2018年大专毕业生士兵军考部队专升本真题分析及命题趋势

20 18年解放军高中军考数学真题分析关键词：2018年军考真题，2019考军校，德方军考，军考复习，军考辅导，军考资料各位战友们，2018年的军考仿若昨天刚结束，转眼间就来到了“八一”，德方君在这里先祝大家节日快乐！今天也是我们给广大在部队考军校的战士们送福利的时刻，上篇文章中德方君刚贡献了一篇18年数学真题考试原题占124分的惊喜，今天就给大家分析一下究竟是哪个部分考查的原题，以帮助大家更好的备战2019年军考。

欢迎各位战友们随时关注和分享德方君家的真诚奉献！！！一2018年军考数学原题分析2018年军考数学真题题型设置与往年相比没有发生变化，总体来说，基础题、中档题与拔高题的分值比例为5:3:2，难度布局合理，紧扣2018年军考大纲和军考教材。

延续往年数学原题较多的传统，2018年军考数学真题仍有大量的原题，其中来源于教材的原题或改编题的分值共计124分（其中18年教材原题96分，17年教材28分）。

具体分布如下：（1）选择题共9道，其中6道题目出自2018年军考教材原题（或改编），3道题目出自2017年军考教材；（2）填空题共8道，其中6道出自2018年教材原题（或改编），2道出自2017年教材；（3）解答题共7道大题，有4道题目是2018年军考教材原题，一道来自于2017年教材。

这与我们德方军考2018年3月份在军考通A P P上公布的《数学2018年备考指南》视频课中对2018年考试命题趋势的预测一致，预计2019年军考数学仍将延续这一趋势。

此外，军考通A P P还于2018年推出了《数学教材精讲视频课》，该视频课全面、系统、细致的讲解了2018年军考数学教材（国防工业出版社）上的全部习题，而且还有2017年教材（长征出版社）上的部分经典习题，可以说该视频课全部覆盖了2018年军考数学真题的原题分值，是各位军考学员数学考取高分的利器！需要各位2019年军考考生格外注意的是，要关注军考教材原题的改编。

2019 年工化75旅（高中）学员苗子选拔语文试卷单位：姓名：座位号：一、单项选择题。

（共21 分）1.下加点字的注音，完全正确的是（）A.皈．依guī拓．片tuò长颈．鹿jǐng戛．然而止jiáB.稗．官bài 掮．客qián 有血．性xiè暴殄．天物tiǎnC.悚．然sǒng戏谑．xuè冠．心病guān怙恶不悛．quānD.绦．虫tāo悖．逆bèi 入场券．quàn 淙．淙流水zōng2．下列没有错别字的是（）A.诵读掂量辩证法揭杆而起B.观摩幅员哈密瓜独辟蹊径C.安祥驰骋录像机对簿公堂D.寒喧通讯座谈会临渊羡鱼3.依次为下列两副对联选填词语，正确的一项是（）1936 年鲁迅先生逝世时，美国作家斯诺撰写了一副挽联，托人送到鲁迅先生追悼会上。

挽联是：译著尚未成书，惊闻陨星，何人领呐喊？先生作古，痛忆旧雨，文坛从此感彷徨！1990 年德高望重的徐向前元帅逝世，越共领导人黄文欢即书一联以悼之，挽联是：军心暖，威震沙场敌胆寒。

A．中国已经身先士卒B．中国不幸同甘共苦C．寰宇已经同甘共苦D．寰宇不幸身先士卒4.下列句子中加点的成语，适用恰当的一项是（）A.科隆新年夜发生的耸．人．听．闻．的群体犯罪事件，再度引发德国民众对外来难民的恐慌情绪，科隆市长发言人说，政府绝不容许执法“无人区”出现。

