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湖南省长沙市雅礼中学2024-2025学年高三上学期入学考试数学试题

湖南省长沙市雅礼中学2024-2025学年高三上学期入学考试数学试题学校:___________姓名：___________班级：___________考号：___________A ．4B ．5．以正方体的顶点为顶点的三棱锥的个数为（A ．70B ．64．已知定义域为R 的函数()f x 则（）A ．()2e 11f -<C ．1e 2f æö>ç÷èø三、填空题(1)当BD长度变化时，理由．(2)记ABD△的面积分别为△与BCD16．函数()e4sinxf x l=-(1)求l的值；()2*Δ0n a n =ÎN 或数列{}2Δna 是等比数列．(3)设数列{}n a 的前n 项和为n S ，如果{}na 和{}n S 都是“优分解”的，并且123346a a a ===，，，求{}n a 的通项公式．2212S S +有最大值为14．16．(1)1l =(2)()f x 在(0,)+¥上仅有1个零点【分析】（1）利用导数的几何意义，求得切线的斜率，和切点，然后得到切线方程，利用对应相等，即可求得l 的值；（2）利用一次求导和二次求导分析原函数和导函数的单调性，分πx ³与0πx <<两种情况讨论，结合单调性和零点存在性定理，即得证.【详解】（1）因为()e 4sin 2,()e 4cos x x f x x f x x l l l l ¢=-+-=-，所以(0)4f l ¢=-，所以切线斜率为4l -，即4a l =-，所切线方程为()41y x l l =--+又(0)1f l =-，所以切点坐标为(0,1)l -，代入得则11l l -=-+，解得1l =.（2）由（1）得()e 4sin 1,()e 4cos x x f x x f x x ¢=--=-，令()()e 4cos x g x f x x ==-¢，则()e 4sin x g x x =+¢，当πx ³时，()e 4cos 0x f x x ¢=->恒成立，所以()f x 在[)π,+¥上递增，所以ππ()(π)e 4sin 1e 50f x f x ³=--³->，因此()f x 在[π,)+¥无零点；当0πx <<时，()e 4sin 0x g x x ¢=+>恒成立，所以()f x ¢单调递增，（3）设()*n n n S B C n =+ÎN ，可得{}2Δn S 是首项为2，公比为()1Q Q ¹的等比数列，设()*n n n a b c n =+ÎN ，可得()21Δ1nn S d c q q =+-，可得()()()223111111d c q q d c q q d c q q éùéùéù+-=+-×+-ëûëûëû，可得数列{}Δn a 是首项121Δ1a a a =-=，公比为q 的等比数列，可求{a n)的通项公式．【详解】（1）{}naQ 是等差数列，\设()()111111n a a n d a n d éù=+-=-+-+ëû，令()111,1n n b a n d c =-+-=，则{b n)是等差数列，{}nc 是等比数列，所以数列{a n)是“优分解”的．（2）因为数列{a n)是“优分解”的，设()*n n n a b c n =+ÎN ，其中()()11111,0,0n n n b b n d c c q c q -=+-=¹¹，则()12121111Δ1,ΔΔΔ(1)n n n n n n n n a a a d c qq a a a c q q --++=-=+-=-=-．当1q =时，()2*Δ0n a n =ÎN ；当1q ¹时，{}2Δna 是首项为21(1)c q -，公比为q 的等比数列．（3）一方面，Q 数列{}nS是“优分解”的，设()*n n n S B C n =+ÎN ，其中()()11111,0,0n n n B B n D C C Q C Q -=+-=¹¹，由（2）知2121Δ(1)n n S C Q Q -=-因为12122323Δ4,Δ6S S S a S S S a =-===-==，所以2121ΔΔΔ2S S S =-=．{}221(1)2,1,Δn C Q Q S \-=\¹\是首项为2，公比为()1Q Q ¹的等比数列．另一方面，因为{a n)是“优分解”的，设()*n n n a b c n =+ÎN ，其中()()11111,0,0n n n b b n d c c q c q -=+-=¹¹，()2111211Δ,ΔΔΔ1n n n n n n n n n n S S S a S S S a a d c q q +++++=-==-=-=+-{}2Δn S Q 是首项为2，公比为()1Q Q ¹的等比数列，0,1q q \¹¹，且()()()2222213ΔΔΔS S S =×，()()()223111111d c q q d c q q d c q q éùéùéù\+-=+-×+-ëûëûëû化简得()311111(1)0,0,0,1,0,Δ1n n n n c dq q c q q d a a a c q q -+-=¹¹¹\=\=-=-Q ，即数列{}Δna是首项121Δ1a a a =-=，公比为q 的等比数列．又232Δ2,2a a a q =-=\=Q ，又()211Δ2,12,0,2,S d c q q d q =\+-===\Q Q 解得11111,312c b a c =\=-=-=，综上所述，()1111122n n n a b n d c q --=+-+=+．【点睛】关键点点睛：本题考查数列新定义，弄清题意，并充分应用等比和等差数列的性质是解题的关徤.。

精品解析：湖南省长沙市雅礼中学2022-2023学年高一下学期入学考试英语试题(解析版)

2022-2023-2雅礼书院高一入学考试英语第一部分听力（共两节，满分30分）略第二部分阅读（共两节，满分50分）第一节（共15小题；每小题2.5分，满分37.5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。

AWe are excited to announce that Brandon Hobson-author of Where the Dead Sit Talking,a National Book Award Finalist-will judge our2023American Short(er)Fiction Prize.General GuidelinesStories must be1,000words or fewer.You are allowed to include up to three stories per entry.Please submit(提交)all stories in one document.Each story must begin on a new page and be clearly titled.For the title of your submission,list the story titles,separated by a comma.The first-place winner will receive a＄1,000prize and publication(出版)in a future issue of American Short Fiction(ASF).All entries will be considered for publication.Please submit your$17entry fee and your work through Submittable.We no longer accept submissions by post.You may submit multiple entries.accept only previously unpublished works.Submit your entry online between November24,2022-February1,2023.Conflicts(冲突)of InterestStaff and volunteers currently working with ASF are not fit for consideration or publication.Additionally, students,former students,and colleagues of the judge’s are not admitted to participate(参加).We ask that previous winners wait three years after their winning entry is published before entering again.About writing,Hobson has said,“I’m always more interested in language than I am certainly in plot.Most of us who write literary fiction are interested in experimenting in more ways than just looking at it,especially a traditional storyline or plot that we all learned in school.”With those words of encouragement and wisdom,good luck!We can’t wait for your submissions!1.How many stories can a participant submit at most?A.One.B.Two.C.Three.D.Four.2.What may the first-place prize winner get?A.A$1,000prize.B.A return of$17entry fee.C.Meeting with Brandon Hobson.D.Publication in a past issue of ASF.3.Which of the following may be qualified to participate?A.Volunteers of ASF.B.A new fiction writer.C.Prize winners last year.D.Students of the judge’s.【答案】1.C 2.A 3.B【解析】【导语】本文是一篇应用文。

湖南省雅礼中学中考自主招生考试物理试题

C．微波炉正常工作时的电功率大于电视机正常工作时的电功率
D．每月在微波炉上用的电费一定比在电视机上用的电费多
14．如图甲所示是某校九年級的同学们在参加“青羊区中学生物理科技创新大赛”时设计的空气质量测仪的原理，电源电压恒为3V，R0为10 的定值电阻，R为可以感知空气污染指数的可变电阻，其阻值随污染指数交化的情况如图乙所示。用电压表示数反映污染指数，污染指数在50以下为空气质量优，90-102之间为空气质量良，100~150为轻微污染，151~200为轻度污染，201~250为中度污染，251~300为轻度重污染，300以上为重度污染，下列分析正确的是（）
湖南省雅礼中学中考自主招生考试物理试题
一、选择题
1．用水银温度计测量热水温度时，温度计内水银液面慢慢升高，在“水银液面升高”的过程中，有关温度计内水银的物理量不变的是
A．温度B．体积C．密度D．质量
2．某大学两位研究生从蚂蚁身上得到启示，设计出如图所示的“都市蚂蚁”概念车．这款概念车小巧实用，有利于缓解城市交通拥堵．下列关于正在城市中心马路上行驶的此车说法正确的是（）
A．污染指数越小，电压表示数越大B．比赛当天电压表示数为1V时，属于轻微污染
C．污染指数越大，电路中消耗的总功率越小D．污染指数为50时，电压表的示数为2.5V
15．如图所示，为樊振东参加2020年3月8日国际乒联卡塔尔公开赛时的情景。下列说法中正确的是（）
A．乒乓球减速向上运动时，重力势能增大
B．乒乓球在空中运动过程中不受重力作用
C．雪的形成是凝华现象D．雾在形成过程中吸收热量
7．如图所示，电源两端的电压不变，电表均完好，闭合开关S1，两灯都发光，接着再闭合开关S2，则比较闭合开关S2前后，关于电路中各元件情况描述正确的是（）

湖南省长沙市雅礼中学2022-2023学年高一上学期入学考试数学试卷含答案

又由旋转知
所以 .
【小问2详解】
当时，
当时，
当时， .
【小问3详解】
.
,
过点作于点（如图），
因为为等边三角形，
，
所以，
，
，
，
当时，（舍去） .
当时，（舍去），
当时，（舍去），
综上所述，当为或或时，△MNC为等腰三角形.
19.随着我校选修课的全面开展，我校决定围绕在“科技、阅读、书法、演讲和英语”活动项目中，你最喜欢哪一项（每人只限一项）活动的问题，采用随机抽样的方式进行问卷调查，根据调查情况绘制成了如图所示的两幅不完整的统计图．由图中所给出的信息解答下列问题：
（1）求在此次调查活动中一共抽查了多少名学生，并将不完整统计图补充完整；
4. ________．
5 已知，则 ____________.
6.如图，在中，，，，，则 ________.
7.已知，求的值________．
8.如图，边长为20 正方形ABCD中，以BC为直径画一个半圆，直线DE与半圆相切，交AB于E点，则DE=________．
9.不等式的解集是全体实数，求实数a的取值范围________．
（3）如图③，在△B1C1D1移动过程中，直线D1C1与线段AB交于点N，直线B1C1与线段BD交于点M．是否存在某一时刻t，使△MNC为等腰三角形，若存在，求出时间t；若不存在，请说明理由．
参考答案
一、填空题
1.【答案】8.5
2.【答案】
3.【答案】3
4.【答案】
5.【答案】12
6.【答案】70°
21.如图，△ABC内接于⊙O，BD为⊙O的直径，BD与AC相交于点H，AC的延长线与过点B的直线相交于点E，且∠A=∠EBC．

