2020西城诊断性测试含答案
2020年北京市西城区5月诊断测试数学试卷答案
化简，得 m = 3n2 − 4n + 2 = 3(n − 2)2 + 2 ， 33
因为 m ， n 是大于 1 的正整数，且 m n ， 所以当 n = 2 时， m 取到最小值 6． 选择 ③： (Ⅰ) 由 2an+1 = an + an+2 ，得 an+1 − an = an+2 − an+1 .
22 因为 m ， n 是大于 1 的正整数，且 m n ， 所以当 n = 2 时， m 有最小值 5 ．
……………… 11 分 ……………… 14 分
……………… 2 分
……………… 4 分 ……………… 6 分 ……………… 8 分 ……………… 9 分 ……………… 11 分 ……………… 14 分
18．（本小题满分 14 分）
解：（Ⅰ）设事件 M 为：“从这些康乃馨种子中随机抽取一种，且该种子不是“C 级”种子”，
……………… 1 分 由图表，得 (0.4 +1.2 + a + 4.0 + 6.0 + 4.4 +1.2 + 0.4) 0.05 = 1，
解得 a = 2.4 .
……………… 2 分
……………… 2 分 ……………… 3 分 ……………… 5 分
……………… 6 分 ……………… 8 分 ……………… 9 分 ……………… 11 分
……………… 14 分
……………… 2 分 ……………… 4 分 ……………… 6 分 ……………… 8 分 ……………… 9 分
北京市西城区诊断性测试 高三数学参考答案 第2页（共8页）
西城区高三诊断性测试
数学参考答案
2020.5
2020年北京市西城区高三数学诊断性测试试卷含参考答案
O 0.486 0.536 0.586 0.636 0.686 0.736 0.786 0.836 0.886 发芽率
企业对康乃馨的种子进行分级，将发芽率不低于 0.736 的种子定为“A 级”，发芽率低于 0.736 但不低于 0.636 的种子定为“B 级”，发芽率低于 0.636 的种子定为“C 级”.
解析： (x 2)2 ( y 1)2 5 a ，半径大于等于 2 即可， 5 a 4 ， a 1 ，选 A.
9.若向量 a 与 b 不共线，则“ a b 0 ”是“ 2 | a b || a | | b | ”的
（A）充分而不必要条件 （C）充要条件
（B）必要而不充分条件 （D）既不充分也不必要条件
A.第一象限
B.第二象限
C.第三象限
解析： z 1 i (1 i) (i) 1 i ，选 A.
i
i (i)
3.下列函数中，值域为 R 且在区间 (0, ) 上单调递增的是(
D.第四象限 )
A. y x3
B. y x x
C. y x1
解析：值域为 R，排除 C、D， (0, ) 上单调递增排除 A，选 B.
C. y x1
4.抛物线 x2 4y 的准线方程为（
）
A. x 1
B. x 1
C. y 1
5.在 ABC 中，若 a : b : c 4 : 5 : 6 ，则其最大内角的余弦值为（
A. 1
B. 1
8
4
C. 3 10
6.设 a 30.2 ， b log3 2 ， c log0.2 3 ，则（ ）
12.若双曲线
x2 a2
y2 16
1(a
北京西城区高三诊断性考试(5月)英语试题 含答案
2020 西城诊断性考试1西城区高三年级英语诊断性考试试卷 C第一部分：知识运用（共两节，45 分）第一节语法填空（共10 小题；每小题1.5 分，共15 分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1 个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AMia rushed home and threw open the front door. Her mother turned around, surprised that Mia was home from school so early. “I won first place in the art contest!” she said (1) pride and raised her head, expecting praise. Though Mia (2) (work) eagerly on her art submission for weeks, her mother wasn’t sure (3) the project involved. “That’s wonderful, Mia! What was the subject of your art project?” her mother asked. Smiling from ear to ear, Mia handed over her artwork. It was a portrait of her mother.BA study found that adults aged 18 to 33 checked their smartphones 85 times a day, or once every 10 minutes. As I learned during my experiment, (4) (place) some distance between myself and my device helped me devote myself to my work more (5) (easy). By not having my smartphone, my distraction(消遣) time went down and thus my work time (6) (spend) more efficientlyand effectively. On numerous occasions, I found (7) (I) wondering what to do with the afternoon since I had already completed my high-impact tasks for the day. With the extra time, I can finally enjoy the pleasures of life.In June 2012, China’ s first manned deep-sea submersible(潜水器), Jiaolong,set a world diving record for submersibles of its kind by reaching a (8) (deep) of 7,062 meters in the Mariana Trench in the Pacific Ocean. In 2017, China successfully tested a submersible (9) (call) Shenhai Yongshi, capable of diving 4,500 meters. (10) much of Jiaolong’s equipment was imported, about 95 percent of Shenhai Yongshi and its core components were produced domestically, said Xu Qinan, the chief designer of Jiaolong.第二节完形填空（共20 小题；每小题1.5 分，共30 分）“Expert advisers often make surprisingly inaccurate predictions about the future, yet people (27) their suggestions nevertheless,” concludedOne morning in July 2011, a taxi sat wandering outside Petco Park stadium in San Diego. And Wade LeBlanc, a (an) (11) pitcher (棒球投手) for the Padres, climbed in.” To the airport, please,” he told the driver. LeBlanc was headed to Tucson, Arizona, home of the club’s A-level branch organization at the time. He’d been sent down to the minors. Again. For the eighth time in three years.“You’re Wade LeBlanc,” the taxi driver said.“Right.”“You got some good stuff.”Stanford University psychologists in a study published last year.Now, not everyone took experts’ advice. The more (28) people become, the smaller the pool of advisers they (29). Participants in positions of power ignored almost two thirds of the advice they received, according to one Harvard University study. Other participants—the control and low power groups—ignored advice about half as often. So it required a massive increase of modesty (谦虚) to do what Wade LeBlanc did: hear what the taxi driver was offering him and accept it as a(an) (30).This performance. (12) the pitcher, after the previous night’s disastrous11. A. excellent B. struggling C. ambitious D. awkward12. A. surprised B. concerned C. disturbed D. angered“I think there are some things you should think about (13),” the driver continued.” I don ’t know; I ’m not a (14). Maybe something like going over your head in your windup (摆臂动作)”Wait, what? This guy was offering…(15)? Earlier in his career, 13. A. avoiding B. making C. trying