武汉市2007届高三年级二月调研考试

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湖北省武汉中学2007届高三年级调研考试数学试题(理)

湖北省武汉中学2007届高三年级调研考试数学试题(理)

湖北省武汉中学2007届高三年级调研考试数学试题(理)说明:本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

考试时间为120分钟。

第Ⅰ卷(选择题,共50分)一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的. 1.已知全集U =R ,集合},3|{},,2|{3R x x x y y B R x y y A x ∈-==∈-==,则 ( ) A .}049|{<<-x x B .}49|{-<x xC .{(1,-2)}D .}49|{-≤x x2.已知平面上三点A 、B 、C 满足⋅+⋅+⋅===则,5||,4||,3||的值等于( )A .25B .24C .-25D .-24 3.=+--3)2)(1(ii i( )A .3 + iB .-3-iC .-3+1D .3-i4.在△ABC 中,a 、b 、c 分别为角A 、B 、C 的对边,ccb A 22cos 2+=,则△ABC 的形状为( ) A .正三角形 B .直角三角形C .等腰直角三角形D .等腰三角形或直角三角形5.已知等比数列{a n }的前n 项和为S n ,首项1512=a ,且==⋅+⋅∞→n n S a a a a lim ,41813229则( )A .230B .215C .15)21(D .2166.已知随机变量ξ~ B (n ,p )且E ξ= 2.4,D ξ= 1.44,,则参数n ,p 的值为 ( )A .n = 4, p = 0.6B .n = 6, p = 0.6C .n = 6, p = 0.4D .n = 24, p = 0.17.如图所示,在正方体ABCD —A 1B 1C 1D 1的侧面AB 1内有一动点P 到平面A 1C 1的距离是直线BC 的距离的2 倍,点M 是棱BB 1的中点,则动点P 所在曲线的大致形状为 ( )8.已知函数0)1(),0()(2=>++=f a c bx ax x f ,则“b > 2a ”是“f (-2) < 0”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9.椭圆122=+by ax 与直线x y -=1交于A 、B 两点,过原点与线段AB 中点的直线的斜率为ba则,23的值为 ( )A .23 B .332 C .239 D .2732 10.一次研究性课堂上,老师给出函数)(||1)(R x x xx f ∈+=,三位同学甲、乙、丙在研究此函数时分别给出命题:甲:函数f (x )的值域为(-1,1); 乙:若x 1≠x 2,则一定有f (x 1)≠f (x 2);丙:若规定||1)()),(()(),()(11x n x x f x f f x f x f x f n n n +===-则对任意*∈N n 恒成立.你认为上述三个命题中正确的个数有 ( )A .0个B .1个C .2个D .3个第Ⅱ卷(非选择题,共100分)二、填空题:本大题共5小题,每小题5分,共25分. 11.已知7)(3123-+xx 的展开式中5x 的系数为 .(用数字作答)12.已知x ,y 满足约束条件132,12340++⎪⎩⎪⎨⎧≤+≥≥x y y x xy x 则的取值范围是 . 13.已知双曲线)0,0(12222>>=-b a by a x 的右焦点为F ,右准线与一条渐近线交于点A ,△OAF 的面积为263a (O 为坐标原点),则双曲线的两条渐近线的夹角为 . 14.若函数(]31,)(log )(221-∞---=在a ax x x f 上增函数,则实数a 的取值范围是 . 15.直角坐标系中横坐标、纵坐标均为整数的点称为格点,如果函数f (x )的图象恰好通过k个格点,则称函数f (x )为k 阶格点函数.下列函数:①x x f sin )(=;②3)1()(2+-=x x f π;③xx f )31()(=;④.l og)(6.0x x f =其中是一阶格点函数的有 .(填上所有满足题意的序号)三、解答题:本大题共6小题,共75分.解答应写出文字说明,证明过程或演算步骤. 16.(本小题满分12分) 已知)()().0)(1),(sin(),sin ,cos 2(R x x f x b x ∈⋅=<<--+==定义ϕπϕϕ,且)4()(x f x f -=π对任意实数x 恒成立.(Ⅰ)求ϕ的值;(Ⅱ)求函数)(x f y =的单调增区间. 17.(本小题满分12分)设p :不等式1|2|>-+m x x 的解集为R ;q :函数6)34()(23++++=x m mx x x f 在R 上有极值.求使命题“p 且q ”为真的实数m 的取值范围.18.(本小题满分12分)如图,在正四棱柱ABCD —A 1B 1C 1D 1中,AB = a ,AA 1 = 2a ,M ,N 分别是棱BB 1,DD 1的中点.(Ⅰ)求异面直线A 1M 与B 1C 所成的角的余弦值;(Ⅱ)求证:平面A 1MC 1⊥平面B 1NC 1;(Ⅲ)若正四棱柱ABCD —A 1B 1C 1D 1的体积为V ,三棱锥N —A 1B 1C 1的体积为V 1,求VV 1的值. 19.(本小题满分12分)有一种密码,明文是由三个字符组成,密码是由明文对应的五个数字组成,编码规则如下表:明文由表中每一排取一个字符组成,且第一排取的字符放在第一位,第二排取的字符放在第二位,第三排取的字符放在第三位,对应的密码由明文对应的数字按相同的次序排成一组成.(Ⅰ)求P (ξ=2)(Ⅱ)求随机变量ξ的分布列和它的数学期望. 20.(本小题满分13分) 如图,已知直线l 与半径为1的⊙D 相切于点C ,动点P 到直线l 的距离为d ,若.||2PD d = (Ⅰ)求点P 的轨迹方程;(Ⅱ)若轨迹上的点P 与同一平面上的点G 、M 分别满足0,3,2=⋅+⋅==PM GM PG GM PD MP DC GD ,求以P 、G 、D 为项点的三角形的面积.21.(本小题满分14分)设无穷数列{a n }具有以下性质:①a 1=1;②当.,1+*≤∈n n a a N n 时(Ⅰ)请给出一个具有这种性质的无穷数列,使得不等式2312423322221<+++++n n a a a a a a a a 对于任意的*∈N n 都成立,并对你给出的结果进行验证(或证明);(Ⅱ)若111)1(++-=n n n n a a a b ,其中*∈N n ,且记数列{b n }的前n 项和B n ,证明:.20<≤n B参考答案二、填空题 11.35 12.]11,1945[ 13.60° 14.[)2,322- 15.①②④ 三、解答题16.解:(Ⅰ)])sin[()sin(cos 2sin )sin(cos 2)(x x x x x x x f -+-+=-+=ϕϕϕϕ ).2sin(sin )(cos cos )sin(ϕϕϕ+=+++=x x x x x x ……………2分 由题意知)2cos(])4(2sin[)2sin(ϕϕπϕ-=+-=+x x x 对任意实数x 恒成立,得0,0)4sin(2cos sin <<-=-=-ϕππϕϕϕ而,.43,4πϕππϕ-=-=-∴即 ………………………………………………………6分(Ⅱ)由(Ⅰ)知).432sin()(π-=x x f由)(2243222Z k k x k ∈+≤-≤+-πππππ,解得).(858Z k k x k ∈+≤≤+ππππ所以,)(x f y =的单调增区间为).(]85,8[Z k k k ∈++ππππ……………………12分17.解:由m m x x m x m m x m x m x x 2|2|,)2(2)2(22|2|≥-+⎩⎨⎧<≥-=-+知,由题意,.21,12,1|2|>>∴>-+m m m x x 即恒成立…………………………4分 又由函数6)34()(23++++=x m mx x x f 在R 上有极值,知 03423)(2=+++='m mx x x f 有解,即△≥0. 由△= 0,得m =-1或m = 4.此时函数没有极值.由△>0,得m <-1或m >4.要使“p 且q ”为真命题,则 ……………………8分4,4121>⎪⎩⎪⎨⎧>-<>m m m m 解得或,m ∴的取值范围为).,4(+∞…………………………12分 18.解:(Ⅰ)∵A 1D ∥B 1C ,D MA 1∠∴是异面直线A 1M 与B 1C 所成的角(或补角). 又.510cos ,3,5,2111=∠∴===D MA MD D A MA C B M A 11与∴所成的角的余弦值为.510…………………………………………4分 (Ⅱ)取AA 1的中点P ,联结B 1P ,NP ,MP ,则B 1PNC 1为平行四边形,∴B 1P ∥C 1N 又A 1B 1MP 1为正方形,N C M A P B M A 1111,⊥∴⊥∴ 又B 1C 1⊥平面A 1B ,A 1M ⊂平面A 1B , .111M A C B ⊥∴ ⊥∴M A 1平面B 1NC 1.又⊂M A 1平面A 1MC 1, ∴平面A 1MC 1⊥平面B 1NC 1. ………………………8分 (Ⅲ).121,612131,21323111=∴=⋅==-V V a a a V a V C B A N ……………………12分 (注意:若用向量法相应给分)19.解:(Ⅰ)密码中不同数字的个数为2的事件为密码中只有两个数字,注意到密码的第1,2列分别总是1,2,即只能取表格第1,2列中的数字作为密码..8142)2(33===∴ξP …………………………………………………………………4分(Ⅱ)由题意可知,ξ的取值为2,3,4三种情形.若ξ= 3,注意表格的第一排总含有数字1,第二排总含有数字2则密码中只可能取数字1,2,3或1,2,4..32194)122(2)3(323132=++==∴C A P ξ 若3294)4(,4322232213=+===∴A A A A P ξξ则(或用)3()2(1=-=-ξξP P 求得). ………………………………………………8分 ξ∴的分布列为:.3232432382=⨯+⨯+⨯=∴ξE ………………………………………………12分 20.解:(Ⅰ)).1,0(22|||,|2∈=∴=d PD PD d ∴点P 的轨迹是D 为焦点,l 为相应准线的椭圆.由.1.1,2,1,222====-==b c a c ca a c e 于是解得又 以CD 所在直线为x 轴,以CD 与⊙D 的另一个交点O 为坐标原点建立直角坐标系.∴所求点P 的轨迹方程为.1222=+y x ………………………………………………6分 (说明:其它建系方式相应给分)(Ⅱ)∴==,2||,2 G 为椭圆的左焦点. 又.0)(,0=+⋅∴=⋅+⋅由题意,,0≠+≠(否则P 、G 、M 、D 四点共线与已经矛盾) .||3||||.0,0)()(22==∴=-=+⋅-∴又∵点P 在椭圆上, .223||,22||,222||||====+∴a 又 90,,2||=∠∆∴=PDG Rt PDG GD 为.2222221=⨯⨯=∴∆P D G S ……………………………………………………13分21.解:(Ⅰ)令112242332222131,,31,31,1-+====n n n a a a a a a a a ,则无穷数列{a n }可由a 1 = 1,)1(3211≥=-+n a a n n n 给出. 显然,该数列满足)(,1*11N n a a a n n ∈≤=+,且23)311(2331311112322221<-=+++=+++-+n n n n a a a a a a ……………………6分(Ⅱ).0,,1)1(111≥∴≤-=+++n n n n n n n b a a a a a b .021≥+++=∴n n b b b B ………………………………………………8分 又)11(1)1(1111++++-=-=n n n n n n n n a a a a a a a b )11)(11(111++++-=n nn nn n a a a a a a).11(2))(11(1111++++-≤+-=n n n n n n n na a a a a a a a .22)11(2111=<-≤∴+a a a B n n.20<≤∴n B。

2007届高三第二次调研考试理科数学试题答案及评分标准(正式版)

2007届高三第二次调研考试理科数学试题答案及评分标准(正式版)

