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2019-2020学年哈尔滨三中高一下学期期末数学试卷一、单选题（本大题共12小题，共60.0分）1.以下对于几何体的描述，错误的是()A. 以半圆的直径所在直线为旋转轴，半圆面旋转一周形成的旋转体叫做球B. 一个等腰三角形绕着底边上的高所在直线旋转180°形成的封闭曲面所围成的图形是圆锥C. 用平面去截圆锥，底面与截面之间的部分叫做圆台D. 以矩形的一边所在直线为旋转轴，其余三边旋转形成的面所围成的旋转体叫做圆柱2.8.下列命题为真命题的是A. 已知，则“”是“”的充分不必要条件B. 已知数列为等比数列，则“”是“”的既不充分也不必要条件C. 已知两个平面，，若两条异面直线满足且//，//，则//D. ，使成立3.已知一水平放置的四边形的平面直观图是边长为1的正方形，那么原四边形的面积为()A. √2B. 2C. 2√2D. 44.等差数列中，，则的值是()A. 12B. 24C. 36D. 485.已知函数f(x)=2|cosx|sinx+sin2x，给出下列四个命题：①函数f(x)的图象关于直线x=π4对称；②函数f(x)在区间[−π4,π4]上单调递增；③函数f(x)的最小正周期为π；④函数f(x)的值域为[−2,2].其中真命题的个数是()A. 0个B. 1个C. 2个D. 3个6.已知命：∃x∈R，使tan x1中正确的是()A. ¬p：∃x∈R，使tanx≠1B. ¬p：∃x∉R，使tanx≠1C. ¬p ：∀x ∈R ，使tanx ≠1D. ¬p ：∀x ∉R ，使tanx ≠17.某几何体的三视图如图所示，则在该几何体的所有顶点中任取两个顶点，它们之间距离的最大值为( )A. √3B. √6C. 2√3D. 2√68.设x >2，则y =x +1x−2取得最小值时，x 、y 的值是( )A. 4，3B. 3，4C. 3，3D. 4，49.圆台侧面展开图是一个内外半径分别为2和4的半圆环，则此圆台的全面积是( )A. 6πB. 10πC. 11πD. 14π10. 用六个完全相同的正方形围成的立体图形叫正六面体．已知正六面体ABCD −A 1B 1C 1D 1的棱长为4，则平面AB 1D 1与平面BC 1D 间的距离为( )A. √3B. √63C. 4√33D. 2√311. 在△ABC 中，3CD⃗⃗⃗⃗⃗ =BD ⃗⃗⃗⃗⃗⃗ ，AD 为BC 边上的高，O 为AD 的中点，若AO ⃗⃗⃗⃗⃗ =λAB ⃗⃗⃗⃗⃗ +μAC ⃗⃗⃗⃗⃗ ，则λ⋅μ=( )A. −34B. −316C. 34D. 31612. 在△ABC 中，BC =1，∠B =π3，△ABC 的面积S =√3，则sinC =( )A. √1313B. 35C. 45D. 2√3913二、单空题（本大题共4小题，共20.0分）13. 如图所示，在▱ABCD 中，已知AB =3，AD =2，∠BAD =120°.若AE ⃗⃗⃗⃗⃗ =13AB ⃗⃗⃗⃗⃗ ，BF ⃗⃗⃗⃗⃗ =12BC ⃗⃗⃗⃗⃗ ，则AF⃗⃗⃗⃗⃗ ⋅DE ⃗⃗⃗⃗⃗⃗ =______． 14. 在三棱锥D −ABC 中，平面ABC ⊥平面ABD ，AB ⊥AD ，AB =AD =4，∠ACB =π6，若三棱锥D −ABC 的四个顶点都在同一个球面上，则该球的表面积为______ ． 15. 13、数列满足，，则____________。
2019-2020年高一下学期学段检测数学试题含答案高一数学试题第Ⅰ卷（选择题共50分）一、选择题（本大题共10小题，每小题5分，共50分.在每小题给出的四个选项中，只有一项是符合题目要求的.1.有20位同学，编号从1至20，现从中抽取4人作问卷调查，用系统抽样方法确定的编号有可能是A. B. C. D.2.圆与圆的位置关系是A. 相交B. 内切C. 相离D.外切3.样本中共有五个个体，其值分别为，若该样本的平均值为1，则样本的标准差为A. B. C. D.4.某校1000名学生的高中数学学业水平考试成绩的频率分布直方图如图所示，规定不低于90分为优秀等级，则该校学生优秀等级的人数是A. B. C. D.5.若一口袋中装有4个白球和3个红球，现从中任取两球，则取出的两球中至少有一个白球的概率为A. B. C. D.6.过点作圆的两条切线，切点分别为，为原点，则的外接圆方程是A. B.C. D.7.分别写上数字1,2,3，…，9的9张卡片中，任取2张，观察上面的数字，则两数之积为完全平方数的概率是A. B. C. D.8.阅读下边的程序框图，若输出S的值为-7，则判断框内可填写A. B. C. D.9.已知蚂蚁在三边长分别为3,4,5的三角形内爬行，某时刻此蚂蚁距离三角形三个顶点距离均超过1的概率为A. B. C. D.10.已知直线过点，P是上的一动点，是圆的两条切线，A,B为切点，若四边形PACB的最小面积为2，则直线的斜率为A. B. C. D.第Ⅱ卷（非选择题共100分）二、填空题：本大题共5小题，每小题5分，共25分.11.一幅混合后的扑克牌（无大小王）共52张，从中随机抽取1张，事件A为“抽得红桃K”，事件B为“抽得黑桃”，则概率（结果用分数表示）.12.已知圆与圆相交，则交点连成的直线方程为 .13.一束光线从点出发，经轴反射到圆上的最短距离是 .14.两艘轮船都要停靠在同一泊位，它们可能在一昼夜的任意时刻到达.设两船停靠泊位的时间分布为1h和2h，则有一艘船停靠泊位时必须等待一段时间的概率是 .15.对任意非零实数，若的运算规则如右图的程序框图所示，则的值是 .三、解答题：解答应写出文字说明、证明过程或演算步骤.16. (本小题满分12分)求经过点，圆心在直线上的圆的方程.17.(本小题满分12分)某市风景区为了做好宣传工作，准备在A和B两所大学分别招募8名和12名志愿者，将这20名志愿者的身高编成如右图所示的茎叶图（单位：）.若身高在以上（包括）定义为“高精灵”，身高在以下（不包括）定义为“帅精灵”.已知A大学志愿者的身高的平均数为，B大学志愿者身高的中位数为.（1）求的值；（2）如果用分层抽样的方法从“高精灵”和“帅精灵”中抽取5人，再从这5人中选2人.求至少有一人为“高精灵”的概率.18.(本小题满分12分)月份12345甲的纯收入 2.9 3.3 3.6 4.4 4.8乙的纯收入 2.8 3.4 3.8 4.5 5.5（1）由表中数据直观分析甲、乙二人中谁的纯收入比较稳定？（2）求关于的线性回归方程，并推测甲在6月份的纯收入；（3）现从这5个月的纯收入中随机抽取两个月，求恰好有1月的纯收入在区间中的概率.19.(本小题满分12分)已知圆与直线交于M,N两点，O为坐标原点，问是否存在实数，使，若存在，求出的值，若不存在，请说明理由.20.(本小题满分12分)在某高校自主招生考试中，所有选报Ⅱ类志向的考生全部参加了“数学与逻辑”和“阅读与表达”两个科目的考试，成绩分为A,B,C，D,E五个等级，某考场的两科考试成绩数据统计如下图所示，其中“数学与逻辑”科目的成绩为B的考生有10人.（1）求该考场考生中，“阅读与表达”科目中成绩为A的人数；（2）若等级A,B,C,D,E分别对应5分，4分，3分，2分，1,分，求该考场考生“数学与逻辑”科目的平均分；（3）已知参加考场测试的考生中，恰有两人的两科成绩均为A,在至少一科成绩为A的考生中，随机抽取两人进行访谈，求这两人的两科成绩均为A的概率.21.(本小题满分12分)已知圆O的方程为，直线过点且与圆O相切.（1）求直线的方程；（2）设圆O与轴交于P,Q两点，M是圆O上异于P,Q的任意一点，过点A且与轴垂直的直线为，直线交直线于点，直线交直线于点，求证：以为直径的圆总过定点，并求出定点的坐标.xx 学年度第二学期学段检测高一数学答案一、选择题： ABDCC AADBD二、填空题：11.726 12. 13. 4 14. 139115215. 三、解答题：16解：设所求圆的方程为 ………2分则 ………6分解得 ………11分所求圆的方程为 ………12分17.解：（1）由题意得： 1768191187182176170170168159=++++++++x ………2分 ………4分解得 ………5分（2）由题意得“高精灵”有8人，“帅精灵”有12人，如果用分层抽样的方法从“高精灵”和“帅精灵”中抽取5人，则抽取的“高精灵”和“帅精灵”人数分别为和 ………6分记抽取“高精灵”为，抽取“帅精灵”为.