高考真题数学_2022高考真题数学

       大家好，今天我想和大家探讨一下关于高考真题数学的问题。在这个话题上，有很多不同的观点和看法，但我相信通过深入探讨，我们可以更好地理解它的本质。现在，我将我的理解进行了归纳整理，让我们一起来看看吧。

1.全国甲卷高考数学试卷真题和答案解析[Word文字版]

2.今年安徽高考数学难不难

3.求2012云南高考数学试卷及答案

4.2006上海高考数学 英语试卷和答案

5.新高考I卷高考数学试卷真题和答案解析[Word文字版]

6.求08年江苏数学高考试卷 word 版（带答案）

全国甲卷高考数学试卷真题和答案解析[Word文字版]

       一、全国甲卷高考数学试卷真题和答案解析全国甲卷高考数学试卷真题和答案解析正在快马加鞭的整理当真，考试结束后我们第一时间发布word文字版。考生可以在线点击阅览： ic.

       10. A. He's unable to finish his homework. B. He can’t give the woman his computer.

       C. He's to remove the virus. D. He's infected with some disease.

       Part B Passages

       Directions: In part B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.

       Questions 11 through 13 are based on the following passage.

       11. A. Some engineers. B. The landlord of the pub.

        C. The former employees. D. Some customers of the company.

       12.A.Threeyears ago. B. Five years ago. C. Last year. D. This year.

       13. A. Why a company lost its customers. B. Why a company went out of business.

        C. How a company went from bad to worse. D. How a company got out of its difficult situation

       Questions 14 through 16 are based on the following report.

       14. A. Physics. B. chemistry. C. English Literature. D. Media Studies

       15. A. More than 144,000. B. About 147,500.

       C. 7.5％ of all the test takers. D. 4.6％of all the test takers.

       16. A. Few students avoid harder subjects. B. Each subject has the same level of difficulty.

        C. Some subjects are more difficult than others. D. Pupils are important to t11e country’s development.

       Part C Longer Conversations

       Directions: In Part C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in me numbered blanks with the information you have heard. Write your answers on your answer sheet.

       B1anks l 7 through 20 are based on the following conversation.

       Taxi Order Form

       Name: John Smith

       Time: 5:30 a.m., ___17___, June 8th

       To: The ___18___

       From: 99 Kent Street, near Carlington ___19_____

       Phone Number: ____20____

       Complete the form. Write ONE WORD for each answer.

       Blanks 21 through 24 are based on the following conversation.

       What does the woman complain about? ______21_______

       What does the man suggest the woman do first? She should __22__ all the way to the right.

       Why is the engineer sent up? He is __23__ for maintaining buildings.

       When is it suitable for the engineer to come? ___24___ later.

       Complete the from. Write NO MORE THAN THREE WORDS for each answer.

       Ⅱ. Grammar and Vocabulary

       Directions: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.