D. crossing14. A. player B. director C. joker D. loser15. A. service B. advice C. chances D. courses16. A. accepted B. worried C. smiled D. laughedLeBlanc might have (16). Or been angry. But today, he just 17. A. explained B. interrupted C. listened D. guessed(17). He couldn’t afford to dismiss anything. His caree r was on the line.The next day, in Tucson, LeBlanc met his (18). He said he was thinking about making (19) to his windup. His coach agreed. Instead of keeping his hands tight to his chest at the beginning of his delivery, LeBlanc raised them briefly over his head, as the taxi driver had (20).LeBlanc included the new (21) into his next start. And he was(22), allowing only one hit over seven innings ( 回合). It was the turning point in his career. Eight years later, LeBlanc is a pitcher for the Seattle Mariners. He signed the first contract extension of his Major League Baseball career—at age 33.The funny thing about advice: We so often take it from the (23) people. That is, we (24) the advice of experts, while undervaluing the input of regular folk. Wade LeBlanc (25) that trend, and he obtained the (26). 18. A. parents B. coach C. driver D. fans19. A. changes B. contributions C. additions D. objectives20. A. included B. announced C. suggested D. resisted21. A. aim B. effect C. hobby D. move22. A. patient B. optimistic C. brilliant D. justified23. A. attractive B. popular C. humble D. wrong24. A. overvalue B. skip C. ignore D. involve25. A. identified B. supported C. opposed D. started26. A. qualifications B. benefits C. prize D. degree27. A. follow B. abandon C. provide D. improve28. A. literary B. successful C. careful D. negative29. A. tolerate B. help C. know D. trust30. A. job B. example C. excuse D. gift第二部分：阅读理解（共两节，40 分）A eight recipes each week, so there isn’t a lot of flexibility for different dietary needs, but the recipes are full of flavor and give subscribers generous portions. If you’re looking for an affordable way to get into meal kits, EveryPlate is a good option.Which meal kit service is right for you?As the simple act of shopping and preparing food for dinner becomes harder to fit in, a way to help meet consumer needs and change the way we shop and eat has grown: meal-delivery plans. Here’s a quick review of some popular options: 1. HelloFreshHelloFresh provides high-quality ingredients （烹饪原料）and generous portions（份量）, with recipes that are generally easy to prepare. The clear, step-by-step instructions get even the newest home chefs up to speed, and the recipe cards are well-made, so you can refer to your favorite recipes again and again.There are meals for almost any lifestyle, including vegetarian（素食）options, low-calorie meals and “quick” recipes that get dinner on the table fast.Cost: $8.75 to $9.99 per serving, with up to 16 servings per week.2. FreshlyGet fresh, home-cooked food without the trouble of actually cooking. This subscription service delivers comfort foods to your doorstep, and the meals are prepared right before delivery. Never frozen and only requiring minimal reheating, they’re nutritious and cost less than many standard takeout options.Cost: $7.99 to $11.50 per serving, with up to 12 servings per week.3. Blue ApronBlue Apron is full of fresh ingredients, with traditional or vegetarian options. Like many of the plans, the food is delivered in one big box and the recipe card is separate from the meal ingredients. The variety is good and the recipes are generally easy to prepare.Cost: $7.49 to $9.99 per serving, with up to 16 servings per week.4. EveryPlateEveryPlate offers simpler meals for a lower cost. Users can choose betweenCost: $4.99 per serving, with up to 12 servings per week.5. Daily HarvestDaily Harvest specializes in delicious smoothies. The meals are packed with fruits and vegetables, making nutrition easy and tasty. Smoothies just require the addition of liquid, so feel free to add your favorite type of milk or water to the blend and get your day started.Cost: $6.99 per serving, with between 9 and 26 servings available.31. Which meal kit service is right for a vegetarian?A. Daily Harvest and EveryPlate.B. HelloFresh and Blue Apron.C. EveryPlate and Freshly.D. HelloFresh and Freshly.32. Each meal-delivery plan is available with .A. fruits and vegetablesB. unlimited servingsC. easy preparationD. separate recipes33. The meal-delivery plans meet the customer needs of .A. living an environmentally friendly lifeB. cutting down on daily food costsC. adapting to a new lifestyleD. improving cooking skillsB account," she said.Kylie Kirkpatrick was getting ready for work when her 9-year old son, Ryan Kyote, burst into her bedroom. The Napa, California-based third-grader had just watched a news story about a kindergarten student in Indiana who was forced to return her school lunch because her account