华附、省实、深中、广雅2020届高三年级四校联考(文数)(含答案)
【写作范文】2020名校联考4篇英语满分作文
2020名校联考4篇英语满分作文模拟（一）[写作题目]（华附、省实、深中、广雅2020届高三年级四校联考）假定你是李华，学生会主席。
你校和英国某中学是友好学校。
对方学校将举办“中国文化周”，邀请你校派学生参加。
请你给负责该项目的老师Jason写一封电子邮件表示感谢邀请并询问相关事宜。
内容如下：1. 活动开始时间；2. 活动内容；3. 学生住宿安排。
注意：1．词数100左右；2．可以适当增加细节，以使行文连贯。
Dear Jason,____________________________________________________________________ _Yours sincerely,Li Hua[参考范文]Dear Jason,I’m Li Hua, chairman of the students’ union. On behalf of the students, I’d like to express our heartfelt gratitude for inviting us to your school’s upcoming Chinese Culture Week. To get further information, I’m writing to make some inquiries concerning the event.Firstly, I’m wondering on what date the event is scheduled to start so that we can apply for visas and book air tickets in advance. Also, I want to ask about the specific activities throughout the week, because the information can help us make better preparations and promote our participation. Lastly, could you please tell us what type of accommodation(s) will be provided? If possible, we hope to stay in the school dormitory, which will offer us more opportunities for cultural exchange with your students.Thanks again for your kind invitation. It would be highly appreciated if you could deal with my inquiries at your convenience. Looking forward to your early reply. Yours sincerely,Li Hua模拟（二）[写作题目]（2020届高考实战卷一）假定你是李华，你的美国朋友Tristan 对你校正在举行的"中华好书分享"活动很感兴趣，希望你介绍此活动，并推荐好书。
2020届广东省华南师范大学附属中学、实验中学、广雅中学、深圳高级中学高三上学期期末联考英语试题 word版
华附、省实、广雅' 深中2020届高三上学期期末联考英语本试卷10页，满分120分。
考试用时120分钟注意事项：1.答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的校名、姓名、考号、座位号等相关信息填写在答题卡指定区域内。
2.选择题每小题选出答案后，请用2B铅笔把答题卡上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其他答案；不能答在试卷上。
.3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液，不按以上要求作答的答案无效。
4. 考生必须保证答题卡的整洁。
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A、B、C和D四个选项中，选出最佳选项。
AOccasions like anniversaries, weddings and reunions call for special event venues （场地）.The following places may have a way out. There's no need to spend money creating atmosphere at special event venues. It's built right in!Hard Rock Cafe Anchorage415 E. STREET, ANCHORAGE, ALASKA 99501Events, like great music are born of inspiration. Featuring a 13,600-square-foot facility that will seat 275 guests with private event space, we pride ourselves on delivering an exceptional experience with a rock and roll twist for each of our guests. Business Expo Center1960 S. ANAHEIM WAY, ANAHEIM, CALIFORNIA 92805The Business Expo Center is Orange County's premier event venue in Anaheim, California. Our flexible 36,000-square-foot expo center is home to space for conferences, trade shows and celebrations. We pride ourselves on providing a memorable experience with excellent flexibility, services, and cost savings. We won't charge customers for on-site parking and provide high-speed Wi-Fi.Automobile Driving Museum610 LAIRPORT STREET, EL SEGUNDO, CALIFORNIA 90245Centrally located in the South Bay beach community of El Segundo, California, the ADM offers a wonderful venue for private parties and corporate events. Conveniently located 5 minutes south of LAX, right off the 405 and 105 Freeways, the 610 Lairport space has a vintage feel