佛山市高考数学模拟试卷及答案3篇

佛山市高考数学模拟试卷及答案1　　一、选择题：本大题共12个小题,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.　　1.已知为实数集，集合，则()　　A.B.C.D.下面是小编为大家整理的佛山市高考数学模拟试卷及答案3篇,供大家参考。

佛山市高考数学模拟试卷及答案1

　　一、选择题：本大题共12个小题,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.

　　1.已知 为实数集，集合 ，则 ( )

　　A. B. C. D.

　　2.复数 (其中 为虚数单位)， 为 的共轭复数，则下列结论正确的是( )

　　A. B. C. D.

　　3.已知实数 ， 满足 ，则 的最小值是( )

　　A.0 B.1 C.2 D.3

　　4.已知等比数列 的前 项和为 ，则“ ”是“ ”的( )

　　A.充分不必要条件 B.必要不充分条件

　　C.充分必要条件 D.既不充分也不必要条件

　　5.已知 ，则 ( )

　　A. B. C. D.

　　6.某几何体的三视图如图所示，则该几何体的表面积为( )

　　A. B. C. D.

　　7.若将函数 的图象向左*移 ( )个单位，所得图象关于原点对称，则 最小时， ( )

　　A. B. C. D.

　　8.现行普通高中学生在高一升高二时面临着选文理科的问题，学校抽取了部分男、女学生意愿的一份样本，制作出如下两个等高堆积条形图：

　　根据这两幅图中的信息，下列哪个统计结论是不正确的( )

　　A.样本中的女生数量多于男生数量

　　B.样本中有理科意愿的学生数量多于有文科意愿的学生数量

　　C.样本中的男生偏爱理科

　　D.样本中的女生偏爱文科

　　9.运行如图所示的程序框图，输出 和 的值分别为( )

　　A.2，15 B.2，7 C.3，15 D.3，7

　　10.直角 中， 为斜边 边的.高，若 ， ，则 ( )

　　A. B. C. D.

　　11.已知双曲线 ： ( ， )的一条渐近线为 ，圆 ： 与 交于 ， 两点，若 是等腰直角三角形，且 (其中 为坐标原点)，则双曲线 的离心率为( )

　　A. B. C. D.

　　12.设函数 ( )满足 ，现给出如下结论：

　　①若 是 上的增函数，则 是 的增函数;

　　②若 ，则 有极值;

　　③对任意实数 ，直线 与曲线 有唯一公共点.

　　其中正确结论的个数为( )

　　A.0 B.1 C.2 D.3

　　第Ⅱ卷(共90分)

　　二、填空题(每题5分，满分20分，将答案填在答题纸上)

　　13.若直线 与曲线 相切，则 .

　　14.有3女2男共5名志愿者要全部分到3个社区去参加志愿服务，每个社区1到2人，甲、乙两名女志愿者需到同一社区，男志愿者到不同社区，则不同的分法种数为 .

　　15.已知点 ，抛物线 ： ( )的准线为 ，点 在 上，作 于 ，且 ， ，则 .

　　16.某沿海四个城市 、 、 、 的位置如图所示，其中 ， ， ， ， ， 位于 的北偏东 方向.现在有一艘轮船从 出发以 的速度向 直线航行， 后，轮船由于天气原因收到指令改向城市 直线航行，收到指令时城市 对于轮船的方位角是南偏西 度，则 .

　　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.已知数列 满足 ， ，数列 的前 项和为 ，且 .

　　(Ⅰ)求数列 ， 的通项公式;

　　(Ⅱ)设 ，求数列 的前 项和 .

　　18.某保险公司针对企业职工推出一款意外险产品，每年每人只要交少量保费，发生意外后可一次性获赔50万元.保险公司把职工从事的所有岗位共分为 、 、 三类工种，根据历史数据统计出三类工种的每赔付频率如下表(并以此估计赔付概率).

　　(Ⅰ)根据规定，该产品各工种保单的期望利润都不得超过保费的20%，试分别确定各类工种每张保单保费的上限;

　　(Ⅱ)某企业共有职工20000人，从事三类工种的人数分布比例如图，老板准备为全体职工每人购买一份此种保险，并以(Ⅰ)中计算的各类保险上限购买，试估计保险公司在这宗交易中的期望利润.

　　19.如图，矩形 中， ， ， 在 边上，且 ，将 沿 折到 的位置，使得*面 *面 .

　　(Ⅰ)求证： ;

　　(Ⅱ)求二面角 的余弦值.

　　20.已知椭圆 ： ( )的焦距为4，左、右焦点分别为 、 ，且 与抛物线 ： 的交点所在的直线经过 .

　　(Ⅰ)求椭圆 的方程;

　　(Ⅱ)分别过 、 作*行直线 、 ，若直线 与 交于 ， 两点，与抛物线 无公共点，直线 与 交于 ， 两点，其中点 ， 在 轴上方，求四边形 的面积的取值范围.

　　21.设函数 ，其中 ， 是自然对数的底数.

　　(Ⅰ)若 是 上的增函数，求 的取值范围;

　　(Ⅱ)若 ，证明： .

　　请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分.

　　22.选修4-4：坐标系与参数方程

　　在*面直角坐标系 中，曲线 ： ，曲线 ： ( 为参数)，以坐标原点 为极点， 轴正半轴为极轴，建立极坐标系.

　　(Ⅰ)求曲线 ， 的极坐标方程;

　　(Ⅱ)曲线 ： ( 为参数， ， )分别交 ， 于 ， 两点，当 取何值时， 取得最大值.

　　23.选修4-5：不等式选讲

　　已知函数 .

　　(Ⅰ)当 时，求不等式 的解集;

　　(Ⅱ)设 ，且存在 ，使得 ，求 的取值范围.

佛山市高考数学模拟试卷及答案3篇扩展阅读

——届广东佛山市高考英语模拟试卷及答案

届广东佛山市高考英语模拟试卷及答案1

　　I. Listening Comprehension

　　Section A

　　听力(略)

　　II. Grammar and Vocabulary

　　Section A

　　Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.

　　Whether in the workplace or the football field , effective teamwork can produce amazing results , However , _____21_______(work) successfully as a team is not as easy as it may seem. Effective teamwork certainly does not just happen automatically , it takes a great deal of hard work and compromise . There are a number of factors ____22___must be in place to make a good team.

　　Effective leadership is one of the most important factors of good teamwork . The team’s leader should possess the skills ____23____(create) a positive working environment and motivate and inspire the team members to talk a positive approach to work and be committed. An effective team leader will promote a high level of spirit and make them feel ____24_____(value)

　　Communication is a vital factor of all interpersonal relationship and especially that of a team . Team members must be able to express their feelings , share ideas and see each other’s opinions.

　　Conflicts will arise ____25____well a team functions together . The best way to deal with conflicts is to have some organized methods of handling conflicts. Team members should be able to voice their concerns ____26_____fear of offending others. Instead of avoiding conflict issues , a practical approach that ____27____(settle) them quickly is much better . It is often advised that the team leader sit with the conflicting parties and help work out their differences without taking sides and try to remain objective if possible .

　　The team leader ___28____set a good example to create good teamwork . In order to keep team members positive and motivated , the team leader ____29_____needs to show these qualities . The team turns to the leader for support and guidance . So any negative words or behaviors on the leader’s part can be disastrous.

　　Regardless of ___30_____type of work you are in , knowing how to effectively work on and with a team is going to be extremely important to your success and that of your team.

　　Section B

　　Directions: Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.

　　A. approach B. shape C. previously D. evident E. secret F. date

　　G. hardly H.remains I. irrelevant J. potential K. particularly

　　Swedish Archaeologists Make New Discoveries

　　Archaeologists have begun exploring an unknown ancient city at a village called Vlochos , five hours north of Athens . The Archaeological ____31______are scattered on and around the Strongiloveni hill on the great Thessaliam plains and can be traced to several historical periods.

　　“What used to be considered remains of some _____32____settlement can now be upgraded to remains of a city higher significance than _____33______thought,” says Robin Ronnland , PhD student in Classical Archaeology and Ancient History at the university of Gotheoburg and leader of the firework.

　　“We came across the site which has never been explored before in connection with another project last year and retailed the great __34_____right away .”

