长沙市雅礼中学招生试题整理
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
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
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。
最新雅礼中学理科实验班招生考试试题(英语)
长沙市雅礼中学理科实验班招生试题英语考生注意：本卷满分120分，考试时间90分钟，请将答案写在答题卡上。
一、单项选择（每题1分，共计20分）1.His father possesses a________factory，which does most of the pollution to this river.A.paper-makeB.paper-makingC.papers-madeD.paper-made2. The letter “b” in the word “doubt” is________.A.soundB.silentC.silenceD.sounded3.—I knocked into a tree when I went to the railway station for my friend.---I suppose you _____too fast.A. driveB.are drivingC.droveD.were driving4. ---What should I do, doctor?---_____healthy, you should take more exercise.A.KeepB.KeepingC.To keepD.Having kept5. ---Have you found the information about famous people____you can use for the report?---Not yet.I’ll search some on the Internet.A.whichB.whoC.whatD.whom6. ---Oh.Mary’s not here these days.Is she ill?---_____.Her mother told me that she was in hospital.A.I am afraid soB.I hope notC.I don’t mindD.I don’t think so7.---It looks like a television.Do you think so?---Yes,I________.A.understandB.knowC.meanD.agree8.---I don’t know how to use this machine.---It doesn’t matter. Here is the ________.A.instructionB.directionrmationD.advertisement9. He _______ go to sleep _______ his father came back.A. won’t; unlessB. doesn’t; untilC. didn’t; untilD. didn’t; when10. She can solve the problem, _______ is often the case.A. ItB. AsC.That D. Which11. --- Did you enjoy yourself at the party?--- Yes. I've never been to ________ one before.A. a more excitedB. the most excitedC. a moreexciting D. the most exciting12. The telephone _______ four times in the last hour, and each time it _____ for the student doing a part-time job.A. has rung; wasB. has been ringing; isC. rang; had beenD. had rung; was13. –They’re really nice. I’ll ________ these two.-Anything else?-N o, that’s all. __________?A. buy; How much is itB. get; How much does it costC. take; How much do they come toD. want; How much is that altogether14. –Do you know _______?-They moved here soon after their son was born.A. when would the Smiths move hereB. when the Smiths moved hereC. the Smiths would move hereD. when the Smiths would move here15. –What does Tom often do at school?-He often plays _______ football after _______ school?A. /;/B. /; theC. the;/D. a; a16. —What do you think of store shopping in the future?—Personally, I think it will exist along with home shopping but ______.A. will never replace B .would never replaceC .will never be replacedD .would never be replaced17. Please call my secretary to arrange a meeting this afternoon, or _____ it is convenient to you.A .wheneverB .howeverC .whicheverD .where ver18. Not until ______, ______ settle the problem.A. he returns; can weB. he returns; we canC .does he returns; we can D. does he can; we can19. I’ll go to the library as soon as I finish what I _____.A. was doing B .am doing C .have done D. had been doing20. English is a language shared by several diverse cultures, each of _____ uses it somewhat differently.A .whichB .what C. them D .those二、完形填空（每题1分，共计20分）A Happy Memory to Lift You UpI hear some actors keep sad memories to help them with scenes where they might need to cry. I think we should each try to find the opposite to 21 us up every day. I’m saying this because I just 22 mine!I had some work in Glasgow today. I was on such a 23 schedule that I had no time for myself all day.Walking across the square, I fished(取出) some 24 from my pocket. There was __25__ someone at the exit selling The Big Issue, a magazine helping homeless folk 26 a living.At the exit, I saw 27 selling The Big Issue. Her clothes were 28 and she obviously hadn’t had a bath for quite a while.As I 29 , I saw she was also rocking from side to side. At first I thought maybe she was trying to keep 30 against the biting wind. But she wasn’t. She was movin g in time to a tune. I couldn’t 31 her, but I could see her lips 32 .As I got closer, I