中考最后一卷二
2024年中考英语最后一卷(广东卷)-2024年中考英语逆袭冲刺名校模拟真题速递(广东专用)
2024年中考最后一卷（广东卷）英语说明:1. 全卷满分为90分,考试用时为70分钟。
2.答卷前,考生务必用黑色字迹的签字笔或钢笔在答题卡填写自己的准考证号、姓名、考场号、座位号。
用2B铅笔把对应该号码的标号涂黑。
3.选择题每小题选出答案后,用2B铅笔把答题卡上对应题目选项的答案信息点涂黑,如需改动,用橡皮擦干净后,再选涂其他答案,答案不能答在试题上。
4.非选择题必须用黑色字迹钢笔或签字笔作答,答案必须写在答题卡各题目指定区域内相应位置上;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。
一、语法选择（本题有10小题，每小题1分，共10分）通读下面短文，掌握其大意，然后按照句子结构的语法和上下文连贯的要求，从每题所给的三个选项中选出一个最佳答案，并将答题卡上对应题目所选的选项涂黑。
Dear Lucy,First I’d like to say that I love your name. When my teacher asked us to choose 1 pen pal, I chose a girl named Lucy. I think the name seems very friendly. I have a happy family. My father 2 in a factory two years ago, and now he is a successful businessman. Mom is a teacher. She 3 English for eighteen years. She takes care of us very well. My father always says 4 my mom is the best cook in the world. I have a sister. She is 5 than me. She thinks she knows more than I do, so she can always tell me what 6 . It really drives me mad.I live in Chongqing. It 7 the Mountain City. It is a “hot” city, too. It is famous for its hotpot and8 . And it is really hot in summer here. The people here are kind and hardworking. Every year many people come to have a visit. Welcome 9 Chongqing. If you come, I’ll be glad to be 10 guide.I hope you can write back soon.Your pen pal，Isabel 1．A．a B．an C．the2．A．work B．works C．worked3．A．is teaching B．will teach C．has taught4．A．that B．if C．how5．A．old B．older C．oldest6．A．do B．doing C．to do7．A．calls B．is calling C．is called8．A．noodle B．noodles C．noodles’9．A．to B．at C．in10．A．you B．your C．yours二、完形填空（本大题有10小题，每小题1分，共10分）通读下面短文，掌握其大意，然后在每小题所给的四个选项中，选出一个最佳答案，并将答题卡对应题目所选的选项涂黑。
2023年安徽省中考数学最后一卷及参考答案
2023年中考最后一卷（考试时间：120分钟试卷满分：150分）学校:___________姓名：___________班级：___________考号：___________ 一、单选题(本大题共10小题，每小题4分，满分40分)．．．．BC的长为（）二、填空题（本大题共4小题，每小题5分，满分20分）FC三．解答题（共9小题，15-1814分，共计90分）15．解方程16．如图，在平面直角坐标系中，(1,1)A ，(4,2)B ，(2,3)C ．（1）请画出将△ABC 向下平移3个单位得到的111A B C △；（2）请画出以点O 为旋转中心，将△ABC 逆时针旋转90°得到的222A B C ； （3）请直接写出1A 、2A 的距离．请结合以上信息回答下列问题：(1)直接写出a＝，b＝；(2)本次抽查的学生平均每天睡眠时间的中位数落在组；(3)根据“通知”要求，初中生睡眠时间要达到9小时．该校有1800名学生，根据抽样调2023年中考最后一卷学校:___________姓名：___________班级：___________考号：___________ 一、单选题【详解】解：5125000 1.2510=× 故选A ． 【点睛】本题主要考查了科学记数法，解题的关键在于能够熟练掌握科学记数法的定义． 4．如图是教师每天在黑板上书写用的粉笔，它的主视图是( )A ．B ．C ．D ．【答案】C【详解】该几何体是圆台，主视图即从正面看到的图形是等腰梯形．故选C ． 5．如图，将一张矩形纸片和一张直角三角形纸片叠放在一起，∠1+∠2的值是（ ）A ．180°B ．240°C ．270°D ．300°【答案】C 【分析】过B 点作BE AF ∥，进而可得：AF BE CD ∥∥，然后利用平行线的性质即可求出∠1+∠2的值．【详解】过B 点作BE AF ∥，∵AF CD ∥，BC的长为（）二、填空题11．已知数据1，2，3，4，a的众数是2，则它们的中位数是___．【答案】2【分析】先根据众数的定义求出a的值，再根据中位数的定义求解即可．【详解】∵数据1，2，3，4，a的众数是2，∴a=2，∴数据1，2，2，3，4的的中位数是2．故答案为：2．【点睛】本题属于基础题，考查了确定一组数据的中位数和众数的能力．一组数据中出现次数最多的数据叫做众数．注意找中位数的时候一定要先排好顺序，然后再根据奇数和偶数个来确定中位数，如果数据有奇数个，则正中间的数字即为所求，如果是偶数个则找中间两位数的平均数．FC1三、解答题．解方程请结合以上信息回答下列问题：(1)直接写出a＝，b＝；(2)本次抽查的学生平均每天睡眠时间的中位数落在组；(3)根据“通知”要求，初中生睡眠时间要达到9小时．该校有1800名学生，根据抽样调查结果，估计该校学生平均每天睡眠时间低于9小时的人数．【答案】(1)20，36%(2)C。
2024年江苏省镇江丹阳市中考语文考前最后一卷含解析
2024年江苏省镇江丹阳市中考语文考前最后一卷注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
回答非选择题时，将答案写在答题卡上，写在本试卷上无效。
3．考试结束后，将本试卷和答题卡一并交回。
一、积累1．下列词语中没有错别字．．．．．的一项是 ( )A．战粟煞风景兴高采列自圆其说B．辐射马前足格物致知心无旁鹜C．枯燥化妆品浮想联翩金榜题名D．决择竞技场消声匿迹震耳欲聋2．下列句子中加点成语使用正确的一项是（）。
A．所谓学习，不一定限于书本或是某种技术，随时随地学习，这是不断提升自我的不二法门。
．．．．．B．在读书汇报会上，张山同学旁征博引，断章取义．．．．，赢得了同学们的一致好评。
C．三月撄花节期间，磁湖南岸，樱花盛开，如云如霞，游人鳞次栉比．．．．。
D．长沙以“湘江新区”获批国家级新区为契机，提质大河西生态文明建设，让自然景观惟妙惟肖．．．．。
3．下列各组词语中加点的字，注音或字形有误的一组是（）A．栈．桥（zhàn）悲天悯．人大气磅礴．（bó）喟．叹B．饶．舌（ráo）鸦．雀无声钟灵毓．秀（yù）羸．弱C．喟．叹（kuì）入不敷．出汗流浃．背（jiā）张皇．D．板滞．（zhì）言简意赅．浪敛．波平（jiǎn）慰籍．4．下列关于文学常识的表述，正确．．的一项是（）A．《变色龙》的作者是俄国短片小说巨匠契诃夫，代表作有小说《我的叔叔于勒》和剧本《万尼亚舅舅》。
B．孟子是我国战国时代伟大的思想家、教育家，他文章的语言喜欢使用比喻，能把道理说得深入浅出、生动有趣，具有气势充沛，感情强烈的特点，例如《鱼我所欲也》。
C．朱自清是我国现代散文家、诗人、学者、民主战士，他是著名散文有《背影》《荷塘月色》和《秋天的怀念》等。
2023年安徽省滁州市凤阳县中学中考物理最后一卷(有解析)
2023年安徽省滁州市凤阳县中学中考物理最后一卷一、选择题（本大题共7小题，共14分）1. 物理兴趣小组的同学对一些物理现象进行讨论，其中错误的是( )A. 高压锅是利用水的沸点随气压增大而升高的特点制成的B. 根据乒乓球被弹开的幅度，探究声音的响度与振幅的关系C. 向两张纸之间吹气，两纸会向中间靠拢，是因为两纸中间部分的气压比两侧高D. 利用铅垂线确定竖直方向，这是利用重力的方向总是竖直向下的道理2.如图是小明用手机、透镜和纸盒自制的简易投影仪，能将手机上的画面放大投射到白色墙上。
下列说法不正确的是( )A. 手机屏幕到透镜的距离应大于透镜的一倍焦距小于二倍焦距B. 如果想使墙上的画面再大一些，则需要让手机适当远离透镜C. 若用不透明的硬纸板遮住透镜的一部分，白色墙上的画面仍然完整D. 从各个角度都能清楚地看到白色墙上的像，是因为光在墙面上发生了漫反射3. 如图所示，图中阴影部分的面积描述相应物理量正确的是( )A. 物体的密度B. 物体运动的路程C. 力做功的功率D. 物体所受的压强4. 高速列车在泸州运行以来，以其高速、便捷、舒适的优点，成为越来越多泸州市民出行选择的交通工具。
下列图示中的实验，与高速列车动力系统工作原理相同的是( )A. B.C. D.5.如图所示，是探究“二力平衡的条件”实验，小车置于水平桌面，两端的轻质细绳绕过定滑轮挂有等重钩码。
F1是小车受到的向左的拉力，F2是小车受到的向右的拉力，F1与F2在同一水平直线上。
下列说法不正确的是( )A. 因为摩擦可忽略，小车在水平方向上只受到F1、F2作用B. 增减钩码个数，是探究二力大小对小车平衡的影响C. F1、F2大小相等时，小车一定处于平衡状态D. 将小车水平扭转90°时，F1、F2仍在同一直线上6. 某学习小组在物理实验室，做了如甲、乙两图的探究实验，以下说法正确的是( )A. 探究物体的动能与质量的关系B. 探究物体的动能与斜面高度的关系C. 探究物体的动能与速度的关系D. 探究结论可用于解释汽车超载带来的危害7.如图所示，电源电压保持不变，图中的三个电阻完全相同，闭合开关S1，当开关S2由1掷到2时，下列说法正确的是( )A. 电流表示数变小，电压表示数变小B. 前后两次电流表示数之比为1：2C. 电路的总电阻变小D. 电路的总功率变大二、填空题（本大题共8小题，共16分）8. 唐代诗人王之焕在《登鹳雀楼》中写到“白日依山尽，黄河入海流”。
2025届平顶山市重点中学中考语文考前最后一卷含解析
2025届平顶山市重点中学中考语文考前最后一卷 注意事项 1．考试结束后，请将本试卷和答题卡一并交回． 2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置． 3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符． 4．作答选择题，必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效． 5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗．
一、积累 1．下列句中加点词语运用不恰当的一项是( )。 A．因为教书育人的巨大贡献，于漪老师荣膺．．“改革先锋”称号。
B．现在社会上好多年轻人找工作总是挑挑拣拣，这山望着那山高．．．．．．．，总不满意。
C．这些经典之作，都是不刊之论．．．．，应该好好地阅读。
D．班主任王老师三顾茅庐．．．．苦口婆心，终于让刘丽同学打消了辍学打工的念头。
2．下列句子中加点成语使用不恰当．．．的一项是（ ） A．在教育系统新春茶话会上，市局领导与教师代表们谈笑风生．．．．，其乐融融。
B．城乡医疗制度改革需要循序．．渐进．．地推进，操之过急只会适得其反。
C．市博物馆用一组栩栩如生．．．．的蜡像生动地展示了柳州多民族聚居的风貌。
D．辩论赛上，李明引经据典，夸夸其谈．．．．，最终毫无悬念地夺得“最佳辩手”称号。
3．宣传标语既要有较强的针对性和一定的思想性，也要讲究语言，力求形式新颖、朗朗上口。下面四条以“和”为主题的宣传标语中，最恰当的一项是（ ） A．和以处众，平以养心，独以思我。
B．阳光甘泉及时雨，博爱慈善人间情。
C．尊老爱幼，亲仁善邻；一团和气，和气生财。
D．各美其美，方有个性；美人之美，自能和谐。
4．下列内容赏析有误的一项是（ ） A．“湖中人鸟声俱绝”，写出大雪后一片静寂，湖山封冻，一个“绝”字，传出万籁无声的森然寒意。这种写意手
2024届山东省东营市中考生物考前最后一卷含解析
2024届山东省东营市中考生物考前最后一卷注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
回答非选择题时，将答案写在答题卡上，写在本试卷上无效。
3．考试结束后，将本试卷和答题卡一并交回。
1、下列关于人体健康的相关叙述，不正确的是（）A．非处方药虽然可以自行购买，但服药前一定要认真阅读药品说明书B．烟草中的尼古丁能使血液中的红细胞数量减少，血液变稠，容易引发心脏病C．青春期应当适当学习性知识，悦纳自己的性别及性征，有效调节自己的情绪D．健康的生活方式能够有效预防心血管疾病，保持心血管健康2、2019年5月25日，四川阿坝卧龙国家级自然保护区管理局发布了拍摄到的白色大熊猫照片，照片中大熊猫通体白色，没有了“黑眼圈”。
专家认为，这只白色的大熊猫患上了“白化病”。
