2011届江苏省海安高级中学、金陵中学、南京外国语学校高三三校联考英语试题

南京市金陵中学2011届高三第四次模拟考试数学I 试题参考公式：锥体的体积公式：V锥体＝错误!Sh，其中S是锥体的底面面积，h是高．一、填空题:本大题共14小题，每小题5分，共70分．请把答案填．写在答题卡相应的位置上Array．．．．．．．．．1．在复平面内,复数－3＋i和1－i2．命题：“若a，b,c34．用半径为R圆锥的高是▲．5．为了调查高中学生眼睛高度近视的原因，某学校研究性学习小组用分层抽样的方法从全校三个年级行深入研究，有关数据见右表（单位:人)：若从高一与高三抽取的人选中选2人进行跟踪式家访调研，则这2人都来自高三年级的概率是▲．6．双曲线x2－错误!＝1的渐近线被圆x2＋y2－6x－2y＋1＝0所截得的弦长为▲．7．在共有2013项的等差数列｛a n}中，有等式(a1＋a3＋…＋a2013)－（a2＋a4＋…＋a2012）＝a1007成立;类比上述性质，在共有2011项的等比数列｛b n｝中，相应的有等式▲成立．8．已知向量p的模是错误!，向量q的模为1，p与q的夹角为错误!,a＝3p＋2q，b＝p－q，则以a、b为邻边的平行四边形的长度较小的对角线的长是▲．9．若x，y满足不等式组错误!且z＝2x＋4y的最小值为－6,则k的值为▲．10．已知等差数列｛a n｝和｛b n｝的前n项和分别为S n，T n,且错误!＝错误!对任意n N*恒成立，则错误!的值为▲．11．已知A＝｛x｜1≤x≤2}，B＝{x|x2＋2x＋a≥0}，A，B的交集不是空集，则实数a的取值范围是▲．12．定义在R上的函数f（x)的图象过点M（－6，2）和N(2，－6），对任意正实数k,有f（x＋k)＜f（x）成立,则当不等式｜f(x－t)＋2｜＜4的解集为(－4，4）时，实数t的值为▲．13．平面四边形ABCD中，AB＝错误!，AD＝DC＝CB＝1,△ABD和△BCD的面积分别为S，T，则S2＋T2的最大值是▲．14．在直角坐标系xOy中，点P（x P，y P）和点Q(x Q,y Q）满足错误!,按此规则由点P得到点Q，称为直角坐标平面的一个“点变换”．此变换下，若错误!＝m，∠POQ＝，其中O为坐标原点，则y＝m sin(x＋）的图象在y轴右边第一个最高点的坐标为▲．二、解答题：本题共6小题，共计90分，请在答题卡指定区域内作答，解答时应写出文字说明、证明过程或演算步骤．15．（本小题满分14分）已知函数f(x）＝，3sin2x＋sin x cos x－错误!（x R）．(1）若x(0，错误!)，求f(x）的最大值；（2）在△ABC中，若A＜B，f(A)＝f(B)＝错误!，求错误!的值．16．（本小题满分14分）已知在直四棱柱ABCD －A 1B 1C 1D 1中，底面ABCD 为直 角梯形,且满足AD ⊥AB ,BC ∥AD ，AD ＝16，AB ＝8，BB 1＝8．E ，F 分别是线段A 1A ，BC 上的点． （1)若A 1E ＝5,BF ＝10，求证:BE ∥平面A 1FD ． （2）若BD ⊥A 1F ，求三棱锥A 1－AB 1F 的体积．17．（本小题满分14分）省环保研究所对市中心每天环境放射性污染情况进行调查研究后,发现一天中环境综合放射性污染指数f （x )与时刻x （时)的关系为f （x ）＝|错误!－a |＋2a ＋错误!，x ［0，24]，其中a 是与气象有关的参数，且a［0，错误!]，若用每天f （x )的最大值为当天的综合放射性污染指数，并记作M （a ）． （1）令t ＝错误!，x [0,24］，求t 的取值范围；（2）省政府规定，每天的综合放射性污染指数不得超过2，试问目前市中心的综合放射性污染指数是否超标?18．(本小题满分16分）已知椭圆C ：错误!＋错误!＝1(a ＞b ＞0)，⊙O ：x 2＋y 2＝b 2，点A ，F分别是椭圆C 的左顶点和左焦点．点P 是⊙O 上的动点．（1）若P (－1,错误!)，PA 是⊙O 的切线，求椭圆C 的方程；（2）是否存在这样的椭圆C ，使得错误!是常数?AF POyx （第16题图）A B C DA 1B 1C 1D 1FE如果存在，求C的离心率;如果不存在，说明理由．19．（本小题满分16分）(第18已知函数f(x)＝错误!ax2－(2a＋1）x＋2ln x(a为正数）．（1）若曲线y＝f(x）在x＝1和x＝3处的切线互相平行,求a的值；(2）求f（x)的单调区间；（3)设g(x）＝x2－2x，若对任意x 1（0，2],均存在x 2（0，2]，使得f(x1）＜g（x2），求实数a的取值范围．20．(本小题满分16分）设数列｛a n}满足:a1＝1，a2＝2，a n＋2＝错误!(n≥1，n N*）．(1)求证：数列｛错误!｝是常数列;(2）求证：当2≥n时，2＜a错误!－a错误!≤3;(3）求a2011的整数部分．M DBAO数 学 Ⅱ（附 加 题)21．【选做题】本题包括A 、B 、C 、D 四小题，请选定其中两题．．．．．．．,．并．在相应的答题区域内作答．．．．．．．．．．．．若多做,则按作答的前两题评分．解答时应写出文字说明、证明过程或演算步骤．A ．选修4－1：几何证明选讲 （本小题满分10分)如图,设AB 为⊙O 的任一条不与直线P 是⊙O 与l 的公共点,AC ⊥l ,BD ⊥l PC ＝PD ．求证：（1)l 是⊙O 的切线；（2）PB 平分∠ABD ． B ．选修4－2：矩阵与变换 （本小题满分10分）已知点A 在变换：T ：错误!→错误!＝错误!作用后,再绕原点逆时针旋转90°，得到点B ．若点B 坐标为(－3，4)，求点A 的坐标． C ．选修4－4:坐标系与参数方程 （本小题满分10分）求曲线C 1：错误!被直线l ：y ＝x －错误!所截得的线段长． D ．选修4－5：不等式选讲 （本小题满分10分）已知a 、b 、c 是正实数,求证：错误!≥错误!．【必做题】第22题、第23题，每题10分,共计20分．请在答题卡．．．指．定区域．．．内作答．解答时应写出文字说明、证明过程或演算步骤．22．（本小题满分10分）如图，在四棱锥O－ABCD中,底面ABCD是边长为1的菱形,∠ABC＝45°，OA⊥底面ABCD，OA＝2，M为OA的中点．（1）求异面直线AB与MD所成角的大小;（2）求平面OAB与平面OCD所成二面角的余弦值．23．(本小题满分10分）已知构成某系统的元件能正常工作的概率为p（0＜p＜1)，且各个元件能否正常工作是相互独立的．今有2n（n大于1）个元件可按下图所示的两种联结方式分别构成两个系统甲、乙．（1)试分别求出系统甲、乙能正常工作的概率p1,p2;（2）比较p1与p2的大小,并从概率意义上评价两系统的优劣．系统甲系统乙南京市金陵中学2011届高三第四次模拟考试数学I 试题评分细则1．2错误!2．2 3．－9 4．错误!R5．错误!6．4 7．错误!＝a10068．错误!9．0 10．错误!11．[－8，＋∞）12．2 13．错误! 14．（错误!,错误!）15．（1）f（x)＝错误!＋错误!sin2x－错误!＝错误!sin2x－错误!cos2x＝sin（2x－π)．………4分3∵0＜x＜错误!，∴－错误!＜2x－错误!＜错误!．……………………………6分∴当2x－错误!＝错误!时，即x＝错误!时，f（x）的最大值为1．……………………………7分(2）∵f(x)＝sin(2x－错误!），x是三角形的内角，则0＜x＜，－错误!＜2x－错误!＜错误!．令f（x）＝错误!,得sin(2x－错误!）＝错误!，∴2x－错误!＝错误!，或2x －错误!＝错误!，解得x＝错误!,或x＝7．……………………………9分12由已知，A,B是△ABC的内角，A＜B且f（A）＝f（B）＝错误!，∴A＝错误!，B＝错误!．∴C＝－A－B＝错误!．……………………………11分由正弦定理，得错误!＝错误!＝错误!＝错误!＝2． ……………………………14分16．(1）过E 作EG ∥AD 交A 1D 于G ,连结GF ． ∵错误!＝错误!,所以错误!＝错误!，∴EG ＝10＝BF ． ∵BF ∥AD ，EG ∥AD ，∴BF ∥EG ． ∴四边形BFGE 是平行四边形．∴BE ∥FG ．…………………………………4分 又FG平面A 1FD ，BE 平面A 1FD , ∴BE ∥平面A 1FD ． …………………………………6分（2)∵在直四棱柱ABCD －A 1B 1C 1D 1中,A 1A ⊥面ABCD ，BD 面ABCD ，∴A 1A ⊥BD ．由已知，BD ⊥A 1F ，AA 1∩A 1F ＝A 1，∴BD ⊥面A 1AF ．∴BD ⊥AF ． ………………………………8分∵梯形ABCD 为直角梯形，且满足AD ⊥AB ，BC ∥AD ,∴在Rt △BAD 中,tan ∠ABD ＝错误!＝2．在Rt △ABF 中,tan ∠BAF ＝错误!＝错误!．∵BD ⊥AF ，∴∠ABD ＋∠BAF ＝错误!，∴错误!＝错误!，BF ＝4． ………………10分∵在直四棱柱ABCD －A 1B 1C 1D 1中，A 1A ⊥面ABCD ， GA B C D A 1 B 1 C 1D 1F E∴面AA1B1B⊥面ABCD，又面ABCD∩面AA1B1B＝AB，∠ABF＝90°，∴FB⊥面AA1B1B，即BF为三棱锥F－A1B1A的高．………………12分∵∠AA1B1＝90°,AA1＝BB1＝8，A1B1＝AB＝8，∴S错误!＝32．∴V错误!＝V错误!＝错误!×S错误!×BF＝错误!． (14)分17．（1)当x＝0时，t＝0；………………2分当0＜x≤24时，错误!＝x＋错误!．对于函数y＝x＋错误!，∵y′＝1－错误!，∴当0＜x＜1时，y′＜0，函数y＝x＋错误!单调递增，当1＜x≤24时，y′＞0，函数y＝x＋错误!单调递增，∴y［2，＋∞）．∴错误!(0，错误!］．综上，t的取值范围是［0，错误!]．………………5分(2）当a［0,错误!]时,f(x）＝g（t)＝｜t－a｜＋2a＋错误!＝错误!………………8分∵g(0）＝3a＋错误!,g(错误!）＝a＋错误!,g（0)－g（错误!）＝2a－错误!．故M(a)＝错误!＝错误!．………………10分当且仅当a≤错误!时，M(a)≤2，………………12分故a[0,错误!]时不超标，a（错误!，1]时超标．………………14分18．（1)∵P(－1，错误!）在⊙O：x2＋y2＝b2，∴b2＝4．……………………………2分又∵PA是⊙O的切线，∴PA⊥OP,∴错误!·错误!＝0,即（－1，错误!)·（－1＋a，错误!)＝0，解得a＝4．∴椭圆C的方程为错误!＋错误!＝1．……………………………5分(2）设F(c，0),c2＝a2－b2,设P(x1,y1），要使得PAPF是常数,则有(x1＋a）2＋y12＝[（x1＋c）2＋y12］，是常数．即b2＋2ax1＋a2＝(b2＋2cx1＋c2），……………………………8分比较两边, b2＋a2＝（b2＋c2）,a＝c，……………………………10分故cb2＋ca2＝a(b2＋c2)，即ca2－c3＋ca2＝a3，即e3－2e＋1＝0， (12)分（e－1)( e2＋e－1)＝0，符合条件的解有e＝错误!，即这样的椭圆存在，离心率为，5－12．……………………………16分19．f ′(x )＝ax －(2a ＋1）＋2x(x ＞0）． （1） f′（1）＝ f ′（3),解得a ＝错误!． ……………………………4分(2）f ′(x )＝错误!(x ＞0)． ①当0＜a ＜错误!时，错误!＞2，在区间(0，2）和（错误!，＋∞）上，f ′（x )＞0；在区间(2,错误!)上f ′(x )＜0,故f （x ）的单调递增区间是（0，2）和(错误!,＋∞)，单调递减区间是(2，错误!）． ……6分②当a ＝错误!时，f ′（x )＝错误!≥0，故f (x )的单调递增区间是（0，＋∞)． ………8分③当a ＞错误!时，0＜错误!＜2，在区间(0，错误!）和（2，＋∞）上，f ′（x )＞0；在区间(错误!，2）上f ′（x ）＜0，故f （x ）的单调递增区间是(0，1a）和(2,＋∞),单调递减区间是（错误!，2）． ……10分 （3）由已知，在(0,2］上有f (x )max ＜g（x )max ． ……………………………11分 由已知，g(x ）max ＝0,由(2）可知,①当0＜a≤错误!时，f（x)在(0，2］上单调递增，故f（x)max＝f(2)＝2a－2(2a＋1)＋2ln2＝－2a－2＋2ln2,∴－2a－2＋2ln2＜0，解得a＞ln2－1，ln2－1＜0，故0＜a≤错误!．……13分②当a＞错误!时,f(x)在（0，错误!]上单调递增，在[错误!，2]上单调递减，故f（x）max＝f(错误!)＝－2－错误!－2ln a．由a＞错误!可知ln a＞ln错误!＞ln错误!＝－1，2ln a＞－2，－2ln a＜2，∴－2－2ln a＜0，f(x）max＜0，……………………………15分综上所述，a＞0．……………………………16分20．（1）易知,对一切n≥1，a n≠0，由a n＋2＝错误!，得错误!＝错误!．依次利用上述关系式，可得错误!＝错误!＝错误!＝…＝错误!＝错误!＝1，从而数列{错误!}是常数列；……………………………4分（2）由(1）得a n＋1＝a n＋错误!．又a1＝1，∴可知数列{a n}递增，则对一切n≥1，有a n≥1成立,从而0＜错误!≤1． (6)分当2≥n时,a n2＝(a n－1＋错误!）2＝a错误!－1＋错误!＋2，于是a n2－a错误!－1＝错误!＋2，∴2＜a2n－a2，n－1≤3；……………………………8分（3）当2≥n时,a n2＝a错误!－1＋错误!＋2,∴a错误!＝错误!＋…＋错误!＋a错误!＋2（n－1)．a错误!＝1,a错误!＝4，则当n≥3时,a错误!＝错误!＋…＋错误!＋a错误!＋2（n－1）＝错误!＋…＋错误!＋1＋1＋2(n－1）＝错误!＋…＋错误!＋2n＞2n．a错误!＝错误!＋…＋错误!＋2（2011－1）＋1＞4021＞3969＝632，……………………10分a错误!＝错误!＋…＋错误!＋2（2011－1）＋1＝4021＋错误!＋…＋错误!＜4020＋11＋错误!＋错误!＋…＋错误!＝4022＋错误!（错误!＋错误!＋…＋错误!）＝4022＋错误![（错误!＋错误!＋…＋错误!）＋(错误!＋错误!＋…＋错误!)＋（错误!＋错误!＋…＋错误!）]＜4022＋错误!［(错误!＋错误!＋…＋错误!)＋(错误!＋错误!＋…＋错误!）＋（错误!＋错误!＋…＋错误!）]＝4022＋错误!（错误!×38＋错误!×160＋…＋错误!×1811)＜4022＋错误!(19＋4＋10)＜4039＜4096＝642．……………………14分∴63＜a2011＜64，即a2011的整数部分为63．……………………16分数学Ⅱ(附加题)评分细则21－A：证明：（1)连结∵AC⊥l，BD⊥l，∴又OA＝OB，PC＝PD∴OP∥BD，从而OP⊥l．∵P在⊙O上，∴l是⊙O的切线．……………………6分（2）连结AP,∵l是⊙O的切线，∴∠BPD＝∠BAP．又∠BPD＋∠PBD＝90o，∠BAP＋∠PBA＝90o，∴∠PBA＝∠PBD,即PB平分∠ABD．……………………10分21－B：解：错误!错误!＝错误!． (6)分设A（a，b)，则由错误!错误!＝错误!，得错误!∴错误!即A（－2，3）．……………………10分21－C：解:C1:错误!．错误!得t＝错误!，代入①，化简得x2＋y2＝2x．又x＝错误!≠0,∴C1的普通方程为(x－1）2＋y2＝1(x≠0）．……………………6分圆C1的圆心到直线l：y＝x－错误!的距离d＝错误!＝错误!．所求弦长＝2错误!＝错误!．……………………10分21－D：证明:由错误!≥0，得2（错误!)－2(错误!）≥0，∴错误!≥错误!．……………………10分z 22．解:作AP ⊥CD 于点P ，分别以AB 、AP 、AO 所在直线为x 、y 、z 轴建立坐标系，则A (0，0，0）,B （1，0，0），P （0，错误!，0），D (－错误!，错误!，0），O (0，0，2），M (0，0，1）．（1）错误!＝（1,0，0)，错误!＝(－错误!，错误!，－1),则cos ＜错误!,错误!＞＝－12， 故AB 与MD 所成角为错误!． 4分（2）OP →＝(0，错误!，－2)，错误!）， 设平面OCD 法向量n ＝(x ，y ，n ·错误!＝0， 即错误!，取z ＝错误!，则n ＝(0,4，错误!6分 易得平面OAB 的一个法向量为m ＝(0，1，0)，cos＜n ,m ＞＝错误!， ……………………9分故平面OAB 与平面OCD 所成二面角的平面角余弦值为错误!．………………10分23．解：(1)p 1＝p n （2－p n ）, ……………………2分 p 2＝p n (2－p )n ； ……………………4分（2）(用二项式定理证明) p 2－p 1＝p n {［1＋(1－p ）］n －2＋［1－（1－p )］n＝p n ｛［1＋C 错误!(1－p )＋C 错误!(1－p ）2＋C 错误!(1－p )3＋…＋C 错误!（1－p ）n ]－2 O学必求其心得，业必贵于专精＋［1－C1n（1－p)＋C错误!(1－p)2－C错误!（1－p)3＋…＋（－1）n C错误!（1－p)n］｝＝p n[C错误!(1－p）2＋C错误!(1－p）4＋…]＞0．…………………10分说明：作差后化归为用数学归纳法证明:(2－p)n＞2－p n也可．。

