2017—2018学年度第二学期期末考试试卷
2017-2018学年第二学期期末考试数学试卷
）））））））2017—2018学年第二学期期末考试数学试题高二数学(文科)一.选择题,本题共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。
M?{x|?2?x?2},N?{0,1,2}，则等于（1.若集合）NMI{1}{0,1}2}{0,1,A.C. D. B. }{0i2,Rb?a,(a?bi)?（）是虚数单位，若2.已知，则bi?i?2?a3?4i C. A. D. B. i43?i?344?3i2??x,xx?1?f(f(?2))的值为3.已知函数,则( )?x)f(?11?,x?x?1?1111 D. C.A. B. ??2255?3??tan）4.已知，则（???)?,(sin,? 253443 A. B. C. D. ??4343?a??a s8a?,?sa?3a （前n项和为），已知，则5.等比数列1n n4231 A. 2 B. 1 C. 8 D. 4??03y??x?xy,?yzx??的最小值为（满足约束条件，则）6.已知0?2x6??y??1?0?x?y2? A. 1 B. C. D. 33?1?(1,1)2处的切线与，若函数的图像在点7.设函数bxx?lnxf()?a)f(x y轴垂直，则实数（）?ab?））））））））、．）））））））11 D. 1A. B. C. 1?4291的最小，则，-2）8.若直线过点（10)n?0(?2?m?0,2mx?ny?nm值为（）A. 6B. 2C. 16D. 12若角所对的边分别是,9.在中,o ABC?3c?3,,a?bA?60?cb,a,CB,A,( ) 则的面积为ABC?33 B. 2 C.A. D. 342rrrrr rr），则有（若向量与的夹角为，且10.o ba b??a?1,|b|?2,c|a|120rr rr rrrr bc? C. D.B. A.a?c ba/c/c//给出下列四个是两条不同的直线，是两个不同的平面，11.设??,nm,则②若，命题：①若，则??????/n?///m//nm//,m?,m，则③若，则④若???????m?mn//,?//m//n,m）其中真命题的个数为（A. 1 B. 2 C. 3 D. 4x为椭轴上，12. 如图，椭圆的中心在坐标原点，焦点在B,,A,BA2112B 与ABF为钝角，，圆顶点，为右焦点，延长若交于点PABF?P2122212则该椭圆离心率的范围是（）B25?15?1BA．．)(0,,1)(ｐ22A2FAF25?25?211．． DC(0,),1)(22B1））））））））、．）））））））二.填空题：本小题共4个小题，每小题5分，共20分。
2017～2018年度第二学期期末考试试题
2017～2018年度第二学期期末考试试题第I卷第一部分：听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）请听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What can we learn from the conversation?A. The woman is leaving for America.B. The woman comes from London.C. The woman is surprised at what the man said.2. Where does the conversation most probably take place？A. In a zoo.B. In a forest.C. In a pet store.3. What can we know about Peter?A. He has heart disease.B. He is resting at home.C. He has got enough exercise.4. What are the speakers talking about?A. Play.B. Music.C. Hobbies.5. What are the speakers probably going to do?A. Go on a trip.B. Buy some food.C. Wait for a taxi第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中做给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
2017-2018学年度第二学期期末考试.doc
2017-2018学年度第二学期期末考试汽车发动机构造与维修姓名_______ 班级____________ 成绩 ___________一、填空题（每题3分，共30分）1 •根据发动机中各运动副工作条件的不同，发动机一般采用___________ 润滑和________ 润滑方式。
2润滑系统_般由_______ _________ __________ __________ __________ ________ 和_____________ 等组成。
3•汽车上的常用机油泵有______________ 和____________ ，它们都属于________ 泵，都是依靠__________ 的变化完成吸油和泵油。
4•与主油道串联的滤清器称为________________ 一般为___________ ，与主油道并联的滤清器称为_______________ _ 般为___________ .5. ______________________________________________ 曲轴箱通风装置有两种通风方式，一种是______________________________________________________ ，另一种是__________6•从曲轴箱抽出的气体直接导入大气中的通风方式称为 ____________ -7. ___________________ 柴油机多采用通风方式。
8. _____________________________________________________ 冷却系的作用是.9. 通常，冷却水在冷却系内的循环路线有两条，一条为，另一条为________ •不经过____________ 的为 __________ .经过____________ 的为____________ .10•目前，汽车发动机一般采用___________ 节温器。
2017—2018学年度第二学期期末考试试卷
2017—2018学年度第二学期期末考试试卷高二文科数学（时量：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，在每个小题给出的四个选项中，只有一项是符合题目要求的．1．设回归方程为x y 32-=，则变量x 增加一个单位时（ ）A ．y 平均增加2个单位B ．y 平均增加3个单位C ．y 平均减少3个单位D ．y 平均减少2个单位 2．复数223(1)()m m m i m R +-+-∈为纯虚数，则（ ） A ．m=1或m=－3B ．m=1C ．m=－3D ．m=33．圆sin )ρθθ=+的圆心坐标是（ ）A ．（1，4π）B ．（21，4π） C ．（2，4π） D ．（2，4π）4．将函数y=f(x)的图象上各点的横坐标缩短到原来的一半（纵坐标不变），再将其纵坐标伸长到原来的3倍（横坐标不变）得到的图象对应的函数解析式为（ ） A ．1(2)3y f x =B ．y=3f(2x)C ．1()32x y f =D ．3()2x y f =5．回归分析中，相关指数R 2的值越大，说明残差平方和（ ） A ．越小 B ．越大 C ．可能大也可能小 D ．以上全都不对6．若执行右下的程序框图，输入6,4n m ==，则输出的p 等于（ ） A ．720 B ．360C ．240D ．1207．复数i i 21121-++-的虚部是（ ） A ．i 51 B ．51C ．i 51- D ．51-8．下面几种推理是合情推理的是（ ）①由圆的性质类比出球的有关性质；②由直角三角形、等腰三角形、等边三角形的内角和是0180归纳出所有三角形的内角和是0180；③一班所有同学的椅子都坏了，甲是1班学生，所以甲的椅子坏了； ④三角形内角和是0180，四边形内角和是0360，五边形内角和是0540， 由此得出凸n 边形内角和是0180)2(⋅-n ．A ．①②④B ．①③④C ．②④D ．①②③④ 9．满足条件|z －i|=|3+4i| 的复数z 在复平面上对应点的轨迹是（ ） A ．一条直线 B ．两条直线 C ．圆 D ．椭圆10．已知点（x,y ）满足曲线方程⎪⎩⎪⎨⎧+=+=θθsin 26cos 24y x （θ为参数），则x y 的最小值是（ ） A ．23B ．23 C ．3 D ．111．在参数方程⎩⎨⎧+=+=θθsin cos t b y t a x (t 为参数)所表示的曲线上有B 、C 两点，它们对应的参数值分别为12,t t ，则线段BC 的中点M 对应的参数值是（ ）A ．122t t - B ． 122t t+ C ． 122t t -D ． 122t t +12．设△ABC 的三边长分别为,,a b c ，△ABC 的面积为S ，内切圆半径为r ，则2Sr a b c=++．类比这个结论可知：四面体ABCD 的四个面的面积分别为1234,,,S S S S ，四面体ABCD 的体积为V ，内切球的半径为，则=（ ）A ．1234V S S S S +++ B ． 12342VS S S S +++C ．12343V S S S S +++ D ． 12344VS S S S +++二、填空题：本大题共4小题，每小题5分，共20分.13．极坐标方程(cos sin )10ρθθ+-=化为直角坐标方程是 ． 14. 曲线x x x f ln )(=在点1=x 处的切线方程为 ．15.直线2()1x t t y t=-+⎧⎨=-⎩为参数被圆22(3)(1)25x y -++=所截得的弦长为 ．16．半径为r 的圆的面积s(r)= 2r π，周长c(r)=2r π，若将r 看作),0(+∞上的变量，则)(2'r π=2r π①①式可用文字语言叙述为，圆的面积函数的导数等于圆的周长函数； 对于半径为R 的球，若将R 看作),0(+∞上的变量，请你写出类似于①的式子 ． ②该式可用文字语言叙述为 ．