湖北省咸宁四校2013届高三12月联考英语试题

高中英语真题:2013届高三第三次段考（12月）英语试题时间：120分钟总分：150分第Ⅰ卷（选择题）第一部分英语知识运用（共两节，满分45分）第一节单项填空（共15小题；每小题1 分，满分15分）从A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

1．---What about ____ passage?---It's too difficult ____ passage for me．A．a, a B．a, the C．the, a D．the, the 2．Developing science and technology must ____ people rather than harm them．A．support B．benefit C．consider D．serv e3．---You shouldn't have said that．Look! She is getting _____．--- But I meant no harm．A．unfair B．unconcerned C．unmoved D．uneasy4．---What did you do last weekend, Jack?--- Well, I ____ to see a film, but in the end I stayed home doing n othing．A．was going B．has gone C．went D．h ad gone5．--- How was your family's party?--- We didn't plan like that, but it ____ very well．A．tried out B．went out C．worked out D ．carried out6．_____ he thought he was helping us with the work, he was a ctually in the way．A．Since B．When C．Because D．If 7．Tom is a hard-working student．In fact, you cannot find anyone in the class __ __．A．diligent B．more diligent C．the most diligent D．the more diligent8．The weather in London is so changeable that people always take their umbrellas with them ____ rain．A．for fear of B．in hope ofC．in spite of D．because of9．--- I think George doesn't really care for TV plays．--- Right, ____ he still watches the program．A．and B．so C．but D．for10．When designing your house, you'd better ____ land for a g arden．A．develop B．save C．spare D．share 11．Jenny worked hard before the final examination, and ____．She got an A．A．took off B．showed off C．put off D．paid off12．They gave me so much help, without ____ I couldn't have s ucceeded last year．A．them B．which C．it D．that 13．The girl seriously injured in the Wenchuan earthquake was so well taken care of in the hospital that she could ____ get out of bed without help．A．nearly B．hardly C．merely D．barely 14．As a reporter, you should first decide what events ____ bef ore you make some interviews．A．reported B．to be reported C．reporting D ．to report15．Mrs Green was so pleased ____ her daughter won the first place in the singing competition．A．as B．that C．when D．if 16．If a book is in French, ____ will be a challenge for me．A．which B．it C．what D．as 17．Holiday shopping ___be a tiring experience．There are so many places to visit and choices to make．A．can B．may C．shall D．will 18．I can hardly remember any occasions ____ I get caught in a traffic jam in our town．A．which B．that C．where D．when 19．---Jack can't concentrate on his study recently．--- Yes, that might ____ why he did so badly in the last test． A．answer for B．apply for C．call for D．account for20．--- What are you busy with?---The exhibition ____ in the city next week．A．held B．will be held C．to be held D．b eing held二．完形填空：（每题1.5分，共30分）第二节完形填空 (共20小题；每小题1.5分，满分30分)阅读下面短文，从短文后各题所给的四个选项 (A、B、C和D) 中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

绝密★启用前2013年普通高等学校招生全国统一考试（湖北卷）英语本试题卷共16页，81题。

全卷满分150分。

考试用时120分钟。

★祝考试顺利★注意事项：1. 答卷前，考生务必将自己的姓名、准考证号填写在试题卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

用统一提供的2B铅笔将答题卡上试卷类型A后的方框涂黑。

2. 选择题的作答：每小题选出答案后，用统一提供的2B铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其它答案标号。

答在试题卷、草稿纸上无效。

3. 完成句子和短文写作题的作答：用统一提供的签字笔直接答在答题卡上对应的答题区域内。

答在试题卷、草稿纸上无效。

4. 考生必须保持答题卡的整洁。

考试结束后，请将本试题卷和答题卡一并上交。

第一部分：听力（共两节，满分30分）做题时，先将答案划在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分)听下面5段对话。

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

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A. £ 19.15．B. £ 9.15．C. £ 9.18．答案：B1. Why doesn’t John go to school today?A. It’s the weekend.B. He’s too tired for school.C. His school is closed down.2. What will the man do tomorrow morning?A. Give Frank a bath.B. Cook Frank a meal.C. Take Frank to a vet.3. What is the male speaker?A. A student.B. A president.C. A professor.4. What does the man mean?A. The door is unlocked.B. He is not the one to blame.C. Somebody has just left the lab.5. On which floor is the woman’s apartment?A. The second.B. The fourth.C. The sixth.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。

