九年级一摸试题

2024年各省市九年级英语联考统考一模试题（中考）精选阅读理解15篇（含答案解析）bcdeSwitzerland were able to guide lightning tor meters.The heat from the laser creates a path of air that is less thick than the air around it. The path also has a special charge (电荷). The lightning can follow this path almost as if it were a lightning rod. Scientist Matteo Clerici said, “The fact that we managed to do it in an outdoor environment is a very big step.”But the laser still didn’t guide the lightning as far as the scientists would like. Besides, the laser is also very expensive. The scientists say it cost about $2 billion. It will probably take 10 or more years before a laser like this is truly able to protect large buildings.6．To know how powerful lightning can be, which paragraph can we read?A．Paragraph 2.B．Paragraph 3.C．Paragraph 4.D．Paragraph 5.7．What is the laser technology expected to protect?A．High-rise buildings.B．Large buildings.C．Beautiful buildings.D．Important buildings.8．Why are lasers not used widely for changing the path of lightning strike now?A．Putting metal rods on the buildings is the best way.B．Some buildings are so large that it’s difficult to protect.C．Lasers are only able to guide lightning for a short distanceD．Lasers are so expensive that scientists can’t pay for experimenting.9．What can we learn from what Matteo Clerici said?A．Scientists still need to work harder to achieve a greater success.B．It is not easy for scientists to guide lightning with lasers outside.C．Scientists need to change working environment in next experiments.D．It is a great progress for scientists to guide lightning with lasers outside.10．What can we get to know at the end of the passage?A．Behind bad luck comes good luck.B．A journey of a thousand miles begins with a single step.C．There is still a long way to go before a laser can really work.D．For scientists, working together is better than working alone.CHave you ever dreamed of travelling all the way over the rainbow? Well, it’s easier than you think.All you need to do is to book a plane ticket to Rainbow Mountain in Peru (秘鲁).Rainbow Mountain is a beautiful natural wonder. It lies in the Andes in Cusco (库斯科的安第斯山脉). As its name suggests, the mountain has different colours.But why is it in yellow, green, red and purple? The reason is the ice that covered the area centuries ago. When it started to melt (融化), the water mixed with the minerals (矿物质) in the ground and turned the earth into many colours.If you plan your trip to the mountain, try to go during warmer months when there is less rain or snow. Rain or snow makes the climbing more difficult and the colours will look less beautiful. The best time is from March to November, when there are blue skies and pleasant weather. At the same time, visit it in the morning or evening, either right after sunrise or right before sunset. Very sunny days may make you not take nice photos.To get to Rainbow Mountain, you should first travel to Cusco—a province in the south of Peru. Then you can take a drive to Qesoyuno. From there you can start the journey on foot. It takes about a two-or-three-hour walk to the top. This is really the best way, but the trip is very difficult. Because the mountain sits at a very high altitude (海拔) about 5,200 meters above the sea level, so bring enough water and take your time.11．How does the writer start the passage?A．By listing a fact.B．By asking a question.C．By telling a story.D．By giving an example.12．What can we learn about Rainbow Mountain?A．It has seven different colours.B．It’s a man-made wonder.C．It was covered by ice in the past.D．It’s the most famous place of Peru.13．Which of the following is best time for a trip to Rainbow Mountain?A．At noon of a cold day in December.B．On the evening of a rainy day in August.C．On the afternoon of a snowy day in January.D．On the morning of a sunny day in September.14．Which of the following is TRUE?A．Rainbow Mountain lies in the Andes in Cusco.B．Very sunny days will help you take nice photos on Rainbow Mountain.18．What did Fu Lei think of Fu Cong’s future?A．It would be uncertain.B．It would be hopeful.C．It would be difficult.D．It would be interesting.19．Why was Fu Cong advised to read famous Chinese texts?A．To be a richer man.B．To do more academic training.C．To help more people.D．To become a better person.20．What’s the Chinese meaning of the underlined word “impact” in the last paragraph?A．改变B．影响C．