四川省绵阳南山实验高中2015届高三一诊模拟考试试题 英语 Word含答案

绵阳市高中2015级第一次诊断性考试英语第I卷（选择题，共90分）第一部分：英语知识运用（共两节，满分40分）第一节：语法和词汇知识（共10小题；每小题1分，满分10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. ——Mum, can you drive faster to the airport?——Honey, ______, for we still have one and a half hour.A. take it easyB. take your timeC. forget itD. with pleasure2. The School Art Festival has set up a stage ______students can show their talents.A. whichB. whereC. thatD. when3. E-Commerce ______ mislead customers at times even though it's more convenient and faster in general.A. shallB. shouldC. can D must4. Hello, Tom. What a coincidence! I ______ about you. And here you are.A. was just thinkingB. just thoughtC. have just thoughtD. would just think5. She had to work deep into the night, ______she couldn't have spread the messages to all the relevant people successfully.A. whileB. butC. otherwiseD. so6. US house prices has risen by 12.4% over the 12 months to the end of July, completely ______his plan to buy another apartment.A. ruinedB. ruiningC. to ruinD. ruins7. ——How many of you made it to the top of the mountain in the end?——______. It was really tough.A. No oneB. NeitherC. NoneD. Nobody8. ______you are always optimistic and self-confident, I can't wait to make friends with you.A. ThoughB. SinceC. WhileD. So9. With a lot of work ______, she weren't allowed to leave her office.A. doB. done .C. to be doneD. to do10. Diligence is ______ it takes for the post-90's generation to win competitions.A. whatB. whereC. whichD. when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。

“一诊”模拟考试英语答案一、单选（10分）1-5 BDADD 6-10 CCCDB二、完型填空（30分）11~15 DBCBA 16~20 CDABC 21~25 CACBD26~30 AAABD三、阅读理解（40分）A篇：ABAC B篇：CDBD C篇：BADB D篇：CCAA E篇：BDDC四、补全对话（10分）EDGBA五、任务型阅读（10分）56. A dog called Mole.57. He lost his footing while looking for shade.58. He was very dehydrated and hardly conscious.59. Between four and six days.60. He will recover completely.六、短文改错（15分）Dear manager,I’m one of your customer. The day before yesterday I bought a walkman in your customersshop. Before I left, I do check it carefully and everything was all right. When I gotdidhome, therefore, I found a fault with it. The problem is what the “Play”doesn’t however thatwork at all. Probable it’s not your fault and so is mine. Anyhow, I can’t solve the Probably neither/norproblem in person.You see, a walkman is of great useful for me to learn English and I cannot waitusefor too long before this problem is solved. Hopefully you will deal with the walkman without delay, when you accept my letter.receiveHoping to hear of you in the earliest possible time!fromYour sincerely,Li Hua七、作文（35分）Fast foodDear friends,Nowadays, fast food is becoming more and more popular among children and teenagers. I think there are several reasons for its popularity.First, it’s very convenient and can save a lot of time. You can go into a fast restaurant to order your food and it is ready in no time. Besides, you can take it away or eat there. What’s more, it offers excellent service and tasty food.However, fast food is not good for people’s health, especially children.There is too much fat in the food and you can’t get enough fresh vegetables.Also the food is very expensive, which may cost you much money.We are what we eat. Therefore, it’s very important for us to form he althy eating habits and eat fast food as little as possible. It’s only a ch oice when you are really in a hurry.That’s all. Thank you! (132词)“一诊”模式考试英语答案第1页共 1 页。

绝密★启用前2015年普通高等学校招生全国统一考试英语本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