2007届高三第二次调研考试数学试题(理科)答案及评分标准一、选择题答案 BACBC ADB 二、填空题三、解答题16.(本题满分12分)解(Ⅰ): ()2sin()2cos 2sin cos2cos sin2cos 666f x a b x x x x x πππ=⋅=+-=+-…2分cos 2sin()6x x x π=-=-.…………………………………………5分由22262k x k πππππ-+≤-≤+ 得 22263k x k ππππ-+≤≤+ …………………………………………7分2[2,2]63x k k ππππ∈-++ k Z ∈ ()f x 增函数………………………………8分(Ⅱ)由(Ⅰ)知()2sin()6f x x π=-,即3sin()65x π-=,.……………………………10分∴27cos(2)12sin ()3625x x ππ-=--=-..……………………………………………12分17.(本题满分14分)(Ⅰ)证明:1111D C B A ABCD - 为长方体,AE D A ⊥∴11 ………………………1分 又 E 是1BB 的中点,且11===AB EB BE ,21==∴AE E A又AE E A AA E A AE EA A AA ⊥∴=+∆=12121211,,,2中在……………..3分又E D A E A D A A E A D A 111111111,平面且⊄=⋂E D A AE 11平面⊥∴……………………………………………………..5分 (Ⅱ)解:D D AA A EA 111平面平面⊥ ,取A A 1的中点F ,连EF ,则11D AA EF 平面⊥ 作1AD FG ⊥交1AD 于点G ,连EG ,则………………………………….7分由三垂线定理知EGF ∠为所求二面角的平面角……………………….8分易知1,51==EF FG ,则5511tan ==∠EGF 故所求二面角的正切值为5. ………………………………………10分(Ⅲ)解:连1BC ,由于1111B BCC D EC 平面平面⊥,交线为1BC 过E 作1BC EH ⊥于H 点,则51=EH ,且为E 到平面11D AC 的距离…12分又2515212111111=⨯⨯=⋅=∆D C AD S D AC 则6151253131111111=⨯⨯=⋅==∆--h S V V D AC D AC E E D C A 故所求的三棱锥的体积为61……………………………………………14分18.(本题满分12分)解: (Ⅰ)设(,)M x y ……………………………………………………………………………1分 因为2AM BM k k ⋅=-,..3分 化简得:()22221x y x +=≠±. ……………………………………………………………..4分 (Ⅱ) 设1122(,),(,)C x y D x y 当直线l ⊥x 轴时,直线l 的方程为12x =,则11((,22C D ,其中点不是N ,不合题意…………………………………………6分 设直线l 的方程为11()2y k x -=-将1122(,),(,)C x y D x y 代入()22221x y x +=≠±得221122x y +=…………(1) 222222x y +=…………(2) ……………………………….8分(1)-(2)整理得:12121212122()12()212y y x x k x x y y ⨯-+==-=-=--+⨯ ……………………………11分直线l 的方程为111()22y x -=-- 即所求直线l 的方程为230x y +-=……………………………………………12.分解法二: 当直线l ⊥x 轴时,直线l 的方程为12x =,则11(,(,2222C D -,其中点不是N ,不合题意.故设直线l 的方程为11()2y k x -=-,将其代入()22221x y x +=≠±化简得222(2)2(1)(1)2022k kk x k x ++-+--=由韦达定理得222212221224(1)4(2)[(1)2]0(1)222(1)2(2)2(1)22(3)2k k k k k k x x k k x x k ⎧--+-->⎪⎪⎪-⎪+=-⎨+⎪⎪--⎪⋅=⎪+⎩,又由已知N 为线段CD 的中点,得122(1)222kk x x k -+=-+12=,解得12k =-, 将1k =-代入(1)式中可知满足条件.此时直线l 的方程为111()22y x -=--,即所求直线l 的方程为230x y +-=.19. (本题满分14分)解法一:设2,MN x O =为正方形的中心,总造价为y 万元……………………………………….1分 过M 作MP AF ⊥,垂足为P ,则1,1,MP AP x AM ==-==……………………………….3分故6203060y AM MN x =⋅+⋅=…………………………………….6分'60y =+…………………………………………………………………….8分令'02(1)y x =⇒-2123620111x x x x ∴-+=∴==+>(舍去)………………………………………………………………………………………….10分当(0,1'0;(1'0x y x y ∈<∈>…………………………………………12分故当13x =-0.423()km ≈时, min 60(1164y =≈(万元) 答: 当中心主干道约为0.423()km 公里时,才能使道路总造价最低. 道路总造价最低约为164万元………………………………………………………………………………………….14分 解法二: (三角法)设2,MN x O =为正方形的中心,((0,))2FAM πθθ∠=∈过M 作//MQ AC 交AF 于Q , 在Rt AQM ∆中,1QM =1,cot 1cot ,1cot sin AM AQ x x θθθθ∴==∴-==- 1202cos 6203060(1cot )6060sin sin y AM MN θθθθ-=⋅+⋅=+-=⋅+令2cos cos sin 2sin()sin t t θθθθφθ-=⇒+=⇒+=又sin()1,t θφ+≤∴≥故60(1y ≥+,故min 60(1164y =≈ 此时: 3πθ=,故1x =0.423()km ≈ 答: 当中心主干道约为0.423()km 公里时,才能使道路总造价最低. 道路总造价最低约为164万元20. (本题满分14分) (Ⅰ)证明: 1111212222n n n n n nnb a a b b b b ++====--+---1210n n a a +++=……………………………………………………………... 3分(Ⅱ)121n n a a +=-- ∴ 111233n n a a ++=-+()……………………….………..5分又 11203a +=-≠ ∴ 1{}3n a +为等比数列………………………………………….6分∴ 13n n a +=(-2)∴ 13nn a =-(-2) ……………………………………………………8分(Ⅲ)11221(2)3n n nb a =+=+-- ∴ 1(1)2(1)12(1)3n n n n nb -=⋅-+-⋅-…………………. 10分当n 为奇数时11(1)(1)nn n n b b ++-+-111112233n n +=++-11111222211112222(2)(2)33n n n n n n n n n n +++++++=<=+⋅+- … 12分①当n 为偶数时,212(1)(1)(1)n n b b b -+-++-2111112222n n -<++++121112<=- ……………………13分②当n 为奇数时,212(1)(1)(1)n n b b b -+-++-2211111121222223n n n--<++++-++1122111223n<-+-+111123n =-<+ 综上所述,212(1)(1)(1)1n n b b b -+-++-<……………………………………………..14分21. (本题满分14分) (Ⅰ)当-2≤a <41时,由'()f x =0得x 12x = ………………..3分 显然-1≤x 1<21,21<x 2≤2,1211,2,,2.22x x ⎡⎤⎡⎤∴∉∈⎢⎥⎢⎥⎣⎦⎣⎦又'()f x =-()()122x x x x x --当21≤x ≤x 2时,'()f x ≥0,()f x 单调递增; 当x 2<x ≤2时,'()f x<0,()f x 单调递减,………………………………..5分∴()f x max =f (x 211ln 22+-+………………………………………………………..7分 (Ⅱ)答: 存在(,13)a ∈-∞符合条件……………………………………………………..8分解: 因为2()[()ln ]g x f x x x =-⋅=3ax x -不妨设任意不同两点111222(,),(,)p x y p x y ,其中12x x <则332212122111221212()()()y y a x x x x k a x x x x x x x x --+-===-++--……………………11分由 1k <知:a < 1+221122()x x x x ++<1223x +…………………12分又22144x ≤≤ 故74a <故存在(,13)a ∈-∞符合条件.………………………14分解法二:据题意在()y g x =图象上总可以在找一点00(,)P x y 使以P 为切点的切线平行图象上任意两点的连线,即存在2120012()()'()31g x g x k g x a x x x -===-<-207134a x ∴<+≤故存在7(,)4a ∈-∞符合条件。

湖北省武汉中学2007届高三年级调研考试历史试题

湖北省武汉中学2007届高三年级调研考试历史试题

湖北省武汉中学2007届高三年级调研考试历史试题说明:本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

共100分;考试时间90分钟。

答卷前,考生务必将学校、班级、考号、姓名等在答题卷上填写清楚;答案一律在答题卷上书写。

考试结束后请将答题卷交回。

第Ⅰ卷(选择题,共50分)一、选择题(本大题共25小题,每小题2分,共计50分。

在每小题列出的四个选项中,只有一项是最符合题目要求的。

)专制主义中央集权制度,是我国封建社会的基本政治制度。

回答1—3题。

1.秦朝是我国封建专制主义中央集权制度的创立时期,下列对秦朝颁布的政策措施叙述正确的是A.确立皇权至高无上B.规定丞相执掌奏章C.开创郡县制D.由太尉处理政务2.历代封建王朝的统治者不断完善和强化专制主义中央集权,按其相同职能分组不正确的是A.御使大夫、刺史B.丞相、参知政事C.太尉、军机处D.郡县、行省3.下列叙述中,表明明太祖的皇权空前加强的是A.实行八股取士B.颁布《大明律》C.设置锦衣卫D.废除了丞相制度我国古代思想深邃,流派各异,影响深远。

回答4—7题。

4.战国时期思想界出现了百家争鸣,其中对我们建设社会主义和谐社会的现实意义最为突出的是A.庄子主张“无用”的思想B.孟子主张“政在得民”的思想C.墨子主张“非攻”的思想D.荀子主张“制天命而用之”的思想5.韩非子是法家的集大成者,下列属于韩非子法家思想主张的是①要“以法为本”来治理国家②臣民不论贵贱都要受法律约束③法律面前人人平等④应顺应时代进行改革A.①②③④ B.①②③C.①③④D.②③④6.宋代新儒学是中国儒学的一大进步,它完成了更为理论化、思辩化的过程,主要是因为它汲取了下列哪些思想中的有益内容A.道教、佛教B.法家、墨家C.墨家、佛教D.法家、道教7.明末清初黄宗羲等早期民主启蒙思想和法国启蒙思想相比较,表述不正确的是A.都批判了封建思想束缚 B.都提倡法治反对人治C.都提出了把权力还给人民D.都主张实行君主立宪制民族融合是中国历史上的进步现象,对于中华民族的形成和发展,对于多民族封建国家统一都有重要的作用。

