncommitted.Eachsaysthefollowing
ininterrogation:
A:Ididit.B:Ididn’tdoit.C:Adidn’tdoit.
Ifonlyoneistruthful,whodidit?
7
A)A
B)B
C)C
D)CannotBeDetermined E)Answernotgiven.
Aboxcontains7pinkpensand15bluepens.Juanitatakestwopensoutofthebox,without
replacement.Whatistheprobabilitythatshechoosesnomorethan1pinkpen?
A)
)
*1+
%
B) ++
*,%
C)
*U*
+U
D) ,,
E)Answernotgiven.
8
IfSetTisthesetofmultiplesof7lessthan50,howmanysubsetsofTcontainatleastone
elementcontainingthedigit“1”?
9
A)32
B)64
C)96
D)128
E)Answernotgiven.
JackandJill’sfarmhasBLUNICORNS,amythicalbluebeastwithonehead,fourwings,andtwo
legs,andonehorn;andCHICKENS,alessmythicalbeastwithonehead,twowings,twolegs,
andnohorns.Jillcounts56legsand82wings.HowmanyBLUNICORNSdoesthefarmhave?
A)10
B)11
C)12
Evaluate:9 ∗ (33+ ) − 4 ∗ (49+ )
10 A)177
D)13
E)Answernotgiven.
D)207
E)Answernotgiven.
B)187
C)197
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
TeamContest
1
2
3
4
5
6
7
8
9
10
Whatisthesumofallthenumbersbetween60and360whicharenotmultiplesof2nor
multiplesof3?
Mr.BrandswritesdownaquadraticequationoftheformO9 + + :9 + F = 0andasksthree
studentstosolveforx.RachelmistakenlywritesdownthewrongvalueofO,andfindsthather
equationhasasolutionof9 = 1or9 = 6.Stevemistakenlywritesdownthewrongvalueof:,
andfindsthathisequationhasasolutionof9 = 1or9 = 3.Tristanmistakenlywritesdown
%
thewrongvalueofF,andfindsthathisequationhasasolutionof9 = 1or9 = .Assuming
+
thateachstudentcorrectlysolvedtheirmiscopiedquadraticequation,whatvaluesof9solve
Mr.Brand’soriginalequation?
Findtherealroot(s)of:9 , – 99 + + 279 = 54
Whatisthesumofthevalue(s)of: 0 ≤ : < 2N satisfy2 cos + 2: + sin 2: = 2?
Whenfourcardsaredrawnfromastandard52-carddeck,whatistheprobabilityofdrawing4
aces?
Atessellationofaplaneconsistsofonlyequilateraltrianglesandregular12-gons.What
fractionoftheshapesaretriangles?
Whatisthesurfacearea,insquaremeters,ofarightrectangularpyramidwithabase
measuring28mby40mandaheightof48m?
AcirclewitharadiusofonehasachordoflengthonewithendpointsAandB.PointsPandQ
arechosensuchthatPQisadiameterandtheareaofAPBismaximized.Whatistheratioof
theareasofAQBandAPB?
Whatistheequation,intheformL9 + M7 + Vq = 1,oftheplanethroughthepoints(4, 4, 5),
(−1, 2, 9),and(2, −1, −6)?
Inthesetofpositiveintegers{56,8,91,70,3,21,x,y,z},themedianisgreaterthanthemean,
whichisgreaterthanthemode.Whatisthelargestpossiblevalueof9 + 7 + q?
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
PressureRoundContest
1 Whatistheleastcommonmultipleof846and348?
Inaclassof6students,theresultsofatestare70,80,90,x,yandz.If
2 themedianis93,themeanis89andtherangeis30,whatisxyz?
Whatistheareaoftheellipsewithequation9 + 47 − 89 + 647 =
3 0?
Inanewcasinogame,aplayerflipsafaircoinrepeatedly.Ifshegets
4 threeheadsinarowbeforeshegetstwoTailsinarow,shewins;
+
5
+
otherwisesheloses.Whatistheprobabilityshewins?
Ifaparallelogramhasverticesontheorigin,(7,4),(5,1),and(12,5),
whatistheareaoftheparallelogram?