湖南省长沙市雅礼中学2025届高三上学期语文入学考试卷及答案

湖南省长沙市雅礼中学2025届高三上学期入学考试语文试题一、现代文阅读（35分）（一）现代文阅读I（本题共5小题，19分）阅读下面的文字，完成1-5题小题。

什么是龙，确乎是一个谜。

龙像马，所以马往往被呼为龙。

《月令》“驾苍龙”，《周礼·庾人》“马八尺以上为龙”，皆其例。

龙有时又像狗。

《后汉书·孔僖传》“画龙不成反类狗”，所以狗也被呼为龙。

此外还有一种有鳞的龙像鱼，一种有翼的又像鸟，一种有角的又像鹿。

至于与龙最容易相混的各种爬虫类的生物，更不必列举了。

然则龙究竟是个什么东西呢？我们的答案是：它是一种图腾（Totem），并且是只存在于图腾中而不存在于生物界中的一种虚拟的生物，因为它是由许多不同的图腾糅合成的一种综合体。

因部落的兼并而产生的混合的图腾，古埃及是一个最显著的例子。

在我们历史上，五方兽中的北方玄武本是龟蛇二兽，也是一个好例。

不同的是，这些是几个图腾单位并存着，各单位的个别形态依然未变，而龙则是许多单位经过融化作用，形成了一个新的大单位，其各小单位已经是不复个别的存在罢了。

前者可称为混合式的图腾，后者则为化合式的图腾。

部落既总是强的兼并弱的，大的兼并小的，所以在混合式的图腾中总有一种主要的生物或无生物，作为它的基本的中心单位，同样的在化合式的图腾中，也必然是以一种生物或无生物的形态为其主干，而以其他若干生物或无生物的形态为附加部分。

龙图腾，不拘它局部的像马也好，像狗也好，或像鱼，像鸟，像鹿都好，它的主干部分和基本形态却是蛇。

这表明在当初那众图腾单位林立的时代，内中以蛇图腾为最强大，众图腾的合并与融化，便是这蛇图腾兼并与同化了许多弱小单位的结果。

金文龙字的偏旁皆从已，而已即蛇，可见龙的基调还是蛇。

大概图腾未合并以前，所谓龙者只是一种大蛇。

这种蛇的名字便叫作“龙”。

后来有一个以这种大蛇为图腾的团族（Klan）兼并了吸收了许多别的形形色色的图腾团族，大蛇这才接受了兽类的四脚，马的头，鬣的尾，鹿的角，狗的爪，鱼的鳞和须……于是便成为我们现在所知道的龙了。

湖南省长沙市雅礼中学2022-2023学年高二下学期入学考试英语试题

湖南省长沙市雅礼中学2022-2023学年高二下学期入学考试英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解The Red Cross is known for doing some of the most heroic acts in the world. There arehuman suffering in the face of sudden serious situations by organizing the power of volunteers and asking people to donate.In 1860, Swiss businessman and social activist, Jean Henri Dunant, saw the effects of wars, and countries not prepared or able to deal with the suffering of those who had been injured in the Battle of Solferino during the Second War of Italian Independence. Dunant organized a group of volunteers to help bring water and food to the injured, to help with medical treatment, or to write letters to the families of those who were dying. After that moment, he knew that more had to be done, and he wrote the book, A Memory of Solferino, which encouraged the public to create an organization which would help the wounded. His writing encouraged more people to support him in creating the International Federation of the Red Cross. And in 1863, the International Committee of the Red Cross was founded.The modern-day Red Cross does more than nursing soldiers during wartime. The group began to spend most of its time on disaster relief and epidemic(流行病) treatment. It has achieved even greater service in humanitarian(人道主义的) programs that serve continuously in both peace and war.One of the easiest ways you can help the Red Cross is to make sure you are able to donate blood and make an appointment at the Red Cross website. But, donating blood isn’t the only way you can help out — the Red Cross also encourages you to donate your time if you can, along with other things the modern-day Red Cross wants you to know.1．What does the underlined word “alleviate” in paragraph 1 mean?A．Lighten.B．Report.C．Express.D．Find.2．Why did Dunant write A Memory of Solferino?A．To make more people know the Red Cross.B．To ask more people to help the wounded.C．To let people see the effects of wars.D．To call on people to stop wars.3．What is the purpose of the last paragraph?A．To introduce the Red Cross website.B．To explain the Red Cross’s future work.C．To encourage people to offer help in the Red Cross.D．To show how the Red Cross helps needy people.When Adora Svitak was twelve years old, she spoke on the TED stage, saying she hates the word "childish" if it's being used to describe irrational （不合理的）demands or irresponsible behavior. She said she has seen enough of that in the adult world, so she knows irrational demands and irresponsible behavior aren't limited to children. In fact, she made the point that adults could learn a thing or two if they'd only open their mind to the possibility that kids have a lot to offer the world.Even as a kid, Svitak often spoke to educators, making the point that there should be more of a reciprocal （互惠的）relationship between teachers and students. "It shouldn't just be teachers at the head of the classroom telling them to do this or that. The students should teach their teachers," she said.But she wasn't naive（幼稚的）, and she knew that isn't how many classrooms and schools operate in that way. Her theory is that it's all about trust. Adults always seem to have a restrictive （约束的）attitude towards kids. "Kids have no or very little say in making the rules," Svitak joked.As a young child, Svitak loved to write. When her mom gave her a computer she wrote over 300 short stories on it. She wanted to get them published, and she was lucky because her parents were on her side. Even though she was turned down by many publishers, eventually she did have a book of short stories published. She was only seven years old then.After that first success, Svitak has gone on to do more impressive things, something she wishes more kids had the support to do. She says it's important for kids to be heard and contribute when they're young, so they grow up to become a better kind of adult. "The goal is not to turn kids into your kind of adults, but rather better adults than you guys have been. Progress happens because new generations and new eras grow and develop, and they become better than the previous ones. It's the reason we aren't in the Dark Ages anymore," she said. 4．What does Svitak think of using "childish" to describe irrational demands?A．It is unfair for children.B．It can lead to positive effects.C．It takes no account of adults' needs.D．It can result in irresponsible behavior. 5．What is a good reciprocal relationship between teachers and students according to Svitak?A．Students get along with teachers.B．Students teach instead of learning.C．Teachers keep telling students what to do.D．Teachers and students learn from each other.6．How did Svitak's parents react to her dream?A．They supported her.B．They had doubt about it.C．They were greatly shocked.D．They hardly took it seriously. 7．What can we infer from the last paragraph?A．Children need to stick to their dreams.B．Parents should satisfy their children's needs.C．Children are advised to imitate their parents.D．Parents should support and expect more from children.Reflexology is a natural treatment dating back to ancient times. It is based on the idea that there are zones, or areas, in the feet and hands that are related to other parts and systems of the body. For example, the tips of the toes and fingers are related to the head and neck, and the ball of the foot is related to the heart and chest. A reflexologist applies pressure to specific areas in a patient’s feet and hands to relieve symptoms or pain in other related areas.This type of treatment does not cure or diagnose specific health problems, and it does not involve any medicine or drugs. Yet many patients find that it successfully relieves symptoms of stress and disease. Reflexology is effective for pain, headaches, and sleeping difficulties, among other ilnesses. Applying pressure to the feet and hands relieves tension, improves blood circulation, and relaxes muscles. It promotes the natural, healthy functions and well-being of the entire body. Reflexology is often used along with other types of treatments, including conventional medicine.This gentle therapy is safe and simple. A reflexologist’s only tools are his or her hands. Pressure is strong, but not uncomfortable. It’s not uncommon for patients to fall asleep during treatments.A typical treatment session lasts one hour. Treatment is usually focused on the feet for most of the session. A patient is asked to remove his or her shoes and socks, to sit in acomfortable reclining chair, and then to relax as the reflexologist warms the patient’s feet with his or her hands and applies pressure to the appropriate parts of the foot. The last ten minutes of the session are dedicated to the hands.After relieving specific problems, many patients continue a regular program of treatment to maintain good health. Some reflexologists suggest building at least a five-minute reflexology session into every day for long-term relief of stress and pain.8．What is a reflexologist?A．a scientist who studies reflexology practice.B．a patient who receives reflexology treatment.C．a person who provides reflexology treatment.D．a person who supports the reflexology theory.9．Which of the following is true about reflexology according to the article?A．It can deal with problems with the feet.B．It works wonderfully with some diseases.C．It is often combined with other treatments.D．Many people do it at least five minutes daily.10．In a typical session of reflexology, about how much time is spent on the feet?A．One hour.B．Fifty minutes.C．Ten minutes.D．Half the time. 11．In ideas, which of the following is similar to reflexology?A．Chinese herbal therapy.B．Spiritual healing method.C．Traditional western medicine.D．Chinese acupuncture (针灸).Pieter Bruegel’s iconic 1565 painting The Harvesters hangs at the Metropolitan Museum of Art. The work showed people harvesting wheat nearly as tall as they were.“nowadays, however, if you walk through a wheat field, you basically see that wheat is about knee-height. The reduced height is essentially a consequence of breeding (培育)along with genes for increasing production to feed a growing population,” biologist De Smet explained.De Smet says wheat is just one example of how historical artwork can allow us to track the transformation of food crops over time. He teamed up with art historian Vergauwen, a friend since childhood, to document such artwork around the world. They have been mainly looking at things where they can spot changes in shape, color and size.Their interest in plants in artwork began with a visit to the Hermitage Museum, wherethey noticed an odd-looking watermelon in an early-17th-century painting. It appeared to be pale and white on the inside. Biologist De Smet assumed the painter had done a poor job. But art historian Vergauwen had a different idea. “No, this is one of the best painters ever from that era. So if he painted it like that, that’s the way it must have looked like,” he explained.Other paintings revealed that both red and white watermelons were grown during the 17th century.“With all the genetic knowledge we now have, we can look in more detail how something comes about,”De Smet said. “For example, until the 18th century, European strawberries appeared tiny in paintings-they then grew in size as they were crossbred with North American varieties.”Ultimately, the team hopes to create an online research database of historical plant artwork. They seek the contributions of art enthusiasts around the world via the social media. “However,” Vergauwen reminds, “if you’re going to use, for example, Picasso to try and understand how a pear looked in the early 20th century, you might be misled.”12．What can we learn about the painting The Harvesters?A．It shows how people successfully grew wheat.B．It proves that wheat was much shorter in the past.C．It explains the consequence of different breeding methods.D．It gives clues about how wheat in the 16th century looked like.13．What inspired the research team to start their study?A．Their preference for food crops.B．Their friendship since childhood.C．Their divided views on an old painting.D．Their shared interest in Hermitage Museum.14．What is the message from Vergauwen in the last paragraph?A．Art enthusiasts are not careful enough.B．Abstract paintings often mislead people.C．The source paintings need to be realistic.D．Picasso’s paintings are hard to understand.15．What is the purpose of the text?A．To comment on historical plant paintings.B．To tell interesting stories behind plant artwork.C．To inform readers of a scientific breakthrough.D．To introduce a study on food crop transformation.二、七选五What makes you cry? Being moved by a sad movie, waving a loved one off, or getting emotional after splitting up with your partner can all cause tears to roll down our faces.16When you think about it, shedding tears from your eyes can cause embarrassment or confusion. But it seems to be an automatic reaction when we get sad or upset.17 However, the feeling is the same – your cheeks puff up, your eyes tighten and before you know it, tears are streaming down your face. Some of us may weep a little while others might cry like a baby.A study in the UK in 2017 found that women admitted they cry 72 times a year. This was, on average, more than men. Adam Rutherford, lead researcher, says that the result has been pretty much consistent with previous research. 18 Are they just more embarrassed about showing their true feelings? The debate continues.One place where we experience emotional and tearful outbursts is in the workplace. 19 Someone might be stressed with a heavy workload. And, as therapist Joanna Cross put it, “crying is often a build-up of frustration and undealt-with situations and it’s a bit of a final straw moment.” She describes how someone might start weeping when they’re just asked to make a cup of tea. Actually, their stress has accumulated to the breaking point.But crying in the office or elsewhere can be an effective stress reliever. It can actually make you feel better. 20 Crying your eyes out shows others how you feel, so perhaps it’s a crying shame that more of us, particularly men, don’t cry more often.A．Then how do we cope with it?B．This can be where emotions run high.C．People reach their breaking point in different ways.D．We all have the power to cry, but is that a good thing?E．Maybe it dissolves or clears the negative feelings you’ve had.F．What brings about this reaction differs from person to person.G．But does this mean men don’t get as upset or emotional as women?三、完形填空When you are storm chasing, most mornings start off in a cheap hotel trying to remember where you ended up the night before. This morning, we were in Wichita, Kansas,the middle of the United States every spring.We loaded the car with our 22 , and off we went, driving under cloudless blue skies for hundreds of miles. Then we reached the border of our targeted storm and entered a dark scene of clouds and occasional rain. As we 23 the heart of the storm, we found ourselves 24 with high winds, violent rain, and severe hail (冰雹). Photographer Krystle, at the wheel, 25 to get in front of the storm, but it was moving too fast. We could 26 keep pace with it.Then we caught sight of something 27 , created by the storm: a rain-wrapped tornado half a mile to our right. The chaotic conditions made it 28 for us to keep it in sight. We lost our cellphone signals and all the data we were desperately 29 for communication. We couldn’t see beyond 20 feet. That was when Nick, our expedition (探险) leader and weather expert, called, “We have to flee.” Krystle 30 changed direction, driving the car north onto a country road, 31 the madness of that dangerous chase.We weren’t done. After a stretch of clear skies, we found another 32 waiting for us. This time, we 33 to get in front of it, stopping to photograph it and racing back to the car to 34 its extreme anger.A little past midnight, we let the storm go. We watched as the lightning-filled cloud rolled away, displaying the night sky — a beautiful 35 for those reckless (不顾危险的) enough to seek it.21．A．recognize B．transform C．photograph D．forecast 22．A．nutrients B．flavor C．equipment D．documents 23．A．mentioned B．identified C．captured D．approached 24．A．struggling B．comparing C．engaged D．filled 25．A．pretended B．accelerated C．deserved D．hesitated 26．A．instantly B．gradually C．exactly D．hardly 27．A．disgusting B．frightening C．annoying D．embarrassing 28．A．efficient B．contradictory C．fundamental D．tough29．A．dependent on B．absorbed in C．satisfied with D．curious about 30．A．deliberately B．frequently C．rigidly D．abruptly 31．A．predicting B．tolerating C．escaping D．witnessing 32．A．cloud B．storm C．car D．road 33．A．regretted B．devoted C．managed D．proposed 34．A．calm B．ignore C．challenge D．avoid 35．A．reward B．excuse C．appetite D．thought四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

