上海重点中学2011-2012学年下学期高二年级
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上海重点中学2011-2012学年度第二学期 高二语文期末试卷答案 (满分150分,150分钟完成,答案一律写在答题纸上) 一、阅读80分 (一)阅读下文,完成第1--6题。
(16分) 文化是一种怎样的教育力量 ①眼下,“文化”成为国家发展的一项重要内容,提出了文化体制改革,还有深化、推动、繁荣文化的目标,这当然是一件好事。
有人说,现在的中国人讲实惠,重功利,不买书(烹调、股票、考试参考书除外),不看戏剧(电视剧除外),不听音乐会(红歌除外),不欣赏舞蹈(公共空地上锻炼身体的“群舞”除外)。
一句话,对文化不感兴趣。
我不太同意这种看法。
前面提到的那些“除外”也都是文化,中国不是没有文化,只是看得见的似乎都是“大众文化”。
②大众文化的特点是实用:娱乐、消遣、调剂劳累,或者用时兴的话来说是“振奋精神”(抽烟、喝酒也可以振奋精神,也是一种“文化”)。
照目前的情况来看,深化、推动、繁荣的目标,对于大众文化应该说是已经达到了。
③不仅政府和商家在为此共同努力,连高等学府也加入进来。
比如,最近网上很红火的“化学歌”就是一个例子。
歌中唱道,“化学究竟是什么,化学就是你!化学究竟为什么,化学为了我!……父母生下的你我,是化学过程的结果。
你我的消化系统,是化学过程的场所。
”□□是把化学元素周期表编成歌,至少还得有初中化学知识的人才能唱,□北大的“化学歌”,□□有嘴巴,有肠胃消化体验的人都能唱,还需要怎么个推动呢? ④真正需要深化、推动的,是文化对国民的心灵教育。
这并不是什么新点子,而是人类自古以来为什么看重文化的原因。
两千多年前,希腊人的教育目标就已经是培养“有文化”的,也就是完整的人了。
希腊文化推崇自由教育(全面的人文教育)。
希腊化时代,希腊教育传到罗马,罗马人注重的是实用教育,虽然后来学校里也开设文法、修辞、演说的课程,但只是技能而非希腊人所看重的那种文化。
⑤希腊文化注重人的心灵和公民精神。
例如,希腊人的“文法教育”不是今天语文课上教的语法、句法,而是□、□□和□□。
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初二年级233班 陈庚艺 指导教师:张苹华 在王忆安的《我读我看》中,她说过这样一段话:“在持有自己经验与结论的同时,善解并诚挚的去观看别人的人生所得,看到人类无穷多的人生景观,这时候,我们应当如同相信自己一样的去读书,书会和我们融为一体。
我们其实也是在读自己。
”人人都认为读书是什么常事,看通一遍句子就完事了,但是大家都错了,真正的去“读”一本书,不仅仅是简单的略读,而且,要体会书中的意境,感受书中的生活,学会理解文字的韵味,在文字的碎影里找出真实。
一篇好的文章就犹如一座神殿。
表面优美的文字是神殿上金碧辉煌的瓦砾,文中的意境是神殿中鸟语花香,树木荫绿的大花园,加上那大喷水池的修饰,这就犹如一片天堂,而文章中真正的内涵,则是在这个神殿中数不胜数,美不胜收的“宝藏”:精美的壁画,精致的雕刻,以及神殿中的那一份和谐、安宁与欢乐,如仙境般的美好。
书籍是人类进步的阶梯。
对于收集书的知识,几辈子也不会够,在书架前徘徊,指尖划过一本本书,那些书的有着共同的气息:洁净的笔墨,幽默的人与事,平静中的忧伤和哀怜,敏锐的心灵和孩童无暇的眼光…… 对于阅读书籍,我能够说些什么呢? 写过《昨日的世界》的奥地利作家斯蒂芬·茨威格对书发出过由衷的礼赞——“一个人与书籍接触得愈亲密,他便愈感受到生活的统一,因为他的人格复化了:他不仅用自己的眼睛观察,而且运用着无数心灵的眼睛,由于他们这种崇高的帮助,他将怀着挚爱的同情踏遍整个世界。
” 在上世纪三十年代出生在意大利乡村的卡尔洛·斯戈隆,他在小说《木头宝座》中借主人公朱利安诺说过“我对世界的了解完全来自书本,那是因为我不厌其烦地阅读各种书籍。
就像一个打捞海绵的渔民不停地潜入水底一样。
” 陶渊明说过:“好读书,不求甚解,每会有意,便欣然忘食。
”所以北大教授说;挂在口头的轻松与压在纸背的沉重,二者合而观之,才是真正的读书生活。
读书是人生一大乐趣。
当你悲伤时,一本书籍是一片“创可贴”为你抚平心灵的伤口;当你感到前途迷茫时,书籍是一盏耀眼明亮的探照灯,为你指引道路;当你感到世界一片寒冷时,书籍是一杯热腾腾的咖啡,让你感到温暖,并且精神百倍,用一颗热情的心,去驱走世界的寒冷。
南京师范大学附属实验学校2011—2012学年度第二学期高二年级期中考试历史试卷第Ⅰ卷一、选择题(本题共20小题,每题3分,共60分。
每题只有一个正确答案,把答案填涂在答题卡上)1.中国古代有一位大臣向皇帝进言:“臣闻殷、周之王千馀岁,封子弟功臣,自为枝辅。
今陛下有海内,而子弟为匹夫,卒有田常、六卿之臣,无辅拂,何以相救哉?”此大臣主张A.分封制 B.郡县制 C.中央集权制 D.皇帝制2.1851年与1911年都是辛亥年,在中国都发生了大规模的革命运动,这两场革命运动的相似之处有:①都以暴力推翻清政府为首要目标②发动者都希望按照西方的政治模式改造中国②参加革命者都是为生计所迫,才揭竿而起的④革命都从中国南方开始,高潮发生在长江流域A.①②③④ B.①②④ C.②③ D.①④3.国史中会经常碰到“近代化”一词。
百度词条对此解释:近代化就是指资本主义化。
它包括:政治上的民主化、法制化,经济上的工业化、商品化,思想上的理性化、科学化。
下列观点与近代化理念背道而驰的有①立国之道,尚礼义不尚权谋,根本之图在人心,不在技艺②男练义和团,女练红灯照。
砍倒电线杆,扒了火车道③今为机器之世,多机器则强,少机器则弱④立宪政体,取决公论;上下议院,实为行政之本⑤我们现在认定只有这两位先生,可救治中国政治上、道德上、学术上的一切黑暗A.② B.①② C.①③④ D.①②③⑤4.右图是1953年由西安市选举委员会印发的一张选民证,其历史背景是A.第一届中国人民政治协商会议的召开B.民族区域自治制度建立起来C.政治协商制度逐渐建立D.第一届全国人民代表大会即将召开5. 1950年中苏两国签署《中苏友好同盟互助条约》,2001年中俄等六国签署《上海合作组织成立宣言》。
这两次外交活动表明中国始终A.坚定独立自主和平外交方针 B.坚定奉行友好结盟政策C.积极开展多边外交活动 D.坚定打击国际恐怖主义势力6.公元的5世纪的雅典步入“黄金时代”。
邢台一中2011---2012学年下学期第四次月考高二年级历史试题命题人:安维玲第Ⅰ卷(选择题,共50分)一、选择题(本题共25小题,每小题2分,共50分)1.中国古代地名命名,多遵循《周易》所谓宇宙万物皆合于阴阳又分于阴阳的二元法则,根据各地所处位置、方向和地势等条件的不同,或直接贯以阴阳法则,或间接贯以阴阳法则,从而出现大批带‚阴‛字或‚阳‛字的地名。
这些地名的分布与古代文化中心的分布密切相关。
商朝定都于殷,在19世纪末在殷墟王陵地区发现了大量甲骨文,成为研究商朝重要的资料。
从‚阴‛‚阳‛位置来看你认为殷有可能位于A.黄河南岸B.秦陵北坡C.长江北岸D.太行山南麓2.1975年在陕西岐山董家村出土的铜器中,有裘卫四器的铭文记载:共王三年,裘卫用价值八十朋的一块玉璋,租得矩伯的十田;共王五年,裘卫用自己的五田与邦君的四田相交换;共王九年,矩伯取裘卫一辆车子和车马的饰件,裘卫另外送给矩妻四卷帛,矩伯便把一片土地和林木送与裘卫。
下列对此解读最准确的是A.西周商品经济繁荣 B.铭文是研究西周历史的主要史料C.分封制瓦解 D.我国奴隶社会土地国有制被破坏3.汉乐府《孔雀东南飞》中焦仲卿妻:‚十三能织素,鸡鸣入机织,夜夜不得息。
‛她身上打扮是‚妾有绣腰糯,威蕤自身光。
‛她床上装饰是‚红罗夏斗帐,四角垂香囊。
香帘六七寸,碧绿青丝绳。
‛这些描述主要反映了A.汉代丝织业生产的普及和发达程度B.中国古代男尊女卑思想严重,女子倍受压迫,日夜劳作C.汉代吏治腐败,焦仲卿为普通小吏,家里竟可以布置得如此富丽堂皇D.汉代家庭手工业在手工业生产中占据主导地位4.据古碑记载:‚汉建成二十年设沛国于相(今淮北市),颁布‘酒榷’,在濉溪口、柳孜专设税官,征收盐酒税。
‛材料表明汉代A.开始推行重农抑商政策 B.盐酒税成为财政收入的主要来源C.实行坊市完全分置政策 D.对市场交易已经进行了严格管理5.当代史学家对封建国家权力运行的规律作出如下总结:皇帝从资历较浅、地位不高的心腹近侍或仆从中选拔一些人来承担政务,逐渐演变成正式的辅助机构,当这些辅助机构和官员的权力较重时,皇帝又从更新宠的近侍或仆从中另选一些人来承担政务,有意架空原有的辅助机构,剥夺其实权……皇帝的权力更加强。
2021-2022学年上海市市北中学高二下学期期末数学试题一、单选题1.已知物体做直线运动的方程为()s s t =,则()410s '=表示的意义是( ) A .经过4s 后物体向前走了10m B .物体在前4秒内的平均速度为10m/s C .物体在第4秒内向前走了10m D .物体在第4秒末的瞬时速度为10m/sD【分析】根据导函数的定义判断可得选项.【详解】解:由导数的意义知()410s '=表示物体在第4秒时的瞬时速度为10m/s . 故选:D.2.若(1)x +7280128(12)x a a x a x a x -=++++,则127a a a +++的值是( )A .-2B .-3C .125D .-131C【详解】试题分析:令0x =,得01a =;令1x =,得01282a a a a -=++++,即1283a a a +++=-.又7787(2)128a C =-=-,所以12783125a a a a +++=--=,故选C .二项式定理.3.如图,在杨辉三角中,虚线所对应的斜行的各数之和构成一个新数列,则数列的第10项为A .55B .89C .120D .144A【分析】根据杨辉三角中,虚线所对应的斜行的各数之和构成一个新数列,找出规律,即可求出数列的第10项,得到答案.【详解】由题意,可知1234561,1,112,123,235,358a a a a a a ===+==+==+==+=, 789105813,81321,132134,213455a a a a =+==+==+==+=,故选A.本题主要考查了归纳推理的应用,其中解答中读懂题意,理清前后项的关系,准确计算是解答的关键,着重考查了推理与运算能力,属于基础题. 二、多选题4.对于函数()f x ,若()02f x '=,则当h 无限趋近于0时,在下列式子中无限趋近于2的式子有( ) A .()()00f x h f x h+-B .()()002f x h f x h+-C .()()002f x h f x h+-D .()()0022f x h f x h+-AD【分析】利用平均变化率的定义以及导数的定义对四个选择逐一判断即可. 【详解】解:因为0000()()lim ()2h f x h f x f x h→+-='=,故选项A 正确;因为0000()()1lim ()122h f x h f x f x h →+-='=,故选项B 错误;因为0000(2)()lim 2()4h f x h f x f x h →+-='=,故选项C 错误;因为0000(2)()lim ()22h f x h f x f x h→+-='=,故选项D 正确.故选:AD . 三、填空题5.1150除以7的余数是___________.1【分析】由()111150491=+结合二项式定理可求得1150除以7的余数.【详解】()111111110210101111115049149C 49C 49C 491=+=+⋅+⋅++⋅+,而111102101011111149C 49C 49C 49+⋅+⋅++⋅能被7整除,故1150除以7的余数是1. 故答案为.16.6(1)x +展开式的中间项是___________. 320x【分析】根据二项式展开式的通项公式,即可求解.【详解】解:展开式的通项为:16C k kk T x +=,展开共有7项,故中间项是第4项,33346C 20T x x ==,故答案为.320x7.函数32e x y x =的导数为___________.1231e 2x x ⎛⎫+ ⎪⎝⎭【分析】根据导数四则运算,即可求解.【详解】解:()'331'2223e e 1e 2x x x y x x x ⎛⎫⎛⎫=+=+ ⎪ ⎪⎝⎭⎝⎭' ,故1231e 2xx ⎛⎫+ ⎪⎝⎭8.