贡献D．挑战EI’m Nancy. Do you remember the name of your kindergarten (幼儿园) teacher? I do. Her name was Mrs. White. And I remember I thought she must be a sister of Snow White, because she had the same bright blue eyes, short dark hair and fair skin as her.I don’t remember much about what we learned in her class, but my mother once told me that we used to write a lot. And I would bring back what I wrote and she would look at it and see there were so many mistakes. But no red corrections (改正), and always a star. Sometimes even a Good, which would make me fly with happiness. So one day when my mother went to meet Mrs. White for one of those parent-teacher meetings, she asked her why she never corrected my mistakes in the right spellings of words or pointed out grammatical mistakes.“The children are just beginning to get excited about using words and forming (形成) sentences. I don’t want my students to lose interest because of red ink (墨水). Spelling and grammar can wait, the wonder of words won’t...”Mrs. White said.Later I knew that if Mrs White had used her red pen often, I probably wouldn’t be telling you about this now. I look back now and think she must have been a rather unusual teacher to use as less red pen as possible.I used to misspell (拼错) “beautiful” a lot, and could never remember that the “e”goes before the “a”. It made my teacher in high school angry. She asked me to use “pretty” when I was writing. I didn’t listen to her. To my eyes, “pretty” is easier to spell, but it doesn’t hold as much as we mean sometimes.And thanks to Mrs. White, I never worried about writing what I meant even if I couldn’t quite spell it out, because life isn’t “pretty”. It’s “beautiful”.21．How might Nancy’s mother feel before she went to meet Mrs. White?A．Worried.B．Pleased.C．Proud.D．Embarrassed.22．Which one is right according to what Mrs. White said in Paragraph 3?A．Children don’t have the patience in spelling words.B．Red corrections are used to draw children’s attention.C．Children’s interest of learning words is very important.D．Grammar and spelling should be paid more attention to.23．What is the correct order according to the text?a. Nancy did badly in her schoolwork.b. Nancy’s mother understood what Mrs. White had done.c. Nancy would never mind misspelling to express herself.d. Mrs. White explained why she never corrected Nancy’s mistakes.e. Nancy’s high school teacher was not satisfied with her for misspelling.A．a-d-b-e-c B．b-e-a-d-c C．c-d-a-e-b D．d-a-e-c-b24．What can we learn from the text?A．One should help children spell correct words.B．We should never pay attention to spelling and grammar.C．Children should know how to use simple words to express themselves.D．Using words to express is more important than just correcting spelling.25．What’s the best title for the text?A．Mother’s Love.B．“Beautiful” Life.C．My Childhood.D．Growing up in Mistakes.FA man had a little dog, and he liked it a lot. He would pat (拍) its head, put it on his knee and talk to it. Then he would give it some food from his own plate.A donkey looked in through the window and saw the man and the dog.“Why doesn’t he choose me as his pet?” said the donkey. “It is not fair. I work hard, but the dog only shakes its tail, barks and jumps onto the master’s knee. It is not fair.”Then the donkey said to himself, “If I do what the dog does, the master may choose me as his pet.”As we walked about halfway down the hillside, she fell over a stone. I jogged up to where she tripped. Suddenly, I saw a lion about ten feet up on a huge rock watching me. It was making a long deep angry sound.I stood perfectly still, holding my breath, wondering what to do. Christina was crying down below.I couldn’t shout to her to be quiet, or the lion might attack me.Then, remembering Dad’s words, I slowly dropped my backpack and took off my T-shirt. With the pack on one arm and the T-shirt on the other, I spread my arms, trying to look as wide and big as I could. Carefully I moved away down the hillside toward Christina, keeping my eyes on the lion.“Christina,” I called. “Stop crying. Get up slowly and catch my belt. We’re going down the hill. There’s a lion at the top.”We moved quietly and slowly down the hill. Once back to the forest, with the lion out of view, I removed the sweat (汗水) from my face with my T-shirt before putting it on, and looked at Christina. Hatless, red eyes, a few small cuts but nothing major.I pulled out the map. The campground was on the other side of the hill. We had hiked for miles before we finally made our way back to our site.Dad saw me first.