集合姓名____________班级___________学号____________分数______________一、选择题1 ．（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）若集合},4|{2R y x y x A ∈==,1{|0}2x B x x-=≥+,则A B = A . [0,1]. B .(2,1]-. C . (2,)-+∞. D . [1,)+∞.2 ．（2013届浦东二模卷理科题）从集合{}2013,,4,3,2,1 中任取3个元素组成一个集合A ,记A 中所有元素之和被3除余数为i 的概率为)20(≤≤i P i ,则210,,P P P的大小关系为 210)(P P P A == 210)(P P P B =>210)(P P P C =< 210)(P P P D >>二、填空题 3 ．（四区（静安杨浦青浦宝山）联考2012学年度第二学期高三（理））已知全集R U =,集合{}0322>--=x x x A ,则=A C U _____________.4 ．（上海市十二校2013届高三第二学期联考数学（理）试题 ）已知全集{12345}U =，，，，,集合2{|320}A x x x =-+=,{|2}B x x a a A ==∈，,则集合()U A B ð=_______.5 ．（上海市长宁、嘉定区2013年高考二模数学（理）试题 ）(理)已知集合{}{}331,,0,1<<=-=x x B a A ,若A B ≠∅,则实数a 的取值范围是____.6 ．（2013届浦东二模卷理科题）已知集合A ={}2,1,2-,B ={}1,a a ,且B A ⊆,则实数a 的值是_______.7 ．（2013届闵行高三二模模拟试卷（数学）理科）已知集合{}2|4,M x x x =<∈R ,{}2|log 0N x x =>,则集合M N =I ________.一、选择题1. A2. B二、填空题[-;3. ]3,14. {3,5}5. )1,0(6. 11,2;7. ()。
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 ++≥++。
高中数学学习材料唐玲出品一、填空题 (本大题共有14题，满分56分)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. 二阶行列式ii i ++-1101的值是 . （其中i 为虚数单位）【答案】2 【解析】2. 已知j i,是方向分别与x 轴和y 轴正方向相同的两个基本单位向量，则平面向量j i +的模等于 .3．二项式7)1(+x 的展开式中含3x 项的系数值为_______________.4. 已知圆锥的母线长为5,侧面积为π15,则此圆锥的体积为__________.(结果中保留π) 【答案】12π 【解析】5. 已知集合{}sin ,A y y x x R ==∈，{}21,B x x n n Z ==+∈，则AB = .6. 在平面直角坐标系xOy 中，若圆22(1)4x y +-=上存在A ，B 两点，且弦AB 的中点为(1,2)P ，则直线AB 的方程为 .【答案】30x y +-= 【解析】7. 已知1log log 22=+y x ，则y x +的最小值为_____________.8. 已知首项31=a 的无穷等比数列{}n a )(*N n ∈的各项和等于4，则这个数列{}n a 的公比是 ． 【答案】14【解析】试题分析：首项31=a 的无穷等比数列{}n a )(*N n ∈，设公比为q ,由各项和等于4.即341q=-.解得14q =. 考点：无穷等比数列的求和公式.9．在平面直角坐标系xOy 中，曲线1C 的参数方程为⎩⎨⎧==,sin 2,cos 2ααy x （α为参数），O 为坐标原点，M 为1C 上的动点，P 点满足2OP OM =，点P 的轨迹为曲线2C ．则2C 的参数方程为.10. 阅读右面的程序框图，运行相应的程序，输出的结果为 .结束开始输出y x1,1x y ==y z =z x y =+x y = 20z <否是第10题图学期望是30151639()23565656568E ξ=+⨯+⨯==. 考点：1.概率问题.2.数学期望.12．【上海静安】设各项均不为零的数列{}n c 中，所有满足01<⋅+i i c c 的正整数i 的个数称为这个数列{}n c 的变号数.已知数列{}n a 的前n 项和442+-=n n S n ，nn a b 41-=（*N n ∈），则数列{}n b 的变号数为 . 【答案】3 【解析】13. 已知定义在[)+∞,0上的函数)(x f 满足)2(3)(+=x f x f .当[)2,0∈x 时x x x f 2)(2+-=.设)(x f 在[)n n 2,22-上的最大值为n a ，且数列}{n a 的前n 项和为n S ，则=∞→n n S lim . （其中*N n ∈）【答案】32【解析】14．正方形1S 和2S 内接于同一个直角三角形ABC 中，如图所示，设α=∠A ，若4411=S ，4402=S ，则=α2sin .【答案】110【解析】二、选择题(本大题共有4题，满分20分)每题有且只有一个正确答案，考生应在答题纸相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分．15. 在实数集R 上定义运算*：(1)x y x y *=⋅-．若关于x 的不等式()0x x a *->的解集是集合{|11}x x -≤≤的子集，则实数a 的取值范围是…………………（ ）. )(A [0,2] )(B [2,1)(1,0]---)(C [0,1)(1,2] )(D [2,0]- 【答案】D 【解析】16．“1=ω”是“函数x x x f ωω22cos sin )(-=的最小正周期为π”的…………（ ）.)(A 充分必要条件 )(B 充分不必要条件)(C 必要不充分条件 )(D 既不充分又必要条件【答案】B 【解析】试题分析：因为x x x f ωω22cos sin )(-=可化为()cos 2f x x ω=-.所以可得1=ω是函数()f x 最小正周期为π的充分条件.由于函数的最小正周期为π,则2,12T ππωω==∴=±.所以必要性不成立.故选B. 考点：1.三角函数的恒等变形.2.充要条件的知识.17. 若圆柱的底面直径和高都与球的直径相等,圆柱、球的表面积分别记为1S 、2S ,则1S :2S =………………………………………………………………（ ）. )(A 1:1 )(B 2:1 )(C 3:2 )(D 4:1【答案】C 【解析】18. 函数()f x 的定义域为实数集R ，⎪⎩⎪⎨⎧<≤--≤≤=.01,1)21(,10,)(x x x x f x 对于任意的x R ∈都有(1)(1)f x f x +=-.若在区间[1,3]-上函数()()g x f x mx m =--恰有四个不同的零点，则实数m 的取值范围是…………………………………………（ ）.)(A 10,2⎡⎤⎢⎥⎣⎦ )(B 10,4⎡⎫⎪⎢⎣⎭ )(C 10,2⎛⎤ ⎥⎝⎦ )(D 10,4⎛⎤ ⎥⎝⎦【答案】D 【解析】考点：1.分段函数的性质.2.函数的周期性.3.函数的等价变换.三、解答题(本大题共有5题，满分74分)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）如图，四棱锥P ABCD -中，底面ABCD 是平行四边形，︒=∠90CAD ，PA ⊥平面ABCD ，1PA BC ==，2AB =，F 是BC 的中点.(1) 求证：DA ⊥平面PAC ；（2）若以A 为坐标原点，射线AC 、AD 、AP 分别是x 轴、y 轴、z 轴的正半轴，建立空间直角坐标系，已经计算得)1,1,1(=n 是平面PCD 的法向量，求平面PAF 与平面PCD 所成锐二面角的余弦值.【答案】（1）参考解析；（2）155【解析】试题分析：（1）需证明DA ⊥平面PAC ，转化为证明AD ⊥AC,AD ⊥PA.因为PA 垂直平面ABCD ，由题意可得AD ⊥AC,AD ⊥PA 显然成立，即可得结论.（2）如图建立空间直角坐标系，因为)1,1,1(=n 是平面PCD 的法向量，所以求出平面PAF 的法向量(1,2,0)m =u r，再根据两平面的法向量的夹角的余弦值，即可得到平面PAF 与平面PCD 所成锐二面角的余弦值，∴所求二面角的余弦值为155. 考点：1.线面垂直的证明2.二面角.3.空间向量的运算.4.运算的能力.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分某公司承建扇环面形状的花坛如图所示，该扇环面花坛是由以点O 为圆心的两个同心圆弧AD 、弧BC 以及两条线段AB 和CD 围成的封闭图形．花坛设计周长为30米，其中大圆弧AD 所在圆的半径为10米．设小圆弧BC 所在圆的半径为x 米（100<<x ），圆心角为θ弧度． （1）求θ关于x 的函数关系式；（2）在对花坛的边缘进行装饰时，已知两条线段的装饰费用为4元/米，两条弧线部分的装饰费用为9元/米．设花坛的面积与装饰总费用的比为y ，当x 为何值时，y 取得最大值？ 