计算:33333456C C C C +++=___________.35【分析】直接求解.【详解】33333456C C C C 14102035+++=+++=,故35.9.设常数0,1a a >≠,在空格内,写出左边到右边的推导过程:()log a x '=___________1ln x a=. ()ln 1ln ln ln x x a a'⎛⎫'=⋅ ⎪⎝⎭ 【分析】根据基本初等函数的导数及导数的运算,即可求解. 【详解】()()ln 1log ln ln ln a x x x a a'⎛⎫''==⋅ ⎪⎝⎭1ln x a =. 故答案为.()ln 1ln ln ln x x a a'⎛⎫'=⋅ ⎪⎝⎭ 10.将4本不同的书分给3所不同的学校,其中一所学校分得2本,另两所学校各分得1本,则分书的种数为___________. 36【分析】这是部分均匀分配问题,先分堆,后分配.【详解】解:分书的种数为211342132236C C C A A ⨯=(种). 故36.11.曲线12e x y -=在点1,12⎛⎫⎪⎝⎭处的切线方程为___________.220x y +-=【分析】根据导数求切线斜率,即可求解.【详解】解:122e x y --'=,所以切线斜率为:2k =-,切线方程为112()2y x -=--, 整理得:220x y +-=, 故220x y +-=12.已知函数()f x 的定义域为R ,其导函数()'f x 的图象如图所示,则对于任意()1212,x x x x ∈≠R ,下列结论正确的是___________.(填序号)①()0f x <恒成立;②()()()1212[]0x x f x f x --<; ③()()()1212[]0x x f x f x -->; ④()()121222f x f x x x f ++⎛⎫> ⎪⎝⎭;⑤()()121222f x f x x x f ++⎛⎫< ⎪⎝⎭②⑤【分析】由导数的图象,分析原函数的图象,根据图象的单调性判断①②③选项,根据图象的凹凸性判断④⑤选项.【详解】由题中图象可知,导函数()'f x 的图象在x 轴下方,即()0f x '<,且其绝对值越来越小,因此过函数()f x 图象上任一点的切线的斜率为负,并且从左到右切线的倾斜角是越来越大的钝角,由此可得()f x 的大致图象如图所示.选项①,导函数只能反映原函数的单调性,不能反映原函数的正负,故①错;选项②表示12x x -与()()12f x f x -异号,即()f x 图象的割线斜率()()1212f x f x x x --为负,故②正确,选项③表示12x x -与()()12f x f x -同号,即()f x 图象的割线斜率()()1212f x f x x x --为正,故③不正确;122x x f +⎛⎫ ⎪⎝⎭表示122x x+对应的函数值,即图中点B 的纵坐标,()()122f x f x +表示当1x x =和2x x =时所对应的函数值的平均值,即图中点A 的纵坐标,显然有()()121222f x f x x x f ++⎛⎫< ⎪⎝⎭,故④不正确,⑤正确.故答案为:②⑤. 四、双空题13.有8名学生排成一排,甲、乙相邻的排法种数为___________,甲不在排头,乙不在排尾的排法种数为___________.(用数字作答) 10080 30960【分析】(1)把甲乙两人捆绑在一起看作一个复合元素,再和另外6人全排列; (2)可采用间接法得到;【详解】(1)把甲乙两人捆绑在一起看作一个复合元素,再和另外6人全排列,故有77210080A =种情况;(2)利用间接法,用总的情况数减去甲在排头、乙在排尾的情况数,再加上甲在排头同时乙在排尾的情况,故有876876A 2A A 30960-+=种情况故10080;3096014.在一块正三角形的铁板的三个角上分别剪去三个全等的四边形,然后折成一个正三棱柱,尺寸如图所示当x 为___________时,正三棱柱的体积最大,最大值是___________.6a 354a【分析】先设内部小三角形的边长为2a x -,根据三棱柱的体积的表达式,构建函数,利用导函数求最值,即可. 【详解】解:由题意得:内部小三角形的边长为2a x -,又20a x ->,所以02a x <<,三棱柱的体积为()()22212sin 60tan 3024x a x V a x x -=-⨯⨯=,令()2322()244(0),2a f x x a x x ax a x x =-=-+<<()()22()12862f x x ax a x a x a '=-+=--,所以0,,()0,,,()0,662a a a x f x x f x ⎛⎫⎛⎫''∈>∈< ⎪ ⎪⎝⎭⎝⎭故3max 2()()627a f x f a ==, 所以33max1242754a V a =⨯=. 故6a ;354a ; 五、解答题15.求函数()tan f x x =的导函数,并由此确定正切函数的单调区间.单调递增区间为:,,22k k k Z ππππ⎛⎫-+∈ ⎪⎝⎭【分析】根据导函数及定义域,即可求解单调区间.【详解】解:2222sin cos sin 1()(tan )()0cos cos cos x x x f x x x x x+'''====>,又定义域为 |,2x x k k Z ππ⎧⎫≠+∈⎨⎬⎩⎭,所以单调递增区间为:,,22k k k Z ππππ⎛⎫-+∈ ⎪⎝⎭,无单调递减区间.16.一个罐子中有同样大小及重量的20个玻璃球,其中4个是红色的,6个是黑色的,10个是白色的.经充分混合后,从罐子中同时取出2个球,求下列事件的概率: (1)两个球都是黑色的; (2)两个球的颜色不同. (1)338(2)6295【分析】(1)根据组合数公式即可求解,(2)先算出摸出的两个球是同色的概率,再用排除法即可求解.【详解】(1)两个球都是黑色的概率为26220C 3C 38P ==(2)两个球的颜色不同的概率为2226104222202020C C C 621C C C 95P =---=.17.设n 展开式的各项系数和为t ,其二项式系数和为h ,若4160t h +=,求: (1)展开式中x 的无理项个数;(2)展开式中系数最大的项. (1)5 (2)1361458x【分析】(1)由二项式系数和与各项系数和可得n ,再由通项公式,即可求解. (2)假设第1r +项系数最大,再由不等式,即可求解.【详解】(1)解:各项系数和为()24,2,42224160n n n n n n t h t h ==+=+=+=,解得:()()2642650n n-+=,解得2646n n =⇒=,展开式通项公式为12666166(3r r rr rr r T C C x+--+==,0,1,2,3,4,5,6r =,当0,6r =时,126r +是整数,1,2,3,4,5r =时,126r+不是整数,系数是无理数,共有5项.(2)假设第1r +项系数最大,则61566617663333r r r r r r r r C C C C -+----⎧⋅≥⋅⎨⋅≥⋅⎩,即()()()()()()6!6!3!6!1!5!6!6!3!6!1!7!r r r r r r r r ⎧⋅≥⎪⋅-+⋅-⎪⎨⎪≥⋅⎪⋅--⋅-⎩,解得:3744r ≤≤,又*r Z ∈,所以1r =,所以系数最大的项为.131351662631458T C x x ==18.(1)若x N ∈,解不等式2996x x P P ->;(2)在()(2030)n a b n +<<的展开式中,第k 项,第1k +项,第2k +项的系数成等差数列,求n 和k 的值;(3)设计一道排列组合的应用题,验证下面这个等式成立:()1122C C C C C C C C 1,,,m m m k m k m n k n k nk n n k k m n k m n ---*+++++=≤≤≤∈N(1) {}234567,,,,,;(2) 914k =或,23n =.(3)过程见解析; 【分析】(1)利用排列数公式,即可求解; (2)列用二项式展开式的通项公式,即可求解;(3)根据(1)n k x ++的展开式中m x 项的系数设计题目,即可证明.【详解】解:(1) ()299296x x P P x ->≤≤得,()()9!9!69!11!x x >--,化简得2211040x x -+>,又92x ≤≤,所以234567x =,,,,,(2)1C k n kk k n T a b -+=,所以有112C C +C ,k k k n n n -+=展开得:()()()()()!!!2!!1!1!1!1!n n n k n k k n k k n k ⨯=+---++--,化简得:211k n k n k k -=+-++,整理得()2241420n k n k -++-=,且()()2241442890k k k ∆=+--=+>,解得: n =n =所以89k +只能是一个奇数的平方, 令2*89(21),k m m N +=+∈,所以228(21)9448k m m m =+-=+-,222m m k +-=, 此时22212n m m n m =+-=-或, 所以,2220213042392023052314m m m n k m m n k <+-<===<-<===,,,或,,,.(3)题目为: “求(1)n k x ++的展开式中m x 项的系数为多少? ()1,,,k m n k m n *≤≤≤∈N ”,解:由题意可得: 展开式中含m x 项为m mn k C x +,也可以拆开为(1)(1)n k x x ++,故展开式中含m x 项可以按照前面提供m 个x ,后面提供0个x , 前面提供1m -个x ,后面提供1个x,……以此类推,即可得展开式中含m x 项为1122(C C C C C C )C m m m m k m k n k n k n k n x ---++++,所以()1122C C C C C C C C 1,,,m m m k m k m n k n k n k n n k k m n k m n ---*+++++=≤≤≤∈N 得证.19.已知函数21()ln 2f x x a x =+. (1)若1a =-,求函数()f x 的极值,并指出是极大值还是极小值; (2)若1a =,求函数()f x 在[1,e]上的最大值和最小值;(3)若1a =,求证:在区间[1,)+∞上,函数()f x 的图象在函数32()3g x x =的图象的下方;由此启发,给出以下结论成立的一个判断依据,“在区间[,)a +∞(a 为常数)上,可导函数()f x 的图象在可导函数()g x 的图象上方”(不必证明). (1)极小值()112f =(2)min 1()2f x =,2max 1()e 12f x =+(3)见解析【分析】(1)代入1a =-,从而化简()f x 并求其定义域,再求导判断函数的单调性及极值即可;(2)代入1a =,从而化简()f x 并求其定义域,再求导判断函数的单调性及求函数的最值;(3)代入1a =,令3221()()()ln 32F x g x f x x x x =-=--,从而化在区间[1,)∞+上,函数()f x 的图象在32()3g x x =的图象下方为()0F x >在[1,)∞+上恒成立,再化为函数的最值问题即可.【详解】(1)解:当1a =-时,21()ln 2f x x x =-的定义域为(0,)+∞, 1(1)(1)()x x f x x x x-+'=-=, 当01x <<时,()0f x '<,当1x >时,()0f x '>, 所以()f x 在(0,1)上是减函数,在(1,)+∞上是增函数, 所以()f x 在1x =处取得极小值()112f =;(2)解:当1a =时,21()ln 2f x x x =+的定义域为(0,)+∞, 1()0f x x x'=+>, 故()f x 在[1,e]上是增函数,故()min 1()12f x f ==,()2max 1()e e 12f x f ==+;(3)证明:令3221()()()ln 32F x g x f x x x x =-=--,则221(1)(21)()2x x x F x x x x x-++'=--=,[1x ∈,)∞+,2(1)(21)()0x x x F x x-++'∴=≥,()F x ∴在[1,)∞+上是增函数,故()211()10326F x F ≥=-=>,故在区间[1,)∞+上,函数()f x 的图象在32()3g x x =的图象下方, 要使在区间[,)a +∞(a 为常数)上,可导函数()f x 的图象在可导函数()g x 的图象上方, 只需要函数()()0f x g x ->在区间[,)a +∞(a 为常数)上恒成立即可.。