“Where have you been?” he shouted.“We were so worried,” Mother cried.“Mommy, you didn’t have to worry. Sean is real smart.” Christina said.I caught Dad’s eye. He smiled. At that moment I realized I was a big brother.45．How did Christina feel before she fell over a stone?A．Happy.B．Proud.C．Nervous.D．Worried.46．What did Sean do when he first saw the lion?A．He started crying.B．He picked up a huge rock.C．He remained still.D．He jogged up to his sister.47．Why did Sean try to look wide and big?2. The free buses for theand Spring Town57．It is obvious that Andy Lee left his ________ when he booked his ticket.A．home addressB．mobile phone numberC．email addressD．company address58．The travellers who got the letter from NR ________.A．bought the tickets onlineB．wanted to travel to Black TownC．worked for National RailwayD．booked the tickets on August 1459．National Railway writes this letter because ________.A．there is a train ticket saleB．a train line will be closed in JulyC．it will open a new train line in AugustD．some of its trains will run on different lines60．What is true about NR’s trains between August 14 and 28?A．No trains will stop at Spring Town.B．Trains that change lines will all stop at Black Town.C．People can take the free buses to any station on the Sand Town-Spring Town line.D．People can go to Hill Town on any train that runs between Green City and Cloud City. 61．From the reading material, we can infer (推断) that National Railway will ________ from August 24 to August 28.A．carry a lot of travellers to Gray Village by using their free busesB．fix the railway between Sand Town and Spring TownC．make a lot of mistakes in carrying travellers to wrong placesD．stop the Green City-Cloud City line trains62．James lives in Smoke Town. He wants to go to Black Town on August 19. How can he get there?A．Take Train RL202 to Green City, get off there, and take the free bus.B．Take Train RL103 to Green City, get off there, and take the free bus.C．Take Train RL102 to Spring Town, get off there, and take Train RL201.D．Take Train RL101 to Cloud City, get off there, and take the free bus.63．What have led to the death of coral reefs this year?A．Ocean animals.C．Sea creatures.64．What does the underlined word “ones” in Paragraph 2 refer to?67．Where can we probably find the passage?A．In a film review.B．In a science report.C．In a travel guide.D．In an art magazine.OI walked into a stranger as he passed by me.“Excuse me,” I said.He replied with a smile and said, “Please excuse me, too. I didn’t notice you.” We apologized and went for our own ways.Later that day, when I was cooking, my daughter was standing too near. When I turned to reach for some milk, I nearly knocked her over. “Move out of the way!” I shouted.She walked away sadly. But I didn’t feel like I had to apologize to her.While I was in bed that evening, my husband said to me. “While dealing with a stranger, you were polite. But with a daughter you love, you were unkind. Your daughter brought you some flowers that she picked herself this afternoon. You will find them in the kitchen by the door. Have you seen the tears in her eyes?”I quietly went and sat down by my daughter’s bed.“Honey, I am sorry,” I said. “Are these the flowers you picked for me?”She said, “I found them by the tree. I picked them because they’re pretty like you. I knew you’d like them, especially the blue ones.”I tearfully replied, “Sweetie, I’m really sorry for the way I acted today. I shouldn’t have shouted at you.”68．The writer was ________ to the stranger who she walked into.A．mad B．honest C．unkind D．polite69．Where were they when the writer shouted at her daughter?A．In the kitchen.B．By the tree.C．In the bedroom.D．In the garden.70．What did the writer’s husband think when he saw her action?A．The little girl shouldn’t cry.B．She shouldn’t shout at their daughter.C．She shouldn’t say sorry to the stranger.D．Both he and his wife should apologize to their daughter.71．What may be the writer’s favorite color according to the passage?A．Yellow.B．Pink.C．Blue.D．Red.72．What can be the best title for the passage?A．Be Friendly to Strangers B．Mothers Like FlowersC．Be Kind to Loved Ones D．Love Between Parents and Children参考答案1．B 2．A 3．C 4．B 5．B【导语】本文主要介绍了首批五个国家公园。