　　Working together with the Swedish Institute at Athens and the local archaeological service in Karditsa , the Vlochos Archacological Project (VLAP) was started with an aim to explore the remains . The project’s research team completed the first field season during two weeks in September 2016.

　　Ronnlund says that the hill is hiding many ____35_____. Remains of towers , walls and city gates can be found on the mountaintop and slopes , but __36_____anything is visible on the ground below . The ambition is to avoid digging and instead use ____37____such as ground—penetrating radar. This will enable the team to leave the site in the same ____38____as it was in when they arrived. The success of this method is _____39____from the results of the first field season.

　　“ We found a town square and a street network that indicate that we are dealing with quite a large city . The area inside the city wall measured over 40 hectares . We also found ancient pottery and coins that can help to ___40____the city . Our oldest finds are from around 500 BC, but the city seems to have flourished mainly from the fourth to the third century BC before it was abandoned for some reason , maybe in connection with the Roman conquest of the area.

　　Ronnlund believes that the Swedish-Greek project can provide important clues as to what happened during this violent period in Greek history.

　　III. Reading Comprehension

　　Section A

　　Directions: For each blank in the following passage 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.

　　Why College is Not Home

　　The college years are supposed to be a time for important growth in autonomy (自主性) and the development of adult identity . However , now they are becoming an ___41____period of adolescence , during which many of today’s students are not shouldered with adult _____42____.

　　In the past two decades , continued connections with and ___43____on family , thanks to cell phones , email and social media , have increased significantly . Some parents go so far as to help with coursework . Instead of promoting the idea of college as a passage from the shelter of the family to autonomy ,universities have ____44_____to the idea that they should provide the same environment as that of the home.

　　To prepare for increased autonomy and responsibility , college need to be a time of ___45____and experimentation . This process involves “trying on” new ways of thinking about oneself both intellectually and personally ._____46_____we should provide “safe spaces” within colleges , we must also make it safe to express opinions and challenge majority views.____47_____ growth and flexibility are fostered by strict debate and questioning .

　　Learning to deal with the ___48____world is equally important . Because a college community (群体) differs from the family , many students will struggle to find a sense of ____49___. If students rely on administrations to ___50_____their social behavior and thinking pattern ,they are not facing the challenge of finding an identity ,within a larger and complex community .

　　______51___,the tendency for universities to monitor and __52_____student behavior runs up against another characteristic of young adults: the response to being controlled by their elders . If acceptable social behavior is too strictly defined (规定)， the insensitive or aggressive behavior that administrators are seeking to minimize many actually be _____53___. It is not surprising that young people are likely to burst out , particularly when there are reasons to do so .

　　Our generation once joined hands and stood from at times of national emergence . What is lacking today is the _____54____between desire for autonomy and their understanding of an unsafe world. Therefore , there is the desire for their home to be replacement homes and not places to experience growth .But Every college discussion about community values ,social climates and behavior should include ___55__of the development importance of students autonomy and self-regulation.

　　41. A. expanded B. educational C. expected D. extended

　　42. A. responsibilities B. abilities C. knowledge D. experience

　　43. A. concentration B. dependence C. influence D. decision

　　44. A. give up B. give away C. give in D. give out

　　45. A. instruction B. exploration C. reflection D. preparation

　　46. A. When B. While C. Since D. If

　　47. A. Intellectual B. Spiritual C. Logical D. Psychological

　　48. A. adult B. virtual C. real D. social

　　49. A. satisfaction B. duty C. belonging D. curiosity

　　50. A. understand B. train C. protect D. regulate

　　51. A. Therefore B. Moreover C. Thus D. However

　　52. A. change B. criticize C. shape D. motivate

　　53. A. encouraged B. challenged C. agreed D. realized

　　54. A. difference B. tension C. balance D. conflict

　　55. A. observation B. recognition C. determination D. judgment

　　Section B

　　Directions:

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

　　(A)

　　The Right Thing

　　“ Hi , Mrs , Grady ,” said Mark when their neighbor opened her door. “ Would you like us to shovel your sidewalk and driveway ?” Shoveling was Jamie’s idea , a way to earn enough money for the new Ocean Kingdom video game that came out the next day .

　　Mrs .Grady was happy , “ That would be wonderful , boys . I think the job is getting to be too much for me .

　　“It will cost 10 dollars ,” Jamie said .” If that’s OK “, Mark added .

　　‘ Oh dear , “ Mrs. Grady said disappointedly , “ I haven’t been able to get to the bank . I can offer homemade cookies ,but I realize that’s not what you had in mind .”

　　Mark was going to say that Mrs . Grady could pay them another time , but Jamie cut him off .“ We’ll come back later .”

　　Mrs. Grady doesn’t look like the person who’d come to his rescue last summer when Mr. Dunn’s collie , Goldie had just wanted to play , but Mark didn’t feel comfortable around big dogs . He wanted to call for help , but his tongue seemed locked behind his teeth. Then Mrs . Grady ‘s front door had flown open . She must have seen him from across the street. ‘ Hold on , Mark . I’m coming !” “ Goldie” she’d called . As soon as Goldie had turned her head , Mrs . Grady had slipped between Mark and the dog . She wasn’t much taller than Mark , but she’d stood firm as a rock in front of him. ‘ Goldie , go home!” Then she’d swept her broom to hurry the dog along .” Get!” Goldie had obeyed.

　　When Mark showed thanks to Mrs.Grady , Mrs. Grady laughed .” It was nothing . Good neighbors watch out for each other , don’t they ? “

　　And now Mrs. Grady needed Mark as much as he’d needed her last summer. He smiled and waved at Mrs. Grady , then his shovel deep into the snow.

　　“ Hey!” Jamie shouted . “What are you doing ?” Mark couldn’t explain about Goldie and watching out for neighbors .” I like Mrs. Grady’s cookies ,” he said .

　　56. Why did Jamie and Mark plan to clear the snow for Mrs .Grany at first?

　　A. To help the lady B. To earn pocket money

　　C. To do volunteer work D. To visit New Kingdom

　　57. Mrs . Grady couldn’t pay them most probably because ________.

　　A. she didn’t have enough cash B. she couldn’t find the bank

　　C. she thought it was worthless D. she couldn’t afford it

　　58. According to the story, which of the following word can not be used to describe Mrs.Grady ?

　　A. Positive B. Helpful C. Brave D. Hopeful

　　59. Which of the following proverb can best summarize the story ?

　　A. A penny saved is a penny earned B. Kindness is repaid with kindness

　　C. A clear conscience D. Actions speak louder than work

　　B

　　This is What a Real Sliver Dollar Looks Like

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　　You Can"t Afford to Lose

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　　Timing is Everything

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　　60. Suppose you want to purchase seven 2017 U.S . Mint Sliver Engles by post , you should pay at least _________.

　　A. $ 273.55 B. $263.55 C. $275.65 D. $266.55

　　61. The 2017 Sliver Eagle is worth purchasing mainly because _________

　　A. the price of the coin is favorable B. the coin is of lasting high quality

　　C. the coin is popular among collectors D. it can be circulated as a currency

　　62. If you are not willing to pay for the service , you can purchase the silver coin by _________.

　　A. shopping on .New York Mint .com B. dialing the number 1-888-201-7143

　　C. writing to the enterprise D. lining up in front of the stores in person

　　C

　　"Today, technical innovations dominate our everyday life in many areas. New technologies, however, always are associated with risks -- and these are also seen by laymen," says Christoph Böhmert, first author of the recently published study and researcher of the Science Communication Group of KIT"s Institute for German Studies. "It is crucial to enable adequate communication between science and society, which does not only consider scientific findings, but also concerns of the population." The study clearly showed that communication of risks may be complicated sometimes. Information on efficient precautions was found to lead to an increased risk perception by the recipients of the information.

　　In their study, the researchers *yzed communication about a technology that has become indispensable in our life -- mobile communications and the electromagnetic fields (电磁场)on which it is based. All over the world, radiation protection authorities, such as the German Federal Office for Radiation Protection, communicate the current state of research into risks of electromagnetic fields as follows: Investigations made and all findings obtained so far do not allow any conclusions to be drawn with respect to mobile communications being a risk for human health. But, the experts continue, there still are knowledge gaps as regards long-term impacts. Then, measures are recommended to reduce exposure of the individual to electromagnetic fields.

