中考冲刺主题训练(二)

14 命题作文专题（知识点思维导图+习题训练）一、（2022·广西贺州·一模）题一：请以“美好，在那一刻绽放”为题，写一篇文章。

要求：（1）按要求作文。

（2）除诗歌，戏剧外，自选文体，文章不少于600字，严禁抄袭。

（3）文中不得出现真实的人名、校名和地名。

【答案】参考例文美好，在那一刻绽放一颗种子在泥土中慢慢发芽，逐渐靠时间的推移，告别黑暗，获得光明，长成一株小苗。

不久在上面藏着一个细小，柔美的小花苞。

在春风的吹拂下，轻轻摇动着身子，好像在展示自己那柔美的曲线……花终于开了。

我家边上有一个小女孩，整天放学回家第一件事就是直奔阳台。

我由于好奇，便有一次去她家问问。

一上楼，空旷的阳台上有一盆泥土，小女孩看着那泥土，问我：“姐姐，我种下了一颗种子，都好多天了，连根芽的影子也没有。

”她失望地看着我。

我说：“不要着急，有可能这颗种子的发芽时间很长，说不定再过些日子就会长出嫩芽了，所以耐心等待吧！”我刚说完，她用那激动的`目光注视着那盆花，等待着嫩芽的出现。

这个小女孩每天起床时都看看花盆，随后就跑去浇水，晚上回来后又会立马去看它。

可日子渐渐过去了，花盆还是没有什么动静，伤心的她便跑来问我：“姐姐，你不是说它不久后会发芽的吗？可是都好几天了，不会是我浇的水多了，或者是没帮它松松土，或者……”她很着急的说着话，看着手中捧着的花盆，又非常失望。

此刻的我不知道说什么来安慰她，便随口跳出一句：“快了，就快要长出来了，相信这颗种子在你辛勤的照顾下，一定会绽放出那碧绿的嫩叶的。

”她带着我的安慰回了家。

突然有一天，女孩兴冲冲的跑来，手里拿着花盆，指我看盆中的那一株碧绿的嫩芽，脸上露出了灿烂的笑容，两只眼睛总是盯着那株小苗。

我也很开心。

在温暖的阳光下，女孩的笑容就在种子发芽的那一刻绽放了出来。

这种天真、纯洁的笑容我永远无法忘记，想起来还是美美的。

【解析】本题是命题作文。

第一，审题：“美好”，可以是“成功”“微笑”“情谊”，还有“心情”“理想”“梦想”等生活中的很多事物。

专题02 词语运用重点讲解1．邓稼先可歌可泣：值得歌颂，使人感动得流泪，指悲壮的事迹使人非常感动。

鲜为人知：很少有人知道。

至死不懈：直到失去生命也不松懈。

比喻对某件事（信念）有着执着的追求。

鞠躬尽瘁：指小心谨慎，贡献出全部精力。

当之无愧：完全当得起，没有什么可以惭愧的地方。

家喻户晓：每家每户都知道。

锋芒毕露：指锐气和才干全都表现出来。

多形容人气盛逞强。

妇孺皆知：妇人和孩子都知道。

形容事情散播得非常广，大家都知道。

2．说和做——记闻一多先生言行片段锲而不舍：不停地雕刻，比喻有恒心，有毅力。

群蚁排衙：指整齐地排列着。

迭起：一次又一次地兴起、出现。

昂首挺胸：昂起头，挺起胸。

形容精神振奋，意气昂扬。

疏懒：形容词，懒散而不惯受拘束。

赫然：形容令人惊讶或引人注目的事物突然出现。

慷慨淋漓：形容情绪十分激动；说话、写文章意气昂扬，言辞畅快。

气冲斗牛：形容气势之盛可以直冲云霄。

斗、牛，星宿名，借指天空。

兀wù兀穷年：用心劳苦地一年到头这样做。

3．回忆鲁迅先生（节选）安顿：安详，安稳。

揩：擦、抹。

旷代：历时长久。

抹杀：彻底勾销；完全去掉。

草率：（工作）粗枝大叶，敷衍了事。

校对：查对、订正。

悠然：安闲、闲适的样子。

疙瘩：①皮肤上突起的或肌肉上结成的硬块。

②不容易解决的问题等。

不以为然：不认为是对的。

表示不同意或否定。

然，是，对。

深恶痛绝：指对某人或某事物极端厌恶、痛恨。

5．黄河颂巅：山顶。

劈：文中指用力分开。

气魄：气势；魄力。

狂澜：文中指巨大的波浪。

浊流：浑浊的水流。

宛转：文中指弯弯曲曲地延伸。

屏障：像屏风那样遮挡着的东西（多指山岭、岛屿等）。

哺育：喂养；比喻培养。

榜样：作为仿效的人或事例（多指好的）。

浩浩荡荡：形容水势浩大的样子。

6．老山界惊惶：惊慌，害怕慌张。

惶，恐慌。

呜咽：低声哭泣或形容凄切的水声或琴声。

酣然入梦：甜美、畅快入睡。

酣然：喝酒畅快的样子。

矗立：高耸地立着。

苛捐杂税：指反动统治下的繁重捐税。

贵州省贵阳市2020年数学中考基础冲刺训练（二）一．选择题（每题3分，满分30分）1．已知x﹣2y＝﹣2，则3+2x﹣4y的值是（）A．0 B．﹣1 C．3 D．52．如图，在△ABC中有四条线段DE，BE，EF，FG，其中有一条线段是△ABC的中线，则该线段是（）A．线段DE B．线段BE C．线段EF D．线段FG3．下面是几个一样的小正方体摆出的立体图形的三视图，由三视图可知小正方体的个数为（）A．6个B．5个C．4个D．3个4．以下问题，适合用普查的是（）A．调查某种灯泡的使用寿命B．调查中央电视台春节联欢会的收视率C．调查我国八年级学生的视力情况D．调查你们班学生早餐是否有喝牛奶的习惯5．如图，在菱形ABCD中，AB＝2，∠B＝60°，E、F分别是边BC、CD中点，则△AEF 周长等于（）A．B．C．D．36．数轴上的点A表示的数是a，当点A在数轴上向右平移了6个单位长度后得到点B，若点A和点B表示的数恰好互为相反数，则数a是（）A．6 B．﹣6 C．3 D．﹣37．如果方程x2﹣8x+15＝0的两个根分别是Rt△ABC的两条边，△ABC最小的角为A，那么tan A的值为（）A．B．C．D．或8．用蓝色和红色可以混合在一起调配出紫色，小明制作了如图所示的两个转盘，其中一个转盘两部分的圆心角分别是120°和240°，另一个转盘两部分被平分成两等份，分别转动两个转盘，转盘停止后，指针指向的两个区域颜色恰能配成紫色的概率是（）A．B．C．D．9．在平面直角坐标系xOy中，若一次函数y＝kx﹣1（k≠0）的图象经过点P，且y的值随x 值的增大而减少，则点P的坐标可以为（）A．（2，1）B．（﹣2，1）C．（﹣2，﹣1）D．（2，﹣1）10．如图，抛物线y＝x2﹣7x+与x轴交于点A、B，把抛物线在x轴及其下方的部分记作C1，将C1向左平移得到C2，C2与x轴交于点B、D，若直线y＝x+m与C1、C2共有3个不同的交点，则m的取值范围是（）A．﹣＜m＜﹣B．﹣＜m＜﹣C．﹣＜m＜﹣D．﹣＜m＜﹣二．填空题（每题4分，满分20分）11．一次数学测试后，某班40名学生的成绩被分为5组，第1﹣4组的频数分别为12、10、6、8，则第5组的频率是．12．如图，点P是反比例函数y＝（k≠0）的图象上任意一点，过点P作PM⊥x轴，垂足为M．若△POM的面积等于2，则k的值等于．13．如图，正六边形ABCDEF的顶点B、C分别在正方形AGHI的边AG、GH上，如果AB＝4，那么CH的长为．14．若不等式组的解集是﹣1＜x≤1，则a＝，b＝．15．如图，在矩形ABCD中，AB＜BC，点E为CD边的中点，连接AE并延长与BC的延长线交于点F，过点E作EM⊥AF交BC于点M，连接AM与BD交于点N，现有下列结论：①AM＝MF；②ME2＝MC•AM；③＝（sin∠DAE）2；④点N是四边形ABME 的外接圆的圆心，其中正确结论的序号是．三．解答题16．（10分）体育老师为了解本校九年级女生1分钟“仰卧起坐”体育测试项目的达标情况，从该校九年级136名女生中，随机抽取了20名女生，进行了1分钟仰卧起坐测试，获得数据如下：收集数据：抽取20名女生的1分钟仰卧起坐测试成绩（个）如下：38 46 42 52 55 43 59 46 253835 45 51 48 57 49 47 53 5849（1）整理、描述数据：请你按如下分组整理、描述样本数据，把下列表格补充完整：范围25≤x≤2930≤x≤3435≤x≤3940≤x≤4445≤x≤4950≤x≤5455≤x≤59人数（说明：每分钟仰卧起坐个数达到49个及以上时在中考体育测试中可以得到满分）（2）分析数据：样本数据的平均数、中位数、满分率如下表所示：平均数中位数满分率46.8 47.5 45%得出结论：①估计该校九年级女生在中考体育测试中1分钟“仰卧起坐”项目可以得到满分的人数为；②该中心所在区县的九年级女生的1分钟“仰卧起坐”总体测试成绩如下：平均数中位数满分率45.3 49 51.2%请你结合该校样本测试成绩和该区县总体测试成绩，为该校九年级女生的1分钟“仰卧起坐”达标情况做一下评估，并提出相应建议．17．（8分）某商场销售进价为每件x元的上衣，先按进价的2倍作为定价，而实际销售时按定价打八折出售．（1）试用代数式表示：①每件上衣最初的定价为元；②每件上衣打八折后的销售价为元；③n件上衣打八折后的利润为元；（2）若该商场这次共购进每件120元的上衣100件，按以上办法售出80件后，其余按定价的六折销售全部卖完，问该商场在这批上衣买卖中，除支付销售费用1000元外，盈亏情况如何？18．如图，在Rt△ABC中，∠ACB＝90°，AC＝4，BC＝3，点D是边AC的中点，CF⊥BD，垂足为点F，延长CF与边AB交于点E．求：（1）∠ACE的正切值；（2）线段AE的长．19．（10分）某水果店2400元购进一批葡萄，很快售完；又用5000元购进第二批葡萄，所购件数是第一批的2倍，但进价比第一批每件多了5元．（1）求第一批葡萄每件进价多少元？（2）若以每件150元的价格销售第二批葡萄，售出80%后，为了尽快售完，决定打折促销，要使第二批葡萄的销售利润不少于640元，剩余的葡萄每件售价至少打几折（利润＝售价﹣进价）？20．（10分）如图，在等腰Rt△ABC中，∠BAC＝90°，延长BA至点D，连结DC，过点B 作BE⊥DC于点E，F为BC上一点，FC＝FE．连结AF，AE．（1）求证：FA＝FE．（2）若∠D＝60°，BC＝10，求△AEF的周长．21．（10分）某种机器使用若干年后即被淘汰，该机器有一易损零件，为调查该易损零件的使用情况，随机抽取了100台已被淘汰的这种机器，经统计：每台机器在使用期内更换的该易损零件数均只有8，9，10，11这四种情况，并整理了这100台机器在使用期内更换的该易损零件数，绘制成如图所示不完整的条形统计图．（1）请补全该条形统计图；（2）某公司计划购买一台这种机器以及若干个该易损零件，用上述100台机器更换的该易损零件数的频率代替一台机器更换的该易损零件数发生的概率．①求这台机器在使用期内共更换了9个该易损零件的概率；②若在购买机器的同时购买该易损零件，则每个200元；若在使用过程中，因备用该易损零件不足，再购买，则每个500元．请你帮该公司用花在该易损零件上的费用的加权平均数进行决策：购买机器的同时应购买几个该易损零件，可使公司的花费最少？22．（10分）为满足市场需求，某超市在新年来临前夕，购进一款商品，每盒进价是40元．超市规定每盒售价不得少于45元．根据以往销售经验发现；当售价定为每盒45元时，每天可以卖出700盒，如果每盒售价每提高1元，则每天要少卖出20盒．（1）试求出每天的销售量y（盒）与每盒售价x（元）之间的函数关系式；（2）当每盒售价定为多少元时，每天销售的利润P（元）最大？最大利润是多少？23．如图，AB为⊙O的直径，且AB＝4，点C在半圆上，OC⊥AB，垂足为点O，P为半圆上任意一点（不与点C重合），过P点作PE⊥OC于点E，设△OPE的内心为M，连接OM、PM．（1）求∠OMP的度数；（2）当点P在半圆上从点B运动到点A时，求内心M所经过的路径长．24．我们知道：在小学已经学过“正方形的四条边都相等，正方形的四个内角都是直角”，试利用上述知识，并结合已学过的知识解答下列问题：如图1，在正方形ABCD中，G是射线DB上的一个动点（点G不与点D重合），以CG 为边向下作正方形CGEF．（1）当点G在线段BD上时，求证：∠DCG＝∠BCF；（2）连接BF，试探索：BF，BG与AB的数量关系，并说明理由；（3）若AB＝a（a是常数），如图2，过点F作FT∥BC，交射线DB于点T，问在点G 的运动过程中，GT的长度是否会随着G点的移动而变化？若不变，请求出GT的长度；若变化，请说明理由．25．如图，直线y＝x+2与x轴交于点B，与双曲线C1：（x＞0）交于点A，且A点的横坐标为2．（1）求双曲线C1的函数解析式；（2）若P为C1上的一动点，连接PO．①将PO绕O点顺时针旋转90°，得到点P′，问P′是否在某定曲线C1上运动，若是，试求C1的解析式，若不是，说明理由；②若△AOP的面积为，直接写出P点坐标为．参考答案一．选择题1．解：由x﹣2y＝﹣2，得到原式＝3+2（x﹣2y）＝3﹣4＝﹣1．故选：B．2．解：根据三角形中线的定义知线段BE是△ABC的中线，故选：B．3．解：综合三视图，这个立体图形的底层应该有3个，第二层应该有1个小正方体，因此构成这个立体图形的小正方体的个数是3+1＝4个．故选：C．4．解：A、调查某种灯泡的使用寿命，不能使用普查，错误；B、调查中央电视台春节联欢会的收视率被调查的对象都较大，不能使用普查，错误；C、调查我国八年级学生的视力情况被调查的对象都较大，不能使用普查，错误；D、调查你们班学生早餐是否有喝牛奶的习惯被调查的对象较小，故D宜使用普查；故选：D．5．解：如图，连接AC，∵菱形ABCD，∠B＝60°，∴△ABC是等边三角形，∵点E是BC的中点，∴AE＝，∠EAC＝30°，同理可得：AF＝，∠FAC＝30°，∴AE＝AF，∠EAC＝∠FAC，∴△AEF是等边三角形，∴△AEF的周长＝3×＝3．故选：B．6．解：由题意可得：B点对应的数是：a+6，∵点A和点B表示的数恰好互为相反数，∴a+a+6＝0，解得：a＝﹣3．故选：D．7．解：x2﹣8x+15＝0，（x﹣3）（x﹣5）＝0，则x﹣3＝0，x﹣5＝0，解得x＝3或5，①当3和5为直角边时：tan A＝．②当5为斜边时，另一直角边为4，tan A＝．故选：D．8．解：列表如下：红红蓝红紫蓝紫紫共有6种情况，其中配成紫色的有3种，所以恰能配成紫色的概率＝＝，故选：A．9．解：把（2，1）代入一次函数y＝kx﹣1得：2k﹣1＝1，k＝1，因此不可以；把（﹣2，1）代入一次函数y＝kx﹣1得：﹣2k﹣1＝1，k＝﹣1，因此可以；故选：B．10．解：∵抛物线y＝x2﹣7x+与x轴交于点A、B∴B（5，0），A（9，0）∴抛物线向左平移4个单位长度∴平移后解析式y＝（x﹣3）2﹣2当直线y＝x+m过B点，有2个交点∴0＝+mm＝﹣当直线y＝x+m与抛物线C2相切时，有2个交点∴x+m＝（x﹣3）2﹣2x2﹣7x+5﹣2m＝0∵相切∴△＝49﹣20+8m＝0∴m＝﹣如图∵若直线y＝x+m与C1、C2共有3个不同的交点，∴﹣＜m＜﹣故选：C．二．填空题11．解：根据题意得：40﹣（12+10+6+8）＝40﹣36＝4，则第5组的频率为4÷40＝0.1，故答案为：0.1．12．解：∵△POM的面积等于2，∴|k|＝2，而k＜0，∴k＝﹣4，故答案为：﹣4．13．解：正六边形的内角的度数＝＝120°，则∠CBG＝180°﹣120°＝60°，∴∠BCG＝30°，∴BG＝BC＝2，CG＝BC＝2，∴AG＝AB+BG＝6，∵四边形AGHI是正方形，∴GH＝AG＝6，∴CH＝HG﹣CG＝6﹣2，故答案为：6﹣2．14．解：∵解不等式①得：x＞1+a，解不等式②得：x≤﹣∴不等式组的解集为：1+a＜x≤﹣∵不等式组的解集是﹣1＜x≤1，∴1+a＝﹣1，﹣＝1，解得：a＝﹣2，b＝﹣3故答案为：﹣2，﹣3．15．解：∵四边形ABC都是正方形，∴AD∥BF，∴∠DAE＝∠F，∵∠AED＝∠FEC，DE＝EC，∴△ADE≌△FCE（AAS），∴AE＝EF，∵ME⊥AF，∴MA＝NF，故①正确，∵∠EMC＝∠EMF，∠ECM＝∠MEF，∴△MEC∽△MFE，∴ME：MF＝MC：ME，∴ME2＝MC•MF＝MC•AM，故②正确，∵∠AEM＝90°，∠ADE＝∠ECM＝90°，∴∠AED+∠MEC＝90°，∠MEC+∠EMC＝90°，∴∠AED＝∠EMC，∴△ADE∽△ECM，∴＝（）2＝（）2＝（tan∠DAE）2，故③错误，∵∠ABM＝∠AEM＝90°，∴A，B，M，E四点共圆，∴四边形的外接圆的圆心是线段AM的中点，显然点N不是AM的中点，故④错误．故答案为①②．三．解答题16．解：（1）补充表格如下：范围25≤x≤2930≤x≤3435≤x≤3940≤x≤4445≤x≤4950≤x≤5455≤x≤59人数 1 0 3 2 7 3 4 （2）①估计该校九年级女生在中考体育测试中1分钟“仰卧起坐”项目可以得到满分的人数为136×≈61，故答案为：61；②从平均数角度看，该校女生1分钟仰卧起坐的平均成绩高于区县水平，整体水平较好；从中位数角度看，该校成绩中等水平偏上的学生比例低于区县水平，该校测试成绩的满分率低于区县水平；建议：该校在保持学校整体水平的同时，多关注接近满分的学生，提高满分成绩的人数．17．解：（1）①每件上衣最初的定价为2x（元）；②每件上衣打八折后的销售价为2x•0.8＝1.6x（元）；③n件上衣打八折后的利润为n•（1.6x﹣x）＝0.6xn（元）；（2）0.6×120×80+2×120×0.6×20﹣120×20﹣1000＝5240（元），所以该商场在这批上衣买卖中盈利5240元．故答案为2x，1.6x，06xn．18．解：（1）∵∠ACB＝90°，∴∠ACE+∠BCE＝90°，又∵CF⊥BD，∴∠CFB＝90°，∴∠BCE+∠CBD＝90°，∴∠ACE＝∠CBD，∵AC＝4且D是AC的中点，∴CD＝2，又∵BC＝3，在Rt△BCD中，∠BCD＝90°．∴tan∠BCD＝＝，∴tan∠ACE＝tan∠CBD＝；（2）过点E作EH⊥AC，垂足为点H，在Rt△EHA中，∠EHA＝90°，∴tan A＝，∵BC＝3，AC＝4，在Rt△ABC中，∠ACB＝90°，∴tan A＝＝，∴＝，设EH＝3k，AH＝4k，∵AE2＝EH2+AH2，∴AE＝5k，在Rt△CEH中，∠CHE＝90°，∴tan∠ECA＝＝，∴CH＝k，∴AC＝AH+CH＝k＝4，解得：k＝，∴AE＝．19．解：（1）设第一批葡萄每件进价x元，根据题意，得：×2＝，解得x＝120．经检验，x＝120是原方程的解且符合题意．答：第一批葡萄每件进价为120元．（2）设剩余的葡萄每件售价打y折．根据题意，得：×150×80%+×150×（1﹣80%）×0.1y﹣5000≥640，解得：y≥7．答：剩余的葡萄每件售价最少打7折．20．（1）证明：∵BE⊥DC，∴∠EBC+∠ECB＝∠CEF+∠BEF＝90°，∵FC＝FE，∴∠ECB＝∠CEF，∴∠EBC＝∠BEF，∴BF＝FE＝FC，在Rt△BAC中，AF是斜边BC上的中线，∴FA＝FC，∴FA＝FE；（2）解：∵∠D＝60°，∠BAC＝90°，∴∠ACD＝30°，∵△ABC为等腰直角三角形，∴∠ABC＝∠ACB＝45°，∴∠ECF＝∠ACD+∠ACB＝30°+45°＝75°，由（1）得：FA＝FE，AF是斜边BC上的中线，∴AF⊥BC，AF＝BC＝5，∵FC＝FE，∴∠EFC＝180°﹣2∠ECF＝180°﹣2×75°＝30°，∴∠AFE＝90°﹣30°＝60°，∴△AEF是等边三角形，∴△AEF的周长＝3AF＝3×5＝15．21．解：（1）100﹣20﹣50﹣20＝10，补全的条形统计图如图所示：（2）①这台机器在使用期内共更换了9个该易损零件的概率为：P＝＝；②购买机器的同时购买8个该易损零件200×0.2+500×0.8＝440元，购买机器的同时购买9个该易损零件200×0.5+500×0.5＝350元，购买机器的同时购买10个该易损零件200×0.1+500×0.9＝470元，购买机器的同时购买11个该易损零件200×0.2+500×0.8＝440元，因此，购买机器的同时应购买9个该易损零件，可使公司的花费最少．22．解：（1）由题意得销售量y＝700﹣20（x﹣45）＝﹣20x+1600（x≥45）；（2）P＝（x﹣40）（﹣20x+1600）＝﹣20x2+2400x﹣64000＝﹣20（x﹣60）2+8000，∵x≥45，a＝﹣20＜0，＝8000元∴当x＝60时，P最大值即当每盒售价定为60元时，每天销售的利润P（元）最大，最大利润是8000元．23．解：（1）∵△OPE的内心为M，∴∠MOP＝∠MOC，∠MPO＝∠MPE，∴∠PMO＝180°﹣∠MPO﹣∠MOP＝180°﹣（∠EOP+∠OPE），∵PE⊥OC，即∠PEO＝90°，∴∠PMO＝180°﹣（∠EOP+∠OPE）＝180°﹣（180°﹣90°）＝135°，（2）如图，∵OP＝OC，OM＝OM，而∠MOP＝∠MOC，∴△OPM≌△OCM，∴∠CMO＝∠PMO＝135°，所以点M在以OC为弦，并且所对的圆周角为135°的两段劣弧上（和）；点M在扇形BOC内时，过C、M、O三点作⊙O′，连O′C，O′O，在优弧CO取点D，连DC，DO，∵∠CMO＝135°，∴∠CDO＝180°﹣135°＝45°，∴∠CO′O＝90°，而OA＝2cm，∴O′O＝OC＝×2＝，∴弧OMC的长＝＝π（cm），同理：点M在扇形AOC内时，同①的方法得，弧ONC的长为πcm，所以内心M所经过的路径长为2×π＝πcm．24．解：（1）∵四边形ABCD和四边形EFCG是正方形，∴CD＝CB，CG＝CF，∠BCD＝∠FCG＝90°，∵∠DCG＝90°﹣∠BCG，∠BCF＝90°﹣∠BCG，∴∠DCG＝∠BCF；（2）BF+BG＝AB，理由：在Rt△CDG和△CBF中，，∴△CDG≌CBF（SAS），∴DG＝BF，在Rt△ABD中，AD＝AB，∴BD＝AB，∵BD＝DG+BG＝BF+BG，∴BF+BG＝AB；（3）∵BD是正方形ABCD的对角线，∴∠CBD＝∠CDB＝45°，由（2）知，△CDG≌CBF（SAS），∴DG＝BF，∠CDG＝∠CBF＝45°，∴∠DBF＝∠CBD+∠CBF＝90°，∴∠FBT＝90°，∵FT∥CB，∴∠BTF＝∠CBD＝45°，∴∠BFT＝45°＝∠BTF，∴BF＝BT，∴DG＝BT，∴GT＝BG+BT＝BG+DG＝BD＝AB＝a．25．解：（1）当x＝2时，y＝x+2＝2+2＝4，∴点A坐标为（2，4），则k＝2×4＝8，∴双曲线C1的函数解析式为y＝；（2）①点P′在双曲线C2：y＝﹣上运动，设P （m ，） （m ＞0），如图，过点P 作PC ⊥x 轴于点C ，过点P ′作P ′D ⊥y 轴于点D ，则∠PCO ＝∠P ′DO ＝∠POP ′＝90°，∴∠POC ＝∠P ′OD ，又∵OP ＝OP ′，∴△OPC ≌△OP ′D （AAS ），∴OD ＝OC ＝m ，P ′D ＝PC ＝，∴P ′（m ，﹣），则点P ′在双曲线C 2：y ＝﹣上运动．②设P （n ，），如图2，过点A 作AE ⊥y 轴于点E ，作PF ⊥x 轴于点F ，延长EA 、FP 交于点M ，则四边形OEMF 是矩形，M （n ，4），∵A （2，4），∴AM ＝n ﹣2，PM ＝4﹣，∵S △AOP ＝S 矩形OEMP ﹣S △AOE ﹣S △POF ﹣S △AMP ， ∴＝4n ﹣4﹣4﹣（n ﹣2）（4﹣），整理，得：3n2﹣16n﹣12＝0，解得n＝6或n＝﹣（舍），当n＝6时，＝，∴点P（6，）．故答案为：（6，）．。

