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德州市2022-2023学年高二下学期期中考试语文试题含答案

德州市2022-2023学年下学期期中考试高二语文2023.4 本试卷满分150分，考试时间150分钟。

注意事项：1．答卷前，考生务必将自己的姓名、考生号等填写在答题卡和试卷指定位置上。

2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号；回答非选择题时，将答案写在答题卡上。

写在本试卷上无效。

3．考试结束后，将本试卷和答题卡一并交回。

一、现代文阅读（35分）（一）现代文阅读Ⅰ（本题共5小题，17分）阅读下面的文字，完成1～5题。

材料一：马克思主义和中国优秀传统文化相结合的过程，实际上属于一种“有选择性的亲和”，并非一一对应的机械复制粘贴。

这势必需要中国共产党人既要善于进行“传统的发现”，找到中华优秀传统文化与马克思主义基本原理的契合处，为科学理论深深扎根中国筑牢基石；又当善于进行“传统的发明”，用马克思主义基本原理激活长存华夏文明之内的文化基因，为优秀文化久久承继弘扬创造条件。

二者间的高度契合大致包括以下四个层面。

二者在世界本原的认识上相契合。

马克思主义的理论基石是唯物论，认为世界是物质的，物质决定意识，意识对物质具有能动的反作用，因此一切事物的发展变化皆有其客观规律。

中华优秀传统文化中蕴含着丰富的朴素唯物主义思想资源。

比如，在世界的本原、人的起源等问题上，儒家讲“万物本乎天，人本乎祖”“天生烝民”，道家讲“道生一、一生二、二生三、三生万物”，亦包含类似的思想元素。

二者就辩证方法的理解相契合。

唯物辩证法是马克思主义研究自然、社会、历史和思维的科学方法，核心内容是对立统一规律、量变质变规律、否定之否定规律；主张坚持发展地而非静止地、全面地而非片面地、普遍联系地而非孤立地观察事物、看待问题；主张人们在认识和实践活动中，要一切从实际出发，按客观规律办事。

中华优秀传统文化中的朴素的辩证法思想丰富而深邃，比如《周易·系辞》中倡导“穷则变，变则通，通则久”，《论语》有云“举一隅不以三隅反，则不复也”。

广东省广州市2024-2025学年高二上学期期中考试物理试卷(含解析)

2024学年第一学期高二年级期中考试试卷物理命题人：高二物理备课组审题人：高二物理备课组本试卷共4页，满分100分，考试用75分钟注意事项：1．开考前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名、班级、考号等信息填写在答题卡指定区域内。

2．选择题每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案；不能答在试卷上。

3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案须写在答题卡各题目指定区域内的相应位置上，不得使用涂改液，不得使用计算器。

不按以上要求作答的答案无效。

4．考生必须保持答题卡的整洁。

一、单选题（7小题，每题4分，共28分）1．如图为某型号的干电池，在其外壳上标注有“9伏”的字样，这表示（）A．电池短路时，该电池输出的电流为9AB．该电池在单位时间内有9J的化学能转化为电能C．将该电池接入电路后，电池两端的电压始终为9VD．1C正电荷通过该电池的过程中，有9J的化学能转化为电能2．静电透镜被广泛应用于电子器件中，在一些电子显示设备中，让阴极发射的电子束通过适当的非匀强电场，可以使发散的电子束聚集。

如图所示，图中带箭头的实线表示电场线，虚线表示电子的运动轨迹，a、b、c为其轨迹上的三点，电子仅在电场力作用下从a点运动到c点，在此过程中，下列说法正确的是（）A．a点的电势高于b点的电势B．b点的电场强度小于在c点的电场强度C．从a到c的运动过程中，电子的动能一直增大D．从a到c的运动过程中，电子的电势能先减少后增加3．关于生活生产中的静电应用，下列四副插图说法正确的是（）A ．图甲为静电除尘装置的示意图，带负电的尘埃被收集在线状电离器B 上B ．图乙为给汽车加油前要触摸一下的静电释放器，其目的是导走加油枪上的静电C ．图丙中摇动起电机，烟雾缭绕的塑料瓶顿时清澈透明，其工作原理为静电吸附D ．图丁中优质的话筒线外面包裹着金属网，目的是为了增强话筒线的导电性能4．如图，是小丽家的太阳能电池，因户外使用时间较久，厂家标记的参数已模糊不清。

人教版高二下学期英语期中考试(含答案)

高二年级英语学科考试试题考试时间：120分钟试卷总分：150分注意：1、答卷前，考生务必将自己的姓名和考号填写或填涂在答题卷指定的位置。

2、选择题答案用2B铅笔把答题卡上对应题目的答案标号涂黑；如需改动，用橡皮擦干净后，再选涂其他答案；不能答在试题卷上。

3、主观题必须用黑色字迹的钢笔或签字笔在答题卷上作答，答案必须写在答题卷各题目指定区域内的相应位置上，超出指定区域的答案无效；如需改动，先划掉原来的答案，然后再写上新的答案。

