高二学年周测

2022-2023学年高二上学期网课英语周测一、阅读理解（每题2.5分，共37.5分）With summer break coming up for children across the United States，now it 's time to plan a fantastic summer trip for your family.Her are a few of the best places you can take your family to this year and any year for that matter.Montgomery，AlabamaMontgomery is an important site for learning about the history of the Civil Rights Move-ment. Children with their families can visit the Civil Rights Memorial Center to take a tour of the exhibits and learn about the hopes and dreams and the struggle for equality in the country.Kenai Peninsula，AlaskaIf you are looking for a wonderful outdoor adventure，the Kenai Peninsula in Alaska is a fantastic trip. While visiting this region of Alaska，you can explore the Kenai Mountains in Kenai Fjords(峡湾）National Park，where your kids can see glaciers，fjords and especially the Harding Icefield Fishing is another wonderful activity to enjoy at this destination.Channel Islands，CaliforniaThe Channel Islands are an amazing archipelago (群岛）) off the coast of California. Here visitors can enjoy the Channel Islands National Park. The Channel Islands National Park protects five of the islands. Within the protection of the park there is a wide variety of wildlife，as well as natural and cultural resources. You should keep an eye out for seals，sea lions，dolphins,and many more.Memphis，TennesseeMemphis is a fantastic destination for families that enjoy music. This city played a great role in the evolution of Blues music. You certainly won't want to miss out on a trip to Graceland while exploring Memphis.The home of Elvis Presley is open to visitors for tours,where you can travel through the life and rise of Elvis.1．Where can you enjoy exhibitions during your trip?A．Montgomery B．Kenai Peninsula. C．Channel Islands. D．Memphis.2．What can you do in the Kenai Peninsula?A．Listen to some music. B．Explore various wildlife.C．Try risking outdoors. D．Watch all kinds of fishes.3．What’s the main purpose of the text?A．To give children some instructions.B．To introduce some trip sites for families.C．To advertise some famous attractions.D．To encourage children to learn in summer.Born in Shanghai in 1981, Yang Ji studied accounting in college before becoming a civil servant in 2005, fulfilling his parents’ wishes of him securing a stable job. But he only lasted a year in that role. “I’ve loved animals since I was a child. I raised many animals, such a s goldfish, turtles and pigeons during my school years,” he says. “Raising animals was my hobby and my dream.”Yang made a career switch in 2006, and started working at a chicken farm to learn about breeding (培育) birds.“The first five years were very difficult for me. I made many mistakes along the way, but I also learned a lot,” he says. “For example, there are huge differences between raising a chicken and a swan.”He shared that the first swans he bought eventually became crippled (瘸的), and some even died, even though he went to great lengths to feed them good food and ensure that their pens were warm. But after consulting with experienced experts, he learned that the animals just needed to eat grass. In addition, the swans should not have been cooped up in their pens but let out to exercise in the cold water.He then went to learn more about the trade with experienced bird keepers and experts from zoos, working alongside them for days and observing how they raised the animals.In 2011, Yang bought a small, deserted zoo and renovated (改造) it for his rare-bird breeding center. In 2014, he received his license to breed first-tier protected animals from the National Forestry and Grassland Administration. He has since introduced several endangered birds to his center.“They’re all native species in China and I’ve succeeded in breeding and raising their babies,” he says. His breeding center, which supplies birds to zoos around China, isn’t all about profit. Yang says that he is planning to release some endangere d birds to help grow the population in the wild. “I am passionate with my work and never feel exhausted,” he says. “Living with the birds and seeing them every day makes me a happy man.”4．Yang Ji started working at a chicken farm because ___________.A．he loved raising chickensB．he wanted to learn bird raisingC．chickens were much easier to raiseD．he had a preference for small animals5．What mistake did Yang Ji make when he first started breeding swans?A．He fed wrong food to the swans.B．He didn’t keep the swans warm.C．He bought some crippled swans.D．He let the swans swim in cold water.6．What do we know about Yang Ji’s breeding center?A．It was rebuilt on an open grassland.B．It has kept all kinds of endangered animals since 2014.C．It intends to increase the number of some endangered birds by setting them free.D．It aims at making money out of supplying endangered birds to zoos all over China.7．Which of the following can be the best title of this passage?A．Yang Ji and His Birds B．From Chickens to SwansC．A Successful Career Switch D．Flying High with His DreamsTo give a tip or not? If so, how much? They can be headaches even for the most experienced tourists. This week, the main political parties in the UK have finally come to rescue by passing laws to forbid bars and restaurants taking tips from the customers.However, not every country in the world takes the matter as seriously as the British, who are believed to have invented the custom in the 17th century — originally as a noble practice of giving small gifts to the so-called “inferior (低等的) classes”. Later, tipping has become a habit widely accepted in the world, although it is influenced by a nation’s culture and values.A common joke among Americans is that only getting tax return is more confusing than tipping. Tips were imported into the country in the 19th century, when wealthy Americans began travelling to Europe. The custom was originally disapproved in the US. Critics accused tippers of creating a class of p eople who “begged for favors”. Fast forward to the 21st century and you will still find Americans debating the pros and cons. But tipping is now completely ingrained (根深蒂固的) in the national soul.Like many Asian countries, China is largely a no-tipping culture for decades it was actually prohibited and considered illegal. To this day, it remains relatively uncommon.Japan’s complex manner system includes tipping. It is socially acceptable on special occasions such as weddings, but on the other occasions, it can actually make the receiver feel ashamed, if not abused. Even onoccasions where tips are expected,the money is expected to be sealed in special envelopes as a sign of gratitude and respect. Otherwise, it will be refused because tips are usually included in the payment for the service.8．What’s the original purpose of tipping?A．To please the ordinary people. B．To praise people’s good deeds.C．To indicate people’s thanks to the poor. D．To show noble kindness to the lower class.9．What does the underlined sentence in paragraph 3 mean?A．Americans are used to giving tips. B．It is quite normal to tip in America.C．Tipping is very complex in the US. D．Getting tax return is simpler than tipping.10．What can be inferred about tipping in Asia?A．Tips are totally forbidden in China. B．Tipping will become popular very soon.C．Good services should be put before tips. D．Tips can be accepted for special celebrations.11．In which section of a newspaper may this text appear?A．Law B．Culture C．Economy D．TourismElon Musk has expressed his company – Neuralink is close to announcing the first brain-machine interface (接口) to connect humans and computers. Musk told followers in Twitter the technology would be “coming soon” –though he failed to provide details.Neuralink was set up in 2016 with the ambitious goal of developing hardware to strengthen the human brain. However, little about how this will work has been made public. Neuralink describes the interface as an extremely high-speed connection between the human brain and computers.Musk has frequently claimed the rapid rise of artificial intelligence poses an existential risk to humanity. Such an interface, he says, is essential if humans are to compete with such technology in the future. At a technology conference in 2016, Mr Musk said humans risked being treated like house pets by AI machines if a brain-computer interface was not built. Last year on the Joe Rogan Experience podcast, Musk said Neuralink’s technolo gy would allow humans to “effectively combine with AI”.A paper published in Nature Nanotechnology in 2015 described a concept for this connection, explaining how a flexible circuit (回路) could be injected into a living brain. “We’re trying to lessen the di stinction between electronic circuits and neural circuits,” said Harvard researcher Charles Lieber, who co-authored the study. Despite the technology’s potential to increase the human brain, experts have warned that brain-computer interfaces risk being controlled by vicious (恶意的) artificial intelligence.Such an action could lead to AI controlling the thoughts, decisions and emotions of a person using abrain-computer link. “Technological developments mean that we are on a path to a world in which it will b e possible to discover people’s mental processes and directly operate the brain mechanisms underlying their intentions, emotions and decision,” stated a Nature comment piece written by 27 scientists and machine intelligence engineers. “The possible medical and social benefits in it are vast. But we must guide their development in a way that respects, protects and enables what is best in humanity.”12．What message did Musk convey about his Neuralink?A．It sells brain-machine interfaces.B．It offers rich data about interfaces.C．It has followers to connect humans and computers.D．Its new technology will be accessible to the public soon .13．What can we know from Paragraph Two?A．Neuralink aims to know the human brain better.B．How the hardware functions is already known.C．The brain-machine interface was invented in 2016.D．The interface is expected to link the human brain and computers rapidly.14．According to Musk, why are brain-machine interfaces important?A．Because they may treat human like house pets.B．Because they may make AI serve human better.C．Because they build neural circuits in human brains.D．Because they rapidly develop artificial intelligence.15．What is the attitude of Nature to brain-machine interfaces?A．Objective B．FavorableC．Opposed D．Indifferent二、七选五（每题2.5分，共12.5分）Winter is connected with fun and games: snowball fights, skiing, and, every four years, the Winter Olympics. But what will a winter sports enthusiast do if the snow doesn’t make an appearance? ____16____ Artificial snow is more like a tightly packed frozen snow that is partly melt. ____17____ They are broken up by a high-pressure pump at first and then turn into small frozen pieces. Most artificial snow is made using snowcannons. As the air’s cooling capacity falls, so doe s the amount of water that can be pumped through the machine. ____18____ At -4℃ a snow cannon can operate at around 80% humidity. But if the outside temperature is -1℃, this must be reduced to around 30% humidity.In 1980, the Olympics held in America became the first Winter Games to use machine-made snow.____19____ Artificial snow also appeared at the two recent Winter Olympics, in Sochi, Russia (2014), and Vancouver, British Columbia (2010). And the 2022 Winter Olympics in Beijing is the first to rely entirely on artificial snow.____20____ The International Olympic Committee states that it creates a more consistent surface. In addition, the snow that comes from a cannon is icier than natural snow. It melts more slowly, and provides a harder surface for athletes looking for speed. The first Olympics using entirely artificial snow will probably not be the last. A．But they weren’t the last.B．It is made from waterdrops.C．That’s when artificial snow comes in.D．What is artificial snow, and how is it made?E．Temperature also plays a significant role in snowmaking.F．Artificial snow can be applied into a wide range of fields.G．Artificial snow is well worth using in the Winter Olympics.四、用单词的适当形式完成短文（每题1.5分，共15分）阅读下面材料, 在空白处填入适当的内容(1个单词)或括号内单词的正确形式。