湖南省长沙市雅礼中学2024-2025学年高三上学期入学考试数学试题(含答案)

雅礼中学2025届高三上学期入学考试试卷数学时量：120分钟分值：150分一､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、已知集合{}240A x x =-≤，则A =N （）A ．{}0B ．{}0,1C ．{}0,1,2D ．{}1,22、）A B C D3、（暑假作业原题）若正数x ，y 满足 ²20x xy -+=，则x y +的最小值是（）A ．B ．C ．4D ．6【答案】C【分析】根据已知条件及基本不等式即可求解.4、过椭圆22:1169x yC+=的中心作直线l交椭圆于,P Q两点，F是C的一个焦点，则PFQ△周长的最小值为（）A．16 B．14 C．12 D．10所以PFQ△的周长为PF当线段PQ为椭圆短轴时，故选：B5、已知圆C的方程为22(2)x y a+-=，则“2a>”是“函数y x=的图象与圆C有四个公共点”的（）A．充分不必要条件B．必要不充分条件C．充要条件D．既不充分也不必要条件【答案】B6、（暑假作业原题）如图是一块高尔顿板的示意图，在一块木板上钉着若干排相互平行但相互错开的圆柱形小木钉，小木钉之间留有适当的空隙作为通道，前面挡有一块玻璃．将小球从顶端放入，小球下落的过程中，每次碰到小木钉后都等可能地向左或向右落下，最后落入底部的格子中．记格子从左到右的编号分别为0，1，2，⋯，10，用X 表示小球最后落入格子的号码，若0()()P X k P X k == ，则0(k = )A ．4B ．5C ．6D ．7【分析】小球在下落过程中，共10次等可能向左或向右落下，则小球落入格子的号码X 服从二项分布，且落入格子的号码即向右次数，即1~(10,)2X B ，则10101()()(02kP X k C k ===，1，2...，10)，然后由二项式系数对称性即可得解．【解答】解：小球在下落过程中，共10次等可能向左或向右落下，则小球落入格子的号码X 服从二项分布，且落入格子的号码即向右次数，即1~(10,2X B ，所以10101010111()()(1()(0222k k k kP X k C C k -==-==，1，2...，10)，由二项式系数对称性知，当5k =时，10kC 最大，故05k =．故选：B ．【点评】本题考查了二项分布及二项式系数的性质的应用，属于中档题．7、（教材原题）以正方体的顶点为顶点的三棱锥的个数是( ) A ．70B ．64C ．60D ．58【分析】从8个顶点中选4个，共有48C 种结果，在这些结果中，有四点共面的情况，6个表面有6个四点共面，6个对角面有6个四点共面，用所有的结果减去不合题意的结果，得到结论．【解答】解：首先从8个顶点中选4个，共有48C 种结果，在这些结果中，有四点共面的情况，6个表面有6个四点共面，6个对角面有6个四点共面， ∴满足条件的结果有4488661258C C --=-=．故选：D ．【点评】本题是一个排列问题同立体几何问题结合的题目，是一个综合题，这种问题实际上是以排列为载体考查正方体的结构特征．8、（暑假作业原题）已知定义域为R 的函数()f x ，其导函数为()f x '，且满足()2()0f x f x '-<，(0)1f =，则( )A ．2(1)1e f -<B ．()21f e >C ．1(2f e >D ．1(1)(2f ef <【分析】构造函数2()()xf xg x e =，由()2()0f x f x '-<得()0g x '<，进而判断函数()g x 的单调性，判断各选项不等式．【解答】解：2()()x f x g x e=，则22222()2()()2()()()x x x x f x e f x e f x f x g x e e '⋅-'-'==，因为()2()0f x f x '-<在R 上恒成立，所以()0g x '<在R 上恒成立，故()g x 在R 上单调递减，所以220(1)(0)(1)(0),(1)1f f g g e f e e --->=->=，故A 不正确；所以g （1）(0)g <，即20(1)(0)f f e e<，即f （1）22(0)e f e <=，故B 不正确；1()(0)2g g <，即101()(0)21f f e e<=，即1(2f e <，故C 不正确；1()(1)2g g >，即121()(1)2f f e e >，即1(1)()2f ef <，故D 正确．故选：D ．【点评】本题考查了利用导数研究函数的单调性，考查了函数思想，属中档题．二､选择题：本题共3小题，每小题6分，共18分.在每小题给出的选项中，有多项符合题目要求.全部选对的得6分，部分选对的得部分分，有选错的得0分.9、已知复数12,z z ，下列说法正确的是（）A ．若12=z z ，则2212z z =B ．1212z z z z =C ．1212z z z z -≤+D ．1212z z z z +≤+10、已知函数()ππ)02,22f x x ωϕωϕ⎛⎫=+<≤-<< ⎪⎝⎭，函数()()12g x f x =+的部分图象如图所示，则下列说法中正确的是（）A ．()f x 的表达式可以写成()24f x x π⎛⎫=- ⎪⎝⎭B ．()f x 的图象向右平移3π8个单位长度后得到的新函数是奇函数 C ．()()1h x f x =+的对称中心ππ,182k ⎛⎫-+⎪⎝⎭，Z k ∈ D ．若方程()1f x =在()0,m 上有且只有6个根，则5π13π,24m ⎛⎫∈ ⎪⎝⎭11、如图，过点(C a ，0)(0)a >的直线AB 交抛物线22(0)y px p =>于A ，B 两点，连接AO 、BO ，并延长，分别交直线x a =-于M ，N 两点，则下列结论中一定成立的有( )A ．//BM ANB ．以AB 为直径的圆与直线x a =-相切C ．AOB MON S S ∆∆=D ．24MCN ANC BCM S S S ∆∆∆=⋅【分析】设出直线与抛物线联立，利用韦达定理及斜率公式，结合三角形的面积公式及直线与圆的位置关系的判断方法即可求解．【解答】解：对于A ，令直线:AB x my a =+，1(A x ，1)y ，2(B x ，2)y ，联立22x my a y px=+⎧⎨=⎩，消x 可得2220y pmy pa --=，则△2(2)80pm pa =+>，122y y pa =-，122y y pm +=，则21212()222x x m y y a pm a +=++=+，则1111,:OA y y k OA y x x x ==则直线，∴11(,)ayM a x --，故12211122212220()BMay pay y x y y y pak x a x a y x a +++====+++，同理0AN k =，//BM AN ∴，故A 正确；对于B ，如图，设AB 中点1212(,22x x y y Q ++，即2(Q pm a +，)pa -，则Q 到直线x a =-的距离22d pm a =+，以AB为直径的圆的半径12||||2AB y y =-=，所以222||(2)(2)4AB d p a a p m -=+-，当2pa =时相切，当2p a ≠时不相切，故B 错误；对于C ，设x a =-与x 轴交于P ，PON AOC S S ∆∆=，MOP BOC S S ∆∆=，则PON MOP AOC BOC S S S S ∆∆∆∆+=+，则AOB MON S S ∆∆=，故C 正确；对于D ，112211(),()22ANC BCM S x a y S x a y ∆∆=+=-+，则1212121211()()(2)(2)44ANC BCM S S x a x a y y my a my a y y ∆∆⋅=-++=-++221212121[2()4]4m y y am y y a y y =-+++22221[(2)2(2)4](2)(2)4m pa am pm a pa pa pm a =--++-=+，而121212||||2MCN MPC NPC S S S a y y a y y ∆∆∆=+=⋅-=-，所以2222222121212()[()4]4(2)4MCN ANC BCM S a y y a y y y y pa pm a S S ∆∆∆=-=+-=+=⋅，故D 正确．故选：ACD ．【点评】本题考查了已知两点求斜率，由斜率判断两条直线平行，判断直线与圆的位置关系，根据韦达定理求参数，属于中档题．三､填空题：本题共3小题，每小题5分，共15分.12、已知随机变量X 服从正态分布()25,N σ，若(56)0.27P X <≤=，则(4)P X <= .13、已知向量()sin ,cos a θθ=，()3,1b =，若a b ∥，则2sin sin 2θθ+的值为 .14、设0k ＞，若存在正实数x ，使得不等式14log 20kx x k --⋅≥成立，则k 的最大值为 .四､解答题：本题共6小题，共70分.解答应写出文字说明､证明过程或演算步骤.15、（13分）平面多边形中，三角形具有稳定性，而四边形不具有这一性质．如图所示，四边形ABCD 的顶点在同一平面上，已知2,AB BC CD AD ====(1)当BD cos A C -是否为一个定值？若是，求出这个定值；若否，说明理由．(2)记ABD △与BCD △的面积分别为1S 和2S ，请求出2212S S +的最大值．【答案】cos A C -为定值，定值为1 (2)14【详解】（1）法一：在ABD △中，由余弦定理222cos 2+-=⋅AD AB BD A AD AB，得cos A =2168BD A -=①，同理，在BCD △中，22222cos 222BD C +-=⨯⨯，即28cos 8BD C -=②，①-②cos 1A C -=，所以当BD cos A C -为定值，定值为1；法二：在ABD △中，由余弦定理2222cos BD AD AB AD AB A =+-⋅得222222cos BD A =+-⨯⨯，即216BD A =-，同理，在BCD △中，2222cos 88cos BD CD CB CD CB C C =+-⋅=-，所以1688cos A C -=-1cos A C -=cos 1A C -=，所以当BD cos A C -为定值，定值为1；（2）222222221211sin sin 44S S AB AD A BC CD C +=⋅⋅+⋅⋅ 222212sin 4sin 12sin 44cos A C A C =+=+-2212sin 41)A A =+--224cos 12A A =-++，令()cos ,1,1A t t =∈-，所以2224122414y t t ⎛=-++=-+ ⎝⎭，所以t =cos A = 2212S S +有最大值为14．