从已抽取的5人中任选两人的所有可能(,) ,( ,) ,( ,),(,),(,),(,),(,),(,),(,),(,),共10种, ………8分设选取的两人中至少有一人为“高精灵”为事件A,则事件A 包括(,) ,( ,) ,( ,),(,),(,),(,),(,),共7种 ………10分所以 为所求. ………12分18. 解(1) 甲的纯收入稳定 ……2分(2), ∴=0.49……5分 , =2.33 ……6分=0.49+2.33 ……………………………………………………………………………7分令,得=5.27,即推测甲在6月份的纯收入为5.27千元 ……8分.(3) 现从乙这5个月的纯收入中,随机抽取两个月的基本事件有:(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5) 共10种 ……10分. 记:恰有一个月的纯收入在区间(3,3.5)为事件A,其中,有:(1,2),(2,3),(2,4),(2,5)共4种.∴恰有一个月的纯收入在区间(3,3.5)的概率为 ……12分.19. 设点,当时，有,(1) ……………………2分又直线与圆相交于M 、N ，联立 ,消可得：,则有：,，· (2) ……4分又M 、N 在直线上， 故1212121264(9)(32)(32)96()4955m y y x x x x x x -=--=-++=-+ (3) ……6分 由 (1)(2)(3)得： ………………………………………………………………………10分且检验成立 ………………………………………………11分故存在，使OM ⊥ON ………………………………………………………………12分20. 解：（1）因为“数学与逻辑”科目中成绩等级为B 的考生有10人，所以该考场有人 ……………………2分所以该考场考生中“阅读与表达”科目中成绩等级为A 的人数为……………………4分（2）该考场考生“数学与逻辑”科目的平均分为……………………8分（3）因为两科考试中，共有6人得分等级为A，又恰有两人的两科成绩等级均为A，所以还有2人只有一个科目得分为A，设这四人为甲，乙，丙，丁，其中甲，乙是两科成绩都是A的同学，则在至少一科成绩等级为A的考生中，随机抽取两人进行访谈，基本事件空间为{甲，乙}，{甲，丙}，{甲，丁}，{乙，丙}，{乙，丁}，{丙，丁},有6个基本事件设“随机抽取两人进行访谈，这两人的两科成绩等级均为A”为事件B，所以事件B中包含的基本事件有1个，则. ……………………13分21.解：（1）∵直线过点，且与圆：相切，设直线的方程为，即，…………………………2分则圆心到直线的距离为，解得，∴直线的方程为，即．………………………4分（2）对于圆方程,令，得,即．又直线过点且与轴垂直，∴直线方程为，设，则直线方程为解方程组,得同理可得, ………………10分∴以为直径的圆的方程为，又，∴整理得，………………………12分若圆经过定点，只需令，从而有，解得，∴圆总经过定点坐标为．……………………………………………14分.。
哈三中2019-2020学年度下学期高一学年第一模块考试莫语试卷第一部分＜阅读理解（共两节•满分40分）第- V/：（共15小题：毎小题2分.满分30分）阅读卜列短文，从每题所给的以个选项（A. B、C^II））中•选出⅛M圭选项•井在答题卡I •将该项涂然•岛一英IS第I页共10天I ・ WhiCh event requires booking In advance9A. CaSa ROnWntiCa PoCtr) RCading SCriCs.B Orange COUnty MIlSCIlm Of Art ViSiOnarieS IxCtUre SeneSC DiSCOVei> SCiCnCC CCnICr PrCSClns: Mexico: FeStiVal OfTOySD. DOnna O'Neil) Land Conscnancy—Hike OtT YOllr ThankSgiVIng FeaSt-2. A StUdent Of an UhO WantS (o Ieanl alx)ut art hιstoπ, WilI go to 一.A. 850 San CIemente Drive, NeWPOrt BCaChB. 2500 N. MaIn St. Santa Ana. CΛ 92705C the Donn<ι O'Neill l>an<l CoiiscrvancyD. 415 AVenida Granada, San Clemente, CA 926723. A Inother WhO VVantS her kid to Ieam about CUhUre ir a fun VVay Will CaIl _____________ f or moreinfbπnationA. 949.759∙1122 B 714-542-2823 C. 949∙489∙9778 D 949∙498∙21394. A IneInber IOgeIIIer WitI) his VVite aικl 12-year-old SOn WalnS to take a IIIke Wlll Pay ___________ ・Λ $20 B. S25 C.SI5 D.SIOBIl WaS NeW Year time・ but I WaSlVt IOOking forward to it. That winter, Iny mother and Iny StePfather moved OUr family to SOUthem CaIifbmia. My brother and I Were IeaVing OUr rural Alabama behind ThiS WoUId be Ollr flret NCW YCar away from Alabama. My mother took to CalifbnIia Iike a SWau to a Ioyal Iake- My atlιle(ic IilIle brotlιer. Paul, WaS excited at a CIiIlIate that allowed him to go to the beach WheneVer he Hanted 1, IIOWeVer, was a Iat Chlld ∖vιlħ a heavy SOUtll ell) prominciation My first day In Ihe new CIaSS. 1 ImrodUCCd myself In a IOVV VOiCe- All I SaId WaS ιnv name and WherC 1 WaS from. Γhc CIaSS buιst into Iauglitcr. U He talks fuιmily.v 1 WaS So helpless Ihat 1 WenI to a PIaCe 10 CalI Granny Smlth after SChOOLwhG VVaS Iny biggest SuPIX)It BUt I didn't get throιιglι.On SUIKIay evening, the PhonC rang. It was Granny. 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IlOU did he author's Broilier IeeI Uhen tlιe∖ Uere moving to California?Λ. UnCOnCemCd. B. JOyfUI C. GratefUL D. Upset.6. Why did the ClUthOl S ClaSSmateS IaUgh at him?A He had a StrOng accentB He Inade A humorous talkC. 