三、解答题（本大题共6小题，共70分，解答应写出文字说明、证明过程或演算步骤）17．（本小题满分10分）已知数列{}n a 满足1a 1=，且nnn a a a +=+11 （,3,2,1=n …，） (Ⅰ)求432,,a a a 的值，并猜想出这个数列的通项公式； (Ⅱ)求12233478S a a a a a a a a =++++的值．18.（本小题满分12分）已知曲线C 的极坐标方程是1ρ=，以极点为原点，极轴为轴的正半轴建立平面直角坐标系，直线的参数方程为12t x y ⎧=+⎪⎪⎨⎪=⎪⎩ （ t 为参数）.（Ⅰ）写出曲线C 的直角坐标方程与直线的普通方程；（Ⅱ）设直线l 与曲线C 相交于,A B 两点，求,A B 两点之间的距离．x l l19．(本小题满分12分)(Ⅰ)2> (Ⅱ)已知,a b 为正实数，请用反证法证明：与中至少有一个不小于2．20．(本小题满分12分）近年来我国电子商务行业迎来篷勃发展的新机遇，2016年双11期间，某购物平台的销售业绩高达一千多亿人民币．与此同时，相关管理部门推出了针对电商的商品和服务的评价体系．现从评价系统中选出200次成功交易，并对其评价进行统计，对商品的好评率为0.6，对服务的好评率为0.75，其中对商品和服务都做出好评的交易为80次． (Ⅰ)请完成如下列联表；(Ⅱ)是否可以在犯错误的概率不超过0.1%的前提下，认为商品好评与服务好评有关？(Ⅲ)若针对商品的好评率，采用分层抽样的方式从这200次交易中取出5次交易，并从中选择两次交易进行客户回访，求只有一次好评的概率．2()0.150.100.050.0250.0100.0050.0012.072 2.7063.841 5.024 6.6357.87910.828P K k k≥（22()()()()()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++）b a 1+ab 1+21．（本小题满分12分）如图所示, 四棱锥P A B C -底面是直角梯形,,,2,BA AD CD AD CD AB PA ⊥⊥=⊥底面ABCD , E 为PC 的中点, 1PA AD AB ===.(Ⅰ)证明: //EB PAD 平面; (Ⅱ)证明: BE PDC ⊥平面; (Ⅲ)求三棱锥B PDC -的体积. 22．（本小题满分12分）如图，有一块半椭圆形钢板，其长半轴为2r ，短半轴为r ，计划将此钢板切割成等腰梯形的形状，下底AB 是半椭圆的短轴，上底CD 的端点在椭圆上，记2CD x =，梯形面积为S ．(Ⅰ)求面积S 关于变量x 的函数表达式，并写出定义域； (Ⅱ)求面积S 的最大值．2017—2018学年度第二学期期末考试试卷高二数学(文)参考答案一、选择题：本大题共12小题，每小题5分，共60分.1．C 2．C 3．A 4． B 5． A 6． B 7．B 8．A 9．C 10．D 11．B 12．C 二、填空题：本大题共4小题，每小题5分，共20分.13．10x y +-= 14．1 1516．324()'43R R ππ= , 球的体积函数的导数等于球的表面积函数三、解答题：本大题共6小题，共70分. 17．（本题满分10分） 解：⑴ 41,311,211,142231121==+==+=∴=a a a a a a a a 猜想)(,1*∈=N n na n …………………………………………4分 ⑵ 111112233478S =++++⨯⨯⨯⨯ 111111117(1)()()()1223347888=-+-+-++-=-= ………10分18．(本小题满分12分)解：曲线C 的直角坐标方程为：直线0y - (6)分 （2）||1AB = …………………12分19．(本小题满分12分)(1) 要 证2>只要证222)>即 证而上式显然成立，故原不等式成立.…………………6分1:22=+y x C l（2）假设结论不成立，则112,2a bb a+<+<，所以114a bb a+++<，即11(2)(2)0a ba b+-++-<，即220+<，矛盾！故假设不成立，所以与中至少有一个不小于2.…………………12分20.(本题满分12分）解析：(1)由题意可得关于商品和服务评价的列联表：…………………4分(2)22200(80104070)11.11110.8281505012080K⨯⨯-⨯=≈>⨯⨯⨯，故可以认为在犯错误的概率不超过0．1%的前提下，商品好评与服务好评有关；…………………8分（3）若针对商品的好评率，采用分层抽样的方式从这200次交易中取出5次交易，则好评的交易次数为3次，不满意的次数为2次，令好评的交易为A，B，C，不满意的交易为a，b，从5次交易中，取出2次的所有取法为(,)A B，(,)A C，(,)A a，(,)A b，(,)B C，(,)B a，(,)B b，(,)C a，(,)C b，(,)a b，共计10种情况，其中只有一次好评的情况是(,)A a，(,)A b，(,)B a，(,)B b，(,)C a，(,)C b，共计6种，因此，只有一次好评的概率为63105= .…………………12分21．（本小题满分12分）证明:（1）取PD中点Q, 连EQ , AQ ,则12QE CD AB==//////QE CDCD AB QE ABQE AB⎫⎪⇒⎬⎪=⎭//ABEQ BE AQ⇒⇒四边形是平行四边形ba1+ab1+////BE AQAQ PAD BE PAD BE PAD ⎫⎪⊂⇒⎬⎪⊄⎭平面平面平面…………………6分(2) PA ABCD CD ABCD ⊥⎫⇒⎬⊂⎭平面平面//AQ PCD BE PCD BE AQ ⊥⎫⇒⊥⎬⎭平面平面 .（3）1112122BDC S AD DC ∆⨯⨯＝＝＝1133B PDC P BDC BDC V V PA S --∆＝＝＝.…………………12分22．（本小题满分12分）（Ⅰ）解：由题意可知，半椭圆方程为222214y x r r+= (0)y ≥∵2CD x =∴ 设C 点的横坐标为x ，则纵坐标y =∴ 221(22)22S r x r x =+-等腰梯形2(r x =+(0,)x r ∈…………………5分（II ） 解：∵ 2(S r x =+(0,)x r ∈ ∴ 22224()()S r x r x =+-令 222()()()f x r x r x =+- x ∈ ∴ 4334()22f x x rx r x r =--++ ∴ 323'()462f x x rx r =--+22()(2)x r x r =-+-CD PA CD AD AD PA A ⊥⎫⎪⊥⇒⎬⎪⋂⎭＝CD PAD AQ CD AQ PAD PA AD AQ PDQ PD CD PD D⊥⎫⇒⊥⎬⊂⎭⎫⇒⊥⎬⎭⋂平面平面＝为的中点＝⇒∴ 4max ()()216f x f r ==∴ 2max2S =…………………12分。
2017-2018学年度第二学期期末
2017-2018学年度第二学期期末分值：150分时间：120分钟第一部分听力（共两节，满分30分）第一节（共5小题，每小题1.5分）听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What does the woman think of cloning?A. It has no side effect at all.B. It should be strictly for bidden.C. It may cause trouble for humans.2. What’s the possible relationship between the two speakers ?A. Friends.B. Husband and wife.C. Teacher and student.3. What do they hope to do?A. Stop cigarette production.B. Advise people not to smoke.C. Stop young people smoking.4. What teacher are they talking about?A. Their Chinese teacher.B. Their history teacher.C. Their politics teacher.5. What does the man think the weather will be like in April?A. Cool.B. Hot.C. Windy.第二节（共15小题，每小题1.5分）听下面5段对话,每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟;听完后，各小题将给出5秒钟的作答时间。
2017—2018学年第二学期期末试题
2017—2018学年第二学期期末试题满分：150分考试时间：100分钟第I卷第一部分：听力（略）第二部分：阅读理解（共两节，满分40分）（共15小题；每小题2分，满分30分）AThe summer holidays are coming up. It's time to fill the books helves with quality literature for the kids. Here are some great books.Josephine Wants to Dance by Jackie FrenchPrice: A$14.99 (for ages 4+)Josephine is a kangaroo who loves to dance. Her little brother , Joey, tells her that kangaroos don't dance; they jump. But Jo sephine continues to point her toes and leap through the air. When aballet group comes to town and the lead ballerina (芭蕾舞演员) is injured, Josephine is called upon to help save the day. Can she do it, and, more importantly, does it matter that she's a kangaroo?House of Secrets by Chris ColumbusPrice: A$19.99 (for ages 9+)The Walker kids —Caroline, Brendan and Nell—may