       25. —It’s atop secret. —Yes, I see. I will keep the secret _____ you and me

       A. with B. around C. among D. between

       26. Black holes ______ not be seen directly, so determining the number of them is a tough task.

       A. can B. should C. must D. need

       27. Send my regards to your lovely wife when you _______ home.

       A. wrote B. will write C. have written D. write

       28. A typhoon swept across tiffs area with heavy rains and winds_____ strong as 113 miles per hour.

       A. too B. very C. so D. as

       29. I made so many changes in my composition mat only I could read it. To ____ else, it was hard to make out.

       A. none B. everyone C. someone D. anyone

       30. A dozen ideas were considered _____ the chief architect decided on the design of the building.

       A. because B. before C. whether D. unless

       31. Eugene's never willing to alter any of his opinions. It’s no use ____ with him.

       A. to argue B. arguing C. argued D. having argued

       32. When he turned professional at the age of 11, Mike _____ to become a world champion by his coach and parents.

       A. expected B. was expecting C. was expected D. would be expected

       33. Energy drinks are not allowed _____ in Australia but are brought in from New Zealand.

       A. to make B. to be made C. to have been made D. to be making

       34. Russ and Earl were auto mechanics _____ the same pay, but Earl had more ambition.

       A. to earn B. to have earned C. earning D. earned

       35. One advantage of playing the guitar is _____ it can give you a great deal of pleasure.

       A. how B. why C. that D. when

       36. The mother felt herself ____ cold and her hands trembled as she read the letter from the battlefield.

       A. grow B. grown C. to grow D. to have grown

       37. In an hour, we can travel to places _____ would have taken our ancestors days to reach.

       A. where B. when C. which D. what

       38. My parents were quarrelling about me ____ I could not quite tell why.

       A. since B. though C. if D. until

       39. He spoke proudly of his part in the game, without mentioning ____ his teammates had done.

       A. what B. which C. why D. while

       40. _____ automatically the e-mail will be received by all the club members.

       A. Mailed out B. Mailing out C. To be mailed out D. Having mailed out

       41. You can see the stars on a clear night, but in the daytime they are _____.

       A. unavoidable B. invisible C. inaccessible D. unavailable

       42. When Jane began to take swimming lessons, her main _____ was the fear of water.

       A. evidence B. crisis C. obstacle D. danger

       43. Try not to start every sentence with “the”. _____ the beginnings of your sentences.

       A. Vary B. Decorate C. Form D. Describe

       44. I hope I will not be called on in class as I’m not yet _______ prepared.

       A. attentively B. readily C. actively D. adequately

       III. Cloze

       Directions: For each blank in the following passages there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.

       (A)

        Several years ago, well-known writer and editor Norman Cousins became very ill. His body ached and he felt constantly tired. It was difficult for him to even __45__ around. His doctor told him that he would lose the ability to move and eventually die from the disease. He was told he had only a 1 in 500 chance of survival.

        __46__ the diagnosis(诊断), Cousins was determined to overcome the disease and survive. He had always been interested in medicine and had read a book, which discussed the idea of how body chemistry and health can be damaged by emotional stress and negative __47__. The book made Cousins think about the possible __48__ of positive attitudes and emotions. He thought, “Is it possible that love, hope, faith, laughter, confidence, and the __49__ to 1ive have positive treatment value?”

        He decided to concentrate on positive emotions as a way to treat some of the symptoms of his disease. In addition to his traditional medical treatment, he tried to put himself in situations that would __50__ positive emotions. “Laugh therapy” became part of his treatment. He __51__ time each day for watching comedy films, reading humorous books, and doing other activities that would draw out __52__ emotions. Within eight days of starting his ‘‘laugh therapy” program his pain began to __53__ and he was able to sleep more easily. He was able to return to work in a few months’ time and __54__ reached complete recovery after a few years.

       45. A. run B. pass C. move D. travel

       46. A. Besides B. Despite C. Without D. Beyond

       47. A. attitudes B. beliefs C. goals D. positions

       48. A. shortcoming B. harm C. benefit D. interest

       49. A. emotion B. pain C. fear D. will

       50. A. bring about B. set about C. put up D. make up

       51. A. afforded B. appointed C. offered D. arranged

       52. A. positive B. approving C. strong D. mixed

       53. A. escape B. decrease C. shrink D. end

       54. A. generally B. especially C. actually D. presently

       (B)

        “When a customer enters my store, forget me. He is King, ’’said John Wanamaker, who in l876 turned an abandoned railway station in Philadelphia into one of me world’s first department stores. This revolutionary concept __55__ the face of retailing(零售业) and led to the development of advertising and marketing as we know it today.

       But convincing as that slogan was, __56__ the shopper was cheated out of the crown. __57__ manufacturing efficiency increased the variety of goods and lowered prices, people still relied on advertisements to get most information about products. Through much of the past century, ads spoke to an audience restricted to just a few radio or television channels or a __58__number of publications. Now media choice, has __59__ too, and consumers select what they want from a far greater variety of sources—especially with a few clicks of a computer mouse. __60__ the internet, the consumer is finally seizing power.

