福建省晋江市养正中学2017届高三上学期期中试题（6科6份）.zip

- 1 -福建省晋江市养正中学 2017 届高三数学上学期期中试题 理第Ⅰ卷 (选择题 共 60 分)一、选择题：本大题共 2 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.请把答案涂在答题卡的相应位置. 1、若集合 ，则 （ ）1,0|cos,MNxkZMCNA． B．0 C． D．01,2、已知命题 ，命题 ，则下列命题为真命题的是（ ）12:,logpx3:,xqxRA． B． C． D．qqppq3、设函数 ，若 ，则 （ ）,21xbf142fbA．-1 B． C．-1 或 D． 2334、角 的终边过函数 的定点 P，则 =（ ）log()ayxsincosA． B. C.4 D.575655、函数 的图象大致为（ ）2()sin()fxA B C D6、已知 m， n 表示两条不同直线， α 表示平面．下列说法正确的是( )A．若 ，则 B．若 则 m⊥ n/,//n,C．若 ，则 D．若 ， 则/7、由曲线 xy，直线 2xy及 轴所围成的封闭图形的面积为（ ）A． 316 B． 310 C．4 D．68、使 sin()yx在区间 ],[至少出现 2 次最大值，则 ω 的最小值为（ ）- 2 -A． 25 B． 45 C．  D． 239、已知三棱锥 ABCD 的棱长都相等， E 是 AB 的中点，则异面直线 CE 与 BD 所成角的余弦值为( )A. B. C. D.16 36 13 3310、 的值为2sin47si1coA． B． C． D．13311.设函数 ，若 是 的极大值点，则 的取值范围为（ ）21lnfxaxbxfaA． B． C． D．1,0,0,,0,12.若函数 在区间 上，对 ， ， ， 为一个三角形的三边长，()fxAcA， ， ()fafb()fc则称函数 为“三角形函数”.已知函数 在区间 上是“三角形函数” ，lnxm21[,]e则实数 的取值范围为（ ）mA． B． C. D．21(,)e2(,)e1(,)e2(,)e第Ⅱ卷（非选择题 共 90 分）二、填空题:本大题共 4 小题，每小题 5 分，满分 20 分.请把答案填在答题纸的相应位置.13、若幂函数 21mfxx在 0,上为增函数，则实数m的值是 ．14、多面体的三视图如图所示，则该多面体的体积为 ．3cm15、已知 为正实数，函数 在 的最大值为 4，则 的最小,ab3()2xfxab[0,1]()fx在 [1,0]值为 16、已知函数 ，若 对任意的xfsin)( 0)2()sin(co2 ff恒成立，则实数 的取值范围为 (0,2m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）设集合 ， ．{|12}Ax22{|()0}Bxm- 3 -(1)当 时，化简集合 ；12mB(2) ，命题 ，且命题 是命题 的必要不充分条件，求实数 的取值范围．:pxA:qxpqm18、 （本小题满分 12 分）已知函数  2 2sin3sincos0,fxxx的图象相邻两条对称轴的距离为 。fx4（1）求 的值；4f（2）将 的图象上所有点向左平移 个长度单位 ，得到 的图象，若fx0mygx图象的一个对称中心为 ，当 取得最小值时，求 的单调递增区间.yg,619、 （本小题满分 12 分）经研究发现，学生的注意力随着老师讲课时间的变化而变化，讲课开始时，学生的兴趣激增；中间有一段时间，学生的兴趣保持较理想的状态，随后学生的注意力开始分散.设 表示学生注意力随时间 （分钟）的变化规律（ 越大，表明学生注意力越集中） ，经过)(tf t )(tf实验分析得知：2680,1()4,24tftkt（1）求出 k 的值，并指出讲课开始后多少分钟，学生的注意力最集中？能坚持多久？（2）一道数学难题，需要讲解 24 分钟，并且要求学生的注意力至少达到 185，那么经过适当安排，老师能否在学生达到所需的状态下讲授完这道题目？20、 （本小题满分 12 分）如图，在四棱锥 中，侧棱PABCD,PABCD底 面， 是棱 的中点。/,ADBC90,2,1AM（1）求证： ；/MD平 面（2）设点 是线段 上的一动点，当点 在何处时，直线 与NNN平面 所成的角最大？并求出最大角的正弦值。PAB21、 （本小题满分 12 分）设函数 ，已2())ln,()xfxageA DCBPMN- 4 -知曲线 在 处的切线过点()yfx1(2,3).（1） 求实数 的值。a（2） 是否存在自然数 ，使得函数 在 内存在唯一的零点？如果存在，k()yfxg(,1)k求出 ；如果不存在，请说明理由。（3） 设函数 ，对于实数 ，()min{(),},(min{,})hxfxgpq其 中 表 示 中 的 较 小 值 m使得 成立，求实数 的取值范围。0,0请考生在 22，23 题中任选一题作答，如果多做，则按所做的第一题计分，作答时请写清题号。22（10 分 坐标系与参数方程）已知直线 的参数方程为 ，以坐标原点为极l12,(xty为 参 数 )点， x 正半轴为极轴，建立极坐标系，曲线 C 的极坐标方程是 2sin.（1） 写出直线 的极坐标方程与曲线 C 的直角坐标方程。l（2） 若点 P 是曲线 C 上的动点，求点 P 到直线 的距离的最小值，并求出此时点 P 的坐标。l23（10 分 不等式选讲 ）设函数 (),0fxa（1） 证明： 1()2fx（2） 若不等式 的解集非空，求实数 的取值范围。()f a高三期中联合考试数学（理）科试卷参考答案- 5 -一、选择题 CDAAA BAABD BD二、填空 13、 2 14、 15、 16、 323212m三、解答题17. 【解析】∵不等式 ………2 分22()0()[()]0xmx(1)当 时， ， ∴集合 B＝ ． …………4 分1m{|1}(2)依题意得则 ，…………5 分BAØ∵ A＝{ x|－1≤ x≤2}，①当 m 时， ，12 {|}xm此时 ；……………11 分2综上所述， m 的取值范围是 ……………12 分118、解：（1）由题意 2 2sin3sincosfxxx． ． ． ． ． ． ． ． ． ． ．3 分22cosin3i6x因为 的图象相邻两条对称轴的距离为 ，所以周期 ． ． ． ． ． ． ． ． ． ．4 分fx42T由 ，可得 ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 5 分22所以 ，故 ． ． ． ． ． ． ． ． ． ．6 分sin46fxx2sinsin1446f（2）由（1）知 ，则 ． ． ． ． ． ． ．7 分2sifigxxm因为 为 的一个对称中心，所以 ． ． ． ． ． ． ． ．8 分,06gx2sin406- 6 -故 ， ，当 时， 取得最小值 ． ． ． ． ． ． ． ． ．10 分46mkZ48km1km8此时 ，2sin43gxx由 ，可得： ，2kkZ 52424kkxZ故 的单调递增区间 为 ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．12 分gx 5,4Z19、 （1） ，则有 得 …….3 分20,()tft20k8当 单调递增，且2(,]68t(10)24f[)4tft单调递减，20,](0()f讲课开始 10 分钟后学生的注意力最集中，能持续 10 分钟……6 分。