一、阅读理解（共15小题；每小题2分，满分30分）ABefore traveling around the world, take some time and find out what sightseeing destinations are. Some of those spots that most guides mention are the following thrilling attractions.Victoria FallsVictoria Falls has always been considered to be an incredible place worth taking pictures of. There are a lot of spots that tourists love. Some of them are very dangerous for people. Yet the brave are ready to overcome their fear for a shot of lifetime.Arctic Cliff FaceA cliff does not make the most comfortable place for camping. Camping on the ground is far safer anyway. Despite all the inconvenience, the new trend is rapidly gaining popularity among climbing enthusiasts and outdoor addicts.Auckland’s Sky TowerAuckland’s Sky Tower is popular with bungee jumpers. Some celebrities, such as Beyonce, have already tried it, which proves that the place is not only safe but popular as well. The tower is 630 feet tall. At the top of the structure there is an observation deck. Trust us, most of those reading this article would prefer to stay on the ground rather than climb up this scary structure.North Yungas RoadThe Road of Death is the right name given to a road in Bolivia. Hundreds of people die here every year. The major cause of all those accidents is the road. The problem is that it is too narrow and badly maintained while here the traffic is heavier than anywhere else. Nevertheless, it seems like tourists will continue visiting this strange road despite its scary nickname.1. What is Victoria Falls famous for?A. Its narrow and badly maintained roadB. Its dangerous but attractive spots for taking picturesC. Its scary structureD. Its thrilling camping2. North Yungas Road is called “the Road of Death” because ________. .A. the traffic is the heaviestB. it is built on the edge of the rockC. each year many people lose their lives thereD. there is no necessary protection equipment3. If you like bungee jumping, you can go to ________. .A. Victoria FallsB. Arctic Cliff FaceC. Auckland’s Sky TowerD. North Yungas Road4. What do the four places have in common?A. They are a bit life-threatening.B. They all have beautiful scenery.C. They are popular with climbers.D. They have been visited by celebrities.BHow do young children learn to have good values? How can parents teach their children about the importance of kindness and patience? At a time more and more parents worry about the violent images (暴力形象) their children see on TV and on the Internet. So many parents are turning to fairy tales. They want to teach their children how to behave in society by this way.It is believed that fairy tales have a great influence on children because they describe the two sides of good and evil (邪恶) very clearly. When children hear the tales, they learn to care about others’ feelings. In each tale, they can see that there are many different kinds of people in the world and that we all have a choice about what kind of person we want to be. We can choose to do good actions, rather than bad ones, in our lives.What kind of values can children learn from fairy tales? In The Princess and the Pea (《豌豆公主》), a poorly dressed girl says she is a princess. Few people believe her, so she is given a difficult test. When she passes the test, we learn that her dream comes true because she stays true to herself. In the Little Mermaid (《小美人鱼》), the mermaid, who lives under the sea, wishes to be with the humans on land. Through her experiences, we learn about the importance of living with and accepting other cultures.Teaching values is probably the main reason for encouraging children to read fairy tales. These tales can teach children lessons about human relationships that have been accepted around the world for many centuries. This might be the reason why they have been around for so long and will not disappear any time soon.5. Why do fairy tales have a great influence on children?A. Because fairy tales can teach them how to make a choice.B. Because fairy tales can help them get higher scores at school.C. Because they can learn how to avoid most difficulties in their lives.D. Because good and evil are shown in a way they can easily understand.6.The Little Mermaid may be helpful when children ________.A. are given a difficult testB. make friends with foreignersC. wish to be a princess or princeD. are going to lie to their parents7.The author writes the text mainly to ________.A. introduce some fairy talesB. talk about the history of fairy tales.C. discuss how to improve human relationshipsD. show how fairy tales help children shape valuesCMetro Pocket GuideMetrorail (地铁)Each passenger needs a farecard to enter and go out. Up to two children under age five may travel free with a paying customer .Farecard machines are in every station. Bring small bills because there are no change machines in the stations and farecard machines only provide up to $5 in change.Get one day of unlimited Metrorail rides with a One Day Pass. Buy it from a farecard machine in Metro stations. Use it after 9:30 a.m. until closing on weekdays, and all day on weekends and holidays .Hours of serviceOpen: 5a.m. Monday--- Friday 7 a.m. Saturday --- SundayClose: midnight Sunday --- Thursday 3 a.m. Friday --- Saturday nightsLast train times vary. To avoid missing the last train, please check the last train times posted in stations.MetrobusWhen paying with exact change, the fare is $1.35. When paying with a SmarTripⓇcard, the fare is $1.25.Fares for senior/disabled customersSenior citizens 65 and older and disabled customers may ride for half the regular fare. On Metrorail and Metrobus, use a senior/disabled farecard or SmarTripⓇcard. For more information about buying senior/disabled farecards, SmarTripⓇcards and passes, please visit MetroOpensDoors. com or call 202-637-7000 and 202-637-8000.Senior citizens and disabled customers can get free guide on how to use proper Metrobus and Metrorall services by calling 202-962-1100.Travel tipsAvoid riding during weekday rush periods --- before 9:30 a.m. and between 4 and 6 p.m.If you lose something on a bus or train or in a station, please call Lost & Found at 202-962-1195.8.What should you know about farecard machines?A. They start selling tickets at 9:30 a.m.B. They are connected to change machines.C. They make change for no more than $5.D. They offer special service to the elderly.9. At what time does Metrorail stop service on Saturday ?A. At midnight.B. At 5 a.m.C. At 7 a.m.D. At 3 a.m.10. What is good about a SmarTripⓇcard ?A. It saves money for its user.B. It is convenient for old people .C. It is sold on the Internet.D. It can be bought at any time.11. Which number should you call if you lose something on the Metro?A. 202-637-7000B. 202-637-8000C. 202-962-1100D. 202-962-1195DI work with Volunteers for Wildlife, a rescue and education organization at Bailey Arboretum in Locust Valley. Trying to help injured, displaced or sick creatures can be heartbreaking; survival is never certain. However, when it works, it is simply beautiful.I got a rescue call from a woman in Muttontown. She had found a young owl(猫头鹰) on the ground. When I arrived, I saw a 2-to 3-week-old owl. It had already been placed in a carrier for safety.I examined the chick(雏鸟) and it seemed fine. If I could locate the nest, I might have been able to put it back, but no luck. My next work was to construct a nest and anchor(固定) it in a tree.The homeowner was very helpful. A wire basket was found. I put some pine branches into the basket to make this nest safe and comfortable. I placed the chick in the nest, and it quickly calmed down.Now all that was needed were the parents, but they were absent. I gave the homeowner a recording of the hunger screams of owl chicks. These advertise the presence of chicks to adults; they might also encourage our chick to start calling as well. I gave the owner as much information as possible and headed home to see what news the night might bring.A nervous night to be sure,but sometimes the spirits of nature smile on us all! The homeowner called to say that the parents had responded to the recordings. I drove over and saw the chick in the nest looking healthy and active. And it was accompanied in the nest by the greatest sight of all —LUNCH! The parents had done their duty and would probably continue to do so.12.What is unavoidable in the author’s rescue work according to paragraph 1？A. Getting injured in his work.B. Efforts made in vain.C. Creatures forced out of their homes.D. Feeling uncertain about his future.13. Why was the author called to Muttontown？A.To look at a baby owl.B. To cure a young owl.C. To rescue a woman.D. To take care of a woman.14. What made the chick calm down？A. Its parents.B. A recording.C.Some food.D. A new nest.15. How would the author feel about the outcome of the event？A.It’s unexpected.B. It’s humorous.C. It’s beautiful.D. It’s discouraging二、阅读七选五（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。

高二数学期中考试真题

高二数学期中考试真题高二数学期中考试真题：一、选择题：（每题5分共60分）1.已知a，b，c是△ABC三边之长，若满足等式＝ab，则角C的大小为A．60 B．90 C．120 D．1502.已知椭圆的长轴长是短轴长的2倍，则椭圆的离心率等于A.12B.22C.2D.323.在△ABC中，已知sin Acosplay B＝sin C，那样△ABC肯定是A．直角三角形 B．等腰三角形 C．等腰直角三角形 D．正三角形4.假如 ,那样下列不等式成立的是（）A． B． C． D．5.目的函数，变量满足，则有（）A． B．无最小值C．无最大值 D．既无最大值，也无最小值6.下列有关命题的说法正确的是A．命题若，则的否命题为：若，则；B．命题使得的否定是：均有；C．在中，是的充要条件；D．或是的非充分非必要条件.7..设f＝2＋24＋27＋210＋＋23n＋1，则f等于（）A.27B.27C.27D.278.已知等差数列的前项和为，，，获得最小值时的值为（）A． B． C． D．9.设等差数列{an}的前n项和为Sn，则a6＋a70是的A．充分但非必要条件B．必要但不充分条件[出处:学|科|网Z|X|XC．充要条件 D．既不充分也非必要条件10.若点O和点F分别为椭圆x24＋y23＝1 的中心和左焦点，点P为椭圆上的任意一点，则OPFP的最大值为A．2 B．3 C．6 D．8二.填空题（每题5分共20分）[来13.不等式的解集是，则a＋b的值是14.已知数列满足，，则的最小值为____.15 .已知椭圆的焦点是 ,Ｐ为椭圆上一点，且是和的等差中项.若点P在第三象限，且＝120，则 .16.已知椭圆x2a2＋y2b2＝1的左，右焦点分别为F1，F2 ，若椭圆上存在点P使asinPF1F2＝csinPF2F1成立，则该椭圆的离心率的取值范围为________．三、解答卷17.命题P：关于x的不等式对于所有恒成立，命题Q：若为真，为假，求实数a的取值范围。

德州市2022-2023学年高二下学期期中考试化学试题含答案

德州市2022-2023学年下学期期中考试高二化学试题2023．4本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

满分100分，考试时间90分钟。

可能用到的相对原子质量：H 1O 16S 32Cu 64 P 31In 115第Ⅰ卷（选择题共40分）一、选择题：本题共10小题，每小题2分，共20分。

每小题只有一个选项符合题目要求。

1．下列关于有机物的说法正确的是（） A ．某有机物的名称为3-甲基1-，3-丁二烯 B ．乳酸（2-羟基丙酸）的核磁共振氢谱有4组峰 C ．3CHCl 只有一种结构可证明4CH 为正四面体形 D ．苯乙烯分子中所有碳原子一定共面 2．下列说法错误的是（） A ．金属键无方向性和饱和性 B ．基态2Fe +的价电子排布式为63dC ．只含非金属元素的化合物不一定是共价化合物D ．第4周期过渡元素基态原子未成对电子数为1的有3种 3．下列化学用语正确的是（）A ．4CF 的电子式：FFF C F ∶∶ B ．3CH +中C 原子的杂化方式为：3spC ．基态2Mn +的价电子轨道表示式为：D ．丙炔的键线式为：4．下列关于微粒间相互作用的说法错误的是（） A ．氧化银溶于氨水的过程中有配位键形成B ．24N H 和66C H 常温下均为液态，因为两种物质都存在分子间氢键C ．金属良好的导电性、导热性以及金属光泽均与金属键密切相关D ．加热法分离4NH Cl 和NaCl 的过程中，破坏了离子键和共价键 5．设A N 为阿伏伽德罗常数的值，下列说法正确的是（） A ．36g 冰中含有氢键最多为A 8N B ．64g 2SO 的中心原子价电子对数为A 3N C ．1mol 苯中含有的σ键为A 6ND ．1mol 基态铬原子中含有的未成对电子数为A 4N6．Ti 被称为21世纪金属，其离子可以和多种配体形成配位化合物。