       As our survey shows, __61__ has great implications for companies, because it is changing the way the world shops. Many firms already claim to be “customer-driven” or “consumer-centred”. Now their __62__ will be tested as never before. Taking advantage of shoppers’ __63__ will no longer be possible: people will know—and soon tell others, even those without the internet—that prices in the next town are cheaper or that certain goods are inferior. The internet is working wonders in __64__ standards. Good and Good and honest firms should benefit most.

       55. A. changed B. maintained C. restored D. rescued

       56. A. in time B. in truth C. in case D. in theory

       57. A. Just as B. The moment C. If D. Although

       58. A. 1imited B. minimum C. sufficient D. great

       59. A. disappeared B. existed C. exploded D. survived

       60. A. According to B. Thanks to C. But for D. Apart from

       61. A. consumer power B. product quality C. purchasing habit D.manufacturing efficiency

       62. A. information B. investment C. claims D. shops

       63. A. generosity B. knowledge C. curiosity D. ignorance

       64. A. raising B. lowering C. abandoning D. carrying

       IV. Reading Comprehension

       Directions： Read the following four passages. Each passage is followed by several questions or unfinished statements. For each of them mere are four choices marked A, B, C and D. Choose the one mat fits best according to me information given in me passage you have just read.

       (A)

        Cara Lang is 13. She lives in Boston, Massachusetts, in me U. S. Last Thursday, she didn't go to school. She went to work with her father instead. Every year, on the fourth Thursday in April, millions of young girls go work. This is Take Our Daughters to Work Day. The girls are between me ages of 9 and 15. They spend the day at work with an adult, usually a mother, father, aunt, or uncle. They go to offices, police stations, laboratories, and other places where their parents or other family members work. Next year, the day will include sons, too.

        The Ms. Foundation, an organization for women, started the program about ten years ago. In the U.S., many women work outside the home. The Ms. Foundation wanted girls to find out about many different kinds of jobs. Then, when the girls grow up, they can choose a job they like.

        Cara's father is a film director. Cara says, “It was very exciting for me to go to the studio with my dad. I saw a lot of people doing different jobs.” Many businesses have special activities for girls on this day. Last year, Cara went to work with her aunt at the University of Massachusetts. In the engineering department, the girls learned to build a bridge with toothpicks and Candy. In the chemistry department, they learned to use scales. They learned about many other kinds of jobs, too.

        Right now, Cara does not know what job she will have when she grows up. But because of Take Our Daughters to Work Day, she knows she h2Ls many choices.

       65. What is Cara's father?

       A. An engineer. B. An official. C. A moviemaker. D. A professor.

       66. According to the passage, Take our Daughters to work Day is ______.

       A. on every Thursday in April B. a holiday for girls of all ages

       C. a day for girls to know about jobs D. a day for girls to get a job easily

       67. On this special day, Cara has done all the following EXCEPT that ____.

       A. she learned to use scales B. she worked as an actress

       C. she went to work with her aunt D. she used toothpicks and Candy to build a bridge

       68. What is probably the best title for the passage?

       A. Cara Lang, a Fortunate Girl B. Take Our Daughters to Work Day

       C. Children's Day and Work Day D. Ms. Foundation, an Organization for Women

       (B)

        Nervous suspects(嫌疑犯) locked up in Britain's newest police station may feel relieved by a pleasant yellow Colour on the door. If they are close to confessing a crime, the blue on the wall might tip the balance.

        Gwent Police have abandoned colours such as greys and browns of the 20th-century police cell(牢房) and have used colour psychology to decorate them.

        Ystrad Mynach station, which recently opened at a cost of￡5 million, has four cells with glass doors for prisoners who suffer from claustrophobia(幽闭恐怖症). Designers have painted the frames yellow, which researchers say is a calming colour. Other cells contain a royal blue line because psychologists believe that the colour is likely to encourage truthfulness.

        The station has 31 cells, including 12 with a “live scan” system for drunken or disturbed prisoners, which detects the rise and fall of their chest. An alarm alerts officers if a prisoner's breathing stops and carries on ringing until the door is opened.

        Designers and psychologists have worked for years on colour. Blue is said to suggest trust, efficiency, duty, logic, coolness, thinking and calm. It also suggests coldness and unfriendliness. It is thought that strong blues will stimulate clear thought and lighter, soft colours will calm the mind and aid concentration.