下图为大熊猫的白化病遗传图，下列分析错误．．的是（）A．大熊猫的正常体色和白色体色在遗传学上称为相对性状B．若用A表示显性基因，a表示隐性基因，则亲代的基因组成都为AaC．大熊猫的白化是由隐性基因控制D．若这两只亲代大熊猫再生一只大熊猫，则表现正常的可能性为50%3、纪实片《穹顶之下》引起了全社会对环境污染的广泛关注．PM2.5是造成雾霾的主要因素，呼吸道对其几乎没有净化作用．下列说法正确的是（）A．PM2.5通过扩散作用由外界空气进入肺泡B．雾霾天气里，人呼出气体中二氧化碳的含量高于氧气C．减少雾霾改善空气质量的根本措施是大规模植树造林D．PM2.5吸入人体后，干扰肺部的气体交换，引发哮喘等疾病4、下列关于生物遗传的描述中，错误的是（）A．已知水稻的卵细胞中染色体的数目12条，则水稻的精子、受精卵、叶肉细胞中含有的染色体数目分别为12条、12条、24条B．在生物体的细胞中，染色体、基因可以成对存在也可以成单存在的C．性状的遗传实质上是亲代通过生殖过程把基因传递给了子代D．含有异型染色体的受精卵将来发育成男性5、当膈肌收缩时，下列叙述正确的是（）A．膈顶部上升B．胸廓容积缩小C．肺内气压增大D．气体进入肺内6、用显微镜观察植物细胞的过程中，若视野从甲调整为乙，需要移动装片的方向以及应先后调节的显微镜结构一般是（）A．向上③②B．向下④①C．向下③①②D．向下③②7、抢救救上岸后的溺水者的第一步是( )。
2024届广东省梅州市丰顺县中考英语考前最后一卷含答案
2024届广东省梅州市丰顺县中考英语考前最后一卷含答案考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。
2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。
3．考生必须保证答题卡的整洁。
考试结束后，请将本试卷和答题卡一并交回。
Ⅰ. 单项选择1、—I can’t believe Jim got first in the competition.— As you know, God helps those who help ______.A．yourself B．himself C．yourselves D．themselves2、—Jolin, how long have you been a teacher as a pop star?—________ the end of last month, after Jolin’s English Diary Book came out.A．Since B．In C．By D．At3、The accident happened ____ the night of March 12.A．on B．from C．in4、— Is the food enough? — I think so. It will _______ four hungry peopleA．support B．serve C．sore D．cover5、—Mom, what does the word “attention”mean?—Oh, my dear, you should the dictionary and then you will get the meaning.A．look for B．look up C．look at D．look out6、— ____ is your mother?— She is in the kitchen.A．Where B．What C. When D．How7、-Must I stay here with you, Mum?-No, you _ .You may go home now, but you _ go to the net-bar.A．mustn't; needn't B．needn't; mustn'tC．must; need D．need; must8、______ the help of Mr. Wang, these poor children have the chance to go back to school.A．With B．In C．From D．For9、—Must I put on the sweater?— No, you _____. It’s up to you.A．needn’t B．can’t C．shouldn’t D．mustn’t10、________it’s Sunday tomorrow, we have to go to school.A．Though B．Since C．As D．BecauseⅡ. 完形填空11、After medical school, Michael moved to Southern California. He became a 1 at Mission Community Hospital. There Michael was known for his hard work. Many patients were helped by Michael, including a little baby called Chris.In August 1985, Chris entered the world earlier than expected, weighing only 1.5 kg. A few months later, he was back in the hospital. His temperature rose quickly with all the symptoms of meningitis(脑膜炎症状). Michael didn't 2 this young patient's side. "Anything could have gone wrong at that point, so I stayed there through the night to make sure everything was done 3 ," Michael said. What Michael did meant the world to Chris' parents, especially the next day when Michael 4 to them that their baby's fever had gone. Then Chris' parents chose Michael to be their son's doctor for his childhood. When Chris finished primary school, the two lost 5 . What Michael could never expected was how Chris would reenter （重返）his life 30 years later.At around 5 a.m. on March 29, 2015, Michael was driving home when suddenly a truck 6 control and hit his car badly in front of him. "Then I felt heat and looked down and could see fire around my legs!" As he tried to open the door, he realized it was 7 . He was trapped in his car watching fire rise up around his legs. After more than 40 years helping others as a doctor, suddenly he needed 8 . But he could never have imagined where it would come from.Luckily, less than a mile away, a group of firefighters were coming. Guess who was in this group? It was Chris. They arrived there in time. They helped Michael out of the car and sent him to the hospital. As Chris learned the name of the person he had just saved, he said, "I surely 9 him. But I couldn't believe it." When Michael realized that the little baby he once saved had just saved him, all he could do was to hold back tears."It really makes you think about 10 ," Michael says, "Everything we do is so important and affects （影响）so many others."1．A．teacher B．driver C．doctor D．worker2．A．miss B．pass C．leave D．follow3．A．fast B．right C．warmly D．slowly4．A．reported B．listened C．showed D．complained5．A．hope B．touch C．trust D．message6．A．had B．kept C．lost D．took7．A．open B．shut C．safe D．cold8．A．help B．wish C．chance D．effort9．A．record B．interrupt C．encourage D．remember10．A．study B．dream C．time D．lifeⅢ. 语法填空12、This is Tammela School, a primary school in Finland. The students are having a math class with their robot teacher.The “teacher” is1．small, blue machine about 25cm high, Reuters reported.Whenever students have problems, it helps them very2．(patient) and never gets bored.“The robot can make students3．(active) in class than usual. I see Eliasas one of the 4．(tool) to get different kinds of practice and activities into the classroom,” a teacher told Reuters.So far the school5．(introduce) four robot teachers, one of whom is a language teacher that can speak 23 languages and dance to music." 6．is necessary to encourage kids to come up7．new ways to make use of technology in school life," the head of the school 8．(add) in the interview.The robot teachers are used9．(help) improve learning. This doesn't mean that human teachers will lose their jobs. The robots can teach well,10．they are not able to keep class in order. The school still needs human teachers.Ⅳ. 阅读理解A13、In Canada and the United States, there is a new group of children called “satellites kids”, who live in one place but whose parents live in another place.Asians are immigrating (移居) to Canada and the United States in larger numbers than ever before. Most Asians immigrate because they believe that they can give their children a better education in the west. In Asia, especially in China, Japan and Korea, it is difficult to go to university. Students must first pass the strict national examination. However, in Canada and the United States, it is easy to go to university, and anyone who wants to go can go. As a result. Asian parents decide to leave their countries so that their children can go to university.The problem is that when Asians arrive, they discover that finding a job and making money are more difficult in the West. So these children become “satellite kids”, and most of their parents do not know how sad it is to be a “satellite kids”.Only until now are Canadians and Americans discovering the “satellite kids” problem. Because these child ren do not speak English and because their parents are not there to take care of them, they are often absent from school. To be a “satellite kids” means to grow up in such a country, you know you are different and you can’t make friends because you do not speak English well. Also, it means to grow up lonely, because your parents are not here.1．