balance couldn't cover the meal."Ryan was upset," Kirkpatrick told TODAY Parents. “He said, 'Mom, how does something like this happen?' Then he asked what he could do to help."After a bit of brainstorming, Kyote-pronounced “coyote" -decided he would use six months' worth of allowance he had saved up to pay off the lunch debt of his entire class at West Park Elementary School. The bill came up to S74.50.Though Kyote had been eyeballing a new pair of basketball sneakers, this was far more important to him. So, on May 24, he happily donated his six months of savings to the Napa Valley Unified School District food services department."Ryan told them, 'Please let my friends know that they no longer owe any money," Kirkpatrick recalled. "Lunch is his favorite part of the day and it broke his heart to think that it's a stressful time for some children."The fourth-grader-to-be wanted his act of kindness to be unknown to others, but his proud mother couldn't resist sharing a photo on Twitter, where it spread quickly."Give this kid his money back. No child should be covering lunch debt for his class with his allowance," wrote one person. Added another: "Love this story ... Special kid."Practicing good deeds is nothing new for Kyote. " I'll go into the garage and Ryan's bike is missing because he gave it to a friend in need," Kirkpatrick, a sign language interpreter, told TODAY parents. "One time, a friend didn't have any shoes that fit, so Ryan gave him a pair of his own shoes."Recently, an investor got wind of what Kyote had done for his classmates and he contacted Kirkpatrick. “He wanted to give Ryan money to put in his savingsKyote, who recently lost his father to ALS, had another idea."Ryan told the man to pay it forward," Kirkpatrick said. "So he made a donation to the ALS Association. I can't even begin to tell you what that meant to Ryan. All he wants is to make the world a better place."34. How did Ryan feel after watching the news story, about a kindergarten student?A. Shocked.B. Relieved.C. Excited.D. Bored.35. Instead of buying a new pair of sneakers, Ryan was more concernedabout .A. his school lunchB. his account balanceC. his six months of savingsD. his classmates’ lunch debt36. What do we know about Ryan Kyote from the passage?A. He tried his best to help his friends in need.B. He couldn't resist sharing his photos on TwitterC. He accepted a donation from the ALS Association.D. He argued against negative reviews on social media.37. What does the story intend to tell us?A. Life is always tough for school children.B.A kid can make a difference in the world.C. Social media can make young people popular.D. Friendship is an important part of being a youth.B actually speak English, he says.A crucial period for learning the rules and structure of a language lasts up to around age 17 or 18, say psychologist Joshua Hartshorne of MIT and his colleagues.Previous research had suggested that grammar-learning ability developed in early childhood before hitting a dead end around age 5. However, Hartshorne’s team reports online in Cognition that people who started learning English as a second language in an English-speaking country by age 10 to 12 ultimately mastered the new tongue as well as folks who had learned English and another language at the same time from birth. Both groups, however, fell somewhat short of the grammatical fluency displayed by English-only speakers. After ages 10 to 12, new-to-English learners reached lower levels of fluency than those who started learning English at younger ages because time ran out when their grammar-absorbing ability fell starting around age 17.Aiming for a sample of tens of thousands of volunteers, Hartshorne began by contacting friends on Facebook to take an online English grammar quiz, which used a person’s responses to guess his or her native language and dialect (方言) of English. Then volunteers filled out a questionnaire asking where they had lived, languages they had spoken from birth, the age at which they began learning English and the number of years they had lived in an English-speaking country.In the end, the researchers analyzed responses of 669,498 native and nonnative English speakers. Statistical calculations focused on estimating at what ages people with varying amounts of experience peaking English reached peak grammar ability.Researchers who study language learning regard the new study as fascinating, but exploratory. According to psycholinguist David Barner of the University of California, San Diego, Hartshorne’s team can’t yet say that language skill develops along a single timeline. Different elements of grammar, such as using correct word order or subjects and verbs that agree with one another, might be learned at different rates, Barner says. It’s also unclear whether the responses of volunteers