B.不言而喻，物理学家和数学家阐发问题，提出理论的途径往往有差异，甚或大．相．径．庭．，物理学家重在理念的物质基础，数学家重在数学逻辑的严密。

C.进入工业革命时代后，民众生活明显改变，咖啡成为下．里．巴．人．的重要食品。

当时，工人生活环境恶劣，工作时间长，咖啡成为保持精力的必需品。

D.那是一张两人的合影，左边是一位英武的解放军战士，右边是一位文弱的莘．莘．学．子．。

5．下列各句中没有语病的一项是（）A．我们知道，魏晋人在思想上崇尚放任、崇尚自由，因此其文学、艺术、哲学皆能彰显个性。

2018年解放军军考英语真题关键词：2018军考真题，2019军考，德方军考，军考英语，军考资料，军考视频，军考辅导一、选择填空（共20分，每小题1分）1.—May I open the window to let in some fresh air?—____.A. Come onB. Take careC. Go aheadD. Hold on2.In order to find ____ better job, he decided to study ____ second foreign language.A. the; aB. a; aC. the ; theD. a; the3.He told us whether ____a picnic was still under discussion.A. to haveB. havingC. haveD. had4.Nowadays people are more concerned about the environment ____ they live.A. whatB. whichC. whenD. where5.Hurry up, kids! The school bus ____ for us!A. waitsB. was waitingC. waitedD. is waiting6.All visitors to this village ____ with kindness.A. treatB. are treatedC. are treatingD. had been treated7.Of the two coats, I’d choose the ____one to spare some money for a book.A. cheapestB. cheaperC. more expensiveD. most expensive8.I knew that ____would ever discourage him, he would never give up wanting to be a director.A. somethingB. anythingC. everythingD. nothing9.You will never gain success ____ you are fully devoted to your work.A. whenB. becauseC. afterD. unless10.You have to ____a choice. Are you going to leave the job or stay?A. decideB. getC. doD. make11. Not until I came home last night ____ to bed.A. Mum did goB. did Mum goC. went MumD. Mum went12. ____ which university to attend, the girl asked her teacher for advice.A. Not knowingB. Knowing notC. Not knownD. Known not13. It is reported that two schools, ____ are being built in my hometown, will open next year.A. they bothB. which bothC. both of themD. both of which14. I haven’t seen Ann for ____ long that I’ve forgotten what she looks like.A. suchB. veryC. soD. too15. —I feel so nervous about the National English Speech Competition tomorrow.—____.A. I really envy youB. Glad to hear thatC. Sounds greatD. Take it easy16. Every year, ____ makes the most beautiful kite will win a prize in the Kite Festival.A. whateverB. whoeverC. whomeverD. whichever17. If I ____ it with my own eyes, I wouldn’t have believed it.A. didn’t seeB. weren’t seeingC. wo uldn’t seeD. hadn’t seen18. Always ____ in mind that your main task is to get this company running smoothly.A. to keepB. to have keptC. keepD. have kept19. You and I could hardly work together because of differences in character, ____?A. could weB. couldn’t IC. couldn’t we`D. could you20. I love the weekend, because I ____ get up early on Saturdays and Sundays.A. needn’tB. mustn’tC. wouldn’tD. shouldn’t二、阅读理解（共40分，每小题2分）Passage1There are stock markets in large cities in many countries. Stock markets in Paris, London, Tokyo, Shanghai and New York are among the largest and most well-known. The stock market also called stock exchange, is a place where people can buy or sell the shares of a factory or company. And each share means part ownership of a factory or company.Different people go to the stock markets. Some are rich, who want to get more money than they have. Others are not very rich who buy stocks and try to become rich. Still others buy stocks as part of their plan to save money.Of course, investing money in the stock market is not the safest way to make money. No one can tell exactly whether the shares will be doing well. The factory or company may do badly. Then the stocks will go down, and investors will lose money. The stock may go up or down for a number of untold reasons. Everyone wants the stock to go up but sometimes even if a factory or a company does a good job, the stock may still go down.No wonder going to the stock market is often compared to gambling. All are eager t o make money by “gambling” in the stock market. Factories and companies that need money are pleased that so many people are willing to “gamble”. Indeed, the stock market is an attractive and complex part of the business world.21.The following people go to the stock market EXCEPT those who ____ .A. want to become richerB. want to get rid of povertyC. want to save moneyD. want to find jobs22. Which of the following statements is true?A. A good investor can affect the change in stock prices.B. A good investor can tell exactly when the stock goes up or down.C. A good investor will sometimes lose money.D. A good investor knows how to choose a company which does a good job.23.In the passage the writer ____.A. encourages people to go to the stock marketB. assures people that buying stocks is a good investmentC. warns people to be careful in buying stocksD. Explains how stock goes up when factories or companies run well24.The word “complex” in the last sentence probably means____.A. completeB. strangeC. difficultD. modern25.The passage mainly tells us about____.A. the ABCs of stock marketsB. gambling in stock marketsC. how to make money in stock marketsD. how to buy or sell shares in stock marketsPassage2You wake up in the morning, the day is beautiful and the plans for the day are what you have been looking forward to for a long time. Then the telephone rings, you say hello, and the drama starts. The person on the other end has a depressing tone in his voice as he starts to tell you how terrible his morning is and that there is nothing to look forward to. Are you still in a wonderful mood? Impossible!Communicating with negative people can wash out your happiness. It may not change what you think, but communicating long enough with them will make you feel depressed for a moment or a long time.Life brings ups and downs, but some people are stuck in the wrong idea that life has no happiness to offer. They only feel glad when they make others feel bad. No wonder they can hardly win others' pity or respect.When you communicate with positive people, your spirit stays happy and therefore more positive things are attracted. When the dagger of a negative person is put in you, you have the heavy feeling that, all in all, brings you down.Sometimes we have no choice but to communicate with negative people. This could be a co-worker, or a relative. In this case, say what needs to be said as little as possible. Sometimes it feels good to let out your anger back to the negative person, but all this is to lower you to that same negative level and they won't feel ashamed of themselves about that.Negativity often affects happiness without even being realized. The negative words of others at the start of the day can be cling to you throughout the rest of your day, which makes you feel bad and steals your happiness. Life is too short to feel negative. Stay positive and avoid negativity as much as possible.26. The purpose of the first paragraph is to____.A. make a comparisonB. offer an evidenceC. introduce a topicD. describe a daily scene27. How can negative people have effect on us?A. By influencing our emotion.B. By telling us the nature of life.C. By changing our way of thinking.D. By comparing their attitudes to life with ours.28. Some negative people base their happiness on____.A. other people's pity for themB. making other people unhappyC. building up a positive attitudeD. other people's respect for