【2013上海徐汇、松江、金山二模】上海市徐汇、松江、金山区2013届高三下学期二模物理试题

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[精品]上海市三区徐汇、松江、金山2013届高三二模化学及答案

2012年第二期徐汇区习能力诊断卷高三年级（满分150分，时间120分钟）20134说明：本卷分试题卷与答题卷两部分，将正确答案写在答题卷上，写在试题卷上一律不给分。

本卷可能用到的相对平均原子质量：H-1 -12 O-16 -355 N-23 -39 M-55 F-56 -64第Ⅰ卷 (共66分)一、选择题（本题共10分，每小题2分，只有一个正确选项）。

1．发生变时，下列所述各项会改变的是①原子的种类，②原子的目，③原子间的排列方式，④分子的种类A．①②③④ B．②③④ ．②④ D．③④2．下列工生产过程中发生的反应不属于氧还原反应的是A．用氯气制漂白粉 B．用石灰石制生石灰．从卤水中提取溴单质 D．用氨气制硝酸3．某些无水试剂可用加入金属钠除去少量水的方法制取，以下不能如此制取的无水试剂是A．苯 B．甲苯．乙醇 D．己烷4．下列有关硝酸盐的说法中正确的是A．都是强氧剂B．受热分解都能生成NO2．都是无色晶体D．溶液都呈中性5．某炔烃经催加氢后可得到2-甲基丁烷，则该炔烃的名称是A．2-甲基-1-丁炔 B．2-甲基-3-丁炔．3-甲基-1-丁炔 D．3-甲基-2-丁炔二．选择题（本题共36分，每小题3分，只有一个正确选项）。

6．利用下列各组物质制备和收集少量相应气体，能采用下图实验装置的是A ．浓氨水与固体OB ．FS 与稀硫酸．稀硝酸与铜片 D ．电石与水7．下列条件变会使H 2O 的电离平衡向电离方向移动，且pH ＜7的是A ．将纯水加热到100℃B ．向水中加少量H ．向水中加少量NOH D ．向水中加少量N 2O 38．下列反应中，调节反应物的用量或浓度以后，不会改变反应产物的是 A ．酒精在氧气中燃烧B ．在硫酸中加入铝粉．将二氧硫气体通入氨水中 D ．在(HO 3)2溶液中加入澄清石灰水 9．下列操作可得到纯净A 2O 3的是A ．向NAO 2溶液中加入适量稀H 2SO 4蒸干并灼烧B ．向NAO 2溶液中通入过量O 2后蒸干并灼烧．向A 3溶液中加入过量氨水后蒸干并灼烧 D ．向A 3溶液中加入适量NAO 2溶液, 蒸干并灼烧 10．已知：CH 3CH 3HH(顺-2-丁烯)H CH 3HCH 3(反-2-丁烯)4.0KJ/mol +。