2010年南外、金中、海中三校联考英语2010.5 本试卷分第一卷（选择题）和第二卷（非选择题）两部分。

共120分。

考试用时为120分钟。

注意事项：答题前，考生务必将自己的学校、姓名、考试号写在答题卡上。

考试结束后，将答题卡交回。

第一卷（三部分，共85分）第二部分英语知识运用 (共两节，满分35分)第一节单项填空 (共15小题；每小题1分，满分15分)请认真阅读下面各题，从题中所给的从A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

21.China’s economic development has made ______ rapid progress in the past 10 years, and youngpeople have made ______ great contribution to this progress.A. a; aB. the; /C. /; aD. /; /22.Susan was expecting her favourite singers, but to her disappointment, _______ appeared.A. someB. noneC. everyoneD. no one23.Y our essay is fairly good and yet it leaves something ______.A. to desireB. desireC. desiringD. to be desired24.The police have offered a large _______ for information leading to the robber’s arrest.A. prizeB. compensationC. priceD. reward25.Even though they have worked side by side in the same office for 9 years, the two ladies ______ ongood terms.A. are notB. were notC. have not beenD. will not be26.I feel sure that ______ qualification, ability and experience, you are abundantly suited to the positionwe have in mind.A. on account ofB. in spite ofC. in terms ofD. by means of27.To my mind, she is the most wonderful teacher that I’ve ever known, _________ is able to get acrossto her students ________ she really thinks and means.A. which; thatB. that; asC. who; whatD. who; that28.―We didn’t see Robert at the opening ceremony yesterday.―No, he _______ it.A. mustn’t have attendedB. needn’t have attendedC. needn’t attendD. didn’t need to attend29.Out of the crowded bus __________, who was dressed in a black suit and waving to a woman.A. stepped a tall man in his thirtiesB. a tall man in his thirties steppedC. did a tall man in his thirties stepD. did a tall man step in his thirties30.After several rounds of competition, the little girl ______ because of her excellent English and quickwit.A. stood outB. picked outC. turned outD. came out31.― I’m sorry to bother you at this time of night.― _________. It’s just so happened that I’m not engaged right now.A. All rightB. That’s OKC. Y ou’re welcomeD. Please don’t be bothered32._______ is the strength of union that all the dilemmas, if any, can be dealt with.A. ThatB. ItC. SuchD. So33.― I'm afraid I have to give it up.― Don't be discouraged. Remember ______ sticks to his work will succeed one day.A. those whoB. whoC. whoeverD. whomever34.I went to bed early, but I left my bedroom lamp on ______ my parents think I _______.A. making; would studyB. to make; was studyingC. to make; had studiedD. making; had been studying35.― Have you ever talked to your fiancée about the wedding yet?― No, I’d like to, ______.A. indeedB. yetC. anywayD. though第二节完形填空(共20小题；每小题1分，满分20分)请认真阅读下面短文，从短文后各题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