them29. According to the passage, to reduce negative people's influence on us, we are advised to____.A. change negative people's attitude to lifeB. show our dissatisfaction to negative peopleC. make negative people feel ashamed of themselvesD. communicate with negative people as little as possible30. What is the author’s attitude towards negative people?A. Favorable.B. Critical.C. Indifferent.D. Supportive.Passage 3I have been hearing- impaired(听力弱的) all my life. By the time I was five years old, putting on hearing aids（助听器）in the morning was just as normal as brushing my teeth. However, I never believed that it should limit my success in any way.During my 17 years , I have met many people who don’t know about hearing disabilities and deal with this by stereotyping(对某人有成见) me. My classmates told me something was wrong with my brain. My teachers would not let me sit past the second row because they worried I would not be able to hear. My “learning expert” tried to teach me sign language, though I had no need for it. People tend to speak louder than normal when they see my thick plastic hearing aids in my ears. Almost every month I hear someone say that hearing aids are for old people.However, my hearing disability has made me a stronger person. Because I wear hearing aids, I have to prove that I am not physically or mentally(精神上) limited. I have to work harder and earn top grades in school to earn the respect of my teachers. In sports, I’ve had to score more points to prove I am not physically challenged.I still don’t know a w ord of sign language. I consider myself no different from anyone else. I wear hearing aids, but I can hear without them. And I am not “half dead”. With my hearing aids on, I can hear just as well as anyone else.I truly believe I would not be the strong and ambitious person I am today if I did not have a hearing disability.31. When I was very young, hearing aids ____.A. made my life difficultB. became a part of my lifeC. limited my successD. hurt my feelings32. Which of the following is NOT the stereotyped view?A. My classmates thought something went wrong with my brain.B. My teachers had me sit at the back of the classroom.C. People spoke louder than normal to me.D. Someone said hearing aids were for old people33. Para.3 shows that the effects of my hearing disability on me are ____.A. comfortingB. encouragingC. troublingD. damaging34. According to Para.4, the writer doesn’t ____.A. think he or she is specialB. like deaf peopleC. learn sign language wellD. hear clearly with hearing aids35. How does the writer feel about the public’s attitude toward hearing disabilities?A. The public is worried.B. The public is critical.C. The public is helpfulD. The public looks down upon people with hearing disabilities.Passage 4Want to improve your writing skills? New Writing South is directing the way!●Towner Writer Squad (班组）for kids aged 13-17Led by comedy and TV writer, Marian Kilpatrick, Towner Writer Squad will meet once a month at the contemporary art museum for 11 months, starting 12 October, 2014.The FREE squad sessions will include introductions to a wide range of writing styles, from poetry to play writing and lyrics (抒情诗）to flash fiction, to support the development of young writers.Application & SelectionIf you would like to apply to be part of the Towner Writer Squad, please send a sample piece of your writing (about 500 words), responding to the title ‘LUNCH,’ with your name, age, address and e-mail address to: debo@.Once all applications are in, you will be invited to an open selection event on 17 September，4-5 pm, at the gallery of Towner. This will be an informal opportunity to meet the Squad Leader, Squad Associate and other young people.You will also have a chance to get to know the fantastic gallery space and get a taste of what’s to come.Deadline for applications: 8 September, 2014For further information go to: /towner or or Any questions 一feel free to send your e-mail to Towner Writer Squad Associate: whame@﹡﹡﹡﹡﹡﹡﹡﹡﹡●Beginner Writing Project for kids aged 10-13Due to popular demand, a writing project will be started for eager beginners.Start time: 6 September, 2014Meet every other Saturday，2-4 pm, at the Towner Study Centre.Study and write at your own pace 一you do not have to rush 一as you have a year to go through the project. Practise under the guidance of some experienced writers and teachers who can help you with basic writing skills. Most importantly, build confidence and have fun while writing!No previous experience or special background is required. Many others have been successful this way. If they can do it, why can’t you?Fee: £179For more information go to: or .36. Towner Writer Squad will be started ____.A. to train comedy and TV writersB. to explore the fantastic gallery spaceC. to introduce a contemporary art museumD. to promote the development of young writers37. To join the Writer Squad，each applicant should first ____.A. provide a piece of their writingB. meet the Writer Squad LeaderC. offer their family informationD. complete an application form38. Applications for the Writer Squad should be e-mailed no later than ____.A. 6 September, 2014B. 8 September, 2014C. 17 September, 2014D. 12 October, 201439. What is most important for the beginners?A. Practising as much as possible.B. Gaining confidence and having fun.C. Studying and writing at their own pace.D. Learning skills from writers and teachers.40. More information about Beginner Writing Project can be found at ____.A. /townerB. C. D. 三、完型填空（共15分，每小题1分）Overhead bridges can be seen in many parts of Singapore, in the place where traffic is very heavy and crossing the road is 41 .These bridges can make people 42 roads safely. Overhead bridges are used in very much the same way as zebra crossings.They are more efficient, 43 less convenient because people have to climb up a lot of steps. This is inconvenient to the old. When people 44 an overhead bridge, they do not hold up traffic. But when they cross a 45 road using a zebra crossing, traffic is held up. This is 46 the government has 47 many overhead bridges to help people and 48 traffic moving at the same time.The government of Singapore has 49 a lot of money building these bridges. For their own safety, people shouldbe given hope to use them 50 rushing across the road. Old people may find it a little 51 climbing up and down the steps, but it is still much safer than walking across the road 52 all the moving traffic.Overhead bridges are very useful. People, 53 old and young, should 54 use them. This will stop accidents 55 happening.41. A. noisy B. not safe C. crowded D. not busy42. A. cross B. crossing C. across D. through43. A. though B. or C. if D. till44. A. pass B. use C. visit D. build45. A. wide B. narrow C. busy D. free46. A. what B. why C. when D. where47. A. made B. let C. built D. asked48. A. see B. keep C. find D. feel49. A. used B. made C. spent D. borrowed50. A. full of B. fond of C. in spite of D. instead of51. A. difficult B. different C. worried D. exited52. A. past B. along C. about D. with53.A. both B. either C. neither D. not54.A. almost B. always C. nearly D. hardly55. A. in B. at C. with D. from四、翻译（共15分，每小题3分）56. 由于下大雨，到处都出现了交通堵塞。

