深圳外国语学校高一新生入学摸底试卷

2023-2024学年广东省深圳市高一下学期开学摸底考试英语试题第一部分听力（共两节，满分15分）第一节（共4小题；每小题1分，满分4分）听下面4段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一个小题。

每段对话仅读一遍。

1. What will the man do on Friday morning?A. Give a lecture.B. Go on a business trip.C. Attend a parents’ meeting.2. What caused the woman to come home late?A. Attending an interview.B. Seeing a doctor.C. Visiting Peter.3. Where will the speakers go?A. To the woman’s house.B. To the man’s company.C. To a restaurant.4. What are the speakers talking about?A. William’s travel experiences.B. The woman’s views on travelling.C. The importance of making travel plans.第二节（共11小题；每小题1分，满分11分）听下面5段对话或独白。

每段对话或独白后有几个小题，从所听到的内容中获取信息，回答相应小题。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第5段材料，回答第5、6题。

5. When did Jack begin reading?A. At 4:40.B. At 5:00.C. At 5:30.6. What does the woman want Jack to do?A. Relax his eyes.B. Read more books.C. Go shopping with her.听第6段材料，回答第7至9题。

深外高中园2022—2023学年度高一第一学期学段（二）考试英语试卷本试卷分选择题和非选择题两部分，共10页，满分为150分。

考试用时120分钟。

注意事项：1、答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名和学号填写在答题卡密封线内相应的位置上， 用2B铅笔将自己的学号填涂在答题卡上。

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

3、非选择题必须用黑色字迹的钢笔或签字笔在答题卡上作答，答案必须写在答卷纸各题目指定区域内的相 应位置上，超出指定区域的答案无效；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅 笔和涂改液。

不按以上要求作答的答案无效。

4、考生必须保持答题卡的整洁和平整。

第一部分听力（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷 的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What do we learn from the conversation?A.The man hates to lend his tools to other people.B.The man lost those tools.C.The man hasn’t finished working on the bookshelf.2.What are the two speakers talking about?A. A trip.B. A park.C. A cinema.3.What does the man mean?A.He would like to make an appointment for the woman.B.He thinks it worthwhile to try Santerbale’s.C.He knows a less expensive place for a haircut.4.What do we learn from this conversation?A The man wants to go to Los AngelesB The man wants to go to San Francisco.C There are no flights to Los Angeles for the rest of the day.5.What is the woman’s opinion of the research paper?A. Only a few changes should be made in it.B. It’s fine as it is.C. Major revisions are needed in it.第二节（共15小题：每小题1分，满分15分）听下面5段对话或独白。

广东省深圳外国语学校2023-2024 学年高一下学期开学检测考试英语试题学校:___________姓名：___________班级：___________考号：___________ 一、单项选择1．With her attention ________ on the book, the girl sat there quietly. A．to be fixed B．fix C．fixed D．fixing2．________to achieving a big, seemingly impossible goal reconnects us to a burning passion.A．Being committed B．Committed C．Committing D．To commit 3．The Chinese tech giant has launched its new operating system, ______an alternative app ecosystem to Google’s Android. A．creating B．to create C．having created D．creates4．The shop owner will get all these goods ordered ___________ to the customers today.A．to deliver B．delivering C．deliver D．delivered5．The girl is so proud that she can’t stand ___________ down upon. A．looking B．to look C．to be looked D．being looked 6．When he saw the mists rising from the river and the soft clouds the mountain tops, he was reduced to tears.A．being surrounded B．surrounded C．surrounding D．to surround 7．In the Chinese market, many foreign brands, ________ their reputations over decades, are facing new challenges due toCOVID-19.A．being developed B．developingC．having developed D．developed8．________ to think critically is an important skill today’s children will need for the future.A．Learn B．LearnedC．Learning D．Having learned9．When ______ different cultures, we often pay attention only to the differences without noticing many similarities.A．being compared B．comparingC．Compared D．having been compared10．（2015·江苏）Much time ________sitting at a desk, office workers are generally troubled by health problems.A．being spent B．having spentC．spent D．spending11．_________in Avebury, England, the monument is so large that it can only be seen from the sky.A．Located B．Locating C．Being located D．To locate 12．When Tom got home he saw a note on the table _______that don’t be discouraged, everything will turn out well soon. A．reading B．reads C．to read D．read13．_____ and caught the mouse.A．Up the cat jumped B．The cat up jumpedC．Up jumped the cat D．Jumped up the cat14．You say he works hard. ______ , and ______.A．So he does; so you do B．So he does; so do youC．So does he; so do you D．So does he; so you do15．So absorbed ________ the work that she often forgot to ________ her meals.A．had she been in; do B．she was in; makeC．was she in; take D．she had been in; have16．Hardly ________ his homework when he went out. A．finished he B．he had finished C．did he finish D．had he finished 17．It was not until near the end of the letter ________ she mentioned her own plan.A．that B．whereC．why D．when18．Was it in 1969 _____ the American astronaut succeeded ____ landing on the moonA．when; on B．that; on C．when; in D．that; in19．The computer was used in teaching. As a result, not only _____, but students became more interested in the lessons.A．sav ed was teachers’ energyB．was teachers’ energy savedC．teachers’ energy was savedD．was saved teachers’ energy20．________ who was wounded in the stomach.A．Among them were a soldier B．Among them was a soldier C．Among them a soldier was D．Among they was a soldier二、阅读理解There are many podcasts(播客)that teach English and you can listen to them anytime. Here is a list of some of the best podcasts that you must see.Learn English PodcastThis podcast has three levels. The first is for beginners, the second is for intermediates(中级学生)and the third is for upper intermediates. If a person wants to learn Business English, then episodes are also made for him. Every podcast is short but very informative. Worksheets(活页练习题)and vocabulary tasks are also included.Speaking BroadlyThis podcast is made for advanced learners. Explained through discussion and interviews, each episode has non-native English speakers and every recording also has expert feedback. You will see some common mistakes made by English learners and you can improve your English by learning from those mistakes.The English We SpeakThis podcast airs one episode daily and every episode is only three to four minutes, which talks about phrases and idioms. There are two people in each episode who communicate with each other. Whatever level you are, you will find it rewarding.Elementary PodcastThis podcast is mainly for beginners and intermediate level learners. The length of a podcast is around 25 minutes but you can pause it anytime and continue whenever you want. The hosts of each episode are different.21．Which podcast provides exercises going with it A．Speaking Broadly. B．Elementary Podcast.C．The English We Speak. D．Learn English Podcast.22．What do we know about Speaking BroadlyA．It records just expert speakers. B．It targets beginners.C．It presents some typical mistakes. D．It provides feedback from listeners.23．What do The English We Speak and Elementary Podcast have in commonA．They are both interactive. B．They cater for beginners. C．They have the same length. D．They share the same contents.I work with Volunteers for Wildlife, a rescue and educationorganization at Bailey Arboretum in Locust Valley. Trying to help injured, displaced or sick creatures can be heartbreaking; survival is never certain. However, when it works, it is simply beautiful.I got a rescue call from a woman in Muttontown. She had found a young owl(猫头鹰) on the ground. When I arrived, I saw a 2-to 3-week-old owl. It had already been placed in a carrier for safety.I examined the chick(雏鸟) and it seemed fine. If I could locate the nest, I might have been able to put it back, but no luck. My next work was to construct a nest and anchor it in a tree.The homeowner was very helpful. A wire basket was found. I put some pine branches into the basket to make this nest safe and comfortable. I placed the chick in the nest, and it quickly calmed down.Now all that was needed were the parents, but they were absent. I gave the homeowner a recording of the hunger screams of owl chicks. These advertise the presence of chicks to adults; they might also encourage our chick to start calling as well. I gave the owner as much information as possible and headed home to see what news the night might bring.A nervous night to be sure, but sometimes the spirits of nature smile on us all! The homeowner called to say that the parents had responded to the recordings. I drove over and saw the chick in thenest looking healthy and active. And it was accompanied in the nest by the greatest sight of all — LUNCH! The parents had done their duty and would probably continue to do so.24．What is unavoidable in the author’s rescue work according to paragraph 1A．Efforts made in vain.B．Getting injured in his work.C．Feeling uncertain about his future.D．Creatures forced out of their homes.25．Why was the author called to MuttontownA．To rescue a woman.B．To take care of a woman.C．To look at a baby owl.D．To cure a young owl.26．What made the chick calm downA．A new nest.B．Some food.C．A recording.D．Its parents.27．How would the author feel about the outcome of the event A．It’s unexpected.B．It’s beautiful.C．It’s humorous.D．It’s discouraging.You are given many opportunities in life to choose to be a victim or creator. When you choose to be a victim, the world is a cold and difficult place. “They” did things to you which caused all of your pain and suffering. “They” are wrong and bad, and life is terrible as long as “they” are around. Or you may blame yourself for all your problems, thus internalizing (内化) your victimization. The truth is, your life is likely to stay that way as long as you feel a need to blame yourself or others.Those who choose to be creators look at life quite differently. They know there are individuals who might like to control their lives, but they don’t let this get in the way. They know they have their weaknesses, yet they don’t blame themselves when they fail. Whatever happens, they have choice in the matter. They believe their dance with each sacred (神圣的) moment of life is a gift and that storms are a natural part of life which can bring the rain needed for emotional and spiritual growth.Victims and creators live in the same physical world and deal with many of the same physical realities, yet their experience of life is worlds apart. Victims relish (沉溺) in anger, guilt, and other emotions that cause others- -and even themselves--to feel likevictims, too. Creators consciously choose love, inspiration, and other qualities which inspire not only themselves, but all around them. Both victims and creators always have choice to determine the direction of their lives.In reality, all of us play the victim or the creator at various points in our lives. One person, on losing a job or a special relationship, may feel as if it is the end of the world and sink into terrible suffering for months, years, or even a lifetime. Another with the same experience may choose to first experience the grief, then accept the loss and soon move on to be a powerful creative force in his life.In every moment and every circumstance, you can choose to have filler, richer life by setting a clear intention to transform the victim within, and by inviting into your life the powerful creator that you are.28．What does the word “They” in paragraph 1 probably refer to A．People and things around you. B．Opportunities and problems. C．Creators and their choices. D．Victims and their sufferings. 29．According to Paragraph 2, creators ________.A．seem willing to experience failures in life B．possess the ability to predict future lifeC．handle ups and downs of life wisely D．have potential to createsomething new30．The examples mentioned in Paragraph 4 show that ________. A．different reactions to sufferings lead to different life paths. B．people need family support to deal with challengers in life. C．it takes creators quite a long time to get rid of their pains. D．one’s experiences determine his attitude toward life. 31．What is the author’s purpose in writing this passageA．To define victims and creators.B．To evaluate victims against creators.C．To explain the relationship between victims and creators. D．To suggest the transformation from victims to creators.Why do some men settle down to form families with the mothers of their children, and others don’t Biology plays a role. Work published by Lee Gettler of the University of Notre Dame, in Indiana, clarifies how testosterone, the principal male hormone (荷尔蒙), operates.Previous studies suggest that high levels of testosterone are bad for family life. Fathers with lower testosterone levels provide more child care while high-testosterone males are less likely to stick around. Dr. Gettler has shown something further. This is that a man’s adult testosterone level seems correlated with whether his father was present during his teenage years.His data come from a survey begun in the Philippines in 1983. This monitored the health and nutrition of 966 men enrolled as babies. It also collected extensive information on whether the fathers of these men were around and providing parental care in the households. It further documented whether participants got married, had children and whether they participated in child care. Crucially, it also measured their testosterone levels at the ages of 21, 26 and 30.Overall, Dr. Gettler and his colleagues found that on becoming fathers, men had lower testosterone levels if their own fathers had been involved in their care during their teenage years. It has two possible explanations. One is that it is directly genetic (基因的). The other is that teenage experience actually modulates (调节) testosterone levels. This explanation, which Dr. Gettler favors, could lead to high-testosterone men abandoning their sons, who thus become high-testosterone in their turn.He also found some of those in the survey whose fathers were absent during their adolescence, and who ended up with high levels of the hormone, did become caring fathers. Why this pattern should exist is an unanswered question. But a zoologist looking at these data might take it as an example of developmental plasticity (可塑性), in which the same genes produce different, butappropriate, outcomes in different circumstances.Dr. Gettler’s discovery throws a useful light on the problem of fatherless families,and how to try to end it.32．What is Gettler’s study mainly aboutA．Family life. B．Fathers’ roles.C．Adult testosterone. D．Child care.33．What can be learnt about Dr. Gettler’s studyA．It was conducted among babies.B．The finding is far from satisfactory.C．The data used were relatively reliable.D．It monitored the nutrition of participants.34．Why is the zoologist mentioned in the passageA．To suggest a follow-up study.B．To contradict Gettler’s ideas.C．To point out the study limitations.D．To give a possible explanation.35．Which of the following is a suitable title for the textA．Like Father, Like SonB．Caring Father, Happy SonC．Good Father, Good SonD．Love Me, Love My SonTechnology is here to stay. 36 . However, they are often unsure onhow to help children use technology responsibly and keep a balance between online and offline time. Here are some tips. Have a device contractHaving a device usage contract allows parents and children to work through what responsible technology usage looks like in your family and ensure that everyone is aware. 37 . Kids are more likely to make sense of the reasons you have for restriction.38Although this tip seems like common sense, it is often difficult due to the demand of work and the expectation of being constantly connected. By ensuring you build offline time into your own day and communicate that with your children, they will see the value and benefits. Whether you are reading a book or just taking a walk, letting your children be aware of your offline actions will encourage them to do the same!Encourage non-tech activitiesOne great way to keep kids off their screens is to ensure that they have other activities to fill their time. 39 . These activities are also great ways to help children to develop their social skills and confidence.Tech-free family timeOnce a week, pencil-in a “tech-free family time” in your schedule. Itcan be a meal or trip. To help increase the success of outings, try designing special activities, i. e., going to the beach to build a sand castle that looks the same as a photo you have found online. 40 A．Model good technology useB．Communicate with childrenC．A little extra planning goes a long wayD．The contract is helpful to the settlement of conflicts E．Parents are seeing more technology in their homes and jobs F．Also, drafting the contract together promotes understanding G．This can come in a variety of forms: soccer, fencing and more 三、完形填空My first caregiving experience involved driving 180 miles every day to see my grandmother who was terminally ill. I was certainly 41 as the weeks turned into months, but the desire to 42 my grandmother in her last days was overwhelming (无法抗拒的). Years later, my 87-year-old father required more 43 skills than I could provide. As he lived 700 miles away from me, I deeply 44 that I couldn’t take care of him myself, but I though t my nightly phone calls, filled with laughter and family news, provided him with 45 support.Then, 46 , because of cancer, I became the one who needed 47 . Friends provided meals, house cleaning, and rides to appointments.The gratitude I felt for these acts of 48 was beyond words. It was also because of their thoughtfulness that I could focus all my energy on healing (治愈) my body and mind.Soon afterwards, in trying to find a meaningful purpose, I 49 the idea of offering assistance to other caregivers. I was 50 with both sides of the struggle, and this 51 me to pay it forward for the incredible amount of support I had received.A(n) 52 arose when a caregiver I knew for years was unable to travel to her winter home in Florida. While recovering from surgery, she was 53 to drive. When she asked me to be the driver, I didn’t 54 , so we headed south on an adventure.Now, due to the pandemic, I have to suspend the program, but I look forward to 55 my journey of caring for caregivers soon. I welcome the chance to lift the burden off their shoulders, even if it’s for just a minute.41．A．relieved B．delighted C．frustrated D．exhausted 42．A．rescue B．comfort C．please D．protect 43．A．communication B．survival C．nursing D．working 44．A．regretted B．assumed C．feared D．appreciated 45．A．professional B．physical C．financial D．emotional 46．A．unfortunately B．gradually C．eventually D．surprisingly 47．A．encouragement B．attention C．care D．guidance48．A．bravery B．modesty C．honesty D．kindness 49．A．reflected on B．came upon C．went over D．focused on 50．A．faced B．occupied C．acquainted D．associated 51．A．allowed B．required C．advised D．forced 52．A．problem B．crisis C．opportunity D．emergency 53．A．forbidden B．expected C．supposed D．determined 54．A．respond B．hesitate C．struggle D．compromise 55．A．extending B．planning C．finishing D．continuing四、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。