2021河南中考英语考前冲刺：阅读理解题组训练（二）1.One morning, a very successful businessman who had a big company was getting ready to go to his office. When he reached into his car and opened the door, a dog sleeping under his car suddenly came out and bit（咬）on his leg. The businessman quickly picked up a few stones and threw at the dog, but none hit the dog. The dog ran away.As soon as he reached his office, the businessman called a meeting of his managers to ask about their tasks, and during the meeting he put anger of the dog on them. The managers also got upset by the anger of their boss and they put their anger on the workers under them. The chain of this reaction kept going, and finally the anger reached to the office cleaner.Now, there was no one working under the cleaner! So, when the office time was over, he reached his home, and his wife opened the door. She asked him, "Why are you so late today?" The cleaner said loudly, "I didn't go to the office to play football. I went to work so don't irritate me with your stupid questions!"So, the wife got upset for no reason. She put her anger on her son who was watching TV, saying, "This is all you do. You have no interest in studying! Turn off the TV now."The son got upset too! He walked out of his house and saw a dog passing by looking at him. He picked up a stone and hit the dog in anger. The window of the businessman's car in front of the building was broken unluckily.（1）The businessman got angry at the meeting because ________.A.the company had a lot of problemsB.the managers didn't finish the tasks on timeC.his leg was bitten by a dogD.the window of his car was broken（2）We can infer（推断）from the passage that ________.A.the anger kept going to the lower level of the workersB.the cleaner knew why his leader put anger on himC.It's not bad for the managers to attend the meetingD.something enjoyable happened in the company（3）What does the underlined word "irritate" mean?A.安慰B.激怒C.照顾D.侮辱（4）The wife asked her son to turn off the TV because ________.A.he wasn't interested in studyingB.the family had a poor lifeC.he should go out for exerciseD.she was upset and tried to put her anger on him（5）What can we learn from the passage?A.Be careful of a sleeping dog under a car.B.Hold in your anger and don't hurt those around you.C.Take a few moments to collect your thoughts.D.Anger itself isn't a problem.2.If you like nature, Mona Island is a wonderful place to take a vacation. There are beautiful beaches and caves for you to explore. Some of the animals living there are not found anywhere else in the world. There are many things that make Mona Island an unusual place.Mona Island is very small. The only way to get there is by taking a long boat ride from the Island of Puerto Rico.The government of Puerto Rico takes care of Mona Island and has made it a natural reserve. Mona Island is different from most places because people mustn't live there. There are only a few forest ranges for people to stay in.The forest rangers' job is to keep Mona Island safe and beautiful. They make people follow the rules here. One rule is that only 100 people each time can visit the island.Visitors to Mona Island have to prepare carefully for their trip. Visitors can only sleep in some areas and must bring their own tents. And if they want anything to eat or drink, they have to bring that along too. But if you are glad to take the trouble to come to Mona Island, you will enjoy many wonderful sights. I'm sure.（1）What is Paragraph 1 mainly about?A.The location of Mona Island.B.The weather of Mona Island.C.Why people should go to Mona Island.D.Why people should protect Mona Island.（2）How can people get to Mona Island from the Island of Puerto Rico?A.By plane.B.By boat.C.On foot.D.By car.（3）What should visitors do before going to Mona Island?A.Read about Puerto Rico.B.Find a comfortable hotel.C.Collect information about the animals there.D.Make sure they have a tent, enough food and water.3.One day a man went to the market and brought home some peaches. He said to his four sons, "I have bought a peach for each of you, and one for your mother." They took the fruit and thanked their father. It was not often that they could have such fine peaches.In the evening the father said, "Well, boys, what did you do with those peaches?"The eldest son said, "I ate mine, and found it very sweet and juicy. I have put the stone away, and in the spring I will plant it. If it grows, I will have a peach tree of my own.""You have done right," said his father. "It is a good thing to think of having something for yourself tomorrow."Theyoungest son then said," I ate my peach and threw away the stone, and Mother gave me half of hers. It tasted so good.""Well," said his father, "you are a little boy. But you should not have been so quick to eat the peach and throw away the stone."The second son said, "I picked up the stone which he threw away. I broke it open and ate the kernel. Then I sold my peach for enough to buy three peaches the next time I go down the street."The father wasn't very happy with this answer. He said, "It is right to think of having something for yourself, but you have acted in a way that I am afraid will make you selfish and greedy."The third son said, "I did not eat my peach. I gave it to the little sick boy who lives next door. The doctor said peaches would do him good, but his mother is too poor to buy any for him."The other three boys felt that this boy had made the best use of his peach.（1）What can we learn about the father from Paragraph 1?A.He didn't like eating peaches.B.He brought home five peaches.C.He often bought peaches for his sons.D.He picked the peaches from a peach tree.（2）What did the eldest son think of his peach?A.It was big.B.It was fresh.C.It looked beautiful.D.It tasted good.（3）What did the second son do with his peach?A.He sold it.B.He ate it.C.He gave it to his mother.D.He traded it for something else.（4）Who was thought to make the best use of his peach?A.The eldest son.B.The second son.C.The third son.D.The youngest son.4.Mary is eleven. She has long hair and brown eyes. Her ears are small.Mary lives in the center of the city. There is a post office next to her house. There is a coffee shop behind her house and a supermarket in front of her house. But there aren't any schools near her house. Mary often goes to the supermarket to buy fruit. She likes apples and bananas, but she likes strawberries best.Now Mary is in her bedroom. The room is in a mess! Her jeans are on the floor. There is one sock on the sofa and the other one is gone（不在的）. Her mom is very angry. She says to Mary, "Tidy up your room! Put the jeans away and find the socks."Mary likes playing table tennis and she often plays with her classmates after school. She doesn't like playing basketball, because she is not tall. In spring, Mary likes to help her grandma work in the garden（花园）. And in summer, she would like to go camping（去野营）with her grandpa. She thinks they' re interesting.（1）You can't find ________ near Mary's house.A.a coffee shopB.a schoolC.a supermarket（2） ________ are Mary's favorite fruit.A.ApplesB.BananasC.Strawberries（3）The underlined words " in a mess " in Paragraph 3 mean "________" in Chinese.A.破旧不堪B.嘈杂喧闹C.杂乱无章（4）From the passage we know Mary ________.A.isn't tallB.has small eyesC.never works in the garden5.Lisa SantoriSpaghetti Street2462 CRome, Italy（1）How is the weather in Shanghai now?A.Sunny.B.Rainy.C.Windy.（2）Who is Lisa?A.Sophie's friend in Italy.B.Sophie's friend in China.C.Sophie's aunt in China.（3）Which of the following is TRUE?A.Sophie comes to China to learn Chinese.B.Sophie would like to travel around Shanghai tomorrow.C.Sophie thinks her brother is lazy because he doesn't cook.6."Love is still alive!" Wang Zhiru from Jiangxi Academy of Forestry, said excitedly when receiving a picture of a white crane（鹤）on January 3rd2019. The white crane they named Love was saved and set free in early 2018.Love was first found on April 24th 2018, when Li Zengming, a farmer, drove past a reservoir（水库）in the countryside of Nanchang, capital of Jiangxi Province. Seeing ittrying to fly but falling again and again, Li thought that it might be hurt. He drove to the shore and went into the water to save it. "I saw the white crane with dull eyes and a weak body. It was probably hurt. If I let it alone, it would be in danger," Li recalled. After more than half an hour, Li finally took the white crane back to the shore.Then he called his uncle, an experienced animal saver for help. "Come over immediately and let's send it to the police station right away" said his uncle. When seeing the weak wild crane, Jiang Qingchun from the Five-Star Police Station, put down his work and checked it carefully."At the end of April, migratory（迁移的）birds usually return to the north. It's abnormal for a white crane to still be living nearby. It may be left behind because of its poor health." Jiang said. He contacted Wang at the Jiangxi Academy of Forestry for help. Wang's team found Love did not seem to be hurt or have illness, but it suffered（遭受）from hunger and tiredness. After five days' treatment, its weight rose from 3.75 kg to 4 kg.Being kept for long will be bad for birds' ability to live in the wild. Wang's team decided on May 2nd to set it free at a place in northern China so that it could join the migrating group heading for Siberia in Russia. On May 8th, Love was set free at the Momoge National Nature Reserve.（1）When did the farmer find Love for the first time?A.On May 2nd, 2019.B.On May 8th, 2019.C.On April 24th, 2018.D.On January 3rd, 2019.（2）The underlined word "abnormal" in Paragraph 4 means ________.A.unhappyB.unusualC.unknownD.unlucky（3）What was wrong with Love?A.It was hurt.B.It was weak and lost.C.It was dead.D.It was hungry and tired.（4）What does the underline words "set free" mean?A.释放B.逮捕C.饲养D.杀害（5）What is the best title of the passage?A.Love hurtB.Love lostC.Love foundD.Love gone7.Perhaps you have heard the expression "When in Rome, do as the Romans do". So when you want to do business in France, you have to get to know French culture, to make marketing plans, and to run your business by local laws.Language should be the focus of anyone planning to do business in France. The French take great pride in their language, so anyone who does not speak it may run the risk of being disrespected（不尊敬）by his French workmates or business partners. Also, another reason why learning French is important is that it is a great way to show every possible French business partner that you care and respect their country's culture and language.The first thing that you should do when meeting someone new is to shake his hand and always look the person in the eye. In social meetings with friends, kissing is common.Use first names only after being invited to. Use Monsieur or Madame before the familyname. The French will sometimes introduce themselves using their family name first, followed by their first name.Dress well. The French get information about people based on their appearance（外貌）. Your business clothing is a reflection（反映）of your success and social status. Always try to be tasteful and stylish. Women are advised to dress simply but elegantly. Business women usually wear make-up.Lunches are common in doing business in France, which usually have an appetizer, main meal with wine, cheese, dessert and coffee. Don't eat quickly. French lunches usually last two or three hours. This is a time to build relationship.Do not begin eating until the host says, "bon appetite". Pass dishes to the left, keep hands above the table and try to eat everything on the plate. Be careful with adding salt, pepper or sauces to your food. This may suggest that you find the food tasteless. If eating in a restaurant, the person who invites always pays.（1）Paragraph 2 mainly talks about ________ if you plan to do business in France.A.why it is important to learn FrenchB.what French culture you should knowC.how you can learn the language wellD.how you can get on with your partners（2）In France, when you meet someone for the first time, you are supposed to ________.A.kissB.bowC.shake handsD.look the person in the eye（3）If a French man named Alban Martin is introduced to you, you'd better call him________.A.AlbanB.MartinC.Monsieur AlbanD.Monsieur Martin（4）What does the underlined word "elegantly" in Paragraph 5 most probably mean in Chinese?A.雅致地B.复杂地C.邋遢地D.随意地（5）According to the last paragraph, what are you supposed to do while you are having a meal at a table with other people?A.Pass dishes with your left hand.B.Eat all the food on the plate.C.Add salt or pepper to your food.D.Let the host start eating first.8.Space vegetables are grown from seeds（种子）that have been taken to space and brought back to the earth. The seeds are affected（影响）by the radiation（辐射）and low gravity（重力）in space. When they are brought back to the earth, these seeds produce vegetables that are bigger and healthier than normal vegetables. However, some people worry about eating space vegetables. They think that space vegetables might not be good for us andcould make us get sick because of the radiation in space. However, people should not be frightened because space vegetables are very healthy.Here are some facts that you should know about space vegetables.Space vegetables are grown from seeds that are carefully chosen. When seeds are brought back from space they are tested to make sure that they will be safe to eat.Space vegetables are better for you than normal vegetables. For example, space tomatoes stay fresh for twenty days, which is one week longer than normal tomatoes.After genetically modified（转基因）food appeared in the market, people worried that they were eating unknown things. For example, if nut genes（坚果基因）are put inside potatoes, people allergic（过敏的）to nuts might get sick from eating these potatoes because they do not know they are also eating nuts. Unlike genetically modified food, space vegetables have not been genetically changed. This means that no new genes are put into the vegetables. Therefore, there are no dangers of eating unknown.（1）According to Paragraph One, how are the space vegetables?A.More delicious.B.Healthier and bigger.C.More dangerous.D.Cheaper and healthier.（2）According to Paragraph 4, how long can normal tomatoes stay fresh?A.For seven day.B.For twenty days.C.For thirteen days.D.For twenty-seven days.（3）What's the difference between space vegetables and genetically modified food?A.Space vegetables have no new genes.B.Space vegetables are grown in space.C.Space vegetables have nothing unknown.D.Space vegetables are genetically changed.（4）What does the writer want to tell us?A.The seeds of space vegetables are taken to space.B.Everybody worries about eating space vegetables.C.Space vegetables are safe and good for people to eat.D.Space vegetables bring us illness because of the radiation.参考答案1.【答案】CABDB2.【答案】CBD3.【答案】BDAC4.【答案】BCCA5.【答案】BAB6.【答案】CBDAC7.【答案】ACDAB8.【答案】BCAC。

