枫叶国际学校入学测试数学模拟试题

Page1of5MATHPROFICIENCYTESTName_________________________Date_____________________Recordyouranswerontheanswersheetprovided.1.Simplify:(2x4y5)³a)6x12y15b)2x12y15c)8x64y125d)8x12y15e)8x7y82.Rewrite4−3usingpositiveexponentsonlyandevaluatetheresult.a)311464=b)−3×41=−12c)34=64d)−34=−64e)34=123Evaluate:12449−a)72b)72−c)27d)27−e)249−4Simplifyandrewriteusingonlypositiveexponents:()22342xy−a)464xyb)644yxc)624yx−d)61ye)6y5.WriteanalgebraicequationforthefollowingAfter7isaddedtoanumberthesumisdividedby4.Theresultis12.a)7124n=b)4127n+=c)7124n+=d)7124n+=e)7124n+=6.Solveforxgiven4(3x−7)=−7a)76b)0c)3512−d)74e)35127.Solveforxgiven4−2(3x−4)=1−(5x+4).a)−9b)−1c)15d)3e)78.Whatisthevalueoftheexpression−3x2+4xwhenx=−5?a)−55b)−95c)50d)95e)559.Evaluate−2a3b−4a4fora=−3andb=−2a)432b)−432c)−128d)144e)−14410.Solve:3x−7≥−22a)x≤5b)x≤−5c)x≤283−d)x≥−5e)x≥511.Solve:1523x−7a)x18b)x18c)x−3d)x−3e)x312.Simplify:(4x²−8xy+2y²)−(9x²−4xy−7y²)a)−5x²−4xy−5y²b)−5x²−4xy+9y²c)−5x²+12xy+4y²d)−5x²+4xy+9y²e)−5x²−12xy+9y²13.HowlongisBC?a)22x²-19x-23b)-16x²+8x-5c)16x²-8x-5d)16x²-24x+5e)16x²-8x+514.Simplify:(−7a−19c)−(−12a+30c)−(−21a−11c)a)26a−38cb)−26a−22cc)−16a−60cd)2a+22ce)26a+38c15.When6x³y−10x²y²iscompletelyfactored,oneofthefactorswillbe_____a)3x−5yb)2xy²c)2xyd)3x−5y²e)3x−516.Simplify:(2x4y³)×(6x³y²)a)12x12y6b)12x7y5c)12x4y3d)8x12y6e)8x7y517.Simplify:6243066xxxx−+³a)4x5−5x²+xb)4x6−5x3+1c)4x5−5x²+1d)4x5−5xe)18x5−36x²Page2of518.When(4x−1)(2x+7)isexpandedandwrittenintheformAx²+Bx+C,whatisthevalueofA+B+C?a)31b)27c)12d)−27e)−3119.Expandandsimplify:7922xx+−a)216342xx−−b)2634xx+−c)2634xx−−d)263xx−−e)2632xx−−20.Multiply:(4x−3)(3x³−5x+3)a)12x4−9x³−20x²−27x−9b)12x4−9x³−20x²+27x−9c)12x4+9x³−20x²+27x−9d)12x4−9x³+20x²+27x−9e)12x4+9x³+20x²+27x−921.Expandandsimplify:(3x+4)²−3(x+5)a)9x²+18x+1b)9x²+21x+1c)9x²+9x+1d)9x²+21x+31e)9x²+9x+3122.Factor:x²−4x−12a)(x+6)(x−2)b)(x+12)(x−1)c)(x+2)(x−6)d)(x+7)(x−3)e)(x−4)(x+3)23.Factor:2x²−7xy−15y²a)(2x+3y)(x−5y)b)(2x−3y)(x+5y)c)(2x−y)(x−15y)d)(2x−5y)(x+3y)e)(2x+5y)(x−3y)24.When6x²+x−15isfactoredcompletely,oneofthefactorswillbe_____a)2x+5b)2x+3c)2x−3d)2x−5e)3x−525.When(4x−7)²−10(4x−7)+24isfactoredcompletely,oneofthefactorswillbe______a)4x+13b)4x+3c)x+6d)x+4e)4x−1126.Factorcompletely:xy−5y−2x+10a)(x+5)(y−2)b)(x−5)(y+2)c)(x+2)(y+5）d)(x−5)(y−2)e)(x−2)(y−5)27.Findtheareaofthefigure,insquaremeters,to1decimalplace.a)935.6m²b)1691.1m²c)362.2m²d)557.8m²e)271.1m²28.Findthevolume,incubiccentimeters,ofthesolidshownwhereh=12cm,s=7cm,andd=8cm.Expressyouranswertotwodecimalplaces.a)2077cm³b)435.63cm³c)1742.54cm³d)217.82cm³e)1258.96cm³29.Inthediagramshown,△A'B'Cistheimageof△ABC.Whichtypeoftransformationisshownintheillustration?a)dilationb)translationc)slided)rotatione)reflection30.Findthelengthofsidex.a)20b)34c)26d)25e)3531.AtrianglehasverticesA(−5,2),B(−3,5),andC(−2,1).Whichofthefollowingtranslationswillplacetheimagetriangleinthefourthquadrant?a)5unitsleft,7unitsdownb)6unitsright,7unitsdownc)4unitsleft,7unitsupd)6unitsright,7unitsupe)4unitsright,7unitsdownPage3of532.Inthediagramshown,△ABC~△DEF,c=5,e=7,andf=9.Finda.a)34b)839c)2123d)265e)31533.Giventhe△DEFiscongruentto△PQR,findtheanglethatiscongruentto∠Ra)∠Pb)∠Fc)∠Dd)∠Qe)∠E34.ExpresstanAasaratioofthevariablesgivenin△ABC.a)cab)cbc)bad)ace)ab35.In△ABC,whichofthefollowingisequalto1213?a)sinCb)tanCc)cosAd)cosCe)tanA36.Whichofthefollowingequationscanbeusedtofindthelengthofx?a)cos35º=20xb)sin35º=14xc)tan55º=30xd)cos35º=20xe)sin35º=14x37.Whichequationcanbeusedtocorrectlydeterminethelengthofsider?a)r=15tan25ºb)r=15sin25ºc)r=15sin25°d)r=15cos25ºe)r=15cos25°38.A2.5metreladderleansagainstahouseforminga30ºanglewiththehouse.Exactlyhowfaristhebaseoftheladderfromthehouse?a)1.35mb)1.50mc)2.25md)1.75me)1.25m39.ThescaleshownonamapofCanadais1cm=120km.OnthemapthedistancebetweenWinnipegandSaskatoonis5.7cm.HowfarapartareWinnipegandSaskatoontothenearestkilometre?a)444kmb)516kmc)684kmd)276kme)660km40.Evaluate:()12235−−−+a)−34b)134−c)22534d)34e)3422541.Evaluate:()()48354333−×a)1b)6c)127d)13e)942.Findthevalueofxinthisdiagram.a)8.8b)12.8c)9.6d)10.2e)7.243.FindtheareaoftheshadedregionwhereS=12.a)12.65units²b)30.90units²c)43.56units²d)3.90units²e)115.73units²44.Arighttrianglehasonelegoflengthaandahypotenuseoflengthc.Expresstheareaofthistriangleintermsofaandc.Page4of5a)222acaA+=b)()2acaA−=c)222cacA−=d)2acA=e)222acaA−=45.IfAx³+7x²+Bx+30isevaluatedforx=−1theresultis54.Whentheexpressionisevaluatedforx=2theresultis6.WhatisthevalueofA?a)3b)-3c)2d)-2e)446.Theperimeterofarectangleis18x+24andthewidthis2x-9.Whatisthelength?a)7x−3b)7x+3c)16x−15d)7x+21e)16x+3347.Aguywireattachedtothetopofan84mradioantennaisboltedtotheground52mfromthebaseofthetower.Ifthewireistight,howlongisthewire?Expressyouranswertothenearesthundredthofametre.a)98.79cmb)93.30cmc)95.56cmd)89.35cme)136.00cm48.Arectanglehasbothofitssidesincreasedby20%.Bywhatpercentdoseitsareaincrease?a)40%b)44%c)140%d)84%e)144%49.Aconewithradiusr=3cmandheighth=9cmjustfitsinsideacylinderwiththesameheightandradius.Howmanycubiccentimetresareinthespacebetweenthetwof