2012年浙江高考自选模块试题

绝密★考试结束前2012年普通高等学校招生全国同一考试（浙江卷）数 学（理科）本试题卷分选择题和非选择题两部分．全卷共5页，选择题部分1至3页，非选择题部分4至5页．满分150分，考试时间120分钟．请考生按规定用笔将所有试题的答案涂、写在答题纸上．选择题部分（共50分）注意事项：1．答题前，考生务必将自己的姓名、准考证号用黑色字迹的签字笔或钢笔分别填写在试卷和答题纸规定的位置上．2．每小题选出答案后，用2B 铅笔把答题纸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。

不能答在试题卷上．参考公式：如果事件A ，B 互斥，那么 柱体的体积公式()()()P A B P A P B +=+ V Sh =如果事件A ，B 相互独立，那么 其中S 表示柱体的底面积，h 表示柱体的高()()()P A B P A P B ⋅=⋅ 锥体的体积公式如果事件A 在一次试验中发生的概率是p ，那么 13V Sh =n 次独立重复试验中事件A 恰好发生k 次的概率 其中S 表示锥体的底面积，h 表示锥体的高()()()1,0,1,2,,n kk kn n P k C p p k n -=-= 球的表面积公式台体的体积公式 24πS R = ()1213V h S S = 球的体积公式其中12,S S 分别表示台体的上底、下底面积， 34π3V R =h 表示台体的高 其中R 表示球的半径一、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．设集合A ＝{x |1＜x ＜4}，B ＝{x |x 2－2x －3≤0}，则A ∩(C R B )＝A ．(1，4)B ．(3，4)C ．(1，3)D ．(1，2) 【解析】A ＝(1，4)，B ＝(－3，1)，则A ∩(C R B )＝(1，4)．【答案】A2．已知i 是虚数单位，则3+i1i-＝ A ．1－2i B ．2－i C ．2＋i D ．1＋2i 【解析】3+i 1i -＝()()3+i 1+i 2＝2+4i 2＝1＋2i ． 【答案】D3．设a ∈R ，则“a ＝1”是“直线l 1：ax ＋2y －1＝0与直线l 2：x ＋(a ＋1)y ＋4＝0平行”的A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件【解析】当a ＝1时，直线l 1：x ＋2y －1＝0与直线l 2：x ＋2y ＋4＝0显然平行；若直线l 1与直线l 2平行，则有：211a a =+，解之得：a ＝1 or a ＝﹣2．所以为充分不必要条件． 【答案】A4．把函数y ＝cos2x ＋1的图像上所有点的横坐标伸长到原来的2倍(纵坐标不变)，然后向左平移1个单位长度，再向下平移1个单位长度，得到的图像是【解析】把函数y ＝cos2x ＋1的图像上所有点的横坐标伸长到原来的2倍(纵坐标不变)得：y 1＝cos x ＋1，向左平移1个单位长度得：y 2＝cos(x —1)＋1，再向下平移1个单位长度得：y 3＝cos(x —1)．令x ＝0，得：y 3＞0；x ＝12π+，得：y 3＝0；观察即得答案．【答案】B5．设a ，b 是两个非零向量．A．若|a＋b|＝|a|－|b|，则a⊥bB．若a⊥b，则|a＋b|＝|a|－|b|C．若|a＋b|＝|a|－|b|，则存在实数λ，使得a＝λbD．若存在实数λ，使得a＝λb，则|a＋b|＝|a|－|b|【解析】利用排除法可得选项C是正确的，∵|a＋b|＝|a|－|b|，则a，b共线，即存在实数λ，使得a＝λb．如选项A：|a＋b|＝|a|－|b|时，a，b可为异向的共线向量；选项B：若a⊥b，由正方形得|a＋b|＝|a|－|b|不成立；选项D：若存在实数λ，使得a＝λb，a，b可为同向的共线向量，此时显然|a＋b|＝|a|－|b|不成立．【答案】C6．若从1，2，2，…，9这9个整数中同时取4个不同的数，其和为偶数，则不同的取法共有A．60种B．63种C．65种D．66种【解析】1，2，2，…，9这9个整数中有5个奇数，4个偶数．要想同时取4个不同的数其和为偶数，则取法有：4个都是偶数：1种；2个偶数，2个奇数：225460C C=种；4个都是奇数：455C=种．∴不同的取法共有66种．【答案】D7．设S n是公差为d(d≠0)的无穷等差数列{a n}的前n项和，则下列命题错误．．的是A．若d＜0，则数列{S n}有最大项B．若数列{S n}有最大项，则d＜0C．若数列{S n}是递增数列，则对任意的n∈N*，均有S n＞0D．若对任意的n∈N*，均有S n＞0，则数列{S n}是递增数列【解析】选项C显然是错的，举出反例：—1，0，1，2，3，…．满足数列{S n}是递增数列，但是S n＞0不成立．【答案】C8．如图，F1，F2分别是双曲线C：22221x ya b-=(a，b＞0)的左右焦点，B是虚轴的端点，直线F1B与C的两条渐近线分别交于P ，Q 两点，线段PQ 的垂直平分线与x 轴交于点M ．若|MF 2|＝|F 1F 2|，则C 的离心率是 ABCD【解析】如图：|OB |＝b ，|O F 1|＝c ．∴k PQ ＝b c ，k MN ＝﹣bc．直线PQ 为：y ＝b c (x ＋c )，两条渐近线为：y ＝b a x ．由()b y x c c b y x a ⎧⎪⎪⎨⎪⎪⎩＝＋＝，得：Q (ac c a -，bc c a -)；由()b y x c cb y x a ⎧⎪⎪⎨⎪⎪⎩＝＋＝-，得：P (ac c a -+，bc c a +)．∴直线MN 为：y －bc c a +＝﹣bc(x －ac c a -+)， 令y ＝0得：x M ＝322c c a -．又∵|MF 2|＝|F 1F 2|＝2c ，∴3c ＝x M＝322c c a -，解之得：2232a c e a ==，即e． 【答案】B9．设a ＞0，b ＞0．A ．若2223a b a b +=+，则a ＞bB ．若2223a b a b +=+，则a ＜bC ．若2223a b a b -=-，则a ＞bD ．若2223a b a b -=-，则a ＜b【解析】若2223a b a b +=+，必有2222a b a b +>+．构造函数：()22x f x x =+，则()2l n 220x f x '=⋅+>恒成立，故有函数()22x f x x =+在x ＞0上单调递增，即a ＞b 成立．其余选项用同样方法排除． 【答案】A10．已知矩形ABCD ，AB ＝1，BC∆ABD 沿矩形的对角线BD 所在的直线进行翻着，在翻着过程中，A ．存在某个位置，使得直线AC 与直线BD 垂直B ．存在某个位置，使得直线AB 与直线CD 垂直C ．存在某个位置，使得直线AD 与直线BC 垂直D ．对任意位置，三直线“AC 与BD ”，“AB 与CD ”，“AD 与BC ”均不垂直【解析】最简单的方法是取一长方形动手按照其要求进行翻着，观察在翻着过程，即可知选项C 是正确的．【答案】C绝密★考试结束前2012年普通高等学校招生全国同一考试（浙江卷）数 学（理科） 非选择题部分（共100分）注意事项：1．用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上．2．在答题纸上作图，可先使用2B 铅笔，确定后必须使用黑色字迹的签字笔或钢笔描黑． 二、填空题：本大题共7小题，每小题4分，共28分． 11．已知某三棱锥的三视图(单位：cm)如图所示，则该三棱锥的体积等于___________cm 3．【解析】观察三视图知该三棱锥的底面为一直角三角 形，右侧面也是一直角三角形．故体积等于11312123⨯⨯⨯⨯=． 【答案】112．若程序框图如图所示，则该程序运行后输出的值是______________． 【解析】T ，i 关系如下图：【答案】112013．设公比为q (q ＞0)的等比数列{a n }的前n 项和为{S n }．若2232S a =+，4432S a =+，则q ＝______________．【解析】将2232S a =+，4432S a =+两个式子全部转化成用1a ，q 表示的式子． 即111233111113232a a q a q a a q a q a q a q +=+⎧⎨+++=+⎩，两式作差得：2321113(1)a q a q a q q +=-，即：2230q q --=，解之得：312q or q ==-(舍去)． 【答案】3214．若将函数()5f x x =表示为()()()()250125111f x a a x a x a x =+++++++其中0a ，1a ，2a ，…，5a 为实数，则3a ＝______________． 【解析】法一：由等式两边对应项系数相等．即：545543315544310100a C a a a C a C a a =⎧⎪+=⇒=⎨⎪++=⎩． 法二：对等式：()()()()2550125111f x x a a x a x a x ==+++++++两边连续对x 求导三次得：2234560624(1)60(1)x a a x a x =++++，再运用赋值法，令1x =-得：3606a =，即310a =．【答案】1015．在∆ABC 中，M 是BC 的中点，AM ＝3，BC ＝10，则AB AC ⋅＝______________． 【解析】此题最适合的方法是特例法．假设∆ABC 是以AB ＝AC 的等腰三角形，如图， AM ＝3，BC ＝10，AB ＝ACcos ∠BAC ＝3434102923434+-=⨯．AB AC ⋅＝cos 29AB AC BAC ⋅∠= 【答案】2916．定义：曲线C 上的点到直线l 的距离的最小值称为曲线C 到直线l 的距离．已知曲线C 1：y ＝x 2＋a到直线l ：y ＝x 的距离等于C 2：x 2＋(y ＋4) 2 ＝2到直线l ：y ＝x 的距离， 则实数a ＝______________．【解析】C 2：x 2＋(y ＋4) 2 ＝2，圆心(0，—4)，圆心到直线l ：y ＝x的距离为：d ==故曲线C 2到直线l ：y ＝x的距离为d d r d '=-=-= 另一方面：曲线C 1：y ＝x 2＋a ，令20y x '==，得：12x =，曲线C 1：y ＝x 2＋a 到直线l ：y ＝x 的距离的点为(12，14a +)，74d a '==⇒=． 【答案】7417．设a ∈R ，若x ＞0时均有[(a －1)x －1]( x 2－ax －1)≥0，则a ＝______________． 【解析】本题按照一般思路，则可分为一下两种情况： (A )2(1)1010a x x ax ≤⎧⎨≤⎩－－－－， 无解； (B )2(1)1010a x x ax ≥⎧⎨≥⎩－－－－， 无解． 因为受到经验的影响，会认为本题可能是错题或者解不出本题．其实在x ＞0的整个区间上，我们可以将其分成两个区间(为什么是两个？)，在各自的区间内恒正或恒负．(如下答图) 我们知道：函数y 1＝(a －1)x －1，y 2＝x 2－ax －1都过定点P (0，1)． 考查函数y 1＝(a －1)x －1：令y ＝0，得M (11a -，0)，还可分析得：a ＞1；考查函数y 2＝x 2－ax －1：显然过点M (11a -，0)，代入得：211011a a a ⎛⎫--= ⎪--⎝⎭，解之得：a =，舍去a =，得答案：a =【答案】a =三、解答题：本大题共5小题，共72分，解答应写出文字说明、证明过程或演算步骤． 18．(本小题满分14分)在∆ABC 中，内角A ，B ，C 的对边分别为a ，b ，c ．已知cos A ＝23，sin BC ． (Ⅰ)求tan C 的值；(Ⅱ)若a∆ABC 的面积．【解析】本题主要考察三角恒等变换，正弦定理，余弦定理及三角形面积求法等知识点。