to an online, 132-item grammar test reflect how well of poorly theyW hat’s more, language learning involves more than a crucial period for acquiring grammar, cautions linguist David Birdsong of the University of Texas at Austin. For instance, growing up speaking two languages at once puts still poorly understood burdens on the ability to grasp grammar, he says.In the new study, people who were bilinguals from birth fell short of peak English grammar scores achieved by English-only speakers. That’s consistent with evidence that bilinguals cannot easily turn off one language while speaking another, Birdsong says. Interactions between tongues spoken by one person may slightly depress how much can be learned about both languages, even if bilingual communication still reaches high levels, he suggests.38. Hartshorne and his colleagues found that .A. one reaches a higher level of fluency at age 10B. one learns a second language fastest at about age 12C. one gets a good grasp of English grammar before age 5D. one’s ability to master grammar declines at around age1739. Hartshorne collected data through .A. social mediaB. experiments in the labC. literature reviewD. face-to-face interviews40. David Barner believes that .A. language skill develops along a single timelineB. online volunteers do not cover a wide enough rangeC. different grammar items may be acquired at different pacesD. the quiz in the new study does not include enough questions41. What can we know about bilinguals from the last two paragraphs?A. They can achieve a perfect grammar score.B. Grammar learning is the biggest burden for them.C. They are able to make a swift shift between languages.D. Speaking two languages affects their language acquisition.B about that threat, Taiz says.The last decade saw the rise of the field of “plant neurobiology (神经生物学)”. That debatable field is based on the idea that plants——which do not possess brains ——handle information in ways similar to complicated animal nervous systems. This thinking implies that plants could feel happiness or sorrow or pain, make intentional decisions and even possess consciousness. But the chances of that are “effectively zero," Lincoln Taiz and colleagues write in an opinion piece in Trends in Plant Science. "There's nothing in the plant remotely comparable to the complexity of the animal brain," says Taiz, from the University of California, Santa Cruz.Some plants are capable of complicated behavior. Wounded leaves can send warning signals to other parts of the plant, and harmful chemicals can warn animals that eat them. Some plants may even have a version of short-term memory: Tiny sensing hairs can count the number of touches that come from a clumsy insect. But plants perform these with equipment that's very different from the nervous systems of animals, no brain required, Taiz argues.He and colleagues point out methodological (方法的) faults in some of the studies that claim plants have brain-like command centers, animal-like nerve cells and changing patterns of electricity that are similar to activity found in animal brains. But beyond the debate over how these studies are conducted, Taiz's team argues that plant consciousness doesn't even make sense from an evolutionary (进化的) point of view.Complicated animal brains advanced in part to help a living being catch a meal and avoid becoming one, Taiz says. But plants are rooted to the ground and rely on sunlight for energy, an inactive lifestyle that doesn't require quick thinking or outsmarting a predator (捕食者)——or the energetically expensive nervous systems that enable those behaviors.“What use would consciousness be to a plant?” Taiz asks. The energy required to power awareness would be too costly, and the benefit from such awareness too small. If a plant worried and suffered when faced with a threat, it would be wasting so much energy that it wouldn't have any left to do anythingImagine a forest fire. "It's unbearable to even consider the idea that plants would be conscious beings aware of the fact that they're being burned to ashes, watching the young trees die in front of them," Taiz says. The frightening scene illustrates "what it would actually cost a plant to have consciousness."Furthermore, plants have plenty to do without having to be conscious, too. With sunlight, carbon dioxide and water, plants create the compounds (化合物) that sustain much of the rest of life on Earth, Taiz points out. "Isn't that enough?"42. According to Paragraph 1, a plant neurobiologist would most probably agree that .A. plants are capable of independent thinkingB. plants are as biologically complex as animalsC. plants developed nervous systems for survivalD. plants feel emotions in the same way as animals43. What does the underlined "one” in Paragraph 4 refer to?A. A predator.B. A meal.C. An inactive