        Yellow is linked with confidence, self-respect and friendliness. Get the colour wrong and it could cause fear, depression and anxiety, but the right yellow can lift spirits and self-respect.

        Ingrid Collins, a psychologist who specializes in the effects of colour, said that colour was an “energy force”. She said: “Blue does enhance communication but I am not sure it would enhance truthful communication.”

        Yellow, she said, affected the mind. Red, on the other hand, should never be considered because it could increase aggression. Mrs Collins praised the designers for using colours in the cells. Gwent is not the first British force to experiment with colour to calm down or persuade prisoners to co-operate. In the 1990s Strathclyde Police used pink in cells based on research carried out by the US Navy.

       69. The expression “tip the balance” in paragraph 1 probably indicates that the blue might ____.

       A. let suspects keep their balance B. help suspects to confess their crimes

       C. make suspects cold and unfriendly in law court D. enable suspects to change their attitudes to colours

       70. Which of the following colours should NOT be used in cells according to me passage?

       A. Pink. B. Yellow C. Blue. D. Red.

       71. Which of the following helps alert officers if someone stops breathing?

       A. Scanning equipment. B. Royal blue lines. C. Glass doors. D.Yellow frames.

       72. The passage is mainly concerned with ______

       A. the relationship between colours and psychology B. a comparison of different functions of colours

       C. the use of colours in cells to affect criminals’ psychology

       D. scientific ways to help criminals reform themselves in prison

       73. The word “talion” in introducing the book Eye for an Eye is probably a concept of ______.

       A. medicine B. trade C. avenging D. striving

       74. The book entitled A History of Modern Indonesia has focus on _______.

       A. 1andscapes and tourist attractions in Indonesia B. its fourth largest population in the world

       C. its relatively unfamiliar and understudied economy D. its social and political aspects in modern times

       75. What do these books have in common?

       A. Their authors are introduced in detail. B. They all have a hard back and a paperback.

       C. Each of them is commented by a professor. D. They are published by the same publishing house.

       (D)

        The “Bystander Apathy Effect” was first studied by researchers in New York after neighbours ignored—and in some cases turned up the volume on their TVs—the cries of a woman as she was murdered(over a half-hour period). With regard to helping those in difficulty generally, they found that:

       (1) women are helped more than men;

       (2) men help more than women;

       (3) attractive women are helped more than unattractive women.

        Other factors relate to the number of people in the area, whether the person is thought to be in trouble through their own fault, and whether a person sees himself as being able to help.

        According to Adrian Furnham, Professor 0f University College, London, there are three reasons why we tend to stand by doing nothing:

       (1) “Shifting of responsibility”一the more people there are, the less likely help is to be given. Each person excuses himself by thinking someone else will help, so that the more “other people’ there are, the greater the total shifting of responsibility.

       (2) “'Fear of making a mistake'’一situations are often not clear. People think that those involved in an accident may know each other or it may be a joke, so a fear of embarrassment makes them keep themselves to themselves.

       (3) “Fear of the consequences if attention is turned on you, and the person is violent.”

        Laurie Taylor, Professor of Sociology at London University, says: “In the experiments I’ve seen on intervention(介入), much depends on

求08年江苏数学高考试卷 word 版（带答案）

       一、新高考I卷高考数学试卷真题和答案解析新高考I卷高考数学试卷真题和答案解析正在快马加鞭的整理当中，考试结束后我们第一时间发布word文字版。考生可以在线点击阅览： /zt/gaokao/daxuepaiming.html

       二、新高考I卷高考数学卷答题技巧

        一、规范书写

        高考文科数学答题技巧之一就是规范书写，这一点是文理通用的技巧。卷面评分标准就是规范度，这就要求不但要对、而且要全且规范。会而不对，令人惋惜；对而不全，得分不高；表述不规范、字迹不工整又是造成高考数学试卷非智力因素失分的一大方面。因为字迹潦草，会使阅卷老师的第一印象不良，“感情分”也就相应低了，所以高考答题书写要工整，保证卷面能得分。