2012年浙江高考自选模块试题题号：13 科目：物理“物理3-3”模块（10分）一定质量的理想气体，状态从A →B →C →D →A 的变化过程可用如图所示的P-V 图描述，图中P 1、P 2、V 1、V 2和V 3为已知量。

（1）气体状态从A 到B 是____过程（填“等容”、“等压”或“等温”）；（2分）（2）状态从B 到C 的变化过程中，气体的温度_____（填“升高”、“不变”或“降低”；）（2分）（3）状态从C 到D 的变化过程中，气体___（填“吸热”或“放热”）；（2分）（4）状态从A →B →C →D 的变化过程中，气体对外界所做的总功为____。

（4分）题号：14 科目：物理“物理3-5”模块（10分）一个静止的钚核23994pu 自发衰变成一个铀核23592U 和另一个原子核X ，并释放出一定的能量。

其核衰变方程为：2392359492Pu U X →+。

（1）方程中的“X ”核符号为_______；（3分）（2）钚核的质量为239.0522u ，铀核的质量为235.0439a ，X 核的质量为4.0026u ，已知1u 相当于931MeV ，则该衰变过程放出的能量是_____，MeV ；（3分）（3）假设钚核衰变释放出的能量全部转变为铀核的X 核的动能，则X 核与铀核的动能之比是_____。

（4分）题号:15 科目：化学《物质结构与性质》模块（1）可正确表示原子轨道的是： ① 。

A ．2sB ．2dC ．3pzD ．3f（2）写出基态镓（Ga ）原子的电子排布式： ② 。

（3）下列物质变化，只与范德华力有关的是 ③ 。

A ．干冰熔化B ．乙酸汽化C ．乙醇与丙酮混溶D ．H C N O CH 3CH 3溶于水 E ．碘溶于四氯化碳 F ．石英熔融（4）下列物质中，只含有极性键的分子是 ④ ，既含离子键又含共价键的化合物是 ⑤ ，只存在σ键的分子是 ⑥ ，同时存在σ键和π键的分子是 ⑦ 。

东阳中学2012届高三5月模拟考试自选模块试题本卷共18题，满分60分,考试时间90分钟注意事项：1．将选定的题号按规定要求写在答题卡的题号内；2．考生可任选6题作答,所答试题应与题号一致；多答视作无效.语文题号：01“中国古代诗歌散文欣赏”模块（10分）阅读下面的诗歌，回答问题。

灵魂选择自己的伴侣文/ 狄金森（美国）灵魂选择自己的伴侣，然后，把门紧闭，她神圣的决定，再不容干预。

发现车辇停在她低矮的门前，不为所动，一位皇帝跪在她的席垫,不为所动。

我知道她从一个民族众多的人口选中了一个，从此封闭关心的阀门，象一块石头.(1）如何理解诗歌题目中的“灵魂”?(4分）▲.（2）结合诗歌内容，分析本诗表达的思想感情。

（6分）▲.题号：02“中国现代诗歌散文欣赏”模块（10分）阅读下面的文言文，回答问题.墨池记曾巩临川之城东，有地隐然而高，以临于溪,曰新城。

新城之上,有池洼然而方以长,曰王羲之之墨池者，荀伯子《临川记》云也。

羲之尝慕张芝，临池学书，池水尽黑,此为其故迹，岂信然邪？方羲之之不可强以仕，而尝极东方,出沧海,以娱其意于山水之间，岂其徜徉肆恣，而又尝自休于此邪？羲之之书晚乃善,则其所能，盖亦以精力自致者，非天成也。

然后世未有能及者，岂其学不如彼邪？则学固岂可以少哉！况欲深造道德者邪？学必求其心得，业必贵于专精 墨池之上，今为州学舍。

教授王君盛，恐其不章也，书“晋王右军墨池"之六字于楹间以揭之.又告于巩曰:“愿有记！”推王君之心，岂爱人之善，虽一能不以废，而因以及乎其迹邪?其亦欲推其事，以勉学者邪？夫人之有一能，而使后人尚之如此，况仁人庄士之遗风馀思，被于来世者如何哉! 庆历八年九月十二日曾巩记. (1）曾巩出自欧阳修门下,接受了欧阳修先道而后文的古文创作主张。

试就本文分析。

(2)请用提要钩玄的方法，赏析上面的文章。

（150字左右）数 学题号：03“数学史与不等式选讲”模块（10分) (1)已知,,x y z 为正实数，满足2x y z ++=,求证：23999x y z ++≥。

宁波市2012年高三“十校”联考自选模块试题本卷共18题，满分60分，考试时间90分钟注意事项：1．将选定的题号按规定要求写在答题卡的题号内：2．考生可任选6题作答，所答试题应与题号一致；多答视作无效。

语文题号：01“中国古代诗歌散文欣赏”模块（10分）张长史草书颓然天放，略有点画处而意态自足，号称神逸。

今世称善草书者或不能真行，此大妄也。

真生行，行生草；真如立，行如行，草如走。

未有未能行立而能走者也。

今长安犹有长史真书《郎官石柱记》，作字简远如晋宋间人。

颜鲁公书雄秀独出，一变古法，如杜子美诗，格力天纵，奄有汉魏晋宋以来风流，后之作者，殆难复措手。

柳少师书本出于颜而能自出新意，一字千金，非虚语也。

其言“心正则笔正者”，非独讽谏，理固然也。

世之小人，书字虽工而其神情终有睢盱侧媚之态，不知人情随想而见，如韩子所谓窃斧者乎，抑真尔也?然至使人见其书而犹憎之，则其人可知矣。

（节选自苏轼《书唐氏六家书后》）注：张长史即张旭，颜鲁公即颜真卿，柳少师即柳公权苏轼在书法上与黄庭坚、米芾、蔡襄并称“宋四家”。

试结合本文，分析苏轼在书法艺术上有哪些基本的主张？（10分）题号：02“中国现代诗歌散文欣赏”模块（10分）如雾起时[中国台湾]郑愁予我从海上来，带回航海的二十二颗星。

你问我航海的事儿，我仰天笑了……如雾起时，敲叮叮的耳环在浓密的发丛找航路，用最细最细的嘘息，吹开睫毛引灯塔的光。

赤道是一痕润红的线，你笑时不见。

子午线是一串暗蓝的珍珠，当你思念时即为时间的分隔而滴落。

我从海上来，你有海上的珍奇太多了……迎人的编贝，嗔人的晚云，和使我不敢轻易近航的珊瑚的礁区。

（1）试分析“赤道”与“子午线”这两个意象的妙处。

（6分）（2）“如雾起时”在全诗中有何作用？（4分）数 学题号：03“数学史与不等式选讲”模块（10分）已知实数x ，y ，z 满足22212(1)1,[,]33ax a y z a +-+=∈其中。

（1）求证：||xyz ≤ （2）若x ，y ，z 又满足(1)1ax a y z +-+=，求z 的取值范围．题号：04“矩阵与变换和坐标系与参数方程”模块（10分）已知圆O 的参数方程为2cos ()2sin x y θθθ=⎧⎨=⎩为参数 直线l 1的参数方程为1cos (,)1sin 63x t t y t θππθθ=+⎧≤≤⎨=+⎩为参数 直线l 2的参数方程为1cos (,)1sin 63x t t y t θππθθ=-⎧≤≤⎨=+⎩为参数（I ）以直角坐标原点O 为极点，以x 轴的正半轴为极轴建立极坐标系，过点P ，1）作圆O 的切线，求该切线的极坐标方程；（II ）直线l 1与圆O 相交于A ，B 两点，直线l 2与圆O 相交于C ，D 两点，求|AB|·|CD|的最大和最小值。

2012年浙江高考自选模块试题题号：01 科目：语文“中国古代诗歌散文欣赏”模块（10分）阅读下面的散文，然后回答问题。

吃野菜说清·龚鼎孳新雨后,绿芜如发,园蔬叶叶,青满畦径。

启扉视之，知一年春事又将烂漫矣，家人间撷作羹，劣得一饱。

野香拂拂，从匕箸间出，诚有如子瞻所谓饱霜雪之精、味含土膏①者。

独怜此物没蓬蒿中，与贫士为伍，寒窗一嚼，胜十日太牢②，甚不可进于达官贵人、钟鸣鼎食、芍药撰、朱砂羹之口。

今中原嗷嗷，道殣相望，雁粪榆皮，所在仰以为命。

甚且折骨解肢，与乌鸢争攫啄之利。

吁，可悲也！彼达官贵人日啖浓鲜，当翠袖，奉卮华茵，度梦时亦曾念及野人藜藿③不继无耶？昔人曰：民不可有此色，士大夫不可无此味。

知信哉！【注】①土膏：土地中的膏泽。

⑦太牢：古时祭祀用的猪、牛、羊，泛指美味佳肴。

③藜藿：野菜。

（1）结合全文，理解文中画线句子的含义。

（4分）（2）赏析这篇散文的写作特色。

（6分）题号：02 科目：语文“中国现代诗歌散文欣赏”模块（10分）阅读下面的诗歌，然后回答问题。

采采卷耳朱巧玲采采卷耳。

不盈顷筐嗟我怀人。

置彼周行——《诗经﹒周南﹒卷耳》用群山、河流和铁轨衡量我们之间的距离三千诗句，算不算长？我相信爱的辽阔一如采采卷耳覆盖每一寸肌肤细微的感觉你知道吗每当老虎从白雪里跃出 我会获得释放,像蒲公英 散落四方用地理和祖国容纳我们之间的落差 每一棵树木都是升起的太阳 每一只小兽都是可爱的孩子 走在天穹下什么在呼唤我的名字我相信爱的自由一如采采卷耳 当我抬头，那些洁白的云朵聚拢而来 挡住了倾斜的光线（1）本诗以《诗经﹒周南﹒卷耳》为引子有什么作用？（4分）（2）从意象、手法、结构中选择一个方面，结合具体诗句进行赏析。

（6分） 题号：03 科目：数学“数学史与不等式选讲”模块(10分)已知a R ∈，设关于x 的不等式2324x a x x -++≤+的解集为A ， (1)若a=1,求A;(2) 若A=R,求a 的取值范围。