上海市16区2013届高三数学二模试题分类汇编2 函数及其应用理

上海2013届高三理科最新数学试题精选（13份含16区二模）分类汇编2：函数及其应用一、选择题1 ．（上海徐汇、松江、金山区2013年高考二模理科数学试题）已知函数()1,00,01,0x f x x x >⎧⎪==⎨⎪-<⎩,设2()()F x x f x =⋅,则()F x 是（）A ．奇函数,在(,)-∞+∞上单调递减B ．奇函数,在(,)-∞+∞上单调递增C ．偶函数,在(),0-∞上递减,在()0,+∞上递增D ．偶函数,在(),0-∞上递增,在()0,+∞上递减2 ．（四区（静安杨浦青浦宝山）联考2012学年度第二学期高三（理））已知集合{})(),(x f y y x M ==,若对于任意M y x ∈),(11,存在M y x ∈),(22,使得02121=+y y x x 成立,则称集合M 是“Ω集合”. 给出下列4个集合: ① ⎭⎬⎫⎩⎨⎧==x y y x M 1),( ②{}2),(-==xe y y x M ③{}x y y x M cos ),(== ④ {}x y y x M ln ),(== 其中所有“Ω集合”的序号是（）A ．②③ .B ．③④ .C ．①②④.D ．①③④.3 ．（上海市黄浦区2013年高考二模理科数学试题）函数21()1(2)2f x x x =+<-的反函数是（）A．3)y x =≤< B．3)y x => C．3)y x =≤<D．3)y x =>4 ．（上海市长宁、嘉定区2013年高考二模数学（理）试题）(理)已知0>a 且1≠a ,函数)(log )(2b x x x f a ++=在区间),(+∞-∞上既是奇函数又是增函数,则函数b x x g a -=||log )(的图象是5 ．（上海市八校2013届高三下学期联合调研考试数学（理）试题）受全球金融危机和国家应对金融危机政策的影响,某公司2012年一年内每天的利润()Q t (万元)与时间t (天)的关系如图所示,已知该公司2012年的每天平均利润为35万元,令()C t (万元)表示时间段[0,]t 内该公司的平均利润,用图像描述()C t 与t之间的函数关系中较准确的是6 ．（2013年上海市高三七校联考（理））若()sin f x x =在区间()()a b a b <，上单调递减,则()x a b ∈，时,（）A ．sin 0x <B ．cos 0x <C ．tan 0x <D ．tan 0x >7 ．（2013届浦东二模卷理科题）已知以4为周期的函数(](]⎪⎩⎪⎨⎧∈--∈-=3,1,2cos1,1,1)(2x x x x m x f π,其中0>m .若方程3)(x x f =恰有5个实数解,则m 的取值范围为)(A 8)3 )(B )(C 48,33⎛⎫⎪⎝⎭)(D 4(3.二、填空题8 ．（上海徐汇、松江、金山区2013年高考二模理科数学试题）设函数()f x x x =,将()f x 向左平移a (0)a >个单位得到函数()g x ,将()f x 向上平移a (0)a >个单位得到函数()h x ,若()g x 的图像恒在()h x 的图像的上方,则正数a 的取值范围为_____________.9 ．（上海徐汇、松江、金山区2013年高考二模理科数学试题）若函数()(0,1)x f x a a a =>≠的反函数图像过点(2,1)-,则a =____________.10．（四区（静安杨浦青浦宝山）联考2012学年度第二学期高三（理））已知函数)(x f y =和函数)1(log 2+=x y 的图像关于直线0=-y x 对称,则函数)(x f y =的解析式为_____________.11．（四区（静安杨浦青浦宝山）联考2012学年度第二学期高三（理））若关于y x 、的二元一次方程组⎩⎨⎧=-+-=+-04)12(03y x m y mx 有唯一一组解,则实数m 的取值范围是_____________. 12．（上海市闸北区2013届高三第二学期期中考试数学(理)试卷）某商场在节日期间举行促销活动,规定:(1)若所购商品标价不超过200元,则不给予优惠;(2)若所购商品标价超过200元但不超过500元,则超过200元的部分给予9折优惠; (3)若所购商品标价超过500元,其500元内(含500元)的部分按第(2)条给予优惠,超过500元的部分给予8折优惠.某人来该商场购买一件家用电器共节省330元,则该件家电在商场标价为_____. 13．（上海市闸北区2013届高三第二学期期中考试数学(理)试卷）设)(x f y =为R 上的奇函数,)(x g y =为R 上的偶函数,且)1()(+=x f x g ,2)0(=g .则=)(x f ________.(只需写出一个满足条件的函数解析式即可)14．（上海市十二校2013届高三第二学期联考数学（理）试题）函数xxa y x=(01)a <<的图像的大致形状是 ( )15．（上海市十二校2013届高三第二学期联考数学（理）试题）下列各对函数中表示相同函数的是 ( ) A.①③④ B.④⑤ C.③⑤ D.①④①()f x =2x,g (x )=x ;②()f x =x ,g (x )=xx 2;③()f x =24x -,g (x )=22x x -+④ ()f x =x , g (x )=33x ; ⑤ ()f x =|1|x +,1,1()1,1x x g x x x +≥-⎧=⎨--<-⎩16．（上海市十二校2013届高三第二学期联考数学（理）试题）幂函数αx y =,当α取不同的正数时,在区间[]1,0上它们的图像是一族美丽的曲线(如图).设点)1,0(),0,1(B A ,连接AB,线段AB 恰好被其中的两个幂函数βαx y x y ==,的图像三等分,即有.NA MN BM ==那么,αβ=_________.17．（上海市十二校2013届高三第二学期联考数学（理）试题）已知定义在R 上的奇函数)(x f ,满足(4)()f x f x -=-,且在区间[0,2]上是增函数,若函数()()F x f x m =-(0)m >在区间[]8,8-上有四个不同的零点1234,,,x x x x ,则1234_________.x x x x +++=18．（上海市十二校2013届高三第二学期联考数学（理）试题）设函数21(0)()2(0)x x f x x x ⎧+≥=⎨<⎩,那么1(10)f -=________. 19．（上海市普陀区2013届高三第二学期（二模）质量调研数学（理）试题）若点)2,4(在NMyB A x幂函数)(x f 的图像上,则函数)(x f 的反函数)(1x f -=________.20．（上海市普陀区2013届高三第二学期（二模）质量调研数学（理）试题）函数2log (1)y x =-的定义域为_________.21．（上海市黄浦区2013年高考二模理科数学试题）已知1()4f x x=-,若存在区间1[,](,)3a b ⊆+∞,使得{}(),[,][,]y y f x x a b ma mb =⊆=,则实数m 的取值范围是___________.22．（上海市黄浦区2013年高考二模理科数学试题）设a 为常数,函数2()43f x x x =-+,若()f x a +在[0,)+∞上是增函数,则a 的取值范围是______. 23．（上海市黄浦区2013年高考二模理科数学试题）函数()1lg(42)f x x x =++-的定义域为___________.24．（上海市虹口区2013年高考二模数学（理）试题）已知函数aax x a x a x x f 2222)1()(22-++--+=的定义域是使得解析式有意义的x 的集合,如果对于定义域内的任意实数x ,函数值均为正,则实数a 的取值范围是________________. 25．（上海市虹口区2013年高考二模数学（理）试题）函数1)12()(+-=x k x f 在R 上单调递减,则k 的取值范围是__________. 26．（上海市奉贤区2013年高考二模数学（理）试题）如图放置的等腰直角三角形ABC 薄片(∠ACB =90°,AC =2)沿x 轴滚动,设顶点A (x ,y )的轨迹方程是y =f (x ),当∈x [0,224+]时y =f (x )= _____________27．（上海市奉贤区2013年高考二模数学（理）试题）设()f x 是定义在R 上以2为周期的偶函数,已知(0,1)x ∈,()()12log 1f x x =-,则函数()f x 在(1,2) 上的解析式是____________ 28．（上海市奉贤区2013年高考二模数学（理）试题）若实数t 满足f (t )=-t ,则称t 是函数f (x )的一个次不动点.设函数()x x f ln =与反函数的所有次不动点之和为m ,则m =______29．（上海市奉贤区2013年高考二模数学（理）试题）已知直线y t =与函数()3x f x =及函)14(图数()43x g x =⋅的图像分别相交于A 、B 两点,则A 、B 两点之间的距离为________30．（上海市长宁、嘉定区2013年高考二模数学（理）试题）(理)函数1sin )1()(22+++=x xx x f 的最大值和最小值分别为m M ,,则=+m M ______.31．（上海市长宁、嘉定区2013年高考二模数学（理）试题）(理)设定义域为R 的函数⎪⎩⎪⎨⎧=≠-=)1(1)1(|1|1)(x x x x f ,若关于x 的方程)()(2=++c x bf x f 有三个不同的实数解321,,x x x ,则232221x x x ++=____________. 32．（上海市八校2013届高三下学期联合调研考试数学（理）试题）)(x f 为R 上的偶函数,)(x g 为R上的奇函数且过()3,1-,)1()(-=x f x g ,则=+)2013()2012(f f _______________.33．（上海市八校2013届高三下学期联合调研考试数学（理）试题）已知(1)22x f x +=-,那么1(2)f -的值是_______.34．（上海市八校2013届高三下学期联合调研考试数学（理）试题）函数0.5log y x =的定义域为_________.35．（2013年上海市高三七校联考（理））函数()M f x 的定义域为R ,且定义如下: 1() M x x M f x x M x∈⎧⎪=⎨∉⎪⎩(其中M 是实数集R 的非空真子集),若{||1|2} {|11}A x x B x x =-≤=-≤<，,则函数2()1()()()1A B A B f x F x f x f x +=++的值域为_________.36．（2013年上海市高三七校联考（理））已知1122arcsin ()22x x x xxf x +--++=+的最大值和最小值分别是M 和m ,则M m +=____.37．（2013年上海市高三七校联考（理））若函数()8xf x =的图像经过点1()3a ，,则1(2)f a -+=________.38．（2013届浦东二模卷理科题）如果M 是函数)(x f y =图像上的点,N 是函数)(x g y =图像上的点,且N M ,两点之间的距离MN 能取到最小值d ,那么将d 称为函数)(x f y =与)(x g y =之间的距离.按这个定义,函数x x f =)(和34)(2-+-=x x x g 之间的距离是____________.39．（2013届浦东二模卷理科题）函数x x f 2log 1)(+=与)(x g y =的图像关于直线xy =对称,则=)3(g _______.40．（2013届闵行高三二模模拟试卷（数学）理科）设()f x 是定义在R 上的函数,若81)0(=f ,且对任意的x ∈R,满足(2)()3,(4)()103x x f x f x f x f x +-≤+-≥⨯,则)2014(f =_______________.41．（2013届闵行高三二模模拟试卷（数学）理科）用二分法研究方程3310x x +-=的近似解0x x =,借助计算器经过若干次运算得下表:若精确到0.1,至少运算n 次,则0n x +的值为_________________.三、解答题 42．（上海市普陀区2013届高三第二学期（二模）质量调研数学（理）试题）本大题共有2小题,第1小题满分6分,第2小题满分8分.已知0>a 且1≠a ,函数)1(log )(+=x x f a ,xx g a-=11log )(,记)()(2)(x g x f x F +=(1)求函数)(x F 的定义域D 及其零点;(2)若关于x 的方程0)(=-m x F 在区间)1,0[内仅有一解,求实数m 的取值范围.43．（上海市奉贤区2013年高考二模数学（理）试题）三阶行列式xbx x D 31302502-=,元素b ()R b ∈的代数余子式为()x H ,(){}0≤=x H x P , (1) 求集合P ;(2)函数()()22log 22f x ax x =-+的定义域为,Q 若,P Q ⋂≠∅求实数a 的取值范围; 44．（上海市长宁、嘉定区2013年高考二模数学（理）试题）(本题满分14分,第1小题满分4分,第2小题满分10分)设函数)10()1()(≠>--=-a a a k a x f xx且是定义域为R 的奇函数.(1)求k 的值; (2)(理)若23)1(=f ,且)(2)(22x f m a a xg x x ⋅-+=-在),1[∞+上的最小值为2-,求m 的值. 45．（2013年上海市高三七校联考（理））本题共有3小题,第(1)小题4分,第(2)小题4分,第(3)小题8分.已知函数2()2(0)f x x ax a =->.(1)当2a =时,解关于x 的不等式3()5f x -<<;(2)对于给定的正数a ,有一个最大的正数()M a ,使得在整个区间[0 ()]M a ，上,不等式|()|5f x ≤恒成立. 求出()M a 的解析式;(3)函数()y f x =在[ 2]t t +，的最大值为0,最小值是4-,求实数a 和t 的值. 46．（2013届浦东二模卷理科题）本题共有2个小题,第(1)小题满分6分,第(2)小题满分8分.设函数()()||f x x a x b =-+(1)当2,3a b ==,画出函数()f x 的图像,并求出函数()y f x =的零点; (2)设2b =-,且对任意[1,1]x ∈-,()0f x <恒成立,求实数a 的取值范围.47．（2013届闵行高三二模模拟试卷（数学）理科）本题共有3个小题,第(1)小题满分4分,第(2)小题满分6分,第(3)小题满分6分.已知()||,=-+∈R f x x x a b x .(1)当1,0a b ==时,判断()f x 的奇偶性,并说明理由; (2)当1,1a b ==时,若5(2)4xf =,求x 的值; (3)若0b <,且对任何[]0,1x ∈不等式()0f x <恒成立,求实数a 的取值范围. 