16、（15分）（暑假作业原题）函数()e 4sin 2xf x x λλ=-+-的图象在0x =处的切线为3,y ax a a =--∈R .（1）求λ的值；（2）求()f x 在(0,)+∞上零点的个数. 解析【小问1详解】因为()e 4sin 2,()e 4cos x x f x x f x x λλλλ'=-+-=-，所以(0)4f λ'=-，所以切线斜率为4λ-，即4a λ=-，所切线方程为()41y x λλ=--+又(0)1f λ=-，所以切点坐标为(0,1)λ-，代入得则11λλ-=-+，解得1λ=.【小问2详解】由（1）得()e 4sin 1,()e 4cos x x f x x f x x '=--=-，令()()e 4cos xg x f x x ==-'，则()e 4sin xg x x =+'，当πx ≥时，()e 4cos 0x f x x '=->恒成立，所以()f x 在[)π,+∞上递增，所以ππ()(π)e 4sin 1e 50f x f x ≥=--≥->，因此()f x 在[π,)+∞无零点；当0πx <<时，()e 4sin 0xg x x '=+>恒成立，所以()f x '单调递增，又π(0)30,(π)e 40f f ''=-<=+>，所以()f x '在(0,π)上存在唯一的零点0x ，当()00,,()0,()∈<'x x f x f x 单调递减；当()0,π,()0,()x x f x f x '∈>单调递增；又()0(0)0,(0)0f f x f =<=，π(π)e 10f =->，因此()f x 在(0,π)上仅有1个零点；综上，()f x 在(0,)+∞上仅有1个零点.17、（15分）如图，四面体ABCD 中，,,AD CD AD CD ADB BDC ⊥=∠=∠，E 为AC 的中点．(1)证明：平面BED ⊥平面ACD ；(2)设2,60AB BD ACB ==∠=︒，点F 在BD 上，当AFC △的面积最小时，求CF 与平面ABD 所成的角的正弦值．【详解】（1）因为AD CD =，E 为AC 的中点，所以AC DE ⊥；在ABD △和CBD △中，因为,,B A C D CD ADB DB DB D ∠=∠==，所以ABD CBD ≌△△，所以AB CB =，又因为E 为AC 的中点，所以AC BE ⊥；又因为,DE BE ⊂平面BED ，DE BE E ⋂=，所以AC ⊥平面BED ，因为AC 平面ACD ，所以平面BED ⊥平面ACD .（2）连接EF ，由（1）知，AC ⊥平面BED ，因为EF ⊂平面BED ，所以AC EF ⊥，所以1=2AFC S AC EF ⋅△，当EF BD ⊥时，EF 最小，即AFC △的面积最小. 因为ABD CBD ≌△△，所以2CB AB ==，又因为60ACB ∠=︒，所以ABC 是等边三角形，因为E 为AC 的中点，所以1AE EC ==，BE =AD CD ⊥，所以112DE AC ==, 在DEB 中，222DE BE BD +=，所以BE DE ⊥.以E 为坐标原点建立如图所示的空间直角坐标系E xyz -，则()()()1,0,0,,0,0,1A B D ，所以()()1,0,1,AD AB =-=-，设平面ABD 的一个法向量为(),,n x y z = ，则0n AD x z n AB x ⎧⋅=-+=⎪⎨⋅=-=⎪⎩，取y =()n =，又因为()31,0,0,4C F ⎛⎫- ⎪ ⎪⎝⎭，所以34CF ⎛⎫= ⎪ ⎪⎝⎭ ，所以cos ,n CF n CF n CF⋅===，设CF 与平面ABD 所成的角的正弦值为02πθθ⎛⎫≤≤ ⎪⎝⎭，所以sin cos ,n CF θ==CF 与平面ABD(1)求C 的方程；(2)记双曲线C 的左右顶点分别为1A ，2A ，直线1A M ，2A N 的斜率分别为1k ，2k ，求12k k 的值. (3)探究圆E ：224410x y x y +---=上是否存在点S ，使得过S 作双曲线的两条切线1l ，2l 互相垂直.【答案】(1)22143x y -=； (2)13-； (3)存在.【详解】（1）由对称性知，双曲线C 过点(4,3)，则221691b a a b ⎧=⎪⎪⎨⎪-=⎪⎩，解得2a b =⎧⎪⎨=⎪⎩，所以双曲线C 的方程为22143x y -=. （2）由（1）得12(2,0),(2,0)A A -，设()()1122,,,M x y N x y ，显然直线MN 不垂直于y 轴，设直线MN 的方程为4x my =+，由2243412x my x y =+⎧⎨-=⎩消去x 得220(34)2436m y my -++=，显然22340,144(4)0m m -≠∆=+>，1212222436,3434m y y y y m m -+==--，则121223my y y y +=-，即()121232my y y y =-+，所以()()()()11212112212222222262y y x y my k x y k x y y my x -++===++-()()1211211221223221236362y y y my y y my y y y y y -+++===-+-++.（3）圆22:4410E x y x y +---=上存在点S ，使得过S 作双曲线的两条切线互相垂直. 若双曲线的两条切线有交点，则两条切线的斜率存在且不为0，设双曲线的两条切线分别为1122,y k x n y k x n =+=+，将y kx n =+代入22143x y -=消去y 得：22(3484120)k knx n ----=，由0'∆=得()()2222644344120k n k n +-+=，解得2243n k =-，因此2222112243,43n k n k =-=-，设两条切线的交点坐标为()00,x y ，则01010202y k x n y k x n -=⎧⎨-=⎩，即有()22010143y k x k -=-，且()22020243y k x k-=-，即()()2222220100100200204230,4230x k x y k y x k x y k y --++=--++=，于是12,k k 是方程()22200004230x k x y k y --++=的两根，而121k k =-，则2020314y x +=--，即22001x y +=，从而两条切线们交点的轨迹为圆221x y +=，而221x y +=的圆心为(0,0)O ，半径为1，圆222:(2)(2)3E x y -+-=的圆心(2,2)E ，半径为3，显然||OE ==，满足31||31OE -<<+，即圆O 与圆E 相交，所以圆22:4410E x y x y +---=上存在点S ，使得过S 作双曲线的两条切线互相垂直.19、（17分）对于数列{}n a ，如果存在等差数列{}n b 和等比数列{}n c ，使得()n n n a b c n *=+∈N ，则称数列{}n a 是“优分解”的．(1)证明：如果{}n a 是等差数列，则{}n a 是“优分解”的．(2)记()2*11ΔΔΔΔn n n n n n a a a a a a n ++=-=-∈N ，，证明：如果数列{}n a 是“优分解”的，则()2*Δ0n a n =∈N 或数列{}2Δn a 是等比数列．(3)设数列{}n a 的前n 项和为n S ，如果{}n a 和{}n S 都是“优分解”的，并且123346a a a ===，，，求{}n a 的通项公式．【答案】(1)证明见解析 (2)证明见解析 (3)122n n a -=+【详解】（1）{}n a 是等差数列，∴设()()111111n a a n d a n d ⎡⎤=+-=-+-+⎣⎦，令()111,1n n b a n d c =-+-=，则{}n b 是等差数列，{}n c 是等比数列，所以数列{}n a 是“优分解”的．（2）因为数列{}n a 是“优分解”的，设()*n n n a b c n =+∈N ，其中()()11111,0,0n n n b b n d c c q c q -=+-=≠≠，则()12121111Δ1,ΔΔΔ(1)n n n n n n n n a a a d c q q a a a c q q --++=-=+-=-=-．当1q =时，()2*Δ0n a n =∈N ；当1q ≠时，{}2Δn a 是首项为21(1)c q -，公比为q 的等比数列．（3）一方面，数列{}n S 是“优分解”的，设()*n n n S B C n =+∈N ，其中()()11111,0,0n n n B B n D C C Q C Q -=+-=≠≠，由（2）知2121Δ(1)n n S C Q Q -=-因为12122323Δ4,Δ6S S S a S S S a =-===-==，所以2121ΔΔΔ2S S S =-=．{}221(1)2,1,Δn C Q Q S ∴-=∴≠∴是首项为2，公比为()1Q Q ≠的等比数列．另一方面，因为{}n a 是“优分解”的，设()*n n n a b c n =+∈N ，其中()()11111,0,0n n n b b n d c c q c q -=+-=≠≠，()2111211Δ,ΔΔΔ1n n n n n n n n n n S S S a S S S a a d c q q +++++=-==-=-=+- {}2Δn S 是首项为2，公比为()1Q Q ≠的等比数列， 0,1q q ∴≠≠，且()()()2222213ΔΔΔS S S =⋅，()()()223111111d c q q d c q q d c q q ⎡⎤⎡⎤⎡⎤∴+-=+-⋅+-⎣⎦⎣⎦⎣⎦化简得()311111(1)0,0,0,1,0,Δ1n n n n c dq q c q q d a a a c q q -+-=≠≠≠∴=∴=-=- ，即数列{}Δn a 是首项121Δ1a a a =-=，公比为q 的等比数列．又232Δ2,2a a a q =-=∴= ，又()211Δ2,12,0,2,S d c q q d q =∴+-===∴ 解得11111,312c b a c =∴=-=-=，综上所述，()1111122n n n a b n d c q --=+-+=+．。