（2） 2(,])681510tfttt解 得[)415………9 分0,](80tft解 得 t26.87即从讲课后 5 分钟到 26.875 分钟这段时间内学生的注意力不低于 185，则学生的注意力最低保持在 185 的时间为 26.71.5所以不能在所需状态下讲解完这道题。………………12 分。20、以 A 为坐标原点，建立如图所示的空间直角坐标系，则(0,)(,20)(,)(1,0)(,2)(0,1)BCDPM,1,,MP设平面 PCD 的法向量是 (,)nxyz……………3 分0202(,1)nDnC 得 令 得………………4 分AMn得- 7 -又 ………………5 分AM/PCD平 面平 面（2）由点 N 是线段 CD 上的一点，可设…………7 分(,20),[,1],,)AM平面 PAB 的一个法向量为 (10AD设 MN 与平面 PAB 成 角，则…………8 分2sin|co,| |53NB令 1[,2]t2 2211sin ,[1]0375()(1)35()5t ttt当 …………11 分max13sin),73tt即 时 (此 时当点 N 是线段 CD 上靠近点 C 的三等分点时，MN 与平面 PAB 所成角最大，最大角的正弦值值为。…………12 分5721、 (1)ln1afx,()0a过() ()1fxyax在 处 的 切 线 方 程 为 (2,3)……2 分312得(2)存在 符合题意，证明如下：……3 分k令2()())lnxxfgxe当 20,1]88()4lnl04e- 8 -可得 ，使得 ……5 分0(1,2)x0()x2)ln()(1,2()110xex e时 ， 2(2)[,)(ln1,0())xxx即 在 单 调 递 增可得 在 有唯一实根。(,2所以存在 使得函数 在 内存在唯一的零点。……7 分1k()yfxg(,1)k（3） 使得 成立，则 ……8 分0(,)x0hmmax(h由（2）知，函数 在 内存在唯一的零点()yfx,)k0当0 002(,)()())ln,(](),]() 9))xxgf xxhe 时 ，时 ， 分00 00,](1()2,]ln1,(),](,()xxfhhx时时 ， 在 递 增0)xxe可得 (,2,()+)0h递 增， 递 减0 028(,(,()2xxhxe且可得 ma)h时 使得 成立。……12 分28e0(,)x0()xm- 9 -22、 （1） ，2,(xty为 参 数 )1xy直线 的极坐标方程为 ……….3 分lcosin2cos()14即由 得2sin.12 in得 ………5 分(0)yx（2）设 ，则,P20()yx点 P 到直线 的距离为l22200001313|()|()|1| 442xxxd当 ………8 分0min13,(,)284xP时 此 时当 P 到直线 的距离最小，最小 ………….10 分(,)4lmin328d23、 （1） 111())())fxxaxa……………4 分2(2) ……….6 分3,()2202,axyfxxax可得 ………8 分min,2axy的解集非空，所以 又因为 …….10 分1()f12a即 01a得1福建省晋江市养正中学 2017 届高三英语上学期期中试题本试卷分第 I 卷（选择题）和第 II 卷（非选择题）两部分。第 I 卷（选择题 共 100 分）第一部分 听力（共两节，满分 30 分）第一节 听下面 5 段对话。每段对话后有一个小题，从题中所给的 A、B、C 三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有 10 秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。1. What does the man suggest the woman do?A. Buy a new book.B. Take the novel out of the library.C. Borrow a novel from her teacher.2. Where does the man want to go? A. The supermarket. B. The bridge. C. The bookshop.3. What does the woman need? A. A new fish tank.B. Someone to take care of her fish.C. Someone to help water the garden.4. What are the speakers doing? A. Watching a movie. B. Enjoying a concert. C. Buying some tickets.5. What will the speakers probably do during the holidays? A. Get away and have fun. B. Listen to some lectures. C. Write some essays.第二节 听下面 5 段对话或独白。每段对话或独白后有几个小题，从题中所给的 A、B、C 三个选项中选出最佳选项，并标在试卷的相应位置。听第 6 段材料，回答第 6、7 题。6. Why does the woman want to stop? A. To get some gas for her car. B. To talk with a policeman. C. To get something to eat.7. How does the man feel about the situation? 2A. Worried. B. Confident. C. Frustrated.听第 7 段材料，回答第 8、9 题。8. When does the woman’s head hurt the most?A. When she is in class. B. After she does sports.C. Before she goes to bed.9. What does the man think Michelle needs? A. More exercise. B. Some medicine. C. Glasses.听第 8 段材料，回答第 10 至 12 题。10. What is the probable relationship between the speakers? A. Brother and sister. B. Husband and wife. C. Parent and kid.11. What do we know about the trip with Uncle George? A. The man didn’t go fishing.B. The woman was six years old then.C. The woman brought lots of shells back.12. What are the speakers doing in the end? A. Taking a photo. B. Making a toast. C. Saying goodbye.听第 9 段材料，回答第 13 至 16 题。