【附17套高考模拟卷】北京市东直门中学2020-2021学年高三下学期期中考试数学试题含解析
2020届北京东直门中学高三英语期中考试试题及答案解析
2020届北京东直门中学高三英语期中考试试题及答案解析第一部分阅读（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、D四个选项中选出最佳选项AMy mother and her best friend Martha were in their mid-80s when they saw each other for the last time.They had been friends since they were 18, both of them students atWesleyanCollegeinMacon,Georgia. My mother was the dreamy one, who loved to read and dream herself as an actress. Martha, however, was more practical. I’m not sure what they had in common except that they trusted each other, helped each other, and stayed in touch even when life separated them.Martha spent most of her adulthood inAtlanta, where she raised three kids. My mother, meanwhile, raised eight children, and moved many times during her financially and emotionally troubled marriage, which included several months living with her family inseedymotels.I sensed my mother hid her troubles from most people, but not from Martha, and I knew from my mother that Martha carried her own sorrows. Their willingness to share sorrow without judgment was part of what bond them.The best friendships can also withstand (抵挡) periods without communication. They didn’t communicate a lot — this was before the ease of emails and texts and yet I knew they were always in each other’s minds.One day in 2008, 1 drove my mother to Martha’s house for their final visit. The moment my mother hobbled (蹒跚) into Martha’s house, they threw their arms around each other and went to sit out in the garden, laughing until they were dizzy. I snapped a photo, and spotted something joyous, young and free on my mom, which existed only in the presence of her best friend.Two years later, my mother died. Of all the people I had to tell, Martha was the hardest because I felt it erased her past. After that, we lost touch. But I still think of her and how that friendship strengthened my mother.1. What does the underlined word “seedy” in Paragraph 3 probably mean?A. largeB. dirtyC. urbanD. bright2. The author’s mother and Martha had a lasting friendship partly because they________.A. were willing to shareB. were constantly in touchC. had much in commonD. had a likeness in personality3. What is the author’s purpose in writing the text?A. To tell the importance of friendship.B. To express his gratitude to his mother.C. To share his standard of choosing a friend.D. To praise the friendship between Martha and his mother.BShanghairesidents passing through the city’s eastern Huangpu district in Octobermight have astonished at an unusual sight: a “walking” building. An 85-year-old primary school has been lifted off the ground in its entirety and relocated using new technology named the “walking” machine.In the city’s latest effort to preserve historic structures, engineers used nearly 200 mobile supports under the five-story building. The supports act like robotic legs. They’re split into two groups which in turns rise up and down, imitating the human step. Attached sensors help control how the building moves forward.TheLagenaPrimary School, which weighs 7,600 tons, faced a new challenge — it’s T-shaped, while previously relocated structures were square or rectangular. Experts and technicians met to discuss possibilities and test a number of different technologies before deciding on the “walking machine”.Over the course of 18 days, the building was rotated 21degrees and moved 62 meters away to its new location. The old school building is set to become a center for heritage protection and cultural protection. The project marks the first time this “walking machine” method has been used inShanghaito relocate a historical building.In recent years,China’s rapid modernization has seen many historic buildingsrazedto clear land for skyscrapers and office buildings. But there has been growing concern about the architectural heritage loss as a result of destruction across the country.Shanghaihas beenChina’s most progressive city when it comes to heritage preservation. The