长沙市雅礼中学招生考试试卷

长沙市雅礼中学理科实验班招生试题数学一、选择题（共8小题，每小题5分，满分40分）1、下列四个图形中，每个小正方形都标上了颜色．若要求一个正方体两个相对面上的颜色都一样，那么不可能是这一个正方体的展开图的是（）A、B、C、D、2、某工厂第二季度的产值比第一季度的产值增长了x%，第三季度的产值又比第二季度的产值增长了x%，则第三季度的产值比第一季度的产值增长了（）A、2x%B、1+2x%C、（1+x%）x%D、（2+x%）x%3、甲从一个鱼摊上买了三条鱼，平均每条a元，又从另一个鱼摊上买了两条鱼，平均每条b元，后来他又以每条元的价格把鱼全部卖给了乙，结果发现赔了钱，原因是（）A、a＞bB、a＜bC、a=bD、与a和b的大小无关4、若D是△ABC的边AB上的一点，∠ADC=∠BCA，AC=6，DB=5，△ABC的面积是S，则△BCD的面积是（）A、B、C、D、5、（2007•玉溪）如图，AE⊥AB且AE=AB，BC⊥CD且BC=CD，请按照图中所标注的数据，计算图中实线所围成的图形的面积S是（）A、50B、62C、65D、686、如图，两个标有数字的轮子可以分别绕轮子的中心旋转，旋转停止时，每个轮子上方的箭头各指着轮子上的一个数字，若左图轮子上方的箭头指着的数字为a，右图轮子上方的箭头指的数字为b，数对（a，b）所有可能的个数为n，其中a+b恰为偶数的不同个数为m，则等于（）A、B、C、D、7、如图，甲、乙两动点分别从正方形ABCD的顶点A、C同时沿正方形的边开始移动，甲点依顺时针方向环行，乙点依逆时针方向环行，若乙的速度是甲的速度的4倍，则它们第2000次相遇在边（）A、AB上B、BC上C、CD上D、DA上8、已知实数a满足，那么a﹣20062的值是（）A、2005B、2006C、2007D、2008二、填空题（共8小题，每小题5分，满分40分）9、小明同学买了一包弹球，其中是绿色的，是黄色的，余下的是蓝色的．如果有12个蓝色的弹球，那么，他总共买了_________个弹球．10、已知点A（1，1）在平面直角坐标系中，在x轴上确定点P使△AOP为等腰三角形．则符合条件的点P共有_________个．11、不论m取任何实数，抛物线y=x2+2mx+m2+m﹣1的顶点都在一条直线上，则这条直线的函数解析式是_________．12、将红、白、黄三种小球，装入红、白、黄三个盒子中，每个盒子中装有相同颜色的小球．已知：（1）黄盒中的小球比黄球多；（2）红盒中的小球与白球不一样多；（3）白球比白盒中的球少．则红、白、黄三个盒子中装有小球的颜色依次是_________．13、在梯形ABCD中，AB∥CD，AC、BD相交于点O，若AC=5，BD=12，中位线长为，△AOB的面积为S1，△COD的面积为S2，则=_________．14、已知矩形A的边长分别为a和b，如果总有另一矩形B，使得矩形B与矩形A的周长之比与面积之比都等于k，则k的最小值为_________．15、已知x、y均为实数，且满足xy+x+y=17，x2y+xy2=66，则x4+x3y+x2y2+xy3+y4=_________．16、（2007•天水）如图，已知在⊙O中，直径MN=10，正方形ABCD的四个顶点分别在⊙O及半径OM、OP上，并且∠POM=45°，则AB的长为_________．三、解答题（共2小题，满分20分）17、甲、乙两班同时从学校A出发去距离学校75km的军营B军训，甲班学生步行速度为4km/h，乙班学生步行速度为5km/h，学校有一辆汽车，该车空车速度为40km/h，载人时的速度为20km/h，且这辆汽车一次恰好只能载一个班的学生，现在要求两个班的学生同时到达军营，问他们至少需要多少时间才能到达？18、如图，已知矩形ABCD，AD=2，DC=4，BN=2AM=2MN，P在CD上移动，AP与DM交于点E，PN交CM于点F，设四边形MEPF的面积为S，求S的最大值．答案与评分标准一、选择题（共8小题，每小题5分，满分40分）1、下列四个图形中，每个小正方形都标上了颜色．若要求一个正方体两个相对面上的颜色都一样，那么不可能是这一个正方体的展开图的是（）A、B、C、D、考点：几何体的展开图。

湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试英语试题

湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解4 Best Places to Travel in 20232023 is the year when travel returns in a big way. To get you started, we’ve rounded up some of the best places to travel in 2023. All you need to do is pick the place that appeals to you.CopenhagenWith its fantastic houses, clean streets and colorful architecture, Copenhagen is regarded as the most livable city on the earth. Named the World Capital of Architecture for 2023, Copenhagen will offer a series of major artistic events and programs sure to delight architects and design lovers.BhutanFor travelers with a sense of adventure and a love of discovery, Bhutan has always been a must-go destination. In 2023, travelers can once again explore the Trans Bhutan Trail, which runs 250 miles from east to west, offering visits to the century-old communities along the journey. The trail spans (横跨)18 major bridges and national parks and connects more than 400 historic and cultural sites.BordeauxThe coming years will be sporty in the historical wine region of Bordeaux in France. In 2023, the city will host the Rugby World Cup, an intense and stressful game. Beyond sports, Bordeaux is one of the favorite historical cities, with more than 350 structures that are either nationally or regionally listed as historical monuments.NamibiaWildlife and adventure lovers looking for a unique path in African Safari trips should head straight to Namibia in 2023 — this country in southern Africa is the perfect place to travel to reconnect with nature and escape the modern stresses of life. On the wildlife front, you may see lions along with giraffes and elephants.1．What is Copenhagen well-known for?A．The natural landscape.B．The adventure travel.C．Eye-catching architecture.D．Famous art designers.2．What can you visit on the Trans Bhutan Trail?A．Modern communities.B．Cultural relics.C．Historical wine regions.D．National monuments.3．Which place attracts those who want to be free from stressful city life?A．Copenhagen.B．Bhutan.C．Bordeaux.D．Namibia.Derek and Shirley walked out of the airport building and into the bright sunshine. Looking up at the brilliant blue sky and then at the faraway mountains rising above the swaying palm trees, they couldn’t wait to start their holiday.A taxi pulled up swiftly and silently. Derek dropped their suitcases into the boot and joined Shirley in the back seat. “Palm Trees Hotel, please,” Derek said excitedly. “Certainly, sir,” replied the driver, as he turned around with a flashing white smile. Derek and Shirley gave each other a puzzled look as the taxi eased smoothly into the traffic. “Excuse me, er, your face seems very familiar—in fact, you remind us of that famous film star, Rocky Overton... but of course, you can’t be.”Derek and Shirley sat in silent disbelief as the driver explained that he was not a real person, but a robot made to look like a famous actor. “Rocky” explained that the taxi company had purchased the latest model of robot drivers since they were programmed to be safer and more reliable than human drivers. “So, here I am,” “Rocky” continued, “your first robot taxi driver!”Derek and Shirley held each other’s hands more lightly. “Relax,” “Rocky” reassured them, “there is nothing for you to worry about. I can assure you that my driving skills are excellent. I’m equipped with perfect vision and superior reactions, and I know every street in the city. I am instantly updated with the latest traffic information so that I can avoid traffic jams and get you to your destination in the quickest and least stressful manner. Please sit back, relax and enjoy the journey.”Derek and Shirley, feeling a little better, leaned back in their seats and closed their eyes. “And another thing,” “Rocky” added, “my line of robots represents the ultimate (最高典范) in computer technology. I am beautifully designed, made from only the best materials and subject to the strictest quality checks. Therefore, you are entirely safe with me. Nothing could possibly go wrong... could possibly go wrong, wrong… go wrong…”4．Why did Derek and Shirley feel puzzled when they got into the taxi?A．Because the driver was a robot.B．Because the driver was Rocky Overton.C．Because the driver gave them a big smile.D．Because the driver looked like a famous actor.5．What do we know about the taxi driver “Rocky”?A．It has the perfect vision and superior reactions.B．It is the first robot taxi driver in the world.C．It is instantly updated with the latest news.D．It has never get stuck in traffic jams.6．What does the underlined word “reassured” in paragraph 4 probably mean?A．Threatened.B．Persuaded.C．Surprised.D．Comforted. 7．What can we infer from the last paragraph?A．Robot drivers are perfectly designed.B．Robot drivers are able to repeat the words.C．Robot drivers are not so reliable as expected.D．Robot drivers are not safer than human drivers.Cetaceans(鲸目动物) communicate through sound to find food and to interact socially. Their sounds vary between species and within communities. The long-finned pilot whales can mimic (模仿) artificial noise, but nobody had previously recorded them. A new study, however, found overlap in the cetacean sound book.Pilot whales and orcas(虎鲸)，the two largest species of cetaceans, are often seen in the same environments and are similar sizes, and both live in social groups with strong union, says Charlotte Cure, a researcher at CEREMA Lab in France, who was not involved in the study. Orcas compete for food with long-finned pilot whales and are potentially their predators.Evidence from orca stomachs shows they do occasionally eat pilot whales. But pilot whales can mob(成群田住) and chase them away, the only cetaceans seen defending themselves from the strong enemies in this way.Mimicry could serve as additional defense; “One assumption is that if they use similar sounds, they may not be recognized as prey," Erbe says. Pilot whales eating orcas' foodremains might go unnoticed if they use orca-like calls. “This is all underwater," she adds, “so these animals rely on sound for detecting their prey and predators.”Long-finned pilot whales have shown an ability to distinguish between orca calls with different meanings; Cure suggests that instead of tricking orcas, the callers could instead be presenting a new orca sound to other group members.Additional work would confirm whether mimicry is actually occurring. Researchers could pair their listening data with direct observations of the animals' interactions in the wild or perhaps even play orca sounds and watch the whales' reactions.But if a future experiment used predatory sounds, it would need to be done. very carefully.“A reaction to a predator can be very strong," Cure says.“In some protected areas, you are not allowed to do more than two predatory playbacks per year."8．Which of the following is NOT shared by the pilot whales and orcas?A．They communicate through sound.B．They often live in the same environments.C．They can defend themselves through mimicry.D．They always live together with other group members.9．What do we know from the fourth paragraph?A．The pilot whales mimic the sounds to detect their prey.B．The pilot whales only mimic one kind of the sounds of the orcas.C．The pilot whales can pretend to be orcas to share the food remains.D．The pilot whales can distinguish different meanings of orca calls to trick them. 10．How do the researchers confirm whether mimicry is actually occurring?A．By observing the whales from the distance.B．By mimicking the sounds in the experiment.C．By analyzing the data from the cetacean sound book.D．By listening or playing the sounds and watching the whales' reactions.11．Which can be a suitable title for the text?A．Pilot Whales: Copy Orca Calls B．How Orcas Mimic Pilot Whale Calls C．How Pilot Whales Defend Themselves D．Orcas and Pilot Whales: Predators and PreyNearly 10 million people worldwide live with Parkinson’s disease. While Parkinson’s isincurable, some of its worst symptoms can be relieved and controlled using medications. A major problem of getting effective treatment at the right time is identifying the disease soon enough, before patients experience the symptoms brought on by irreversible(不可逆转的)neuron loss.But scientists might have just the thing to change the situation. And it involves a nose. In a study published in the journal ACS Omega, researchers from China’s Zhejiang University created an “e-nose, ”a portable device that can detect body smells specific to Parkinson’s patients.It may come as a surprise to learn Parkinson’s patients have their own smells. But after a retired nurse in Scotland made headlines in 2015 for a heightened sense of smell that led to her own husband’s Parkinson’s diagnosis, scientists have been trying hard to create a device that could smell the disease before physical symptoms start to show.Over the years, scientists have found people with Parkinson’s tend to produce more sebum (皮脂)than the average person. This sebum mixes with other overproduced substances to produce certain, unique smells.To track down these smells, the Zhejiang University researchers swabbed(用拭子擦拭)the upper backs of 31 Parkinson’s patients and 32 healthy volunteers. Using machine-learning software, they were able to identify three smell compounds that healthy volunteers lacked. The researchers then tested the e-nose on sebum taken from 12 Parkinson’s patients and 12 healthy people. The device was found to be about 71 percent accurate in distinguishing healthy sebum from Parkinson’s sebum.These are encouraging findings, but before the e-nose is ready for clinical use, the team needs to test it on many more people to improve the accuracy of the models. They will also need to test whether factors like race affect the e-nose’s performance in any way. But for now, as the number of people living with Parkinson’s in the U. S. is expected to rise to 1.2 million by 2030, a nose might be the best option to detect this disease.12．What makes it difficult for Parkinson’s patients to get effective treatment?A．Its medications are in short supply.B．It involves irreversible neuron loss.C．Its early signs are not easy to notice.D．It’s not a curable disease medically.13．What did the Scottish nurse find?A．Her husband’s body gave off a strange smell.B．Her husband had a heightened sense of smell.C．A smell caused her husband to suffer from a disease.D．A smell could relieve her husband’s Parkinson’s symptoms.14．What will the researchers do concerning their invention?A．Put it into clinical use.B．Conduct a broader test.C．Create more lab models.D．Expand its market outside the U. S.15．What is the best title for the text?A．This e-nose can smell Parkinson’sB．Parkinson’s patients produce more sebumC．People living with Parkinson’s are on the riseD．Researchers have found treatment for Parkinson’s二、七选五How to Strengthen Your WillpowerResearchers find willpower is like a muscle—it may get tired from over use. So, if it acts like a muscle, can it also be strengthened? The answer is YES. 161. Ten minutes of reflectionReflection will give you the fater results. 17 Researchers show that after just 2—3 days of practicing thinking for 10 minutes, your brain will be able to focus better, you will have more energy, and you aill be less stressed.2. Work on your postureWork on your posture for a 2-week period. Every time you catch yourself slouching(懒散), correct it by sitting up straight. This simple practice can vastly improve your perseverance.3. Use your opposite handSelect a chunk(块) of the day to use your opposite hand. 18 And from personal experience, if you aim for more than an hour, you will unnecessarily tire out your willpower muscle.4. Correct your speechChange your natural speech. 19 Again, it takes willpower to consciously go against your instincts. It doesn’t matter how you correct your speech, as long as you change natural speech habits.To get started, select a chunk of the day to practice and choose the words you will change. Personally, I tried not using contractions during work hours and it worked very well.Above are some effective ways to strengthen your perseverance. Do not try to do all at once. 20 You should start small and gradually build up as your muscles get stronger.A．Training your willpower muscle is like training for a marathon.B．This even includes resisting the urge to say “hello” instead of “hey”.C．You will be more mentally strong.D．With the right practice willpower can be strengthened.E．It can make your brain focus and resist the urge to wander.F．Be more conscious of your automic decisions.G．It doesn’t need to be more than an hour in order to get results.三、完形填空This year, hundreds of people around the world are applying for a desired job to run Portcommunity. You’ve got to 32 , because you can’t get away from each other very easily. I really love that sort of 33 ,” she said. “And what you can achieve here is 34 . The total experience offers both a different 35 towards the world and a new viewpoint on your function on the planet. ”21．A．centre B．position C．aim D．unit 22．A．requirements B．characteristics C．virtues D．activities 23．A．persuades B．instructs C．encourages D．hires 24．A．exists B．transforms C．doubles D．develops 25．A．tastes B．talents C．roles D．backgrounds 26．A．temporary B．historic C．grand D．magical 27．A．in favor of B．in need of C．in possession of D．in charge of 28．A．paid B．sought-after C．hard-won D．respectable 29．A．annually B．weekly C．monthly D．daily 30．A．invited B．devoted C．related D．drawn 31．A．joy B．lesson C．effort D．shock 32．A．get along B．show off C．break through D．give in 33．A．loneliness B．eagerness C．looseness D．togetherness 34．A．consistent B．rewarding C．potential D．pure 35．A．entrance B．answer C．attitude D．introduction四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

湖南省长沙雅礼中学2024_2025学年高一语文上学期入学考试试题含解析

C.念鬼(念：叨念) 又间令吴广(间：暗地里)
D. 卒中往往语(往往：常常) 皆指目陈胜(目：看着)
8. 下面对《木兰诗》赏析有误的一项是( )
A. “东市买骏马……北市买长鞭。”通过东西南北的排比铺写，表现了木兰购买战马和用具的劳碌，渲染了战前的惊惶气氛。
B. “旦辞爷娘去……但闻燕山胡骑鸣啾啾。”表现了木兰的女儿心思和军情紧迫，使故事更具传奇色影。
4.下列句子中没有语病的一项是（）
A. 言行不一样的人，是一种极不好的习惯。
B. 生活的最重要部分不是去生活，就是对生活的思索。
C. 充溢功利色调的教化，只能培育出只有小聪慧而无大才智。
D. 一个连教化都得不到敬重的民族是很难矗立于世界民族之林的。
【改病句的实力。考生首先要了解病句的六大类型错误：语序不当、搭配不当、成分残缺、成分赘余、结构混乱、表意不明、不合逻辑。
A. 故事揭示了学习要举一反三的道理。
B. 故事告知我们，学习要知其然，更要知其所以然。
C. 关尹子要求列子从学射中自己去探究射中的道理。
D. 治理国家、为人处世和学习射箭的道理是一样的。
11. 请用“/”给【丙】文中的画线部分断句（限两处）.
非独射也为国与身亦皆知之。
12. 用现代汉语翻译下面的句子。
B. “今诚以吾众诈自称公子扶苏、项燕，为天下唱，宜多应者。”写出了陈胜对民心的深刻洞察。
C. “陈胜、吴广喜，念鬼，曰：‘此教我先威众耳。”表现了陈胜对天意的精确领悟和把握。
D. “旦日，卒中往往语，皆指目陈胜。”生动地表现了陈胜的谋略所产生的奇妙效果。
10. 下面对《列子学射》理解有误的一项是（）
A项，“凫水”中“凫”读为fú)，“愧作”中“作”读为zuò；

湖南省长沙市雅礼中学2025届高三上学期入学考试英语试题及答案

湖南省长沙市雅礼中学2024-2025 学年高三上学期入学考试第二部分阅读理解 (共两节，满分50 分)第一节 (共15 小题: 每小题2.5 分, 满分37.5 分)阅读下列短文，从每题所给的A、B 、C 和D四个选项中，选出最佳选项，并在答题纸上将该项涂黑。