深圳外国语学校2024届高三第一次月考试题数学本试卷分选择题和非选择题两部分，共4页，满分150分，考试用时120分钟。

注意事项：1．答题前，考生务必用黑色字迹的钢笔或签字笔将自己的姓名、班级、座位号等相关信息填写在答题卷指定区域内。

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

3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卷各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液.不按以上要求作答的答案无效。

4．考生必须保持答题卷的整洁第一部分选择题(共60分)一、单选题(本题共8小题，每小题5分，共40分．每小题给出的四个选项中，只有一个选项是符合题目要求的)1.已知全集U =R ，集合A ={x x ≥4或x ≤0}，B ={x x >4或x ≤-2}，则图中阴影部分表示的集合为()A ．-2,0B ．-2,0C ．-2,0 ∪4D ．-2,0 ∪42.若复数z 所对应的点在第四象限，且满足z 2-2z +2=0，则z 2=()A.1+iB.1-iC.-2iD.2i3.已知a ⋅b =-24，a +2b =(-5,2)，若a 与b 模相等，则a =( ).A.3B.4C.5D.64.探照灯反射镜的纵断面是抛物线的一部分，光源放在焦点F 处．已知灯口直径为60cm ，光源距灯口的深度为40cm ，则光源到反射镜的顶点的距离为A.5cmB.10cmC.15cmD.20cm5.设函数f x =a -1 x x -b +1 为奇函数且在R 上为减函数，则关于a ,b 的值表述正确的是()A.a >1,b =1B.a >1,b <1C.a <1,b =1D.a <1,b >16.定义函数迭代：f 0x =x f 1 x =f x f 2 x =f f x ⋯f n +1x =f fnx已知f x =3x +2，则f nx =()A.3n x +3n -1B.3n x +3n +1C.3nx +3n -1D.3n x -3n +17.如图，F 1､F 2是双曲线C ：x 2a 2-y 2b2=1a >0,b >0 的左､右焦点，过F 2的直线与双曲线C 交于A ､B 两点.若A 是BF 2中点且BF 1⊥BF 2则该双曲线的渐近线方程为()A.y =±23xB.y =±22xC.y =±3xD.y =±2x8.若∃m ∈R ，对于∀x ∈a ,b 恒有2m 2-22sin x +π4 ⋅m +sin2x ≤0，则b -a 的最大值是()A.3π4B.πC.4π3D.2π二、多选题(本题共4小题，每小题5分，共20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5分，部分选对的得2分，有选错的得0分)9.已知函数f (x )和g (x )分别为奇函数和偶函数，且f (x )+g (x )=2x ，则()A.f (x )-g (x )=2-xB.f (x )在定义域(-∞,+∞)上单调递增C.f (x )的导函数f (x )≥1D.g (x )≥110.给出下列说法，其中正确的是()A.数据0，1，2，4的极差与中位数之积为6B.已知一组数据x 1,x 2,⋯,x n 的方差是5，则数据4x 1-1,4x 2-1,⋯,4x n -1的方差是20C.已知一组数据x 1,x 2,⋯,x n 的方差为0，则此组数据的众数唯一D.已知一组不完全相同的数据x 1,x 2,⋯,x n 的平均数为x 0，在这组数据中加入一个数x 0后得到一组新数据x 0,x 1,x 2,⋯,x n ，其平均数为x ，则x=x 011.已知函数f x 定义域为R ，f x +1 是奇函数，g x =1-x f x ，函数g x 在1,+∞ 上递增，则下列命题为真命题的是()A.f -x -1 =-f x +1B.函数g x 在-∞,1 上递减C.若a <2-b <1，则g 1 <g b <g aD.若g a >g a +1 ，则a <1212.如图AD 与BC 分别为圆台上下底面直径，AD ⎳BC ，若AB =3，AD =2，BC =4，则()A.圆台的母线与底面所成的角的正切值为22B.圆台的全面积为14πC.圆台的外接球(上下底面圆周都在球面上)的半径为2D.从点A 经过圆台的表面到点C 的最短距离为33第二部分非选择题(90分)三、填空题(本题共4小题，每小题5分，共20分)13.钥匙掉了，掉在宿舍里､掉在教室里､掉在路上的概率分别是50%、30%和20%，而掉在上述三处被找到的概率分别是0.8、0.3和0.1，则找到钥匙的概率为.14.已知圆柱体的底面半径为32cm ，高为5πcm ，一只蜗牛从圆柱体底部开始爬行，绕圆柱体4圈到达顶部，则蜗牛爬行的最短路径长为．15.测量地震级别的里氏是地震强度(即地震释放的能量)的常用对数值．显然级别越高，地震的强度也越高，如日本1923年地震是8.9级，旧金山1906年地震是8.3级，问日本1923年地震强度是8.3级的倍．(lg2≈0.3)16.已知椭圆E 的中心为O ，E 上存在两点A ，B ，满足△OAB 是以半焦距为边长的正三角形，则E 的离心率为.四、解答题(本题共6小题，共70分，其中17题10分，其余各题12分.解答应写出文字说明、证明过程或演算步骤)17.已知数列a n 满足a 1=1，a n +13a n =1+1n ．(1)求数列a n 的通项公式；(2)求数列a n 的前n 项和S n ．18.如图，多面体ABCDEF 中，四边形ABCD 为矩形，二面角A -CD -F 的大小为45°，DE ⎳CF ，CD ⊥DE ，AD =2，DC =3.(1)求证：BF ⎳平面ADE ；(2)求直线AC 与平面CDEF 所成角的正弦值.19.已知抛物线C 的焦点F 到准线l 的距离为2.(1)求抛物线的标准方程；(2)过焦点F 的直线(斜率存在且不为0)交抛物线C 于A ,B 两点，线段AB 的中垂线交抛物线的对称轴于点P ，求FPAB.20.如图，某景区绿化规划中，有一块等腰直角三角形空地ABC ，∠BAC =π2，BC =30m ，Q 为BC 上一点，满足BQ =2CQ .现欲在边界AB ，AC (不包括端点)上分别选取M ，N 两点，并在四边形AMQN 区域内种植花卉，且∠MQN =π2，设∠NQC =θ.(1)证明：QMQN =2；(2)tan θ为何值时，花卉种植的面积占整个空地面积的一半？21.高尔顿板又称豆机、梅花机等，是英国生物统计学家高尔顿设计用来研究随机现象的模型．如图所示的高尔顿板为一块木板自上而下钉着6层圆柱形小木块，最顶层有2个小木块，以下各层小木块的个数依次递增，各层小木块互相平行但相互错开，小木块之间留有适当的空隙作为通道，前面挡有一块透明玻璃．让小球从高尔顿板上方的通道口落下，小球在下落过程中与层层小木块碰撞，且等可能向左或者向右滚下，最后落入高尔顿板下方从左至右编号为1，2，⋯，6的球槽内．(1)某商店将该高尔顿板改良成游戏机，针对某商品推出促销活动．凡是入店购买该商品一件，就可以获得一次游戏机会．若小球落入X 号球槽，该商品可立减Y 元，其中Y =20-5X ．若该商品的成本价是10元，从期望的角度考虑，为保证该商品总体能盈利，求该商品的最低定价．(结果取整数)(2)将79个小球依次从高尔顿板上方的通道口落下，试问3号球槽中落入多少个小球的概率最大？附：设随机变量ξ~B (n ,p )，则ξ的分布列为P (ξ=k )=C k n p k (1-p )n -k ，k =0,1,2,⋯,n ．P (ξ=k )P (ξ=k -1)=C k n p k(1-p )n -k C k -1n p k -1(1-p )n -k +1=1+(n +1)p -kk (1-p )．22.设函数f x =-x ln x+ax2+x a∈R.(1)若函数f x 有两个不同的极值点，求实数a的取值范围；(2)若a=1，k∈N*，g x =x2+2x，当x>2时，不等式2k x-2+f x <g x 恒成立，试求正整数k的最大值.深圳外国语学校2024届高三入学测试数学试卷参考答案选择题：共12小题，每小题5分，满分60分题号123456789101112答案DCCACAABBDACDBCDABD1.D【详解】因为A ={x x ≥4或x ≤0}，B ={x x >4或x ≤-2}，所以A ∪B ={x x ≥4或x ≤0}∪{x x >4或x ≤-2}={x x ≥4或x ≤0}，A ∩B ={x x ≥4或x ≤0}∩{x x >4或x ≤-2}={x x >4或x ≤-2}.由题意可知阴影部分对于的集合为∁U A ∩B ∩A ∪B ，所以∁U A ∩B ={x -2<x ≤4 ，∁U A ∩B ∩A ∪B ={x -2<x ≤0或x =4}.故选：D .2.C【详解】因为复数z 满足：z 2-2z +2=0，即(z -1)2=-1，故z =1+i 或z =1-i ，因为复数z 所对应的点在第四象限，故复数z =1-i ，所以z 2=-2i. 故选:C .3.C故a +2b 2=a 2+4b 2+4a ⋅b =29，而又已知a ⋅b =-24，且a =b ，所以a 2+4a 2-96=29，解得a =5.故选：C4.A【详解】以抛物线的顶点为坐标原点建立平面直角坐标系如下图所示，设F p2,0，则抛物线上一点的坐标为p 2+40,30，代入抛物线方程y 2=2px p >0 得302=2p p 2+40 ，解得p =10,p 2=5，所以光源到反射镜的顶点的距离为5cm.故选：A5.C【详解】因为函数f x =a -1 x x -b +1 为R 上的奇函数，且递减，所以a -1≠0且f -1 =-f 1 ，即-a -1 -b =-a -1 2-b ，所以-b =2-b ，解得b =1，经检验符合题意，故f x =a -1 x x =a -1 x2,x ≥0-a -1 x 2,x <0因为函数f x =a -1 x x 在R 上为减函数，所以a -1<0，所以a <1.故选：C .6.A【详解】对于∀x 0∈R ，设a n =f nx 0 n ∈N ∗，则a 1=f 1x 0 =f x 0 =3x 0+2，且a n +1=3a n +2，所以a n +1+1=3a n +3=3a n +1 ，所以a n +1 是以3x 0+3为首项，公比为3的等比数列.a n +1=f nx 0 +1=3x 0+3 3n -1=3n x 0+3n ，即f nx 0 =3n x 0+3n -1.所以f nx =3n x +3n -1，故选：A .7.A【详解】设AB =AF 2 =m ,AF 1 =AF 2 +2a =m +2a ,BF 1 =BF 2 -2a =2m -2a ，BF 12+BA 2=AF 1 2,BF 1 2+BF 2 2=F 1F 2 2,2m -2a 2+m 2=m +2a 2①，2m -2a 2+4m 2=4c 2②,由①可得m =3a ,代入②式化简得：13a 2=c 2,∴12a 2=b 2,∴ba=23,所以双曲线的渐近线方程为y =±bax =±23x .故选：A8.B【详解】由2m 2-22sin x +π4⋅m +sin2x ≤0，得m 2-sin x +cos x ⋅m +sin x ⋅cos x ≤0，即m -sin x m -cos x ≤0,由几何意义可知，函数y =m 的图像在函数y =sin x ，y =cos x 的图像之间，如下图所示，-22≤m ≤22，要使b -a 达到最大，仅需要m =-22或m =22，此时b -a =π4--3π4=π.故选：B .9.BD【详解】由f (x )+g (x )=2x 得f (-x )+g (-x )=2-x ，由于函数f (x )和g (x )分别为奇函数和偶函数，所以-f (x )+g (x )=2-x，因此f x =2x -2-x 2,g x =2x +2-x 2，对于A , f (x )-g (x )=-2-x ,故A 错误，对于B ，由于函数y =2x 在(-∞,+∞)单调递增，y =2-x在(-∞,+∞)单调递减，所以f x =2x -2-x 2在(-∞,+∞)单调递增，故B 正确，对于C ，fx =2x ln2+2-x ln22=2x +2-xln22≥22x ×2-x ln22=ln2,当且仅当x =0时取等号，而ln2<1，所以C 错误，对于D ，g x =2x +2-x 2≥22x ×2-x2=1，当且仅当x =0时取等号，所以D 正确，故选：BD 10.ACD【详解】对于A ，极差为4-0=4，中位数为1+22=32，所以极差与中位数之积为4×32=6，A 对；对于B ，根据方差的性质可知，数据4x 1-1,4x 2-1,⋯,4x n -1的方差是42×5=80，B 错；对于C ，由方差s 2=1n x 1-x 2+x 2-x 2+⋯x n -x 2 =0，可得x 1=x 2=⋯=x n =x，即此组数据众数唯一，C 对；对于D ，∵x 1+x 2+⋯+x n n =x 0,∴x 1+x 2+⋯+x n =nx 0，∴x 0+x 1+x 2+⋯+x n n +1=x 0+nx 0n +1=x 0，D 对.故选：ACD11.BCD【详解】对于A ，因为f x +1 是奇函数，所以f -x +1 =-f x +1 ，故A 错误；因为f x +1 是奇函数，所以y =f x 的图象关于点1,0 对称，即有f x =-f 2-x ，所以g 2-x =1-2-x f 2-x =x -1 f 2-x =(1-x )f (x )=g x ，所以y =g x 的图象关于直线x =1对称，函数g x 在x ∈1,+∞ 上单调递增，所以g x 在x ∈-∞,1 上单调递减，故B 正确；因为a <2-b <1，所以g 1 <g 2-b <g a ，即g 1 <g b <g a ，故C 正确；因为g a >g a +1 ，且a <a +1，由函数y =g x 的图象关于直线x =1对称，得a +a +12<1，解得a <12，故C 正确.故选：BCD .12.ABD【详解】取圆台的轴截面ABCD ，设AD 、BC 的中点分别为O 1、O 2，连接O 1O 2，分别过点A 、D 在平面ABCD 内作AE ⊥BC ，DF ⊥BC ，垂足分别为点E 、F ，由题意可知，O 1O 2与圆台的底面垂直，易知四边形ABCD 为等腰梯形，且AB =CD =3，AD =2，BC =4，在△ABE 和△DCF 中，AB =DC ，∠ABE =∠DCF ，∠AEB =∠DFC =90°，所以，△ABE ≌△DCF ，所以，BE =CF ，因为AD ⎳BC ，AE ⊥BC ，DF ⊥BC ，则四边形ADFE 为矩形，且EF =CD =2，同理可证四边形AEO 2O 1为矩形，则O 1O 2=AE ，且AE ⎳O 1O 2，所以，AE 与圆台的底面垂直，则圆台的母线与底面所成的角为∠ABE ，所以，BE =CF =AB -EF 2=4-22=1，则AE =AB 2-BE 2=32-1=22，所以，tan ∠ABE =AEBE=22，A 对；对于B 选项，圆台的全面积为π×12+π×22+π×1+2 ×3=14π，B 对；对于C 选项，易知圆台的外接球球心在梯形ABCD 内，且CE =BC -BE =4-1=3，由勾股定理可得AC =AE 2+CE 2=8+9=17，且sin ∠ABE =AE AB=223，所以，圆台的外接球直径为2R =AC sin ∠ABE =17223=3344，则R =3348，B 错；对于C 选项，将圆台沿着轴截面ABCD 切开，将圆台的侧面的一半展开如下图所示：延长BA 、DC 交于点M ，在圆台的轴截面等腰梯形ABCD 中，AB ⎳CD 且AB =12CD ，易知A 、D 分别为BM 、CM 的中点，所以，AM =DM =AB =3，设∠AMD =θ，则AD =3θ=π，则θ=π3，在△ACM 中，AM =3，CM =6，∠AMD =π3，由余弦定理可得AC =AM 2+CM 2-2AM ⋅CM cos π332+62-2×3×6×12=33，因此，从点A 经过圆台的表面到点C 的最短距离为33，D 对.