        二、讲究策略

        对于高考文科数学题要力求做的对、全、得满分，高考文科数学有两种常用方法：

        1。分步解答：对于疑难问题，考生可以将它划分为一系列的步骤，先解决问题的一部分，能解到几步就写几步，每进行一步就可得到这一步的分数，也可以把条件和目标译成数学表达式，设应用题的未知数，设轨迹题的动点坐标，依题意正确画出图形等，都能得分。从局部到整体，形成思路，获得解题成功。在高考文科数学答题过程中尽量多的列举应用到的公式。

        2。跳步解答：当文科数学在解题的某一环节出现问题时，可以跳过这一步，写出后继各步，一直做到底；另外，若题目有两问，第一问做不上，可以第一问为“已知”，完成第二问，这都叫跳步解答。也许后来由于解题的正迁移对中间步骤想起来了，或在时间允许的情况下，经努力而攻下了中间难点，可在相应题尾补上。

        三、合理分配时间

        1、文科数学就是和时间的斗争。高考文科数学试卷一发下来后，首先把全部问题看一遍。找出其中看上去最容易解答的题，然后假定步骤，思考怎么样的顺序解题才最好。

        2、切忌不看题目盲目背题，要仔细审题，清楚题目要求你解决什么问题，然后有条不紊迅速解题，提高准确率。

        3、解题格式要规范，重点步骤要突出。

        4、选择题时间控制在35分中以内。小题小做、巧做、简单做，选择题和填空题要多用数形结合、特殊值验证法等技巧，节约时间。

        5、保持心静，以不变应万变。切莫因旁人的翻卷或其他行为干扰自己的解决思路。这些都是高考文科数学应试答题高分技巧。

        四、掌握文科数学失分原因

        ①对题意缺乏正确的理解，应做到慢审题快做题；

        ②公式记忆不牢，考前一定要熟悉公式、定理、性质等；

        ③思维不严谨，不要忽视易错点；

        ④解题步骤不规范，一定要按课本要求，否则会因不规范答题失分，避免“对而不全”如解概率题，要给出适当的文字说明，不能只列几个式子或单纯的结论，表达不规范、字迹不工整等非智力因素会影响阅卷老师的“感情分”；

        ⑤计算能力差失分多，会做的一定不能放过，不能一味求快，例如平面解析中的圆锥曲线问题就要求较强的运算能力；

        ⑥轻易放弃试题，难题不会做，可分解成小问题，分步解决，如最起码能将文字语言翻译成符号语言、设应用题未知数、设轨迹的动点坐标等，都能拿分。也许随着这些小步骤的罗列，还能悟出解题的灵感。

        正确运用高考文科数学答题技巧，不仅可以预防各种心理障碍造成的不合理丢分和计算失误及笔误，而且能运用科学的检索方法，考出最佳成绩。

        三、新高考I卷哪些省份使用

        适用地区：山东、福建、湖北、江苏、广东、湖南、河北

        四、新高考I卷难吗

        河北考生：

        考完数学，从考场出来那一刻，头都是沉重的，心里说不出的滋味，感觉填空看着都是灰色。今年的数学试题，总体上出的是中规中矩，但是题型很新颖，很抽象，和平时做的题目完全不是一个水平的题目。选择题部分，也比平时难一些，看着题目很简单，但就是不知道怎么入手解题，大题部分，就更崩溃了，只有两道是有点把握得，剩下的都只答了一半。

        总体来讲，试题是比平时要难的，至少难个20分左右。平时也都能考个100来分，这下估计七八十就算幸运了。

        山东考生：

        我觉得数学试题难度还行，今年发挥的还可以，平时都能考个120分，这次感觉会少一些，题目比去年要难一些。我有做过去年的数学试卷，考了127，今年的数学，能110就很知足了。主要是题目比较烧脑，不像平时的题目那样，一看就知道大概咋解题，高考的数学题，估计很多考生都要比平时低一些，今年的考生应该更明显，确实题目是难了一些。 五、安徽高考数学试卷答案解析 一.2022年新高考I卷高考语文试卷真题和答案解析[Word文字版] ;