have saved the world, but they can' t save their home an d must leave Kristoff House. Things can't get any worse, but t hen it turns out that the Wind Witch is still alive and planning a n attack. To defeat her. the Walkers must return to the book w orld.The Walkers always help each other, but they must go it alone in their most important mission yet. And this time, if they fail, there's no chance of coming back.Edge of Extinction Book 1 by Laura MartinPrice: AS 16.00 (for ages 9+)If you like The Land of the Dinosaurs. You will love this boo k. Two hundred years ago, the first dinosaur was successfully cloned (克隆). Soon after, humans realized they'd made a big mistake. T hirteen-year-old Sky Mundy's father suddenly disappeared five years ago. Along with her best friend，Shawn，she steps out into the world above --a world of dinosaurs --to look for him. Then she learns that everything she's been ta ught has been a lie.21．Which book will you choose if your child is five years old?A. House of Secrets.B. Josephine Wants t o Dance.C. The Land of the Dinosaurs.D. Edge of Extinction Book 1.22．What can we learn about the Walker kids from the text?A. They live in a secret house.B. They hate each oth er.C. They are afraid of the Wind Witch.D. They have to carry o ut the task alone.23．What is the world like in the last book?A. It is full of dinosaurs.B. Animals live happily together .C. Many dinosaurs attack the earth.D. Many adults are killed by the dinosaurs.24．The text is especially helpful for those who .A. are interested in raising animalsB. want to make friends during the holidaysC. plan to educate their children during the holidaysD. want to explore an unknown world during the holidaysBIt was one of the hottest days of the dry season. We had not seen rain in almost a month. The crops were dying. Cows had stopped giving milk. The streams were long gone back into th e earth. If we didn't see some rain soon we would lose everyt hing.I was in the kitchen making lunch for my husband and his brot hers when I saw my six-year old son, Billy, walking toward the woods. He was obvious ly walking with a great effort... trying to be as still as possible. Minutes after he disappeared into the woods, he came runnin g out again, toward the house.Moments later, however, he was once again walking in that sl ow purposeful long step toward the woods. This activity went on for over an hour: walking cautiously to the woods, then run ning back to the house. Finally, my curiosity got the best of m e. I crept out of the house and followed him on his journey.He was cupping both hands in front of him as he walked; bein g very careful not to spill(洒出) the water he held in them. Branches and thorns slapped hi s little face but he did not try to avoid them. He had a much gr eater purpose. As I leaned in to spy on him, I saw the most amazing site.Several large deer appeared threatening in front of him. But B illy walked right up to them. I almost screamed for him to get a way. And I saw a baby deer lying on the ground, obviously suf fering from heavy loss of water and heat exhaustion, lift its he ad with great effort to lap up the water cupped in my beautiful boy's hand.I stood on the edge of the woods watching the most beautiful heart I have ever known working so hard to save a life. As the tears that rolled down my face began to hit the ground, they were suddenly joined by other drops... and more drops... and more. I looked up at the sky. It was as if God, Himself, was w eeping with pride.25. Why did the author follow her son?A. Because there might be danger.B. Because her son was doing a good deed.C. Because she was curious.D. Because she intended to help.26. Which of the following statements is Not True according to the passage?A. Rain was in great need.B. Billy carried water with his s mall hands.C. Billy walked into the woods and then returned over and ove r again.D. There were few trees in the woods.27. Which of the following is the best title for the passage?A. Importance of waterB. The water of lifeC. How to sa ve animalsD. Animals in dangerCGrowing up in Philadelphia, Lieberman started cooking with hi s stay-at-home dad when he was seven. His food-loving family had two kitchens, and he quickly learned what w as the best way to bake his cakes. Lieberman improved his kit chen skills greatly during a year abroad before college, learni ng from a cook in Italy and studying local specialties（地方特色菜）in Germany, Spain and France. At Yale, he was known for thr owing dinner