1 单词拼写 一、根据汉语及首字母填空 1．（2023·安徽合肥·统考一模）Mike missed several good chances to s_______（得分）in the first half.

2．（2023·安徽合肥·统考一模）He’s always an active man and always e_______ (期待) that things are going the right way. 3．（2023·安徽合肥·统考一模）It’s necessary for children to learn some b_______ (基本的) life skills. 4．（2023·安徽合肥·统考一模）Confucius said, “Behave toward everyone as if receiving a great g_______（客

人）.” 5．（2023·安徽合肥·模拟预测）Her voice is too l________ (低的). I can’t hear what she says clearly. 6．（2023·安徽合肥·模拟预测）She thinks life in a foreign c________ (国家) is very different. 7．（2023·安徽合肥·模拟预测）The problem is that we write them down, but f________ (忘记) them soon. 8．（2023·安徽合肥·模拟预测）Now some people are used to buying m________ (餐) from restaurants. 9．（2023·安徽合肥·统考一模）Steven Hawking is one of the greatest scientists a________ (活着的) in the world. 10．（2023·安徽合肥·统考一模）Mr.Wang g________ (毕业) from Beijing University when he was 24 years old. 11．（2023·安徽合肥·统考一模）Our government has made several laws to p________ (保护) teachers. 12．（2023·安徽合肥·统考一模）You’d better know a lot about their c________ (风俗) before you go abroad. 13．（2023·安徽芜湖·统考一模）It seemed impolite that I r________ (拒绝) her invitation yesterday morning. 14．（2023·安徽芜湖·统考一模）The book is well w________ (值得) reading for a second time. 15．（2023·安徽芜湖·统考一模）He decided to d________ (奉献) the rest of his life to art. 16．（2023·安徽芜湖·统考一模）We must take p________ (积极的) steps to deal with the problem. 17．（2023·安徽芜湖·统考一模）I am facing a c________ (选择) between staying with my family or studying abroad. 18．（2023·安徽马鞍山·校考一模）I believe you will make progress in Chinese if you read these p____________（诗歌）aloud every day. 19．（2023·安徽马鞍山·校考一模）Saying “no” is a b________________（基本的）right for everyone. 20．（2023·安徽马鞍山·校考一模）A true friend r________（伸手） for your hand and touches your heart. 21．（2023·安徽淮北·校考一模）She was told not to s________ (传播) this secret around. 22．（2023·安徽淮北·校考一模）The Caspian Sea is the d________ (最深的) of all the salt lakes. 23．（2023·安徽淮北·校考一模）He went to Chongqing for a trip w________ (没有) telling me. 24．（2023·安徽淮北·校考一模）Can you tell me the r________ (理由) why you are late for school? 2

2024年3月学情调研九年级语文试卷(本试题卷共8页，满分 120分，考试时间150分钟)祝考试顺利温馨提示：1. 答卷前，考生务必将自己的姓名、准考证号填写在试卷和答题卡上，并将准考证号条形码粘贴在答题卡上指定位置。