13. What is NOT one of George Clooney’s movies? A. Ocean’s Eleven. B. Batman. C. 364 Days.14. Why does George Clooney do commercials(商业广告)? A. It’s what he really loves to do.B. He does it to make money.C. It has made him more famous.15. What do many actors do according to George Clooney? A. They act in bad movies for higher payment.B. They do TV and radio ads.C. They produce films besides acting.16. What does George Clooney think of the life in Los Angeles? A. It’s cheap. B. It’s a little hard. C. It’s uncomfortable.3听第 10 段材料，回答第 17 至 20 题。17. How many people live in the speaker’s hometown? A. A few thousand. B. A few hundred. C. Only a few dozen or so.18. What can you find on Main Street? A. A couple of markets. B. A hospital. C. A hairdresser.19. Where is the post office? A. At the end of Main Street. B. Five miles away. C. In a nearby city.20. According to the speaker, what is the most fun thing to do? A. Running around in the fields.B. Going fishing in the river.C. Going climbing in the mountains.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）阅读下列短文，从每题所给的四个选项（A、B、C、和 D）中，选出最佳选项，并在答题卡上将该项涂黑。AFallingwater is a house built over a waterfall in Southwestern Pennsylvania. Frank Lloyd Wright,America’s most famous architect, designed the house in 1935. It instantly became famous, and today it is a National Historic Landmark.Guided House TourThis tour features all the major rooms of the house and lasts about one hour. Photography is notpermitted during this tour. The Guided House Tour allows children six-year-old and older to enjoy the house with their parents.Adults ---- $ 20. 00 with advance purchase---- $ 23. 00 when purchased on site4Youth (ages 6〜12) ---- $ 14. 00 with advance purchase---- $ 17. 00 when purchased on siteDaily from 10:00 a.m. to 4:00 p.m., except Wednesday.In-Depth TourThe tour is best if you desire a greater understanding of what Wright was seeking to create with his masterwork. The number of visitors on each tour is limited and photography is permitted for personal use only. Children nine years and older may accompany adults on this tour.$ 65. 00 per person (Available by advance ticket purchase only)Daily from 10:00 a.m. to 4:00 p.m.Sunset TourAs afternoon turns to evening, the changing light allows you to see Fallingwater from an entirely new perspective(视角). The number of visitors is limited and photography is permitted for personal use only. Children under nine-years-old are not permitted on this tour.$ 110. 00 per person (Available by advance ticket purchase only)May, June, & September ---- Saturdays at 4:30 p.m.July & August ---- Fridays and Saturdays at 4:45 p.m.Brunch TourThe guests join their guide for brunch before they leave. Children nine years and older may accompany adults on this tour. Please allow three hours total for this experience.$ 115. 00 per person (Available by advance ticket purchase only)May through September ---- Saturdays & Sundays at 9:00 a.m.21. How much will a father and his two children (one is 9, the other is 15) spend if they buy the Guided House Tour tickets ahead of time?A. $ 48 B. $ 54 C. $ 63 D. $ 5122. What can we know about Sunset Tour?5A. The number of visitors is not limited. B. It is not accessible in August.C. It is only open for teenagers. D. The ticket isn’t available on site.23. What do the four tours mentioned have in common?A. They encourage advance tickets. B. They offer brunch free of charge.C. They