南京三中2011届高三英语试题 2011.4 说明：1.本卷分第Ⅰ卷和第Ⅱ卷两部分，满分120分，考试时间120分钟。

2.所有答案必须填写到答题卡和答卷纸上，否则无效。

第Ⅰ卷一部分　听力（共两节，满分20分） 第一节（共5小题：每小题1分，满分5分） 听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What does the man think of the cake?A. Delicious.B. Not very good.C. It’s OK. 2. Who is in the hospital?A. Tom’s sister.B. Tom.C. Betty. 3. What is the woman’s occupation?A. A student.B. A salesperson.C. A teacher. 4. When will the speakers get to Beijing?A. At 8:30.B. At 8:50.C. At 9:00. 5. How much should the woman pay if she buys two T-shirts?A. Ten dollars.B. Eleven dollars.C. Six dollars. 第二节（共15小题：每小题1分，满分15分） 听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，每小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，回答第6至8题6. Where is the flat?A. In the central part of the town.B. Near a busy road.C. Beside a park. 7. How much is the rent?A. 13 pounds a week.B. 120 pounds a month.C. 300 pounds a year. 8. What does the man think of the flat?A. He likes it very much.B. He doesn’t like it.C. He wants to see it first. 听第7段材料，回答第9至11题9. How many languages can the woman speak?A. Two.B. Three.C. Four. 10. What do we know from the text? A. The woman can write French. B. The woman can’t write German. C. The woman can not only speak German but also write it. 11. What does the man think of Japanese?A. It’s difficult.B. It’s easy.C. It is the same as German. 听第8段材料，回答第12至13题12. Who called whom?A. James called John.B. John called James.C. Jane called John. 13. Where will they meet? A. At the entrance of the stadium. B. At the entrance of the museum. C. At the entrance of the theater. 听第9段材料，回答第14至16题14. What do you think is the possible relationship between the two speakers? A. The man is the woman’s husband. B. The man is a guest to the woman’s flat. C. The woman is a guest to the man’s house. 15. What were others doing and why did the woman go out? A. Having dinner; because she wanted to see her old house. B. Having a concert; because she thought of her parents. C. Having a party; because she wanted to look at the lights. 16. What can we learn from the woman? A. She worked hard and was successful. B. She lived a poor life in the past. C. Both A and B. 听第10段材料，回答第17至20题17. Why will strange things happen to time when you travel? A. Because of time zone, a day has always less than twenty-four hours. B. Because of time zone, a day has always more than twenty- four hours. C. Because of time zone, a day is longer or shorter than twenty- four hours. 18. Which of the following statements is TRUE? A. If we travel around the world, we will get into trouble in telling the time. B. If we travel west across the Atlantic Ocean, we will have twenty-three hours a day. C. If we travel by ship across the Atlantic Ocean, we will cross the international date line. 19. What’s the time difference between two time zones?A. Seven days.B. Twenty-four hoursC. One hour 20. Where can you find the international date line?A. In the Pacific OceanB. In the Atlantic OceanC. Both are OK 第二部分 英语知识运用(共两节满分5分)习网第一节：语法和词汇知识(共15小题；每小题1分，满分15分)习网从A、B、C、D四个选项中，选出可以填入空白处的最佳选项ince we have entered____ industrial age, our economic development model has to keep pace with____ times.A. a; aB. the; theC. a; theD. the; / 22. Helpless and unable to care for himself, he had no ______ except for nursing home care.A. alternativeB. assumptionC. approvalD. allowance 23. ---Why ? Can’t you just post your letter into any post box on the street? --- _______, I need to pay my telephone bill and the post office ________ in 10 minutes.A. Yes, is to closeB. No, closesC. Yes, will closeD. No, has closed 24. I’m most awfully grateful to you. I can’t think what I ________ without you.A. could doB. would doC. should have doneD. must have done 25. So far, more than 1300 hotels in Europe, Africa, Middle East region have committed to _________ in the event, with many more ________ to join the effort.A. participating; expectingB. participate; to expectC. participating; expectedD. participate; to be expected 26. Yidixiang, which ________ means one-drop fragrance, aroused public concern after media reported that it was used by many restaurants and was harmful to health.A. appropriatelyB. rigidlyC. originallyD. literally 27. Within even the weakest of human bodies lies a life that is precious indeed--- ____ needs to be respected and honored.A. something thatB. oneC. one thatD. something 28. Not even when _____through the darkest valley ____be afraid, for you are close beside me.A. do I walk; will IB. do I walk; I willC. I walk ; I willD. I walk; will I 29. No one came to purchase any of the meat products this morning and sales ________ sharply during the past few days.A. fellB. fallC. have fallenD. had fallen 30. ________ I put on, I’m never dressed properly for the day. I believe that’s the reason I’m often sick.A. HoweverB. WhateverC. WhicheverD. Whenever 31. There was a code on the card __________ school students could log on to the website and receive online education.A. on whichB. whichC. of whichD. through which 32. Since then, central and local governments have been called on to help migrant workers to settle down in cities where they will be _________ to social welfare and other benefits.A. entitledB. lostC. transferredD. opposed 33. The program, I think, should teach people _______ the threat can be dealt with, and _____ blind fear can be challenged and got over.A. how, thatB. how, howC. what, what,D. what, how 34. By working together, each of us can make a positive impact in this fight against climate change, ____ our future and that of future generations.A. protectingB. having protectedC. to protectD. protect 35. --- I’m afraid the company will not hire me. --- Come on, Bill, relax! You have a lot of experience and fine references and your college work is ideal background for them. ______________A. It'll be no sweat.B. All good things come to an end.C. Words pay no debts.D. Don't give me any jaw. 第二节 完型填空(共20小题：每题1分，满分20分) 阅读下面短文，掌握其大意，然后从36--55各题所给的四个选项(A、B、C和D)中，选出最佳选项，并在答题卡上将该项涂黑。

M:Yes,certainly,well,we're a sort of social club for people from different countries.It'squite a new club-we have about 50 members at the moment,but we're growing allthe time.
Overall,cloud tourism will work wonders,making us free on the move on cloud nine.
听力材料录音稿：
注意：回答听力部分时，请先将答案标在试卷上。听力部分结束前，你将有两分钟的时间将你的答案转涂到客观题答题卡上。
停顿00'5”
（反对）I am against it.First,it costs us the real joy we would otherwise get fromreal-life travelling,of which the value lies not in the places we will reach,but the wondersand diversities nature and our life can offer on the way.Pictures shared or stored on thecloud can never match the picturesque memories imprinted under the cloud.Second,beit personal or rational,it will no doubt cloud the travel where family and friends aresupposed to gather together.Buried in your desired places online,you happen to findyour beloved ones on cloud nine doing the same thing as yours.No more sweet blamesabout irrational choices of routes or collective decisions.No more.