1 Ic IOOkCd overweight.D. He SPOke In a Very IOW voice・7. What does the UfKlCrlined Hord U taCky M In ParagTaPh ? probably mean oA. SUitable.B. Large.C. ChCaP.D. AttraCtiVC-& WhlCh Of Ihe （OIlOVVlng Can be the best title Of Ihe text9Λ Granny5s Care PaCkage B An UnfbReuable HOlidayC. OUr MOVe to CalItbmIaD. A Telephone Call from GrannyCE∖ery animal SPeCiCS CarrieS UnIqUe VinlSeS that have SPeCIfiCally adapted to infecting it. OVer time, SOme Of IheSe have jumped to humans——these are known as "zoonotic （动物传染的）VirUSCS ・AS the POPllIatIOn grows. VVC move IntO Wlld areas. NhlCh bπngs US into InOlC contact Wlth animals v⅜c don't ικ）∏nally IIaVe COntaCt VVith l ThUS. VIrIlSeS Can jump from animal to huπιans and they Can SPlCad between humans・ through ClOSC COnIaCt Wlth body fluids （体液）like blood Or uruιe （尿液）.BeCaUSe every virus has evolved to target a PartiCUIar species, it's rare for a VinlS to be able IOJUmP to another SPeCieS、WhCn this does happen, it's by ChanCC・ and It USUaIly requires a Iarge amount Of COntaCt Unth the ViruaΛl first, Ihe VinIS IS USUalIy not WeII-SInICd Io its new host and doesn't SPread easily, （）∖cr time. ho\、c、ci\ it Can CVOlVC in the new host to PrOdUCC VariantS （变M i） that arc better adaptedWhCn VirUSeS jump to a new host, they Often CaUSe InOre SeVere disease・ TlIiS is because VirUSeS aικl theu IlrSt IK）StS IIaVe e∖ohed IOgether, aικl IhC SPeCIeS has time to build UP resistance （抵抗Z/）・Tħc new host SlXCieS. On Ihe Other hand. miglιt not have evolved IhC ability to deal VVlth Ihe virus. FOr example, When VVe come IntO COntaCt Wlth bats and their viruses, we may develop rabies （壮犬炳）Eboh MnlS （埃博荷柄毒）disease. Whll C the bats themselves arc ICSS a∏ected.It s IIkeIy that bats are Ihe OrigInal SOUrCe Of three recently known coronaviruses: SARS- COV （2003）. MERS-COV （2012） and SARS-COV-2 （WhOSC CUrrCnI Onkial name is COvTD-19）. All Of these JUnIP ITonI bats to humans Vla an Intennedia:e animal; In the CaSe Of SARS-CoV-2, IhIS may have been PangOIinS （穿山r P）, but more research IS needed∣⅛英语第J页共10页9. Why IS It rare for a VInIS to InfeCt another species?人TIIe new host Can deal With the virus.B The new SPeCieS builds UP resistance.C. NOIIC Of the VinlS Can adapt to the new SPCCiCS.D EaCh VHUS d已∖ek^∣)s to Iaf gel a SPeCifiC species.10. What is the fifth ParagraPh mainly about?A. ThC rcs∣sta∣κx Ofthe Old SPyClCs.ThC ability OflhC new host SPCClCS・C l he InfeCtlOn PrOCeSS Of VlnISD IIIe CaUSe Of Stronger disease・11. WIIat Can We Infel from Ihe text?Λ HUmanS ShOIIId not move into Wild areasB Wlld animals are actuallv OlIr best friends.C. A VlnIS Can SPread from animals to hιπnansO. A VinlS Call CVOIVe io infect another species.DClnIdlen IOVe PlaJing games. Ihat IS a Uell-known fact. KldS Ieanl IIOW to Play games at a very* early age, and OnCe they find a game they IOVe. they Can Play for hours and IIollrS on end. In tact, kids games arc SO POPUIal e that there IS an CntirC mdust∏f dcx,otcd to dcsigιmιg and SClIing them. There ScCmS to be a iun game for kιdδ for every OCCaSlon. ChnStnlaS and birthdays arc Often Celebrated Wi(I) IIle family (radilion Of gi∏ing a new game.OId games handed down IrOnl generation to gcnσation iικlude SllCh fa∖oriιes SUCh as hops cotch. FCd rover. LondOn BrldgC and (IUCk-(IUCk-g<M>sc. they arc always big hits and StiIl Played at Hlany SChoOlS during recreation tnne.In recent years, though. Intemet games and gaming S)StClnS SeCm to have taken Ihe kids, WOrld by StOrm. Kids' Online games ha∖ e quickly become a VerY POPUIar Way to PaSS the tune With Small ChildrCn and teens alike OnImC games arc a great VVay to have hιn. and they Can be quite CdUCatiOnal as WeIl Many Online games CIealed Rir SpeCifiC age groups CnCoUragC gιade appropπa te de∖elopιnent and educational skills.HUndrCdS Of IntemCt SltCS OffCr fiιn and CdllCatiOnal games fbr kids SomC games need them to USe brains, WhlIe OtherS InVOh e hands and ieet. Many Of IheSe SlteS are Created by big names. SIICh as NatiOlIaI GeOgraPhi e, WhiCh We CaJI tnιst ThCy Ofler