解:48 ．（四区（静安杨浦青浦宝山）联考2012学年度第二学期高三（理））本题共有2小题,第1小题满分7分,第2小题满分7分 . 已知函数a x x f +=2)(. (1)若12)()(++=bx x f x F 是偶函数,在定义域上ax x F ≥)(恒成立,求实数a 的取值范围;(2)当1=a 时,令)())(()(x f x f f x λϕ-=,问是否存在实数λ,使)(x ϕ在()1,-∞-上是减函数,在()0,1-上是增函数?如果存在,求出λ的值;如果不存在,请说明理由.49 ．（上海市八校2013届高三下学期联合调研考试数学（理）试题）(本题满分16分;第(1)小题4分,第(2)小题6分,第(3)小题6分)已知下表为函数d cx ax x f ++=3)(部分自变量取值及其对应函数值,为了便于研究,根据表中数据,研究该函数的一些性质: (1) 判断)(x f 的奇偶性,并证明;(2) 判断)(x f 在[]6.0,55.0上是否存在零点,并说明理由; (3) 判断a 的符号,并证明)(x f 在(]35.0,-∞-是单调递减函数.50 ．（上海市虹口区2013年高考二模数学（理）试题）定义域为D 的函数)(x f ,如果对于区间I 内)(D I ⊆的任意两个数1x 、2x 都有)]()([21)2(2121x f x f x x f +≥+成立,则称此函数在区间I 上是“凸函数”.(1)判断函数x x f lg )(=在+R 上是否是“凸函数”,并证明你的结论; (2)如果函数xax x f +=2)(在]2,1[上是“凸函数”,求实数a 的取值范围; (3)对于区间],[d c 上的“凸函数”)(x f ,在],[d c 上任取1x ,2x ,3x ,,n x .① 证明: 当k n 2=(*∈N k )时,)]()()([1)(2121n n x f x f x f nn x x x f +++≥+++ 成立;② 请再选一个与①不同的且大于1的整数n , 证明:)]()()([1)(2121n n x f x f x f nn x x x f +++≥+++ 也成立.上海2013届高三理科数学最新试题精选（13份含16区二模）分类汇编2：函数及其应用参考答案一、选择题 1. B 2. A3. D4. A5. D6. B7. B 二、填空题8. 2a >9.1210. 12-=x y ;11. 31≠m ; 12. 200013. x x f 2sin 2)(π= 14. D 15. B 16. 1 17. 8- 18. 3 19. =-)(1x f2x (0≥x )20. }2|{≥x x 21. []3,422. [)2,+∞23. [)1,2- 24. 07≤<-a 或2=a ; 25. )21,(∞-; 26. ()()()()()⎪⎩⎪⎨⎧+≤≤--≤≤--=224248202822x x x x x f (每空2分)27. ()1log 21-=x y28. 0;29. 4log 3; 30. 2 31. 5 32. 3- 33. 3 34. (0,1]35. 21[1]13， 36. 4 37.2338.127- 39. 440. 832014.41. 5.3; 三、解答题42.解:(1))()(2)(x g x f x F +=xx aa -++=11log )1(log 2(0>a 且1≠a ) ⎩⎨⎧>->+0101x x ,解得11<<-x ,所以函数)(x F 的定义域为)1,1(- 令)(x F 0=,则011log )1(log 2=-++xx aa (*)方程变为 )1(log )1(log 2x x a a -=+,x x -=+1)1(2,即032=+x x解得01=x ,32-=x经检验3-=x 是(*)的增根,所以方程(*)的解为0=x 所以函数)(x F 的零点为0 (2)xx m aa -++=11log )1(log 2(10<≤x )=m )4141(log 112log 2--+-=-++x x x x x a a4141--+-=xx a m 设]1,0(1∈=-t x ,则函数tt y 4+=在区间]1,0(上是减函数当1=t 时,此时1=x ,5min =y ,所以1≥ma①若1>a ,则0≥m ,方程有解; ②若10<<a ,则0≤m ,方程有解 43.解:(1)、()xx x x H 1252-+==2522+-x x⎭⎬⎫⎩⎨⎧≤≤=221x x P(2)、若,P Q ⋂≠∅则说明在1,22⎡⎤⎢⎥⎣⎦上至少存在一个x 值,使不等式2220ax x -+>成立,即在1,22⎡⎤⎢⎥⎣⎦上至少存在一个x 值,使222a x x >-成立,令222,u x x =-则只需min u a >即可又22221112.22u x x x ⎛⎫=-=--+ ⎪⎝⎭当1,22x ⎡⎤∈⎢⎥⎣⎦时,11,2,2x ⎡⎤∈⎢⎥⎣⎦4,21,4min -=⎥⎦⎤⎢⎣⎡-∈u u 从而4min -=u由⑴知, min 4,u =- 4.a ∴>-44. (本题满分14分,第1小题满分4分,第2小题满分10分)解:(1)由题意,对任意R ∈x ,)()(x f x f -=-, 即x x x xa k a a k a---+-=--)1()1(,即0)())(1(=+-+---x x xxa a aa k ,0))(2(=+--x x a a k ,因为x 为任意实数,所以2=k解法二:因为)(x f 是定义域为R 的奇函数,所以0)0(=f ,即0)1(1=--k ,2=k .当2=k 时,xxa a x f --=)(,)()(x f a ax f x x-=-=--,)(x f 是奇函数.所以k 的值为2 (2)由(1)xxa a x f --=)(,因为23)1(=f ,所以231=-a a , 解得2=a . 故x xx f --=22)(,)22(222)(22x x x xm x g ----+=,令x x t --=22,则222222+=+-t x x ,由),1[∞+∈x ,得⎪⎭⎫⎢⎣⎡∞+∈,23t , 所以2222)(22)()(m m t mt t t h x g -+-=+-==,⎪⎭⎫⎢⎣⎡∞+∈,23t 当23<m 时,)(t h 在⎪⎭⎫⎢⎣⎡∞+,23上是增函数,则223-=⎪⎭⎫⎝⎛h ,22349-=+-m , 解得1225=m (舍去) 当23≥m 时,则2)(-=m f ,222-=-m ,解得2=m ,或2-=m (舍去). 综上,m 的值是245.解:(1)2a =时,{224503()5430x x f x x x --<-<<⇔-+>①②由①得,15x -<<,由②得,1x <或3x >,∴(1 1)(3 5)-，，为所求(2)∵0a >,当25a -<-,即a ,()M a a =当250a -≤-<,即0a <,()M a a =∴()a a M a a a ⎧=⎨<⎩(3)22()()(2)f x x a a t x t =--≤≤+,显然(0)(2)0f f a ==①若0t =,则1a t ≥+,且min [()]()4f x f a ==-,或min [()](2)4f x f ==-, 当2()4f a a =-=-时,2a =±,2a =-不合题意,舍去当2(2)2224f a =-⨯=-时,2a =②若22t a +=,则1a t ≤+,且min [()]()4f x f a ==-,或min [()](22)4f x f a =-=-,当2()4f a a =-=-时,2a =±,若2a =,2t =,符合题意; 若2a =-,则与题设矛盾,不合题意,舍去当2(22)(22)2(22)4f a a a a -=---=-时,2a =,2t = 综上所述,{20a t ==和{22a t ==符合题意46.解:(1)22230()23x x x f x x x x ⎧-+≥⎪=⎨-+<⎪⎩,画图正确当0x ≥时,由()0f x =,得2230x x -+=,此时无实根;当0x <时,由()0f x =,得2230x x --=,得1,3(x x =-=舍）. 所以函数的零点为1x =- (2)由()x f <0得,()||2x a x -<. 当0x =时,a 取任意实数,不等式恒成立当01x <≤时,2a x x >-.令2()g x x x=-,则()g x 在01x <≤上单调递增, ∴max ()(1)1a g x g >==-; 当10x -≤<时,2a x x >+,令2()h x x x=+, 则()h x在上单调递减,所以()h x 在10x -≤<上单调递减. ∴ max ()(1)3a h x h >=-=- 综合 1a >-47. [解](理)(1)当1,0a b ==时,()|1|f x x x =-既不是奇函数也不是偶函数 ∵(1)2,(1)0f f -=-=,∴(1)(1),(1)(1)f f f f -≠-≠- 所以()f x 既不是奇函数,也不是偶函数 (2)当1,1a b ==时,()|1|1f x x x =-+, 由5(2)4xf =得52|21|14x x-+= 即2211(2)204x x x ⎧≥⎪⎨--=⎪⎩或2211(2)204x x x⎧<⎪⎨-+=⎪⎩解得111222222xx x ===（舍），或所以221log log (112x +==+-或1x =- (3)当0x =时,a 取任意实数,不等式()0f x <恒成立, 故只需考虑(]0,1x ∈,此时原不等式变为||bx a x--< 即b b x a x x x +<<- 故(]max min ()(),0,1b bx a x x x x+<<-∈又函数()b g x x x =+在(]0,1上单调递增,所以max ()(1)1bx g b x +==+;对于函数(](),0,1bh x x x x=-∈①当1b <-时,在(]0,1上()h x 单调递减,min ()(1)1bx h b x-==-,又11b b ->+,所以,此时a 的取值范围是(1,1)b b +-②当10b -≤<,在(]0,1上,()bh x x x=-≥当x =,min ()bx x-=此时要使a 存在,必须有110b b ⎧+<⎪⎨-≤<⎪⎩即13b -≤<,此时a 的取值范围是(1b +综上,当1b <-时,a 的取值范围是(1,1)b b +-;当13b -≤<时,a 的取值范围是(1b +;当30b ≤<时,a 的取值范围是∅48. 本题共有2小题,第1小题满分6分,第2小题满分8分 .解:(1)12)(2+++=bx a x x F 是偶函数,0=∴b 即2)(2++=a x x F ,R x ∈ 又ax x F ≥)(恒成立即2)1(222+≤-⇒≥++x x a ax a x 当1=x 时R a ∈⇒当1>x 时,213)1(122+-+-=-+≤x x x x a ,232+≤a当1<x 时,213)1(122+-+-=-+≥x x x x a , 232+-≥a综上: 232232+≤≤+-a (2))())(()(x f x f f x λϕ-=)2()2(24λλ-+-+=x x)(x ϕ∴是偶函数,要使)(x ϕ在()1,-∞-上是减函数在()0,1-上是增函数,即)(x ϕ只要满足在区间()+∞,1上是增函数在()1,0上是减函数.令2x t =,当()1,0∈x 时()1,0∈t ;()+∞∈,1x 时()+∞∈,1t ,由于()+∞∈,0x 时,2x t =是增函数记)2()2()()(2λλϕ-+-+==t t t H x ,故)(x ϕ与)(t H 在区间()+∞,0上有相同的增减性,当二次函数)2()2()(2λλ-+-+=t t t H 在区间()+∞,1上是增函数在()1,0上是减函数,其对称轴方程为1=t 4122=⇒=--⇒λλ. 49.036.03675.0212122>->+++∴acx x x x50. 解:(1)设1x ,2x 是+R 上的任意两个数,则01lg )(4lg 2lg 2lg lg )2(2)()(2212121212121=≤+=+-+=+-+x x x x x x x x x x f x f x f ∴)]()([21)2(2121x f x f x x f +≥+.∴函数x x f lg )(=在+R 上是 “凸函数” (2)对于]2,1[上的任意两个数1x ,2x ,均有)]()([21)2(2121x f x f x x f +≥+成立,即)]()[(212)2(22212121221x a x x a x x x a x x +++≥+++,整理得)()(21)(2121221221x x x x x x a x x +--≤-若21x x =,a 可以取任意值. 若21x x ≠,得)(212121x x x x a +-≤, 1)(2182121-<+-<-x x x x ,∴8-≤a . 综上所述得8-≤a (3)①当1=k 时由已知得)]()([21)2(2121x f x f x x f +≥+成立. 假设当mk =)(*∈N m 时,不等式成立即)]()()([21)2(2211221m kx f x f x f x x x f mm +++≥++++ 成立. 那么,由d x x x c mm≤+++≤2221 ,d x x x c mmm m m ≤+++≤+++2222212得]}22[21{)2(22221222112211mm m mm m m m m x x x x x x f x x x f +++++++++++=++++)]2()2([21222212221mm m m m m m x x x f x x x f ++++++++++≥ )]}()()([21)]()()([21{21122212221++++++++≥++m m m m x f x f x f x f x f x f m m )]()()([2112211++++=+m x f x f x f m . 即1+=m k 时,不等式也成立.根据数学归纳法原理不等式得证②比如证明3=n 不等式成立.由①知d x c ≤≤1,d x c ≤≤2,d x c ≤≤3,d x c ≤≤4,有)]()()()([41)4(43214321x f x f x f x f x x x x f +++≥+++成立.d x c ≤≤1,d x c ≤≤2,d x c ≤≤3,d x x x c ≤++≤)(31321,∴)43()3(321321321x x x x x x f x x x f +++++=++)]()()()3([41421321x f x f x f x x x f +++++≥, 从而得)]()()([31)3(321321x f x f x f x x x f ++≥++。