考生作答时，将答案答在答题卡上，在本试卷上答题无效。

考试结束后，将本试卷和答题卡一并交回。

注意事项：1．答题前，考生务必先将自己的姓名、准考证号填写在答题卡上，认真核对条形码上的姓名、准考证号，并将条形码粘贴在答题卡的指定位置上。

2．选择题答案使用2B铅笔填涂,如需改动，用橡皮擦干净后，再选涂其他答案的标号；非选择题答案使用0.5毫米的黑色中性（签字）笔或碳素笔书写，字体工整、笔迹清楚。

3．请按照题号在各题的答题区域(黑色线框)内作答，超出答题区域书写的答案无效。

4．保持卡面清洁，不折叠，不破损。

第I卷第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。

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. ￡19.15B. ￡9.18C.￡9.15答案是C。

1. What is the weather like today?A. Cloudy.B. Rainy.C. Sunny.2. How does the woman’s sister go to university?A. On foot.B. By subway.C. By bus.3. Where are the speakers?A. On a plane.B. On a bus.C. In a car.4. What are the two speakers talking about in general?A. A pool.B. A book.C. A holiday.5. What does the man mean？A. He is too busy to have breakfast.B. He doesn’t like to eat breakfast.C. He disagrees with the woman.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。

绵阳一诊-2015级-2017年11月一诊--英语----参考答案绵阳一诊-2015级-2017年11月一诊--英语----参考答案绵阳市高中2015级第一次诊断性考试参考答案英语第一部分听力（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）1—5 CABCB第二节（共15小题；每小题1.5分，满分22.5分）6—10 CACCB 11—15 BCABC 16—20 ABCAB第二部分阅读理解（共两节, 满分40分）第一节 (共15小题；每小题2分, 满分30分)21—25 ACBDD 26—30 CDDBC31—35 ABADA第二节(共5小题；每小题2分, 满分10分)36—40 ADGFE第三部分英语知识运用（共两节, 满分45分）第一节完型填空（共20小题；每小题1.5分，满分30分）41—45 DBCBC 46—50 BCABC 51—55 BDABD56—60 ABBCA第二节（共10小题；每小题1.5分，满分15分）61. to take 62. jobs63. greater64. themselves 65. has come66. using 67. mainly68.by/through69. the70. that/which第四部分写作（共两节，满分35分）第一节短文改错（共10小题；每小题1分，满分10分）We are required to collect our smart phones and keep it in the teacher’s d u r i n g t h ethemweekdays. In fact the most of us obey this regulation, but some still play various t r i c k高三英语一诊参考答案第3页tricksagainst it. I’m among those. Once, I hand in a waste phone. Mr. Li, our head t e a c h e r,handedseemed∧ignore all that. So I felt very luckily to have an extra phone with me. And to luckyBut/Yetg ood times don’t last long. “Can I use your phone as a while? I forgot to take mine b yforchance.”Mr. Li said, pick out my waste phone and dialing. You can see how e m b a r r a s s i n gpickingembarrassedI was at the scene!第二节书面表达（满分25分）Dear Mike,I am sorry to bother you, but I have to ask a favor of you in the hope that you will be so kind to help me.Recently I am writing a paper about the culture and customs of native Americans, but I am stuck as not many English reference books are available in China. Therefore, would you please buy some for me in America if it is convenient for you? Two or three books are just enough, and I would appreciate it if you could send them to me before Nov. 9.As to the expense of books and postage, I will transfer them to your account via online banks. Looking forward to your early reply.Yours,Li Hua一、各档次评分参考标准档次给分范围语言及要点要求第五档21～25 要点齐全，语言基本无误，行文连贯，表达清楚第四档16～20 包含绝大部分要点，语言有少量错误，行文基本连贯，表达基本清楚第三档11～15 包含多数要点，语言有一些错误，尚能表达高三英语一诊参考答案第4页第二档6～10 只涉及少数要点，语言错误很多，影响表达第一档0～5 只能写出与要求内容有关的一些单词二、扣分参考依据1、其表达未能达成正确句意的，不给分, 如：写出了主语或谓语等关键词，但未能达成符合要点要求、意义正确的句子。