海安中学，南外，金陵中学三校联考四模2016.5单项选择21. Her husband went so wild that he was so desperate to know why he had been kept ______ estate sales up to now.A. in defense ofB. in ignorance ofC. in possession ofD. in recognition22. Do not make complaints about being left out______ you shy away from sharing your joys and sorrows with others.A. whenB. unlessC. onceD. until23. ---Andy, how do you find your present occupation?--- Just so-so. I’ve decided to resign my job July, by when I ______ for five years.A. have workedB. will be workingC. workedD. will have worked24. Step on it, or you won’t complete the graduation essay in time. If you take the term ―step on it‖_______, it will bring disastrous consequences.A. alternativelyB. seriouslyC. literallyD. sensitively25.---How shall we go to Pudong International Airport?---By subway! Trying to call a taxi in such rush hours______ spell a frustration.A. shouldB. willC. canD. has to26. Following the hot ―A4 Waist‖trend, _______ Chinese women posted their photos to prove they were as skinny as an A4 sheet of paper, the ―iPhone 6 Legs ‖ have taken the Chinese Internet by storm now.A. thatB. whichC. whereD. what27. A great collection left in private hands was the subject of crazy bidding at Southby’s in Hong Kong on Wednesday, which_______HK$502 million, well over twice the top estimate.A. fetchedB. chargedC. affordedD. valued28. Such a passionate speech______ at the school opening ceremony that we each were deeply moved and strongly inspired.A. did we makeB. madeC. had he madeD. he had made29. ---It seems that people are becoming more and more selfish.--- How much happier life would be if we _______ to the values of past!A. would returnB. had returnC. returnD. were to return30. What matters most is not to_______ more products but to polish up the quality and reduce the cost.A. make outB. turn outC. take outD. give out31. ―Wallet threat‖ is the_______ act of pulling one’s wallet out as a sign of willingness to pay for a meal that assumed to be a treat.A. reluctantB. initialC. aggressiveD. appealing32. _______ from the Song Dynasty, the Confucian Temple of Nanjing has now developed into a famous scenic spot, _______sightseeing, shopping and tasty foods.A. Having dated; featuredB. Dating; featuringC. Dating; having featuredD. Dated; featuring33. Getting your _______in order is a good way not to waste energy on meaningless matters.A. potentialsB. privilegesC. prejudicesD. priorities34. Tony always works out development schemes faster than others. Is it_______ he graduated from a top university_______ counts?A. because; thatB. that; whichC. that; thatD. why; what35.--- The car crash hasn’t brought any traffic inconvenience, has it?--- Yes. The road_______ with several miles of vehicles within a few minutes.A. has been blockedB. was blockedC. had been blockedD. is blocked第二节：完形填空For the past 2 years, I’ve had the privilege of traveling to various countries in Asia, specifically Indonesia and China. These trips weren’t the 36 vacations that last for roughly two weeks and 37 hurrying from one destination to the next. 38 , I was completely absorbed in the culture, staying in both Indonesia and China for approximately 6 weeks.After two continuous years of 39 to the Asian countries, however, I’m staying at home.My desire to travel, 40 , makes me incredibly impulsive（冲动的）. One day, I was watching my old friend Andrew Zimmern travel to Cambodia. I watched him taste the special foods and 41 down a massive man-made lake, staying with locals trying to find dinner. The 42 the show ended, I ran upstairs to my computer and looked up plane tickets to Phnom Penh（金边）. It’s43 , I know.I apologize for this sob story that’s been a good portion of my article. Let me try to 44things around.Though I’m upset about not being able to travel for the summer, staying in place does have its 45 . I graduated from high school just recently. As I walked across the stage, reaching out for my high school principal’s hand with my right and taking my 46 with my left, I graduated. As I walked across the stage, suddenly I realized I had just completed one of the most important 47 in my life. I was soon entering the real world, but I had one last summer that see-sawed in between the real world and the world my 48 and I had just left. I had one last summer to make memories with high school friends that I 49 recall during old age.50 , I am pleased to say I have found a job this summer. I work at the Seneca Hill Animal Hospital and Resort where I look after dogs whose owners have left for summer vacation. The work may be hard, but at least I’m 51 .All in all, life at home so far has not been all that 52 . I’m spending time with old friends, and earning for myself. Although I would have wanted to spend the summer in a magical land with 53 foods, languages, and people, I have to realize that life is what you 54 of it. That’s why I’m going to make my time at home the best 55 I’ve ever had.36. A. original B. critical C. typical D. magical37. A. consist of B. account for C. amount to D. make up38. A. Otherwise B. Thus C. Indeed D. Rather39. A. returning B. escaping C. attending D. catering40. A. in contrast B. in fact C. in consequence D. in all41. A. fly B. flee C. flow D. float42. A. way B. day C. second D. fact43. A. pitiful B. sympathetic C. enthusiastic D. imaginative44. A. hang B. turn C. move D. get45. A. rights B. limits C. downs D. ups46. A. diploma B. license C. prize D. scholarship47. A. memories B. achievements C. stages D. homework48. A. teachers B. parents C. associates D. peers49. A. would B. ought to C. must D. shall50. A. Surprisingly B. Particularly C. Additionally D. Temporarily51. A. compensated B. comforted C. occupied D. depressed52. A. colorful B. complicated C. interesting D. difficult53. A. familiar B. foreign C. fancy D. fashionable54. A. think B. love C. make D. take55. A. experience B. vacation C. job D. trip第三部分阅读理解(共15小题；每小题2分，满分30分)A56. Which buttons directly control the movement of the Rocket Ball?A. LAUNCH and FLIPPERSB. STAR and FLIPPERSC. START/PAUSE and FLIPPERSD. LAUNCH and SELECT57. The most action-packed variation would be__________.A. Game One with a blue starB. Game Two with a black starC. Game One with a yellow starD. Game Two with a red star58. Rocket Ball could best be described as a game of__________.A. space voyageB. quick responseC. skills & strengthD. scientific knowledgeBThe Harry Potter author JK Rowling has shared some rejection letters publishers sent to her alter ego Robert Galbraith, in an effort to comfort aspiring authors.Rowling posted the letters on Twitter after a request from a fan. They related to The Cuckoo’s Calling, her first novel as Galbraith. But Rowling also saw Harry Potter turned down several times before the boy wizard became one of the greatest phenomena in children’s literature, with sales of more than 400m copies worldwide.Asked how she kept moti vated, she tweeted: ―I had nothing to lose and sometimes that makes you brave enough to try.‖ When she pitched under the name Galbraith without revealing her true identity, she faced many more snubs. Since then, Galbraith has published three successful novels but the first was rejected by several publishers, and Rowling was even advised to take a writingcourse.Rowling erased the signatures when she posted the letters online, saying her motive was ―inspiration not revenge‖. She did not reveal the full text of the most brutal brush-off, which came by email from one of the publishers who had also rejected Harry Potter.Rowling said she could not share the Potter rejections because they ―are now in a box in my attic‖ before offering the Galbraith letters. The kindest and most detailed rejection came from Constable & Robinson, who – despite the advice about a writing course – included helpful tips on how to pitch to a publisher (―as on book jackets –don’t give away the ending!‖). The publisher added: ―I regret that we have reluctantly come to the conclusion that we could not publish it without commercial success.‖ The short note from publishers Crème de la Crime said the firm had become part of another publishing group and was not accepting new submissions.When The Cuckoo’s Calling eventually found a publisher in 2013, it was achieving respectable sales before the secret of its authorship broke, and it then shot to the top of the bestseller lists. Joanne Harris, author of a string of hit novels, joined the Twitter discussion to say she had so many rejections for her 1999 book Chocolat, later adapted as a Hollywood movie, that she had piled them up and ―made a sculpture‖.Rowling, Harris and their literary disciples are in excellent company. Eimear McBride, the 2014 Bailey’s prizewinner for her first novel A Girl is a Half-formed Thing, accumulated a drawer full of rejection letters before a chance conversation led to her book being published by Galley Beggar,a tiny independent publisher in Norwich.59. Which of the following is the name of a prize for fiction?A. Robert Galbraith.B. Chocolat.C. Bailey’sD. Crème de la Crime60. JK Rowling’s novels were rejected for the following reasons EXCEPT that _________.A. the writer needs to learn some techniques about how to writeB. books are meant to be published for bringing in moneyC. the publisher for the time being denies new submissionsD. those that can be adapted for movies are worth considering61. Why did JK Rowling post some rejection letters on the Twitter?A. To inform readers that hardships make a man stronger.B. To inspire ambitious writers never to give up halfway.C. To take her revenge on those publishers who ever rejected her.D. To carry out an academic discussion with other fellow writers.CTwo things that Starbucks has discovered about mothers: first, our bodies are 90 per cent made up of milky coffee, which requires constant refilling; and second, we very much want to be wanted. Hence, its new ―parent-friendly‖ pledge.With the help of the National Childbirth Trust, baristas at more than 800 Starbuck outlets around Britain are being trained in how to handle tired and emotional parents. Breastfeeding will be encouraged; bottles will be warmed on request; high chairs and changing tables will be supplied in abundance; there will even be emergency nappies on hand, for when your baby’s having one of those hundred-poo days and you only packed supplies for 99. ―It’s important that parents feel reassured they have the support of staff and won’t be judged,‖ says an NCT spokeswoman.In return for these efforts, Starbucks branches will be able to display a special NCT window sticker bearing the logo: ―Parent Friendly Place.‖ This has t he double advantage of implying that other cafes, lacking the official sticker, might be Parent Unfriendly, or at least a little Parent Standoffish. And indeed, some are. Who can blame them? Where there are parents, there are children – crying, running about, pouring out salt into little mounds, sucking their fingers and then sticking them in the sugar bowl.On the other hand, there’s always money to be made from society’s desperate. Catering to parents, literally or figuratively, makes sense for those businesses already paying rents on the high street. It brings in customers all through the day, instead of just at lunch and supper. Cinemas have cottoned onto this too: the big chains have all introduced daytime ―parent and baby‖ screenings, where you and your screaming bundle of reflux can pretend to watch a whole grown-up film and no one is allowed to tut.Even the swankiest restaurants are getting in on the act. The Michelin-starred Pollen Street Social in London, and the equally feted Delaware and Hudson in New York, have both hosted ―dining clubs for mothers‖. You take your child along with you to eat posh food from posh plates, and pretend the last two years of living off cold fish fingers and squirts of Ella’s Kitchen straight from the sachet were just a bad dream.There is, I can’t help feeling, something slightly depressed about all this. Why are we so reluctantto give up our old habits? Is it because so many of us come to motherhood late, by which time our habits have come to define us? I remember, soon after having my first child, fretting that I had ―lost myself‖, as if I’d left my ID somewhere along with my car keys. I tried all sorts of things to recover it: spa weekends with girlfriends, date nights with the husband, writing book proposals in a vain attempt to restart my ambition.But, after eight years and two more children, I have come to realise –you can’t ever get your old life back. It’s no use looking for it in restaurants and cinemas and down the back of the sofa. That person – the one who could leave the house without having to hire someone to take her place, and gossip at leisure without being tugged at on all sides by tiny, insistent hands, like a bosomy, Breton-striped Gulliver –is no more. And the strangest thing is, you don’t even mi ss her.62. How do you understand the sentence ―We very much want to be wanted" in the first paragraph?A.Mothers want society to be considerate of the uniqueness of their identity.B.Mothers hope to get rid of traditional roles and go to work.C.Mothers expect their kids to think of them frequently when they grow up.D.Mothers desire to have the same social position as men.63. Which of the following measures is used to attract mothers to restaurants?A.Some businesses pay rents on the high street.B.Free spa weekends and date nights are provided for them.C.They can enjoy cold fish fingers and squirts of Ella’s kitchen in restaurants.D.Dining clubs are hosted and nappies are even supplied on request.64. Which of the following has the closest meaning to the underlined phrase ―getting in on the act‖?A. responding accordinglyB. joining the lineup of businessC. taking the critical attitudeD. preventing the act happening65. Which is the best title for the passage?A. Mother’s New Appeal: Cozier LifeB. A Study on Mothers’ Likings and DislikingsC. Easy Money from New ParentsD. On Restaurants’ Marketing StrategiesDIn the film The Revenant the Leonardo DiCaprio adventuretakes the basic facts of real-life frontiersman Hugh Glass'ssufferings and adds extra characters, extra ultra violence andmore horse guts.Hugh Glass was a frontiersman working in the upper Missouririver area in the early years of the 19th century. On a fur trapping expedition in 1823, he was attacked and injured by a grizzly bear.1. _____________Hugh Glass (Leonardo DiCaprio) is one of a group of men finishing up a fur trapping expedition in the wilderness. They are attacked by Ree (Arikara) warriors. Whoosh！Someone gets impaled on a spear. Bang！Someone gets shot off his horse. Crack！Someone's bones shatter. There's a fearless close-up of an arrow thwacking into a face, a gun butt bashing into a face, a flying kick to a face. A horse gets shot in the face. It's exceptionally well choreographed (取景) and filmed. This scene is based on a real-life incident: In June 1823, Ashley's band of around 70 men was attacked by Arikara warriors –they estimated around 600, though in the film it's more like a dozen.2. CharactersIn the film, 10 men get away. Fitzgerald is fighty and racist, so he's the bad guy. Glass is the good guy, because he loves his son (who is half-Pawnee) in a gruff, manly way that involves telling him off a lot. The back story abo ut Glass’s love for a Pawnee woman is fiction. It has been suggested the real Glass had such a relationship, but there's no firm evidence –and no evidence that he had any children.3. WildlifeAs the men make their way through a forest, Glass happens upon two bear cubs and their angry mama. If you felt pale after the face-smashing scene at the start, reach for the smelling salts. Chomp！Growl！Shake！The bear sniffs him to see if he's dead, then jumps up and down on his back. Splinter！Howl！Slash！Glass shoots the bear. Anyway, while historians are not certain of the precise details, the real Glass did get into a fight with a real bear, sometime in August 1823. 4. MurderThe men find Glass in a rum old state. Captain Henry pays Fitzgerald, Bridger and Hawk to staybehind until it is time for Glass's inevitable burial. When the captain leaves, Fitzgerald tries to bump Glass off. Hawk interrupts, so Fitzgerald bumps him off instead. This didn't happen in real life, because Hawk didn't exist. In the film, the weak Glass sees Fitzgerald kill his son, giving him an extra motivation to stay alive and seek revenge.5. SurvivalThe real Glass survived his abandonment and dragged his battered body over hundreds of miles of terrain in pursuit of the men who left him for dead. Though he could read and write, Glass never set his story down in his own hand. It was first published by another writer in a Philadelphia journal in 1825. It may well have been modified then. It has been modified many times since.6. HardshipThe film has invented some extra obstacles for Glass: it is snowing throughout, even though in real life his trek took place between August and October; the Arikara track him and chase him into a tree; he has to hollow out a dead horse to make himself a sleeping bag. As for the ending, it has been changed in one significant way: in real life, nobody got killed.66. We can know for sure after reading the passage that real Hugh Glass _____.A. finally survived for he was determined to take revenge on Fitzgerald killing HawkB. fell in love with a Pawnee woman and soon after they had a clever and brave boyC. wrote nothing about his suffering despite the fact that he was actually educatedD. nearly got killed by Fitzgerald and Hawk under the instruction of Captain Henry67. To play the role of Hugh Glass, Leonardo DiCaprio must have ______.A. fought against three bears courageouslyB. walked in snow with great difficultyC. rode a horse time and time againD. grasped skills for surviving in the wild68. Which of the following can be the best subtitle for the 4th and 5th paragraphs?A. ViolenceB. SettingC. HorrorD. Special effects69. We can see here and there in the passage that the writer thinks of the movie as a _____ adaptation.A. faithfulB. disappointingC. successfulD. heartless70. The passage is intended to inform readers _____.A. how tragic Hugh Glass's experience isB. how well Leonardo DiCaprio performs in The RevenantC. how bloody the movie The Revenant isD. how historically accurate The Revenant is第四部分任务型阅读(共10小题，每小题1分，满分10分)请认真阅读下列短文，并根据所读内容在文章后表格中的空格里填入一个最恰当的单词。

2011年南外、金中、海中三校联考英语2011.05本试卷分第一卷（选择题）和第二卷（非选择题）两部分。

共120分。

考试用时120分钟。

注意事项：答题前，考生务必将自己的姓名、班级、学号写在答卷纸的密封线内。

选择题答案按要求填涂在答题卡上；非选择题的答案写在答卷纸上对应题目的答案空格内，答案不写在试卷上。

考试结束后，将答题卡、答卷纸一并交回。

第一卷（选择题，共85分）第一部分听力理解(共两小节，满分20分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题；每小题1分，满分5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例: How much is the shirt?A. ￡19.15.B. ￡9.15.C. ￡9.18.答案是B。

1.What are they probably talking about?A. An apartment.B. A park.C. Food.2.What is the woman doing?A. Asking for directions.B. Giving directions.C. Shopping.3.What can we know about Jeffrey?A.He is a trouble maker.B. He is talkative.C. He is strict.4.What is the probable relationship between the two?A. Manager and secretary.B. Teacher and student.C. Doctor and patient.5.How would the man describe himself now?A. Fat.B. Slim.C. Wonderful.第二节(共15小题；每小题1分，满分15分)听下面5段对话或独白。

江苏省海安高级中学高三年级第三次统测试题预览江苏省海安高级中学高三年级第三次统测第I卷（共85分）第一部分：听力（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1．What do we know about the woman?A．She took the job．B．She refused the job．C．She failed to get the job．2．How did the woman feel about the English programme?A．It’s interesting． B．It’s difficult． C．It’s important．3．Where will the man probably have been at?A．In the front row． B．In the back row． C．In the middle．4．What is the relationship between the two speakers?A．Mother and son．B．Doctor and patient．C．Teacher and student．5．Why will the man go to the airport?A．T o meet a girl from London．B．To catch Flight 587．C．T o see a girl off．第二节（共15小题；每题1分，满分15分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，每小题将给出5秒钟的作答时间。