parties, single-handedly frying and baking while mixing drinks for dozens of f riends. Just for fun, he and some friends decided to tape a sh ow named Campus Cuisine about his cooking. Lieberman wa s a real college student showing his classmates how to do thi ngs like make drinks out of dining-hall fruit. That helped the show become very popular among t he students. They would stop Lieberman after classes to ask f or his advice on cooking. Tapes of the show were passed aro und, with which his name went beyond the school and finally t o the Food Network.Food Network producer Flay hopes the young cook will find a place on the network television. He says Lieberman’s chari sma is key.“Food TV isn’t about food anymore,” says Flay. “It’s about your personality（个性）and finding a way to keep people’s eyeballs on your show.”But Lieberman isn’t putting all his eggs in one basket. After taping the first season of the new show, Lieberman was back in his own small kitchen preparing sandwiches. An airline com pany（航空公司）was looking for someone to come up with a tasteful, inexpensi ve and easy-to-make menu to serve on its flights, Lieberman got the job.28. We can learn from the text that Lieberman’s family ____.A. have relatives in EuropeB. love cooking at home C . often hold parties D. own a restaurant29. The Food Network got to know Lieberman ____.A. at one of his partiesB. from his teachersC. through his taped showD. on a television program30. What does the word “charisma” underlined in the text refer to?A. A natural ability to attract others.B. A way to show one’s a chievement.C. Lieberman’s after-class interest. D. Lieberman’s fine cooking skill.31. Why did the airline company give Lieberman the job?A. He could prepare meals in a small kitchen.B. He was famo us for his shows on Food TV.C. He was good at using eggs to make sandwiches.D. He could cook cheap, delicious and simple meals.DIt’s nothing new that you can find many files or services you c an download or use from the Internet. The question is : Is dow nloading legal or not? In most cases the answer is negative, b ecause sharing and downloading are illegal. Of course, you c an find files for legal downloading, but you have to pay for the m.It seems innocent if you click on the download mark, but it is n’t. It should be compared with stealing in a store. Would you steal a magazine, an MP3 player or a car? Downloading from the Internet is a theft, and sharing files, once you have stolen them, only makes it worse. For example, if everybody only downloaded, movies wouldn’t make money and the studios woul dn’t invest millions of dollars to make new ones.Many people may think it better, easier and cheaper to do do wnloading. I think, that is the main reason why Internet users prefer sharing something to buying them. In the modern world we love convenience and what could be more convenient tha n getting music, films and games without having to leave your house? You don’t need to pay for what you get, there is no re gistration, and you don’t have to wait until shops open or the CD/DVD you want is posted to you. However, you could be in big trouble if you are caught. You could go to prison as a resul t of acting unlawfully, but so far only a tiny amount of people h ave been charged for downloading illegally. The majority of pe ople who download illegally, and use the files for their person al use, will not get in trouble. And that’s why it’s important for people to understand what the long-term consequences are if they don’t want to pay for their musi c, films and TV. Will film and music companies still spend milli ons of pounds every year if they have no chance of making a profit? The answer is plainly “no”.Finally I would like to say that the Internet offers a lot of servi ces for money, but people will always try to get them for free. To summarize my thoughts I’d like to highlight that illegal downloading is both unfair towards producers and dangerous for t hose who practise this kind of activity. You have to decide wh ether to buy or download.Many people download files free from the Internet because__ _______.A. They follow others’ examples to do such things.B. They don’t think they may be charged by the producer.C. They think everything on the Net can be shared by others.D. They think it is legal, convenient and easy.What can be inferred from Paragraph 2?A. Downloading helps movies become more popular.B. Downloading free files is as illegal as stealing.C. Sharing files on the Internet is dangerous.D. Sharing files on the Internet can make a profit.What does the underlined word “highlight” in paragraph 4 mea n?A. StressB. ExplainC. AdmitD. Deny What is the author’s purpose of writing this text?A. He advises readers to download legal files.B. He asks readers to limit the amount of free downloading.C. He wants to make it clear that downloading for free is against the law.D. He tells readers how to avoid being charged for downloadi ng.第二节（共5小题；每小题2分，共10分）根据短文内容，从短文后的七个选项中选出能填入空白处的最佳选项。