2018年军考解放军数学真题分析及备考建议2019年军考复习资料关键词：2018年军考真题，2019考军校，德方军考，军考复习，军考辅导，军考资料你知道，今年军考，数学考了多少原题吗历年军考，数学大致会考100-120分的教材原题。

今年军考，数学考了124分的原题。

其中，96分来自18年教材，28分来自17年教材。

对于数学这一科来说，最有效率的复习方式不用说，大家都知道了，刷教材。

无论你是自学还是外出辅导，把教材上的每一道题目搞懂，都是你数学复习的最终目标。

教材上的题目都有解析和答案，一般题目不会做时，看一看解析和答案，也许就会有思路；如果还不行，与一起考学的战友讨论一下，兴许也能解决。

还不行，手机搜题软件上，多看几种解析，对于这道题可能会有不同角度的认识。

这样学，到底行不行？行不行，我们要看会了没有。

学的目的就是要会，若没有学会就是浪费时间。

如何检验自己会不会？一道题，只有你能在没有任何辅助工具的帮助下，自己独立做出来，才能说真正会了。

所以，我们最好再准备一套空白教材，学会一章就做一章，看自己是不是真正的会。

自学要想成功，首先你要有超乎常人的意志力和自制力。

能忍住不看答案，这都不值一提。

更重要的是，能耐得住寂寞，守得住孤独。

别的战友外出放松，你自己在挑灯夜读。

要想考上军校，没有强大的意志力是不行的。

而对于有一定基础的学员来说，拥有强大的意志力和自制力能让你通过自学考上军校。

但如果你的学习基础比较薄弱，那么要想自学，光有意志力还不够，你学习能力的欠缺，不是你单打独斗可以应付得了的。

这时你就需要高人指点。

换句话说，你需要有老师的指导。

如果你有士官假，你有条件外出辅导，那么与老师面对面紧密沟通，是最有效率的学习方式。

如果你没有这个条件，那么视频课自学，是你实现高人指点的一种选择。

今年军考数学考的原题，德方全部押中了。

为什么能全押中？很简单，从2017年开始，我们就开始做《教材精讲视频课》。

所以不止今年教材里的原题，连往年教材里的原题，视频课里都有。

21 .2019 年工化75旅（高中）学员苗子选拔数学试卷单位： 姓名： 座位号：一、单项选择（每小题 4 分，共 36 分）1.设集合S = {a ，b ，c ，d ，e }，则包含元素a ，b 的S 的子集共有 .A.2 个B.3 个C.4 个D.8 个2.下列函数中，满足“f (x + y ) = f (x )f (y )”的单调递增函数是.1A. f (x ) = x 2B. f (x ) = x3C. f (x ) = 3xD. f (x ) = (1)x3.设a , b 为正实数，则“a > b > 1”是“log 2 a > log 2 b > 0”的 .A.充要条件B.充分不必要条件C.必要不充分条件D.既不充分也不必要条件4.若a > 0，b > 0，且函数f (x ) = 4x 3 − ax 2 − 2bx + 2在x = 1处有极值，则ab 的最大值等于 .A.9B.6C.3D.21 5.直线l 经过椭圆的一个顶点和一个焦点，若椭圆中心到l 的距离为其短轴长的 ，则该椭圆的离心率为 .41 123 A.3B.2C.3 D. 46.记S n 为等差数列{a n }的前n 项和.若a 4 + a 5 = 24，S 6 = 48，则{a n }的公差为 .A.1B .2C.4D.87.在一个袋子中装有分别标注数字 1，2，3，4，5 的五个小球，这些小球除标注的数字外完全相同.现从中随机取出 2 个小球，则取出的小球标注的数字之和是 3 或 6 的概率是 .1 31A.B.C D.51010128.若直线a ∥平面α，直线b ∥平面α，则a 与b 的位置关系是 .A.平行B.相交C.异面D.以上都有可能9.已知直线y = kx + 1与曲线y = x 3 + ax + b 切于点(1，3)，则b 的值为 .A. 3B.−3C. 5D. −5二、填空题（每小题 4 分，共 32 分）− 9 ( ) 10.设a ，b 的夹角为120°，|a | = 1，|b | = 3，则|3a − b | =. 11.设θ为第二象限角，若tan(θ + π) = 1，则sin θ + cos θ =.42x 2 y 212.若双曲线C : 2 2a 2 为.b2 = 1 a > 0，b > 0 的一条渐近线被圆(x − 2) + y = 4所截得的弦长为 2，则C 的离心率 13.若曲线y = 2x 2的一条切线l 与直线x + 4y − 8 = 0垂直，则切线l 的方程为.14.若（2x 2 − 1n (n ∈ N ∗)展开式中存在常数项，则n 的最小值是x3 ）.15. 有 3 位司机，6 位售票员分配到 3 辆公共汽车上工作，每一辆汽车分别有一位司机和两位售票员，那么所有不同的分配方法有 种.16. 在极坐标系中，点（2 π ， 6）到直线 ρ sin θ = 2的距离等于 .17. 若复数(1 + mi )(3 + i )（i 是虚数单位，m.m +2i 是实数）是纯虚数，则复数1−i的模等于三、解答题（共 7 小题，共 82 分，解答应写出文字说明，演算步骤或证明过程）18.（8 分）已知f (x ) = 2x 2 + bx + c ，不等式f (x ) < 0的解集是（0，5）. （1）求f (x )的解析式；（2）对于任意x ∈ [−1，1]，不等式f (x ) + t ≤ 2恒成立，求t 的取值范围.19.（10 分）设△ABC 的内角A ，B ，C 所对的边分别为a ，b ，c ，且a + c = 6，b = 2，cos B = 7.（1）求a ，c 的值； （2）求sin (A − B )的值.20.（12 分）设等差数列{a n }的公差为d ，点(a n ，b n )在函数f (x ) = 2x 的图像上(n ∈ N ∗). （1）若a 1 = −2，点(a 8，4b 7)在函数f (x )的图像上，求数列{a n }的前n 项和S n ；x−2 （2）若a = 1，函数f (x )的图像在点(a ，b )处的切线在x 轴上的截距为2 −1，求数列{a n }的前n 项和T .122ln 2b nn21.（12 分）甲、乙、丙三人参加了一家公司的招聘面试，面试合格者可正式签约，甲表示只要面试合格就签约， 1 乙、丙则约定：两人面试都合格就一同签约，否则两人都不签约.设每人面试合格的概率都是 ，且面试是否合格互2不影响.求：（1） 至少有 1 人面试合格的概率；（2） 签约人数ξ的分布列和数学期望.22.（14 分）已知椭圆x 2 + 2y 2 = 1，过原点的两条直线l 1和l 2分别与椭圆交于A 、B 和C 、D ，设△A OC 的面积为S . （1）设A (x 1，y 1)，C (x 2，y 2)，用A 、C 的坐标表示点C 到直线l 1的距离，并证明S = 1|x y − x y |；2 1 22 1（2）设l ：y = kx ， 3 ， 3)，S = 1，求k 的值；1C ( 333（3） 设l 1与l 2的斜率之积为m ，求m 的值，使得无论l 1与l 2如何变动，面积S 保持不变.23.（12 分）某店销售进价为 2 元/件的产品A ，该店产品A 每日的销量y （单位：千件）与销售价格x （单位：元/件） 满足关系式y =10+ 4(x − 6)2，其中2 < x < 6.（1） 若产品A 销售价格为 4 元/件，求该店每日销售产品A 所获得的的利润；（2） 试确定产品A 的销售价格，使该店每日销售产品A 所获得的的利润最大（保留 1 位小数）.24.（14 分）如图所示，在三棱锥P− ABC中，PA⊥底面ABC，∠BAC = 90°.点D，E，N分别为棱PA，PC，BC的中点，M是线段AD的中点，PA = AC = 4，AB = 2.（1）求证：MN∥平面BDE；（2）求二面角C− EM− N的正弦值；√7（3）已知点H在棱PA上，且直线NH与直线BE所成角的余弦值为21，求线段AH的长.29，所以 93 272018 年军队院校招生士兵高中数学真题答案一、单项选择（每小题 4 分，共 36 分）1.D2.C3.A4.A5.B6.C7.B8.D9.A二、填空题（每小题 4 分，共 32 分）√1010.3√3 11.− 512.2 13.4x − y − 2 = 0√26 14.515.54016.117. 2三、解答题（共 7 小题，共 82 分）18. 本题满分 8 分解：（1）∵不等式2x 2 + bx + c < 0的解集是（0，5），∴方程2x 2 + bx + c = 0的两根为0，5.∴0 + 5 = − b，0 × 5 = c ，即b = −10，c = 0，故f (x ) = 2x 2 − 10x .（2）∀x ∈ [−1，1]，不等式f (x ) + t ≤ 2恒成立，只需f max (x ) ≤ 2 − t 即可.