According to the passage, parents in _______ don’t send their kids abroad.A．China B．Japan C．Korea D．America2．“Satellite kids” refer to the Asian kids ______.A．without parents B．living abroad aloneC．with university education D．not speaking English3．Some Asian immigrant children become “satellite kids” because their parents______.A．want to leave their own country B．want them to go to universityC．return to their countries to work D．want them to be depend on themselves4．The following problems of “satellites kids” are right except ______.A．They grow up lonely. B．The don’t often go to school.C．They can make friends easily. D．Their parents can not look after them.5．What is the main idea of the passage?A．Parents feel lonely abroad.B．Parents want a better education for their kids.C．Canadians and Americans’ kids can’t find jobs easily.D．Kids in foreign counties alone are very in need of care from families.B1．How many books are written for children among the books?A．One B．Two C．Three D．Four2．Which of the following books is the latest in print?A．Deceptively Delicious B．The RoadC．Harry Potter and the Deathly Hallows D．Rich Dad, Poor Dad3．If Nancy buys 3 copies of Harry Potter and the Deathly Hallows and 2 copy of Rich Dad, Poor Dad, how much should she pay?A．$3.65. B．$59.50. C．$64.50. D．$74.45.C15、Giving someone good news is easy, but what about bad news? Are there any good ways to give bad news without making people too upset? The following steps might help:Say something positive. Try to start or end the conversation with some good news, so that it’s not all bad. For examp le, “ You did very well in the interview, but unfortunately we’ve given the job to somebody else.”Prepare your listener for the news. Use phrases to introduce what you’re going to say, like “Unfortunately, …”, “ I’m really sorry , but…” or “ I’m afraid I’ve got some bad news.” This gives the listener time to prepare for what you’re going to say.Try to give a reason. People like know why things go wrong. Try to explain the decision. If someone doesn’t get the job, can you explain why? If you have to cancel an appointment, try to give a reason.Use a softtone of voice. If you’re giving someone bad news, try to use a soft, calm voice to make your sound kind. Say things to show you understand, like “I’m really sorry.” Or “I know this must be disappointing.”1．W hich step isn’t mentioned in the passage?A．Talk about problemsB．Try to give a reasonC．Say something positiveD．Prepare your listener for the news2．What does the underlined word “ tone” mean in Chinese?A．词语B．语气C．眼神D．手势3．Linda failed the te st. She could tell her mum the news beginning with “__________”.A．Y ou lucky thing!B．Y ou’ll never guess what.C．Bad news, I’m afraid.D．That’s really wonderful.4．Which of the following is NOT true according to the passage?A．“Unfortunately” can be used t o tell the bad news.B．Y ou can start the conversation with some good news.C．Tone of voice is important when giving the bad news.D．Nobody likes to know the reason why things go wrong.5．The best title for the passage is “ _______”.A．Bad news can be good newsB．Good ways to give bad newsC．It’s easy to give bad newsD．Giving bad news without any troubleD16、Rome, Paris and New York are the world's top fashion cities, all of which have produced some of the top trends, form high-low skirts to the hottest new shoes. However, have you ever wondered the negative(消极的)ideas that they've broughtIn April 2016, the Advertising Standard Authority(ASA) in Britain stopped an ad from Gucci that has models dancing around and having fun, because the models in the ad were all quite thin. (Gucci, a famous brand(品牌)in the fashion industry and the company in question, said, "It was a personal idea as to whether a model looked unhealthily thin." It isn't new to us. The ASA stopped an ad in the year 2015 for the same reason. In France, it has been ruled that models are to provide a doctor's note which could prove that they are at a healthy weight.This brings up the question of weight, a hot topic for some people. What is the healthy weight for models? While I couldn't find an exact number, I did find this. According to ABC News, "Twenty years ago, the average(平均)fashion model weighed 8 percent less than the average woman. Today, she weighs 23 percent less." This is worrying. When has it ever been okay for anyone, models included, to weigh less than the average?People may think that being at an unhealthy weight will help him have the advantages that the models do. This provides a standard of beauty, and therefore people who want to achieve those things may try to do this through unhealthy ways. People may also think that they are overweight, compared to the images(形象)of models' thin bodies. They see something wrong with their bodies, whether they are overweight or not. This may make people feel bad, unconfident about their bodies. Sometimes people may have eating problems.I'm not blaming(指责)the fashion industry. It's not their fault(错误)that many people look up to the models and expect to live a life like their. I am glad that the ASA is raising its voices when discussing the growing problem of body image in the fashion industry. By stopping the photos and videos, speaking out against them and pushing for doctors' notes from the videos, it's pushing for the idea that the traditional fashion industry's body image standard should be changed and something more needy to be questioned.1．What does Gucci mean by what it says?A．Gucci has the right to choose models they like.B．Gucci has lost a lot of money.C．Gucci feels sorry for not choosing the right models.D．Gucci shouldn't be blamed as there're no exact weight standards.2．The numbers mentioned in Paragraph 3 show that .A．people don't know why models weigh lessB．many women are eating less to become thinnerC．weight problems of the models are more seriousD．being too thin causes health problems to models3．What does the fourth paragraph mainly talk about?A．The advantages of having a thin figure.B．The bad influence of models' thin images.C．The methods for having a good image.D．People's thoughts towards models' images.4．