surrounded by our primary automobile collection. We offer several different venues inside and outside our facility for diverse events. To better our service, reservations are needed.Yamashiro Hollywood1999 N. SYCAMORE AVE., LOS ANGELES, CALIFORNIA 90068Yamashiro Hollywood is a restaurant and therefore, all food and beverages must be handled in house. However, guests are allowed to bring in outside wine and champagne for a corkage fee.21.What can you do in Business Expo Center?A. Enjoy free parking.B. Bring in outside wine.C. Experience a rock and roll twist.D. See some automobile collections.22.Which venue do you need to book in advance?A. Business Expo Center.B. Yamashiro Hollywood.C. Hard Rock Cafe Anchorage.D. Automobile Driving Museum.23.What do the four venues have in common?A. They offer optional places.B. They are open to special events.C. They are located in the same state.D. They enjoy convenient transportation.BKyle Cassidy and three other members of the Annenberg Running Group were stretching on the grounds of the University of Pennsylvania, waiting for a few latecomers. The Penn colleagues and other community members meet three days a week for a roughly 30-minute jog and an occasional lecture. That's right― d uring some runs, one of them delivers a talk. Topics range from the brain to Bitcoin.But on this day last January, it would not be their normal run. The first clue that something was off was the man who sprinted past them. "Running at an amazing pace,"Cassidy told Runner's World admiringly. Cassidy discovered why the sprinter was so fleet of foot when another man ran by, yelling, “Help! He took my phone and laptop!"At that, the group did what running clubs do: They ran, trailing the suspect down the streets of Philadelphia until he ducked into a construction site. The runners split up. Cassidy ran around to the far side of the site to cut the thief off while the others wandered the neighborhood hoping he had dumped the loot （赃物）in a backyard.No luck. So they decided to ask residents whether they'd seen the guy. When they knocked on the door of one row house, they were in for a surprise. Unknown to them, he had already emerged from the construction site—and was hiding behind a bush by that very house. As the owner opened the door, the suspect darted out from behind the bush ... and right into the arms of campus police, who'd joined the chase shortly behind the runners.The members of this running group are not hard-core athletes. But they do understand the benefit of a little exercise. ''Running is typically a useless sport where you turn fat cells into heat," Cassidy told The Philadelphia Inquirer. "But occasionally it can be useful, and here was one of those opportunities."24. Why do the group members gather together?A. To do some stretching.B. To have a regular run.C. To deliver a lecture.D. To cover some topics.25. What does the underlined word "sprinted" in Paragraph 2 probably mean?A. Dashed.B. Pushed.C. Jumped.D. Escaped.26. We can infer that the success of the chase is mainly due to _________ .A. the assistance of the runnersB. the owner of the row houseC. the campus police on patrolD. the joint efforts of the people27. Which of the following best describes