绵阳市高二级第一次诊断性考试参考答案英语第一部分听力（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）1—5 CABCB第二节（共15小题；每小题1.5分，满分22.5分）6—10 CACCB 11—15 BCABC 16—20 ABCAB第二部分阅读理解（共两节, 满分40分）第一节 (共15小题；每小题2分, 满分30分)21—25 ACBDD26—30 CDDBC31—35 ABADA第二节(共5小题；每小题2分, 满分10分)36—40 ADGFE第三部分英语知识运用（共两节, 满分45分）第一节完型填空（共20小题；每小题1.5分，满分30分）41—45 DBCBC 46—50 BCABC51—55 BDABD56—60 ABBCA第二节（共10小题；每小题1.5分，满分15分）61. to take62. jobs63. greater64. themselves 65. has come66. using67. mainly68.by/through69. the70. that/which第四部分写作（共两节，满分35分）第一节短文改错（共10小题；每小题1分，满分10分）We are required to collect o ur smart phones and keep it in the teacher’s during t h ethemweekdays. In fact the most of us obey this regulation, bu t some still play various tricktricksagainst it. I’m among those. Once, I hand in a waste phone. Mr. Li, our head teacher,handedseemed∧ignore all that. So I felt very luckily to have an extra phone with me. And to luckyBut/Yetgood times don’t last long. “Can I use your phone as a while? I forgot to take mine byforchance.” Mr. Li said, pick out my waste phone and dialing. You can see how e m b a r r a s s i n gpickingembarrassedI was at the scene!第二节书面表达（满分25分）Dear Mike,I am sorry to bother you, but I have to ask a favor of you in the hope that you will be so kind to help me.Recently I am writing a paper about the culture and customs of native Americans, but I am stuck as not many English reference books are available in China. Therefore, would you please buy some for me in America if it is convenient for you? Two or three books are just enough, and I would appreciate it if you could send them to me before Nov. 9.As to the expense of books and postage, I will transfer them to your account via online banks. Looking forward to your early reply.Yours,Li Hua一、各档次评分参考标准只涉及少数要点，语言错误很多，影响表达二、扣分参考依据1、其表达未能达成正确句意的，不给分, 如：写出了主语或谓语等关键词，但未能达成符合要点要求、意义正确的句子。

四川省绵阳市高中高三第一次诊断性考试英语试卷（word版）本试卷分为第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

满分150分，考试时间120分钟。

注意事项：1．答题前，考生务必将自己的学校、班级、姓名、考号用0 5毫米的黑色签字笔填写在答题卡上，并检查条形码粘贴是否正确。

2．选择题（1-65）使用2B铅笔填涂在答题卡对应题目标号的位置上，非选择题用0．5毫米黑色签字笔书写在答题卡的对应题框内，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