湖北省武汉市华中科技大学附属中学2022-2023学年高二（上）数学周测（8）一、选择题：本题共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. 如图所示，直线l 1、l 2、l 3的斜率分别为k 1、k 2、k 3，则A ．k 1＜k 2＜k 3B ．k 1＜k 3＜k 2C ．k 3＜k 2＜k 1D ．k 3＜k 1＜k 22.某调查机构对某高科技行业进行调查统计，得到该行业从业者的学历分布扇形图以及从事该行业岗位的人数分布条形图，如图所示．给出下列三种说法：①该高科技行业从业人员中学历为博士的占一半以上；①该高科技行业中从事技术岗位的人数超过总人数的30%；①该高科技行业中从事运营岗位的人员主要是本科生．其中正确说法的个数为A. 0B. 1C. 2D. 33.如图所示，已知三棱锥O ­ABC ，点M ，N 分别为AB ，OC 的中点，且,,OA a OB b OC c ===，用,,a b c 表示MN ，则MN 等于A ．()12c a b --B ．()12a b c ++ C ．()12a b c -+ D ．()12b c a +- 4. 已知直线02534:=+-y x l ，直线023:=-y ax m 与直线l 平行，则直线l 与m 之间的距离为 A ．85B ．2C ．5D ．45. 甲、乙两人独立地破译一份密码，已知两人能破译的概率分别是31，41，则 A. 两人都成功破译的概率为127 B. 两人都成功破译的概率为125 C. 密码被成功破译的概率为127 D. 密码被成功破译的概率为216．在直三棱柱ABC A B C '''-中，侧棱长为2，底面是边长为2的正三角形，则异面直线AB '与BC '所成角的余弦值为A ．14 B ．33 C ．12D ．557. 如图所示，“嫦娥五号”月球探测器飞行到月球附近时，首先在以月球球心F 为圆心的圆形轨道①上绕月球飞行，然后在P 点处变轨进入以F 为一个焦点的椭圆轨道①绕月球飞行，最后在Q 点处变轨进入以F 为圆心的圆形轨道①绕月球飞行，设圆形轨道①的半径为R ，圆形轨道①的半径为r ，则下列结论中不正确的是A. 轨道①的焦距为R r -B. 若R 不变，r 越大，轨道①的短轴长越小C.轨道①的长轴长为R r +D. 若r 不变，R 越大，轨道①的离心率越大 8. 设集合}4),({2x y y x M -==,})4()3(),({222r y x y x N =-+-=（0>r ）.若N M 中有且只有一个元素，则r 所有取值组成的集合为A ．}41,17{B ．}4117{≤<r r C ．}3{}4117{ ≤<r r D ．}3{}4117{ ≤≤r r二、选择题：本题共4小题，每小题5分，共20分。

遂宁中学高2024届高二下期周考（三）政治试题一、单选题（共48分）1．“检验真理的标准只能是社会实践，理论与实践的统一是马克思主义最基本的原则，任何理论都需要不断接受实践的检验。

”我国42年前一场关于真理标准问题的大讨论，揭开了改革开放的序幕，具有划时代意义。

“实践是检验真理的唯一标准”是因为①实践是客观见之于主观的物质性活动②实践具有把主观认识和客观事物联系起来加以对照的特点③真理具有反复性、无限性和上升性④真理是标志主观同客观相符合的范畴A．①②B．①③C．②④D．③④2．获诺贝尔奖以来，屠呦呦团队在深入研究中发现，双氢青蒿素对红斑狼疮有独特效果。