Cassidy?A. Athletic and generous.B. Courageous and ambitious.C. Helpful and humorous.D. Thoughtful and demanding.CFood experts say washing could spread the germs on your turkey in the kitchen sink or nearby food.But it's been a challenge trying to convince cooks to stop rinsing （冲洗）off raw poultry. Germs that can make people sick are common in the guts of healthy poultry and are legally allowed to be on raw turkey and chicken. The assumption is that nobody eats their poultry raw, and that thorough cooking will kill the bacteria.The do — not — wash raw poultry advice from the USDA is relatively new and perhaps hasn't caught on because it goes against the common belief that washing makes things clean, said Chapman. Benjamin Chapman, a study author and food safety expert atNorth Carolina State University, said the instinct to wash raw poultry goes back at least decades when people relied more on visual clues to spot problems with poultry. Meanwhile, washing hands and surfaces are also important.But food preparation is a complicated act, and germs from poultry can be spread even if it's not washed, especially when birds are removed from packaging.The USDA-funded study stresses that point. Researchers sprayed raw chicken with a harmless strain of E. coli （大肠杆菌）and watched volunteer cooks at test kitchens. Among those who washed their raw chicken, about a quarter ended up spreading the bacteria to their lettuce. But even some of those who did not rinse the chicken got germs on the lettuce. And there are other opportunities for germs to survive on turkeys: melting and cooking.To ensure a bird is thoroughly cooked, they say to use a thermometer to check that the deepest and thickest parts of it have reached 165 degrees. Even after the meal is cooked, you aren't out of the danger zone. To keep turkeys and other leftovers safe, experts say they should be refrigerated after two hours.28. People don't accept USDA's advice because __________ .A. the advice is relatively newB. cleaning seems more trustworthyC. cooks clean the turkey before cooking itD. heat can kill most germs and no one eats raw food29. What can be concluded from Paragraph 4?A. Food packages carry germs.B. Hands and surfaces are easy to get E. coli.C. Germs from a turkey can be spread whether it is washed or not.D. Multiple methods should be applied to food to get rid of germs.30. Which way may help to cook a turkey safely?A. Rinse off the turkey before it is heated.B. Keep the turkey away from the lettuce and refrigerator.C. Wash hands and packages before taking out the turkey.D. Use a thermometer to check the temperature of the turkey.31. From which section of a magazine is the text probably taken?A. Culture.B. Science.C. Education.D. Medicine.DMicroplastics are everywhere in our environment. It's hardly surprising that the tiny fragments have also been found in humans. A new study shows that America ns are consuming as many as 121,000 particles each year.Measuring 50 to 500 microns in length, microplastics come from a variety ofsources, including large plastics that break down into smaller and smaller pieces. Therefore, much remains unknown about the common existence of these materials within the human body, as