       绝密★启用前

       2008年普通高等学校招生全国统一考试（江苏卷）

       数 学

       本试卷分第I卷（填空题）和第II卷（解答题）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

       准考证号、姓名，并将条形码粘贴在指定位置上．

       2.选择题答案使用2B

       铅笔填涂，如需改动，用橡皮擦干净后，再选涂其他答案标号；非选择

       题答案使用0.5毫米的黑色中性（签字）笔或炭素笔书写，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．

       5.作选考题时，考生按照题目要求作答，并用2B铅笔在答题卡上把所选题目对应的标号涂黑．

       参考公式:

       样本数据 , , , 的标准差

       其中 为样本平均数

       柱体体积公式

       其中 为底面积， 为高

       一、填空题：本大题共1小题，每小题5分，共70分．

       1. 的最小正周期为 ，其中 ，则 = ▲ ．

       解析本小题考查三角函数的周期公式.

       答案10

       2．一个骰子连续投2 次，点数和为4 的概率 ▲ ．

       解析本小题考查古典概型．基本事件共6×6 个，点数和为4 的有(1,3)、(2,2)、(3,1)共3 个，故

       答案

       3. 表示为 ，则 = ▲ ．

       解析本小题考查复数的除法运算．∵ ，∴ ＝0， ＝1，因此

       答案1

       4.A= ，则A Z 的元素的个数 ▲ ．

       解析本小题考查集合的运算和解一元二次不等式．由 得 ,∵Δ＜0，∴集合A 为 ，因此A Z 的元素不存在．

       答案0

       5. ， 的夹角为 ， ， 则 ▲ ．

       解析本小题考查向量的线性运算．

       = ， 7

       答案7

       6.在平面直角坐标系 中，设D是横坐标与纵坐标的绝对值均不大于2 的点构成的区域， E是到原点的距离不大于1 的点构成的区域，向D 中随机投一点，则落入E 中的概率 ▲ ．

       解析本小题考查古典概型．如图：区域D 表示边长为4 的正方形的内部（含边界），区域E 表示单位圆及其内部，因此．

       答案

       7.算法与统计的题目

       8.直线 是曲线 的一条切线，则实数b＝ ▲ ．

       解析本小题考查导数的几何意义、切线的求法． ，令 得 ，故切点（2，ln2），代入直线方程，得，所以b＝ln2－1．

       答案ln2－1

       9在平面直角坐标系中，设三角形ABC 的顶点分别为A(0,a),B(b,0),C (c,0) ，点P（0，p）在线段AO 上（异于端点），设a,b,c, p 均为非零实数，直线BP,CP 分别交AC , AB 于点E ,F ，一同学已正确算的OE的方程： ，请你求OF的方程：

       （ ▲ ） .

       解析本小题考查直线方程的求法．画草图，由对称性可猜想填 ．事实上，由截距式可得直线AB： ，直线CP： ，两式相减得 ，显然直线AB与CP 的交点F 满足此方程，又原点O 也满足此方程，故为所求直线OF 的方程．

       答案

       10．将全体正整数排成一个三角形数阵：

       1

       2 3

       4 5 6

       7 8 9 10

       ． ． ． ． ． ． ．

       按照以上排列的规律，第n 行（n ≥3）从左向右的第3 个数为 ▲ ．

       解析本小题考查归纳推理和等差数列求和公式．前n－1 行共有正整数1＋2＋…＋（n－1）个，即 个，因此第n 行第3 个数是全体正整数中第 ＋3个，即为 ．

       答案

       11.已知 ， ，则 的最小值 ▲ ．

       解析本小题考查二元基本不等式的运用．由 得 ，代入 得

        ，当且仅当 ＝3 时取“＝”．

       答案3

       12.在平面直角坐标系中，椭圆 1( 0)的焦距为2，以O为圆心， 为半径的圆，过点 作圆的两切线互相垂直，则离心率 = ▲ ．

       解析设切线PA、PB 互相垂直，又半径OA 垂直于PA，所以△OAP 是等腰直角三角形，故 ，解得 ．

       答案

       13．若AB=2, AC= BC ，则 的最大值 ▲ ． ?