武汉市2007届高中毕业生二月调研测试理科数学试卷

武汉市2007届高中毕业生二月调研测试理科数学试卷

武汉市2007届高中毕业生二月调研测试理科数学试卷 2007.2.5一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的. 1.复数z=ii -1的值为( ) A. 12(1+i) B. -12(1+i) C. 12(1-i) D. -12(1-i) 2.在等比数列{a n }中, a 3= 32, S 3= 92 , 则首项a 1=( )A. 32B. -32C. 6或-32D. 6或323.已知角α的正切线是单位长度的有向线段,那么角α的终边在( ) A. x 轴上 B. y 轴上 C.直线y=x 上 D.直线y=x 或y=-x 上4.已知全集U=R, A= {x|x +1x≥0}, 则C u A=( ) A.{x|-1<x ≤0} B. {x|-1<x<0} C. {x|-1≤x<0} D. {x|-1≤x ≤0} 5.在正方体ABCD -A 1B 1C 1D 1中, E 、F 、M 分别为AA 1,C 1D 1,BC 的中点,那么直线B 1E 与FM 所成角的余弦值为( ) A.0 B.1 C. 12 D. 136.若AB 过椭圆 x 225 + y 216 =1 中心的弦, F 1为椭圆的焦点, 则△F 1AB 面积的最大值为( ) A. 6 B.12 C.24 D.487.在△ABC 中, D 为AC 边的中点, E 为AB 上一点, BC 、CF 交于一点F, 且2BF FD =, 若,BE BA λ=, 则实数λ的值为( )A. 34B. 12C. 23D. 138.将4个相同的小球投入3个不同的盒内, 不同的投入方式共有( )A 1B 1C 1D 1ABCD FMA. 43种B. 34种C. 15种D. 30种9.如果实数x 、y 满足4303x+5y 250x 1x y -+≤⎧⎪-≤⎨⎪≥⎩, 目标函数z=kx +y 的最大值为12, 最小值3, 那么实数k 的值为( )A. 2B. -2C. 15 D.不存在10. 函数y=|cos2x|+|cosx|的值域为( )A. [12, 2]B. [22,2]C. [22, 98 ]D.[32,2]二.填空题:本大题共5小题,每小题5分,共25分. 11.(1+x)6(1-x) 展开式中x 2项的系数是________12. x →1lim 11x -= _________ 13.如果直线l 过定点M(1,2)且与抛物线y=2x 2有且仅有一个公共点, 那么直线l 的方程为_______14.正四棱锥S -ABCD 内接于一个半径为R 的球, 那么这个正四棱锥体积的最大值为_____15. 函数f(x)=x 3-3x 2+6x -7的图象是中心对称图形, 其对称中心的坐标为_________ 三.解答题:本大题共6小题,共75分.解答应写了文字说明,证明过程或演算步骤. 16.(本小题满分12分)如图, 在平面四边形ABCD 中, AB=AD=1, ∠BAD=θ, 而△BCD 是正三角形, (1) 将四边形ABCD 面积S 表示为θ的函数; (2) 求S 的最大值及此时θ角的值.ABCD17. (本小题满分12分)如图, 在斜三棱柱ABC-A1B1C1中AB=BC=2, ∠ABC= 120°, 又顶点A1在底面ABC上的射影落在AC上, 侧棱AA1与底面成60°的角, D为AC的中点.(1) 求证: AA1⊥BD;(2)若面A1DB⊥面DC1B, 求侧棱AA1之长.18. (本小题满分12分)A袋中装有大小相同的红球1个, 白球2个, B袋中装有与A袋中相同大小的红球2个, 白球3个. 先从A中取出1个球投入B中, 然后从B中取出2个球. 设ξ表示从B中取出红球的个数.(1) 求ξ=2时的概率;(2)求ξ的分布列和数学期望19. (本小题满分13分)如图, 直线l : y= 43(x-2) 和双曲线C:x2a2-y2b2= 1 (a>0,b>0) 交于A、B两点, |AB|=1211,又l关于直线l1: y= ba x对称的直线l2与x轴平行.(1)求双曲线C的离心率;(2)求双曲线C的方程. A BCDA1B1C1l220. (本小题满分13分)已知数列{a n}的前n项之和S n与a n满足关系式: nS n+1=(n+2)S n+a n+2 (n∈N+)(1)若a1=0 , 求a2,a3的值;(2) 求证: a1=0是数列{a n}为等差数列的充要条件.21. (本小题满分13分)已知函数f(x)=x2+2x+alnx(1)若函数f(x)在区间(0,1)上恒为单调函数, 求实数a的取值范围;(2) 当t≥1时, 不等式f(2t-1) ≥2f(t)-3恒成立, 求实数a的取值范围.参考答案1.C2.D3.D4.A5.A6.B7.B8.C9.A 10.B11.9 12. 1313.x=1 或y=4x-2 14.6481R315. (1,-3)16.解: (1)△ABD的面积S= 12absinC=12·1·1·sinθ=12sinθ∵△BDC是正三角形, 则△BDC面积=34BD2 : 而由△ABD及余弦定理可知:BD 2=12+12+2·1·1·cos θ= 2-2cos θ于是四边形ABCD 面积S=12 sin θ +34 (2-2cos θ)S=32 + sin(θ-π3) 其中0<θ<π (2)由 S=32 + sin(θ-π3) 及0<θ<π 则-π3<θ-π3< 2π3在θ-π3= π2时, S 取得最大值 1+32 此时θ= π3+π2 = 5π617.(1) 在斜三棱柱ABC -A 1B 1C 1中, 因为A 1在底面ABC 上射影落在AC 上, 则平面A 1ACC 1经过底面ABC 的垂线 故侧面A 1C ⊥面ABC.又 BD 为等腰△ABC 底边AC 上中线, 则BD ⊥AC, 从而BD ⊥面AC . ∴BD ⊥面A 1C 又AA 1⊂ 面A 1C ∴AA 1⊥BD (2)在底面ABC, △ABC 是等腰三角形, D 为底边AC 上中点, 故DB ⊥AC, 又面ABC ⊥面A 1C∴DB ⊥面A 1C , 则DB ⊥DA 1,DB ⊥DC 1 , 则∠A 1DC 1是二面角A 1-OB -C 1的平面角 ∵面A 1DB 面DC 1B, 则∠A 1DC 1=Rt ∠, 将平面A 1ACC 1放在平面坐标系中(如图), ∵侧棱AA1和底面成60°, 设A 1A=a , 则A 1=(a 2 , 32a), C 1(a2 +23,32a) A(0,0) , C(23, 0), AC 中点D(3, 0), 由110A D DC = 知: (a 2-3, 32a)·(a 2 +3, 32a)=0 , ∴a 2=3, a= 3故所求侧棱AA 1长为 318.(1) ξ=2表示从B 中取出两个红球.① 从A 中取一红球放入B 中, 再从B 中取2红球的概率P= 13·C 32C 62 = 115② 从A 中取一白球放入B 中, 再从B 中取2红球的概率P=23·C 22C 62 = 245∴P(ξ=2)=115+245 = 19(2) 由(1)的方式可知: P(ξ=0)= 13·C 32C 62 +23·C 42C 62 = 131 xP(ξ=1)= 13·C 31·C 31C 62 + 23·C 21·C 41C 62= 59∴ξ的概率分布列为:E ξ=1·2545 + 2·545 = 3545 = 7919. 解: (1) 设双曲线一、三象限渐近线l 1: x a - yb =0 的倾 斜角为α ∵l 和l 2关于直线l 1对称, 记它们的交点为P. 而l 2与x 轴平行, 记l 2与y 轴交点为Q 依题意有∠QPO=∠POM=∠OPM=α(锐角)又AB: y= 43(x -2), 故tan2α=43 则 2tan α1-tan 2α = 43 , 求得tan α= 12 , tan α=-2(舍) ∴ b a = 12 , e 2= c 2a 2 = 1+(b a )2 = 54 ,因此双曲线C 的离心率 52. (2) ∵ b a = 12 , 故设所求双曲线方程 x 24k 2 - x 2k 2 =1 将 y= 43(x -2),代入 x 2-4y 2=4k 2,消去y 得:5536x 2- 649x +649+ k 2=0 设A(x 1,y 1), B(x 2,y 2) |AB| = 1+k 2|x 1-x 2| = 1+k 2·(x 1+x 2)2-4x 1x 2 = 1+169·(649)2-4·5536(649+k 2)5536= 1211 , 化简得到: 464-55k 211 = 1211 , 求得k 2=1 . 故所求双曲线C 的方程为: x 24 -y 2=120.解: (1)由 nS n +1=(n +2)S n +a n +2 (*)变形为n(S n +1-S n )=2S n +a n +2, 而S n 是{a n }前n 项和, 于是有na n +1=2S n +a n +2, a 1=0, 在n=1, a 2=2a 1+a 1+2=2, 则a 2=2 , 在n=2, 2a 3=2(a 1+a 2)+a 2+2=4+4=8, 则a 3=4 (2)充分性: 由(1)可猜测到: a n =2n -2. 下面先用数学归纳法证明: a n =2n -2 ① 在n=1时, a 1=2×1-2=0 与已知 a 1=0一致 故n=1时, a n =2n -2成立. ②假设n ≤k 时, a n =2n -2成立,∴S k =a 1+a 2+……+a k =0+2+4+…+(2k -1)=k(k -1)∵ (*)式 na n +1=2S n +a n +2恒成立, 则ka n +1=2S k +a k +2 = 2k(k -1)+(2k -2)+2=2k 2 ∴ a k +1=2k=2[(k +1)-1]故n=k+1时, a n=2n-2成立, 综合①②可知: a n=2n-2成立对n∈N*恒成立.∴数列{a n}的通项为a n=2n-1, ∴a n-a n-1=2(n≥2, n∈N+)由等差数列定义可知{a n}是等差数列, 从而充分性得证.必要性: 由(1)可知na n+1=2S n+a n+2恒成立, 则(n-1)a n=2S n-1+a n-1+2(n≥2)(**) 若{a n}是等差数列, 则a n-a n-1=d(n≥2),且a n=a1+(n-1)d. 代入(**) 式中有:n(a n+1-a n)=2a n-a n-1 ∴nd=a n+d=a1+(n-1)d+d ∴a1=0 从而必要性得证.因此a1=0 是数列{a n}为等差数列的充分条件.21. 解: (1)由f(x)=x2+2x+alnx 求导数得f '(x)=2x+2+a xf(x)在(0,1)上恒单调,只需f '(x) ≥0 或≤0在(0,1)上恒成立.只需2x2+2x+a≥0 , 或2x2+2x+a≤0恒成立即只需a ≥-(2x2+2x) 或a≤-(2x2+2x) 在(0,1)上恒成立.又记g(x)=-2x(x+1) , 0<x≤1 可知: -4 ≤g(x)<0 ∴所求a≥0 或a≤-4 (2) ∵f(x) =x2+2x+alnx 由f(2t-1)≥2f(t)-3得到:(2t-1)2+2(2t-1)+aln(2t-1)≥2(t2+2t+alnt)-3化简为: 2(t-1)2≥a·ln t22t-1①∵t>1时, 有t2>2t-1, 则ln t22t-1>0 . a≤2(t-1)2lnt22t-1②构造函数m(x)=ln(1+x)-x(x>-1), 求导m '(x) =11+x-1=-x1+x则m(x)在x=0时取极大值, 同时也是最大值.故m(x)≤m(0). 从而ln(1+x)≤x在x>-1上恒成立.∴lnt22t-1= ln(1+(t-1)22t-1)≤(t-1)22t-1< (t-1)2③在t>1时恒成立, 而t=1时③式取等号.∴lnt22t-1≤(t-1)2④在t≥1时恒成立. 因此由②④可知实数a取值范围: a≤2.。

武汉市2007届高中毕业生二月调研测试语文考试题

武汉市2007届高中毕业生二月调研测试语文考试题

高三语文考试题2007年一、(30分,每小题5分)1.下列词语中加点的字,读音有错误的一组( )A.悖(bèi)谬筚(bì)路蓝缕亵(xiè)渎虚与委蛇(yí)B.勾(gōu)当夙(sù)兴夜寐葳蕤(ruí)退避三舍(shě)C.巨擘(bî)羽扇纶(guān)巾编纂(zuǎn) 暴戾恣睢(suī)D.央浼(měi) 未雨绸缪(mïu) 玷(diàn)辱时乖命蹇(jiǎn)2.下列词语中,没有错别字的一组是( )A.脉博徇情枉法招揽妍媸毕露B.威慑垂手可得羁押仗义疏财C.寥落虚无缥缈滂沱庸人自扰D.澹泊捉发难数饿殍铺张浪费3.依次填入下列各句横线处的词语,恰当的一项是( )①第六届“世界华商大会”在南京揭幕。