3．考试结束以后，将答题卡收回。

第Ⅰ卷（选择题，共100分）第一部分：英语知识运用（共两节，满分50分）第一节：【2012届四川省绵阳市高三第一次诊断性考试】语法和词汇知识（共20小题；每小题1分，满分20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．—I enjoyed myself so much at your birthday party last Sunday.—!A．Oh, that’s kind of you B．CongratulationsC．It’s a pleasure D．Oh, I’m glad to hear that2．—Is Johnson in the office?—I didn’t see there.A．anyone B．each one C．everyone D．someone3．I’d appreciate if you could call back tomorrow and tell us your final decision.A．it B．you C．them D．that4．There are to show that a new, different village is coming out of its dark past.A．marks B．signals C．signs D．symbols5．Nowadays, a large number of college students home and abroad some part time jobs in their spare time.A．done B．do C．did D．does6．People in western countries celebrate ____ Christmas, while people in China observe ____ Spring Festival．A．the; the B．不填; the C．the; 不填 D．不填; 不填7．Because of the reform, the economic situation of China has ____ to be much better than it was 30 years ago．A．turned up B．turned down C．turned out D．turned in8．—I was on the highway when their car went past followed by a police car．—They ____ at least 150 kilometers an hour．A．should have been driving B．must have been drivingC．could have driven D．would have driven9．____ I accept that he is not perfect, 1 do actually like the person．A．While B．Since C．Before D．Unless 10．The earth is believed ____ by an object the size of Mars at some point in the past before its surface cooled down．A．to be hit B．to have hit C．to have been hit D．to hit 11．—Tommy is such a selfish person．—I agree．Never again ____ with him．A．do I deal B．I do deal C．will I deal D．I will deal 12．By the time you have completed the essential training, you ____ exposed to virtually every new feature of the course．A．are B．will have been C．have been D．will be 13．My interests include football, bowling and surfing the web ______ studying my favorite subjects．A．instead of B．as well asC．less than D．rather than14．—Your pardon, but I didn't quite catch you．—Oh, I ____ myself．A．would talk to B．talked toC．had talked to D．was talking to15．It makes little difference to me ____ we go or stay．A．whether B．where C．that D．how16．—Why was Professor Smith unhappy recently?—Because the theory he insisted on ____ wrong．A．proved B．proving C．being proved D．was proved 17．— What do you think of leaching．Bob?—I find it fun and challenging．It is a job _____ you are doing something serious but interesting．A．when B．which C．that D．where 18．—Andrew won’t like it, you know．—______? I don't care what Andrew thinks!A．So what B．So where C．So why D．So how19．Ten years ago, the population of our village was ____ that of theirs．A．as twice large as B．twice as large asC．twice as much as D．as twice much as20．Meals in Spain are quite different from _____ they have here in China．A．what B．which C．that D．whom第二节【2012届四川省绵阳市高三第一次诊断性考试】完型填空（共20小题；每小题1．5分，满分30分）阅读下面短文，掌握其大意，从短文后各题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题卡上涂黑。

绵阳市高中2015 级第一次诊断性考试英语本试卷分为试题卷和答题卡两部分其中试题卷由第I卷(选择题) 和第II卷(非选择题) 组成，共12页; 答题卡共2页。

满分150分，考试时间120分钟。

注意事项:1.答题前，考生务必在答题卡上将自己的学校、班级、姓名用0.5毫米黑色签字笔填写清楚，同时用2B铅笔将考号准确填涂在“考号“栏目内。

2.选择题使用2B铅笔填涂在答题卡对应题目标号的位置上，如需改动，用橡皮擦擦干净后再选涂其它答案非选择题用0.5毫米黑色签字笔书写在答题卡的对应框内，超出答题区域书写的答案无效: 在草稿纸、试愿卷上答题无效。

3.考试结束后将答题卡收回。

第I卷(选择题，共100分)第一部分听力(共两节，满分30分)回答听力部分时，先将答案标在试卷上。

听力部分结束前，你将有两分钟的时间将你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并阅读下一小题。

每段对话仅读一遍。

例: How much is the shirt?A. £ 19.15.B. £ 9.18.C. £ 9.15.答案是C.1. Who wants to borrow a camera?B. Jane. A. Mary.C. Alice.2. What is the man doing?A. Attending an appointmentB. Discussing an agreement.C. Applying for a position.3. Where are the two speakers talking?A. Ina shop.B. In a bank.C. In a cinema.4. How long did Eric stay abroad in all?A. 9 days.B. 11 days.C. 16 days.5. Why will Mr. Rogers be off work next week?A. To make his holiday.B. To attend a wedding.C. To travel on business.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。

秘密★启用前【考试时间：2017年11月1日15:00—17:00】绵阳市高中2015级第一次诊断性考试英语本试卷分为试题卷和答题卡两部分，其中试题卷由第I卷（选择题)和第II卷（非选择题）组成，共12页；答题卡共2页。

满分150分，考试时间120分钟。

注意事项：1.答题前，考生务必在答题卡上将自己的学校、班级、姓名用0.5毫米黑色签字笔填写清楚，同时用2B铅笔将考号准确填涂在“考号”栏目内。

2.选择题使用2B铅笔填涂在答题卡对应题目标号的位置上，如需改动，用橡皮擦擦干净后再选涂其它答案；非选择题用0.5毫米黑色签字笔书写在答题卡的对应框内;超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