　　It had been known from previous studies already that information on precautions may increase worries. It had been suspected that people conclude from the recommendation of precautions that there really is a risk. This effect was not confirmed by the recent study. The scientists rather attributed the increased worries to a lack of knowledge about the propagation(传播) of electromagnetic fields.

　　Within the framework of the study, the recommended precautions were submitted to 1717 Australians, together with one of six information brochures providing scientific background information. When test persons were given not only the recommendations, but also explained why observation of these tips strongly reduces their exposure to electromagnetic fields, worries increased. For example, scientists explained to the test persons that telephone conversations with a headset largely reduce exposure. When a mobile phone is located ten centimeters instead of just one centimeter away from the ear, the electric power absorbed by the ear is about one hundredth of the initial value. Hence, the own mobile phone usually causes an exposure that by far exceeds that of mobile communications stations that are generally referred to as "cellphone towers." While the scientists wanted to explain the effectiveness of precautions, test persons mainly considered this information to be an indication of their mobile phone -- not the transmission towers -- being dangerous. As a result, they perceived increased risk potentials for telephone conversations with their mobile phones.

　　"The study reveals that messages on precautions and information are a double-edged sword in terms of subjective risk perception. Their use should be far better understood," Boehmert says.

　　63. Which of the following statements is TRUE according to the passage ?

　　A. Adequate information on efficient precautions can relieve the concerns of the public

　　B. Mobile communications definitely do harm to people’s health in the long run.

　　C. Information about technologies and their risks may have undesired side effects.

　　D. Observation of the precautions can help reduce the concerns of the public

　　66. According to the passage ,we can conclude that the best way to relieve the inappriate worries is to __________.

　　A. enable the users to know better of science and technology .

　　B. produce new electric products with a lower radiation value

　　C. provide the public with less information on effective precaution

　　D. inform the public about the potential risks with more patience

　　65. The word “ precaution” ( first appears in paragraph 1) in bold letters has the closets meaning to _______-

　　A. introduction B. intention C. recommendation D. prevetion

　　66. Which of the following might be the best title of the passage ?

　　A. Science and Technology : A Double –edged Sword

　　B. Technical Innovation : Worries and Information

　　C. Science and Technology: Security Tips for Users

　　D. Technical Innovations : Effectiveness of Precautions .

　　Section C

　　Directions: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.

　　To Please Your Friends, Tell Them What They Already Knew

　　The research emeraged out of some real-life observations shared by Gilbert and co-authors Gus Cooney and Timothy D. Wilson：“Conversation is the most common of all human social activities, and doing it well requires that we know what our conversation partners most want to hear.___67___”says psychological scientist Daniel T, Gilbert of Harvard University.

　　“When our friends try to tell us about movies we’ve never seen or albums we’ve never heard, we usually find ourselves bored, confused, and underwhelmed. ___68___. And yet, as soon as it’s our turn to speak, we do exactlly the same thing to our friends – with exactly the same consequences. We wanted to understand why this happens.”Gilbert explains. The researchers decided to do this by conducting a series of experiments.

　　In their first experiment, the researchers assigned participants to groups of three, with one person acting as the speaker and the other two acting as listeners. Speakers watched a video and then tried do describe it to the listeners. Some of the listeners had seen the video the speakere was describing, and others had not.

　　___69___. When the speakers were done speaking, the listeners rated them on these aspects. The results showed that speakers’ predictions were exactly backwards. Speakers expected listeners to respond more positively to their stories when the listeners had not seen the video they were describing ___70___. Although speakers expected listeners to enjoy hearing about a novel experience more than a familiar one, it was actually the other way around.

　　A second study showed that when asked to predict their own reactions before hearing the story, listeners made the same mistake that speakers did.

　　Ⅳ. Summary Writing

　　Directions：Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.

　　Moving My Curfew

　　For some time now , I have had an 8:00 p.m. curfew ---the time by which I have to be at home , even on weekends. When I was younger , I didn’t really complain . But now I have reached an age when this curfew is no longer suitable . For several reasons , it is clearly time to move my curfew to 10:00 p.m. on weekends.

　　First of all , I ’m soon going to be an adult , like all teenagers , I need practice handling the greater freedom that goes along with being an adult . When teenagers don’t get practice handling freedom , they often make many serious mistakes. For example , some teenagers go away to college and suddenly they don’t know how to handle it , and they get into trouble . I believe it is better to increase freedom gradually . That may the teenager learners how to handle freedom responsibly . I believe I could handle a later curfew without making serious mistakes in judgment.

　　A later curfew is also important to me because I’m an active student . As you know , I am often on the committee in charge of running extra-curricular activities .Because of my present curfew , I have to finish school activities over an hour before they are over. Others students must take over for me when I leave . A 10:00 curfew would allow me to stay until the end of school functions and give me enough time to get home without rushing .

　　Finally , I am a teenager who can be trusted to handle a 10:00 p.m curfew . I know that many teenagers cannot handle much responsibility . However , I am clearly not that kind of teenager. I have proven myself to be a very responsible person . For example , I have never been in serious trouble , either at school or in the company . I also hold a part-time job and still manage to maintain a “B” average in school . In other words , I am a person who uses my time wisely , meets responsibilities an stays out of trouble .

　　V. Translation

　　Directions: Translate the following sentences into English, using the words given in the brackets.

　　72. 现如今人们越来越关注自己的生活品质。(concerned)

　　73. 春游的"小学生们没能抵制住商贩们的花言巧语。(resist)

　　74. 只有通过参与志愿者活动才能有效地增强中学生服务大众的责任感。(Only )

　　75. 家用轿车普及带来的便利不容否认，但随之产生的能源浪费、空气污染和交通拥堵等问题发人深思。(While)

　　VI. Guided Writing

　　Directions: Write an English composition in 120-150 words according to the instructions given below in Chinese.

　　假如你是某英语报读者信箱栏目的编辑Alex. 请你根据Tom 来信反映的问题写一封信。

　　Dear Alex,

　　I got a mean message online from someone at school . They say I ’m stupid and ugly . I feel sad and worried . I don’t know what to do . Please help me .

　　From Tom

　　你的回信须包含以下要点：

　　①安慰Tom

　　② 提出解决问题的办法

——届襄阳市高考数学模拟试卷及答案

届襄阳市高考数学模拟试卷及答案1

　　一、选择题(本大题共12个小题，每小题5分，共60分.在每小题给出的四个选项中，只有一个选项是符合题目要求的).

　　1. 设集合 ， ，则 ( )

　　A. B. C. D.

　　2. 已知复数 在复*面上对应的点在直线 上，复数 ( 是虚数单位)，则 ( )

　　A. B. C. D.

　　3. 若 ，则 的值为( )

　　A. B. C. D.

　　4. 在 内随机取出两个数，则这两个数满足 的概率为( )

　　A. B. C. D.

　　5. 若圆 与直线 交于不同的两点，则实数 的取值范围为( )

　　A. B. C. D.

　　6. 70年代中期，美国各所名牌大学校园内，人们都像发疯一般，夜以继日，废寝忘食地玩一个数学游戏.这个游戏十分简单：任意写出一个自然数 ，并且按照以下的规律进行变换：如果是个奇数，则下一步变成 ;如果是个偶数，则下一步变成 .不单单是学生，甚至连教师、研究员、教授与学究都纷纷加入.为什么这个游戏的魅力经久不衰?因为人们发现，无论 是怎样一个数字，最终都无法逃脱回到谷底 .准确地说，是无法逃出落入底部的 循环，永远也逃不出这样的宿命.这就是著名的“冰雹猜想”.按照这种运算，自然数 经过十步运算得到的数为 (　　)

　　A. B. C. D.

　　7. 在 中， ， ， 分别为内角 ， ， 的对边，且 ，则 的值为( )

　　A. B. C. D.

　　8. 某几何体的三视图如图所示，若该几何体的体积为 ，则图中 的值为( )

　　A. B. C. D.

　　9. 运行如下程序框图，如果输入的 ，则输出 属于( )

　　A. B. C. D.

　　10. 已知向量 ， ， ，若 与 的夹角为60°，且 ，则实数 的值为( )

　　A. B. C. 6 D. 4

　　11. 如图，在四边形 中， ， ， .现沿对角线 折起，使得*面 *面 ，且三棱锥 的"体积为 ，此时点 ， ， ， 在同一个球面上，则该球的体积是( )

　　A. B. C. D.

　　12. 已知函数 存在极值，若这些极值的和大于 ，则实数 的取值范围为( )

　　A. B. C. D.

　　第Ⅱ卷

　　本试卷包括必考题和选考题两部分.第13题～第21题为必考题，每个试题考生都必须作答.第22题～第23题为选考题，考生根据要求作答.