湖北省咸宁市四校2013届高三数学12月联考试题文（扫描版）新人教A版高三年级数学（文科）参考答案1.D2.B3.D4.B5.C6.B 解答：据题意知()()1033110f a b f '=⎧=⎧⎪⇒⎨⎨=-=⎩⎪⎩或411a b =-⎧⎨=⎩, 但当33a b =⎧⎨=-⎩时()()2310f x x '=-≥,函数在1=x 处不存在极值.故选B.7.C 解答：两向量垂直且模都为21m +，∴)1(212m S ABC +=∆ 8.B 解答：方程083492sin sin =-+⋅+⋅a a a x x有解，等价于求134928sin sin +⋅+⋅=xx a 的值域 ∵]3,31[3sin ∈x∴13492sin sin +⋅+⋅x x ]31,923[∈则a 的取值范围为2372318≤≤a 9.A10.B 11.4 12.213.{}210><<x x x 或14.32π 15.2012402316.]16,4[解答：在函数)2(xf 中，定义域为[1，2]即,422,21≤≤≤≤xx ∴)(x f 的定义域为[2，4] 则164,4log 22≤≤≤≤x x ∴)(log 2x f 的定义域]16,4[ 17.1-解答：设)0)(2,(0000>+x x x x P ，则点P 到直线x y =和y 轴的距离分别为 00022|)2(|||x x x x PA =+-=，0||x PB =.∵O 、A 、P 、B 四点共圆，所以43ππ=∠-=∠AOB APB . ∴⋅=143cos200-=⋅⋅πx x 18.解答：(1)由图象知,34,2π==T A 则,342πωπ⨯=∴23=ω……（2分）又0)4sin(2])6(23sin[2)6(=+-=+-⨯=-ϕπϕππf ∴0)4sin(=+-ϕπ，∵20πϕ<<，444ππϕπ<-<-∴404πϕπϕ=⇒=-∴)(x f 的解析式为)423sin(2)(π+=x x f . ………………（5分）(2)由(1)可得]4)12(23sin[2)12(πππ+-=-x x f ),823sin(2π+=x ∴2)43cos(14)]12([)(2ππ+-⨯=-=x x f x g ＝),43cos(22π+-x …（8分）∵],3,6[ππ-∈x ∴45434πππ≤+≤-x ， ∴当ππ=+43x ，即4π=x 时，4)(max =x g …………………（12分）19.解答:(1)由题意:13+=-t kx ，将1,0==x t 代入得2=k ∴123+-=t x , 当年生产x (万件)时，年生产成本3)123(32332++-⋅=+=t x , 当销售x (万件)时，年销售收入150=％t t 21]3)123(32[+++-⋅⋅, 由题意，生产x 万件产品正好销完∴年利润=年销售收入-年生产成本-促销费即)0()1(235982≥+++-=t t t t y .………（6分） (2)∵4216250)13221(50=-≤+++-=t t y (万件) 当且仅当13221+=+t t 即7=t 时，42max =y , ∴当促销费定在7万元时，利润最大. ………（12分）20.解答：(1)取C A 1的中点E 点，取AC 的中点F ，连,DE EF BF ,.由此知:DE ∥BF ，又∵面⊥BAC 面C C AA 11且相交于AC ，易知AC BF ⊥， ∴⊥BF 面C C AA 11 ∴直线DE ⊥面C C AA 11又DE 在面C DA 1内，且面C DA 1∩面C C AA 11＝C A 1 ∴面⊥C DA 1面C C AA 11；………6分(2)延长D A 1与直线AB 相交于G ，易知⊥CB 面B B AA 11, 过B 作G A BH 1⊥于点H ，连CH 知:CH G A ⊥1,由此知CBH ∠二面角C D A A --1的平面角； ………9分 设;,21a BC AB b AA === 在AG A Rt 1∆中，易知BG AB =.A 1C 1B 1ACBDHEFG在DBG Rt ∆中,DGBGBD BH ⋅=22ba ab +⋅=，在CHB Rt ∆中，=∠CHB tan =BHBCbb a 22+， 据题意有：360tan 022==+b b a ,解得:22=ab， 所以=ABAA 12. ………13分21. 解：（Ⅰ）c bx ax x x f +++=23)(，b ax x x f ++='23)(2，由题意，知2=m ，,21)1(=+++=c b a f 023)1(=++='b a f ，即.4,32+=--=a c a b ………… 2分).321)(1(3)32(23)(2ax x a ax x x f ++-=+-+=' ……………3分 ① 当3-=a 时，0)1(3)(2≥-='x x f ，函数)(x f 在区间),(+∞-∞上单调增加， 不存在单调减区间； ……………………5分 ② 当3->a 时，121<--a，有∴当3->a 时，函数)(x f 存在单调减区间，为;1,321⎥⎦⎤⎢⎣⎡--a ……………6分 ③ 当3-<a 时， 121>--a，有∴当3-<a 时，函数)(x f 存在单调减区间，为;321,1⎥⎦⎤⎢⎣⎡--a …………8分 （Ⅱ）由（Ⅰ）知：若1=x 不是函数)(x f 的极值点，则3-=a ，,1,3==c b .2)1(133)(323+-=++-=x x x x x f …………………10分设点),(00y x P 是函数)(x f 的图像上任意一点，则2)1()(3000+-==x x f y ，点),(00y x P 关于点)2,1(M 的对称点为)4,2(00y x Q --，∵,4222)1(2)12()2(0030300y y x x x f -=+-=+--=+--=-（或 002030020300200302000203004)133(43331363121261281)2(3)2(3)2()2(y x x x x x x x x x x x x x x x x f -=++--=+-+-=+-+-+--+-=+-+---=-Θ）∴点)4,2(00y x Q --在函数)(x f 的图像上.