survival of a number of 1930s buildings in the famous Bund district and 19th-century “Shikumen” houses in the repaired Xintiandi neighborhood has offered examples of how to give old buildings new life. The city also has a track record of relocating old buildings. In 2018, the city relocated a 90-year-old building in Hongkou district, which was then considered to beShanghai’s most complex relocation project to date.4. How did the primary school get moved?A. By reducing the weight of it.B. By using movable supports.C. By dividing it into several parts.D. By using robotic legs.5. What does the underlined word “razed” probably mean in Paragraph 5?A. Replaced.B. Burnt.C. Protected.D. Destroyed.6. What can we infer about the heritage preservation inChina?A. The use of advanced technology leads to growing concern.B. Shanghai is the pioneer in preserving architectural heritage.C.A number of old buildings have been given new life.D. Many historic buildings will be relocated.7. What is the passage mainly about?A. New preservation campaigns are launched inChina.B. New technology gives new life to historic buildings.C. A building inShanghai“walks” to a new location.D. “Walking machine” makes heritage protection simpler.CWhile the start of a new school year is always exciting, this year was even more so for some elementary school students inAuckland,New Zealand. They became the world’s first kids to be “taught” by a digital teacher.Before you start imagining a human-like robot walking around the classroom, Will is just an avatar that appears on the student’s desktop, or smartphone screen, when ordered to come.The autonomous animation platform has been modeled after the human brain and nervous system, allowing it to show human-like behavior. The digital teacher is assigned to teach Vector’s “Be sustainable with energy”— a free program forAucklandelementary schools.Just like the humans it replaced, Will is able to instantly react to the students’ responses to the topic. Thanks to a webcam and microphone, the avatar not only responds to questions the kids may have, but also picks up non-verbal cues. For instance, if a student smiles at Will, he responds by smiling back. This two-way interaction not only helps attract the students’ attention, but also allows the program’s developers to monitor their engagement, and make changes if needed.Nikhil Ravishankar believes that Will-like avatars could be a novel way to catch the attention of the nextgeneration. He says, “I have a lot of hope in this technology as a means to deliver cost-effective, rich, educational experience in the future.”The program, in place since August 2018, has been a great success thus far. Ravishankar says, “ What was fascinating to me was the reaction of the children to Will. The way they look at the world is so creative and different, and Will really captured their attention.” However, regardless of how popular it becomes, Will is unlikely to replace human educators any time soon.8. What was special for some elementary school students inAuckland?A. A digital teacher taught them.B. They first saw something digital.C. This was the start of a new school year.D. They could get close to smartphone screen.9. What is the benefit of this two-way interaction?A. It can smile back.B. It can use microphone.C. It can talk any topic for free.D. It can change if necessary.10. What’s Ravishankar’s attitude to Will’s replacing Human educators soon?A. Optimistic.B. Doubtful.C. Unclear.D. Disapproving.11. What might be the best title for the passage?A. New High-tech Contributes to EducationB. The World’s First Digital Teacher Appears in Classroom.C. The World’s First Digital Teacher, a Help to StudentsD.New ZealandWill Replace Teachers in ClassroomsDIt was the first day of spring here but it didn't feel like it. The COVID-19 epidemic (流行病) was sweeping the globe and everywhere there were feelings of fear and loneliness. “Social Distancing” had become the new norm. Here the schools had been closed, the restaurant