plant.D. A living being.44. Which statement does Linchol Taiz believe?A. Plants possess brain-like command centers.B. The lifestyle of plants requires nervous systems.C. It is unnecessary for plants to have consciousness.D. Nervous systems enable plants to fight their predators.45. Lincoln Taiz introduces a forest fire to .A. suggest new ways to study the behaviors of plantsB. discuss the possibility of plants escaping a disasterC. illustrate how plants make decisions in face of dangersD. prove consciousness would do plants more harm than good第二节（共5 小题；每小题2 分，共10 分）Rain sounds are also comforting. The rhythmic pattern of rain hitting a roof,umbrella, or the ground below is called "pink noise." Pink noise is a category of 根据短文内容，从短文后的七个选项中选出能填入空白处的最佳选项。
北京市西城区2020诊断性测试高三西城试题Word版及答案.doc
45°空气 介质30° 西 城 区 高 三 诊 断 性 测 试物 理 2020.5本试卷共8页，100分。
考试时长90分钟。
考生务必将答案写在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分本部分共14小题，每小题3分，共42分。
在每小题列出的四个选项中，选出最符合题目要求的一项。
1. 下列说法正确的是A ．液体中悬浮微粒的无规则运动称为布朗运动B ．液体分子的无规则运动称为布朗运动C ．物体温度降低，其内能一定增大D ．物体温度不变，其内能一定不变2．一束光从某种介质射入空气，折射光路如图所示，则 A ．该介质的折射率约为0.71 B ．该介质的折射率约为1.41C ．进入空气后这束光的速度变慢，波长变长D ．进入空气后这束光的频率增高，波长变短3. 处于n = 3能级的大量氢原子，向低能级跃迁时A ．能辐射2种频率的光，其中从n =3能级跃迁到n =2能级放出的光子频率最大B ．能辐射2种频率的光，其中从n =3能级跃迁到n =1能级放出的光子频率最大C ．能辐射3种频率的光，其中从n =3能级跃迁到n =2能级放出的光子波长最长D ．能辐射3种频率的光，其中从n =3能级跃迁到n =1能级放出的光子波长最长4．关于气体的压强，下列说法正确的是A ．单位体积内的分子数越多，气体的压强就越大B ．分子的平均动能越小，气体的压强就越小C ．一定质量的理想气体，体积越大，温度越低，气体的压强就越小D ．一定质量的理想气体，体积越大，温度越高，气体的压强就越大5．一交流电源的输出电压为u=U m sin ωt ，其中U m = 311V ，ω = 100π rad/s ，下列表述正确的是A ．该电源输出的交流电的频率是100HzB ．该电源输出的交流电的周期是0.05sC ．若用交流电压表测量这一电源的输出电压，电压表示数为311VD ．若将一电阻为50 Ω的电热器接在这一电源上，电热器的电功率约为968W6．手持软绳的一端O 点在竖直方向上做简谐运动，带动绳上的其他质点振动形成沿绳水平传播的简谐波，P 、Q 为绳上的两点。
西城北京市2020年高三二模数学试题及答案(WORD版)
北 京 西 城 区 高 三 诊 断 性 测 试数 学2020.5第Ⅰ卷（选择题 共40分）一、选择题：本大题共10小题，每小题4分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项． 01．设集合{}3A x x =<，{}2,B x x k k ==∈Z ，则AB =（A ）{}0,2（B ）{}2,2-（C ）{}2,0,2- （D ）{}2,1,0,1,2--02．若复数z 满足i 1i z ⋅=-+，则在复平面内z 对应的点位于（A ）第一象限 （B ）第二象限 （C ）第三象限 （D ）第四象限03．下列函数中，值域为R 且区间(0,)+∞上单调递增的是（A ）3y x =-（B ）y x x =（C ）1y x -=（D ）y =04．抛物线24x y =的准线方程为（A ）1x = （B ）1x =-（C ）1y = （D ）1y =-05．在ABC ∆中，若::4:5:6a b c =，则其最大内角的余弦值为（A ）18（B ）14（C ）310 （D ）3506．设0.23a =，3log 2b =，0.2log 3c =，则（A ）a c b >> （B ）a b c >> （C ）b c a >> （D ）b a c >>07．某几何体的三视图如图所示，则该几何体的体积是（A ）6（B ）4（C ）3（D ）208．若圆22420x y x y a +-++=与x 轴，y 轴均有公共点，则实数a 的取值范围是（A ）(,1]-∞（B ）(,0]-∞（C ）[0,)+∞（D ）[5,)+∞09．若向量a 与b 不共线，则“0•<a b ”是“2->+a b a b ”的（A ）充分而不必要条件 （B ）必要而不充分条件（C ）充要条件（D ）既不充分也不必要条件10．设函数()(1)e x f x x =-．若关于x 的不等式()1f x ax <-有且仅有一个整数解，则正数a 的取值范围是（A ）(0,e]（B ）2(0,e ]（C ）2e 1,2⎛⎤ ⎥⎝⎦（D ）2e 11,2⎛⎤+ ⎥⎝⎦第Ⅱ卷（非选择题 共110分）二、填空题：本大题共5小题，每小题5分，共25分． 11．设平面向量(1,2)=-a ，(,2)k =b 满足⊥a b ，则=b ____．12．若双曲线2221(0)16x y a a -=>经过点(2,0)，则该双曲线渐近线的方程为____．13．设函数2()sin 22cos f x x x =+，则函数()f x 的最小正周期为____；若对于任意x ∈R ，都有()f x m ≤成立，则实数m 的最小值为____．14．甲、乙、丙、丁四人参加冬季滑雪比赛，其中有两人最终获奖．在比赛结果揭晓之前，四人的猜测如下表，其中“√”表示猜测某人获奖，“×”表示猜测某人未获奖，而“○”则表示对某人是否获奖____，____．15．在四棱锥P -，,,E F H 分别是棱,,PB BC PD①截面的面积等于②截面是一个五边形；③截面只与四棱锥P ABCD -四条侧棱中的三条相交． 其中，所有正确结论的序号是______．三、解答题：本大题共6小题，共85分．解答应写出必要的文字说明、证明过程或演算步骤． 16．（本小题满分14分）如图，在几何体ABCDEF 中，底面ABCD 是边长为2的正方形，DE ⊥平面ABCD ，DE BF ∥，且22DE BF ==．（Ⅰ）求证：平面BCF ∥平面ADE ； （Ⅱ）求钝二面角D AE F --的余弦值．17．（本小题满分14分）从①前n 项和2()n S n p p =+∈R ，②13n n a a +=-，③611a =且122n n n a a a ++=+这三个条件中任选一个，补充到下面的问题中，并完成解答．在数列{}n a 中，11a =，_______，其中*n ∈N ． （Ⅰ）求{}n a 的通项公式；（Ⅱ）若1,,n m a a a 成等比数列，其中*,m n ∈N ，且1m n >>，求m 的最小值．注：如果选择多个条件分别解答，按第一个解答计分． 18．（本小题满分14分）某花卉企业引进了数百种不同品种的康乃馨，通过试验田培育，得到了这些康乃馨种子在当地环境下的发芽率，并按发芽率分为8组：[0.486,0.536)，[0.536,0.586)，…，[0.836,0.886)加以统计，得到如图所示的频率分布直方图．企业对康乃馨的种子进行分级，将发芽率不低于0.736的种子定为“A 级”，发芽率低于0.736但不低于0.636的种子定为“B 级”，发芽率低于0.636的种子定为“C 级”．（Ⅰ）现从这些康乃馨种子中随机抽取一种，估计该种子不是“C 级”种子的概率； （Ⅱ）该花卉企业销售花种，且每份“A 级”、“B 级”“C 级”康乃馨种子的售价分别为20元、15元、10元．某人在市场上随机购买了该企业销售的康乃馨种子两份，共花费X 元，以频率为概率，求X 的分布列和数学期望；（Ⅲ）企业改进了花卉培育技术，使得每种康乃馨种子的发芽率提高到原来的1.1倍，那么对于这些康乃馨的种子，与旧的发芽率数据的方差相比，技术改进后发芽率数据的方差是否发生变化？若发生变化，是变大了还是变小了？（结论不需要证明）．19．（本小题满分14分）已知椭圆2222:1(0)x y C a b a b +=>>的离心率为12，右焦点为F ，点(,0)A a ，且1AF =．（Ⅰ）求椭圆C 的方程；（Ⅱ）过点F 的直线l （不与x 轴重合）交椭圆C 于点,M N ，直线,MA NA 分别与直线4x =交于点P ，Q ，求PFQ ∠的大小．20．（本小题满分15分）设函数()e cos x f x a x =+，其中a ∈R ． （Ⅰ）已知函数()f x 为偶函数，求a 的值； （Ⅱ）若1a =，证明：当0x >时，()2f x >；（Ⅲ）若()f x 在区间[0,π]内有两个不同的零点，求a 的取值范围． 21．（本小题满分14分）设N 为正整数，区间[,1]k k k I a a =+（其中k a ∈R ，1,2,,k N =）同时满足下列两个条件：①对任意[0,100]x ∈，存在k 使得k x I ∈； ②对任意{}1,2,,k N ∈，存在[0,100]x ∈，使得i x I ∉（其中1,2,,1,1,,i k k N =-+）． （Ⅰ）判断(1,2,,)k a k N =能否等于1k -或12k-；（结论不需要证明）． （Ⅱ）求N 的最小值；（Ⅲ）研究N 是否存在最大值，若存在，求出N 的最大值；若不在在，说明理由．西城区高三诊 断 性测试数学参考答案2020.5一、选择题：本大题共10小题，每小题4分，共40分. 1．C 2．A 3．B 4．D 5. A 6. B7. D8. A9. A10. D二、填空题：本大题共5小题，每小题5分，共25分. 11．12．2y x =± 13．π1 14．乙，丁15．②③注：第14题全部选对得5分，其他得0分；第15题全部选对得5分，不选或有错选得0分，其他得3分. 三、解答题：本大题共6小题，共85分. 其他正确解答过程，请参照评分标准给分. 16．（本小题满分14分）解：（Ⅰ）因为//DE BF ，DE ⊂平面ADE ，BF ⊄平面ADE ，所以//BF 平面ADE . ………………3分 同理，得//BC 平面ADE . 