作为一个非政治性的论坛,“世界华商大会”已成为联系、_______五大洲华人的纽带和桥梁。

②对鲁迅,我们似乎知道的够多了。

不是吗?他留下的数以百万字计的著作,都有详尽的注解;他生平的每一个细节,都有详尽的________。

③美国国务院立即发表一项_______,告诫美国人警惕由于美国对阿富汗的军事打击,可能导致的针对美国人或美国利益的恐怖袭击。

A.沟通考证声明B.勾通考证申明C.沟通考订声明D.勾通考订申明4.下列各句中,加点的成语使用不正确的一句是( )A.第24届大众电影百花奖评选今天揭晓,曾在放映期间赢得了数百万观众,掀起了国产电影多年少见的热潮的《生死抉择》,在本届评选中不负众望,摘取了最佳故事片桂冠。

B.由于高考政策的放宽,现在参加高考的不仅仅有浩浩荡荡的中学生大军,而且还有一支年龄参差不齐,婚姻状况各异的应考队伍。

C.极端恐怖主义用这样惨烈的“宣战”方式,拉开了文明发展“全球化”阶段的新型世界大战的序幕,正像二次大战期间罗斯福政府千方百计仍无法调动美国国人的战争动员,而珍珠港事件却轻而易举地替他完成了一样。

湖北省武汉市2007届高中毕业生二月调研考试语文试题-新人教

湖北省武汉市2007届高中毕业生二月调研考试语文试题-新人教

武汉市2007届高中毕业生二月调研考试语文试卷第Ⅰ卷(选择题,共36分)一、(15分,每小题3分)1、下列词语中加点的字,读音全都不同的一组是A、苍.穹寒伧.凄怆.满目疮.痍沧.海桑田B、蒿.草篙.子缟.素膏.腴之地犒.赏三军C、枝柯.坎坷.苛.责一气呵.成百舸.争流D、贿赂.搁.浅骨骼.恪.守不渝络.绎不绝2、下列词语中,没有错别字的一组是A、世外桃源桃园结义和颜悦色察言观色B、手屈一指首当其冲真知灼见远见卓识C、欢呼雀跃声誉鹊起心无旁鹜趋之若骛D、山清水秀青山绿水振耳欲聋震聋发聩3、下列各句中,加点的成语使用不恰当的一句是A、听到这个消息,不祥的预感涌上四个老人的心头,他们又沿路返回,细细寻找蛛丝马迹....。

B、那时严福祥和全楼的人们正在熟睡,谁也没想到他们在香甜的梦中要和突如其来的大火不期而遇....。

C、在以后的岁月里,埃菲尔的一些不同凡响....的设计不断涌现,这些设计既结构简便,又造价低廉。

D、医院有关人员不是采取积极措施救人,而是欲置患者于死地,掩盖事故真相,干了伤天害理、耸人听闻....的事。

4、下列各句中,没有语病的一句是A、《英国医学杂志》的一篇评论说,中国的肥胖问题“令人担忧”,有近15%的人口体重超标,儿童肥胖在5年里增加乐8倍。

B、21世纪,文化创意产业成为全球最有前景的产业之一。

从“超级女声”到“百家讲坛”,处于起步阶段的中国文化创意产业势头强劲。

C、本次评选活动,所以的一切都只能等到颁奖晚会上才能揭开全部谜底,这就更增添了这项活动的神秘感和吸引力。

D、在春节来临之际,人们有理由为这一利好政策的出台而高兴,春运期间数以千万计乃至近亿的南来北往的人流,将从中受益。

5、下列各项中,标点符号的使用合乎规范的一项是A、据报道,今年年底之前,世界知名学府、美国麻省理工学院全部约1800门课程将通过互联网免费向全世界开放。

B、游客质疑:若只参观故居,岂不花冤枉钱?旅游公司的导游却霸气十足:“那没有办法”,“可以打投诉电话,去投诉嘛。

湖北省武汉市2007届高三语文调研考试卷

湖北省武汉市2007届高三语文调研考试卷

湖北省武汉市2007届高三语文调研考试卷本试卷共150分,考试用时150分钟。

本卷1—12题为选择题,共36分,13—23题为非选择题,共114分。

一、(15分,每小题3分)1.下列词语中加点的字,读音全部正确的一组是()A.胳臂.(bō)一叶扁.舟(piān)辟.邪(pì)万乘.之国(shèng)B.摒.弃(bǐng)当.机立断(dāng)菲.薄(fēi)待.一会儿(dāi)C.供.养(gōng)横.加阻拦(héng)行.伍(háng)少.安毋躁(shǎo)D.埋.怨(mái)虚与委蛇.(yí)拓.本(tuò)欺人蒙.上(mēng)2.下列各组词语中,没有错别字的一组是()A.安民告事部署树阴再接再励匮乏B.班师回营伸张荟萃不肖子孙流连C.苍海横流湮没委曲瞋目结舌遐想D.攻城掠地沉缅荒诞坚苦卓绝塞暄3.下列各句中,加点成语使用恰当的一组是()A.旧城改造,张大爷从旧宅搬出来,住进马路边的一栋商住楼,以为可以安定下不再搬家了。

可是还没有住满三年,他又接到了通知,要他安土重迁,再次搬家。

B.消极避世毕竟和儒家的入世哲学相悖,面对光怪陆离的统治者,报国无门、才华难展的文人们内心矛盾重重,总是在自嘲中流露出满心凄苦。

C.李仁义和王霞平新婚不久就劳燕分飞,李仁义到北京读博士,王霞平去深圳一家外资企业工作。

他们最大的心愿是能够尽快地生活在一起。

D.朱自清先生对春天景物的描写堪称一绝,任何素材到了他的笔下,他都能着手成春,惟妙惟消,创造出生动的意象。

4.下列各句中,没有语病的一句是()A.在共产党的领导下,不仅中国人民从根本上改变了1840年以来的半殖民地、半封建社会的困境,而且经过团结奋斗,使国民经济得到了恢复和好转。

B.国家安全问题,从美伊战争和紧张的台海局势看,发展我国的海军和空军,获得制海权和制空权,已经是刻不容缓的了。

C.结实的王经理的办公桌搬到宽大办公室的中央,再把高背老板椅往办公桌后面一摆,人们立即感觉到一种威严。

湖北省武汉市二月份月考文综试题人教版

湖北省武汉市二月份月考文综试题人教版

武汉市2007届高中毕业生二月调研测试文科综合试卷2007. 2. 6第Ⅰ卷(选择题,共140分)注意事项:1.本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(综合题)两部分。

满分300分。

考试用时150分钟。

2.答卷前,考生务必将自己的姓名、准考证号填在试卷的答题卡上,并认真核对条形码上的准考证号,在规定的位置贴好条形码。

3.每小题选出答案后,用2B铅笔把答题卡上对应题目的答案标号涂黑,如果需要改动,用橡皮擦干净后,再选涂其它答案标号,答在试卷上无效。

一、本卷共35小题,每小题4分,共140分。

在每小题列出的四个选项中,只有一项是符合题目要求的。

北京时间2006年11月15日19点15分左右,在某海域(46.6°N,153.3°E)发生8.1级强烈地震,并引发周边沿海2起小规模海啸。

回答1~2题。

1.地震发生时,东半球所处区域A.全部处在11月15日B.大部分处在11月15日C.少部分处在11月15日D.全部处在11月14日2.地震发生地区当天与下列几个日期的正午太阳高度角最接近的是A.1月28日B.4月15日 C.6月18日 D.10月17日图1为“我国某山地剖面图”,读图1回答3~5题。

3.根据图中资料可以判断该地区属于A.热带季风气候B.亚热带季风气候C.温带季风气候D.温带大陆性气候4.该地区七月份气温A.从南向北依次递减B.从北向南依次递减C.随海拔增加而增加D.随海拔增加而减少5.有图中信息可知A.山地的南坡为夏季风的迎风坡B.该地的蒸发量与地形有密切关系C.该地冬季降水量大于夏季降水量D.该地的风向为偏北风下图中甲是我国东部河流某河段示意图,乙是EF河段河床示意图,丙是河流A、B两水文站测得的水位变化图。

据此完成6~8题。

6.甲图中AB段河流A.由西北流向东南B.有东南流向西北C.水位A处低于B处D.不能确定7.丙图中河流出现最高水位时,可能是由于出现下列现象中的造成的A.气旋活动频繁B.梅雨连绵C.冰雪融化D.春雨霏霏8.关于乙图EF的河床剖面的描述及形成理由正确的是①E岸河床较缓,F河床较陡②E岸河床较陡,F河床较缓③由于地球的自转使河水发生偏向,F岸遭受冲蚀力大④由于该处河流是弯道,E岸遭受冲刷力大A.①③B.①④C.②④D.②③下图为陕西宝鸡(34°N,107°N)到四川巴中(32°N,107°E)一线降水量和1月平均气温曲线图,完成9~11题。

湖北省五市2007届高三年级第二次联考调研英语-旧人教[整理]全国通用-三轮冲刺

湖北省五市2007届高三年级第二次联考调研英语-旧人教[整理]全国通用-三轮冲刺

湖北省五市2007届高三年级第二次联考调研英语2007.4本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共150分.考试时间120分钟.第Ⅰ卷(选择题,三部分,共30分)第一部分听力(共两节,满分30分)第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话。

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

听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What did the man buy yesterday?A. ShirtsB. ShoesC. Trousers.2. When can the woman get the computers?A.On Tuesday.B.On Wednesday.C.On Thursday.3. What is the woman doing now?A. Changing her clothes.B. Watering the flowers.C. Starting for a meal.4. Where are Lisa's parents?A. At the airport.B. In California.C. In hospital.5. What are the speakers talking about?A. A plan for sightseeing in London.B. A plan for Thursday morning.C. The man's family's arriving.第二节(共15小题;每小题1.5分,满分22.5分)听下面对话或独白。

每段对话或独白后有几道小题,从每题所给的A、B、C三个选项中选出最佳选项。

并标在试卷的相应位置。

听每段对话或独白前,你将有5秒钟时间阅读各小题。

听完后,每小题将给出5秒钟的作答时间。

武昌区2007届高三年级调考数学试卷及答案(文科)

武昌区2007届高三年级调考数学试卷及答案(文科)