【答案】（1）10210xxθ+=+；（2）参考解析 【解析】装饰总费用为()9108(10)17010x x x θ++-=+，所以花坛的面积与装饰总费用的比22550550==1701010(17)x x x x y x x -++---++， 令17t x =+，则3913243()101010y t t =-+≤，当且仅当t =18时取等号， 此时121,11x θ==． 答：当1x =时，花坛的面积与装饰总费用的比最大． 考点：1.扇形的面积.2.函数的最值.3.基本不等式的应用.21．（本题满分14分）本题共有2个小题，第1小题满分5分，第2小题满分9分已知椭圆2222:1x y C a b+=(0)a b >>的右焦点为F (1,0)，短轴的端点分别为12,B B ,且12FB FB a ⋅=-.（1）求椭圆C 的方程；（2）过点F 且斜率为k (0)k ≠的直线l 交椭圆于,M N 两点，弦MN 的垂直平分线与x 轴相交于点D .设弦MN 的中点为P ，试求DPMN的取值范围． 【答案】（1）22143x y +=；（2）1(0,)4【解析】解得2,3a b ==.所以椭圆C 的方程为22143x y +=. （2）依题意直线l 的方程为(1)y k x =-.由22(1),143y k x x y =-⎧⎪⎨+=⎪⎩得2222(34)84120k x k x k +-+-=.直线PD 的方程为222314()4343k k y x k k k +=--++，由0y =，得2243k x k =+，则22(,0)43k D k +， 所以2223(1)43k k DP k +=+. 所以22222223(1)14312(1)4143k k DP k k k MN k k ++==+++211141k =-+. 又因为211k +>，所以21011k <<+. 所以211101414k <-<+. 所以DP MN 的取值范围是1(0,)4. 考点：1.向量的数量积.2.椭圆的性质.3.等价转化的数学思想.4.运算能力.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分设函数x x g 3)(=，x x h 9)(=.（1） 解方程：)9)((log )8)(2(log 33+=-+x h x g x ；（2）令3)()()(+=x g x g x p ，3)(3)(+=x h x q ，求证： )20142013()20142012()20142()20141()20142013()20142012()20142()20141(q q q q p p p p ++++=++++ （3）若bx g a x g x f +++=)()1()(是实数集R 上的奇函数，且0))(2()1)((>⋅-+-x g k f x h f 对任意实数x 恒成立，求实数k 的取值范围.【答案】（1）2=x ；（2）参考解析；（3）2<k【解析】试题分析：（1）由于函数x x g 3)(=，xx h 9)(=，所以解方程0)1()(8)(=--h x g x h .通过换元即可转化为解二次方程.即可求得结论.（2）由于3)()()(+=x g x g x p 即得到3()33xx P x =+.所以()(1)1p x p x +-=.所以两个一组的和为1，还1393399399399)1()(11=+++=+++=-+--x x x x x x x x q x q 所以，211006)20142013()20142()20141(+=+++p p p ， 211006)20142013()20142()20141(+=+++q q q ． )20142013()20142()20141(p p p +++ =)20142013()20142()20141(q q q +++ ． （3）因为bx a x x f +++=)()1()(ϕϕ是实数集上的奇函数，所以1,3=-=b a .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小题满分8分设各项都是正整数的无穷数列{}n a 满足：对任意*N n ∈，有1+<n n a a ．记n a n a b =．（1）若数列{}n a 是首项11a =，公比2=q 的等比数列，求数列{}n b 的通项公式；（2）若n b n 3=，证明：21=a ；（3）若数列{}n a 的首项11a =，1+=n a n a c ，{}n c 是公差为1的等差数列．记n n n a d ⋅-=2，n n n d d d d S ++++=-121 ，问：使5021>⋅++n n n S 成立的最小正整数n 是否存在？并说明理由．【答案】（1）142n n b -=；（2）参考解析；（3）存在5 【解析】试题分析：（1）由于数列{}n a 是首项11a =，公比2=q 的等比数列，所以通项公式为12 (*)n n a n N -=∈.由于数列{}n a 为递增数列，所以都符合1+<n n a a .即可得到数列{}n b 的通项公式.（2）由于各项都是正整数的无穷数列{}n a ，所以利用反正法的思想，反证法排除11a =和*113()a a N ≥∈即可得到证明.（3）由{}n a 各项都是正整数，所以由1n n a a +>可得到11n n a a +≥+.所以可得到1111[1(1)]n n a a n n a a a a ++++≥++-+.从而可得到{}n a 是公差为1的等差数列.再根据求和公式以及解不等式的知识求出结论.试题解析：（1）1111a b a a ===，242112211--====--n a n n n n a a b ；两边乘以2，得14322232222+⋅--⋅-⋅--=n n n S两式相减得=⋅-++++=+13222222n n n n S 22211-⋅-++n n n。
静安、杨浦、青浦、宝山区2013届高三4月高考模拟英语试卷考生注意：1、本试卷分为第Ⅰ卷和第Ⅱ卷两部分。
全卷共11页。
满分150分。
考试时间120分钟。
2、答第一卷前，考生务必在答题卡上用钢笔或水笔清楚填写学校、班级、姓名、准考证号，并用铅笔在答题卡上正确涂写准考证号。
3、第I卷（1—16小题，25 —80小题）由机器阅卷，答案必须全部涂写在答题卡上。
考生应将代表正确答案的小方格用铅笔涂黑。
注意试题题号和答题卡编号一一对应，不能错位。
答案需要更改时，必须将原选项用橡皮擦去，重新选择。
答案不能涂写在试卷上，涂写在试卷上一律不给分。
第I卷中的第17—24小题、81—84小题和第II卷的试题在电脑上阅卷，其答案用黑色或蓝色钢笔或水笔写在答题卡上，如用铅笔答题，或写在试卷上也一律不给分。
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第I卷（共105分）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. 8:15. B. 8:45. C. 9:13. D. 9:30.2. A. Terrible. B. Regretful. C. Exhausted. D. Satisfied.3. A. Its quality. B. Its space. C. Its design. D. Its price.[来源:]4. A. Husband and wife. B. Doctor and patient.[来源:]C. Customer and waitress.D. Boss and employee.5. A. At a nursery school. B. At a studio. C. In a cinema. D. In a store.6. A. He doesn’t like living in the suburbs.B. The suburbs make lots of noise.C. He can’t afford to stay there.D. He has to pay a lot to take a taxi.7. A. He gave the woman the wrong information.B. He added salt to the coffee.C. He put the sugar in the black container.D. He broke the two containers.8. A. Take some medicine. B. Stay in hospital.C. Take his temperature.D. Have some soft drink.9. A. The woman is good at maths. B. The man has problem with maths.C. The man is the cheerleader in school.D. The woman is a trouble maker.10. A. Sam applied for the job first.B. Christina is supposed to be in charge of the department.C. Sam is capable enough of taking the responsibility.D. Christina is the right person for the job vacancy.