江苏省海安中学2011届高三二轮复习检测 英语 第I卷 (选择题 三部分 共85分) 第一部分 听共两节，第一节 共5小题；每小题1分，满分5分1. Where is Mr. Black now?A. He’s at the Friendship Hotel.B. He is at lunch.C. He is at another hotel. 2. How much does one chair cost if you buy a pair?A. 35 yuan.B. 40 yuan.C. 70 yuan. 3. Where does the talk probably take place?A. In a library.B. In a restaurant.C. In a hospital. 4. What is the most probable result of the conversation? A. The woman accepts the man’s opinion. B. The woman puts on the hat. C. The woman throws away the hat. 5. When will the headmaster come back?A. 11:45.B. 9:30.C. 12:40. 第二节 (共15小题；每小题1分，满分15分) 5段对话或独白。

每段对话或独白后有几个小题, 从题中所给的A、B、C三个选项中选出最佳选项, 并标在试卷的相应位置。

听每段对话或独白前, 你将有5秒钟的时间阅读各个小题；听完后, 各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

请听第6段材料，回答第6至8题。

6. When will the plane take off A. At 5:00. B. At 4:30. C. At 5:30. 7. Where is Jane going? A. She is going straight to New York. B. She is going straight to Washington. C. She is going to New York then to Washington. 8. What is Jane probably going to do in Washington?A. To go to school.B. To go to work.C. To stay with her sister. 请听第7段材料，回答第9至11题。

金陵中学2011/2012学年第一学期高三年级期中考试英语试题本试卷共120分，考试时间120分钟。

第一部分听力（共两节，满分20分）第一节(共5小题；每小题1分，满分5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试题卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What do the speakers need to buy?A. A fridge.B. A dinner table.C. A few chairs,2. Where are the speakers?A. In a restaurant.B. In a hotel.C. In a school.3. What does the woman mean?A. Cathy will be at the party.B. Cathy won’t be invited.C. Cathy is going to be invited.4. Why does the woman plan to go to town?A. To pay her bills in the bank.B. To read books in a bookstore.C. To get some money from the bank,5. What is the woman trying to do?A. Finish some writing.B. Print a newspaper.C. Find a newspaper.第二节(共15小题；每小题1分，满分15分)请听下面4段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试题卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

江苏省南京市金陵中学、海安高级中学、南京外国语学校2018届高三三校联考语文试题本试卷包含语文I 和语文II（附加题）两部分。

语文I 满分160 分，考试时间150 分钟。

语文II 满分40 分，考试时间30 分钟。

请按照题号将答案填涂或书写在答题纸相对应的答题区域内，将答案直接书写在本试卷上无效。

语文I 试题一、语言文字运用（15 分）1．在下面一段话空缺处依次填入词语，最．恰．当．的一组是（3分）与众多欧西事物的“迁地弗良”不同，文学史这一著述形式进入中国以后，很快便，而今已经变得枝繁叶茂。

欧洲十九世纪兴盛一时的文学史，在十九世纪末遭遇了来自审美主义的；二十世纪中叶，在美国学院占据主流的“新批评”更是公然拒绝文学史；尽管后来随着文学社会学、接受美学、新历史主义等研究路径的展开，文学史一度有复兴之势，但对这一学科进行理论反思的声音，一直。

A．落地生根置疑不绝如缕B．入乡随俗质疑若隐若现C．落地生根质疑不绝如缕D．入乡随俗置疑若隐若现2．下列各句中，没．有．语．病．的一组是（3分）A．为促进广大同学自觉养成文明排队、有序就餐、遵守公共秩序规则，现长期面向全校招募食堂引导志愿者。

B．联合国开发计划署准备设立一个信息共享平台，以便成员单位及时应对并了解在抵抗山区生态灾害时可能遇到的危险。

C．专家表示，我国房地产今后一段时间还将保持稳健发展的势头，仍是国人投资、抵御通胀的主要手段。

D．历史上看，现代西方人是罗马文化与基督教文化的直接后裔，跟古希腊文化是八竿子打不着的，但是他们甘愿宣称自己是希腊文化之子。

3．学校举办对联展览，下面是某学生收集的四副对联，对联与人物对应最．恰．当．的一项是（3分）著作最谨严，岂徒中国小说史；遗言犹沉痛，莫作空头文学家。

狂到世人皆欲杀，醉来天子不能呼。

世事洞明皆儿女情事，人情练达即释道真理。

功名事业清流山，道德文章丰乐亭。

A．老舍李白曹雪芹韩愈B．鲁迅李白曹雪芹欧阳修C．鲁迅柳永庄子欧阳修D．老舍柳永庄子韩愈4．在下面一段文字横线处填入语句，衔接最．恰．当．的一项是（3分）颇有意味的是，。

江苏省南京外国语、金陵中学、海安中学2022届高三下学期考前模拟英语试题（含听力）一、听力选择题1.A．He is in urgent need of a talk.B．He is fully occupied right now.C．He runs a lab in the middle of the city.D．He is doing an experiment at the moment.2. What are the speakers talking about?A．How to get to Manchester.B．Where to eat.C．What to do in Chinatown.3.A．His dream university.B．His interest.C．His memory.D．His past experience.4. Where is the woman eager to go?A．The Nile.B．The Pyramids.C．Egypt.5. Which name did the woman’s husband suggest?A．Amy.B．Louise.C．Elizabeth.二、听力选择题6. 听下面一段较长对话，回答以下小题。

1. What is the woman’s concern about the man?A．His idea of honesty.B．His absence from classes.C．His explanation of basics.2. What does the woman suggest the man do?A．Join a history club.B．Memorize some tricks.C．Read up on some books.3. What’s the probable relationship between the speakers?A．Classmates.B．Mother and son.C．Teacher and student.7. 听下面一段较长对话，回答以下小题。

2016届英语试卷2016.5第一部分听力 (共两节，满分20分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题；每小题1分，满分5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Who is the man looking for?A. Tami.B. Dr. Maxwell.C. Alison Simpson.2. What will the woman probably do?A. Call the airline soon.B. Stay at home for a while.C. Leave for the airport before lunch.3. What does the man think of his current book?A. It’s exciting.B. It’s relaxing.C. It’s long.4. When does the man hope to see the woman?A. This afternoon.B. Tomorrow night.C. Tomorrow afternoon.5. What does the man mean?A. He didn’t put in any sugar.B. He added some natural flavors.C. He also thinks the coffee tastes strange.第二节(共15小题；每小题1分，满分15分)听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

江苏省金陵中学、海安中学、南京外国语学校2024届高三三模数学试题学校:___________姓名：___________班级：___________考号：___________一、单选题1．已知全集U =R ，集合{}{}21,3xM x N x x =≥=≤，则M N ⋂=（ ）A ．](-,3∞B ．[]0,1C ．[]0,3D ．[]1,32．已知复数z 满足()1i 5i z +=+，则复数z 在复平面内所对应的点位于（ ） A ．第一象限B ．第二象限C ．第三象限D ．第四象限3．下列结论中正确是（ ）A ．若直线a ，b 为异面直线，则过直线a 与直线b 平行的平面有无数多个B ．若平面α//平面β，直线m ⊂α，点M ∈β，则过点M 有且只有一条直线与m 平行C ．若直线m 与平面α内无数条直线平行，则直线m 与平面α平行D ．若直线l ⊥平面α，则过直线l 与平面α垂直的平面有且只有一个4．抛物线26y x =上一点M 到其焦点的距离为92，则点M 到坐标原点的距离为（ ）AB ．C ．D ．5．对于函数()y f x =，部分x 与y 的对应关系如下表：数列{}n x 满足12x =，且对任意*n N ∈，点()1,n n x x +都在函数()y f x =的图象上，则1232016x x x x +++⋯+的值为（ ）A ．9400B ．9408C ．9410D ．94146．定义：一对轧辊的减薄率-=输入该对的面带厚度输出该对的面带厚度输入该对的面带厚度.如图所示，为一台擀面机的示意图，擀面机由若干对轧辊组成，面带从一端输入，经过各对轧辊逐步减薄后输出.已知擀面机没对轧辊的减薄率都为0.2（轧面的过程中，面带宽度不变，且不考虑损耗）.有一台擀面机共有10对轧辊，所有轧辊的横截面积均为2640000mm π，若第k 对轧辊有缺陷，每滚动一周在面带上压出一个疵点，在擀面机输出的面带上，疵点的间距为k L ，则（ ）A ．1016000.2mm k k L -=⨯B ．1016000.2mm k k L -=⨯C ．1016000.8mm k k L -=⨯D ．1016000.8mm k k L -=⨯7．已知函数()f x 的大致图象如图所示，则其解析式可能为（ ）A ．2()e e -=+x x f xB ．e e ()2-+=x xf xC ．2()e e-=-x x f xD ．e e ()2--=x xf x8．已知双曲线22136x y -=，O 为坐标原点，P ，Q 为双曲线上两动点，且OP OQ ⊥，则2211||||OP OQ +=（ ） A ．2 B ．1C ．13D ．16二、多选题9．已知平面α的一个法向量为111,2,2n ⎛⎫=-- ⎪⎝⎭u r ，平面β的一个法向量为()21,0,2n =--u u r ，直线l 的方向向量为()1,0,2a =r ，直线m 的方向向量为()0,1,2b =-r，则（ ） A ．//l α B ．αβ⊥C ．l 与m 为相交直线或异面直线D ．a r 在b r 向量上的投影向量为480,,55⎛⎫⎪⎝⎭10．已知函数()π1sin sin 34f x x x ⎛⎫=⋅+- ⎪⎝⎭的定义域为[](),m n m n <，值域为11,24⎡⎤-⎢⎥⎣⎦，则n m-的值不可能是（ ）A ．5π12B ．7π12C ．34π D ．11π1211．钻石是金刚石精加工而成的产品，是世界上最坚硬的、成分最简单的宝石，它是由碳元素组成的、具有立方结构的天然晶体．如图，已知某钻石形状的几何体由上、下两部分组成，上面为一个正六棱台 111111ABCDEF A B C D E F -（上、下底面均为正六边形，侧面为等腰梯形），下面为一个正六棱锥P -ABCDEF ，其中正六棱台的上底面边长为a ，下底面边长为2a ，且P 到平面111A B C 的距离为3a ，则下列说法正确的是（ ）（台体的体积计算公式：(1213V S S h =+，其中1S ，2S 分别为台体的上、下底面面积，h 为台体的高）A ．若平面PAF ⊥平面11AFF A ，则正六棱锥P -ABCDEFB ．若PA =2C ．该几何体存在外接球，且外接球的体积为350081a πD ．若该几何体的上、下两部分体积之比为7：83三、填空题12．已知5723456701234567(1)(1)x x a a x a x a x a x a x a x a x -++=-+-+-+-，则246a a a ++的值为 ．13．已知3,,sin cos 4πθπθθ⎛⎫∈-= ⎪⎝⎭1sin 2cos 2θθ-= ．14．已知()f x 是定义在R 上的函数，1(1)0f =，且对于任意x ∈R 都有(20)()20f x f x +≥+，(1)()1f x f x +≤+，若()()1g x f x x =-+，则(10)g = ．四、解答题15．记n S 是等差数列{}n a 的前n 项和，已知632a S =+，654S a =. (1)求{}n a 的通项公式；(2)设234111111111n n T S S S S +⎛⎫⎛⎫⎛⎫⎛⎫=---⋅⋅- ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭L ，证明：1324nT <≤. 16．佛山顺德双皮奶是一种粤式甜品，上层奶皮甘香，下层奶皮香滑润口，吃起来，香气浓郁，入口嫩滑，让人唇齿留香．双皮奶起源于清朝末期，是用水牛奶做原料，辅以鸡蛋和白糖制成．水牛奶中含有丰富的蛋白质，包括酪蛋白和少量的乳清蛋白，及大量人体生长发育所需的氨基酸和微量元素．不过新鲜的水牛奶保质期较短．某超市为了保证顾客能购买到新鲜的水牛奶又不用过多存货，于是统计了50天销售水牛奶的情况，获得如下数据：假设水牛奶日销售量的分布规律保持不变，将频率视为概率． (1)求接下来三天中至少有2天能卖出3件水牛奶的概率；(2)已知超市存货管理水平的高低会直接影响超市的经营情况．该超市对水牛奶实行如下存货管理制度：当天营业结束后检查存货，若存货少于2件，则通知配送中心立即补货至3件，否则不补货．假设某天开始营业时货架上有3件水牛奶，求第二天营业结束后货架上有1件存货的概率．17．如图，在四棱锥P ABCD -中，底面ABCD 为正方形，PD ⊥底面ABCD ，M 为线段PC 的中点，1PD AD ==，N 为线段BC 上的动点．（1）证明：MD PN ⊥；（2）当N 为线段BC 的中点时，求三棱锥A MND -的体积．18．若函数()3f x ax bx =+，当2x =-时函数()f x 有极值163. (1)求函数()f x 的解析式；(2)求曲线()y f x =过点()3,3P -的切线方程.19．某兴趣小组对小球在坚直平面内的匀速圆周运动进行研究，将圆形轨道装置放在如图1所示的平面直角坐标系中，此装置的圆心O 距离地面高度为2m ，装置上有一小球P （视为质点），P 的初始位置在圆形轨道的最高处，开启装置后小球P 按逆时针匀速旋转，转一周需要6min ．小球P 距离地面的高度H （单位：m ）与时间t （单位：min ）的关系满足()sin (0,0,02π)H r t h r ωϕωϕ=++>>≤<．(1)写出H 关于t 的函数解析式，并求装置启动1min 后小球P 距离地面的高度；(2)如图2，小球Q （视为质点）在半径为1m 的另一圆形轨道装置上，两圆形轨道为同心圆，Q 的初始位置在圆形轨道的最右侧，开启装置后小球Q 以角速度为πrad /min 3顺时针匀速旋转．两装置同时启动，求,P Q 两球高度差的最大值．。