free games that ParClItS know arc appropriate Ibr kids. ParentS are encouraged to go Online and research Online games appropriate fbr their kids' age before allowing their kids to PIay these games ParentS Want to have the ability to Set Or InOnItOr their kids* PIay time, WhiCh is a PrObIeln NationaI GeOgraPhiC is UOrking to SolVeWlth So Inany OPtiO<ιs to ChOOse from. ParCntS and CInIdrCn will find it easy to find IiIn games and activities On the InternCt And nowadays, bein g able to USC a COmPlltCr is a Wy iιn∣x>rtant SkiIl for your Iiltle One to Iearn a SO PIaying on Ihe COn)PUter is definitely both educational and fun. YOUr Chlld is SUre to Ieanl neu- SkiIIS about any SUbjeCt Wilh Ihe right, IrUSIed WebSIte岛一英ifi第J页共IC页12 ITie IndlIStn r OfkidL games is PrOSPerOlIS ProbabIy because ___________Λ. there are all kinds Of games ∏)r ChiIdrenB. ChIICIren are mostly CraZy about gamesC IxX)PlC WOUId IikC to PIay games IOgCthCrL). paients IOVe to buy gifts for IheiI CiUld13. WC Can inlcι fr om IhC third ParagraPh that OnIinC games arc __________ ・Λ. POPUIar and PraCtlCaI B. COfnPliCatCd and CXPCnSiVCC. SimiIar and edιιcarional D fiιnnv and instπιctive■14 WhlCh Of ll>e IbIIovMtig IS true Of NatIonal GeOgraPhICeA. The news is UPdated e∖ery dayB ThCrC is(i IargC (ImOIInt OfinfbmuUionC. I he games are good for kids' InenIal aικl PhySICal l⅞ealthD. It c<ιn help ParelItS to COntIOl kids, PIay time.15. According to IhIS passage, IhC author's altitude to Playlng ConlPUtCr games isA. SUPPOrtiVe B ObjeCtiVe C. negative D・ PeSSimiStiC第二节：(共5小每小魅2分•満分1()分)HiiKm文内容•从短文后的选项中选出能填入空白处的最佳选项•选项中有两顶为多余选项.TIK OXfbrd EngliSll DiCtiOnary iικlιιdes InOrC than 170,000 EngIiSh entries (词条).LUCkil∖. you don't need to ICam SO Tnany WordS BUt as a Rircign bngιιagc Ieamcr. you have to ICam a CCnalIl number Of WOrdS to communicate CflfeCtiVCIy. 16 ThC following are the most InIPortaDt ones.NarrOW it do、Vn. The first SteP is to identify what you Want to focus On and Set goals17 PerhaPS you VVant to read about ⑷CCer Or Ieam how to COok IIke a native Chef The best learners are motivated to StUdJ f because they ChooSC ∖ocabulafy based On their IntereStS and needs・18 Iiley refer to tlιe InOSI WideIy USed WOrdS in any kind Of SPeeCll or writing. Generally, there arc four CategOriCS Of words in any language: high-frequency words, academic words, technical words aικi IOW・fbequency words. 19 These are the WOrdS PeOPIe USe most IU CVeAday Wntmg and speech. SO IeafuUIg them CaU IUakC you UUdCrStalId What you Ilear aud respond appropriately. An OIIllne SearCh for the PhniSe **tlιe InOSt COnHnon WOrdS In X IangUage ' Can help you identity a IlSt Of high-frequency WordS to focus On Seek OUt OI)POrtllnitlCS to USe ι>eu WOrdS Learning the ∖xxzabulary, involves two processes: lo be able to recognize a U Ord and to Use It We IyPiCally Iearn to recogmze ∖¼ords In Untlng Or SPCCCh before WC re able to USe them It takes additional. COnCCntratCd PraCtiCe to ICam a new UOrd 20 _ SuCh OPPortUnIlieS include Wnting CmaiIS to and Chatling With native SPCakCrSA. DlVIde UOldS IntO dιilerent categories.B. FOCUS On the most COtnnlOn WOrdS髙一英语3B页共】0页C. If you IIaVC a sirong interest in a PartiCUlar subject. Start With thatD. YOU will Ieanl new v¼ords better if you SPeak rather tlιan StInPIy read them.E. With SomC StrategieS・you Can ICanl IaStCr Iind IllOrC CaSiIy th<ιn you have IllIaginCd I∖ High-frequency WOrdS help to quickly ImPrOVC your ability to COmmlmicate.G. That's v∖hy iΓs important to find OUt πιore ChanCeS OrPnXhlCtiVe Iangllage PraCliCe第二部分英语知识运用第一节，完型填空(共2U小题，毎小题IS分，满分30分)In 1982 SteVen Callahan WaS CrOSSing the Ailanlic alone in his SailbOal When