故选：ABD .三、填空题：共4小题，每小题5分，满分20分．13.0.5114. 13π(cm )15. 416. 3-1或6313.0.51【详解】记事件A 1为“钥匙掉在宿舍里”，A 2为“钥匙掉在教室里”，A 3为“钥匙掉在宿舍里”，事件B 为“找到钥匙”，由全概率公式得P (B )=P (A 1)P B A 1 +P (A 2)P B A 2 +P (A 3)P B A 3 =0.5×0.8+0.3×0.3+0.2×0.1=0.5114.13π(cm )【详解】根据题意，从圆柱底部M 点绕圆柱体的侧面旋转4圈到达顶部的N 点，沿MN 将侧面展开后，最短路程，如图所示，其中矩形的高等于圆柱的高5πcm ，矩形的宽等于圆柱的底面圆的周长的4倍，即4×2π×32=12πcm ，所以蜗牛爬行的最短路径为MN =(5π)2+(12π)2=13π(cm ).故答案为：13π(cm ).15.4【详解】设地震强度为x ，则地震级别为f (x )=lg x ，由题意可令lg x =8.9,lg t =8.3，则lg x -lg t =8.9-8.3=0.6，由于lg2≈0.3，故lg x -lg t =2lg2=lg4,∴lg x t =lg4,xt=4，即日本1923年地震强度是8.3级的4倍，故答案为：416.3-1或63【详解】不妨设椭圆方程为x 2a 2+y 2b2=1(a >b >0)，因为△OAB 是以半焦距为边长的正三角形，根据椭圆的对称性，可知AB 平行于x 轴或AB 平行于y 轴；当AB 平行于x 轴时，A ,B 关于y 轴对称，不妨设点A 在第一象限，所以∠AOx =60°，OA =c ，所以A c 2,3c 2 ，所以c 24a 2+3c 24b2=1，即c 2(a 2-c 2)+3a 2c 2=4a 2(a 2-c 2)，所以c 4-8a 2c 2+4a 4=0，即e 4-8e 2+4=0，解得e 2=4-23或e 2=4+23(因为0<e <1，故舍去)，所以e =3-1；当AB 平行于y 轴时，A ,B 关于x 轴对称，所以∠AOx =30°，OA =c ，不妨设点A 在第一象限，所以A 3c 2,c 2 ，所以3c 24a 2+c 24b2=1，即3c 2(a 2-c 2)+a 2c 2=4a 2(a 2-c 2)，即3c 4-8a 2c 2+4a 4=0，所以3e 4-8e 2+4=0，而0<e <1，解得e 2=23或e 2=2(舍去)，故e =63，所以椭圆的离心率为3-1或63，故答案为：3-1或63四．解答题(共6小题)17.【详解】(1)由a n +13a n =1+1n ，得a n +1n +1=3×a n n，------------2分又a 11=1，∴a n n 是以1为首项，3为公比的等比数列，------3分∴an n=3n -1，a n =n ×3n -1，即数列a n 的通项公式为a n =n ×3n -1.------5分(2)由(1)知，a n =n ×3n -1，则S n =1×30+2×31+⋅⋅⋅+n ×3n -11--------------6分1×3得3S n =1×31+2×32+⋅⋅⋅+n ×3n 2-----------7分1-2得-2S n =1+31+32+⋅⋅⋅+3n -1-n ×3n --------------8分=1-3n 1-3-n ×3n =3n -12-n ×3n ------------------------9分故S n =2n -1 ×3n+14．---------------10分18.【详解】(1)证明：因为四边形ABCD 是矩形，所以，BC ⎳AD ，因为BC ⊂平面BCF ，AD ⊄平面BCF ，所以AD ⎳平面BCF ， --------------------2分因为DE ⎳CF ，CF ⊂平面BCF ，DE ⊄平面BCF ，所以DE ⎳平面BCF ， ----------4分因为AD ∩DE =D ，AD 、DE ⊂平面ADE ，则平面BCF ⎳平面ADE ，---------------5分因为BF ⊂平面BCF ，所以，BF ⎳平面ADE .------------------------------6分(2)解：因为CD ⊥AD ，CD ⊥DE ，所以，二面角A -CD -F 的平面角为∠ADE ，----------7分由题意可得∠ADE =45°，又因为AD ∩DE =D ，AD 、DE ⊂平面ADE ，所以，CD ⊥平面ADE ，过点A 在平面ADE 内作AO ⊥DE ，垂足为点O ，因为AO ⊂平面ADE ，所以CD ⊥AO ，-----------------8分又因为CD ∩DE =D ，CD 、DE ⊂平面CDEF ，所以AO ⊥平面CDEF ，连接CO ，所以直线AC 与平面CDEF 所成角为∠ACO ， -----9分因为CD ⊥AD ，AD =2，DC =3，则AC =AD 2+DC 2=22+32=13，因为AO ⊥DE ，则AO =AD sin ∠ADE =2×22=2，-----------------11分所以sin ∠ACO =AO AC =213=2613.直线AC 与平面CDEF 所成角的正弦值为2613-------12分19.【详解】(1)因为抛物线C 的焦点F 到准线l 的距离为2，所以p =2，----------2分根据建系方案的不同，抛物线的标准方程有四种可能，分别是y 2=4x ，y 2=-4x ，x 2=4y ，x 2=-4y .------------------4分(2)在平面直角坐标系中，抛物线的位置并不影响FP AB的取值，因此不妨取抛物线的方程为y 2=4x ，此时焦点F 1,0 ，根据题意，直线AB 的斜率存在且不为0，因此设直线AB 的方程为x =my +1，---5分与抛物线y 2=4x 联立，得关于y 的一元二次方程y 2-4my -4=0，-----------6分则Δ=16m 2+16>0，设A x 1,y 1 、B x 2,y 2 ，则y 1+y 2=4m ，y 1y 2=-4，y 1-y 2 =16m 2+16，-----------7分x 1+x 2=m y 1+y 2 +2=4m 2+2，-----------------------8分则AB =1+m 2y 1-y 2 =41+m 2 ，--------------------9分线段AB 的中点坐标为2m 2+1,2m ，中垂线方程为y -2m =-m x -2m 2-1 ，令y =0，解得x =3+2m 2，即中垂线与x 轴交于P 3+2m 2,0 ，---------10分所以FP =2+2m 2，------------------------11分则FP AB=12.-------------------------------12分20.【详解】(1)由题意得BQ =20m ，QC =10m ，∠B =∠C =π4，∵∠MQN =π2，∠BAC =π2，四边形内角和等于2π，所以∠AMQ +∠ANQ =π，又∠AMQ +∠BMQ =π,∠ANQ +∠CNQ =π，--------------------1分∴∠CNQ +∠BMQ =π，sin ∠CNQ =sin ∠BMQ ，-------------------------2分在△BMQ 中，由正弦定理得MQ sin B =BQ sin ∠BMQ，-------------------------3分在△CQN 中，由正弦定理得NQ sin C =CQ sin ∠CNQ，--------------------4分∴MQ NQ =BQ QC=2，证毕；-------------------------5分(2)由题意得AB =AC =152m ，故S △ABC =12AB ⋅AC =225m 2，-----------6分∵∠MQN =π2，∠NQC =θ，∴∠BQM =π2-θ，∴∠C =π4，∴∠QNC =3π4-θ，-------------7分设QN =xm ，则QM =2xm ，在△CQN 中，由正弦定理得NQ sin C =CQ sin ∠CNQ，即x sin π4=10sin 3π4-θ ，解得x =10sin π4sin 3π4-θ =52sin 3π4-θ ①，-------8分由三角形面积公式得S △CNQ =12CQ ⋅QN sin ∠CQN =5x sin θ，S △BMQ =12BQ ⋅QM sin ∠BQM =20x sin π2-θ =20x cos θ，--------------------9分故S △CNQ +S △BMQ =5x sin θ+20x cos θ=12S △ABC =2252，∴x =452sin θ+4cos θ②，--------10分由①②得52sin 3π4-θ =452sin θ+4cos θ ，化简得sin θ+4cos θsin θ+cos θ=92，-----------11分分子分母同除以cos θ得tan θ+4tan θ+1=92，解得tan θ=-17---------12分21.【详解】(1)X 的取值可能为1，2，3，4，5，6．--------1分P (X =1)=P (X =6)=12 5=132，P (X =2)=P (X =5)=C 15×12×12 4=532，P (X =3)=P (X =4)=C 25×12 2×12 3=516．------------------2分因为Y =|20-5X |，所以Y 的取值可能为0，5，10，15．P (Y =0)=P (X =4)=516，P (Y =5)=P (X =3)+P (X =5)=1532，P (Y =10)=P (X =2)+P (X =6)=316，P (Y =15)=P (X =1)=132．----------3分Y 的分布列为Y051015P 5161532316132E (Y )=0×516+5×1532+10×316+15×132=7516≈4.7，----------------------4分则顾客玩一次游戏，立减金额的均值约为4.7元，又该商品成本价是10元，所以该商品的最低定价约为15元．----------------------------5分(2)由(1)得P (X =3)=516．进行79次试验，设小球落入3号球槽的个数为ξ，则ξ~B 79,516．----------6分P (ξ=k )P (ξ=k -1)=1+(79+1)×516-k k 1-516 =1+25-k 11k 16．------8分当k <25时，P (ξ=k )P (ξ=k -1)>1，即P (ξ=k )>P (ξ=k -1)；------------9分当k =25时，P (ξ=k )P (ξ=k -1)=1，即P (ξ=k )=P (ξ=k -1)；-----------10分当k >25时，P (ξ=k )P (ξ=k -1)<1，即P (ξ=k )<P (ξ=k -1)．------------------11分所以当k =25时，P (ξ=25)=P (ξ=24)，此时这两项概率均为最大值．故3号球槽中落入24或25个小球的概率最大．--------------------------12分22.【详解】(1)由题意可知，f x 的定义域为0,+∞ ，f x =-ln x +2ax .令f x =0，可得2a =ln x x ，-------------1分令ℎx =ln x x x >0 ，ℎ x =1-ln x x2，令ℎ x =0得x =e ，----------2分当0<x <e 时，ℎ x >0，当x >e 时，ℎ x <0，可知ℎx 在0,e 上单调递增，在e ,+∞ 上单调递减，--------3分所以ℎx max =ℎe =1e，又当0<x <1时，ℎx <0，当x >1时，ℎx >0，根据以上信息，作出ℎx 的大致图象，-----------4分则由题意可知y =2a 与函数ℎx 的图象有两个不同的交点，∴2a ∈0,1e ，∴a ∈0,12e.-----------------5分(2)当a =1时，f x =-x ln x +x 2+x ，由2k x -2 +f x <g x 得2k x -2 <x ln x +x ，因为x >2，所以2k <x ln x +x x -2.----------------------------------6分设F x =x ln x +x x -2x >2 ，则F x =x -4-2ln x x -22，------------7分令m x =x -4-2ln x x >2 ，则m x =1-2x>0，所以m x 在2,+∞ 上单调递增，------------------------------------8分又m 8 =4-2ln8<4-2ln e 2=0，m 10 =6-2ln10>6-2ln e 3=0，所以m x 在8,10 上有唯一的零点x 0，即x 0-4-2ln x 0=0，--------------9分当2<x <x 0时，m x <0，即F x <0，当x >x 0时，m x >0，即F x >0，所以F x min =F x 0 =x 0ln x 0+x 0x 0-2=x 01+x 0-42 x 0-2=x 02，---------------------10分所以2k <x 02，又x 0∈8,10 ，所以x 02∈4,5 ，-------------11分又k ∈N *，所以k 的最大值为2.----------------12分。

2020-2021学年深圳市外国语高级中学高一入学考试
物理模拟试卷解析版
一、解答题（共9小题，满分36分）
1．（4分）下列物理量中，不是矢量的是（）
A．加速度B．位移C．瞬时速度D．路程
【解答】解：加速度、位移和瞬时速度都是既有大小又有方向的矢量，而路程只有大小没有方向，是标量，故ABC错误，D正确。

故选：D。

2．（4分）在杭宁高速公路上，分别有图示的甲、乙两块告示牌，告示牌上面数字的意思是（）
A．甲是指位移，乙是平均速度
B．甲是指路程，乙是平均速度
C．甲是指位移，乙是瞬时速度
D．甲是指路程，乙是瞬时速度
【解答】解：告示牌甲是量程牌，表示路程。

限速是指瞬时速度不能超过多大，告示牌乙上面的数字是瞬时速度。

故选：D。

3．（4分）皮球从3m高处落下，被地板弹回，在距地面1m高处被接住，则皮球通过的路程和位移的大小分别是（）
A．4m、4m B．3m、1m C．3m、2m D．4m、2m
【解答】解：位移是指从初位置到末位置的有向线段，所以此时物体的位移的大小是：x ＝3m﹣1m＝2m
路程是指物体所经过的路径的长度，此时的路程为：s＝3m+1m＝4m。