2012浙江高考英语真题及答案(全word版)2012年浙江高考英语试题选择题部分，（共80分）第一部分：英语知识运用（共两节，满分30分）第一节：（共20小题；每小题0．5分，满分10分）1. ----- Is there anything else to discuss?------ _________, I guess.A. Not at allB. No ,that’s allC. Yes , I ‘m sureD. Yes , of course2. The development of industry has been _______ gradual process throughout ______human existence from stone tools to modern technology.A, / , the B, the , a C, a, / D, a, a3. No matter how bright a talker you are , there are times when it ‘s better ______ silent.A, remain B, be remaining C, having remained D, to remain4. I made a promise to myself _______ this year, my first year in high school , would be different.A, whether B, what C, that D, how5. Studying Wendy’s menu , I found that many of the items are similar to ______ of McDonald’s .A, those B, ones C, any D, all6. _______ all the animals I ‘ve ever had ,those two dogs are the most sensitive to spoken word.A. FromB. OfC. ForD. With7. Your _______ as a student will be excellent if you develop a habit of reflecting on how you learn.A, opinion B, growth C, performance D, character 8. I think Tom, as the head of a big department, should either study regualrly or ______ his job.A, quits B, to quit C, quitting D, quit17. Ellen was a painter of birds and nature, _______, for some reason, had withdrawn from all human society.A, which B, who C, where D, whom18. Mike was usually so careful, ________this time he made a small mistake.A, yet B, still C, even D, thus19. Had they known what was coming next, they ________ second thoughts.A, may have B, could have C, must have had D, might have had20. ----- I’m going to San Francisco for a coup le of days.------ ________, I wish I could get away for a while.A. It doesn’t matterB. Forget it.C. I really envy youD. I can’t agree more第二节：完形填空（共20小题；每小题1分，满分20分）“Just sign here, sir,” the d eliveryman said as he handed Oscar Reyna a package.The package consisted of a long , narrow box___21____ wrapped in brown paper. __22___ the box, Oscar saw an umbrella inside—— a very old one with a beautifully carved handle. ____23___He had not seen it in more than 20 years, he recognized it ____24____.Oscar was 16 when he first saw the ___25____ umbrella. He had gone to a concert with his grandparents. As they were leaving, he noticed an umbrella on an empty seat. Impressed by its ____26____, Oscar felt a strong desire to find its ___27____.Oscar ___28____ the manager to look in the record of advance ticket sales. Just as he thought, a name matched the seat ____29___ Oscar had found the umbrella . The name was Mrs. Katie O’brien.Oscar talked his grandparents into going by MrsO’brien’s ___30____ on their way home. He rang the bel l, the door opened, and an elderly woman appeared. “May I __31___ you ? “she asked.“I’d like to return it if its yours,” Oscar said,____32____ the umbrella as if presenting a ___33___ that had long been wished for.“Why , yes! it’s mine, “replied Mrs. Brien with a___34____ smile and shining eyes. “ It was given to by my father years ago. Thank you so much for returning it. May I offer you a reward for your ____35____ ? ““ No, ma’am , “ he said “ my grandmother says a good deed is its own rewar d.”“ Well, that ‘s ____36_____ my father used to say. What is your name , Young man ?”Years later, Oscar was staring at the finely carved handle of the umbrella as he remember Mrs. O’ Brien . It was in perfect condition, considering how__37__ it was. Why had it arrived here today?As if ___38____, a note fell from the paper. It read: Mrs O’brien wanted you to ___39___ this umbrella as a present for a kind, __40___gesture long ago.21. A. strictly B. carefully C. roughlyD. casually22. A. opening B. seizing C. observing D. searching23. A. After B. When C. Since D. Although24. A. clearly B. fully C. immediatelyD. suddenly25. A. average B. unusual C. plain D. typical26. A. beauty B. shape C. origin D. history27. A. designer B. seller C. user D. owner28. A. convinced B. forced C. encouragedD. advised29. A. until B. before C. which D. where30. A. family B. theater C. house D. neighborhood31. A. invite B. help C. bother D. know32. A. putting up B. turning out C. picking upD. holding out33. A. chance B. fact C. gift D. result34. A. wide B. confident C. proud D. shy35. A. patience B. kindness C. courage D. determination36. A. obviously B. naturally C. exactlyD. probably37. A. old B. rare C. precious D. nice38. A. in contrast B. in return C. in exchangeD. in answer39. A. possess B. accept C. carry D. value40. A. attractive B. significant C. unselfishD. sympathetic第二部分：阅读理解（第一节20小题，第二节5小题；每小题2分，共50分）A Easter (复活节) is still a great day for worship, candy in baskets and running around the yard finding eggs, but every year it gets quite a bit worse for bunnies.And no, not because the kids like to pull their ears. The culprit is climate change, and some researchers found that rising temperatures are having harmful effects on at least five species of rabbit in the US,Take the Lower Keys Marsh rabbit, for instance. An endangered species that lives in the Lower Florida Keys, this species of cottontail is a great swimmer -- it lives on the islands! -- but it is already severely affected by development and now by rising sea levels. According to the Center for Biological Diversity, an ocean level rise of only 0.6 meters will send these ~ys jumping to higher ground and a 0.9-meter rise would wipe out their habitat (栖息地) completely.The snowshoe hare, on the other hand, has a color issue. Most of these rabbits change their fur color from white inthe wintertime to brown in the summer, each designed to give them better cover from predators (~I~’) ~ As the number of days with snow decreases all across the country, however, more and more bunnies are being left in white fur during brown dirt days of both fall and spring, making them an easier mark for predators. Researchers know that the color change is controlled by the number of hours of sunlight, but whether the rabbit will be able to adapt quick enough to survive is a big question. The National Wildlife Federation has reported that hunters have noticed their numbers are already markedly down.American pikas or rock rabbits, a relative of rabbits and hares, might be the first of these species to go extinct due to climate change. About 7-8 inches long, pikas live high in the cool. damp mountains west of the Rocky Mountains. As global temperatures rise, they would naturally migrate (J~2~) to higher ground -- but they already occupy the mountaintops. They can’t go any higher. The National Wildlife Federation reports that they might not be able to stand the new temperatures as their habitat heats up.The volcano rabbit has the same problem. These rabbits live on the slopes of volcanoes in Mexico, andrecent studies have shown that the lower range of their habitat has already shifted upward about 700 meters, but there are not suitable plants for them to move higher, so they are stuck in the middle. Scientists are concerned about their populations.Native to the US, pygmy rabbits weigh less than 1 pound and live in the American West. They are believed to be the smallest rabbits in the world. Their habitats have been destroyed by development. Several populations, such as the Columbia Basin pygmy, almost went extinct and were saved by zoo breeding programs. Pygmy rabbits also rely on winter cover by digging tunnels through the snow to escape predators, but lesser snowfall is leaving them exposed.All of this gives new meaning to dressing up in a giant bunny costume this Easter.41. The writer mentions Easter at the beginning of the passage in order toA. show the importance of Easter DayB. introduce the issue about bunniesC. remind people of Easter traditionsD. discuss the relationship between Easter and bunnies42. The word “culprit” (Paragraph 2) is closest inmeaning to_________A. criminalB. judgeC. victimD. producer43. According to the passage, some rabbits can now be easily discovered by predators because theyA. are exposed to more skillful huntersB. have moved to habitats with fewer plantsC. haven’t adapted themselv es to climate changeD. can’t change their fur color into white in the fall and the spring44. The problem faced by volcano rabbits and rock rabbits is thatA. both are affected by less snowB. both are affected by rising sea levelsC. neither can find enough foodD. neither can migrate to higher places45. Which best describes the writer’s tone in the passage?A. Approving.B. Concerned.C. Enthusiastic.D. Doubtful.BBelow is a selection about Guinness（吉尼斯）World Records.Top 6 Unusual Guinness World Records♦Fastest 100 m running on all foursThe 2008 Guinness World Records Day was, according to CWR, their biggest day of record-breaking ever, I- h more than 290.000 people taking put in record attempts in 15 different countries. Kenichi Ito's record attempt was port of this special day. He is just another example of Japanese with "super powers". His "super power" is to run with great speed on all fours. Kenichi Ito ran 100 m on all fours in 18.58 seconds. The Japanese set this record at Setagaya Kuritsu Sogo Undojyo, Tokyo, in 2008.♦Most people inside a soap bubbleThe Discovery Science Center in Santa Ana, Califomia celebrated this year the 15th anniversary of the Bubble (泡泡) Festival. A bubble's math principles and science were presented and demonstrated at the three-week-long exhibition. The intriguing Bubble Show was also part of the program. Fan Yang and Deni Yang impressed the audience with their awesome skills for bubble making. The Yang family cooperated with the Discovery Science Center to set a new Guinness World Record for mow people inside a scup bubble and they succeeded.The family that has been working with soap bubbles for27 years created a huge soap bubble and got 118 people inside it. The record was set or. April 4, 2011.♦Longest ears on a dogA bloodhound from Illinois has the longest ears ever measured a dog. The right ear is 13.75 inches long and the left one 13.5 inches. The dog named Tigger earned this title in 2004 and is owned by Christina and Bryan Flessner. Mr. Jeffries is the previous record holder of this title. Each of his ears measured approximately 11. 5 inches long. His grandfather used to hold this amazing world record, but when he died Mr.Jeffries look over.♦M ost living generationsDid you ever wonder what is the Guinness World Record for most living generation in one family? Seven is the answer.The ultimate authority on record-breaking mentions on the website that the youngest great-great- great-great grandparent of this family was Augusta Bung "aged 109 years 97 days, followed by her daughter aged 89, her granddaughter aged 70, her great grand-daughter aged 52, her great-great grand-daughter aged 33 and her great-great-great granddaughter aged 15 on the birth of her great-great-great-great grandson on January 21, 1989"♦M ost T shirts worn at onceBelieve it or not, there is a record also for this category. Krunoslav Budiseli set a new world record on May 22, 2010 for wearing 245 T-shirts at the same time. The nun from Croatia was officially recognized as the new record bolder by Guinness World Records after he managed to put on 245 different T-shirts in 1ess than two hours. . The T-shirts weighted 68 KG and Budiseli said he began struggling around T-shirt No. 120. He dethroned the Swedish Guinness record holder who wore 238 T-shirts.♦ Heaviest pumpkinGuinness World Records confirmed on October 9. 2010 that a gigantic pumpkin （南瓜）grown in Wisconcin was officially the world’s heaviest. It weighed 1,810 pounds 8 ounces and was unveiled by Chris Stevens at the Stillwater Harvest Festival in Minnesota. Stevens' pumpkin was 85 pounds Javier than the previous re I, another huge pumpkin grown in Ohio. The proud farmer said his secret is a precise of rain, cow mature, good soil, sea grass and fish emulsion. Some of the world's heaviest pumpkins, including the record bolder, were on public display at the Bronx Botanical Gardens in New Yost for a dozen days. 46. Why is Kenichi Ito described «s a man with a "superpower"?A. H e set a good example to all Japanese.B. He made record attempts in 15 different countries.C. H e set a new record for "Fastest 100 m running on all fours".D. H e participated in the 2008 Guinness World Records Day activities.47. _________ Jeffries is the name of .A. _________ the owner of the dog with the longest earsB. _________ the grandfather of the dog with the longest careC. _________ the present holder of the record for "Longest care on a dog"D.the former holder of the record for " longest care on a dog'48. How many T-shirts had Krunoslav Budiseli put on before he felt it difficult to go on?A. 68.B. 120.C. 238.D. 245.49. According to the given information. which Guinness World Record was most recently set?A. T he record for "Most people inside a soup bubble".B. The record for "Most living generations'".C. T he record for "Most T-shirts worn at once".D. T he record for " Heaviest pumpkin".CTwo friends have an argument that bleaks up their friendship forever, even though neither one can remember how the whole thing got started. Such sad events happen over and over in high schools across the country. In fact, according to an official report on youth violence, "In our country today, the greatest threat to the lives of children and adolescents is not disease or starvation or abandonment, but the terrible reality of violence". Given that this is the case, why aren't students taught to manage conflict the way they are taught to solve math problems, drive cars, or stay physically fit?First of all, students need to realize that conflict is unavoidable. A report on violence among middle school and high school students indicates that most violent incidents between students begin with a relatively minor insult (侮辱). For example, a fight could start over the fact that one student eats a peanut butter sandw ich each lunchtime. Laughter over the sandwich can lead to insults, which in turn can lead to violence. The problem isn't in the sandwich, but in the way students deal with the conflict. Once students recognize that conflict is unavoidable,they can practice the golden rule of conflict resolution (解决) stay calm. Once the student feels calmer, he or she should choose words that will calm the other person down as well. Rude words, name-calling, and accusation only add fuel to the emotional fir On the other hand, soft words spoken at a normal sound level can put out the fire before it explodes out of control.After both sides have calmed down, they can use another key strategy for conflict resolution; listening. Listening allows the two sides to understand each other. One person should describe his or her side, and the other person should listen without interrupting. Afterward, the listener can ask non-threatening questions to clarify the speaker's position. Then the two people should change roles.Finally, students need f. consider what they are hearing. This doesn't mean trying to figure out what's wrong with the other person. It means understanding what the real issue is and what both sides are trying to accomplish. For example, a shouting match over a peanut butter sandwich might happen because one person thinks the other person is unwilling to try new things. Students need to ask themselves questions such as these: How did this start?What do I really want? What am I afraid off As the issue becomes clearer, the conflict often simply becomes smaller. Even if it doesn't, careful thought helps both sides figure out a mutual solution.There will always be conflict in schools, but that doesn't mean there needs to be violence. After students in Atlanta started a conflict resolution program, according to Educators for Social Responsibility, "64 percent of the teachers reported less physical violence in the classroom;75 percent of the teachers reported an increase in student cooperation; and 92 percent of the students felt better about themselves". Learning to resolve conflicts can help students deal with friends,. teachers. parents, bosses, and coworkers. In that way, conflict resolution is a basic life skill that should be taught in schools across the country.50. ___________ This article is mainly about .A. the lives of school childrenB. the cause of arguments in schoolsC. how to analyze youth violenceD. how to deal with school conflicts51. ______________ From Paragraph 2 we can learn that________ _____ .A. ______________ violence is more likely to occur atlunchtimeB. ______________ a small conflict can lead to violenceC. ______________ students tend to lose their temper easilyD. ______________ the eating habit of a student is often the cause of a fight52. Why do students need to ask themselves the questions stated in Paragraph 5?A. T o find out who to blame.B. To get ready to buy new things.C. T o make clear what the real issue is.D. To figure out how to stop the shouting match.53. ____________________________ After the conflict resolution program was started in Atlanta, it was found that______.A. there was a decrease in classroom violenceB. there was less student cooperation in the classroomC. m ore teachers fell better about themselves in schoolsD. t he teacher-student relationship greatly improved54. _________________ T he writer’s purpose for writing this article is to_______.A. complain about problems in school educationB. teach students different strategies for school lifeC. advocate teaching conflict management in schoolsD. inform teachers of the latest studies on school violenceDAs a young boy, I sometimes traveled the country roads with my dad. He was a rural mill carrier, and on Saturdays he would ask me to go with him. Driving through the countryside was always an adventure: There were animals to see, people to visit, and chocolate cookies if you knew where to stop, and Dad did.In the spring, Dad delivered boxes full of baby chickens, and when 1 was a boy it was such a fun to stick your finger 'through one of the holes of the boxes and let the baby birds peck on your fingers.On Dad' s final day of work, it took him well into the evening to complete his rounds because at least one member from each family was waiting at their mailbox to thank him for his friendship and his years of service. "Two hundred and nineteen mailboxes on my route." he used to say, "and a story at every one. " One lady had no mailbox, so Dad took the mail in to her every day because she was nearly blind. Once inside, he read her mail and helped her pay her bills.Mailboxes were sometimes used for things other than mail. One note left in a mailbox read. "Nat, take these eggs to Marian; she's baking a cake and doesn't have any eggs. " Mailboxes might be buried in the snow, or broken, or lying on the groom:. bat the mail was always delivered On cold days Dad might find one of his customers waiting for him with a cup of hot chocolate. A young wrote letters but had no stamps, so she left a few button on the envelope in the mailbox; Dad paid for the stamps. One businessman used to leave large amounts of cash in his mailbox for Dad to take to the bank. Once, the amount came to 8 32,000.A dozen years ago, when I traveled back to my hometown on the sad occasion of Dad’s death, the mailboxes along the way reminded me of some of his stories. I thought I knew them all, but that wasn't the case. As I drove home, I noticed two lamp poles, one on each side of the street. When my dad was around, those poles supported wooden boxes about four feet off the ground. One box was painted green and the other was red, and each had a long narrow hole at the top with white lettering: SANTA CLAUS, NORTH POLE. For years children had dropped letters to Santa through those holes.I made a turn at the comer and drove past the post officeand across the railroad tracks to our house. Mom and I were sitting at the kitchen table when I heard footsteps. There, at the door, stood Frank Townsend, Dad's postmaster and great friend for many years. So we all sat down at the table and began to tell stories.At one point Frank looked at me with tears in his eyes. " What are we going to do about the letters this Christmas?" he asked."The letters?"'I guess you never knew. ""Knew what?"" Remember, when you were a kid and you used to put your letters to Santa in those green and red boxes on Main Street? It was your dad who answered all those letters every year. "I just sat there with tears in my eyes. It wasn’t hard for me to imagine Dad sitting at the old table in our basement reading those letters and answering each one. I have since spoken with several of the people who received Christmas letters during their childhood, and they told me how amazed they were that Santa had known so much about their homes and families.For me, just knowing that story about my father was thegift of a lifetime.55. ____________________________ I t can be inferred from the passage that the writer regarded his travels with Dad us_____.A. great chances to help other peopleB. happy occasions to play with baby chickensC. exciting experience* with a lot of funD. good opportunities to enjoy chocolate cookies56. ______________________ The writer provides the detail about the businessman to show that_____.A. Dad had a strong sense of dutyB. Dad was an honest and reliable manC. Dad had a strong sense of honorD. Dad was a kind and generous man57. According to the passage, which of the following impressed the writer most?A. Dad read letters for a blind lady for years.B. Dad paid for the stamps for a young girl.C. Dad delivered some eggs to Marian.D. Dad answered children's Christmas letters every year.58. The method the writer uses to develop Paragraph 4 is______.A. offering analysesB. providing explanationsC. giving examplesD. making comparisons59. What surprised the children most when they received letters in reply from Santa Claus every year?A. Santa Claus lived alone in the cold North Pole.B. Santa Claus answered all their letters every year.C. Santa Claus had unique mailboxes for the children.D. Santa Claus had so much information about their families.60. Which of the following is the best title for the passage?A. The MailB. Christmas LettersC Special Mailboxes D. Memorable Travels第二节下面文章中有5处（第61~65题）需要添加小标题，请从以下选项中选出符合各段意思的小标题，并在答题卡上将该项涂黑,选项中一项为多余选项.A. S low Down Your LifeB. Escape Now and ThenC. S eparate Your ActionsD. A llow Yourself to Be WeakE. Relieve Pressure by Firmly Saying " No"F. Stop Expecting Everything to Be PerfectHow to Simplify Your LifeLess is more. This is why we say: reduce things by half instead of doubling them, get rid of junk instead of piling it up, relax instead of stressing, slow down instead of speeding up. Apply these principles in your everyday life in a conscious way. You will then find yourself well along on your journey to simplification.61. _When you concentrate on one task, you find you have energy that you didn't even know you had. Just imagine: you arc at a fair and you have to carry two heavy pigs over 100 yards. If you keep grabbing one and then the other, it will take forever, because one of them will keep slipping out from under your arm and running off. But if you tie one pig in a place, pick up the other, gather all your strength and make a dash for the finish line, pause for a moment, run bock and get the other one, and with great determination, carry the second pig to the finish line, then you can be sure of succcss.62. ______The pressure at work is on the increase in all occupations. In the modem nuclear family, the expectations that formerly would have been shared amongall the relatives are now concentrated on the individual partner.If you have the feeling that 24 hours per day are not enough for nil the things you need to do, then it’s not because the day has too few hours, but because you have too many activities. A simple fact that overloaded people often tend to forget. The solution is equally simple; refuse to accept so many work assignments in your private life or your working life.63. _“I can handle stress” is regarded as a positive statement in the world of work. People who can handle stress are given more and more to cope with —until one day they break.Pay careful attention to the signs that tell you that you arc under more stress than you can cope with. These signals came from various areas of life. You become ill, or your work efficiency decreases.If you have any of these symptoms, change your life goals and decrease your tolerance of stress. Say quite openly, "I can't manage that. "64. _"If only I were slimmer, more beautiful, richer, moreclever, then I would be happier. " This is a dream that makes a lot of people ill, depressed, and unhappy. Life has its flaws, defects, comets, and edges. Only those who accept this reality can lead a really full life.Of course there are activities in which errors are dangerous; driving a car, crossing the road. But life doesn't consist entirely of these things. In among them there is a lot of room for small and large mistakes.65.Successful people ail have their own places where they can withdraw in order to work. Find out which places improve your creativity. For me it's the train. When I know that I'm going to be traveling for four hours without phone calls and people knocking on my door, I find my mind is free and I can read or write complex articles. There can be problems working on the train, of course: if the person sitting opposite you keeps talking away, or if train trips make you tired (some people fall asleep after a few miles).（非选择题，共40分）第三部分:写作（共二节,满分40分）第一节:短文改错（共10小题；每小题1分，满分10分）假如英语课上老师要求同学们交换修改作文，请你修改你同桌写的以下作文。