( ) 2( 2)5 2 25∵f x = 2x − 10x = 2 x − 5x= (x − 2) − 2，x ∈ [−1，1]，∴f max (x ) = f (−1) = 12.故12 ≤ 2 − t ，即t ≤ 10.19. 本题满分 10 分解：（1）由余弦定理b 2 = a 2 + c 2 − 2ac cos B ，得b 2 = (a + c )2 − 2ac (1 + cos B )，又(a + c ) = 6，b = 2，cos B = 7ac = 9， 解得a = 3，c = 3.（2）在△ABC 中，sin B = √1 − cos 2 B =4√2，由正弦定理得sin A =a sin B = 2√2b3因为a = c ，所以A 为锐角，所以cos A = √1 − sin 2 A = 1，因此sin (A − B ) = sin A cos B − cos A sin B =10√220. 本题满分 12 分解：（1）因为点(a n ，b n )在函数f (x ) = 2x 的图像上，所以b n = 2a n ，b n +12a n +1a −ad可得b n= 2a n= 2 n +1n= 2 .，b ， = . n因为点(a 8，4b 7)在函数f (x )的图像上，所以4b 7 = 2a 8 = b 8. 所以2d =b 8= 4 ⇒ d = 2，又a 1 = −2，所以数列{a n }的前n 项和为 7S n = na 1 + n (n − 1)d = −2n + n 2 − n = n 2 − 3n2（ 2 ）由f (x ) = 2x ⇒ f ′(x ) = 2x ln 2 ， 所以函数f (x ) 的图像在点(a 2，b 2) 处的切线方程为y − b 2 = (2a 2 ln 2)(x − a 2)， 故切线在x 轴上的截距为a 2 −1 ，从而a2 − 1 = 2 − 1，故a 2 = 2.从而a= n ，bln 2= 2na n n ln 2 ln 2nnb n 2n1 2 3 nT n = 2 + 22 + 23 + ⋯ + 2n1 上式两边同乘以 ，可得21 T= 1 + 2 + 3 + ⋯ + n两式右边错项相减可得2 n 22 23 24 2n +111 1 1 1 1 n 1 n n + 22 T n = 2 + 22 + 23 + 24 + ⋯ + 2n − 2n +1 = 1 − 2n − 2n +1 = 1 − 2n +1 故T n = 2 − n +2.221. 本题满分 12 分.解：用A 、B 、C 分别表示事件甲、乙、丙面试合格，由题意可知A 、B 、C 相互独立，且P (A ) = P (B ) = P (C ) = 12（1）至少有 1 人面试合格的概率是1 3 71 − P (A B C) = 1 − P (A )P (B )P (C) = 1 − (2) = 8（2）ξ的可能取值为 0，1，2，3.P (ξ = 0) = P (ABC ) + P (A BC ) + P (A B C ).= P (A )P (B )P (C ) + P (A )P (B )P (C ) + P (A )P (B )P (C ) 1 3 = ( ) 2 1 3 + ( ) 2 1 3 + ( )2 = 3.8P (ξ = 1) = P (ABC ) + P (ABC ) + P (AB C )1 3 1 31 3 3= P (A )P (B )P (C ) + P (A )P (B )P (C ) + P (A )P (B )P (C ) = ( ) 2 + ( ) 2 + ( ) 2 = 8.( ) ( ) ( ) 1P ξ = 2 = P (ABC ) = P (A )P B P C= 8.( ) ( ) ( ) ( ) ( ) 1P ξ = 3 = P A B C = P A P B P C = 8.1 所以，ξ的分布列如下表ξ的期望是( )3 3 1 122. 本题满分 14 分E ξ = 0 × 8 + 1 × 8 + 2 × 8 + 3 × 8= 1.解：（1）直线l 1的方程为y 1x − x 1y = 0，由点到直线的距离公式可知点C 到直线l 1的距离为d = |y 1x 2 − x 1y 2| ，√x 12 + y 12因为|OA | = √x 12 + y 12，所以，S = 1|OA | ∙ d = |y 1x 2 − x 1y 2|.（2）由{y = k x 2 22 2，消去y 解得 x + 2y = 1x 2 =1 ，由（1）得11 + 2k 2S = 1 ||1 √3 √3√3|k − 1|由题意知2 x 1y 2 − x 2y 1 = | x −2 3 3 kx 1| = 6√1 + 2k 2 ，√3|k − 1| = 1 ，6√1 + 2k 2 31解得k = −1 或k = − 5.(3)设l ：y = kx ，则 l ：y = mx ，设A (x ，y )，C (x ，y )1 2 k 1 1 2 2y = k x 由{，得x 2 = 1 ， x 2+ 2y 2= 11 1 + 2k 2同理x 22= 1m k 2 2 = k 2 + 2m 2 ，1 +2 ( k ) ( ) 1|| 1 x 1 ∙ mx 11 |k2 − m | | |由 1 知 ，S = 2 x 1y 2 − x 2y 1 = 2 | k − x 2 ∙ kx 1| = 2 ∙ |k | ∙x 1x 2 |k 2 − m |= ， 2√1 + 2k 2 ∙ √k 2 + 2m 2整理得(8S 2 − 1)k 4 + (4S 2 + 16S 2m 2 + 2m )k 2 + (8S 2 − 1)m 2 = 0， 由题意知S 与k 无关，则{ 8S 2− 1 = 0，解得{ S 2 = 1 8 1 ，所以4S 2 + 16S 2m 2 + 2m = 0 m = − 1 2m = − 2.23. 本题满分 12 分解：(1)当x = 4 时，y = 10+ 4 × (4 − 6)2 = 21，2此时该店每日销售产品A 所获得的利润为(4 − 2) × 21 = 42千元.(2)该店每日销售产品A 所获得的利润为f (x ) = (x − 2) ∙ [ 10 x − 2+ 4(x − 6)2]= 10 + 4(x − 6)2(x − 2) = 4x 3 − 56x 2 + 240x − 278(2 < x < 6)，从而f ′(x ) = 12x 2 − 112x + 240 = 4(3x − 10)(x − 6) (2 < x < 6)，令f ′(x ) = 0，得x = 10 ，易知在(2， 10上，f ′(x ) > 0，函数f (x )单调递增；3 3 )在(10，6)上，f ′(x ) < 0，函数f (x )单调递减. 3 所以x = 10是函数f (x )在（2，6）内的极大值点，也是最大值点.3即当x = 10≈ 3.3 时，函数f (x )取得最大值.3 故当销售价格为3.3元/件时，利润最大. 24. 本题满分 14 分（1）证明：取 AB 中点 F ，连接 MF 、NF ， ∵M 为 AD 中点，∴MF ∥BD ，∵BD ⊂平面 BDE ，MF ⊄平面 BDE ，∴MF ∥平面 BDE ． ∵N 为 BC 中点，∴NF ∥AC ，又 D 、E 分别为 AP 、PC 的中点，∴DE ∥AC ，则 NF ∥DE ． ∵DE ⊂平面 BDE ，NF ⊄平面 BDE ，∴NF ∥平面 BDE ． 又 MF ∩NF =F ．∴平面 MFN ∥平面 BDE ，则 MN ∥平面 BDE ；（2）解：∵PA ⊥ 底面ABC ，∠BAC = 90°．∴ 以A 为原点，分别以AB 、AC 、AP 所在直线为x 、y 、z 轴建立空间直角坐标系．∵PA = AC = 4，AB = 2，∴A （0，0，0），B （2，0，0），C （0，4，0），M （0，0， 1）， N （1，2，0），E （0，2，2），→→则MN = (1，2， − 1)，ME = (0，2，1)，→设平面MEN 的一个法向量为m = (x ，y ，z )，→→x + 2y − z = 0→ 由{m ⋅ MN = 0，得{ ，取z =2，得m = (4， − 1，2)． → → 2y + z = 0 m ⋅ ME = 0→由图可得平面CME 的一个法向量为n = (1，0，0)．→ →→→m⋅n 4 4√21 ∴cos ＜m ，n ＞= → →= √21×1 = 21 ．|m ||n |4√21√105∴二面角C ﹣EM ﹣N 的余弦值为21，则正弦值为 →21 ；→（3）解：设 AH = t ，则 H （0，0，t ），NH = (−1， − 2，t )，BE = (−2，2，2)．∵直线 NH 与直线 BE√7所成角的余弦值为21，→→→ → ∴|cos ＜ NH⋅BE2t−2 √7 NH ，BE ＞|=| → → |=| 2 |=21．解得：t =81或t = ．52|NH ||BE |√5+t ×2√3 8 1∴线段 AH 的长为 或 ．5 2。