下列相关说法正确的是（） A ．已知2222222TiCl (H NCH CH NH )]Cl [中含有环状结构，Ti 为6+价 B ．1mol 配合物2422[Ti(H O)Cl Cl 2H O ]⋅中有26mol H O 做为配体 C ．352Ti(NH )Cl 1ol []Cl m 含有σ键的数目为A 15N D ．上述选项中涉及的配合物，中心离子的配位数均为6 7．下列说法正确的是（）A ．蒸馏制备无水乙醇B ．检验产物中的HBrC ．鉴别邻二甲苯和环己烯D ．除去甲烷中的乙烯8．下列关于晶体的说法错误的是（）A ．利用X 射线衍射实验可以测定物质中原子的空间排布B ．共价键的键能越大，共价晶体熔沸点越高C ．干冰晶体中，1个2CO 分子周围有12个2CO 紧邻D ．离子晶体内可能含有共价键，分子晶体内可能含有离子键 9．下列对物质性质变化规律的叙述正确的是（） A ．3NF 、3NH 、2H O 的键角依次减小B ．2H O 、2H S 、2H Se 的键能依次增大C ．3AlCl 、2MgCl 、MgO 的熔点依次增高D ．乙烷、乙烯、乙炔的碳碳键长依次增大10．铁是应用最广泛的金属，在不同条件下能形成不同的晶体结构，分别称为Fe α-，Fe γ-，Fe δ-，其晶胞如下图所示，下列说法错误的是（）A ．晶胞参数最长的是Fe δ-B ．密度最小的是Fe α-C ．铁原子配位数最大的是Fe γ-D ．上述三种铁之间的转化是化学变化二、不定项选择题：本题共5小题，每小题4分，共20分。

期中专题01 数列大题综合高二下学期期中考试真题必刷强化训练(新高考广东卷)原卷版

a3 a4 24 .
(1)求数列 an 的通项公式；
(2)在 an 与 an1 之间插入 n 个数，使这 n 2 个数组成一个公差为 dn 的等差数列，求证：
1 1 d1 d2
1 L 1
d3
dn
3 .
8．（2022 春·广东佛山·高二校考期中）已知数列an 、bn 满足 a1a2a3 an 3bn ，若数
，求数列
1 bn
的前
n
项和 Tn
.
25．（2022 秋·广东广州·高二校考期中）已知等差数列an 满足，a1 10 ，且 a2 10 ，a3 8 ，
a4 6 成等比数列．
(1)求数列 an 的通项公式；
(2)若数列bn 的通项公式为 bn 2n ，求数列anbn的前 n 项和．
26．（2022 春·广东江门·高二台山市华侨中学校考期中）已知数列an为单调递增的等
比数列，且 a1a4 32 ， a2 a3 12.
(1)求数列 an 的通项公式；
(2)记 bn an log2 an ，求数列bn 的前 n 项和 Tn .
27．（2022 春·广东韶关·高二校考期中）已知an 为等差数列，bn为等比数列，
a1 b1 1, a5 5a4 a3 ,b5 4b4 b3 ．
.
21．（2022 春·广东揭阳·高二普宁市华侨中学校考期中）已知 Sn 为等差数列{an}的前 n
项和，若 a3＋a5＝5，S4＝7．
(1)求 an； 1
(2)记 bn＝ a2n a2n2 ，求数列{bn}的前 n 项和 Tn. 22．（2022 春·广东佛山·高二校联考期中）“绿水青山就是金山银山”是时任浙江省委书
(1)求 a2 ，并证明an n 为等比数列； (2)求数列an 的前 n 项和 Sn . 15．（2022 春·广东佛山·高二佛山市顺德区郑裕彤中学校考期中）已知数列an 中，a1 2 ，

高二第二学期期中考试(英语)试卷含答案

高二第二学期期中考试（英语）（考试总分：120 分）一、阅读理解（本题共计4小题，总分30分）1.（8分）1 .What does Ms. Hooper do?A. She's an architectB. She's a studentC. She's a teacherD. She's a designer2. What is Ms. Hooper hoping to use as content entry?A Her final assignmentB The sketch she made last yearC A new restoration designD last-minute drawing3. What does Mr. Muri apologize for?A His promptnessB His lack of detailsC His hastily made adD His late reply4. What is Muri's concern for Ms. Hooper?A That she might be too busy to do this wellB That she is too young and inexperiencedC That she is a professional and this is not designed for themD That the requested designs might be different from what she has learned.2.（6分）When I was young, I had an old neighbor nam ed Dr. Gibbs. He didn’t look like any doctor I’d ever known. He never shouted at us for playing in his yard. I remembered him as a neighbor who was nicer than anyone else in the neighborhood.When Dr. Gibbs was happy, he was planting trees. And his life’s goal was to make it a forest. Dr. Gibbs had some interesting theories about planting. He talked about trees that weren’t watered would grow deep roots in search of water. So he never watered his trees. He planted an oak (橡树) and, instead of watering it every morning, he beat it with the rolled-up newspaper. I asked him why he did that, and he said it was to get the tree’s attention.Dr. Gibbs died a couple of years. Every now and again, I walk by his house and look at the trees that he planted twenty-five y ears ago. They’re very strong now.I planted a couple of trees a few years later. I watered them regularly and took good care of them. Whenever a cold wind blows, they shake their leaves and branches.The funny thing about those trees of Dr. Gibbs was that difficulty seemed to help them in ways comfort and ease never could.1．What was Dr. Gibbs’ life goal?A. To study plants.B. To save more lives.C. To make a lot of money.D. To build a forest.2．One of Dr. Gibbs’ theories about planting was that ______.A. he often talked to the treesB. he never watered the treesC. he kicked the trees heavilyD. he buried the leaves around the roots 3．What does the writer mainly want to tell us?A. Trees are not as weak as we think.B. Difficulty is necessary for growth.C. We should listen to others’ adviceD. Planting trees is good for the environment.3.（8分）New law lets students sleep inWhen your alarm clock rings and you drag yourself out of bed, you probably wonder: Why on earth does school have to start so early?Fortunately, there is a new law to back you up―or better still, science.A law in California, passed on Oct 13, requires that public middle schools begin classes no earlier than 8:00 am and that high schools start no earlier than 8:30 am. The law will go into effect by July 1, 2022.Starting school at 8:00 or 8:30 in the morning may not sound like too big of a change, but it could mean one more hour of sleep for students who used to start school at 7:30 or even earlier.“The e ffect of that one hour is something they will be feeling as 40-year-old adults,” Sumit Bhargava, a sleep expert at Stanford University told The New York Times. He said that not having enough sleep can affect students’ mental health and increase the risk of getting fat and diabetes (糖尿病).In the short run, students’ school performances should improve almost immediately. Kyla Wahlstrom, a researcher at the University of Minnesota’s College of Education, found that students who have enough sleep are more alert (机敏的) in class and get better grades.Some might say that urging students to go to bed earlier could have been a much easier solution than changing the school timetable across an entire state. But according to the American Academy of Sleep Medicine, teenagers go through biological changes when they enter puberty (青春期), which makes it difficult for them to fall asleep before 11: 00 pm. So when school starts at 8: 00 or earlier, they can hardly get the ideal 8.5-9.5 hours of sleep that experts suggest they need to do their best in the daytime.This is why when the new law came out, its author, Anthony Portantino, said, “Generations of children will come to appreciate ( 感激) this historic day and our governor for taking bold action.1.When should public high schools start classes according to the California’s new law?A.No earlier than 8:30 am..B.No earlier than 8:00 am.C.No earlier than 7:30 am.D.No earlier than 9:00 am.2.What can we learn from Bhargava’s words?A. The amount of sleep people need changes with age.B. Lack of sleep could lead to health problems.C. Lack of sleep affects adults more than children.D. Sleep problems are one of the leading causes of diabetes3.What do we know about teenagers’ sleep patterns?A. Ideally, they need eight hours of sleep a night..B. Less sleep is needed when they enter pubertyC. They often wake up at midnight due to biologicalD. They may have difficulty falling asleep before11.pm4.Where does this passage probably come from?A. A n ewspaperB. A b iographyC. A textbookD. An advertisement4.（8分）Many people have long dreamed of being able to fly around as simply as riding a bicycle. Yet the safety and strength of a flying bike was always a big problem. Over the past 10 years，development in technology has moved the dream of personal flying vehicles closer to reality. Now，two groups of inventors say such vehicles may be available soon.The British company Malloy Aeronautics has developed a prototype(原型) of its flying bicycle. Grant Stapleton，marketing sales director of Malloy Aeronautics，says the Hoverbike is able to get in and out of small spaces very quickly.“It can be moved across continents very quickly because it can be folded and packed，” he adds.Mr. Stapleton says safety was the company’s main concern. He says the designers solved the safety issue by using overlapping rotors(交叠式旋翼) to power the vehicle.The company is testing a fullsize prototype of the Hoverbike，which will most likely be used first by the police and emergency rescue teams.In New Zealand，the Martin Aircraft Company is also testing a fullsize prototype of its personal flying device，called Jetpack(喷气背包).It can fly for more than 30 minutes，up to 1,000 meters high and reach a speed of 74 kilometers per hour.Peter Coker is the CEO of Martin Aircraft Company. He said Jetpack “is built around safety from the start”.In his words，“reliability is the most important element of it. We have safety built into the actual structure itself，very sim ilar to a Formula One racing car.”Jetpack uses a gasolinepowered engine that produces two powerful jet streams. Mr Coker says it also has a parachute(降落伞) that can be used should there be an emergency. “It starts to work at very low altitude and actually saves both the aircraft and the pilot，” he adds. Mr Coker says Jetpack will be ready for sale soon.1.We can learn from the passage that the Hoverbike __________.A. has been used by the police and emergency rescue teamsB. can be transported quickly after being folded and packedC. can hardly get in and out of small spaces quicklyD. can fly for over 30 minutes，up to 1,000 meters high2.The writer uses the example of Formula One racing car to show that .A.Jetpack’s engine is powerfulB.Jetpack is very safe and reliableC.Jetpack’s actual structure is uniqueD.Jetpack can reach a great speed and height3.The underlined word “it” in the last paragraph refers to “ ”.A.the parachuteB.the engineC.JetpackD.the jet stream4.What is th e author’s main purpose of writing the passage?A.To describe the problems of inventing flying vehicles.B.To show the differences between the two personal flying vehicles..C.To introduce the latest development of flying vehicles.D.To advertise the two personal flying vehicles.二、阅读七选五（本题共计1小题，总分10分）5.（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,并在答题卡上将该项涂黑。