故选：D。

4．（4分）如图所示的时间轴，下列关于时刻和时间的说法中正确的是（）
第 1 页共7 页。

深圳外国语学校高中园2025届高三年级第二次调研考试数学答案1．D 2．B 3．D 4．B 5．C 6．C 7．B【详解】当x <1时，则f (x )=−ax 2+2ax −a +3=−a (x −1)2+3， 且a >0，所以f (x )=−a (x −1)2+3<3，若函数()f x 的值域为R ，可知当1x ≥时，则f (x )=a x +a 的值域包含[)3,+∞， 若0<a <1，则f (x )=a x +a 在1,+∞)内单调递减， 可得f (x )≤f (1)=2a ，不合题意；若a >1，则f (x )=a x +a 在1,+∞)内单调递增， 可得f (x )≥f (1)=2a ，则2a ≤3，解得1<a ≤32；综上所述：实数a 的取值范围是31,2⎛⎤⎥⎝⎦.故选：B. 8．A【详解】由()f x 的图象关于点(1,0)对称可得f (x +2)=−f (−x )． 由f (x +1)+f (x +2)=0，可得f (x +1)=−f (x +2)=f (−x )， 故函数()f x 的图象关于直线12x =对称， 且f (x +2)=−f (x +1)=−(−f (x ))=f (x )，得()f x 的周期为2．当10,2x ⎡⎤∈⎢⎥⎣⎦时，()()()()()22221222log 31log 31log 312111x x f x x x x x x x +−=++=++=+−++++， ()f x 单调递增，且f (13)=32，则f (43)=f (13+1)=−f (13)=−32，f (53)=f (2−13)=−f (13)=−32，画出()f x 在一个周期内的大致图象如图所示： 当012m <+<时，结合图象可得45133m <+<，即1233m <<．故实数m 的取值范围为()122,233k k k ⎛⎫++∈ ⎪⎝⎭Z ．故选：A. 9．ABD 10．AD 11．BCD【详解】对于A ，若函数()f x 在R 上单调递增，则{−a2≥0−2a ≤1−a ，解得a ∈[−1,0]，故A错误；对于B ，若函数()f x 有3个零点，则当0x <时，2(2)x ax a f x −−=−有2个零点12,x x ， 所以{Δ=a 2−8a >0x 1+x 2=−a <0x 1x 2=2a >0，解得8a >，当0x ≥时，f(x)=e x −a 有1个零点，则1a ≥， 所以()8,a ∈+∞，故B 正确；对于C ，设函数()f x 的3个零点分别是1x ，2x ，3x （123x x x <<）， 由B 知，()8,a ∈+∞，12x x a +=−，令e 0()x f a x =−=，解得ln x a =，即3ln x a =，设1231l 3)13n (a a h a x x x −+==−−，()8,a ∈+∞，得()h a 在()8,+∞上单调递减，所以()(),8ln 2h a ∈−∞−−，故C 正确；对于D ，当[)0,1x ∈时，()e x f x a =−单调递增，[)()1,e f x a a ∈−−， 当()1,0x ∈−时，2(2)x ax a f x −−=−，对称轴为直线2ax =−， ①当122a −≥−，即1a ≤时，()(1)1211f x f a a a a <−=−+−=−−<−，无最小值； ②当122a −<−，即1a >时，((2)0)a f x f <=−， 若()f x 有最小值，则12a a −≤−，解得1a ≤−，与1a >矛盾，故无最小值； 综上任意实数a ，函数()f x 在()1,1−内无最小值，故D 正确； 故选：BCD ． 12．(-1，2)13．1− 14．2±【详解】由题意()12y f x =+为奇函数， 所以()11[()]22f x f x −+=−+，则112222xx n n m m −=+++−−， 所以202(2221)(12)(2)122(12)(2)10x x x x x x x x xn n n m m m m m m m ⋅+⋅+++=⋅+++⋅++++⇒=⋅， 所以22()2(21)20x x n m m mn n m ++++⋅++=恒成立， 故2012101m n m m mn n +==−⎧⎧⇒⎨⎨++==⎩⎩或11m n =⎧⎨=−⎩，所以2m n −=±.故答案为：2±。

广东省深圳市福田外国语高级中学2022-2023学年高一上学期入学考试英语试题学校:___________姓名：___________班级：___________考号：___________一、完形填空When I first arrived in Santiago, Chile, and took a walk around the city center, one of the first things I noticed was how many street dogs there were.On every corner there was a sleeping 1 . At every traffic light there was a dog 2 to cross. By every shop there was a dog waiting for 3 . At first I was 4 as I thought they might be 5 or unfriendly. However, I have been here for more than a year now and every street dog I have seen has been quiet and 6 .The dogs are 7 and welcomed here in Chile. They are 8 given food and water by the public. Some people even 9 jackets for the dogs or put out beds for them to sleep in.There are an estimated 2.5 million street dogs in Chile and the canine (犬的) population is 10 . Some people believe that the 11 is getting out of control and that it is 12 to have so many dogs on the streets. The dogs can sometimes cause 13 such as car accidents if they run into the road. Many Chileans think that all the street dogs should be sterilized(使绝育) so that they cannot 14 . Others think that the street dog population should be culled (i.e. reducing the population by killing them).The future of street dogs is 15 , but for now it looks like they are here to stay, with their population expanding year by year.1．A．man B．cat C．dog D．boy 2．A．jumping B．waiting C．hesitating D．refusing 3．A．partners B．owners C．toys D．food 4．A．disappointed B．nervous C．shocked D．angry 5．A．aggressive B．thirsty C．hungry D．sensitive 6．A．lonely B．weak C．friendly D．strong 7．A．controlled B．accepted C．caught D．received 8．A．often B．never C．merely D．barely 9．A．wear B．make C．change D．sell 10．A．aging B．raising C．growing D．declining11．A．policy B．position C．behavior D．situation 12．A．unacceptable B．reasonable C．unusual D．interesting 13．A．diseases B．fears C．problems D．questions 14．A．bite B．breed C．bark D．grow 15．A．bright B．different C．promising D．uncertain二、阅读理解Dorothy and her friends the Scarecrow (稻草人), the Tinman (铁皮人) were walking through the forest with Toto. Suddenly, a great Lion came running at them from the trees. With one blow of his paw, he turned the Scarecrow over and over to the edge of the road, and then he struck at the Tinman with his sharp claws. But, to the Lion’s surprise, he could make no impression on the tin, although the Tinman fell over in the road and lay still. Then little Toto ran up to the Lion and started barking. The Lion was going to hit him too, but Dorothy came between him and the dog, shouting:“Don’t you dare to bite Toto! A big animal like you is going to bite this poor little dog? You are nothing but a coward (胆小鬼)!”The Lion’s face suddenly changed from mad to sad.“I know it,” said the Lion, hanging his head in shame. “I’ve always known it. But how can I help it?” he sighed.“Look at what you did to Scarecrow!” said Dorothy. She picked up the Scarecrow and set him upon his feet, while she put him into shape again.“I’m terribly sorry, Scarecrow,” said the Lion. “You seemed so scary that I had to try and make you run away. Usually, when people and animals see me, they run, but you didn’t.”“Why are you so scared of us?” asked Dorothy. “You’re a lion! Lions are the kings of the forests.”“I can’t help being scared. Whenever there is danger, my heart beats fast.”“Well,” said the Tinman, “maybe you can join us. I have no heart and Scarecrow has no brain. Dorothy and the little dog are dying to go home, very far away. We are going to find the Wizard of Oz for help. Why not come with us and ask him for courage?”“But I am scared to go!” said the Lion.“Everything will be fine,” comforted Dorothy. “There’s nothing to fear when we are alltogether. We’ll all become better.”“Then, if you don’t mind, I’ll go with you,” said the Lion. “As long as I know myself to be a coward, I shall be unhappy!”16．What does the underlined “him” in paragraph 1 refer to?A．The Scarecrow.B．The Tinman.C．The Lion.D．Toto. 17．Which of the following can best describe the Lion in the text?A．Strong but not brave.B．Wild but open-minded.C．Smart but not honest.D．Shy but warm-hearted.18．Why did the Lion try to hit Dorothy and her friends?A．They tried to beat it.B．It was afraid of them.C．They wanted to catch it.D．It was the king of the forest. 19．What do we know about the Tinman?A．He could free the Wizard of Oz.B．He wanted to go home far away.C．He invited the Lion to join them.D．He was a robot with no thoughts. 20．What can we infer about the Lion from the last paragraph?A．It hated to work for long.B．It would live a simple life.C．It minded joining the team.D．It would try to find courage.Rainforests provide much of the world’s oxygen. People have been trying to protect them for years. But another type of forest, the cloud forest, is just as important to humans.These forests are at the tops of mountains, generally near the equator (赤道). These wet, wooded mountaintops are mainly in African and Central and South American countries. They are called “cloud forests” because their height allows for the formation of clouds among the trees. The trees in these forests pull water out of the clouds. The water gathers on the leaves and falls into small rivers below, which flow into towns at the bottom of the mountain. The yearly rainfall in these areas is about 180 centimetres. Cloud forests can pull in up to 60 percent of that. The water is important to the plants and the people in the area. It helps them survive.Cloud forests are also home to countless species of plants that can’t be found anywhere else. One small cloud forest has as many types of plants as there are in all of Europe. In fact, there are so many that scientists haven’t made a complete list of them yet.These forests are being destroyed at an increasing speed. Trees are being cut down, androads are being built in their place. Some people have a goal to get government money to protect the forests. But they have had little success so far. Another way is to take the place of the destroyed plants with new ones. That, too, has been difficult because the plants are so special. There’s plenty of work to be done, but saving the cloud forests is still possible with creative solutions.21．Where can you probably find cloud forests?A．In North America.B．Far from the equator.C．In an African country.D．At the foot of mountains.22．How much rainfall is pulled in by the cloud forests in those areas every year?A．About 60 cm.B．About 108 cm.C．About 180 cm.D．About 300 cm.23．What is the main idea of paragraph 3?A．Europe is short of plant types.B．Scientists are working on a list.C．Cloud forests are getting smaller.D．Cloud forests house many plants.24．What will be discussed in the following part of the text?A．Ways to protect cloud forests.B．Goals of cloud forest protectors.C．Difficulties in planting new trees.D．Successes of getting wide support.25．Where can we probably find the text?A．In a storybook.B．In a travel guide.C．In a chemistry textbook.D．In a geography magazine.Colourful felt (毛毡) flowers have been “planted” at different street corners throughoutGuangzhou by young local sculptor (雕塑家) Luo Shengtian. Starting as a graduation project in April, his efforts have now become a group activity in both China and Europe.Luo said he always wanted to repair the city’s “scars”, such as damaged walls or stone stairs by art. Luo mentioned that these colourful felt plants are like a “beautiful warning” to people as they walk by, reminding them to be aware of these damaged street corners.Within one month, Luo “planted” more than 20 flowers in his community. These flowers attracted more than 300 volunteers to join a WeChat group to spread the repair tasks to other places such as Beijing and Fuzhou. “The meaning of the project is to bring art into people’s everyday lives. Sculptures or other works of fine arts are no longer just an idea in the air,” Luo noted. Following the increase of volunteers, it even spread to European cities such as Venice, and Paris.Luo shared an interesting story in Venice, where one of his fans “planted” a felt flower to see how people would respond to the project. The flower was picked up by someone only a day after it appeared in public, but later three new ones were “planted” by a mysterious person overnight. “I was touched by that. Such an artistic focus on our living environment seems to be shared by global creators,” Luo said.Luo is not the only young creator in the city to focus on creatively renewing people’s everyday experiences. More similar projects have been launched, showing younger generations’ care and social responsibility.26．Why does Luo Shengtian “plant” felt flowers in Guangzhou?A．To protect the flowers.B．To fix broken walls.C．To start a group activity.D．To warn people in streets.A．Hard stones.B．Waste buildings.C．Strange shapes.D．Woundedsurfaces.28．What can we learn from paragraph 3?A．Luo created 300 volunteer groups.B．Luo “planted” 20 flowers in Beijing.C．The project’s influence spread abroad.D．The project made art appear in the air. 29．What is the purpose of the story in Venice in paragraph 4?A．To show the art works’ acceptance in Italy.B．To praise a kind stranger whospread the idea.C．To test if people value their living environment.D．To state the flowers have beenwidely “planted”.30．What’s the best title of this text?A．Felt Flowers Beautify Old Cities B．Luo Shengtian, a Gifted SculptorC．A Beautiful Warning from Flowers D．A Project Famous in European Countries三、其他Gardening has been around for as long as humans have been growing food. Today it is known for its health benefits (益处). Taking part in gardening can reduce our bad feelings andyou don’t like to work out in the gym, gardening is an enjoyable way for you to keep fit.We can include gardening in our life in many ways.Decide which plant to grow. Do you have a favourite flower, fruit, or vegetable?32 . Choose a plant that you want to grow according to how much time you have and how much money and energy you can put into.33 . A community garden is a shared place where people grow plants in a large piece of land together. Search online for a community garden near you. It is a good place to ask questions and learn from experienced gardeners.Grow plants indoors.You don’t have to own land to start gardening. 34 . All you need is just a window or artificial (人造的) lightening source, pots, soil, and any other thing that helps a plant grow.Mistakes happen. Not every plant will grow exactly how you want or expect. Almost everyone will experience problems or failure in growing a plant. Don’t lose heart. 35 .A．Find a community garden.B．Turn to experienced gardeners for help.C．Different plants need different amounts of care.D．Plenty of plants grow well indoors in small pots.E．Even standing near a green plant can help you feel more relaxed.F．Learn from your mistakes, and don’t let them keep you from continuing to garden.四、信息匹配下面的材料A~F介绍的是六个周末活动的好去处。

罗湖外国语新高一入学摸底预测题（90分钟，满分100分）姓名________班级________分数________一、单项选择（共10小题；每小题2分，满分20分）()1.As________matter of fact,_________beauty of__________nature there made an excellent impression on me.A.a;the;不填B.a;the;theC.the;the;不填D.a;不填；the()2.The harder you__________,the better progress you___________.A.will workB.work;have madeC.work;will makeD.will work;make()3._________for his good skill,this doctor has a lot of visitors calling for help all the time.A.KnowingB.To knowC.KnownD.To have known()4.It was a cold winter night,and there wasn’t anyone__________the boy could turn for help in the street.A.thatB.whichC.whomD.what()5.He looked very confident and calm during the test,but_____he was extremely nervous.A.in troubleB.in dangerC.in realityD.in surprise()6.Have you determined___________?A.next to do whatB.what to do nextC.how to do nextD.next how to do()7.They are looking forward to_____________to the lecture by the famous professor. A.send B.be sent C.being sent D.sending()8.It was until last year that he___________.A.left his hometown for a new startB.came to realize the important of learning EnglishC.worked as an English teacher at a middle schoolD.set out to build a new house of his town()9.---Jane wasn’t in when Jack came,was she?---_____,but she returned a few minutes later.A.No,she wasB.No,she wasn’tC.Yes,she wasD.Yes,she wasn’t.()10.He has already gone home.But before he left,he____all the mistakes in his translation.A.had correctedB.has correctedC.correctedD.would correct二、完形填空（共15小题；每小题1分，满分15分）阅读下面短文，按照句子结构的语法性和上下文连贯的要求，从11~25各题所给的A、B、C和D项中选出最佳选项。