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questionson 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 the middle of the hall. B. At the back of the room.C. Next to the gate.D. At the information desk.12. A. Speak without permission. B. Note down the agenda (议程).C. Read the agenda carefully.D. Fill out a “Speaker Card”.13. A. Just share the ideas with the partner in the meeting room.B. Interrupt the speaker whenever he just talks nonsense.C. Keep quiet when somebody else is giving his opinions.D. Talk on the cell phone in a low voice during the meeting.Questions 14 through 16 are based on the following passage.14. A. 6a.m.-8a.m., 9p.m.-11p.m.. B. 5a.m.-7a.m., 5p.m.-7p.m..C. 5a.m.-6a.m., 5p.m.-6p.m..D. 6a.m.-7a.m., 8p.m.-9p.m..15. A. To make the town cleaner and better the environment.B. To reduce the amount of the waste.C. To introduce a new resource-recycling company.D. To try some new way out to decrease its negative effects.16. A. They have to help clean the streets for a whole day.B. They have reached an agreement with the local residents.C. They travel a lot to look after family businesses.D. They come back home late and miss the waste collection time.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.What is the name of the book? __17 and the Modern Age.Who asks the librarian to make sure every student can read the book? The 18 .Where is the book now? In the 19 room.Which floor can students find the book? On the 20 floor.Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.What kind of store is Radio Shack? 21 .What is the advantage of shopping in Radio Shack besides good quality? It provides 22 . What is the disadvantage of shopping in the bookstores? 23 .What does “shopping around” mean?Going to different stores and 24__ goods at the cheapest price.II. Grammar and vocabularySection ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. choose the one answer that best completes the sentence.25. The start of a new year brings hope — hope _____ better health, more happiness and greater success.A. amo ngB. forC. overD. on26. –What is the man, actually?–I don’t know for sure. But I think he can be _____ but a policeman.A. nothingB. somethingC. everythingD. anything27. –Do you know where David is? I couldn’t f ind him anywhere.– Well. He _____ have gone far — his glasses are still here.A. shouldn’tB. mustn’tC. can’tD. wouldn’t28. I suppose you are unwilling to change your idea, _____?A. aren’t youB. do IC. don’t ID. are you29. At the moment of the car accident, Jason’s life _____ in the blink of an eye.A. changesB. had changedC. was changingD. changed30. The law says that all public buildings must be accessible to people who have trouble _____.A. walkingB. walkC. to walkD. walked31. Many students apply for a position at that company, but only a few _____.A. are being acceptedB. are acceptedC. have acceptedD. accept32. Desserts made from apples, such as pies, apple pancakes and apples _____ in sugar are available for sampling.A. dippingB. dipC. dippedD. to dip33. Tom’s resolution _____ up drinking alcohol lasted only two days.A. givenB. givingC. giveD. to give34. The boy, one of the so-called rich second generation, forced his parents to buy a new car _____ it might cost.A. no matter howB. however highC. no matter how muchD. how much35. A business plan should be a strategic outline of _____ you are going to do, why and how you are going to do it.A. whatB. whichC. howD. that36. The teacher left word with our monitor _____ she would explain the problem again next time.A. whoB. whichC. asD. that37. They will pay a visit to Europe in a couple of years _____ they have enough money.A. for fear thatB. on condition thatC. even thoughD. as well as38. Every time Gina catches her employees _____ time, she reminds them that time is money.A. to wasteB. wastingC. wastedD. waste39. Not until 2012 _____ to a Chinese writer for the first time.A. the Nobel Prize in literature was awardedB. was awarded the Nobel