备战2021年九年级中考复习数学高分冲刺训练——几何综合：《四边形综合》（二）1．如图，矩形ABCD中，AB＝6cm，AD＝8cm，点P从点A出发，以每秒一个单位的速度沿A→B→C的方向运动；同时点Q从点B出发，以每秒2个单位的速度沿B→C→D的方向运动，当其中一点到达终点后两点都停止运动．设两点运动的时间为t秒．（1）当t＝时，两点停止运动；（2）设△BPQ的面积面积为S（平方单位）①求S与t之间的函数关系式；②求t为何值时，△BPQ面积最大，最大面积是多少？2．共顶点的正方形ABCD与正方形AEFG中，AB＝13，AE＝5．（1）如图1，求证：DG＝BE；（2）如图2，连结BF，以BF、BC为一组邻边作平行四边形BCHF．①连结BH，BG，求的值；②当四边形BCHF为菱形时，直接写出BH的长．3．如果将（1）中的条件“▱ABCD”改为“四边形ABCD的对角线AC⊥BD”（如图②）．试探索：S1：S2与S4：S3之间的关系；（3）如果将（2）中的对角线AC⊥BD的条件去掉（如图③），试探索S1，S2，S3，S4之间的关系．4．如图1，在等腰直角△ABC和△DCE中，AC＝BC，DC＝EC，∠ACB＝∠DCE＝90°．（1）求证：△ACD≌△BCE；（2）如图2，将△DCE绕点C顺时针旋转n°（0＜n＜45），使点A、D、E在同一直线上，AF平分∠BAE交CE延长线与F，探究AB、DE、EF之间的数量关系；（3）如图3，在正方形ABCD中，CD＝．若点P满足PD＝1，且∠BPD＝90°，请直接写出点A到BP的距离．5．如图，△ABC是一块铁皮余料．已知底边BC＝160cm，高AD＝120cm．在铁皮余料上截取一个矩形EFGH，使点H在AB上，点G在AC上，点E，F在BC上，AD交HG 于点M．（1）设HG＝ycm，HE＝xcm，试确定用x表示y的函数表达式．（2）当x为何值时，矩形EFGH的面积S最大？（3）以面积最大时的矩形EFGH为侧面，围成一个无底圆桶，怎样围，圆桶的体积较大？请说明理由，（接缝处忽略不计，结果可保留π）6．类比、转化、从特殊到一般等思想方法，在数学学习和研究中经常用到，请利用上述有关思想，解答下列问题．如图1，在▱ABCD中，E是BC的中点，AE与BD相交于点F．若△BEF的面积为2，求四边形CDFE的面积．【类比延伸】如图2，在▱ABCD中，E是BC的一点，且BE：BC＝m：n（n＞m＞0），AE与BD相交于点F．求△ABF的面积与四边形CDFE的面积的比．（用含m、n的代数式表示）【拓展迁移】如图3，在▱ABCD中，E是BC的一点，且BE：BC＝，点G是线段CD的中点，AE 与BD相交于点F．则△ABF的面积与四边形CGFE的面积的比等于．（直接写出答案）7．，四边形OBCD是矩形，O，B，D三点的坐标分别是（0，0），（b，0），（0，d），求点C 的坐标．（2）如图（2），四边形ABCD是菱形，C，D两点的坐标分别是（c，0），（0，d），点A，B在坐标轴上，求A，B两点的坐标．（3）如图（3），四边形OBCD是正方形，O，D两点的坐标分别是（0，0），（0，d），求B，C两点的坐标．8．如图，四边形ABCD是正方形，E是正方形ABCD内一点，F是正方形ABCD外一点，连结BE、CE、DE、BF、CF、EF．（1）若∠EDC＝∠FBC，ED＝FB，试判断△ECF的形状，并说明理由．（2）在（1）的条件下，当BE：CE＝1：2，∠BEC＝135°时，求BE：BF的值．（3）在（2）的条件下，若正方形ABCD的边长为（3+）cm，∠EDC＝30°，求△BCF的面积．9．如图，矩形OABC在平面直角坐标系中，若OA、OC的长满足方程x2﹣（2+2）x+4＝0的两根．（1）求B、C两点的坐标．（2）把△ABC沿AC对折，点B落在点B′处，线段AB′与x轴交于点D，求直线BB′的解析式．（3）在直线BB′上是否存在点P，使△ADP为直角三角形？若存在，请直接写出P点坐标；若不存在，请说明理由．10．四边形ABCD是正方形（提示：正方形四边相等，四个角都是90°）（1）如图1，若点G在BC边上时（不与点B、C重合），连接AG，作BF⊥AG于点F，DE⊥AG于点E，求证：△ABF≌△DAE；（2）直接写出（1）中，线段EF与AF、BF的等量关系是；（3）①如图2，若点G在CD边上时（不与点C、D重合），连接AG，作BF⊥AG于点F，DE⊥AG于点E，则图中全等三角形是，线段EF与AF、BF的等量关系是；②如图3，若点G在CD延长线上任意一点，连接AG，作BF⊥AG于点F，DE⊥AG于点E，线段EF与AF、BF的等量关系是；（4）若点G是BC延长线上任意一点，连接AG，作BF⊥AG于点F，DE⊥AG于点E，请画图、探究线段EF与AF、BF的等量关系．参考答案1．解：（1）∵四边形ABCD是矩形，∴AD＝BC＝8cm，AB＝CD＝6cm，∴BC+AD＝14cm，∴t＝14÷2＝7，故答案为7．（2）①当0＜t＜4时，S＝（6﹣t）×2t＝﹣t2+6t．当4≤t＜6时，S＝（6﹣t）×8＝﹣4t+24．当6＜t≤7时，S＝（t﹣6）（2t﹣8）＝t2﹣10t+24．②当0＜t＜4时，S＝（6﹣t）×2t＝﹣t2+6t＝﹣（t﹣3）2+9，∵﹣1＜0，∴t＝3时，△PBQ的面积最大，最小值为9．当4≤t＜6时，S＝（6﹣t）×8＝﹣4t+24，∵﹣4＜0，∴t＝4时，△PBQ的面积最大，最大值为8，当6＜t≤7时，S＝（t﹣6）（2t﹣8）＝t2﹣10t+24＝（t﹣5）2﹣1，t＝7时，△PBQ的面积最大，最大值为3，综上所述，t＝3时，△PBQ的面积最大，最大值为9．2．（1）证明：∵四边形ABCD和四边形AEFG是正方形，∴AD＝AB＝CB，AG＝AE，∠DAB＝∠GCE＝90°，∴∠DAB﹣∠GAF＝∠GCE﹣∠GAF，即∠DAG＝∠BAE，在△DAG和△BAE中，，∴△DAG≌△BAE（SAS），∴DG＝BE；（2）解：①连接GH，延长HF交AB于N，设AB与EF的交点为M，如图2所示：∵四边形BCHF是平行四边形，∴HF∥BC，HF＝BC＝AB，∵BC⊥AB，∴HF⊥AB，∴∠HFG＝∠FMB，又AG∥EF，∴∠GAB＝∠FMB∴∠HFG＝∠GAB，在△GAB和△GFH中，，∴△GAB≌△GFH（SAS），∴GH＝GB，∠HGF＝∠BGA，∴∠HGF﹣∠BGF＝∠BGA﹣∠BGF，∴∠HGB＝∠AGF＝90°，∴△GHB为等腰直角三角形，∴BH＝BG，∴＝；②分两种情况：a、如图3所示：连接AF、EG交于点O，连接BE，∵四边形BCHF为菱形，∴CB＝FB，∵AB＝CB，∴AB＝FB＝13，∴点B在AF的垂直平分线上，∵四边形AEFG是正方形，∴AF＝EG，OA＝OF＝OG＝OE，AF⊥EG，AE＝FE＝AG＝FG，∴点G、点E都在AF的垂直平分线上，∴点B、E、G在一条直线上，∴BG⊥AF，∵AE＝5，∴AF＝EG＝AE＝10，∴OA＝OG＝OE＝5，∴OB＝＝＝12，∴BG＝OB+OG＝12+5＝17，由①得：BH＝BG＝17；b、如图4所示：连接AF、EG交于点O，连接BE，同上得：点B、E、G在一条直线上，OB＝12，BG＝OG+OB﹣OG＝12﹣5＝7，由①得：BH＝BG＝7；综上所述，BH的长为17或7．3．解：（1）∵四边形ABCD是平行四边形，∴OA＝OC，∵△AOB，△BOC的边OA，OC上的高相同，∴S1＝S2，同理S2＝S3，S3＝S4，S4＝S1，∴S1＝S2＝S3＝S4；（2）∵AC⊥BD，垂足为O，∴S1＝OAOB，S2＝OBOC，S3＝OCOD，S4＝ODOA，∴S1S3＝S2S4，∴；（3）设点B到线段AC所在直线的距离为h1，点D到线段AC所在直线的距离为h2，∴S1＝OAh1，S2＝OCh1，S3＝OCh2，S4＝OAh2，∴S1S3＝S2S4；4．（1）证明：如图1中，∵∠ACB＝∠DCE＝90°，∴∠ACD＝∠BCE，在△ACD和△BCE中，，∴△ACD≌△BCE．（2）结论：AB﹣DE＝EF，理由：如图2中，∵CD＝CE，∠DCE＝90°，∴∠CED＝45°，DE＝CE，∵CA＝CB，∠ACB＝90°，∴∠CAB＝45°，AB＝CA，∵∠CED＝∠F+∠EAF，∴∠F＝45°﹣∠EAF，∵∠CAF＝∠CAB﹣∠F AB＝45°﹣∠F AB，∵∠EAF＝∠F AB，∴∠CAF＝∠F，∴CA＝CF，∵EF＝CF﹣CE＝CA﹣CE，∴EF＝CA﹣CE＝AB﹣DE．∴AB﹣DE＝EF．（3）如图3中，以D为圆心1为半径作⊙D，过点B作⊙D的切线BP、BP′，连接BD，作AE⊥BP′于E，AF⊥BP于F．∵四边形ABCD是正方形，CD＝BC＝AB＝AD＝，∴BD＝DC＝2，∠ABC＝90°，在Rt△PBD中，∵∠BPD＝90°，BD＝2，DP＝1，∴∠PBD＝30°，同理∠P′BD＝30°，∴∠ABE＝∠CBP＝15°，在△ABE和△BAF中，，∴△ABE≌△BAF，∴∠ABE＝∠OAB＝15°，∴∠AOE＝∠FOB＝30°，∴AO＝OB＝2AE，设AE＝a，则AO＝OB＝2a，EO＝a，∴EB＝AF＝2a+a，∵AB2＝AE2+BE2，∴2＝a2+（2a+a）2，∴a＝（负根已经舍弃），∴AE＝，AF＝BE＝2a+a＝．故答案为或．5．解：（1）∵四边形GHEF为矩形，∴GH∥FE，∴△AHG∽△ABC，∵AM和AD分别是△AHG和△ABC的高，∴，∴，∴y ＝﹣x +160；（2）∵S ＝xy ，∴S ＝﹣+160x ＝﹣（x 2﹣120x ）＝﹣（x 2﹣120x +3600﹣3600）＝﹣（x ﹣60）2+4800．∴当x ＝60cm 时，Smax ＝4800cm 2；（3）围圆柱形铁桶有两种情况：当x ＝60cm 时，y ＝﹣×60+160＝80cm ．第一种情况：以矩形EFGH 的宽HE ＝60cm 作铁桶的高，长HG ＝80cm 作铁桶的底面周长．则底面半径R ＝cm ，铁桶体积V 1＝π（）260＝（cm 3），第二种情况：以矩形EFGH 的长HG ＝80cm 作铁桶的高，宽HE ＝60cm 作铁桶的底面周长，则底面半径r ＝cm ，铁桶体积V 2＝π（）280＝（cm 3）．因为V 1＞V 2．所以矩形EFGH 的宽HE ＝60cm 作铁桶的高，长HG ＝80cm 作铁桶的底面周长围成的圆柱形铁桶的体积较大．6．解：（1）∵点E 是平行四边形ABCD 中BC 边的中点，∴AD ＝BC ＝2BE ，BE ∥AD ，∴△BEF ∽△DAF ，∴＝，∴＝（）2＝， ∵△BEF 的面积为2，∴S △ABF ＝2S △BEF ＝4，S △ADF ＝4S △BEF ＝8，∴S △ABD ＝S △ABF +S △ADF ＝12，∴S 四边形DCEF ＝S △BCD ﹣S △BEF ＝S △ABD ﹣S △BEF ＝12﹣2＝10；（2）【类比延伸】∵在▱ABCD 中，E 是BC 的一点，且BE ：BC ＝m ：n ，∴AD ＝BC ，BE ∥AD ，∴△BEF ∽△DAF ，∴＝，∴＝（）2＝，设△BEF 的面积为a ，∴S △ABF ＝S △BEF ＝，S △ADF ＝S △BEF ＝，∴S △ABD ＝S △ABF +S △ADF ＝＝a ，∴S 四边形DCEF ＝S △BCD ﹣S △BEF ＝S △ABD ﹣S △BEF ＝a ﹣a ＝a ， ；△ABF 的面积与四边形CGFE 的面积的比＝：（a ）＝； （3）【拓展迁移】设△BEF 的面积为a ，∵由（2）得：m ＝2．n ＝3，∴△ABF 的面积＝a ，四边形CDFE 的面积＝a ，连接CF ，如图所示： ∵△ABF 的面积+△CDF 的面积＝△ABD 的面积，∴△CDF 的面积＝△ADF 的面积＝a ，∵G 是CD 的中点，∴△DGF 的面积＝△CDF 的面积＝a ，∴四边形CGFE 的面积＝a ﹣a ＝a ，∴△ABF 的面积与四边形CGFE 的面积的比＝a ：a ＝， 故答案为：．7．解：（1）如图1中，∵B（b，0），D（0，d），∴OB＝b，OD＝d，∵四边形OBCD是矩形，∴∠CDO＝∠CBO＝90°，CD＝OB＝b，BC＝OD＝d，∴C（b，d）．（2）如图2中，∵四边形ABCD是菱形，∴OA＝OC，OB＝OD，∵C（c.0），D（0，d），∴OA＝OC＝c．OB＝OD＝d，∴A（﹣c，0），B（0，﹣d）．（3）如图3中，∵四边形OBCD是正方形，∴OB＝BC＝CD＝OD，∠CDO＝∠CBO＝90°，∵D（0，d），∴OD＝d，∴OB＝BC＝CD＝d，∴B（d，0），C（d，d）．8．（1）证明：在正方形ABCD中，CD＝CB，∠DCE+∠BE＝∠BCD＝90°，∵EC⊥CF，∴∠BCF+∠BCE＝90°，∴∠BCF＝∠DCE，在△BCF和△DCE中，∴△BCF≌△DCE（ASA），∴EC＝FC，∴∠ECD＝∠BCF，∵∠DCE+∠BCE＝90°，∴∠ECF＝90°，∴△ECF是等腰直角三角形；（2）解：∵BE：CE＝1：2，∴设BE＝a，CE＝2a，∵△ECF是等腰直角三角形，∴EF＝2a，∵∠BEC＝135°，∠CEF＝45°，∴∠BEF＝90°，∴BF＝＝3a，∴BE：BF＝1：3；（3）解：如图所示：作FM⊥BC垂足为M，设BF＝3b，FC＝2b，∵∠EDC＝30°，∴∠CBF＝30°，在Rt△BFM中，∴MB＝×3b＝b，MF＝b，∴MC＝＝b，∴b+b＝3，∴b＝2，则FM＝×2＝3，∴△BCF的面积是：×BC×FM＝×（3+）×3＝+．9．解：（1）∵x2﹣（2+2）x+4＝0，∴（x﹣2）（x﹣2）＝0，解得：x1＝2，x2＝2，∴OA＝2，OC＝2∴B点坐标为：（2，2），C点坐标为（2，0）．（2）∵△ABC≌△AB′C．∴AB＝AB′＝2，CB′＝CB＝2，∵A（0，2），C（2，0）∴设B′的坐标为（x，y），则，解得：B′的坐标为（，﹣1），由两点式解出BB′的解析式为y＝x﹣4．（3）假如存在设P（a，a﹣4），D（，0），又A（0，2），∴AD2＝（）2+22＝，PD2＝（a﹣）2+（a﹣4）2，AP2＝a2+（a﹣4﹣2）2＝4a2﹣12a+36，①当∠ADP为直角时，AD2+PD2＝AP2，解得a＝，则P（，1）；②当∠APD为直角时，AP2+PD2＝AD2，此时无解；③当∠P AD为直角时，AD2+P A2＝PD2，解得a＝3，则P（3，5）；综上可得，P为（3，5）或（，1）．10．证明：（1）∵DE⊥AG，BF⊥AG，∴∠BF A＝∠DEA＝90°．∵∠BAF+∠ABF＝90°，∠BAF+∠EAD＝90°，∴∠EAD＝∠FBA．在△ABF和△DAE中，，∴△ABF≌△DAE．（2）EF+BF＝AF．理由：∵△ABF≌△DAE，∴AE＝BF．∵AE+EF＝AF，∴BF+EF＝AF．（3）①由（1）可知：△ABF≌△DAE，∴AE＝BF．∵AF+EF＝AE，∴AF+EF＝BF．②∵BF⊥AG，DE⊥AG，∴∠BF A＝∠DEA＝90°．∵∠BAF+∠ABF＝90°，∠BAF+∠EAD＝90°，∴∠EAD＝∠FBA．在△ABF和△DAE中，，∴△ABF≌△DAE．∴FB＝AE．∵EF＝AE+AF，∴AF+BF＝EF．（4）如图所示：∵BF⊥AG，DE⊥AG，∴∠BF A＝∠DEA＝90°．∵∠BAF+∠ABF＝90°，∠BAF+∠EAD＝90°，∴∠EAD＝∠FBA．在△ABF和△DAE中，，∴△ABF≌△DAE．∴FB＝AE．∵AE＝EF+AF，∴AF+EF＝BF．。