3.考试结束后将答题卡收回。

第I卷（选择题，共100分）第一部分听力（共两节，满分30分）回答听力部分时，先将答案标在试卷上。

听力部分结束前，你将有两分钟的时间将你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并阅读下一小题。

每段对话仅读一遍。

例:How much is the shirt?A. £ 19.15.B.£9.18.C.£9.15.答案是C。

1 . Who wants to borrow a camera?A. Mary.B. Jane.C. Alice.2. What is the man doing?A. Attending an appointment.B. Discussing an agreement.C. Applying for a position.3. Where are the two speakers talking?A. In a shop.B. In a bank.C. Ina cinema.4. How long did Eric stay abroad in all?A. 9 days.B. 11 days.C. 16 days.5. Why will Mr. Rogers be off work next week?A. To make his holiday.B. To attend a wedding.C. To travel on business.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。

秘密★启用前【考试时间：2017年11月1日15:00—17:00】绵阳市高中2015级第一次诊断性考试英语本试卷分为试题卷和答题卡两部分，其中试题卷由第I卷（选择题)和第II卷（非选择题）组成，共12页；答题卡共2页。

满分150分，考试时间120分钟。

注意事项：1.答题前，考生务必在答题卡上将自己的学校、班级、姓名用0.5毫米黑色签字笔填写清楚，同时用2B 铅笔将考号准确填涂在“考号”栏目内。

2.选择题使用2B铅笔填涂在答题卡对应题目标号的位置上，如需改动，用橡皮擦擦干净后再选涂其它答案；非选择题用0.5毫米黑色签字笔书写在答题卡的对应框内;超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

3.考试结束后将答题卡收回。

第I卷（选择题，共100分）第一部分听力（共两节，满分30分）回答听力部分时，先将答案标在试卷上。

听力部分结束前，你将有两分钟的时间将你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并阅读下一小题。

每段对话仅读一遍。

例:How much is the shirt?A. £ 19.15.B.£9.18.C.£9.15.答案是C。

1 . Who wants to borrow a camera?A. Mary.B. Jane.C. Alice.2. What is the man doing?A. Attending an appointment.B. Discussing an agreement.C. Applying for a position.3. Where are the two speakers talking?A. In a shop.B. In a bank.C. Ina cinema.4. How long did Eric stay abroad in all?A. 9 days.B. 11 days.C. 16 days.5. Why will Mr. Rogers be off work next week?A. To make his holiday.B. To attend a wedding.C. To travel on business.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。