Prize in literatureC. was the Nobel Prize in literature awardedD. the Nobel Prize was awarded in literature40. BrainPOP is an educational program consisting of brief animated videos _____ a man named Tim and his robot friend Moby discuss various subjects.A. in whichB. whichC. asD. in thatSection 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. concentratedB. possibleC. revisedD. applicationsE. figuresF. connectG. benefitsH. globalI. contributeJ. topsMore than two million people in Europe now have fiber broadband（光纤宽带）direct to their home, suggests a survey. The latest __41__ on superfast broadband delivered by fiber to the home (FTTH) show 18% growth over the last survey compiled in late 2008.The continued growth suggests that the __42__ economic decline has not hit plans to build fiber networks. Sweden __43__ the list of nations applying the technology, with 10.9% of its broadband customers using fiber. Karel Helsen, president of Europe’s Fiber-To-The-Home Council, said the growth matched predictions that were __44__ when the credit crisis started to make itself felt. “The numbers in 2009 are in line with the latest forecasts,” said Mr. Helsen.By 2012, the FTTH Council expects that 13 million people across 35 European nations will have their broadband delivered by fiber. Such services would start at a speed of 100 megabits per second (mbps), said Mr. Helsen. Around Europe more than 233 projects were underway to lay the fibers that would __45__ homes or buildings to the net, said Mr. Helsen. Many of those, he said, were being operated by local governments or smaller net firms. Local governments were interested in FTTH because of the economic and social __46__ it brought in its wake, said Mr. Helsen.The low delay in high-speed fiber networks made __47__ new uses of broadband, he said. “No delay is very important,” he said, “specifically if you talk about __48__ that are time-dependent such as personal communications, conference calls or video calls where delays cause a lot of trouble.” While early FTTH services were__49__ in cities, said Mr. Helsen, many more were reaching out to rural areas for e-health and e-learning projects.III. Reading ComprehensionSection ADirections: For each blank in the following passage 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.Large companies need a way to reach the savings of the public at large. The same problem, on a smaller__50__, faces practically every company trying to __51__ new products and create new jobs. There can be little prospect of raising the sort of sums needed from friends and people we know. While banks may agree to provide short-term finance, they are generally __52__ to provide money on a permanent basis for long-term projects. So companies turn to public, inviting people to lend them money, or take a share in the business in __53__ for a share in future profits. This they do by __54__ stocks and shares in the business through the Stock Exchange. By doing so they can put into circulation the savings of __55__ and organizations, both at home and overseas. When the saver needs his money back, he does not have to go to the company with whom he originally placed it. __56__, he sells his shares through a stockbroker to some other saver who is seeking to __57__ his money.Many of the __58__ needed both by industry and by each of us are provided by the government or by local authorities. Without hospitals, electricity, telephones, railways, this country could not __59__. All these require __60__ spending on new equipment and new development if they are toserve us properly, requiring more money than is raised through taxes alone. The government, local authorities, and nationalized industries __61__ frequently need to borrow money to finance major capital spending, and they, too, come to the Stock Exchange.There is __62__ a man or woman in this country whose job or whose standard of living does not __63__ the ability of his or her employers to raise money to finance new development. In