2007届高三调考数学试题参考答案及评分标准(文科)二.填空题11. 15-. 12. ⎥⎦⎤⎢⎣⎡7,1933. 13.60. 14. ()1,0. 15. ①②④.三.解答题16. 解:(Ⅰ)()1,220=∴==a a f . 又2,23214323=∴+=+=⎪⎭⎫⎝⎛b b af π. ()142sin 212cos 2sin cos sin 2cos 22+⎪⎭⎫ ⎝⎛+=++=+=∴πx x x x x x x f . …4分()21max +=∴x f ,()21min -=x f . ……………………………6分(Ⅱ)由πππππk x k 224222+≤+≤+-()Z k ∈,解得()Z k k x k ∈+≤≤+-ππππ883. 所以,函数()x f y =的单调增区间为()Z k k k ∈⎥⎦⎤⎢⎣⎡++-ππππ8,83. ……………12分17. 解:(Ⅰ)由题意知()022=++='b ax x x f 的两根分别为1-=x 或3=x .()()⎩⎨⎧=⨯--=+-∴b a31231,解得3,1-=-=b a .()133123+--=∴x x x x f . ……………………………4分 由题意知函数()x f 的单调递增区间为()1,-∞-和()+∞,3,递减区间为()3,1-.…6分 (Ⅱ)根据(Ⅰ)的分析知,函数()x f 的极大值为()381=-f ,极小值为()83-=f .在同一坐标系内分别作()k y x f y ==和的大致图象.∴当38=k 或8-=k 时,原方程有且仅有两个不相等的实数根; 当8-<k 或38>k 时,原方程有且仅有一个不相等的实数根;当388<<-k 时,原方程有且仅有三个不相等的实数根. …………………………12分18. 解:(Ⅰ)若获得冠军,则需每轮过关,其概率为612132435465=⨯⨯⨯⨯. ………6分(Ⅱ)前两轮过关第三轮被淘汰或前三轮过关第四轮被淘汰,其概率为313214354654315465=⎪⎭⎫ ⎝⎛-⨯⨯⨯+⎪⎭⎫ ⎝⎛-⨯. …………………………12分 (说明:没有文字说明扣2分)19. 解:(Ⅰ) C B D A 11//,D MA 1∠∴是异面直线M A 1与C B 1所成的角(或补角). 又3,5,211===MD D A MA ,由余弦定理,得510cos 1=∠D MA ∴M A 1与C B 1所成的角的余弦值为510. ……………………………6分 (Ⅱ)取1AA 的中点P,联结MP NP P B ,,1,则11PNC B 为平行四边形,N C P B 11//∴ 又MP B A 11为正方形,P B M A 11⊥∴,N C M A 11⊥∴. 又B A M A B A C B 11111,平面平面⊂⊥,M A C B 111⊥∴.111A NC B M 平面⊥∴.又111MC A M A 平面⊂, 1111NC B MC A 平面平面⊥∴. …………………………12分 (注意:若用向量法相应给分)20. 解:(Ⅰ) 0,11≠⋅=-=--n n n n n n S S S S S a ()2≥n1111-=-∴-n n S S .又2911=S⎭⎬⎫⎩⎨⎧∴n S 1为以29为首项,1-为公差的等差数列. ……………………………5分(Ⅱ)由(Ⅰ)知,()()221111291nn S n -=-⨯-+= nS n 2112-=∴.当2≥n 时,()()n n S S a n n n 21321141--=-=-,()()()()⎪⎪⎩⎪⎪⎨⎧≥--==∴22132114192n n n n a n . …………………………9分 由()()02132114<--n n ,解得213211<<n ,而*∈N n ,6=∴n .故所求n 的集合为{}6. ……………………13分21.解:(Ⅰ)()1,022,2∈=∴=dPD PD d . ∴点P 的轨迹是以D 为焦点,l 为相应准线的椭圆.由22==a c e ,又12=-c c a ,解得1,2==c a . 以CD 所在直线为x 轴,以CD 与⊙D 的另一个交点O 为坐标原点建立直角坐标系.∴所求点P 的轨迹方程为1222=+y x . ……………………………6分(说明:其它建系方式相应给分)(Ⅱ)22== ,G ∴为椭圆的左焦点. 又()0,0=+⋅∴=⋅+⋅ .由题意,0,0≠+≠PM PG GM (否则P 、G 、M 、D 四点共线与已知矛盾)()()0,022=-=+⋅-∴PG PM PM PG PG PM .=.又 点P 在椭圆上,22322222====+a .又PDG ∆∴=,2为直角三角形,90=∠PDG .2222221=⨯⨯=∴∆PDG S . ……………………………14分。

2007届湖北武汉武汉中学高三年级调研试卷

2007届湖北武汉武汉中学高三年级调研试卷

2007届湖北省武汉市武汉中学高三年级调研试卷第Ⅰ卷(选择题,共50分)一、单项选择题(本大题共25小题,每小题2分,共50分。

在每小题给出的四个选项中,只有一项是符合题目要求的。

)下图为某国家轮廓图。

读图回答下列1—3题。

1.该国家国民经济的主要支柱产业是()A.渔业B.森林工业C.种植业D.畜牧业2.在以下各种资源中,该国可以充分开发利用的自然资源是()A.铁矿资源B.森林资源C.地热资源D.野生动物资源3.该岛屿的东西方向跨距最大约是()A.320km B.540km C.760km D.1100km下图为南极洲示意图。

读图回答下列4—6题。

4.我国长城站位于图中②所在国家的A.西北方B.东南方C.西南方D.东北方5.在图中①、②、③、④的所在国家中,修建了东水西调工程的国家是()A.①B.②C.③D.④6.在南极洲上空出现臭氧层空洞的季节,①所在国家从事的农业活动可能是()A.收获咖啡B.收获可可C.播种玉米D.收割小麦下图为“洋流分布图”(局部)。

读图回答下列7—10题。

7.下列四幅图等温线分布图中(等温线数值①>②>③),能正确反映乙地沿岸洋流的是()8.比较图中①②③④四地盐度,由大到小排列正确的是()A.④>①>②>③B.①>②>③>④C.④>③>②>①D.④>③>①>②9.图中甲处成为渔场的主要原因是()A.有温带浅海冷海水上泛带来营养盐类 B.有沿岸河流带来营养盐类C.有上升补偿流从海底带来营养盐类D.位于寒暖流交汇处10.图中乙处气候的典型特征是多雾干旱,多雾的主要原因是()①沿岸有暖流经过②沿岸有寒流经过③山地背风坡降水少④距海近,空气中有成雾所需水汽A.①③B.②③C.①④D.②④下面一组图反映四个地区的不同地貌景观。

读图回答下列11—13题。

11.在四幅地貌景观图中,表示喀斯特地貌景观的是()A.①图B.②图C.③图D.④图12.组成图③地貌景观的岩石比较单一,按其成因它属于()A.沉积岩B.变质岩C.侵入型岩浆岩D.喷出型岩浆岩13.在四幅图中的地层里,最不可能找到化石的是()A.①图B.②图C.③图D.④图下图为“我国部分地区7月份平均气温图(单位:℃)。

2007届湖北武汉武汉中学高三年级调研试卷文

2007届湖北武汉武汉中学高三年级调研试卷文

2007届湖北省武汉市武汉中学高三年级调研试卷(文)考试时间为120分钟 第Ⅰ卷(选择题,共50分)一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的.1.已知全集U =R ,集合},3|{},,2|{3R x x x y y B R x y y A x ∈-==∈-==,则 ( ) A .}049|{<<-x x B .}49|{-<x xC .{(1,-2)}D .}49|{-≤x x2.5人站成一排,甲、乙两人相邻的不同站法的种数为 ( )A .24B .36C .48D .603.已知等比数列{a n }若883=⋅a a 则数列{a n }前10项的积T n 等于 ( )A .230B .215C .15)21(D .2164.在△ABC 中,a 、b 、c 分别为角A 、B 、C 的对边,ccb A 22cos 2+=,则△ABC 的形状为( ) A .正三角形B .直角三角形C .等腰直角三角形D .等腰三角形或直角三角形5.已知平面上三点A 、B 、C 满足⋅+⋅+⋅===则,5||,4||,3||的值等于 ( )A .25B .24C .-25D .-246.已知函数0)1(),0()(2=->++=f a c bx ax x f ,则“b<0”是“f (1) < 0”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7.如图所示,在正方体ABCD —A 1B 1C 1D 1的侧面AB 1内有一动点P 到平面A 1C 1的距离是直线BC 的距离的2倍,点M 是棱BB 1的中点,则动点P 所在曲线的大致形状为 ( )8.椭圆122=+by ax 与直线x y -=1交于A 、B 两点,过原点与线段AB 中点的直线的斜率为ba则,23的值为 ( )A .23B .332C .239D .2732 9.已知函数c bx x g ax x x f +=+=23)(2)(与的图象都过点P (2,0),且在点P 处有公共切线,则函数g (x )的表达式为( )A .2x 2-4xB .6x 2-24C .-4x 2+ 16D .4x 2-1610.一次研究性课堂上,老师给出函数)(||1)(R x x xx f ∈+=,三位同学甲、乙、丙在研究此函数时分别给出命题:甲:函数f (x )的值域为(-1,1);乙:若x 1≠x 2,则一定有f (x 1)≠f (x 2);丙:若规定||1)()),(()(),()(11x n x x f x f f x f x f x f n n n +===-则对任意*∈N n 恒成立.你认为上述三个命题中正确的个数有 ( )A .0个B .1个C .2个D .3个第Ⅱ卷(非选择题,共100分)二、填空题:本大题共5小题,每小题5分,共25分. 11.10)211(x -的展开式中x 3的系数为 .(用数字作答)12.已知x ,y 满足约束条件132,12340++⎪⎩⎪⎨⎧≤+≥≥x y y x xy x 则的取值范围是 . 13.已知双曲线)0,0(12222>>=-b a by a x 的右焦点为F ,右准线与一条渐近线交于点A ,△OAF 的面积为263a (O 为坐标原点),则双曲线的两条渐近线的夹角为 . 14.若函数(]2,)2(log )(2∞-+-=在ax x f 上是减函数,则实数a 的取值范围是 . 15.直角坐标系中横坐标、纵坐标均为整数的点称为格点,如果函数f (x )的图象恰好通过k 个格点,则称函数 f (x )为k 阶格点函数.下列函数:①x x f sin )(=;②3)1()(2+-=x x f π;③xx f )31()(=;④.lo g )(6.0x x f =其中是一阶格点函数的有 .(填上所有满足题意的序号)三、解答题:本大题共6小题,共75分.解答应写出文字说明,证明过程或演算步骤. 16.(本小题满分12分)已知函数.2321)3(,2)0(,cos sin cos 2)(2+==+=πf f x x b x a x f 且 (Ⅰ)求函数f (x )的最大值与最小值; (Ⅱ)求函数f (x )的单调增区间.17.(本小题满分12分)已知函数131)(23+++=bx ax x x f 在1-=x 处取得极大值,在x = 3处取极小值. (Ⅰ)求f (x )的解析式并指出其单调区间; (Ⅱ)讨论方程f (x )=k 的实根的个数.18.(本小题满分12分)武昌区某中学举行春季运动会,高三某班李萍同学参加女子乒乓球单打比赛.假定从开始的小组淘汰赛到最后决定出冠亚军共经过5轮比赛.若李萍同学在5轮比赛中顺利过关的概率依次为.21,32,43,54,65试问: (Ⅰ)李萍同学获得该项冠军的可能性有多大? (Ⅱ)李萍同学在第二轮或第三轮被淘汰的概率是多少?19.(本小题满分12分)如图,在正四棱柱ABCD —A 1B 1C 1D 1中,AB = a ,AA 1 = 2a ,M ,N 分别是棱BB 1,DD 1的中点.(Ⅰ)求异面直线A 1M 与B 1C 所成的角的余弦值; (Ⅱ)求证:平面A 1MC 1⊥平面B 1NC 1;20.(本小题满分13分)已知数列{a n }的前n 项和为S n ,且.92),0,2(11=≠≥⋅=-a S n S S a n n n n (Ⅰ)求证:数列}1{nS 为等差数列; (Ⅱ)求满足0<n a 的自然数n 的集合.21.(本小题满分13分)如图,已知直线l 与半径为1的⊙D 相切于点C ,动点P 到直线l 的距离为d ,若.||2PD d = (Ⅰ)求点P 的轨迹方程;(Ⅱ)若轨迹上的点P 与同一平面上的点G 、M 分别满足0,3,2=⋅+⋅==,求以P 、G 、D 为项点的三角形的面积.。