What's the possible purpose of the ASA′s measures(措施)?A．To improve the working conditions models are traced with.B．To set new standard of model's body imageC．To make people have a proper idea of body image.D．To keep us the good tradition in the fashion industry.E17、A young man entered the last interview of a company. The director found the young man’s academic grade were very good.“Did you get any scholarships(奖学金) in school?” The director asked. “None.” The young man answered.“Was it your father who paid for your school fees(学费)?” the director asked. “My father passed away when I was one year old, so it was my mother who paid for my school fees.” the young man answered.“Where did your mother work?” the director asked. “My mother cleaned clothes.” th e young man said. The director looked the young man’s hands. He had a pair of smooth and perfect hands.“Have you ever helped your mother wash the clothes before?” the director asked. “Never,” the young man answered. “I have a request,” the director said.“When you go back home today, go and clean your mother’s hands, and then see me tomorrow morning.”The young man felt that his chance of getting the job was high. When he went back, he happily asked his mother to let him clean her hands. His mother felt strange; happy but with mixed feelings. She showed her hands to the kid. The young man cleaned his mother’s hands slowly. His tears fell as he did that. It was the first time he had noticed his mother’s hands were so wrinkled. He realized it was this pair of hands that helped him pay the fees.The next morning, the young man went to the director’s office.“I cleaned my mother’s hands, and I know that without my mother, I would not be the person I am today.” he said.“This is what I am looking for in my manager.” the director said. “I want a person who can appreciate (感激) ” the help of others to get things done. You get the job!”1．What did the director ask the young man to do that night?A．to help his mother wash the clothes B．To wash his mother’s handsC．To chat with his mother D．To hug his mother2．The underlined word “wrinkled” in paragraph 6 probably means ______.A．soft B．rough C．dirty D．smooth3．What can we learn from the passage about the young man?A．The young man had good academic grades and got scholarships.B．His parents worked hard to pay the fees.C．The young man had a pair of hands that looked just like his mother’s.D．The young man finally got the job as a manager.4．Which of the following is wrong about the young man’s mother?A．Her son never helped her with her work before the interview.B．Life was difficult but she managed to support her son.C．She couldn’t help crying when her son washed her hands that night.D．Her son learned a lot from what she had done for him.5．What did the director value most from the young man?A．Working ability. B．Academic grades.C．Communication skills. D．Appreciation.F18、On Saturday Patrick woke up with a little shock，knowing that this was a special day. For a moment he couldn’t think exactly why，and then，with an excited flutter of his stomach，he remembered. At ten o’clock today he was going to find out the final result of the programme called Super Brain. He got dressed more carefully than usual，went downstairs and turned on the TV. Quickly he switched channels. Cartoons，cartoons，advertisements，man talking，snow，snow… and still nothing at all on Channel 8.“Patrick，turn it off，darling，if you’re going to watch.” Judith walked past with the newspaper under her arm and her eyes half closed. She headed for the kitchen. Patrick turned off the TV and followed.“What’s for breakfast，Mum?”“We will see，” Judith said in a low voice，turning on the electric kettle (水壶). She looked sleepily at him and smiled. “You look nice，darling，” She said. “You’re all ready. But we can’t go till eight-thirty at the earliest，you know. Nothing will be open till then.”Patrick’s stomach seemed to feel a little sick. “We aren’t going out，are we?” He asked. Judith began to make the tea. “Don’t say you’ve forgotten!” she said，“I promised you，last Saturday. Your new trainers，remember?”“Oh—oh，but I can’t go out this morning，Mum. There’s something I’ve got to watch on TV. At ten o’clock. I’ve got to! My trainers will be all right for another week.” Patrick sai d with excitement，looking quite worried.Judith faced him，hands on hips，“Patrick，” she said with great dislike，“it’s all organized.”1．This Saturday was very special for Patrick because ________.A．he was allowed to watch TV this morningB．he was dressed more carefully than beforeC．he would go shopping with his mother this morningD．he would get the result of the programme he was waiting for2．What did Patrick mean by saying “My trainers will be all right for another week”?A．He didn’t need a pair of n ew trainers at all.B．He wanted his mother to put off the shopping plan.C．He would like his mother to start off to buy the trainers.D．He had another pair of trainers which could last another week.3．How did Judith feel about Patrick’s requests?A．She felt happy with his request.B．She felt sad about his request.C．She felt surprised at his request.D．She was not satisfied with his request.4．What’s the best title for the passage?A．What to choose B．What to wearC．What to eat D．What to buyⅤ.书面表达19、对于中学生来说，朋友是我们初中生涯的一笔宝贵财富。
2024年浙江中考数学最后一卷终极押题卷及答案
2024年浙江中考最后一卷数学注意事项：1．本试卷共有三个大题，分为单项选择题、填空题、解答题，满分120分，考试时间100分钟。
2．本试卷上不要答题，请按答题卡上注意事项的要求直接把答案填写在答题卡上，答在试卷上的答案无效。