it StrUCk Something and Sank. He ∖sas OUt Of IlK ShiPPing IaneS and floating in a Ilfe rail. 21 HiS SUPPIieS Were ftnv. HiS 22 WerC SnIalI YCt Uhen three fishermen found him Sevent)-SiX days Iaier4 he WaS much SkInnICr (han he UaS When he 23 、but aliveΓhe thing that 24 my eye WaS how he managed to keep himself going When all hope SeeIned IOSL When there Seemed no ______________________ 25 _ in COntinUing Ihe struggle, WlIen he WaS SUftenng greatly. When his IIfeboal WaS broken Ulth a hole and after more Ihan a Week StrUggllng Wnh his WCak body to _26_ it, It WilS Stlll IeakIng Water Ilc WaS _27_ and thoroughly CXhaUSted・28 VVOUId have SeenIed the Only wise ChOiCeWhen PCOPlC SUn Z iVC these kinds Of circumstances, they do SOlnCthlng With their _29_ that gives them the CoUragC to keep going Many PCoPIC In 30 desperate ClrCUnlStanCCS give in Or go mad・ SOmCthing Ihe SUlXiVOrS do WitlI Iheir J)OuglltS helps IIIeIn find IhC 31 to carr> on.T tell InySclf I Can 32 it/' WrOtC CaIIahan in his account. w4Comparcd to What OthCrS IIaS r e gone 33_, Γm Ibrtwnate. 1 tell mysell* IhCSe things OVer and over. _34 my deteπninalion to keep going.,,1 Wrote IIlat down after I Iead it. It 35 InC as SOmet hmg important And Γve IOId myself the SamC thing WhCn my Own goals SCClnCd 36 off. And CYCry time I Say it. I always COmC back to my _37_.SO here, CofniI)g io US from Ihe extreme edge Of 38 are UOrdS that Can give US strength.39 you w re going through. tell yourself you Can handle it. TCll this to yourself OVCr and over, and it Will help you get thιoιιgl) Ihe 40 SPOtS With a IiItle InOre deteπninauon.21. Λ aloud B alone C. aside D. aboard22. A. fish B. holes C. CreW D ChaI)CeS23. A. StartCd B. arrived C. ross D. disappeared24. A CoVered B IIUrt C. Callgln D. Cntered25. A. SaIIOr B companion C. POint D. OPPOrtUnity26. Λ. board B- abandon C. ObSCrVC D. fix27. A Staned B embaιτassed C. COrfilSed I) SatlSfied28. Λ. GiVing OUt B GiVing UP C. Giving away D. GiVing OfT29. A tools B dreams C. minds D. hearts高一英语第6页共10页30 A. SiInilarIy B. PhySiCaIIy C mentally D. differentlyd 31. Λ. IUCk B. direction C. COUrage D PnVIlege32 A. handle B. delavd C. realize D iιnaginc33. A. into B. for C. against D. IhroUgl)34 A. PIIttIng UP B building 叩 C. bringing IIP D taking IIP35. A. frightened B. SIrUCk C. disappointed D. PrCSCrVCd36 A. far B IoW C heavy D bright37. A. StatUS B- CrOSSrOadS C. IlOnIeS L>. SelISeS38 A. CXPenment B IHirnCane C (IOOd D SUniVal39. Λ. HOWeVeI B. Whoe∖er C. WhateVer D. WhiCheVer40 A. SlnOOth B.rough C. CaSy D ColnfbrtabIe第二节：单项选择（共30个小趣■每小SSl分■満分30分）从下列乞題中所给的四个选项 5、Ik C和D〉中，选出最佳选项，并在答题卡上将该项涂黑C41. WC II InCet again ill IlIe IUOrumg aιιd We Can Where WC Ieft off.A. PiCk UP B PUt down C take In D CUt OfT42. OlIr PIaHe didn t take Off On time, because OnC Of the CUgineS •A. VVere On tireB. CaIlgllt fire C HCiS CaUglIt fire D Set On fire43 He Said he UaS goinι* (o build a Plane in his back yard, bill I didifl take Ililn !A. ObViOUSlVW B. SeliOUSIy C CntlrCly D heavily44 NOt UntiI T Ixgan to WOrk how much time T had wasted.A. didn’t 1 realize B did 1 realize C had I realized L) I realized45. Don,ι IeaVe IOOIS ______ ; PUt IIIem in order.A .lying about B. being Iaid alx>ut C. IayIng about D Io Iie about46. DeSPite the tact that the PandenIiC (瘟疫)is Clr from over. ClUlIa's CCOlIOmy is beginning toShOW ______ Of recovery.A. SignaISB. SyInIX)IS C mark D. SignS47. In the dark forests ________ . SOmC Iarge CnOUgh to hold SCVCral EngliSh towns.A. Stand many lakesB. lie InalIy IakeS C Inany IakeS Iie D many IakeS Stand48 I hoiigli the gul had been SUflenng from tlιc blood disease. She acted as If I)OtIUlIg toher Uhile lacing her friends and relationsA. happened B WOUld happen C WaS IIaPPCnCd D Ilad IIaPPened49 TheSe teenagers (Iolft know much Ofthe Worid yet; that*s Why they are So easily _______________Λ. Iaken in B. taken OVer C. taken after D. taken OfT50 him not to do so、he WOllkln't have made SlICh a SCrioUS mistake.