       解析本小题考查三角形面积公式、余弦定理以及函数思想．设BC＝ ，则AC＝ ，

       根据面积公式得 = ，根据余弦定理得

        ，代入上式得

        =

       由三角形三边关系有 解得 ，

       故当 时取得 最大值

       答案

       14. 对于 总有 ≥0 成立，则 = ▲ ．

       解析本小题考查函数单调性的综合运用．若x＝0，则不论 取何值， ≥0显然成立；当x＞0 即 时， ≥0可化为，

       设 ，则 ， 所以 在区间 上单调递增，在区间 上单调递减，因此 ，从而 ≥4；

       当x＜0 即 时， ≥0可化为 ，

        在区间 上单调递增，因此 ，从而 ≤4，综上 ＝4

       答案4

       二、解答题：解答应写出文字说明，证明过程或演算步骤．

       15．如图，在平面直角坐标系 中，以 轴为始边做两个锐角 , ，它们的终边分别与单位圆相交于A,B 两点，已知A,B 的横坐标分别为 ．

       （Ⅰ）求tan( )的值；

       （Ⅱ）求 的值．

       解析本小题考查三角函数的定义、两角和的正切、二倍角的正切公式．

       由条件的 ，因为 , 为锐角，所以 =

       因此

       （Ⅰ）tan( )=

       （Ⅱ） ，所以

       ∵ 为锐角，∴ ，∴ =

       16．在四面体ABCD 中，CB= CD, AD⊥BD，且E ,F分别是AB,BD 的中点，

       求证：（Ⅰ）直线EF ‖面ACD ；

       （Ⅱ）面EFC⊥面BCD ．

       解析本小题考查空间直线与平面、平面与平面的位置关系的判定．

       （Ⅰ）∵ E,F 分别是AB,BD 的中点，

       ∴EF 是△ABD 的中位线，∴EF‖AD，

       ∵EF 面ACD ，AD 面ACD ，∴直线EF‖面ACD ．

       （Ⅱ）∵ AD⊥BD ，EF‖AD，∴ EF⊥BD.

       ∵CB=CD, F 是BD的中点，∴CF⊥BD.

       又EF CF=F，∴BD⊥面EFC．∵BD 面BCD，∴面EFC⊥面BCD ．

       17．某地有三家工厂，分别位于矩形ABCD 的顶点A,B 及CD的中点P 处，已知AB=20km,

       CB =10km ，为了处理三家工厂的污水，现要在矩形ABCD 的区域上（含边界），且A,B 与等距离的一点O 处建造一个污水处理厂，并铺设排污管道AO,BO,OP ，设排污管道的总长为 km．

       （Ⅰ）按下列要求写出函数关系式：

       ①设∠BAO= (rad)，将 表示成 的函数关系式；

       ②设OP (km) ，将 表示成x 的函数关系式．

       （Ⅱ）请你选用（Ⅰ）中的一个函数关系式，确定污水处理厂的位置，使三条排污管道总长度最短．

       解析本小题主要考查函数最值的应用．

       （Ⅰ）①由条件知PQ 垂直平分AB，若∠BAO= (rad) ，则 , 故

        ，又OP＝ 10－10ta ，

       所以 ，

       所求函数关系式为

       ②若OP= (km) ，则OQ＝10－ ，所以OA =OB=

       所求函数关系式为

       （Ⅱ）选择函数模型①，

       令 0 得sin ，因为 ，所以 = ，

       当 时， ， 是 的减函数；当 时， ， 是 的增函数，所以当 = 时， 。这时点P 位于线段AB 的中垂线上，且距离AB 边

        km处。

       18．设平面直角坐标系 中，设二次函数 的图象与两坐标轴有三个交点，经过这三个交点的圆记为C．求：

       （Ⅰ）求实数b 的取值范围；

       （Ⅱ）求圆C 的方程；

       （Ⅲ）问圆C 是否经过某定点（其坐标与b 无关）？请证明你的结论．

       解析本小题主要考查二次函数图象与性质、圆的方程的求法．

       （Ⅰ）令 ＝0，得抛物线与 轴交点是（0，b）；

       令 ，由题意b≠0 且Δ＞0，解得b＜1 且b≠0．

       （Ⅱ）设所求圆的一般方程为

       令 ＝0 得 这与 ＝0 是同一个方程，故D＝2，F＝ ．

       令 ＝0 得 ＝0，此方程有一个根为b，代入得出E＝―b―1．

       所以圆C 的方程为 .