本文部分内容来自网络整理，本司不为其真实性负责，如有异议或侵权请及时联系，本司将立即删除！== 本文为word格式，下载后可方便编辑和修改！ ==军校考试试题篇一：现役士兵考军校试题现役士兵考军校试题第二部分物理一、本题共5小题，每小题4分，共20分. 对于有多个正确选项的题，全选对得4分，选不全的得2分，有选错的得0分.1. 加速度不变的运动（）.A. 一定是直线运动B. 可能是曲线运动C. 可能是匀速圆周运动D. 若初速度为零，一定是直线运动2. 对于一定质量的理想气体，可能发生的过程是（）.A. 气体的压强增大，温度升高，气体对外界做功B. 气体的压强增大，温度不变，气体对外界放热C. 气体的压强减小，温度降低，气体从外界吸热D. 气体的压强减小，温度升高，外界对气体做功3. 一个运动物体，在任何相等的时间内，动量的变化量相同，则物体的运动可能是（）. ．．．．．．A. 匀减速曲线运动B. 只受某一恒力作用的曲线运动C. 匀速圆周运动D. 任何只有重力做功的运动4. 某人在高h处抛出一个质量为m的物体. 不计空气阻力，物体落地时的速度是v，则人对物体做的功是（）.A. mghB. 1211mvC. mv2?mghD. mv2?mgh 2225. 如图所示，质点S为波源，做上下振动，形成向左、向右传播的简谐波，振动频率为20Hz，波速为16m/s，已知PS?15.8m，QS?14.6m. 足够长的时间后的某时刻，质点S恰好通过平衡位置向上运动，此时（）.A. P在波峰B. P在波谷C. Q在波峰D. Q在波谷二、本题共3小题，每空3分，共15分. 不要求写过程.P SQ 出演算6. 两行星A、B各有一颗卫星a和b，卫星的圆轨道接近各自行星表面，如果两行星的质量比MA:MB?p，两行星半径之比RA:RB?q，则两卫星的周期之比Ta:Tb?.7. 一个质量为1kg的物体，在0时刻以速度v0?5m/s向东运动. 物体同时受两个恒力的作用：，方向向西. 则2秒末物体的动F1?2N，方向向南；F2?0.5N．量．大小为kg?m/s，方向为.8. 23892U经过2次?衰变和3次?衰变后，得到的原子核中质子数为，中子数为 .三、（12分）9. 某登山运动员在一次攀登珠穆朗玛峰的过程中，在接近山顶时他裸露在手腕上的防水手表的表盘玻璃突然爆裂了. 而手表没有受到任何撞击，该手表出厂时给出的参数为：27℃时表内气体压强为1.0?105Pa（常温下的大气压强值），当内外压强差超过6.0?104Pa时表盘玻璃将爆裂. 当时登山运动员携带的温度计的读数是?21℃，表内气体体积的变化可忽略不计.(1) 手表的表盘是向外爆裂还是向内爆裂的？通过计算判断.(2) 当时外界的大气压强为多少？四、（13分）现役士兵大专生考军校资料网站/———军考网！10. 用线绳悬挂质量M?1kg的木块，木块重心到悬点的距离L?1m，有一质量m?0.01kg的子弹以v0?500m/s的水平速度射入木块，以v1?100m/s的速度从木块中射出，子弹穿过前后木块的质量变化忽略不计. 求：(1) 木块能摆动多高？(2) 此过程中有多少机械能转化为内能？第三部分化学注意：可能用到的相对原子质量：H: 1 C: 12 N: 14 O: 16 Na: 23 Mg: 24 Al: 27 S: 32 Cl: 35.5 Ca: 40一、选择题（每小题3分，共21分。