10 散文专题（知识点思维导图+习题训练）一、（2022·江苏连云港·中考真题）文学作品阅读课，老师选择了徐则臣的一篇散文，请完成下面小题。

当家园只剩下一个籍贯①家园是个美好的词，美好到可以独立地被抽象出来，作为游子的乡愁与情感寄托永远存在于内心。

②在农业文明时代及其文学里，充满了此类坚实的叙述。

这种叙述基本上成立，田园牧歌式的家园：采菊东篱下，悠然见南山，现实安稳，血脉相关，此心安处是吾乡，仅仅是想到那片熟悉的土地，你都是笃定的。

中国有不少古话和俗语与此有关：出门靠墙，在家靠娘；在家千日好，出门一时难；叶落归根，等等。

家园乃是身之所系、心之所系、生之所系、根之所系。

它是世界上最后一块可靠的厚土。

③但是今天，很多坚固的东西都烟消云散了，家园也不能幸免。

在城市化和现代化的进程中，我们正在失去家园，因为家园正在被迫失去它自己。

④十八岁出门远行，我自认是一个情感上患有严重“古典病”的人，从不相信“家园”有朝一日也能崩塌。

祖先的坟墓在那里，父母至今生活在那里，我的童年和少年时光在那里。

判断这世上的一切，我都会以家园为最初也是最终的参照；它是我判别这个世界最重要的标尺。

但是这些年，我发现正在失去这些参照和这把标尺。

⑤从二十多岁的某一年开始，每次回到故乡的村庄，我都发现它正在被简化。

先是少一条河，再是少一条路，接着又少一条河，又少一条路，然后是我能一一叫出名字的庄稼和野草，也在一个种一个科地消失。

它的简化源于被篡改。

这些年故乡的确出现了很多新东西，它被裹挟在某个不可逆的潮流中，笨拙地执行着“现代化”的规定动作，迅速向那些城镇样板靠拢。

它变得和其他所有的城镇与现代村庄一样，横平竖直，条分缕析，板着一张被整过容的制式的脸。

“从来如此”不一定就对，但这制式的脸，肯定有问题。

⑥故乡在水泥化、标准化、去泥土化……既是实实在在泥土的减少，也是人与土地的关系正在消失，建基于土地之上的人际关系和伦理也正在消失。

2021年中考生物冲刺专题训练——专题2细胞的分裂、分化、生长一．选择题（共20小题）1．（2021•广东模拟）如图为人体的四种组织，下列说法错误的是（）A．唾液腺主要由①组成，具有保护、分泌等功能B．①至④依次是上皮组织、肌肉组织、神经组织和结缔组织C．神经元由细胞体和突起组成，短的突起是神经纤维的主要部分D．④是结缔组织，具有保护、支持、连接、营养等功能2．（2021•福建模拟）小小的受精卵能分裂分化成多种多样的细胞，与此过程无关的是（）A．细胞分裂B．细胞生长C．细胞衰老D．细胞分化3．（2021•陕西模拟）如图为植物细胞分裂过程示意图，下列有关叙述，错误的是（）A．植物细胞分裂过程的先后顺序为a→c→bB．植物细胞的染色体是由DNA和蛋白质组成的C．动物细胞的分裂过程与植物细胞完全相同D．新细胞与原细胞所含的遗传物质是一样的4．（2021•江西模拟）如图表示某植物体内细胞的一系列变化过程，①②③分别表示不同的生理活动，下列叙述错误的是（）A．生物体由小长大与①②③均有关系B．①是细胞生长，受细胞核的控制C．②是细胞分裂，使细胞数量增加D．③是细胞分化，细胞遗传物质发生改变5．（2021•兖州区模拟）每年的3月5日是我国学雷锋日，雷锋在生前日记中写道：“人的生命是有限的，可是，我要把有限的生命投入到无限的为人民服务之中去”。

从一个受精卵发育成一个可爱的宝宝，让我们看到了生命的神奇过程（）A．①②③表示细胞分裂，④表示细胞分化B．大脑皮层主要由图中的神经组织构成C．人体内的血液属于图中的结缔组织D．细胞分化可导致细胞中遗传物质改变6．（2021•平阴县一模）如图是某种生物受精卵分裂和分化过程的示意图，据图判断下列说法正确的是（）A．①过程表示细胞分裂，②过程表示细胞分化B．a、b、c三种细胞继续分裂可产生更多的细胞C．细胞核中的DNA数量在b细胞和受精卵中不相等D．因为各细胞中携带的基因不同，所以a、b、c三种细胞的形态、功能不同7．（2021•槐荫区一模）如图表示植物细胞分裂和分化的过程。

2020数学中考冲刺专项练习【难点突破】着眼思路，方法点拨, 疑难突破；新定义问题：是指题目提供一定的材料,或介绍一个新概念,或给出一种解法等,在理解材料的基础上,获得探索解决问题的方法,从而加以运用,解决问题. 这类问题一般由“阅读材料”和“提出问题”两个部分组成．解决此类题的步骤: ①理解“新定义”——明确“新定义”的条件、原理、方法、步骤和结论；②重视“举例”,利用“举例”检验是否理解和正确运用“新定义”;归纳“举例”提供的解题方法.归纳“举例”提供的分类情况；③类比新定义中的概念、原理、方法,解决题中需要解决的问题。

解决此类题的关键是（1）深刻理解“新定义”——明确“新定义”的条件、原理、方法、步骤和结论;（2）重视“举例”，利用“举例”检验是否理解和正确运用“新定义”；归纳“举例”提供的做题方法；归纳“举例”提供的分类情况；（3）依据新定义，运用类比、归纳、联想、分类讨论以及数形结合的数学思想方法解决题目中需要解决的问题。

类型1：方法模拟型，该类题目是指通过阅读所给材料，将得到的信息通过观察、分析、归纳、类比，作出合理的推断，大胆的猜测，从中获取新的思想、方法或解题途径，进而运用归纳与类比的方法来解答题目中所提出的问题．类型2：新知识学习型，这类题目就是由阅读材料给出一个新的定义、运算等，涉及的知识可能是以后要学到的数学知识，也有可能是其他学科的相关内容，然后利用所提供的新知识解决所给问题．解答这类问题的关键是要读懂题目提供的新知识，理解其本质，把它与已学的知识联系起来，把新的问题转化为已学的知识进行解决．类型3：信息处理型，这类题目主要是根据提供的表格，从中获得信息，并结合题意进行解答，这就需要我们将表格内容转化为数学信息或者已知条件。

类型4：阅读操作型，这类题目就是由阅读材料给出一个新的定义、运算等，涉及的知识可能是以后要学到的数学知识，也有可能是其他学科的相关内容，然后利用所提供的新知识解决所给问题．解答这类问题的关键是要读懂题目提供的新知识，理解其本质，把它与已学的知识联系起来，把新的问题转化为已学的知识进行解决．【名师原创】原创检测，关注素养，提炼主题；【原创1】2018年某省积极推进乡村规划和特色小城镇建设，各市地将结合本地实际，因地制宜培育一到三个设施完善、特色鲜明的典型示范镇，全面推进特色小城镇建设。