根据现有临床试验，青蒿素对盘状红斑狼疮的有效率超90%、对系统性红斑狼疮有效率超80%。

研究人员还证明了青蒿素在治疗肿瘤、白血病、类风湿性关节炎、多发性硬化、变态反应性疾病等方面也有一些效果。

这表明A．尊重客观规律，能把“不可能”转变成“可能”B．尊重客观规律与发挥人的主观能动性相互作用、相互制约C．规律的客观性要求人们必须按客观规律办事D．发挥主观能动性有助于我们正确认识和利用规律3．回溯地球上的气候变迁历史，我国自主研制的超级计算机“天河二号”可以模拟到5000年前甚至更远，从而大大提高天气预报的准确率。

从哲学看，这一成果佐证了A．客观世界具有物质统一性B．思维和存在具有同一性C．意识对物质有依赖性D．人类认识有限世界的可能性4．今年是阿波罗登月51周年，人类正是以月球为起点，前往更远的星球探索。

阿波罗登月对促进科学发展、推动技术进步等起到了巨大作用，将永载人类史册。

这佐证了（）A．运动是物质的唯一特性B．人类能创造并利用规律C．实践是认识的根本任务D．实践是认识发展的动力5．在中央美院最近举行的一场画展上，人工智能“微软小冰”一次创造了7个人工智能画家，这些画家能将人生背景与情感贯穿在生成的每一幅作品中，使观众能通过作品进入创作者的“人生”。