又因为BCBF B =，BC ⊂平面BCF ，BF ⊂平面BCF ，所以平面//BCF 平面ADE . ………………6分 （Ⅱ）由DE ⊥平面ABCD ，底面ABCD 为正方形，得,,DA DC DE 两两垂直，故分别以,,DA DC DE 为x 轴，y 轴，z 轴，如图建立空间直角坐标系， ………………7分则(0,0,0)D ，(0,0,2)E ，(2,2,1)F ，(2,0,0)A ， 所以(2,0,2)AE =-，(0,2,1)AF =. ………8分 设平面AEF 的法向量(,,)x y z =n ， 由0AE ⋅=n ，0AF ⋅=n ，得220,20,x z y z -+=⎧⎨+=⎩令1y =，得(2,1,2)=--n .………………11分 平面DAE 的法向量(0,1,0)=m .设钝二面角D AE F --的平面角为θ，则1|cos ||cos ,|||||||3θ⋅=<>==⋅m n m n m n ，所以1cos 3θ=-，即钝二面角D AE F --的余弦值为13-. ………………14分17．（本小题满分14分） 解：选择 ①：(Ⅰ) 当1n =时，由111S a ==，得0p =. ……………… 2分 当2n ≥时，由题意，得21(1)n S n -=-， ……………… 3分所以121n n n a S S n -=-=-（2n ≥）. ……………… 5分 经检验，11a =符合上式，所以21()n a n n =-∈N *. ……………… 6分(Ⅱ)由1,,n m a a a 成等比数列，得21nm a a a =，……………… 8分 即2(21)1(21)n m -=⨯-. ……………… 9分化简，得22112212()22m n n n =-+=-+，……………… 11分因为m ，n 是大于1的正整数，且m n >， 所以当2n =时，m 有最小值5．……………… 14分选择 ②:(Ⅰ)因为13n n a a +=-，所以13n n a a +-=．………………2分所以数列{}n a 是公差3d =的等差数列． ………………4分所以1(1)32()n a a n d n n =+-=-∈N *. ………………6分(Ⅱ)由1,,n m a a a 成等比数列，得21n m a a a =，……………… 8分即2(32)1(32)n m -=⨯-. ……………… 9分化简，得22223423()33m n n n =-+=-+，………………11分因为m ，n 是大于1的正整数，且m n >， 所以当2n =时，m 取到最小值6．………………14分 选择 ③：(Ⅰ) 由122n n n a a a ++=+，得121n n n n a a a a +++-=-. 所以数列{}n a 是等差数列．……………… 2分又因为11a =，61511a a d =+=， 所以2d =． ……………… 4分所以1(1)21()n a a n d n n =+-=-∈N *. ………………6分(Ⅱ) 因为1,,n m a a a 成等比数列，所以21nm a a a =，………………8分 即2(21)1(21)n m -=⨯-. ……………… 9分化简，得22112212()22m n n n =-+=-+，……………… 11分因为m ，n 是大于1的正整数，且m n >， 所以当2n =时，m 有最小值5．……………… 14分18．（本小题满分14分）解：（Ⅰ）设事件M 为：“从这些康乃馨种子中随机抽取一种，且该种子不是“C 级”种子”， ……………… 1分由图表，得(0.4 1.2 4.0 6.0 4.4 1.20.4)0.051a +++++++⨯=， 解得 2.4a =.……………… 2分由图表，知“C 级”种子的频率为(0.4 1.2 2.4)0.050.2++⨯=，………… 3分 故可估计从这些康乃馨种子中随机抽取一种，该种子是“C 级”的概率为0.2.因为事件M 与事件“从这些康乃馨种子中随机抽取一种，且该种子是“C 级”种子”为对立事件，所以事件M 的概率()10.20.8P M =-=.……………… 5分（Ⅱ） 由题意，任取一种种子，恰好是“A 级”康乃馨的概率为(4.4 1.20.4)0.050.3++⨯=， 恰好是“B 级”康乃馨的概率为(4.0 6.0)0.050.5+⨯=，恰好是“C 级”的概率为(0.4 1.2 2.4)0.050.2++⨯=. ……………… 7分 随机变量X 的可能取值有20，25，30，35，40， 且(20)0.20.20.04P X ==⨯=，(25)0.20.50.50.20.2P X ==⨯+⨯=，(30)0.50.50.30.20.20.30.37P X ==⨯+⨯+⨯=， (35)0.30.50.50.30.3P X ==⨯+⨯=， (40)0.30.30.09P X ==⨯=.……………… 9分所以X 的分布列为：……………… 10分故X 的数学期望()200.04250.2300.37350.3400.0931E X =⨯+⨯+⨯+⨯+⨯=. ……………… 11分（Ⅲ）与旧的发芽率数据的方差相比，技术改进后发芽率数据的方差变大了.…… 14分19．（本小题满分14分） 解：（Ⅰ）由题意得1,21,c a a c ⎧=⎪⎨⎪-=⎩解得2a =，1c =， …………… 3分 从而b =所以椭圆C 的方程为22143x y +=．… 5分（Ⅱ）当直线l 的斜率不存在时，有3(1,)2M ，3(1,)2N -，(4,3)P -，(4,3)Q ，(1,0)F ，则(3,3)FP =-，(3,3)FQ =，故0FP FQ ⋅=，即90PFQ ∠=．…………6分 当直线l 的斜率存在时，设:(1)l y k x =-，其中0k ≠． ……………… 7分 联立22(1),3412,y k x x y =-⎧⎨+=⎩得2222(43)84120k x k x k +-+-=． ……………… 8分 由题意，知0∆>恒成立，设11(,)M x y ，22(,)N x y ，则2122843k x x k +=+，212241243k x x k -=+．………… 9分直线MA 的方程为11(2)2yy x x =--． ……………… 10分令4x =，得1122P y y x =-，即112(4,)2y P x -． ……………… 11分同理可得222(4,)2y Q x -． ……………… 12分 所以112(3,)2y FP x =-，222(3,)2y FQ x =-． 因为121249(2)(2)yy FP FQ x x ⋅=+--212124(1)(1)9(2)(2)k x x x x --=+--2121212124[()1]92()4k x x x x x x x x -++=+-++22222222241284(1)434394121644343k k k k k k k k k --+++=+--+++22222224[(412)8(43)]9(412)164(43)k k k k k k k --++=+--++0=， 所以90PFQ ∠=． 综上，90PFQ ∠=.……………… 14分20．（本小题满分15分） 解：（Ⅰ）函数()f x 为偶函数，所以(π)(π)f f -=，即ππe 1e 1a a --=-， ……………… 2分 解得0a =.验证知0a =符合题意. ……………… 4分 （Ⅱ）()e sin x f x x '=-. ……………… 6分 由0x >，得e 1x >，sin [1,1]x ∈-， ……………… 7分 则()e sin 0x f x x '=->，即()f x 在(0,)+∞上为增函数.故()(0)2f x f >=，即()2f x >. ………………9 分 （Ⅲ）由()e cos 0xf x a x =+=，得a = 设函数cos ()e xxh x =-，[0,π]x ∈ ……………… 10分 则sin cos ()e xx xh x +'=. ……………… 11分令()0h x '=，得3π4x =.随着x 变化，()h x '与()h x 的变化情况如下表所示：所以()h x 在3(0,)4上单调递增，在(,π)4上单调递减. ……………… 13分又因为(0)1h =-，π(π)e h -=，3π43π()4h -=， 所以当3ππ4[e ,)a --∈时，方程cos e x x a =-在区间[0,π]内有两个不同解，且在区间3π[0,)4与3π(,π]4上各有一个解.即所求实数a 的取值范围为3ππ4[e ,)2--. ……………… 15分21．（本小题满分14分）解：(Ⅰ)k a 可以等于1k -，但k a 不能等于12k-. ……………… 3分 (Ⅱ) 记b a -为区间[,]a b 的长度，则区间[0,100]的长度为100，k I 的长度为1.由①，得100N ≥. ……………… 6分 又因为1[0,1]I =，2[1,2]I =，，100[99,100]I =显然满足条件①，②.所以N 的最小值为100. ……………… 8分 (Ⅲ)N 的最大值存在，且为200. ……………… 9分 解答如下：（1）首先，证明200N ≤. 由②,得12,,,N I I I 互不相同，且对于任意k ，[0,100]kI ≠∅.不妨设12n a a a <<<<.如果20a ≤，那么对于条件②，当1k =时，不存在[0,100]x ∈，使得i x I ∉(2,3,,)i N =.这与题意不符，故20a >. ……………… 10分 如果111k k a a +-+≤，那么11k k k I I I -+⊆，这与条件②中“存在[0,100]x ∈，使得i x I ∉(1,2,,1,1,)i k k N =-+”矛盾，故111k k a a +->+.所以4211a a >+>，6412a a >+>，，200198199a a >+>，则2001100a +>. 故12200[0,100]I I I ⊇.若存在201I ，这与条件②中“存在[0,100]x ∈，使得i x I ∉(1,2,,200)i =”矛盾，所以200N ≤. ……………… 12分 （2）给出200N =存在的例子 .令1100(1)2199k a k =-+-，其中1,2,,200k =，即12200,,,a a a 为等差数列，公差100199d =.由1d <，知1kk I I +≠∅，则易得122001201[,]22I I I =-，所以12200,,,I I I 满足条件①.西城区2020年高三二模数学试题及答案(WORD 版)11 / 11 又公差10011992d =>， 所以100(1)199k k I -∈，100(1)199i k I -∉(1,2,,1,1,)i k k N =-+.（注：100(1)199k - 为区间k I 的中点对应的数）所以12200,,,I I I 满足条件②.综合（1）（2）可知N 的最大值存在，且为200. ……………… 14分。
2020.5西城诊断性测试(1.5模)试题及解析
三、解答题（6 题，共 85 分）
16.（本小题满分 14 分）如图，在几何体 ABCDEF ,底面 ABCD 是边长为 2 的正方形， DE 丄平面 ABCD,DE//BF,旦 DE = 2BF = 2. （I）求证：平面 BCF//平面 ADEf （II）求顿二面角 D AE F 的余弦值.