2012年普通高等学校招生全国统一考试（浙江卷）理科综合测试（物理）一．单项选择部分(每题6分)14．如图所示，与水平面夹角为30°的固定斜面上有一质量m =1.0 kg 的物体。

细绳的一端与物体相连，另一端经摩擦不计的定滑轮与固定的弹簧秤相连．物体静止在斜面上，弹簧秤的示数为4.9 N ．关于物体受力的判断(取g =9.8 m/s 2)，下列说法正确的是( )A ．斜面对物体的摩擦力大小为零B ．斜面对物体的摩擦力大小为4.9 N ，方向竖直向上C ．斜面对物体的支持力大小为4.9 3 N ，方向竖直向上D ．斜面对物体的支持力大小为4.9 N ，方向垂直斜面向上 【答案】A【解析】由弹簧秤的示数为4.9 N 可知细绳对物体的拉力大小也为4.9 N ，刚好等于物体的重力沿斜面向下的分力，因此物体在重力、绳子的拉力和斜面的支持力下能够保持平衡状态，故选项A 正确，选项B 错误；由平衡条件，斜面对物体的支持力F N ＝mg cos30°＝4.93N ，方向垂直斜面向上，故选项C 、D 错误。

15．如图所示，在火星与木星轨道之间有一小行星带．假设该带中的小行星只受到太阳的引力，并绕太阳做匀速圆周运动。

下列说法正确的是( )A ．太阳对各小行星的引力相同B ．各小行星绕太阳运动的周期均小于一年C ．小行星带内侧小行星的向心加速度值大于外侧小行星的向心加速度值D ．小行星带内各小行星圆周运动的线速度值大于地球公转的线速度值【答案】C【解析】各小行星质量以及其与太阳的距离不一定相同，故太阳对各小行星的引力不一定相同，选项A 错误；由a n ＝GMr 2可知，内侧小行星与太阳的距离较近，向心加速度较大，选项C 正确；各小行星绕太阳运动的半径均大于地球绕太阳运动的半径，由开普勒第三定律可知，各小行星绕太阳运动的周期均大于地球绕太阳运动的周期，选项B 错误；根据G Mm r 2＝mv 2r ，得v ＝GMr，可知各小行星运动的线速度均小于地球公转的线速度，故选项D 错误。