上海市徐汇、松江、金山区2013届高三数学下学期二模试题理(上海徐汇、松江、金山二模)沪教版

20132012学年第二学期徐汇、松江、金山区高三年级数学学科学习能力诊断卷（理科试卷）（考试时间：120分钟，满分150分）一．填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分.1．若函数()(0,1)xf x a a a =>≠的反函数图像过点(2,1)-，则a = . 2．已知函数[]13(),8,64f x x x =∈的值域为A ，集合43|01x x B x x ⎧-⎫=<⎨⎬⎩⎭，则A B = .3．已知(,0)2πα∈-，且4cos 5α=，则tan 2α=___________.4．已知圆锥的母线长为5，侧面积为π15，则此圆锥的体积为__________（结果保留π）. 5．已知32i x =--（i 为虚数单位）是一元二次方程20x ax b ++= (,a b 均为实数)的一个根，则a b +=__________.6．如图给出的是计算1111352013++++的值的一个程序框图，图中空白执行框内应填入i = .7. 在极坐标系中,过圆6cos ρθ=的圆心,且垂直于极轴的直线的极坐标方程是__________.8. 将参数方程212cos x y θθ⎧=⎪⎨=+⎪⎩（θ为参数，R θ∈）化为普通方程，所得方程是_____ _____.9. 在二项式63()()ax a R x +∈的展开式中，常数项的值是20-，则23lim()n n a a a a →∞++++= .10．一质地均匀的正方体三个面标有数字0，另外三个面标有数字1.将此正方体连续抛掷两次，若用随机变量ξ表示两次抛掷后向上面所标有的数字之积，则数学期望ξE =___________.第6题图11．已知椭圆2212516x y +=内有两点()()1,3,3,0,A B P为椭圆上一点，则PA PB+的最大值为 .12.如图，O 为直线02013A A 外一点，若0123452013,,,,,,,A A A A A A A 中任意相邻两点的距离相等，设02013,OA a OA b ==，用,a b 表示0122013OA OA OA OA ++++，其结果为 . 13.设函数()f x x x=，将()f x 向左平移a (0)a >个单位得到函数()g x ，将()f x 向上平移a (0)a > 个单位得到函数()h x ,若()g x 的图像恒在()h x 的图像的上方，则正数a 的取值范围为 .14.如图，现将一张正方形纸片进行如下操作：第一步，将纸片以D 为顶点，任意向上翻折，折痕与BC 交于点1E ，然后复原，记11CDE α∠=；第二步，将纸片以D 为顶点向下翻折，使AD与1E D重合，得到折痕2E D,然后复原，记22ADE α∠=；第三步，将纸片以D 为顶点向上翻折，使CD 与2E D重合，得到折痕3E D，然后复原，记33CDE α∠=；按此折法从第二步起重复以上步骤……，得到12,,,,n ααα，则lim n n α→∞=.二．选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15．已知,a b 为实数，命题甲：2ab b >，命题乙：110b a <<，则甲是乙的（）A.充分不必要条件B.必要不充分条件C.充要条件D.既不充分也不必要条件16．已知函数()1,00,01,0x f x x x >⎧⎪==⎨⎪-<⎩，设2()()F x x f x =⋅，则()F x 是（） A.奇函数，在(,)-∞+∞上单调递减 B.奇函数，在(,)-∞+∞上单调递增 C.偶函数，在(),0-∞上递减，在()0,+∞上递增 D.偶函数，在(),0-∞上递增，在()0,+∞上递减17．气象意义上从春季进入夏季的标志为：“连续5天的日平均温度均不低于22 (0C)”.现有甲、乙、丙三地连续5天的日平均温度的记录数据（记录数据都是正整数）： ① 甲地：5个数据的中位数为24，众数为22； ② 乙地：5个数据的中位数为27，总体均值为24；③ 丙地：5个数据中有一个数据是32，总体均值为26，总体方差为10.8；则肯定进入夏季的地区有 ( ) A. 0个 B. 1个 C. 2个 D. 3个18. 如图所示，向量BC 的模是向量AB 的模的t 倍，AB BC 与的夹角为θ,那么我们称向量AB 经过一次(),t θ变换得到向量BC .在直角坐标平面内，设起始向量()14,0OA =，向量1OA 经过1n -次12,23π⎛⎫⎪⎝⎭变换得到的向量为()1*,1n n A A n N n -∈>，其中*12,,()i i i A A A i N ++∈为逆时针排列，记iA 坐标为()(),*i i a b i N ∈，则下列命题中不正确的是（）A. 2b =B. 3130k k b b +-=()*k N ∈ C. 31310k k a a +--=()*k N ∈D.()()43180k k k k a a a a +++-+-=()*k N ∈三．解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19．(本题满分12分)在ABC ∆中，,,a b c 分别是角,,A B C 的对边，且sin cos cos sin 2A C A C +=,若b =ABC ∆的面积ABC S ∆=a c +的值.20．(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分. 某轮船公司的一艘轮船每小时花费的燃料费与轮船航行速度的平方成正比，比例系数为k .轮船的最大速度为15海里/小时.当船速为10海里/小时，它的燃料费是每小时96元，其余航行运作费用（不论速度如何）总计是每小时150元.假定运行过程中轮船以速度v 匀速航行．（1）求k 的值；（2）求该轮船航行100海里的总费用W （燃料费+航行运作费用）的最小值.21．(本题满分14分) 本题共有2个小题，第1小题满分6分，第2小题满分8分. 如图，已知111ABC A B C -是正三棱柱，它的底面边长和侧棱长都是2，D 为侧棱1CC 的中点．（1）求异面直线1A D与BC 所成角的大小（结果用反三角函数值表示）；（2）求直线11A B 到平面DAB 的距离.22．(本题满分16分) 本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分6分.已知数列{}*()na n N ∈的前n 项和为n S ,数列n S n ⎧⎫⎨⎬⎩⎭是首项为0，公差为12的等差数列.（1）求数列{}n a 的通项公式；（2）设()*42()15n an b n N =⋅-∈，对任意的正整数k ，将集合{}21221,,k k k b b b -+中的三个元素排成D BCAB 1C 1A 1第21题图一个递增的等差数列，其公差为kd ，求证：数列{}k d 为等比数列；（3）对（2）题中的kd ，求集合{}1,kk x d x d x Z +<<∈的元素个数.23．(本题满分18分) 本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题有三个问题情形，每位考生只能选择一个作答，若多答，只对所答情形中最前面的一个记分，情形一、二、三满分依次为5分、6分、8分.已知双曲线C 的中心在原点，()1,0D 是它的一个顶点，d =是它的一条渐近线的一个方向向量. 求双曲线C 的方程；若过点(3,0-)任意作一条直线与双曲线C交于,A B两点(,A B都不同于点D)，求证：DA DB⋅为定值；对于双曲线Γ:22221(0,0,)x ya b a ba b-=>>≠，E为它的右顶点，,M N为双曲线Γ上的两点(都不同于点E)，且EM EN⊥，那么直线MN是否过定点？若是，请求出此定点的坐标；若不是，说明理由.然后在以下三个情形中选择一个，写出类似结论（不要求书写求解或证明过程）.情形一：双曲线22221(0,0,)x ya b a ba b-=>>≠及它的左顶点；情形二：抛物线22(0)y px p=>及它的顶点；情形三：椭圆22221(0)x ya ba b+=>>及它的顶点.数学（理）参考答案一．填空题:(本题共有14题，每小题4分)1．12 2.[)2,3 3. 247-4. 12π5. 19 6．2i + 7. cos 3ρθ=8. 23y x =-+(x ≤≤) 9.14-10. 14 11.15 12.1007()a b +13.2a > 14.6π二．选择题：（本题共有4小题，每小题5分） 15. B 16. B 17. C 18.D 三．解答题 19．（本题12分）解：由条件可得sin()A C +=，…………… 2分即sin B =，……………4分1sin 2ABC S ac B ∆== 3.ac ∴=………………………………8分由余弦定理B ac c a b cos 2222-+=,得22()22cos ,b a c ac ac B =+--………………10分于是，217()23(1).2a c =+-⋅+4a c ∴+=. ………………………………………12分 20.（本题14分）本题共有2小题，第（1）小题6分，第（2）小题8分. 解：（1）由题意得燃料费21W kv =，………………………………2分把v =10，196W =代入得0.96k =.………………………………………………6分（2）21001001500.96W v v v ⨯=⋅+，……………………………………9分=15000962400v v +≥=，………………………11分其中等号当且仅当1500096v v =时成立，解得12.515v ==<， (13)分所以，该轮船航行100海里的总费用W 的最小值为2400（元）. ……………………………cos5θ==14分21．（本题14分）本题共有2题，第(1)小题6分,第(2)小题8分.解：（1）方法一：以11A B中点O为坐标原点，如图建立空间直角坐标系.………1分由题意得()(()(11,0,0,,1,2,0,A DB C-则()(11,1,3,A D BC=-=. .............3分1A D与设θ为向量，.....5分异面直线1A D与BC所成角的大小为arccos...... 6分方法二：取1B B中点E，连结1,A E DE.//DE CB………………………………….2分1A DE∴∠（或其补角）为异面直线1A D BC与所成的角. ……3分由题意得:在11Rt A B E∆中，1A E=;在11Rt A C D∆中，1A D;……………………4分在等腰三角形1A DE中，………5分所以异面直线1A D与BC所成角的大小为. .... 6分（2）方法一：由题意可得11//A B ABD平面,所以，11A B到平面DAB的距离即为1A到平面DAB的距离，设为h. …………….8分设平面ABD的法向量为n，(),,1n x y=,由()(()1(1,0,0),1,2,0,,1,2,0A A D B-得()()(1200113AB AD A D=-=--=-，，，，，，,…………………11分EDBCAB1C1A1arccos5112cos5DEA DEA D∠==1222,2ABD S ∆=⋅⋅=即()0,3,1n =. ……………………………………………………12分所以线11A B 到平面DAB 的距离为故直.…………………………………14分方法二：由题意可得11//A B ABD平面,所以，11A B 到平面DAB的距离即为1A 到平面DAB 的距离，设为h .…………….8分由题意得12A D AD BD AB ====，等腰ADB ∆底边AB 2=，则12AA B S ∆=， 11ABB A 的距离为且D 到平面，………………………………………12分由11A ABD D A ABV V --=得……………………………………………………………13分，则h =所以，直线11A B 到平面DAB .……………14分22．(本题满分16分) 本题共有3个小题，第（1）小题满分4分，第（2）小题满分6分, 第（3）小题满分6分.解：(1)由条件得10(1)2n S n n =+-，即(1)2n n S n =-,…………………………..2分所以，*1()n a n n N =-∈. ……………………………………………………..4分200000x x AB n x y y AD n ⎧-==⎧⎧⋅=⎪⎪⎪⇒⇒⎨⎨⎨--+==⎪⎪⋅=⎪⎩⎩⎩10n A Dh n+⋅===11133ABD A AB S h S ∆∆⋅⋅=(2) 由（1）可知1*4(2)()15n n b n N -=⋅-∈所以，22222144(2)21515k k k b ---=-=⋅，2121244(2)21515k k k b --=-=-⋅,222144(2)21515k k k b +=-=⋅，…………………………..7分由212212k k k b b b -+=+及22121k k k b b b -+<<得22121,,k k k b b b -+依次成递增的等差数列,……………..8分所以22221214442215155k k k k k k d b b -+-=-=⋅-⋅=，…………………………..9分满足14k k d d +=为常数，所以数列{}k d 为等比数列. …………………………..10分（3）①当k 为奇数时，112211223101555(1)4(51)55515555(1)5k k k k k k kk k k k k k k k k k C C d C C C --------+-+--====-+-+--，…………………………..12分同样，可得111122011114(51)15555(1)555k k k k k k k k k k k d C C C ++--++++-===-+-+-+,所以，集合{}1,k k x d x d x Z +<<∈的元素个数为111()()155k k d d +--++ 133(41)55k k k d d ++=-+=；……..13分②当k 为偶数时，同理可得集合{}1,k k x d x d x Z +<<∈的元素个数为3(41)5k ⋅-. (16)分23．(本题满分18分) 本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题有三个问题情形，每位考生只能选择一个作答，若多答，只对所答情形中最前面的一个记分，情形一、二、三满分依次为5分、7分、8分。