1华二附中2024学年第一学期高二年级数学测试2024.09一、填空题（本大题共有12题,满分54分,第1-6题每题4分,第7-12题每题5分） 1.直线l 上存在两点在平面α上，则l α(填一符号). 2.函数324y sin x π⎛⎫=+ ⎪⎝⎭的圆频率是 .3.已知{}n a 是等差数列,若75230a a −−=,则9a 的值是 .4.两条异面直线所成角的取值范围是 .5.已知复数z a i =−的实部与虚部相等,则z i −= .6.函数213y tan x π⎛⎫=−+ ⎪⎝⎭的对称中心是 .7.三个互不重合的平面能把空间分成 . 8.数列{}n a 满足1111,12n n a a a +==−,则2024a = . 9.在ABC ∆中,::5:7:8sinA sinB sinC =,则该三角形外接圆与内切圆的面积之比是 . 10.如图,摩天轮的半径为50m,圆心O 距地面的高度为60m.已知摩天轮按逆时针方向匀速转动,每15min 转动一圈.游客在摩天轮的舱位转到距离地面最近的位置进舱.则游客进舱5min 时他距离地面的高度为 m.11.已知ABC ∆中,过中线AD 的中点E 任作一条直线分别交边,AB AC 于,M N 两点,设,(0,0)AM x AB AN yAC x y ==>>,则4x y +的最小值为 .12.对任意0,4π⎡⎤ϕ∈⎢⎥⎣⎦,函数()()f x sin x =ω+ϕ在区间2,π⎡⎤π⎢⎥⎣⎦上单调递增,则实数ω的取值范围是 .2二、选择题（本大题共有4题,满分18分,第13,14题每题4分,第15,16题每题5分） 13.设扇形的圆心角为α,半径为r ,弧长为l ,而积为S,周长为L ,则下列说法不正确的 是（ ）.A.若,r α确定,则,L S 唯一确定B.若,l α确定,则L S 唯一确定C.若,S L 确定，则,r α唯一确定D.若,1S 确定,则,r α唯一确定14.过正方体1111ABCD A B C D −的顶点A 作直线l ,使l 与棱1,,AB AD AA 所成的角都相等，这样的直线l 可以作（ ）.A.1条B.2条C.3条D.4条15.数列{}{},n n a b 满足21,32n n n a b a n n ⋅==++,则{}n b 的前10项之和等于（ ）. A.13 B.512 C.12 D.712 16.如图所示,角02x ,π⎛⎫∈ ⎪⎝⎭的终边与单位圆O 交于点(),10,P A ,PM x ⊥轴,AQ x ⊥轴,M 在x 轴上，Q 在角x 的终边上.由正弦函数、正切函数定义可知，sin ,tan x x 的值别等于线段,MP AQ 的长，且ΔOAP ΔOAQ OAP S S S <<扇形，则下列结论不正确的是（ ）. A.函数y tanx sinx x =++在22,ππ⎛⎫− ⎪⎝⎭内有1个零点B.函数y tanx x =−在32222,,ππππ⎛⎫⎛⎫−⋃ ⎪ ⎪⎝⎭⎝⎭内有2个零点C.函数y sinx x =−有3个零点D.函数y tanx sinx tanx sinx =+−−在22,ππ⎛⎫− ⎪⎝⎭内有13三、解答题(本大题满分78分)本大题共有5题, 17.(本题满分14分,第1小题6分,第2小题8分) 已知3,052sin ,π⎛⎫α=α∈ ⎪⎝⎭. （1）求23sin π⎛⎫α+ ⎪⎝⎭的值;（2）在平面直角坐标系xOy 中，以Ox 为始边，已知角β的终边与角α的终边关于y 轴对称,求()cos α+β的值.18.(本题满分14分,第1小题6分,第2小题8分)如图所示,在长方体1111ABCD A B C D −中,2AB BC ==,14,AA P =为线段11B D 上一点. (1)求证:AC BP ⊥;(2)当P 为线段11B D 的中点时,求点A 到平面PBC 的距离.419.(本题满分14分,第1小题6分,第2小题8分)在直角梯形ABCD 中,//,90,224AB CD DAB AB AD DC ∠====,点F 是BC 边上的中点. (1)若点E 满足2DE EC =,且EF AB AD =λ+μ,求λ+μ的值; (2)若点P 是线段AF 上的动点(含端点),求AP DP ⋅的取值范围.20.(本题满分18分,第1小题4分,第2小题6分,第3小题8分) 如图，正方体的棱长为1,''B C BC O ⋂=，求： (1)AO 与''A C 所成角的度数; (2)AO 与平面ABCD 所成角的正切值; (3)B OA C −−的度数.521.(本题满分18分,第1小题4分,第2小题6分,第3小题8分) 若有穷数列{}n a 满足:10ni i a ==∑且11ni i a ==∑，则称其为"n 阶01−数列".（1）若"6穷01−数列"为等比数列,写出该数列的各项;（2）若某"21k +阶01−数列"为等差数列,求该数列的通项(121n a n k ≤≤+,用,n k 表示)； （3）记"n 阶01−数列"{}n a 的前k 项和为()123k S k ,,,,n =,若存在{}123m ,,,,n ∈,使12m S =,试问:数列{}()123i S i ,,,,n =能否为"n 阶01−数列"?若能,求出所有这样的数列{}n a ；若不能,请说明理由.6参考答案一、填空题1.⊂;2.2;3.3;4.0,2π⎛⎤⎥⎝⎦;5. 6.,1,46k k Z ππ⎛⎫+∈ ⎪⎝⎭; 7.4678或或或; 8.2; 9.499; 10.85； 11.94 12.13042,⎛⎤⎧⎫⋃−⎨⎬ ⎥⎝⎦⎩⎭11.已知ABC ∆中,过中线AD 的中点E 任作一条直线分别交边,AB AC 于,M N 两点,设,(0,0)AM x AB AN yAC x y ==>>,则4x y +的最小值为 . 【答案】94 【解析】()12AD AB AC =+,且E 为AD 的中点,()1124AE AD AB AC ∴==+,11,,(0,0),AM x AB AN y AC x y AB AM AC AN x y==>>∴==,,,M E N 三点共线,11144x y∴+=, ()1111944111444444y x x y x y x y x y ⎛⎫∴+=++=+++++= ⎪⎝⎭…故答案为:94 12.对任意0,4π⎡⎤ϕ∈⎢⎥⎣⎦,函数()()f x sin x =ω+ϕ在区间2,π⎡⎤π⎢⎥⎣⎦上单调递增,则实数ω的取值范围是 . 【答案】13042,⎛⎤⎧⎫⋃−⎨⎬ ⎥⎝⎦⎩⎭【解析】对任意0,4π⎡⎤ϕ∈⎢⎥⎣⎦,函数()()f x sin x =ω+ϕ在区间2,π⎡⎤π⎢⎥⎣⎦上单调递增,12,222ππ∴⨯π−∴ωω厔 ①0ω>时,此时,()02,y sin x <ω=ω+ϕ…单调递增,可得222,22k k Z k ππω+ϕ≥−+π∈ππω+ϕ≤π⎧⎪⎪⎨⎪⎩+⎪,则22222k k ⎧⎪⎪⎨⎪⎪ππϕ≥π−−ωπϕ≤+−ω⎩ππ71120,,24441kk ⎧ω≤−+π⎪⎡⎤ϕ∈∴⎨⎢⎥⎣⎦⎪ω≥−⎩当0k =时，可得104<ω≤； ②0ω<时,此时,20−ω<…,()y sin x =ω+ϕ单调递增, 即()y sin x =−−ω−ϕ在区间2,π⎡⎤π⎢⎥⎣⎦上单调递减；可得222322,k k Z k ππ−ω−ϕ≥+ππ−πω−ϕ≤π⎧⎪⎪∈⎨⎪+⎪⎩,则222322k k ⎧⎪⎪⎨⎪⎪ππϕ≤−π−ω−πϕ≥π−πω⎩−− 14120,,3422k k ⎧ω≤−−−⎪π⎪⎡⎤ϕ∈∴⎨⎢⎥⎣⎦⎪ω≥−−⎪⎩当0k =时，可得32ω=−； 综上,则实数ω的取值范围是13042,⎛⎤⎧⎫⋃−⎨⎬ ⎥⎝⎦⎩⎭.二、选择题13.C 14.D 15.B 16.C15.数列{}{},n n a b 满足21,32n n n a b a n n ⋅==++,则{}n b 的前10项之和等于（ ）. A.13 B.512 C.12D.712 【答案】B【解析】由题意得()()12,n a n n =++()()11112112n n b a n n n n ===−++++1210b b b ∴++⋯⋯+11111123341112=−+−+⋯⋯+−11521212=−= 综上所述,答案选择:B16.如图所示,角02x ,π⎛⎫∈ ⎪⎝⎭的终边与单位圆O 交于点(),10,P A ,PM x ⊥轴,AQ x ⊥轴,M 在x 轴上，Q 在角x 的终边上.由正弦函数、正切函数定义可知，sin ,tan x x 的值别等于线段,MP AQ 的长，且ΔOAP ΔOAQ OAP S S S <<扇形，则下列结论不正确的是（ ）.8A.函数y tanx sinx x =++在22,ππ⎛⎫− ⎪⎝⎭内有1个零点B.函数y tanx x =−在32222,,ππππ⎛⎫⎛⎫−⋃ ⎪ ⎪⎝⎭⎝⎭内有2个零点C.函数y sinx x =−有3个零点D.函数y tanx sinx tanx sinx =+−−在22,ππ⎛⎫− ⎪⎝⎭内有1【答案】C【解析】对于选项A ,函数()g x y tanx sinx x ==++在22,ππ⎛⎫− ⎪⎝⎭为增函数,又()00g =,即函数y tanx sinx x =++在22,ππ⎛⎫− ⎪⎝⎭内有1个零点,即选项A 正确;对于选项B ,函数()f x y tanx x ==−,则()21'1f x cos x =−,则函数在3,2222,,ππππ⎛⎫⎛⎫− ⎪ ⎪⎝⎭⎝⎭为减函数,又()3300,0,042f f f ππ⎛⎫⎛⎫=<> ⎪ ⎪⎝⎭⎝⎭,即函数在3,2222,,ππππ⎛⎫⎛⎫− ⎪ ⎪⎝⎭⎝⎭各有一个零点, 即函数y tanx x =−在32222,,ππππ⎛⎫⎛⎫−⋃ ⎪ ⎪⎝⎭⎝⎭内有2个零点,即选项B 正确;对于选项C ,因为y sinx x =−,则'10y cosx =−…,即函数为减函数, 又当0x =时,0y =,即函数y sinx x =−有1个零点,即选项C 错误；对于选项D,当02x ,π⎛⎫∈− ⎪⎝⎭时,sin tanx x <,即2y tanx =,显然无零点,当02x ,π⎛⎫∈ ⎪⎝⎭时,sin tanx x >,即2y sinx =,显然无零点,又当0x =时,0y =,即函数y tanx sinx tanx sinx =+−−在22,ππ⎛⎫− ⎪⎝⎭内有1个零点,即选项D 正确,故选C三．解答题 17.（1）（2）1− 18.（1）证明略（219.（1）112− （2）1,810⎡⎤−⎢⎥⎣⎦20.(本题满分18分,第1小题4分,第2小题6分,第3小题8分)9如图，正方体的棱长为1,''B C BC O ⋂=，求： (1)AO 与''A C 所成角的度数; (2)AO 与平面ABCD 所成角的正切值; (3)B OA C −−的度数.【答案】（1）30（2（3）90 【解析】(1)连接'AB ,则由正方体性质,可得''AB AC B C ====且O 为'B C 的中点,所以1'2OC B C ==AO OC ⊥,所以12OC sin OAC AC ∠===,故30OAC ∠=,又由正方体性质可知'//'AA CC 且''AA CC =,所以四边形''AA C C 是平行四边形， 所以//''AC A C 所以OAC ∠是AO 与''A C 所成角,故AO 与''A C 所成角的度数为30; (2)如图,在平面''BCC B 内作OE BC ⊥交BC 于点E ,连接AE , 由正方体性质可知平面''BCC B ⊥平面ABCD ,又平面''BCC B ⋂平面,ABCD BC OE =⊂平面''BCC B ,所以OE ⊥平面ABCD , 所以E 为BC 中点,AE 为AO 在平面ABCD 上的射影, 所以OAE ∠为OA 与平面ABCD 所成的角, 由题意,在Rt OAE ∆中,12OE BE ==,AE ==所以1OEtan OAEAE∠===所以AO与平面ABCD;(3)由(1)知AO OC⊥,又由正方体性质可知AB⊥平面''BB C C,而OC⊂平面''BB C C,所以AB OC⊥,又,,AO AB A AO AB⋂=⊂平面ABO,所以OC⊥平面ABO,又OC⊂平面AOC,所以平面ABO⊥平面AOC,所以B OA C−−的度数为90.21.(本题满分18分,第1小题4分,第2小题6分,第3小题8分)若有穷数列{}n a满足:10niia==∑且11niia==∑，则称其为"n阶01−数列".（1）若"6穷01−数列"为等比数列,写出该数列的各项;（2）若某"21k+阶01−数列"为等差数列,求该数列的通项(121na n k≤≤+,用,n k表示)；（3）记"n阶01−数列"{}n a的前k项和为()123kS k,,,,n=,若存在{}123m,,,,n∈,使12mS=,试问:数列{}()123iS i,,,,n=能否为"n阶01−数列"?若能,求出所有这样的数列{}na；若不能,请说明理由.【答案】（1）111111,,,,,666666−−−或1111111,,,,,666666−−−;（2）当0d>时,()()*1211nna n N,n kk k k∴=−∈≤++当0d<时,()()*1211nna n N,n kk k k=−+∈≤++（3）数列{}()123iS i,,,,n=不为"n阶01−数列".【解析】(1)设123456,,,,,a a a a a a成公比为q的等比数列,显然1q≠,则有123456a a a a a a+++++=,得()6111a qq−=−,解得1q=−,由1234561a a a a a a+++++=，得161a=,解得116a=±,1011所以数列为111111,,,,,666666−−−或1111111,,,,,666666−−−;(2)设等差数列()12321,,,,1k a a a a k +…的公差为d ,123210,k a a a a +++++=()()11221210,0,2k k dk a a kd +∴++=+=即120,,k k a a d ++=∴=当0d =时,矛盾, 当0d >时,(23211212k k k a a a a a ++++++==−++)k a +()1122k k kd d −∴+=,即()11d k k =+, 由()11100,1k a a k k k +=+⋅=+得即11,1a k =−+ ()()()111111n na n k k k k k ∴=−+−⋅=+++()*121n N ,n k k−∈≤+ 当0d <时,同理可得()1122k k kd d −+=−,即()11d k k =−+由10k a +=得()1101a k k k −⋅=+，即111a k =+ ()()()111111n na n k k k k k ∴=−−⋅=−+++()*121n N ,n k k+∈≤+ 综上所述,当0d >时,()()*1211n n a n N ,n k k k k∴=−∈≤++当0d <时,()()*1211n n a n N ,n k k k k=−+∈≤++(3)记12,,,n a a a 中非负项和为A ,负项和为B ,则0,1A B A B +=−=,得1111,,2222k A B B S A ==−−=≤≤=，即()11232k S k ,,,,n ≤=，若存在{}123m ,,,,n ∈,使12m S =,可知:1210,0,,0,0m m a a a a +厖厔21210,,0,,2m n m m n a a a a a ++++++=−且剟1,0,0;k k k m a S ∴时剟厖 1,0,0k k n m k n a S S +<=时剟?123123n n S S S S S S S S ∴++++=++++12又1230n S S S S ++++=与1231n S S S S ++++=不能同时成立数列{}()123i S i ,,,,n =不为"n 阶01−数列".。