高二期中考试(数学)试卷含答案解析

高二期中考试（数学）（考试总分：150 分）一、单选题（本题共计12小题，总分60分）1.（5分）1．2i12i-=+（）A．1 B．−1 C．i D．−i2.（5分）2．函数f（x）＝x4﹣2x3的图象在点（1，f（1））处的切线方程为（）A．y＝﹣2x﹣1B．y＝﹣2x+1C．y＝2x﹣3D．y＝2x+13.（5分）3．6名同学到甲、乙、丙三个场馆做志愿者，每名同学只去1个场馆，甲场馆安排1名，乙场馆安排2名，丙场馆安排3名，则不同的安排方法共有（）A．120种B．90种C．60种D．30种4.（5分）4．某中学的学生积极参加体育锻炼，其中有96%的学生喜欢足球或游泳，60%的学生喜欢足球，82%的学生喜欢游泳，则该中学既喜欢足球又喜欢游泳的学生数占该校学生总数的比例是（）A．62% B．56%C．46% D．42%5.（5分）5．设一组样本数据x1，x2，…，x n的方差为0.01，则数据10x1，10x2，…，10x n的方差为（）A．0.01B．0.1C．1D．106.（5分）6．从一批零件中抽取80个，测量其直径（单位：mm），将所得数据分为9组：[)[)[)[]5.31,5.33,5.33,5.35,,5.45,5.47,5.47,5.49，并整理得到如下频率分布直方图，则在被抽取的零件中，直径落在区间[5.43,5.47)内的个数为（）A．10B．18C ．20D ．367.（5分）7．在5(2)x -的展开式中，2x 的系数为（）．A ．5-B ．5C ．10-D ．108.（5分）8．要安排3名学生到2个乡村做志愿者，每名学生只能选择去一个村，每个村里至少有一名志愿者，则不同的安排方法共有（） A ．2种B ．3种C ．6种D ．8种9.（5分）9．北京2022年冬奥会和冬残奥会色彩系统的主色包括霞光红､迎春黄､天霁蓝､长城灰､瑞雪白；间色包括天青､梅红､竹绿､冰蓝､吉柿；辅助色包括墨､金､银.若各赛事纪念品的色彩设计要求：主色至少一种､至多两种，间色两种､辅助色一种，则某个纪念品的色彩搭配中包含有瑞雪白､冰蓝､银色这三种颜色的概率为（） A ．8225B ．245C ．115D ．21510.（5分）10．如图，将钢琴上的12个键依次记为a 1，a 2，…，a 12.设1≤i <j <k ≤12．若k –j =3且j –i =4，则称a i ，a j ，a k 为原位大三和弦；若k –j =4且j –i =3，则称a i ，a j ，a k 为原位小三和弦．用这12个键可以构成的原位大三和弦与原位小三和弦的个数之和为（） A ．5B ．8C ．10D ．1511.（5分）11．在新冠肺炎疫情防控期间，某超市开通网上销售业务，每天能完成1200份订单的配货，由于订单量大幅增加，导致订单积压.为解决困难，许多志愿者踊跃报名参加配货工作.已知该超市某日积压500份订单未配货，预计第二天的新订单超过1600份的概率为0.05，志愿者每人每天能完成50份订单的配货，为使第二天完成积压订单及当日订单的配货的概率不小于0.95，则至少需要志愿者（） A ．10名B ．18名C ．24名D ．32名12.（5分）12．已知定义在（0，+∞）上的连续函数()y f x =满足：()()x xf x f x xe '-=且(1)3f =-，(2)0f =．则函数()y f x =（）A ．有极小值，无极大值B ．有极大值，无极小值C ．既有极小值又有极大值D ．既无极小值又无极大值二、填空题（本题共计4小题，总分20分）13.（5分）13．设函数e ()xf x x a =+．若(1)4e f '=，则a =_________．14.（5分）14．262()x x+的展开式中常数项是__________（用数字作答）．15.（5分）15．设复数1z ，2z 满足12||=||=2z z ，12i z z +=，则12||z z -=__________.16.（5分）16．已知22451(,)x y y x y R +=∈，则22x y +的最小值是_______．三、解答题（本题共计6小题，总分70分）17.（10分）17．（10分）已知函数2()|21|f x x a x a =-+-+.（1）当2a =时，求不等式()4f x 的解集；（2）若()4f x ，求a 的取值范围.18.（12分）18．（12分）某沙漠地区经过治理，生态系统得到很大改善，野生动物数量有所增加.为调查该地区某种野生动物的数量，将其分成面积相近的200个地块，从这些地块中用简单随机抽样的方法抽取20个作为样区，调查得到样本数据(x i ，y i )(i =1，2，…，20)，其中x i 和y i 分别表示第i 个样区的植物覆盖面积(单位：公顷)和这种野生动物的数量，并计算得20160i ix==∑，2011200i i y ==∑，2021)80i i x x =-=∑（，2021)9000i iy y =-=∑（，201))800i i i x y x y =--=∑（（.（1）求该地区这种野生动物数量的估计值（这种野生动物数量的估计值等于样区这种野生动物数量的平均数乘以地块数）；（2）求样本(x i ，y i )(i =1，2，…，20)的相关系数（精确到0.01）；（3）根据现有统计资料，各地块间植物覆盖面积差异很大.为提高样本的代表性以获得该地区这种野生动物数量更准确的估计，请给出一种你认为更合理的抽样方法，并说明理由.附：相关系数r =12211))))ni iiiin ni i x y x x y y y x ===----∑∑∑（（（（，≈1.414.19.（12分）19．（12分）已知函数3()6ln f x x x =+，()'f x 为()f x 的导函数．（Ⅰ）求曲线()y f x =在点(1,(1))f 处的切线方程；（Ⅰ）求函数9()()()g x f x f x x'=-+的单调区间和极值； 20.（12分）20．（12分）甲口袋中装有2个黑球和1个白球，乙口袋中装有3个白球．现从甲、乙两口袋中各任取一个球交换放入另一口袋，重复n 次这样的操作，记甲口袋中黑球个数为X n ，恰有2个黑球的概率为p n ，恰有1个黑球的概率为q n ．（1）求p 1、q 1和p 2、q 2；（2）求X 2的分布列和数学期望E (X 2) ．21.（12分）21．（12分）为加强环境保护，治理空气污染，环境监测部门对某市空气质量进行调研，随机抽查了100天空气中的PM2.5和2SO 浓度（单位：3μg/m ），得下表：（1）估计事件“该市一天空气中PM2.5浓度不超过75，且2SO 浓度不超过150”的概率；（2）根据所给数据，完成下面的22⨯列联表：（3）根据（2）中的列联表，判断是否有99%的把握认为该市一天空气中PM2.5浓度与2SO 浓度有关？附：22()()()()()n ad bc K a b c d a c b d -=++++，22.（12分）22．（12分）已知12a <≤，函数()e xf x x a =--，其中e =2.71828…为自然对数的底数．（Ⅰ）证明：函数()y f x =在(0)+∞，上有唯一零点；（Ⅰ）记x 0为函数()y f x =在(0)+∞，上的零点，证明：（Ⅰ0x ≤≤；（Ⅰ）00(e )(e 1)(1)x x f a a ≥--．答案一、单选题（本题共计12小题，总分60分） 1.（5分）1D 2.（5分） 2B 3.（5分） 3 C 4.（5分） 4C 5.