Λ. Did I PCrSUadC B Ifl PCrSUadC C. IfI ShOUld PCrSUadC D I Iad I PCrSUaded51. On the 70lh birthday Oflhe PRC, many POliCeinen aιιd POIiCeWOInen Were Called Ollt toA. take actionB. keep Order C make SenSe D. v%atch OUt髙一英禹第7页共10页52. The athlete's years Of hard training _________ WlIeII SlIe finally Won the OlylnPiC gold InedalA. PiCked OUtB. Paid OfTC. got IIIrOUghD. ended UP 53 HCnrV WOUld rather his mother in the SClIOOl Where he is StUdying. A. no( WOrkB. not WorkedC. didn't WOrkD. not WOrking 54 that he found it ditlicult to StOP at the red light. A. SO fast ħc WaS (IriVing B. SO fast he CirOVCC. SO fast WaS he drivingD. SO IaSt drove he55 Eatiiig too InUCIl (at Can ________ heart disease aιιd CalKe IIigIl blood PreSSUre A. result from B. COntnbUtC to C ・ attend Io Lλ devot e to56 ThaIIk you for your directions to the ħouse; We WOllIdlft have IbUnd it ____________A. nowhereB. OthCrwlSC C ・ howeverD. instead 57 2020 is a bad year for film CofnPanieS _________ box OffiCe returns A. but for B. regardless Of C. In acditιon to D. In IermS Of58 TUm On the television Or IhC applications in your mobile PhonC and youthe news Of ChineSe PeOPle fightmg agamsι COrOna ∖irus bravely.A. SeeB. have SeenC. are SeeingD. Will See 59. Tibet IieSthe WeSt Of ChiIla WhiIe JaPan IieS the CaSt Of China. A. to; toB. in. inC. in; toD. to; in 60 Mr WhIte is _________ OlIr EngliSh Ieachcr. He OnCllhClpS IIS to deal With SOIne PerSOnaI affairsA in Other WOrdS B. On the Olher hand C. as a Inaner Of fact D. for anotherΛ. TO face B. IIaVing faced C. FaCCdD. FaCing 66. 一It's many years SinCe I SaW you last. 1you at all. I WoUIdrft have. either, if SomCOne _________ you by the name.A dιdn t recognize; hadn't CaIledB. didn't recognize; didn't CaII C IIaVen t recognized; (Iidn t CaIID haven^t recognized; hadιft CaIled 67 If I K ： his ICgS in the Iabt training, he the COming WOrId Cup, WhiCh he hasbeen IOnging to COlnPete inΛ. didn't hurt; WoUId go in R )rB. hadn't hurt, WoUld IlaVe taken Part in C hadn't hurt; UOUld join in D didn t hurt; UOUld have taken Parl in岛-英讯第8更共ID 页68 It's time youthe fact Ihat it's a dangerous WOrICi OlIt there Be brave and OPtimiStiC A I)Ut UP WithB. WOke Ul) toC. t∞k the PlaCe OfD. IoOked down UPOnΛ no more than B OthCr than C. mon: Ihan D rather tlιan61 ・ I Want to SCIl IhC house, butCan t bear Ihe thouglπ Of moving. 62. I'll tiever agree What he SaId IhaI point.A. with; withB WitIE On C. on: On 63. ChHla has POPUIatiOn Of 1.1 bιllιoik 80 PCrCCnt Of Wholnhome during the epidemic (疫情)Of COronaVinis.A. a; WaSB. /; WaSC. a; WeTe 64 ThC PnCCS Of the sh<x^> in this ShoPPmg mall S25 to $100 A. range betweenB. range IrOlnC. Vary in 65. D OnI With ____ a sked to Stay atD. the; Were DVary at With a difficult SitUation, ArnOld decided to ask his IeaClIer for advice69. J haven't SeCn you for a COUPIC Of days. What have you been UP ________ ?A in B. to C. Wth D. for70 DUe to the O(ItbrCak Of the CPKlenliC in China. a kιrge (IUantity Of foreign IeaChCrS andStUdentS abroad.A StUCkB Were SnICk C. WaS S IlCk D. have StlICk第三节：单句语法填空(共W个小题，每小βl.5分，满分15分)阅读下面材料•在空门处塡入适匕的内容或括号刚丫I词的正确形式•71 After years Of WOrklng With children, Man (PrOVe) qualified as a teacher.72. OCCaSionS arc quite rare the teachers doιft assign US Iioineuork during Ihe holidays.73. Dark ClOUdS WamCd the fanners the approaching StOnIL74. _____ SlIddenly OCCUned to Miranda that PerhaPS no One WOUld believe her StOn75. PeoPIe SlIOuld Change IIIeiI IIabIt Of OIdCIUlg loυ IIlUCJ IbOd in IeStalIlalltS・ because a lot Offood ended UP (waste).76. He s been resting today, SO _______ (Ik)PC) he WlIl feel better totnoπ,ow.77 By the time TOm got up. his father (PrePare) breakfast for him78. TOm (UIned away, ____ (bury ) his (ace in his hand、・79. Tlle SCiCnCe Of medicine, WhiCh Ue ov¼c a great deal, is PCrhaPS the InOSt importantOf all IhC branches Of science.80. DeSPite the rapid economic development In SOIne WeStern countries, Inany CIderly PCOPleStllI IiVe In (poor),第三部分写作第一节、单旬攻笛(M IO小題•毎小題1分，満分IO分)卜列毎个句子中有一处说言错谋。
哈32中2019-2020学年度下学期中测试高一数学试题一、选择题（每小题只有1个选项符合题意，每小题4分，共40分） 1、 15sin 75sin 15cos 75cos += （ ） A 、 100cos B 、 100sin C 、23 D 、21 2、已知41sin -=x ，则=x 2cos （ ） A 、87B 、87- C 、415 D 、415-3、函数x x y 2cos 2sin =的最小正周期是 （ ） A 、π2 B 、π4 C 、4πD 、2π 4、函数x x y 4cos 34sin 3+=的最大值是 （ ） A 、3 B 、32 C 、3 D 、6 5、︒︒︒︒-+50tan 70tan 350tan 70tan = （ ） A 、3 B 、33 C 、33- D 、3- 6、关于零向量，下列说法中错误的是 （ ） A 、零向量是没有方向的 B 、零向量的长度为0 C 、零向量与任一向量平行 D 、零向量的方向是任意的 7、BC DA CD AB +++= ( ) A 、 B 、 C 、 D 、 8、在ABC ∆中，bc c b a ++=222，则A 等于 A ︒︒︒︒30.45.60.120.D C B9、已知)1,2(),,6(-=-=y ，且与共线，则y = （ ） A 、-6 B 、6 C 、3 D 、-310、已知向量、满足4||,1||==b a ，且,2=∙b a 则与的夹角为（ ） A 、6π B 、4π C 、3π D 、2π 二、填空题（每空4分，共20分） 11、已知33)6cos(=-απ，则=+)65cos(απ； 12、已知2||||==，,2)()2(-=-∙+则a 与b 的夹角为 ； 13．若3sin 5θ=，θ为第二象限角，则≡θ2sin _______. 14．等差数列{}n a 中，若377,3a a ==，则10a = ． 三、解答题（每题10分，共40分）15．求函数)32sin(π-=x y ，的周期及单调递减区间；16．已知πβαββαα<<<==0),sin ,(cos ),sin ,(cos b a ， （1）求||的值；（2）求证：+与-互相垂直。
哈三中2018-2019学年度下学期高一学年第一次验收考试数学试卷一、选择题：本大题共12小题，每小题5分，共60分. 在每小题给出的四个选项中，只有一项是符合题目要求的.1.在中，若，，，则A. B. C. D.【答案】B【解析】试题分析：在中，由正弦定理可知，∴.考点：正弦定理的应用.2.在平行四边形中，下列结论错误的是A. B. C. D.【答案】C【解析】分析】画出图像，根据向量加法运算，对选项逐一分析判断，由此得出正确选项.【详解】画出图像如下图所示.对于A选项，大小相等方向相反，，结论正确.对于B选项，根据向量加法的平行四边形法则可知，，结论正确.对于C选项，由于，故结论错误.对于D选项，，大小相等方向相反，，结论正确.故选C.【点睛】本小题主要考查向量加法运算，考查平行四边形的几何性质，属于基础题.3.在中，根据下列条件解三角形，其中有两个解的是A. ，，B. ，，C. ，，D. ，，【答案】D【解析】【分析】根据全等三角形的判断方法，判断A,B两个选项有一个解.根据判断C选项有一个解.根据判断D选项有两个解.【详解】根据“有两个角两角相等，且有一边相等的两个三角形全等”可知A选项有一个解.根据“两边对应相等，且这两边的夹角相等，则这两个三角形全等”可知B选项有一个解.由于为锐角，且，故C选项有一个解.对于D选项，由于，所以D选项有两个解.故选B.【点睛】本小题主要考查解三角形过程中，三角形解得个数的判断，属于中档题.4.设是两个不共线向量，若则（）A. 三点共线B. 三点共线C. 三点共线D. 三点共线【答案】A【解析】因为+==2，故三点共线.故答案为：A.5.已知向量与的夹角为120°，则（）A. 5B. 4C. 3D. 1【答案】B【解析】即解得（舍去）故选B6.的三内角所对边的长分别为设向量,,若,则角的大小为( )A. B. C. D.【答案】B【解析】试题分析：因为两向量平行，所以等价于，整理为，所以，所以角考点：1．向量平行的坐标表示；2．余弦定理．7.．已知与为互相垂直的单位向量，，且与的夹角为锐角，则实数的取值范围是（）A. B.C. D.【答案】A【解析】由题意，得，，，根据向量数量积的计算公式，得，解得，又与不共线，则，所以正确答案为A,8.在中，点在边上，且，，则的值为A. B. C. D.【答案】C【解析】【分析】画出图像，利用向量减法的运算，表示出，由此求得的值，进而求得的值.【详解】依题意，故，故.故选C.【点睛】本小题主要考查向量减法运算，考查平面向量基本定理，属于基础题.9.在中，，则的形状是A. 直角三角形B. 锐角三角形C. 钝角三角形D. 不确定【答案】C【解析】【分析】利用正弦定理和二倍角公式，求得的值，由此判断角的大小，进而判断出角的大小，从而判断出三角形的形状.【详解】由正弦定理得，由于，故,，由于，故，故，所以三角形为钝角三角形.故选C.【点睛】本小题主要考查正弦定理，考查二倍角公式，考查三角形形状的判断，属于中档题.10.已知是平面内两个互相垂直的单位向量，若向量满足，则的最大值是A. B. C. D.【答案】A【解析】【分析】以分别为轴正方向建立平面直角坐标系，设出的坐标，代入，利用模的坐标表示出，进而求得的最大值.【详解】以分别为轴正方向建立平面直角坐标系，如下图所示，，设，则有得，化简得，故向量对应的点在以为圆心，半径为的圆上.由于圆过原点，故圆上的点到原点的距离的最大值为直径，也即的最大值为.故选A.【点睛】本小题主要考查平面向量的坐标运算，考查数形结合的数学思想方法，考查运算求解能力以及化归与转化的数学思想方法，属于中档题.11.在中,已知,分别为所对边,则为A. B. 1 C. 或1 D. 无法确定【答案】B【解析】【分析】将通分后，利用余弦定理化简，求得化简的结果.【详解】由余弦定理得.由通分得，故选B.【点睛】本小题主要考查余弦定理的运用，考查化归与转化的数学思想方法，属于中档题.12.已知，为三角形所在平面上的一点，且点满足：，则点为三角形的A. 外心B. 垂心C. 重心D. 内心【答案】D【解析】【分析】在上分别取单位向量，记，则平分，用表示出，代入条件所给等式，用表示出，则可证明三点共线，即平分.同理证得在其它两角的平分线上，由此求得是三角形的内心.【详解】在，上分别取点使得，则，作菱形，则由所以为的平分线.因为，所以，所以，所以三点共线，即在的平分线上. .同理证得在其它两角的平分线上，由此求得是三角形的内心.，故选D.【点睛】本小题主要考查平面向量的加法运算，考查三点共线的证明，考查数形结合的数学思想方法，属于中档题.二、填空题：本大题共4小题,每小题5分,共20分.13.已知向量，，若，则_____________．【答案】【解析】【分析】先求得，然后利用两个向量垂直的坐标表示列方程，解方程求得的值.【详解】依题意，由于，所以，.