       （Ⅲ）圆C 必过定点（0，1）和（－2，1）．

       证明如下：将（0，1）代入圆C 的方程，得左边＝0 ＋1 ＋2×0－（b＋1）＋b＝0，右边＝0，

       所以圆C 必过定点（0，1）．

       同理可证圆C 必过定点（－2，1）．

       19.（Ⅰ）设 是各项均不为零的等差数列（ ），且公差 ，若将此数列删去某一项得到的数列（按原来的顺序）是等比数列：

       ①当n =4时，求 的数值；②求 的所有可能值；

       （Ⅱ）求证：对于一个给定的正整数n(n≥4)，存在一个各项及公差都不为零的等差数列 ，其中任意三项（按原来顺序）都不能组成等比数列．

       解析本小题主要考查等差数列与等比数列的综合运用．

       （Ⅰ）①当n＝4 时， 中不可能删去首项或末项，否则等差数列中连续三项成等比数列，则推出d＝0．

       若删去 ，则有 即

       化简得 ＝0，因为 ≠0，所以 =4 ；

       若删去 ，则有 ，即 ，故得 =1．

       综上 =1或－4．

       ②当n＝5 时， 中同样不可能删去首项或末项．

       若删去 ，则有 ＝ ，即 ．故得 =6 ；

       若删去 ，则 ＝ ，即 ．

       化简得3 ＝0，因为d≠0，所以也不能删去 ；

       若删去 ，则有 ＝ ，即 ．故得 = 2 ．

       当n≥6 时，不存在这样的等差数列．事实上，在数列 ， ， ，…， ， ， 中，

       由于不能删去首项或末项，若删去 ，则必有 ＝ ，这与d≠0 矛盾；同样若删

       去 也有 ＝ ，这与d≠0 矛盾；若删去 ，…， 中任意一个，则必有

        ＝ ，这与d≠0 矛盾．

       综上所述，n∈{4，5}．

       （Ⅱ）略

       20.若 ， ， 为常数，

       且

       （Ⅰ）求 对所有实数成立的充要条件（用 表示）；

       （Ⅱ）设 为两实数， 且 ,若

       求证： 在区间 上的单调增区间的长度和为 （闭区间 的长度定义为 ）．

       解析本小题考查充要条件、指数函数与绝对值函数、不等式的综合运用．

       （Ⅰ） 恒成立

        （*）

       因为

       所以，故只需 （*）恒成立

       综上所述， 对所有实数成立的充要条件是：

       （Ⅱ）1°如果 ，则的图象关于直线 对称．因为 ，所以区间 关于直线 对称．

       因为减区间为 ，增区间为 ，所以单调增区间的长度和为

       2°如果 .

       （1）当 时. ，

       当 ， 因为 ，所以 ，

       故 =

       当 ， 因为 ，所以

       故 =

       因为 ，所以 ，所以 即

       当 时，令 ，则 ，所以 ，

       当 时， ，所以 =

        时， ，所以 =

        在区间 上的单调增区间的长度和

       =

       （2）当 时. ，

       当 ， 因为 ，所以 ，

       故 =

       当 ， 因为 ，所以

       故 =

       因为 ，所以 ，所以

       当 时，令 ，则 ，所以 ，

       当 时， ，所以 =

        时， ，所以 =

        在区间 上的单调增区间的长度和

       =

       综上得 在区间 上的单调增区间的长度和为

       好了，今天关于“高考真题数学”的话题就讲到这里了。希望大家能够对“高考真题数学”有更深入的认识，并从我的回答中得到一些启示。如果您有任何问题或需要进一步的信息，请随时告诉我。