dining rooms had been shut, and people had been told to work from home whenever they could. Even the sheltered workshop where my oldest son worked had been closed until further notice. People had made a run on the stores and large areas of the shelves were bare. On the news the numbers of the sick and dead continued to rise. It felt like there was a weight on the souls of everyone in the world.My family were staying at home as much as possible and as I looked out of my window I wondered how long this crisis would last. It was then, however, that I saw something that lifted that weight off of my soul, made me smile, and made my heart feel happy again. On the street below my house there was an old friend of mine from high school who was a teacher there. With him was my younger son's former aide from the high school as well. They were delivering the school lunches door to door to the hungry children who were stuck at home. Watching them made me think of something everyone's childhood television neighbor, Mr. Roger's once said: "In the bad times, always look for the helpers."I have no doubt that this crisis will pass as all the crisis before. But it is our choice on whether it brings out the best in us or the worst in us. Let it bring out the best in you. Use it to strengthen your faith. Use it to free yourself from fear. Use it to grow kinder, more giving, and more loving. Become a helper to all those in need and you will be a happy person today and all the days to come.12. Why didn't the author like the first day of spring?A. He had to work at home instead of at office.B. There wasn't social distance between each other.C. There was an epidemic everywhere in the world.D. His own company had been closed for a long time.13. How did people feel in the face of the epidemic?A. Disappointed.B. TenseC. Confident.D. Cheerful.14. What made the author happy?A. Seeing someone delivering lunches from door to door.B. Talking with his old friend in the street.C. Watching a childhood television at home.D. Staying together with his family.15. What do Mr. Roger's words actually mean?A. It's not necessary for us to find helpers in bad times.B. In good times we needn't do much to help others.C. We should ask more people to help us in bad times.D. We are supposed to help each other in bad times.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2021届北京东直门中学高三语文下学期期中试题及参考答案
2021届北京东直门中学高三语文下学期期中试题及参考答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的小说，完成各题。
老丁扶贫金光精准扶贫中，局里每名干部包扶一个贫困户，还剩一户没人帮扶。
局长拿着花名册盯了良久，对办公室主任说，让老丁去吧。
老丁是个退伍兵，来到单位二十多年连个副科级都没混上。
办公室主任把局长的决定告诉老丁，老丁只说了一个字：中！老丁包扶的是苗家沟唐大石一家。
这家就大石一个劳力，上有79 岁卧病在床的母亲，下有两个在镇上读书的娃娃，妻子两条腿畸形，只能坐在矮凳子上，以手代脚挪着前行。
老丁见唐家的光景确实愁人，就从家里拿来一些衣服被褥，又自掏腰包买了些生活必需品送到唐家。
局长批评老丁说：“你这接济式的扶贫是不行的，要扑下身子，与贫困户一起研究致富项目，只有搞产业扶贫才是出路。
”老丁就和唐大石琢磨项目，想一个被否定一个，末了对大石说：“不行咱们养猪吧，这个项目简单又不用花太多的本钱。
”大石说：“猪要吃饲料，没钱买可咋办？”老丁指着门前沟渠上长的两排灰灰菜说：“这后山沟里的草就足够养百十头猪了，还让它吃什么饲料，再说了，这猪吃草长出的肉可是难得的原生态猪肉。
”老丁领着唐大石在唐家屋后的洼地上挖八个土坑，用石头垒成猪圈，自己又掏钱买了八头猪崽，养起了猪。
老丁重新收拾了一下唐家的生活用品，又在山墙边续了一间简易房。
每周五老丁都随单位的扶贫车过来，帮着割猪草、馇猪食，白天和唐家人一起吃饭，夜里就宿在简易房里，到了周日下午才坐班车回到县城。
这样，一周保证三天住在唐家。
那天夜里，突然天降暴雨，猪圈灌满了水；老丁的简易房也漏了雨，被褥被雨淋得湿透了。
老丁赶紧把大石叫起来，两人摸黑把猪崽从水里捞出来，放到安全的地方，然后一个挨一个地把猪圈扒个小豁口，将水排放出去。
他们折腾了一夜，才将猪崽重新又安臵到猪圈里。
老丁被雨水淋病了，发高烧，回到县城住了五天医院。
当他出院随扶贫车来到唐家时，反少了一头猪崽，他问大石，大石说：“后山沟有红毛狼，夜里听见猪崽叫，起来追时，红毛狼叼着一头猪崽上山坡了。
2020年北京东直门中学高三生物下学期期中试卷及参考答案
2020年北京东直门中学高三生物下学期期中试卷及参考答案一、选择题：本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求。
1. 生物界在基本组成上的高度一致性表现在（）①组成生物体的化学元素基本一致①各种生物体的蛋白质都相同①构成核酸的碱基都相同①各种生物体的核酸都相同①构成蛋白质的氨基酸都相同．A. ①①①B. ①①①C. ①①①D. ①①①2. 下列关于显微镜使用的叙述，正确的是A. 目镜越长放大倍数越高B. 要观察位于视野右上方的细胞，需要将装片向右上方移动C. 换上高倍镜后，观察到的视野范围更大D. 如果视野亮度太低，需要将反光镜调成平面镜3. 下列关于免疫失调的叙述，正确的是（）A.过敏反应是免疫系统异常敏感，将自身物质当做外来异物进行攻击而引起的疾病B.艾滋病、类风湿性关节炎、系统性红斑狼疮等都属于免疫缺陷病C.因为过敏不会破坏组织细胞，也不会引起组织严重损伤，所以不危及生命D.艾滋病患者由于免疫力很低，最终常常死于病菌感染或者恶性肿瘤4. 由新冠病毒引起的新冠肺炎流行病，给世界人民的生命安全造成了巨大危害。
下列关于新冠病毒的叙述正确的是（）A.新冠病毒在活细胞外能大量增殖B.新冠肺炎患者的血液中可以检测出新冠病毒C.新冠病毒的遗传物质主要存在于细胞核中D.新冠病毒仅含有核糖体这一种细胞器5. 某个鼠群有基因纯合致死现象(在胚胎时期就使个体死亡)，该鼠群的体色有黄色(Y)和灰色(y)，尾巴有短尾(D)和长尾(d)。
任意取雌雄两只黄色短尾鼠经多次交配，F1的表现型为黄色短尾①黄色长尾①灰色短尾①灰色长尾＝4①2①2①1。