一、单选题（本大题共有10小题，每小题3分，共30分）1．下列各数中最大的数是（）A．5−B．0 C．1−D2．下面计算正确的是（）A．3a﹣2a＝1 B．2a2+4a2＝6a4C．（x3）2＝x5D．x8÷x2＝x63．今年春节电影《热辣滚烫》《飞驰人生2》《熊出没•逆转时空》《第二十条》在网络上持续引发热议，根据国家电影局2月18日发布数据，我国2024年春节档电影票房达80.16亿元，创造了新的春节档票房纪录．其中数据80.16亿用科学记数法表示为（）A．8×80.16108.01610×B．9C．10×80.1610×D．100.8016104．下列立体图形中，主视图是三角形的是（）A．B．C．D．5．在数轴上表示不等式x﹣2≤0的解集，正确的是（）A．B．C ．D ．6．随着自动驾驶技术的不断发展，某知名汽车制造公司近期对研发的自动驾驶汽车进行了一次大规模的路测，有45辆自动驾驶汽车参与了这次测试．测试结束后，技术部门对每辆汽车的性能进行评估（车辆的自动驾驶技术、安全性、反应速度等综合表现），得分如下：得分（分） 75 80 85 90车辆（辆） 5 16 14 10得分的中位数和众数分别是（ ）A ．80，80B ．82.5，80C ．80，85D ．85，807．如图，线段CD 是O 的直径，CD AB ⊥于点E ，若8AB =，3OE =，则CE 的长是（ ）A ．8B ．7C ．6D ．58．《九章算术》中曾记载：“今有牛五羊二，直金十两；牛二羊五，直金八两．问牛、羊各直金几何？”译文：“假设有5头牛，2只羊，值金10两；2头牛、5只羊，值金8两．问：每头牛、每只羊各值金多少两？若设每头牛值金x 两，每只羊值金y 两，则可列方程组为（ ）A ．5210258x y x y += +=B ．2510528x y x y += +=C ．51058x y x y += +=D ．21028x y x y += +=9．二次函数2y =的图象如图所示，点O 为坐标原点，点A 在y 轴的正半轴上，点B ，C 在函数图象上，四边形OBAC 为菱形，且120ABO ∠=°，则点C 的坐标为（ ）A ．14 −B ．14 −C ． −D ．(− 10．如图，四边形ABCD 是一张矩形纸片．折叠该矩形纸片，使AB 边落在AD 边上，点B 的对应点为点F ，折痕为AE ，展平后连接EF ；继续折叠该纸片，使FD 落在FE 上，点D 的对应点为点H ，折痕为FG ，展平后连接HG ．若矩形HECG ∽矩形ABCD ，1AD =，则CD 的长为（ ）．A ．0.5B 1−C D二、填空题（本大题共有6小题，每小题4分，共24分）11．因式分解： 34t t −=12．实现中国梦，必须弘扬中国精神．在如图所示除正面图案不同外，其余无差别的四张不透明卡片上分别写有“红船精神”、“长征精神”、“延安精神”、“特区精神”，将卡片置于暗箱摇匀后随机抽取一张，则所抽取卡片为“特区精神”的概率为 ．13x 的值可以是 ．（写出一个即可） 14．如图，《掷铁饼者》是希腊雕刻家米隆于约公元前450年雕刻的青铜雕塑，掷铁饼者张开的双臂与肩宽可以近似看像一张拉满弦的弓，若弧长为2π3米，“弓”所在圆的半径1．2米，则“弓”所对的圆心角θ的度数为 ．15．如图，点A 为反比例函数(0,0)k y k x x=<<的图象上一点，AB x ⊥轴于点B ，点C 是y 轴正半轴上一点，连接BC ，AD BC ∥交y 轴于点D ，若0.5ABCD S =四边形，则k 的值为 ．16．如图，正方形ABCD 的边长为2，以AB 边上的动点O 为圆心，OB 为半径作圆，将AOD △沿OD 翻折至A OD ′ ，若O 过A OD ′ 一边上的中点，则O 的半径为 ．三、解答题（本大题共有8小题，共66分）（共66分）17．（本题6分）计算或化简：(1)()201253π− +−−+−； (2)()()()2m n n m m n +−−−．18．（本题6分）如图，在平面直角坐标系中，ABC 的顶点坐标分别为()2,4A ，()3,1B ，()5,3C ．(1)作ABC 关于y 轴对称的111A B C △；(2)将ABC 绕原点O 顺时针旋转90°，得到222A B C △，作出222A B C △并求点C 旋转到点2C 所经过的路径长．19．（本题6分）2023年全国教育工作会议提出要把开展读书活动作为一件大事来抓．引导学生爱该书．读好书，善读书，贵阳市某校为了推进这项工作，对全校学生一周内平均读书时间进行抽样调查．将调查结果的数据分成A 、B 、C 、D 、E 五个等级并绘制成表格和扇形统计图如下．等级 周平均读书时间t （单位：小时） 人数A01t ≤< 4 B12t ≤< a C23t ≤< 20 D34t ≤< 15 E 4t ≥5 每个等级人数扇形统计图(1)求统计图表中=a ______，m =______．(2)已知该校共有2800名学生，试估计该校每周读书时间至少3小时的人数为______．(3)请写出一条你对读书的建议．20．（本题8分）我国是世界上最早发明历法的国家之一，《周礼》中记载：垒土为圭，立木为表，测日影，正地中，定四时，如图1，圭是地面上一根水平标尺，指向正北，表是一根垂直于地面的杆，正午，表的日影（即表影）落在圭上，根据表影的长度可以测定节气．在一次数学活动课上，要制作一个圭表模型，如图2，地面上放置一根长2米的杆AB ，向正北方向画一条射线BC ，在BC 上取点D ，测得 1.5m BD =， 2.5m AD =．(1)判断：这个模型中AB 与BC 是否垂直．答：______（填“是”或“否”）；你的理由是：______．(2)利用这个圭表模型，测定某市冬至正午阳光与日影夹角30°，夏至正午阳光与日影夹角为60°，请求出这个模型中该市冬至与夏至的日影的长度差（结果保留根号）．21．（本题8分）如图，在矩形ABCD 中，沿EF 将矩形折叠，使A 、C 重合，AC 与EF 交于点H ．(1)求证：AE ＝AF ；(2)若AB ＝4，BC ＝8，求△ABE 的面积．22．（本题10分）我市某镇组织20辆汽车装运完A 、B 、C 三种脐橙共100吨到外地销售．按计划，20辆车都要装运，每辆汽车只能装运同一种脐橙．且必须装满，根据下表组织的信息，解答以下问题．脐橙品种A B C 每辆汽车运载量（吨） 6 5 4每吨脐橙获利（元） 1200 1600 1000(1)设转运A 种脐橙的车辆数为x ，转运B 种脐橙的车辆数为y ，求y 与x 的函数表达式；(2)如果转运每种脐橙的车辆数都不少于4，那么车辆的安排方案有几种？(3)若要使此次销售获利最大，应采用哪种安排方案？并求出此时最大利润的值．23．（本题10分）定义：平面直角坐标系xOy 中，当点N 在图形M 的内部，或在图形M 上，且点N 的横坐标和纵坐标相等时，则称点N 为图形M 的“梦之点”．(1)如图①，矩形ABCD 的顶点坐标分别是(1,2)A −，(1,1)B −−，(3,1)C −，(3,2)D ，在点1(2,2)P −−，2(0,0)P ，3(1,1)P ，4(2,2)P 中，是矩形ABCD “梦之点”的是________；(2)如图②，已知A 、B 是抛物线21922y x x =−++上的“梦之点”，点C 是抛物线的顶点： ①求出AC ，AB ，BC 三条线段的长度；②判断ABC 的形状，并说明理由．24．（本题12分）如图，ABC 内接于圆O ，AD 是ABC 的高线，9AD =，12CD =，tan 3ABD ∠=，连接OC ．(1)求证：ABC 是等腰三角形；(2)求证：BCO BAD ∠=∠；(3)若点E 是OC 上一动点，EF AB ∥交BC 于点F ．①若OEF 与ABD △相似，求EF 的长；②当OEF 的面积与CEF △的面积差最大时，直接写出此时CF 的长．2024年浙江中考最后一卷数学解析及参考答案一、单选题1．D【分析】此题考查了实数的大小比较法则：正数大于零，零大于负数，两个负数绝对值大的反而小，据此判断．【详解】∵510−<−<<故选：D ．2．D【分析】根据各个选项中的式子可以计算出正确的结果，本题得以解决．【详解】解：∵3a ﹣2a ＝a ，故选项A 错误；∵2a 2+4a 2＝6a 2，故选项B 错误；∵（x 3）2＝x 6，故选项C 错误；∵x 8÷x 2＝x 6，故选项D 正确；故选D ．【点睛】本题考查整式的混合运算，解答本题的关键是明确整式混合运算的计算方法．3．B【分析】此题考查科学记数法的表示方法．科学记数法的表示形式为10n a ×的形式，其中110a ≤<，n 为整数．确定n 的值时，要看把原数变成a 时，小数点移动了多少位，n 的绝对值与小数点移动的位数相同．当原数绝对值10≥时，n 是正数；当原数的绝对值1<时，n 是负数．【详解】解：80.16亿98.01610×，故选：B ．4．B【分析】本题考查立体几何的三视图．根据题意，逐项判断即可．【详解】解：A.主视图为长方形，此项不符合题意；B.主视图为三角形，此项符合题意；C.主视图为圆，此项不符合题意；D.主视图为长方形，此项不符合题意．故选：B ．5．C【分析】先解不等式，求出解集，然后在数轴上表示出来．【详解】解：不等式x ﹣2≤0，得：2x ≤ ，把不等式的解集在数轴上表示出来为：．故选：C【点睛】本题主要考查了解不等式，并在数轴上表示解集，解题的关键是熟练掌握解不等式的步骤，不等式的解集在数轴表示时空心圈不包含该点，实心圈包含该点．6．D【分析】本题为统计题，考查众数与中位数的意义，根据众数的定义，找到该组数据中出现次数最多的数即为众数；根据中位数定义，将该组数据按从小到大依次排列，处于中间位置的两个数的平均数即为中位数．【详解】有45辆自动驾驶汽车参与了这次测试，45个分数，按大小顺序排列最中间的数据是第23个数：85，故得分的中位数是85（分），得80分的人数最多，有16人，故众数为80，故选D ．7．A【分析】本题考查了垂径定理和勾股定理的应用，根据垂径定理求出AE 的长是解此题的关键．连接OA ，根据垂径定理求出AE ，再根据勾股定理求出OA ，最后根据线段的和差求解即可．【详解】解：如图，连接OA ，线段CD 是O 的直径，CD AB ⊥于点E ，∴12AE AB =，8AB =， ∴4AE =，3OE =，∴5OA ，∴5OC OA ==，∴8CE OC OE =+=，故选：A ．8．A【分析】本题考查由实际问题抽象出二元一次方程组，解答本题的关键是设每头牛、每只羊分别值金x 两、y 两，根据“5头牛，2只羊，值金10两；2头牛，5只羊，值金8两”列出方程组即可得答案．【详解】解：设每头牛值金x 两，每只羊值金y 两，则可列方程组为5210258x y x y += +=， 故选A ．9．B【分析】本题考查了菱形的性质、二次函数图象上点的坐标特征，根据二次函数图象上点的坐标性质得出BD 的长是解题关键．连接BC 交OA 于D ，如图，根据菱形的性质得BC OA ⊥，60OBD ∠=°，利用含30度的直角三角形三边的关系得OD =，设BD t =，则OD =，()B t ，利用二次函数图象上点的坐标特征得2=，得出14BD =，OD =C 点坐标． 【详解】解：连接BC 交OA 于D ，如图，四边形OBAC 为菱形，BC OA ，120ABO ∠=° ，60OBD ∴∠=°，OD ∴，设BD t =，则OD =，()B t ∴，把()B t 代入2y =,得2=，解得10t =（舍去）， 214t =，14BD ∴=，OD =故C 点坐标为：14 − ．故答案为：B ．10．C【分析】本题考查的是矩形的性质、翻折的性质及相似多边形性质，熟练应用矩形和相似多边形性质是解题关键，设CD x =，则()1,1EC x CG x x =-=--，根据两矩形相似求出即可．【详解】解：在矩形ABCD 中，设CD x =，则ABCD x ==，1AD BC ==， 由翻折得,90AB AF x AFE B BAF ==∠=∠=∠=︒，∴四边形ABEF 是正方形，同理，四边形DFHG 是正方形，,1BE AB x DF DG x ∴====-，()1,121CE x CG x x x ∴=-=--=-，矩形HECG ∽矩形ABCD ，EC CG BC CD∴=，即1211x x x --=，解得：x =，经检验，xCD ∴ 故选：C ．二、填空题11．()()22t t t +−【分析】本题考查了因式分解，先提取公因式，再利用公式法即可求解，熟练掌握提公因式法及公式法分解因式是解题的关键．【详解】解：()()()324422t t t t t t t −=−=+−，故答案为：()()22t t t +−．12．14/0.25 【分析】本题考查了概率公式的应用，用到的知识点为：概率所求情况数与总情况数之比．全部情况的总数是四种，符合条件的情况的是一种，二者的比值就是其发生的概率．【详解】由于概率为所求情况数与总情况数之比，而抽取卡片为“特区精神”的情况数只有一种，从暗箱随机抽取一张的情况数为四种，故抽取卡片为“特区精神”的概率为14， 故答案为14． 13．0（答案不唯一）【分析】本题主要考查了二次根式有意义的条件，分式有意义的条件，根据二次根式有意义的条件的条件是被开方数大于等于0，分式有意义的条件是分母不为0进行求解即可．∴10x −>，解得1x <．∴x 的值可以是0，故答案为：0（答案不唯一）．14．100°/100度【分析】本题考查的是已知弧长与半径求解弧所对的圆心角，熟记弧长公式是解本题的关键．直接利用弧长公式计算即可．【详解】解： 设“弓”所在的圆的弧长圆心角度数是n °， 则1.2π2π1803n =， 解得：100n =，故答案为：100°．15．0.5−【分析】本题考查了反比例函数k 值的几何意义，熟练掌握k 值的几何意义是解答本题的关键.根据反比例函数k 值的几何意义进行解答即可.【详解】AB x ⊥ 轴于点B ，CD x ⊥轴，∴AB CD ，又 AD BC ，∴四边形ABCD 是平行四边形，过点作AM y ⊥轴，则四边形ABOM 是矩形， ∴0.5,ABOMABCD S S k ===矩形平行四边形∵反比例函数图象在第二象限，0.5k ∴=−，故答案为：0.5−.16．23、54【分析】本题考查了折叠的性质，正方形的性质，勾股定理，圆的定义；分三种情况讨论，设O 的半径为r ，分别根据勾股定理，即可求解．【详解】设O 的半径为r ，当O 经过A O ′的中点，即经过AO 的中点， ∴1233r AB =，当O 经过OD 的中点，则12r OB OD ==， ∴2OD r =，2AO AB OB r =−=−， 在Rt AOD 中，222AD AO OD +=∴()()222222r r +−=解得：r = 当O 经过A D ′的中点，即经过AD 的中点，设AD 的中点为M ，∴2,1,AO r AM OM r =−== ∴()22221r r −+= 解得：54r =综上所述，半径为23、54故答案为：23、54 三、解答题17．(1)5(2)222m mn −+【分析】此题考查了实数的运算以及整式的混合运算，熟练掌握运算法则是解本题的关键．（1）原式利用零指数幂、绝对值的代数意义以及负整数指数幂法则计算即可求出值；（2）根据平方差公式和完全平方公式化简，再合并同类项即可．【详解】（1）解：原式159=-+5=；（2）原式()22222n m m mn n =−−−+22222n m m mn n =−−+−222m mn =−+18．(1)图见解析(2)【分析】本题考查作图-轴对称变换，旋转变换，以及求弧长，熟练掌握相关作图方法是解题关键； （1）根据点关于y 轴对称的性质分别找到对应的点1A ，1B ，1C ，然后进一步连接即可；（2）利用旋转变换的性质分别作出A ，B ，C 的对应点2A ，2B ，2C ，再顺次连接即可，利用弧长公式求得点C 经过的路径长．【详解】（1）解：如图，111A B C △即为所求；（2）如图，222A B C △即为所求，由题意可知，OC∴点C 旋转到点2C =． 19．(1)6，40(2)1120(3)全校学生一周内平均读书时间23t ≤<(答案不唯一)【分析】本题考查了扇形统计图，样本估计总体等知识．（1）由等级得到学生总数，即可得出a ，再求C 等级的占比即可；（2）用样本估计总体即可得出结果；（3）根据表格可题建议合理即可．【详解】（1）解：由等级D 得到学生总数1530%50÷=人， ∴504201556a −−−−，()%2050100%40%m =÷×=，40m =，故答案为：6，40．（2）1552800112050+×=人， 故该校2800名学生每周读书时间至少3小时的人数为1120人．故答案为：1120．（3）根据表格可建议：全校学生一周内平均读书时间23t ≤<．