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#1–
#1
#
1
2
3
4
5
6
7
8
9
10
SET1
Problem
Atrianglehassidesoflengthsixcentimeters,eightcentimeters,and
tencentimeters.Whatisthearea,insquarecentimeters,ofthe
triangle?
Answer
24[cm2]
Whatisthearea,insquaremeters,ofanequilateraltrianglewitha
perimeterofthirty-sixmeters?
36 3[m2]
What is the product of four-hundred ninety-eight and three-hundred
twelve?
155,376
Jack and Jill flip a coin, and then roll three fair, six-sided dice to decide
)%
who has to carry the pails of water. Jack will carry the pail either if
)1
Heads is flipped OR the product of the numbers on the three dice is a
multiple of two. What is the probability Jack carries the pail of water?
What is the smallest integer value of B satisfying six-to-the-B-power
[PAUSE], plus seven-thousand nine-hundred twenty-four [PAUSE],
6
is-greater-than-or-equal-to [PAUSE], forty-one-thousand threehundred sixty-six?
Howmanypositiveintegersarefactorsofone-thousandsevenhundredeighty?
12[integers]
Whatisthearithmetic(“air-ith-MET-ic”)meanoftwo-X-minus-three,
four-X,andtwelve-X-plus-nine?
69 + 2
SetRisthesetofpositivemultiplesofninelessthanone-thousand
andsetSisthesetofpowersofthreegreaterthanten.Howmany
elementsareintheintersectionofsetsRandS?
Themeanclassscoreforanassignmentwasninetypoints.Thereare
fifteenstudentsintheclassandthirteenofthemhadacombined
scoreofone-thousandone-hundred.Whatisthecombinedscoreof
theremainingtwostudents?
Whatistheeighthtermofageometricsequencewithfirstterm
thirteenandcommonratiotwo?
4
250[points]
1664
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#2–
SET2
#2
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer
Whatisthemedianofthedataset{51,2,68,9,34,6,78}?
34
Whatistheproductoftherootsofeight-G-cubed[PAUSE]minusfiveG-squared[PAUSE]plusseven-G[PAUSE]plustwenty-three[PAUSE]
equalszero?
Therearesix-hundredFrisbees.Five-hundredforty-twoofthemare
red,andtwo-hundredthreeofthemhavepicturesonthem.Every
Frisbeeiseitherred,hasapicture,orboth.HowmanyFrisbeesare
bothredandhaveapicture?
+,
− U
145[Frisbees]
Inafieldofsheepandchickens,therearetwentyheadsandfifty-four
feet.Howmanychickensarethere?
13[chickens]
Penelopevisitsarestaurantthathasenormousfoodandordersa
pizzathathasadiameterofsixfeet.Thesmallersizehasaradiusof
twofeet.Howmuchmoreareadoesthelargersizepizzahavethan
thesmallersize,insquarefeet?
5π[ft2]
Five-pi
Evaluatethree-hundredseventy-eightsquaredminustwo-hundred
twenty-twosquared.
93,600
Whatarethecoordinates,intheformX-comma-Y,oftheleftmostXinterceptofY-equals-two-X-squared-minus-seven-X-minus-thirty?
Whatistheeccentricity(“ex-en-TRISS-it-ee”)oftheconic
X-squared-plus-two-X[PAUSE]plus-Y-squared-minus-fifty-six-Y
[PAUSE]
plus-one-hundred-twenty-four-equals-zero?
Sarahdrawsasquare,whichisinscribedinsideacircle,whichisitself
inscribedinsideofasquare.Iftheinnermostsquarehasasidelength
ofonemeter,whatisthearea,insquaremeters,oftheoutermost
square?
Youdropaballfromaheightofonemeter.Onthefirstbounce,it
goesuppoint-ninemetersabovetheground,thenfallsbackdown.
Ontheoneafterthat,itbouncespoint-eight-onemetersupandthen
backdown.Oneachsuccessivebounce,itrisestonine-tenthsthe
heightofthepreviousbounce.Whatisthetotaldistanceinmeters
(bothup&down)coveredbytheballasitbounces?