（A）充分而不必要条件 （C）充要条件
（B）必要而不充分条件 （D）既不充分也不必要条件
10.设函数 f (x) (x 1)e x . 若关于 x 的不等式 f (x) ax 1有且仅有一个整数解，则正数 a
的取值范围是
（A） (0,e]
（B） (0,e2 ]
（C） (1, e2 ] 2
（D） (1, e2 1] 2
6.0 4.4 4.0 a 1.2 0.4
O 0.486 0.536 0.586 0.636 0.686 0.736 0.786 0.836 0.886 发芽率
企业对康乃馨的种子进行分级，将发芽率不低于 0.736 的种子定为“A 级”，发芽率低于 0.736 但不低于 0.636 的种子定为“B 级”，发芽率低于 0.636 的种子定为“C 级”.
4
19（. 本小题满分
14
分）已知椭圆
C
:
x2 a2
y2 b2
1(a
b 0) 的离心率为 1 ，右焦点为 F,点 2
A(a, 0) .
且 AF 1 .
(I)求椭圆 C 的方程； (II)过点 F 的直线 l （不与 x 轴重合）交椭圆 C 于点 M, N，直线 MA, NA 分别与直线 x = 4 相交 于点 P, Q.求 PFQ 的大小.
2020北京西城高三诊断性测试语文试卷答案逐题解析
一、本大题共5小题，共18分。
阅读下面的材料，完成1－5题。
材料一历史建筑作为人类文化遗产的重要组成部分，是人类历史变迁的物质载体，包含着城镇、村庄的文化发展脉络，封存着本地居民的集体记忆和特殊情感，具有鲜明的地域特色与文化内涵。
作为不可再生的文化资源，历史建筑保护已经成为全球性课题。
始建于公元前6世纪的庞贝古城，因维苏威火山喷发而被掩埋于地下，两千多年后才重见天日。
在持续两百多年的发掘中，意大利对遗址采取了“原真性”保护策略，即在原地保留古城出土时的残损形貌和原初场景，不移动废墟中的任何残件，店铺、钱庄以及神庙都保持着灾难发生时的倒塌状态。
这就不仅再现了当时的规划建设、文化艺术以及日常生活画面，还能透过建筑破损直观地展现出古罗马时期建筑的材料、构造及建造工艺。
经此保护的古城遗址，既是一件历史的“活化石”，也是一部关于建筑的“活的教科书”。
从17世纪起，北京琉璃厂便集中了许多出售书籍、笔墨纸砚、古玩字画的店铺，有着浓厚的传统文化氛围。
上世纪八十年代经过综合整治，琉璃厂保持了清代建筑风貌，文化商业街的功能得以延续，居民生活环境也得到了改善。
但是对这种“仿古一条街”的做法，至今仍然存在着两种对立的观点。
一种观点认为“原真性”的清代历史建筑已不复存在，留下的只是做工地道的清式“新建筑”，那么这里只能算作历史风貌区，而不能算作历史文化街区。
另一种观点则认为，琉璃厂历史地段原来的砖木结构建筑年久失修，若局限于静态的“原真性”，完全保留屋舍凋敝的真实，对城市发展和街区居民也未必有什么意义。
而且，经过翻新改造的琉璃厂，既保持了传统建筑风格，又延续了历史建筑街区的传统功能和文化活力，是否也可以理解为保持了历史地段的“原真性”。
（取材于陈思等作者的文章）1．根据材料一，下列表述不符合．．．文意的一项是（3分）A．历史建筑能够反映本地的历史变迁和文化发展脉络。
B．对历史建筑废墟的原真性保护意味着不能翻修重建。
C．原真性保护指的是要保持历史建筑原初的倒塌状态。
2020年 西城区 高三 二模 化学 附答案
西城区高三诊断性测试化学2020.5 本试卷共 9 页，100 分。
考试时长 90 分钟。
可能用到的相对原子质量：H 1 O 16 Cu 63.5第一部分本部分共14 题，每题3 分，共42 分。
在每题列出的四个选项中，选出最符合题目要求的一项。
1．下列图示的混合物不．属．于．胶体的是2．糖类、油脂、蛋白质是重要的营养物质，下列说法正确的是A．糖类、油脂、蛋白质均可水解B．纤维素和淀粉互为同分异构体C．油脂属于酯类物质可发生皂化反应D．NH4Cl 溶液和 CuSO4 溶液均可使蛋白质变性3．化学与生产生活密切相关，下列说法不正确的是A．铁粉有还原性可作吸氧剂B．生石灰能与水反应可作干燥剂C．福尔马林能杀菌防腐可作食品保鲜剂D．明矾能水解形成胶体可作净水剂4．117 号元素 Ts 的原子最外层电子数是 7，下列说法不．正．确．的是A．Ts 是第七周期第ⅦA 族元素B．还原性：I−＜Ts−C．原子半径：I＜Ts D．中子数为 176 的 T S 的核素符号：5．蜂胶中某活性物质 X 的结构简式如下，下列关于 X 的说法正确的是A．X 不具有顺式和反式结构B．X 不能与浓溴水发生取代反应C．1 mol X 最多能与 2 mol NaOH 反应D．一定条件下 X 可发生加聚反应6．下列化学用语的表述正确的是A．乙酸与乙醇的酯化反应：CH3COOH+C2H518OH CH3COOC2H5+H218OB．镁离子的结构示意图：C．二氧化碳分子的比例模型：D．NaCl 溶液导电：7．下列说法不．正．确．的是A．常温常压下，3.2 g O2 和 O3 的混合气体中含有氧原子的数目约为 0.2×6.02×1023B．1 L 0.5 mol·L−1 CH3COONa 溶液中含有CH3COOH 和CH3COO−的总数约为0.5×6.02×1023C．标准状况下，1.12 L HCl 气体中含有电子的数目约为 0.9×6.02×1023D．0.1 mol 环氧乙烷（）中含有共价键的总数约为 0.3×6.02×10238．以氮气和水蒸气为原料，电化学合成氨装置（电极不参与反应）示意图如下。
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西城区高三诊断性测试英语2020.5本试卷共11页，120分。
考试时长100分钟。
考生务必将答案写在答题卡上，在试卷上作答无效。
考试结束后，将本试卷和答题卡一并交回。
第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分，共15分）阅读下列短文，根据短文内容填空。
在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。
AMia rushed home and threw open the front door. Her mother turned around, surprised that Mia was home from school so early. “I wonfirst place in the art contest!” she said 1prideand raised her head, expecting praise. Though Mia 2 (work) eagerly on her art submission for weeks, her mother wasn’t sure 3 the project involved. “That’s wonderful, Mia! What was the subject of your art project?” her mother asked. Smiling from ear to ear, Mia handed over her artwork. It was a portrait of her mother.BA study found that adults aged 18 to 33 checked their smartphones 85 times a day, or once every 10 minutes. As I learned during my experiment, 4 (place) some distance between myself and my device helped me devote myself to my work more 5 (easy). By not having my smartphone, my distraction (消遣) time went down and thus my work time 6 (spend) more efficiently and effectively. On numerous occasions, I found 7 (I) wondering what to do with the afternoon since I had already completed my high-impact tasks for the day. With the extra time, I can finally enjoy the pleasures of life.CIn June 2012, China’s first manned deep-sea submersible (潜水器), Jiaolong, set a world diving record for submersibles of its kind by reaching a 8 (deep) of 7,062 meters in the Mariana Trench in the Pacific Ocean. In 2017, China successfully tested a submersible 9 (call) Shenhai Y ongshi, capable of diving 4,500 meters. 10 much of Jiaolon g’s equipment was imported, about 95 percent of Shenhai Y ongshi and all its core components were produced domestically, said Xu Qinan, the chief designer of Jiaolong.第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。
