(A)-1/2(B)1/2(C)1(D)-1(E)2
Question#6:
Ifintegersm>2andn>2,howmany(m,n)pairssatisfytheinequalitymn<100
(A)2(B)3(C)4(D)5(E)7
Question#7:
TheUSdeerpopulationincreaseis50%every20years.Howmaytimeslargerwillthedeerpopulationbein60years
(A)(B)(C)(D)(E)
Question#8:
Findthevalueofxifx+y=13andx-y=5.
(A)2(B)3(C)6(D)9(E)4
Question#9:
US
UK
Medals
3
2
gold
1
4
silver
4
1
bronze
Thenumberofmedalswonatatrackandfieldchampionshipisshowninthetableabove.WhatisthepercentageofbronzemedalswonbyUKoutofallmedalswonbythe2teams
(A)20%(B)%(C)%(D)%(E)10%
Question#10:
Theedgesofacubeareeach4incheslong.Whatisthesurfacearea,insquareinches,ofthiscube
(A)66(B)60(C)76(D)96(E)65
Question#1:
Thesumofthetwosolutionsofthequadraticequationf(x)=0isequalto1andtheproductofthesolutionsisequalto-20.Whatarethesolutionsoftheequationf(x)=16-x?
(a)x1=3andx2=-3(b)x1=6andx2=-6
(c)x1=5andx2=-4(d)x1=-5andx2=4
(e)x1=6andx2=0
Question#2:
Inthe(x,y)coordinateplane,threelineshavetheequations:
l1:
y=ax+1
l2:
y=bx+2
l3:
y=cx+3
Whichofthefollowingmaybevaluesofa,bandc,iflinel3isperpendiculartobothlinesl1andl2
(a)a=-2,b=-2,c=.5(b)a=-2,b=-2,c=2
(c)a=-2,b=-2,c=-2(d)a=-2,b=2,c=.5
(e)a=2,b=-2,c=2
Question#3:
Themanagementteamofacompanyhas250menand125women.If200ofthemanagershaveamasterdegree,and100ofthemanagerswiththemasterdegreearewomen,howmanyofthemanagersaremenwithoutamasterdegree
(a)125(b)150(c)175(d)200(e)225
Question#4:
Inthefigurebelow,theareaofsquareABCDisequaltothesumoftheareasoftrianglesABEandDCE.IfAB=6,thenCE=
(a)5(b)6(c)2(d)3(e)4
Question#5:
Ifαandβaretheanglesoftherighttriangleshowninthefigureabove,thensin2α+sin2βisequalto:
(a)cos(β)(b)sin(β)(c)1(d)cos2(β)(e)-1
Question#6:
Theaverageofnumbers(a+9)and(a-1)isequaltob,whereaandbareintegers.Theproductofthesametwointegersisequalto(b-1)2.Whatisthevalueofa
(a)a=9(b)a=1(c)a=0(d)a=5(e)a=11
Question#1:
Iff(x)=xandg(x)=√x,x≥0,whatarethesolutionsoff(x)=g(x)
(A)x=1(B)x1=1,x2=-1
(C)x1=1,x2=0(D)x=0
(E)x=-1
Question#2:
WhatisthelengthofthearcABinthefigurebelow,ifOisthecenterofthecircleandtriangleOABisequilateralTheradiusofthecircleis9
(a)π(b)2·π(c)3·π(d)4·π(e)π/2
Question#3:
Whatistheprobabilitythatsomeonethatthrows2dicegetsa5anda6Eachdicehassidesnumberedfrom1to6.
(a)1/2(b)1/6(c)1/12(d)1/18(e)1/36
Question#4:
AcyclistbikesfromtownAtotownBandbacktotownAin3hours.HebikesfromAtoBataspeedof15miles/hourwhilehisreturnspeedis10miles/hour.Whatisthedistancebetweenthe2towns
(a)11miles(b)18miles(c)15miles(d)12miles(e)10miles
Question#5:
Thevolumeofacube-shapedglassC1ofedgeaisequaltohalfthevolumeofacylinder-shapedglassC2.TheradiusofC2isequaltotheedgeofC1.WhatistheheightofC2
(a)2·a/π(b)a/π(c)a/(2·π)(d)a/π(e)a+π
Question#6:
Howmanyintegersxaretheresuchthat2x<100,andatthesametimethenumber2x+2isanintegerdivisiblebyboth3and2
(a)1(b)2(c)3(d)4(e)5
Question#7:
sin(x)cos(x)(1+tan2(x))=
(a)tan(x)+1(b)cos(x)
(c)sin(x)(d)tan(x)
(e)sin(x)+cos(x)
Question#8:
If5xy=210,andxandyarepositiveintegers,eachofthefollowingcouldbethevalueofx+yexcept:
(a)13(b)17(c)23(d)15(e)43
Question#9:
Theaverageoftheintegers24,6,12,xandyis11.Whatisthevalueofthesumx+y
(a)11(b)17(c)13(d)15(e)9
Question#10:
Theinequality|2x-1|>5mustbetrueinwhichoneofthefollowingcases
I.x<-5II.x>7III.x>0
1.Threeunitcirclesarearrangedsothateachtouchestheothertwo.Findtheradiiofthetwocircleswhichtouchallthree.
2.Findallrealnumbersxsuchthatx+1=|x+3|-|x-1|.
3.
(1)Givenx=(1+1/n)n,y=(1+1/n)n+1,showthatxy=yx.
(2)Showthat12-22+32-42+...+(-1)n+1n2=(-1)n+1(1+2+...+n).
4.Allcoefficientsofthepolynomialp(x)arenon-negativeandnoneexceedp(0).Ifp(x)hasdegreen,showthatthecoefficientofxn+1inp(x)2isatmostp
(1)2/2.
5.Whatisthemaximumpossiblevalueforthesumoftheabsolutevaluesofthedifferencesbetweeneachpairofnnon-negativerealnumberswhichdonotexceed1
6.ABisadiameterofacircle.XisapointonthecircleotherthanthemidpointofthearcAB.BXmeetsthetangentatAatP,andAXmeetsthetangentatBatQ.ShowthatthelinePQ,thetangentatXandthelineABareconcurrent.
7.Fourpointsonacircledivideitintofourarcs.Thefourmidpointsformaquadrilateral.Showthatitsdiagonalsareperpendicular.
8.Findthesmallestpositiveintegerbforwhich7+7b+7b2isafourthpower.
9.Showthattherearenopositiveintegersm,nsuchthat4m(m+1)=n(n+1).
10.ABCDisaconvexquadrilateralwitharea1.ThelinesAD,BCmeetatX.ThemidpointsofthediagonalsACandBDareYandZ.FindtheareaofthetriangleXYZ.
11.Asquarehastensdigit7.Whatistheunitsdigit
12.Findallorderedtriples(x,y,z)ofrealnumberswhichsatisfythefollowingsystemofequations:
13.xy=z-x-y
14.xz=y-x-z
15.yz=x-y-z