模块综合检测(一)

《计算机文化基础》检测试题模块1 认识计算机一、单项选择题（每题1分，47小题，共47分。

每题所给的四个选项中，只有一个正确答案，请将你的答案填在答题卡上）1、世界上第一台电子计算机诞生于（ B ）。

A.1943B.1946C.1956D.19602、计算机软件系统由（ C ）组成。

A.数据库软件和工具软件B.编辑软件和应用软件C.系统软件和应用软件D.程序、相应数据和文档3、Windows7是计算机系统中的（ B ）。

A.主要硬件B.系统软件C.工具软件D.应用软件4、计算机硬件的五大主要部件包括：运算器、控制器、（ B ）、输出设备和输入设备。

A.键盘B.存储器C. CPUD.显示器5、下列叙述中，正确的是（ C ）。

A.计算机病毒只在可执行文件中传染B.只要删除所有感染了病毒的文件就可以彻底消除病毒C.计算机病毒主要通过读/写移动存储器或Internet网络进行传播D.计算机杀病毒软件可以查出和清除任意已知的和未知的计算机病毒6、度量处理器CPU时钟频率的单位是（ B ）。

A.MIPSB.HzC.MBD.Mbps7、计算机的主要技术性能指标（ C ）。

A.硬盘的容量和内存的容量B.显示器的分辨率、打印机的性能等配置C.计算机所配备的语言、操作系统、外部设备D.字长、运算速度、内/外存容量和CPU的时钟频率8、将二进制数“11010101001”转换为十进制数为（ D ）。

A.1001B.1025C.1757D.17059、组成计算机指令的两部分是（ B ）。

A.数据和字符B.操作码和地址码C.运算符和运算数D.运算符和运算结果10、ANIAC所采用的电子元件是（ A ）。

A．电子管 B．晶体管C．中小规模集成电路D．大规模集成电路11、利用计算机系统时行生产设备的管理、控制和操作的过程一般被称为（ D ）。

A．计算机辅助设计B．计算机辅助测试C．计算机辅助教学D．计算机辅助制造12、大写字母“A”的ASCII码为41H，则大写字母“N”的ASCII码是（ B ）。

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模块综合检测(一)选修3-3(90分钟 100分)1.(6分)关于布朗运动的说法正确的是( )A.布朗运动是液体分子的运动B.悬浮在液体中的颗粒越大,其布朗运动越明显C.布朗运动是悬浮颗粒内部分子无规则运动的反映D.悬浮在液体中的颗粒越小,液体温度越高,布朗运动越明显2.(2013·天水模拟)(6分)相互作用的分子间具有势能,规定两分子相距无穷远时两分子间的势能为零。

设分子a固定不动,分子b以某一初速度从无穷远处向a运动,直至它们之间的距离最小。

在此过程中,a、b之间的势能( )A.先减小,后增大,最后小于零B.先减小,后增大,最后大于零C.先增大,后减小,最后小于零D.先增大,后减小,最后大于零3.(6分)在下列叙述中正确的是( )A.物体的温度越高,分子热运动越剧烈,分子平均动能越大B.布朗运动就是液体分子的热运动C.对一定质量的气体加热,其内能一定增加D.当分子间距r<r0时,分子间斥力比引力变化得快;当r>r0时,引力比斥力变化得快4.(6分)下列说法正确的是( )A.某种液体的饱和蒸汽压与温度无关B.物体内所有分子热运动动能的总和就是物体的内能C.气体的温度升高,分子的平均动能增大D.所有晶体都具有各向异性的特点5.(6分)热力学第二定律常见的表述方式有两种,其一:不可能使热量由低温物体传递到高温物体而不引起其他变化;其二:不可能从单一热源吸收热量并把它全部用来做功,而不引起其他变化。

第一种表述方式可以用图甲来表示,根据你对第二种表述的理解,如果也用类似的示意图来表示,你认为图乙中正确的是( )6.(6分)设合力为零时分子间距为r0,分子之间既有引力也有斥力,它们与分子间距的关系有以下说法,其中正确的是( )A.随着分子间距的增加,分子间的引力减小得快,斥力减小得慢B.随着分子间距的增加,分子间的引力减小得慢,斥力减小得快C.分子间距大于r0时,距离越大,分子力越大D.分子间距等于r0时,分子力最大7.(2013·广州模拟)(6分)下列说法正确的是( )A.在黑暗、密闭的房间内,在窗外射入的阳光下,可以看到灰尘在飞舞,这些飞舞的灰尘在做布朗运动B.小木块浮在水面上是由于液体表面张力的作用C.大颗粒的盐磨成细盐,就变成了非晶体D.对于一定质量的饱和蒸汽,当温度不变,体积减小一半时,压强不变8.(6分)水蒸气达到饱和时,水蒸气的压强不再变化,这时( )A.水不再蒸发B.水不再凝结C.蒸发和凝结达到动态平衡D.以上都不对9.(6分)某充有足量空气的足球,在从早晨使用到中午的过程中,其体积的变化忽略不计,则其内部气体的压强随温度变化的关系图像应遵循图中的(设足球不漏气)( )10.(2013·潮州模拟)(6分)夏天将密闭有空气的矿泉水瓶放进低温的冰箱中会变扁,此过程中瓶内空气(可看成理想气体)( )A.内能减小,外界对其做功B.内能减小,吸收热量C.内能增加,对外界做功D.内能增加,放出热量11.(6分)如图所示,活塞将汽缸分成两个气室,汽缸壁、活塞、拉杆是绝热的,且都不漏气,U A和U B分别表示A、B气室中气体的内能。

［网络构建］本模块话题是“世界不同地方人们的生活”。

内容涉及世界各地的人在同一时间正在进行的活动及如何写明信片等内容。

通过听、说、读、写的语言实践活动，加深对世界各地风土人情方面的了解，鼓励学生了解世界，加强交流，促进世界和平。

/m/, /n/, //;典例分析例1用动词的适当形式填空。

1. She__________(drive) a car now.2. Look! They__________(take) photos.3. Listen! The children__________(sing).4. —What are you doing? —I__________(wait) for you.5. It’s ten o’cloc k. We__________(wash) the clothes.思维分析：本题考查现在进行时的谓语动词的构成。

首先看其特征标志词，谓语动词一定是be+v.-ing。

答案：1. is driving 2. are taking 3. are singing 4. am waiting 5. are washing例2按照要求进行句型转换。

1. She is doing her homework.(改为否定句)She __________ __________ her homework.2. They are looking at the blackboard.(改为一般疑问句)__________ __________ __________at the blackboard?3. Tom is playing basketball.(对画线部分提问)What __________ __________ __________?思维分析：现在进行时的谓语动词的构成是：助动词be+v.-ing，在变为否定或疑问句时，be后加not变为否定句，把be提前变为一般疑问句。

模块综合检测(一)第一部分阅读(共两节，满分50分)第一节(共15小题；每小题2.5分，满分37.5分)阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。