下列相关说法不正确的是()A．两个亲本的基因型均为YyDdB．F1中黄色短尾个体的基因型为YyDdC．F1中的纯合子在胚胎时期均死亡D．F1中黄色长尾和灰色短尾的基因型分别是Yydd和yyDd6. 2022年北京冬奥会吉祥物“冰墩墩”，大熊猫是其设计原型。
2021届北京东直门中学高三语文期中试卷及答案
2021届北京东直门中学高三语文期中试卷及答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成下面小题。
科学与艺术是人类认识世界的两种有效方式，它们各具特点，相互补充，缺一不可，共同构成人类文明发展的动力和基石。
科学思维善于把复杂的世界概念化、明确化、单纯化。
科学家能够从纷繁多变的客观现象中去寻找规律，发现本质，归纳概念，变混沌为清晰，变偶然为必然。
艺术思维则善于把现实世界形象化、模糊化、丰富化，艺术家喜欢用感性的方式捕捉现实的生动瞬间和个性差异，描绘生活的点点滴滴、精彩多样，追求个人的精神世界和自我感受，变点滴为大海，变平淡为神奇。
科学思维和艺术思维认识世界的关系就好比数码相机成像过程，科学思维犹如把丰富多彩的景色编码成简单的数字符号，记录在相机储存卡里面，看上去非常的简单枯燥，但它记载着纷繁生动的客观对象；而艺术思维犹如把内存卡里的数码符号转化为图片的形象化过程，它会让无生命的数字转化成有生命活力的充满美感的图像。
在当今的艺术创作中，科学元素如影随形。
一是科学领域的很多研究方向，已经成为艺术创作的主题。
在科技时代，当代艺术家的视野有了很大的拓展，不论是航空航天、宇宙奥秘，还是基因细胞、微观世界；无论是机械动能，还是光学电子，这些都成了艺术家创作的题材和主题。
二是科技领域的研究成果已成为当今艺术关注的焦点。
人类文明进程中的很多科技的发明和研究成果，时时都会在艺术家的作品中找到它的身影，无论是飞机、汽车还是家用电器，无论是信息技术还是人工智能，都成为艺术家的兴趣点和关注点，成为他们艺术构思、艺术创作的灵感来源。
三是科研领域的创新突破，成为艺术实验探索的动因和引领。
艺术像科学一样需要不断创新，不断探索。
当代的影像、装置、观念等多种艺术的实验与探索，无不是基于当代科技的革命，如信息技术、虚拟现实、人工智能等技术的创新与突破。
由此可见，科学主题已经成为当代艺术创作的重要方面。
科技时代的艺术在表现方式与方法上有三大特征。
2020届北京东直门中学高三语文下学期期中考试试卷及参考答案
2020届北京东直门中学高三语文下学期期中考试试卷及参考答案一、现代文阅读（36分）(一)现代文阅读I(9分)阅读下面的文字，完成下面小题。
杜甫之所以能有集大成之成就，是因为他有可以集大成之容量。
而其所以能有集大成之容量，最重要的因素，乃在于他生而禀有一种极为难得的健全才性——那就是他的博大、均衡与正常。
杜甫是一位感性与理性兼长并美的诗人，他一方面具有极大极强的感性，可以深入到他接触的任何事物，把握住他所欲攫取的事物之精华；另一方面又有着极清明周至的理性，足以脱出于一切事物的蒙蔽与局限，做到博观兼美而无所偏失。
这种优越的禀赋表现于他的诗中，第一点最可注意的成就，便是其汲取之博与途径之正。
就诗歌体式风格方面而言，古今长短各种诗歌他都能深入撷取尽得其长，而且不为一体所限，更能融会运用，开创变化，千汇万状而无所不工。
我们看他《戏为六绝句》之论诗，以及与当时诸大诗人，如李白、高适、岑参、王维、孟浩然等，酬赠怀念的诗篇中论诗的话，都可看到杜甫采择与欣赏的方面之广；而自其《饮中八仙歌》《曲江三章》《同谷七歌》等作中，则可见到他对各种诗体运用变化之神奇工妙；又如从《自京赴奉先县咏怀五百字》《北征》及“三吏”“三别”等五古之作中，可看到杜甫自汉魏五言古诗变化而出的一种新面貌。
就诗歌内容方面而言，杜甫更是无论妍媸巨细，悲欢忧喜，宇宙的一切人物情态，都能随物赋形，淋漓尽致地收罗笔下而无所不包，如写青莲居士之“飘然思不群”，写空谷佳人之“日暮倚修竹”；写丑拙则“袖露两肘”，写工丽则“燕子风斜”；写玉华宫之荒寂，予人以一片沉哀悲响；写洗兵马之欢忭，写出一片欣奋祝愿之情、其涵蕴之博与变化之多，都足以为其禀赋之博大、均衡与正常的证明。
其次值得注意的，则是杜甫严肃中之幽默与担荷中之欣赏，我以为每一位诗人对于其所面临的悲哀与艰苦，都各有其不同的反应态度，如渊明之任化，太白之腾跃，摩诘之禅解，子厚之抑敛。
东坡之旷观，六一之遣玩，都各因其才气性情而有所不同，然大别之，不过为对悲苦之消融与逃避。
2021届北京东直门中学高三生物下学期期中考试试卷及参考答案
2021届北京东直门中学高三生物下学期期中考试试卷及参考答案一、选择题：本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求。
1. 噬菌体、烟草、HIV病毒的核酸中具有碱基和核苷酸的种类分别是（）A. 4种、8种、4种和4种、8种、4种B. 4种、5种、4种和4种、8种、4种C. 4种、5种、4种和4种、5种、4种D. 4种、8种、4种和4种、5种、4种2. 图中①～①表示某细胞的部分细胞器。
下列叙述错误的是（）A.①中通过内膜折叠的方式增大膜面积B.①对来自内质网的蛋白质进行加工、分类和包装C.①若处于游离状态可合成血红蛋白等胞内蛋白D.由①可判断该细胞为动物细胞3. 下列有关水和无机盐的调节不正确的是（）A. 当细胞外液渗透压降低时，内环境中的抗利尿激素相对减少B. 当细胞外液渗透压升高时，垂体分泌抗利尿激素增多C. 血钾升高时，肾上腺皮质分泌的醛固酮增加D. 水和无机盐的调节器官主要是肾脏4. 将某活组织放入适宜的完全营养液中，置于适宜的条件下培养。
培养液中甲、乙两种离子的浓度保持相等且恒定，定期测定细胞中两种离子的含量，得到如图所示曲线。
据图分析下列叙述中正确的是A. 该组织的细胞吸收甲、乙两种离子的方式分别是自由扩散和主动运输B. 该组织细胞运输离子甲的载体数量比运输离子乙的载体数量多C. 两种离子均只能从低浓度的一侧运输到高浓度的一侧D. 曲线mn段和ab段表明两种离子浓度的升高抑制了细胞对水的吸收5. 如下图①~①表示甲刺激所引起的调节过程，乙表示参与调节的重要器官，下列有关叙述正确的是（）A.图中乙表示下丘脑，①过程主要通过神经调节实现B.若甲刺激为血糖浓度升高，则“甲刺激→乙→胰岛”过程属于体液调节C.若甲刺激为寒冷条件，则“甲刺激→乙→垂体→甲状腺”过程中存在分级调节D.若甲刺激为食物过咸，则在乙处下丘脑产生渴觉，且垂体释放抗利尿激素增多6. 下列物质通过细胞膜时需要载体的是A. 水分子进入根毛细胞B. 氧进入肺泡细胞C. 二氧化碳进入毛细血管D. K＋被吸收进入小肠绒毛上皮细胞7. 某同学从室温20①的家中来到0①户外的一小时内，其体温调节的情况将会是A.体温维持恒定不变B.甲状腺激素分泌量增加C.毛细血管舒张以减少散热D.可能会出现打寒颤的条件反射8. 下列有关生物膜系统的描述错误的是（）A.原核细胞不具有生物膜系统B.生物膜系统由具膜的细胞器构成C.各种生物膜的化学组成和结构相似D.丰富的生物膜为酶的附着提供了大量位点9. 某人足部突然扎到钉子而迅速抬腿的相关反射弧如图所示。
2021届北京东直门中学高三生物下学期期中试卷及答案
2021届北京东直门中学高三生物下学期期中试卷及答案一、选择题：本题共15小题，每小题2分，共30分。
每小题只有一个选项符合题目要求。
1.已知水稻高秆(T)对矮秆(t)为显性，抗病(R)对感病(r)为显性，两对基因独立遗传。
现将一株表现型为高秆、抗病植株花粉授给另一株表现型相同的植株，F1高秆∶矮秆＝3∶1，抗病∶感病＝3∶1。
再将F1中高秆抗病类型分别与矮秆感病类型进行杂交，则产生的F2表现型之比理论上为( )A. 9∶3∶3∶1B. 1∶1∶1∶1C. 4∶2∶2∶1D. 3∶1∶3∶12.某兴趣小组用不同浓度的生长素处理刚开始发芽的大豆芽，三天后观察到的胚轴生长情况如下图（“－”表示未用生长素处理，“＋”表示用生长素处理，“＋”越多表示激素浓度越高），该实验可作为探究生长素促进胚轴伸长的最适浓度的预实验。
下列相关叙述正确的是（）A. 预实验能检测实验设计的科学性和可行性，减少实验误差B. 在正式实验时还需设计不含生长素的空白对照组C. 图示结果说明生长素的作用具有两重性D.D组比C组生长慢可能由于生长素浓度升高诱导乙烯产生有关3.关于现代生物进化理论的叙述，正确的是（）A. 一个池塘内所有生物构成生物进化的基本单位B. 进化的原材料只能由基因突变和基因重组产生C. 二倍体草莓与四倍体草莓存在生殖隔离D. 若种群中显隐性个体的数量保持不变，则没有发生进化4.下列有关实验的叙述，错误的是（）A. 换成高倍镜观察叶绿体，图像不清晰要调细准焦螺旋B. 蛋白质变性后，加入双缩脲试剂仍呈现紫色反应C. 质壁分离及复原实验中先后用低倍和高倍显微镜观察三次，形成自身前后对照D. 洋葱表皮细胞浸润在一定浓度的甘油溶液中可发生质壁分离和质壁分离复原5.下图所示去掉尖端的胚芽鞘一侧放置含适宜浓度的生长素的琼脂块，将花盆放入暗箱中，以一定速度匀速旋转一段时间后，在图示的位置停止。
胚芽鞘的生长情况是A. 直立生长B. 向右弯曲生长C. 向左弯曲生长D. 不生长不弯曲6.下图某反射弧结构的模式图，其中乙表示神经中枢，甲、丙未知。
2020年北京东直门中学高三英语下学期期中考试试题及答案解析