湖北省五市2007届高三年级第二次联考调研

湖北省五市2007届高三年级第二次联考调研

湖北省五市2007届高三年级第二次联考调研语文2007.4本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分,共150分.考试时间150分钟.第Ⅰ卷(选择题,共30分)一、(12分,每小题3分)1.下列词语中没有错别字的一组是()A.辐射戎马倥偬计日程功无耻斓言B.撕打声名鹊起相辅相成功亏一篑C.赝品忧柔寡断高屋建瓴唇枪舌剑D.斡旋开源节流备受青睐好高骛远2.下列各句中,加点的成语使用恰当的一句是()A.南京的首场古董挂表拍卖会结果差强人意,美国收藏家协会会员项明华收藏的23款古董挂表昨天仅仅拍出了一块——华生1906年产的银壳钻挂表以底价1300元拍出。

B.姚明本赛季不仅能内线强打得分,而且也能外线投篮命中,表现近乎完美。

他能取得今天的成功,并不是一挥而就的,而是与他过去几个赛季的努力分不开的。

C.为提高公路建设质量,省交通厅去年11月专门出台《河南省公路建设从业单位业绩信誉动态管理暂行办法》,旨在用“阳光作业”遏制“暗箱操作”。

D.著名学者吴组缃教授生前说过,《红楼梦》的思想艺术成就被人们认识到的只是‘表里山河’,藏在水下的更多。

”3.下列各句子,没有语病的一句是( )A.照片拍得好,诗歌写得有味,是由一个人的思想认识、艺术水平的高低决定的。

B.这套护身服可比“护身符”管用,到了太空,一旦发生真空、低压以及缺氧、低温等恶劣环境,航天服就是宇航员的“救身符”。

C.花明天的钱过今天的日子,国外盛行的这种消费理念在郑州人买房问题上表现得最为抢眼,郑州大约有七成左右的市民买商品房选择了按揭贷款。

D.以一种轻松平等的方式取代毕恭毕敬的心情,在呼朋引伴的称呼中表现彼此友好的姿态,这不能不说是“朋友”一词的魅力所在。

4.依次填入下面一段文字中横线处的语句,最恰当的一组是()儿童时代放牛为业,每天最大的心愿是给牛找到丰盛的野草。

当在林中、溪边、田埂之上看到青翠鲜嫩的水草,便有如获大发现时的激动感。

①因此期待田里应该长野草而非庄稼,这是源于对牛的心爱②这种激动源于对牛的心爱,因此也期待田里应该长野草而非庄稼③由此也想到美的本源,特别是对园艺美的反思④由此也想到园艺美的本源,特别是对美的反思⑤野草是美的,因为和庄稼或鲜花在本质上并没有区别⑥因为和庄稼或鲜花在本质上并没有区别,所以野草也是美的A.①④⑤B.②③⑤C.①③⑥D.②④⑥二、阅读下文,完成5—7题。

武汉市高三级二月调研考试英语试卷

武汉市高三级二月调研考试英语试卷

武汉市⾼三级⼆⽉调研考试英语试卷武汉市2007届⾼三年级⼆⽉调研考试英语试题考试时间:2007年2⽉6⽇3:00—5:00考⽣注意:本试题由第⼀卷和第⼆卷两部分构成。

满分150分,考试时间120分钟。

第1卷(三部分,共115分)注意事项:1.本试卷分第1卷(选择题)和第Ⅱ卷(⾮选择题)两部分。

共150分:考试⽤时120分钟。

2.答题前,考⽣务必将⾃⼰的姓名、准考证号填写在试卷和答题卡上,并将准考证号条形码粘贴在答题卡上的指定位置。

3.每⼩题选出答案后,⽤2B铅笔把答题卡上对应题⽬的答案标号涂⿊。

如需改动,⽤橡⽪擦⼲净后,再选涂其它答案标号。

答在试卷上⽆效。

考试结束,监考A员将本试卷和答题卡⼀并交回。

第⼀部分:听⼒(共两节,满分30分)做题时,先将答案划在试卷上。

录⾳内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第⼀节(共5⼩题,每⼩题1.5分,满分7.5分)·听下⾯5.段对话。

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

听完每段对话后,你都有10秒钟的时间来回答有关⼩题和阅读下⼀⼩题。

每段对话仅读⼀遍。

1. What is the most probable relationship between the two speakers?A. Mother and son.B. Teacher and student.C. Bus driver and passenger.2. How do they like the film?A. The music is good, but not the movie.B. The music is good, as well as the movie.C. The movie is good, but not the music.3. What is the man speaker most probably?A. A librarian.B. A geography teacher.C. A customer.4. How can the man help the girl?A. He may find something for her.B. He will have a look at the racks.C. He can do nothing for her.5. What' s Sandra planning to do?A. Leave the basketball team.B. Start a different sport.C. Never play basketball any more.第⼆节(共15⼩题;每⼩题1.5分,满分22.5分)听下⾯5段对话或独⽩。

高三年级调研考试数学文

高三年级调研考试数学文

高三年级调研考试数学文湖北省武汉市2007届高三年级调研考试文科数学试题本试卷150分,考试用时120分钟。

注意事项:1.本卷1—10题为选择题,共50分;11—21题为非选择题,共100分。

请把答案全部写在答题卷上,答在试题卷上无效。

考试终止后,监考人员将答案卷收回。

2.答卷前,考生务必将自己的学校、班级、姓名、准考证号填写在试题卷和答题卷指定的位置。

3.选择题选出答案后,用2B 铅笔把答题卷上对应题目的答案标号涂黑。

如需改动,请用橡皮擦洁净后,再选涂其它答案标号。

4.非选择题请用0.5毫米黑色签字笔答在答题卷上每题所对应的答题区域内,答在指定区域外无效。

参考公式:假如事件A 、B 互斥,那么P (A +B )=P (A )+P (B ) 假如事件A 、B 相互独立,那么P (A · B )=P (A )·P (B )假如事件A 在一次试验中发生的概率是p ,那么n 次独立重复试验中恰好发生k 次的概率kn k k n n P P C k P --=)1()(.球的表面积公式 24R S π= 其中R 表示球的半径 球的体积公式 334R V π=球 其中R 表示球的半径一、选择题:本大题共10题,每小题5分,共50分。

在每小题给出的四个选项中,只有一项是符合题目要求的。

1.设全集U=R ,集合M=}|{},0|{2x x x N x x ≤≥,则下列关系中正确的是 ( )A .M ∩N=MB .M ∩N=NC .M ∪N=RD .M ∪N=N 2.316tanπ的值是( )A .33 B .-33 C .3 D .-33.记函数)1(log 2+=x y 的反函数为)3(),(g x g y 则== ( )A .2B .3C .7D .84.为了了解某校高三调考学生成绩,用简单随机抽样的方法从中抽取了100名学生的成绩进行统计分析,在那个问题中,100被称为 ( )A .总体B .个体C .从总体中抽取的一个样本D .样本容量5.已知两个非零向量22),2,3(),6,3(,--=--=+则若与= ( )A .-3B .-24C .21D .126.在等差数列}{n a 中,若1210159331,72a a a a a -=++则的值为 ( )A .15B .16C .17D .187.若直线)0,(022>=+-b a by ax 始终平分圆014222=+-++y x y x 的圆周,则ba 11+ 的最小值是( )A .4B .2C .41 D .21 8.棱长为a 的正四面体中,高为h ,斜高为m ,相对棱间的距离为d ,则a 、m 、h 、d 的大小关系正确的是( )A .d h m a >>>B .h m d a >>>C .m d h a >>>D .m h d a >>>9.在锐角△ABC 中,A >B , 则有下列不等式:①sin A>sinB ;②cos A <cos B ;③sin2A >sin2B ;④cos2A <cos2B A .①③ B .②③ C .①②③ D .①②④ 10.定义在R 上的函数)2,(),(-∞=在x f y 上是增函数,且函数)2(+=x f y 是奇函数,当 )()(,|2||2||2|,2,22122121x f x f x x x x x +-<-<-><则时且的值( )A .可能为0B .恒大于0C .恒小于0D .可正可负二、填空题:本大题共5小题,每小题5分,共25分.11.不等式0112≥+-x 的解集为 . 12.在32)2(xx -的展开式中,常数项为 .(用数字作答)13.在约束条件⎪⎪⎩⎪⎪⎨⎧≤+≤+≥≥42,3,0,0y x y x y x 下,目标函数y x z 23+=的最大值是 .14.直线AB 过抛物线y 2=x 的焦点F ,与抛物线交于A 、B 两点,且|AB |=3,则线段AB 的中点到y 轴的距离为 . 15.定义运算2)32()(,)()(*x x x f b a b b a a b a *+=⎩⎨⎧<≥=则函数的最小值是 .三、解答题:本大题共6小题,共75分. 解承诺写出文字说明、证明过程或演算步骤. 16.(本小题满分12分)设函数.1sin 22sin )(2+-=x x x f(1)求f (x )的单调递增区间; (2)设θθ2sin ,57)2(求=f 的值. 17.(本小题满分12分) 箱子中有红、黄两种颜色的卡片各4张,现有甲、乙两人从箱子中轮番抽取卡片,甲先抽,乙后抽,然后甲再抽,…,抽取后不放回,直到两人中有一人抽到红色卡片时就终止. 假设每张卡片在每一次被抽取的机会是等可能的. (1)求甲恰好在第二次抽到红色卡片的概率; (2)求甲抽到红色卡片的概率. 18.(本小题满分12分)如图,四棱锥P —ABCD 的底面为正方形,P A ⊥底面ABCD ,AB =1,P A =6,E 为CP 的中点.(1)求直线DE 与平面ABCD 所成角的大小. (2)求二项角E —AD —C 的正切值.(3)在线段PC 上是否存在一点M ,使PC ⊥平面MBD ?假如存在,求出MC 的长;假如不存在,请说明理由.19.(本小题满分12分)已知单调递增的等比数列234322,28,}{a a a a a a n 是且中+=++、a 4的等差中项.(1)求数列}{n a 的通项公式; (2)若}1{,log 12+=n n n n b b a b 求数列的前n 项和T n .20.(本小题满分13分)已知函数)0(1232)(3<-+=k kx x x f . (1)求函数)(x f 的单调区间;(2)当实数k 在什么范畴内变化时,函数)(x f y =的图象与直线y =3只有一个公共点. 21.(本小题满分14分)已知双曲线122=-x y ,过上焦点F 2的直线与下支交于A 、B 两点,且线段AF 2、BF 2的长度分别为m 、n .(1)写出直线AB 的斜率k 的取值范畴; (2)证明mn ≥1;(3)当直线AB 的斜率]55,31[∈k 时,求mn 的取值范畴.参考答案一、选择题1.B 2.C 3.C 4.D 5.C 6.B 7.A 8.A 9.D 10.B 二、填空题11.),1(]1,(+∞--∞ 12.12 13.7 14.4515.1 三、解答题16.(1))42sin(22cos 2sin )(π+=+=x x x x f…………3分由224222πππππ+≤+≤-k x k ,得单调增区间为)](8,83[Z k k k ∈+-ππππ.…………6分(2)由57cos sin ,57)2(=+=θθθ得f平方得.25242sin =θ…………12分17.(1)记“甲恰好在第二次抽到红色卡片”的为事件A ,则71)(381424==A A A A P…………4分(2)甲抽到红色卡片分为三类: 第一类:甲第一次抽到红色卡片,概率为;21841==P第二类:甲第二次抽到红色卡片,概率为;712=P第三类:甲第三次抽到红色卡片,概率为7015814443==A A A P ;…………10分因此,甲抽到红色卡片的概率为.3523321=++=P P P P …………12分18.(1)如图,连结AC ,BD 交于点0,连结OE ,则OE//PA. ∵PA ⊥底面ABCD , ∴OE ⊥面ABCD. ∠EDO 为DE 与平面ABCD 所成的角. …………2wv60,3tan ,2621=∴=∠==EDO EDO PA OE …………4分(2)过点0作OF ⊥AD 于F ,连结EF ,由三垂线定理得EF ⊥AD ,则∠EFO 为二面角E —AD —C 的平面角. …………6分6tan ,21=∠∴=EFO OF . …………8分(3)过点O 作OM ⊥PC 于M ,由△COM~△CPA ,得 42=CM . …………10分∵PC ⊥OM , ∴PC ⊥面MBD.因此,求M 存在,且使CM=42. …………12分方法二:向量法(参照给分).19.解:(1)由2342423432)2(228a a a a a a a a a =⋅⎩⎨⎧+=+=++及,解得 424242(416164a a a a a a >⎩⎨⎧==⎩⎨⎧==或不合题意,舍去). …………4分从而a 1=2,q =2.n n a 2=∴…………6分 (2)n b nn ==2log 2 .…………8分132211111111)1(11+++++=∴+-=+=∴n n n n n b b b b b b T n n n n b b)111()3121()211(+-++-+-=n n.1111+=+-=n nn…………12分20.解:(1).23)(2k x x f +='由k x x f -±=='得,0)(.…………2分);,(),,()(0)(,0)(,+∞----∞∴<'-<<-->'->--<k k x f x f k x k x f k x k x 的单调递增区间是时当时或当递减区间为),(k k --.…………6分(2)由(1)知,当1)(34)()(,3--=----=k k f x f k x 取得极大值时, 当1)(34)()(,3---=--=k k f x f k x 取得极小值时 …………8分依题意,要使函数3)(==y x f y 与只有一个公共点,须.3)(,3)(><极小极大或x f x f…………10分.31)(3409,31)(34333无解而解得由>---<<-<--k k k因此,所求实数k 的取值范畴是)0,9(3-.…………13分21.解:(1)所求斜率的范畴是11<<-k . (说明:只要写出范畴,不需考查过程) …………2分(2)易知双曲线上焦点为)2,0(. 设直线AB 的方程为).,(),,(,22211y x B y x A kx y +=当k=0时,A 、B 两点的横坐标分别为1和-1, 现在mn=1. …………4分当2,0+=≠kx y k 将时代入双曲线方程,消去x 得0222)1(222=++--k y y k .…………6分由双曲线的第二定义,知121y m +-=,221y n +-=…………8分因此,.1112111)(2212222121>-+=-+=+-+=k kk y y y y mn 综上,知mn ≥1.…………10分(3)记,λ=mn 由(2)知,,1122λ=-+kk 解得.112+-=λλk 由2354,51912≤≤≤≤λ解得k 为所求. …………14分欢迎访问 :// k12zy。