高二政治下学期第六次周测一、选择题（每小题3分，共75分）1.下列社会关系中属于民事法律关系的是①买卖关系②师生关系③借贷关系④税收关系A.①②B.①③C.②④D.①④2.双11过后，杨女士接到多个推销商品的电话和短信，原来是某快递公司的收派员和仓库管理员小张利用职务便利，从快递单中嗅出商机，将大量快递单直接出售，或以拍照的方式出售给他人，共计获利9.08万元。

小张的行为侵犯了杨女士的A.隐私权B.姓名权C.名誉权D.肖像权3.甲公司就其生产的一款S型高档轿车造型和颜色组合获得了外观设计专利权，又将其设计的“飞鹰”造型注册为汽车的立体商标，并将该造型安装在车头。

某车行因车主陈某请求，将陈某低价位旧车改装成S型高档轿车的造型和颜色，并从报废轿车上拆下“飞鹰”标志安装在改装车上。

陈某使用该改装车提供专车服务，收费高于普通轿车。

据此，判断正确的是①陈某的行为侵犯了甲公司的专利权②车行的行为侵犯了甲公司的专利权③陈某的行为侵犯了甲公司的商标权④车行的行为未侵犯甲公司的商标权A.①③B.②③C.①④D.②④4.作家钱某创作完成《青春》剧本，电影制片人孙某经钱某允许将该剧本拍成同名电影。

未经钱某、孙某同意，网络商赵某根据该电影制作网络剧在网络上传播，出版商顾某出版发行了《青春》电影的影碟出售。

下列对赵某、顾某的侵权行为认识正确的是①顾某侵犯了孙某的复制、发行权②起某侵犯了孙某的改编权③赵某侵犯了钱某的改编、发行权④顾某侵犯了钱某的放映权A.①②B.②③C.③④D.①④5.在疫情防控期间，浙江省很多企业为职工提供必要的防护用品和保障设施，确保职工身体健康和工作场所安全，落实职工隔离期和医疗期的工资待遇。

企业采取这些措施，意在①协调劳动关系，维护劳动者的权益②承担社会责任，塑造良好形象③完善社会保障制度，恢复生产能力④推进复工复产，增加就业岗位A.①②B.①④C.②③D.③④6.关于全面履行原则，下列说法中正确的是①又称正确履行原则②也叫适当履行原则③它要求当事人必须按照合同约定的要求正确行使自己的合同权利④只有合同得到全面履行，合同的订立才有意义A.①②③B.①②④C.①③④D.①②③7.下列行为构成侵犯知识产权的是A.小王把李某的一首诗配上音乐背景供自己和朋友欣赏B.王老师把李某的诗作为范文在课堂讲授C.某报刊转载其他报刊上发表的作品D.张某把李某的诗稍作修改署上自己的姓名发表在当地一家报纸上8.小猛与小丽登记结婚后不久由于夫妻矛盾重重提出离婚。

海南热带海洋学院附属中学2022-2023学年高二年级第一学期九月第二次周测试题第一部分完形填空（共20小题；每小题2分，满40分）阅读下面的短文，从短文后各题所给的四个选项（A、B、C和D）中，选出可以填入空白处的最佳选项。