2020年北京东直门中学高三英语下学期期中考试试题及答案解析第一部分阅读（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、D四个选项中选出最佳选项ABrecon Beacons YAC has an amazing opportunity for budding (崭露头角的) archaeologists(考古学家) of all ages, in Sunderland in Tyne and Wear. Thanks to funding from the Heritage Lottery Fund, professional archaeologists from Wardell Armstrong will be investigating an archaeological mystery and they need your help. Romans?“The site is a bit of a mystery”, Frank Giecco from Wardell Armstrong said. “There is a very nice cropmark recorded on the site that has got lots of people very excited. Geophysicists(地质物理学家) failed to find anything related to the cropmark. There is anecdotal (传闻的)evidence of Roman material being found, but nothing is officially recorded. We hope to finally answer the question of what is in this field, during the two weeks on site. Is there evidence of any Roman occupation on the site? Can you help us find out?"Get involvedThis is an opportunity for both adults and children to take part in field walking and trial trenching (small hand-dug test pits for children). No experience is necessary, training will be provided by the professional archaeologists from Wardell Armstrong, and all equipment will be provided. Volunteers can attend for as few or as many days as they wish, but they do need to book a place.For more information, and to book your place, please contact Norman Kirtlan at ***********************************.1.Who is the activity probably intended for?A.OfficialsB.ExpertsC.FamiliesD.Romans.2.If you take part in the activity, you ________.A.will be coached by experts in the fieldB.will be charged for using equipmentC.should have worked with archaeologists beforeD.should spare two weeks to stay at the site3.What's the main purpose of the activity?A.To seek funding for archaeological research.B.To appeal for help inproving findings based on anecdotal evidence.C.To find volunteers to help solve an archaeological mystery.D.To organize volunteers to help sort our data on the Roman occupation.BThe history of the flying car is almost as old as that of powered flight itself. It started with the Curtiss Autoplane of 1917, an awkward-looking machine with removable wings. It never left the ground. Later machines made it into the skies but failed to take off commercially. Money is now pouring into flying taxis. On March 30th Lilium, a German company that develops them, announced a merger with SPAC, an acquisition company that values it at $3. 3 bn -- a sign that investors think the business will fly.Thanks to better batteries and lightweight materials, some of them are ready to carry passengers. Up to 300 firms are working on short-range battery-powered craft that take off and land vertically. Carmakers, tech companies and others are investing money into the field. The government isoffering a glide pathto certification.America's Federal Aviation Administration is engaged in the process with around 30 firms, says Natasha Santha of LEK, a consulting company.Midway between a cab and a helicopter, flying taxis have distinct advantages over both. Quiet electric motors allow them to operate frequent services. They require only a patch of concrete to land, unlike noisy helicopters, which face severe operating restrictions in most cities. They can fly four or five times faster than a cab can drive and do not get stuck in traffic. Prices can be kept low by ride-sharing. Joby, based inCalifornia, says its five-seater machine will enter commercial service in 2024. The firm calculates the initial cost of around $4 per person per mile may soon fall by 25%. A trip fromManhattanto JFK airport would then cost $30-40 per passenger.The real revolution will come when full autonomy takes out the cost of a pilot. Archer hopes to run such aircraft by 2028. They face fewer obstacles in the air than earth-bound cars do on the road; airliners mostly fly on autopilot as it is. Still, as one industry insider puts it, it is probably best to accustom passengers and regulators to airborne taxis before getting