绵阳南山中学. 南山中学实验学校绵阳市“一诊”模拟考试试题理科数学本试卷分I 卷（选择题）和第II 卷（非选择题）两部分，满分150分，考试时间为120分钟。

考试结束后，将试卷和答题卡一并交回。

注意事项：1．答题前，考生必须将自己的姓名、准考证号填写清楚，将条形码准确粘贴在条形码区域内。

2．选择题必须用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

第I 卷（共50分）一、选择题（本大题共10小题，每小题5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.集合{}2,0,1,2M -=，{}211N x x =->,则N M ⋂=( ) A.｛-2,1,2｝ B.｛0,2｝ C.｛-2，2｝ D.［-2，2］2.已知a =(2,1), (),3b x =,且 b a//，则x 的值为（ ）A.2B.1C.3D.63.在各项均为正数的等比数列{}n a 中，13213,,22a a a 成等差数列，则1113810a aa a +=+（ ）A.1-或3B.3C.1或27D.27 4.下列说法错误的是 （ ）A ．若2:,10p x R x x ∃∈-+=，则 2:,10p x R x x ⌝∀∈-+≠；B ．“1sin 2θ=”是“30θ=”的充分不必要条件；C ．命题“若0a =，则0ab =”的否命题是：“若0a ≠，则0ab ≠”；D ．若1cos ,:=∈∃x R x p ，01,:2>+-∈∀x x R x q ，则“q p ⌝∧”为假命题.8.已知函数(){2014sin ,01log ,1x x x x f x π≤≤>=若,,a b c 互不相等,且()()()f a f b f c ==,则a b c++的取值范围是( ).A.(1,2014)B.(1,2015)C.[2,2015]D.(2,2015)9.已知定义为R 的函数()f x 满足()()4f x f x -=-+，且函数()f x 在区间()2,+∞上单调递增.如果122x x <<，且124x x +<，则()()12f x f x +的值（ ） A. 恒小于0B.恒大于0C ．可能为0D ．可正可负10.设函数()f x 的导函数为()'f x ，对任意x R ∈都有()()'f x f x >成立，则（ ） A. 3(ln 2)2(ln3)f f > B. 3(ln 2)2(ln3)f f <C. 3(ln 2)2(ln3)f f =D. 3(ln 2)f 与2(ln 3)f 的大小不确定第Ⅱ卷二、填空题(本大题共5小题，每小题5分，共25分．) 11.幂函数2(33)m y m m x =-+过点()2,4，则m = . 12. 计算31log 4233log 6log 243-+- 的结果为 .13已知菱形ABCD 的边长为2，120BAD ︒∠=，点,E F 分别在边,BC DC 上，3BC BE =，DC DF λ=. 若1AE AF ⋅=，则λ的值为 .14.已知22,,12y x y R x +∈+=，则12的最大值为 . 15.已知()()()112212,,,A x y B x y x x >是函数()3f x x x=-图象上的两个不同点，且在,A三、解答题（解答应写出文字说明，证明过程或演算步骤共75分） 16. （本小题满分12分）已知函数()2cos sin 333f x x x x πππ⎡⎤⎛⎫⎛⎫⎛⎫=+++ ⎪ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎝⎭⎣⎦.（Ⅰ）求()f x 的值域和最小正周期；（Ⅱ）若对任意0,6x π⎡⎤∈⎢⎥⎣⎦，使得()20m f x ⎡++=⎣恒成立，求实数m 的取值范围.17.（本小题满分12分）设公差不为0的等差数列{}n a 的首项为1，且2514,,a a a 构成等比数列． （Ⅰ）求数列{}n a 的通项公式； （Ⅱ）若数列{}n b 满足12121 (12)n n n b b b a a a +++=-，*n N ∈，求{}n b 的前n 项和n T18. （本小题满分12分）已知函数())(0,)22f x x ππωϕωϕ=+>-≤<的图像关于直线3x π=对称，且图像上相邻两个最高点的距离为π. （I ）求ω和ϕ的值；（II ）若()2f α= ,( 263ππα<<)，求3cos()2πα+的值.19. （本小题满分12分）已知二次函数2()(0),(1)3,f x Ax Bx A f =+≠=其图象关于1x =-对称，数列{}n a 的前n 项和为n S ,点()()*,n n S n N ∈均在()y f x =图象上. （Ⅰ）求数列{}n a 的通项公式，并求n S 的最小值； （Ⅱ）数列{}n b , 1n nb S =, {}n b 的前n 项和为n T ,求证：11313443n T n n -<<-+.20．