2. 选择题的作答：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。

写在试卷、草稿纸和答题卡上的非答题区域均无效。

3. 非选择题的作答：用黑色签字笔直接答在答题卡上对应的答题区域内，写在试卷、草稿纸和答题卡上的非答题区域均无效。

4. 考试结束后，请将本试卷和答题卡一并交回。

一、积累与运用(20 分)班级开展“君子自强不息”学习活动，特邀请你一起来参与。

1. (2分) 在朗诵会环节中，同学们纷纷展示，请你选出以下朗读处理不合适的一项。

A. 小忠这样朗读下面的诗句：我是你雪被下古莲的胚(pēi)芽……是绯(fēi)红的黎明/正在喷薄(pēn bó)——祖国啊!B. 小华朗诵小诗《苔》，这样处理节奏：白日/不/到处，青春/恰自/来。

苔花/如/米小，也学/牡丹/开。

C. 小宇在朗诵“为什么我的眼里常含泪水?因为我对这土地爱得深沉……”时，为了表现出沉痛悲壮的感情，语速缓慢，语调低沉凝重。

D. 小玟认为“——让∨暴风雨∨来得更猛烈些．．．吧！”这一祈使句是革命者的战斗宣言，在朗读时要饱含激情，读得坚定有力，鼓舞人心。

(“V”表示停顿，加点的词要重读)2. (2分) 小忠写了个“莫”字，请你分别加上偏旁组成新的汉字，填入相应括号内。

A. □然回首B. 羡□不已C. 朝思□想D. 落下帷□3. (2分) 小华在活动前想到了一副对联：A. 励志求学展抱负 B. 勤学苦练创辉煌，但他不知如何分辨上下联，请你帮其作出选择。

(填序号)上联: 下联:4. (3分) 下面是小玟在“初三当自强”演讲环节中所写讲演稿的部分内容，请你帮其完善。

中考已悄然来到眼前，2024年的春天，是我们人生的春天，我们将迎战中考，【A】这既是我们追求梦想的起点，又是我们初中生涯的终点。

九年级数学一、选择题（每小题3分，共30分）下列各小题均有四个选项，其中只有一个是正确的．1．如图，数轴上点所表示的数的相反数是 A．B．3C．D．2．砚台与笔、墨、纸是中国传统的文房四宝，是中国书法的必备用具．如图是一方寓意“规矩方圆”的砚台，它的俯视图是 A B C D3．中原熟，天下足．处于中原的河南一直是我国重要的粮食大省，最近几年粮食总产量更是连续突破1300亿斤，为保证国家粮食安全做出了突出贡献．数据“1300亿”用科学记数法表示为 A．B．C．D．4．甲、乙两个学校统计男女生人数，分别绘制了扇形统计图（如图），下列说法正确的是 A．甲校的男生人数比乙校的男生人数多B．甲、乙两个学校的人数一样多C．乙校的女生人数比甲校的女生人数多D．甲校的男女生人数一样多5．如图，直线，，，则的度数是（）A．B．C．D．6．对任意整数，都能 A．被3整除B．被4整除C．被5整除D ．被6整除7．如图，点是中优弧的中点，，为劣弧上一点，则的度数是 A()3-13-13()()111.310⨯101.310⨯120.1310⨯100.1310⨯()//a b231∠=︒28A∠=︒1∠61︒60︒59︒58︒n2(21)25n+-()A OBAD70ABD∠=︒C BD BCD∠()第2题第5题第4题A ．110°B ．C ．D ．8．一配电房示意图如图所示，它是一个轴对称图形．已知，，，则房顶离地面的高度为 A ．B ．C ．D ．9．如图，在中，，AB =2，AD =2AB ，点，分别是边，上的动点，连接，，点为的中点，点为的中点，连接，则的最小值为 A ．2BC ．1D10．生物兴趣小组在研究校园内银杏树植株年内的高度时，将得到的数据通过描点、连线得到相应的图象如图所示．现要根据这些数据选用合适的函数模型来描述植株在年内的生长规律．若选择的函数模型是，则a ______0，b ______0；若选择的函数模型是，则a ______0，b ______0．以上四处填入的不等号依次为 A ．，，，B ．，，，C ．，，，D ．，，，二、填空题（每小题3分，共15分）11之间的整数是　　．12．鱼缸里要饲养A ，B 两种鱼，经了解，A 种鱼生长温度的范围是，B 种鱼生长温度的范围是，那么鱼缸里的温度应该控制在　　的范围内．13．小明笔袋里有两支红笔和两支黑笔支笔的款式相同），上课做笔记时，他随机从笔袋中抽出两支笔，刚好是一红一黑的概率是　　．120︒130︒140︒6m BC =4m BE =ABC α∠=A EF ()(43sin )m α+(43tan )m α+3(4sin α+3(4)m tan α+ABCD 120C ∠=︒H G DC BC AH HG E AH F GH EF EF ()1~51~52y ax bx c =++ay b x=+()<><><>><><<>>><<C x ︒2028x ……C x ︒1925x ……C x ︒(4第7题第8题第9题第10题14．如图，是的直径，与⊙O 相切于点，的延长线交直线于点，连接，．若，，则的长度是___________.15．如图，在Rt △ABC 中，∠ACB =90°，BC =3，AC =4，点D ，E 分别是边AB ，AC 的中点，连接DE ．将△ADE 绕点D 按顺时针方向旋转()，点A ，E 的对应点分别为点G ，F ，GF 与AC 交于点P ．当直线GF 与△ABC 的一边平行时，CP 的长为．三、解答题（本大题共8个小题，满分75分）16．(10分)（1）计算：； （2）化简：．17．(7分)中小学午餐配送是郑州教育的“暖心服务”工程. 某校午餐原来由甲公司配送，为了提高饭菜质量，新学期午餐由乙公司配送. 学生会为了解用餐学生对甲、乙两家公司配送饭菜的满意情况，组织学生对两家公司的饭菜质量进行分数评价（满分为10分）. 学生会随机抽取了10位学生的评价分数：学生A学生B 学生C 学生D 学生E 学生F 学生G 学生H 学生I 学生J 甲公司76769798109乙公司65878889810学生会同学在进行数据分析时首先计算了各公司得分的平均数：甲公司7.8分；乙公司7.7分.