2012浙江高考英语真题及答案(全word版)2012年浙江高考英语试题选择题部分，（共80分）第一部分：英语知识运用（共两节，满分30分）第一节：（共20小题；每小题0．5分，满分10分）1. ----- Is there anything else to discuss?------ _________, I guess.A. Not at allB. No ,that’s allC. Yes , I ‘m sureD. Yes , of course2. The development of industry has been _______ gradual process throughout ______human existence from stone tools to modern technology.A, / , the B, the , a C, a, / D, a, a3. No matter how bright a talker you are , there are times when it ‘s better ______ silent.A, remain B, be remaining C, having remained D, to remain4. I made a promise to myself _______ this year, my first year in high school , would be different.A, whether B, what C, that D, how5. Studying Wendy’s menu , I found that many of the items are similar to ______ of McDonald’s .A, those B, ones C, any D, all6. _______ all the animals I ‘ve ever had ,those two dogs are the most sensitive to spoken word.A. FromB. OfC. ForD. With7. Your _______ as a student will be excellent if you develop a habit of reflecting on how you learn.A, opinion B, growth C, performance D, character 8. I think Tom, as the head of a big department, should either study regualrly or ______ his job.A, quits B, to quit C, quitting D, quit9. We live in an age ________ more information is available with great ease than ever before.A, why B, when C, to whom D, on which10. The research lacks ________ evidence ,and therefore , its conclusions are doubtful.A, solid B, fierce C, severe D, potential11. “ It’s such a nice place,” Mother said as she sat at the table______ for customers.A, to be reserved B, having reserved C, reserving D, reserved12. According to scientists, our mental abilities begin to ___ from the age of 27 after reaching the highest level at 22.A, differ B, shrink C, fail D, decline13. Peter had intended to take a job in business, but______ that plan after the unpleasant experience in Canada in 2010.A, had abandoned B, abandoned C, abandon D, will abandon14. Brown said he was by no means annoyed; _______ he was glad to be able make himself clearly understood.A, all in all B, for one thing C, on the contrary D, by the way15. Armed with the information you have gathered , you can ________ preparing your business plan.A, set out B, set about C, set off D, set up16. ----- Alvin , are you coming with us?------ I’d love to , but something unexpected__________.A, has come up B, was coming up C, had come up D, would come up17. Ellen was a painter of birds and nature, _______, for some reason, had withdrawn from all human society.A, which B, who C, where D, whom18. Mike was usually so careful, ________this time he made a small mistake.A, yet B, still C, even D, thus19. Had they known what was coming next, they ________ second thoughts.A, may have B, could have C, must have had D, might have had20. ----- I’m going to San Francisco for a coup le of days.------ ________, I wish I could get away for a while.A. It doesn’t matterB. Forget it.C. I really envy youD. I can’t agree more第二节：完形填空（共20小题；每小题1分，满分20分）“Just sign here, sir,” the d eliveryman said as he handed Oscar Reyna a package.The package consisted of a long , narrow box___21____ wrapped in brown paper. __22___ the box, Oscar saw an umbrella inside—— a very old one with a beautifully carved handle. ____23___He had not seen it in more than 20 years, he recognized it ____24____.Oscar was 16 when he first saw the ___25____ umbrella. He had gone to a concert with his grandparents. As they were leaving, he noticed an umbrella on an empty seat. Impressed by its ____26____, Oscar felt a strong desire to find its ___27____.Oscar ___28____ the manager to look in the record of advance ticket sales. Just as he thought, a name matched the seat ____29___ Oscar had found the umbrella . The name was Mrs. Katie O’brien.Oscar talked his grandparents into going by MrsO’brien’s ___30____ on their way home. He ran g the bell, the door opened, and an elderly woman appeared. “May I __31___ you ? “she asked.“I’d like to return it if its yours,” Oscar said,____32____ the umbrella as if presenting a ___33___ that had long been wished for.“Why , yes! it’s mine,“replied Mrs. Brien with a___34____ smile and shining eyes. “ It was given to by my father years ago. Thank you so much for returning it. May I offer you a reward for your ____35____ ? ““ No, ma’am , “ he said “ my grandmother says a good deed is its own reward.”“ Well, that ‘s ____36_____ my father used to say. What is your name , Young man ?”Years later, Oscar was staring at the finely carved handle of the umbrella as he remember Mrs. O’ Brien . It was in perfect condition, considering how__37__ it was. Why had it arrived here today?As if ___38____, a note fell from the paper. It read: Mrs O’brien wanted you to ___39___ this umbrella as a present for a kind, __40___gesture long ago.21. A. strictly B. carefully C. roughlyD. casually22. A. opening B. seizing C. observing D. searching23. A. After B. When C. Since D. Although24. A. clearly B. fully C. immediatelyD. suddenly25. A. average B. unusual C. plain D. typical26. A. beauty B. shape C. origin D. history27. A. designer B. seller C. user D. owner28. A. convinced B. forced C. encouragedD. advised29. A. until B. before C. which D. where30. A. family B. theater C. house D. neighborhood31. A. invite B. help C. bother D. know32. A. putting up B. turning out C. picking upD. holding out33. A. chance B. fact C. gift D. result34. A. wide B. confident C. proud D. shy35. A. patience B. kindness C. courage D. determination36. A. obviously B. naturally C. exactlyD. probably37. A. old B. rare C. precious D. nice38. A. in contrast B. in return C. in exchangeD. in answer39. A. possess B. accept C. carry D. value40. A. attractive B. significant C. unselfishD. sympathetic第二部分：阅读理解（第一节20小题，第二节5小题；每小题2分，共50分）A Easter (复活节) is still a great day for worship, candy in baskets and running around the yard finding eggs, but every year it gets quite a bit worse for bunnies.And no, not because the kids like to pull their ears. The culprit is climate change, and some researchers found that rising temperatures are having harmful effects on at least five species of rabbit in the US,Take the Lower Keys Marsh rabbit, for instance. An endangered species that lives in the Lower Florida Keys, this species of cottontail is a great swimmer -- it lives on the islands! -- but it is already severely affected by development and now by rising sea levels. According to the Center for Biological Diversity, an ocean level rise of only 0.6 meters will send these ~ys jumping to higher ground and a 0.9-meter rise would wipe out their habitat (栖息地) completely.The snowshoe hare, on the other hand, has a color issue. Most of these rabbits change their fur color from white inthe wintertime to brown in the summer, each designed to give them better cover f rom predators (~I~’) ~ As the number of days with snow decreases all across the country, however, more and more bunnies are being left in white fur during brown dirt days of both fall and spring, making them an easier mark for predators. Researchers know that the color change is controlled by the number of hours of sunlight, but whether the rabbit will be able to adapt quick enough to survive is a big question. The National Wildlife Federation has reported that hunters have noticed their numbers are already markedly down.American pikas or rock rabbits, a relative of rabbits and hares, might be the first of these species to go extinct due to climate change. About 7-8 inches long, pikas live high in the cool. damp mountains west of the Rocky Mountains. As global temperatures rise, they would naturally migrate (J~2~) to higher ground -- but they already occupy the mountaintops. They can’t go any higher. The National Wildlife Federation reports that they might not be able to stand the new temperatures as their habitat heats up.The volcano rabbit has the same problem. These rabbits live on the slopes of volcanoes in Mexico, andrecent studies have shown that the lower range of their habitat has already shifted upward about 700 meters, but there are not suitable plants for them to move higher, so they are stuck in the middle. Scientists are concerned about their populations.Native to the US, pygmy rabbits weigh less than 1 pound and live in the American West. They are believed to be the smallest rabbits in the world. Their habitats have been destroyed by development. Several populations, such as the Columbia Basin pygmy, almost went extinct and were saved by zoo breeding programs. Pygmy rabbits also rely on winter cover by digging tunnels through the snow to escape predators, but lesser snowfall is leaving them exposed.All of this gives new meaning to dressing up in a giant bunny costume this Easter.41. The writer mentions Easter at the beginning of the passage in order toA. show the importance of Easter DayB. introduce the issue about bunniesC. remind people of Easter traditionsD. discuss the relationship between Easter and bunnies42. The word “culprit” (Paragraph 2) is closest inmeaning to_________A. criminalB. judgeC. victimD. producer43. According to the passage, some rabbits can now be easily discovered by predators because theyA. are exposed to more skillful huntersB. have moved to habitats with fewer plantsC. haven’t adapted themselves to climate changeD. can’t change their fur color into white in the fall and the spring44. The problem faced by volcano rabbits and rock rabbits is thatA. both are affected by less snowB. both are affected by rising sea levelsC. neither can find enough foodD. neither can migrate to higher places45. Which best describes the writer’s tone in the passage?A. Approving.B. Concerned.C. Enthusiastic.D. Doubtful.BBelow is a selection about Guinness（吉尼斯）World Records.Top 6 Unusual Guinness World Records♦Fastest 100 m running on all foursThe 2008 Guinness World Records Day was, according to CWR, their biggest day of record-breaking ever, I- h more than 290.000 people taking put in record attempts in 15 different countries. Kenichi Ito's record attempt was port of this special day. He is just another example of Japanese with "super powers". His "super power" is to run with great speed on all fours. Kenichi Ito ran 100 m on all fours in 18.58 seconds. The Japanese set this record at Setagaya Kuritsu Sogo Undojyo, Tokyo, in 2008.♦Most people inside a soap bubbleThe Discovery Science Center in Santa Ana, Califomia celebrated this year the 15th anniversary of the Bubble (泡泡) Festival. A bubble's math principles and science were presented and demonstrated at the three-week-long exhibition. The intriguing Bubble Show was also part of the program. Fan Yang and Deni Yang impressed the audience with their awesome skills for bubble making. The Yang family cooperated with the Discovery Science Center to set a new Guinness World Record for mow people inside a scup bubble and they succeeded.The family that has been working with soap bubbles for27 years created a huge soap bubble and got 118 people inside it. The record was set or. April 4, 2011.♦Longest ears on a dogA bloodhound from Illinois has the longest ears ever measured a dog. The right ear is 13.75 inches long and the left one 13.5 inches. The dog named Tigger earned this title in 2004 and is owned by Christina and Bryan Flessner. Mr. Jeffries is the previous record holder of this title. Each of his ears measured approximately 11. 5 inches long. His grandfather used to hold this amazing world record, but when he died Mr.Jeffries look over.♦M ost living generationsDid you ever wonder what is the Guinness World Record for most living generation in one family? Seven is the answer.The ultimate authority on record-breaking mentions on the website that the youngest great-great- great-great grandparent of this family was Augusta Bung "aged 109 years 97 days, followed by her daughter aged 89, her granddaughter aged 70, her great grand-daughter aged 52, her great-great grand-daughter aged 33 and her great-great-great granddaughter aged 15 on the birth of her great-great-great-great grandson on January 21, 1989"♦M ost T shirts worn at onceBelieve it or not, there is a record also for this category. Krunoslav Budiseli set a new world record on May 22, 2010 for wearing 245 T-shirts at the same time. The nun from Croatia was officially recognized as the new record bolder by Guinness World Records after he managed to put on 245 different T-shirts in 1ess than two hours. . The T-shirts weighted 68 KG and Budiseli said he began struggling around T-shirt No. 120. He dethroned the Swedish Guinness record holder who wore 238 T-shirts.♦ Heaviest pumpkinGuinness World Records confirmed on October 9. 