ATeenagers who spend hours in front of the television may have a poorer diet as young adults.A study, which involved nearly 1,400 high school students found those who watched TV for five hours or more every day had less healthy diets than other students five years later. Why does this happen? Should the parents take any measures?On the one hand, people who spend a lot of time in front of the TV, especially teenagers, may snack (吃零食) more, and that may influence their long­term diet quality.On the other hand, TV ads for fast food, sweets and snacks make teenagers eat more of those foods. TV time might also replace exercise time for some kids.The researchers found a clear relationship between TV time during high school and diet quality of the young. While the heaviest TV viewers were eating the most junk food, those who'd watched fewer than two hours every day had the most fruits and vegetables.As far as I am concerned, children should watch no more than two hours of television per day. And parents should set a good example by eating right, being physically active and curbing their own TV time.【语篇解读】本文是一篇说明文。

Ⅰ.语言知识及应用(共两节，满分45分)第一节完形填空(共15小题；每小题2分，满分30分)阅读下面短文，掌握其大意，然后从1～15各题所给的A、B、C和D项中，选出最佳选项。

I work for a company that has cut a lot of staff in the past year.I was employed as the Director of New Business Development.As business__1__，I employed a young man with whom I’d__2__for several years at my previous company to be my staff leader，as his knowledge and experience was__3__.He was employed at a rate of $10 per hour，which was__4__lower than the pay，$16.50，he had previously been paid at our__5__company，but with the__6__that he would receive a pay increase in 3 months.3 months later，when the young man was given the promised__7__，the manager came to me__8__.“Jen，that boy has more__9__than anyone I’ve ever worked with.”He__10__the many hours the boy had worked off the clock and his__11__to the company.“The boy thanked me，and said that he__12__the acknowledgment(承认)very much，then said，‘Nate works really hard and is really struggling.Earning more money would make a lot of__13__to him.I know you can’t give everyone who deserves it a raise，so please give mine to Nate.He needs it more than I do.’I couldn’t__14__，and I gave the raise to Nate.”For a person of the boy’s age，with nothing but the clothes on his back，to give to someone with even less was__15__.【解题导语】一个对公司贡献很大的员工并没有要求公司履行三个月后给他涨工资的承诺，因为他理解公司大量裁员、资金紧张的状况，因此主动要求把给自己涨的那部分分给更需要钱的人。

模块综合检测(一)(时间：45分钟满分：100分)一、选择题(每小题5分，共60分)1．右图是《红楼梦》中“元春省亲”一节中的图片(局部)。

面对贵妃元春的到来，身为祖母的贾母也不得不率众跪迎。

这一现象表明( )A．元春违背了纲常伦理B．宗法关系要服从政治隶属关系C．当时宗法关系已经崩溃D．贾母等以此表示对元春的喜爱解析：选B 根据宗法制强调尊老爱幼的特征，理应由元春跪拜作为祖母的贾母，但情形恰恰相反。

身为贵妃的元春代表了皇权，这说明宗法关系要从属于政治隶属关系。

A、D 两项错误，不能简单地凭借人物之间的血缘关系来分析这一现象；C项错误，这体现的是等级关系，并未表明宗法关系崩溃。

2．中国古代先后产生了多种选官制度，下列最能体现西汉时期主流选官制度的是( ) A．“在每州设置大中正，郡县设小中正，中正官以在中央任官的本地人充任。

郡县中正官评定本地人的等第，作为政府用人授官的准则”B．“为了摧毁门阀，拔擢人才，故特准士人自行报名，参加策试，及第者得任官职”C．“令天下郡国每年举孝子、廉吏各一人；孝廉之举，遂成定制”D．“题目囿于四书五经，文章须依八股形式，造成士人只读闱墨制义的风气”解析：选C 西汉的选官制度为察举制，孝廉是当时士大夫做官的主要途径，“天下郡国每年举孝子、廉吏各一人”与察举制相符合，C项正确；A项为设“中正”评定本地人等第的九品中正制度，不符合题意；B项是打击门阀士族的科举制度，不符合题意；D项为明清时期的八股取士制度，不符合题意。

3．(2012·乌鲁木齐模拟)“史实”“史论”“史识”是构成史学的“三要素”。

史实即历史事实，史论即对历史事件和历史人物的评论，史识即是以科学的史观作指导，来分析大量可靠的史实，然后得出的科学结论。

下列对唐朝三省六部制的叙述属于“史识”的是( ) A．“三省”指的是中书省、门下省、尚书省，三省的长官都是宰相B．三省六部制的基本运作程序是中书省→门下省→尚书省→六部C．三省六部制排除了相权过大威胁皇权而出现的政治危机，并且提高了行政效率D．三省六部制是中国古代政治制度的重大创造，此后历朝基本沿袭这种制度解析：选D A、B两项是史实；C项是史论；D项是史识。