20172018学年第二学期期末考试题六年级试题及答案
20172018学年第二学期期末考试题六年级试
题及答案
2017-2018学年第二学期期末考试题六年级试题及答案
为了满足您的要求，我将按照考试题及答案的格式为您呈现试题和答案。
请注意，以下内容是虚构的试题和答案，仅用于示范目的。
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## 语文试题
### 一、填空题（每题2分，共10分）
1. 中国的首都是__北京__。
2. 《红楼梦》是__曹雪芹__创作的。
3. 诗歌《庐山谣》的作者是__杨洪基__。
4. 成语“一鸣惊人”中的“一鸣”意指__第一次发声__。
5. “春江水暖鸭先知”中的“鸭先知”是指__鸭子__。
### 二、选择题（每题4分，共20分）
6. 下面哪个词是正确的？
- A. 龙卷风
- B. 龍捲風
- C. 龘捲風
- D. 龙巻風
答案：A
7. 以下哪位历史人物是中国的开国皇帝？
- A. 孔子
- B. 刘备
- C. 秦始皇
- D. 孟子
答案：C
8. 《三国演义》中的主要故事发生在中国的哪个历史时期？ - A. 春秋时期
- B. 唐朝
- C. 三国时期
- D. 战国时期
答案：C
9. 下面哪个句子使用了比喻修辞？
- A. 月亮像一轮银盘悬挂在夜空。
- B. 太阳升起，照亮大地。
- C. 雨水滴答滴落在窗户上。
- D. 小鸟在树上歌。
2017-2018学年度第二学期期末考试初一数学试题及答案
2017—2018学年度第二学期期末考试初一数学试题一、填空题（每空1分，共22分）1、如果下降5米，记作－5米，那么上升4米记作（）米；如果＋2千克表示增加2千克，那么－3千克表示（）。
2、从80减少到50，减少了（）%；从50增加到80，增加了（）%。
3、某班有60人，缺席6人，出勤率是（）%。
4、如果3a=5b（a、b≠0），那么a：b=（）。
5、一个圆锥的体积12dm3 ,高3dm，底面积是（）。
6、甲、乙两数的比是5:8，甲数是150，乙数是（）。
7、比较大小：－7○－5 1.5○5 20○－2.4 －3.1○3.18、某服装店一件休闲装现价200元，比原价降低了50元，相当于打（）折。
照这样的折扣，原价800元的西装，现价（）元。
9、一个圆柱和一个圆锥的体积相等，底面积也相等，圆柱的高是4米，圆锥的是高（）米。
10、一桶油连桶称7.5千克，用去一半油后，连桶称还重4.5千克。
桶重（）千克，油重（）千克。
11、13只鸡放进4个鸡笼里，至少有（）只鸡要放进同一个笼子里。
12、一个圆柱形的木料，底面半径是3厘米，高是8厘米，这个圆柱体的表面积是（）平方厘米。
如果把它加工成一个最大的圆锥体，削去部分的体积是（）立方厘米。
13、找出规律，填一填。
3，11，20，30，（），53,（）。
二、判断题：对的在括号打√，错的打×。
（每小题1分共5分）1、0是负数。
（）2、书店以50元卖出两套不同的书，一套赚10%，一套亏本10%，书店是不亏也不赚。
（）3、时间一定，路程和速度成正比例。
（）4、栽120棵树，都成活了，成活率是120%。
（）5、圆柱的体积大于与它等底等高的圆锥的体积。
（）三、选择题（每题3分，共15分）1、规定10吨记为0吨，11吨记为＋1吨，则下列说法错误的是（）A、9吨记为－9吨B、12吨记为＋2吨C、6吨记为－4吨D、＋3吨表示重量为13吨2、在a12=13中，a的值是（）A、12B、4C、6D、83、把长1.2米的圆柱形钢材按2:3:7截成三段，表面积比原来增加56平方厘米，这三段圆钢中最长的一段比最短的一段体积多（）A、700立方厘米B、800立方厘米C、840立方厘米D、980立方厘米4、小刚把1000元钱按年利率2.4%存入银行，存期为两年，那么计算到期时她可以从银行取回多少钱（不计利息税），列式正确的是（）。
2017—2018学年度第二学期期末试题_1
2017—2018学年度第二学期期末试题时间：100分钟，满分：120分第I卷第一部分：阅读理解（共两节，满分40分）（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项（A、B、C、D）中，选出最佳选项。
AA HALF - EMPTY BASKETOnce there was a poor farmer and his farm belonged to a r ich man. One day he brought a basket of apples to the rich m an’s house. On the doorsteps, he met two monkeys dressed li ke children. They jumped onto the basket to eat the apples an d threw some on the ground. The farmer politely took off his h at and asked the monkeys to get off. They obeyed(服从) and the farmer went into the house. He asked to see the ri ch man. A servant took him to the room where the rich man w as sitting."I have brought you the basket of apples you asked for," h e said."But why have you brought a half-empty basket?" the rich man asked."I met your children outside, and they stole some of the ap ples."1. Why did the farmer bring apples to the rich man? Because ___________A. he was poorB. he liked the rich manC. his farm belonged to the rich manD. the rich man’s c hildren liked apples2. What did the monkeys do when the farmer was on the door steps?A. They jumped and jumped.B. They played.C. They ran away.D. They ate some of the apples3. The monkeys left the basket because ___________they had thrown apples on the groundB. the farmer had politel y asked them to get offC. they were afraid of the hatD. the farmer was angry with the m4. How did the rich man feel when he saw the basket? He felt ________.A. unhappyB. pleasedC. excitedD. movedBAll over the world people enjoy sports. Sports help to keep pe ople healthy, happy and help them to live longer.Sports change with the seasons. People play different games in winter and summer.Games and sports often grow out of people's work and every day activities. The Arabs use horses or camels in much of thei r everyday life; they use them in their sports, too.Some sports are so interesting that people everywhere go in f or them. Football, for example, has spread around the world. Swimming is popular in all countries near the sea or in those with many rivers.Some sports or games go back thousands of years, like runni ng or jumping. Chinese boxing, for example, has a very long h istory. But basketball and volleyball are rather new. Neither on e is a hundred years old yet. People are inventing new sports or games all the time.People from different countries may not be able to understand each other, but after a game they often become good friends. Sports help to train a person's character. One learns to fight hard but fight fair, to win without pride and to lose with grace.5．