（本小题满分13分）设函数x ax x a x f ln 21)(2-+-=（R a ∈）． （Ⅰ）当1=a 时，求函数)(x f 的极值； （Ⅱ）当R a ∈时，讨论函数)(x f 的单调性；（Ⅲ）若对任意(2,3)a ∈及任意1x ，[]2,12∈x ，恒有12ln 2()()ma f x f x +>-成立，求实数m 的取值范围．21.（本小题满分14分） 已知()ln ()f x x mx m R =-∈.（Ⅰ）若曲线()y f x =过点P(1,1)-，求曲线在P 点处的切线方程； （Ⅱ）求()f x 在区间[]1,e 上的最大值；（Ⅲ）若函数()f x 有两个不同的零点12,x x ，求证212x x e >.绵阳南山中学. 南山中学实验学校绵阳市“一诊”模拟考试试题理科数学参考答案一、CDDBA CADAB 二、填空题11.2 12. -1 13．2 14. 3815.（-1,0）三、解答题16.解： (1)f(x)＝2sin ⎝ ⎛⎭⎪⎫x ＋π3cos ⎝ ⎛⎭⎪⎫x ＋π3－23cos2⎝ ⎛⎭⎪⎫x ＋π3＝sin ⎝ ⎛⎭⎪⎫2x ＋2π3－3⎣⎢⎡⎦⎥⎤cos ⎝ ⎛⎭⎪⎫2x ＋2π3＋1＝sin ⎝ ⎛⎭⎪⎫2x ＋2π3－3cos ⎝ ⎛⎭⎪⎫2x ＋2π3－ 3＝2sin ⎝ ⎛⎭⎪⎫2x ＋π3－ 3.∵－1≤sin ⎝⎛⎭⎪⎫2x ＋π3≤1. ∴－2－3≤2sin ⎝ ⎛⎭⎪⎫2x ＋π3－3≤2－3，T ＝2π2＝π，即f(x)的值域为[－2－3，2－3]，最小正周期为π. (2)当x ∈⎣⎢⎡⎦⎥⎤0，π6时，2x ＋π3∈⎣⎢⎡⎦⎥⎤π3，2π3，故sin ⎝ ⎛⎭⎪⎫2x ＋π3∈⎣⎢⎡⎦⎥⎤32，1，此时f(x)＋3＝2sin ⎝⎛⎭⎪⎫2x ＋π3∈[3，2].由m[f(x)＋3]＋2＝0知，m≠0，∴f(x)＋3＝－2m，即3≤－2m ≤2，即⎩⎪⎨⎪⎧2m ＋3≤0，2m ＋2≥0，解得－233≤m≤－1.即实数m 的取值范围是⎣⎢⎡⎦⎥⎤－233，－1.17.解：（I ）设等差数列{}n a 的公差为d,(d 0≠),则2514,,a a a 构成等比数列，∴22145a a a =，即2(14)(1))113)d d d +=++ 解得d=0（舍去）或d=2, ∴n a =1+2(n-1)=2n-1 ……………….3分（II ）由已知1212...n nb b b a a a +++112n =-（*n N ∈） 当n=1时，11b a =12； 当2n ≥时，n nb a =（112n -）11(1)2n ---=12n ，∴n nb a ==12n ，（*n N ∈） 由（I ），n a =2n-1（*n N ∈），∴212n nn b -=（*n N ∈）…………7分 12313521...2222n nn T -=++++ 2341113521 (22222)n n n T +-=++++ 两式相减得234111222221(...)2222222n n n n T +-=+++++-，=113121222n n n -+---， ∴n T =2332nn +- …………….12分 18.解：（I ）6π-φ2ω,.6π-φ)6π-2sin(3)12π-(2sin 3f(x)∴2πφ≤2π-0)12π()4-3π(∴3π2ω⇒|ω|π2∴π=====<======，所以，，且为对称轴由题可知，周期x x f T f x T T ………………………….5分（II ）8153)23παcos(,.8153214152341)23παcos(∴.415)6π-αcos(2π6π-α0∴32πα6π21)6π-αcos(23)6π-αsin(]6π)6π-αsin[(αsin )23παcos(41)6π-αsin(43)6π-αsin(3∴43)2α(+=++=•+•=+=<<<<•+•=+==+===所以，，即 f……………………12分 19.解：（1）(1)3,12Bf A B A=+=-=-, ∴21,2,,()2A B f x x x ===+ ……………..1分点()()*,n n S n N ∈均在y=f(x)图象上，∴22n S n n =+①………………..2分21(1)2(1)n S n n -=-+-（2n ≥）②①-②得121n n S S n --=+，即n a =2n+1 （2n ≥）……………………….4分， 又113a s == ……………5分∴n a =2n+1（*n N ∈） ………………6分 （2）211111()(2)222n b n n n n n n===-+++ ………………….7分 111111[(1)()...