江苏省南京市金陵中学、海安高级中学、南京外国语学校2025届语文高三上期末调研模拟试题注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗．1．阅读下面的文字，完成下面小题。

中华民族的文化博大精深、包罗万象，在上下五千年的历史长河中形成了民族独有的特质。

国宝作为历史文物，承载着民族的记忆与文明，它的诞生与流传皆源于文化血脉的精髓，同时又反哺于发展着的博大文化。

作为一种器物媒介，不仅仅为今天的人们所欣赏和收藏，更是华夏文明的表征。

“历史作为一种记忆，使先民的事迹、经验与思想存活于今，它充当着不同时代的纽带。

”每种文化都会形成一种“凝聚性结构”，历史作为一种“凝聚性结构”，对中华民族的向心力、归属感起着重要的促进作用。

《国家宝藏》以博物馆的文化底蕴为依托，用文物衔接历史与当下，采用舞台剧与小话剧的展演方式，集中展现文明古国文化的博大精深。

故事讲述、舞台演绎与观众互动，环环相扣，层层递进，激活了中华民族的文化记忆。

不同的个人和文化通过语言、图像和重复的仪式等方式进行交际，从而互动地建立起他们的记忆。

个人和文化两者都需要借助外部的存储媒介和文化实践来组织他们的记忆。

用舞台剧演绎国宝的“前世传奇”，让观众有身临其境之感，是《国家宝藏》的节目特色之一。

如在第五期对国宝辛追墓T形帛画的前世传奇的演绎中，雷佳一开嗓，便将辛追所思之人、所念之世深情道来，听者皆入其境。

《帛画魂》是根据T形帛画的内容作的曲，大致分为天国之美、人世之欢、炼狱之苦。

2016年南外、金中、海中三校联考英语试卷参考答案1—5 CBABA6—10 ACABC11—15 ABCCA16—20 BCBCB21—25 BADCC26—30 CAADB31—35 ABDCB36—40 CADBB 41—45 DCABD 46—50 ACDAC 51—55 ADBCB56—58 ADB59—61CDB62—65 ADBC66—70 CBACD71. Procedure(s) / Process / Steps72. Analyzing / Analysing73. exceeds / surpasses/ overtakes74. burying75. opposite / contrary76. control77. Failure / Lack / Absence78. made / accounted79. though / although80. focused81. Possible versions:A father’s concern that smartphone is depriving him of his precious family time does not stand alone. Favorable opinions as there are, the majority of Americans today view technology as hazardous. (31 words)【选“是”】However, no pains, no gains. The world evolves as human technology leaps forward, along whose process there is bound to be sacrifices. The definition of happiness may vary, but a more connected, convenient, and creative society is undeniably nothing a modern man wouldn’t have desired. With digital devices booming around, we are given so many choices that our minds have been freed to a degree our ancestors could never anticipated.That being said, to make sure technology doesn’t get in the way, you need to unplug from the information highway and share your journey with your family and friends from time to time. A balance between man and computers will lead to an ultimate happiness. (115 words)【选“否”】True, a high-tech world seems a new Eden, but it won’t last any longer than the old one. Putting down their phones, lifting up their misty eyes, and waking up at night, people suddenly realize that, with all their family living by, they are alone. Children forgot how and why they should return their parents’ love because it were never given; classic literature is left rotten on the shelves because no one bothers to look away from their screen.To stop yourself getting “high” instead of “happy”, read a book, go outdoors, or simply pay a visit to your parents. There are things to pursue in life other than thumbing up tweets. Enjoy a tech-free day and see what real happiness means. (122 words)听力录音原文：W: Hello, this is Dr. Maxwell’s office. My name is Tami. How may I direct your call?Text 2Text 3Text 4Text 5Text 6Text 7Text 8。