　　二、填空题(本大题共4小题，每小题5分，共20分)

　　13. 若 ，其中 ，则 的值为 .

　　14. 已知函数 ，若 ，实数 满足约束条件 ，则目标函数 的最大值为 .

　　15. 过点 的直线交抛物线 于 两点，若抛物线的焦点为 ，则 面积的最小值为 .

　　16. 以下四个命题：

　　①已知随机变量 ，若 ，则 的值为 ;

　　②设 ，则“ ”是“ ”的充分不必要条件;

　　③函数 的零点个数为1;

　　④命题 ，,则 为 .

　　其中真命题的序号为 .

　　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12分)

　　已知数列 为公差不为0的等差数列，满足 ，且 成等比数列.

　　(1)求 的通项公式;

　　(2)若数列 满足 ，且 ，求数列 的前 项和 .

　　18. (本小题满分12分)

　　已知在四棱锥 中， *面 , , 是边长为 的等边三角形， ， 为 的中点.

　　(1)求证： ;

　　(2)若直线 与*面 所成角的正切值为 ，

　　求二面角 的大小.

　　19. (本小题满分12分)

　　近年来，微信越来越受欢迎，许多人通过微信表达自己、交流思想和传递信息，微信是现代生活中进行信息交流的重要工具.而微信支付为用户带来了全新的支付体验，支付环节由此变得简便而快捷.某商场随机对商场购物的 名顾客进行统计，其中 岁以下占 ，采用微信支付的占 ， 岁以上采用微信支付的占 .

　　(1)请完成下面 列联表：

　　岁以下 岁以上 合计

　　使用微信支付

　　未使用微信支付

　　合计

　　并由列联表中所得数据判断有多大的把握认为“使用微信支付与年龄有关”?

　　(2)采用分层抽样的方法从 名顾客中抽取 人参与抽奖活动，一等奖两名，记 “ 岁以下”得一等奖的人数为 ，求 的分布列及数学期望.

　　参考公式: ， .

　　参考数据：

　　20. (本小题满分12分)

　　已知椭圆的两个焦点为 ， ， 是椭圆上一点，若 ， .

　　(1)求椭圆的方程;

　　(2)点 是椭圆上任意一点， 分别是椭圆的左、右顶点，直线 与直线 分别交于 两点，试证：以 为直径的圆交 轴于定点，并求该定点的坐标.

　　21. (本小题满分12分)

　　已知函数 .

　　(1)如果对于任意的 ， 恒成立，求实数 的取值范围;

　　(2)若 ，过点 作函数 的图象的所有切线，令各切点的横坐标按从小到大构成数列 ，求数列 的所有项之和.

　　请考生在第22、23两题中任选一题作答.注意：只能做所选定的题目.如果多做，则按所做的第一个题目计分.

　　22. (本小题满分10分)选修4-4：坐标系与参数方程

　　在直角坐标系 中，点 ，以原点为极点， 轴正半轴为极轴建立极坐标系，曲线 的极坐标方程为 .直线 的参数方程为 为参数 .

　　(Ⅰ)写出曲线 的直角坐标方程和直线 的普通方程;

　　(Ⅱ)设直线 与曲线 的两个交点分别为 ，求 的值.

　　23. (本小题满分10分)选修4-5：不等式选讲

　　已知函数 .

　　(Ⅰ)解不等式 ;

　　(Ⅱ)若关于 的不等式 在 上的解集为 ，求实数 的取值范围.

——届佛山市高考英语模拟试卷及答案

届佛山市高考英语模拟试卷及答案1

　　第Ⅰ卷

　　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)

　　阅读下面短文，从每题所给的ABCD四个选项中，选出最佳答案，并在答题卡上将该项涂黑。

　　A

　　Mobile phones and iPads are now wonderful tools for learning and teaching English. With the help of the thousands of education and language apps available online, students can make effective use of them to learn in an interactive environment. Given below is a list of some of the best apps for learning and teaching English.

　　Grammar Up

　　Grammar is the heart of any language and, thus, the Grammar Up app is one of the most highly recommended apps for English learners. This app is specifically designed for people who want to improve their grammar, vocabulary and word selection. It consists of more than 1,800 multiple-choice questions grouped under twenty different grammar categories.

　　iFPoems

　　iFPoems is a fantastic app for poetry lovers. This app consists of a great collection of poems from famous poets around the world. It also allows users to save their favorites along with recording their own readings of the poems.

　　iBooks

　　iBooks is a complete book library for the iPad users. It includes the iBookstore and allows users to download and read books. The app features a beautiful bookshelf, on which you can browse various books or even add notes to your favorite paragraphs in the book. You can also create your own texts and upload them into the app.

　　SpeakingPal

　　Recommended as one of the best apps for English educators and learners, SpeakingPal allows you to record your speech and compare it with a native English speaker. This amazing app combines video with automatic speech recognition software that tests your English speaking skills. You just have to speak with a video character and get immediate response on how well you speak English.

　　21. What do these apps have in common?

　　A. They can be found online. B. They are free of charge.

　　C. They improve users’ grammar. D. They’re designed by teachers.

　　22. What can we do with iBooks?

　　A. Download books for free. B. Write notes on it with pens.

　　C. Save notes and texts. D. Create a bookstore.

　　23. What is special about SpeakingPal?

　　A. It offers video call service. B. It evaluates users’ speech.

　　C. It offers talks with a native speaker. D. It includes English speaking contests.

　　B

　　I don’t want kids. I know I wouldn’t make for a very good mother. It’s not that I’d drop them or forget them at the grocery store or anything like that but they’re not a good fit for me and the life I’ve created for myself. I’d rather be in Cambodia kissing elephants or cage diving with sharks in Cape Town, or wandering the streets of Paris, a city that has become my second home, than trapped at home doing the mom thing.

　　The itch to become a mother isn’t in me but the itch to travel, and travel far and often, is.

　　If the urge isn’t there, I don’t think it’s fair to live a life I don’t want and have a baby because someone else thinks I should. That would be awful.

　　I like children. To say I love them wouldn’t be completely accurate. It’s not because I’m a monster — the same monster people who feel women should have children will call me — but I sim* don’t love them because I’m not around them much. Very few of my friends have children, and the ones who do I don’t see much because, well, they have children.

　　I have two nephews in Colorado whom I love to pieces, but I don’t see them very often. I don’t go out there as often as I probably should because I’d rather be traveling. Some people may call this selfish, but I call it “living my best life.”

　　When I talk to my sister about my nephews, everything they do and say is exciting to her. The joy my sister feels by just playing with them in the yard is the same joy I feel every time I get off a plane in a new country. I’d rather be on the beaches of Spain every summer while she prefers to spend her days at home with them, climbing trees and such. I’m fulfilled one way, while she’s fulfilled another way.

　　I’m very much certain that at this point in my life my greatest fulfillment comes in the form of traveling and being free of kids. I can go anywhere at anytime; I don’t have to put my life on hold for someone else. It’s complete and total freedom.

　　24. What does the underlined word “itch” in Paragraph Two mean?

　　A. tradition B. competence C. plan D. desire

　　25. Why is the author regarded as a monster?

　　A. Because she doesn’t like kids. B. Because she doesn’t want children.

　　C. Because she’s different from her friends. D. Because she rarely stays with children.

　　26. Which is “living my best life” according to the author?

　　A. To stay with her family. B. To see her nephews often.

　　C. To visit a new country. D. To talk with her sister.

　　27. What is the author’s purpose of writing the passage?

　　A. To explain her choice of life. B. To persuade people to travel.

　　C. To share her happiness in life. D. To introduce a unique lifestyle.

　　C

　　Long school holidays help students clear their heads, relax a little and stretch their brains in different ways.