（5分） 5C 6.（5分）6B 7.（5分） 7C 8.（5分） 8 C 9.（5分） 9 B 10.（5分） 10C 11.（5分） 11 B 12.（5分） 12 A二、填空题（本题共计4小题，总分20分） 13.（5分）13．1 14.（5分） 14． 24015.（5分） 15． 16.（5分） 16．45三、解答题（本题共计6小题，总分70分）17.（10分）17．（10分）【解】（1）当2a =时，()43f x x x =-+-.当3x ≤时，()43724f x x x x =-+-=-≥，解得：32x ≤；当34x <<时，()4314f x x x =-+-=≥，无解；当4x ≥时，()43274f x x x x =-+-=-≥，解得：112x ≥；综上所述：()4f x ≥的解集为32x x ⎧≤⎨⎩或112x ⎫≥⎬⎭.……（5分）（2）()()()()22222121211f x x a x a x a x a aa a =-+-+≥---+=-+-=-（当且仅当221a x a -≤≤时取等号），()214a ∴-≥，解得：1a ≤-或3a ≥，a ∴的取值范围为(][),13,-∞-+∞.……（10分）18.（12分）18．（12分）【答案】（1）12000；（2）0.94；（3）详见解析【解】（1）样区野生动物平均数为201111200602020i i y ==⨯=∑，地块数为200，该地区这种野生动物的估计值为2006012000⨯=……（4分）（2）样本(,)i i x y (i =1，2，…，20)的相关系数为20()()0.943iix x y y r --===≈∑……（4分）（3）由（2）知各样区的这种野生动物的数量与植物覆盖面积有很强的正相关性，由于各地块间植物覆盖面积差异很大，从俄各地块间这种野生动物的数量差异很大，采用分层抽样的方法较好地保持了样本结构与总体结构得以执行，提高了样本的代表性，从而可以获得该地区这种野生动物数量更准确的估计. ……（4分）19.（12分）19．（12分）【答案】（Ⅰ）98y x =-；（Ⅰ）()g x 的极小值为(1)1g =，无极大值；【解】(Ⅰ) ∵()36ln f x x x =+，()26'3f x x x=+.可得()11f =，()'19f =， ∴曲线()y f x =在点()()1,1f 处的切线方程为()191y x -=-，即98y x =-.…4分（Ⅰ）依题意，()()32336ln ,0,g x x x x x x=-++∈+∞. 从而可得()2263'36g x x x x x =-+-，整理可得：323(1)(1)()x x g x x '-+=，令()'0g x =，解得1x =.当x 变化时，()()',g x g x 的变化情况如下表：，+∞)； g (x )的极小值为g (1)=1，无极大值. ……（12分）20.（12分）20．（12分）【答案】（1）112212716,,332727p q p q ====；；（2）；详见解析【解】（1）11131232,333333p q ⨯⨯====⨯⨯， 211131211227++3333333927p p q ⨯⨯=⨯⨯=⨯⨯=⨯⨯， 211231122222516+0+3333333927q p q ⨯⨯+⨯=⨯⨯+=⨯⨯=⨯⨯.……（8分）（2）227(2)27P X p ===；2216(1)27P X q ===；22124(0)33327P X ==⨯⨯=；∴2X 的分布列为故210()9E X =.；……（12分） 21.（12分）21．（12分）【答案】（1）0.64；（2）答案见解析；（3）有.【解】（1）由表格可知，该市100天中，空气中的 2.5PM 浓度不超过75，且2SO 浓度不超过150的天数有32618864+++=天，所以该市一天中，空气中的 2.5PM 浓度不超过75，且2SO 浓度不超过150的概率为640.64100=；……（4分）（2）由所给数据，可得22⨯列联表为：（3）根据22⨯列联表中的数据可得222()100(64101610)()()()()80207426n ad bc K a b c d a c b d -⨯⨯-⨯==++++⨯⨯⨯36007.4844 6.635481=≈>，因为根据临界值表可知，有99%的把握认为该市一天空气中 2.5PM 浓度与2SO 浓度有关. ……（12分）22.（12分）22．（12分）【答案】（I ）证明见解析，（II ）（i ）证明见解析，（ii ）证明见解析. 【解】（I ）()1,0,1,()0,()x x f x e x e f x f x ''=->∴>∴>∴在(0,)+∞上单调递增，2212,(2)240,(0)10a f e a e f a <≤∴=--≥->=-<，所以由零点存在定理得()f x 在(0,)+∞上有唯一零点；……（4分）（II ）（i ）000()0,0xf x e x a =∴--=，002000012(1)xxx e x x e x ≤⇔--≤≤--，令22()1(02),()1(02),2xxx g x e x x x h x e x x =---<<=---<<一方面：1()1(),xh x e x h x '=--= 1()10x h x e '=->，()(0)0,()h x h h x ''∴>=∴在(0,2)单调递增，()(0)0h x h ∴>=，2210,2(1)2xx x e x e x x ∴--->-->，另一方面：1211a a <≤∴-≤，所以当01x ≥0x ≤成立，因此只需证明当01x <<时2()10x g x e x x =---≤，因为11()12()()20ln 2x x g x e x g x g x e x ''=--==-=⇒=，当(0,ln 2)x ∈时，1()0g x '<，当(ln 2,1)x ∈时，1()0g x '>，所以()max{(0),(1)},(0)0,(1)30,()0g x g g g g e g x ''''''<==-<∴<，()g x ∴在(0,1)单调递减，()(0)0g x g ∴<=，21x e x x ∴--<，综上，002000012(1),x xex x e x x ∴--≤≤--≤≤（8分）（ii ）0000000()()()[(1)(2)]xa a t x x f e x f x a x e x a e ==+=-+-，00()2(1)(2)0a a t x e x a e '=-+->0x ≤，0()(2)](1)(1)2)a a a a t x t e a e e a e ∴≥=--=--+-，因为12a <≤，所以,2(1)ae e a a >≥-，0()(1)(1)2(2)a t x e a a e ∴≥--+--，只需证明22(2)(1)(1)a a e e a --≥--，即只需证明224(2)(1)(1)ae e a -≥--，令22()4(2)(1)(1),(12)as a e e a a =----<≤，则22()8(2)(1)8(2)(1)0aas a e e e e e e '=---≥--->，2()(1)4(2)0s a s e ∴>=->，即224(2)(1)(1)a e e a -≥--成立，因此()0x 0e (e 1)(1)x f a a≥--.……（12分）。

江苏省扬州市扬州中学2024-2025学年高二上学期11月期中考试数学试题(含答案)