rid of the driver.4. What can we learn from Paragraph 1?A. The flying car can date back to the 1920s.B. Investors see the potential of the business of the flying car.C. The flying car never left the ground successfully in history.D. A German company has launched a new flying car into the market.5. What does "offering a glide path" in Paragraph 2 probably refer to?A. Giving the green light.B. Providing timely assistance.C. Presenting legal guidance.D. Conducting strict management.6. Which of the following is the strength of flying taxis?A. Costing as little as cabs.B. Saving passengers from the traffic jam.C. Reducing air pollution.D. Having no operating restrictions.7. What can be inferred about the flying taxis from the last paragraph?A. They will develop faster than cars.B. Passengers will quickly get used to taking them.C. The regulators will take measures to promote them.D. Autopilot flying taxis will probably replace those with pilots.CWhen you say the word donkey, whatthings come to your mind? A few people might say they’re cute, but the majority think they’re stubborn, dumb and all-round less capable than their horse s.However, this wasn’t the case for a recently unearthed ancient Chinese noblewoman who was unexpectedly found buried with her donkeys. Published in the journal Antiquity in March, Chinese archaeologists (考古学家) first discovered the tomb in Xi’an, Shaanxi, in 2012. The team examined the remains and identified the body as Cui Shi, a Tang Dynasty high-born lady who died in 878 AD.Speaking to Science Magazine in 2012, the study’s co-author, Fiona Marshall, said the finding caused confusion as “donkeys … are not associated with high-status people”.However, following years of further research, the team discovered artworks and artifacts that showed a sport known as “Lvju”. This was similar to modern-day polo (马球)and was popular among noble (高贵的) women at the time. They preferred to use donkeys instead of full-sized horses for safety reasons, due to their smaller size and slower speed.Speaking to CNN, Marshall later said, “Historical documents also showed that ladies of the late Tang court loved to play donkey polo.”At that time in Chinese history, animals were often placed in tombs so that they could be used for a specific purpose in the afterlife. The study determined that Cui Shi likely requested that her beloved donkeys be buried with her, so that she could continue her favorite sport after death. In total, three donkeys were found inside her tomb with riding gear (装备), including stirrups (马镫). “This context provides evidence that the donkeys in her tomb were for polo, not transport,” lead author Hu Songmei of the Shaanxi Academy of Archaeology told ScienceMagazine.Before the study, it was believed that donkeys were only used to carry loads, but now it may be time to see them as a sign of achieving high social status(地位), well, in ancient times.8. What do most people think of donkeys, according to the text?A. They are as adorable(可爱的) as horses.B. They are stubborn and not so capable.C. They were necessary in ancient sports.D. They were a sign of high social status.9. Why did Fiona Marshall feel confused when she discovered the donkeys?A. She didn’t connect donkeys with nobles.B. She hadn’t seen donkeys in ancient tombs before.C. She didn’t expect to find donkeys in a woman’s tomb.D. She didn’t understand why animals were in human tombs.10. What do we know about the sport “Lvju” from the text?A. Horses were preferred in Lvju.B Lvju was similar to modern-day soccer.C. Lvju was popular among common people.D. Donkeys were preferred in the sport for safety.11. The donkeys were found in the tomb of Cui Shi probably because _______.A. she intended to use them for transport after deathB. her family didn’t want her to be lonely after deathC. she wanted to continue to play Lvju after deathD. noble women needed donkeys to maintain their dignityDThereare two days that set you on your path in life: the day you’re born, and the day you realize