2020-2021学年深圳外国语学校高一入学考试物理模拟试卷一、单项选择题（本大题10小题，每小题3分，共30分．在每小题给出的四个选项中只有一个是符合要求的．）1．（3分）下面关于质点的正确说法有（）A．乒乓球运动员在研究乒乓球的运动时可把乒乓球看成质点B．研究沿地面翻滚前进的体操运动员的动作可把运动员看成点C．计算火车通过站台的时间虽然不能忽略火车的大小但仍可把火车看成质点D．小的物体运动可看成质点，大的物体运动就不能看成质点【解答】解：A、乒乓球运动员研究乒乓球在旋转的时候，是不能看成质点的，但研究乒乓球运动的轨迹时，可以把乒乓球可知质点。

故A正确；B、在体操比赛中，评委要看运动员的形体动作的情况，此时人的形状是不能忽略的，所以不能看成质点，故B错误；C、研究一列火车通过站台的时间时，火车的长度相对于站台来说是很大的，此时不能忽略火车的长度，不能看成质点，故C错误；D、能否看成质点，与质量大小无关，质量很小的物体不一定能看成质点，如其大小和形状对所研究的问题影响很大，就不能看成质点，而某些情况下地球也可以看成质点，比如地球的公转，故D错误；故选：A。

2．（3分）下列关于参考系的正确说法有（）A．研究地面上物体的运动，必须选取地面为参考系B．被选为参考系的物体是一定不动的C．质点运动的轨迹是直线还是曲线，与参考系的选取无关D．质点运动的时间，与参考系选取无关【解答】解：A、研究物体的运动时，参考系是可以任意选取的（但不能选研究对象本身为参考系），故A错误；B、自然界中的一切物体都处在永恒的运动中，被选做参考系的物体只是被假定不动，故B错误；C、同一物体的运动，选择不同的参考系所观察到的轨迹可能不同，故C错误；D、质点运动的时间，与参考系选取无关，故D正确。

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广东省深圳市罗湖外国语新2020-2021学年高一上学期入学分班模拟考试英语试题（90 分钟，满分100 分）一、单项选择（共10 小题；每小题2 分，满分20 分）( ) 1. As ________matter of fact, _________ beauty of __________ nature there made an excellent impression on me.A. a; the; 不填B. a; the; theC. the; the; 不填D. a; 不填；the( ) 2. The harder you__________, the better progress you ___________.A. will workB. work; have madeC. work; will makeD. will work; make( ) 3. _________for his good skill, this doctor has a lot of visitors calling for help all the time.A. KnowingB. To knowC. KnownD. To have known( ) 4. It was a cold winter night, and there wasn’t anyone __________the boy could turn for help in the street.A. thatB. whichC. whomD. what( ) 5. He looked very confident and calm during the test, but _____ he was extremely nervous.A. in troubleB. in dangerC. in realityD. in surprise( ) 6. Have you determined ___________?A. next to do whatB. what to do nextC. how to do nextD. next how to do( ) 7. They are looking forward to _____________ to the lecture by the famous professor.A. sendB. be sentC. being sentD. sending( ) 8. It was until last year that he ___________.A. left his hometown for a new startB. came to realize the important of learning EnglishC. worked as an English teacher at a middle schoolD. set out to build a new house of his town( ) 9. ---Jane wasn’t in when Jack came, was she?---_____, but she returned a few minutes later.A. No, she wasB. No, she wasn’tC. Yes, she wasD. Yes, she wasn’t.( ) 10. He has already gone home. But before he left, he____ all the mistakes in his translation.A. had correctedB. has correctedC. correctedD. would correct二、完形填空（共15 小题；每小题1 分，满分15 分）阅读下面短文，按照句子结构的语法性和上下文连贯的要求，从11~25 各题所给的A、B、C 和D项中选出最佳选项。

罗湖外国语新高一入学摸底预测题答案:一、单选1—5ACCCC6—10BCCBA二、完形11-15DACBB16—20ADBBC21—25CAA BC三、阅读26—30CABBC31—35BCDBA36—40DABCA41—45DEBCA四、语法填空46.when47.before48.neatly49.the50.in51.had worked52.where53.one54.their55.Getting五、写作Chinese style of crossing streets has been a hot topic on the Internet recently.Now many people cross streets without looking at the traffic lights.Why?I think there aretwo main reasons.Some people lack awareness of traffic safety.Besides,some people are sobusy that they don’t want to wait for the green light.However,it has brought danger to themselves as well as to others.So I hope something mustbe done to avoid traffic accidents.For example,whoever breaks the traffic rules should be punished.As middle school students,we should obey the traffic rules.What’s more,I will try my bestto advise people to obey the rules.Only in this way can we cross streets safely.作文：（满分15分）1.评分原则：1)本题总分15分，按4个档次评分。

2015-2016高一新生英语水平测试一. 单项选择(1’*20)1.It’s not wise of him to say ______ comes into his head. That’s why he doesn’t leave people a good impression.A. whatB. whateverC. no matter whatD. anything what2.The reason ________ he was absent from school was not the reason ________ he explained to the teacheryesterday.A. why; becauseB. because; thatC. why; thatD. that; because3.The hotel wasn’t particularly good, but I ________ in many worse hotels.A. had stayedB. stayedC. was stayingD. would stay4. A witness reported having seen a police car ________ a truck on the highway yesterday.A. running inB. running afterC. running awayD. running across5.Just in front of our house ________ with a history of 1,000 years.A. does a tall tree standB. a tall tree is standingC. a tall tree standsD. stands a tall tree6.It is now quite ________ for women to hold the top positions in big companies.A. ordinaryB. commonC. usualD. average7.If you have no more modern music ______ , fetch so me from my brother’s.A. listeningB. listening toC. to listenD. to listen to8.In the hope of _________ to the ball, Mathilde borrowed the necklace from her friend.A. invitingB. being invitedC. to inviteD. to be invited9.He must be the man you told me about, ________?A. mustn’t heB. needn’t heC. isn’t heD. doesn’t he10.The doctor _________ me to eat less meat and take more exercise. But I find it difficult to do what the doctortold me.A. suggestedB. hopedC. advisedD. persuaded11.Chicago is on ________ Lake Michigan. There is nothing in the world like ________ Chicago meat industry.A. the；theB. /；/C. the；/D. /；the12.My parents used ________they had to get a new car for my brother.A. whichB. all whatC. whatD. /13.________ the bad weather, the construction of the two railway lines is now behind schedule.A. According toB. Up toC. Due toD. As to14.While building a tunnel through the mountain, ________ .A. an underground lake was discoveredB. there was an underground lake discoveredC. a lake was discovered undergroundD. the workers discovered an underground lake15.Paper produced every year is ________ the world's production of vehicles.A. the three times weight ofB. three times the weight ofC. as three times heavy asD. three times as heavier as16.We have done things we ought not to have done and ________ undone things we ought to have done.A. leftB. leaveC. will leaveD. leaving17.--- Why weren't you at the meeting?--- I ________ for a long distance call from my sister in America.A. was waitedB. was waitingC. has waitedD. have been waiting18.She will have to find some other work for she can't ________ this loud noise any more.A. come up withB. keep up withC. grow up withD. put up with19.I've just seen no more than one copy of "Gone with the Wind" in the bookshop opposite. Tom, go andbuy______ back.A. oneB. anyC. itD. some20.Have you ever been in a situation _____ you know the other person is right yet you cannot agree with him?A. by whichB. thatC. in whereD. where二. 语法填空(1’*10)Every afternoon, lots of youths rush into Internet cafes, switch on game consoles(游戏机), ___21____ sit down to involve themselves in intense fantasy worlds.Games are often ____22_____ (excite) and dramatic, but they generally aren’t very intellectual. We don’t learn as much from them as we would ____23____ simply reading a book, and spending too much time ____24____ (play) them can take away our study time. We need to remember that we are students first and ____25____ should get in the way of proper studying.Video games can also have a bad influence on younger children ___26____ may be watching. Many video games are ____27_____ (violence). This does not send the right message to children, who are supposed ____28_____ (tell) that violence is not acceptable, and need to be taught _____29_____ to handle situations maturely. Even if we do decide to sit down and play ___30_____ wild video game, we need to make sure that it is not influencing younger children around us.三. 完形填空(2’*15)A friend of mine met with an accident driving in darkness. His legs were so hurt that he couldn't move. What was __31__, he found himself unable to ask for help --- his mobile phone went out of __32__ as a result of exhausted battery. Nothing could be done but to __33__ in cold wilderness. It was 8 hours later that day broke，and then the __34__ of the rescue.It is almost __35__ that he could stand the horror in the darkness for so long. Even more surprising was his explanation: “First of all I checked up my _36__ conditions and found myself not in mortal (致命的) danger. As there was no__37__ to call for help，I leaned back in my seat trying my best to keep the wound from __38__. In this way I dozed (打盹)off.”His story put an end to my regret for the failure of an exploration adventure that happened last year. A group of young men __39__ to explore a mountain cave and got lost. __40__ to find a way out in the dark cave they were frightened and ran anxiously without a sense of __41__.Finally they fell dead in fear and exhaustion . According to the __42__ people that found them, the place where they got lost was only about 10 meters away from the opening of the cave. If they stayed on the spot when they lost their way and tried to __43__ themselves，they would probably sense a faint light glimmering not far away.Don't you think that you can compare it with __44__ itself? When you meet with obstacles in life and work，you are lost in darkness. Mind you it's unclear yet and you needn't put up struggle __45__. It seems to be a negative attitude, but a person who can afford to do so must have foresight as well as a great courage in the first place.31. A. hopeless B. worse C. more D. best32. A. service B. way C. control D. work33. A. cry B. lie C wait D. sleep34. A. delay B. success C. team D. arrival35. A. untrue B. unimaginable C. true D. useless36. A. physical B. mental C. working D. medical37. A. method B. way C. tools D. strength38. A. rotting B. spreading C. hurting D. bleeding39. A. had B. managed C. tried D. planned40. A. Willing B. Unable C. Determined D. Deciding41. A. hearing B. sight C. feeling D. direction42. A. rescue B. village C. local D. brave43. A. save B. help C. stop D. calm44. A. adventure B. work C. life D. mankind45. A. really B. immediately C. carefully D. hopefully四．阅读（2’*25）（一）阅读理解AResearchers in London and Bristol have found that men are particularly likely to give way to depression if their partners are also depressed（沮丧的）.The finding highlights the importance of paying attention to the partners of depressed mothers, as young children themselves are vulnerable (容易受伤的) to social problems if both parents are depressed.Researchers in London and at the University of Bristol launched their study to investigate whether family structure affects the likelihood of depression in men around the time their child is born. They looked at men from traditional families, men with children from a previous relationship, men whose partners had children by a former partner, and men who were not living with their partners.All 7018 participants filled out a questionnaire on depression, and answered questions about their age, education level and employment status. Details about the quality of their relationships with their partners, networks of friends and previous life events were also recorded.About 3.5 per cent of the men and 13 per cent of their partners suffered depression around the time their child was born. While men in step-families or who were not living with their partners were twice as likely to get depressed as those in traditional families, this could be explained by other factors that are more common in non-traditional families, such as poor education and relationship conflicts.Even allowing for all these factors, however, the partners of women who were suffering from prenatal (产前的) depression were significantly more likely to become depressed themselves, the researchers report in an American Journal. Ten per cent of women who were depressed had depressed partners. For the healthy women, the figure was only 2.6 