模块综合检测(一)(时间120分钟，满分150分)一、选择题(共12小题，每小题5分，共60分) 1．方程C x 14＝C 2x －414的解集为( )A ．{4}B ．{14}C ．{4,6}D ．{14,2}解析：选C 由C x 14＝C 2x －414得x ＝2x －4或x ＋2x －4＝14，解得x ＝4或x ＝6.经检验知x ＝4或x ＝6符合题意．2．设X 是一个离散型随机变量，则下列不能成为X 的概率分布列的一组数据是( ) A ．0，12，0,0，12 B ．0.1,0.2,0.3,0.4C ．p,1－p (0≤p ≤1) D.11×2，12×3，…，17×8解析：选D 利用分布列的性质推断，任一离散型随机变量X 的分布列都具有下述两共性质：①p i ≥0，i ＝1,2,3，…，n ；②p 1＋p 2＋p 3＋…＋p n ＝1.选C 如图，由正态曲线的对称性可得P (a ≤X <4－a )＝1－2P (X <a )＝0.36. 3．已知随机变量X ～N (2，σ2)，若P (X <a )＝0.32，则P (a ≤X <4－a )等于( ) A ．0.32 B ．0.68 C ．0.36 D ．0.64解析：选C 如图，由正态曲线的对称性可得P (a ≤X <4－a )＝1－2P (X <a )＝0.36.4．已知x ，y 取值如下表：x 0 1 4 5 6 8 y1.31.85.66.17.49.3从所得的散点图分析可知：y 与x 线性相关，且y ^＝0.95x ＋a ，则a 等于( ) A ．1.30 B ．1.45 C ．1.65 D ．1.80解析：选B 依题意得，x －＝16×(0＋1＋4＋5＋6＋8)＝4，y －＝16×(1.3＋1.8＋5.6＋6.1＋7.4＋9.3)＝5.25.又直线y ^＝0.95x ＋a 必过样本中心点(x －，y －)， 即点(4，5.25)，于是有5.25＝0.95×4＋a ， 由此解得a ＝1.45.5．甲、乙两人独立地对同一目标各射击一次，其命中率分别为0.6,0.5，现已知目标被击中，则它是被甲击中的概率是( )A ．0.45B ．0.6C ．0.65D ．0.75 解析：选D 目标被击中P 1＝1－0.4×0.5＝0.8， ∴P ＝0.60.8＝0.75. 6．从6名男生和2名女生中选出3名志愿者，其中至少有1名女生的选法有( ) A ．36种 B ．30种 C ．42种 D ．60种解析：选A 直接法：选出3名志愿者中含有1名女生和2名男生或2名女生和1名男生，故共有C 12C 26＋C 22C 16＝2×15＋6＝36种选法；间接法：从8名同学中选出3名，减去全部是男生的状况，故共有C 38－C 36＝56－20＝36种选法．7.⎝ ⎛⎭⎪⎫x ＋2x 2n 的开放式中只有第6项二项式系数最大，则开放式中的常数项是( )A ．180B ．90C ．45D ．360 解析：选A 由已知得，n ＝10，T r ＋1＝C r10(x )10－r⎝ ⎛⎭⎪⎫2x 2r ＝2r ·C r 10x 5－52r ，令5－52r ＝0，得r ＝2，T 3＝4C 210＝180.8．(四川高考)六个人从左至右排成一行，最左端只能排甲或乙，最右端不能排甲，则不同的排法共有( )A ．192种B ．216种C ．240种D ．288种解析：选B 当最左端排甲时，不同的排法共有A 55种；当最左端排乙时，甲只能排在中间四个位置之一，则不同的排法共有C 14A 44种．故不同的排法共有A 55＋C 14A 44＝9×24＝216种．9．箱子里有5个黑球和4个白球，每次随机取出一个球．若取出黑球，则放回箱中，重新取球，若取出白球，则停止取球．那么在第4次取球之后停止的概率为( )A.C 35C 14C 45 B .⎝ ⎛⎭⎪⎫593×49C.35×14D ．C 14⎝ ⎛⎭⎪⎫593×49解析：选B 记“从箱子里取出一球是黑球”为大事A ，“从箱子里取出一个球是白球”为大事B ，则P (A )＝59，P (B )＝49，在第4次取球后停止，说明前3次取到的都是黑球，第4次取到的是白球，又每次取球是相互独立的，由独立大事同时发生的概率公式，在第4次取球后停止的概率为59×59×59×49＝⎝ ⎛⎭⎪⎫593×49.10．下列说法：①将一组数据中的每个数据都加上或减去同一个常数后，方差恒不变； ②设有一个回归方程y ^＝3－5x ，变量x 增加一个单位时，y 平均增加5个单位；③线性回归直线y ^＝b ^x ＋a ^必过(x －，y －)； ④曲线上的点与该点的坐标之间具有相关关系；⑤在一个2×2列联表中，由计算得k ＝13.079.则其两个变量间有关系的可能性是90%. 其中错误的个数是( ) A ．1 B ．2 C ．3D ．4解析：选C 由方差的定义知①正确，由线性回归直线的特点知③正确，②④⑤都错误． 11．对两个变量y 和x 进行线性相关检验，已知n 是观看值组数，r 是相关系数，且已知： ①n ＝10，r ＝0.953 3；②n ＝15，r ＝0.301 2；③n ＝17，r ＝0.999 1；④n ＝3，r ＝0.995 0. 则变量y 和x 具有线性相关关系的是( ) A ．①和② B ．①和③ C ．②和④D ．③和④解析：选B 相关系数r 的确定值越接近1，变量x ，y 的线性相关性越强．②中的r 太小，④中观看值组数太小．12．某市政府调查市民收入与旅游欲望时，接受独立性检验法抽取3 000人，计算发觉k ＝6.023，则依据这一数据查阅下表，市政府断言市民收入增减与旅游欲望有关系的把握是( )P (K 2≥k )… 0.25 0.15 0.10 0.025 0.010 0.005 … k…1.3232.0722.7065.0246.6357.879…A.90% B ．95% C ．97.5%D ．99.5%解析：选C ∵k ＝6.023＞5.024，∴可断言市民收入增减与旅游欲望有关的把握为97.5%. 二、填空题(共4小题，每小题5分，共20分)13．有5名男生和3名女生，从中选出5人分别担当语文、数学、英语、物理、化学学科的科代表，若某女生必需担当语文科代表，则不同的选法共有________种．(用数字作答)解析：由题意知，从剩余7人中选出4人担当4个学科的科代表，共有A 47＝840(种)选法． 答案：84014．某射手对目标进行射击，直到第一次命中为止，每次射击的命中率为0.6，现共有子弹4颗，命中后剩余子弹数目的均值是________．解析：设ξ为命中后剩余子弹数目，则P (ξ＝3)＝0.6，P (ξ＝2)＝0.4×0.6＝0.24，P (ξ＝1)＝0.4×0.4×0.6＝0.096，P (ξ＝0)＝0.4×0.4×0.4＝0.064，E (ξ)＝3×0.6＋2×0.24＋0.096＝2.376.答案：2.37615．抽样调查表明，某校高三同学成果(总分750分)X 近似听从正态分布，平均成果为500分．已知P (400＜X ＜450)＝0.3，则P (550＜X ＜600)＝________.解析：由下图可以看出P (550＜X ＜600)＝P (400＜X ＜450)＝0.3.答案：0.316．某高校“统计初步”课程的老师随机调查了选该课的一些同学状况，具体数据如下表：专业性别非统计专业统计专业 男 13 10 女720为了推断主修统计专业是否与性别有关系，依据表中的数据，计算得到K 2＝________(保留三位小数)，所以判定________(填“能”或“不能”)在犯错误的概率不超过0.05的前提下认为主修统计专业与性别有关系．