　　Traditionally, schooling schedules have long been based more on the needs of society than on efficient education strategies. For instance, in Iceland it was traditionally arranged to allow children to help out with harvest. Other countries have long summer vacations because it is sim* too hot to study. In other areas where religion plays an important role in the holiday season, the religion calendar then calls for the break, so that students can have ample time to participate in the religious ceremonies and traditions of seasonal holidays.

　　There are some obvious advantages to a vacation that lasts longer. Families who live a long distance from relatives are able to travel together, sometimes across the ocean, in order to connect with their loved ones. Even if there is no visiting family far away, a long holiday is a great opportunity for kids to interact with the community. From an educational point of view, a child that is able to experience another culture can gain valuable language, history, and social skills.

　　Long school holidays are also needed in schools that have become overly academic and too exam-focused in recent years, which requires a considerably longer holiday break from such a “marathon pumping (灌输) of knowledge,” and it makes great sense!

　　Great psychologists, like Freud and Piaget, have stressed play’s central role in the formation of fully-rounded (全面发展的`) individuals, so the long holiday achieves this by allowing students to explore the world outside school. The students get to participate in activities that would be difficult to do during a regular school term.

　　As a consequence, long school holiday can be quite constructive to our students!

　　28. What traditionally determines the arrangement of school holidays?

　　A. Local needs. B. Cultural activities.

　　C. Religious customs. D. Academic performance.

　　29. Which is one of the advantages of long holidays?

　　A. Students run away from exams. B. Children can learn science and history.

　　C. Fewer courses are required at school. D. Family bonds are strengthened.

　　30. Freud and Piaget may probably agree that ________________.

　　A. schools need longer holidays B. holiday activities are necessary

　　C. play is more important than learning D. students should travel around the world

　　31. What is the best title of the passage?

　　A. Traditional School Holidays B. Activities for Long Holidays

　　C. Benefits of Long Holidays D. Advice from Psychologists

　　D

　　Every February 14, people worldwide demonstrate their affection for family members, friends, teachers, and significant others with a gift or two. However, this display of love does not come cheap. 55% of Americans celebrate Valentine’s Day in 2017 by spending an average of 136.57 dollars each. It is no wonder that retailers (零售商) love the holiday.

　　In 1861, Richard Cadbury, a man from a British chocolate company came up with the idea of packaging chocolates in heart-shaped boxes for Valentine’s Day. Not surprisingly, they were an instant success, and a tradition was born. Today, Americans spend over one billion dollars handing out boxes of chocolates to their loved ones. Sweethearts, the heart-shaped candy, are also very popular. According to the manufacturer, a majority of the 8 billion pieces of candy made annually are sold between January 1 and February 14.

　　Massachusetts businesswoman Esther Howland popularized Valentine’s Day greeting cards in America. Often called “The Mother of the American Valentine”, the artist was the first to sell handmade paper cards with messages of love to retailers. With over 145 million cards bought in the US and over a billion worldwide, Valentine’s Day is now one of the biggest business chances for greeting card companies. It is no wonder that the day is often referred to as a “Hallmark Holiday”.

　　Flowers are also very popular. About 51% of people, mainly men, buy red roses for their loved ones. Given that Valentine’s Day is very popular for wedding proposals (求婚), it should not come as a surprise that a lot of the money spent on this day is used to buy fine jewelry. With a quarter of Americans treating their loved ones to a romantic meal, the day is also much welcomed by restaurant owners.

　　Pope Gelasius, the man who made February 14 Valentine’s Day in 496 AD, would have never imagined that this festival would change into such an expensive celebration!

　　32. What does the first paragraph mainly tell us?

　　A. People buy their friends gifts on February 14.

　　B. Valentine’s Day is celebrated every year.

　　C. Valentine’s Day is a good time to show love.

　　D. A lot of money is spent on Valentine’s Day.

　　33. Which is true about Richard Cadbury’s idea?

　　A. It resulted in a new taste of chocolate.

　　B. It led to the birth of a new tradition.

　　C. It was put forward on Valentine’s Day.

　　D. It helped the company earn one billion dollars.

　　34. Valentine’s Day is referred to “Hallmark Day” because _______________.

　　A. people get greeting cards on that day

　　B. it was popularized by Miss Howland

　　C. it offers cards companies big business chances

　　D. retails help send messages of love on that day

　　35. What is probably a necessary gift for a wedding proposal according to the passage?

　　A. Heart-shaped candy. B. Messages of love.

　　C. A romantic meal. D. A piece of jewelry.

　　第二节 (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入空白处的最佳选项。选项中有两项为

　　多余选项。

　　Information Overload

　　In modern society, if we’re trying to make a decision, we often have so much information that we get confused, and we don’t know what to do. This state is known as information overload. 36 It can cause stress, frustration and reduced productivity. But what can we do in the face of information overload?

　　• Plan for only one time each day to check e-mail, social messaging sites, chat rooms, etc. Don’t allow yourself to check multiple times, unless you truly are waiting for an important e-mail. 37 And that eats up your valuable time before getting away.

　　• If you are suffering from too many electronic interruptions during the weekday, ask people to call or text you during work hours only if it’s really an emergency. 38

　　• Remind yourself that it’s okay to not know everything. In fact, it’s impossible to keep up with the pace of the information superhighway. The sooner you accept that, the happier you’ll be. 39 It is good to fall behind on the information that really isn’t worth your attention.

　　• 40 Set aside a regular time each week where you and other family members do not use any kind of electronic media technologies, including television. It could be something you do every weekend, or perhaps an hour or two every evening.

　　A. Just catch up with the happiest moment.

　　B. Know what’s worth knowing and what isn’t.

　　C. Almost everyone suffers from it to some degree.

　　D. Spend time with your family free from electronic products.

　　E. We need to find some effective ways to process the information.

　　F. Each time you go online, you run the risk of being addicted to it.

　　G. Otherwise they and you end up stealing time from your employer.

　　第三部分 英语知识运用 (共两节，满分45分)

　　第一节 完形填空(共20小题;每小题1.5分，满分30 分)

　　阅读下面短文，从每题所给的A、B、C 和 D 四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

　　Most 7-year-old girls are playing Barbie and jumping rope. Though Sailor Gutzler may have enjoyed those 41 , she was also an active participant in 42 activities with her father. He was a pilot and he taught her 43 skills. She actually used these 44 when her family’s twin-engine plane 45 upside down in rural Kentucky. They’d been traveling 46 to Illinois in cold weather from a Christmas vacation in Key West, Florida.

　　Sailor had broken bones, but when she couldn’t 47 her father, mother, sister or cousin after the crash, she 48 herself from the remains, lit a stick on the burning wing of the plane and walked 49 for a mile through the cold darkness of the wooded Kentucky 50 .

　　Sailor 51 the nearest house, hoping to get help for her 52 . She told the woman who answered the 53 that she’d been in a(n) 54 and that her parents were dead.

　　Though the temperature was 5℃ below zero, Sailor was wearing clothing meant for the

　　55 Florida and only had on one sock. 56 , she’s a survivor.

　　Though her father had been 57 since he was 16 and was a flight 58 for more than 4,000 hours, disaster still struck. He had made the same exact 59 many times but still, the weather won. 60 , he’d taught his daughter what to do and she did it.