20．(1)是；222AB BD AD +=，由勾股定理的逆定理可知AB BC ⊥．(2)．【分析】本题考查的勾股定理的逆定理的应用，解直角三角形的应用，理解题意是解本题的关键． （1）利用勾股定理的逆定理判断即可；（2）先画图，利用三角函数再计算BE=BF =，从而可得答案． 【详解】（1）解：是， 理由：由测量结果可知得 1.5m BD =， 2.5m AD =，而2m AB =，∴2226.25AB BD AD +==，∴90ABD ，∴AB BC ⊥．故答案是：是；222AB BD AD +=，由勾股定理的逆定理可知AB BC ⊥．（2）如图，由题意可得：90ABC ∠=°，2AB =，30AFB ∠=°，60AEB ∠=°，∴tan tan 60AB AEB BE∠=°=，∴BE =， 同理：tan tan 30AB AFBBF ∠=°=，∴BF =，∴FE BF BE =−==． 21．(1)证明见解析(2)6【分析】（1）依据平行线的性质以及矩形的性质，即可得到∠AFE =∠AEF ，进而得出AE =AF ．（2）设BE =x ，则AE =EC =8-x ，在Rt △ABE 中，根据勾股定理可得方程，即可得到BE 的长，再根据三角形面积计算公式求解．【详解】（1）证明：∵四边形ABCD 矩形，∴AD ∥BC ，∴∠AFE =∠FEC ，由折叠的性质得：∠AEF =∠FEC ，∴∠AFE =∠AEF ，∴AE =AF ．（2）解：根据折叠的性质可得AE =EC ，设BE =x ，则AE =EC =8-x ，在Rt △ABE 中，根据勾股定理可得：222AB BE AE +=，即()22248x x +=−，解得：x =3，∴BE =3，∴ABE S = 12AB •BE =12×4×3=6． 【点睛】本题主要考查了折叠问题以及矩形的性质的运用，解题的方法是设要求的线段长为x ，然后根据折叠和轴对称的性质用含x 的代数式表示其他线段的长度，选择适当的直角三角形，运用勾股定理列出方程求出答案．22．(1)220y x =−+ (2)5种(3)当转运A 种脐橙的车4辆，转运B 种脐橙的车12辆，转运C 种脐橙的车4辆时，利润最大为140800元【分析】（1）根据题意列式：()20651040x x y y −−=++，整理后即可得到220y x =−+； （2）根据装运每种水果的车辆数都不少于4辆，4x ≥，2204x −+≥，解不等式组即可；（3）设利润为W 元，则()480016000048W x x =−+≤≤，根据一次函数的增减性求解即可． 【详解】（1）根据题意，装运A 种水果的车辆数为x ，装运B 种水果的车辆数为y ，∴装运C 种水果的车辆数为()20x y −−，∴()20651040x x y y −−=++， 整理得220y x =−+． （2）由（1）知，装运A ，B ，C 三种水果的车辆数分别为x ，220x −+，x ，由题意得2204x −+≥，解得8x ≤，∵4x ≥，∴48x ≤≤．∵x 为整数，∴x 的值为4，5，6，7，8，∴安排方案共有5种．（3）设利润为W 元，∴()612005220160041000W x x x =×+−+×+× 4800160000x =−+，因为48000−<，且x 的值为4，5，6，7，8，∴W 的值随x 的增大而减小，∴当4x =时，销售利润最大．当装运A 种水果4车，B 种水果12车，C 种水果4车，销售获利最大．最大利润48004160000140800W =−×+=（元）．【点睛】主要考查利用一次函数的模型解决实际问题的能力．要先根据题意列出函数关系式，再代数求值．解题的关键是要分析题意根据实际意义求解．注意要根据自变量的实际范围确定函数的最值．23．(1)2(0,0)P ，3(1,1)P ，4(2,2)P(2)①AC =BC =AB =ABC 是直角三角形，理由见解析【分析】本题考查了二次函数的图象与性质、勾股定理以及勾股定理逆定理：（1）根据“梦之点”的定义判断这几个点是否在矩形的内部或者边上即可得到答案；（2）①根据“梦之点”的定义求出A ，B 的坐标，再求出顶点的坐标，计算出AC ，AB ，BC 的长； ②根据勾股定理逆定理，即可求解．【详解】（1）解：∵矩形ABCD 的顶点坐标分别是(1,2)A −，(1,1)B −−，(3,1)C −，(3,2)D ，∴矩形ABCD 的“梦之点”(),x y 满足2,131x y −−≤≤≤≤，∴点2(0,0)P ，3(1,1)P ，4(2,2)P 是矩形ABCD 的“梦之点”，1(2,2)P −−不是矩形的“梦之点”．故答案为：2(0,0)P ，3(1,1)P ，4(2,2)P（2）解：①A 、B 是抛物线21922y x x =−++上的“梦之点”， ∴21922x x x =−++， 解得：123,3x x ==−，当3x =时，3y =，当3x =−时，=3y −，∴()()3,3,3,3A B −−， ∵()2219115222y x x x =−++=−−+， ∴顶点坐标为()1,5C ，∴AC =BC =AB =； ②ABC 是直角三角形，理由如下：∵AC =BC =AB =∴((2222280AB AC BC +=+==，∴ABC 是直角三角形．24．(1)证明见解析(2)证明见解析(3)①EF =253CF =【分析】本题考查了圆的性质，等腰三角形的判定与性质，相似三角形的判定与性质，锐角三角函数等知识，掌握相关知识是解题的关键．（1）利用勾股和锐角三角函数求得AC BC =即可证明；（2）连接,OA OB ，延长CO 交AD 于点M ，交AB 于点N ，先证明CO 是ACB ∠的角平分线，再证明ANM CDM ∽即可得出结论；（3）①过O 点作OH BC ⊥交BC 于点H ，点E 是OC 上一动点，EF AB ∥交BC 于点F ，先证明CHO CFB ∽，设EF x =3x =即可求解，②要使OEF 的面积与CEF △的面积差最大，必须使EF 和()CE OE −最大，当E 点与O 点重合时，EF 最大，CE OE OC −=最大，先求得EF =即可求出CF ． 【详解】（1）证明：∵AD 是ABC 的高线，∴90ADC ADB ∠=∠=°， ∵9AD =，12CD =，∴15AC ===，∵tan 3ABD ∠=， ∴tan 3AD ABD BD∠==， ∴3BD =，∴31215BC BD CD =+=+=， ∴AC BC =，∴ABC 是等腰三角形．（2）证明：连接,OA OB ，延长CO 交AD 于点M ，交AB 于点N ，如图：∵AC BC =，∴CAB CBA ∠=∠， ∵OA OB =，∴OAB OBA ∠=∠， ∴CAO CBO ∠=∠， ∵OA OC =，∴CAO ACO ∠=∠， ∵OB OC =，∴BCO CBO ∠=∠， ∴ACO BCO ∠=∠， ∴CO 是ACB ∠的角平分线， 又∵ AC BC =，∴CN AB ⊥，∴90ANC BNC ∠=∠=°， ∴90MDC ANE ∠=∠=°， 又∵AMN CMD ∠=∠， ∴ANM CDM ∽，∴DCM NAM ∠=∠， ∴BCO BAD ∠=∠． （3）解：①过O 点作OH BC ⊥交BC 于点H ，点E 是OC 上一动点，EF AB ∥交BC 于点F ，如图：∵,,15OB OC OH BC BC =⊥=， ∴17.52CH BC ==，90CHO CFB ∠=∠=°， ∴CHO CFB ∽，∴COH CBF ∠=∠， ∵tan 3ABD ∠=， ∴tan tan 3CH COH CBF OH∠=∠==， ∴ 2.5OH =，∴OC =， ∵EF AB ∥，90BNC ∠=°， ∴CEF CNB ∽，∴90CEF CNB ∠=∠=°， 设EF x =，∴tan tan 3CE CE CFE CBN EF x∠=∠===， ∴3CE x =，∵OEF ADB ∽，∴OE EF AD BD=， ∵OEOC CE =−， 3x =， 解得：x =∴EF ②∵90CEF ∠=°，即EF OC ⊥， ∴12CEF S CE EF =⋅ ，12OEF S OE EF =⋅ ， ∴()111222CEF OEF S S CE EF OE EF EF CE OE −=⋅−⋅=⋅− ， 由题知，要使OEF 的面积与CEF △的面积差最大，必须使EF 和()CE OE −最大，∴当E 点与O 点重合时，EF 最大，CE OE OC −=最大，如图：∵EF AB ∥，∴CEF CNB ∽，∴CFE CBN ∠=∠，CE OC ==，∴tan tan 3CE CFE CBN EF ∠=∠==，∴EF∴253CF =．。
2024年安徽中考数学试卷最后一题
1、在平面直角坐标系中，点A的坐标为(1,0)，点B的坐标为(0,√3)，以AB为边作等边三角形ABC，则点C的坐标不可能是？A、(1, -√3)B、(-1, √3)C、(1/2, √3/2)D、(1+√3, -1)（答案：C。
解析：通过计算AB的长度和角度，可以确定C点的可能位置，C选项的坐标不满足等边三角形的条件。
）2、已知一个长方体的长、宽、高之比为3:2:1，其体积为72立方厘米，则长方体的表面积为？A、36平方厘米B、48平方厘米C、72平方厘米D、96平方厘米（答案：D。
解析：设长、宽、高分别为3x、2x、x，则体积为3x2xx=72，解得x=2，进而计算表面积。
）3、若关于x的一元二次方程x²+2(k-1)x+k²-1=0有两个不相等的实数根，则k的取值范围是？A、k<0B、k>2C、0<k<2D、k<0或k>2（答案：C。
解析：根据判别式Δ=b²-4ac>0，代入方程的系数进行计算。
）4、在圆O中，弦AB的长度是半径的两倍，则弦AB所对的圆心角∠AOB的度数为？A、30°B、60°C、90°D、120°（答案：B。
解析：利用弦长与半径的关系，结合圆的性质，可知弦AB所对的圆心角为60°。
）5、已知反比例函数y=k/x的图像经过点A(2,3)，则当x=-3时，y的值为？A、-2B、-1C、1D、2（答案：A。
解析：将点A的坐标代入函数，求得k=6，再代入x=-3计算y值。
）6、一个正方体的内切球半径为r，则该正方体的体积为？A、8r³B、24r³D、64r³（答案：A。
解析：正方体的内切球半径等于正方体边长的一半，即边长为2r，计算体积。
）7、在∠ABC中，AB=AC，D是BC的中点，DE∠AB于点E，若∠BDE的面积为1，则∠ABC的面积为？A、2B、3C、4D、6（答案：C。
2024届安徽省亳州地区中考英语考前最后一卷含答案
2024届安徽省亳州地区中考英语考前最后一卷含答案注意事项：1．答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。
2．选择题必须使用2B铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。
3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。
4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。
Ⅰ. 单项选择1、More TV programs, accordi ng to government officials, will be produced _____ people’s attention over food safety. A．to raise B．raising C．to rise D．rising2、Lily Lucy may go with you because one of them must stay at home.A．Not only; but also B．Neither; norC．Both; and D．Either; or3、Susan never gets upset when she has to wait in line. She is very ______ .A．shyB．honestC．funnyD．patient4、— What were you doing when we were playing basketball yesterday afternoon?— I ______ the classroom.A．was cleaning B．have cleanedC．will clean D．clean5、--I saw John in the park this morning..--It _____be him. He has gone to HongKong.A．can’t B．can C．mustn’t D．must6、---Look! The woman is wrinkling her nose at what the waiter brought.--- _______it means she doesn’t like how the food loo ks.A．Must B．Perhaps C．Could D．probably7、---I’m afraid I have to give up my dream of being a dancer.---_______. No dream is too big and no dreamer is too small.A．Don’t lose heart B．Don’t mention itC．Y ou must be joking D．That’s OK8、"I want to know ." said the boy opening the box.A．what's inside the box B．where the box isC．that there's some candy D．how big is the box9、In every computer class,we must use the computer according to our teacher’s .A．standards B．instructions C．tasks10、—Why do you want to stay at home?—Because I ________ good when I am with my family.A．smell B．feel C．taste D．soundⅡ. 