2018年解放军军考数学真题关键词：2018军考真题，2019军考，德方军考，军考数学，军考资料，军考视频，军考辅导一、单项选择（每小题4分，共36分）1.设集合S ={a ，b ，c ，d ，e}，则包含元素a ，b 的S 的子集共有 . A.2个B.3个C.4个D.8个2.下列函数中，满足“f (x +y )=f(x)f(y)”的单调递增函数是 . A. f (x )=x 12B. f (x )=x 3C. f (x )=3xD. f (x )=(12)x3.设a,b 为正实数，则“a >b >1”是“log 2a >log 2b >0”的 . A.充要条件B.充分不必要条件C.必要不充分条件D.既不充分也不必要条件4.若a >0，b >0，且函数f (x )=4x 3−ax 2−2bx +2在x =1处有极值，则ab 的最大值等于 . A.9B.6C.3D.25.直线l 经过椭圆的一个顶点和一个焦点，若椭圆中心到l 的距离为其短轴长的14，则该椭圆的离心率为 . A. 13B. 12C. 23D. 346.记S n 为等差数列{a n }的前n 项和.若a 4+a 5=24，S 6=48，则{a n }的公差为 . A.1B .2C.4D.87.在一个袋子中装有分别标注数字1，2，3，4，5的五个小球，这些小球除标注的数字外完全相同.现从中随机取出2个小球，则取出的小球标注的数字之和是3或6的概率是 . A.15B.310C .110D.1128.若直线a ∥平面α，直线b ∥平面α，则a 与b 的位置关系是 . A.平行B.相交C.异面D.以上都有可能9.已知直线y =kx +1与曲线y =x 3+ax +b切于点(1，3)，则b 的值为 . A. 3B.−3C. 5D. −5二、填空题（每小题4分，共32分）10.设a ，b 的夹角为120°，|a |=1，|b |=3，则|3a −b |= . 11.设θ为第二象限角，若tan(θ+π4)=12，则sin θ+cos θ= . 12.若双曲线C :x 2a 2−y 2b 2=1(a >0，b >0)的一条渐近线被圆(x −2)2+y 2=4所截得的弦长为2，则C 的离心率为 .13.若曲线y =2x 2的一条切线l 与直线x +4y −8=0垂直，则切线l 的方程为 .14.若（2x 2−1x3）n(n ∈N ∗)展开式中存在常数项，则n 的最小值是 .15.有3位司机，6位售票员分配到3辆公共汽车上工作，每一辆汽车分别有一位司机和两位售票员，那么所有不同的分配方法有 种.16.在极坐标系中，点（2，π6）到直线ρsin θ=2的距离等于 . 17. 若复数(1+mi )(3+i )（i 是虚数单位，m 是实数）是纯虚数，则复数m+2i 1−i的模等于.三、解答题（共7小题，共82分，解答应写出文字说明，演算步骤或证明过程） 18.（8分）已知f (x )=2x 2+bx +c ，不等式f(x)<0的解集是（0，5）. （1）求f(x)的解析式；（2）对于任意x ∈[−1，1]，不等式f (x )+t ≤2恒成立，求t 的取值范围.19.（10分）设△ABC 的内角A ，B ，C 所对的边分别为a ，b ，c ，且a +c =6，b =2，cos B =79 . （1）求a ，c 的值； （2）求sin (A −B )的值.20.（12分）设等差数列{a n }的公差为d ，点(a n ，b n )在函数f (x )=2x 的图像上(n ∈N ∗). （1）若a 1=−2，点(a 8，4b 7)在函数f (x )的图像上，求数列{a n }的前n 项和S n ；（2）若a 1=1，函数f (x )的图像在点(a 2，b 2)处的切线在x 轴上的截距为2−1ln2，求数列{a n b n}的前n 项和T n .21.（12分）甲、乙、丙三人参加了一家公司的招聘面试，面试合格者可正式签约，甲表示只要面试合格就签约，乙、丙则约定：两人面试都合格就一同签约，否则两人都不签约.设每人面试合格的概率都是12，且面试是否合格互不影响.求：（1）至少有1人面试合格的概率； （2）签约人数ξ的分布列和数学期望.22.（14分）已知椭圆x 2+2y 2=1，过原点的两条直线l 1和l 2分别与椭圆交于A 、B 和C 、D ，设△AOC 的面积为S . （1）设A(x 1，y 1)，C(x 2，y 2)，用A 、C 的坐标表示点C 到直线l 1的距离，并证明S =12|x 1y 2−x 2y 1|；（2）设l 1：y =kx ，C (√33，√33)，S =13，求k 的值； （3）设l 1与l 2的斜率之积为m ，求m 的值，使得无论l 1与l 2如何变动，面积S 保持不变.23.（12分）某店销售进价为2元/件的产品A ，该店产品A 每日的销量y （单位：千件）与销售价格x （单位：元/件）满足关系式y =10x−2+4(x −6)2，其中2<x <6. （1）若产品A 销售价格为4元/件，求该店每日销售产品A 所获得的的利润；（2）试确定产品A 的销售价格，使该店每日销售产品A 所获得的的利润最大（保留1位小数）.24.（14分）如图所示，在三棱锥P−ABC中，PA⊥底面ABC，∠BAC=90°.点D，E，N分别为棱PA，PC，BC的中点，M是线段AD的中点，PA=AC=4，AB=2.（1）求证：MN∥平面BDE；（2）求二面角C−EM−N的正弦值；（3）已知点H在棱PA上，且直线NH与直线BE所成角的余弦值为√721，求线段AH的长.2018年解放军军考数学真题答案一、单项选择（每小题4分，共36分） 1.D 2.C 3.A 4.A 5.B 6.C 7.B 8.D 9.A 二、填空题（每小题4分，共32分） 10.3√3 11.−√10512.2 13.4x −y −2=014.515.54016.117.√262三、解答题（共7小题，共82分） 18. 本题满分8分解：（1）∵不等式2x 2+bx +c <0的解集是（0，5）， ∴方程2x 2+bx +c =0的两根为0，5. ∴0+5=−b2，0×5=c ，即b =−10，c =0，故f (x )=2x 2−10x .（2）∀x ∈[−1，1]，不等式f (x )+t ≤2恒成立，只需f max (x )≤2−t 即可. ∵f (x )=2x 2−10x =2(x 2−5x )=(x −52)2−252，x ∈[−1，1]，∴f max (x )=f (−1)=12.故12≤2−t ，即t ≤10.19.