According to this passage we know that________. A．people began to play pingpong about one hundred years agoB．about 100 years ago people ran or jumped when they play edC．basketball has a longer history than volleyballD．not all the games have a long history6．The writer didn't tell us in this passage that________. A．basketball was invented inB．sports change with the seasonsC．games and sports often grow out of people's work and ev eryday activitiesD．football is played all over the world7．According to this passage, which of the following is NOT tr ue?A．Sports help to train a person's character.B．People swim only because there are a lot of rivers in their country.C．People from different countries may not be able to underst and each other before a game.D．Sports and games can develop the friendship between people all over the world.8．A lot of people have more free time from their work to enjo y sports because________.A．they like sports very muchB．they want to live longer C．they want to make a lot more friendsD．they don't have to go to work on Saturday or Sunday as b eforeCIf English means endless new words, difficult grammar and s ometimes strange pronunciation, you are wrong. Haven’t you noticed that you have become smarter since you started to le arn a language? According to a new study by a British univers ity, learning a second language can lead to an increase in you r brain power. Researchers found that learning other languag es changes grey matter. This is the area of the brain which pr ocesses information. It is similar to the way that exercise build s muscles.The study also found the effect is greater when the younger p eople learn a second language. A team led by Dr. Andrea Me chelli, from University College London, took a group of Britons who only spoke English. They were compared with a group of “early bilinguals” who had learnt a second language before t he age of five, as well as a number of later learners.Scans showed that grey matter density (密度) in the brain was greater in bilinguals than in people withou t a second language. But the longer a person waited before m astering a new language, the smaller the difference.“Our findings suggest that the structure of the brain is change d by the experience of learning a second language,” said the scientists. It means that the change itself increases the ability to learn. Professor Dylan Vaughan Jones of the of , has rese arched the link between bilingualism and math skills. “Having two languages gives you two windows on the world and make s the brain more flexible (灵活的),” he said. “You are actually going beyond language and h ave a better understanding of different ideas.”The findings were matched in a study of native Italian speake rs who had learned English as a second language between th e ages of two and thirty-four. , writing, and comprehension were all tested. The results showed that the younger they started to learn, the better. “St udying a language means you get an entrance to another worl d,” explained the scientists.9.The main subject talked about in this passage is ________.A. science on learning a second languageB. man’s ability of learning a second languageC. that language can help brain powerD. language learn ing and math study10. The underlined word “bilingual” probably means _______.A. a researcher on language learningB. a person wh o can speak two languagesC. a second language learnerD. an active langu age learner11. We may know from the scientific findings that ________.A. the earlier you start to learn a second language, the higher the grey matter density is.B. there is no difference between a later second language lea rner and one who doesn’t know a second language.C. the experience of learning a second language has bad effe ct on people’s brain.D. the ability of learning a second language is changing all the time.DTomato FestivalStarted in 2005, the Tomato Festival has grown into a local tr adition in . In recent years, the festival has added amusementpark-style rides and a yearly Creature Feature, which screens old h orrible movies. There are also dance competitions, parades a nd pancake breakfast. Third weekend in August.Address: 833 Tinkham Rd, Fountain Park, Wilbraham, Massa chusetts 01095 Phone：(413)599-0010Brat DaysDon't mistake this festival