江苏省扬州中学2024-2025学年第一学期期中试卷高二数学 2024.11一、单项选择题: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．圆的圆心和半径分别是（）A ．，1B ．，3C ．，2D ．，22．经过两点，的直线的斜率为（）A ．B ．C ．D ．3．椭圆x 225+y 216=1的焦点为为椭圆上一点，若，则（）A ．B ．C ．D ．4．已知双曲线的离心率大于实轴长，则的取值范围是（）A ．B ．C ．D．5．两平行直线与之间的距离为（）ABCD6．已知圆关于直线对称，则实数（）A ．1或B ．1C ．3D ．或37．已知抛物线C :y 2=2px (p >0)的焦点为，若抛物线上一点满足|MF |=2，∠OFM =60°，则（）A ．3B ．4C ．6D ．88．如图，双曲线的左右焦点分别为、，过的直线与该双曲线的两支分别交于、两点（在线段上），⊙与⊙分别为与的内切圆，其半径分别为、，则的取值范围是（）A ．B ．C ．D ．(0，+∞)二、多项选择题:本题共3小题，每小题6分，共18分.在每小题给出的四个选项中，有多项符合题目要求，全部选对得6分，部分选对的得部分分，选对但不全的得部分分，有选错的得0分.9．下列说法正确的是（）A ．若，且直线不经过第二象限，则，.()()22232x y +++=()2,3-()2,3-()2,3--()2.3-(2,7)A (4,6)B 12-2-12212,,F F P 13PF =2PF =435722:1y C x m -=m (3,)+∞)+∞(0,3)320mx y --=4670x y --=22:330C x y mx y +-++=:0l mx y m +-=m =3-1-F M p =2218y x -=1F 2F 1F l A B A 1F B 1O 2O 12AF F △2ABF △1r 2r 12r r 1132⎛⎫ ⎪⎝⎭，1233⎛⎫⎪⎝⎭，1223⎛⎫ ⎪⎝⎭，0abc ≠0ax by c ++=0ab >0bc <B ．方程（）表示的直线都经过点.C ．，直线不可能与轴垂直.D ．直线的横、纵截距相等.10．已知曲线．点，，则以下说法正确的是（）A ．曲线C 关于原点对称B ．曲线C 存在点P，使得C ．直线与曲线C 没有交点D ．点Q 是曲线C 上在第三象限内的一点，过点Q 向作垂线，垂足分别为A ，B ，则.11．已知集合.由集合中所有的点组成的图形如图中阴影部分所示，中间白色部分形如美丽的“水滴”.给出下列结论，正确的有（）A ．白色“水滴”区域（含边界）任意两点间距离的最大值为B ．在阴影部分任取一点，则到坐标轴的距离小于等于3.C ．阴影部分的面积为.D ．阴影部分的内外边界曲线长为.三、填空题:本题共3小题，每小题5分，共15分.12．若双曲线的离心率为2，则其两条渐近线所成的锐角的大小为 .13．已知椭圆的左、右焦点分别为F 1、F 2，过点的直线交椭圆于A 、B 两点，若，则该椭圆的离心率为 .14．已知为曲线y =1+4―x 2上的动点，则的最大值为 .四、解答题:本题共5小题，共77分.解答题写出文字说明、证明过程或演算步骤.15．已知△ABC 的顶点坐标是为的中点.(1)求中线的方程；(2)求经过点且与直线平行的直线方程.16．已知双曲线C :x 2a2―y 2b 2=1(a >0,b >0)的离心率为为双曲线的右焦点，且点到直线的()()21250x y λλ++--=R λ∈()2,1m ∈R 220m x y ++=y 3310x y +-=:44C x x y y =-1F 2(0,F 124PF PF -=2y x =2y x =±45QA QB ⋅=(){}22,(cos )(sin )4,0πP x y x y θθθ=-+-=≤≤∣P 1M M 8π8π()222210,0y x a b a b -=>>22221(0)x y a b a b+=>>2F 1AB F B ⊥，14sin 5F AB ∠=(),P a b 223a b a b --++()()()2,0,6,2,2,3,A B C M --AB CM B AC ()5,,03F c F 2a x c=距离为.(1)求双曲线的方程；(2)若点，点为双曲线左支上一点，求的最小值.17．已知，是抛物线：上的两点．(1)求抛物线的方程；(2)若斜率为的直线经过的焦点，且与交于，两点，求的最小值．18．椭圆与椭圆：有相同的焦点，且经过点.(1)求椭圆的方程；(2)椭圆的右焦点为，设动直线与坐标轴不垂直，与椭圆交于不同的，两点，且直线和的斜率互为相反数.①证明：动直线恒过轴上的某个定点，并求出该定点的坐标.②求△OMN 面积的最大值.19．定义：M 是圆C 上一动点，N 是圆C 外一点，记的最大值为m ，的最小值为n ，若，则称N 为圆C 的“黄金点”；若G 同时是圆E 和圆F 的“黄金点”，则称G 为圆“”的“钻石点”.已知圆165C ()12,0A P C PA PF +()6,2A m +()24,8B m +C ()221y px p =>C ()0k k ≠l C C P Q 2PQ k +C 1C 2212x y +=31,2Q ⎛⎫ ⎪⎝⎭C C B l l C M N BM BN l x MN MN 2m n =E F -A ：，P 为圆A 的“黄金点”(1)求点P 所在曲线的方程.(2)已知圆B ：，P ，Q 均为圆“”的“钻石点”.①求直线的方程.②若圆H 是以线段为直径的圆，直线l ：与圆H 交于I ，J 两点，对于任意的实数k ，在y 轴上是否存在一点W ，使得y 轴平分？若存在，求出点W 的坐标；若不存在，请说明理由.()()221113x y +++=()()22221x y -+-=A B -PQ PQ 13y kx =+IWJ ∠江苏省扬州中学2024-2025学年第一学期期中试卷高二数学（参考答案）2024.11参考答案：题号12345678910答案C A D A C C A C BD CD 题号11 答案ABD8．【详解】设，∴S △AF 1F 2=12r 1(8+2m )=(4+m )r 1，S △ABF 2=12r 2(2m +2p )=(m +p )r 2，.在△与△中：，即，，当双曲线的斜率为正的渐近线时，取最大，此时，，当与轴重合时，取最小，此时，经上述分析得：，.故选：C.10．【详解】当时，曲线，即；当时，曲线，即；不存在；时，曲线，即；时，曲线，即；画出图形如右：对于A ，由图可得A 错误，故A 错误；对于B ，方程是以为上下焦点的双曲线，当时，曲线C 存在点P ，使得，故B 错误；对于C ，一三象限曲线的渐近线方程为，所以直线与曲线C 没有交点，故C 正确；对于D ，设，设点在直线上，点在直线，11222,,6,2,2AF m BA p F F AF m BF m p ====+=+-()()11224m r S m S p m p r +∴==+12AF F 2AF B 122cos cos F AF F AB ∠=-∠()()()()()2222222262222224m m m p m p m p m m m pm++-++-+-=-⇒=⋅⋅+⋅+⋅-32212324444444m m r m mp m m m r p mp m m m++-∴===+++--//l m p →+∞404m m ∴-=⇒=l x m 2m =()2,4m ∈1212,23r r ⎛⎫∴∈ ⎪⎝⎭0,0x y ≥>22:44C x y =-2214y x -=0,0x y ≥<22:44C x y =--2214y x +=-0,0x y ≤≥22:44C x y -=-2214y x +=0,0x y <≤22:44C x y -=--2214y x -=2214y x -=12,F F 0,0x y ≥>214PF PF -=2y x =2y x =()00,Q x y A 2y x =B 2y x =-又点Q 是曲线C 上在第三象限内的一点，代入曲线方程可得，故D 正确；故选：CD.11．