2021年江苏中考数学冲刺专题训练——专题2整式、因式分解一．选择题（共2小题）1．（2021•龙岗区模拟）如图，矩形ABCD的周长是10cm，以AB，AD为边向外作正方形ABEF和正方形ADGH，若正方形ABEF和ADGH的面积之和为17cm2，那么矩形ABCD 的面积是（）A．3cm2B．4cm2C．5cm2D．6cm2 2．（2019•安徽）已知三个实数a，b，c满足a﹣2b+c＝0，a+2b+c＜0，则（）A．b＞0，b2﹣ac≤0B．b＜0，b2﹣ac≤0C．b＞0，b2﹣ac≥0D．b＜0，b2﹣ac≥0二．填空题（共8小题）3．（2021春•鼓楼区期中）如图是A型卡片（边长为a的正方形）、B型卡片（长为a、宽为b的长方形）、C型卡片（边长为b的正方形）．现有4张A卡片，11张B卡片，7张C 卡片，选用它们无缝隙、无重叠地拼正方形或长方形，下列说法正确的是．（只填序号）①可拼成边长为a+2b的正方形；②可拼成边长为2a+3b的正方形；③可拼成长、宽分别为2a+4b、2a+b的长方形；④用所有卡片可拼成一个大长方形．4．（2021春•南京月考）三种不同类型的地砖的长、宽如图所示，若现有A型地砖4块，B 型地砖4块，C型地砖2块，要拼成一个正方形，则应去掉1块地砖；这样的地砖拼法可以得到一个关于m，n的恒等式为．5．（2020秋•江汉区期末）将两张边长分别为6和5的正方形纸片按图1和图2的两种方式放置在长方形ABCD内，长方形ABCD内未被这两张正方形纸片覆盖的部分用阴影表示，设图1中的阴影面积为S1，图2中的阴影面积为S2，当AD﹣AB＝3时，S2﹣S1的值是．6．（2020春•沭阳县期末）因式分解：2m2﹣4mn+2n2＝．7．（2020•张家界）因式分解：x2﹣9＝．8．（2020•浙江自主招生）若m2＝n+2，n2＝m+2（m≠n），则m3﹣2mn+n3的值为．9．（2019春•江宁区期中）已知a=12018+2017，b=12018+2018，c=12018+2019，则代数式a2+b2+c2﹣ab﹣bc﹣ca＝．10．（2019•徐州二模）因式分解4x2﹣4＝．三．解答题（共20小题）11．（2021春•南京期中）探究活动：（1）如图①，可以求出阴影部分的面积是（写成两数平方差的形式）；（2）如图②，若将图①中阴影部分裁剪下来，重新拼成一个长方形，面积是（写成多项式乘法的形式）；（3）比较图①，图②阴影部分的面积，可以得到公式．知识应用：运用你得到的公式解决以下问题：（4）计算：（Ⅰ）（a+b﹣2c）（a+b+2c）；（Ⅱ）（2a+b﹣3c）（﹣2a+b+3c）．12．（2021春•鼓楼区校级月考）阅读：若x满足（80﹣x）（x﹣60）＝30，求（80﹣x）2+（x﹣60）2的值．解：设（80﹣x）＝a，（x﹣60）＝b，则（80﹣x）（x﹣60）＝ab＝，a+b＝（80﹣x）+（x﹣60）＝，所以（80﹣x）2+（x﹣60）2＝a2+b2＝（a+b）2﹣2ab＝．请仿照上例解决下面的问题：（1）补全题目中横线处；（2）已知（30﹣x）（x﹣20）＝﹣10，求（30﹣x）2+（x﹣20）2的值；（3）若x满足（2021﹣x）2+（2020﹣x）2＝2019，求（2021﹣x）（x﹣2020）的值；（4）如图，正方形ABCD的边长为x，AE＝10，CG＝25，长方形EFGD的面积是400，四边形NGDH和MEDQ都是正方形，PQDH是长方形，求图中阴影部分的面积（结果必须是一个具体数值）．13．（2021春•秦淮区校级期中）先化简，再求值：（3a﹣2b）（2a+3b）−12（3a+2b）2﹣a（32a﹣2b），其中|a+12|+|b+1|＝0．14．（2021春•宜兴市期中）计算或化简：（1）﹣22+（23）﹣1+（π﹣3）0（2）a⋅a2⋅a3+（﹣2a3）2﹣a9÷（﹣a）3（3）（x+3）（x﹣3）﹣（x﹣2）2（4）（m+2n﹣3）（m﹣2n+3）15．（2021•滨湖区一模）（1）计算：|3−2|﹣（12）﹣2+2sin60°；（2）化简：（a+b）2﹣a（a+2b）．16．（2021春•徐州期中）计算：（1）（﹣1）2021+（﹣2）0+（12）﹣3；（2）a•a3•a4﹣4a10÷a2+（﹣3a4）2；（3）（x+5）（x﹣3）﹣x（x+2）；（4）20212﹣2020×2022．17．（2021春•鼓楼区校级月考）计算：（1）（﹣3a3）2÷a2；（2）（﹣2a）3﹣（﹣a）•（3a）2；（3）﹣22+30﹣（−12）﹣1；（4）（318）12×（825）11×（﹣2）3．18．（2021春•鼓楼区校级月考）计算：（1）（﹣3y）5÷（﹣3y）2；（2）2a2•4a4﹣（﹣3a2）3；（3）（π﹣3）0﹣（−12）﹣2+25×（﹣1）﹣2021；（4）x（x+y）﹣（2x+3y）2；（5）（3a﹣2b）（2b+3a）﹣（2a）2．19．（2021春•邗江区月考）规定两数a，b之间的一种运算，记作（a，b）；如果a c＝b，那么（a，b）＝c．例如：因为23＝8，所以（2，8）＝3．（1）根据上述规定，填空：①（5，125）＝，（﹣2，﹣32）＝；②若( ，116)=−4，则x＝．（2）若（4，5）＝a，（4，6）＝b，（4，30）＝c，试说明下列等式成立的理由：a+b＝c．20．（2021春•南京月考）计算：（1）|−2|+( −3)0−(13)−2+(−1)2021；（2）（﹣2×1012）×（﹣2×102）3÷（0.5×103）3；（3）(−12 2)×(23 2 −6 )；（4）（a﹣2b+3c）×（a+2b﹣3c）；（5）（﹣2m﹣3）2（3﹣2m）2；（6）4×1.632+6.52×6.74+6.742．（用乘法公式计算）21．（2021•滨湖区模拟）计算：（1）2﹣1﹣（﹣0.5）0−4；（2）（x﹣3）2+x（x﹣2）22．（2020秋•江都区期末）先化简，再求值：12x﹣2（x−13y2）+（−32 +13 2），其中x＝﹣2，y=23．23．（2020秋•渑池县期末）乘法公式的探究及应用．（1）如图1，可以求出阴影部分的面积是（写成两数平方差的形式）；（2）如图2，若将阴影部分裁剪下来，重新拼成一个长方形，它的宽是，长是，面积是．（写成多项式乘法的形式）（3）比较左、右两图的阴影部分面积，可以得到乘法公式．（用式子表达）（4）运用你所得到的公式，计算下列各题：①10.3×9.7②（2m+n﹣p）（2m﹣n+p）24．（2021春•秦淮区校级期中）因式分解：（1）25（a+b）2﹣9（a﹣b）2；（2）16ab2﹣6a3﹣4ab2；（3）（x2﹣4x）2+8（x2﹣4x）+16．25．（2021春•玄武区期中）把下列各式分解因式：（1）ax3﹣16ax；（2）（2x﹣3y）2﹣2x（2x﹣3y）+x2；（3）（m2+1）2﹣4m2．26．（2021春•吴江区期中）整式乘法与多项式因式分解是既有联系又有区别的两种变形．例如，a（b+c+d）＝ab+ac+ad是单项式乘多项式的法则；把这个法则反过来，得到sb+ac+ad ＝a（b+c+d），这是运用提取公因式法把多项式因式分解．又如（a±b）2＝a2±2ab+b2、（a+b）（a﹣b）＝a2﹣b2是多项式的乘法公式；把这些公式反过来，得到a2±2ab+b2＝（a±b）2、a2﹣b2＝（a+b）（a﹣b），这是运用公式法把多项式因式分解．把多项式乘多项式法则（a+b）（c+d）＝ac+ad+bc+bd反过来，将得到什么呢？事实上，ac+ad+bc+bd＝a（c+d）+b（c+d）＝（a+b）（c+d），这样多项式ac+ad+bc+bd 就分解为两个因式（a+b）与（c+d）的乘积．类似地，ac+bc+3a+3b＝c（a+b）+3（a+b）＝（a+b）（c+3）．问题一：因式分解：（1）a2﹣ab+ac﹣bc；（2）9a2﹣6a+2b﹣b2．问题二：探究对x、y定义一种新运算F，规定：F（x，y）＝（mx+ny）（3x﹣y）（其中m，n均为非零常数）．当x2≠y2时，F（x，y）＝F（y，x）对任意有理数x、y都成立，试探究m，n 的数量关系．27．（2020春•赣榆区期中）对于一个平面图形，通过两种不同的方法计算它的面积，可以得到一个数学等式，例如：图1可以得到（a+b）2＝a2+2ab+b2，请解答下列问题：（1）写出图2所表示的数学等式：＝；（2）已知上述等式中的三个字母a，b，c可取任意实数，若a＝7k﹣5，b＝﹣4k+2，c ＝﹣3k+4，且a2+b2+c2＝37，请利用（1）所得的结论求ab+bc+ac的值；（3）小明同学用图3中2张边长为a的正方形，3张边长为b的正方形和m张邻边长分别为a、b的长方形纸片拼出一个长方形，通过拼图求出m的值．（求出1个即可）28．（2020春•玄武区期中）把几个图形拼成一个新的图形，再通过两种不同的方式计算同一个图形的面积，可以得到一个等式，也可以求出一些不规则图形的面积．例如，由图1，可得等式：（a+2b）（a+b）＝a2+3ab+2b2．（1）由图2，可得等式；（2）利用（1）所得等式，解决问题：已知a+b+c＝11，ab+bc+ac＝38，求a2+b2+c2的值．（3）如图3，将两个边长为a、b的正方形拼在一起，B，C，G三点在同一直线上，连接BD和BF，若这两个正方形的边长a、b如图标注，且满足a+b＝10，ab＝20．请求出阴影部分的面积．（4）图4中给出了边长分别为a、b的小正方形纸片和两边长分别为a、b的长方形纸片，现有足量的这三种纸片．①请在下面的方框中用所给的纸片拼出一个面积为2a2+5ab+2b2的长方形，并仿照图1、图2画出拼法并标注a、b．②研究①拼图发现，可以分解因式2a2+5ab+2b2＝．29．（2019秋•海门市期末）我们知道，任意一个正整数n都可以进行这样的分解：n＝p×q （p，q是正整数，且p≤q），在n的所有这种分解中，如果p，q两因数之差的绝对值最小，我们就称p×q是n的完美分解．并规定：F（n）= ．例如18可以分解成1×18，2×9或3×6，因为18﹣1＞9﹣2＞6﹣3，所以3×6是18的完美分解，所以F（18）=36=12．（1）F（13）＝，F（24）＝；（2）如果一个两位正整数t，其个位数字是a，十位数字为b﹣1，交换其个位上的数与十位上的数得到的新数减去原来的两位正整数所得的差为36，那么我们称这个数为“和谐数”，求所有“和谐数”；（3）在（2）所得“和谐数”中，求F（t）的最大值．30．（2019秋•柘城县期末）下面是某同学对多项式（x2﹣4x+2）（x2﹣4x+6）+4进行因式分解的过程．解：设x2﹣4x＝y，原式＝（y+2）（y+6）+4（第一步）＝y2+8y+16（第二步）＝（y+4）2（第三步）＝（x2﹣4x+4）2（第四步）（1）该同学第二步到第三步运用了因式分解的．A．提取公因式B．平方差公式C．两数和的完全平方公式D．两数差的完全平方公式（2）该同学因式分解的结果是否彻底？．（填“彻底”或“不彻底”）若不彻底，请直接写出因式分解的最后结果．（3）请你模仿以上方法尝试对多项式（x2﹣2x）（x2﹣2x+2）+1进行因式分解．2021年江苏中考数学冲刺专题训练——专题2整式、因式分解参考答案与试题解析一．选择题（共2小题）1．【解答】解：设AB＝x，AD＝y，∵正方形ABEF和ADGH的面积之和为17cm2∴x2+y2＝17，∵矩形ABCD的周长是10cm∴2（x+y）＝10，∵（x+y）2＝x2+2xy+y2，∴25＝17+2xy，∴xy＝4，∴矩形ABCD的面积为：xy＝4cm2，故选：B．2．【解答】解：∵a﹣2b+c＝0，a+2b+c＜0，∴a+c＝2b，b= + 2，∴a+2b+c＝（a+c）+2b＝4b＜0，∴b＜0，∴b2﹣ac=( + 2)2− = 2+2 + 24−ac= 2−2 + 24=( − 2)2≥0，即b＜0，b2﹣ac≥0，故选：D．二．填空题（共8小题）3．【解答】①（a+2b）2＝a2+4ab+4b2，要用A型卡片1张，B型卡片4张，C型卡片4张，所以可拼成边长为a+2b的正方形．②（2a+3b）2＝4a2+12ab+9b2，要用A型卡片4张，B型卡片12张，C型卡片9张，因为B型卡片只有11张，C型卡片只有7张，所以不能拼成边长为2a+3b的正方形．③（2a+4b）（2a+b）＝4a2+2ab+8ab+4b2＝4a2+10ab+4b2，可得A型卡片4张，B型卡片10张，C型卡片4张，所以可拼成长、宽分别为2a+4b、2a+b的长方形．④所有卡片面积和为4a2+11ab+7b2＝（4a+7b）（a+b）．所以所有卡片可拼长长为（4a+7b），宽为（a+b）的长方形．故答案为：①③④．4．【解答】解：4块A的面积为：4×m×m＝4m2；4块B的面积为：4×m×n＝4mn；2块C的面积为2×n×n＝2n2；那么这三种类型的砖的总面积应该是：4m2+4mn+2n2＝4m2+4mn+n2+n2＝（2m+n）2+n2，因此，多出了一块C型地砖，去掉一块C型地砖，这两个数的平方为（2m+n）2．这样的地砖拼法可以得到一个关于m，n的恒等式为：4m2+4mn+n2＝（2m+n）2故答案为：4m2+4mn+n2＝（2m+n）2．5．【解答】解：设AB＝CD＝x，AD＝BC＝y，则S1＝6（AB﹣6）+（CD﹣5）（BC﹣6）＝6（x﹣6）+（x﹣5）（y﹣6），S2＝6（BC﹣6）+（BC﹣5）（CD﹣6）＝6（y﹣6）+（y﹣5）（x﹣6），∴S2﹣S1＝6（y﹣6）+（y﹣5）（x﹣6）﹣6（x﹣6）﹣（x﹣5）（y﹣6）＝6y﹣36+xy﹣6y﹣5x+30﹣6x+36﹣xy+6x+5y﹣30＝5y﹣5x＝5（y﹣x），∵AD﹣AB＝3，∴y﹣x＝3，∴原式＝5×3＝15，故答案为：15．6．【解答】解：原式＝2（m2﹣2mn+n2）＝2（m﹣n）2，故答案为：2（m﹣n）27．【解答】解：原式＝（x+3）（x﹣3），故答案为：（x+3）（x﹣3）．8．【解答】解：∵m2＝n+2，n2＝m+2（m≠n），∴m2﹣n2＝n﹣m，∵m≠n，∴m+n＝﹣1，∴原式＝m（n+2）﹣2mn+n（m+2）＝mn+2m﹣2mn+mn+2n＝2（m+n）＝﹣2．故答案为﹣2．9．【解答】解：∵a=12018+2017，b=12018+2018，c=12018+2019，∴a﹣b＝﹣1，a﹣c＝﹣2，b﹣c＝﹣1，∴a2+b2+c2﹣ab﹣bc﹣ca=12×(2 2+2 2+2 2−2 −2 −2 )=12[( − )2+( − )2+( − )2]=12×[(−1)2+(−1)2+(−2)2]=12×(1+1+4)=12×6＝3，故答案为：3．10．【解答】解：原式＝4（x2﹣1）＝4（x+1）（x﹣1），故答案为：4（x+1）（x﹣1）三．解答题（共20小题）11．【解答】解：（1）阴影部分的面积为两个正方形的面积差，即a2﹣b2；故答案为：a2﹣b2；（2）拼成的长方形的长为（a+b），宽为（a﹣b），所以面积为（a+b）（a﹣b）；故答案为：（a+b）（a﹣b）；（3）由（1）（2）可得，a2﹣b2＝（a+b）（a﹣b）；故答案为：a2﹣b2＝（a+b）（a﹣b）；（4）（Ⅰ）（a+b﹣2c）（a+b+2c）＝[（a+b）﹣2c][（a+b）+2c]＝（a+b）2﹣（2c）2＝a2+2ab+b2﹣4c2；（Ⅱ）（2a+b﹣3c）（﹣2a+b+3c）＝[b+（2a﹣3c）][b﹣（2a﹣3c）]＝b2﹣（2a﹣3c）2＝b2﹣4a2+12ac﹣9c2．12．【解答】解：（1）设（80﹣x）＝a，（x﹣60）＝b，则（80﹣x）（x﹣60）＝ab＝30，a+b＝（80﹣x）+（x﹣60）＝20，所以（80﹣x）2+（x﹣60）2＝a2+b2＝（a+b）2﹣2ab＝400﹣60＝340；故答案为：30，20，340；（2）设30﹣x＝a，x﹣20＝b，则ab＝﹣10，a+b＝10，∴（30﹣x）2+（x﹣20）2＝a2+b2＝（a+b）2﹣2ab＝102﹣2×（﹣10）＝120；（3）设2021﹣x＝m，2020﹣x＝n，则m2+n2＝2019，m﹣n＝1，∵（m﹣n）2＝m2﹣2mn+n2，∴1＝2019﹣2mn，∴mn＝1009，即（2021﹣x）（x﹣2020）＝﹣1009；（4）由题意得：DE＝x﹣10，DG＝x﹣25，则（x﹣10）（x﹣25）＝400，设a＝x﹣10，b＝x﹣25，则a﹣b＝15，ab＝400，＝（a+b）2＝（a﹣b）2+4ab＝152+4×400＝1825．∴S阴13．【解答】解：原式＝6a2+9ab﹣4ab﹣6b2−12（9a2+12ab+4b2）−32a2+2ab ＝6a2+9ab﹣4ab﹣6b2−92a2﹣6ab﹣2b2−32a2+2ab＝ab﹣8b2，∵|a+12|+|b+1|＝0，∴a+12=0，b+1＝0，解得：a=−12，b＝﹣1，当a=−12，b＝﹣1时，原式=−12×（﹣1）﹣8×（﹣1）2＝﹣712．14．【解答】解：（1）﹣22+（23）﹣1+（π﹣3）0＝﹣4+32+1=−32；（2）a⋅a2⋅a3+（﹣2a3）2﹣a9÷（﹣a）3＝a6+4a6﹣a9÷（﹣a3）＝a6+4a6+a6＝6a6；（3）（x+3）（x﹣3）﹣（x﹣2）2＝x2﹣9﹣x2+4x﹣4＝4x﹣13；（4）（m+2n﹣3）（m﹣2n+3）＝[m+（2n﹣3）][m﹣（2n﹣3）]＝m2﹣（2n﹣3）＝m2﹣4n2+12n﹣9．15．【解答】解：（1）原式＝3−3−4+2＝3−3−4+3＝﹣1；（2）原式＝a2+2ab+b2﹣a2﹣2ab＝b2．16．【解答】解：（1）（﹣1）2021+（﹣2）0+（12）﹣3＝（﹣1）+1+8＝8；（2）a•a3•a4﹣4a10÷a2+（﹣3a4）2＝a8﹣4a8+9a8＝6a8；（3）（x+5）（x﹣3）﹣x（x+2）＝x2+2x﹣15﹣x2﹣2x＝﹣15；（4）20212﹣2020×2022＝20212﹣（2021﹣1）×（2021+1）＝20212﹣20212+1＝1．17．【解答】解：（1）原式＝9a6÷a2＝9a4；（2）原式＝﹣8a3+a•9a2＝﹣8a3+9a3＝a3；（3）原式＝﹣4+1+2＝﹣1；（4）原式=258×（258×825）11×（﹣8）=258×111×（﹣8）=258×1×（﹣8）＝﹣25．18．【解答】解：（1）原式＝（﹣3y）3＝﹣27y3；（2）原式＝8a6+27a6＝35a6；（3）原式＝1﹣4+32×（﹣1）＝1﹣4﹣32＝﹣35；（4）原式＝x2+xy﹣（4x2+12xy+9y2）＝x2+xy﹣4x2﹣12xy﹣9y2＝﹣3x2﹣11xy﹣9y2；（5）原式＝9a2﹣4b2﹣4a2＝5a2﹣4b2．19．【解答】解：（1）①因为53＝125，所以（5，125）＝3；因为（﹣2）5＝﹣32，所以（﹣2，﹣32）＝5；②由新定义的运算可得，x﹣4=116，因为（±2）﹣4=1(±2)4=116，所以x＝±2，故答案为：①3，5；②±2；（2）因为（4，5）＝a，（4，6）＝b，（4，30）＝c，所以4a＝5，4b＝6，4c＝30，因为5×6＝30，所以4a•4b＝4c，所以a+b＝c．20．【解答】解：（1）|−2|+( −3)0−(13)−2+(−1)2021＝2+1﹣9+（﹣1）＝﹣7；（2）（﹣2×1012）×（﹣2×102）3÷（0.5×103）3＝（﹣2×1012）×（﹣23×106）÷（123×109）＝27×109＝128×109＝1.28×1011；（3）(−12 2)×(23 2 −6 )=−13x3y3+3x2y3；（4）（a﹣2b+3c）×（a+2b﹣3c）＝[a﹣（2b﹣3c）][a+（2b﹣3c）]＝a2﹣（2b﹣3c）2＝a2﹣4b2+12bc﹣9c2；（5）（﹣2m﹣3）2（3﹣2m）2＝（2m+3）2•（3﹣2m）2＝[（3+2m）（3﹣2m）]2＝（9﹣4m2）2＝81﹣72m2+16m4；（6）4×1.632+6.52×6.74+6.742＝（2×1.63）2+2×3.26×6.74+6.742＝3.262+2×3.26×6.74+6.742＝（3.26+6.74）2＝102＝100．21．【解答】解：（1）2﹣1﹣（﹣0.5）0−4=12−1﹣2=−52；（2）（x﹣3）2+x（x﹣2）＝x2﹣6x+9+x2﹣2x＝2x2﹣8x+9．22．【解答】解：原式=12x﹣2x+23y2−32x+13y2=12x﹣2x+23y2−32x+13y2＝﹣3x+y2，把x＝﹣2，y=23代入得：原式＝649．23．【解答】解：（1）利用正方形的面积公式可知：阴影部分的面积＝a2﹣b2；故答案为：a2﹣b2；（2）由图可知矩形的宽是a﹣b，长是a+b，所以面积是（a+b）（a﹣b）；故答案为：a﹣b，a+b，（a+b）（a﹣b）；（3）（a+b）（a﹣b）＝a2﹣b2（等式两边交换位置也可）；故答案为：（a+b）（a﹣b）＝a2﹣b2；（4）①解：原式＝（10+0.3）×（10﹣0.3）＝102﹣0.32＝100﹣0.09＝99.91；②解：原式＝[2m+（n﹣p）]•[2m﹣（n﹣p）]＝（2m）2﹣（n﹣p）2＝4m2﹣n2+2np﹣p2．24．【解答】解：（1）25（a+b）2﹣9（a﹣b）2＝（5a+5b）2﹣（3a﹣3b）2．＝（5a+5b+3a﹣3b）[5a+5b﹣（3a﹣3b）]＝（8a+2b）（2a+8b）．＝4（4a+b）（a+4b）．（2）16ab2﹣6a3﹣4ab2＝12ab2﹣6a3＝6a（2b2﹣a2）＝6a（2b+a）（2b﹣a）．（3）原式＝（x2﹣4x+4）2＝[（x﹣2）2]2＝（x﹣2）425．【解答】解：（1）原式＝ax（x2﹣16）＝ax（x+4）（x﹣4）；（2）原式＝（2x﹣3y﹣x）2＝（x﹣3y）2；（3）原式＝（m2+1+2m）（m2+1﹣2m）＝（m+1）2（m﹣1）2．26．【解答】解：问题一、（1）a2﹣ab+ac﹣bc＝a（a﹣b）+c（a﹣b）＝（a﹣b）（a+c）；（2）9a2﹣6a+2b﹣b2，＝（3a+b）（3a﹣b）﹣2（3a﹣b）＝（3a﹣b）（3a+b﹣2），问题二、∵F（x，y）＝（mx+ny）（3x﹣y），F（y，x）＝（my+nx）（3y﹣x），又∵F（x，y）＝F（y，x），∴（mx+ny）（3x﹣y）＝（my+nx）（3y﹣x），3mx2+（3n﹣m）xy﹣ny2＝﹣nx2+（3n﹣m）xy+3my2，∵x2≠y2，∴3m＝﹣n．27．【解答】解：（1）正方形的面积可表示为＝（a+b+c）2；正方形的面积＝各个矩形的面积之和＝a2+b2+c2+2ab+2bc+2ac，∴（a+b+c）2＝a2+b2+c2+2ab+2bc+2ac，故答案为（a+b+c）2；a2+b2+c2+2ab+2bc+2ac；（2）∵a＝7k﹣5，b＝﹣4k+2，c＝﹣3k+4，a2+b2+c2＝37，∴（7k﹣5﹣4k+2﹣3k+4）2＝37+2（ab+bc+ac），∴ab+bc+ac＝﹣18；（3）如图所示：2a2+7ab+3b2＝（a+3b）（2a+b）．∴m＝7．28．【解答】解：（1）由题意得，（a+b+c）2＝a2+b2+c2+2ab+2bc+2ac，故答案为，（a+b+c）2＝a2+b2+c2+2ab+2bc+2ac；（2）∵a+b+c＝11，ab+bc+ac＝38，∴a2+b2+c2＝（a+b+c）2﹣2（ab+ac+bc）＝121﹣76＝45；（3）∵a+b＝10，ab＝20，∴S＝a2+b2−12（a+b）•b−12a2=12a2+12b2−12ab=12（a+b）2−32ab=12×102−32×20＝阴影50﹣30＝20；（4）①根据题意，作出图形如下：②由上面图形可知，2a2+5ab+2b2＝（a+2b）（2a+b）．故答案为（a+2b）（2a+b）．29．【解答】解：（1）∵13＝1×13，∴F（13）=113∵24＝1×24＝2×12＝3×8＝4×624﹣1＞12﹣2＞8﹣3＞6﹣4∴F（24）=46=23故答案为：113；23．（2）原两位数可表示为10（b﹣1）+a，新两位数可表示为10a+b﹣1∴10a+b﹣1﹣10（b﹣1）﹣a＝36∴10a+b﹣1﹣10b+10﹣a＝36∴9a﹣9b＝27∴a﹣b＝3∴a＝b+3（1＜b＜6且b为正整数）∴b＝2，a＝5；b＝3，a＝6，b＝4，a＝7，b＝5，a＝8b＝6，a＝9∴和谐数为15，26，37，48，59（3）∵F（15）=35，F（26）=213，F（37）=137，F（48）=68=34，F（59）=159．∵34＞35＞213＞137＞159，∴所有“和谐数”中，F（t）的最大值是34．30．【解答】解：（1）该同学第二步到第三步运用了因式分解的两数和的完全平方公式；故选：C；（2）该同学因式分解的结果不彻底，原式＝（x2﹣4x+4）2＝（x﹣2）4；故答案为：不彻底，（x﹣2）4；（3）（x2﹣2x）（x2﹣2x+2）+1＝（x2﹣2x）2+2（x2﹣2x）+1＝（x2﹣2x+1）2＝（x﹣1）4．。