完形填空11、One day, a farmer was walking along a road with his son Thomas when they saw a horseshoe (马蹄铁) on the ground. The father said to his son, “Look at the horseshoe on the ground. Go and 1 the horseshoe and put it in your bag, my son.” But Thomas said, “If I do so, it will waste my time.” His father said nothing but picked it up himself. When they 2 a nearby town, they had a rest. There the farmer sold the horseshoe and 3 some strawberries with the money.The father and the son went on walking. The sun was well up in the 4 They soon drank up all their water and there was not a house or even a tree for them to have a rest. Thomas felt 5 thirsty to walk on. At this time, his father gave him a strawberry and he quickly ate it. After a while, his father gave him 6 strawberry and once again, his son got it quickly and put it in his mouth.And so they 7 The old farmer gave the strawberries and the son ate them. When Thomas had eaten up all the strawberries, his father said to him, “My dear son,8 ____ you picked up that horseshoe, you would have your own 9 to eat. Always remember the lesson: if you don't worry about the little things, you will find it difficult 10 ____ the great things.1．A．give up B．put up C．pick up D．take up2．A．got on B．got to C．got off D．got down3．A．threw B．bought C．sold D．found4．A．sky B．sea C．river D．ground5．A．so B．very C．quite D．too6．A．another B．other C．else D．the other7．A．carried on B．turned on C．went on D．worked on8．A．Or B．If C．Unless D．Until9．A．water B．money C．horseshoe D．strawberries10．A．to do B．to use C．to eat D．to drinkⅢ. 语法填空12、(B) Complete the passage with the proper forms of given words.Zengzi was a famous thinker in Chinese history. His 1．(teach) was Confucius (孔子).One day, Zengzi’s wife was going to the market to sell somethi ng for money without their son. The boy kept 2．(cry)and shouting. She said to her son, “When I come back, I’ll kill our pig to make a meal for you.”But she didn’t do as she said. “How can you cheat a child?” Zengzi said 3．(serious) “The small child only 4．(follow) the example of his parents. If you cheat him, he may cheat 5．(other) like you.” Having said this, Zengzi raised the knife and killed the pig.Ⅳ. 阅读理解A13、We can express thoughts and feelings and send sounds and pictures on our smart phones today. We also communicate by using programs like Skype and Face Time. We can't send tastes, smells or touch, of course. But scientists in Britain are trying to develop a way for smart phones to do just that.Adrian David Cheok is a professor at City University in London. He wants people to experience communication using all of their senses. He said "In the real world, we can open up the glass, open the window. We can touch, we can taste, we can smell in the real world."To give users a sense of taste, researchers designed two electrodes (电极）that are placed on the tongue. A chemical process creates different tastes through molecules (微粒)on the surface of the tongue. This chemical process sends electrical signals that convince the brain that a person is tasting something. They have already created sour, salty, sweet and bitter tastes."You put these two silver electrodes in your mouth, you put your tongue in between and then it stimulates electrically your tongue and you get a virtual taste perception in your brain."A device(设备）called "Scentee" permits users to have the sense of smell. Scentee plugs into a smart phone and can spray tiny clouds of fragrances, including flowers, fruits and coffee. Professor Cheok says the person speaking can activate the device.Scentee holds a container with about 100 different smells. The container must be replaced when all the scents （pleasant smells) run out.1．Where could the passage most probably be taken from?A．A news story.B．An advertisement.C．A science fiction.D．A science magazine.2．Which of the following is the right order according to the passage?a. Electrical signals are sent to brain.b. Two electrodes are placed on the tongue.c. The brain is convinced that a person is tasting something.d. Different tastes are created through molecules on the surface of the tongue. A．a-b-c-dB．b-d-a-cC．c-a-d-bD．b-d-c-a3．What will be most probably talked about in the next paragraph?A．The bright future of the smart phones.B．How the sense of touch will be achieved.C．The different attitudes towards the smart phones.D．The advantages of the smart phones with new functions.B14、Deng Yu：In 2050, China will be richer than it is now. Beijing will be getting ready for the 40th Olympic Games in 2052. We will see the blue and clear sky and smell the fresh air. There will be more pandas living happily in China. I believe that 2050 will be the year of China.Liu Yuan：A holiday trip to the moon will no longer(不再) be a dream. We can also travel far to other planets and talk with the spacemen. We might also eat something like pills instead of meals. Everyone will enjoy a longer life.Sun Wei：Robots will be very popular. They will do what people don’t want to do. We’ll build new homes on other planets. By then, I’ll be sixty ye ars old. Maybe we will have an exciting talk in my new home on another planet!Zhang Lan：By the year of 2050, cloning(克隆) will be used in many ways. It will bring back animals which disappeared(消失) many years ago. There will be no pollution(污染). The whole world will be one big family. There will be no wars. As time passes, we’ll live a much easier and better life.1．It is the _______ Olympic Games in 2048.A．38th B．39th C．40th D．41st 2．According to Liu Yuan, everyone will live a(n) _______ life.A．boring B．exciting C．longer D．interesting3．_______ thinks that people can spend their holidays on the moon in the future.A．Deng Yu B．Zhang Lan C．Sun Wei D．Liu Yuan4．What does Zhang Lan think will happen in the future?A．People will live in a world without wars.B．Robots will do the things that people don’t want to do.C．People can talk with the spacemen.D．There will be more pandas living happily in China.5．From the talk, we can know that _______.A．people are still polluting the earth todayB．the 50th Olympic Games will take place in 2052C．we will have the same food in 2050 as we do nowD．all the people will move to another planet in the futureC15、These days the hit South Korean TV drama“My Love from the Stars”attracts thousands of Chinese TV viewers．It’s about a love story between a woman and a 400-year-old alien．