江苏省海安高级中学、南京外国语学校、金陵中学2015届高三第四次模拟考试数学11.已知集合A ={－1，0，2}，B ={x |x ＝2n －1，n ∈Z}，则A ∩B = .2.已知复数z 1=1－2i ，z 2=a ＋2i(其中i 为虚数单位，a ∈R ).若z 1·z 2是纯虚数，则a 的值为 .3.从集合{1，2，3}中随机取一个元素，记为a .从集合{2，3，4}中随机取一个元素，记为b ，则a ≤b 的概率为 .方图，根据产品标准，单件产品长度在区间[25，30)的为一等品，在区间[20，25)和[30,35)的为二等品，其余均为三等品，则样本中三等品的件数为 .5.右图是一个算法的伪代码，其输出的结果为 .6.若函数f (x )=sin(ωx )(0ω>)在区间[0,]3π上单调递增，在区间[,]32ππ上单调递增，则ω的值为 .7.在平面直角坐标系xOy 中，若双曲线C ：22221(0,0)x y a b a b-=>>C的渐近线方程为 .8.已知实数x ，y 满足10,30,330.x y x y x y -+⎧⎪+-⎨⎪--⎩≥≥≤，则当2x －y 取得最小值时，x 2＋y 2的值为 .9.在平面直角坐标系xOy 中，P 是曲线C ：y =e x 上一点，直线l ：x ＋2y ＋c =0经过点P ，且与曲线C 在点P 处的切线垂直，则实数c 的值为 .10.设x >0，y >0，向量a =(1－x ，4)，b =(x ，－y )，若a //b ，则x ＋y 的最小值为 .11.已知f (x )是定义在区间[－1，1]上的奇函数，当x <0时，f (x )=x (x －1).则关于m 的不等式f (1－m )＋f (1－m 2)<0的解集为 .12.设S n 为数列{a n }的前n 项和，若S n =na n －3n (n －1)(n ∈N*)且a 2=11，则S 20= .13.在△ABC 中，已知sin A =13sin B sin C ，cos A =13cos B cos C ，则tan A ＋tan B ＋tan C 的值为 . 14.在平面直角坐标系xOy 中，设A ，B 为函数f (x )=1－x 2的图象与x 轴的两个交点，C ，D 为函数f (x )的图象上的两个动点，且C ，D 在x 轴上方(不含x 轴)，则AC BD ⋅的取值范围为 .15.△ABC中，a，b，c分别为角A，B，C所对边的长.若a cos B=1，b sin A，且A－B＝4．(1)求a的值；(2)求tan A的值.16.如图，在四面体ABCD中，AD=BD，∠ABC=90°，点E、F分别为棱AB、AC上的点，点G 为棱AD的中点，且平面EFG//平面BCD.求证：(1)EF=12BC；(2)平面EFD⊥平面ABC.ABCDGEF17.某企业拟生产一种如图所示的圆柱形易拉罐(上下底面及侧面的厚度不计)，易拉罐的体积为108π mL，设圆柱的高度为h cm，底面半径为r cm，且h≥4r，假设该易拉罐的制造费用仅与前表面积相关.已知易拉罐的侧面制造费为m元/cm2，易拉罐上下底面的制造费用为n元/cm2 (m，n 为常数).(1)写出易拉罐的制造费用y(元)关于r(cm)的函数表达式，请求求定义域；(2)求易拉罐制造费最低时r(cm)的值.18.在平面直角坐标系xOy中，设椭圆C：22221(0)x ya ba b+=>>的左焦点为F，左准线为l，P为椭圆上任意一点，直线OQ⊥FP，垂足为Q，直线OQ与l交于点A.(1)若b=1，且b<c，直线l的方程为x=－52．①求椭圆C的方程；②是否存有点P，使得110FPFQ=？若存有，求出点P的坐标；若不存有，说明理由；(2)设直线FP圆O：x2＋y2=a2交于M、N两点，求证：直线AM，AN均与圆O相切.19.设函数f(x)=(x－a)ln x－x＋a，a∈R.(1)若a=0，求函数f(x)的单调区间；(2)若a<0，试判断函数f(x)在区间(e－2，e2)内的极值点的个数，并说明理由；(3)求证：对任意的正数a，都存有实数t，满足：对任意的x∈(t,t＋a)，f(x)<a－1.20.定义：从一个数列{a n}中抽取若干项(很多于三项)按其在{a n}中的次序排列的一列数叫做{a n}的子数列，成等差(比)的子数列叫做{a n}的等差(比)子列.(1)求数列11111,,,,2345的等比子列；(2)设数列{a n}是各项均为实数的等比数列，且公比q≠1.①试给出一个{a n}，使其存有无穷项的等差子列(不必写出过程)；②若{a n}存有无穷项的等差子列，求q的所有可能值.江苏省海安高级中学、南京外国语学校、金陵中学2015届高三第四次模拟考试数学221B.在平面直角坐标系xOy 中，先对曲线C 作矩阵A =cos sin (02)sin cos θθθπθθ-⎡⎤<<⎢⎥⎣⎦所对应的变换，再将所的曲线矩阵B =10(01)0k k ⎡⎤<<⎢⎥⎣⎦所对的变换，若连续实施两次变换所对应的矩阵为01102-⎡⎤⎢⎥⎢⎥⎣⎦，求k ，θ的值.21C.在极坐标系中，已知A (1,)3π，B (9,)3π，线段AB 的垂直平分线l 与极轴交于点C ，求l 的极坐标方程及△ABC 的面积.22.如图，在四棱锥P —ABCD 中，已知棱AB ，AD ，AP 两两垂直，长度分别为1，2，2.若DC AB λ=(λ∈R )，且向量PC 与BD夹角的余弦值为15. (1)求λ的值；(2)求直线PB 与平面PCD 所成角的正弦值.23.设数列{a n }的通项公式]n n n a =-，n ∈N*，记S n =11n C a ＋22n C a ＋…＋nn n C a ．(1)求S 1，S 2的值；(2)求所有正整数n ，使得S n 能被8整除.BPDCA数学参考答案及评分标准 2015.05说明：1．本解答给出的解法供参考．如果考生的解法与本解答不同，可根据试题的主要考查内容比照评分标准制订相对应的评分细则．2．对计算题，当考生的解答在某一步出现错误时，如果后续部分的解答未改变该题的内容和难度，可视影响的水准决定给分，但不得超过该部分准确解答应得分数的一半；如果后续部分的解答有较严重的错误，就不再给分．3．解答右端所注分数，表示考生准确做到这个步应得的累加分数． 4．只给整数分数，填空题不给中间分数．一、填空题：本大题共14小题，每小题5分，共70分．1．{－1} 2．－4 3．89 4．100 5．10116．32 7．y ＝±3x 8．5 9．－4－ln2 10．9 11．[0，1) 12．1240 13．196 14．(－4，332－94]【解析】： 1．答案：{－1}．2．因为z 1·z 2＝(1－2i)(a ＋2i)＝a ＋4＋(2－2a )i ，所以a ＋4＝0，a ＝－4．3．a ＞b 的取法只有一种：a ＝3，b ＝2，所以a ＞b 的概率是19，a ≤b 的概率是1－19＝89．4．根据频率分布直方图可知，三等品的数量是[(0.0125＋0.025＋0.0125)×5]×400＝100(件)． 5．S ＝0＋11×2＋12×3＋…＋110×11＝(1－12)＋(12－13)6．由已知条件得f (x )＝sin(ωx )的周期T 为4π3，所以7．因为(c a )2＝1＋(b a )2＝10，所以ba ＝38．令z ＝2x －y ，如图，则当直线z ＝2x －y x ＋y －3＝0的交点A 时，z 取得最小值．此时x 2＋y 2＝5．9．由题意y'＝e x ，所求切线的斜率为2，设切点为以x 0＝ln2，y 0＝e ln2＝2．所以直线x ＋2y ＋c ＝010．因为a ∥b ，所以4x ＋(1－x )y ＝0，又x ＞0，y ＞0，所以1x ＋4y ＝1，故x ＋y ＝(1x ＋4y )(x ＋y )＝5＋y x ＋4xy≥9． 当y x ＝4x y ，1x ＋4y＝1同时成立，即x ＝3，y ＝6时，等号成立．(x ＋y )min ＝9． 11．由题意，奇函数f (x )是定义在[－1，1]上的减函数，不等式f (1－m )＋f (1－m 2)＜0，即f (1－m )＜f (m 2－1)，所以⎩⎪⎨⎪⎧－1≤1－m ≤1，－1≤1－m 2≤1，1－m ＞m 2－1，解得m ∈[0，1)．12．由S 2＝a 1＋a 2＝2a 2－3×2(2－1)和a 2＝11，可得a 1＝5．解法1：当n ≥2时，由a n ＝S n －S n －1，得a n ＝na n －3n (n －1)－[(n －1)a n －1－3(n －1)(n －2)]，所以(n －1)a n －(n －1)a n －1＝6(n －1)，即a n －a n －1＝6(n ≥2，n ∈N *)，所以数列{a n }是首项a 1＝5，公差为6的等差数列，所以S 20＝20×5＋20×192×6＝1240．解法2：当n ≥2时，由S n ＝na n －3n (n －1)＝n (S n －S n －1)－3n (n －1)，可得(n －1)S n －nS n －1＝3n (n －1)，所以S n n －S n －1n －1＝3，所以数列{S n n }是首项S 11＝5,公差为3的等差数列，所以S 2020＝5＋3×19＝62，即S 20＝1240．13．由题意cos A ，cos B ，cos C 均不为0，由sin A ＝13sin B sin C ，cos A ＝13cos B cos C ，两式相减得tan A＝tan B tan C ，又由cos A ＝13cos B cos C ，且cos A ＝－cos(B ＋C )＝sin A sin B －cos A cos B ，所以sin A sin B ＝14cos A cos B ，所以tan B tan C ＝14．又tan B ＋tan C ＝tan(B ＋C )(1－tan B tan C )＝－tan A (1－tan B tan C )，所以tan A ＋tan B ＋tan C ＝tan A tan B tan C ＝196．14．由题意A (－1，0)，B (1，0)，设C (x 1，1－x 12)，D (x 1，1－x 12)，－1＜x 1，x 2＜1，则AC →·BD →＝(x 1＋1)(x 2－1)＋(1－x 12)(1－x 22)＝(x 2－1)[(x 2＋1)x 12＋x 1－x 2]．记f (x )＝(x 2＋1)x 2＋x －x 2，－1＜x ＜1．（1）当－1＜x 2≤－12时，则0＜2(x 2＋1)≤1，－12(x 2＋1)≤－1，又x 2＋1＞0，所以f (x )在(－1，1)上单调递增，因为f (－1)＝0，f (1)＝2，所以0＜f (x )＜2．又x 2－1＜0，所以2(x 2－1)＜AC →·BD→＜0．根据－1＜x 2≤－12，则－4＜AC →·BD →＜0．（2）当－12＜x 2＜1时，则1＜2(x 2＋1)＜1，－1＜－12(x 2＋1)＜－14．又x 2＋1＞0，所以f (x )在(－1，1)上先减后增，x ＝－12(x 2＋1)时取的最小值f (－12(x 2＋1))＝－[x 2＋14(x 2＋1)]，又f (1)＝2，所以x 2＋14(x 2＋1)＜f (x )＜2．又x 2－1＜0，所以2(x 2－1)＜AC →·BD →≤[x 2＋14(x 2＋1)](1－x 2)．令g (x )＝x (1－x )＋1－x 4(x ＋1)，则g (x )＝－x 2＋x －14＋12(x ＋1)，g'(x )＝1－2x －12 (x ＋1)2＝－4x 3＋6x 2－12(x ＋1)2＝－(2x ＋1)(x －3－12)(x ＋3＋12)2(x ＋1)2，当－12＜x ＜3－12时，g'(x )＞0；3－12＜x ＜1时g'(x )＜0；所以g (x )在(－12，1)上先增后减，所以g (x )max ≤g (3－12)＝332－94．又2(x 2－1)＞－3，所以－3＜AC →·BD →≤332－94．综上，AC →·BD →的取值范围是(－4，332－94]．二、解答题：本大题共6小题，共90分．15．解：（1）由正弦定理知，b sin A ＝a sin B ＝2，① …………………………………………………… 2分 又a cos B ＝1， ②①，②两式平方相加，得(a sin B )2＋(a cos B )2＝3， ………………………………………… 4分 因为sin 2B ＋cos 2B ＝1，所以a ＝3（负值已舍）；……………………………………………………… 6分（2）①，②两式相除，得sin Bcos B＝2,即tan B ＝2,…………………………………………………8分因为A －B ＝π4，所以tan A ＝tan(B ＋π4)＝tan B ＋tanπ41－tan B tanπ………………………………………………………12分A BCDE FG＝1＋21－2＝－3－22．………………………………………………………14分16．证明：（1）因为平面EFG ∥平面BCD ，平面ABD ∩平面EFG ＝EG ，平面ABD ∩平面BCD ＝BD ，所以EG //BD ， ………………………………… 4分又G 为AD 的中点， 故E 为AB 的中点， 同理可得，F 为AC 的中点，所以EF ＝12BC ．……………………………… 7分（2）因为AD ＝BD ，由（1）知，E 为AB 的中点， 所以AB ⊥DE ，又∠ABC ＝90°，即AB ⊥BC ， 由（1）知，EF //BC ，所以AB ⊥EF ， 又DE ∩EF ＝E ，DE ，EF ⊂平面EFD ，所以AB ⊥平面EFD ， ……………………………………………………………………… 12分 又AB ⊂平面ABC ，故平面EFD ⊥平面ABC ． ……………………………………………………………………14分17．解：（1）由题意，体积V ＝πr 2h ，得h ＝V πr2＝108r 2．y ＝2πrh ×m ＋2πr 2×n ＝2π (108mr ＋nr 2)． ……………………………………………………4分因为h ≥4r ，即108r 2≥4r ，所以r ≤3，即所求函数定义域为(0，3]．…………………6分（2）令f (r )＝108m r ＋nr 2，则f'(r )＝－108mr 2＋2nr ．由f'(r )＝0，解得r ＝332mn．①若32mn ＜1，当n ＞2m 时，332mn∈(0，3]，由得，当r ＝332mn时，f (r )有最小值，此时易拉罐制造费用最低． …………………10分②若32mn≥1，即n ≤2m 时，由f'(r )≤0知f (r )在(0，3]上单调递减， 当r ＝3时，f (r )有最小值，此时易拉罐制造费用最低．……………………………14分18．