My husband used to be a workaholic(工作狂) . Nothing seemed to be more __1__to him than his work, not even his family.He usually 2 at 6 o’clock, and our 3 and I were still asleep then, and then left 4 having breakfast, I asked him to have breakfast 5, but he said it’s a waste of 6. I didn’t know what kept him so 7. He even couldn’t finish all his work in the office. He came back at ten at night. However, I never expected that he would give me a kiss. 8 he got home, he would start to 9 . The kids had already been in bed, of course.“Mom, where is Dad? Why I 10 see him?” the kids often asked.“Well, Dad has to work, He is busy,” I always 11 like this. As time went by, they didn’t ask where their dad was again. Perhaps they had 12 that they had a dad. However, the situation changed several months ago.Jenny, our daughter, suddenly became 13 . I sent her to the hospital. The 14 told me that she was seriously ill and that she was calling 1 5 all the time. Tears burst into my eyes when I 16 that. I finally called my 17 and told him about that. Half an hour later, he came to the hospital and held Jenny’s little hands.He 18 another job two weeks later.“I Just wanted to make as much 19 as possible for you and our kids. But now, I just want to 20 as much time as possible with you and the kids,” he said and that’s what he is doing now.1. A. possible B. interesting C. important D. relaxing2. A. sat down B. got up C. stoop up D. came up3. A. kids B. pets C. neighbors D. parents4. A. on B. with C. without D. after5. A. in the office B. on the way C. in school D. at home6. A. money B. time C. energy D. food6. A. tired B. busy C. fast D. excited8. A. As soon as B. In the end C. Long before D. Long after9. A. eat B. sleep C. work D. write10. A. often B. never C. sometimes D. cheated11. A. shouted B. asked C. replied D. cheated12. A. thought B. forgotten C. ignored D. minded13. A. fine B. worse C. ill D. angry14. A. teacher B. boss C. officer D. doctor15. A. mom B. sir C. dad D. madam16. A. noticed B. realized C. heard D. felt17. A. mother B. child C. brother D. husband18. A. received B. lost C. changed D. found19. A. money B. happiness C. value D. laughter20. A. spend B. make C. set D. steal第二部分（共20小题，每小题2分，满分40分）第一节阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项（共15小题；每小题2分，满分30分）（A）Valencia is in the east part of Spain(西班牙). It has a port on the sea, two miles away on the coast. It is the capital of a province that is also named Valencia.The city is a market centre for what is produced by the land around the city. Mo st of the city’s money is made from farming. It is also a busy business city, with ships, railways, clothes and machine factories.Valencia has an old part with white buildings, colored roofs, and narrow streets. The modern part has long, wide streets and new buildings. Valencia is well known for its parks and gardens. It has many old churches and museums. The University in the centre of the city was built in the 13th century.The city of Valencia has been known since the 2nd century. In the 8th century it was the capital of Spain. There is also an important city in Venezuela（委内瑞拉）named Valencia.21. From the text, how many places has the name Valencia?.A. One.B. Two.C. Three.D. Four.22. What is the main difference between the two parts of the city?.A. The color of the buildings.B. The length of the streets.C. The age of the buildings.D. The color of the roofs.23. When was Valencia the most important city in Spain?.A. 2nd century.B. 8th century .C. 13th century.D. 20th century.24.What is Valencia famous for?.A. Its seaport.B. Its University.C. Its churches and museums.D. Its parks and gardens25. The main income of the city of Valencia is from its.A. markets.B. business.C. factories.D. farming.(B)Sam and Joe were astronauts. There was once a very dangerous trip and the more experienced astronauts knew there was only a small chance of coming back alive （活着）. Sam and Joe, however, thought it would be exciting though a little dangerous. “We’re the best men for the job,” they said tothe boss. “There may be problems, but we can find the answers.” “They’re the last people I’d trust,” thought the boss. “But all the other astronauts have refused to go.”Once they were in space, Joe had to go outside to make some repairs. When the repairs were done, he tried to get back inside the spaceship. But the door was locked. He knocked but there was no answer. He knocked again, louder this time, and again no answer came. Then he hit the door as hard as he could and finally a voice said, “Who’s there?” “It’s me! Who else could it be?” shouted Joe. Sam let him in all right but you can imagine that Joe never asked to go on a trip with Sam again!26. Most of the astronauts were unwilling to go on the trip because.A. there was little chance of being selectedB. they weren’t experienced enoughC. they thought they might get killedD. it wasn’t exciting enough27.Why were Sam and Joe chosen?A.The boss wanted them to get more experience.B.The boss trusted them more than anyone else.C.They were the last people who wanted to go.D.They were the only men who offered to go.28.What did Sam and Joe think the trip would be like?A. There would be serious problems.B. There wouldn’t be any danger.C. It would be long and tiring.D. It would be exciting.29.Joe didn’t want to work with Sam again probably because he thought Sam.A. was very slow and possibly deafB. didn’t know how to operate the doorC. was less experienced than he wasD. didn’t know how to do repairs30.The writer tells this story to .A.show the dangerous side of the astronauts’lifeB.show the funny side of the astronauts’lifeC.make people laughD.make people think(C)One Sunday, Mark decided to go sailing in his boat with his friend Dan, but Dan happened to be away. Dan’s brother John offered to go instead though he did not know anything about sailing. Mark agreed and they set out to sea.Soon they found themselves in a thick fog. Mark was sure they would be hit by a big ship.Fortunately he saw a large buoy（浮标）through the fog and decided to tie the boat to it for safety.As he was getting onto the buoy, however, he dropped the wet rope. The boat moved away in the fog carrying John, who did not know how to use the radio. He drifted（漂流）about and was not seen until twelve hours later.Mark spent the night on the buoy. In the early morning he fell asleep. He was having a bad dream when a shout woke him up. A ship, the Good Hope, came up and he climbed onto it and thanked the captain. The captain told him that John had been picked up by another ship and the ship’s captain had sent out a message. “Without the message I would not have found you on the buoy,” he said.31.Why didn’t Mark and Dan go sailing together?A. Dan asked his brother to go instead.B. Dan was in some other place.C. Mark was in some other place.D. Mark would like to go with John.32. Mark tried to tie the boat to the buoy so that.A. he could spend the night on it while John was looking for helpB. he and John could go sailing again when the fog clearedC. it wouldn’t be hit by other shipsD. he might be picked up by a passing ship33. John and Mark became separated because.A. there wasn’t room for both John and Mark on the buoyB. John couldn’t control the boat and it drifted awayC. Mark thought it safe to stay on the buoy but John didn’tD. John had to stay in the boat to radio for help34. What made it possible for Mark to be found on the buoy?A. John told people where to look for him.B. John radioed to the Good Hope to get him.C. He shouted when he caught sight of the Good Hope.D. The captain saw him as the fog cleared.35. The word he in the last sentence refers to .A. the captain that got the messageB. the captain that sent the messageC. JohnD. Mark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。