forbid visitors taking photos. D. They have the same price of tickets. BTo Chinese immigrants, in the mid-1800s, California was “The Land of the Golden Mountain.” In their homeland they had heard the words, “There’s gold in California.” They sailed 7,000 miles to join the gold rush and strike it rich. Between 1849 and 1882, more than 30,000 Chinese came to California. Most were men. They had been farmers in China. They came here to be miners and laborers. They ended up doing many other jobs, too.Like many other immigrants, they did not plan to stay in America. They came because of their ties to their homeland and their families. They planned to return to China with their fortunes and help their families.Only a few Chinese gold miners struck it rich. Most picked over the areas that had been mined already. But still, white miners resented the Chinese. Slowly, they drove the “yellow people” from the mining camps.By the end of the 1850s, many Chinese returned home. Those who stayed found other jobs. Few women had come west in the gold rush. The Chinese saw a good business opportunity. They began doing the jobs women would have done. Many became house servants. Many more opened laundries.The Chinese opened restaurants. Chop suey(炒杂碎) and chow mein are popular Chinese-American dishes. The Chinese probably created these dishes to serve to the white miners. Other Chinese became fishermen, farmers, and even cigar makers. 624. Why did Chinese go to America in the mid-1800s?A. Because they could find good jobs there. B. Because they had found gold there.C. Because they wanted to seek fortunes there. D. Because they could open laundries and restaurants there.25. Which of the following words can replace the underlined word “resented”? A. liked B. hated C. helped D. served26. Which of the following statements is true according to the passage?A. Many Chinese returned to China with great fortunes. B. Many Chinese women became servants to their white miners. C. White-miners made popular Chinese-American dishes.D. The Chinese made livings in all walks of life. 27. Which should be the title of the passage?A. Early Chinese Immigrants in America B. Dream to Strike It RichC. The Difference Between Men and Women D. Gold Miners in AmericaCFlyingEver since I was old enough to dream, I have imagined myself soaring with the eagles. My love of flying has shaped the way I live and the person I have become. Two years ago, that passion rocketed to new heights when I had the opportunity to visit Embry Riddle Aeronautical University in Arizona. For a whole week I lived in a college dorm, roomed with a total stranger and ---- best of all ---- I flew!My group took part in activities ranging from learning about the history of aviation(航空) to flying in advanced pilot training simulators(模拟装置). At least once a day, I devoted myself to learning one of the world’s best training aircrafts, the Cessna 182. Not only did I receive thorough ground instruction, but I also got to fly. In total, I flew five hours to receive my private pilot’s license. In that one 7joyous and oh-so-short week, my passion for aviation grew even stronger. Now, whenever I see a plane flying overhead, I feel a sense of pride thinking I’ve done that.During