　　41. A. ropes B. sports C. activities D. dolls

　　42. A. outdoor B. social C. school D. daily

　　43. A. repair B. flight C. communication D. survival

　　44. A. skills B. tricks C. thoughts D. activities

　　45. A. flew B. landed C. swung D. appeared

　　46. A. around B. home C. abroad D. everywhere

　　47. A. wake up B. struggle for C. call out to D. get contact with

　　48. A. hid B. supported C. pulled D. protected

　　49. A. fast B. steadily C. heavily D. endlessly

　　50. A. countryside B. tunnel C. wonderland D. desert

　　51. A. got ready for B. went on for C. made it to D. looked forward to

　　52. A. fear B. loss C. plane D. family

　　53. A. question B. request C. girl D. door

　　54. A. crash B. attack C. holiday D. dilemma

　　55. A. remote B. warm C. rainy D. famous

　　56. A. Actually B. Besides C. Finally D. Still

　　57. A. practicing B. flying C. studying D. fighting

　　58. A. agent B. planner C. steward D. instructor

　　59. A. decision B. trip C. mistake D. plan

　　60. A. Previously B. Accidentally C. Fortunately D. Amazingly

　　第 II 卷

　　第三部分 英语知识运用(共两节 满分45)

　　第二节 (共10小题;每小题1.5 分，满15分)

　　阅读下面短文，在空白处填入 1个适当的内容或括号内单词的正确形式。

　　A balanced diet means the nutrition of three meals in a day should be balanced, and breakfast is very important to achieve that goal. Skipping breakfast 61 (cause) damage to health, apart from reducing work performance. 62 (study) have showed that if a person does not eat breakfast 63 (regular), he or she will be 64 a higher risk of various diseases.

　　However, many people do not eat breakfast. A recent survey shows that 8.6 percent of people do not eat breakfast every day. The situation is even 65 (bad) in poverty-stricken areas.

　　While most people are used to 66 (eat) breakfast, the quality of their meal is in question. About 25 percent of people do not eat a homemade breakfast, 67 more than 80 percent of people do not consume a healthy breakfast.

　　Children, women, and people living in poverty-stricken areas are most likely to be affected 68 it comes to eating unhealthy breakfasts. However, old people 69

　　(age) above 60 tend to have healthy breakfast, because this group, mostly retired, have time and 70 (patient) to cook breakfast themselves.

　　第四部分 写作(共两节，满分 35)

　　第一节 短文改错(共 10小题;每小题1分，满分10 分)

　　假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。文*有10处语言错误，每句中最多有两处。每处错误仅涉及一个单词的增加、删除或修

　　改。

　　Ms. Trump is my history teacher. She loves a subject that she teaches and has a completely knowledge of it, too. History comes alive in his class, where no one talks about something but the topic. She likes to teach by telling stories, what always makes her lessons so interesting but easy to understand. Ms. Trump also has a good knowledge of other subject and often links it to what she teaches about. The best part about her is that she’s always nice to those students who needs more time to grasp the subject, encouraging them ask questions so that they can understand the subject better.

　　第二节 书面表达(满分 25分)

　　假定你是李华，是你校“读书俱乐部”的负责人，计划在下个月组织“英语读书节”。

　　请给你的美国笔友Tony写信，介绍本次活动，并请他为本次读书节推荐阅读书目。

　　注意：

　　1. 词数100左右;

　　2. 可以适当增加细节，以使行文连贯;

　　3. 信的开头和结尾已给出，不计入总词数。

　　Dear Tony,

　　...........................................................................................................................................................................................................................

　　Looking forward to your early re*!

　　Yours,

　　Li Hua

——届乌鲁木齐市高三数学模拟试卷及答案

届乌鲁木齐市高三数学模拟试卷及答案1

　　一、选择题：本大题共12个小题，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.

　　1.设集合A={x|x2﹣3x+2<0}，B={x|1

　　A.A=B B.A⊇B C.A⊆B D.A∩B=∅

　　2.若复数 为纯虚数(i为虚数单位)，则实数m等于(　　)

　　A.﹣1 B. C. D.1

　　3.等差数列{an}中，已知a1=2，a3+a5=10，则a7等于(　　)

　　A.5 B.6 C.8 D.10

　　4.“log2a>log2b”是“ ”的(　　)

　　A.充分不必要条件 B.必要不充分条件

　　C.充要条件 D.既不充分也不必要条件

　　5.明朝数学家程大位将“孙子定理”(也称“*剩余定理”)编成易于上口的《孙子歌诀》：三人同行七十稀，五树梅花廿一支，七子团圆正半月，除百零五便得知.已知正整数n被3除余2，被5除余3，被7除余4，求n的最小值.按此歌诀得算法如图，则输出n的结果为(　　)

　　A.53 B.54 C.158 D.263

　　6.下列函数中，以 为最小正周期的偶函数是(　　)

　　A. B.y=sin22x﹣cos22x

　　C.y=sin2x+cos2x D.y=sin2xcos2x

　　7.已知实数x，y满足 ，则z=﹣3x﹣y的最大值为(　　)

　　A.﹣19 B.﹣7 C.﹣5 D.﹣4

　　8.已知x，y∈R，x2+y2+xy=315，则x2+y2﹣xy的最小值是(　　)

　　A.35 B.105 C.140 D.210

　　9.某几何体的三视图如图所示，则该几何体的表面积为(　　)

　　A.8+2π B.8+3π C.10+2π D.10+3π

　　10.已知双曲线 的左，右焦点分别为F1，F2，点A在双曲线上，且AF2⊥x轴，若△AF1F2的内切圆半价为 ，则其离心率为(　　)

　　A. B.2 C. D.

　　11.球O与棱长为2的正方体ABCD﹣A1B1C1D1的各个面都相切，点M为棱DD1的中点，则*面ACM截球O所得截面的面积为(　　)

　　A. B.π C. D.

　　12.已知对任意实数k>1，关于x的不等式 在(0，+∞)上恒成立，则a的最大整数值为(　　)

　　A.0 B.﹣1 C.﹣2 D.﹣3

　　二、填空题(每题5分，满分20分，将答案填在答题纸上)

　　13.若单位向量 满足 ，则向量 的夹角的余弦值为　　.

　　14.学校拟安排六位老师至5 月1日至5月3日值班，要求每人值班一天，每天安排两人，若六位老师中王老师不能值5月2日，李老师不能值5月3日的班，则满足此要求的概率为　　.

　　15.若P是抛物线y2=8x上的动点，点Q在以点C(2，0)为圆心，半径长等于1的圆上运动.则|PQ|+|PC|的最小值为　　.

　　16.已知定义在R上的奇函数f(x)满足 ，Sn为数列{an}的前n项和，且Sn=2an+n，则f(a5)+f(a6)=　　.

　　三、解答题(本大题共5小题，共70分.解答应写出文字说明、证明过程或演算步骤.)

　　17.△ABC中，角A，B，C的对边分别是a，b，c，已知(2a+b)sinA+(2b+a)sinB=2csinC.

　　(Ⅰ)求C的大小;

　　(Ⅱ)若 ，求△ABC周长的最大值.

　　18.如图，在直三棱柱ABC﹣A1B1C1中，△ABC是正三角形，E是棱BB1的中点.

　　(Ⅰ)求证*面AEC1⊥*面AA1C1C;

　　(Ⅱ)若AA1=AB，求二面角C﹣AE﹣C1的*面角的余弦值.

　　19.对某地区儿童的身高与体重的一组数据，我们用两种模型①y=bx+a，②y=cedx拟合，得到回归方程分别为 ， ，作残差分析，如表：

　　身高x(cm) 60 70 80 90 100 110

　　体重y(kg) 6 8 10 14 15 18

　　0.41 0.01 1.21 ﹣0.19 0.41

　　﹣0.36 0.07 0.12 1.69 ﹣0.34 ﹣1.12

　　(Ⅰ)求表中空格内的值;

　　(Ⅱ)根据残差比较模型①，②的拟合效果，决定选择哪个模型;

　　(Ⅲ)残差大于1kg的样本点被认为是异常数据，应剔除，剔除后对(Ⅱ)所选择的模型重新建立回归方程.

　　(结果保留到小数点后两位)

　　附：对于一组数据(x1，y1)，(x2，y2)，…(xn，yn)，其回归直线y=bx+a的斜率和截距的最小二乘法估计分别为 ， .

　　20.在*面直角坐标系xOy中，M，N是x轴上的动点，且|OM|2+|ON|2=8，过点M，N分别作斜率为 的两条直线交于点P，设点P的轨迹为曲线E.

　　(Ⅰ)求曲线E的方程;

　　(Ⅱ)过点Q(1，1)的两条直线分别交曲线E于点A，C和B，D，且AB∥CD，求证直线AB的斜率为定值.

　　21.设函数 .

　　(Ⅰ)讨论f(x)的单调性;

　　(Ⅱ)当a<﹣2时，讨论f(x)的零点个数.