The heroine(女主角) Cheon Song-yi likes to have“fried chicken and Beer”，especially on snowy days，which made fried chicken and beer become one of the most popular kinds of food on Valentine’s Day th is year．However，it is reported that overeating them is bad for our health．As the saying goes，“____________．”It means food is the most important to people．In today’s society，many hotels where they stand，rush from all kinds of food，in Fujian，Sichuan，Guangdong，Shandong…even dishes of Italy，Japanese cuisine，Korean food and so on．We all know that health is closely connected with the food．Today，We take a look at the food on the table now．Food is divided into many kinds such as vegetables and fruit，beans，meat，cereals，dairy and so on，and they all influence our health．Therefore．in order to achieve a reasonable meal，We have to remember that eating till 80％full，not being choosy food anorexia，not overeating and eating clean food are very important．we all hope to be happy, so we should take good care of our health．Health is much more important than anything else．Money can do many things，but it can’t buy happiness．However，if man has good health，he can enjoy the pleasures of human life．Therefore，we must pay attention to three things to make sure of good health．They are healthy food，fresh air and enough exercise．That’s why we have to stay away from fried chicken and beer from now on．1．“My Love from the Stars”is．A．a new movie B．a TV dramaC．a new book D．a hit CD2．“Hunger breeds discontent”means in Chinese．A．饥饿让人开心B．人们喜欢饥饿C．民以食为天D．人们不满意食物3．If we want to achieve a reasonable meal，we should ．A．eat 80％of the food on the tableB．be choosy food anorexiaC．eat things we like as much as possibleD．never eat too much4．Which is wrong according to this passage?A．Fried chicken and beer became popular on Valentine’s Day this year．B．Our health is influenced by different kinds of food．C．Healthy food，fresh air and enough money can keep us in good health．D．Health is much more important than money．D16、1．How much is the writing course?A．￡30. B．￡60. C．￡95. D．￡125. 2．On Sunday a student can ________________.A．take a writing course B．meet the native teachers C．practice listening skills D．have a speaking class3．A writing course will last ____________ hour.A．10 B．20 C．30 D．50 4．You can learn about the school in many ways EXCEPT_______________. A．making a phone call B．visiting its website C．sending an email D．follow（关注）its public -hat5．This is a(n) _____________.A．travel guide B．advertisement C．science report D．instructionsE17、Almost every day, we discuss the topic of health, especially for kids. But what is health?"Health" means eating well, getting enough exercise, and having a healthy weight. Let's read the following rules. They can help you stay healthy.▲Eat a variety of food, especially fruits and vegetables. We all know that eating fruits and vegetables can help us stay healthy, but many of us only eat our favorite food. Remember that we can only get the nutrition（营养）we need by eating different kinds of food, especially fruits and vegetables.▲ Drink water and milk most often. Everyone knows that water is important. Besides that, kids need plenty of calcium（钙）to grow strong bones, and milk is rich in it. Every day, you should drink at least three cups of milk, when you are 9 years old or older. You should also try to have less sugary drinks, like soda and coca. They include a lot of sugar. Sugar only includes calories（热量）, not important nutrition.▲ Listen to your body. When you are eating, notice how your body feels. When your stomach feels comfortably full, stop eating. Eating too much makes you feel uncomfortable. If you do it too often, it can make unhealthy and fat.▲ Limit screen time. What's screen time? It's the amount of time you spend watching TV, movies and playing computer games. The more time you spend on these sitting-down activities, the less time you spend playing sports, like basketball, and doing other activities like riding and swimming. Try to spend no more than 2 hours a day on screen time.1．How many rules of keeping healthy are listed in the passage?A．two B．three C．four D．untold2．The underlined phrase "a variety of' means _______________.A．all kinds of B．plenty of C．the rest of D．a lot of3．In this passage, "health" includes all of the following EXCEPT _____________.A．eating well B．doing more exerciseC．having a healthy weight D．wearing comfortable clothes4．Screen time is the time that you spend _____________________.A．playing computer games B．watching moviesC．watching TV D．All of the above5．What's the main idea of the passage?A．How to eat healthy food. B．Suggestions for staying healthyC．Eating and playing are both important. D．Health is very important.F18、I bought a jasmine plant for my office. When I bought it, I was told it would bloom（开花）and the sweet smell would fill my office. I had the plant for two months, and every day I looked at it, but there weren't any flowers or pleasant smell. I was not happy, so I gave the plant to my friend Linda.One day, another friend Mary called and invited me to her office. When I walked in, her jasmine flowers surprised me. I reached out to touch the flowers. Mary cut some and gave them to me. I couldn't help smelling them. Surrounded by the sweet smell of only a handful of these flowers, I suddenly understood something.Mary bought her plant the same time I did. It took a year for her jasmine to bloom. I was so impatient for mine to bloom; regretfully, I gave it away.In a way my life is like the jasmine plant. I need to be patient and let things happen.Last Sunday Linda told me that she was going abroad the next week. Before she left, she returned the plant to me. This time I am going to wait. I have learned that when we want something in our life, we have to be patient. I am slowly learning to have that patience to wait for my jasmine to bloom.1．Before she gave the jasmine away, the writer had it for .A．one day B．one year C . two weeks C．two months2．When the writer saw Mary's jasmine, she felt____________ .A．unhappy B．peaceful C．hopeful D．surprised3．What has the writer learned from her experience?A．Patience is needed in life.B．Flowers can make life better.C．Friendship is necessary for us.D．Jasmine can be a wonderful plant.Ⅴ.书面表达19、假定你是李华，你的英国笔友Mike最近因视力减退而感到不安，请你用英文给他写封电子邮件，谈谈你在保护视力方面的一些做法。