for a day filled with poorly behaved children. Begun in 1953, the gathering is the biggest festival i n the city each year and features more than 50 stands (摊位) selling the sausage, as well as a contest to see who can q uickly eat the most bratwurst (德国式小香肠) in ten minutes. Early August.Address: 17th and New Jersey sts, Kiwanis Park, , Phone: (920)457-9491Hope Watermelon FestivalThe festival dates back to the 1920s, when many trains went t hrough this small town and local watermelon growers would s ell their watermelon to parched travelers. These days, the fest ival sees a Watermelon Queen crowned(加冠的) and sometimes a world-record watermelon grown. There are also more than 300 stands selling arts and crafts from a six-state area, as well as a car show and the Watermelon Olympi cs. Early August.Address: , , Phone: (870) 777-3640Oyster Festival (牡蛎节)Featuring appearances from tall ships and oyster boats, this f estival has regularly drawn 60,000 visitors a year since it beg an in 1978.More than 3,000 volunteers make the festival poss ible each year. Norwalk is less than a two-hour drive from many of New England's larger cities, making it easy to attend the festival during a trip to New York or . Week end after Labor Day.Address: Sea view Ave, Veteran's Park, East , Phone: (800) 866-792512．Which of the following festivals has the longest history?A. Oyster Festival. ?B．Hope Watermelon Festival.C. Brat Days.D．Tomato Festival.13．The underlined word “parched” in the third passage mea ns________.A. tired B．hungry C．thirsty D．excited14．In which of the following activities can you enjoy the fright ening films?A．The Creature Feature B．The Watermelon Olympics C．The Eating-bratwurst Contest D．Dance Competitions 15．If it is August 15 today this year, you might still attend ___ _____.A．Brat Days B．Oyster FestivalC．Hope Watermelon Festival ? D．Tomato Festival七选五（共5小题；每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填人空白处的最佳选项。
2017-2018学年度第二学期期末考试.docx
2017— 2018 学年度第二学期期末考试七年级数学试题第Ⅰ卷（满分 100 分）一、选择题（共 10 小题，每小题 3 分，共 30 分）1. 下面的四个图形中，∠ 1 与∠ 2 是对顶角的是（）2. 1的平方根是（）4A.1B.1 C.1 D.1 216223. 点 P 在 y 轴上，位于原点的下方，距离坐标原点5 个单位长度，则点 P 的坐标是（）A. （ -5 ，0）B.（0， -5 ）C.（ 0， 5）D.（ 5，0）4.x 4x y3 方程组的解为y，其中一个方程是 ，另一个方程可以是（）1A. 3x 4 y 16B.y x 3C.x 3y 8D.2 x y 6 y5. 一个不等式组中两个不等式的解集如图所示，则这个不等式组的解集是（）A.0≤ x ﹤ 1B.0﹤ x ﹤ 1C.0≤ x ≤ 1D.0﹤ x ≤ 16. 我市七年级有 10000 名学生参加某项考试，为了了解这些学生的考试成绩，从中抽取了500 名考生的考试成绩进行统计分析 . 下列说法：①这 10000 名学生的考试成绩是总体；②每个学生的考试成绩是个体；③抽取的500 名考生的考试成绩是总体的一个样本；④样本容量是 10000.正确的有（）个 .A.4B.3C.2D.1 7. 如图，以下说法错误的是（ ）A. 若∠ EAD=∠ B ，则 AD ∥ BCB. 若∠ EAD+∠ D=180°，则 AB ∥CDC.若∠ CAD=∠ BCA ，则 AB ∥ CDD.若∠ D=∠EAD ，则 AB ∥ CD 8. 下列说法正确的是（）A. 若 ab 0 ，则点 P （ a ， b ）表示原点B. 点（ -1 ， a 2 ）在第三象限C. 已知点 A （ 3， -3 ）与点 B （ 3， 3），则直线 AB ∥ x 轴D. 若 ab 0 ，则点 P b）在第一、三象限（ a ，9. 五边形的五个外角的度数之比 1:2:3:4:5 ，那么该五边形的最小的内角的度数是（ ）A.24 °B.36 °C.48°D.60°点，设车速为 x10. 一辆匀速行驶的汽车在11:20 距离A 地 ，到达A 地时时间已经过了 12（x），50kmkm/h则车速应满足的条件是（）A.2 x50B.2x 50C.50 3 D.50 ≥ 333x 2x2二、填空题（共 6 小题，每小题 3 分，共 18 分）11. x 的 2 倍与 5 的和不小于 3，用不等式表示为 .12. 2x 3y 5 y 的值为 .已知 x ， y 满足方程组4 y，则 xx 413. 一个长方形在平面直角坐标系中三个顶点的坐标为（ -1 ， -1 ），（ -1 ， 3），（ -3 ， -1 ），则第四个顶点的坐标为 .14. 如果 x 2 2 x ，那么 x 的取值范围是 .15. 某校学生来自甲，乙，丙三个地区，其人数比为2:3:7 ，如图所示的扇形图表示上述分布情况，其中甲所对应扇形的圆心角是° .16. 观察算式：3， 238 ， 33 27 ， 4364 ， 53 125 ， 63 216 ， 73343 ， 83 512 ， 93 729 ，1 1103 1000 ， 2038000 ， 303 27000 ， 403 64000 ， 503125000 .319683 ， 3110592 .三、解答题（共 5 题，共 52 分）17. （本题满分 10 分，每小题 5 分）解下列方程组或不等式组 .x y 35x2 4 x 1（ 2）（ 1）8 y141 x 1 7 3 x 3x2 218. （本题满分 10 分）某校开设了足球、篮球、乒乓球和羽毛球四个课外体育活动小组，有512 名学生参加，每人只参加一个组.为了了解学生参与的情况，对参加的人员分布情况进行抽样调查，并绘制了下面两幅不完整的统计图，请根据图中提供信息，解答下面问题：（ 1）此次共抽查了多少名同学？（ 2）将条形统计图补充完整；在扇形统计图中的括号中填写百分数；（ 3）请估计该校参加篮球运动小组的学生人数19.（本题满分 10 分）如图 ,BE 平分∠ ABD,DE平分∠ BDC,且 BE⊥ ED,E 为垂足 , 求证 :AB ∥ CD.20.（本题满分 10 分）如图，把△ ABC向上平移 4 个单位长度，再向右平移 3 个单位长度得A1B1C1,其中A（-1，2），B（-3，-2），C（ 4， -2 ）.（1）在图上画出A1B1C1；（2）写出点A1，B1，C1的坐标；（3）请直接写出线段 AC在两次平移中扫过的总面积 .21.（本分 12 分）小要一种价 5 元的本，学校旁有甲、乙两个文具店正在做促活，甲商店的惠条件是：一次性超10 本，超的部分按价的70%售；乙商店的惠条件是：活期所有文具按价的85%售；(1)小要20 本本，他若甲商店，需花元，他若乙商店，需花元.(2)若小有120 元，他最多可多少本本?(3)分析小如果要 x 本本，到哪个商店省?第Ⅱ卷（满分50 分）四、填空题（共 4 小题，每小题 4 分，共 16 分）22.了解某校九年女生 1 分仰卧起坐的次数 , 从中随机抽了 50 名女生参加 , 并制成数分布直方（如）. 如果被抽的女生中有90%的女生 1 分仰卧起坐的次数大于等于30 且小于 50，那么 1分仰卧起坐的次数在40～45 的数是 ______.23.如 , 点 A,B 定点 , 直 l ∥AB， P 是直 l 上一点。