上海市上海中学2022--2023学年高二下学期英语期中试卷一、单项选择1.________health experts'belief that giving people access to their health data will inspire them to eat better and exercise more,there's evidence________their promise isn't quite paying off.A.Despite of;/B.Despite;thatC.Though;that D.In spite of;for2.When humans develop machines that are smarter than they are and machines begin to improve themselves, they risk________the mathematician IJ Good called an"intelligence explosion".A.what B.that what C.even if D.whatever3.His technique has developed to the point_____he can help kill the latest computer virus going round the city.A.that B.which C.when D.where4.Only when the war,with all its unexpected consequences,is over________.A.that any political impacts will beginB.will any political impacts beginC.and any political impacts will beginD.any political impacts will begin5.Addicted to shopping,I found that the items I bought lost their appeal right around________a new item caught my eye.A.the second when B.a second whenC.the second D.a second6.The collectors dreamed of________a place to show off the collection in Latin America as a way to spark dialogue among artists across the diverse regions.A.there to be B.there being C.there having D.there would be 7.Researching findings show we spend about two hours dreaming every night,no matter what we________ during the day.A.would have done B.should have doneC.may have done D.must have done8.The invention of telegram________the transmission of messages to any part of the world within a few seconds.A.made possible B.made it possibleC.made possibly D.made it possibly9.With the meeting________in just a couple of hours,I didn't have the time to worry about those unimportant things.A.beginning B.begun C.to begin D.would begin 10.Yesterday,the storm delayed us.________the storm we would have been here in time.A.If it were not for B.But forC.Unless D.But that11.In our discussion of instincts,we saw that there was reason to believe________we inherit must be of some very simple sort rather than any complicated or very definite kind of behavior.A.how B.when C.whatever D.since12.The dress proved such a hit________the London company who made the original for Diana turned it into an off-the-peg line.A.whenever B.as C.since D.that13.________your phone is a worthy assistant,there's no substitute for a real camera when it comes to________the perfect picture.A.As;taking B.Whether;take C.Though;take D.While;taking 14.The economist argues that no society can surely be flourishing and happy,________of the members are poor and miserable.A.of which the far greater part B.of which far greater partC.of whom the far greater part D.of whom far greater part15.It is likely that we may________great benefits from such releases of genetically engineered organisms into the environment—providing they do what we expect them to.A.invalidate B.derive C.prohibit D.reserve16.His election campaigns were infamous for their cruelty—he often made sure that those who did not vote for him would never vote again—but the________of his involvement has never been clear.A.vision B.vulnerability C.depth D.misconception 17.In contrast to Barbie's fantasy figure and fashionable high heels,these dolls are________on girls from historical eras and come with storybooks about themselves.A.modeled B.synthesized C.popularized D.imposed二、选用适当的单词或短语补全短文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.petenceB.repetitiveC.dramaticallyD.paceE.routinely AB.Beating AC.blowing AD.worthy AE.shallowly BC.ease BD.readinessHow to prevent and fight anxiety?Lingering anxiety can keep you up at night,make you easily annoyed,weaken your ability to concentrate,and ruin your appetite.And the constant state of18.generated by anxiety—adrenaline(肾上腺素)pumping,heart racing,palms sweating-may contribute to high blood pressure and heart disease.How to prevent anxiety then?Meditate.Maybe you're just nervous.If so,meditation is19.of a try.It cultivates a calmness that will20.anxious feelings and offer a sense of control.A study at the University of Massachusetts found that volunteers who took an8-week meditation course,were considerably less anxious afterward. People who are nervous find that they are21.calmer with20minutes of meditation in the morning and another20minutes after dinner.Jog,walk,swim,or cycle.If you can't make time for meditation,be sure to make time for regular exercise.Exercise can have the same calming effect as meditation,particularly if it's something22.like running or swimming laps.Treatment?Remember to breathe.When you're anxious,you tend to hold your breath or breathe too23..That makes you feel more anxious.Breathing slowly and deeply can have a calming effect.Let's say you are anxious about your24.on the job.Ask yourself"What,in particular,am I afraid that I'll mess up?"Maybe you're afraid that you get further behind and miss your deadlines.Or maybe you're worried that you're25.it whenever you present your ideas in meetings.Are your worries reasonable?Have you had several near misses with deadlines?Are your suggestions26.rejected?If not,the anxiety is needless.If there is a real problem,work on a solution: 27.yourself to better meet deadlines,or join a public speaking class.