one way or another this new money must come from the savings of the country. The Stock Exchange __64__ to provide a channel through which these savings can reach those who need finance.50. A. level B. extent C. scale D. basis51. A. programme B. provide C. develop D. prepare52. A. unexpected B. unwilling C. unbelievable D. uncertain53. A. search B. exchange C. value D. comfort54. A. issuing B. allowing C. producing D. acquiring55. A. immigrants B. investigators C. inheritors D. individuals56. A. Indeed B. In fact C. In addition D. Instead57. A. eliminate B. reflect C. invest D. profit58. A. properties B. appliances C. foundations D. services59. A. function B. experience C. share D. launch60. A. invisible B. continuous C. l imited D. economical61. A. therefore B. however C. nevertheless D. otherwise62. A. definitely B. almost C. hardly D. probably63. A. turn down B. depend on C. take over D. put off64. A. releases B. forces C. leaves D. existsSection BDirections: Read the following three 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)A voyaging ship was wrecked during a storm at sea and only two of the men aboard were able to swim to a small, desert-like island. Not knowing what else to do, the two survivors agreed that they had no alternativethan to pray to God.However, to find out whose prayers were more powerful, they agreed to divide the territory between them a nd stay on opposite sides of the island.The first thing they prayed for was food. The next morning, the first man saw a fruit-bearing tree on his side of the island, and he was able to eat its fruit. But the other man’s parcel of land remained barren.After a week, the first man became lonely and decided to pray for a wife. The next day, another ship was wrecked and the only survivor was a woman who swam to his side of the island. But on the other side of the island, there was nothing.Soon thereafter the first man prayed for a house, clothes and more food. The next day, like magic, all of these things were given to him. However, the second man still had nothing.Finally, the first man prayed for a ship so that he and his wife could leave the island, and in the morning he found a ship docked at his side of the island.The first man boarded the ship with his wife and decided to leave the second man on the island, considering the other man unworthy to receive God’s blessings since none of his prayers had be enanswered.As the ship was about to leave, the first man heard a voice from Heaven booming, “Why are you leaving your companion on the island?”“My blessings are mine alone since I was the one who prayed for them,” the first man answered. “His prayers were all unanswered and so he doesn’t deserve an ything.”“You are mistaken!” the voice rebuked him. “He had only one prayer, which I answered. If not for that, you would not have received any of my blessings.”“Tell me,” the first man asked the voice, “what did he pray for that I should owe him anything?”“He prayed that all your prayers would be answered.”For all we know, our blessings are not the fruits of our prayers alone, but those of another praying for us. So what you do for others is more important than what you do for yourself.65. The first man’s wife is _____.A. a swimmer who got to the island by accidentB. an angel sent by God to keep him companyC. a survivor from another wrecked shipD. a native person on the desert-like island66. The underlined word “barren” in Paragraph 3 is closest in meaning to _____.A. isolatedB. unproductiveC. fertileD. dry67. Which of the following is true about the second man?A. He didn’t deserve any blessing from God.B. None of his prayers was answered by God.C. He is not brave enough to tell God his needs.D. His prayer helped his companion get out of trouble.68. What’s the moral of the story?A. Never judge a person by appearance.B. Don’t lose heart in trouble.C. Helping others is helping ourselves.D. Greed is the root of all evil.