%
− , 0 +
0(it’sacircle)
2
19[meters]
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#3–
#
1
2
3
4
5
6
7
SET3
#3
8
9
10
Problem
Answer
Expressthebasesixnumeralthree-five-one-two-base-sixasabase
tennumeral.
836
Whatisthemeasure,indegrees,ofaninteriorangleofaregular
twenty-four-gon?
165[degrees]
Arectangularrosegardenmeasuresfivemetersbytenmeters,andis
surroundedbyarectangularwalkwaythatistwometerswideonall
sidesofthegarden.Whatisthearea,insquaremeters,ofthe
walkway?
76[m2]
Whatistheprimefactorizationoftheproductofthefirstfivetermsof )D )%
2 ⋅ 3 ageometricsequencewithfirsttermtwelveandcommonratiothree?
Whatisthesumofthenumberofbagelsinabaker’sdozen,the
numberofdaysinaleapyear,andthenumberofprimenumbersless 387
thantwenty?
Twenty-seventothefifthpowerequalsthreetotheninthpower
timesninetowhatpower?
3
JackandJillareplayingpokerwithoneoftheirBLUNICORNS.
BLUNICORNSonlyplaywiththeredcardsinthedeck.Ifthe
BLUNICORNisdealtafive-cardhand,whatistheprobabilityithasa
0
fullhouse?Note:afullhouseistwoofonerankandthreeofanother
rank.
Whenthesecretnumberismultipliedbysevenandthisresultis
decreasedbyfive-hundredseventy-four,thefinalresultisone263
thousandtwo-hundredsixty-seven.Whatisthesecretnumber?
Whatisthearea,insquaremeters,ofacirclecircumscribedabouta
rectanglemeasuringtwenty-sixmetersbyseventy-eightmeters?
1690N[m2]
Ajacketshopsellsjacketsfortwentydollarseach.Asalestaxoften
percentisimposedonthejackets.Theshopthendecidestoholda
sale,reducingthecostsofalljacketsbytwenty-fivepercent.Whatis
thefinalcostofajacket,asadecimalnumberofdollars?
$16.50
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#4–
SET4
#4
#
1
2
3
4
5
6
7
8
9
10
Problem
InwhichquadrantoftheCartesianPlanedoesthepointninethousandone-hundredthirty-fourCOMMAnegativefifty-sixthousandseven-hundredeighty-ninelie?
CarlwantstoimpressagirlnamedElla.Duringlunch,hewalksupand
askshertothinkaboutherfavoritewholenumber.Hetellsherto
cubeit,subtractoneanddividebyonelessthanthenumbershe
originallypicked(fortunately,herfavoritenumberwasn'tone,sothis
operationwaspossible).WhenheasksEllaforherresult,sheshrugs
andtellsCarlthatshegotten-thousandone-hundredone.ThenCarl
uttersherfavoritenumberanddabs(asoneshouldwhen
accomplishingsuchafeat).Whatisthisnumber?
AregularN-sidedpolygoncantessellatetheplane.Findthesumofall
possiblevaluesofN.
Answer
Findthemedianfortheset{9,12,28,37,12,74,24}
24
Whatisthemostspecificnamethatappliestoallquadrilateralswith
diagonalsthatbisectoneanother?
Parallelogram
Whatisthemodeofthedataset{5,8,5,2,6,90}?
5
IVor4or4th
100
13
Sharondahassixfour-sideddice.Ifsherollsallofherdice,whatisthe ,
,+
chancethatshewillgetexactlyfiveevennumbers?
JackandJillleavetheirhousesandarewalkingtowardseachother(to
gofetchapailofwater).JackcanwalkfromhishousetoJill’shouse
intenminutesandJillcanwalkfromherhousetoJack’shousein
6[min]
fifteenminutes.Iftheybothleavehomeatthesametimeandwalk
towardseachother,howmanyminuteswillittakethemtomeet?
Howmanynon-congruentrectangleshaveperimetersofeighty
20
metersandintegersidelengthswhenmeasuredinmeters?
Jackgetstherightmedicationandspendsafewnightsinthehospital
withaconcussion,butwantstogetbacktohistennisteam.His
doctorrecommendsagraduatedreturntoplayafterwards.Thefirst 1+%
[hrs]
%)+
week,Jackplaysthirtyminutes,andeachweekheplaystwenty-five
percentmorethanthepriorweek.Howmanyhourswillplayinthe
fifthweek,asafraction?