解：（1）（i ）由题意，b ＝1，a 2c ＝52，又a 2＝b 2＋c 2，所以2c 2－5c ＋2＝0，解得c ＝2，或c ＝12(舍去)．故a 2＝5．所求椭圆的方程为x 25＋y 2＝1．…………………………………………………3分（ii ）设P (m ，n )，则m 25＋n 2＝1，即n 2＝1－m 25．当m ＝－2，或n ＝0时，均不符合题意； 当m ≠－2，n ≠0时，直线FP 的斜率为nm ＋2，直线FP 的方程为y ＝nm ＋2(x ＋2)． 故直线AO 的方程为y ＝－m ＋2n x ，Q 点的纵坐标y Q ＝2n (m ＋2)(m ＋2)2＋n 2．…………………………………………………5分所以FP FQ ＝|ny P |＝|(m ＋2)2＋n 22(m ＋2)|＝|(m ＋2)2＋1－m 252(m ＋2)|＝|4m 2＋20m ＋2510(m ＋2)|．令FP FQ ＝110，得4m 2＋21m ＋27＝0 ①，或4m 2＋19m ＋23＝0 ② ． ………………………7分由4m 2＋21m ＋27＝0，解得m ＝－3，m ＝－94，又－5≤m ≤5，所以方程①无解．由于△＝192－4×4×23＜0，所以方程②无解，故不存在点P 使FP FQ ＝110．………………………………………………………………10分（3）设M (x 0，y 0)，A (－a 2c ，t )，则FM →＝(x 0＋c ，y 0)，OA →＝(－a 2c ，t )．因为OA ⊥FM ，所以FM →·OA →＝0，即(x 0＋c )(－a 2c )＋ty 0＝0，由题意y 0≠0，所以t ＝x 0＋c y 0·a 2c ．所以A (－a 2c ，x 0＋c y 0·a 2c)．……………………………………………………12分因为AM →＝(x 0＋a 2c ，y 0－x 0＋c y 0·a 2c )，OM →＝(x 0，y 0)，所以AM →·OM →＝(x 0＋a 2c )x 0＋(y 0－x 0＋c y 0·a 2c )y＝x 02＋y 02＋a 2c x 0－x 0＋c y 0·a 2c y 0 ＝x 02＋y 02＋a 2c x 0－a 2cx 0－a 2 ＝x 02＋y 02－a 2． 因为M (x 0，y 0)在圆O 上，所以AM →·OM →＝0． ………………………………………………15分 即AM ⊥OM ，所以直线AM 与圆O 相切． 同理可证直线AN 与圆O 相切．……………………………………………………16分19．解：（1）当a ＝0时，f (x )＝x ln x －x ，f’(x )＝ln x ， 令f’(x )＝0，x ＝1，列表分析故f (x )的单调递减区间为(0，1)，单调递增区间为(1，＋∞)． …………………………3分（2）f (x )＝(x －a )ln x －x ＋a ，f ’(x )＝ln x －ax ，其中x ＞0，令g (x )＝x ln x －a ，分析g (x )的零点情况．g ’(x )＝ln x ＋1,令g ’(x )＝0，x ＝1e，列表分析g (x )min ＝g (1e )＝－1e－a ，…………………………5分而f’(1e )＝ln 1e －a e ＝－1－a e ，f’(e －2)＝－2－a e 2＝－(2＋a e 2)，f ’(e 2)＝2－a e 2＝1e2(2e 2－a )，①若a ≤－1e ，则f’(x )＝ln x －ax ≥0，故f (x )在(e －2，e 2)内没有极值点；②若－1e ＜a ＜－2e 2，则f’(1e )＝ln 1e －a e ＜0，f’(e －2)＝－(2＋a e 2)＞0，f’(e 2)＝1e2(2e 2－a )＞0， 因此f’(x )在(e －2，e 2)有两个零点，f (x )在(e －2，e 2)内有两个极值点；③若－2e 2≤a ＜0，则f’(1e )＝ln 1e －a e ＜0，f’(e －2)＝－(2＋a e 2)≤0，f’(e 2)＝1e 2(2e 2－a )＞0，因此f’(x )在(e －2，e 2)有一个零点，f (x )在(e －2，e 2)内有一个极值点； 综上所述，当a ∈(－∞，－1e]时，f (x )在(e －2，e 2)内没有极值点；当a ∈(－1e ，－2e2)时，f (x )在(e －2，e 2)内有两个极值点；当a ∈[－2e2，0)时，f (x )在(e －2，e 2)内有一个极值点.. ………………………10分（3）猜想：x ∈(1，1＋a )，f (x )＜a －1恒成立． ……………………………………………11分 证明如下：由（2）得g (x )在(1e，＋∞)上单调递增，且g (1)＝－a ＜0，g(1＋a )＝(1＋a )ln(1＋a )－a ．因为当x ＞1时，ln x ＞1－1x (*)，所以g(1＋a )＞(1＋a )(1－1a ＋1)－a ＝0．故g (x )在(1，1＋a )上存在唯一的零点，设为x 0．由知，x ∈(1，1＋a )，f (x )＜max{f (1)，f (1＋a )}． …………………………………………13分 又f (1＋a )＝ln(1＋a )－1，而x ＞1时，ln x ＜x －1(**)， 所以f (1＋a )＜(a ＋1)－1－1＝a －1＝f (1)． 即x ∈(1，1＋a )，f (x )＜a －1．所以对任意的正数a ，都存在实数t ＝1，使对任意的x ∈(t ，t ＋a )，使 f (x )＜a －1．……………………………………………15分补充证明（*）：令F (x )＝ln x ＋1x －1，x ≥1．F ’(x )＝1x －1x 2＝x －1x2≥0，所以F (x )在[1，＋∞)上单调递增． 所以x ＞1时，F (x )＞F (1)＝0，即ln x ＞1－1x ．补充证明（**）令G (x )＝ln x －x ＋1，x ≥1．G ’(x )＝1x－1≤0，所以G (x )在[1，＋∞)上单调递减．所以x ＞1时，G (x )＜G (1)＝0，即ln x ＜x －1． ……………………………………………16分20．解：（1）设所求等比子数列含原数列中的连续项的个数为k （1≤k ≤3，k ∈N *），当k ＝2时，①设1n ，1n ＋1，1m 成等比数列，则1(n ＋1)2＝1n ×1m ，即m ＝n ＋1n ＋2，当且仅当n ＝1时，m ∈N *，此时m ＝4，所求等比子数列为1，12，14；②设1m ，1n ，1n ＋1成等比数列，则1n 2＝1n ＋1×1m ，即m ＝n ＋1＋1n ＋1－2 N *；…… 3分当k ＝3时，数列1，12，13；12，13，14；13，14，15均不成等比，当k ＝1时，显然数列1，13，15不成等比；综上，所求等比子数列为1，12，14． ………………………………………………………5分（2）（i ）形如：a 1，－a 1，a 1，－a 1，a 1，－a 1，…（a 1≠0，q ＝－1）均存在无穷项等差子数列： a 1，a 1，a 1，… 或－a 1，－a 1，－a 1， ……………………………………7分（ii ）设{a n k}(k ∈N *，n k ∈N *)为{a n }的等差子数列，公差为d ， 当|q |＞1时，|q |n ＞1，取n k ＞1＋log |q ||d ||a 1|(|q |－1)，从而|q |n k－1＞|d ||a 1|(|q |－1)，故|a n k ＋1－a n k|＝|a 1qn k ＋1－1－a 1qn k －1|＝|a 1||q |n k －1·|qn k ＋1－n k－1|≥|a 1||q |n k －1(|q |－1)＞|d |，这与|a n k ＋1－a n k|＝|d |矛盾，故舍去； ………………………………………………………12分 当|q |＜1时，|q |n ＜1，取n k ＞1＋log |q ||d |2|a 1|，从而|q |n k－1＜|d |2|a 1|， 故|a n k ＋1－a n k|＝|a 1||q |n k －1|qn k ＋1－n k－1|≤|a 1||q |n k －1||q |n k ＋1－n k＋1|＜2|a 1||q |n k －1＜|d |，这与|a n k ＋1－a n k|＝|d |矛盾，故舍去；又q ≠1，故只可能q ＝－1，结合(i)知，q 的所有可能值为－1．……………………………………………………16分数学附加题参考答案及评分标准 2015.0521．【选做题】在A 、B 、C 、D 四小题中只能选做2题，每小题10分，共20分． A ．选修4—1：几何证明选讲解:延长AO ､AD ，分别交圆O 于点E ､F ，连接EF ､BF ． 因为AE 为圆O 的直径，所以∠AFE ＝90°， 又AD ⊥BC ，所以EF //BC ，所以∠CBF ＝∠BFE ， 又∠CBF ＝∠CAF ，∠BAE ＝∠BFE ， 所以∠CAF ＝∠BAE ，∠CAO ＝∠BA D ． 在△ABC 中，AB ＝4，AD ＝2，AD ⊥BC ， 所以∠BAD ＝60°，所以∠CAO ＝60°．……………………………………………… 10分B ．选修4—2：矩阵与变换解：依题意，BA ＝⎣⎡⎦⎤1 00 k ⎣⎡⎦⎤cos θ －sin θsin θ cos θ＝⎣⎢⎢⎡⎦⎥⎥⎤0 －112 0， …………………………………… 5分从而⎩⎪⎨⎪⎧cos θ＝0－sin θ＝－1，k sinθ＝12，k cosθ＝0．因为0＜θ＜2π，所以⎩⎨⎧θ＝π2 ，k ＝12．…………………………………………………… 10分C ．选修4—4：坐标系与参数方程解：易得线段AB 的中点坐标为(5，π3)，……………………………………………………2分设点P (ρ，θ)为直线l 上任意一点，在直角三角形OMP 中，ρcos(θ－π3)＝5，EF所以，l 的极坐标方程为ρcos(θ－π3)＝5， ……………………………………………………6分令θ＝0，得ρ＝10，即C (10，0)．…………………………………………………… 8分所以，△ABC 的面积为：12×(9－1)×10×sin π3＝203． ……………………………………10分D ．选修4—5：不等式选讲 证明：因为|a ＋b |≤2，所以|a 2＋2a －b 2＋2b |＝|a ＋b ||a －b ＋2| ＝|a ＋b ||2a －(a ＋b )＋2| ≤|a ＋b |(|2a |＋|a ＋b |＋2) ≤4(|a |＋2)． ……………………………………10分【必做题】第22题、第23题，每题10分，共20分．22．解：依题意，以A 为坐标原点，AB ，AD ，AP 分别为x ，y ，z 轴建立空间直角坐标系A －xyz （如图），则B (1，0，0)，D (0，2，0)，P (0，0，2)， 因为DC →＝λAB →，所以C (λ，2，0)，……………………………………2分 （1）从而PC →＝(λ，2，－2)，BD →＝(－1，2，0)，则cos ＜PC →，BD →＞＝PC →·BD →|PC →|·|BD →|＝4－λλ2＋8×5＝1515，解得λ＝2；（2）易得PC →＝(2，2，－2)，PD →＝(0，2，－2)， 设平面PCD 的法向量n ＝(x ，y ，z )， 则n ·PC →＝0，且n ·PD →＝0， 即x ＋y －z ＝0，且y －z ＝0， 所以x ＝0，不妨取y ＝z ＝1，则平面PCD 的一个法向量n ＝(0，1，1)， …………………………………… 8分又易得PB →＝(1，0，－2)，（第22题）故cos ＜PB →，n ＞＝PB →·n |PB →|·|n |＝－22×5＝－105，所以直线PB 与平面PCD 所成角的正弦值为105． ……………………………………10分23．解：（1）S 1＝C 11f 1＝1，S 2＝C 12f 1＋C 22f 2＝3．……………………………………2分（2）记α＝1＋52，β＝1－52．则S n ＝15∑n i ＝1C i n (αi －βi )＝15∑n i ＝0C i n (αi －βi)＝15(∑n i ＝0C i n αi －∑n i ＝0C i n βi )＝15[(1＋α)n －(1＋β)n ]＝15[(3＋52)n －(3－52)n]．……………………………………6分注意到(3＋52)×(3－52)＝1．故S n ＋2＝15{[(3＋52)n ＋1－(3－52)n ＋1][ (3＋52)＋(3－52)]－[(3＋52)n －(3－52)n ]}＝3S n ＋1－S n ．因此，S n ＋2除以8的余数完全由S n ＋1，S n 除以8的余数确定．由（1）可以算出{S n }各项除以8的余数依次是1，3，0，5，7，0，1，3，…，这是一个以6为周期的周期数列．从而S n 能被8整除，当且仅当n 能被3整除． (10)。

2011年普通高等学校招生全国统一考试(江苏卷)英语试卷总分120 试卷时间90第一部分：听力（共两节，满分20分）做题时，先将答案标在试卷上，录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题：每小题1分，满分5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A.￡19.15B. ￡.9.15 C . ￡9.18答案是B.1.What does the man like about the play?A.The storyB. The endingC. The actor2.Which place are the speakers trying to find?A. A hotel .B. A bank .C.A restaurant.3.At what time will the two speakers meet?A.5:20 .B.5:10 .C.4:40.4.What will the man do?A.Change the plan.B.Wait for a phone.C.Sort things out.5.What does the woman want to do?A. See a film with the man .B. Offer the man some help.C.Listen to some great music.第二节 (共15小题;每小题1分，满分15分)听下面5段对话。

每段对话后有几个小问题，从题中所给的A、B、C、三个选项中选出最佳选项，并标在试卷的相应位置，听每段对话前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题给出5秒钟的作答时间。