三、完形填空完形填空There has,in recent years,been an outpouring of information about the impact of buildings on the natural rmation which explains and promotes green construction design strives to 28.others of its effectiveness and warns of the dangers of ignoring the issue.Seldom do these documents offer any advice to practitioners,such as those designing mechanical and electrical systems for a building,on how to use this knowledge on a29.level.Although there are a good many advocates of"green"construction in the architectural industry,able to list enough reasons why buildings should be designed in a(n)30.way,that doesn't translate into a booming green construction industry.Likewise,the fact that plenty of architectural firms have experience in green design is not enough to make green construction31..The driving force behind whether a building is constructed with minimal environmental impact32.the owner of the building;that is,the person financing the project.If the owner considers green design unimportant,or of secondary importance, then more than likely,it will not be33.into the design.The commissioning(委任)process plays a key role in34.the owner gets the building he wants, in terms of design,costs and risk.Owners who35.the commissioning process,or fail to take"green" issues into account when doing so,often run into trouble once their building is up and running.Materials and equipment are installed as planned,and,at first glance,appear to fulfil their purpose adequately.36., in time,the owner realizes that operational and maintenance costs are higher than necessary,and that the occupants are dissatisfied with the results.These factors in turn lead to higher ownership costs as well as increased environmental impact.In some cases,an owner may be37.of the latest trends in green building design,which, however,does not necessarily lead to an interpretation that the client already has an idea of how green he intends the structure to be.Indeed,this initial interaction between owner and firm is the ideal time for a designer to outline and38.the ways that green design can meet the client's objectives.In this way, he may turn a project originally not39.green design into a potential candidate.Typically,when condiering whether or not to adopt a green40.,an owner will ask about additional costs or return for investment.In a typical project,landscape architects,mechanical and electrical engineers are not involved until a much later stage.However,in green design,they have a role to play from they outset,since green design demands41.between these disciplines,which requires additional cost. However,there are examples of green design which have demonstrated42.costs for long-term operation,ownership and even construnction.28.A.preserve B.convince C.exploit D.accuse 29.A.pracical B.measured C.tremendous D.theoretial 30.A.professional B.groundbreaking C.innovative D.sustainable 31.A.tap into experience B.live up to its nameC.rise to fame D.come into being32.A.refers to B.lies with C.races against D.calls on 33.A.knocked B.loaded C.factored D.stuffed 34.A.concluding B.stressing C.ensuring D.acknowledging 35.A.skip B.transport C.isolate D.cover 36.A.As a result B.On the contraryC.What's more D.However37.A.ignorant B.aware C.critical D.capable 38.A.promote B.perceive C.attribute D.impose 39.A.applited to B.anxious for C.destined for D.specific about 40.A.gesture B.approach C.origin D.patent 41.A.competition B.calculation C.cooperation D.distinction 42.A.increased B.extra C.fixed D.lower四、阅读理解阅读理解St Kilda is a tiny archipelage(群岛)of the North Atlantic Ocean.The islands are among the most spectacular,but the greatest fascination is that,for over a thousand years,people lived there and possessed a sense of community.Cut off from the mainland,the islanders had a distinct way of living their lives,mainly eating the seabirds that returned to breed on the rocks.Isolation also had a big effect upon St Kildans'attitudes and ideas.The people sacrificed themselves year in and year out,in a constant battle to secure a livelihood.In such harsh conditions,life was only possible because the whole community worked together.In the19th century St Kilda was subject to pressures from the outside cation,religion and tourism all attempted to throw the St Kildans'way of life into doubt.In the early20th century,the strength of the community became weakened as contact with the rest of Britain increased.When disease cut their numbers,and wind and sea made it difficult to get adequate food,the St Kildans were forced to turn to the mainland for assistance.In1930,the St Kildans finally agreed to abandon their homes.They settled on the Scottish mainland, not realizing it meant throwing themselves into the20century.As adults,they had to accept those values most Scots believe in.For instance,the islanders found difficult to base their existence upon money.They had never lived in a world where they bought goods and services from each other.The islanders showed themselves indifferent to the jobs they were given on the mainland.The labours asked of them were unskilled compared with the spectacular skills they had once performed in order to kill seabirds.Moreover,killing