【解析版】上海市徐汇、松江、金山区2013届高三二模数学理试题

2013年上海市徐汇、松江、金山区高考数学二模试卷（理科）参考答案与试题解析一．填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分.1．（4分）（2006•上海）若函数f（x）=a x（a＞0，且a≠1）的反函数的图象过点（2，﹣1），则a=．故答案为2．（4分）（2013•松江区二模）已知函数的值域为A，集合B={x|＜0}，则A∩B=[2，3）．解：由函数3．（4分）（2013•松江区二模）已知=﹣．﹣（﹣，∴±±，故答案为﹣．4．（4分）（2013•松江区二模）已知圆锥的母线长为5，侧面积为15π，则此圆锥的体积为12π（结果保留π）．h=∴h==4V=π×π×5．（4分）（2013•松江区二模）已知x=﹣3﹣2i（i为虚数单位）是一元二次方程x2+ax+b=0（a，b均为实数）的一个根，则a+b=19．，解得．6．（4分）（2013•松江区二模）如图给出的是计算的值的一个程序框图，图中空白执行框内应填入i=i+2．由已知中该程序的功能是计算该程序的功能是计算7．（4分）（2013•松江区二模）在极坐标系中，过圆ρ=6cosθ的圆心，且垂直于极轴的直线的极坐标方程为ρcosθ=3．8．（4分）（2013•松江区二模）将参数方程（θ为参数，θ∈R）化为普通方程，所得方程是y=﹣x2+3（）．，，则9．（4分）（2013•松江区二模）在二项式的展开式中，常数项的值是﹣20，则=．，解：由题意二项式的展开式的通项为=a==故答案为：10．（4分）（2013•松江区二模）一质地均匀的正方体三个面标有数字0，另外三个面标有数字1．将此正方体连续抛掷两次，若用随机变量ξ表示两次抛掷后向上面所标有的数字之积，则数学期望Eξ=．=．，=．=故答案为11．（4分）（2013•松江区二模）已知椭圆内有两点A（1，3），B（3，0），P为椭圆上一点，则|PA|+|PB|的最大值为15．椭圆方程为10+|AB'|=10+=10+5=1512．（4分）（2013•松江区二模）如图，O为直线A0A2013外一点，若A0，A1，A2，A3，A4，A5，…，A2013中任意相邻两点的距离相等，设，用表示，其结果为1007（）．=2同理可得=2（13．（4分）（2013•松江区二模）设函数f（x）=x|x|，将f（x）向左平移a（a＞0）个单位得到函数g（x），将f（x）向上平移a（a＞0）个单位得到函数h（x），若g（x）的图象恒在h（x）的图象的上方，则正数a的取值范围为a＞2．，==14．（4分）（2013•松江区二模）如图，现将一张正方形纸片进行如下操作：第一步，将纸片以D为顶点，任意向上翻折，折痕与BC交于点E1，然后复原，记∠CDE1=α1；第二步，将纸片以D为顶点向下翻折，使AD与E1D重合，得到折痕E2D，然后复原，记∠ADE2=α2；第三步，将纸片以D为顶点向上翻折，使CD与E2D重合，得到折痕E3D，然后复原，记∠CDE 3=α3；按此折法从第二步起重复以上步骤…，得到α1，α2，…，αn，…，则=．依此类推：（．若；若{是以为首项，解：由第二步可知：；由第三步可知：，（∴∴，则，此时{是以为首项，∴，即．∴=．综上可知：．故答案为依此类推：（二．选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分.15．（5分）（2013•松江区二模）已知a，b为实数，命题甲：ab＞b2，命题乙：，若命题乙：16．（5分）（2013•松江区二模）已知函数，设F（x）=x2•f（x），则﹣17．（5分）（2013•松江区二模）气象意义上从春季进入夏季的标志为：“连续5天的日平均温度均不低于22 （℃）”．现有甲、乙、丙三地连续5天的日平均温度的记录数据（记录数据都是正整数）：①甲地：5个数据的中位数为24，众数为22；②乙地：5个数据的中位数为27，总体均值为24；③丙地：5个数据中有一个数据是32，总体均值为26，总体方差为10.8；18．（5分）（2013•松江区二模）如图所示，向量的模是向量的模的t 倍，的夹角为θ，那么我们称向量经过一次（t ，θ）变换得到向量．在直角坐标平面内，设起始向量，向量经过n ﹣1次变换得到的向量为，其中为逆时针排列，记A i坐标为（a i ，b i ）（i ∈N *），则下列命题中不正确的是（）．变换的定义，推导知的向量坐标，然：解：向量，则=，三．解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤. 19．（12分）（2013•松江区二模）在△ABC 中，a ，b ，c 分别是角A ，B ，C 的对边，且，若，△ABC 的面积，求a+c 的值．由条件可知的面积可知，，∵，20．（14分）（2013•松江区二模）某轮船公司的一艘轮船每小时花费的燃料费与轮船航行速度的平方成正比，比例系数为k．轮船的最大速度为15海里/小时．当船速为10海里/小时，它的燃料费是每小时96元，其余航行运作费用（不论速度如何）总计是每小时150元．假定运行过程中轮船以速度v匀速航行．（1）求k的值；（2）求该轮船航行100海里的总费用W（燃料费+航行运作费用）的最小值．，得燃料费为小时，可燃料费为海里的总费用为）由题意，设燃料费为小时，可得其余航行运作费用为=（∵当且仅当时，即21．（14分）（2013•松江区二模）如图，已知ABC﹣A1B1C1是正三棱柱，它的底面边长和侧棱长都是2，D为侧棱CC1的中点．（1）求异面直线A1D与BC所成角的大小（结果用反三角函数值表示）；（2）求直线A1B1到平面DAB的距离．为向量arccos；在中，；．arccos由题意得上的高为，则，的距离为h=××∴的距离为22．（16分）（2013•松江区二模）已知数列的前n项和为S n，数列是首项为0，公差为的等差数列．（1）求数列{a n}的通项公式；（2）设，对任意的正整数k，将集合{b2k﹣1，b2k，b2k+1}中的三个元素排成一个递增的等差数列，其公差为d k，求证：数列{d k}为等比数列；（3）对（2）题中的d k，求集合{x|d k＜x＜d k+1，x∈Z}的元素个数．）由条件得，∴．）可知∴为常数，所以数列23．（18分）（2013•松江区二模）已知双曲线C的中心在原点，D（1，0）是它的一个顶点，=是它的一条渐近线的一个方向向量．（1）求双曲线C的方程；（2）若过点（﹣3，0）任意作一条直线与双曲线C交于A，B两点（A，B都不同于点D），求证：为定值；（3）对于双曲线Γ：，E为它的右顶点，M，N为双曲线Γ上的两点（都不同于点E），且EM⊥EN，那么直线MN是否过定点？若是，请求出此定点的坐标；若不是，说明理由．然后在以下三个情形中选择一个，写出类似结论（不要求书写求解或证明过程）．情形一：双曲线及它的左顶点；情形二：抛物线y2=2px（p＞0）及它的顶点；情形三：椭圆及它的顶点．的方程为，由顶点坐标、渐近线方程及的方程为，则的方程为．，得由，则+9k．综上，，则，化简得，过定点（中，若）在椭圆中，若过定点（，）在椭圆中，若过定点（）在椭圆中，若））在椭圆中，若，。