well as their impact on human health.Hoping to fill in some of these gaps, a research team led by Kieran Cox, a PhD candidate at theUniversity of Victoria, looked at 26 papers assessing the amount of microplastics in commonly consumed food items, among which are seafood, sugars, salts, honey, alcohol and water. The team also evaluated the potential consumption of microplastics through inhalation （吸入）using previously reported data on microplastic concentrations in the air and the Environmental Protection Agency's reported respiration rates. Based on these data, the researchers calculated that our annual consumption of microplastics via food and drink ranges from 39,000 to 52,000 particles. When microplastics taken in through inhalation are taken into account, the range jumps to between 74,000 and 121,000 particles per year.The authors of the study found that people who drink exclusively from plastic water bottles absorb an additional 90,000 microplastics each year, compared to 4,000 among those who only consume tap water. "This shows that small decisions, over the course of a year, really matter and have an impact." Cox says. The new study, according to its authors, was the first to investigate "the accumulative human exposure" to microplastics. But in all likelihood, the research tells only a small part of the entire story. Collectively, the food and drink that the researchers analyzed represent 15 percent of Americans' caloric intake. The team could not account for food groups like fruits, vegetables and grains because there simply is not enough data on their microplastic content.For those worried about microplastic consumption, cutting down bottled water is a good place to start. But to the heart of the problem, we have to stop producing and using so much plastic.32. What makes it difficult to know microplastics commonly exist in the human body?A. The quality.B. The quantity.C. The shape.D. The size.33. How did Kieran Cox's team calculate the potential consumption of microplastics?A. By studying papers.B. By comparing the impacts.C. By analyzing the data.D. By conducting experiments.34. Which of the following is true according to the text?A. Drinking less plastic bottled water helps to take in fewer microplastics.B. The study is among the earliest to investigate human exposure to microplastics.C. Cox's team gained comprehensive information of microplastics taken in by humans.D. People consume 74,000 to 121,000 particles of microplastics per year from food and drink.35. What is the best title for the text?A. The Potential Problems of MicroplasticsB. Microplastics Coming From Various SourcesC. Microplastics Found Within Human BodiesD. The Impact of Microplastics on Human Health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。
2020届四校联考语文答案8(1)
华附、省实、广雅、深中2020届高三上学期期末联考语文参考答案及评分标准1.B（B项错误，原文第②段只是说古典美学的主要审美对象是大自然、乡村，没有指出现代美学是否存在大自然这个审美对象，所以不存在现代美学“不再以大自然为审美对象”。
）2.D（D项中的“发展前景”不是文章重点论述的内容。
）3.A（ B项推断错误，文章论述两者之间的审美对象有不同，而没有评价价值的高低；C项错误，强加因果，二者为并列关系；D项错误，逻辑关系错误，原文第四段是“只有……才……”的必要条件。
）4.C（“消费者不再为交通的便利性担忧”的原因解释错误，原文是“我国部分城市已经开始推行延长公共交通服务时间的做法，这将很大程度上解决夜间居民城市出行难题”，时间上是“未然”，不是“已然”，这只是“部分城市”而非所有消费者。
）5.D（材料中表述的是“相比于欧美夜间经济对线下消费（尤其是酒吧、餐饮、娱乐等）的倚重”，这并不意味着欧美的夜间经济只局限于线下消费。