birds had once provided the community with food to survive.On the mainland, however,the tasks they were asked to perform did not provide them immediately with what was needed to keep them fed and warm.The history of the St Kildans after the evacuation(撤离),of their inability and lack of resolution to fit into urban society,makes sad reading.When they were resettled on the mainland,the St Kildans were forced to live in a society whose values were unacceptable and incomprehensible to the majority of them.For many, the move was a tragedy.43.According to Paragraph3,the following factors lead to St Kildans seeking help from outside EXCEPT ________.A.unbearable wind B.insufficient food supplyC.contact with Britain D.worsening health44.After the St Kildans inhabited Scotland,they________.A.soon learned how to buy goods and services from othersB.had trouble adapting to the value of dominant societyC.exhibited willingness to carry out their given jobsD.had the opportunity to show their skills of killing seabirds45.Which of the following is NOT about how people used to live on St Kilda?A.The major source of food was found locally.B.It was essential for people to help each other.C.Very few people had visited mainland Scotland.D.Money played an insignificant role in life.46.What is the passage mainly concerned with?A.The role of money in modern communities.B.How a community adapted to a different form of life.C.The destruction of an old-fashioned community.D.How a small community fight against opposite conditions.阅读理解Depression hurts,Prozac can help Depression isn't just feeling down.It's a real illness with real causes.Depression can be triggered by stressful life events,like divorce or a death in the family.Or it can appear suddenly,for no apparent reason.Some people think you can just will yourself out of a depression.That's not true.Many doctors believe that one thing that may cause depression is an imbalance of serotonin—a chemical in your body.If this happens,you may have trouble sleeping.Feel unusually sad or irritable easily.Find it hard to concentrate.Lose your ck energy.Or have trouble feeling pleasure.These are some of the symptoms that can point to depression—especially if they last for more than a couple of weeks and if normal,everyday life feels like too much to handle.To help fight depression,the medicine doctors now prescribe(开处方)most often is Prozac.Prozac isn't a"happy pill."It's not a tranquilizer(镇静剂).It won't turn you into a different person.Some people do experience mild side effects,like upset stomach,headaches,difficulty sleeping, sleepiness,anxiety and nervousness.These tend to go away.within a few weeks of starting treatment, and usually aren't serious enough to make most people stop taking it.However,if you are concerned about a side effect,or if you develop a rash(皮疹),tell your doctor right away.And don't forget to tell your doctor any other medicines you are taking.Some people should not take Prozac,especially people on MAO inhibitors(单胺抑制剂).As you start feeling better,your doctor can suggest therapy or other means to help you●through your depression.Prozac has been carefully studied for nearly10years.But remember,Prozac is a prescription medicine,and it isn't right for everyone.Only your doctor can decide if Prozac is right for you—or for someone you love.Prozac has been prescribed for more than17million Americans.Chances are someone you know is feeling sunny again because of it.47.All the following are true EXCEPT________.A.Tremendous determination is essential to getting rid of depression.B.Sleep disorder is one of the signs characteristic of depression.C.Depression can be caused by a combination of factors.D.Depression is a psychological state taking the form of low mood.48.What can we learn about Prozac from this piece of information?A.Prozac infuses depression patients with energy at the cost of modest side effects.B.Taking Prozac together with other prescriptions may give you a rash.C.A medical prescription must be acquired if you intend to take Prozac.D.Over17million Americans have been involved in studies of Prozac so far.49.This piece of information is most probably________.A.an introduction to a scientific projectB.a part of prescription drug instructionsC.a part of a research report in a medical journalD.an advertisement of a medicine for depression阅读理解Why do so many Americans distrust what they read in their newspapers?The American Society of Newspaper Editors is trying to answer this painful question.The organization is deep into a longself-analysis known as the journalism credibility project.Sad to say,this project has turned out to be mostly low-level findings about factual errors and spelling and grammar mistakes,combined with lots of head-scratching puzzlement about what in the world those readers really want.But the sources of distrust go way deeper.Most journalists learn to see the world through a set of standard patterns into which they plug each day's events.in other words,there is a conventional story line in the newsroom culture that provides a backbone and a ready-made narrative structure for otherwise confusing news.There exists a social and cultural disconnect between journalists and their readers,which helps explain why the"standard patterns"of