本题满分10分解：（1）由余弦定理b 2=a 2+c 2−2ac cos B ，得b 2=(a +c )2−2ac (1+cos B )， 又(a +c )=6，b =2，cos B =79，所以ac =9，解得a =3，c =3.（2）在△ABC 中，sin B =√1−cos 2B =4√29， 由正弦定理得sin A =asin B b=2√23， 因为a =c ，所以A 为锐角，所以cos A =√1−sin 2A =13，因此sin (A −B )=sin A cos B −cos A sin B =10√22720.本题满分12分解：（1）因为点(a n ，b n )在函数f (x )=2x 的图像上，所以b n =2a n ，可得b n+1b n=2a n+12a n=2a n+1−a n =2d .因为点(a 8，4b 7)在函数f (x )的图像上，所以4b 7=2a 8=b 8. 所以2d =b 8b 7=4 ⇒d =2，又a 1=−2，所以数列{a n }的前n 项和为 S n =na 1+n(n −1)d2=−2n +n 2−n =n 2−3n （2）由f (x )=2x ⇒f ′(x )=2x ln 2，所以函数f (x )的图像在点(a 2，b 2)处的切线方程为y −b 2=(2a 2ln 2)(x −a 2)，故切线在x 轴上的截距为a 2−1ln2，从而a 2−1ln2=2−1ln2，故a 2=2. 从而a n =n ，b n =2n ，a n b n =n2n .T n =12+222+323+⋯+n2n 上式两边同乘以12，可得12T n =122+223+324+⋯+n 2n+1 两式右边错项相减可得12T n =12+122+123+124+⋯+12n −n 2n+1=1−12n −n 2n+1=1−n +22n+1 故T n =2−n+22n . 21.本题满分12分.解：用A 、B 、C 分别表示事件甲、乙、丙面试合格，由题意可知A 、B 、C 相互独立，且P (A )=P (B )=P (C )=12（1）至少有1人面试合格的概率是1−P(A B C)=1−P(A)P(B)P(C)=1−(12)3=78（2）ξ的可能取值为0，1，2，3.P (ξ=0)=P(ABC)+P(A BC)+P(A B C).=P(A)P (B )P(C)+P(A)P(B)P (C )+P(A)P(B)P(C) =(12)3+(12)3+(12)3=38.P (ξ=1)=P(ABC)+P(ABC)+P(AB C)=P (A )P (B )P(C)+P (A )P(B)P (C )+P (A )P(B)P(C)=(12)3+(12)3+(12)3=38.P (ξ=2)=P(ABC)= P(A)P (B )P (C )=18.P (ξ=3)=P (ABC )= P (A )P (B )P (C )=18.所以，ξ的分布列如下表ξ的期望是E(ξ)=0×38+1×38+2×18+3×18=1.22.本题满分14分解：（1）直线l1的方程为y1x−x1y=0，由点到直线的距离公式可知点C到直线l1的距离为d=|y x−x y|√x12+y12因为|OA|=√x12+y12，所以，S=12|OA|∙d=|y1x2−x1y2|2.（2）由{y=kxx2+2y2=1，消去y解得x12=11+2k2，由（1）得S=12|x1y2−x2y1|=12|√33x1−√33kx1|=√3|k−1|6√1+2k2由题意知√3|| 6√1+2k2=1 3，解得k=−1或k=−1 5 .(3)设l1：y=kx，则 l2：y=mkx，设A(x1，y1)，C(x2，y2)由{y=kxx2+2y2=1，得x12=11+2k2，同理x22=11+2(mk)2=k2k2+2m2，由(1)知，S=12|x1y2−x2y1|=12|x1∙mx1k−x2∙kx1|=12∙|k2−m||k|∙|x1x2|=|2|2√1+2k2∙√k2+2m2整理得(8S2−1)k4+(4S2+16S2m2+2m)k2+(8S2−1)m2=0，由题意知S与k无关，则{8S2−1=04S2+16S2m2+2m=0，解得{S2=18m=−12，所以m=−12.23.本题满分12分解：(1)当x=4时，y=102+4×(4−6)2=21，此时该店每日销售产品A所获得的利润为(4−2)×21=42千元.(2)该店每日销售产品A所获得的利润为f(x)=(x−2)∙[10x−2+4(x−6)2] =10+4(x−6)2(x−2)=4x3−56x2+240x−278(2<x<6)，从而f′(x)=12x2−112x+240=4(3x−10)(x−6) (2<x<6)，令f′(x)=0，得x=103，易知在(2，103)上，f′(x)>0，函数f(x)单调递增；在(103，6)上，f′(x)<0，函数f(x)单调递减.所以x=103是函数f(x)在（2，6）内的极大值点，也是最大值点.即当x=103≈3.3时，函数f(x)取得最大值.故当销售价格为3.3元/件时，利润最大.24.本题满分14分（1）证明：取AB中点F，连接MF、NF，∵M为AD中点，∴MF∥BD，∵BD⊂平面BDE，MF⊄平面BDE，∴MF∥平面BDE．∵N为BC中点，∴NF∥AC，又D、E分别为AP、PC的中点，∴DE∥AC，则NF∥DE．∵DE⊂平面BDE，NF⊄平面BDE，∴NF∥平面BDE．又MF∩NF=F．∴平面MFN∥平面BDE，则MN∥平面BDE；（2）解：∵PA⊥底面ABC，∠BAC=90°．∴以A为原点，分别以AB、AC、AP所在直线为x、y、z轴建立空间直角坐标系．∵PA=AC=4，AB=2，∴A（0，0，0），B（2，0，0），C（0，4，0），M（0，0，1），N（1，2，0），E（0，2，2），则MN →=(1，2，−1)，ME →=(0，2，1)， 设平面MEN 的一个法向量为m →=(x ，y ，z)，由{m →⋅MN →=0m →⋅ME →=0，得{x +2y −z =02y +z =0，取z =2，得m →=(4，−1，2)． 由图可得平面CME 的一个法向量为n →=(1，0，0)． ∴cos ＜m →，n →＞=m →⋅n→|m →||n →|=√21×1=4√2121． ∴二面角C ﹣EM ﹣N 的余弦值为4√2121，则正弦值为√10521； （3）解：设AH =t ，则H （0，0，t ），NH →=(−1，−2，t)，BE →=(−2，2，2)． ∵直线NH 与直线BE 所成角的余弦值为√721， ∴|cos ＜NH →，BE →＞|=|NH →⋅BE→|NH →||BE →||=|√5+t 2×2√3|=√721． 解得：t =85或t =12．∴线段AH 的长为85或12．。