AFour of the world’s greatest national parksKomodoLocation: IndonesiaArea: 1,733km²Home to the world’s largest lizard ( 蜥蜴), the Komodo dragon, Komodo National Park is made up of 29 islands in the centre of the Indonesian archipelago (群岛). The park’s three main islands of Komodo, Rinca and Padar make ideal destinations for divers, as the surrounding coral reefs support a vast amount of oceanic diversity. With over 1,000 species of fish, 260 species of coral, and countless sea animals, this is an ideal spot to swim with sharks, whales, dolphins and more.Namib-NaukluftLocation: NamibiaArea: 49,768km²In the world’s oldest desert, the landscape moves. The golden dunes (沙丘) shift as winds blow and seasons pass. Visitors come to explore the dunes and it can be a real adventure. Jump in a 4×4 or hike across the sands on foot for a multi-day trail and you’ll soon find yourself deep in the Namibian wilderness. You’ll need a permit and doctor's letter to take on the longer hikes, but one-day hikes give anyone a chance to see more of the Namib.TongariroLocation: New ZealandArea: 795km²As New Zealand’s oldest national park, Tongariro National Park is home to three active volcanoes. And here’s the Tongariro Alpine Crossing, a 19.4-kilometre hike that takes you across beautiful landscapes. This park also draws in skiers during the winter seasons. The biggest ski area, Whakapapa, covers 5.5km² and has 15 lifts in all.TeideLocation: Tenerife, SpainArea: 190km²This park is home to Mount Teide, the highest peak in Spain. With a height of 3,718 metres, Mount Teide is also the third largest volcanic structure on the planet. Besides, Teide National Park possesses unique plants. The most unusual among the 139 recorded species is red bugloss, which has become the symbol of the park.21. What can visitors do in Komodo National Park?A. Play with the Komodo dragon.B. Go diving on its 29 islands.C. Have an up-close encounter with ocean life.D. Hike across the biggest ski area Whakapapa.22. Which of the following parks is the biggest?A. Teide National Park.B. Komodo National Park.C. Tongariro National Park.D. Namib-Naukluft National Park.23. What do the last two parks have in common?A. Both are well-known for their volcanoes.B. Both own more than 100 plant species.C. Both are perfect choices for skiers.D. Both feature golden dunes.BLindsey Stallworth, a high school student from Alabama, is on her way to a promising career in paleontology (古生物学) due to an unexpected discovery on family property. For years, she had been collecting fossils on their land in Monroe County, unaware of significant scientific value. However, her teacher at the Alabama School of Math and Science, Dr. Andrew Gentry, a paleontologist himself, took an interest when she showed him her collection.“Upon examining the fossil shark teeth Lindsey presented, I quickly identified one and became eager to learn about its origin,” said Andrew.Lindsey guided her teacher through the rural area where she had unearthed various relics, including shark teeth. Before long, they encountered an especially significant find on the grounds: a large bone from a 34-million-year-old whale skeleton! This led the pair to launch the huge project of uncovering the rest of the bones. After two months of hard work, they’ve managed to find the animal’s skull (颅骨).“Assuming the entire skeleton is present, it may require several years for us to have the entire animal back in the lab,” Andrew explained.Lindsey secured a research scholarship to persist in her fossil-digging expeditions alongside her instructor. Her enthusiasm for the project was at an all-time high, though she had never imagined a childhood pastime would lead her down this road. “We would go out and pick up shark teeth and fossil shells, but we never knew anyone that could tell us anything about them,” she recalled.“ We just thought they were cool.”“The Research Fellows Program allows Lindsey to gain real-world experience in scientific research and even present that research at professional conferences,” Andrew said. “It’s a once-in-a-lifetime opportunity for a high school student to stand out when applying to college and maybe even discover a new career path.”24. Why was Andrew fascinated by Lindsey’s finds?A. He had a personal interest in geography.B. He recognized the significance of one fossil.C. He was hoping to be financially independent.D. He wanted to start a paleontology club at school.25. What inspired Andrew and Lindsey to start a fossil uncovering project?A. A primitive whale’s bone.B. Some fossil shells.C. An animal’s skull.D. Some shark teeth.26. Which of the following best describes Andrew and Lindsey’s project?A. Risky but interesting.B. Dangerous but rewarding.C. Demanding but motivating.D. Boring but groundbreaking.27. What is the last paragraph mainly about?A. The unexpected joy of discovering fossils.B. The additional benefits of applying to college.C. Lindsey’s potential to become a high school teacher.D. Lindsey’s unique opportunities for future development.CWhen driving, Clara-Marina Martinez makes a note of any unusual behaviour she sees on the road. She then feeds these into machine-learning algorithms (算法), a form of AI, which she is helping develop for Porsche Engineering.Those algorithms are intended to produce a system reliable enough for a car to drive itself. Such a fully autonomous car, known in the industry as Level 5, should be able to complete an entire journey without any intervention (介入) from the driver, and deal with all situations on the road. But this is proving hard to achieve, and many attempts to do so are being abandoned. Last year, for instance, Uber sold off its unit developing self- driving cars.Autonomous vehicles are said to be not just convenient but potentially safer. However, just as people take time to learn how to drive safely, so do machines. And machines are not quick learners. The RAND Corporation calculates that to develop a system 20% safer than a human driver, 100 self-driving cars would have to operate 24 hours a day, 365 days a year.Carmakers such as Porsche therefore speed up the development process using simulators (模拟器 ). These teach software about dangers rarely encountered in reality. Dr Martinez and her colleagues employ “game engines” to do this. These are used to create virtual worlds through which the software can drive. Objects in these virtual worlds are assigned their physical characteristics (ie, buildings are hard, people are soft) so that the sensors in vehicles respond in the appropriate way. Once the software has been trained, it is tested in real autonomous vehicles by re-creating those situations on a test track.How quickly all this will translate into reality remains to be seen. Both regulators and customers will need to overcome the doubt that a software driver really can be safer than a human being.From Porsche’s point of view, though, there is another question. Given that much of the reason owning a sports car is for owners to show off their driving skills, just how big a market will there be for a version where software takes those bragging (炫耀的) rights away?28. What does Clara-Marina Martinez intend to do?A. Market Porsche cars.B. Improve an AI technology.C. Learn to be a responsible driver.D. Enjoy riding in a self- driving car.29. What is the problem with self- driving cars?A. They learn as slowly as human beings.B. They have to be monitored by human drivers.C. They operate for a very short period of time.D. They need a long time to reach a certain safety level.30. What are Dr Martinez and her colleagues doing?A. Fixing sensors in autonomous vehicles.B. Re-creating road situations on a test track.C. Enabling software to identify road dangers.D. Separating the real world from the virtual world.31. What worries Porsche according to the last paragraph?A. The quality of self-driving cars.B. The future of the sports car market.C. The driving skills of human beings.D. The reliability of car software.DImagine this. You need an image of a balloon for a work presentation and turn to an AI text-to-image generator, like Midjourney or DALL-E, to create a suitable image. You enter the prompt (提示词) “red balloon against a blue sky”but the generator returns an image of an egg instead.What’s going on? The generator you’re using may have been “poisoned”.What does this mean? Text-to-image generators work by being trained on large datasets that include millions or billions of images. Some of the generators have been trained by indiscriminately (任意地) scraping online images, many of which may be under copyright. This has led to many copyright infringement ( 侵害) cases where artists have accused big tech companies of stealing and profiting from their work.This is also where the idea of “poison” comes in. Researchers who want to empower individual artists have recently created a tool named “Nightshade”to fight back against unauthorised image scraping. The tool works by slightly changing an image’s pixels (像素) in a way that confuses the computer vision system but leaves the image unchanged to ahuman’s eyes. If an organization then scrapes one of these images to train a future AI model, its data pool becomes “poisoned”.This can result in mistaken learning, which makes the generator return unintended results. As in our earlier example, a balloon might become an egg.The higher the number of “poisoned”images in the training data, the greater the impact. Because of how generative AI works, the damage from “poisoned”images also affects related prompt keywords. For example, if a “poisoned”image of a Picasso work is used in training data, prompt results for masterpieces from other artists can also be affected.Possibly, tools like Nightshade can be abused by some users to intentionally upload “poisoned”images in order to confuse AI generators. But the Nightshade’s developer hopes the tool will make big tech companies more respectful of copyright. It does challenge a common belief among computer scientists that data found online can be used for any purpose they see fit.Human rights activists, for example, have been concerned for some time about the indiscriminate use of machine vision in wider society. This concern is particularly serious concerning facial recognition. There is a clear connection between facial recognition cases and data poisoning, as both relate to larger questions around technological governance. It may be better to see data poisoning as an innovative solution to the denial of some fundamental human rights.32. What does the underlined word “scraping” in paragraph 2 probably mean?A. Facilitating.B. Polishing.C. Damaging.D. Collecting.33. According to the text, what may adding poisoned data lead to?A. Affecting the training of generative AI.B. Discriminating against great masterpieces.C. Causing users to forget the prompt key words.D. Increasing the accuracy of returned information.34. What can be inferred from the last two paragraphs?A. Computer scientists have learned to respect the copyright of most artists.B. Nightshade is being abused by human rights activists to recognize faces.C. Data poisoning is somehow justified to direct attention to human rights.D. The issue of technological governance has aroused the lawyers’ interest.35. Which of the following might be the best title of the passage?A. Data Poisoning: Restricting Innovation or Empowering ArtistsB. Data Poisoning: Risks and Rewards of Generative AI Data TrainingC. Data Poisoning: Addressing Facial Recognition Issues Among ArtistsD. Data Poisoning: Government Empowering Citizens to Protect Themselves第二节 (共5小题; 每小题2.5 分, 满分12.5 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。

湖南省长沙雅礼中学2024届招生全国统一考试·物理试题

湖南省长沙雅礼中学2024届招生全国统一考试·物理试题卷注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、单项选择题：本题共6小题，每小题4分，共24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，在0≤x ≤3a 的区域内存在与xOy 平面垂直的匀强磁场，磁感应强度大小为B 。

在t ＝0时刻，从原点O 发射一束等速率的相同的带电粒子，速度方向与y 轴正方向的夹角分布在0°～90°范围内。

其中，沿y 轴正方向发射的粒子在t ＝t 0时刻刚好从磁场右边界上P （3a ，3 a ）点离开磁场，不计粒子重力，下列说法正确的是（）A ．粒子在磁场中做圆周运动的半径为3aB ．粒子的发射速度大小为04a t π C ．带电粒子的比荷为043Bt π D ．带电粒子在磁场中运动的最长时间为2t 02、下列说法正确的是（）A ．牛顿第一定律并不是在任何情况下都适用的B ．根据F =ma 可知，物体的加速度方向一定与物体所受拉力F 的方向一致C ．绕地球飞行的宇航舱内物体处于漂浮状态是因为没有受到重力作用D ．人在地面上起跳加速上升过程中，地面对人的支持力大于人对地面的压力3、某行星为质量分布均匀的球体，半径为R ，质量为M 。