the newsroom seem alien to many readers.In a recent survey,questionnaires were sent to reporters in five middle-size cities around the country,plus one large metropolitan area.Then residents in these communities were phoned at random and asked the same questions.Replies show that compared with other Americans,journalists are more likely to live in upscale neighborhoods,have maids,own Mercedeses,and trade stocks,and they're less likely to go to church,do volunteer work,or put down roots in a community.Reporters tend to be part of a broadly defined social and cultural elite(精英),so their work tends to reflect the conventional values of this elite.The astonishing distrust of the news media isn't rooted ininaccuracy or poor reportorial skills but in the daily conflict of world views between reporters and their readers.This is an explosive situation for any industry,particularly a declining one.Here is a troubled business that keeps hiring employees whose attitudes vastly annoy the customers.Then it sponsors lots of conferences and a credibility project dedicated to wondering why customers are annoyed and fleeing in large numbers. But it never seems to get around to noticing the cultural and class biases that so many former buyers are complaining about.If it did,it would open up its diversity program,now focused narrowly on race and gender,and look for reporters who differ broadly by outlook,values,education,and class.50.What is the passage mainly about?A.The objectives and findings of a journalism credibility project.B.The personnel structure of the declining newspaper industry.C.The causes of the public disappointment in newspapers.D.The indefinite needs of newspaper readers in America.51.The results of the journalism credibility project turned out to be________.A.somewhat conflicting B.rather trustworthyC.quite superficial D.very enlightening52.According to the author,the fundamental problem of journalists lies in their________. A.conventional lifestyle in upscale communitiesB.inflexible approach to handling news storiesC.contradictory ways of making sense of the worldD.shared values disconnected from general readers53.Which one of the following statements is TRUE about the newspaper industry?A.It fails to satisfy its readers due to annoying reporters.B.It hasn't realized the real problem despite its efforts.C.It's urgent that it focus on accurate and skillful reporting.D.It should be aware of underlying prejudice in race and gender.五、六选四Read the following passage.Fill in each blank with a proper sentence given in the box.Each sentence can be used only once.Note that there are two more sentences than you need.The Minoans:A Forgotten PeopleThe first advanced culture in ancient Greece was the Minoan culture.For thousands of years,knowledgeof these people survived only in Greek myths.In the late19h century,archaeologists began to unearth ruins. This inspired Arthur Evans to begin digging on the island of Crete near mainland Greece.On a dig in Kbossos,Evans found an ancient palace Experts think that it was the palace of King Minos,acentral figure in many Greek myths.54.With his team,he uncovered a vast structure,varied works of art,and many hieroglyphic records.These finds,together with later finds,comprise all that experts know about Minoan culture.From the evidence experts gathered,it is clear that the Minoans were ahead of their time.The palace at Knossos was five floors high with hundreds of rooms.Buildings throughout the ancient city had plumbing and flush toilets.Stone pavement lined the surfaces of the roads.In addition,the Minoans possessed a highly developed naval fleet for long-distance trade.55.These records confirm the central role of commerce in culture.Their analysis of the evidence also offers insight into some aspects of Minoan society.56.Ruins and artwork suggest that people of all classes enjoyed a high degree of social and gender equality.Religious icons(图符)show that Minoans worshiped bulls,the natural world,and many female gods.An unusual feature of Minoans culture was the pursuit of leisure interests.Sport and visual arts were central to Minoan life.Boxing and bull jumping,a sport in which players jumped over live bulls,were popular.Although bull jumping may have served some ritual purpose,experts believe that it was done mostly for fun.Similarly,although some works of art showed political and religious themes,other works served only as pleasant decor(装饰品).57.The Minoans met their demise after a series of natural disasters.Experts believe that group from the Greek mainland capitalized on these events and looked over the island.A.Some experts think that the wealth gained from trade allowed for such leisure in sports and the artsB.Experts believe that a king and mostly a female priest ruled the government and controlled trade.C.In ancient Greek myths,Minoan society was quite prosperous and highly civilizedD.The palace that Evans unearthed a century ago was the first proof of Minoan culture.E.Minoan culture didn't exist before Arthur Evans discovered the palace under the earthF.Although not yet decoded,written script on clay tablets appears to list trade accounts.