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#5–
#5
#
1
2
3
4
5
6
7
8
9
10
SET5
Problem
Answer
Whatisthequotientwhenninety-four-thousandone-hundredfifteen
2,689
isdividedbythirty-five?
Howmanynumbersbetweenoneandtwenty,includingoneand
twenty,haveanoddnumberofpositivefactors?
4
Thereareone-hundredsocksinasockdrawer,withthirtyofthem
green,thirtyofthemblue,andtherestwhite.Howmanysocksdo
71[socks]
youhavetotakeoutofthedrawertohaveguaranteedthatatleast
onesockofeachcolorwastakenout?
Linisonvacation.Shefirstdrivestwelvemilesdirectlyeastfromher
housebeforeturninganddrivingsixteenmilesdirectlynorth.She
337[miles]
thendrivesthreemilesdirectlywesttothehotelwhereshewillstay
thenight.HowmanymilesisLinfromherhouseatthispoint?
Whatisthetwelfthtermofthesequencedefinedas“H-sub-JequalsJsquaredminusthree-Jplusseven”?AssumethatH-sub-1isthefirst
115
term.
Whatistheareaofacirclewithacircumferenceofeighty-six-pi?
1849N
Solveforx:“three-X-squaredminussixteen-Xplussixteenequals
zero”.
[9 =] ,4
IftheprobabilityofTombreakingapiñataispoint-sixonthefirsttry,
andeverysuccessivetryhasthechanceofthepiñatabreaking
increasingbypoint-one,whatistheprobabilityasadecimalthatit
willtakeTomexactlythreehitstobreakthepiñata?
0.096
Saraissixtimesasoldasherbrother.Infouryears,Sarawillbeonly
twiceasoldasherbrother.HowoldisSaranow?
6[yearsold]
Ifyou'vealreadydrawnajackofclubs,aqueenofdiamonds,anace
ofhearts,andatenofclubsfromastandardfifty-two-carddeck,what
arethechancesthatyourfifthdrawcompletesastraight?Note:a
straightisfivecardsoffiveconsecutiveranks.
)+
*
,
)
“MathisCool”Masters–2016-17
Sponsoredby:
11th&12thGrade–December10,2016
COLLEGEKNOWLEDGEBOWLROUND#6–
SET6
#6
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer
Whatisthesumofsix-hundredseventy-nineandeight-hundred
thirty-five?
1,514
Afterthreetests,Joanna’stestaveragewaseighty-eight.Afterthe
fourthtest,Joanna’stestaveragewasninety.Ifallfourtestscount
equallyintheaverage,whatdidJoannascoreonherfourthtest?
96
Evaluateone-hundred-fourtimesninety-six.
9,984
Whatistheslopeofalineperpendiculartotheline“fifty-six-Xplus
forty-nine-Yequalsthirteen-thousandeight-hundredninety”?
'
Howmanyonesareinthebinaryrepresentationofeight-hundred
forty-seven?
U
7
TriangleABCandTriangleDEFaresimilartriangles.Iftheratioofthe
anglesinTriangleABC(innoparticularorder)areone-to-two-to-three 60[degrees]
whatistheaverageoftheanglesintriangleDEF?
Jackhasabagthatcontainsthreefaircoinsandtwocoinsthathavea
'+t
sixtypercentchanceofreturningheads.Ifhepullstwocoins,with
+%DD
replacement,andflipsthem,whatistheprobabilitythatbothcoins
areheads?
Wendellhasadancefloorintheshapeofaparallelogram.Thedance
floor’sdiagonalsmeasuretwelvefeetandsixteenfeet,andare
perpendiculartooneanother.IfWendellwantstoputastringalights 40[ft]
aroundtheperimeterofthedancefloorforagreatervisualeffect,
howmanyfeetlongdoesthestringoflightsneedtobe?
Whatisthesumofthetwentysmallestpositiveintegersthatarenot
multiplesofseven?