my time in and above the Arizona desert, I learned not only about the mechanics and techniques of aviation, but also about myself and how I see the world. As I floated in that seemingly endless sea of air, I became aware of the variety and complexity of the humanity below. On the roadways, each tiny car carried people with hopes and dreams. I wondered if any of those people had ever wished to fly like an eagle. Then I realized that each must have his or her own dreams and ambitions. That’s what makes us unique. We try to respond to something special inside us. I also realized that I was especially fortunate to be making my own dream come true.Everywhere I go, I hear, “Do what makes you happy and you will be happy.” It sounds like standardadvice, but I’ve really thought about it and taken it to heart. I couldn’t care less about how much money I make or what benefits I receive. I know that I am already in hot pursuit(追逐) of my dreams. And, even if they change, even if they finally don’t involve aviation, I’ll always aim to fly with the eagles.28. What happened to the author two years ago?A. He was admitted to a university. B. He stayed in a university for one week.C. He saw the launch of the rocket. D. He made good friends with an astronaut.29. What is Paragraph 2 mainly about?A. Which aircraft the author got to fly. B. How the author learned to fly.C. What the author learned about simulators. D. Why the author got a pilot’s license.30. What makes people unique according to the author?A. Flying like an eagle. B. Trying something special.C. Having their own dreams. D. Learning unusual techniques.31. What can we learn from the last paragraph about the author?8A. He cares a lot about money and benefits. B. He brings happiness to others.C. He pursues his aims whatever happens. D. He offers advice wherever he goesDMachines could put more than half the world’s population out of work in the next 30 years, according to a computer scientist who said on Saturday that artificial intelligence’s threat to the global economy should not be ignored. Physicist Stephen Hawking and the tech billionaires Bill Gates and Elon Musk issued a similar warning last year.Moshe Vardi, a professor at Rice University, said that AI (artificial intelligence) could drive global unemployment to 50%. He said the AI revolution will not be a matter of physically powerful machines that do better than human laborers, but rather a contest between human wisdom and mechanical intelligence and strength. In his talk, Vardi referred to economist John Maynard Keynes’ rosy view of a future in which billions worked only a few hours a week, with intelligent machines to support their easy lifestyles ---- a prediction accepted by Google head of engineering Ray Kurzweil, who also believes that AI could bring about a promising future for mankind. Vardi insisted that even if machines make life easier, humanity will face an existential(关于生存的) challenge. “I do not find this a promising future,” he said. “I believe that work is essential to human wellbeing.”Last year, the consultant company McKinsey published a research about which jobs are at risk thanks to intelligent machines, and found that some jobs ---- or at least well-paid careers like doctors ---- are better protected than others. The researchers also concluded that some low-paying jobs, including health care assistants, are also less likely to be changed than others. By comparison, they concluded that 20% of a CEO’s working time could be automated with existing technologies, and nearly 80% of a file clerk’s job could be automated. They argued that as much as 45% of the work people are paid to do could be automated by existing technology.32. Who held a different opinion about AI’s influence? A. Stephen Hawking. B. Ray Kurzweil. C. Elon Musk. D. Moshe 9Vardi.33. What does the underlined word “rosy” in the third paragraph mean? A. Similar. B. Amazing. C. Pessimistic. D. Optimistic.34. What is the best title for the text?A. Advantages and Disadvantages of AI B. AI’s Threat to Global EconomyC. How AI Replaces Human Workers D. AI Could Leave Half of World Unemployed35. Where does this text probably come from? A. An advertisement. B. A job poster. C. A newspaper. D. A science textbook.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。Learning to set goals plays an important role as your child starts to gain independence. However, setting goals doesn’t come naturally to your child, so helping him to learn the process should probably be one of your goals.Explain the word “goal”. Your child may know what a goal is when it comes to soccer, but he may not understand what it means in everyday life. 36 Listen to your child. Ideally, you want your child to be able to decide for himself what his goals are. 37 Let him talk about what he thinks he does well and what he thinks needs to improve. If he's stuck, you can provide some examples of your own personal goals.Help keep goals achievable. Don't throw cold water on your child. 38 For example, if your child wants to be a champion swimmer, but can’t swim an entire lap of the pool yet, you can suggest he start by making that his first goal.39 Help your child write down his goals in an easy-to-follow form. Being able to see and check off the steps on the way to his goal is key in keeping him motivated. A really simple way is to have your child draw a ladder on a piece of paper, 10writing his goal at the top and each step to that goal on the rungs (横木). 40 A. Change goals every so often.B. Make a visual goal reminder.C. Don’t always tell him what you think.D. He’s climbing to the top as he gets closer to his goal.E. You can take sports as an example to help explain it to him.F. Once he has set up a goal，he may find it very difficult to achieve it.G. When a goal is beyond his reach, help him break it down into smaller pieces.第三部分 完形填空（共 20 小题；每小题 1.5 分，满分 30 分）阅读下面短文，掌握其大意，然后从 41—60 题所给的四个选项（A、B、C、D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。Six-year-old Matthew Parker was in need of a kidney(肾) transplant, and his family looked all over the country for a suitable donor. Up to 80 people signed up to give up a living 41 for the first-grader. Coincidentally, the person 42 to donate a kidney to Matthew was his teacher, Lindesy Painter.Matthew had been on the transplant 43 for a long time and developed antibodies(抗体) to most kidneys. It was 44 to find a match for him. The doctor had warned the family to be “ 45 ” and used the term “needl