2010 that a gigantic pumpkin （南瓜）grown in Wisconcin was officially the world’s heaviest. It weighed 1,810 pounds 8 ounces and was unveiled by Chris Stevens at the Stillwater Harvest Festival in Minnesota. Stevens' pumpkin was 85 pounds Javier than the previous re I, another huge pumpkin grown in Ohio. The proud farmer said his secret is a precise of rain, cow mature, good soil, sea grass and fish emulsion. Some of the world's heaviest pumpkins, including the record bolder, were on public display at the Bronx Botanical Gardens in New Yost for a dozen days. 46. Why is Kenichi Ito described «s a man with a "superpower"?A. H e set a good example to all Japanese.B. He made record attempts in 15 different countries.C. H e set a new record for "Fastest 100 m running on all fours".D. H e participated in the 2008 Guinness World Records Day activities.47. _________ Jeffries is the name of .A. _________ the owner of the dog with the longest earsB. _________ the grandfather of the dog with the longest careC. _________ the present holder of the record for "Longest care on a dog"D.the former holder of the record for " longest care on a dog'48. How many T-shirts had Krunoslav Budiseli put on before he felt it difficult to go on?A. 68.B. 120.C. 238.D. 245.49. According to the given information. which Guinness World Record was most recently set?A. T he record for "Most people inside a soup bubble".B. The record for "Most living generations'".C. T he record for "Most T-shirts worn at once".D. T he record for " Heaviest pumpkin".CTwo friends have an argument that bleaks up their friendship forever, even though neither one can remember how the whole thing got started. Such sad events happen over and over in high schools across the country. In fact, according to an official report on youth violence, "In our country today, the greatest threat to the lives of children and adolescents is not disease or starvation or abandonment, but the terrible reality of violence". Given that this is the case, why aren't students taught to manage conflict the way they are taught to solve math problems, drive cars, or stay physically fit?First of all, students need to realize that conflict is unavoidable. A report on violence among middle school and high school students indicates that most violent incidents between students begin with a relatively minor insult (侮辱). For example, a fight could start over the fact that one student eats a peanut butter sandw ich each lunchtime. Laughter over the sandwich can lead to insults, which in turn can lead to violence. The problem isn't in the sandwich, but in the way students deal with the conflict. Once students recognize that conflict is unavoidable,they can practice the golden rule of conflict resolution (解决) stay calm. Once the student feels calmer, he or she should choose words that will calm the other person down as well. Rude words, name-calling, and accusation only add fuel to the emotional fir On the other hand, soft words spoken at a normal sound level can put out the fire before it explodes out of control.After both sides have calmed down, they can use another key strategy for conflict resolution; listening. Listening allows the two sides to understand each other. One person should describe his or her side, and the other person should listen without interrupting. Afterward, the listener can ask non-threatening questions to clarify the speaker's position. Then the two people should change roles.Finally, students need f. consider what they are hearing. This doesn't mean trying to figure out what's wrong with the other person. It means understanding what the real issue is and what both sides are trying to accomplish. For example, a shouting match over a peanut butter sandwich might happen because one person thinks the other person is unwilling to try new things. Students need to ask themselves questions such as these: How did this start?What do I really want? What am I afraid off As the issue becomes clearer, the conflict often simply becomes smaller. Even if it doesn't, careful thought helps both sides figure out a mutual solution.There will always be conflict in schools, but that doesn't mean there needs to be violence. After students in Atlanta started a conflict resolution program, according to Educators for Social Responsibility, "64 percent of the teachers reported less physical violence in the classroom;75 percent of the teachers reported an increase in student cooperation; and 92 percent of the students felt better about themselves". Learning to resolve conflicts can help students deal with friends,. teachers. parents, bosses, and coworkers. In that way, conflict resolution is a basic life skill that should be taught in schools across the country.50. ___________ This article is mainly about .A. the lives of school childrenB. the cause of arguments in schoolsC. how to analyze youth violenceD. how to deal with school conflicts51. ______________ From Paragraph 2 we can learn that________ _____ .A. ______________ violence is more likely to occur atlunchtimeB. ______________ a small conflict can lead to violenceC. ______________ students tend to lose their temper easilyD. ______________ the eating habit of a student is often the cause of a fight52. Why do students need to ask themselves the questions stated in Paragraph 5?A. T o find out who to blame.B. To get ready to buy new things.C. T o make clear what the real issue is.D. To figure out how to stop the shouting match.53. ____________________________ After the conflict resolution program was started in Atlanta, it was found that______.A. there was a decrease in classroom violenceB. there was less student cooperation in the classroomC. m ore teachers fell better about themselves in schoolsD. t he teacher-student relationship greatly improved54. _________________ T he writer’s purpose for writing this article is to_______.A. complain about problems in school educationB. teach students different strategies for school lifeC. advocate teaching conflict management in schoolsD. inform teachers of the latest studies on school violenceDAs a young boy, I sometimes traveled the country roads with my dad. He was a rural mill carrier, and on Saturdays he would ask me to go with him. Driving through the countryside was always an adventure: There were animals to see, people to visit, and chocolate cookies if you knew where to stop, and Dad did.In the spring, Dad delivered boxes full of baby chickens, and when 1 was a boy it was such a fun to stick your finger 'through one of the holes of the boxes and let the baby birds peck on your fingers.On Dad' s final day of work, it took him well into the evening to complete his rounds because at least one member from each family was waiting at their mailbox to thank him for his friendship and his years of service. "Two hundred and nineteen mailboxes on my route." he used to say, "and a story at every one. " One lady had no mailbox, so Dad took the mail in to her every day because she was nearly blind. Once inside, he read her mail and helped her pay her bills.Mailboxes were sometimes used for things other than mail. One note left in a mailbox read. "Nat, take these eggs to Marian; she's baking a cake and doesn't have any eggs. " Mailboxes might be buried in the snow, or broken, or lying on the groom:. bat the mail was always delivered On cold days Dad might find one of his customers waiting for him with a cup of hot chocolate. A young wrote letters but had no stamps, so she left a few button on the envelope in the mailbox; Dad paid for the stamps. One businessman used to leave large amounts of cash in his mailbox for Dad to take to the bank. Once, the amount came to 8 32,000.A dozen years ago, when I traveled back to my hometown on the sa d occasion of Dad’s death, the mailboxes along the way reminded me of some of his stories. I thought I knew them all, but that wasn't the case. As I drove home, I noticed two lamp poles, one on each side of the street. When my dad was around, those poles supported wooden boxes about four feet off the ground. One box was painted green and the other was red, and each had a long narrow hole at the top with white lettering: SANTA CLAUS, NORTH POLE. For years children had dropped letters to Santa through those holes.I made a turn at the comer and drove past the post officeand across the railroad tracks to our house. Mom and I were sitting at the kitchen table when I heard footsteps. There, at the door, stood Frank Townsend, Dad's postmaster and great friend for many years. So we all sat down at the table and began to tell stories.At one point Frank looked at me with tears in his eyes. " What are we going to do about the letters this Christmas?" he asked."The letters?"'I guess you never knew. ""Knew what?"" Remember, when you were a kid and you used to put your letters to Santa in those green and red boxes on Main Street? It was your dad who answered all those letters every year. "I just sat there with tears in my eyes. It wasn’t hard for me to imagine Dad sitting at the old table in our basement reading those letters and answering each one. I have since spoken with several of the people who received Christmas letters during their childhood, and they told me how amazed they were that Santa had known so much about their homes and families.For me, just knowing that story about my father was thegift of a lifetime.55. ____________________________ I t can be inferred from the passage that the writer regarded his travels with Dad us_____.A. great chances to help other peopleB. happy occasions to play with baby chickensC. exciting experience* with a lot of funD. good opportunities to enjoy chocolate cookies56. ______________________ The writer provides the detail about the businessman to show that_____.A. Dad had a strong sense of dutyB. Dad was an honest and reliable manC. Dad had a strong sense of honorD. Dad was a kind and generous man57. According to the passage, which of the following impressed the writer most?A. Dad read letters for a blind lady for years.B. Dad paid for the stamps for a young girl.C. Dad delivered some eggs to Marian.D. Dad answered children's Christmas letters every year.58. The method the writer uses to develop Paragraph 4 is______.A. offering analysesB. providing explanationsC. giving examplesD. making comparisons59. What surprised the children most when they received letters in reply from Santa Claus every year?A. Santa Claus lived alone in the cold North Pole.B. Santa Claus answered all their letters every year.C. Santa Claus had unique mailboxes for the children.D. Santa Claus had so much information about their families.60. Which of the following is the best title for the passage?A. The MailB. Christmas LettersC Special Mailboxes D. Memorable Travels第二节下面文章中有5处（第61~65题）需要添加小标题，请从以下选项中选出符合各段意思的小标题，并在答题卡上将该项涂黑,选项中一项为多余选项.A. S low Down Your LifeB. Escape Now and ThenC. S eparate Your ActionsD. A llow Yourself to Be WeakE. Relieve Pressure by Firmly Saying " No"F. Stop Expecting Everything to Be PerfectHow to Simplify Your LifeLess is more. This is why we say: reduce things by half instead of doubling them, get rid of junk instead of piling it up, relax instead of stressing, slow down instead of speeding up. Apply these principles in your everyday life in a conscious way. You will then find yourself well along on your journey to simplification.61. _When you concentrate on one task, you find you have energy that you didn't even know you had. Just imagine: you arc at a fair and you have to carry two heavy pigs over 100 yards. If you keep grabbing one and then the other, it will take forever, because one of them will keep slipping out from under your arm and running off. But if you tie one pig in a place, pick up the other, gather all your strength and make a dash for the finish line, pause for a moment, run bock and get the other one, and with great determination, carry the second pig to the finish line, then you can be sure of succcss.62. ______The pressure at work is on the increase in all occupations. In the modem nuclear family, the expectations that formerly would have been shared amongall the relatives are now concentrated on the individual partner.If you have the feeling that 24 hours per day are not enough for nil the things you need to do, then it’s not because the day has too few hours, but because you have too many activities. A simple fact that overloaded people often tend to forget. The solution is equally simple; refuse to accept so many work assignments in your private life or your working life.63. _“I can handle stress” is regarded as a pos itive statement in the world of work. People who can handle stress are given more and more to cope with —until one day they break.Pay careful attention to the signs that tell you that you arc under more stress than you can cope with. These signals came from various areas of life. You become ill, or your work efficiency decreases.If you have any of these symptoms, change your life goals and decrease your tolerance of stress. Say quite openly, "I can't manage that. "64. _"If only I were slimmer, more beautiful, richer, moreclever, then I would be happier. " This is a dream that makes a lot of people ill, depressed, and unhappy. Life has its flaws, defects, comets, and edges. Only those who accept this reality can lead a really full life.Of course there are activities in which errors are dangerous; driving a car, crossing the road. But life doesn't consist entirely of these things. In among them there is a lot of room for small and large mistakes.65.Successful people ail have their own places where they can withdraw in order to work. Find out which places improve your creativity. For me it's the train. When I know that I'm going to be traveling for four hours without phone calls and people knocking on my door, I find my mind is free and I can read or write complex articles. There can be problems working on the train, of course: if the person sitting opposite you keeps talking away, or if train trips make you tired (some people fall asleep after a few miles).（非选择题，共40分）第三部分:写作（共二节,满分40分）第一节:短文改错（共10小题；每小题1分，满分10分）。