上海徐汇区金山区松江区联考高考二模英语试卷

2013学年第二学期徐汇区学习能力诊断卷高三年级英语学科2014.4第I 卷I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. Visit the woman. B. Go to an interview.C. Attend a lecture.D. Work in the office.2. A. At a post office. B. At a fast-food restaurant.C. At a booking office.D. At a check-in desk.3. A. One hour later. B. Thirty minutes later.C. Twenty minutes later.D. Around ten minutes.4. A. $8. B. $12. C. $16. D. $20.5. A. There is something wrong with the yoga class.B. John and Tom are good friends.C. Tom has attended a yoga class.D. The woman may have dialed a wrong number.6. A. What to take up as a hobby. B. How to keep fit.C. How to handle pressure.D. What to play with.7. A. Classmates. B. Lecturers. C. Strangers. D. Relatives.8. A. He has made a careful plan of writing it. B. He hasn’t got a whole picture of it.C. He has quit writing it.D. He is seeking for a publisher now.9. A. A head waiter. B. A shop assistant. C. A customer. D. A receptionist.10. A. He’s not surprised at the woman’s playing at a concert tomorrow.B. He won’t give the woman a surprise at th e concert tomorrow.C. He will also play at the concert tomorrow with the woman.D. He understands the woman’s nervous feeling and thinks it normal.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. In small cups. B. In a boat on a river.C. At the bottom of a river.D. On food stored in the ground.12. A. It came from a river. B. It was extremely pure.C. It was found in large quantities.D. It was dug up from a deep mine.13. A. An early means of travel on rivers. B. An ancient method of fishing in rivers.C. An important discovery at a village.D. The way of trading foods in old times. Questions 14 through 16 are based on the following passage.14. A. She enjoyed removing others’ drinks. B. She became more and more forgetful.C. She preferred to do everything by herself.D. She wanted to keep her house in good order.15. A. She is happy to clean windows. B. She loves to clean used windows.C. She is fond of clean used windows.D. She likes clean windows as my mother did.16. A. My mother often made us confused.B. My family members had a poor memory.C. My mother helped us to form a good habitD. My wife was surprised when she visited my mother.Section CDirections: In section C, you will hear two longer conversations. The conversations will beread twice. After you hear each conversation, you are required to fill in the numbered blankswith the information you hear.Blanks 21 through 24 are based on the following conversation.II. Grammar and VocabularySection ADirections:After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)The California state assembly recently approved the so-called Paris Hilton bill, which prevents dogs 25______ occupying the driver’s seat in a moving vehicle. The bill passed 26______ Democrats wanted to make an example of Miss Hilton. They think she is a “little rich girl” who always gets her way; plus, her daddy is a big contributor to the Republican Party. “The judge 27______ have put her in jail for four months,” said one Democrat when Paris got only a four-day jail sentence for driving while drunk.28______ (drive) around town with her little dog Lovey hanging out the driver's window, Paris is a familiar sight throughout Los Angeles. Pictures of her and Lovey are common in newspapers and magazines.“That dog is a deadly threat to everyone on the streets and the sidewalks,” said assembly leader Fabian Nunez. “We wrote this bill to protect the public. There’s no telling 29______ the dog might cause her to drive into a crowd of pedestrians. 30______ Paris wants to be with her dog, let her chauffeur do the driving. The state assembly is responsible for protecting people, and we take that responsibility seriously.”The assembly bill passed by a vote of 44 to 11. The state senate(参议院) 31______(expect) to approve the bill, and Governor Schwarzenegger has promised to sign it. “I love dogs,” he said, “but when it comes to 32______ (protect) the people of California, dogs will have to t ake a back seat.”The eleven assembly members who objected to the bill were all Republicans. “While Californians,”said Republican Tom Ridge, “are being attacked daily by murderers, rapists, and muggers, who do the Democrats protect citizens from—a 33______ (spoil) little girl and her dog!”(B)He almost killed somebody, but one minute changed his life. This beautiful story comes from Sherman Rogers’ book, Foremen: Leaders or Drivers? .In his true-life story, Rogers illustrates the importance of effective relationships. During his college years, Rogers spent 34______ summer in an Idaho(爱达荷州) logging camp. When the superintendent had to leave for a few days, he put Rogers in charge.“35______ if the men refuse to follow my orders?” Rogers asked. He thought of Tony, an immigrant worker who roared all day, giving the other men a hard time.“Fire them,” the superintendent said. Then, as if 36______ (read) Roger’s mind, he added, “I suppose you think you are going to fire Tony if you get the chance. I’d feel badly about that. I have been logging for 40 years. Tony is the most reliable worker I’ve ever had. I know he hates everybody and everything. But he comes in first and leaves last. There has not been an accident for eight years on the hill 37______ he works.”Rogers took over the next day. He went to Tony and spoke to him.“Tony, do you know I’m in charge here today?” Tony grunted（发哼声）. “I was going to fire you thefirst time we fought, but I want you to know I’m not,”he told Tony, adding what the superintendent 38______ (say).When he finished, Tony dropped the shovelful of sand he had held and tears streamed down his face.“Why he no tell me dat eight years ago?”That day Tony worked harder than ever before --- and he smiled! He later said to Rogers, “My first foreman who ever say, ‘Good work, Tony’ and it made me feel like Christmas.”Rogers went back to school after that summer. Twelve years later he met Tony again who was now superintendent for railroad construction for one of 39______ (large) logging companies in the West. Rogers asked him how he came to California and happened to have such success.Tony replied, “If it not be for the one minute you talk to me back in Idaho, I keel somebody someday. One minute change my whole life.”Effective managers know the importance of taking a moment to point out 40______ a worker is doing well. But what a difference a minute of affirmation can make in any relationship!Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. reassuresB. wellC. distinguishD. encounterE. objectsF. inoffensiveG. revealsH. afterwardsI. implicationJ. genuineK. unpleasantTelling Tales“Here’s a nice bit of gossip!” Do I have your attention? Probably. We listen, but 41______ we often feel terrible with ourselves. That’s the problem with gossip: it’s something that as a social species we are primed to enjoy, but it can also be 42______ and harmful.Not all gossip is bad. Small talk establishes relationships and 43______ the other person that our intentions are friendly. So gossip, in the sense of exchanging bits and pieces of news about ourselves and others, can be perfectly 44______. If I say to you, “L et’s meet for coffee andhave a bit of a gossip,”I’m inviting you to a social 45______ in which twopeople chew the fat. There is nothing wrong with that: life would be verydull if we were unable to talk about what goes on around us.But it’s not that simple. If we say that somebody is a gossip, we do notmean that he or she enjoys gentle social chat: it carries a crueler 46______.A true gossip enjoys spreading stories about other people --- stories in which others do not usually come out 47______. The gossip is one who spreads bad gossip; good gossip is still fine, but it’s not what gossips spread. The distinction between good and bad gossip is not always clear. It would be easy if we could 48______ the two by saying that bad gossip is just about people; but innocent gossip may be about people too. The best way to tell the difference is to look at the intention behind the remarks. Bad gossip 49______ itself in its desire to make the 50______ of the story look foolish. It also intrudes on their privacy. So we all know the difference.Now then, did you hear about ...III. Reading ComprehensionSection ADirections: For each blank in the following passages there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.“What are you going to be when you grow up?” is a question that you may have been asked. You may not even know there are a variety of geography-related jobs.The Association of American Geographers lists nearly 150 different geography jobs. So, if you are interested in people, places, and environments, consider a job in geography. Your work will not be limited to maps—it might range from 51 data to planning projects, or making decisions about the environment.Processing Geographic DataA geographer’s main activity is analyzing geographic information to answer geographic questions. Jobs processing geographic data begin, of course, with collecting the information. One on-the-ground job in data collection is that of a surveyor. Surveyors 52 and measure the land directly. They may mark boundaries, study the shape of the land, or even help find sewer(下水道) and water systems beneath the Earth. High-tech information-gathering jobs include working with Geographic Information Systems (GIS) data. Some examples of these jobs include remote sensing specialists and GIS analysts. Data analysis jobs require the ability to think 53 , high-level computer skills, and a college education.Once data have been processed, a geographer may study the information to use in planning projects such as a new urban area, a(n) 54 evacuation(撤退) plan, or the placement of a new highway. Planners can also help determine how to make a neighborhood a better place to live. These jobs, too, require good critical thinking, writing, and computer skills, as well as a college education. Planners are 55 to the success of a community.Advising Businesses and GovernmentAbout half of jobs using geography are in business and government. All kinds of businesses use geographic information to help build and 56 their operations. A location analyst studies an area to find the best location for a client. The client might be a large retail store chain that wants to know which location would be best for opening a new store. The location analyst can study GIS reports on such elements as transportation networks or population in an area and give the business owners the positive and 57 points about a location being considered.In 1967, the Mexican government was looking for a location to create a new international tourist resort. They used location analysts to find an area that had good beaches and was easy to reach from the United States. The 58 was Cancún, today one of the world’s most desirable vacation sites.Businesses connected with natural 59 such as forests also rely on geographers. Geographers help them understand the relationship between their business and the environment where their business is located.In 1967, Cancún was a small island on Mexico’s Caribbean coast. It had white sand beaches, many birds and mangrove(红树) trees, but few people. After it was selected as a resort site, it was quickly 60 . Today, Cancún has more than 100 hotels and 500,000 permanent residents. Many work in the tourist industry that serves the millions of visitors who come each year from all over the world.Physical and Human GeographyPhysical geographers are sometimes called earth scientists. Some study such topics as geomorphology (地形学), that is, the study of how the shape of the Earth 61 . Others study weather and climate. Still others study water, the oceans, soils, or ecology. Jobs in these fields require 62 scientific training.Some geographers study economic, political, and 63 issues as they relate to place or region. Human geographers are usually hired by government agencies to analyze a specific problem. These geographers work 64 with political scientists, economists, and sociologists.Together, they provide possible solutions to problems from many different aspects of life in an area. And, of course, geographers teach the subject at all levels of 65 , from elementary schools to universities. But no matter what geography jobs people might hold, they are always trying to answer the basic geographic questions: “Where are things located?” and “Why are they there?”51.A. performing B. analyzing C. appreciating D. downloading52.A. map B. mine C. shape D. honour53.A. creatively B. critically C. wildly D. moderately54.A. disaster B. radioactivity C. excursion D. vacation55.A. qualified B. determined C. valuable D. feasible56.A. survive B. expand C. manage D. boom57.A. negative B. effective C. depressive D. profitable58.A. scenery B. destination C. result D. foundation59.A. potentials B. histories C. resources D. sciences60.A. specialized B. polluted C. governed D. transformed61.A. proceeds B. stretches C. extends D. changes62.A. peculiar B. special C. reasonable D. enthusiastic63.A. psychological B. contemporary C. religious D. social64.A. closely B. peacefully C. loyally D. sensitively65.A. demonstration B. revolution C. examination D. educationSection BDirections:Read the following passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)The Dangers of DietingThanks to our modern lifestyle, with more and more time spent sitting down in front of computers than ever before, the number of overweight people is at a new high. As people crazily search for a solution to this problem, they often try some of the popular fad(时尚) diets being offered. Many people see fad diets as harmless ways of losing weight, and they are grateful to have them. Unfortunately, not only don’t fad diets usually do the trick, but they can actually be dangerous for your health.Although permanent weight loss is the goal, few are able to achieve it. Experts estimate that 95 percent of dieters return to their starting weight, or even add weight. While the irresponsible or unwise useof fad diets can bring some initial results, long-term results are very rare.Nonetheless, people who are bored with the difficulties of changing their eating habits often turn to fad diets. Rather than being moderate, fad diets involve extreme dietary changes. They advise eating only one t ype of food, or they prohibit other types of foods entirely. This results in a situation where a person’s body doesn’t get all the vitamins and other things that it needs to stay healthy.One popular fad diet recommends eating lots of meat and animal products, while nearly eliminating carbohydrates（碳水化合物）. A scientific study from Britain found that this diet is very high in fat. According to the study, the increase of damaging fats in the blood can lead to heart disease and, in extreme cases, kidney failure. Furthermore, diets that are too low in carbohydrates can cause the body to use its own muscle for energy. The less muscle you have, the less food you use up, and the result is slower weight loss.Veteran(老兵) dieters may well ask at this point, “What is the ideal diet?” Well, to some extent, it depends on the individual. A United States government agency has determined that to change your eating habits requires changing your psychology of eating, and everyone has a different psychology. That being said, the British study quoted above recommends a diet that is high in carbohydrates and high in fiber, with portions of fatty foods kept low. According to the study, such a diet is the best for people who want to stay healthy, lose weight, and keep that weight of f. And, any dieting program is best undertaken with a doctor’s supervision.66.After losing weight by dieting, what usually happens to people?A. They have kidney failure.B. They gain the weight back again.C. They keep the weight off.D. They have less muscle.67.Which of the following best expresses the essential information in paragraph 3?A. Bored people turn to fad diets, which, being too extreme, don’t give the body everything itneeds.B. People are bored with fad diets and turn to diets which provide what the body needs.C. People prefer fad dieting to moderate dieting because it requires fewer foods to give the body whatit needs.D. Fad diets give boring people the moderate dietary changes they need to get all the requiredvitamins.68.Which is not mentioned as an effect of the meat and animal product diet?A. Heart disease.B. Slower weight loss.C. Psychological changes.D. Kidney failure.69.According to the passage, why does the ideal diet depend on the individual?A. The less muscle you have, the less food you use up.B. Everyone can gain the weight back.C. Everyone has a different psychology.D. Everyone likes different foods.(B)Charlie Bell became chief executive of McDonald’s in April. Within a month doctors told him that he had colorectal cancer. After stock market hours on November 22nd, the fast-food firm said he had resigned; it would need a third boss in under a year. Yet when the market opened, its share price barely dipped then edged higher. After all, McDonald’s had, agai n, shown how to act swiftly and decisively in appointing a new boss.Mr. Bell himself got the top job when Jim Cantalupo died of a heart attack hours before he was due to address a convention of McDonald’s franchisees(获特许经营联营店者). Mr. Cantalupo was a McDon ald’s veteran brought out of retirement in January 2003 to help remodel the firm after sales began falling because of dirty restaurants, indifferent service and growing concern about junk food. He devised a recovery plan, backed by massive marketing, and promoted Mr. Bell to chief operating officer. When Mr. Cantalupo died, a rapidly convened(召集) board confirmed Mr. Bell, a 44-year-old Australian already widely seen as his heir apparent, in the top job. The convention got its promised chief executive’s address, from the firm’s first non-American leader.Yet within weeks executives had to think about what to do if Mr. Bell became too ill to continue. Perhaps Mr. Bell had the same thing on his mind: he usually introduced Jim Skinner, the 60-year-old vice-chair man, to visitors as the “steady hand at the wheel”. Now Mr. Skinner, an expert on the firm’s overseas operations, becomes chief executive, and Mike Roberts, head of its American operations, joins the board as chief operating officer.Is Mr. Roberts now the new heir apparent? Maybe. McDonald’s has brought in supposedly healthier choices such as salads and toasted sandwiches worldwide and, instead of relying for most of its growth on opening new restaurants, has turned to upgrading its 31,000 existing ones. America has done best at this; under Mr. Roberts, like-for-like sales there were up by 7. 5% in October on a year earlier.The new team’s task is to keep the revitalization plan on course, especially overseas, where some American brands are said to face political hostility from consumers. This is a big challenge. Is an in-house succession(交替、继承) the best way to tackle it? Mr. Skinner and Mr. Roberts are both company veterans, having joined in the 1970s. Some recent academic studies find that the planned succession of a new boss from within, such as Mr. Bell and now (arguably) Mr. Roberts, produces better results than looking hastily, or outside, for one. McDonald’s smooth handling of its serial misfortunes at the top certainly seems to prove the point. Even s o, everyone at McDonald’s must be hoping that it will be a long time before the firm faces yet another such emergency.70.The main reason for the constant change at the top of McDonald is _______.A. the constant change of its share priceB. the board’s failure to reach an agreementC. the falling salesD. the physical problems of the chief executives71.The underlined phrase “heir apparent” (in Paragraph 2) in the article most probably means someonewho _______.A. has the same ideas, aims and style with a personB. has the same right to receive the family titleC. is appointed as an executive of a companyD. is likely to take over a person’s position when that person leaves72.Which of the following was NOT a cause of the falling sales of McDonald?A. The change of the chief executive.B. People’s concern about junk food.C. Dirty restaurant.D. Indifferent service.73.In terms of succession at the top, McDonald_______.A. has had to made rather hasty decisionsB. prefers to appoint a new boss from withinC. acts in a quick and unreasonable wayD. surprises all the people with its decisions(C)It is evident that there is a close connection between the capacity to use language and the capacities covered by the verb “to think”. Indeed, some writers have identified thinking with using words: Plato coined the saying, “In thinking the soul is talking to itself”; J. B. Watson reduced thinking to inhibited(拘谨的) speech located in the minute(微小的) movements or tensions of the physiological mechanisms involved in speaking; and although Ryle is careful to point out that there are many senses in which a person is said to think and in which words are not in evidence, he has also said that saying something in a specific frame of mind is thinking a thought.Is thinking reducible to, or dependent upon, language habits? It would seem that many thinking situations are hardly distinguishable from the skillful use of language, although there are some others in which language is not involved. Thought cannot be simply identified with using language. It may be the case, of course, that the non-linguistic skills involved in thought can only be acquired and developed if the learner is able to use and understand language. However, this question is one which we cannot hope to answer in this book. Obviously being able to use language makes for a considerable development in all one’s capacities but how precisely this comes about we cannot say.At the common-sense level it appears that there is often a distinction between thought and the words we employ to communicate with other people. We often have to struggle hard to find words to capture what our thinking has already grasped, and when we do find words we sometimes feel that they fail to do their job properly. Again when we report or describe our thinking to other people we do not merely report unspoken words and sentences. Such sentences do not always occur in thinking, and when they do they are merged with vague imagery and the hint of unconscious or subliminal（潜意识）activities going on just out of rage. Thinking, as it happens, is more like struggling, striving, or searching for something than it is like talking or reading.Again the study of speech disorders due to brain injury disease suggests that patients can think without having adequate control over their language. Some patients, for example, fail to find the names of objectspresented to them and are unable to describe simple events which they witness; they even find it difficult to interpret long written notices. But they succeed in playing games of chess or draughts. They can use the concepts needed for chess playing or draught playing but are unable to use many of the concepts in ordinary language. How they manage to do this we do not know. Presumably human beings have various capacities for thinking situations which are likewise independent of language.74.According to the theory of "thought" devised by J. B. Watson, thinking is_______.A. talking to the soulB. concealed speechC. speaking nonverballyD. a non-linguistic behavior75.What does the author think about the relationship between language and thinking?A. The ability to use language enhances one’s capacity of thinking.B. Words and thinking match more often than not.C. Thinking never goes without language.D. Language and thinking are generally distinguishable.76.According to the author, when we intend to describe our thoughts, we______.A. merely report internal speechB. have to search for proper words in the way we readC. are overwhelmed with vague imageryD. sometimes are not able to find appropriate words77.Why are patients with speech disorders able to think without having adequate control of language?A. They use different concepts.B. They do not think linguistically.C. It still remains an unsolved mystery.D. Thinking is independent of language.Section CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Space Travel and Science FictionSpace travel and science fiction have long been connected. Early science fiction writers such as Jules Verne inspired scientists and engineers to develop new space technologies. Writers of science fiction, as well as creators of science fiction TV shows and movies, often study the latest scientific concepts and use or adapt them to help expose what future space travel, space ships, and space stations might look like. And while many of their predictions have come true, many others have not.Jules Verne (1828-1905) was a French author. He was a pioneer of science fiction. In his novels From the Earth to the Moon(1865) and Around the Moon(1870), a kind of space ship is fired from a 900-foot-long cannon(大炮) at the moon. On their journey, the three travelers are deprived of gravity at one point and float around their small ship. When landing on the moon, rockets are used to slow the ship down.Given the year in which he was writing, Verne’s predictions were very good. The size of his space ship is about the size of the first one to go to the moon, the Apollo, minus its l arge rockets. Both Verne’s ship and the Apollo carried three people into space. Furthermore, rockets were indeed used by the Apollo to slow its descent. However, Verne’s ship, by analogy(相似) with a gun, shot his travelers into space, which never could have worked. The intense pressure of such an event would cause great physiological damage to the crew.During the first half of the 20th century, science fiction novels and comic books were widely distributed in the United States. Their portrayal(描写) of space travel was less far-fetched than Verne’s. Pictures began showing astronauts in space suits, as writers realized that exposure of human beings to space was deadly. Ideas of other planets were still often wrong, though. A 1928 drawing of the surface of a moon of the planet Jupiter shows it covered in plant life. Only later was it discovered that other than Earth, the planets and moons around our sun are without life as we know it. Drawings in the early 20th century showed very large space ships and stations. They were like floating cities. Writers at the time knew that trips to other stars would take hundreds of years. Those who left Earth would die on the journey; their descendants would arrive. Some writers avoided this problem by using the concept of suspended animation —a deep sleep in which a person doesn't grow older. Such travelers would awaken at the end of their journey, hundreds of years in the future. It is not impossible that these ideas could become reality one day.After the American space program had begun, the television show Star Trek became very popular. It follows the adventures of a large space ship with over 400 crew members that flies around the universe at speeds faster than light. This is a wonderful dream, but it will probably never come to fulfillment. The laws of physics tell us that it is quite impossible for any object to travel faster than the speed of light.It’s clear to see that science fiction has progressed along with science and technology. Science fiction writers continue to study scientific concepts and to use them to portray the future. Looking back at their ideas, some were correct and cannot be distinguished from today’s reality; many others were nothing but fiction. But, they have always inspired new generations of humans to dream of someday going into space.78.According to the passage, what did early science fiction writers do to help reveal what future spacetravel might look like?79.If the modern spaceship were shot into space by analogy with a gun, the astronauts in it would___________________________.80.The space travelers in early science fictions didn’t wear space suits, because___________________________________________________.81.According to the passage, suspended animation was a concept used in science fiction to_______________________________(Note: Answer the questions or complete the statements in No More Than Twelve Words.)。