湖北省武汉中学2007届高三年级调研考试(英语)

湖北省武汉中学2007届高三年级调研考试(英语)

湖北省武汉中学2007届高三年级调研考试英语试题说明:本试题分为第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分.共150分;考试用时120分钟.答卷前,考生务必将学校、班级、姓名等在答题卡和第Ⅱ卷上填写清楚;第I卷答案一律用2B铅笔在答题卡上填写,第Ⅱ卷答案一律填写在第Ⅱ卷对应的空白栏上。

考试结束后请将答题卡和第Ⅱ卷一并交回。

第I卷(选择题,共115分)第一部分:听力(共两节,满分30分)做题时,先将答案划在试卷上。

录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题;每小题1.5分,满分7.5分)听下面5段对话。

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

听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What time will the two speakers leave ?A.At 7:30. B.At 8:00. C.At 9:10.2.What are the two speakers talking about ?A.Past experiences . B.Family members . C.Traveling abroad . 3.Where does this conversation most probably take place ?A.At a theatre B.At a restaurant . C.At a gas station .4.What can we know about the woman ?A.She doesn’t’ understand the man .B.She can’t hear the man clearly .C.She is angry with the man .5.Why is the man angry with Anne ?A.She hasn’t turned up . B.She drives too slowly . C.She is rude to him .第二节(共15小题;每题1.5分,满分22.5分)听下面5段对话或独白。

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武汉市2007届高三年级二月调研考试英语试题考试时间:2007年2月6日3:00—5:00考生注意:本试题由第一卷和第二卷两部分构成。

满分150分,考试时间120分钟。

第1卷(三部分,共115分)注意事项:1.本试卷分第1卷(选择题)和第Ⅱ卷(非选择题)两部分。

共150分:考试用时120分钟。

2.答题前,考生务必将自己的姓名、准考证号填写在试卷和答题卡上,并将准考证号条形码粘贴在答题卡上的指定位置。

3.每小题选出答案后,用2B铅笔把答题卡上对应题目的答案标号涂黑。

如需改动,用橡皮擦干净后,再选涂其它答案标号。

答在试卷上无效。

考试结束,监考A员将本试卷和答题卡一并交回。

第一部分:听力(共两节,满分30分)做题时,先将答案划在试卷上。

录音内容结束后,你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题,每小题1.5分,满分7.5分)·听下面5.段对话。

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

听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. What is the most probable relationship between the two speakers?A. Mother and son.B. Teacher and student.C. Bus driver and passenger.2. How do they like the film?A. The music is good, but not the movie.B. The music is good, as well as the movie.C. The movie is good, but not the music.3. What is the man speaker most probably?A. A librarian.B. A geography teacher.C. A customer.4. How can the man help the girl?A. He may find something for her.B. He will have a look at the racks.C. He can do nothing for her.5. What' s Sandra planning to do?A. Leave the basketball team.B. Start a different sport.C. Never play basketball any more.第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或独白。

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

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

每段对话或独白读两遍。

听第6段材料,回答第6---7题。

6. Why doesn' t the woman eat hamburgers?A. She doesn't eat any meat.B. She wants to lose weight.C. She doesn't like oily things.7. What does the man think of the woman' s attitude?A. He understands her.B. He accepts it.C. He doesn't agree with it.听第7段材料,回答第8---9题。

8. What is the woman' s job?A. A language teacher.B. A computer technician.C. A painter.9. What was the woman good at as a student?A. Mathematics.B. Painting.C. Physics.听第8段材料,回答第10---12题。

10. According to the man, when did the area start to develop?A. In 1837.B. In 1860.C. In 1898.11, What do we know about Watlington House?A. Il used to be a hospital.B. It is next to the school.C. It is opposite St John' s Church.12. What do we know about the industries of the area in the past?A. They were. mainly connected to the building industry.B. They mainly produced daily necessities.C. Their products were mainly for office use.听第9段材料,回答第13---16题。

13. Why does Lucy think her parents are too strict with her?A. They don't allow her to choose her clothes herself.B. They foree her to keep away from all her friends.C. They forbid her to go out on weekdays.14. How do Lucy' s parents think of her homework?A. It must be finished before anything else.B. It's not difficult enough yet.C. It'should be out of the way before Saturday.15. What does Lucy mean by saying: "We' re all in the same boat" ?A. Peter is in a very similar situation.B. Her friends' parents are as strict as hers.C. Her parents have the same problems.16. What do Peter' s parents want him to be?A. Independent.B. Brave.C. Honest.听第10段材料,回答第17---20题。