per cent.Previous research suggests that families with two depressed parents may need special attention. A researcher in Atlanta has found that primary schoolchildren with two troubled parents have difficulty relating to their peers. "It's extremely important to look at the whole family," she says.46. What can we conclude from paragraphs one and two of this passage?A. Men often beat their children.B. Depressed women often have depressed partners.C. All young children are vulnerable to social problems.D. Women with children often have depressed partners.47. Why did researchers in London and Bristol carry out such and investigation?A. To see what kind of family environment is ideal for children to grow up in.B. To study whether family structure affects depression in men when their child is born.C. To investigate why so many men get depressed when a child is born.D. To see whether it is true that behind every depressed man there is a depressed woman.48. What kind of men were NOT included as objects in the study?A. Men from traditional families.B. Men with children from a previous relationship.C. Men who were not living with their partners.D. Men who have no children.49. What kind of men are least likely to get depressed when their child was born?A. Men in stepfamilies.B. Men who were not living with their partners.C. Men in traditional families.D. Men in nontraditional families.50. Which of the following statements is NOT true?A. Ten per cent of women who were depressed had depressed partners.B. 2.6 per cent of healthy women were depressed.C. Special attention should be paid to families in which both the father and the mother were depressed.D. Primary schoolchildren whose parents were both depressed couldn't get along well with their peers.BEvery day we lace our talk with measurement words. We ask, “How much?”“How many?” and “How far?” At the store we buy meat by the pound, clothing by the size, and cloth by the yard. All athletic events are played on measured fields or surfaces. Rules are also filled with words of measurement. For example, in football we know that a first down means a gain of at least 10 yards. Words of distance, weight, and size help us understand and visualize what is seen and said.In ancient times, people used parts of the body as units of measurement. The Romans used uncia to name the distance equal to the width of a thumb. The English picked up this word and renamed it an inch.They did not, however, accept the thumb as a unit of measure. They decided instead that an inch should be “three barley corns, round and dry, placed end-to-end lengthwise(纵长).”After this inch was accepted and used, the English then joined 12 inches and called it a foot. As it happened, 12 inches was roughly the length of a man’s foot, so the foot unit was widely used. To measure a room, all you had to do was put one foot in front of the other and count.The inch and foot worked so well that the English introduced a large unit. They put together three lengths of a man’s foot and called it a yard. Again, man had another useful unit---in this case, one he could use to pace off a large field quickly.Then the English made a unit for the women, one especially for measuring cloth. They called this unit a yard too. The distance was from a man’s nose to the tip of his middle finger.Of course, there is a flaw in all this. Not all men are the same size. But no one seems to care.51. This article is mainly concerned with ________.A. Roman measurementB. the development of common units of measurementC. what an inch and a foot are equal toD. understanding measurement52. The Romans decided that________A. thumbs were about an inch wide.B. barley corns were always the same size.C. people are not all the same size.D. a man’s foot measures exactly 12 inches..53. Many units of measurement were developed ________A. to make it easier to figure out common lengths.B. because men were considered more important than women.C. for no particular reason.D. so the English could prove their superiority to the Romans.54. In the first paragraph the author gives ________A. a history of measurement.B. examples of how often we use measures.C. an explanation of football rules.D. a way of figuring out which measures are useful.55. The word “flaw”in the last paragraph is closest in meaning to________A. defect.B. difference.C. change.D. danger.CF ive years ago, David Smith wore an expensive suit to work every day. “I was a clothes addict.” he jokes. “I used to carry a fresh suit to work with me so I could change if my clothes got wrinkled.” Today David wears casual clothes----khaki pants and a sports shirt---to the office. He hardly ever wears a necktie. “I am working harder than ever.”David says, “and I need to feel comfortable.”More and more companies are allowing their office workers to wear casual clothes to work. In the United States, the change from formal to casual office wear has been gradual. In the early 1990s, many companies allowed their employees to wear casual clothes on Friday（but only on Friday. This became known as “dress-down Friday”or “casual Friday”.“What started out as an extra one-day-a-week benefit for employees has really become an everyday thing,” said business consultant Maisly Jones.Why have so many companies started allowing their employees to wear casual clothes? One reason is that it’s easi er for a company to attract new employees if it has a casual dress code. “A lot of young people don’t want to dress up for work,” says the owner of a software company,“so it’s hard to hire people if you have a conservative dress code.” Another reason is that people seem happier and more productive when they are wearing comfortable clothes. In a study conducted by Levi Strauss and Company, 85 percent of employers said that they believe that casual dress improves employee morale（心境，士气）. Only 4 percent of employers said that casual dress has a negative influence on productivity. Supporters of casual office wear also argue that a casual dress code helps them save money. “Suits are expensive, if you have to wear one every day,” one person said, “For the same amo unt of money, you can buy a lot more casual clothes.”56．David Smith refers to himself as having been “a clothes addict,” because _____.A．he often wore khaki pants and a sports shirtB．he couldn’t stand a clean appearanceC．he wanted his clothes to look neat all the timeD．he didn’t want to spend much money on clothes57．David Smith wears casual clothes now, because_____.A．they make him feel at ease when workingB．he cannot afford to buy expensive clothesC．he looks handsome in casual clothesD．he no longer works for any company58．According to this passage, which of the following statements is FALSE?A．Many employees don’t like a conservative dress code.B．Comfortable clothes make employees more productive.C．A casual clothes code is welcomed by young employees.D．All the employers in the U. S. are for casual office wear.59．According to this passage, which of the following statements is TRUE?A．Company workers started to dress down about twenty years ago.B．Dress-down has become an everyday phenomenon since the early 90s.C．“Dress-down Friday” was first given as a favor from employers.D．Many workers want to wear casual clothes to impress people.60．In this passage, the following advantages of casual office wear are mentioned EXCEPT_____.A．saving employees’ moneyB．making employees more attractiveC．improving employees’ motivationD．making employees happierDEvery year thousands of people are arrested and taken to court for shop-lifting. In Britain alone, about HK$3,000,000’s worth of goods are stolen from shops every week. This amounts to something like HK$150 million a year, and represents about 4 percent of the shops’ total stock. As a result of this “shrinkage” as the shops call it, the honest public has to pay higher prices.Shop-lifters can be divided into three main categories: the professionals, the deliberate amateur, and the people who just can’t help themselves. The professionals do not pose much of a problem for the store detectives, who, assisted by closed circuit television, two-way mirrors and various other technological devices, can usually cope with them. The professionals tend to go for high value goods in parts of the shops where security measures are tightest. And, in any case, they account for only a small percentage of the total losses due to shop-lifting.The same applies to the deliberate amateur who is, so to speak, a professional in training. Most of them get caught sooner or later, and they are dealt with severely by the courts.The real problem is the person who gives way to a sudden temptation and is in all other respects an honest and law-abiding citizen. Contrary to what one would expect, this kind of shop-lifter is rarely poor. He steals not because he needs the goods and cannot afford to pay for them. He steals because he simply cannot stop himself. And there are countless others who, because of age, sickness or plain absent-mindedness, simply forget to pay for what they take from the shops. When caught, all are liable to prosecution, and the decision whether to send for the police or not is in the hands of the store manager.In order to prevent the quite incredible growth in ship-lifting offences, some stores, in fact, are doing their best to separate the thieves from the confused by prohibiting customers from taking bags into the store. However, what is most worrying about the whole problem is, perhaps, that it is yet another instance of the innocent majority being penalized（宣告有罪）and inconvenienced because of the actions of a small minority. It is the aircraft hijack situation in another form. Because of the possibility of one passenger in a million boarding an aircraft with a weapon, the other 999,999 passengers must subject themselves to searches and delays. Unless the situation in the shops improves, in ten years’ time we may all have to subject ourselves to a body-search every time we go into a store to buy a tin of beans!61. Why does the honest public have to pay higher prices when they go to the shops?A. There is a “shrinkage” in market values.B. Many goods are not available.C. Goods in many shops lack variety.D. There are many cases of shop-lifting.62. The third group of people steal things because they _____.A. are mentally illB. are quite absent-mindedC. can not resist the temptationD. can not afford to pay for goods63. According to the passage, law-abiding citizens _____.A. can possibly steal things because of their povertyB. can possibly take away goods without payingC. have never stolen goods from the supermarketsD. are difficult to be caught when they steal things64. Which of the following statements is NOT true about the main types of shop-lifting?A. A big percentage of the total losses are caused by the professionals.B. The deliberate amateurs will be punished severely if they get caught.C. People would expect that those who can’t help themselves are poor.D. The professionals don’t cause a lot of trouble to the store detectives.65. The aircraft hijack situation is used in order to show that ____.A. “the professionals do not pose much of a problem for the stores”B. some people “s i mply forget to pay for what they take from the shops”C. “the honest public has to pay higher prices”D. the third type of shop-lifters are dangerous（二）七选五：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，选项中有两项为多余选项。