（1）为了能够更加全面、客观地对甲、乙两家公司配送饭菜的满意情况进行评价，你认为还需要了解中位数、众数、方差中的哪些统计量？请至少选择一个你认为合适的统计量进行数据分析.（2）根据前面的工作，你认为用餐学生对哪家公司的饭菜质量更加满意，为什么？18．(9分)如图，正比例函数的图象与反比例函数的图象的一个交点是．（1）求出这两个函数的表达式，并直接写出这两个函数图象的另一个交点的坐标．（2）写出使反比例函数大于正比例函数的的取值范围．（3）点A （2，y 1）在正比例函数的图象上，点B （2，y 2），点C （-2，y 3），AB O CDCAB CD E AC BC 60ACD ∠=︒3=AC BE α090α︒︒ 01)31(25---+-2)1()1(2---x x x 1y k x =2k y x=(1,3)x 1y k x =第15题点D （-3，y 4）都在反比例函数的图象上，比较y 1，y 2，y 3，y 4的大小关系，并用“<”连接.19．(9分)请你完成命题“等腰三角形两底角的平分线相等”的证明．（提示：证明命题应首先依据命题画出几何图形，再结合几何图形用数学符号语言写出“已知”“求证”，最后写出证明过程．）20．(9分) 2024年植树节来临之际，某学校计划采购一批树苗，参加“保护黄河，远离雾霾” 植树节活动. 已知每棵甲种树苗比每棵乙种树苗贵10元，用400元购买甲种树苗的棵数恰好与用300元购买乙种树苗的棵数相同．（1）求甲、乙两种树苗每棵的价格分别是多少元？（2）学校决定购买甲、乙两种树苗共100棵，实际购买时，甲种树苗的售价打九折，乙种树苗的售价不变．学校用于购买两种树苗的总费用不超过3200元，最多可购买多少棵甲种树苗？21．(9分) 如图，是等边三角形，将沿直线平移到的位置，连接，交AC 于点O ．（1）线段BD 与AC 的数量关系是BD ：AC=___________．（2）判断BD 与AC 的位置关系，并说明理由．（3）请在图中连接AD ，则四边形ABCD 一定是菱形吗？为什么？2k y x=ABC ∆ABC ∆BC DCE ∆BD22．(10分) “诗圣”杜甫出生在郑州巩义市笔架山下的窑洞里，窑洞是黄土高原、黄河中游特有的民居形式．如图，某窑洞口的底部为矩形，上部为抛物线．已知底部矩形的长为4米，宽为2米，窑洞口的最高点P 离地面的距离为4米．（1）请在图中建立适当的平面直角坐标系，并写出P 点的坐标 ．（2）求（1）中所建坐标系中抛物线的表达式．（3）若在窑洞口的上部安装一个矩形窗户ABCD （窗户的边框忽略不计），使得点A ，B 在底部矩形的边上，点C ，D 在抛物线上，且AB =2BC ，那么这个窗户的宽BC 为多少米？23．(12分) 数学社团活动课上，同学们研究一个问题：任意给定一个矩形，是否存在一个新矩形，它的周长和面积分别是原矩形周长和面积的？【阶段一】同学们认为可以先研究给定矩形为正方形的情况，即是否存在一个正方形，其周长和面积都为原正方形周长和面积的？活动一：从特殊的矩形入手，如果已知矩形的长和宽分别为4和2，是否存在一个新矩形，它的周长和面积分别是原矩形周长和面积的？121212分析：设新矩形长和宽为，，根据题意，得 思路一：消去未知数y ，得到关于x 的方程，根据方程的解的情况解决问题．思路二：借助一次函数与反比例函数的图象（画出简单的函数图象即可）研究．结论： ⑤ （“存在”或“不存在”）一个新矩形，使其周长和面积都是长和宽分别为4和2的矩形周长和面积的．活动二：对于一般的矩形，如果已知矩形的长和宽分别为m 和n ，是否存在一个新矩形，它的周长和面积分别是原矩形周长和面积的？若存在，请指出需要满足的条件；若不存在，请说明理由．请你完成以下任务：（1）将【阶段一】中的①~④分别补充完整．（2）分别按照【阶段二】中活动一的思路一、思路二解决问题，并将⑤补充完整．（3）完成对【阶段二】中活动二的研究．九年级数学参考答案一、选择题（每小题3分，共30分）题号12345678910答案ACADCBDBDA二、填空题（每小题3分，共15分）题号1112131415答案2（答案不唯一）1三、解答题（本大题共8个小题，共75分）16．（1）原式……………………………………………………………3分x y 34.x y xy +=⎧⎨=⎩，1:3l y x =-+24:l y x=12122025x (23)2321或1215=+-．………………………………………………………………5分（2）原式 ………………………………………………………3分． …………………………………………………………5分17．（1）中位数： 甲公司7.5分 乙公司8分 众数： 甲公司7分，9分 乙公司8分方差：甲公司1.76乙公司1.81（答案不唯一）∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙4分（2）（略，答案不唯一）.∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙7分18．（1）把代入正比例函数与反比例函数的表达式，得k 1=3，k 2=3．，．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙4分这两个函数图象的另一个交点的坐标是．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙5分（2）或．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙7分（3）y 3<y 4<y 2<y 1.∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙9分19．已知：如图，在中，，，是的角平分线．∙∙1分∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙2分求证：．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙3分证明：，．