　　请考生在22、23两题中任选一题作答，如果多做，则按所做的第一题记分.[选修4-4：坐标系与参数方程]

　　22.已知直线l的参数方程为 (t为参数， )，以坐标原点为极点，x轴正半轴为极轴建立极坐标系，圆C的极坐标方程为ρ=2cosθ.

　　(Ⅰ)讨论直线l与圆C的公共点个数;

　　(Ⅱ)过极点作直线l的垂线，垂足为P，求点P的轨迹与圆C相交所得弦长.

　　[选修4-5：不等式选讲]

　　23.已知函数f(x)=|2x﹣1|+|x+a|.

　　(Ⅰ)当a=1时，求y=f(x)图象与直线y=3围成区域的面积;

　　(Ⅱ)若f(x)的最小值为1，求a的值.

——届扬州市高考数学模拟试卷及答案

届扬州市高考数学模拟试卷及答案1

　　一、填空题(本大题共14小题，每小题5分，共70分，请将答案填写在答题卷相应位置)

　　1.已知 ，则 ▲ .

　　2.若复数 满足 ，则复数 在复*面上对应的点在第 ▲ 象限.

　　3.随着社会的发展，食品安全问题渐渐成为社会关注的热点，为了提高学生的食品安全意识，某学校组织全校学生参加食品安全知识竞赛，成绩的频率分布直方图如下图所示，数据的分组依次为 ， ， ， ，若该校的学生总人数为3000，则成绩不超过60分的学生人数大约为 ▲ .

　　4.在区间 内任取一个实数 , 则满足 的概率为 ▲ .

　　5.如图是一个算法流程图，则输出 的值为 ▲ .

　　6.函数 的定义域为 ▲ .

　　7.已知双曲线 的一条渐近线方程为 ，则该双曲线的焦距为

　　▲ .

　　8.已知 ，则 ▲ .

　　9.已知圆锥的侧面展开图是半径为4，圆心角等于 的扇形，则这个圆锥的体积是 ▲

　　10.已知圆 为常数)与直线 相交于 两点，若 ，则实数 ▲ .

　　11、设等差数列 的前 项和为 ，若 ， ， 则 的最小值为 ▲ .

　　12.若动直线 与函数 ， 的图象分别交于 两点，则线段 长度的最大值为 ▲ .

　　13.在 中， 、 分别是 、 的`中点， 是直线 上的动点.若 的面积为2，则 的最小值为 ▲ .

　　14.已知函数 有两个不相等的零点 ，则 的最大值为 ▲ .

　　二、解答题(本大题共6小题，共90分.解答应写出必要的文字说明、证明过程或演算步骤)

　　15.(本小题满分14分)

　　在 中，角A,B,C的对边分别为a,b,c，若 ， .

　　⑴求 的值;

　　⑵若 ，求 的面积.

　　16.(本小题满分14分)

　　如图，在四棱锥P-ABCD中，底面ABCD为梯形，CD∥AB，AB=2CD， AC交BD于O，锐角 PAD所在*面⊥底面ABCD，PA⊥BD，点Q在侧棱PC上，且PQ=2QC.

　　求证：⑴PA∥*面QBD;

　　⑵BD AD.

　　17.(本小题满分14分)

　　如图是一座桥的截面图，桥的路面由三段曲线构成，曲线 和曲线 分别是顶点在路面 、 的抛物线的一部分，曲线 是圆弧，已知它们在接点 、 处的切线相同，若桥的最高点 到水*面的距离 米，圆弧的弓高 米，圆弧所对的弦长 米.

　　(1)求弧 所在圆的半径;

　　(2)求桥底 的长.

　　18.(本小题满分16分)

　　如图，已知椭圆 的左顶点 ，且点 在椭圆上， 、 分别是椭圆的左、右焦点。过点 作斜率为 的直线交椭圆 于另一点 ，直线 交椭圆 于点 .

　　(1)求椭圆 的标准方程;

　　(2)若 为等腰三角形，求点 的坐标;

　　(3)若 ，求 的值.

　　19.(本小题满分16分)

　　已知函数 ，其中 为参数.

　　(1)当 时，求函数 在 处的切线方程;

　　(2)讨论函数 极值点的个数，并说明理由;

　　(3)若对任意 ， 恒成立，求实数 的取值范围.

　　20.(本小题满分16分)

　　已知各项不为零的数列 的前 项和为 ，且 ， ， .

　　(1)若 成等比数列，求实数 的值;

　　(2)若 成等差数列，

　　①求数列 的通项公式;

　　②在 与 间插入 个正数，共同组成公比为 的等比数列，若不等式

　　对任意的 恒成立，求实数 的最大值.

　　扬州市2017届高三考前调研测试

　　数学Ⅱ(附加题 共40分)

　　21.[选修4-2：矩阵与变换](本小题满分10分)

　　已知矩阵 ，设曲线C： 在矩阵 对应的变换下得到曲线C′，求C′的方程.

　　22.[选修4-4：坐标系与参数方程](本小题满分10分)

　　在极坐标系中，直线 和圆C的极坐标方程为 ( )和 .若直线 与圆C有且只有一个公共点，求a的值.

　　23.(本小题满分10分)

　　某校举办校园科技文化艺术节，在同一时间安排《生活趣味数学》和《校园舞蹈赏析》两场讲座.已知A、B两学习小组各有5位同学，每位同学在两场讲座任意选听一场.若A组1人选听《生活趣味数学》，其余4人选听《校园舞蹈赏析》;B组2人选听《生活趣味数学》，其余3人选听《校园舞蹈赏析》.

　　⑴若从此10人中任意选出3人，求选出的3人中恰有2人选听《校园舞蹈赏析》的概率;

　　⑵若从A、B两组中各任选2人，设 为选出的4人中选听《生活趣味数学》的人数，求 的分布列和数学期望 .

　　24. (本小题满分10分)

　　在数列 中， ( )

　　⑴试将 表示为 的函数关系式;

　　⑵若数列 满足 ( )，猜想 与 的大小关系，并证明你的结论.

——届苏州市高考数学模拟试卷及答案

届苏州市高考数学模拟试卷及答案1

　　一.填空题：本大題共14小败，每小題5分，共70分.不需要写出解答过程

　　1.已知集合U={1，2，3，4，5，6，7}，M={x|x2﹣6x+5≤0，x∈Z}，则∁UM=　　.

　　2.若复数z满足z+i= ，其中i为虚数单位，则|z|=　　.

　　3.函数f(x)= 的定义域为　　.

　　4.如图是给出的一种算法，则该算法输出的结果是

　　5.某高级中学共有900名学生，现用分层抽样的方法从该校学 生中抽取1个容量为45的样本，其中高一年级抽20人，高三年级抽10人，则该校高二年级学生人数为　　.

　　6.已知正四棱锥的底面边长是2，侧棱长是 ，则该正四棱锥的体积为　　.

　　7.从集合{1，2，3，4}中任取两个不同的数，则这两个数的和为3的倍数的槪率为　　.

　　8.在*面直角坐标系xOy中，已知抛物线y2=8x的焦点恰好是双曲线 ﹣ =l的右焦点，则双曲线的离心率为　　.

　　9.设等比数列{an}的前n项和为Sn，若S3，S9，S6成等差数列.且a2+a5=4，则a8的值为　　.

　　10.在*面直角坐标系xOy中，过点M(1，0)的直线l与圆x2+y2=5交于A，B两点，其中A点在第一象限，且 =2 ，则直线l的方程为　　.

　　11.在△ABC中，已知AB=1，AC=2，∠A=60°，若点P满足 = + ，且 • =1，则实数λ的值为　　.

　　12.已知sinα=3sin(α+ )，则tan(α+ )=　　.

　　13.若函数f(x)= ，则函数y=|f(x)|﹣ 的零点个数为　　.

　　14.若正数x，y满足15x﹣y=22，则x3+y3﹣x2﹣y2的最小值为　　.

　　二.解答题：本大题共6小题，共计90分

　　15.在△ABC中，a，b，c分别为角A，B，C的对边.若acosB=3，bcosA=l，且A﹣B=

　　(1)求边c的长;

　　(2)求角B的大小.