广东省深圳外国语学校高中园2025届高三入学摸底考试数学试卷学校：___________姓名：___________班级：___________考号：___________一、选择题1．已知集合，，则( )A. B. C. D.2．已知( )3．已知( )D.4．设非零向量，，则“”是“或”的( )A.充分而不必要条件B.必要而不充分条件C.充要条件D.即不充分也不必要条件5．等比数列的各项均为正数，且，则( )A.12B.10C.5D.6．设抛物线，若将直线绕点F逆时针旋转()A.7．已知正三棱台的高为1，上、下底面边长分别为上，则该球的表面积为( )A. B. C. D.8．设函数，，若存在，，使得，则{}0,1,2M ={}2,0,1N =-{}0M N = M N M= {}0M N⊆ {}0,1M N ⊆ z =πsin 3α⎛⎫+= ⎪⎝⎭π23α⎛⎫-= ⎪⎝⎭2425-a b ()()a b a b +⊥- a b = a b =- {}n a 564718a a a a +=3132310log log log a a a ++⋅⋅⋅+=32log 52:4T y x =4AF 4532----100π128π144π192π()e x f x x =+()ln g x x x =+1x 2x ()()12f x g x =1x -二、多项选择题9．已知函数，则函数( )A.单调减区间为B.在区间上的最小值为C.图象关于点中心对称D.极大值与极小值的和为10．现安排高二年级A ，B ，C 三名同学到甲、乙、丙、丁四个工厂进行社会实践，每名同学只能选择一个工厂，且允许多人选择同一个工厂，则下列说法正确的是( )A.所有可能的方法有种B.若工厂甲必须有同学去，则不同的安排方法有37种C.若同学A 必须去工厂甲，则不同的安排方法有16种D.若三名同学所选工厂各不相同，则不同的安排方法有24种11．已知F 为双曲线的右焦点，过F 的直线l 与圆相切于点M ，且l 与C 及其渐近线在第二象限的交点分别为P ，Q ，则下列说法正确的是( )A.直线l 的斜率为B.直线是C 的一条渐近线三、填空题12．在数列中，，，则数列的通项公式为________.13．已知函数，若在上的最小值为-1，则t 的最大值是________.14．已知函数四、解答题()32112132f x x x x =--+()f x ()2,1-[]3,3-132-11,212⎛⎫- ⎪⎝⎭16-432222:1(0,0)x y C a b a b-=>>222:O x y a +=a b-OM 32y x =±{}n a 14a =()12n n na n a +=+n a =π()2sin (03f x x ωω⎛⎫=+<< ⎪⎝⎭()f x π,4t ⎡⎤-⎢⎥⎣⎦()(1)e e x x f x x =-+15．在中，角A 、B 、C 的对边分别为a ，b ，c.已知（1）求c 的值；（2）求的值；（3）求的值.16．如图，在直三棱柱中，，点D 是的中点，点E 在上，平面.（1）求证：平面平面；（2）当三棱锥的体积最大时，求直线与平面所成角的正弦值.17．随着信息技术的飞速进步，大数据的应用领域正日益扩大，它正成为推动社会进步的关键力量.某研究机构开发了一款数据分析软件，该软件能够精准地从海量数据中提取有价值的信息.在软件测试阶段，若输入的数据集质量高，则软件分析准确的概率为0.8；若数据集质量低，则分析准确的概率为0.3.已知每次输入的数据集质量低的概率为0.1.（1）求一次数据能被软件准确分析的概率；（2）在连续次测试中，每次输入一个数据集，每个数据集的分析结果相互独立.设软件准确分析的数据集个数为X .①求X 的方差；②当n 为何值时，的值最大?（1）求椭圆的方程；ABC △a =2c =cos A =sin B sin(2)A B -111ABC A B C -13AB AC AA ===BC 1AA //AD 1BC E 1BC E ⊥11BB C C 11B BC E -AC 1BC E ()8n n ≥()8P X =(2210y a b b +=>>BF =（2）直线l 与椭圆有唯一的公共点M ，与y 轴的正半轴交于点N ，过N 与垂直的直线交x 轴于点P .若，求直线l 的方程.19．牛顿（1643－1727）给出了牛顿切线法求方程的近似解：如图设r 是的一个零点，任意选取作为r 的初始近似值，过点作曲线的切线，与x 轴的交点为横坐标为，称为r 的1次近似值，过点作曲线的切线，与x 轴的交点为横坐标为，称为r 的2次近似值.一般地，过点作曲线的切线，与x 轴的交点为横坐标为，就称为r的次近似值，称数列为牛顿数列.（1）若的零点为r ，，请用牛顿切线法求r 的2次近似值；（2）已知二次函数有两个不相等的实数根b ，c ，数列为的牛顿数列，数列满足，且.（ⅰ）设，求的解析式；BF //MP BF ()y f x =0x ()()00,x f x ()y f x =1l 1l 1x 1x ()()11,x f x ()y f x =2l 2l 2x 2x ()(),nnx f x ()y f x =1n l+1n l +1n x +1n x +1n +{}n x ()31f x x x =+-00x =()g x ()c b >{}n x ()g x {}n c ()*n n n x bc n x c-=∈-N n x c >()1n n x h x +=()n h x 21112ln n c c c +++<参考答案1．答案：C解析：，，A 、B 错误；，C 正确；不正确，D 错误.故选：C.2．答案：B解析：由，故选：B.3．答案：A解析：令，所以故选：A.4．答案：B解析：因为所以或；但若“或所以“”是“或”的必要不充分条件，故选：B.5．答案：B解析：因为是各项均为正数的等比数列，，所以，即，则{}0,1M N = {}2,0,1,2M N =- {}0M N ⊆ {}0,1M N ⊆ ()21i i 1i i 11i i i 1z --+====---=x α=+2y α=45x =2πy x =-()22π4cos 2cos cos 2πcos 22sin 12135y x x x α⎛⎫⎛⎫-==-=-=-=⨯-= ⎪ ⎪⎝⎭⎝⎭()()a b a b+⊥-()()222200a b a b a b a b +⋅-=⇔-=⇔= b = a b =- a b = a b =- ()()a b a b +⊥- a b = a b =- {}n a 564718a a a a +=564756218a a a a a a +==569a a =11029569a a a a a a ====记，则，两式相加得，所以，即.故选：B.6．答案：A 解析：，设，，，，所以，则故所以，则直线l 的倾斜角，所以直线l 的斜率所以直线l 的方程为，联立，消y 得，，设，，则3132310log log log S a a a =++⋅⋅⋅+3103931log log log S a a a =+⋅⋅⋅++()()()3110329310132log log log 10log 920S a a a a a a =++⋅⋅⋅+=⨯=10S =3132310log log log 10a a a ++⋅⋅⋅+=()1,0F ()00,A x y 00x >00y >014x +=03x =0y =AF k ==60AFx ∠=︒6045α=︒+︒()tan 60452k =︒+︒==-(()21y x =--(()2214y x y x⎧=--⎪⎨=⎪⎩((271870x x +-+++=((((2222Δ184718140=+-+=+-+>()11,C x y ()22,D x y 1230x x +==-12232x x ++=-故选：A.7．答案：A解析：设正三棱台上下底面所在圆面的半径，，所以即，，设球心到上下底面的距离分别为，，球的半径为R ，所以或或，解得符合题意，所以球的表面积为.故选：A.8．答案：B解析：由题意可得，即，所以，又，所以在R 上单调递增，即，所以，令，，则，令，则，1r 2r 12r =2r =13r =24r =1d 2d 1d =2=21d -=12d d +=1-1=225R =24π100πS R ==()()12f x g x =1122e ln x x x x +=+12ln 12e e ln x x x x +=+()1e 0x f x =+>'()f x ()()12ln f x f x =12ln x x =1222ln e ln x x x x -=-=-()ln h x x x =-()0,x ∈+∞()11h x x =-='0>()0h x '=1x =当时，，则单调递增，当时，，则单调递减，所以当时，有极大值，即最大值，所以，.故选：B 9．答案：BCD解析：对于A ，，故，所以在和上，，函数单调递增；在上，，函数单调递减，故A 错误；对于D ，由A 知，函数的极大值为极小值则对于B ，，结合函数在的单调性可知：对于C ，，所以故函数图象关于点中心对称，故C 正确.故选：BCD 10．答案：BCD解析：所有可能的方法有种，A 错误.()0,1x ∈()0h x '>()h x ()1,x ∞∈+()0h x '<()h x 1x =()h x ()()1h x h ≤=-)1x ≥222min min ln 11x x x -=-=-=()32112132f x x x x =--+()()()2221f x x x x x =--=-+'(),1-∞-()2,+∞()0f x '>()f x ()1,2-()0f x '<()f x ()f x ()1112132f -=--++=()822413f =--+=()()12f f -+=()()9133961222f f -=--++=-<[]3,3-()()min 3f x f =-=()()()()321111121132f x x x x -=-----+()()()()()32321111111211213232f x f x x x x x x x -+=-----++--+=()f x 11,212⎛⎫- ⎪⎝⎭34对于B ，分三种情况：第一种：若有1名同学去工厂甲，则去工厂甲的同学情况为，另外两名同学的安排方法有种，此种情况共有种，第二种：若有两名同学去工厂甲，则同学选派情况有，另外一名同学的排法有3种，此种情况共有种，第三种情况，若三名同学都去工甲，此种情况唯一，则共有种安排方法，B 正确.对于C ，若A 必去甲工厂，则B ，C 两名同学各有4种安排，共有种安排，C 正确.对于D ，若三名同学所选工厂各不同，则共有种安排，D 正确.故答案为：BCD 11．答案：ABD解析：对于A ，根据题意，，设直线，，又因为直线l 与圆相切于点M ，所以，，对于B ，根据题意可知，可得，所以直线是C 的一条渐近线，B正确；，联立，解得，同理联立，解得，13C 339⨯=13C 927⨯=23C 23C 39⨯=279137++=4416⨯=34A 24=(c,0)F :0l y kx kc kx y kc =-⇒--=0k <222:O x y a +=2222(1)a a k k c +=222b c a =- k ∴=OM l ⊥OM bk a=:bOM y x a=(c,0)222b y x a x y a⎧=⎪⎨⎪+=⎩2(,a ab M c c b y x a a a y x c b b ⎧=-⎪⎪⎨⎪=-+⎪⎩22222(,a c abc Q a b a b ---，，化简得对于D，设，故，得，故，，，D 正确；故选：ABD12．答案：（n 为正整数），（n 为正整数）.故答案为：（n 为正整数）.解析：函数图象所对应解析式为：，因为，可得，，又，所以，即，223abc a b =-()2223b a =-223c a =2e =00(,P x y 3FM = ()200,3,a ab x c y c cc ⎛⎫-=- ⎪⎝⎭2023x a c c =-0y =2332,a ab P c c c ⎛⎫- ⎪⎝⎭22y b -=2231ab c b⎛⎫ ⎪⎝⎭-===2294b a ==32y x =±()21n n +=14=132112211143412321n n n n n a a a a n n n a a a a a a n n n ---+-∴=⋅⋅⋅⋅⋅=⨯⨯⨯⨯⨯⨯--- ()()142121n n nn +⨯=⨯=+⨯()21n n +π()2sin (03f x x ωω⎛⎫=+<< ⎪⎝⎭ππππ2sin 2sin 123123y x x ωωω⎡⎤⎛⎫⎛⎫=++=++ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦ππ2sin 123y x ωω⎛=++ ⎝ππ3k +=∈Z 122k ω=+k ∈Z 06ω<<2ω=()π2sin 23f x x ⎛⎫=+ ⎪⎝⎭要使在上的最小值为，则在上的最小值为，当时，，又所以14．答案：解析：由函数，可得，，所以，所以，可得或，即或，令，，可得，，当时，可得，在单调递增，且；当时，且；当时，可得，在单调递减；当时，可得，在单调递增，且又当时，，，当时，且；作出函数，的图象，如图所示，要使得有两个实数根，即有两个不同的零点，结合图象，可得或，即实数a 的取值范围为.故答案为：.()f x π,4t ⎡⎤-⎢⎥⎣⎦1-πsin 23y x ⎛⎫=+ ⎪⎝⎭π,4t ⎡⎤-⎢⎥⎣⎦12-π,4x t ⎡⎤∈-⎢⎥⎣⎦πππ2,2363x t ⎡⎤+∈-+⎢⎥⎣⎦π7πsin sin 66⎛⎫⎛⎫-== ⎪ ⎪⎝⎭⎝⎭ππ263t -≤+≤π4t ≤≤1,0(0,e)e ⎛⎫- ⎪⎝⎭()(1)e e x x f x x =-+()0f x =(1)e e 0x x x a -+-=(1)e x a x -=--0a -≥(1)0e x x --≥1x ≤e (1)e x x a x -=-e (1)e x x a x -=-(2)e x a x =-e x a x =()(2)e x g x x =-()e x h x x =()(1)e x g x x =-'()(1)e x h x x +'=1x ≤()0g x '≥()g x (,1]-∞()1e g =x →-∞()0g x >()0g x →1x <-()0h x '<()h x (,1)-∞-11x -<<()0h x '>()h x (1,1)-()1h -=0x <()0g x >()0h x <x →-∞()0h x <()0g x →()y g x =()y h x =(1)e e 0x x x a -+-=()y f x =10e a -<<0e a <<1,0(0,e)e ⎛⎫- ⎪⎝⎭1,0(0,e)e ⎛⎫- ⎪⎝⎭15．答案：（1）；（2）（3）解析：（1）因为，即，而，代入得，解得：.（2）由（1）可求出，而，所以（3）因为，故以而故16．答案：（1）证明见解析；解析：（1）取中点M ，连接、，如图所示：1c =sin B =sin(2)A B -=2222cos a b c bc A =+-22162b c bc =++2b c =22264c c c =++1c =2b =0πA <<sin A ==sin a A =sin b A B a ===cos A =πA <<0B <<A ==1sin 22sin cos 24A A A ⎛⎫==⨯-= ⎪⎝⎭2122cos 12116A A =-=⨯-=sin B =B ==7sin(2)sin 2cos cos 2sin 8A B A B A B ⎛-=-== ⎝1BC EM MD，点D 是的中点，，又M 是的中点，，又在直三棱柱中，有，平面，平面，平面，且面，平面平面，，平面，且平面，，又，且平面，平面，又，平面，平面，面平面.（2）由（1）知平面，则设，则，，AB AC = BC AD BC ∴⊥ 1BC 1//DM CC ∴ 111ABC A B C -11//AA CC 1AA ⊥ABC//DM AE ∴DM ∴⊥ABC //AD 1BC E AD ⊂ADME ADME 1BC E EM =//AD ME ∴1CC ⊥ ABC AD ⊂ABC 1CC AD ∴⊥1CC BC C = 1CC BC ⊂、11BB C C AD ∴⊥11BB C C //AD ME ME ∴⊥11BB C C ME ⊂ 1BC E ∴ABC ⊥11BB C C ME ⊥11BB C C 11113B BC E B V S -=⋅△2BC a =BD a =AD =1112332B BC a a =⨯⋅=△112219332B BC Ea a V a -+-∴=⋅≤=由基本不等式知，当且仅当的体积最大，此时，以D 为坐标原点，所在直线为x轴，所在直线为y 轴，所在直线为z 轴建立空间直角坐标系，如图所示：则有，，，，，，，，设平面的一个法向量为，则有，取，设直线与平面所成的角为，故直线与平面17．答案：（1）；解析：（1）记“输入的数据集质量高”为事件A ，“一次数据能被软件准确分析”为事件Ba =11B BC E -a =DA DB DM A ⎫⎪⎪⎭0,C ⎛⎫ ⎪ ⎪⎝⎭B ⎛⎫ ⎪ ⎪⎝⎭32E ⎫⎪⎪⎭10,C ⎛⎫ ⎪ ⎪⎝⎭AC ⎛⎫∴= ⎪ ⎪⎝⎭ ()13C B =- 32BE ⎫=⎪⎪⎭1BC E ()111,,x n y z =11111130302n C B z n BE x y z ⎧⋅=-=⎪⎨⋅=+=⎪⎩ 1y =()2= AC 1BC E θsin cos ,n AC θ∴=== AC 1BC E 0.7510=，由题意可知：，，则，所以.所以一次数据能被软件准确分析的概率0.75.（2）由（1）可知：①依题意，，所以X 的方差②可知，令，解得，可知当，可得；，解得，可知当，可得；于是所以当时，最大，即时，的值最大.；（2）.解析：（1）易知点、因为椭圆的离心率为，，；（2）设点上一点，先证明直线，()P A =()|0.8B A =()|0.3P B A =()()10.9P A P A =-=()()(()()||0.75P B P B A P P B A P A ==()0.75P B ==3,4X B n ⎛⎫~ ⎪⎝⎭()D X =()88888833318C 1C 4444n n n n P X --⎛⎫⎛⎫⎛⎫⎛⎫==-= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭8831C 44n n n a -⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭878188831C 4431C 44n n n n -+-⎛⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭==⎛⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭1>9n ≤9n ≤1n n a a +>1<10n ≥10n ≥1n n a a +<123101112a a a a a a <<<>>>10n =n a 10n =()8P X =21y +=0x y -=(),0F c (0,B b a ==c e a ==2=1b ==21y +=(00,M x y 21y +=MN 01y y +=联立，消去y 并整理得，，在点.在直线的方程中，令，可得，即点，直线的斜率为的方程为的方程中，令，可得，因为，则，即，所以，，因为，，故所以，直线l 的方程为，即.；（2）（ⅰ）解析：（1），，，，所以当，，，所以00221515x xy y x y ⎧+=⎪⎪⎨⎪+=⎪⎩220020x x x x -+=2200440x x ∆=-=21y +=()00,M x y 01y y +=MN 0x =y =00y >010,N y ⎛⎫⎪⎝⎭BF BF b k c =-=PN 2y x =0y =x =01,02P y ⎛⎫- ⎪⎝⎭//MP BF MP BF k k =200000021212y y x y x y ==++)20050x y +=005x y =-222000615x y y +==00y ∴>0y =0x =1x y =0x y -+=()n h x =()31f x x x =+-()231f x x '=+00x =()01f x =-()01f '=()1:11l y x y x --=⇒=-101y x =⇒=()11f =()14f '=2:14(1)43l y x y x -=-⇒=-当.（2）（ⅰ）因为二次函数有两个不等实根b ，c ，所以不妨设，则，因为，所以，所以在横坐标为的点处的切线方程为，令，则即所以.因为，，所以，所以.令，则，又，，数列是公比为2的等比数列..令，则当时，，所以在单调递减，所以，即，因为，所以.20y x =⇒=()f x ()()()f x a x b x c =--()()()()2n n n n n f x a x b x c ax ab ac x abc =--=-++()()2f x a x b c '=--()()2n n f x a x b c '=--n x ()()()2n n n y f x a x b c x x -=---0y =()()()()2222n n n n n n a x x b c f x ax abc x a x b c a x b c ⋅----===----1n x +=()n x =()()2222222222n n n n n n n n x bc b x b c x bx b x bc c x b c x cx c -----+===-----+21n n c c +=n x c >c b >1n c >()21ln ln 2ln 0n n n c c c +==>ln n n d c =12n n d d +=11ln 0d c =>2={}n d ()11ln 2n n d c -=⋅()()=ln 11g x x x x -+>()11=1xg x x x-'-=1x >()0g x '<()g x ()1,+∞()()g g 1ln1110x <=-+=()ln 11x x x <->1n c >0ln 1n n n c c c <<-<10nc >>1121211111111111ln 22n n n c c c d d d c -⎛⎫+++<+++=+++ ⎪⎝⎭ 1111121211ln ln 212n n c c ⎡⎤⎛⎫-⎢⎥ ⎪⎡⎤⎛⎫⎝⎭⎢⎥==-<⎢⎥⎪⎢⎥⎝⎭⎢⎥⎣⎦-⎢⎥⎣⎦。