2012年普通高等学校招生全国统一考试数学理(浙江卷)本试题卷分选择题和非选择题两部分．满分150分，考试时间120分钟．选择题部分(共50分)参考公式： 球的表面积公式 S ＝4πR 2球的体积公式 V ＝43πR 3 其中R 表示球的半径 锥体的体积公式 V ＝13Sh 其中S 表示锥体的底面积，h 表示锥体的高 柱体的体积公式 V ＝Sh其中S 表示柱体的底面积，h 表示柱体的高 台体的体积公式V ＝13h (S 1＋S 2) 其中S 1，S 2分别表示台体的上、下底面积． h 表示台体的高如果事件A ，B 互斥，那么 P (A ＋B )＝P (A )＋P (B )如果事件A 在一次试验中发生的概率是P ，那么n 次独立重复试验中事件A 恰好发生k次的概率P n (k )＝C k n P k (1－P )n －k(k ＝0,1,2，…，n ) 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．设全集U ＝{1,2,3,4,5,6}，集合P ＝{1,2,3,4}，Q ＝{3,4,5}，则P ∩(U Q )＝()A ．{1,2,3,4,6}B ．{1,2,3,4,5}C ．{1,2,5}D ．{1,2} 2．已知i 是虚数单位，则3i1i+-( ) A ．1－2i B ．2－i C ．2＋i D ．1＋2i 3．设a ∈R ，则“a ＝1”是“直线l 1：ax ＋2y －1＝0与直线l 2：x ＋(a ＋1)y ＋4＝0平行”的( )A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件4．把函数y ＝cos2x ＋1的图象上所有点的横坐标伸长到原来的2倍(纵坐标不变)，然后向左平移1个单位长度，再向下平移1个单位长度，得到的图象是( )5．设a ，b 是两个非零向量，( ) A ．若|a ＋b |＝|a |－|b |，则a ⊥b B ．若a ⊥b ，则|a ＋b |＝|a |－|b |C ．若|a ＋b |＝|a |－|b |，则存在实数λ，使得b ＝λaD ．若存在实数λ，使得b ＝λa ，则|a ＋b |＝|a |－|b |6．若从1,2,3，…，9这9个整数中同时取4个不同的数，其和为偶数，则不同的取法共有( )A ．60种B ．63种C ．65种D ．66种7．设S n 是公差为d (d ≠0)的无穷等差数列{a n }的前n 项和，则下列命题错误的是( ) A ．若d ＜0，则数列{S n }有最大项 B ．若数列{S n }有最大项，则d ＜0C ．若数列{S n }是递增数列，则对任意n ∈N *，均有S n ＞0D ．若对任意n ∈N *，均有S n ＞0，则数列{S n }是递增数列8．如图，F 1，F 2分别是双曲线C ：22221x y a b-=(a ，b ＞0)的左、右焦点，B 是虚轴的端点，直线F 1B 与C 的两条渐近线分别交于P ，Q 两点，线段PQ 的垂直平分线与x 轴交于点M ．若|MF 2|＝|F 1F 2|，则C 的离心率是( )A ．3 B ．2C D 9．设a ＞0，b ＞0，( )A ．若2a ＋2a ＝2b ＋3b ，则a ＞bB ．若2a ＋2a ＝2b ＋3b ，则a ＜bC ．若2a －2a ＝2b －3b ，则a ＞bD ．若2a －2a ＝2b －3b ，则a ＜b10．已知矩形ABCD ，AB ＝1，BC =ABD 沿矩形的对角线BD 所在的直线进行翻折，在翻折过程中，( )A ．存在某个位置，使得直线AC 与直线BD 垂直B ．存在某个位置，使得直线AB 与直线CD 垂直C ．存在某个位置，使得直线AD 与直线BC 垂直D ．对任意位置，三对直线“AC 与BD ”，“AB 与CD ”，“AD 与BC ”均不垂直非选择题部分(共100分)二、填空题：本大题共7小题，每小题4分，共28分．11．已知某三棱锥的三视图(单位：cm)如图所示，则该三棱锥的体积等于__________ cm 3．12若某程序框图如图所示，则该程序运行后输出的值是__________．13．设公比为q (q ＞0)的等比数列{a n }的前n 项和为S n ，若S 2＝3a 2＋2，S 4＝3a 4＋2，则q ＝__________．14．若将函数f (x )＝x 5表示为f (x )＝a 0＋a 1(1＋x )＋a 2(1＋x )2＋…＋a 5(1＋x )5，其中a 0，a 1，a 2，…，a 5为实数，则a 3＝__________．15．在△ABC 中，M 是BC 的中点，AM ＝3，BC ＝10，则AB AC ⋅=__________． 16．定义：曲线C 上的点到直线l 的距离的最小值称为曲线C 到直线l 的距离．已知曲线C 1：y ＝x 2＋a 到直线l ：y ＝x 的距离等于曲线C 2：x 2＋(y ＋4)2＝2到直线l ：y ＝x 的距离，则实数a ＝__________．17．设a ∈R ，若x ＞0时均有［(a －1)x －1］(x 2－ax －1)≥0，则a ＝__________．三、解答题：本大题共5小题，共72分．解答应写出文字说明、证明过程或演算步骤．18．在△ABC 中，内角A ，B ，C 的对边分别为a ，b ，c ．已知2cos 3A =，sinBC ． (1)求tan C 的值；(2)若a =ABC 的面积．19．已知箱中装有4个白球和5个黑球，且规定：取出一个白球得2分，取出一个黑球得1分．现从该箱中任取(无放回，且每球取到的机会均等)3个球，记随机变量X 为取出此3球所得分数之和．(1)求X 的分布列；(2)求X 的数学期望E (X )．20．如图，在四棱锥P －ABCD 中，底面是边长为∠BAD ＝120°，且P A ⊥平面ABCD ，PA =，M ，N 分别为PB ，PD 的中点．(1)证明：MN ∥平面ABCD ；(2)过点A 作AQ ⊥PC ，垂足为点Q ，求二面角A －MN －Q 的平面角的余弦值．21．如图，椭圆C ：22221x y a b+=(a ＞b ＞0)的离心率为12，其左焦点到点P (2,1)的距离．．．．O 的直线l 与C 相交于A ，B 两点，且线段AB 被直线OP 平分．(1)求椭圆C 的方程；(2)求△ABP 面积取最大值时直线l 的方程．22．已知a ＞0，b ∈R ，函数f (x )＝4ax 3－2bx －a ＋b ． (1)证明：当0≤x ≤1时，①函数f (x )的最大值为|2a －b |＋a ； ②f (x )＋|2a －b |＋a ≥0；(2)若－1≤f (x )≤1对x ∈［0,1］恒成立，求a ＋b 的取值范围．【自选模块】3．“数学史与不等式选讲”模块(10分)已知a ∈R ，设关于x 的不等式|2x －a |＋|x ＋3|≥2x ＋4的解集为A ． (1)若a ＝1，求A ；(2)若A ＝R ，求a 的取值范围．4．“矩阵与变换和坐标系与参数方程”模块(10分)在直角坐标系xOy 中，设倾斜角为α的直线l：2cos sin x t y t αα⎧⎪⎨⎪⎩＝＋，(t 为参数)与曲线C ：2cos sin x y θθ⎧⎨⎩＝，＝(θ为参数)相交于不同两点A ，B ． (1)若π3α=，求线段AB 中点M 的坐标；(2)若|P A |·|PB |＝|OP |2，其中P (2，求直线l 的斜率．1． B 2．D 3． A 4． A 5． C 6． D 7． C 8． B 9． A 10． B 11．1 12．1120 13．32 14．10 15．－16 16．94 17．3219．解：(1)由题意得X 取3,4,5,6，且P (X ＝3)＝3539C 5C 42=， P (X ＝4)＝124539C C 10C 21⋅=， P (X ＝5)＝214539C C 5C 14⋅=，P (X ＝6)＝3439C 1C 21=．所以X 的分布列为(2)由(1)知E (X )＝3·P (X ＝3)＋4·P (X ＝4)＋5·P (X ＝5)＋6·P (X ＝6)＝133． 20． (1)证明：因为M ，N 分别是PB ，PD 的中点， 所以MN 是△PBD 的中位线． 所以MN ∥BD ．又因为MN 平面ABCD ， 所以MN ∥平面ABCD ．(2)解：方法一：连结AC 交BD 于O ，以O 为原点，OC ，OD 所在直线为x ，y 轴，建立空间直角坐标系O －xyz ，如图所示．在菱形ABCD 中，∠BAD ＝120°，得AC ＝AB ＝6BD ==． 又因为P A ⊥平面ABCD ， 所以P A ⊥AC ．在直角△P AC中，AC =PA =AQ ⊥PC ，得QC ＝2，PQ ＝4， 由此知各点坐标如下，A (0,0)，B (0，－3,0)，C0,0)，D (0,3,0)，P(0,，M (2-，32-，，N(2-，32)，Q (3，0，3)． 设m ＝(x ，y ，z )为平面AMN 的法向量．由33(2AM =-，33(2AN =，，， 知30230.2x y x y -=++=，取z ＝－1，得m ＝(0，－1)． 设n ＝(x ，y ，z )为平面QMN 的法向量．由3(2QM =-， 3(2QN =，，知30,230.2x y z x y z ⎧-+=⎪⎪⎨⎪+=⎪⎩ 取z ＝5，得n ＝(0,5)． 于是cos 〈m ，n〉＝||||33⋅=⋅m n m n ． 所以二面角A -MN -Q的平面角的余弦值为33． 方法二：在菱形ABCD 中，∠BAD=120°，得AC=AB=BC=CD=DA ，BD= AB ．又因为P A ⊥平面ABCD ，所以P A ⊥AB ，P A ⊥AC ，P A ⊥AD ． 所以PB =PC =PD ． 所以△PBC ≌△PDC ．而M ，N 分别是PB ，PD 的中点， 所以MQ =NQ ，且AM =12PB =12PD =AN ． 取线段MN 的中点E ，连结AE ，EQ ，则AE ⊥MN ，QE ⊥MN ，所以∠AEQ 为二面角A －MN －Q 的平面角．由AB =PA = 故在△AMN 中，AM =AN =3，MN =12BD =3，得2AE =． 在直角△P AC 中，AQ ⊥PC，得AQ =QC =2，PQ =4，在△PBC 中，2225cos 26PB PC BC BPC PB PC +-∠==⋅，得MQ ==在等腰△MQN 中，MQ =NQMN =3，得2QE ==． 在△AEQ中，2AE =，2QE =，AQ =222cos 233AE QE AQ AEQ AE QE+-∠==⋅．所以二面角A －MN －Q． 21．解：(1)设椭圆左焦点为F (－c,0)，则由题意得1,2c a ==⎪⎩得1,2,c a =⎧⎨=⎩ 所以椭圆方程为22143x y +=． (2)设A (x 1，y 1)，B (x 2，y 2)，线段AB 的中点为M ．当直线AB 与x 轴垂直时，直线AB 的方程为x ＝0，与不过原点的条件不符，舍去．故可设直线AB 的方程为y ＝kx ＋m (m ≠0)，由22,3412y kx m x y =+⎧⎨+=⎩消去y ，整理得 (3＋4k 2)x 2＋8kmx ＋4m 2－12＝0，①则∆＝64k 2m 2－4(3＋4k 2)(4m 2－12)＞0，12221228,34412.34km x x km x x k ⎧+=-⎪⎪+⎨-⎪=⎪+⎩所以线段AB 的中点M (2434km k -+，2334mk +)，因为M 在直线OP 上，所以22323434m kmk k -=++， 得m ＝0(舍去)或32k =-．此时方程①为3x 2－3mx ＋m 2－3＝0，则∆＝3(12－m 2)＞0，12212,3.3x x m m x x +=⎧⎪⎨-=⎪⎩所以|AB |·|x 1－x 2|＝6设点P 到直线AB 距离为d ，则d ==设△ABP 的面积为S ，则1||26S AB d =⋅=其中m ∈(-0)∪(0,．令u (m )＝(12－m 2)(m －4)2，m ∈［-，，u ′(m )＝－4(m －4)(m 2－2m －6)＝－4(m －4)·(m －1m －1． 所以当且仅当m ＝1u (m )取到最大值． 故当且仅当m ＝1S 取到最大值．综上，所求直线l 方程为3x ＋2y＋2＝0． 22． (1)证明：①f ′(x )＝12ax 2－2b ＝12a (x 2－6b a)． 当b ≤0时，有f ′(x )≥0，此时f (x )在［0，＋∞)上单调递增．当b ＞0时，f ′(x )＝12a (x ＋6b a )(x －6b a)， 此时f (x )在［0，6b a ］上单调递减，在［6ba，＋∞)上单调递增．所以当0≤x ≤1时，f (x )max ＝max{f (0)，f (1)}＝max{－a ＋b,3a －b }＝3,2,,2a b b a a b b a-≤⎧⎨-+>⎩＝|2a －b |＋a ．②由于0≤x ≤1，故当b ≤2a 时，f (x )＋|2a －b |＋a ＝f (x )＋3a －b ＝4ax 3－2bx ＋2a ≥4ax 3－4ax ＋2a ＝2a (2x 3－2x ＋1)．当b ＞2a 时，f (x )＋|2a －b |＋a ＝f (x )－a ＋b ＝4ax 3＋2b (1－x )－2a ＞4ax 3＋4a (1－x )－2a ＝2a (2x 3－2x ＋1)．设g (x )＝2x 3－2x ＋1,0≤x ≤1，则g ′(x )＝6x 2－2＝6(x－3)(x＋)， 于是所以，g (x )min ＝g＝1＞0，所以，当0≤x ≤1时，2x 3－2x ＋1＞0， 故f (x )＋|2a －b |＋a ≥2a (2x 3－2x ＋1)≥0．(2)由①知，当0≤x ≤1时，f (x )max ＝|2a －b |＋a ， 所以|2a －b |＋a ≤1．若|2a －b |＋a ≤1，则由②知f (x )≥－(|2a －b |＋a )≥－1．所以－1≤f (x )≤1对任意0≤x ≤1恒成立的充要条件是|2|1,0,a b a a -+≤⎧⎨>⎩即20,31,a b a b a -≥⎧⎪-≤⎨⎪>⎩或20,1,0.a b b a a -<⎧⎪-≤⎨⎪>⎩在直角坐标系aOb 中，不等式组所表示的平面区域为如图所示的阴影部分，其中不包括线段BC ．作一组平行直线a +b =t (t ∈R )， 得－1＜a +b ≤3，所以a +b 的取值范围是(－1,3］．【自选模块】3．解：(1)当x ≤－3时，原不等式化为－3x －2≥2x ＋4，得x ≤－3．当－3＜x≤12时，原不等式化为4－x≥2x＋4，得－3＜x≤0．当12x>时，原不等式化为3x＋2≥2x＋4，得x≥2．综上，A＝{x|x≤0或x≥2}(2)当x≤－2时，|2x－a|＋|x＋3|≥0≥2x＋4成立．当x＞－2时，|2x－a|＋x＋3＝|2x－a|＋|x＋3|≥2x＋4，得x≥a＋1或13ax-≤，所以a＋1≤－2或113aa-+≤，得a≤－2．综上，a的取值范围为a≤－2．4．解：设直线l上的点A，B对应参数分别为t1，t2．将曲线C的参数方程化为普通方程24x＋y2＝1．(1)当π3α=时，设点M对应参数为t0．直线l方程为12,2x ty⎧=+⎪⎪⎨⎪=⎪⎩(t为参数)，代入曲线C的普通方程24x＋y2＝1，得13t2＋56t＋48＝0，则1228213t tt+==-，所以，点M的坐标为(1213，．(2)将=2+cossinx ty tαα⎧⎪⎨⎪⎩，代入曲线C的普通方程24x＋y2＝1，得(cos2α＋4sin2α)t2＋(α＋4cosα)t＋12＝0，因为|P A|·|PB|＝|t1t2|＝2212cos4sinαα+，|OP|2＝7，所以22127cos4sinα=+，得25tan16α=．由于∆＝32cosα(α－cosα)＞0，故tan4α=．所以直线l的斜率为4。