why you were born.Growing up south of Chicago in Harvey, Illinois, most people just had their heads down trying to make it from point A to point B. I was the same way, just going with the flow. I played basketball in high school because I was good at it and because other people thought I should until I discovered my talent.I give up basketball and started doing speeches. It wasn’t a popular decision but my grandfather told me to do what made me happy. I fell in love with comedy and performing. And when I discovered the passion, I realized why I was born.I knew I had something to offer —I knew that not only am I powerful, but I can make a difference.I realized a long time ago that my dream is not to be famous or rich. My talent is to entertain. But it’s more than that. I have the chance to reach people, to brighten days, to bring laughter and positive energy into lives and inspire. And I am grateful forit.Acting putting myself out there and having doors closed on me time and time again has taught me a lot about myself. I have learned to trust what I have to offer the world over momentary doubt. I’ve learned to put my faith over my feelings. And I've grown a tough skin. More importantly, I have learned there is a long way towards our goals and that when we put our talents and passion to work, we determine our value.Like a lot of places across the country, there’s poverty, crime, violence and unemployment in Harvey. And growing up there, a lot of people have tragically low expectations for life. But I know that with the right opportunity and with help along the way, everyone can find their passion and go after it. My life is proof.12. What was the author born to do according to the text?A. Be a basketball player.B. Act and perform.C. Make speeches.D. Teach people.13. What does the underlined word “it” in Paragraph 5 refer to?A. Chance.B. Energy.C. Days.D. Laughter.14. What is the author’s purpose of writing this text?A. To help others find their talents.B. To prove his decision was right.C. To inspire people to follow their dreams.D. To encourage people to set a goal.15. What can be the best tile for the text?A. Success Lies in Hard Work.B. How to Achieve the Dream Is Important.C. The Two Important Days in Life.D. The Day I Realized What I Was Born to Do.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
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北京市东直门中学2020-2021学年高三下学期期中考试数学试题注意事项1．考生要认真填写考场号和座位序号。
2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。
第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。
3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。
一、选择题：本题共12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。
1．一场考试需要2小时，在这场考试中钟表的时针转过的弧度数为（ ）A ．3πB ．3π-C ．23πD ．23π- 2．已知命题p ：1m =“”是“直线0x my -=和直线0x my +=互相垂直”的充要条件；命题q ：对任意()2,∈=+a R f x x a 都有零点；则下列命题为真命题的是（ ）A ．()()p q ⌝∧⌝B ．()p q ∧⌝C ．p q ∨D ．p q ∧ 3．为了加强“精准扶贫”，实现伟大复兴的“中国梦”，某大学派遣甲、乙、丙、丁、戊五位同学参加、、A B C 三个贫困县的调研工作，每个县至少去1人，且甲、乙两人约定去同一个贫困县，则不同的派遣方案共有（ ）A ．24B ．36C ．48D ．644．执行如图所示的程序框图，输出的结果为（ ）A ．193B ．4C ．254D ．1325．若0.60.5a ＝,0.50.6b ＝,0.52c ＝,则下列结论正确的是( )A ．b c a >>B ．c a b >>C ．a b c >>D ．c b a >>6．设m ，n 为非零向量，则“存在正数λ，使得λ=m n ”是“0m n ⋅>”的（ ）A ．既不充分也不必要条件B ．必要不充分条件C ．充分必要条件D ．充分不必要条件7．如图，这是某校高三年级甲、乙两班在上学期的5次数学测试的班级平均分的茎叶图，则下列说法不正确的是（ ）A ．甲班的数学成绩平均分的平均水平高于乙班B ．甲班的数学成绩的平均分比乙班稳定C ．甲班的数学成绩平均分的中位数高于乙班D ．甲、乙两班这5次数学测试的总平均分是1038． “2a =”是“直线210ax y +-=与(1)20x a y +-+=互相平行”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 9．复数满足48i z z +=+，则复数z 在复平面内所对应的点在（ ）A ．第一象限B ．第二象限C ．第三象限D ．第四象限10．设复数z 满足()117i z i +=-，则z 在复平面内的对应点位于（ ）A ．第一象限B ．第二象限C ．第三象限D ．第四象限11．运行如图所示的程序框图，若输出的i 的值为99，则判断框中可以填（ ）A ．1S ≥B ．2S >C ．lg99S >D ．lg98S ≥12．如图是正方体截去一个四棱锥后的得到的几何体的三视图，则该几何体的体积是（ ）A．12B．13C．23D．56二、填空题：本题共4小题，每小题5分，共20分。
13．在《九章算术》中，将底面为矩形且有一条侧棱与底面垂直的四棱锥称之为阳马．如图，若四棱锥P ABCD-为阳马，侧棱PA⊥底面ABCD，且3PA=，4BC AB==，设该阳马的外接球半径为R，内切球半径为r，则Rr=__________．14．已知不等式组20202x yx yx-≥⎧⎪-≤⎨⎪≤⎩所表示的平面区域为Ω，则区域Ω的外接圆的面积为______．15．设1234x x x x、、、为互不相等的正实数，随机变量X和Y的分布列如下表，若记DX，DY分别为,X Y的方差，则DX_____DY．（填>，<，=）X1x2x3x4xY122x x+232x x+342x x+412x x+P1414141416．甲、乙两人同时参加公务员考试，甲笔试、面试通过的概率分别为45和34；乙笔试、面试通过的概率分别为23和12．若笔试面试都通过才被录取，且甲、乙录取与否相互独立，则该次考试只有一人被录取的概率是__________．三、解答题：共70分。