(B)Stewart Island Ferry ServicesWhile most visitors spend at least one night on Stewart Island, it is also readily accessible by ferry as a day excursion from Invercargill and Bluff.Experience Foveaux Strait in comfort and style on board our express catamarans. During the one-hour crossing between Bluff and Stewart Island keep a lookout for wildlife, especially seabirds. Watching mollymawks (albatross) soaring behind the ferry is a fantastic sight. Interesting landmarks commonly seen include Dog Island Lighthouse, Ruapuke Island, Titi Islands and Mt Anglem - Stewart Island’s highest point.•Free tea and coffee on board•Interpretation handouts are available (English only).•Wheelchair access available•Personal baggage is carried free on the ferries - max. two bags per person (one stowed and one small carry-on). Additional baggage is by prior arrangement.•Vehicle parking available at Bluff (extra cost - reservations recommended)FERRY TO STEW ART ISLANDDepart BluffAll year 9:30amSep-May 5:00pmOct –Apr 11:00amJun –Aug 4:30pmLate Dec –mid Jan8:00amFERRY TO BLUFFDepart Stewart IslandAll year 8:00amSep –May 3:30pmOct –Mar 6:00pmApr 5:00pmJun-Aug 3:00pmLate Dec –mid Jan 9:30amOther departures as locally advertisedDuration 1hrCheck-in 30 minutes prior to the scheduled departure time. (Check-in and boarding gates are closed 10 minutes prior to times stated above.)“20% Multi-Purchas e REW ARD” on Return Ferry ServicesBuy 2 or more different excursions and SA VE 20% off all lower priced!Kids Go FREE on selected departures during NZ School Holidays!Kids Go FREE for travel 20 April - 5 May 2013.69. If leaving a car at Bluff, a traveler had better _____.A. refer to the handouts firstB. use wheelchair accessC. make a reservationD. park it 30 minutes before departure time70. John, who went to Stewart Island on Dec. 28th, got to the ferry dock at 7:55am. When did he most probably leave Bluff?A. At 8:00a.m..B. At 9:30a.m..C. At 11:00a.m..D. At 3:00p.m..71. Which of the following is false about the ferry services?A. Tea and coffee are free for passengers.B. Children go free for travel for about 15 days.C. Travelers are sure to see some seabirds during the crossing.D. Passengers have to pay extra cost for extra pieces of luggage.(C)Barack Obama urged congressional leaders on Monday to act quickly to pass a huge stimulus package for the U.S. economy. He met with a bipartisan (concerning or involving two different political parties) group of lawmakers on Capitol Hill. Later he met individually with Democratic and Republican House and Senate leaders and spoke to a bipartisan leadership gathering. In comments to reporters early on Monday, he emphasized the urgency of finalizing economic legislation (立法). “We have got an extraordinary econ omic challenge ahead of us,” he said, “Weare expecting a sobering job report at the end of the week. Nancy Pelosi and her staff have been extraordinarily helpful in working with our team so that we can shape an economic recovery and reinvestment plan that starts putting people back to work.”Mr. Obama wants tax cuts for individual Americans and businesses to make up a significant portion of expected legislation. This could involve as much as $300 billion of a bill that is likely to go beyond $700 billion and include aid to cash-poor U.S. states, and money for alternative energy and a range of infrastructure (基础设施) projects. Later, Mr. Obama said he expects to be able to sign legislation as soon as the end of this month, adding that quick action is necessary to “break the drive of the U.S. econo mic depression”.Emerging later from bipartisan talks with Mr. Obama, Nancy Pelosi said lawmakers discussed with the president how to pass a stimulus package as quickly as possible. “An economic recovery package that will create jobs immediately and will grow the economy and that is what we talked about today,” said Nancy Pelosi. “How we could do this fast, deliberatively and to act upon it soon.” Just how soon that would be, Pelosi would not say.How much support Democrats can obtain from Republicans will depend on the details. But the severity of the U.S. economic depression has created considerable bipartisan backing for quick action. Senate Majority Leader, Harry Reid said: “There are investments that we need to make on behalf of the American people to turn around this economy. We felt very good about the meeting; we ar e confident that we can do this and we have to do this.”