解析：依据供应的表格得 K 2＝50×13×20－7×10223×27×20×30≈4.844>3.841.所以可以在犯错误的概率不超过0.05的前提下认为主修统计专业与性别有关系． 答案：4.844 能三、解答题(共6小题，共70分，解答时应写出文字说明、证明过程或演算步骤)17．(本小题满分10分)若⎝⎛⎭⎪⎪⎫6x ＋16x n开放式中第2,3,4项的二项式系数成等差数列．(1)求n 的值．(2)此开放式中是否有常数项？为什么？解：(1)T k ＋1＝C k n·⎝⎛⎭⎫6x n －k·⎝ ⎛⎭⎪⎪⎫16x k ＝C kn ·x n －2k 6，由题意可知C 1n ＋C 3n ＝2C 2n ，即n 2－9n ＋14＝0， 解得n ＝2(舍)或n ＝7.∴n ＝7. (2)由(1)知T k ＋1＝C k7·x 7－2k6. 当7－2k 6＝0时，k ＝72，由于k ∉N *， 所以此开放式中无常数项．18．(本小题满分12分)某篮球队与其他6支篮球队依次进行6场竞赛，每场均决出胜败，设这支篮球队与其他篮球队竞赛胜场的大事是独立的，并且胜场的概率是13.(1)求这支篮球队首次胜场前已经负了2场的概率； (2)求这支篮球队在6场竞赛中恰好胜了3场的概率； (3)求这支篮球队在6场竞赛中胜场数的均值和方差．解：(1)这支篮球队首次胜场前已负2场的概率为P ＝⎝ ⎛⎭⎪⎫1－132×13＝427.(2)这支篮球队在6场竞赛中恰好胜3场的概率为P ＝C 36×⎝ ⎛⎭⎪⎫133×⎝ ⎛⎭⎪⎫1－133＝20×127×827＝160729.(3)由于X 听从二项分布，即X ～B ⎝ ⎛⎭⎪⎫6，13，∴E (X )＝6×13＝2，D (X )＝6×13×⎝⎛⎭⎪⎫1－13＝43.故在6场竞赛中这支篮球队胜场的均值为2，方差为43.19．(本小题满分12分)某商场经销某商品，依据以往资料统计，顾客接受的付款期数X 的分布列为商场经销一件该商品，接受250元；分4期或5期付款，其利润为300元．Y 表示经销一件该商品的利润．(1)求大事：“购买该商品的3位顾客中，至少有1位接受1期付款”的概率P (A )； (2)求Y 的分布列及E (Y )．解：(1)由A 表示大事“购买该商品的3位顾客中至少有1位接受1期付款”知，A 表示大事“购买该商品的3位顾客中无人接受1期付款”．P (A )＝(1－0.4)3＝0.216， P (A )＝1－P (A )＝1－0.216＝0.784.(2)Y 的可能取值为200元，250元，300元．P (Y ＝200)＝P (X ＝1)＝0.4，P (Y ＝250)＝P (X ＝2)＋P (X ＝3)＝0.2＋0.2＝0.4，P (Y ＝300)＝1－P (Y ＝200)－P (Y ＝250)＝1－0.4－0.4＝0.2， Y 的分布列为E (Y )20．(本小题满分12分)为迎接2022年北京冬奥会，推广滑雪运动，某滑雪场开展滑雪促销活动．该滑雪场的收费标准是：滑雪时间不超过1小时免费，超过1小时的部分每小时收费标准为40元(不足1小时的部分按1小时计算)．有甲、乙两人相互独立地来该滑雪场运动，设甲、乙不超过1小时离开的概率分别为14，16；1小时以上且不超过2小时离开的概率分别为12，23；两人滑雪时间都不会超过3小时． (1)求甲、乙两人所付滑雪费用相同的概率；(2)设甲、乙两人所付的滑雪费用之和为随机变量ξ，求ξ的分布列与数学期望E (ξ)． 解：(1)若两人所付费用相同，则相同的费用可能为0元，40元，80元， 两人都付0元的概率为P 1＝14×16＝124，两人都付40元的概率为P 2＝12×23＝13，两人都付80元的概率为P 3＝⎝ ⎛⎭⎪⎫1－14－12×1－16－23＝14×16＝124，则两人所付费用相同的概率为P ＝P 1＋P 2＋P 3＝124＋13＋124＝512. (2)由题意得，ξ全部可能的取值为0,40,80,120,160.P (ξ＝0)＝14×16＝124， P (ξ＝40)＝14×23＋12×16＝14， P (ξ＝80)＝14×16＋12×23＋14×16＝512， P (ξ＝120)＝12×16＋14×23＝14， P (ξ＝160)＝14×16＝124， ξ的分布列为E (ξ)＝0×124＋40×14＋80×12＋120×4＋160×24＝80.21．(本小题满分12分)甲、乙两厂生产同一产品，为了解甲、乙两厂的产品质量，以确定这一产品最终的供货商，接受分层抽样的方法从甲、乙两厂生产的产品中分别抽取14件和5件，测量产品中的微量元素x ，y 的含量(单位：毫克)．下表是乙厂的5件产品的测量数据：编号1 2 3 4 5 x 169 178 166 175 180 y7580777081(1)已知甲厂生产的产品共有98件，求乙厂生产的产品数量．(2)当产品中的微量元素x ，y 满足x ≥175，且y ≥75，该产品为优等品．用上述样本数据估量乙厂生产的优等品的数量．(3)从乙厂抽出的上述5件产品中，随机抽取2件，求抽取的2件产品中优等品数ξ的分布列及其均值． 解：(1)乙厂生产的产品总数为5÷1498＝35. (2)样品中优等品的频率为25，乙厂生产的优等品的数量为35×25＝14.(3)ξ＝0,1,2，P (ξ＝i )＝C i 2C 2－i3C 25(i ＝0,1,2)，ξ的分布列为ξ 0 1 2 P31035110均值E (ξ)＝1×35＋2×110＝45.22．(本小题满分12分)某煤矿发生透水事故时，作业区有若干人员被困．救援队从入口进入之后有L 1，L 2两条巷道通往作业区(如下图)，L 1巷道有A 1，A 2，A 3三个易堵塞点，各点被堵塞的概率都是12；L 2巷道有B 1，B 2两个易堵塞点，被堵塞的概率分别为34，35.(1)求L 1巷道中，三个易堵塞点最多有一个被堵塞的概率；(2)若L 2巷道中堵塞点个数为X ，求X 的分布列及均值E (X )，并依据“平均堵塞点少的巷道是较好的抢险路线”的标准，请你挂念救援队选择一条抢险路线，并说明理由．解：(1)设“L 1巷道中，三个易堵塞点最多有一个被堵塞”为大事A ，则P (A )＝C 03×⎝ ⎛⎭⎪⎫123＋C 13×12×⎝ ⎛⎭⎪⎫122＝12.(2)依题意，X 的可能取值为0,1,2，P (X ＝0)＝⎝⎛⎭⎪⎫1－34×⎝⎛⎭⎪⎫1－35＝110， P (X ＝1)＝34×⎝⎛⎭⎪⎫1－35＋⎝⎛⎭⎪⎫1－34×35＝920，P (X ＝2)＝34×35＝920，所以随机变量X 的分布列为X 0 1 2 P110920920E (X )＝0×110＋1×920＋2×920＝2720.法一：设L 1巷道中堵塞点个数为Y ，则Y 的可能取值为0,1,2,3，P (Y ＝0)＝C 03×⎝ ⎛⎭⎪⎫123＝18，P (Y ＝1)＝C 13×12×⎝ ⎛⎭⎪⎫122＝38，P (Y ＝2)＝C 23×⎝ ⎛⎭⎪⎫122×12＝38， P (Y ＝3)＝C 33×⎝ ⎛⎭⎪⎫123＝18， 所以，随机变量Y 的分布列为Y0 1 2 3 P18383818E (Y )＝0×18＋1×38＋2×38＋3×18＝2，由于E (X )<E (Y )，所以选择L 2巷道为抢险路线为好．法二：设L 1巷道中堵塞点个数为Y ，则随机变量Y ～B ⎝ ⎛⎭⎪⎫3，12， 所以，E (Y )＝3×12＝32，由于E (X )<E (Y )，所以选择L 2巷道为抢险路线为好．。