科研人员研究同一物体在该行星上的重力时，发现物体在“两极”处的重力为“赤道”上某处重力的1.1倍。

湖南省长沙市雅礼中学理实班自主招生考试数学试卷

故根据图形可知：满足阴影部分的不等式组为：．故选：D．
3．正实数a，b，c，d满足a+b+c+d＝1，设p ，则（）
A．p＞5B．p＝5
C．p＜5D．p与5的大小关系不确定
解析：∵a，b，c，d均为正数，且a+b+c+d＝1，
∴必有0＜a，b，c，d＜1
∵p ，
事实上我们在xOy坐标系中作出函数f（x）的图象，
由，得b＜﹣2a，所以2a+b＜0；
由a﹣b+c＜0得（a+c）2﹣b2＝（a+b+c）（a﹣b+c）＜0；
由a+b+c＞0得a+b＞﹣c＞0，因此（a+b）2﹣c2＞0，|b|＞|a|，b2﹣a2＞0．
综上所述，仅有（a+b）2﹣c2，b2﹣a2为正数．故选：A．
5．如图为某三岔路口交通环岛的简化模型，在某高峰时刻，单位时间进出路口A，B，C的机动车辆数如图所示．图中x1，x2，x3分别表示该时段单位时间通过路段AB，BC，CA的机动车辆数（假设单位时间内在上述路段中同一路段上驶入与驶出的车辆数相等），则有（）
A．x1＞x2＞x3B．x1＞x3＞x2C．x2＞x3＞x1D．x3＞x2＞x1
解析：依题意，有x1＝50+x3﹣55＝x3﹣5＝＞x1＜x3，
同理，x2＝30+x1﹣20＝x1+10＝＞x1＜x2，
同理，x3＝30+x2﹣35＝x2﹣5＝＞x3＜x2．故选：C．
6．已知不等式ax+3≥0的正整数解为1，2，3，则a的取值范围是﹣1≤a ．
解析：不等式ax+3≥0的解集为：
（1）a＞0时，x ，正整数解一定有无数个．故不满足条件．

湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试数学试题

湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试数学试题学校:___________姓名：___________班级：___________考号：___________四、解答题15．已知函数()()=+Î．ln,f x x a x a R （1）讨论函数()f x的单调性；(1)判断数列012,,是否具有性质P ，并说明理由；(2)设数列{}n a 具有性质P ，(12)i a i k =L ，，，是{}n a 中的任意一项，证明：k i a a -一定是{}n a 中的项；(3)若数列{}n a 具有性质P ，证明：当5k ³时，数列{}na 是等差数列．【分析】（1）先证明线面垂直，再证明面面垂直即可；（2）以O 为坐标原点，建立空间直角坐标系，再分别求出两平面的法向量，用向量的夹角公式计算即可.【详解】（1）因为底面ABCD 是平行四边形，且AC =BD ，所以底面ABCD 是矩形，所以有AB AD ^,又PD ⊥AB ，且=AD PD D Ç,,AD PD Ì平面P AD ,所以AB ^平面P AD ，又AB Ì平面P AB ，所以平面P AB ⊥平面P AD ；（2）取AD 的中点O ,因为PA PD =，可得PO AD ^,由（1）可得AB PO ^，而=AB AD A Ç，且AB AD Ì，平面ABCD ,所以PO ^平面ABCD .所以以O 为坐标原点，建立如图所示的空间直角坐标系.所以(0,0,3),(3,0,0),(3,3,0),(3,3,0),(3,0,0)P A B C D --.设(,,)M x y z ，由PD =3MD ．有(3,0,3)3(3,,)x y z --=----，可得2,0,1x y z =-==，所以(2,0,1)M -.当2i k ££，证得1k k i i a a a -+-=，当32i k ££-，得到1k k i i a a a ---=，由5k ³时，得到1(11)k k i i a a a i k ---=££-，两式相减得出()1111k k i i a a a a i k -+-=-££-，结合等差中项公式，即可求解.【详解】（1）解：数列0,1,2具有性质P .理由：根据有穷数列{}na 满足：1230k a a a a <<<×××<≤，且对任意的,(1)i j i j k £££，j i a a +或j i a a - 是数列{}n a 中的项，则称数列{}n a 具有性质P ，对于数列0,1,2中，若对任意的,(1)i j i j k £££，可得0j i a a -=或1或2，可得j i a a -一定是数列{}na 中的项，所以数列0,1,2具有性质P .（2）证明：由(1,2,,)i a i k =L 是数列{}na 中的任意一项，因为数列{}n a 具有性质P ，即j i a a +或j i a a - 是数列{}n a 中的项，令j k =，可得k i a a +或k i a a - 是数列{}na 中的项，又因为120k a a a £<<<L ，可得k i a a +一定不是数列{}n a 中的项，所以k i a a -一定是数列{}na 中的项.（3）解：由数列{}n a 具有性质P ，可得{}k k n a a a +Ï，所以{}k k n a a a -Î，则{}0na Î，且10a =，又由{}k i n a a a +Ï，所以{}k i na a a -Î，又由12210k k k k k k k k a a a a a a a a a a --=-<-<-<<-<-L ，①设2i k ££，因为120ka a a £<<<L可得12232110,,,,,k k k k k k k k k k a a a a a a a a a a a a a a ----=-=-=-=-=L ，当5k ³时，可得()111k k i i a a a i k -+-=££-，（*）②设32i k ££-，则112k i k k a a a a a --+>+=，所以{}1k i n a a a -+Ï，由111213320k k k k k k k a a a a a a a a a ------=-<-<<-<-=L ，又由12320k k a a a a --£<<<<L ，可得111122133133,,k k k k k k k k a a a a a a a a a a a a ---------=-=<-=-=L ，所以1(13)k k i i a a a i k ---=££-，因为5k ³，由以上可知：111k k a a a ---=且122k k a a a ---=，所以111k k a a a ---=且122k k a a a ---=，所以1(11)k k i i a a a i k ---=££-，（**）由（*）知，()111k k i i a a a i k -+-=££-两式相减，可得()1111k k i i a a a a i k -+-=-££-，所以当5k ³时，数列{}n a 为等差数列.。

精品解析：湖南省长沙市雅礼实验学校2023-2024学年九年级下学期入学考试物理试题(解析版)

2024年上学期九年级寒假作业纠错检测物理科目考生注意：本试卷共4道大题，24道小题，满分100分，时量60分钟一、选择题（每小题3分，共36分。

第1～10题为单选题，第11、12题为双选题，每小题有两个答案符合题意，选对但少选得2分，错选得0分。

）1. 下列古诗文中加点字段描述的现象，能够说明分子不停做无规则运动的是（）A. 大漠风尘日色昏，红旗半卷出辕门B. 零落成泥碾作尘，只有香如故C. 流水落花春也去，天上人间D. 城阙辅三秦，风烟望五津【答案】B【解析】【详解】A．大漠风尘中的尘是可见的，所以是物体的机械运动，故A不符合题意；B．“香如故”是扩散现象，是花香分子运动的结果，故B符合题意；C．流水落花，描述的是水的流动，花瓣落下，是物体的机械运动，故C不符合题意；D．风烟望五津中的烟是可见的，不是分子的运动，不能说明分子不停做无规则运动，故D不符合题意。

故选B。

2. 如图所示，是不用火不插电，只用一杯冷水就可以加热食物的发热包．将发热包放到水中，会放出大量的热，从而加热食物，下列说法正确的是（）A. 发热包将温度传递给盒中的水B. 食物温度升高的过程伴随着内能的转移C. 被加热的食物吸收热量后自身所含热量增大D. 当加热包和水的温度相同时，它们的内能一定相等【答案】B【解析】【详解】A．发热包将热量传递给盒中的水，故A错误；B．食物温度升高的过程伴随着内能的转移，故B正确；C．热量是过程量，不能说所含热量，故C错误；D．内能与物体的温度、质量、状态等有关，只知道温度高低，不能判断内能的大小，故D错误。

故选B。

3. 自然界中的能量有多种，它们之间的转化也是非常普遍的，下列有关说法正确的是（）A. 电风扇工作，机械能主要转化为电能B. 冬天在室外，我们搓手取暖，将机械能转化为内能C. 水轮机带动发电机发电，是将电能转化为机械能D. 西红柿电池，是将电能转化为化学能【答案】B【解析】【详解】A．电风扇工作，消耗电能，使风扇转动，电能主要转化为机械能，故A错误；B．冬天在室外，我们搓手取暖，通过做功的方式使手的内能增大，温度升高，将机械能转化为内能，故B正确；C．水轮机带动发电机发电，消耗机械能，获得电能，是将机械能转化为电能，故C错误；D．西红柿电池可以提供电能，是将化学能转化为电能，故D错误。

湖南省长沙市雅礼中学2024-2025学年高三上学期入学考试地理试题及答案

雅礼中学2025届高三上学期入学考试试卷地理时量:75分钟分值:100分第Ⅰ卷(选择题)一、单选题(每小题只有一个正确答案，每题3分，共16题，48分)下图为“埃及地图”，其中①②③图均表示同一区域，且其图幅依次减少3/4。

读图，完成下面小题。

1.若①图比例尺为1:N,则②图、③图的比例尺依次为()A.2:N1:2NB.1:2N2:NC.2:N4:ND.1:2N1:4N2.一架飞机走最短航线从开罗飞往杭州(120°E，30°N)，其飞行方向应该是()A.一直向正东方B.先向正北方，后向正南方C.先向东北方，后向东南方D.先向东南方，后向东北方图甲为某地等高线示意图(单位：m)，MN和PQ为两条剖面线，图乙、图丙为沿剖面线的地形剖面图(单位：m)，读图完成下面小题。

3.据图判断，下列说法正确的是()A.图乙为图甲中剖面线MN的剖面图B.C在图甲中剖面线PQ上C.B和D即图甲中的O点D.站在C点看不到A点4.若该地位于一个拟建水库的库区内，当最高蓄水位达海拔150米时，图甲范围内将出现()A.一个岛B.两个岛C.三个岛D.无岛下左图为位于太行山南段东麓某地，该地山势险峻，易发山洪。

为适应当地地理环境，该地形成了西北—东南向的“山—耕—田—村——水”空间格局(下右图)，体现了当地居民的生存智慧。

据此完成下面小题。

5.下列要素与该地易发山洪的关联度最低的是()A.坡面朝向B.坡度大小C.年降水总量D.降水集中度6.关于该地早期a、b、c、d四处民居，说法正确的是()A.a处位于缓坡向阳，距河流近B.b处的地势最平坦，利于劳作C.c处位于河流上游，交通不便D.d处地势高峻崎岖，有利农业7.“宅高田低”是村落的常见格局，而该地“田高宅低”，此处布局农田的主要目的()①获得林区落叶肥田②避开河流洪水③拦截坡面径流④提高水资源利用效率A.①②B.①③C.②④D.③④苋菜，茎叶可作为蔬菜食用，叶色丰富，主要供观赏。