234
Findtherangeofthemean,median,andmodeofthefollowingdata:
{31,17,31,20,16}
11
“MathisCool”Masters–2016-17
Sponsoredby:
HighSchool–December10,2016
COLLEGEKNOWLEDGEBOWLROUND–
#
1
2
3
4
5
6
EXTRA
Problem
Answer
Expressthecuberootofthree-thousandfour-hundredfifty-sixin
simplestradicalform.
12 2
Arrangethefractionsthree-fourths,five-sevenths,andseven-ninthsin
DECREASINGnumericalorder.
Howmanyminutespassbetweentenfifty-fourAMandtwelvethirtyfourPM?
Twoverticallinesaredrawninaplane.Oneofthemisrotatedonehundredthirty-fourdegreesclockwise,andtheotherisrotatedtwohundredforty-sixdegreescounter-clockwise.Whatisthemeasure,in
degrees,ofthesmalleranglebetweenthetwolines?
Whatarethecoordinates,intheformX-comma-Y,ofthecenterofthe
circlewithequation“x-squaredplusy-squaredminusfour-xplussix-y
equalsone-hundred”?
@
' , %
, , thisorder
only
t * '
100
20°
2, −3 Extra
Expressthesumofthebase-eightnumeralsthree-four-fiveandtwofour-sixasabase-eightnumeral.
613U (six-one-threebase
eight)
Final Score:
KEY
“MathisCool”Masters--2016-17
School:
Room# Name:
HighSchool
Team#
Proctor:
(Out of8)
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
1
31
114[m]
55[exchanges]
20
-5
127
-9
Final Score:
MathisCool”Masters–2016-17
KEY
11th&12thGrade–December10,2016
StudentName
ProctorName
First Score
Room#
SCHOOLNAME Team#
(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
B
1
2
3
4
5
6
7
8
9
10
10
-1,0or2
-1,0or2
C
C
A
C
B
E
C
D
C
Final Score:
“MathisCool”Masters–2016-17
KEY
11th&12thGrade–December10,2016
SCHOOLNAME ProctorName
Team#
First Score
Room#
(out of 10)
TeamContest–ScoreSheet
TEAMTEST-15minutes–30%ofteamscore
Whenyouarepromptedtobegin,tearoffthecoloredsheetandgiveacopyofthetesttoeachofyourteammembers
andbegintesting.Eachproblemisscoredas1or0.Recordallanswersonthecoloredanswersheet.
DONOTWRITEINSHADEDREGIONS
Answer
1
2 2, [inanyorder]
3 6
4 6N
5 6 7 4576[m ]
8 7 − 4 3
9 29 − 37 + q = 1
10 254
21,000
,
1or0
1or0
+
)
+'D,'+%
)
+
2
10
Final Score:
“MathisCool”Masters–2016-17
KEY
11th&12thGrade–December10,2016
ProctorName
Room#
SCHOOLNAME Team#
First Score
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
49,068
940,800
136N
,
)D
13[squareunits]
Final Score:
“MathisCool”Masters--2016-17
School:
Room# Name:
HighSchool
Team#
Proctor:
(Out of8)
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
1
31
114[m]
55[exchanges]
20
-5
127
-9
Final Score:
MathisCool”Masters–2016-17
11th&12thGrade–December10,2016
StudentName
ProctorName
First Score
Room#
SCHOOLNAME Team#
(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
B
1
2
3
4
5
6
7
8
9
10
10
-1,0or2
-1,0or2
C
C
A
C
B
E
C
D
C
Final Score:
“MathisCool”Masters–2016-17
11th&12thGrade–December10,2016
SCHOOLNAME ProctorName
Team#
First Score
Room#
(out of 10)
TeamContest–ScoreSheet
TEAMTEST-15minutes–30%ofteamscore
Whenyouarepromptedtobegin,tearoffthecoloredsheetandgiveacopyofthetesttoeachofyourteammembers
andbegintesting.Eachproblemisscoredas1or0.Recordallanswersonthecoloredanswersheet.
DONOTWRITEINSHADEDREGIONS
Answer
1
2 2, [inanyorder]
3 6
4 6N
5 6 7 4576[m ]
8 7 − 4 3
9 29 − 37 + q = 1
10 254
21,000
,
1or0
1or0
+
)
+'D,'+%
)
+
2
10