深圳市福田区外国语高级中学2022-2023学年高一上学期入学考试数学学科试题答题注意事项：1.本试卷满分100分；考试用时90分钟；2.本试卷分二卷,不按要求答卷不得分。

一、选择题（每题3分，共30分）1、下列立体图形中，主视图和左视图不一样的是（）A．B．C．D．2、下列运算正确的是（）A．3x2﹣2x2＝1 B．2m•（﹣2m）2＝8m3C．x10÷x10＝0 D．（2a2b）3＝8a5b33、我国神舟十三号载人飞船和航天员乘组于2022年4月16日返回地球，结束了183天的在轨飞行时间．从2003年神舟五号载人飞船上天以来，我国已有13位航天员出征太空，绕地球飞行共约2.32亿公里．将数据232000000用科学记数法表示为（）A．0.232×109B．2.32×109C．2.32×108D．23.2×1084、如图，将矩形纸片ABCD沿EF折叠后，点D、C分别落在点D1、C1的位置，ED1的延长线交BC于点G，若∠EFG＝64°，则∠EGB等于（）A．128°B．130°C．132°D．136°5、家务劳动是劳动教育的一个重要方面，教育部基础教育司发布通知要求家长引导孩子力所能及地做一些家务劳动．某校为了解七年级学生平均每周在家的劳动时间，随机抽取了部分七年级学生进行调查，根据调查结果，绘制了如下频数分布表：根据表中的信息，下列说法正确的是（）A．本次调查的样本容量是50人B．本次调查七年级学生平均每周在家劳动时间的中位数落在二组C．本次调查七年级学生平均每周在家劳动时间的众数落在四组D．若七年级共有500名学生，估计平均每周在家劳动时间在四组的学生大约有100人4题5题6、下列命题中，是真命题的有（）①对角线相等且互相平分的四边形是矩形②对角线互相垂直的四边形是菱形③四边相等的四边形是正方形④四边相等的四边形是菱形A．①②B．②③C．③④D．①④7、我国古代数学名著《张邱建算经》中记载：“今有清酒一斗直粟十斗，醑酒一斗直粟三斗．今持粟三斛，得酒五斗，问清、醑酒各几何？”意思是：现在一斗清酒价值10斗谷子，一斗醑酒价值3斗谷子，现在拿30斗谷子，共换了5斗酒，问清、醑酒各几斗？如果设清酒x斗，那么可列方程为（）A．10x+3（5﹣x）＝30 B．3x+10（5﹣x）＝30 C．+＝5D．+＝58、如图，∠MON＝60°，以点O为圆心，适当长为半径画弧，交OM于点A，交ON于点B；分别以点A，B为圆心，大于AB的长为半径画弧，两弧在∠MON的内部相交于点P，画射线OP；连接AB，AP，BP，过点P作PE⊥OM于点E，PF⊥ON于点F．则以下结论错误的是（）A．△AOB是等边三角形B．PE＝PF C．△PAE≌△PBF D．四边形OAPB是菱形9、已知抛物线y＝x2﹣bx+c，当x＝1时，y＜0；当x＝2时，y＜0．下列判断：①b2＜2c；②若c＞1，则b＞；③已知点A（m1，n1），B（m2，n2）在抛物线y＝x2﹣bx+c上，当m1＜m2＜b时，n1＞n2；④若方程x2﹣bx+c＝0的两实数根为x1，x2，则x1+x2＞3．其中正确的有（）A．1个B．2个C．3个D．4个10、如图，正方形ABCD中，对角线AC、BD相交于点O，点E是BC的中点，AE交BD于点F，BH⊥AE于点G，连接OG，则下列结论中①OF＝OH，②△AOF∽△BGF，③tan ∠GOH＝，④FG+GH＝GO，正确的个数是（）A．1 B．2C．3 D．4二、填空（每题3分，共15分）11、因式分解：a 3﹣6a 2+9a ＝12、为了疫情防控，某小区需要从甲、乙、丙、丁4名志愿者中随机抽取2名负责该小区入口处的测温工作，则甲被抽中的概率是13、如图，AB 是⊙O 的弦，OC ⊥AB ，垂足为C ，OD ∥AB ，OC ＝OD ，则∠ABD 的度数为 度14、如图，正方形ABCD 的顶点分别在反比例函数y ＝（k 1＞0）和y ＝（k 2＞0）的图象上．若BD ∥y 轴，点D 的横坐标为3，则k 1+k 2＝15、如图，在边长为6的等边△ABC 中，D 、E 分别为边BC 、AC 上的点，AD 与BE 相交于点P ，若BD ＝CE ＝2，则△ABP 的周长为 ．三、计算题（共55分）16、（5分）计算：（1﹣π）0﹣2cos30°﹣|1﹣|﹣（）﹣1．17、（6分）先化简，再求值：（1﹣）÷，其中x ＝+1．18、（8分）教育部在《大中小学劳动教育指导纲要（试行）》中明确要求：初中生每周课外生活和家庭生活中，劳动时间不少于3小时．某走读制初级中学为了解学生劳动时间的情况，对学生进行了随机抽样调查，并将调查结果制成不完整的统计图表，如图： 平均每周劳动时间的频数统计表请根据图表信息，回答下列问题．8题10题14题13题15题（1）参加此次调查的总人数是人，频数统计表中a＝；（2分）（2）在扇形统计图中，D组所在扇形的圆心角度数是°；（1分）（3）该校准备开展以“劳动美”为主题的教育活动，要从报名的2男2女中随机挑选2人在活动中分享劳动心得，请用树状图或列表法求恰好抽到一名男生和一名女生的概率．（5分）19、（8分）某水果店经销甲、乙两种水果，两次购进水果的情况如表所示：（1）求甲、乙两种水果的进价；（4分）（2）销售完前两次购进的水果后，该水果店决定回馈顾客，开展促销活动．第三次购进甲、乙两种水果共200千克，且投入的资金不超过3360元．将其中的m千克甲种水果和3m千克乙种水果按进价销售，剩余的甲种水果以每千克17元、乙种水果以每千克30元的价格销售．若第三次购进的200千克水果全部售出后，获得的最大利润不低于800元，求正整数m的最大值．（4分）20、（9分)如图，在Rt△ABC中，∠C＝90°，AD平分∠BAC交BC于点D，O为AB上一点，经过点A，D的⊙O分别交AB，AC于点E，F，连接DF．（1）求证：BC是⊙O的切线；（3分）（2）连接DE，求证：△BDE∽△BAD；（3分）（3）若BE，sin B，求AD的长，直接写出答案（3分）21、（9分）已知二次函数y＝ax2+bx+3的自变量x的部分取值和对应函数值y如下表：x…﹣1 0 1 2 3 …y… 4 3 0 ﹣5 ﹣12 …（1）求二次函数y＝ax2+bx+3的表达式；（2分）（2）将二次函数y＝ax2+bx+3的图象向右平移k（k＞0）个单位，得到二次函数y＝mx2+nx+q 的图象，使得当﹣1＜x＜3时，y随x增大而增大；当4＜x＜5时，y随x增大而减小，求实数k的取值范围；（3分）（3）A、B、C是二次函数y＝ax2+bx+3的图象上互不重合的三点．已知点A、B的横坐标分别是m、m+1，点C与点A关于该函数图象的对称轴对称，求出∠ACB的度数．（4分）22、（10分）问题提出：如图（1），在△ABC中，AB＝AC，D是AC的中点，延长BC至点E，使DE＝DB，延长ED交AB于点F，探究的值．问题探究（1）先将问题特殊化．如图（2），当∠BAC＝60°时，直接写出的值；（3分）（2）再探究一般情形．如图（1），证明（1）中的结论仍然成立．（4分）问题拓展如图（3），在△ABC中，AB＝AC，D是AC的中点，G是边BC上一点，＝（n＜2），延长BC至点E，点DE＝DG，延长ED交AB于点F．直接写出的值（用含n的式子表示）（3分）．2022年高一年级新生入学考试 数学学科答案一、选择题（每题3分，共30分） 1-5 D B C A B 6-10 D A D B C二、填空题 （每题3分，共15分） 11、 a （a ﹣3）2 ； 12、 （ 21） ； 13、 105 ；14、 18 ； 15、771842+ （或．77186+ ） 9、解：∵a ＝＞0，∴抛物线开口向上，当x ＝1时，y ＜0；当x ＝2时，y ＜0， ∴抛物线 与x 轴有两个不同的交点，∴Δ＝b 2﹣4ac ＝b 2﹣2c ＞0，∴b 2＞2c 故①错误； ∵当x ＝1时，y ＜0；当x ＝2时，y ＜0， ∴﹣b +c ＜0；∴b ＞+c ，当c ＞1时，则b ＞，故②正确；抛物线的对称轴为直线x ＝b ，且开口向上， 当x ＜b 时，y 的值随x 的增大而减小，∴当m1＜m2＜b时，n1＞n2，故③正确；∵方程x2﹣bx+c＝0的两实数根为x1，x2，∴x1+x2＝2b，由②可知，当c＞1时，则b＞，∵c不一定大于1 ∴x1+x2不一定大于3，故④错误；综上，正确的有②③，共2个，故选：B．10、解：∵四边形ABCD是正方形，∴AC⊥BD，AB＝BC＝AD，OA＝OB＝OC＝OD，AD∥BC，∠ABO＝∠ACB＝45°，∴∠AOF＝∠BOH＝90°，∵BH⊥AE，∠AFO＝∠BFG，∴∠OAF＝∠OBH，在△AOF和△BOH中，，∴△AOF≌△BOH（ASA），∴OF＝OH，①正确；∵∠AOF＝∠BGF＝90°，∠OAF＝∠OBH，∴△AOF∽△BGF，②正确；∵点E是BC的中点，∴AB＝BC＝2BE，∵∠AOB＝∠AGB＝90°，∴A、B、G、O四点共圆，∴∠BOG＝∠BAE，∠AGO＝∠ABO＝45°，∵∠BOG+∠GOH＝90°，∠BAE+∠AEB＝90°，∴∠GOH＝∠AEB，∴tan∠GOH＝tan∠AEB＝＝2，③错误；过点O作OM⊥OG，交GH延长线于点M，如图所示：∵∠BOC＝∠GOM＝90°，∴∠FOG＝∠HOM，∵∠OMG+∠OGM＝90°，∠OGF+∠OGM＝90°，∴∠OMH＝∠OGF，由①正确得：OF＝OH，在△OMH和△OGF中，，∴△OMH≌△OGF（AAS），∴OG＝OM，FG＝HM，∴△GOM是等腰直角三角形，∴GM＝OG，∵GM＝GH+HM＝GH+FG，∴FG+GH＝GO，④正确；正确的个数有3个，故选：C．14、解：连接AC交BD于E，延长BD交x轴于F，连接OD、OB，如图：∵四边形ABCD是正方形，∴AE＝BE＝CE＝DE，设AE＝BE＝CE＝DE＝m，D（3，a），∵BD∥y轴，∴B（3，a+2m），A（3+m，a+m），∵A，B都在反比例函数y＝（k1＞0）的图象上，∴k1＝3（a+2m）＝（3+m）（a+m），∵m≠0，∴m＝3﹣a，∴B（3，6﹣a），∵B（3，6﹣a）在反比例函数y＝（k1＞0）的图象上，D（3，a）在y＝（k2＞0）的图象上，∴k1＝3（6﹣a）＝18﹣3a，k2＝3a，∴k1+k2＝18﹣3a+3a＝18；15、解：∵△ABC是等边三角形，∴AB＝BC，∠ABD＝∠C＝60°，在△ABD和△BCE中，∴△ABD≌△BCE（SAS），∴∠BAD＝∠CBE，∴∠APE＝∠ABP+∠BAD＝∠ABP+∠CBE＝∠ABD＝60°，∴∠APB＝120°，在CB上取一点F使CF＝CE＝2，则BF＝BC﹣CF＝4，∴∠C＝60°，∴△CEF是等边三角形，∴∠BFE＝120°，即∠APB＝∠BFE，∴△APB∽△BFE，∴＝＝2，设BP＝x，则AP＝2x，作BH⊥AD延长线于H，∵∠BPD＝∠APE＝60°，∴∠PBH＝30°，∴PH＝，BH＝，∴AH＝AP+PH＝2x+＝x，在Rt△ABH中，AH2+BH2＝AB2，即（x）2+（x）2＝62，解得x＝或﹣（舍去），∴AP＝，BP＝，∴△ABP的周长为AB+AP+BP＝6++＝6+＝，故答案为：．三、计算（共55分）16、（5分）计算：（1﹣π）0﹣2cos30°﹣|1﹣|﹣（）﹣1．-=-+-1（化简对一个得4分，共分）43131分）（1322 --=20、（6分）先化简，再求值：（1﹣）÷，其中x ＝+1．2)1()1)(1(11+-+÷+-+=x x x x x x ）（1)1()1(112-++⨯+=x x x x 分411 -=x 时当12+=x22=原式分）分，无化最简扣（12 18、（8分）（1） 150 人， 60 ；................(2分，1空1分)（2） 36 °；................(1分)（3）画树状图如下：.................(2分)共有12种等可能的结果，其中恰好抽到一名男生和一名女生的结果有8种，.................(2分，写出关键种数各得1分)∴恰好抽到一名男生和一名女生的概率为＝．.................(1分)19、（8分）解：（1）设甲两种水果的进价为每千克a元，乙两种水果的进价为每千克b元．由题意，得，......................................................(2分)解得，..............................(2分)答：甲两种水果的进价为每千克12元，乙两种水果的进价为每千克20元．（2）设第三次购进x千克甲种水果，则购进（200﹣x）千克乙种水果．由题意，得12x+20（200﹣x）≤3360，解得x≥80．......................................................(1分)设获得的利润为w元，由题意，得w＝（17﹣12）×（x﹣m）+（30﹣20）×（200﹣x﹣3m）＝﹣5x﹣35m+2000，..................(1分)∵﹣5＜0，∴w随x的增大而减小，∴x＝80时，w的值最大，最大值为﹣35m+1600，.................(1分)由题意，得﹣35m+1600≥800，解得m≤，∴m的最大整数值为22．.................(1分)20、（9分)【解答】（1）证明：连接OD，如图1所示：∵AD平分∠BAC，∴∠BAD＝∠CAD，∵OA＝OD，∴∠BAD＝∠ODA，∴∠CAD＝∠ODA，∴OD∥AC，∴∠ODB＝∠C＝90°，∴BC⊥OD，又∵OD是圆O的半径，∴BC是圆O的切线；...............................................................（3分，过程酌情给分）（2）证明：连接DE，如图2所示：∵BC是⊙O的切线，∴∠BDO＝90°，∵AE是⊙O的直径，∴∠ADE＝90°，∴∠BDE＝∠ADO＝90°﹣∠EDO，∵OD＝OA，∴∠OAD＝∠ADO，∴∠BDE＝∠OAD，∵∠B＝∠B，∴△BDE∽△BAD；.........................................................................（3分，过程酌情给分）（3）解：在Rt△BOD中，sin B＝＝，设圆O的半径为r，则＝，解得：r＝，∴AE＝2r＝，AB＝AE+BE＝10，在Rt△AEF中，∠AFE＝90°，sin∠AEF＝sin B＝＝，∴AF＝，∵∠B＝∠ADF，∠CAD＝∠BAD，∴△ABD∽△ADF，∴＝，∴AD2＝AF•AB，∴AD＝＝＝3．...................................................（3分,直接写出答案）21、解：（1）将（﹣1，4），（1，0）代入y＝ax2+bx+3得：，解得，.∴二次函数的表达式为y＝﹣x2﹣2x+3；...................................................（2分，没写过程，只给1分）（2）如图：（共3分）∵y＝﹣x2﹣2x+3＝﹣（x+1）2+4，∴将二次函数y＝﹣x2﹣2x+3的图像向右平移k（k＞0）个单位得y＝﹣（x﹣k+1）2+4的图象，∴新图象的对称轴为直线x＝k﹣1，.................................................（1分）∵当﹣1＜x＜3时，y随x增大而增大；当4＜x＜5时，y随x增大而减小，且抛物线开口向下，...........（1分）∴3≤k﹣1≤4，解得4≤k≤5，...................................................（1分）（3）当B在C左侧时，过B作BH⊥AC于H，如图：∵点A、B的横坐标分别是m、m+1，∴y A＝﹣m2﹣2m+3，y B＝﹣（m+1）2﹣2（m+1）+3＝﹣m2﹣4m，∴A（m，﹣m2﹣2m+3），B（m+1，﹣m2﹣m），∵点C与点A关于该函数图像的对称轴对称，而抛物线对称轴为直线x＝﹣1，∴＝﹣1，AC∥x轴，∴x C＝﹣2﹣m，∴C（﹣2﹣m，﹣m2﹣2m+3），过B作BH⊥AC于H，∴BH＝|﹣m2﹣4m﹣（﹣m2﹣2m+3）|＝|﹣2m﹣3|，CH＝|（﹣2﹣m）﹣（m+1）|＝|﹣2m ﹣3|，∴BH＝CH，∴△BHC是等腰直角三角形，∴∠HCB＝45°，即∠ACB＝45°，当B在C右侧时，如图：同理可得△BHC是等腰直角三角形，∴∠ACB＝180°﹣∠BCH＝135°，综上所述，∠ACB的度数是45°或135°．.......................(共4分，过程2分，过程酌情给分，答对一个答案1分）22、（10分）【解答】解：（1）如图，取AB的中点G，连接DG，∵点D是AC的中点，∴DG是△ABC的中位线，∴DG∥BC，∵AB＝AC，∠BAC＝60°，∴△ABC是等边三角形，∵点D是AC的中点，∴∠DBC＝30°，∵BD＝ED，∴∠E＝∠DBC＝30°，∴DF⊥AB，∵∠AGD＝∠ADG＝60°，∴△ADG是等边三角形，∴AF＝AG，∵AG＝AB，∴AF＝AB，∴；.........................................................(3分，直接写出答案) （2）取BC的中点H，连接DH，∵点D为AC的中点，∴DH∥AB，DH＝AB，∵AB＝AC，∴DH＝DC，∴∠DHC＝∠DCH，∵BD＝DE，∴∠DBH＝∠DEC，∴∠BDH＝∠EDC，∴△DBH≌△DEC（ASA），∴BH＝EC，∴，∵DH∥AB，∴△EDH∽△EFB，∴，∴，∴；.........................................................(4分，过程酌情给分，只写答案不给分）问题拓展取BC的中点H，连接DH，由（2）同理可证明△DGH≌△DEC（ASA），∴GH＝CE，∴HE＝CG，∵＝，∴，∴，∴，∵DH∥BF，∴△EDH∽△EFB，∴，∵DH＝AB，∴，∴．.....................................................(3分，直接写出答案）。