第6题图 2020至2021学年高二(上)数学周测试卷 姓名 学号 班级 一、选择题 1.在平面ABCD 中，A (0,1,1)，B (1,2,1)，C (－1,0，－1)，若向量a ＝(x ，y ，z )，且向量a 为平面ABC 的法向量，则y 2等于( )A ．2B ．0C ．1D ．32.已知平面α的一个法向量n ＝(－2，－2,1)，点A (－1,3,0)在α内，则点P (－2,1,4)到α的距离为( )A ．10B ．3 C.83 D. 1033.若点A (2,3,2)关于Ozx 平面的对称点为A ′，点B (－2,1,4)关于y 轴的对称点为B ′，点M 为线段A ′B ′的中点，则|MA |等于( )A.30 B ．3 6 C ．5 D.214.圆x 2＋y 2＝4上的点到直线4x －3y ＋25＝0的距离的取值范围是( )A ．[3,7]B ．[1,9]C ．[0,5]D ．[0,3]5.已知圆C 1：x 2＋y 2－2mx ＋m 2＝4，圆C 2：x 2＋y 2＋2x －2my ＝8－m 2(m >3)，则两圆的位置关系是( )A ．相交B ．内切C ．外切D ．外离6.如图所示，F 1，F 2分别为椭圆x 2a 2＋y 2b2＝1的左、右焦点，点P 在椭圆上，△POF 2是面积为3的正三角形，则b 2的值为( )A. 3 B ．2 3 C ．3 3 D ．437.若椭圆的焦距与短轴长相等，则此椭圆的离心率为( )A.15B.55C.12D.228.若椭圆x 2a 2＋y 2b2＝1(a >b >0)的左、右焦点分别为F 1，F 2，线段F 1F 2被点⎝⎛⎭⎫b 2，0分成5∶3的两段，则此椭圆的离心率为( )A.1617B.41717C.45D.2559.已知双曲线C ：x 2a 2－y 2b2＝1(a >0，b >0)的离心率为2，焦点到渐近线的距离为3，则双曲线C 的实轴长为( )A. 3 B ．3 C ．2 3 D ．610.已知直线l ：(a ＋1)x ＋ay ＋a ＝0(a ∈R )与圆C ：x 2＋y 2－4x －5＝0，则下列结论正确的是( )A ．存在a ，使得l 的倾斜角为90°B ．存在a ，使得l 的倾斜角为135°C ．存在a ，使直线l 与圆C 相离D ．对任意的a ，直线l 与圆C 相交，且a ＝1时相交弦最短二、填空题11.已知a >b >0，椭圆C 1的方程为x 2a 2＋y 2b 2＝1，双曲线C 2的方程为x 2a 2－y 2b 2＝1，C 1与C 2的离心率之积为32，则C 2的渐近线方程为________． 12.设F 1，F 2是双曲线C ：x 2a 2－y 2b2＝1(a >0，b >0)的两个焦点，P 是C 上一点．若|PF 1|＋|PF 2|＝6a ，且△PF 1F 2的最小内角为30°，则C 的离心率为________．13.已知双曲线x 2m －y 2m ＋6＝1(m >0)的虚轴长是实轴长的2倍，则双曲线的标准方程为________． 14.若椭圆x 2a 2＋y 2b 2＝1(a >b >0)的离心率为14，则双曲线x 2a 2－y 2b2＝1的渐近线方程为________． 三、解答题15.已知椭圆x 2a 2＋y 2b 2＝1(a >b >0)经过点A (2,1)，离心率为22，过点B (3,0)的直线l 与椭圆交于不同的两点M ，N .(1)求椭圆的方程；(2)若|MN |＝322，求直线MN 的方程．16.已知双曲线过点(3，－2)，且与椭圆4x 2＋9y 2＝36有相同的焦点．(1)求双曲线的标准方程；(2)若点M 在双曲线上，F 1，F 2为左、右焦点，且|MF 1|＋|MF 2|＝63，试判断△MF 1F 2的形状．。

2022-2023学年高二下学期周考卷D考试时间75分钟满分100分一、单选题（每小题2分，共24分。

在每小题给出的四个选项中，只有一项符合题目要求）1．(2022春·广东佛山·高二统考期末)诗句“也是人间玉，无非香不同。

初闻封鼻孔，细品引馋虫。

”描述的正是腐乳——我国古代劳动人民创造出的一种经过微生物发酵制作的大豆食品。

下列叙述错误的是()A．制作腐乳前需要对各种用具进行清洁和消毒B．腐乳中的蛋白质被分解成小分子，易于人体消化吸收C．腐乳制作过程中起主要作用的微生物是曲霉D．为提高腐乳品质和产量，可利用基因工程改造和选育优良菌种2．(2022春·福建龙岩·高二统考期末)我国制作泡菜历史悠久。

家庭制作泡菜时，主要选择的是芥菜。

在发酵过程中，芥菜产生的亚硝酸盐在特定条件下会转变为致癌物——亚硝胺。

泡菜虽美味，但不宜过量食用。

下列叙述错误的是()A．在发酵过程中，乳酸菌、乳酸和亚硝酸盐的含量均会先增加后减少再趋于稳定B．在发酵初期有气泡产生，原因是微生物呼吸作用产生了CO2和坛中存在空气C．制作过程中需要用食盐，其作用是析出芥菜中的水分并抑制微生物生长D．原料应选用新鲜的芥菜，原因是新鲜的芥菜中亚硝酸盐的含量低3．(2022春·黑龙江绥化·高二校考期末)下列有关制作果酒、果醋所利用的主要微生物的说法，错误．．的是()A．用到的主要微生物分别是酵母菌，醋酸菌B．从微生物的细胞结构来看，用到的主要微生物属于真核生物C．用到的主要微生物的异化作用类型依次是兼性厌氧型、需氧型D．用到的主要微生物都可以通过分裂生殖4．(2022春·四川南充·高二统考期末)用下表培养基成分培养某种微生物，下列有关说法错误的是()A．此培养基可用来培养自养型微生物B．表中的营养成分有水、无机盐和氮源C．用此培养基可直接培养出肉眼可见的菌落D．若加入蛋白胨，则它可提供碳源、氮源和维生素5．(2022春·吉林·高二校联考期末)下列有关无菌技术的叙述，错误是()A．无菌技术包括消毒和灭菌两个方面B．经巴氏消毒法可以杀死牛奶中的绝大多数微生物，基本不破坏牛奶的营养成分C．煮沸消毒法中100℃煮沸5～6min可以杀死所有微生物包括芽孢和孢子D．将接种环直接在酒精灯火焰的燃烧层充分灼烧，可以灭菌6．(2022春·青海西宁·高二校联考期末)以下关于能分解尿素的细菌的说法，正确的是() A．能分解尿素的原因是能合成蛋白酶B．用以尿素为唯一氮源且添加了酸碱缓冲剂的培养基培养该菌后不会使酚红指示剂变红C．环境中含有大量的尿素诱导该细菌产生了分解尿素的特性D．分离该种细菌时以尿素作为唯一碳源7．(2022春·湖南衡阳·高二统考期末)粗饲料经过微生物发酵后，其富含的纤维素、半纤维素和果胶等物质被降解为小分子，易于被畜禽采食和消化吸收，用于饲料发酵的益生菌包括乳酸菌和酵母菌等。