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Support your reading habit without paying a cent or even taking a trip to the library.The Library of CongressIf you're looking for classics online，the Library of Congress has got you covered.With more than 60 classic books available，this is the perfect website if you have a specific classic you're looking to read.It also includes children's classics like Alice in Wonderland and Cinderella.Project GutenbergFounded in 1971，Project Gutenberg is the oldest eBook collection online.While the website asks for donations (捐赠)，no fees are required for reading the free online books they offer.There are more than 56，000 eBooks to choose from，and they are Kindle-compatible and easy to download.BookBubIf you're a book lover who's always looking for something new to read，BookBub is a site you need in your life.To access this site and its thousands of available eBooks you need to create an account (账户)，but it's totally free.Once you've created an account，the site asks you to pick your favorite genres so that it can provide the best reading recommendations (推荐)．If you want to learn more about BookBub，click here.BookRixBookRix allows readers to download free ebooks onto their iPads，tablets，eReaders，and smartphones.The site offers books from self-published authors as well as books that are part of the public domain.The homepage group books into different types including fiction，fantasy，romance，thrillers，so you can easily find a new book to read.1．Which should one choose if they want to read classical fairy tale books?A．The Library of Congress.B．Project Gutenberg.C．BookBub.D．BookRix.2．What makes BookBub different from the other three?A．All the ebooks are totally free.B．Some of the ebooks are classics.C．It recommends books for readers.D．Thousands of ebooks are available.3．Where does this text most probably come from?A．A newspaper.B．The Internet.C．A magazine.D．A notice board.BEmma Watson entered our lives as the perfect Hermione Granger in 2001，and nowadays，we're just as much in love with this charming，intelligent British girl，as ever.You may or may not be a Potter head，but a lot of people are charmed by Emma Watson's perfection.Despite being a star performer at the young age of 11，she's never gone the Hollywood-spoiled-child route.In fact，she made all attempts to stay as normal as possible.She said ，“Ignoring fame was my rebellion，in a funny way.I was insistent on being normal and doing normal things.It probably wasn't advisable to go to college in America and room with a complete stranger.And it probably wasn't wise to share a bathroom with eight other people in a dormitory.Looking back，I think that was crazy.”She added，“I was very well-educated.My dad paid for me to go to a very good school，so I worked hard every single day at that school to make him proud of me.And I did，and I still do.”If we had to imagine what Hermione Granger would have grown up to be like，we would say she'd be the Emma Watson of the Potter universe because there really is noway to separate the two.In the last few years，Emma has added more feathers to her cap than we imagined being humanly possible，which include actor，scholar，model and UN Women Goodwill Ambassador.In her role as a UN Women Goodwill Ambassador，she'd supported powerful causes to the best of her ability and brought them all the attention they deserve.Emma Watson gave us the most accurate description of our favorite girl from the Potter universe.“Young girls are told you have to be a delicate princess.Hermione taught them that you can be a warrior.”4．After Emma Watson became an actress，she________．A．followed the Hollywood child routeB．had a preference for a normal lifeC．became rebellious in a funny wayD．went to a good college instead5．What does the author mean by saying “Emma has added more feathers to her cap”in paragraph 4?A．Emma has earned more titles.B．Emma wears a cap with feathers.C．Emma is expert at designing caps.D．Emma has been more absorbed in her job.6．What can be the best title for the text?A．Emma Watson：You Can Be the Best ActressB．Emma Watson：You Can Be a WarriorC．The Way to Be a Delicate PrincessD．The Way to Be a Good Performer7．What's the author's attitude to Emma Watson?A．Critical.B．Objective.C．Cautious.D．Appreciative.CInstead of going on a trip or buying herself new clothes：Xiao Tong from Wuhan，Hubei Province，chose to celebrate her senior high school graduation in a differentway.She went to a beauty clinic to have plastic surgery on her nose.“I want to make a good impression and start my university life with a brand-new look，”the 18-year-old told Changjiang Daily.Like Xiao Tong，many young Chinese are anxious about their looks，and more and more subject themselves to plastic surgery.Young people do it for different reasons，and improving self-confidence is one of them.Wang Fang，18，from Beijing，felt that her eyes were too small.In 2019，after she got in university，Wang had a minor operation done on her eyelids.“Before I had the surgery，I had a negative view of myself.Therefore，I had no confidence，”Wang told Beijing Youth Daily.But Jiang Wenxiu of the Department of Psychiatry，Zhongda Hospital，Southeast University in Jiangsu，advised that people should think twice before going under the knife.“Medical beauty apps only show how great plastic surgery can be，”Jiang told China Daily.“They leave out all the negative things.”Today beauty clinics are well aware that these young students are mostly short of money，so they use summer discounts，installment plans and other ways to attract their attention.Xiao Zhen，17，from Chengdu，Sichuan Province，is one of the victims.She took out a loan(贷款) of about 20，000 yuan to get plastic surgery.But the large sum of money became a big burden.She had to drop out of school and go to work to pay off the loan.Besides the financial burden，potential health risks of plastic surgery also need to be considered.“If you have big problems with your look，you should wait until you are a full adult，and then decide if you want to do something about it，”Jiang said.“Then，with a stable(稳定的)mind，you can consider inner and outer beauty，and whether plastic surgery is for you.”8．Why does the author mention Xiao Tong in the first paragraph?A．To explain what plastic surgery is.B．To praise her bravery to live a different life.C．To show the popularity of plastic surgery.D．To introduce a new way to start university.9．What does Xiao Zhen lose for her surgery?A．Freedom.B．Education.C．Health.D．Confidence.10．What is Jiang Wenxiu's attitude towards plastic surgery?A．Admiring.B．Worried.C．Cautious.D．Satisfied.11．What is the best title of the passage?A．Popular Plastic Surgery.B．Never Take Plastic Surgery.C．What Makes Plastic Surgery Popular?D．Show Your Confidence in Plastic Surgery.DIt is generally acknowledged that young people from poorer socio-economic backgrounds tend to do less well in the education system.In an attempt to help the children of poor families，a nationwide program called“Headstart” was started in the US in 1965.A lot of money was poured into it.It took children into preschool institutions at the age of three and was supposed to help them succeed in school.But the results have been disappointing，because the program began too late.Many children who entered it at three were already behind their peers in language and intelligence and the parents were not involved in the process.At the end of each day，“Headstart”children returned to the same disadvantaged home environment.To improve the results，another program was started in Missouri that concentrated on parents as the child's first teachers.This program was based on research showing that working with the family is the most effective way of helping children get the best possible start in life.The four-year study included 380 families who were about to have their first child and represented different socio-economic status，age and family structure.The program involved trained educators visiting and working with the parent or parents and the child.The program also gave the parents some guidance，and useful skills on child development.At three，the children involved in the “Missouri” program were evaluated withthe children selected from the same socio-economic backgrounds and family situations.The results were obvious.The children in the program were more advanced in language development，problem solving and other intellectual skills than their peers.They performed equally well regardless of socio-economic backgrounds or family structure.The one factor that was found to affect the child's development was the poor quality of parent-child interaction.That interaction was not necessarily bad in poorer families.The “Missouri”program compares quite distinctly with the “Headstart”program.Without a similar focus of parent education and on the vital importance of the first three years，some evidence indicates that it will not be enough to overcome education unfairness.12．What caused the failure of the “Headstart” program?A．The large number of poor families.B．The disapproval from children.C．The late start of the program.D．The long period of time.13．What do we know about the “Missouri” program?A．It focused on the children's first school teachers.B．It helped the children return to the same home.C．It made the children improved in many aspects.D．It gave the parents advice on their development.14．According to the passage，what is likely to influence children's performance? A．The number of family members.B．The teacher-student relationship.C．The intelligence of their parents.D．The parent-child communication.15．How does the author develop the passage?A．By listing figures.B．By making comparisons.C．By presenting ideas.D．By drawing conclusions.第二节To tell the truth，no one has the right to judge you.People may have heard your stories，but they can't feel what you are going through; they aren't living YOUR life.16 Instead，focus on how you feel about yourself，and do what you think is right.17 Your relationship with yourself is the closest and most important one you will ever have.If you don't take good care of yourself，then you can't take good care of others either.Taking care of yourself is the best thing you can do.Do what you know is right，for YOU.Don't be afraid to walk alone，and don't be afraid to like it.Don't let anyone's words stop you from being the best you can be.18 When you are totally at peace within yourself，nothing can shake you.Follow your own path. 19 Make use of the chance to make life all that you want it to be.Work hard for what you believe，and keep your dreams big and your worries small.Forgive those who have wronged you. 20 It is a special quality of the strong and wise.It allows you to focus on the future instead of the past.Without forgiveness，wounds can never be healed，and moving on can never be achieved.A．Take care of yourself.B．So forget what they say about you.C．Forgiveness is a gift you give yourself.D．Show everyone your love and kindness.E．Every new day is a chance to change your life.F．Keep doing what you know in your heart is right.G．When you are dealing with failure，don't be ashamed.第二部分语言运用第一节Everyday on the way to work I drive down a street lined with pine trees.One tree in particular 21 my attention.It must have suffered some 22 .Part of its trunk grew nearly parallel to the ground，and then in an effort to 23 its own course of life，the trunk took a 90 degree turn 24 to stand tall and stretch toward the sun.This tree became a 25 for me.Each day as I drove by，I saw this bent butdetermined tree and I would be 26 ．It was a reminder to me that 27 I may not have had the best start in life，I could change 28 in the parts of my life at any time.I was planning to stop one day to get a perfect 29 of my kindred-spirit(志趣相同的) tree.But that week I was 30 ．After that busy week，I still didn't take any action.Every time I drove by the tree I would 31 myself，“Tomorrow，I'll stop to take one.”Then one day，as I 32 by “my” tree，I glanced over，and much to my 33 I found a sawed-off stump(树桩) where that symbolic tree had stood.Gone.I had 34 my plan until “tomorrow” and tomorrow proved to be too35 ．A picture of a tree gives me a lesson clearly that if we knew we would never have the opportunity to do it again？Why not do those things that you have been putting off until tomorrow？21.A．paid B．caughtC．fixed D．escaped22．A．damage B．influenceC．experience D．defeat23．A．follow B．designC．change D．imagine24．A．applying B．attemptingC．happening D．learning25．A．shelter B．signalC．sign D．symbol26．A．interested B．satisfiedC．encouraged D．educated27．A．even though B．as ifC．in case D．if only28．A．purpose B．planC．habit D．direction29．A．glance B．viewC．picture D．knowledge30．A．busy B．freeC．worried D．bored31．A．tell B．helpC．call D．see32．A．wandered B．droveC．rode D．ran33．A．surprise B．pleasureC．regret D．happiness34．A．taken off B．cut offC．put off D．called off35．A．cold B．farC．sunny D．late第二节A 90-year-old has been awarded “Woman Of The Year” for 36.________(be) Britain's oldest full-time employee—still working 40 hours a week.Now Irene Astbury works from 9 am to 5 pm daily at the pet shop in Macclesfield，37.________ she opened with her late husband Les.Her years of hard work have 38.________(final) been acknowledged after a customer nominated(提名) her to be Cheshire's Woman Of The Year.Picking up her “Lifetime Achievement”award，proud Irene 39.________(declare) she had no plans 40.________(retire) from her 36-year-old business.Irene said，“I don't see any reason to give up work.I love coming here and seeing my family and all the friends I 41.________(make) over the years.I work not because I have to，42.________ because I want to.”Granddaughter Gayle Parks，31—who works alongside her in the family business—said it remained unknown as to who nominated Irene for the award.She said，“We don't have any idea who put grandma forward.When we got a call 43.________(say) she was short-listed，we thought it was 44.________ joke.But then we got an official letter and we were blown away.We are so proud of her.It's 45.________(wonder)．”第三部分写作第一节假如你是李明，根据学校安排，你给即将到你校任教的外籍教师Jack推荐一名学生助手(assistant)。