17. What does the speaker mainly wants to tell us about?A. Her motherland.B. Her home city.C. A big island.18. Where is Victoria?A. On Vancouver Island.B. On the mainland.C. In the city of Vancouver.19. How is the climate of Victoria?A. Very hot.B. Quite Cold.C. Not very cold.20. How long does the best season last to watch whales in Vietoria?A. About 3 months.B. About 5 months.C. About 8 months.第二部分:英语知识运用(共两节,满分45分)第一节:单项填空(共15小题;每小题1分,满分15分)21. I don' t believe what she told us about meeting Ehon John. I think she is ____ it up.A. makingB. takingC. pretendingD. weaving22. The _____ you sign your name can tell experts a lot about you.A. choieeB. wayC. methodD. means23. I don't like people who try to __ you with how much money they' ve got.A. impressB. showC. pressD. strengthen24. I think we should ______all these old toys to the local children hospital.A. give outB. give inC. give upD. give away25. I was driving my car when __ I heard a loud bang -- I had driven over some glass!A. once in a whileB. all at onceC. the soonestD. in no time26. You should take a few days ______work, you' re not looking at all well.A. ofB. fromC. offD. at27. Mom' s spent the day shopping, cleaning and cooking and now she________A. has worn outB. ts worn outC. is wearing outD. wears out28. - ---After living in a village for so long, Kathy won't want to move to a big city.- ----I don't imagine______.A. soB. tooC. itD. that29. We buy fruit and vegetables at the market, but we get ____bread from ____ bakery near our house.A. 不填; 不填B. the; 不填C. the; aD. 不填; a30. She is not always so friendly. I wonder what sheA. is wantingB. has wantedC. wantsD. will want31. Oxford Street and Tottenham Street are very busy ______in London.A. shop streetsB. streets to shopC. shopping streetsD. streets for shops32. She did worse in the tests __ she expected, but better in the final examination.A. asB. thanC. sinceD. if33. If you ______ require any 'further information, please do not hesitate to contact us.A. shouldB. wouldC. couldD. might34. There was a choice between __ on the plane.A. chickens or fishB. chicken and fishesC. chicken or fishD. chickens and fish35. ------ John, I can' t play tennis at all. [ wonder if you could teach me.-----______ .Just name the day.A. I'm gladB. Go aheadC. If you like itD. With pleasure第二节:完形填空(共20小题,每小题1.5分,满分30分)"Gardening is good for the soul," Grandma always says. She lives in the 36 and hasa big yard with raised fiowerbeds and an organic vegetable patch, but I' m her 37 granddaughter and a fullqime city dweller. I always 38 about planting a garden in my neighborhood, but I never had the 39 Last year, the opportunity came by itself. The brownstone across the way was torn down. The lot remained 40 for months littered with garbage. When I decided to 41 the empty lot into a community garden, I started a difficult42 rewarding adventure.At first, the difficulties I had 43 me. I had to make fifteen phone calls to 44 city offices before the city would give me 45 permission to use the lot. Now with their permission, I put up fiyers(ft$!~-) in local grocery stores and buildings 46 volunteers to help pull weeds and 47 garbage, glass, rocks, an.d bricks. Only two people signed up. I48 doing most of the clearing myself. Not only did i have to clear tons of garbage in thelot, but I also had to use all my persuasive skill to convince a gang of kids to do their hangingout 49No matter what 50 I had, the rewards were far greater. After I had 51 some flowers and trees, the place looked attractive and 52 . More and more people in the community53 me and.wanted to help. Students in our local elementary school planted vegetables. A senior citizens' group started a small herb garden. I' ve gotten to know many 54 people in my community by starting this garden. Grandma was 55 gardening is good for the soul.36. A. city B. greenhouse C. hospital D. country37. A. only B. lofiely C. single D. close38. A. thought B. wondered C. dreamed D. talked.39. A. time B. chance C. desire D. plan40. A. empty B. there C. dark D. still41. A. get B. turn C. develop D. move42. A. and B. or C. therefore D. but43. A. discouraged B. stopped C. frightened D. troubled44. A. other B. different C. various D. all45. A. printed B. written C. oral D. admitted46. A. organizing B. finding out C. encouraging D. asking for47. A. collect B. remove C. transport D. recycle48. A. ended B. insisted on C. remembered D. kept on49. A. somewhere B. anywhere C. elsewhere D. everywhere50. A. difficulties B. problems C. troubles D. disadvantages51. A. bought B. watered C. selected D. planted52. A. quiet B. wild C. cheerful D. natural53. A. found B. called C. questioned D. accepted54. A. more B. old C. new D. strange55. A. bright B. wise C. humorous D. right第三部分:阅读理解(共20小题;每小题2分,满分40分)AThe Beijing municipal government has stepped up efforts to provide an efficient, safe and quick transportation system for the 2008 Olympic Games through planned special transport lines connecting Olympic venues(赛场) with the city external and internal routes.It is estimated that Beijing will receive a maximum of I. 2 million people per day at Olympic venues duringthe IS-day competition period.The transportation lines will mainly depend on a special transportation circle for the Olympics and several other main streets in Beijing. The circle consists of parts of the hmrth and fifth ring roads and their conneeting roads.Beijing provides special bus service anti free public transport services to athletes, coaches and judges. Olympic officials anti other honored guests will receive free car services.As part of the transport layout, the public transport system, especially the urban railway,is the priority project under construction. The length of the urban railway will reach over 100 kilometers later this month with the opening to traffic of the western section of the No. 13 Line.In an effort to speed up the development of public transport, new subway lines totaling 126 kilometers will be constructed from the current 63 kilometer.Among the planned urban railway lines, a high-speed 23 kilometer line will be constructedin the future to connect urban Beijing with the Capital International Airport, which is the first stop for most athletes and visitors to the 2008 Games.56. To make its transportation system more effective, Beijing is __A. replacing the city's old transportation routesB. combining new lines with existing onesC. building all the Olympic stadiums close togetherD. designing a system considered unusual in the world57. The main transportation lines for the Olympics will include __A. all the streets and roads in the cityB. both city streets and country roadsC. only some of the city' s roads and streetsD. only four or five roads at the most58. A cheap and convenient transport for an athlete to go to a particular stadium alone will beA. the taxiB. the free car sen'iceC. the special bus serviceD. the free public bus service59. The new transport line going downtown from Capital International Airport would be _A. the high-speed 23-kilometer railway lineB. the 126-kilometer subway lineC. the current 63-kilometer lineD. the No. 13 lineBAs a foreign visitors you are entitled to claim back the tax you pay on your purchases when you take them home.This service is offered by major retailers(零售商) world-wide.Note: If you are a European Union(EU) resident you cannot use the V AT(增值税) redund service within the EU.The V AT/GST rate in our country is 16%.Your total purchases (V AT/GST include ) in a store must be a minimun of 25%€Your Global Refund Cheque must be validated by Customs at departure within 3 months plus month of purchase.Your refund amount is the V AT/GST less an administrtion fee.1.IN THE STOREShop where you see the Global Refund TAX FREE SHOPPING,sign (over 225,000 stores worldwide) and simply ask for your refund cheque. You’ll find a highly trained member of staff happy to help and advise you.2.THROUGH CUSTOMSIf you leave a country,respectively the European Union,show your purchases,receipts and passport to customs offials and have your Global Refund cheque staped.3 COLLECT YOUR REFUNDYou have several choices:Immediate cash at our nearby Cash Refund Office,the direct crediting of a chosen credit card,a bank cheque sent to a chosen address and even,for certain countries a cash refund when you return home---what could be more convenient?60. The word :refund” in the text refers to _____.A. tichetB. goodsC. luggageD. money61.This text mainly wants to explain to us ____.A.reasons to pay taxB.,steps to claiming refundC. rates of taxexD. process to clear customs62. According to the policy,when you take a computer of 500€back home,how much would you get paid when leaving the country?A. Over 80€B. At most 40€C.About 60 €D.Nearly 120 €CI made a pledge(发誓) to myself on the way down to the vacation beach cottage. For two weeks I would try to be a loving husband and father. Totally loving. No ifs, ands or buts.The idea had come to me as I listened to a talk on my car radio. The speaker was quoting a Biblical(圣经的) passage about husbands being thoughtful of their wives. Then he went on to say, "Love is an act of will. A person can choose to love." To myself, I had tq admit that I had been a selfish husband. Well, for two weeks that would change. And it did. Right from the moment l kissed Evelyn at the door and said, "That new yellow sweater looks great on you.""Oh, Tom, you noticed," she said, surprised and pleased. Maybe a little puzzled.After the long drive, I wanted to sit and read. Evelyn suggested a walk on the beach. I started to refuse, but then I thought, "Evelyn' s been alone here with the kids all week and now she wants to be alone with me. ' We walked on the beach while the Children flew their kites.So it went. Two weeks of not calling the Wall Street firm where I am a director; a visit to the shell museum though I usually hate museums. Relaxed and happy, that' s how the whole vacation passed. I made a new pledge to keep on remembering to choose love.There was one thing that went wrong with my experiment, however. Evelyn and I still laugh about it today. On the last night at our cottage, preparing for bed, Evelyn stared at me with the saddest expression."What's the matter?" I asked her."Tom," she said in a voice filled with distress, "do you know something I don' t?""What do you mean?""Well ... that checkup({体检) I had several weeks ago ... our doctor ... did he tell you something about me? Tom, you' ye been so good to me ..- am I dying?"It took a moment for it all to sink in. Then I burst out laughing."No, honey, ' I said, wrapping her in my arms. "You' re not dying; I' m just starting to live."63. In the first paragraph, "No ifs, ands or buts" probably means_____.A. unnecessarilyB. unexpectedlyC. impossiblyD. unconditionally64. From the story we may infer that Tom drove to the beach cottage ______A. with his familyB. with EvelynC. aloneD. with his children65. During the two weeks on the beach, Tom showed more love to his wife becauseA. she looked lovely in her new clothes______B. he had made a lot of money in Wall StreetC. he was determined to be a good husbandD. she was seriously iii66. The underlined words "one thing" in the text refer to the fact that _A. he praised her sweater, which puzzled her.B. she insisted on visiting a museum, which he ~nated.C. he knew something about her illness but didn' t tell her.D. he was so good to her that she thought she must be dying.67. By saying "l' m just starting to live," Tom means that __A. he is just beginning to understand the real meaning of lifeB. he is just beginning to enjoy life as a loving husbandC. he lived an unhappy life before and is now starting to changeD. he is beginning to feel regret for what he did to his wife beforeDAlthough intelligence has been studied, and the brain has been studied, there is little understanding of how the brain works to produce intelligence. This has something to do with thefact that the brain contains around 100 billion cells( about the number Of stars in the Milky Way).One of the continuing myths about the relationship between intelligence and the brain is that the brains of very clever people are somehow physically different from those of ordinary people. At the beginning of the century an American scientist called E.A. Spitzka produced a list of the weights of the brains of important, well-known men. The heaviest brain on the list was that of Turgenev, the Russian novelist, at 2000g. However, the brain of another genius,Walt Whitman, weighed only 1282g.There are similarities between brains and computers. Computers can do complicated calculations at unbelievable speeds. But they work in a fixed way, because they can' t make memory associations. If we need a screwdriver and there isn' t one, we will think laterally (横向) and use a knife or coin instead. Computers can' t do this. In fact, it is claimed that whent comes to seeing, moving and reacting to stimuli( 刺激), no computer can compete with even the brain power of a fly.Most 'of our mental processes are deeply formed habits. Challenging your brain to do things differently helps it develop. Try changing routines as often as you can: take a bus instead of going by car, sit in a different chair. An extreme but useful exercise is to read something upside down -- you can actually feel your brain at work.Exercise more. Good health and fitness levels give you overall improved energy which leads to better concentration.Cooking is a good all-round mental exercise. It needs mathematical, organizational and scientific skills as well as challenging memory and creative ability. Use recipes at first and then learn to guess amounts, combinations, reactions of ingredients( i~[-d~t) and timing.Do puzzles and play games. Teach yourself to work out codes and expand your vocabulary at the same time.68. The brain is described in the text as a_____A. flyB. piece of art workC. cellD. machine69. The example of Walt Whitman is given to show that _A. he is not as clever as TurgenevB. there' s no relationship between weights of brain and intelligenceC. the bigger the brain, the cleverer the man.D. the brain of the genius is quite different from that of the ordinary70. The author mentions screwdriver to explain that____A. we can use something different instead of itB. only brain remembers the pastC. human brain is more powerful than computersD. brain works the same as computers71. The last 4 paragraphs of the text mainly tell us:_____A. Make your brain workB. Exercise is good for your healthC. Enjoy cooking rather than eatingD. Good habits should not be changedEJust a few weeks ago eight graffiti gang members were convicted (宣判) of causing 5,000 worth of damage on the London Underground. They are among more than 70 hard-core graffiti artists thought to be operating in London today. Most are aged under 20.Graffiti artists, or "grafters", operate in many British towns. They often work at night, covering walls, trains and railway stations in spray paint and marker pen.Some people regard graffiti as a form of vandalism(有意破坏). London Underground says that railusers find it ugly and offensive. It spends£2 m a year dealing with graffiti, and has even introduced trains with graffiti-resistant paint. "We don' t think it' s artistic or creative --it's vandalism. It's a huge nuisance to our customers, and it's ugly and offensive," says Serena Holleyl a spokeswoman for London Underground."It creates a sense 'of disorder," says Richard Mandel, a lawyer who prosecuted起诉) the graffiti gang. "Passengers feel as if the whole rail system is out of control."British Transport Police has a graffiti unit designed to catch grafters in the act. It spent five months tracking down the recently prosecuted gang.Graffiti art can also be a dangerous pastime. London Underground says that some teenagers have died in accidents during night graffiti "raids(突袭) ".However, others say that graffiti at its best is an art form. Art galleries in London and New York have exhibited work by increasingly famous graffiti artists. "Of course graffiti is art.There's no question about that," says David Grob, director of the Grob Gallery in London.Even some of those who think graffiti is wrong admit that graffers are talented. "It' s just that their artistic talent is channeled in the wrong direction,' says Barry Kogan, a lawyer who represented Declan Rooney, one of the gang member.There is a difference between "good graffiti"' and vandalism, says Dean Colman, a 24- year-old graffiti artist. "I' d never spray private property, like someone' s house. Some graffitiare disgusting. There's a big difference between that and graffiti which can brighten up grey walls."Dean makes a living as a graffiti artist. His days of illegal spraying are behind him, he says. He has worked on a television programme about graffiti, designed a series of government posters, and decorated nightclubs. He has exhibited his work at Battersea Arts Centre in Lndon, and he hastaught graffiti-spraying in youth clubs.Dean sees himself as an artist, and thinks that graffiti art does not get due~ recognition. "There' s no graffiti art in the Tare Gallery and there should be," he says. *'Graffiti is as valid as any other art form."72. The attitude of London Underground is that graffiti is __A. kind of art, but a problem because some passengers don' t like itB. something to be stopped at all costsC. annoying but they have more serious problems to worry aboutD. causing the price of tickets to go up and therefore needs to be stopped73. The British Transport Police___A. have killed some "grafters" by accidentB. spent a lot of time trying to catch a group of graffiti artists.C. have recently criticised the behaviour of the London UndergroundD. don't know what to do about the problem74. Barry Kogan, who defended one of th'e convicted graffiti artists, thinks they _____A. should show their work in art galleriesB. should not have been convictedC. should use their abilities in different waysD. should be more careful when working in the Underground75. What do we know about Dean Colman?A. He has never broken the law.B. He's concerned about how little he earns from his work with graffiti.C. He' s worried about young people taking up graffti-spraying.D. He would like to see graffiti taken more seriously by the art world.第Ⅱ卷(共35分)第四部分:写作(共两节,满分35分)第一节短文改错(共10小题,每小题1分,满分10分)此题要求改正所给短文中的错误。

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