“I think the best thing I can do is to decline to comment on what they are going to do going forward,” said Dana Perino. “Obviously, we think that tax cuts were the right way to help our economy get out of the economic depression that this president inherited and we know that tax cuts can stimulate innovation.” Asked by reporters how large the economic stimulus package might be, Senate Majority Leader Reid said Obama indicated that all but one of some 28 economists advising him had said it should range from $800 billion to $1.3 trillion.72. Barack Obama urged congressional leaders and met with bipartisan leaders to _____.A. take over the White HouseB. end economic declineC. understand each other betterD. negotiate political issues73. If the sti mulus package is passed quickly and successfully, it can _____.A. obtain support from RepublicansB. finalize economic legislationC. enhance America’s international pos itionD. provide job opportunities74. What is the bipartisan leaders’ attitude towards this meeting?A. Uncertain.B. Hopeful.C. Disappointed.D. Indifferent.75. What can we infer from the passage?A. The best way out of the economic depression is tax cuts.B. The Republic Party plays the key role in coping with the economic depression.C. Democrats and Republicans will team up in the economic depression.D. When the stimulus package will be passed is known to the lawmakers.Section CDirections: Read the following text and choose the most suitable heading from A-F for each paragraph. There is one extra heading which you do not need.A. Factors that influence reactions to pollutantsB. Possible sources of indoor air pollutionC. Ways to identify diseases with similar symptomsD. Long-term effects after repeated exposureE. A commonly-ignored health threatF. Immediate symptoms and regular treatment76.Most people are aware that outdoor air pollution can damage their health, but many do not know that indoor air pollution can also have significant health effects. Environmental Protection Agency studies indicate that indoor levels of pollutants may be 2-5 times, and occasionally more than 100 times, higher than outdoor levels. These levels of indoor air pollutants may be of particular concern because most people spend about 90％of their time indoors.[来源:]77.There are many sources of indoor air pollution in any home. These include combustion sources such as oil, gas, coal, wood, and tobacco products; building materials and furnishings as diverse as deteriorated asbestos-containing insulation, wet or damp carpet, and cabinetry or furniture made of certain pressed wood products; products for household cleaning and maintenance, personal care, or hobbies; central heating and cooling systems and humidification devices; and outdoor sources such as radon, pesticides, and outdoor air pollution.78.Immediate effects may show up after a single exposure or repeated exposures. These include irritation of the eyes, nose, and throat, headaches, dizziness, and fatigue. Such immediate effects are usually short-term and treatable. Sometimes the treatment is simply eliminating the person's exposure to the source of the pollution, if it can be identified. Symptoms of some diseases, including asthma, hypersensitivity and fever, may also show up soon after exposure to some indoor air pollutants.