Ⅰ.语言知识及应用(共两节，满分45分)第一节完形填空(共15小题；每小题2分，满分30分)阅读下面短文，掌握其大意，然后从1～15各题所给的A、B、C和D项中，选出最佳选项。

A father had a pair of twin sons.The two boys looked like each other.Judging (判断) from the __1__，the two boys were almost the same.But their __2__ were very different，or __3__ speaking，just opposite.One was extremely optimistic (乐观的)，while the other was extremely pessimistic (悲观的)．The father wanted to __4__ their characters to make both of them better. One day，he bought many __5__ toys for the pessimistic child，and closed his __6__ brother the optimistic child in a room the floor of which was covered with dogs’ waste.An hour later，the father came to see the __7__.He was sure he would see the scene he __8__：the pessimistic child was __9__ and the optimistic one was crying.But what he saw __10__ surprised him.He found the face of the pessimistic child was in __11__.He asked him，“Why are you crying? Why don’t you play with these toys？”“They will get dirty if I play with them.” The child was still crying.The father __12__ his head helplessly，entered the other room and __13__ actually that the optimistic child was happily clearing dogs’ waste.“Hey，daddy.The room should really be cleaned.I did a good job，didn’t I？” That child said to the father，with a(n) __14__ face.Between the optimist and the pessimist，the __15__ is very interesting：An optimist says the glass is half full...A pessimist says the glass is half empty...1．A.clothes B．voicesC．names D．looks解析：选D。