2012年普通高等学校招生全国统一考试（浙江卷）理科综合测试（物理）一．单项选择部分(每题6分)14．如图所示，与水平面夹角为30°的固定斜面上有一质量m=1.0 kg的物体。

细绳的一端与物体相连，另一端经摩擦不计的定滑轮与固定的弹簧秤相连．物体静止在斜面上，弹簧秤的示数为4.9 N．关于物体受力的判断(取g=9.8 m/s2)，下列说法正确的是( )A．斜面对物体的摩擦力大小为零B．斜面对物体的摩擦力大小为4.9 N，方向竖直向上C．斜面对物体的支持力大小为4.9 3 N，方向竖直向上D．斜面对物体的支持力大小为4.9 N，方向垂直斜面向上【答案】A15．如图所示，在火星与木星轨道之间有一小行星带．假设该带中的小行星只受到太阳的引力，并绕太阳做匀速圆周运动。

下列说法正确的是( )A．太阳对各小行星的引力相同B．各小行星绕太阳运动的周期均小于一年C．小行星带内侧小行星的向心加速度值大于外侧小行星的向心加速度值D．小行星带内各小行星圆周运动的线速度值大于地球公转的线速度值【答案】C16．用手握住较长软绳的一端连续上下抖动，形成一列简谐横波。

某一时刻的波形如图所示，绳上a、b两质点均处于波峰位置。

下列说法正确的是()A．a、b两点之间的距离为半个波长B．a、b两点振动开始时刻相差半个周期C．b点完成全振动次数比a点多一次D．b点完成全振动次数比a点少一次【答案】D17．功率为10 W的发光二极管(LED灯)的亮度与功率为60 W的白炽灯相当。

根据国家节能战略，2016年前普通白炽灯应被淘汰。

假设每户家庭有2只60 W的白炽灯，均用10 W的LED灯替代，估算出全国一年节省的电能最接近( )A．8×108 kW·h B．8×1010 kW·hC．8×1011 kW·h D．8×1013 kW·h【答案】B18．由光滑细管组成的轨道如图所示，其中AB段和BC段是半径为R的四分之一圆弧，轨道固定在竖直平面内。