六、用单词的适当形式完成短文After reading the passages below,fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word,fill in each blank with the proper form of the given word;for the otherblanks,use one word that best fits each blank.A rare hole has opened up in the ozone layer above the Arctic,in58.scientists say is the result of unusually low temperatures in the atmosphere above the north pole.The hole has reached record dimensions,but is not expected to pose any danger to humans59.it moves further south.60.it extends further south to overpopulated areas,such as southern Greenland,people will be at increased risk of sunburn.However,on current trends the hole is expected to disappear altogether in a few weeks.Low temperatures in the northern polar regions led to an unusual stable polar vortex(极地漩涡),and the presence of ozone-destroying chemicals such as chlorine(氯)in the atmosphere-from human activities-caused the hole61.(form).It is now too early to say62.the unusually stable Arctic polar vortex conditions are linked with the climate crisis,or part of normal stratospheric weather variability.Peuch said there were no direct implications for the climate crisis.Temperatures in the region are already increasing, 63.(slow)the destruction of ozone.64.a hole over the Arctic is a rare event,the much larger hole in the ozone layer over the Antarctic has been a major cause for concern for more than four decades.The production ofozone-destroying chemicals65.(reduce)dramatically,under the1987Montreal Protocol(蒙特利尔协议),but some sources appear still to be functioning.New sources of ozone-destroying chemicals were not a factor in the hole66.(observe) in the Arctic,said Peuch."However,this is a reminder that one should not take the Montreal Protocol measures for granted,and that observations from the ground and from satellites are central to avoiding a situation67.the ozone-destroying chemical level in the stratosphere could increase again."七、汉译英(整句)68.我从未想到,这支管弦乐队会将其人气归功于互联网的兴起。
上海重点中学2011-2012学年度第二学期高二数学期终试卷(文科卷)本试卷共有23道试题,满分150分,考试时间120分钟。
一.填空题(本大题满分56分)本大题共有14题,考生应在答题纸相应编号的空格内直接填写结果,每个空格填对得4分,否则一律得零分. 1. 抛物线2x y =的准线方程是 .2. 方程222424x xC C =的解为 .3. 在5(31)x -的展开式中,设各项的系数和为a ,各项的二项式系数和为b ,则ab= . 4. 若圆锥的侧面展开图是半径为2、 圆心角为90︒的扇形,则这个圆锥的全面积是 . 5. 某同学有同样的画册2本,同样的集邮册3本,赠送给5位朋友,每位朋友1本,则不同的赠送方法共有 种.6. 一只口袋里有5个红球,3个绿球,从中任意取出2个球,则其中有绿球的概率为 .(结果用最简分数表示)7. 已知正四棱柱的一条对角线长为22,底面边长为1,则此正四棱柱的表面积为_________.8. 抛物线24y x =的准线与x 轴的交点为K ,抛物线的焦点为F ,M 是抛物线上的一点,且||2||FM FK =,则△MFK 的面积为 .9. 在圆周上有10个等分点,以这些点为顶点,每3个点可以构成一个三角形,如果随机选择了3个点,刚好构成直角三角形的概率是 . 10. 如图,在由二项式系数所构成的杨辉三角形中, 第_____行中从左至右第14与第15个数的比为3:2.11. 边长分别为a 、b 的矩形,按图中所示虚线剪裁后, 可将两个小矩形拼接成一个正四棱锥的底面,其余恰好拼接 成该正四棱锥的4个侧面,则ba的取值范围是 . 12. 9291除以100的余数是 .第0行 1第1行 1 1 第2行 1 2 1 第3行 1 3 3 1 第4行 1 4 6 4 1 第5行 1 5 10 10 5 1 …… …… ……13. 若对于任意实数x ,都有()()()()2344012342222x a a x a x a x a x =++++++++,则3a 的值为 .14. 如果一个正四位数的千位数a 、百位数b 、十位数c 和个位数d 满足关系()()0a b c d ,则称其为“彩虹四位数”,例如2012就是一个“彩虹四位数”.那么,正四位数中“彩虹四位数”的个数为 .(直接用数字作答)二.选择题(本大题满分20分)本大题共有4题,每题有且只有一个正确答案,考生应在答题纸的相应编号上,填上正确的答案,选对得5分,否则一律得零分. 15. 经过原点且与抛物线23(1)4y x =+-只有一个公共点的直线有多少条? ( ) A. 0 B. 1 C. 2 D. 316. 教室内有一把直尺,无论这把直尺怎样放置,在教室的地面上总能画出一条直线,使这条直线与直尺 ( ) A. 平行 B. 垂直 C. 异面 D. 相交17. 有3个兴趣小组,甲、乙两位同学各自参加其中一个小组,每位同学参加各个小组的可能性相同,则这两位同学参加同一个兴趣小组的概率为 ( ) A.34B.23 C. 12 D. 1318. 给出下列四个命题:(1) 异面直线是指空间两条既不平行也不相交的直线; (2) 若直线l 上有两点到平面α的距离相等,则//l α; (3) 若直线m 与平面α内无穷多条直线都垂直,则m ⊥α;(4) 两条异面直线中的一条垂直于平面α,则另一条必定不垂直于平面α.其中正确命题的个数是 ( ) A. 0个 B. 1个 C. 2个 D. 3个三.解答题(本大题满分74分)本大题共5题,解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤 . 19.(本题满分12分)已知矩形ABCD 内接于圆柱下底面的圆O ,PA 是圆柱的母线,若6AB =,8AD =,异面直线PB 与CD 所成的角为arctan2,求此圆柱的体积.20.(本题满分14分)本题共有4个小题,第1小题满分3分,第2小题满分3分,第3小题满分4分,第4小题满分4分.有8名学生排成一排,求分别满足下列条件的排法种数.要求列式并给出计算结果. (1)甲不在两端; (2)甲、乙相邻;(3)甲、乙、丙三人两两不得相邻; (4)甲不在排头,乙不在排尾.21.(本题满分14分)如图,在北纬60°线上,有A 、B 两地,它们分别在东经20°和140°线上,设地球半径为R ,求A 、B 两地的球面距离.22.(本题满分16分)本题共有2个小题,第1小题满分6分,第2小题满分10分。
2012学年度第二学期上海市新川中学数学教研组工作小结数学组教研工作继续围绕校四年发展规划,以学校“精致教育”课题为主线,落实区教研室开展的各项活动。
以提高学生的数学素养为宗旨,聚焦数学课堂,注重提高数学课堂教学的有效性;减时增效,进一步落实数学课堂文化为抓手,规范教学制度建设,强化教学常规管理,加强督查和反馈;深化教学研究,加强校本开发,提高教学的时效性。
结合学校实际,创建良好的互帮互助教研梯队。
加强教研组备课组建设,努力提升执行力。
我们完成了开学初制定的各项工作任务,现简要总结如下:一、以学习、修订《新川中学数学学科校本化实施基础型课程实施要点》为主线,加强教师对新川数学教研文化的认同。
1、结合学校提出的人人都是德育工作者的工作计划,数学组积极响应“德育导师制”的工作。
2、修订与完善《新川中学数学学科校本化实施基础型课程实施要点》,组织专题讨论,努力提升教师对课程定位、教学进度、教学活动要求等理解。
3、组织本组教师深层次的挖掘高中数学课程中“数学文化”,努力做到数学文化课堂教育目标的正确定位。
细化个单元目标,落实到“知识与技能、过程与方法、情感、态度与价值观”这三个部分。
4、对数学组教师进行培训与自学相结合,使教师掌握教学理念,深化“问题解决”为范式的高中数学课堂文化的实践与研究,建设一支具有一定科研能力的教师队伍。
5、加强高三数学的质量监控、把关制,确实提高教学质量。
我校高三年级克服平行授课的基础上不分文理的现状,高三年级在二模考试中数学文科108.63(位于全区第5名)全区平均87.03,理科106.84(位于全区第7名)全区平均101.7。
二、对近三年来的数学组的工作进行提炼与总结1、完善《新川中学高一数学习题册上、下》,形成《新川中学高二数学习题册上、下》。
2、立足课堂,上好各类课。
课堂教学是科研的主阵地,特别是基础教育的科研,我们围绕课题继续做好以下工作:①公开教学。
上好精致教学研究课,重点探究新观念的体现,新模式的运用,旨在通过公开教学及时传播课题研究的阶段性成果。
求实务实和谐创新--2012年度高二年级部工作总结一年来,高二年级在学校及各处室的正确领导下,本着教学夯实基础、管理狠抓落实、提高教学质量的理念,认真做了教师培养、教学常规的落实、教学质量的提高、学生的养成教育和管理等方面的工作,顺利而圆满地从高一年级跨入高二年级。
各方面都取得了一定的成绩,现将本学期的工作情况作如下总结。
1.继续推进和谐年级组、平安年级组建设近年来点击率最高的词就是胡锦涛总书记提出的“创建和谐社会”。
“创建和谐大社会”,必须先有和谐小社会,作为当代教育工作者,我们有责任有义务将国家的大政方针贯彻于日常行动之中,从我做起,为创建“和谐校园”、“和谐年级组”、“和谐班级”贡献力量,并教育学生做到。
我们追求教师之间的和谐、师生之间的和谐、学生之间的和谐、学生与校园环境的和谐,家校之间和谐等。
即建立良性的年级组运行机制,调动一切资源,形成教师的合力、师生的合力、学生之间的合力、家长和学校的合力,当所有的力量和所有的目标都成为一致时,一个拼搏向上、和谐温馨、充满凝聚力和战斗力的班级和年级将会无往而不胜!我们将继续上学期的布署的“创建和谐年级组,促进和谐校园建设”的有关工作,并要把工作推上层次,提升水平。
进一步纯化年级风气,调动好师生的精神状态。
采取切实有效的措施调动好每一位老师的主动性、积极性和创造性,使每位老师始终以昂扬的姿态去迎接每天的工作;通过竞赛评比、竞争流动、奖励惩戒等举措激发每一位学生的求知欲,强化他们的内驱力,磨炼他们的意志力,集中他们的注意力。
使他们在不断的勤苦细实的学习中得到充实提高,在日渐的“三力”培养和提升中得到锻炼和增强。