【点睛】本小题主要考查平面向量坐标加法运算，考查两个向量垂直的坐标表示，属于基础题.14.在所在的平面内有一点，若，那么的面积与的面积之比是_____________．【答案】【解析】【分析】利用向量加法和减法运算，证得是线段上，靠近点的四等分点，由此求得两个三角形面积的比值.【详解】依题意，所以，即，所以是线段上，靠近点的四等分点，故两个三角形面积的比等于.【点睛】本小题主要考查平面向量加法和减法的运算，考查平面向量方向相反的表示，属于基础题.15.在中,内角所对应的边分别为，若，，则的面积为_________.【答案】【解析】分析：由，，利用余弦定理可得，结合三角形的面积公式进行求解即可.详解：因为，，所以由余弦定理得：，即，因此的面积为，故答案为.点睛：本题主要考查余弦定理及特殊角的三角函数，属于简单题.对余弦定理一定要熟记两种形式：（1）；（2），同时还要熟练掌握运用两种形式的条件.另外，在解与三角形、三角函数有关的问题时，还需要记住等特殊角的三角函数值，以便在解题中直接应用.16.在中，内角，，的对边分别为，，，为边上的高，给出以下结论：（1）；（2）；（3）；（4）．其中正确的序号是__________．【答案】（1）（2）（3）（4）【解析】【分析】利用向量加法、减法和数量积的运算，结合余弦定理，对四个结论逐一分析，由此得出正确的序号.【详解】由于，故（1）正确.由于，故（2）正确.由于，且，故（3）正确.由于，故（4）正确.综上所述，正确的序号是（1）（2）（3）（4）.【点睛】本小题主要考查平面向量加法、减法运算，考查平面向量数量积运算，考查两个向量垂直的表示，考查余弦定理，属于中档题.三、解答题：本大题共4小题，共40分.解答应写出文字说明,证明过程或演算步骤.17.在中，内角的对边分别为，，，已知．（1）求的值；（2）若，,求的面积．【答案】（1）2；（2）【解析】【分析】（1）通过将条件转化为，然后利用三角变换可得结果；（2）由（1）得，由余弦定理得，可解得，，从而解得三角形面积。
哈32中2019-2020学年度下学期中测试高一数学试题一、选择题（每小题只有1个选项符合题意，每小题4分，共40分） 1、 15sin 75sin 15cos 75cos += （ ） A 、 100cos B 、 100sin C 、23 D 、21 2、已知41sin -=x ，则=x 2cos （ ） A 、87B 、87- C 、415 D 、415-3、函数x x y 2cos 2sin =的最小正周期是 （ ） A 、π2 B 、π4 C 、4πD 、2π 4、函数x x y 4cos 34sin 3+=的最大值是 （ ） A 、3 B 、32 C 、3 D 、6 5、︒︒︒︒-+50tan 70tan 350tan 70tan = （ ） A 、3 B 、33 C 、33- D 、3- 6、关于零向量，下列说法中错误的是 （ ） A 、零向量是没有方向的 B 、零向量的长度为0 C 、零向量与任一向量平行 D 、零向量的方向是任意的 7、BC DA CD AB +++= ( ) A 、BD B 、AC C 、0 D 、AB 8、在ABC ∆中，bc c b a ++=222，则A 等于 A ︒︒︒︒30.45.60.120.D C B9、已知)1,2(),,6(-=-=b y a ，且a 与b 共线，则y = （ ） A 、-6 B 、6 C 、3 D 、-3 10、已知向量a 、b 满足4||,1||==b a ，且,2=∙b a 则a 与b 的夹角为（ ） A 、6π B 、4π C 、3π D 、2π 二、填空题（每空4分，共20分） 11、已知33)6cos(=-απ，则=+)65cos(απ； 12、已知2||||==b a ，,2)()2(-=-∙+b a b a 则a 与b 的夹角为 ； 13．若3sin 5θ=，θ为第二象限角，则≡θ2sin _______. 14．等差数列{}n a 中，若377,3a a ==，则10a = ． 三、解答题（每题10分，共40分）15．求函数)32sin(π-=x y ，的周期及单调递减区间；16．已知πβαββαα<<<==0),sin ,(cos ),sin ,(cos b a ， （1）求||a 的值；（2）求证：b a +与b a -互相垂直。
哈32中2019-2020学年度下学期中测试高一数学试题一、选择题（每小题只有1个选项符合题意，每小题4分，共40分） 1、 15sin 75sin 15cos 75cos += （ ）A 、 100cosB 、 100sinC 、23 D 、21 2、已知41sin -=x ，则=x 2cos （ ）A 、87B 、87-C 、415D 、415- 3、函数x x y 2cos 2sin =的最小正周期是 （ ）A 、π2B 、π4C 、4πD 、2π4、函数x x y 4cos 34sin 3+=的最大值是 （ ）A 、3B 、32C 、3D 、6 5、︒︒︒︒-+50tan 70tan 350tan 70tan = （ ）A 、3B 、33C 、33-D 、3- 6、关于零向量，下列说法中错误的是 （ ）A 、零向量是没有方向的B 、零向量的长度为0C 、零向量与任一向量平行D 、零向量的方向是任意的 7、BC DA CD AB +++= ( )A 、B 、C 、D 、8、在ABC ∆中，bc c b a ++=222，则A 等于A ︒︒︒︒30.45.60.120.D C B9、已知)1,2(),,6(-=-=y ，且与共线，则y = （ ）A 、-6B 、6C 、3D 、-310、已知向量、满足4||,1||==b a ，且,2=∙b a 则与的夹角为（ ）A 、6πB 、4πC 、3πD 、2π二、填空题（每空4分，共20分）11、已知33)6cos(=-απ，则=+)65cos(απ；12、已知2||||==，,2)()2(-=-∙+则a 与b 的夹角为 ；13．若3sin 5θ=，θ为第二象限角，则≡θ2sin _______.14．等差数列{}n a 中，若377,3a a ==，则10a = ．三、解答题（每题10分，共40分）15．求函数)32sin(π-=x y ，的周期及单调递减区间；16．已知πβαββαα<<<==0),sin ,(cos ),sin ,(cos b a ，（1）求||的值；（2）求证：+与-互相垂直。
2019-2020学年黑龙江省哈尔滨市第三中学高三数学文联考试题含解析一、选择题：本大题共10小题，每小题5分，共50分。
在每小题给出的四个选项中，只有是一个符合题目要求的1. 已知直线与曲线在点P（1，1）处的切线互相垂直，则为（）A． B． C．D．参考答案：D略2. 已知集合，，则（）A． B． C． D．参考答案：B【知识点】集合的运算【试题解析】所以。
3. 在平面直角坐标系xOy中，直线3x+4y﹣5=0与圆x2+y2=4相交于A、B两点，则弦AB的长等于（）A．3B．2C．D．1参考答案：B【考点】直线与圆相交的性质．【分析】由直线与圆相交的性质可知，，要求AB，只要求解圆心到直线3x+4y﹣5=0的距离【解答】解：由题意可得，圆心（0，0）到直线3x+4y﹣5=0的距离，则由圆的性质可得，，即．故选B4. 设等差数列的前项和为，若，则必有A．且 B．且C．且 D．且参考答案：A试题分析：由题意知，，得，，故答案为A考点：等差数列的前项和公式5. 已知双曲线mx2﹣ny2=1（m＞0，n＞0）的离心率为2，则椭圆mx2+ny2=1的离心率为（）A．B．C．D．参考答案：C【考点】K4：椭圆的简单性质；KC：双曲线的简单性质．【分析】双曲线、椭圆方程分别化为标准方程，利用双曲线mx2﹣ny2=1（m＞0，n＞0）的离心率为2，可得m=3n，从而可求椭圆mx2+ny2=1的离心率．【解答】解：双曲线mx2﹣ny2=1化为标准方程为：∵双曲线mx2﹣ny2=1（m＞0，n＞0）的离心率为2，∴∴m=3n椭圆mx2+ny2=1化为标准方程为：∴椭圆mx2+ny2=1的离心率的平方为=∴椭圆mx2+ny2=1的离心率为故选C．【点评】本题考查椭圆、双曲线的离心率，考查学生分析解决问题的能力，属于中档题．6. 如图,四边形是正方形，延长至，使得.若动点从点出发，沿正方形的边按逆时针方向运动一周回到点，其中，下列判断正确的是……… ………………………………………（）（A）满足的点必为的中点.（B）满足的点有且只有一个.（C）的最大值为3.（D）的最小值不存在.参考答案：C当时，，此时位于处，所以（A）错误。