模块综合检测卷(一)(时间：120分钟 满分：150分)一、选择题(本大题共12小题，每小题5分，共60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．直线x －3＝0的倾斜角是( )A ．45°B ．60°C ．90°D ．不存在 答案：C2．已知点A (x ，1，2)和点B (2，3，4)，且|AB |＝26，则实数x 的值是( ) A ．－3或4 B ．－6或2 C ．3或－4 D ．6或－2答案：D3．一个球的内接正方体的表面积为54，则球的表面积为( ) A ．27π B ．18π C ．9π D ．54π 解析：设正方体的棱长为a ，球的半径为r ， 则6a 2＝54，所以a ＝3. 又由于2r ＝3a ， 所以r ＝32a ＝332，所以S 表＝4πr 2＝4π·274＝27π.答案：A4．在同一个平面直角坐标系中，表示直线y ＝ax 与y ＝x ＋a 正确的是( )答案：C5．某几何体的三视图如图所示，则该几何体的体积为( )A ．12B ．18C ．24D ．30解析：由于三个视图中直角较多，所以可以在长方体中对几何体进行分析还原，在长方体中计算其体积．由俯视图可以推断该几何体的底面为直角三角形，由正视图和左视图可以推断该几何体是由直三棱柱(侧棱与底面垂直的棱柱)截取得到的．在长方体中分析还原，如图①所示，故该几何体的直观图如图②所示．在图①中，V 棱柱ABC -A 1B 1C 1＝S △ABC ·AA 1＝12×4×3×5＝30，V 棱锥P -A 1B 1C 1＝13S △A 1B 1C 1·PB 1＝13×12×4×3×3＝6.故几何体ABC -PA 1C 1的体积为30－6＝24.故选C.答案：C6．已知圆C 1：(x －2)2＋(y －3)2＝1，圆C 2：(x －3)2＋(y －4)2＝9，M ，N 分别是圆C 1，C 2上的动点，P 为x 轴上的动点，则|PM |＋|PN |的最小值为( )A ．52－4 B.17－1 C ．6－2 2D.17解析：先求出圆心坐标和半径，再结合对称性求解最小值，设P (x ，0)，C 1(2，3)关于x 轴的对称点为C 1′(2，－3)，那么|PC 1|＋|PC 2|＝|PC 1′|＋|PC 2|≥|C ′1C 2|＝（2－3）2＋（－3－4）2＝5 2. 而|PM |＝|PC 1|－1，|PN |＝|PC 2|－3， 所以|PM |＋|PN |＝|PC 1|＋|PC 2|－4≥52－4. 答案：A7．直线y ＝kx ＋3与圆(x －2)2＋(y －3)2＝4相交于M 、N 两点，若|MN |≥23，则k 的取值范围是( )A.⎣⎢⎡⎦⎥⎤－34，0 B.⎣⎢⎡⎦⎥⎤－33，33C.[]－3，3D.⎣⎢⎡⎦⎥⎤－23，0 解析：法一：可联立方程组利用弦长公式求|MN |，再结合|MN |≥23可得答案．法二：利用圆的性质知，圆心到直线的距离的平方加上弦长一半的平方等于半径的平方，求出|MN |，再结合|MN |≥23可得答案．答案：B8．若空间中四条两两不同的直线l 1，l 2，l 3，l 4满足l 1⊥l 2，l 2⊥l 3，l 3⊥l 4，则下列结论肯定正确的是( )A ．l 1⊥l 4B ．l 1∥l 4C ．l 1与l 4既不垂直也不平行D ．l 1与l 4的位置关系不确定解析：如图所示，在长方体ABCD -A 1B 1C 1D 1中，记l 1＝DD 1，l 2＝DC ，l 3＝DA ，若l 4＝AA 1，满足l 1⊥l 2，l 2⊥l 3，l 3⊥l 4，此时l 1∥l 4，可以排解选项A 和C.若l 4＝DC 1，也满足条件，可以排解选项B.故选D. 答案：D9.如图所示，在四周体ABCD 中，E ，F 分别是AC 与BD 的中点，若CD ＝2AB ＝4，EF ⊥BA ，则EF 与CD 所成的角为( )A ．90°B ．45°C ．60°D ．30°解析：如图所示，取BC 的中点H ，连接EH ，FH ，则∠EFH 为所求，可证△EFH 为直角三角形， EH ⊥EF ，FH ＝2，EH ＝1， 从而可得∠EFH ＝30°. 答案：D10．若直线y ＝kx ＋1与圆x 2＋y 2＋kx －y ＝0的两个交点恰好关于y 轴对称，则k 等于( )A ．0B ．1C ．2D ．3解析：由⎩⎨⎧y ＝kx ＋1，x 2＋y 2＋kx －y ＝0，得(1＋k 2)·x 2＋2kx ＝0. 由于两点恰好关于y 轴对称， 所以x 1＋x 2＝－2k 1＋k 2＝0， 所以k ＝0. 答案：A11．已知直线l 1：ax ＋4y －2＝0与直线l 2：2x －5y ＋b ＝0相互垂直，垂足为(1，c )，则a ＋b ＋c 的值为( )A ．－4B ．20C ．0D ．24解析：垂足(1，c )是两直线的交点，且l 1⊥l 2，故－a 4·25＝－1，所以a ＝10.l ：10x ＋4y －2＝0.将(1，c )代入，得c ＝－2； 将(1，－2)代入l 2，得b ＝－12. 则a ＋b ＋c ＝10＋(－12)＋(－2)＝－4. 答案：A12．过点A ⎝⎛⎭⎪⎫0，73与B (7，0)的直线l 1与过点(2，1)，(3，k ＋1)的直线l 2和两坐标轴围成的四边形内接于一个圆，则实数k 等于( )A ．－3B ．3C ．－6D ．6 解析：由题意知l 1⊥l 2，所以kl 1·kl 2＝－1，即－13k ＝－1，k ＝3.答案：B二、填空题(本大题共4小题，每小题5分，共20分．将正确答案填在题中的横线上)13．设点A (－1，0)，B (1，0)，直线2x ＋y －b ＝0与线段AB 相交，则b 的取值范围是________．解析：b 为直线y ＝－2x ＋b 在y 轴上的截距，如图所示，当直线y ＝－2x ＋b过点A (－1，0)和点B (1，0)时b 分别取得最小值和最大值．所以b 的取值范围是[－2，2]． 答案：[－2，2]14．已知直线ax ＋y －2＝0与圆心为C 的圆(x －1)2－(y －a )2＝4相交于A ，B 两点，且△ABC 为等边三角形，则实数a ＝________．解析：依据“半径、弦长AB 的一半、圆心到直线的距离”满足勾股定理可建立关于a 的方程，解方程求a .圆心C (1，a )到直线ax ＋y －2＝0的距离为|a ＋a －2|a 2＋1.由于△ABC 为等边三角形，所以|AB |＝|BC |＝2.所以⎝ ⎛⎭⎪⎫|a ＋a －2|a 2＋12＋12＝22.解得a ＝4±15.答案：4±1515．