）6.答案：①中国不断完善的城市基础设施建设。
（2分）（若答“加大轨道交通投资、延长公共交通服务时间”“重视电网建设、城市电力覆盖率高”两点，因没有概括只得1分；若答“不断完善的轨道交通和电网等城市基础设施”得2分。
）②中国未完全释放的夜间经济红利。
（2分）（如没有答出第②点，而答了“中国数量庞大的消费人群”，得1分；这一点应该属于“未完全释放的夜间经济红利”，与第②点不能重复给分。
）③中国移动互联网的发展异军突起。
（1分）④中国政府的政策支持。
（1分）7．C（老班长的故事不属于插叙；“为了表现老班长的技术无人能及”错误，是为了表现老班长的成功除了技术，更多的是热爱、执着和专注的精神。
）8．参考答案：粗犷：①踹石平阳一脚以示惩罚，动作（行为）粗野；②在炮场上脏话丑话连篇，语言粗鲁。
温情：①反复抹大炮上的铅笔线，爱惜大炮（内心细腻）；②给士兵们讲述老班长的故事，以情动人；③查看石平阳手上的烂处与老茧，关心战友；④将自己掌握的技术全部送给石平阳，帮助战士（热心待人、提携后进）。
华附、省实、广雅、深中2024届高三四校联考数学试题与答案
本试卷分选择题和非选择题两部分，共4页，满分150分，考试用时120分钟．注意事项：1．答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名、考号填写在答题卷上。
2．选择题每小题选出答案后，用2B 华附、省实、广雅、深中2024届高三四校联考数学试题铅笔把答题卷上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其它答案；不能答在试卷上。
3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卷各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液.不按以上要求作答的答案无效。
4．考生必须保持答题卡的整洁，考试结束后，将答题卷收回。
一.单项选择题（本大题共8小题，每小题5分，共40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.已知全集U =R ，集合A ，B 满足A ⊆(A⋂B)，则下列关系一定正确的是( )A. A =BB. B ⊆AC. (∁U A)∩B =⌀D. A⋂(∁U B)=⌀2.已知复数z 满足(1)1+=−i z i ，则z 2024=( )A. iB. −1C. 1D. −i3.直线x +2y +3=0关于直线y =−x 对称的直线方程是( )A. x +2y −3=0B. 2x +y −3=0C. x −2y −3=0D. 2x +3y +3=04.已知向量a 在b 方向上的投影向量的模为2，向量b 在a 方向上的投影向量的模为1，且（（+⊥−a b a b )23)，则向量a 与向量b 的夹角为（ ）A ．π6B ．π4C ．π3D ．π345.若椭圆Γ1：x 2a 2+y 2b2=1(a >b >0)的离心率为12，则双曲线Γ2：y 2b2−x 2a 2=1的离心率为( )A.213 B.72C. √ 3D. √ 56. 在平直的铁轨上停着一辆高铁列车，列车与铁轨上表面接触的车轮半径为R ，且某个车轮上的点P 刚好与铁轨的上表面接触，若该列车行驶了距离S ，则此时P 到铁轨上表面的距离为（ ） A ．+R S R(1cos )B ．−R S R (1cos )C ．2sin R S RD ．sin R S R7.若（（ac e c b −=−=1)1)ln 1则a ，b ，c 的大小关系为（ ） A ． c ≤a ＜bB ． c ＜a ＜bC ．c ＜b ＜aD ．b ＜a ≤c8.数列a n {}的前n 项和S n ，且a a a n a n n n n =++−−−1882111，n n N ≥∈+(2,)，若a =11，则 A ．S <<2024523 B ．S <<2024252C ．S <<2024322 D ． S <<2024132二.多项选择题（本题共4小题，每小题5分，共20分.在每小题给出的四个选项中，有多个选项是符合题目要求的，全部选对的得5分，选对但不全的得2分，有选错的得0分） 9.下列结论正确的是( )A. 若a >b,c >d ，则ac 2>bd 2B. 若ac 2>bc 2，则a >bC. “ab >1”是“a >1,b >1”成立的充分不必要条件D. 若a >b >1，则a a b b +<+1log log (1)10. 已知圆C 1：x y +=221，圆C 2：−++=x y r (3)(4)222r >0（），P 、Q 分别是圆C 1与圆C 2上的点，则（ ）A .若圆C 1与圆C 2无公共点，则0＜r ＜4B .当r ＝5时，两圆公共弦所在直线方程为x y −−=6810C .当r ＝2时，则PQ 斜率的最大值为−724D .当r ＝3时，过P 点作圆C 2两条切线，切点分别为A ，B ，则∠APB 不可能等于 π2 11.已知函数f(x)=x 3−3x 2，满足f (x )=kx +b 有三个不同的实数根x 1，x 2，x 3，则( ) A. 若k =0，则实数b 的取值范围是−4<b <0B. 过y 轴正半轴上任意一点仅有一条与函数 y =f (x )−1 相切的直线C. x 1x 2+x 2x 3+x 1x 3=kD.若 x 1，x 2，x 3成等差数列，则k +b =−212.已知正四面体O −ABC 的棱长为3，下列说法正确的是( )A. 若点P 满足OP ⃗⃗⃗⃗⃗ =x OA ⃗⃗⃗⃗⃗ +y OB ⃗⃗⃗⃗⃗⃗ +z OC ⃗⃗⃗⃗⃗ ，且x +y +z =1，则|OP ⃗⃗⃗⃗⃗ |的最小值为6B. 在正四面体O −ABC 的内部有一个可以任意转动的正四面体，则此四面体体积可能为√ 210C. 若正四面体O −ABC 的四个顶点分别在四个互相平行的平面内，且每相邻平行平面间的距离均相等，则此距离为3√ 1010D.点Q 在△ABC 所在平面内且|QO|=2|QA|,则Q 点轨迹的长度为2√ 303π三、填空题（本大题共4小题，共20.0分）13.已知双曲线x y −=2241，则此双曲线的渐近线方程为 ．14.已知等差数列{a n }的前n 项和为S n (n ∈N ∗)，a 4=4，a 7=10，则S n 的最小值为 ． 15.已知函数f x x =−ωπ2()sin (3)(ω>0)的最小正周期为2π，且f (x )在[0,m]上单调递减，在[2m,5π3]上单调递增，则实数m 的取值范围是 ．16. 在同一平面直角坐标系中，M ，N 分别是函数f x x x =−−+−2()43和函数()ln()=−g x ax axe x 图象上的动点，若对任意a ＞0，有|MN |≥m 恒成立，则实数m 的最大值为______________． 四、解答题（本大题共6小题，共70.0分。
【精准解析】广东省华附、省实、深中、广雅2020届高三下学期四校联考数学(文)试题
3 ，则向量 a, b 的夹角为（
）
A. 30° 【答案】B 【解析】
B. 60°
C. 120°
D. 150°【分析】源自由| a b | 3 ,平方求出 a b ,代入向量夹角公式,求出 a, b 的夹角余弦值,即可得结果.
【详解】设 a, b 的夹角为
rr | a b |
3,
|
r a
r b |2
2020
条件为（ ）
-4-
A. n 2020? n 2020 ?
【答案】A 【解析】 【分析】
B. n 2020?
C. n 2020?
D.