saw a white cane (拐杖) hanging from her elbow (肘) and noticed she had sunken (凹陷的) 33 . She was blind, dirty and living on the 34 . I came closer and through the 35 of the traffic and the crowd I heard her 36 the immortal (永恒的) line, “... and I think to myself, what a wonderful world!”I bought her 37 magazine for twice what I’d originally intended. She 38 me, then she picked up her stuff and went tapping off along the pavement — 39 singing!So, I have my happy 40 for the day. And I think it will stay with me a long long time. Feel free to borrow it if you like.21. A. build B. give C. pick D. lift22. A. explained B. found C. invented D. described23. A. tight B. perfect C. free D. short24. A. tickets B. keys C. change D. paper25. A. barely B. sometime C. never D. usually26. A. understand B. earn C. offer D. complete27. A. someone B. anyone C. everyone D. no one28. A. well-known B. sold C. ragged D. packed20. A. stayed B. approached C. disappeared D. escaped30. A. fearless B. calm C. still D. warm31. A. see B. admire C. hear D. trust32. A. moving B. closing C. changing D. falling33. A. ears B. eyes C. mouth D. nose34. A. roofs B. stages C. streets D. trains35. A. cost B. bottom C. window D. noise36. A. writing B. singing C. recording D. retelling37. A. last B. next C. only D. extra38. A. served B. recognized C. thanked D. considered39. A. yet B. thus C. also D. still40. A. memory B. childhood C. adventure D. birthday三、阅读理解（41—53小题每题2分，54—62小题每题3分，共计50分）【A】阅读下面的短文，请根据短文内容从每题中所给的A、B、C、D四个选项中选出最佳答案。
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 --=+-+=+．。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
WORD格式整理版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。
分析：利用正方体及其表面展开图的特点解题．解答：解：选项C中红色面和绿色面都是相邻的，故不可能是一个正方体两个相对面上的颜色都一样，故选C．点评：注意正方体的空间图形，从相对面入手，分析及解答问题．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%考点：一元二次方程的应用。
专题：增长率问题。
分析：设第一季度产值为1，第二季度比第一季度增长了x%，则第二季度的产值为1×（1+x%），那么第三季度的产值是由第二季度产值增长了x%来确定，则其产值为1×（1+x%）×（1+x%），化简即可．解答：解：第三季度的产值比第一季度的增长了（1+x%）×（1+x%）﹣1=（2+x%）x%．故选D．点评：本题考查一元二次方程的应用，关键在于理清第一季度和第二季度的产值增长关系．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的大小无关考点：一元一次不等式的应用。
分析：本题考查一元一次不等式组的应用，将现实生活中的事件与数学思想联系起来，读懂题列出不等式关系式即可求解．解答：解：利润=总售价﹣总成本=×5﹣（3a+2b）=0.5b﹣0.5a，赔钱了说明利润＜0∴0.5b﹣0.5a＜0，∴a＞b故选A点评：解决本题的关键是读懂题意，找到符合题意的不等关系式．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、考点：相似三角形的判定与性质。
分析：先根据相似三角形的判定定理求出△ACD∽△ABC，再根据相似三角形的面积比等于相似比的平方解答．解答：解：∵∠ADC=∠BCA，∠A是公共角，∴∠ABC=∠ACD，∴△ACD∽△ABC，∴AC：AD=AB：AC，∵AB=AD+BD=AD+5，∴AD（AD+5）=36，解得AD=4或﹣9，负值舍去，∴AD=4，△ABC的面积是S，△ACD的面积就是S，△BCD=S．故选C．点评：本题的关键是求得△ACD∽△ABC，根据相似比和已知的条件求得AD的值，然后利用面积比等于相似比的平方求值．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、68考点：全等三角形的判定与性质。
分析：由AE⊥AB，EF⊥FH，BG⊥AG，可以得到∠EAF=∠ABG，而AE=AB，∠EFA=∠AGB，由此可以证明△EFA≌△ABG，所以AF=BG，AG=EF；同理证得△BGC≌△DHC，GC=DH，CH=BG．故FH=FA+AG+GC+CH=3+6+4+3=16，然后利用面积的割补法和面积公式即可求出图形的面积．解答：解：∵AE⊥AB且AE=AB，EF⊥FH，BG⊥FH⇒∠EAB=∠EFA=∠BGA=90°，∠EAF+∠BAG=90°，∠ABG+∠BAG=90°⇒∠EAF=∠ABG，∴AE=AB，∠EFA=∠AGB，∠EAF=∠ABG⇒△EFA≌△ABG∴AF=BG，AG=EF．同理证得△BGC≌△DHC得GC=DH，CH=BG．故FH=FA+AG+GC+CH=3+6+4+3=16故S=（6+4）×16﹣3×4﹣6×3=50．故选A．点评：本题考查的是全等三角形的判定的相关知识．作辅助线是本题的关键．6、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、考点：列表法与树状图法。
分析：先用树状图展示所有可能的结果，共有12种等可能结果数，然后找出和为偶数的个数，这样可得到的值．解答：解：列树状图：∴数对（a，b）所有可能的个数为n=12，其中a+b恰为偶数的不同个数为m=5，∴=，故选C．点评：本题考查了利用树状图展示所有等可能的结果的方法．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上考点：正方形的性质。
专题：动点型；规律型。
分析：因为乙的速度是甲的速度的4倍，所以第1次相遇，甲走了正方形周长的×=；从第2次相遇起，每次甲走了正方形周长的，从第2次相遇起，5次一个循环，从而不难求得它们第2000次相遇位置．解答：解：根据题意分析可得：乙的速度是甲的速度的4倍，故第1次相遇，甲走了正方形周长的×=；从第2次相遇起，每次甲走了正方形周长的，从第2次相遇起，5次一个循环．因此可得：从第2次相遇起，每次相遇的位置依次是：DC，点C，CB，BA，AD；依次循环．故它们第2000次相遇位置与第五次相同，在边AB上．故选A．点评：本题是一道找规律的题目，对于找规律的题目首先应找出哪些部分发生了变化，是按照什么规律变化的．8、已知实数a满足，那么a﹣20062的值是（）A、2005B、2006C、2007D、2008考点：非负数的性质：算术平方根；非负数的性质：绝对值。
专题：计算题。
分析：根据负数没有平方根，得到a﹣2007大于等于0，然后根据a的范围化简绝对值，移项后两边平方即可求出所求式子的值．解答：解：由题意可知：a﹣2007≥0，解得：a≥2007，则|2006﹣a|+=a，化为：a﹣2006+=a，即=2006，两边平方得：a﹣2007=20062，解得：a﹣20062=2007．故选C点评：本题考查平方根的定义，化简绝对值的方法，是一道基础题．学生做题时注意负数没有平方根．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96 个弹球．考点：一元一次方程的应用。