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2024届江西省初中学业水平评估(三)3数学h试卷答案

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W:That'swonderful!听下面一段对话，回答第10至第12三个小题

现在，你有15秒钟的时间阅读这三个小题

(Text8)W:HiDan.DidyouhaveagoodtimeatWorldofMusic?M:Amazing!IhadplannedtotakeabustherebutKieraofferedmearide.Therewasevenasmallplaneflyingintheskyadvertisingthebands.W:Werethereanygoodbandsthere?M:Kierasawherfavoriteband,TheRabbits.PennyandIlistenedtosomehiphoptogether.W:Strange.Ithoughtshedidn'tlikethatkindofmusic.M:IalsosawTobywhileIwastryingtogetticketsforTheBanjos.Theyplaycountrymusic.W:ButTobyhatescountry.M:Iknow.HeboughtaticketforarapbyanAmericanandeveryonesaiditwasamazing.W:Whatdidyouthinkofthejazzband?M:Ididn'tgo.ButSylviasaidtheyweren'tgood.听下面一段对话，回答第13至第16四个小题

现在，你有20秒钟的时间阅读这四个小题

(Text9)M:Goodmorning.ThisisSpaHeaven.HowcanIhelpyou?W:Well,basically,IthinkI'mtootiredandlookingforsomewaytorelax.M:OK,sure.Didyouknowthatwerecentlyhaveaspecialofferwhichallowsnon-memberstouseourfacilitieswithouthavingtopaythemembershipfee?W:Oh,that'sgreat.M:Yeah,buttheofferisjustuntiltheendofthismonth.Anyway,letmetellyoualittleaboutthefacilitiesatSpaHeaven.First,wehaveafitnesscenterwhereyoucanhaveaweighttrainingsothatyoucanlosesomeweight.W:Andthatsoundsgood,butI'mnotreallyinterestedingettingfit.Ijustwanttogetridofmytiredness.Mm,well,I'dliketogoswimmingandIfindthathelpsmerelax.M:Wehavetwo25-meterpoolshere.W:Canyoutellmehowmuchthatcosts?M:Well,fornon-members,itcostsjust$10foreachtime.W:OK.IthinkIneedtodosomethingmorerelaxing,youknow,likeyoga.Doyouhaveanythinglikethat?M:Well,yes.Andduringthespecialofferperiod,non-memberscantakepartforjust35perclass.W:OK.Thanksverymuchforyourhelp.I'llcomedownthisafternoonandarrangeayogaclass.M:Sure,I'mlookingforwardtoseeingyouthen.听下面一段独白，回答第17至第20四个小题

现在，你有20秒钟的时间阅读这四个小题

(Text10)M:I'mPaulHart,abiologist.TodayI'lltellaboutmytripacrossAfrica.Westartedontheeastcoast,andtraveledonfootacrossAfricatoGaboninthewest,collectingplantsandflowersalongtheway.Itwasn'teasy,butmyroutecrossedaregionrichinplants,andIchoseitbecauseitwon'tstaythatwayforlongwhenmoreroadsarebuilt.Wehadateamofsevenscientists,weworkedfromsixinthemorning,buttheforestwassothickthatittookhourstocutourwaythroughit.Fortunately,wecarryspecialequipmentthatwasverylightandwetookasmuchfoodaspossible,butwewerealwaystiredwhenweputthetentsupatnight.Towardstheendofthetrip,Isuddenlydiscoveredthatthefoodhadnearlyallgone;itwasstrangebecauseweboughtenoughdriedfoodwithustolast.Thetripfoodwon'tevergobad,butthenIfoundthatsomeoftheteammateshadeatenmuchmorethantheyweresupposedto.Finally,Ireturnedhome,Iwasaskedtogoonanothertrip,【高二英语·参考答案第3页（共4页）】·23-139B·

分析根据两向量平行的坐标表示，列出方程求出tanθ的值，再化sin2θ为正切函数，从而求出它的值．

解答解：∵θ∈R，向量$\overrightarrow{a}$=（sinθ，cosθ），$\overrightarrow{b}$=（2，1），
且$\overrightarrow{a}$∥$\overrightarrow{b}$，
∴2cosθ-sinθ=0，
∴tanθ=2，
∴sin2θ=2sinθcosθ
=$\frac{2sinθcosθ}{{sin}^{2}θ{+cos}^{2}θ}$
=$\frac{2tanθ}{{tan}^{2}θ+1}$
=$\frac{2×2}{{2}^{2}+1}$
=$\frac{4}{5}$．
故选：A．

点评本题考查了平面向量的坐标运算以及三角函数的恒等变换问题，是基础题目．

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