因为
g
n
1 n2
n
1
nn 1
1 n
1 n 1
，此程序框图是对函数
g
n
求和，利用裂项相消
法求和，可知
S
n
n 1
2019 2020
，可知
2019
满足条件进入循环，2020
在△ BF1F2 中，由余弦定理可得 cos BF2F1
33 22 a
，
3
根据 cos AF2O cos BF2 F1
0 ，可得
1 a
3 2a2 a
0 ，解得 a2
2，
b2 a2 c2 2 1 1．
所以椭圆 C 的方程为： x2 y2 1 ．
2
故选 A ．
【点睛】本题考查了椭圆的定义及余弦定理，属中档题． 第二部分非选择题（共 90 分）
r (a
r b)2
r2 a
r 2a
r b
r2 b
5
rr 2a b
3,
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华附、省实、深中、广雅2020年高三四校联考语文试题-含答案
华附、省实、深中、广雅2020年高三四校联考语文试题本试卷共10页，22小题，满分150分。
考试用时150分钟。
注意事项：1.答卷前，考生务必将条形码粘贴在指定区域，用黑色字迹的钢笔或签字笔将自己的姓名和考生号、试室号、座位号填写在答题卡上。
2.选择题每小题选出答案后，用2B铅笔把答题卡上对应的题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再填涂其他答案。
答案不能答在试卷上。
3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案，不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
4.考生必须保持答题卡的整洁。
一、现代文阅读（36分）（一）论述类文本阅读（本题共3小题，9分）阅读下面的文字，完成1～3题。
都市化进程在深刻改变与重建当今世界经济社会发展方式的同时，也为当代中国美学带来了新的课题，提供了新的学术生长空间。
都市化进程使当代人的审美意识与审美活动发生了巨大变化，应对这一来自理论与实践两大方面的挑战，是中国美学的重要使命。
都市化进程给中国美学带来的影响是多方面的。
以审美对象为例——审美对象即人与世界的一切审美现象和审美活动——古典美学的主要审美对象是大自然与乡村，中国古代的田园诗是这方面最典范的创造；现代美学的主要审美对象是反思、批判工业化及其对古典精神世界的异化，这集中体现在西方现代哲学美学思潮与现代派文学艺术对现代人类异化困境的深刻揭示上。
与此不同，当代都市社会与都市生活中出现了大量的新型精神文化消费品与审美实践活动，如超级市场、广告文化、模特文化、汽车文化、选秀文化、景观设计等，即使作为美学最直接、最重要的研究对象——文学艺术，与其传统形态相比也发生了重要的变迁，并具体再现于以物质和肉体消费为中心的大众文化话语与影像上。
都市化进程给中国美学带来的影响推动了都市美学的理论研究，以当代都市社会中的精神文化消费生态、审美文化及文学艺术为基本研究对象而构建的都市美学的理论研究具有重要意义，也是当下一项亟待开展的研究。
广东省华附省实深中广雅2020届高三数学下学期四校联考试题理含解析
3.已知平面向量 a , b 是非零向量,| a |=2, a ⊥( a +2 b ),则向量 b 在向量 a 方向上的投影为(
)
A. 1
B. -1
C. 2
【答案】B
D. -2
【解析】
【分析】
先根据向量垂直得到 a ( a +2 b ),=0，化简得到 a b =﹣2，再根据投影的定义即可求出．
n
2
，
作出图像如图：
m
圆
12
n
12
1的面积为
，正方形
OABC
的面积为
4
.
则
ab
1
的概率是
4
.
故答案为： 4
【点睛】本题考查了几何概型的概率求法，解题的关键是变量满足的条件，属于基础题.
14.已知两个等差数列
an
和
bn
的前
n
项和分别为
An 和 Bn ，且
An Bn
3n 1 n 1 ，则
a2 a5 a8
1 2
的几何意义是单位圆(在
x
轴及其上方)
上的动点 M (cos ,sin ) 与点 A(2,1) 连线的斜率 k ，由图象，得 0 k 1，即函数 f (x) 的
值域为[0,1]，故选 C.