2021河南中考英语复习冲刺：阅读理解限时训练（二）（限时45分钟）1.We spend hours, days and years of our lives in education. But how perfect do you think your school is? Imagine you could design your ideal school. What would it be like? What would you be doing? We want to find out what teenagers around the world think. Here is what they say:（1）Who wants one more day off in a week?A.Wu Lei.B.Richard.C.Yoko.D.Hannah.（2）In Yoko’s ideal school, she can ________.A.see moviesB.play tennisC.play instrumentsD.do some shopping（3）The four teenagers talk about their ________.A.dream schoolsB.favorite sportsC.hobbiesD.teachers2.Skateboarding makes me feel free, like I’m flying. When I’m in the air, it feels like I can do anything. I started skating when I was two or three, same with surfing. My dad built a mini-ramp in our backyard. He would skate every day after surfing. I would steal his boardand play with it.If I saw my dad doing a cool trick, I’d think “I want to try that.” I’d look it upon Youku and try to learn it. Now I just learn from my friends. It’s nice to skate with your friends because you can teach each other things. I never really thought, “I’m going to get so good at this.” I just got better and better and it happened naturally when I was seven. I’m 12 now.It’s a great feeling, getting a new trick especially if it’s taken a long time to learn. You try it a thousand times and then one day, you finally land it. That’s the feeling I want. It’s what makes me keep trying new things. When I was eight, I became the first female skater to land a frontside 540.Sometimes doing a trick can be scary. But I feel like that falling is just part of skateboarding. I like inspiring other girls to do what they want to do. I don’t want girls to think that boys can do things that they can’t. I want girls to think, “I can do it, because I’m a girl. If I can do it, so can they.”（1）How does skateboarding make the author feel?A.She is frightened.B.She has the feeling of freedom.C.She feels nervous.D.Her mind is focused.（2）How did the author learn tricks at first?A.She asked her father for help.B.She learned the tricks from her friends.C.She watched videos on the Internet.D.She practiced her tricks while surfing.（3）What makes the author keep trying new things?A.Help from friends.B.Father’s support.C.Skills from a training course.D.The feeling of success.（4）Which of the following words best describe the writer?A.Talented and quiet.B.Outgoing and talkative.C.Brave and strong-minded.D.Caring and warm -hearted.（5）What’s the best title of the passage?A.Sky high.B.Doing a trick is scary.C.A professional skater.D.How to be brave.3.For many American 10-year-olds, summer is always a time for goofing around (消磨时光), hanging out with friends, and playing outside until the sun goes down. However, for Liam Hannon, the summer of 2017 was a bit different. That year, Liam did not want to go to summer camp, so he made a deal with his dad to stay busy and active. He joined a program to give back to the community. Specifically, he was given a task to help homeless people.Liam pointed out to his dad that there were a lot of homeless people just outside their home in Cambridge, Massachusetts. These people were hungry and Liam thought he could do something to lift their spirits. Liam and his clad began making sandwiches. Together, they made 20 lunches that first week, which they then handed out to the homeless people. When the week was over, Liam realized he was not ready to put away his bread knife just yet, so Liam’s Lunches of Love was born.“No one should be hungry,” Liam wrote on his GoFundMe page. He created the online page with his father as a way to help raise money for Lunches of Love. Donations that were received through GoFundMe have enabled Liam to buy a better cart (手推车) and make thousands of additional lunches. Liam also gets help from friends and volunteers to make and deliver the lunches. His friends love drawing pictures and writing encouraging messages on the brown paper bags that the lunches and healthy snacks are packed in. “I’ve seen people who are feeling really down. But when we hand them a lunch, their faces just light up,” says Liam.But he didn’t stop there. Liam has another project called Legos (乐高) of Love. People send in their old toys, which are then sorted and given to children who are living at homeless shelters.One thing is certain: This now 12-year-old knows how to pay it forward (让爱传播出去). His Lunches of Love is an example of how even something as simple as a sandwich can change the world.（1）What did Liam Hannon do in the summer holiday of 2017?A.He went to summer camp.B.He hung out with his friends.C.He helped many homeless people with his father and friends.D.He drew pictures and wrote encouraging messages on the paper bags.（2）How did Liam help the children at homeless shelters?A.By raising money for them.B.By making sandwiches for them.C.By buying old toys for them.D.By creating a project called Legos of Love.（3）Liam’s story mainly tells us ________.A.we should ask our friends for helpB.we should enjoy the summer holiday with our familyC.simple help can make a big differenceD.projects make a lot of fun4.What can you make with pieces of paper? Look at Chen Yiyan's work! The 14-year-old boy in Hangzhou Foreign Language School has an amazing talent for paper-folding. He has folded a “fantasy world” with his hands.Chen wasn't born with this talent. When he was a fourth-grader, he found his brother's paper-folding book. It got him interested in it. Following the 50 steps shown in the book, he made his first work—a paper elephant within two hours. Since then, he has read many books about paper-folding and practiced folding paper in his spare time. So far, his fantasy world has many members, such as monsters and robots.He made his favorite work last year. It was a paper dragon that had almost 2,000 steps.Chen used to fold paper himself until he met Li Changnan, an eighth-grader in his school who also loved folding paper. They set up a paper-folding club last year. To their joy, their school sponsored it. With the encouragement and the money provided, they had a paper-folding class every Wednesday afternoon. The club soon attracted a lot of students. Now it has more than 20 members. They showed their works and taught other students how to fold paper. On February 14th this year, the club also held a speech for the kids in Wenzhou Children's Library.“It is really exciting to develop my hobby and share it with others at the same time,” said Chen. “I hope more and more people get to know paper-folding and love the art.”（1）Which work did Chen Yiyan like best?A.A paper monster.B.A paper elephant.C.A paper dragon.D.A paper robot.（2）The underlined word “sponsored” means “________” in Chinese.A.赞助B.阻止C.拒绝D.推迟（3）Which of the following activities did the club hold?①holding competitions①showing their works①giving a speech①reading books in the library①teaching how to fold paper①having paper-folding classesA.①①①①B.①①①①C.①①①①D.①①①①（4）Why did Chen Yiyan put so much effort into paper-folding?A.To develop paper-folding art.B.To build his own fantasy world.C.To find more paper-folding lovers.D.To make himself famous in the school.5.Nearly all students feel both nervous and excited when their big day comes. On the big day, there will be the graduation ceremony. Students will wear graduation costumes and hats that day. Parents, relatives, and friends may also be invited to the ceremony.When students enter the hall of the ceremony,they will see lots of other schoolmates. They will see that all of them are wearing some costumes and hats. This makes them feel that it is a very important and extraordinary day. This kind of feeling is rather hard to describe. It would be better to understand if one can personally experience this.As soon as the ceremony starts,the schoolmaster will give a speech. After the speech,the students will be called to go on stage(舞台) to receive their certificates (证书).This should be the most important part of the whole ceremony. During this moment,most students start to feel nervous,since hundreds of people are watching them. However, this is also the most wonderful moment for them. This marks a very important moment in their lives, as they have finally finished their school years. Besides that,this moment also shows they are going to move onto a new stage of life.（1）What does the big day refer to?A.The time when students graduate.B.The time when schools hold a parents' meeting.C.The time when the new term begins.D.The time when students come in the hall.（2）The underlined word “extraordinary” means “________” in Chinese.A.奇怪的B.消极的C.特别的D.额外的（3）Why is the graduation ceremony important to students?A.Because it helps students get to know themselves better.B.Because it helps students find better jobs.C.Because it helps students do better in their future study.D.Because it shows a new stage of life for students.（4）What can we know from the passage?A.Parents must wear graduation hats to join the graduation ceremony.B.People needn't study after they finish their school years.C.Students have different feelings during their graduation ceremony.D.The schoolmaster gives a speech at the end of the graduation ceremony.6.Parents are often surprised at their children's ability to use technology. A five-year-old child may easily find and use apps on a smart phone. A ten-year-old child can move up through the levels of a video game easily. Their parents may think their children were born geniuses!Natural geniuses, however, are not common. But your parents are right if they think you are smarter than them. Most children are born smarter than their parents. This has been proved on IQ tests around the world recently. These tests have shown that over the last 100years, each new generation has become smarter than the older one. In other words, you are smarter than your parents and your parents are smarter than your grandparents.This increase in intelligence is called the "Flynn Effect". It was named after James Flynn. Flynn is a university professor in New Zealand. He first noticed this in 1980. According to his research, with each new generation, average IQ scores would increase by twenty percent.But why are people getting smarter? Flynn and many other researchers believe this has something to do with technology. New technologies have further developed our brains. They have made us think better. So we may be better at completing the missing parts of a puzzle than our parents.However, being smart doesn't make you wise. Wisdom comes with age and experience. A killer score on a computer game will not help you solve the everyday problems of life. For that, a smart kid will turn to the wisdom of his parents and grandparents.根据材料内容选择最佳答案，并在答题卡上将该项涂黑。

○………………内………………○………………装………………○………………订………………○………………线………………○…………○………………外………………○………………装………………○………………订………………○………………线………………○………… 学校：______________姓名：_____________班级：_______________考号：______________________安徽省2020届中考押题冲刺试卷历 史（考试时间：50分钟 试卷满分：70分）注意事项：本试卷分第Ⅰ卷和第Ⅱ卷两部分。

答卷前，考生务必填写好自己的姓名、准考证号。

第Ⅰ卷一、单项选择（本大题共15小题，每小题2分，共30分）1．“雍正年间，用兵西北，……始设军需房于隆宗门内，选内阁中书之谨密者入直缮写。

后名军机处，地近宫廷，便于宣召。

”上述历史事件对中国历史的主要影响是 A ．加强了对西北边疆的管理 B ．完善了专制主义中央集权制度 C ．巩固了雍正帝的统治D ．使专制主义中央集权制度发展到顶峰2．信阳市九中七（1）班布置的下列图片组成的主题展，反映了A ．科学技术的发展进步B ．华夏文明的广泛影响C ．农耕文明的丰硕成果D ．中华文明的博大精深3．鸦片战争是英国发动的侵略战争，中国进行的是正义反抗，但最终以英国获胜中国失败而告终。

这表明 ①战争的性质是战争胜败的决定因素 ②腐朽的封建主义难以对抗新兴的资本主义 ③综合国力的强弱是决定战争胜负的重要条件 A ．①③ B ．②④ C ．②③④ D ．①②③④4．初二（3）班举办以“近代化探索”为主题的手抄报比赛，下列哪些材料符合这主题 ①林则徐领导虎门销烟 ②太平军抗击洋枪队③李鸿章创办轮船招商局 ④康有为组织公车上书 A ．①②B ．②③C ．③④D ．①④5．在中国民主革命的过程中，毛泽东作出的突出贡献有 ①找到了中国民主革命的正确道路 ②领导人民建立了中华人民共和国 ③领导人民完成了反帝反封建的任务 ④领导人民建立起社会主义制度 A ．①②③B ．①③④C ．①②D ．①②③④6．下图为华成烟草公司在《申报》上对“美丽牌”卷烟的宣传广告。

02 标点符号专题（知识点思维导图+习题训练）依次填入下面一段文字方框内的标点符号，最恰当的一项是（）。

一位九十多岁的篆刻艺术家从16岁起便与篆刻结缘。

他多年潜心于书法古文字和篆刻的研究，同时撰写了多部著作这位篆刻艺术家说：“人活到老学到老，还要贡献到老A.，。

”。

B.、；”。

C.，；。

”D.、。

”【答案】D【解析】第一处：“书法”与“古文字”为表并列关系的短语，中间应使用顿号；第二处：“他多年潜心于书法、古文字和篆刻的研究，同时撰写了多部著作”表达完整句意，句末应使用句号；第三处：“人活到老学到老，还要贡献到老”，是艺术家所说的完整的话，应先写句号再写下引号；故选D。

2.（2022·四川雅安·一模）下列各项中标点使用不当的一项是（）。

A.人还没看见，已经先听到歌声了；或者人已经转过山头望不见了，歌声还余音袅袅。

B.桃树、杏树、梨树，你不让我，我不让你，都开满了花赶趟儿。

C.把报刊亭改造成志愿者服务站？还是生活服务便民亭？人们对此意见不一。

D.在我国的经典文化典籍里，大家认为最重要的是“四书五经”。

【答案】C【解析】C.选择问句，第一个问号应该改为逗号。

故选C。

3.（2022·天津和平·二模）依次填入下面一段文字方框内的标点符号，最恰当的一项是（）。

在天津大学2021年的高考录取通知书里，有一份特别的礼物□一本由知名作家冯骥才主编的□天津文化地图□。

7月12日，在这本书的新书首发式□天津大学2021首批本科生录取通知书签发仪式上，校长金东寒当场签发0001号录取通知书，并将它与这本书交到首批录取的本科新生代表手上。

这份礼物让录取通知书变得格外有文化、有深度、有创意。

A.。

“”、 B.——《》、 C.——“”， D.。

《》，【答案】B【解析】第一空，结合文段“有一份特别的礼物”与“一本由知名作家冯骥才主编……”可知，第一空的后面文字是对前面“特别的礼物”进行解释说明，所以标点符号应填破折号；第二、三空，结合文段“一本由知名作家冯骥才主编的”可知，“天津文化地图”是一本书，所以二、三空应填书名号；第四空，结合文段“7月12日，在这本书的新书首发式”“天津大学2021首批本科生录取通知书签发仪式上”可知，第四空前后分句为并列关系，应填顿号；故选B。

2021年中考语文三轮冲刺卷默写专练（二）1．按要求填写相应的语句（1）__________________，散入春风满洛城。

（李白《春夜洛城闻笛》）（2）马上相逢无纸笔，__________________。

（岑参《逢入京使》）（3）__________________，一山放出一山拦。

（杨万里《过松源晨炊漆公店（其五）》）（4）__________________，青草池塘处处蛙。

（赵师秀《约客》）（5）杨花榆英无才思，__________________。

（韩愈《晚春》）（6）__________________，隔江犹唱后庭花。

（杜牧《泊秦淮》）（7）《木兰诗》中，概述战争旷日持久，战斗激烈悲壮的句子是__________________，__________________。

【答案】（1）谁家玉笛暗飞声（2）凭君传语报平安（3）政入万山围子里（4）黄梅时节家家雨（5）惟解漫天作雪飞（6）商女不知亡国恨（7）将军百战死，壮士十年归【详解】注意“声” “政” “惟” “漫” 等字不要写错。

2．默写(1)杜牧的《泊秦淮》中借用典故表现诗人的忧患意识，抒发爱国情怀的诗句是：__________，____________。

(2)李商隐《贾生》中借古讽今揭示唐晚期皇帝求仙访道，不顾国计民生的现实，寄寓诗人怀才不遇的感慨的句子是：______________，_________________。