　　16.如图，在斜三梭柱ABC﹣A1B1C1中，侧面AA1C1C是菱形，AC1与A1C交于点O，E是棱AB上一点，且OE∥*面BCC1B1

　　(1)求证：E是AB中点;

　　(2)若AC1⊥A1B，求证：AC1⊥BC.

　　17.某单位将举办庆典活动，要在广场上竖立一形状为等腰梯形的彩门BADC (如图)，设计要求彩门的面积为S (单位：m2)•高为h(单位：m)(S，h为常数)，彩门的下底BC固定在广场地面上，上底和两腰由不锈钢支架构成，设腰和下底的夹角为α，不锈钢支架的长度和记为l.

　　(1)请将l表示成关于α的函数l=f(α);

　　(2)问当α为何值时l最小?并求最小值.

　　18.在*面直角坐标系xOy中，已知椭圆 + =l (a>b>0)的焦距为2，离心率为 ，椭圆的右顶点为A.

　　(1)求该椭圆的方程：

　　(2)过点D( ，﹣ )作直线PQ交椭圆于两个不同点P，Q，求证：直线AP，AQ的

　　斜率之和为定值.

　　19.己知函数f(x)=(x+l)lnx﹣ax+a (a为正实数，且为常数)

　　(1)若f(x)在(0，+∞)上单调递增，求a的取值范围;

　　(2)若不等式(x﹣1)f(x)≥0恒成立，求a的取值范围.

　　20.己知n为正整数，数列{an}满足an>0，4(n+1)an2﹣nan+12=0，设数列{bn}满足bn=

　　(1)求证：数列{ }为等比数列;

　　(2)若数列{bn}是等差数列，求实数t的值：

　　(3)若数列{bn}是等差数列，前n项和为Sn，对任意的n∈N*，均存在m∈N*，使得8a12Sn﹣a14n2=16bm成立，求满足条件的所有整数a1的值.

　　四.选做题本题包括A，B，C，D四个小题，请选做其中两题，若多做，则按作答的前两题评分.A.[选修4一1：几何证明选讲]

　　21.如图，圆O的直径AB=6，C为圆周上一点，BC=3，过C作圆的切线l，过A作l的垂线AD，AD分别与直线l、圆交于点D、E.求∠DAC的度数与线段AE的长.

　　[选修4-2：矩阵与变换]

　　22.已知二阶矩阵M有特征值λ=8及对应的一个特征向量 =[ ]，并且矩阵M对应的变换将点(﹣1，2)变换成(﹣2，4).

　　(1)求矩阵M;

　　(2)求矩阵M的另一个特征值.

　　[选修4-4：坐标系与参数方程]

　　23.已知圆O1和圆O2的极坐标方程分别为ρ=2， .

　　(1)把圆O1和圆O2的极坐标方程化为直角坐标方程;

　　(2)求经过两圆交点的直线的极坐标方程.

　　[选修4-5：不等式选讲]

　　24.已知a，b，c为正数，且a+b+c=3，求 + + 的最大值.

　　四.必做题：每小题0分，共计20分

　　25.如图，已知正四棱锥P﹣ABCD中，PA=AB=2，点M，N分别在PA，BD上，且 = = .

　　(1)求异面直线MN与PC所成角的大小;

　　(2)求二面角N﹣PC﹣B的余弦值.

　　26.设|θ|< ，n为正整数，数列{an}的通项公式an=sin tannθ，其前n项和为Sn

　　(1)求证：当n为偶函数时，an=0;当n为奇函数时，an=(﹣1) tannθ;

　　(2)求证：对任何正整数n，S2n= sin2θ•[1+(﹣1)n+1tan2nθ].

——届遂宁市高考文科数学模拟试卷题目及答案

届遂宁市高考文科数学模拟试卷题目及答案1

　　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，只有一个是符合题目要求的.

　　1.若集合A={x∈N|x≤2}，B={x|3x﹣x2≥0}，则A∩B为(　　)

　　A.{x|0≤x≤2} B.{1，2} C.{x|0

　　2.复数z=cos +isin 在复*面内对应的点在(　　)

　　A.第一象限 B.第二象限 C.第三象限 D.第四象限

　　3.已知向量 ， 的夹角为 ，且 ， ，则 =(　　)

　　A. B.61 C. D.7

　　4.我国古代数学名著《九章算术》中记载了公元前344年商鞅督造一种标准量器商鞅铜方升，其三视图如图所示(单位：寸)，若π取3，且图中的x为1.6(寸).则其体积为(　　)

　　A.0.4π+11.4立方寸 B.13.8立方寸

　　C.12.6立方寸 D.16.2立方寸

　　5.已知直线ax+y﹣2=0与圆C：(x﹣1)2+(y﹣a)2=4相交于A，B 两点，且线段AB是圆C的所有弦中最长的一条弦，则实数a=(　　)

　　A.2 B.±1 C.1或2 D.1

　　6.表面积为24的正方体的顶点都在同一球面上，则该球的体积为(　　)

　　A.12π B. C. π D. π

　　7.函数y=Asin(ωx+ϕ) 的部分图象如图所示，则其在区间 上的单调递减区间是(　　)

　　A. 和 B. 和

　　C. 和 D. 和

　　8.某程序框图如图所示，若该程序运行后输出的值是 ，则(　　)

　　A.a=3 B.a=4 C.a=5 D.a=6

　　9.已知cos(α﹣ )+sinα= ，则sin(α+ )的值是(　　)

　　A. B.﹣ C.﹣ D.

　　10.已知函数f(x)=x2﹣x﹣2，x∈，在定义域内任取一点x0，使f(x0)≤0的概率是(　　)

　　A. B. C. D.

　　11.已知直线l过椭圆C： 的左焦点F且交椭圆C于A、B两点.O为坐标原点，若OA⊥OB，则点O到直线AB的距离为(　　)

　　A. B.2 C. D.

　　12.已知函数g(x)的导函数g"(x)=ex，且g(0)g"(1)=e，(其中e为自然对数的底数).若∃x∈(0，+∞)，使得不等式 成立，则实数m的取值范围是(　　)

　　A.(﹣∞，1) B.(﹣∞，3) C.(3，+∞) D.(﹣∞，4﹣e)

　　二、填空题：本大题共4个小题，每小题5分，共20分.

　　13.函数 的值域是　　.

　　14.已知实数x，y满足 ，则z=2x﹣3y的最小值为　　.

　　15.在△ABC中，BC=2，B=60°，若△ABC的面积等于 ，则AC边长为　　.

　　16.已知函数f(x)= 的图象上存在不同的两点A，B，使得曲线y=f(x)在这两点处的切线重合，则实数a的取值范围是　　.

　　三、解答题：本大题共5小题，共70分.解答应写出文字说明、证明过程或演算步骤.

　　17.等比数列{an}的各项均为正数，且 .

　　(1)求数列{an}的通项公式;

　　(2)设bn=log3a1+log3a2+…+log3an，求数列 的前n项和Tn.

　　18.如图，在直三棱柱ABC﹣A1B1C1中，AB=BC=BB1，AB1∩A1B=E，D为AC上的点，B1C∥*面A1BD;

　　(Ⅰ)求证：BD⊥*面A1ACC1;

　　(Ⅱ)若AB=1，且AC•AD=1，求三棱锥A﹣BCB1的体积.

　　19.某公司为了解广告投入对销售收益的影响，在若干地区各投入4万元广告费用，并将各地的销售收益绘制成频率分布直方图(如图所示).由于工作人员操作失误，横轴的数据丢失，但可以确定横轴是从0开始计数的.

　　22.在直角坐标系xOy中，以O为极点，x轴的正半轴为极轴建立极坐标系，已知直线l的参数方程为 ，(t为参数)，曲线C的普通方程为x2﹣4x+y2﹣2y=0，点P的极坐标为(2 ， ).

　　(1)求直线l的普通方程和曲线C的极坐标方程;

　　(2)若将直线l向右*移2个单位得到直线l′，设l′与C相交于A，B两点，求△PAB的面积.

　　23.设f(x)=|x﹣b|+|x+b|.

　　(1)当b=1时，求f(x)≤x+2的解集;

　　(2)当x=1时，若不等式f(x)≥ 对任意实数a≠0恒成立，求实数b的取值范围.

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