()23242n T n n =-+-++-+] =1111[(1)]2212n n +--++=3111()4212n n -+++ ………9分即证313111()434212n n n ->-++++ 即证211()312n n n <++++， 1111,3132n n n n <<++++，所以右边成立……..10分， 又n T 随n 的增大而增大，1111334n T T n>=>-，左边成立…………..11分 所以，原不等式成立 . ……………………….12分 20.解：（Ⅰ）函数的定义域为(0,)+∞，当1a =时，11()ln ,'()1.x f x x x f x x x-=-=-= 令'()0, 1.f x x ==得，当01x <<时，'()0f x <；当1x >时，'()0f x >，()(0,1)f x ∴在单调递减，在(1,)+∞单调递增，()(1)1f x f ∴==极小值，无极大值 ；…… 4分 （Ⅱ）21(1)1[(1)1](1)'()(1)a x ax a x x f x a x a x x x-+--+-=-+-==1(1)()(1)1a x x a x----=………………5分 ①1a ≤时，(1)10a x -+>,()f x 在(0,1)单减，(1,)+∞单增； ②12a <<时，111a >-，()f x 在(0,1)单增，在1(1,)1a -单减，1(,)1a +∞-单增；③当111a =-即2a =时，2(1)'()0,()(0,)x f x f x x -=-≤+∞在上是减函数；④当111a <-，即2a >时，令'()0f x <，得1011x x a <<>-或,令'()0f x >，得111x a <<- ……………9分 （Ⅲ）由（Ⅱ）知，当(2,3)a ∈时，()[1,2]f x 在上单调递减，当1x =时，()f x 有最大值，当2x =时，()f x 有最小值，123|()()|(1)(2)ln 222a f x f x f f ∴-≤-=-+，3ln 2ln 222a ma ∴+>-+ ， 而0a >经整理得13113230,22422m a a a>-<<-<-<由得 0m ∴≥．……13分 21．解：（1）因为点P （1，-1）在曲线上，所以f(1)=-1,得m=1/1()1f x x=-，∴/(1)f =0，故切线方程为y=-1. ……3分 （2） /1()f x m x=-=1mxx-①当m ≤0时，(1,)x e ∈； (1,)x e ∈，/()f x >0, ()f x 单增，max ()f x =f(e)=1-me ； ② 当1e m ≥，即10m e<≤时，(1,)x e∈，/()f x >0, ()f x 单增，max ()f x =f(e)=1-me ；③ 当11e m <<时，即111e m <<时，(1,)x e ∈，()f x 在1(1,)m 单增，在1(,)e m单减， max ()f x =1()f m=ln 1m --④当11m≤即1m ≥时，(1,)x e ∈，/()f x 0<，()f x 单减，max ()f x = f(1)=-m∴()f x 在［1，e ］上的最大值max ()f x=………………………………8分(3)不妨设120x x >>，12()()0f x f x ==，∴11ln 0x mx -=，22ln 0,x mx -=1212ln ln ()x x m x x +=+，1212ln ln ()x x m x x -=-， 要证212x x e >，即证12ln ln x x +2>，即证12()m x x +2>，………10分1212ln ln x x m x x -=-，即证1212ln ln x x x x --122x x >+，即证12ln ln x x -12)122(x x x x ->+，即证1121222(1)ln 1x x x x x x ->+，……………12分 令12x x =t,则1t >，即证1ln 1t t t ->+，1()ln 1t t t t ϕ-=-+，则/()t ϕ=22214(1)0(1)(1)t t t t t --=>--，函数()t ϕ在(1,)+∞单增，∴()t ϕ(1)ϕ>=0，∴原不等式成立. ……………………14分。