2013年高考上海市各区县二模语文试题分类汇编——7作文

2013年高考上海市各区县二模语文试题分类汇编——作文壹、浦东新区卷27．根据要求，写一篇作文。

当你作决定时，更需要．．．接受别人的意见还是坚持自己的见解？请谈谈你的看法和理由。

要求：①自选角度，自拟题目，不要写成诗歌。

②不少于 800 字。

③不得透露个人信息。

贰、徐汇区、松江区卷27．阅读下面文字，选取一个角度立意，自拟题目，写一篇不少于800字的文章（不要写成诗歌）。

明代《菜根谭》书中说：处世不必求功，无过便是功。

也有人说：不作为便无过，无过也无功。

叁、黄浦区卷27．根据以下材料，选取一个角度，自拟题目，写一篇不少于800字的文章(不要写成诗歌)。

南京大学在校庆前夕将移植牛顿故乡林肯郡的苹果树枝，校庆办说，届时，“砸中牛顿的苹果也将有可能砸中南大学生”。

引进牛顿的苹果枝，并非该大学首创。

天津大学校长就曾剪下“牛顿苹果树”的枝条带回校园；李嘉诚转赠的“牛顿苹果树”枝条也已落户汕头大学。

肆、虹口区卷27．根据以下材料，选取一个角度，自拟题目，写一篇不少于800字的文章(不要写成诗歌)。

中国人喜欢争先恐后，常常可以看到这种情况：支援灾区，远在千里之外的人们争抢献血；400米跑道上，运动员在为得到好名次拼命奔跑；斑马线前，行人都下意识地往前拥，绿灯还没亮，人群就漫到了马路上……伍、杨浦区、青浦区、宝山区、静安区卷27．作文学习书法，须认识“三人”、明白“三法”。

三人者，古人，今人，本人也。

三法者，学法，化法、想法也。

请根据上述材料，自选角度，自拟题目，写一篇文章。

要求：⑴不少于800字。

⑵不要写成诗歌。

⑶不要透露个人相关信息。

陆、嘉定区、长宁区卷27．根据以下材料，自选角度，自拟题目，写一篇不少于800字的文章（不要写成诗歌）。

庄子说，高山上看到的山下人，皆如蝼蚁，大小高低如一，何必去争谁高谁低。

胡适先生说，我是山下人，就在山下看人，怎能不计较大小、高低、胖瘦？柒、闸北区卷27、根据以下材料，自选角度，自拟题目，写一篇不少于800字的文章，文体不限（不要写成诗歌）。

【VIP专享】【2013上海徐汇、松江、金山二模】上海市徐汇、松江、金山区2013届高三下学期二模数学(文)试题

ABC 的面积 SABC
3 4
3 ，求 a c 的值.
20．(本题满分 14 分) 本题共有 2 个小题，第 1 小题满分 6 分，第 2 小题满分 8 分. 某轮船公司的一艘轮船每小时花费的燃料费与轮船航行速度的平方成正比，比例系数
8．如图给出的是计算1 1 1 1 的值的一个程序框图，
图中空白执行框内应填入 i
35
9．某国际体操比赛，我国将派 5 名正式运动员和 3 名替补运动员参加, 最终将有 3 人上场比赛,其中甲、乙两名替补运动员均
不上场比赛的概率是
10．满足条件
11.
lim(a a2 a3 an ) =
2012 学年第二学期徐汇、松江、金山区高三年级数学学
科
学习能力诊断卷（文科试卷）
（考试时间：120 分钟，满分 150 分） 2013.4 一．填空题（本大题满分 56 分）本大题共有 14 题，考生应在答题纸相应编号的空格内直接填写结果，每个空格填对得 4 分，否则一律得零分.
1．若函数 f (x) ax (a 0, a 1) 的反函数图像过点 (2, 1) ，则 a =
则肯定进入夏季的地区有
A. 0 个
B. 1 个
C. 2 个
三．解答题（本大题满分 74 分）本大题共有 5 题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.
19．(本题满分 12 分)
b 7,
在 ABC 中， a,b, c 分别是角 A, B,C 的对边，且 sin Acos C cos Asin C
14.如图，对正方形纸片 ABCD 进行如下操作：第一步，过点 D 任作一条直线与 BC 边相
交于点 E1 ,
记 CDE1 1 ；第二步，作 ADE1 的平分线交 AB 边于点 E2 ,记 ADE2 2 ；第

2013徐汇金山松江二模联考题讲解

2012学年第二学期徐汇、金山、松江三区联考高三年级物理学科2013.4．18（考试时间120分钟，满分150分）1．答第Ⅰ卷前，考生务必在答题卷上用蓝色或黑色的钢笔或圆珠笔清楚填写姓名、考号，并用2B 铅笔在答题卷上正确涂写考号。

2．第30、31、32、33题要求写出必要的文字说明、方程式和重要的演算步骤。

只写出最后答案，而未写出主要演算过程的，不能得分。

有关物理量的数值计算问题，答案中必须明确写出数值和单位。

第 Ⅰ 卷（共56分）一．单项选择题（每小题2分，共16分，每小题只有一个正确选项。

） 1．电磁波和机械波的相同之处是（）（A ）都可以在真空中传播（B ）都可以发生干涉和衍射现象（C ）它们在同一介质中传播速度相同（D ）都有纵波和横波 2．物体体积增大时，下列物理量中一定减小的是（）（A ）分子力（B ）分子引力（C ）分子势能（D ）内能3．如图为包含某逻辑电路的一个简单电路图，L 为小灯泡．光照射电阻R ′时，其阻值将变得远小于R ，小灯泡L 发光。

则该逻辑门是（）（A ）与门（B ）或门（C ）非门（D ）与非门4．伴随着某一种粒子X 的发现，人们开始认识到原子核内部可能存在不带电荷的中性粒子Y ，则粒子X 是（）（A ）中子（B ）α粒子（C ）电子（D ）质子5．用单分子油膜法测出油酸分子（视为球形）的直径后，还需要下列哪一个物理量就可以计算出阿伏伽德罗常数（）（A ）油滴的体积（B ）油滴的质量（C ）油酸的摩尔体积（D ）油酸的摩尔质量6．如图所示为α粒子散射实验装置，α粒子打到荧光屏上都会引起闪烁，若将带有荧光屏的显微镜分别放在图中A 、B 、C 、D 四处位置。

则这四处位置在相等时间内统计的闪烁次数可能符合事实的是（）（A ）1305、25、7、1 （B ）202、405、625、825（C ）1202、1010、723、203 （D ）1202、1305、723、203 7．四种颜色的光分别通过同一双缝产生的双缝干涉图案如图中各选项所示，用这四种颜色的光分别照射某金属板，只有两种光能产生光电效应，则能产生光电效应的光线中，光子能量较小的光对应的双缝干涉图案是（）A(A)(B) (C)(D)8．下列四个选项的图中实线为河岸，河水的流速u 方向如图中箭头所示，虚线为小船从河岸M 驶向对岸N 的实际航线，已知船在静水中速度小于水速，且船头方向为船对水的速度方向。

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2012学年第二学期徐汇区学习能力诊断卷高三年级物理学科2013.4（考试时间120分钟，满分150分）1．答第Ⅰ卷前，考生务必在答题卷上用蓝色或黑色的钢笔或圆珠笔清楚填写姓名、考号，并用2B铅笔在答题卷上正确涂写考号。