解答应写出文字说明、证明过程或演算步骤。
17．（12分）在平面直角坐标系中，曲线C的参数方程为cos1sinxyθθ=⎧⎨=+⎩（θ为参数）.以原点为极点，x轴的非负半轴为极轴，建立极坐标系.（1）求曲线C 的极坐标方程；（2）直线1cos :sin x t l y t θθ=+⎧⎨=⎩（t 为参数）与曲线C 交于A ，B 两点，求||AB 最大时，直线l 的直角坐标方程.18．（12分）{}2*112n 11=1=,.n 2n n n n n a a a a n N n ++++∈+已知数列满足， (Ⅰ)证明：22n n a ≥≥当时， ()*n N ∈； (Ⅱ)证明：()1121111=2122312n n n a a a a n n ++++-⋅⋅⋅+(*n N ∈)； (Ⅲ)证明：431,42n a e e <-为自然常数. 19．（12分）已知离心率为12的椭圆2222:1x y M a b+=(0)a b >>经过点31,2D ⎛⎫ ⎪⎝⎭. (1)求椭圆M 的方程；(2)荐椭圆M 的右焦点为F ，过点F 的直线AC 与椭圆M 分别交于,A B ，若直线DA 、DC 、DB 的斜率成等差数列，请问DCF ∆的面积DCF S ∆是否为定值？若是，求出此定值；若不是，请说明理由. 20．（12分）已知动圆过定点(0,1)F ，且与直线:1l y =-相切，动圆圆心的轨迹为C ，过F 作斜率为(0)k k ≠的直线m 与C 交于两点,A B ，过,A B 分别作C 的切线，两切线的交点为P ，直线PF 与C 交于两点,M N ．（1）证明：点P 始终在直线l 上且PF AB ⊥；（2）求四边形AMBN 的面积的最小值．21．（12分）如图，三棱锥P ABC -中，3,2,PA PB PC CA CB AC BC =====⊥（1）证明：面PAB ⊥面ABC ；（2）求二面角C PA B --的余弦值.22．（10分）如图，在三棱柱111ABC A B C -中，1A B ⊥平面ABC ，AB AC ⊥，且12AB AC A B ===.（1）求棱1AA 与BC 所成的角的大小；（2）在棱11B C 上确定一点P ，使二面角1P AB A --25.参考答案一、选择题：本题共12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、B【解析】【分析】因为时针经过2小时相当于转了一圈的16，且按顺时针转所形成的角为负角，综合以上即可得到本题答案. 【详解】因为时针旋转一周为12小时，转过的角度为2π，按顺时针转所形成的角为负角，所以经过2小时，时针所转过的弧度数为11263ππ-⨯=-.故选：B【点睛】本题主要考查正负角的定义以及弧度制，属于基础题.2、A【解析】【分析】先分别判断每一个命题的真假，再利用复合命题的真假判断确定答案即可.【详解】当1m =时，直线0x my -=和直线0x my +=，即直线为0x y -=和直线0x y +=互相垂直， 所以“1m =”是直线0x my -=和直线0x my +=互相垂直“的充分条件，当直线0x my -=和直线0x my +=互相垂直时，21m =，解得1m =±.所以“1m =”是直线0x my -=和直线0x my +=互相垂直“的不必要条件.p ：“1m =”是直线0x my -=和直线0x my +=互相垂直“的充分不必要条件，故p 是假命题．当1a =时，2()1f x x =+没有零点，所以命题q 是假命题．所以()()p q ⌝∧⌝是真命题，()p q ∧⌝是假命题，p q ∨是假命题，p q ∧是假命题．故选：A ．【点睛】本题主要考查充要条件的判断和两直线的位置关系，考查二次函数的图象， 考查学生对这些知识的理解掌握水平.3、B【解析】【分析】根据题意，有两种分配方案，一是3:1:1，二是2:2:1，然后各自全排列，再求和.【详解】当按照3:1:1进行分配时，则有133318C A =种不同的方案；当按照2:2:1进行分配，则有233318C A =种不同的方案.故共有36种不同的派遣方案，故选：B.【点睛】本题考查排列组合、数学文化，还考查数学建模能力以及分类讨论思想，属于中档题.4、A【解析】【分析】模拟执行程序框图，依次写出每次循环得到的,x M 的值，当3x =，1943M =>，退出循环，输出结果. 【详解】程序运行过程如下： 3x =，0M =；23x =，23M =；12x =-，16M =； 3x =，196M =；23x =，236M =；12x =-，103M =；3x =，1943M =>，退出循环，输出结果为193， 故选：A.【点睛】该题考查的是有关程序框图的问题，涉及到的知识点有判断程序框图输出结果，属于基础题目. 5、D【解析】【分析】根据指数函数的性质，取得,,a b c 的取值范围，即可求解，得到答案.【详解】由指数函数的性质，可得0.50.50.610.60.50.50>>>>，即10b a >>>，又由0.512c =>，所以c b a >>.故选：D.【点睛】本题主要考查了指数幂的比较大小，其中解答中熟记指数函数的性质，求得,,a b c 的取值范围是解答的关键，着重考查了计算能力，属于基础题.6、D【解析】【分析】 充分性中，由向量数乘的几何意义得,0m n =，再由数量积运算即可说明成立；必要性中，由数量积运算可得),0,90m n ⎡∈⎣，不一定有正数λ，使得λ=m n ，所以不成立，即可得答案.【详解】充分性：若存在正数λ，使得λ=m n ，则,0m n =，cos00m n m n m n ⋅==>，得证； 必要性：若0m n ⋅>，则),0,90m n ⎡∈⎣，不一定有正数λ，使得λ=m n ，故不成立；所以是充分不必要条件故选：D【点睛】本题考查平面向量数量积的运算，向量数乘的几何意义，还考查了充分必要条件的判定，属于简单题. 7、D【解析】【分析】计算两班的平均值，中位数，方差得到ABC 正确，两班人数不知道，所以两班的总平均分无法计算，D 错误，得到答案.【详解】由题意可得甲班的平均分是104，中位数是103，方差是26.4；乙班的平均分是102，中位数是101，方差是37.6，则A ，B ，C 正确.因为甲、乙两班的人数不知道，所以两班的总平均分无法计算，故D 错误.故选：D .【点睛】本题考查了茎叶图，平均值，中位数，方差，意在考查学生的计算能力和应用能力.8、A【解析】【分析】利用两条直线互相平行的条件进行判定【详解】当2a =时，直线方程为2210x y +-=与20x y ++=，可得两直线平行；若直线210ax y +-=与()120x a y +-+=互相平行，则()12a a -=，解得12a =，21a =-，则“2a =”是“直线210ax y +-=与()120x a y +-+=互相平行”的充分不必要条件，故选A【点睛】本题主要考查了两直线平行的条件和性质，充分条件，必要条件的定义和判断方法，属于基础题． 9、B【解析】【分析】设(,)z a bi a b R =+∈,则48z z a bi i +=+=+,可得48a b ⎧⎪+=⎨=⎪⎩,即可得到z ,进而找到对应的点所在象限.【详解】设(,)z a bi a b R =+∈,则48z z a bi i +=++=+,48a b ⎧⎪+=∴⎨=⎪⎩,6,68i 8a z b =-⎧∴∴=-+⎨=⎩, 所以复数z 在复平面内所对应的点为()6,8-,在第二象限.故选:B【点睛】本题考查复数在复平面内对应的点所在象限,考查复数的模,考查运算能力.10、C【解析】【分析】化简得到34z i =--，得到答案.【详解】()117i z i +=-，故()()()()1711768341112i i i i z i i i i -----====--++-，对应点在第三象限. 故选：C .【点睛】本题考查了复数的化简和对应象限，意在考查学生的计算能力.11、C【解析】【分析】模拟执行程序框图，即可容易求得结果.【详解】运行该程序：第一次，1i =，lg 2S =；第二次，2i =，3lg 2lglg32S =+=； 第三次，3i =，4lg3lg lg 43S =+=， …；第九十八次，98i =，99lg98lglg9998S =+=； 第九十九次，99i =，100lg99lg lg100299S =+==， 此时要输出i 的值为99.此时299S lg =>.故选：C.【点睛】本题考查算法与程序框图，考查推理论证能力以及化归转化思想，涉及判断条件的选择，属基础题. 12、C【解析】【分析】根据三视图作出几何体的直观图，结合三视图的数据可求得几何体的体积.【详解】根据三视图还原几何体的直观图如下图所示：由图可知，该几何体是在棱长为1的正方体1111ABCD A B C D -中截去四棱锥1B ABCD -所形成的几何体，该几何体的体积为321211133V =-⨯⨯=. 故选：C.【点睛】本题考查利用三视图计算几何体的体积，考查空间想象能力与计算能力，属于基础题.二、填空题：本题共4小题，每小题5分，共20分。