(3)《陋室铭》中以“交往之雅”表明“陋室不陋”的语句是：_______________，______________。

(4)孔子有言“登泰山而小天下”，《望岳》中与之相近的诗句是____________，____________。

【答案】商女不知亡国恨隔江犹唱后庭花可怜夜半虚前席不问苍生问鬼神谈笑有鸿儒往来无白丁会当凌绝顶一览众山小【详解】注意“隔”“苍”“儒”“凌”等字的书写。

3．默写古诗文的名句名篇。

（1）__________________，关山度若飞。

题型二函数的实际应用类型1 最优方案问题1．(2019·宁波)某风景区内的公路如图1所示，景区内有免费的班车，从入口处出发，沿该公路开往草甸，途中停靠塔林(上下车时间忽略不计)．第一班车上午8点发车，以后每隔10分钟有一班车从入口处发车．小聪周末到该风景区游玩，上午7︰40到达入口处，因还没到班车发车时间，于是从景区入口处出发，沿该公路步行25分钟后到达塔林．离入口处的路程y(米)与时间x(分)的函数关系如图2所示．(1)求第一班车离入口处的路程y(米)与时间x(分)的函数表达式．(2)求第一班车从入口处到达塔林所需的时间．(3)小聪在塔林游玩40分钟后，想坐班车到草甸，则小聪最早能够坐上第几班车？如果他坐这班车到草甸，比他在塔林游玩结束后立即步行到草甸提早了几分钟？(假设每一班车速度均相同，小聪步行速度不变)(第24题图)类型2 分段函数问题2．(2019·淮安)快车从甲地驶向乙地，慢车从乙地驶向甲地，两车同时出发并且在同一条公路上匀速行驶，途中快车休息1.5小时，慢车没有体息．设慢车行驶的时间为x小时，快车行驶的路程为y1千米，慢车行驶的路程为y2千米，下图中折线OAEC表示y1与x之间的函数关系，线段OD表示y2与x之间的函数关系，请解答下列问题:(1)求快车和慢车的速度；(2)求图中线段EC所表示的y1与x之间的函数表达式；(3)线段OD与线段EC相交于点F，直接写出点F的坐标，并解释点F的实际意义．3．(2019·无锡)“低碳生活，绿色出行”是一种环保，健康的生活方式，小丽从甲地出发沿一条笔直的公路骑行前往乙地，她与乙地之间的距离y(km)与出发时间t(h)之间的函数关系式如图①中线段AB所示，在小丽出发的同时，小明从乙地沿同一条公路骑车匀速前往甲地，两人之间的距离x(km)与出发时间t(h)之间的函数关系式如图①中折线段CD-DE-EF所示．(1)小丽和小明骑车的速度各是多少？(2)求点E坐标，并解释点E的实际意义．类型3 利润最值问题4．(2019·广元)某水果商计划购进甲、乙两种水果进行销售，经了解，甲种水果的进价比乙种水果的进价每千克少4元，且用800元购进甲种水果的数量与用1000元购进乙种水果的数量相同．(1)求甲、乙两种水果的单价分别是多少元？(2)该水果商根据该水果店平常的销售情况确定，购进两种水果共200千克，其中甲种水果的数量不超过乙种水果数量的3倍，且购买资金不超过3420元，购回后，水果商决定甲种水果的销售价定为每千克20元，乙种水果的销售价定为每千克25元，则水果商应如何进货，才能获得最大利润，最大利润是多少？5．(2019·通辽)当今，越来越多的青少年在观看影片《流浪地球》后，更加喜欢同名科幻小说，该小说销量也急剧上升．书店为满足广大顾客需求，订购该科幻小说若干本，每本进价为20元．根据以往经验：当销售单价是25元时，每天的销售量是250本；销售单价每上涨1元，每天的销售量就减少10本．书店要求每本书的利润不低于10元且不高于18元．(1)直接写出书店销售该科幻小说时每天的销售量y(本)与销售单价x(元)之间的函数关系式及自变量的取值范围；(2)书店决定每销售1本该科幻小说，就捐赠a(0＜a≤6)元给困难职工，每天扣除捐赠后可获得最大利润为1960元，求a的值．类型4 抛物线型问题6．(2019·广安)在广安市中考体考前，某初三学生对自己某次实心球训练的录像进行分析，发现实心球飞行高度y(米)与水平距离x(米)之间的关系为y＝－112x2＋23x＋53，由此可知该生此次实心球训练的成绩为________米．7．（2019•襄阳）如图，若被击打的小球飞行高度h（单位：m）与飞行时间t（单位：s）之间具有的关系为h＝20t﹣5t2，则小球从飞出到落地所用的时间为s．8．(2019·临沂)从地面竖直向上抛出一小球，小球的高度h(单位:m)与小球的运动时间t(单位:s)之间的函数关系如图所示，下列结论:①小球在空中经过的路程是40 m；①小球抛出3秒后，速度越来越快；①小球抛出3秒时速度为0；①小球的高度h＝30 m时，t＝1.5 s.其中正确的是()A．①① B．①① C．①①① D．①①类型5 图形面积问题9．(2019·连云港)如图，利用一个直角墙角修建一个梯形储料场ABCD，其中①C＝120°.若新建墙BC与CD总长为12 m，则该梯形储料场ABCD的最大面积是()A．18 m2B．18 3 m2C．24 3 m2 D.4532m210．(2019·绍兴)有一块形状如图的五边形余料ABCDE，AB＝AE＝6，BC＝5，①A＝①B＝90°，①C＝135°，①E＞90°.要在这块余料中截取一块矩形材料，其中一条边在AE上，并使所截矩形材料的面积尽可能大．(1)若所截矩形材料的一条边是BC或AE，求矩形材料的面积．(2)能否截出比(1)中更大面积的矩形材料？如果能，求出这些矩形材料面积的最大值；如果不能，说明理由．题型二 函数的实际应用答案1．思路分析：本题考查了用待定系数法求一次函数解析式，一次函数的生活应用，一元一次不等式，主要考查学生能否把实际问题转化成数学问题．在第(1)小题中，根据(20，0)，(38，2700)这两个特殊点，利用待定系数法可以求出y 关于x 的函数关系式．在第(2)小题中，已知函数值求自变量．第(3)小题中，利用一元一次不等式求出最早可以坐的班车，进而求出时差．解题过程：解：(1)由题意得，可设函数表达式为：y ＝kx ＋b (k ≠0)． 把(20，0)，(38，2700)代入y ＝kx ＋b ，得020270038k b k b，解得1503000k b．①第一班车离入口处的路程y (米)与时间x (分)的函数表达式为 y ＝150x －3000(20≤x ≤38)．(注：x 的取值范围可省略不写) (2)把y ＝1500代入，解得x ＝30，则30－20＝10(分)． ①第一班车到塔林所需时间10分钟． (3)设小聪坐上第n 班车．30－25＋10(n －1)≥40，解得n ≥4.5， ①小聪最早坐上第5班车．等班车时间为5分钟，坐班车所需时间：1200÷150＝8(分)， 步行所需时间：1200÷(1500÷25)＝20(分)，20－(8＋5)＝7(分)． ①小聪坐班车去草甸比他游玩结束后立即步行到达草甸提早7分钟． 2．思路分析：（1）根据函数图象中的数据可以求得快车和慢车的速度；（2）根据函数图象中的数据可以求得点E 和点C 的坐标，从而可以求得1y 与x 之间的函数表达式；（3）根据图象可知，点F 表示的是快车与慢车行驶的路程相等，从而以求得点F 的坐标，并写出点F 的实际意义．解题过程：解：(1)快车速度＝1802＝90(千米/小时)，慢车速度＝1803＝60(千米/小时)．(2)点E 坐标(3.5，180)，点C 坐标(5.5，360)．设直线EC 的表达式为y 1＝kx ＋b (k ≠0)，⎩⎪⎨⎪⎧3.5k ＋b ＝180，5.5k ＋b ＝360，解得⎩⎪⎨⎪⎧k ＝90，b ＝－135，即y 1与x 之间的函数表达式为y 1＝90x －135. (3)F (4.5，270)，F 点的实际意义是出发了4.5小时后两车都行驶了270千米．点拨:直线OD 的表达式为y 2＝60x ，⎩⎪⎨⎪⎧y ＝60x ，y ＝90x －135，解得⎩⎪⎨⎪⎧x ＝4.5，y ＝270.3．思路分析：（1）由点A ，点B ，点D 表示的实际意义，可求解；（2）理解点E 表示的实际意义，则点E 的横坐标为小明从甲地到乙地的时间，点E 纵坐标为小丽这个时间段走的路程，即可求解． 解题过程：解：（1）由题意可得：小丽速度3616(/)2.25km h == 设小明速度为/xkm h 由题意得：1(16)36x ⨯+= 20x ∴=答：小明的速度为20/km h ，小丽的速度为16/km h ． （2）由图象可得：点E 表示小明到了甲地，此时小丽没到，∴点E 的横坐标369205==， 点E 的纵坐标91441655=⨯=∴点9(5E ，144)54．思路分析：（1）根据题意可以列出相应的分式方程，求出甲、乙两种水果的单价分别是多少元；（2）根据题意可以得到利润和购买甲种水果数量之间的关系，再根据甲种水果的数量不超过乙种水果数量的3倍，且购买资金不超过3420元，可以求得甲种水果数量的取值范围，最后根据一次函数的性质即可解答本题．解题过程：解:(1)设乙种水果的单价是x 元/千克，则甲种水果的单价是(x －4)元/千克． 根据题意，得800x －4＝1000x ，解得x ＝20.经检验，x ＝20是原方程的解， 当x ＝20时，x －4＝20－4＝16.答:甲、乙两种水果的单价分别是16元/千克，20元/千克． (2)设水果商购进乙种水果m 千克，获得的利润为w 元．⎩⎪⎨⎪⎧200－m ≤3m ，16（200－m ）＋20m ≤3420，解得50≤m ≤55， w ＝(20－16)(200－m )＋(25－20)m ，即w ＝m ＋800. ①1＞0，①w 随m 的增大而增大．①50≤m ≤55，①当m ＝55时，w 有最大值，此时，200－m ＝200－55＝145，w ＝55＋800＝855. 答:水果商应购进乙种水果55千克，购进甲种水果145千克，才能获得最大利润，最大利润是855元．5．思路分析：（1）根据题意列函数关系式即可；（2）设每天扣除捐赠后可获得利润为w 元．根据题意得到2(20)(10500)10(10700)50010000(3038)w x a x x a x a x =---+=-++--求得对称轴为1352x a =+，若06a <<，则130352a <+，则当1352x a =+时，w 取得最大值，解方程得到12a =，258a =，于是得到2a =．解题过程：解：①当销售单价是25元时，每天的销售量是250本； 销售单价每上涨1元，每天的销售量就减少10本，①销售量y (本)与销售单价x (元)之间的函数关系式为：y ＝250－10×x －251，①y ＝－10x ＋500.①书店要求每本书的利润不低于10元且不高于18元， ①10≤x －20≤18，①30≤x ≤38，即为所求自变量的取值范围． (2)设每天扣除捐赠后可获得的利润为W 元，则W ＝(x －20－a )(－10x ＋500)＝－10x 2＋(10a ＋700)x －500a －1000. ①对称轴为x ＝12a ＋35，且0＜a ≤6，①30＜12a ＋35≤38，①当x ＝12a ＋35时，W 有最大值，①1960＝⎝⎛⎭⎫12a ＋35－20－a ⎣⎡⎦⎤－10⎝⎛⎭⎫12a ＋35＋500， ①a 1＝2，a 2＝58(不符合题意，舍去)． ①a ＝2.6．答案：10．解析：当0y =时，212501233y x x =-++=， 解得，2x =（舍去），10x =．故答案为：10． 7．答案：4．解析：依题意，令h ＝0得 0＝20t ﹣5t 2 得t （20﹣5t ）＝0 解得t ＝0（舍去）或t ＝4即小球从飞出到落地所用的时间为4s 故答案为4．8．答案：D ．解析：由图象可知小球竖直向上达到最大高度40 m 后再下落回来，因此小球在空中经过的路程是80 m ，故①错误；小球抛出3秒时，速度为0，然后落回地面，速度越来越快，故①与①均正确；当小球的高度h ＝30 m 时，即y ＝30，此时函数图象对称轴两侧各有一点纵坐标为30，也就是说存在两个时间点使小球的高度为30 m(小球上升与回落)，故①错误，设抛物线的解析式为y ＝a (x －3)2＋40，把(6，0)代入，得0＝9a ＋40，解得a ＝－409，①y ＝－409(x －3)2＋40，当y ＝30时，－409(x －3)2＋40＝30，解得x 1＝1.5，x 2＝4.5，即当t ＝1.5 s 或t ＝4.5 s 时，小球的高度h ＝30 m ． 9．答案：C ．解析：如图，过点C 作CE AB ⊥于E ，则四边形ADCE 为矩形，CD AE x ==，90DCE CEB ∠=∠=︒， 则30BCE BCD DCE ∠=∠-∠=︒，12BC x =-， 在Rt CBE ∆中，90CEB ∠=︒， 11622BE BC x ∴==-，AD CE x ∴==， 116622AB AE BE x x x =+=+-=+，∴梯形ABCD 面积221113()(6)(63)4)222S CD AB CE x x x x =+=++-=++-+，∴当4x =时，S =最大．即CD 长为4m 时，使梯形储料场ABCD 的面积最大为2； 故选：C ．10．思路分析：（1）①若所截矩形材料的一条边是BC ，过点C 作CF AE ⊥于F ，得出16530S AB BC ==⨯=；①若所截矩形材料的一条边是AE ，过点E 作//EF AB 交CD 于F ，FG AB ⊥于G ，过点C 作CH FG ⊥于H ，则四边形AEFG 为矩形，四边形BCHG 为矩形，证出CHF ∆为等腰三角形，得出6AE FG ==，5HG BC ==，BG CH FH ==，求出1BG CH FH FG HG ===-=，5AG AB BG =-=，得出26530S AE AG ==⨯=；（2）在CD 上取点F ，过点F 作FM AB ⊥于M ，FN AE ⊥于N ，过点C 作CG FM ⊥于G ，则四边形ANFM 为矩形，四边形BCGM 为矩形，证出CGF ∆为等腰三角形，得出5MG BC ==，BM CG =，FG DG=，设AM x =，则6BM x =-，11FM GM FG GM CG BC BM x =+=+=+=-，得出2(11)11S AM FM x x x x =⨯=-=-+，由二次函数的性质即可得出结果．解题过程：解:(1)①若所截矩形材料的一条边是BC ，如图①所示: 过点C 作CF ①AE 于点F ，S 1＝AB ·BC ＝6×5＝30； ①若所截矩形材料的一条边是AE ，如图①所示:过点E 作EF ①AB 交CD 于点F ，过点F 作FG ①AB 于点G ，过点C 作CH ①FG 于点H ， 则四边形AEFG 为矩形，四边形BCHG 为矩形， ①①C ＝135°，①①FCH ＝45°， ①①CHF 为等腰直角三角形，①AE ＝FG ＝6，HG ＝BC ＝5，BG ＝CH ＝FH ， ①BG ＝CH ＝FH ＝FG －HG ＝6－5＝1， ①AG ＝AB －BG ＝6－1＝5， ①S 2＝AE ·AG ＝6×5＝30； (2)能；理由如下:在CD 上取点F ，过点F 作FM ①AB 于点M ，FN ①AE 于点N ，过点C 作CG ①FM 于点G ，则四边形ANFM 为矩形，四边形BCGM 为矩形， ①①C ＝135°， ①①FCG ＝45°，①①CGF 为等腰直角三角形， ①MG ＝BC ＝5，BM ＝CG ，FG ＝CG ， 设AM ＝x ，则BM ＝6－x ，①FM ＝GM ＋FG ＝GM ＋CG ＝BC ＋BM ＝11－x ，①S ＝AM ×FM ＝x (11－x )＝－x 2＋11x ＝－(x －5.5)2＋30.25， ①当x ＝5.5时，S 的最大值为30.25.。

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） 沥尽心血（11） 气冲斗牛（d6u ）3、下列词语中加点字的注音全对的一组是（）下列词语中加点字的注音完全正确的一项是（） 粗犷(kudng) 应和(ying) 抖擞(shu)水藻(zdo)抹杀（m6） 疙瘩（g€） 揩油（kdi ） 校对（jido ）A.朗润(riin)B.贮蓄(zhu)C.澄清(ddng)1).憔悴(cui) 应和粗犷匿笑(h6) 若落(zhao)分歧(qf )(kuong) 静谧(bi)霎时(chd)(nl)絮叨(doo)吝啬（s仓）祷告(ddo)卜列词语在加点字注音无误的•项是（A.诘问(jl )B.(E 若(yti )C.门槛(kdn)D.烦躁(zdo) 粗拙（zhu。

）取缔（(11滞笨(zhi ) 胯骨(kud )攥若(zudn )(hul) )晌午(xidng)自矜(jin)侍弄尴尬(gon)震悚(sdng ) 针灸(zhl) 憎恶(zMg)A・柏树(ji£i)凫水(fii) 蕴茨(ytm) 不惮(dan)B.怠慢(ddi) 潺潺(chdn) 行辈(X] ng) 家眷(judn)C.旺相(xiang) 弥散(M) 纠葛(jiu) 掠掇(chuan)D.归省(shMg) 喝采(诡)舟楫(jD 漂渺(mido)6、下列加点字的注音完全正确的一项是()A.赫然(诡)校补(xiao) 衙门3)气冲斗牛(dbu)B.窥探(9U1) 硕果(shud)卓越(zhu6) 潜心贯注(qidn)C.独裁(cdi) 衰微(shudi) 迭起(did) 慷慨淋漓(kdi)1).弥高(mi) 一剂(ji)深宵(xiao) 锲而不舍(qi)7、下列加点字的读音全都正确的•项是()A. 哺育(bU) 祈祷(ql) 哽住(g$ng) 山涧(jidn)B. 怪诞(dan) 机杼(shu) 可汗(好)途异(chdi)C. 云鬓(bin) 浊流(zhud) 气魄(pb) 惩罚(chdng)D. 肃静(sti) 污秽(hul) 亘古(gM) 胡骑(ji)8、下列词语中加点的字，每对读音都不同的一项是( )A.殷勤/殷红咀嚼/咬文嚼字风调雨顺/南腔北调B.儒雅/惜弱侍奉/侍才傲物咄咄逼人/相形见细C.卡片/关卡屏障/屏气凝神置之度外/度日如年1).譬如/偏僻栅栏/姗姗来迟前仆后继/赴汤蹈火9、卜列加点字注音正确的一项是()A.陋室(1N) 噫(yl) 苔痕(Wi)B.鸿儒(h6ng) 濯(zhu6) 鲜有闻(xian)C.蕃(fan) 清涟(lidn) 亵玩(xi。