襄阳四中2021级高二数学周考测试题（二）一、单选题1、已知向量，且向量与互相垂直，则的值是（）A.B. C. D.2、若平面的一个法向量分别为，，则（）A. B.与相交但不垂直C.或与重合D.3、已知正四面体ABCD，M为BC中点，N为AD中点，则直线BN与直线DM所成角的余弦值为（）A. B. C. D.4、如图，在长方体中，，E为CD的中点，点P在棱AA1上，且平面，则AP的长为（）C.1D.与AB的长有关A. B.5、设、，向量，，且，，则（）A. B. C. D.6、以下命题：①若，则存在唯一的实数，使得；②若，则或；③若{}为空间的一个基底，则构成空间的另一个基底；④一定成立.则其中真命题的个数为（）A.4B.3C.2D.17、直三棱柱中，，，点是线段上的动点（不含端点），则以下各命题中正确的是（）A.与不垂直B.的最小值为D.平面C.的取值范围为8、在棱长为2的正四面体ABCD中，点M满足=x+y-(x+y-1)，点N满足=λ+(1-λ)，当AM、BN最短时，·=（）A.-B.C.-D.二、多选题9、已知，是两条不同的直线，，，是三个不同的平面．下列说法中正确的是（）A.若，，，则B.若，，则C.若，，，则D.若，，，则10、如图，在三棱柱中，侧棱底面，，，是棱的中点，是的延长线与的延长线的交点.若点在直线上，则下列结论错误的是（）A.当为线段的中点时，平面B.当为线段的三等分点时，平面C.在线段的延长线上，存在一点，使得平面D.不存在点，使与平面垂直11、正方体的棱长为，，，分别为，，的中点.则（）A.直线与直线垂直B.直线与平面平行C.平面截正方体所得的截面面积为D.点与点到平面的距离相等12、在三维空间中，叫作向量与的外积，它是一个向量，且满足下列两个条件：①，，且，，三个向量构成右手系（如图所示）；②.在正方体中，已知其表面积为S，下列结论正确的有（）A. B.C. D.与共线三、填空题13、已知向量，若，则实数________．14、已知四棱柱的底面是正方形，底面边长和侧棱长均为2，，则对角线的长为________．15、如图，在三棱锥中，，平面ABC，于点E，M是AC的中点，，则的最小值为______．16、已知球是棱长为2的正八面体(八个面都是全等的等边三角形)的内切球，为球的一条直径，点为正八面体表面上的一个动点，则的取值范围是_____.四、解答题17、已知空间中三点的坐标分别为，，，且，.(1)求向量与夹角的余弦值；(2)若与-互相垂直，求实数的值.18、在中，角所对的边分别为，且满足（1）求角;（2）若外接圆的半径为，且边上的中线长为，求的面积.19、2020年新冠肺炎疫情期间，某区政府为了解本区居民对区政府防疫工作的满意度，从本区居民中随机抽取若干居民进行评分．根据调查数据制成如下表格和频率分布直方图．已知评分在的居民有人．满意度评分满意度等级不满意基本满意满意非常满意（1）求频率分布直方图中的值及所调查的总人数；（2）为了解部分居民不满意的原因，从不满意的居民中用分层抽样的方法抽取名居民，倾听他们的意见，并从人中抽取人担任防疫工作的监督员，求这人中仅有一人对防疫工作的评分在内的概率．20、如图，在底面为菱形的平行六面体中，分别在棱上，且，且．(1)用向量表示向量；(2)当为何值时，．21、如图，在三棱锥中，平面平面，，为的中点．（1）证明：；（2）若是边长为1的等边三角形，点在棱上，，且二面角的大小为，求三棱锥的体积．22.如图，在四棱锥中，底面是平行四边形，，M，N分别为的中点，．(1)证明：；(2)求直线与平面所成角的正弦值．。

河南省南阳市文礼中学2022-2023学年高二下学期第二次周考试卷一．选择题（共30小题，每小题2分）1．传统发酵食品的制作在我国具有悠久的历史，下列关于制作传统泡菜的说法正确的是（）A．制作泡菜利用了乳酸菌发酵产生的乳酸和CO2B．制作泡菜时加入“陈泡菜水”可以缩短发酵时间C．为保证泡菜坛内的无氧环境，腌制时应尽量将泡菜坛装满D．为防止杂菌污染，腌制时要多放盐并将盐水与食材一同煮沸2．唐代苏敬的《新修本草》云：凡作酒醴须曲，而蒲桃（即葡萄）、蜜等酒独不用曲。

下列叙述错误的是（）A．装置密闭发酵过程中，酒精度的变化是先增加后趋于稳定B．“蒲桃、蜜等酒独不用曲”说明葡萄酒的酿制不需要微生物C．酿酒中期起泡现象是微生物无氧呼吸产生的CO2释放形成的D．工业发酵中为降低杂菌污染，发酵前需要对器具、原料等进行灭菌3．某同学将自然发酵的甘蔗汁加入体积分数为3%的无水乙醇中，利用高产菌株酿制甘蔗醋。

下列分析错误的是（）A．醋酸菌可将甘蔗汁中的糖类和乙醇转化为醋酸B．添加高产菌株到发酵液后，应高温处理杀灭杂菌C．发酵过程需要保持通气，温度控制在30～35℃D．培养液中的醋酸浓度不再上升时即可停止发酵4．微生物培养时常用到无菌技术避免杂菌污染，相关叙述正确的是（）A．无菌技术包括对操作者的衣着和手进行灭菌B．倒平板时应该把培养皿盖完全打开，以免培养基溅到培养皿盖上C．配置好的培养基应放入干热灭菌箱中进行灭菌D．接种前后接种环都必须灼烧灭菌5．下列关于分离高产脲酶菌的实验叙述，正确的是（）A．分离目的菌株时以能产生脲酶的刀豆种子研磨液作为样品B．分离菌种所采用的选择培养基需添加尿素和牛肉膏蛋白胨C．利用稀释涂布平板法纯化菌种时常用菌落数作为统计结果D．实施本实验时所用平板和试管的数目不多而且耗时也不长6．精氨酸依赖型谷氨酸棒状杆菌缺乏将鸟氨酸转化为精氨酸的酶，不能在缺少精氨酸的培养基上正常生长，但可作为鸟氨酸发酵的优良菌种。