如图所示，将边长为1的正方形ABCD 沿对角线AC 折起，使得平面ADC ⊥平面ABC ，在折起后形成的三棱锥D -ABC 中，给出下列三种说法：①△DBC 是等边三角形；②AC ⊥BD ；③三棱锥D -ABC 的体积是26.其中正确的序号是________(写出全部正确说法的序号)．解析：取AC 的中点E ，连接DE ，BE ， 则DE ⊥AC ，BE ⊥AC ，且DE ⊥BE . 又DE ＝EC ＝BE ，所以DC ＝DB ＝BC ，故△DBC 是等边三角形． 又AC ⊥平面BDE ， 故AC ⊥BD .又V D -ABC ＝13S △ABC ·DE ＝13×12×1×1×22＝212，故③错误．答案：①②16．已知直线l 经过点P (－4，－3)，且被圆(x ＋1)2＋(y ＋2)2＝25截得的弦长为8，则直线l 的方程是_________________________．解析：由于(－4＋1)2＋(－3＋2)2＝10<25，所以点P 在圆内．当l 的斜率不存在时，l 的方程为x ＝－4，将x ＝－4代入圆的方程，得y ＝2或y ＝－6，此时弦长为8.当l 的斜率存在时，设l 的方程为y ＋3＝k (x ＋4)，即kx －y ＋4k －3＝0，当弦长为8时，圆心到直线的距离为 25－42＝3，则|－k ＋2＋4k －3|k 2＋1＝3，解得k ＝－43.则直线l 的方程为y ＋3＝－43(x ＋4)，即4x ＋3y ＋25＝0.答案：4x ＋3y ＋25＝0或x ＝－4三、解答题(本大题共6小题，共70分．解答时应写出必要的文字说明、证明过程及演算步骤)17．(本小题满分10分)求经过两直线2x －3y －3＝0和x ＋y ＋2＝0的交点且与直线3x ＋y －1＝0平行的直线方程．解：法一：由方程组⎩⎨⎧2x －3y －3＝0，x ＋y ＋2＝0，得⎩⎪⎨⎪⎧x ＝－35，y ＝－75.由于直线l 和直线3x ＋y －1＝0平行， 所以直线l 的斜率k ＝－3.所以依据点斜式有y －⎝⎛⎭⎪⎫－75＝－3⎣⎢⎡⎦⎥⎤x －⎝⎛⎭⎪⎫－35，故所求直线方程为15x ＋5y ＋16＝0.法二：由于直线l 过两直线2x －3y －3＝0和x ＋y ＋2＝0的交点， 所以设直线l 的方程为2x －3y －3＋λ(x ＋y ＋2)＝0， 即(λ＋2)x ＋(λ－3)y ＋2λ－3＝0. 由于直线l 与直线3x ＋y －1＝0平行， 所以λ＋23＝λ－31≠2λ－3－1，解得λ＝112.从而所求直线方程为 15x ＋5y ＋16＝0.18．(本小题满分12分)如图所示，在正三棱柱ABC -A 1B 1C 1中，AA 1＝6，异面直线BC 1与AA 1所成角的大小为30°，求该三棱柱的体积．解：由于CC 1∥AA 1，所以∠BC 1C 为异面直线BC 1与AA 1所成的角， 即∠BC 1C ＝30°.在Rt △BC 1C 中，BC ＝CC 1·tan ∠BC 1C ＝6×33＝23， 从而S △ABC ＝34BC 2＝33，因此该三棱柱的体积为V ＝S △ABC ·AA 1＝33×6＝18 3.19．(本小题满分12分)如图所示，在正方体ABCD -A 1B 1C 1D 1中，E ，F ，P ，Q ，M ，N 分别是棱AB ，AD ，DD 1，BB 1，A 1B 1，A 1D 1的中点．求证：(1)直线BC 1∥平面EFPQ ； (2)直线AC 1⊥平面PQMN .证明：(1)连接AD 1，由ABCD -A 1B 1C 1D 1是正方体， 知AD 1∥BC 1.由于F ，P 分别是AD ，DD 1的中点，所以FP ∥AD 1. 从而BC 1∥FP .而FP ⊂平面EFPQ ，且BC 1⊄平面EFPQ ， 故直线BC 1∥平面EFPQ .(2)如图所示，连接AC ，BD ，则AC ⊥BD .由CC1⊥平面ABCD，BD⊂平面ABCD，可得CC1⊥BD.又AC∩CC1＝C，所以BD⊥平面ACC1.而AC1⊂平面ACC1，所以BD⊥AC1.由于M，N分别是A1B1，A1D1的中点，所以MN∥BD，从而MN⊥AC1.同理可证PN⊥AC1.又PN∩MN＝N，所以直线AC1⊥平面PQMN.20．(本小题满分12分)右图是某几何体的三视图，请你指出这个几何体的结构特征，并求出它的表面积与体积．解：此几何体是一个组合体，下半部是长方体，上半部是半圆柱，其轴截面的大小与长方体的上底面大小全都．表面积为S，则S＝32＋96＋48＋4π＋16π＝176＋20π.体积为V，则V＝8×4×6＋12×22×8π＝192＋16π.所以几何体的表面积为(176＋20π)cm2，体积为(192＋16π)cm3.21．(本小题满分12分)已知点M(x0，y0)在圆x2＋y2＝4上运动，N(4，0)，点P(x，y)为线段MN的中点．(1)求点P(x，y)的轨迹方程；(2)求点P(x，y)到直线3x＋4y－86＝0的距离的最大值和最小值．解：(1)由于点P(x，y)是MN的中点，所以⎩⎪⎨⎪⎧x＝x0＋42，y＝y02，故⎩⎨⎧x0＝2x－4，y0＝2y.将用x，y表示的x0，y0代入到x20＋y20＝4中得(x－2)2＋y2＝1.此式即为所求轨迹方程．(2)由(1)知点P的轨迹是以Q(2，0)为圆心，以1为半径的圆．点Q到直线3x ＋4y－86＝0的距离d＝|6－86|32＋42＝16.故点P到直线3x＋4y－86＝0的距离的最大值为16＋1＝17，最小值为16－1＝15.22.(本小题满分12分)如图所示，在平面直角坐标系xOy中，点A(0，3)，直线l：y＝2x－4，设圆C的半径为1，圆心在l上．(1)若圆心C也在直线y＝x－1上，过点A作圆C的切线，求切线的方程；(2)若圆C上存在点M，使|MA|＝2|MO|，求圆心C的横坐标a的取值范围．解：(1)由题设，圆心C是直线y＝2x－4和y＝x－1的交点，解得点C(3，2)，于是切线的斜率必存在，设过A(0，3)的圆C的切线方程为y＝kx＋3.由题意，得|3k＋1|k2＋1＝1，解得k＝0或k＝－34，故所求切线方程为y＝3或3x＋4y－12＝0.(2)由于圆心在直线y＝2x－4上，设圆心C(a，2(a－2))，所以圆C的方程为(x－a)2＋[y－2(a－2)]2＝1.设点M(x，y)，由于MA＝2MO，所以x2＋（y－3）2＝2x2＋y2，化简得x2＋y2＋2y－3＝0，即x2＋(y＋1)2＝4.所以点M在以D(0，－1)为圆心，2为半径的圆上．由题意，点M(x，y)在圆C上，所以圆C与圆D有公共点，则|2－1|≤CD≤2＋1，即1≤a2＋（2a－3）2≤3.整理，得－8≤5a2－12a≤0.由5a2－12a＋8≥0，得a∈R；由5a2－12a≤0，得0≤a≤125.所以点C的横坐标a的取值范围为⎣⎢⎡⎦⎥⎤0，125.。