2022年河南省中考英语最新题型冲刺卷02第I卷（选择题）一、完形填空（每小题1分，共15小题）（2022·浙江·嘉兴一中一模）While doing shopping one day, I realised I’d spent close to 30 minutes just choosing fruits and vegetables that were good-looking without any spots(斑点). I’m sure I’m not____1____. How did we become so?I’ve also seen ____2____ my action has influenced my daughter. Every time I prepare lunches for her. I make sure I include everything ____3____. But one day when ____4____ refused to eat an apple that was turning a little brown, I ____5____ I had to change my ways.Then one night, I ____6____ a dinner party. The host Josh Treuhaft ____7____to draw public attention to the food waste problem. At the party, the cook Pesha Perlsweig prepared a six-course meal with food bought from Imperfect Store that sells “ugly” fruits and vegetables. The food can be bought there for 30 to 50 percent of the ____8____. Everyone was____9____ at Perlsweig’s creative delicious dishes made from the “ugly” food. Before each dish, he offered guests advice on how to reduce food waste. ____10____, if you cut off the end of a limp carrot and place it in water, it will become fresh again. After the evening’s dinner, I began to rethink the way I shopped for food, and to ____11____ the imperfect and ugly food. ____12____ looking ugly, the food contains no less nutrition than normal food. Furthermore, it’s ____13____. My change ____14____ my daughter to think differently as well. One morning. while she was helping prepare her school lunch, I noticed her choosing cherry tomatoes with spots. “They’re ____15____,”she said.I’m hoping that these small changes can make a big difference to our world.1．A．alone B．afraid C．full D．proud 2．A．why B．how C．whether D．where 3．A．delicious B．typical C．perfect D．clean 4．A．he B．she C．we D．they 5．A．preferred B．agree C．wished D．knew6．A．found B．prepared C．had D．allowed 7．A．wanted B．asked C．allowed D．promised 8．A．size B．spots C．dish D．price 9．A．angry B．amazed C．relaxed D．tired 10．A．As a result B．At first C．For example D．To be honest 11．A．forget B．accept C．avoid D．regret 12．A．Though B．Because C．Unless D．When 13．A．common B．heavy C．cheap D．free 14．A．advised B．reminded C．invited D．encouraged 15．A．special B．ugly C．expensive D．unhealthy 二、阅读理解（每小题2分，共15小题）A（2022·甘肃武威·一模）16．Where can you enjoy red leaves?A．In the Star Stadium B．In the Underwater World C．Downtown Beijing D．In Fragrant Hills Park17．What may the Coffee maker be?A．A shark B．A machine C．A stadium D．A person 18．What time will the match begin?A．At 6 am. B．At 7 pm. C．At 9:30 am. D．At 5:30 pm. 19．What will you find in the Underwater World?A．Leaves B．Teams C．Cats D．Fishes 20．According to the passage, which of the following is TRUE?A．The cats are on sale. B．Only good-looking people can own the cats.C．Five cute cats want good families. D．The Coffee Maker can’t understand what you say.B（2022·广东·江东镇初级中学一模）Deadly flooding has swept China’s central Henan Province. More than hundreds of thousands of people have been influenced. Up to August 2, a total of 302 people have been killed and 50 missing.Like many other natural disasters, floods can happen with little or no warning. Flash floods move quickly and have strong currents (水流). They are known to bring down trees and destroy buildings. Besides, floods can cause power cuts (停电), traffic jams and other problems. But the flood itself isn’t the only problem to deal with. After a flood, its influence can be just as deadly, as it may not be feasible to send basic supplies, such as water and food to the area.So, in the face of a flash flood, how should we save ourselves?Besides, here are also some tips to keep in mind after a flood.Do not drink floodwater, or use it to wash food. Return to your home only after local governments have said it is safe to do so. Use only bottled or boiled water for drinking, cooking and bathing. Avoid driving through flooded areas.21．Before a flood is coming, _________ can be noticed.A．few signs B．power cuts C．traffic jams D．strong currents 22．What does the underlined word “feasible” in Paragraph 2 probably mean? A．Important. B．Dangerous. C．Possible. D．Expensive.23．Which of the following is correct when we are in a flood?①Don’t stay on a bridge to be broken.②Pay attention to the broadcasts.③Don’t get close to power lines.④Move to the roof at once whatever happens.⑤Stay in the car unless the water begins to flood the car itself.A．②③B．③④⑤C．①②④⑤D．①②③⑤24．What’s the main idea of the last paragraph?A．What life is like after a flood. B．What to do or not to do after a flood. C．When we can go back home after a flood. D．How to choose drinkable water after a flood.25．The purpose of the passage is ________ .A．to report the latest news in HenanB．to tell readers how a flood happensC．to remind readers to stay away from flooded areasD．to give readers some advice on keeping safe in floodsC（2022·广西贵港·一模）Our teacher gave us a task called “secret friends” for the coming week. With our eyes closed, we drew (抽取) a name of a classmate from a basket. We were supposed to do nice things for our friends without letting them know who was doing it. We could leave encouraging notes or cards on their desks or in their schoolbags.Soon, the task was turned into a competition of giving gifts instead of notes. Everyone was getting cool presents except me. I received nothing but cards with nice words about me.On the last morning, I finally got a package. When I opened it, the girls around alllaughed. It was perfumed powder (香粉), an “old lady” gift. My face went red.I tried to forget about the embarrassing gift, but when the girls mentioned it again in the washroom, I joined in, “How stupid! My grandmother wouldn’t even want it.” The girls laughed and left the bathroom.“I’m your secret friend.” It was Rachel. “I’m sorry about the gift,” she said to me in a low voice.From a poor family she was often laughed at by those with rich parents. Yet she just bore (忍受) everything silently.I was sick to my stomach as my hurtful words ran through my mind. She had heard everything. How could I have been so cruel?Later I learned that she had felt bad all week about not being able to leave me any cool present and her mum had given up her only luxury (奢侈品).I told her that I had only said those things to try to fit in (融入).“We aren’t that different from each other, are we?” she smiled understandingly. Her simple words, spoken from her heart, found their way straight into mine.26．What was the task given by the teacher?A．Helping their deskmates with their study. B．Sharing lunch with one of their classmates.C．Drawing a picture of one student in their class. D．Doing nice things for a classmate secretly.27．What does the underlined word “it” refer to in the passage?A．The note. B．The card. C．The package. D．The schoolbag. 28．Why did the writer say those hurtful words?A．Because she thought the gift was cheap. B．Because she tried to fit in. C．Because she hated those girls. D．Because she wanted to be the leader.29．How did the writer feel when she heard what Rachel said?A．Sorry. B．Pleased. C．Angry. D．Proud. 30．What’s the best title for the passage?A．Please understand and respect others B．The differences between poor and rich C．Please be brave to tell the truth D．The good relationships between classmates三、阅读还原（每小题2分，共5小题）（2022·河南信阳·一模）Last year, China introduced the “double reduction(双减)” policy in order t o reduce students’ learning burden(负担) by reducing homework andafter-school classes. ____31____“Our homework is clearly less than before,” said 13-year-old Shen Yuzhe from Beijing. “____32____ The exercises are mainly from the textbook.”According to her, teachers now teach at a much slower pace(节奏). ____33____ “Our teachers are also giving us more chances to do experiments and learn from real life,” said Shen.For 13-year-old Zhang Hangming from Tianjin, the best thing about “double reduction” is the increased time in after-school activities. “____34____ I have joined a group called‘leadership development’ where I can learn all kinds of skills beyond academic(学业的) study,” said Zhang.Both Shen and Zhang find there are fewer exams now. ____35____ “Exams push me to study harder. Besides my progress, more importantly, each exam shows my weak points as well,” Zhang said.Shen also pointed out that when burden is lightened, self-discipline(自律) becomes the key. “Some students now spend more time having fun when homework is finished early. But if you use all the free time to relax, you might fall behind your peers(同龄人),” he said.根据材料内容，从下面五个选项中选出能填入文中空缺处的最佳选项，使文章意思通顺，内容完整。

语文中考考点专题训练之说明文阅读（二）（一）“光谱”鼻子探知人体疾病苏格兰斯特拉斯克莱德大学的科学家们正在开发一种称为“光谱”的人造鼻子，这种神奇的鼻子借助探测人体的气味，可告诉当事人是否有病。

科学家们正在探索将这种奇妙鼻子广泛应用于食品、饮料和化妆品的质量控制上，最终让其成为一种交警测试可疑吸毒司机的有效工具。

利用病人身上的气味进行医疗诊断，早在一个世纪前就应运而生。

但是苏格兰的科学家目前正在尝试的是利用先进的化学方法探测不同的气味，然后再利用计算机屏幕给予病人一种免除了忧虑的警报或者告诉他们可能患有什么样的疾病。

斯特拉斯克菜德大学化学系的教授安德鲁.米尔斯说，这些神奇的装置仍在开发阶段。

目前可实用的装置还需一段时日，迄今已经取得了进展。

测试气味和利用气味来医疗的想法，早在100多年前就有人尝试了，现在只不过是重新研究而已。

他还说，人的疾病通常是与化学气味联系在-起的，这种气味可用来快速过滤和大规模的过滤。

比如，天花、肝衰竭、糖尿病等疾病，医生往往可以从病人的呼吸中诊断知道.即使是麻疹，也有一-种化学气味。

人的各种疾病都带有一定的化学气味，这是经过临床实践得出来的。

目前，米尔斯教授正与他的合作人保罗.斯拉文一起致力人造鼻子的开发。

他说这种鼻子将由一系列排列的成分构成.根据所探测到的气味，这些装置将改变颜色和光的强度，他说：“这种显示将会说‘正常或者没问题’1或者一些令人担忧的东西.接着它将有希望识别与其相关的何种疾病，但不一定会让人感到恐惧。

”他还说：“它也许会说“你得去看医生了’。

但是在医院，它会提供全套的诊断建议，说‘我未曾看到过这种气味’，除了患这种或那种疾病的病人之外。

”米尔斯认为，制造一种用于实验室和医院的台式机器，而且还是手提式的，这种机子虽谈不上高质量，但必须是能识别出各种令人关注的明显气味，且不带有主观色彩，无论是冬天还是夏天，无论是当事人是否感冒，这种检测都将是准确的。

目前，科学家们正在开发-一种适用于医院、实验室、医生手术和工作场所的一种桌面装置；同时，再开发一种便携式的装置，可以在家里或野外使用.据悉，一部便携式的装置最初可能要耗资几百英镑，而台式实验室装置则需几千英镑.米尔斯说，如果该装置得到普及，价格就不会成为问题了。

2021年中考英语考点复习冲刺训练题21. The VIPs (very important persons) from 21 countries will ______ the APEC inShanghai this autumn.A. holdB. take part inC. joinD. attend2. The government will _______ some new colleges for more students to receive highereducation.A. set upB. set outC. put downD. put on3. It will _____ them a few years to build the underground.A. spendB. takeC. costD. pay4. The manager _____ that the business would be worse after the stock went down.A. talkedB. toldC. saidD. spoke5. I don’t know Sam’s te lephone number. Will you please _____ in your address bookfor me?A. look up itB. look it upC. look for itD. look at it6. Coffee is ready. How nice it ______! Would you like some?A. looksB. smellsC. soundsD. feels7. Sorry, I can’t hear you clearly. Will you please ______ your e-mail address?I’ll write it down.A. reviewB. reciteC. reportD. repeat8. Don’t ______ your coat, Tom! It’s easy to catch cold in spring.A. take awayB. take offC. take downD.take out9. We are very sad and angry to hear that the bad milk powder(劣质奶粉) _______ thedeaths of over 30 babies.A. madeB. didC. broughtD. caused10. – Shall we call for a taxi?- OK. Let me ______ the phone number in Yellow Page.A. look atB. look forC. look upD. look after11. How magnificent the Bund looks at night when all the lights are _______!A. turned overB. turned offC. turned downD.turned on12. Thousands of spectators came to Shanghai to ______ the 48th World Table Tennis Championships.A. seeB. noticeC. watchD. look13. Millions of Shanghai citizens are learning to ______ English for the 2021 WorldExpo.A) tell B) speak C) say D) talk14. Mr Smith is quite busy today. He has ______ meetings to attend.A) little B) a little C) few D) a few15. To ______ his sick mother, David goes to the hospital after work every day.A) take charge of B〕take hold of C) take care of D) take theplace of各区模拟试题1. Don’t ______ the street when the red light is on.A. crossB. acrossC. throughD. over2. Susan usually walks to work with an umbrella in hand. She uses it to _____the sunlight.A. carry outB. keep offC. take offD. hold in3. Uncle Peter failed to buy a house of his own two years ago _____ the moneyproblem.A. insteadB. instead ofC. becauseD. because of4. I was in such a hurry this morning that I _________ my history book at home.A. forgotB. putC. leftD. found5. The 29th Olympic Games will________ in Beijing in 2021.A. holdB. take placeC. enter forD. give6. I will call you as soon as my cousin _____________in Beijing tomorrow.A. will getB. arrivesC. reachesD. will arrive7. A recorder __________ English when we have English lessons.A. is used to learnB. used to learnC. is used to learningD. used to learning8. I’m afraid it’s to o noisy. Could you please ______ the radio a bit?A. turn onB. turn upC. turn offD. turn down9. --- Have you ever _____ Wuzhen and Taohua Island?--- No, never. But I’m going to either of the places this summer.A. been inB. gone inC. been toD. gone to10. It’s ____ dark. Let’s go home at once.A. soundingB. feelingC. turningD. getting11. Sending that present to my friend _____ me 25 yuan.A.. costB.. spentC.. paidD.. posted12. She has been here for five years. She has made ____ good friends.A.．littleB.．a littleC.．fewD.．a few13. You can’t talk with her like that. _________, she is your mother.A. At firstB. At lastC. At allD. After all14. Wendy ___________ 6 hours a day working on her computer games.A. takesB. paysC. spendsD. costs15. The weather forecast ______ it will be rainy in the late afternoon.A. tellsB. saysC. speaksD. talks16. The technician told us that this machine __________ more than 500 parts.A. was made byB. was made ofC. was made fromD. was made up of17. My brother entered a boarding school this year. At first, he __________ livingat school.A. used not toB. was not used forC. was not used toD. didn't use to18. The 2021 World Expo will be __________ in Shanghai . I want to a volunteerat that time.A. taken placeB. happenedC. holdD. held19. David is a worker and he moves______ furniture to people’s new flats everyday.A. a lot ofB. manyC. a fewD. a little20. I would like to ____ my son to the park this weekend.A. bringB. carryC. sendD. take21. Will you please ____ the radio . The neighbours are having a rest.A turn down B. turn up C. turn overD. turn into22. His successful experience ______ an interesting question.A. raisesB. roseC. risesD. israised23. The teacher often does chemical ______ in chemistry classes.A. expensesB. exhibitionsC. excusesD.experiments24. You can ______ all the new words in your dictionary if necessary.A. look upB. look forC. look outD.look at25. Now my daughter _____ reading a book for a while before sleeping.A. used toB. is used toC. use toD.was used to26. Every day people get _______ information from TV, newspapers and the Internet.A. manyB. a number ofC. a lot ofD. a few27. His brother has ________ London for three years.A. gone toB. been inC. been toD. gone in28. Would you please _________ the rubbish to the bin when you go downstairs?A. find outB. take outC. look outD. think out29. Nowadays lots of old houses __________ to give way to the construction(建立).A. are put offB. are being put upC. are being put onD. arebeing put down30. It’s raining _______. We have to stay at home instead of going fishing.A. badlyB. hardlyC. stronglyD. heavily31. Jack likes to _______ others but never writes to them.A. hearB. hear ofC. hear fromD. hear about32. Mr. Jackson has only ______ money in his pocket.A. moreB. a littleC. a fewD. few33. — Do you have ______ eggs? — Sorry, I only have______ hamburgers.A. any; someB. some; anyC. some; someD. any; any34. Something must be done to ______ the bird flu.A. turn offB. take offC. put offD. keep off35. A special cake was ______ at an exhibition in Japan on December 7 last year.A. in troubleB. at workC. on showD.on business36. The APEC 2021 ______ from Nov. 12 to 19 in Busan, South Korea last year.A. happenedB. takes placeC. was heldD. was taken place37. Sportsmen all over China went to Nanjing to ______ the 10th National Gameslast October.A. attendB. enter forC. take part inD. join38. Please ______ the map before you drive around the city.A. readB. watchC. seeD. notice39. He ______ his keys everywhere but failed to find it.A. looked atB. looked afterC. looked forD. looked forward to40. What about eating _____food before we start again?A. someB. anyC. a lotD. a few41. Tibet ___ people from all over the world with its clean air, unique cultureand pleasant people.A. attractsB. invitesC. catchesD. expects42. We are eating out more often than we ____.A. are used toB. used toC. used fored as43. People ____the tide(潮) on the bank of Qiantang River in Hangzhou.A. seeB. watchC. look atD. read44. The report has _________ questions about pollution.A. riseB. risenC. raiseD. raised45. If you save coins a day, you’ll be able to buy a mobile phone in a year.A. a littleB. littleC. a fewD. few46. Fu Biao, the famous film star, has from us for about 8 months, but we cinemagoers and viewers remember him for ever.A. leftB. been awayC. gone awayD. gone47. Digital(数码) cameras are becoming very popular, though some still too much.A. payB. spendC. sellD. cost48. Mr. Li write articles by hand, but now he doing it with a computer.A. used to; used toB. is used to; is used toC. is used to; used toD. used to; is used to49. To my surprise, she for the Super Girl Contest by email, hoping to bea star.A. cameB. leftC. wentD. entered50. Neither of the coats me. They’re too large. Would you show me one more?A. fitsB. coversC. wearsD. puts on51. Yang Liwei _______ 21 hours and 23 minutes________ in the manned spacecraft in space on October 15 and 16.A. cost, stayB. took, to stayC. paid, to stayD. spent, staying52. Tom_______ it if he doesn’t want to.A. doesn’t need toB. need not to doC. needs not to doD. need not do53. In order to keep healthy, you should eat ______ fast food, _____ freshvegetables and take enough exercises.A. fewer…fewerB. fewer…moreC. less…moreD. less…fewer54. How long will it to build a tunnel across the Yangtze River ?A. spendB. payC. costD.take55. _________ it e asy. You’ll be fine in a day or two.A. CarryB. BringC. TakeD. Say56. Tom likes to his knowledge in front of his classmates.A. put offB. turn offC. give offD. show off57. There are ______ mistakes in Mary’s project, so her teacher is pleased withher work.A. a littleB. littleC. a fewD. few58. Tom’s parents have spent ______ money on his education.A. a lotB. plenty ofC. quite a fewD. a number of59. Many people look ______ going to Beijing for the Olympic Games in 2021.A. atB. afterC. forward toD. out of60. I think these foreign visitors ______ Shanghai for more than two weeks.A. have been inB. have come toC. arrived inD. got to61. You’d better not ______ some unhealthy food to that campsite.A. bringB. takeC. fetchD. get62. The big forest fire in Kunmin was ______ in the end thanks to the bravesoldiers.A. put offB. put upC. put onD. put out63. Can you help me to ______ the word in the dictionary? It confuses me a lot.A. findB. look upC. look forD. find out64. Sam _________ $200 for the I-pod Nano.A. spentB. paidC. tookD. cost65. The little boy is clever enough to ___________ the time.A. sayB. tellC. talkD. speak66. Betty, we have only ___________ milk in the fridge. Would you please buy somenow?A. a littleB. littleC. fewD. a few67. Sarah ____________a bike to work, but now she drives.A. used to rideB. had riddenC. would rideD. is used to riding68. All the street lights ______ because of the power cut〔断电〕 last night.A. put downB. put offC. went outD. went off69. Let Jimmy play with your toy car as well, Peter. You must learn to ____.A.．helpB.．shareC.．likeD.．care70. Mu m, I’ve __________ the table. Can we begin our dinner?A. layB. lainC. laidD. lied励志赠言经典语录精选句；挥动**，放飞梦想。