【详解】对于A ，由于，令时，整理得，解得，“水滴”图形与轴相交，最高点记为A ，则点A 的坐标为，点，白色“水滴”区域（含边界）任意两点间距离的最大值为，故A 正确；对于B ，由于，整理得：，所以，所以到坐标轴的距离为或，因为，所以，，所以到坐标轴的距离小于等于3，故B正确；对于C ，由于，令时，整理得，解得，因为表示以为圆心，半径为的圆，则，且，则在x 轴上以及x 轴上方，故白色“水滴”的下半部分的边界为以为圆心，半径为1的半圆，阴影的上半部分的外边界是以为圆心，半径为3的半圆，根据对称可知：白色“水滴”在第一象限的边界是以以为圆心，半径为2的圆弧，设，则，即AN 所对的圆心角为，同理AM 所在圆的半径为2，所对的圆心角为，阴影部分在第四象限的外边界为以为圆心，半径为2的圆弧，设，可得，DG 所对的圆心角为，同理DH 所在圆的半径为2，所对的圆心角为，故白色“水滴”图形由一个等腰三角形，两个全等的弓形，和一个半圆组成，22004455x y QA QB -⋅==22(cos )(sin )4x y θθ-+-=0x =[]32sin 0,2y yθ=-∈[1]y ∈- y (0,1)B -||1AB =22(cos )(sin )4x y θθ-+-=2cos cos 2sin sin x y αθαθ=+⎧⎨=+⎩2cos cos ,2sin sin )(M αθαθ++M ||2cos cos αθ+|2sin sin |αθ+cos [1,1],sin [0,1]θθ∈-∈2cos cos ||2cos ||cos |213|αθαθ+≤+≤+=|2sin sin ||2sin ||sin |213αθαθ+≤+≤+=M 22(cos )(sin )4x y θθ-+-=0y =[]32cos 2,2y yθ=-∈-[3,1][1,3]x ∈-- 22(cos )(sin )4x y -+-=θθ()cos ,sin Q θθ2r =13r OQ OP OQ r =-≤≤+=0πθ≤≤()cos ,sin Q θθO O ()1,0M -()1,0N 2AN AM MN ===π3π3()1,0N ()()3,0,3,0G H -π1,3ON OD OND ==∠=2π32π3所以它的面积是.轴上方的半圆（包含阴影和水滴的上半部分）的面积为，第四象限的阴影和水滴部分面积可以看作是一个直角三角形和一个扇形的面积的和，且等于所以阴影部分的面积为C 错误；对于D ，轴上方的阴影部分的内外边界曲线长为，轴下方的阴影部分的内外边界曲线长为，所以阴影部分的内外边界曲线长为，故D 正确.故选：ABD.12．13【详解】如图，设，因为，所以．由椭圆定义可知，，由，可得，所以．在Rt △F 1BF 2中，由，可得，即得，故得14．【详解】曲线，由于在曲线上，令，则，（其中），，又，，当时取得最大值15．【详解】（1）因为，所以，212π111π2π1222326S S S S ⎛=++=⨯⨯+⨯+⨯=⎝V 弓形半圆x 219π3π22⨯=2114π21π323⨯⨯+=941116π2(πππ2363++-=+x 1π4132π3223πππ2333⨯⨯+⨯⨯=+=x 111112π1(2π2π2)2π2233⨯⨯+⨯⨯-⨯⨯=13π11π8π33+=π314BF t =1AB F B ⊥，14sin 5F AB ∠=15,3AF t AB t ==21212=25,224AF a AF a t BF a BF a t =--=-=-22493AB AF BF a t t =+=-=13t a =1242,33BF a BF a ==2221212||||||F F BF BF =+222424(()33a a c =+2295c a =c e a ==9+1y =()()22141x y y +-=≥(),P a b ()2cos ,0π12sin a b θθθ=⎧≤≤⎨=+⎩()()222232cos 12sin 32cos 12sin a b a b θθθθ--++=---+++2cos 2sin 454sin 42sin 2cos 54sin θθθθθθ=--++=+-++()96sin 2cos 9θθθϕ=+-=+-sin ϕ=cos ϕ=π0,2ϕ⎛⎫∈ ⎪⎝⎭[][]0,π,πθθϕϕϕ∈∴-∈-- π,02ϕ⎛⎫-∈- ⎪⎝⎭ππ,π2ϕ⎛⎫-∈ ⎪⎝⎭∴π2θϕ-=223a b a b --++9+()()2,0,6,2A B -()4,1M -故的方程是，即；（2）因为直线的斜率，所以经过点且与直线平行的直线方程为，即.16．【详解】（1）由题意知，解得，则，所以双曲线的方程为.（2）记双曲线的左焦点为，则，可得，当三点共线时，最小，且最小值为.故的最小值为.17．【详解】（1）∵，是抛物线C ：上的两点，∴，则，整理得，解得，当时，，解得，不合题意；当时，，解得．故抛物线C 方程为y 2=6x ．（2）由（1）知C 的焦点为，故直线l 的方程为，联立，得，必有，设，，则，∴， ∴，即所以的最小值为18．【详解】（1）椭圆：的焦点坐标为，所以椭圆的焦点坐标也为，即得焦距为，∵椭圆过点，∴，CM 143124y x +-=+--2350x y +-=AC 303224ACk -==---B AC ()3264y x +=--34100x y +-=253165c a a c c ⎧=⎪⎪⎨⎪-=⎪⎩35a c =⎧⎨=⎩4b ==C 221916x y -=C 0F ()05,0F -0026PA PF PA PF a PA PF +=++=++0,,P F A 0PA PF +017AF =PA PF +17623+=()6,2A m +()24,8B m +()221y px p =>()()22212,848m p m p⎧+=⎪⎨+=⎪⎩()()22842m m +=+216m =4m =±4m =-()21224p m =+=113p =<4m =()212236p m =+=31p =>3,02⎛⎫⎪⎝⎭32y k x ⎛⎫=- ⎪⎝⎭2632y xy k x ⎧=⎪⎨⎛⎫=- ⎪⎪⎝⎭⎩()222293604k x k x k -++=0∆>()11,P x y ()22,Q x y 212236k x x k ++=2122236636k PQ x x p k k+=++=+=+222666PQ k k k +=++≥+226k k=2k =2PQ k +6+1C 2212x y +=()1,0±C ()1,0±22c =C 31,2Q ⎛⎫⎪⎝⎭24a +=∴，，∴椭圆的标准方程为.（2）①设直线：（），由，得，设M (x 1,y 1)，N (x 2,y 2)，所以，，所以，因为直线和的斜率互为相反数，所以，所以，所以，所以.即，所以，因为，所以，所以动直线恒过轴上的定点②由①知，，且，即，又S △OMN =12⋅|OT |⋅|y 1―y 2|=12⋅4⋅(y 1+y 2)2―4y1y 2令，则，∴S △OMN=24⋅n (3n +16)2≤24⋅n (2⋅3n⋅16)2=24⋅n 4⋅3n ⋅16=3（当且仅当时取“＝”）∴(S △OMN )max =3.19．【详解】（1）因为点P 为圆A 的“黄金点”，即，所以点P的轨迹是以AP 所在曲线的方程为（2）①因为P 为圆B 的“黄金点”，则所以，即点P 在圆上，则P 是圆和的交点.因为P ，Q 均为圆“”的“钻石点”，所以直线即为圆和的公共弦所在直线，2a =b =22143x y +=l x my t =+0m ≠223412x my t x y =+⎧⎨+=⎩()2223463120m y mty t +++-=122634mt y y m +=-+212231234t y y m -=+()()()()1221121212111111MF NF y x y x y yk k x x x x -+-+=+=----()()()()1221121111y my t y my t x x +-++-=--BM BN 0MB NB k k =+()()()()12211211011y my t y my t x x +-++-=--()()1221110y my t y my t +-++-=()()1212210my y t y y +-+=()22231262103434t mtm t m m --⨯+-⨯=++()640m t -=0m ≠4t =l x ()4,0T 1222434m y y m +=-+1223634y y m =+()()22Δ24434360m m =-+⋅>24m >224==240n m =->24m n =+316n ==PA =()()2211 3.x y +++=()121PB PB +=-||3PB =()()22229x y -+-=()()22113x y +++=()()22229x y -+-=A B -PQ ()()22113x y +++=()()22229x y -+-=两圆方程相减可得，故直线的方程为.②设的圆心为的圆心为，半径为.直线的方程为，得的中点坐标为，点S 到直线，则，所以圆H 的方程为.假设轴上存在点满足题意，设，.若轴平分，则，即，整理得又，所以代入上式可得，整理得①，由可得，所以x 1+x 2=―23k k 2+1,x 1x 2=―89k 2+1，代入①并整理得，此式对任意的都成立，所以.故轴上存在点，使得轴平分.0x y +=PQ 0x y +=22(1)(1)3x y +++=(11),S --()()22229x y -+-=(2,2)T 3ST y x =PQ (0,0)0x y +==12PQ ==221x y +=y (0),W t ()()1122,,,I x y J x y 120x x ≠y IWJ ∠0IM JW k k +=12120y t y tx x --+=()()21120.x y t x y t -+-=11223,113y kx y kx =+=+211211)33(()0x kx t x kx t +-++-=()12121203kx x t x x ⎛⎫+-+= ⎪⎝⎭22131y kx x y ⎧=+⎪⎨⎪+=⎩()22281039k x kx ++-=2203k kt -+=k 3t =y ()0,3W y IWJ ∠。