2．第30、31、32、33题要求写出必要的文字说明、方程式和重要的演算步骤。

只写出最后答案，而未写出主要演算过程的，不能得分。

有关物理量的数值计算问题，答案中必须明确写出数值和单位。

第Ⅰ卷（共56分）一．单项选择题（每小题2分，共16分，每小题只有一个正确选项。

）1．电磁波和机械波的相同之处是（）（A）都可以在真空中传播（B）都可以发生干涉和衍射现象（C）它们在同一介质中传播速度相同（D）都有纵波和横波2．物体体积增大时，下列物理量中一定减小的是（）（A）分子力（B）分子引力（C）分子势能（D）内能3．如图为包含某逻辑电路的一个简单电路图，L为小灯泡．光照射电阻R ʹ时，其阻值将变得远小于R，小灯泡L发光。

则该逻辑门是（）（A）与门（B）或门（C）非门（D）与非门4．伴随着某一种粒子X的发现，人们开始认识到原子核内部可能存在不带电荷的中性粒子Y，则粒子X是（）（A）中子（B）粒子（C）电子（D）质子5．用单分子油膜法测出油酸分子（视为球形）的直径后，还需要下列哪一个物理量就可以计算出阿伏伽德罗常数（）（A）油滴的体积（B）油滴的质量（C）油酸的摩尔体积（D）油酸的摩尔质量金箔ABCD放射源荧光屏显微镜6．如图所示为粒子散射实验装置，粒子打到荧光屏上都会引起闪烁，若将带有荧光屏的显微镜分别放在图中A、B、C、D四处位置。

则这四处位置在相等时间内统计的闪烁次数可能符合事实的是（）（A）1305、25、7、1 （B）202、405、625、825（C）1202、1010、723、203 （D）1202、1305、723、2037．四种颜色的光分别通过同一双缝产生的双缝干涉图案如图中各选项所示，用这四种颜色的光分别照射某金属板，只有两种光能产生光电效应，则能产生光电效应的光线中，光子能量较小的光对应的双缝干涉图案是（）(A)(B)(C)(D)8．下列四个选项的图中实线为河岸，河水的流速u方向如图中箭头所示，虚线为小船从河岸M驶向对岸N的实际航线，已知船在静水中速度小于水速，且船头方向为船对水的速度方向。

则其中可能正确是（）河岸MNu(A)河岸MNu(B)河岸MNu(C)河岸Mu(D)二．单项选择题（每小题3分，共24分，每小题只有一个正确选项。

）9．如图，一质量为M的不均匀三角板AOB，OA⊥OB且OA＝OB＝L，O点为水平固定转动轴，现用一水平拉力拉住A点，维持三角板处于OA竖直的静止状态，拉力大小为F，重力加速度为g，则三角板重心到AO的距离为（）FOAB（A）（B）（C）（D）10．一列沿x轴正方向传播的简谐横波，波速为0.5m/s，在某时刻波形如图中实线所示，经过一段时间后波形如图中虚线所示，在这段时间内，图中P处的质点通过的路程可能是（）x/mPy/m2134Ｏ0.2-0.2（A）0.4m （B）0.5m（C）0.6m （D）0.7m11．如图所示，一气缸竖直倒放，气缸内有一质量不可忽略的活塞，将一定质量的气体封闭在气缸内，活塞与气缸壁无摩擦，通过下列哪种方式可以使封闭气体的体积减小（）（A）升高气体温度（B）用力拉着气缸一起向上加速运动（C）顺时针转30° （D）减小气缸质量12．在光滑绝缘的水平桌面上，存在着方向水平向右的匀强电场，电场线如图中实线所示。

一带正电、初速度不为零的小球从桌面上的A点开始运动，到C点时，突然受到一个外加的水平恒力F作用而继续运动到B点，其运动轨迹如图中虚线所示，v表示小球经过C点时的速度。

则（）CBvE（A）小球在A点的电势能比在B点小（B）恒力F的方向可能水平向左（C）恒力F的方向可能与v方向相反（D）在A、B两点小球的速率不可能相等13．如图所示的电路中，R1、R2、R4皆为定值电阻，R3为滑动变阻器，电源的电动势为E，内阻为r，设理想电流表的示数为I，理想电压表的示数为U，当滑动变阻器的滑臂向a端移动过程中（）AVaR3R4R2R1（A）I变大，U变小（B）I变大，U变大（C）I变小，U变大（D）I变小，U变小14．如图所示，一固定杆与水平方向夹角为，将一质量为m1的滑块套在杆上，通过轻绳悬挂一个质量为m2的小球，杆与滑块之间的动摩擦因数为μ。

若滑块与小球保持相对静止以相同的加速度a一起运动，此时绳子与竖直方向夹角为，且＜，则滑块的运动情况是（）（A）沿着杆加速下滑（B）沿着杆加速上滑（C）沿着杆减速下滑（D）沿着杆减速上滑15．如图，一小球从一半圆轨道左端A点正上方某处开始做平抛运动（小球可视为质点），飞行过程中恰好与半圆轨道相切于B点。

O为半圆轨道圆心，半圆轨道半径为R，OB与水平方向夹角为60°，重力加速度为g，则小球抛出时的初速度为（）ABO60°（A）（B）（C）（D）16．一有界匀强磁场区域如图（甲）所示，abcd是一个质量为m、电阻为R、边长为L、匝数为N的正方形线圈。

线圈一半在磁场内，一半在磁场外。

t=0时刻磁场磁感应强度由B0开始均匀减小，线圈在磁场力作用下运动,v-t图象如图（乙），图中斜向虚线为速度图线在0点的切线，数据由图中给出，不考虑重力影响。

则磁场磁感应强度的变化率为（）LBabcd（甲）vtv0t1（乙）（A）（B）（C）（D）三、多项选择题（每小题4分，共16分. 每小题有两个或三个正确选项。

全选对的，得4分；选对但不全的，得2分；有选错或不答的，得0分。

）17．自然界中某个量D的变化量△D，与发生这个变化所用时间△t的比值，叫做这个量D的变化率。

以下物理量中变化率恒定不变的是（）（A）某质点做匀加速直线运动的位移（B）某汽车匀加速启动中牵引力的功率（C）某质点做匀速圆周运动的速度（D）某感应电流恒定的固定线圈中穿过的磁通量18．甲、乙两列连续简谐横波在同一绳上相向传播，t＝0时的波形图如图所示，则（）x/cmy/cm132-1-2-3乙甲（A）两列波同时传到坐标原点（B）x＝0.2cm处的质点开始振动时的运动方向向-y方向（C）由于两波振幅不等，故两列波相遇时不会发生干涉现象（D）两列波相遇时会发生干涉，且x＝1.5cm处为振动加强点19．静电场方向平行于x轴，其电势φ随x的分布可简化为如图所示的折线。

一质量为m、带电量为＋q的粒子（不计重力），以初速度v0从O 点(x=0)进入电场，沿x轴正方向运动。

下列叙述正确的是（）φxφ0-φ0x1x2x3x4O（A）粒子从O运动到x1的过程中速度逐渐减小（B）粒子从x1运动到x3的过程中，电势能先减小后增大（C）要使粒子能运动到x4处，粒子的初速度v0至少为（D）若v0＝，粒子在运动过程中的最大速度为20．如图（甲）所示，左侧接有定值电阻R＝2的水平粗糙导轨处于垂直纸面向外的匀强磁场中，磁感应强度B＝1T，导轨间距为L＝1m。

一质量m＝2kg，阻值r＝2的金属棒在拉力F作用下由静止开始从CD处沿导轨向右加速运动，金属棒与导轨间动摩擦因数μ＝0.25，g=10m/s2。

金属棒的速度-位移图像如图（乙）所示，则从起点发生s=1m位移的过程中（）0.5（乙）（甲）xRrmLBv/m·s-1x/m112CD（A）拉力做的功W=9.25J （B）通过电阻R的感应电量q=0.125C（C）整个系统产生的总热量Q=5.25J （D）所用的时间t＞1s第Ⅱ卷（共94分）四．填空题.（每小题4分，共20分）本大题中第22题为分叉题，分A、B两类，考生可任选一类答题。

若两类试题均做，一律按A类题计分。

21．油膜被日光照射后呈现彩色条纹是光的____________现象，泊松亮斑是光的____________现象。

（分别填入“干涉”或“衍射”）22（A）．A、B两物体在光滑水平地面上沿一直线相向而行，A质量为5kg，速度大小为10m/s，B质量为2kg，速度大小为5m/s，它们的总动量大小为____________kgm/s，两者相碰后，A沿原方向运动，速度大小为4m/s，则B的速度大小为____________m/s。

22（B）．某双星由质量不等的星体S1和S2构成，两星在相互之间的万有引力作用下绕两者连线上某一定点C做匀速圆周运动。

由天文观察测得其运动的周期为T，S1到C点的距离为r1，S1和S2的距离为r，已知万有引力常量为G，由此可求得S1和S2的线速度之比v1：v2＝____________，S2的质量为____________。

23．如图所示，用两条一样的弹簧吊着一根铜棒，铜棒所在的虚线框范围内有垂直纸面的匀强磁场，棒中通入自左向右的电流。

当棒静止时，每个弹簧的拉力大小均为F1；若将棒中电流反向但不改变电流大小，当棒静止时，每个弹簧的拉力大小均为F2，且F2＞F1，则磁场的方向为____________，安培力的大小为____________。

拉力ACBqQhRI24．如图所示，在光滑小滑轮C正下方相距h的A处固定一电量为Q的点电荷，电量为q的带电小球B，用绝缘细线拴着，细线跨过定滑轮，另一端用适当大小的力拉住，使小球处于静止状态，这时小球与A点的距离为R，细线CB与AB垂直。

（静电力恒量为K，环境可视为真空），则小球所受的重力的大小为____________，若小球所受的重力为G，缓慢拉动细线（始终保持小球平衡）直到小球刚到滑轮的正下方过程中，拉力所做的功为____________。

25．如图所示，倾角为θ的斜面上只有AB段粗糙，其余部分都光滑，AB 段长为3L。

有若干个相同的小方块（每个小方块视为质点）沿斜面靠在一起，但不粘接，总长为L。

将它们由静止释放，释放时下端距A为2L。

当下端运动到A下面距A为L/2时小方块运动的速度达到最大。

则小方块与粗糙斜面的动摩擦因数为____________，小方块停止时下端与A的距离是____________。

θABL五、实验题.（共24分.）N26．（4分）（1）法拉第发现电磁感应现象的实验装置如图所示，软铁环两侧分别绕两个线圈，左侧线圈为闭合回路，在其中一段导线下方附近放置一小磁针，小磁针静止时N极指向北方如图所示，右侧线圈与电池、电键相连。

则在闭合电键后，你将看到小磁针（）（单选题）（A）仍然在原来位置静止不动（B）抖动后又回到原来位置静止（C）抖动后停在N极指向东方位置（D）抖动后停在N极指向西方位置（2）通过归纳得出产生感应电流的条件是27．（4分）在“用单摆测定重力加速度”的实验中：（1）某同学分别选用四种材料不同、直径相同的实心球做实验，各组实验的测量数据如下。