点睛：本题考查利用三角代换、直线的斜率公式求函数的值域，解决本题的关键有两个，一
sin 1 是利用 1 x2 的形式和平方关系联想到三角代换，二是由 cos 2 的形式联想到过两点的
性的判断依次如下，正确的是（ ）
A. 真，假，真
B. 假，假，真
C. 真，真，假
D. 假，假，
假
【答案】B
广东省华附、省实、广雅、深中2020届高三上学期期末联考数学(文)试题Word版含解析
广东省华附、省实、广雅、深中2020届高三上学期期末联考数学（文）试题一、选择题（本大题共12小题，共60.0分）1.若集合，，则A. B. C. D.2.已知为虚数单位，若，则复数的模等于（）．A. B. C. D.3.设，是非零向量，记与所成的角为，下列四个条件中，使成立的充要条件是（）．A. B. C. D.4.随着人民生活水平的提高，对城市空气质量的关注度也逐步增大，下图是某城市1月至8月的空气质量检测情况，图中一、二、三、四级是空气质量等级，一级空气质量最好，一级和二级都是质量合格天气，下面四种说法正确的是（）．①1月至8月空气合格天数超过20天的月份有5个②第二季度与第一季度相比，空气合格天数的比重下降了③8月是空气质量最好的一个月④6月的空气质量最差A. ①②③B. ①②④C. ①③④D. ②③④5.若函数是偶函数，则的单调递增区间是A. B. C. D.6.齐王与田忌赛马，田忌的上等马优于齐王的中等马，劣于齐王的上等马，田忌的中等马优于齐王的下等马，劣于齐王的中等马，田忌的下等马劣于齐王的下等马，现从双方的马匹中各随机选一匹进行一场比赛，则田忌马获胜的概率为（）．A. B. C. D.7.若函数的部分图像如图所示，则的解析式可能是（）．A. B.C. D.8.若，满足约束条件，则的最小值为（）．A. 0B. 2C. 4D. 139.等比数列中，是关于x的方程的两个实根，则（）．A. 8B.C.D.10.若函数有3个零点，则实数的取值范围是（）．A. B. C. D.11.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.12.设，分别是椭圆的左、右焦点，若在直线其中上存在点P，使线段的垂直平分线经过点，则椭圆离心率的取值范围是A. B. C. D.二、填空题（本大题共4小题，共20.0分）13.函数在处的切线方程是____.(其中为自然对数的底数)14.已知双曲线的离心率为2，且它的一个焦点到一条渐近线的距离为，则双曲线的标准方程是____15.等差数列的前n项和为，，，对一切恒成立，则的取值范围为____.16.体积为的正四棱锥的底面中心为，与侧面所成角的正切值为，那么过的各顶点的球的表面积为____.三、解答题（本大题共7小题）17.已知分别是锐角的内角的对边，.(1)求；(2)若，且边上的高为，求的周长.18.如图，在三棱柱中，，，为的中点，点在平面内的射影在线段上.(1)求证：；(2)若是正三角形，求三棱柱的体积.19.为提倡节能减排，同时减轻居民负担，广州市积极推进“一户一表”工程非一户一表用户电费采用“合表电价”收费标准：元度“一户一表”用户电费采用阶梯电价收取，其11月到次年4月起执行非夏季标准如下：单位：单位：元度例如：某用户11月用电410度，采用合表电价收费标准，应交电费元，若采用阶梯电价收费标准，应交电费元．为调查阶梯电价是否能取到“减轻居民负担”的效果，随机调查了该市100户的11月用电量，工作人员已经将90户的月用电量填在下面的频率分布表中，最后10户的月用电量单位：度为：88、268、370、140、440、420、520、320、230、380．（1）在答题卡中完成频率分布表，并绘制频率分布直方图；根据已有信息，试估计全市住户11月的平均用电量同一组数据用该区间的中点值作代表；设某用户11月用电量为x度，按照合表电价收费标准应交元，按照阶梯电价收费标准应交元，20.已知动圆与直线相切且与圆外切。