相信老师们的能力,同学们的潜力!学生安全工作学校把它看作是重中之重,年级组与学校、保卫科的密切协同配合,制订计划和方案,认真履行安全保卫工作,预防为主,切实落实学校安全保卫工作制度,本年度未发生一起安全事故,做到了学校满意、学生满意、家长满意,创立了人心安定、学生学习安心的平安年级部。
上海重点中学2011-2012学年下学期高二年级期末考试数学试卷(理科)本试卷共有23道试题,满分150分,考试时间120分钟。
一、填空题(本大题满分56分)本大题共有14题,每个空格填对得4分,否则一律得零分. 1. 抛物线2x y =的准线方程是 .2. 方程222424x xC C =的解为 . 3. 在5(31)x -的展开式中,设各项的系数和为a ,各项的二项式系数和为b ,则ab= . 4. 若圆锥的侧面展开图是半径为2、圆心角为90︒的扇形,则这个圆锥的全面积是 .5. 某同学有同样的画册2本,同样的集邮册3本,从中取出4本赠送给4位朋友,每位朋友1本,则不同的赠送方法共有 种.6. 将4个不同的球任意放入3个不同的盒子中,则每个盒子中至少有1个球的概率为 .(结果用最简分数表示)7. 已知123F i j k =+- ,223F i j k =-+- ,3345F i j k =-+ ,若1F 、2F 、3F共同作用于一个物体上,使物体从点1M (1,-2,1)移到点2M (3,1,-2),则合力所做的功为 .8. 抛物线24y x =的准线与x 轴的交点为K ,抛物线的焦点为F ,M 是抛物线上的一点,且||2||FM FK =,则△MFK 的面积为 .9. 在圆周上有10个等分点,以这些点为顶点,每3个点可以构成一个三角形,如果随机选择了3个点,刚好构成直角三角形的概率是 .10. 如图,在由二项式系数所构成的杨辉三角形中,第_____行中从左至右第14与第15个数的比为3:2.11. 边长分别为a 、b 的矩形,按图中所示虚线剪裁后,可将两个小矩形拼接成一个正四棱锥的底面,其余恰好拼接成该正四棱锥的4个侧面,则ba的取值范围是 .12. 已知平面α截一球O 得圆M ,圆M 的半径为r ,圆M 上两点A 、B 间的弧长为2rπ,又球心O 到平面α的距离为r ,则A 、B 两点间的球面距离为 .13. 若对于任意实数x ,都有()()()()2344012342222x a a x a x a x a x =++++++++,则3a 的值为 .14. 给n 个自上而下相连的正方形着黑色或白色. 当4n ≤时,在所有不同的着色方案中,黑色正方形互不相邻的着色方案如图所示:由此推断,当6n =时,黑色正方形互不相邻的着色方案共有 种,至少有两个黑色正方形相邻的着色方案共有 种. (直接用数字作答)二、选择题(本大题满分20分)本大题共有4题,每题有且只有一个正确答案,选对得5分,否则一律得零分. 15. 经过原点且与抛物线23(1)4y x =+-只有一个公共点的直线有多少条? ( ) A. 0 B. 1 C. 2 D. 316. 正四面体ABCD 的表面积为S ,其中四个面的中心分别是E 、F 、G 、H .设四面体EFGH 的表面积为T ,则TS等于 ( ) A.49 B. 19 C. 14 D. 1317. 甲乙两人一起去游园,他们约定,各自独立地从1到6号景点中任选4个进行游览,每个景点参观1小时,则最后一小时他们同在一个景点的概率是 ( ) A.136 B. 19 C. 536D. 1618. 给出下列四个命题:(1) 若平面α上有不共线的三点到平面β的距离相等,则//αβ; (2) 两条异面直线在同一平面内的射影可能是两条平行直线;(3) 两条异面直线中的一条平行于平面α,则另一条必定不平行于平面α; (4) a 、b 为异面直线,则过a 且与b 平行的平面有且仅有一个.其中正确命题的个数是 ( ) A. 0个 B. 1个 C. 2个 D. 3个三、解答题(本大题满分74分)本大题共5题,解答下列各题必须写出必要的步骤 . 19.(本题满分12分)已知矩形ABCD 内接于圆柱下底面的圆O ,PA 是圆柱的母线,若6AB =,8AD =,异面直线PB 与CD 所成的角为arctan 2,求此圆柱的体积.20.(本题满分14分)本题共有4个小题,第1小题满分3分,第2小题满分3分,第3小题满分4分,第4小题满分4分.m 个元素环绕在一条封闭曲线上的排列,称为环状排列.已知m 个不同元素的环状排列的所有种数为(1)!m -.请利用此结论来解决下列问题,要求列式并给出计算结果.(1)从10个不同的元素中选出8个元素的环状排列的所有种数为多少?(2)某班8个班干部中有1个班长,2个副班长,现在8个干部围坐一张圆桌讨论班级事务,则分别满足下列条件的此8人的坐法有多少种?(i )班长坐在两个副班长中间; (ii )两个副班长不能相邻而坐; (iii )班长有自己的固定座位.21.(本题满分14分)本题共有2个小题,第1小题满分7分,第2小题满分7分 .如图,在四棱锥P ABCD -中,底面ABCD 是矩形,PA ⊥平面ABCD ,2AP AB ==,4AD =,E F 、依次是PB PC 、的中点.(1)求直线EC 与平面PAD 所成的角(结果用反三角函数值表示); (2)求三棱锥P AFD -的体积.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.如图,点P 为斜三棱柱111C B A ABC -的侧棱1BB 上一点,1BB PM ⊥交1AA 于点M ,1BB PN ⊥交1CC 于点N .(1)求证:MN CC ⊥1;(2)在任意DEF ∆中有余弦定理:DFE EF DF EF DF DE ∠⋅-+=cos 2222.拓展到空间,类比三角形的余弦定理,写出斜三棱柱的三个侧面面积与其中两个侧面所成的二面角之间的关系式,并予以证明.(3)在(2)中,我们看到了平面图形中的性质类比到空间图形的例子,这样的例子还有不少.下面请观察平面勾股定理的条件和结论特征,试着将勾股定理推广到空间去.勾股定理的三角形ABC四面体O -ABC类比条件 AB ⊥AC OA 、OB 、OC 两两垂直 结论AB 2+AC 2=BC 2?请完成上表中的类比结论,并给出证明.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.在平面直角坐标系中,O 为坐标原点. 已知曲线C 上任意一点(,)P x y (其中0x ≥)到定点(1,0)F 的距离比它到y 轴的距离大1.(1)求曲线C 的轨迹方程;(2)若过点(1,0)F 的直线l 与曲线C 相交于A 、B 不同的两点,求OA OB ⋅的值;(3)若曲线C 上不同的两点M 、N 满足0OM MN ⋅=,求ON 的取值范围.上海重点中学2011-2012学年下学期高二年级期末考试数学试卷(理科)参考答案一、填空题(本大题满分56分)1. 14y =-2. 0,2,43. 14.54π5. 106.23434439C P =7. 48. 9.1310. 3411. 1(,)2+∞12. 13. -814. 21;43二、选择题(本大题满分20分) 15. D 16. B 17. D 18. C三、解答题(本大题满分74分) 19.(本题满分12分)解:设圆柱下底面圆O 的半径为r ,连AC ,由矩形ABCD 内接于圆O ,可知AC 是圆O 的直径,……2分于是210r AC ==,得5r =,……………4分 由AB ∥CD ,可知PBA ∠就是异面直线PB 与CD 所成的角, 即arctan 2PBA ∠=,故tan 2PBA ∠=.………………7分 在直角三角形PAB 中,tan 12PA AB PBA =∠=,…………9分故圆柱的体积22512300V r PA =π⋅=π⨯⨯=π.……………12分 20.(本题满分14分)解:(1) 8107!226800C ⋅=----------------------3分(2-i ) 225!240P ⋅= ----------------------6分(2-ii ) 间接法:227!6!3600P -⋅=;插空法:265!3600P ⋅=----------------------10分 (2-iii ) 7!5040= ----------------------14分 21.(本题满分14分)(1)解法一:分别以AB AD AP 、、为x 轴、y 轴、z 轴建立空间直角坐标系,各点坐标分别是(0 0 0)A ,,,(2 0 0)B ,,,(2 4 0)C ,,,(0 4 0)D ,,,(0 0 2)P ,,,∴(1 0 1)E ,,,(1 2 1)F ,,, (1 4 1)EC =-,,, (2分)又∵AB ⊥平面PAD ,∴平面PAD 的法向量为(2,0,0)n AB ==, (4分)设直线EC 与平面PAD 所成的角为α,则sin ||||EC n EC n α⋅===⋅(6分) ∴直线EC 与平面PAD所成的角为. (7分)解法二:∵PA ⊥平面ABCD ,∴CD PA ⊥,又CD AD ⊥,∴CD ⊥平面PAD ,取PA 中点G ,CD 中点H ,联结EG GH GD 、、,则EG AB CD ////且1=12EG AB =,EGHC ∴是平行四边形,∴HGD ∠即为直线EC 与平面PAD 所成的角. (3分) 在Rt GAD ∆中,GD = 在Rt GHD ∆中,tan HD HGD GD ∠==, (6分) ∴直线EC 与平面PAD所成的角为. (7分)(2)解法一:由(1)解法一的建系得,(1 2 1)AF = ,,,(0 4 0)AD =,,,设平面AFD 的法向量为(,,)n x y z = ,点P 到平面AFD 的距离为d ,由0AF n ⋅= ,0AD n ⋅=得20x y z ++=且40y =,取1x =得(1,0,1)n =- , (9分)∴AP n d n⋅=== , (11分)又AF FD ==2AFD S ==△ (13分)∴1433P AFD V -=⨯=. (14分) 解法二:易证PE 即为三棱锥P AFD -底面上的高,且PE = (11分)底面AFD △边AD 上的高等于AE,且AE =AFD S =△(13分)1144323P AFD V -=⨯⨯=. (14分)解法三:依题意,//EF 平面PAD ,∴P AFD F PAD E PAD D PAE V V V V ----=== (11分)11114224322123D PAE V PA AB AD -=⨯⨯⨯⨯⨯=⨯⨯⨯=. (14分) 22.(本题满分16分)(1)证:MN CC PMN CC PN CC PM CC BB CC ⊥⇒⊥∴⊥⊥⇒111111,,//平面 ;(4分)(2)解:在斜三棱柱111C B A ABC -中,有αcos 21111111111222A ACC B BCC A ACC B BCC A ABB S S S S S ⋅-+=,其中α为平面B B CC 11与平面A A CC 11所组成的二面角. (7分)∴⊥,1PMN CC 平面 上述的二面角为MN P ∠,在PMN ∆中,2222cos PM PN MN PN MN MNP =+-⋅∠⇒MNP CC MN CC PN CC MN CC PN CC PM ∠⋅⋅⋅-+=cos )()(211111222222,由于111111111,,BB PM S CC MN S CC PN S A ABB A ACC B BCC ⋅=⋅=⋅=,∴有αcos 21111111111222A ACC B BCC A ACC B BCC A ABB S S S S S ⋅-+=. (10分) (3)空间勾股定理的猜想:已知四面体O -ABC 的三条侧棱OA 、OB 、OC 两两垂直,则有2222OAB OAC OBC ABC S S S S ∆∆∆∆++=.(13分) 证法一:作OD ⊥AB ,垂足为D ,连结CD22222222221111()4444ABC S AB CD AB OC OD AB OC AB OD ∆=⋅⋅=⋅⋅+=⋅⋅+⋅⋅ 222222222222111()444AOB AOB AOC COB AOB OA OB OC S OA OC OB OC S S S S ∆∆∆∆∆=⋅+⋅+=⋅⋅+⋅⋅+=++ (16分) 证法二:作OH ⊥平面ABC ,垂足为H ,易得H 为△ABC 的垂心。