北京四中高二语文期中考试真题

北京四中高二语文期中考试真题（正文部分）一、阅读理解（题目一）阅读下面的文章，根据文章的内容进行选择。

范例：（文章正文）2月4日，国家卫生健康委员会发布了最新疫情通报。

根据最新统计数据，全国累计报告新冠肺炎确诊病例已超过50000例，其中死亡病例超过1000例。

多地医疗资源告急，医院床位不足等问题已经成为突出难题。

在这样的情况下，各级医疗机构调动了大量医护人员支援一线战斗。

仅北京市第十医院就派出了200名医生和护士参与抗疫工作，其中包括5名重症医学科的专家。

此外，还有数百名医护人员主动加入志愿者队伍，为病人们提供援助和照顾。

尽管疫情带来了极大的压力，但是人们看见的并不仅仅是医疗资源匮乏和生活困难，更多的是互助和奉献。

许多志愿者纷纷加入抗疫行列，为疫情防控做出了重要贡献。

问题：根据文章内容，回答下列问题。

1. 我国新冠肺炎确诊病例超过多少例?A. 1000例B. 一万例C. 50000例D. 30000例答案：C2. 北京市第十医院为抗击疫情派出了多少名医护人员?A. 100人B. 200人C. 300人D. 500人答案：B3. 除了医生和护士，还有什么类型的人员参与了抗疫工作?A. 军人B. 大学生C. 志愿者D. 政府官员答案：C（题目二）阅读下面的文章，根据文章的内容填写空白处的信息。

范例：（文章正文）春节是中国最重要的传统节日之一，人们通常会与家人团聚，互相拜年，参加各种庆祝活动。

文化活动：春节联欢晚会是中国人非常期待的一个节目。

除了联欢晚会，传统曲艺、舞龙舞狮等等也都是人们喜爱的文化活动。

特色食品：春节期间，人们喜欢吃一些有特色的食品。

比如饺子、年糕、汤圆等等。

特殊习俗：年年有余、爆竹声声、红包等都是中国春节非常重要的习俗。

问题：根据文章内容，填写下列空白处的信息。

1. 中国春节是什么时候的节日?答案：农历正月初一2. 中国人通常会与谁团聚，互相拜年?答案：家人3. 春节联欢晚会是中国人非常期待的一个什么节目?答案：节目4. 除了春节联欢晚会，还有哪些人们喜爱的文化活动?答案：传统曲艺、舞龙舞狮等等5. 春节期间，人们喜欢吃哪些特色食品?答案：饺子、年糕、汤圆等等6. 年年有余、爆竹声声、红包等都是中国春节的什么?答案：习俗（正文内容到此结束）二、作文（题目）请你写一篇作文，题目为《我眼中的教师》。

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职高第二册英语期中试题第一部分：听力（共两节，满分30分）略第二部分：英语知识运用（共两节，满分45分）第一节: 单项填空（共15小题；每小题1分，满分15分）从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。 21．—Would you like another cup of coffee? —_____． A．Yes, I like some B．Yes, I’d like to C．Yes, go ahead D．Yes, please 22．I don’t think she will come to the meeting on time, ? A．do I B．do you C．will she D．won’t she 23．I simply couldn’t understand how it _____ that you did so much work within such a short time． A．came about B．came back C．came up D．came along 24．—Do you have ___ trouble finishing the work? —The work is not so difficult as you think．We have finished it already． A．much B．any C．some D．no 25．The workers are working very hard __________ they can finish their work ahead of time． A．in order to B．so as to C．as if D．so that 26．They considered a computer, which was considered a great help in their work． A．to buy; to be B．buying; being C．to buy; being D．buying; to be 27．In fact is really a hard job for the police to keep order in an important football match． A．this B．that C．there D．it 28．—Jack, have you been away from your hometown? —Since the end of last February． A．how long B．how soon C．how far D．how often 29．I’m not going to say sorry to him．____I won’t today． A．At first B．At last C．At most D．At least 30．The is just around the comer and you won’t miss it． A．bicycle’s shop B．bicycle shop C．bicycles shop D．bicycles’ shop 31．—Could I speak to Miss Smith, please? —______．She’s gone to the post office． A．I’m afraid not B．I think so C．Certainly you can. D．I’m not sure． 32．I thought there would be many students in the room, but when I got in, I found ____． A．no one B．many C．none D．nothing 33．I still remember the house _____my mother and I used to stay in that evening． A．where B．which C．in that D．the one 34．I prefer studying English at home ______the match． A．to watching B．to watch C．rather than watch D．rather than watching 35．— , may I know your name and address? — , my name is Jack．I live in Dalas． A．Sorry; Yes B．Excuse me; Never mind C．Pardon; Of course D．Excuse me; Certainly

第二节：完形填空（共20小题；每小题1.5分，满分30分）阅读下面短文，掌握其大意，然后从36～55各题所给的四个选项（A、B、C和D）中，选出最佳选项。 Having said goodbye to his parents, Alvin, with his wife and one-year-old son, set off back home．36 excited, Alvin and Clare talked and laughed happily．And even little Alax 37 from time to time．The family were 38 from trip． But about three hours later things began to 39 ．It was starting to snow．Alvin sped up the car, 40 to arrive home before dark．But it was too dangerous to drive fast now．Because it was snowing more and more heavily．So Alvin had to 41 down．The snow on the 42 was getting deeper and deeper until it was hard to 43 on it．Their car slipped（滑落）off the way and got stuck in the deep snow 44 the engine refused to start again． “The snow doesn’t seem to 45 ．Shall we stay in the car waiting to be frozen to death or walk ahead through the snow?” Alvin asked．Clare said she 46 to walk．So they got out of the car with their son and began walking．But 47 was to come．Soon they lost their 48 and had to walk aimlessly on and on． Night came．They were not afraid of the dark．But they were 49 that poor Alax would die of cold．However, their faith to keep Alax 50 made them filled with courage, warmth and strength．They 51 and rested in turn and then continued their walk．They had countless falls but each time true love encouraged them to rise to their 52 again． One, two, three, …seven days passed．On the eighth day, 53 at last came from Alvin’s parents, the police and local people．But the young 54 had to have their feet cut off because of the bad frost-bites（冻伤）．Fortunately, there was 55 seriously wrong with little Alax． 36．A．Still B．Even C．Yet D．Ever 37．A．cried B．jumped C．smiled D．sang 38．A．taking B．having C．enjoying D．starting 39．A．work B．change C．come D．finish 40．A．phoning B．deciding C．thinking D．hoping 41．A．get B．slow C．go D．look 42．A．land B．highway C．fields D．car 43．A．walk B．sit C．stay D．wait 44．A．and B．but C．or D．for 45．A．fall B．end C．continue D．melt 46．A．liked B．preferred C．decided D．wished 47．A．better B．something C．nothing D．worse 48．A．hope B．luck C．way D．money 49．A．certain B．afraid C．sorry D．sure 50．A．happy B．silent C．alive D．dead 51．A．slept B．walked C．watched D．ate 52．A．heads B．eyes C．hands D．feet 53．A．danger B．help C．luck D．news 54．A．husband B．wife C．couple D．baby 55．A．everything B．anything C．something D．nothing

第三部分：阅读理解（共20小题；每小题2分，满分40分）阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。 A There are a lot of public libraries in Britain．These libraries have more than one hundred and fifteen million books, not including（包括）those libraries of public schools． Public libraries not only lend books, music records（唱片）but also help children, patients（病人）in hospitals and others to get special play readings, film shows and so on． The first public libraries were founded in about the year 1850．Today’s public libraries usually have a reading-room, a lending room and a reference room． The greatest and most famous library in Britain is that of the British Library in London．It was founded in 1973 and has over 10, 000, 000 books．It has nearly every magazine（杂志）, newspaper and book published（出版）in Britain and other parts across the world． 56．How many books are there in the British Museum? A．No more than 10, 000, 000． B．10,000,000 or less． C．More than 10, 000, 000． D．Just 10,000,000． 57．The “reference room” means a place for people to __ ． A．borrow books B．look up something C．read magazines D．lend records 58．The British Library ______． A．was founded in the seventeenth century B．was famous only for its rich collection of books and magazines