，分别是，的角平分线，，（角平分线的定义）．即．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙6分在和中，．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙8分65=(1)(21)x x x =--+21x =-(1,3)3y x ∴=3y x=(1,3)--1x <-01x <<ABC ∆AB AC =BD CE ABC ∆BD CE =AB AC = ABC ACB ∴∠=∠BD CE ABC ∠ACB ∠12CBD ABC ∴∠=∠12BCE ACB ∠=∠BCE CBD ∠=∠ BCE ∆CBD ∆EBC DCB BC BC ECB DBC ∠=∠⎧⎪=⎨⎪∠=∠⎩，，，(ASA)BCE CBD ∴∆≅∆．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙9分20．解：（1）设乙种树苗每棵元，则甲种树苗每棵元，∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙1分根据题意，得 .∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙3分解得：.经检验，是原方程的解.答：每棵甲种树苗40元，每棵乙种树苗30元.∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙5分（2）设可购买a 棵甲种树苗，根据题意，得.∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙7分解得：.∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙8分最大取33.答：学校最多可购买棵甲种树苗33棵．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙9分21．（1∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙2分（2）BD ⊥AC ．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙3分理由如下：∵是等边三角形，由平移而得，∴DC =AB =BC ，AB ∥CD ．∴∠ACD =∠A =60°．∵∠ACB =60°，∴∠ACD =∠ACB ．∴OC ⊥BD ．即BD ⊥AC ．（方法不唯一）∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙6分（3）四边形ABCD 一定是菱形．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙7分理由如下：由平移知，AB ∥CD ，AB =CD ．∴四边形ABCD 是平行四边形．由（2）可知，BD ⊥AC ，∴平行四边形ABCD 是菱形．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙9分22．（1）如图所示．BD CE ∴=x (10)x +40030010x x=+30x =30x =10301040x +=+=0.94030(100)3200a a ⨯+⨯- (100)3a …a ∴ABC ∆DCE ∆ABC ∆∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙1分（0，2） （答案不唯一）∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙2分（2）（答案不唯一）∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙4分（3）设B （a ，0），则C ．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙5分矩形ABCD 中，AB =2BC ，即．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙7分解得 （舍去）．答：这个窗户的宽BC为（）米．∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙10分23.（1）①a 2…………………………………………………………………………………1分 …………………………………………………………………………………………2分③不存在 ………………………………………………………………………………………3分④等边三角形（答案不唯一，如圆） ………………………………………………………4分（2）思路一：消去未知数y ，得到关于x 的方程．整理，得 ．∵，∴方程没有实数根．∴不存在这样的新矩形．………………………………………………………6分思路二：如图，∵两个函数的图象没有交点，2212+-=x y ⎪⎭⎫⎝⎛+-221,2a a 2212+-=a a 51,5121--=+-=a a 15-14(3)4x x -=2340x x -+=231670∆=-=-<∴不存在这样的新矩形．………………………………………………………………………8分⑤不存在 …………………………………………………………………………………………9分（3）活动二：给定矩形的长和宽分别为m 和n ，则其周长为，面积为，由题意可知，新矩形的周长为，面积为．设新矩形一边为x ，则．∵．∴当时方程有实数根．∴当时存在这样的新矩形． …………………………………………………12分（方法不唯一）2()m n +mn ()m n +12mn 111()222x m n x mn +-=22113442m n mn ∆=+-226m n mn +≥226m n mn +≥。