[来源:]79.The likelihood of immediate reactions to indoor air pollutants depends on several factors. Age and pre-existing medical conditions are two important influences. In other cases, whether a person reacts to a pollutant depends on individual sensitivity, which varies tremendously from person to person. Some people can become sensitized to biological pollutants after repeated exposures, and it appears that some people can become sensitized to chemical pollutants as well.80.Certain immediate effects are similar to those from colds or other viral diseases, so it is often difficult to determine if the symptoms are a result of exposure to indoor air pollution. For this reason, it is important to pay attention to the time and place the symptoms occur. If the symptoms fade or go away when a person is away from the home and return when the person returns, an effort should be made to identify indoor air sources that may be possible causes.Section DDirections: Read the passage carefully. Then answer the questions or complete the statements inthe fewest possible words.Children and adolescents who watch a lot of television are more likely to have antisocial and criminal behavior when they become adults, according to a new University of Otago, New Zealand, study published online in the journal Pediatrics. The study followed a group of around 1,000 children born in the New Zealand city of Dunedin in 1972-1973. Every two years between the ages of 5 and 15, they were asked how much television they watched. Those who watched more television were more likely to have a criminal conviction and were also more likely to have antisocial personality traits in adulthood.The study found that the risk of having a criminal behavior by early adulthood increased by about 30% with every hour that children spent watching TV on an average weeknight.The study also found that watching more television in childhood was associated, in adulthood, with aggressive personality, an increased tendency to experience negative emotions, and an increased risk of antisocial personality disorder; a psychiatric disorder characterised by persistent patterns of aggressive and antisocial behavior.The researchers found that the relationship between TV viewing and antisocial behavior was not explained by socio-economic status, aggressive or antisocial behavior in early childhood, or parenting factors.A study co-author, Lindsay Robertson, says it is not that children who were already antisocial watched more television. “Rather, children who watched a lot of television were likely to go on to manifest antisocial behavior and personality traits.”Other studies have suggested a link between television viewing and antisocial behavior, though very few have been able to demonstrate a cause-and-effe ct sequence. This is the first ‘real-life’ study that has asked about TV viewing throughout the whole childhood period, and has looked at a range of antisocial outcomes in adulthood. As an observational study, it cannot prove that watching too much television caused the antisocial outcomes, but the findings are consistent with most of the research and provides further evidence that excessive television can have long-term consequences for behavior.Antisocial behavior is a major problem for society. While we’re not saying that television causes all antisocial behavior, our findings do suggest that reducing TV viewing could go some way towards reducing rates of antisocial behavior in society,” says Associate Professor Hancox.The American Academy of Pediatrics recommends that children should watch no more than 1 to 2 hours of quality television programming each day. The researchers say their findings support the idea that parents should try to limit their children's television use.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)81. The aim of the study is to reveal ______________________________________________.82. The researchers chose __________________________________________ as their research subjects（研究对象）.83. What’s the shortcoming of most of the studies on this topic?__________________________________________________________.84. What do you suppose many parents will do after reading this passage?__________________________________________________________.第II卷（共45分）I. Translation。