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2017—2018学年度第二学期期末考试试卷高二理科数学（时量：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，在每个小题给出的四个选项中，只有一项是符合题目要求的．1．已知i 为虚数单位，则(1)i i -=（ ） A ．1i -B ．1i -+C ．1i --D ．1i +2．若*n N ∈，且n ≤19，则（20-n ）(21-n )……(100-n )等于（ ）A ．80100n A -B ．n n A --20100C ．81100n A -D ．8120n A -3．在一次试验中事件A 出现的概率为p ，则在n 次独立重复试验中A 出现k 次的概率（ ）A. 1－k pB. ()k n kp p --1C. 1－()kp -1 D. ()kn k k n pp C --14．在相关分析中，对相关系数r ，下列说法正确的是（ ） A.r 越大，线性相关程度越强 B.r 越小，线性相关程度越强C.r 越大，线性相关程度越弱，r 越小，线性相关程度越强D.1r ≤且r 越接近1，线性相关程度越强，r 越接近0，线性相关程度越弱 5 ．某科研机构为了研究中年人秃发与心脏病是否有关，随机调查了一些中年人的情况，具体数据如下表：根据表中数据得到22775(204505300)25750320455K ⨯⨯-⨯=⨯⨯⨯≈15.968，因为2K ≥10.828,则断定秃发与心脏病有关系,那么这种判断出错的可能性为（ ） 附表：A ．0.1B ．0.05C ．0.01D ．0.0016. 五位同学去听同时进行．．．．的4个课外知识讲座，每个同学可自由选择，则不同的选择种数是（ ） A ．54B ．5×4×3×2C ．45D ．5×47．用反证法证明命题：若整系数一元二次方程有有理根，那么中至少有一个是偶数时，下列假设中正确的是（ ）A ．假设都是偶数B ．假设都不是偶数C ．假设至多有一个是偶数D ．假设至多有两个是偶数 8．曲线32153y x x =-+在1x =处的切线的倾斜角是 （ ） A.6π B. 3π C. 4πD. 34π9．设袋中有80个红球，20个白球．若从袋中任取10个球，则其中恰好有6个红球的概率为（ ）A ．10100610480C C C ⋅B ．10100420680C C C ⋅ C ．10100620480C C C ⋅ D ．10100410680C C C ⋅ 10.四名师范毕业生全部分配到3所中学任教，每校至少有1名，则不同的分配方案有（ ）A. 18种B. 36种C. 54种D. 72种11.随机变量ξ服从正态分布(0,1)N ，则下列结论不正确的是（ ）A. (||)(||)(||)(0)P a P a P a a ξξξ<=<+=> B ．(||)2()1(0)P a P a a ξξ<=<-> C ．(||)12()(0)P a P a a ξξ<=-<> D ．(||)1(||)(0)P a P a a ξξ<=->>12.函数()2ln(3)8f x x x =+，则的值为（ ）A ．-20B ．-10C ．10D ．20二、填空题：本大题共4小题，每小题5分，共20分.20(0)ax bx c a ++=≠a b c，，a b c ，，a b c ，，a b c ，，a b c ，，0(12)(1)limx f x f x∆→-∆-∆13．设随机变量X 等可能取1，2，3，...，这个值，如果(4)0.4P X ≤=，则等于 .14．定理:“平行于同一直线的两直线平行”,可用符号语言表示为:“∵a b ∥，b c ∥，∴a c ∥”,这个推理称为 . (填“归纳推理”、“类比推理”、“演绎推理”之一) 15．220(3)10,x k dx k +==⎰则 ．16．已知)(x g 是各项系数均为整数的多项式，2()21f x x x =-+，且满足432(())24131116f g x x x x x =++++，则)(x g 的各项系数之和为 .三、解答题（本大题共6小题，共70分，解答应写出文字说明、证明过程或演算步骤） 17. （本小题满分10分）现有2名男生和3名女生．(Ⅰ)若其中2名男生必须相邻排在一起，则这5人站成一排，共有多少种不同的排法? (Ⅱ)若男生甲既不能站排头，也不能站排尾, 这5人站成一排，共有多少种不同的排法?18. (本小题满分12分)(Ⅰ) 比较下列两组实数的大小：① 2－1与2－3； ② 2－3与6－5； (Ⅱ) 类比以上结论，写出一个更具一般意义的结论，并给出证明.n n n19．(本小题满分12分)在二项式的展开式中， (Ⅰ)写出其中含的项；(Ⅱ)如果第项和第项的二项式系数相等，求的值．20. (本小题满分12分)如图，直三棱柱ABC-A 1B 1C 1中， AB ＝AC ＝AA 1，AB ⊥AC ，M 是CC 1的中点，N 是BC 的中点，点P 在线段A 1B 1上运动． （Ⅰ）求证：PN ⊥AM ；（Ⅱ）试确定点P 的位置，使直线PN 和平面ABC 所成的角最大．21.（本小题满分12分）设b 和c 分别是先后抛掷一枚骰子得到的点数，用随机变量ξ表示方程2x bx c ++=实根的个数（重根按一个计）．(Ⅰ)求方程20x bx c ++=有实根的概率；1032⎪⎪⎭⎫ ⎝⎛-x x 2x r 32+r r M NC 1 B 1(Ⅱ)求ξ的分布列和数学期望；(Ⅲ)求在先后两次出现的点数中有5的条件下，方程20x bx c ++=有实根的概率．22．（本小题满分12分） 已知函数()1ax x ϕ=+，a 为正常数． (Ⅰ) 若()ln ()f x x x ϕ=+，且92a =，求函数()f x 的单调增区间； (Ⅱ) 若()|ln |()g x x x ϕ=+，且对任意12,(0,2]x x ∈，12x x ≠，都有2121()()1g x g x x x -<--，求a 的的取值范围．2017—2018学年度第二学期期末考试试卷高二数学(理)参考答案一、选择题：本大题共12小题，每小题5分，共60分.1．D 2．C 3．D 4． D 5． D 6． C 7．B 8．D 9．B 10．B 11．C 12．A 二、填空题：本大题共4小题，每小题5分，共20分.13．10 14．演绎推理 15．1 16．5 三、解答题：本大题共6小题，共70分. 17.解：(1) 24!48⨯= ………………………5分(2) 34!72⨯= ………………………10分18. (本小题满分12分)(Ⅰ) 解法一：① (2+3)2－(2+1)2=26－4＞0. 故2+3＞2+1，即2－1＞2－3.② (2+5)2－(6+3)2=45－218=220－218＞0. 故2+5＞6+ 3，即2－3＞6－5. 解法二：分子有理化，略………………………6分(Ⅱ) 一般结论：若n 是正整数，则1+n －n ＞3+n －2+n .或：函数()f x =(0,)+∞上单调递减；或：若正数,,,a b c d 满足：,a b a c >>，且a d b c +=+，则<证明从略. ………………………12分19．(本小题满分12分) 解：（1）= 令10-k=2得k=6 ∴含的项是==13440x 2．…………6分（2）∵．∴3r-1=r+1或 r-1+r+1=10 ∴r=1或r=舍去． ∴r=1 ． …………12分20. (本小题满分12分) 方法一：几何法(Ⅰ) 取AC 的中点Q ，连结A 1Q ，易知AM ⊥A 1Q ，又PN 在平面A 1C 内的射影为A 1Q ，所以AM ⊥PN. ………………6分(Ⅱ) 作PD ⊥AB 于D ，连结DN ，则PND ∠为直线PN 和平面ABC 所成的角。
易知当ND 最短即ND ⊥AB 时，tan PDPND ND∠=最大，从而PND ∠最大，此时D 为AB 的中点，P 为A 1B 1的中点。
………………………12分方法二：向量法，略。
21.（本小题满分12分）【解】（I ）基本事件总数为6636⨯=，若使方程有实根，则240b c ∆=-≥，即b ≥当1c =时，2,3,4,5,6b =； 当2c =时，3,4,5,6b =； 当3c =时，4,5,6b =；kKk xC T -+=10101kx ⎪⎪⎭⎫ ⎝⎛-32k k k k xC 3410102)1(--342x 63410610662)1(∙--x C 261062x C 1101310+-=r r C C 25M NC 1 B 1当4c =时，4,5,6b =； 当5c =时，5,6b =； 当6c =时，5,6b =,目标事件个数为54332219,+++++= 因此方程20x bx c ++= 有实根的概率为19.36…………………4分 (II)由题意知，0,1,2ξ=，则17(0)36P ξ==，21(1),3618P ξ===17(2)36P ξ==， 故ξ的分布列为ξ0 1 2P1736118 1736 ξ的数学期望17117012 1.361836E ξ=⨯+⨯+⨯=…………………8分(III)记“先后两次出现的点数中有5”为事件M ，“方程20ax bx c ++=有实根” 为事件N ，则11()36P M =，7()36P MN =，()7()()11P MN P N M P M ==．…………12分22、（本小题满分12分解：（1） 2221(2)1'()(1)(1)a x a x f x x x x x +-+=-=++，…………………………… 2分∵92a =，令'()0f x >，得2x >，或12x <， ……………………… …3分∴函数()f x 的单调增区间为1(0,)2， (2,)+∞． ……………………… 4分（2）∵2121()()1g x g x x x -<--，∴2121()()10g x g x x x -+<-，∴221121()[()]0g x x g x x x x +-+<-，…………………………… ………………… 5分设()()h x g x x =+，依题意，()h x 在(]0,2上是减函数． 当12x ≤≤时， ()ln 1a h x x x x =+++，21'()1(1)a h x x x =-++， 令'()0h x ≤，得：222(1)1(1)33x a x x x x x+≥++=+++对[1,2]x ∈恒成立， 设21()33m x x x x =+++，则21'()23m x x x=+-， ∵12x ≤≤，∴21'()230m x x x=+->， ∴()m x 在[1,2]上是增函数，则当2x =时，()m x 有最大值为272， ∴272a ≥． …………………………… ………………………………………… 9分 当01x <<时， ()ln 1a h x x x x =-+++，21'()1(1)a h x x x =--++， 令'()0h x ≤，得： 222(1)1(1)1x a x x x x x+≥-++=+--，设21()1t x x x x =+--，则21'()210t x x x=++>，∴()t x 在(0,1)上是增函数，∴()(1)0t x t <=，∴0a ≥，综上所述，272a ≥…………………………………………………12分。