由点P 的任意性知函数)(x f 的图像关于点M 对称. …………………14分22. （Ⅰ）∵44)(+-=x x x f 2)2(-=x (4≥x )，∴)(1x f-2)2(+=x (0≥x )， ……………………………………（2分）∴)(11n n a fa -+=2)2(+=n a ，即21=-+n n a a （∈n N *）． ……………………………（4分） ∴数列{}na 是以11=a 为首项，公差为2的等差数列．………（6分）（Ⅱ）由（Ⅰ）得：12)1(21-=-+=n n a n ，即2)12(-=n a n （∈n N *）． ……………………………（8分）11=b ，当2≥n 时，1131--⎪⎭⎫⎝⎛=-n n n b b ，∴+-+-+=)()(23121b b b b b b n …)(1--+n n b b+⎪⎭⎫ ⎝⎛++=231311 (1)31-⎪⎭⎫⎝⎛+n⎪⎭⎫ ⎝⎛-=n 31123因而⎪⎭⎫⎝⎛-=n n b 31123，∈n N *． ……………………………（10分） n n n b a c ⋅=⎪⎭⎫⎝⎛-⋅-=n n 31123)12(，∴n S ++=21c c …n c +]531[23+++=…+++--+32353331()12(n …)312n n -+ 令=n T +++32353331…nn 312-+ ① 则=n T 31+++432353331…1312332+-+-+n n n n ② ①-②，得=n T 32+++323131(231…1312)31+--+n n n 11312)311(3131+----+=n n n ∴n n n T 311+-=．又+++531 (2))12(n n =-+．∴)311(232n n n n S ++-=． ……………………………（14分）。

Dear friends， Do you want to live in a beautiful world?
Living a low-carbon style of life is playing a more and more important role in energy saving and environmental protection. To fulfill it, we should bear the following in mind. First, it's important to turn off taps and lights and recycle everything recyclable in our daily life. What's more, while sticking to the habit of setting the temperature of your air conditioner at above 26℃ in summer and eating fruits and vegetables in seasons, we should also climb stairs under the fifth floor instead of taking lifts. Let's all take action now and contribute to the prosperity of our mother－the earth.
Thank you!
This passage is about a little hero. Being an orphan, he lived a hard life in early years. He helped the captain and his soldiers but lost his er listening to “A Little Hero”, I was moved and encouraged .The little hero was homeless. He had neither parents nor brothers nor sisters. He lived a poor and hard life by working for another family in his early years. He didn’t study at school, but he loved his country. Compared with the little hero, I had a happy childhood. I have a happy family with many good books,