One morning in July 2011, a taxi sat wandering outside Petco Park stadium in San Diego. And Wade LeBlanc, a (an) 11 pitcher (棒球投手) for the Padres, climbed in. “To theairport, please,” he told the driver. LeBlanc was headed to Tucson, Arizona, home of the club’s A-level bra nch organization at the time. He’d been sent down to the minors. Again. For the eighth time in three years.“You’re Wade LeBlanc,” the taxi driver said.“Right.”“You got some good stuff.”This 12 the pitcher, after the pr evious night’s disastrous performance.“I think there are some things you should think about 13 ,” the driver continued. “I don’t know; I’m not a 14 . Maybe something like going over your head in your windup (摆臂动作).”Wait, what? This guy was offering... 15 ? Earlier in his career, LeBlanc might have 16 . Or been angry. But today, he just 17 . He couldn’t afford to dismiss anything. His career was on the line.The next day, in Tucson, LeBlancmet his 18 . He said he was thinking about making 19 to his windup. His coach agreed. Instead of keeping his hands tight to his chest at the beginning of his delivery, LeBlanc raised them briefly over his head, as the taxi driver had 20 .LeBlanc included the new 21 into his next start. And he was 22 , allowing only one hit over seven innings (回合). It was the turning point in his career. Eight years later, LeBlanc is a pitcher for the Seattle Mariners. He signed the first contract extension of his Major League Baseball career—at age 33.The funny thing about advice: We so often take it from the 23people. That is, we 24 the advice of experts, while undervaluing the input of regular folk. Wade LeBlanc 25 that trend, and he obtained the 26 .“Expert advisers often make surprisingly inaccurate predictions about the future, yet people 27 their suggestions nevertheless,” concluded Stanford University psychologists in a study published last year.Now, not everyone took experts’ advice. The more 28 people become, the smaller the pool of advisers they 29. Participants in positions of power ignored almost two thirds of the advice they received, according to one Harvard University study. Other participants—the control and low power groups—ignored advice about half as often. So it required a massive increase of modesty(谦虚)to do what Wade LeBlanc did: hear what the taxi driver was offering him and accept it as a (an) 30 .11. A. excellent B. struggling C. ambitious D. awkward12. A. surprised B. concerned C. disturbed D. angered13. A. avoiding B. making C. trying D. crossing14. A. player B. director C. joker D. loser15. A. service B. advice C. chances D. courses16. A. accepted B. worried C. smiled D. laughed17. A. explained B. interrupted C. listened D. guessed18. A. parents B. coach C. driver D. fans19. A. changes B. contributions C. additions D. objectives20. A. included B. announced C. suggested D. resisted21. A. aim B. effect C. hobby D. move22. A. patient B. optimistic C. brilliant D. justified23. A. attractive B. popular C. humble D. wrong24. A. overvalue B. skip C. ignore D. involve25. A. identified B. supported C. opposed D. started26. A. qualifications B. benefits C. prize D. degree27. A. follow B. abandon C. provide D. improve28. A. literary B. successful C. careful D. negative29. A. tolerate B. help C. know D. trust30. A. job B. example C. excuse D. gift第二部分：阅读理解（共两节，40分）第一节（共15小题；每小题2分，共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，并在答题卡上将该项涂黑。