专题：一轮复习专项突破

第二章 代数式2.1 整式考点突破考点一 列代数式典例1 10名学生的平均成绩是x ，如果另外5名学生每人得84分，那么整个组的平均成绩是__________分. A.284+x B.1542010+x C.158410+x D.1542010+ 思路导引整个组的平均成绩＝15名学生的总成绩÷15.点拨列代数式，需根据题意，找出题目蕴含的数量关系及正确书写代数式是解决问题的关键. 跟踪训练 11.用代数式表示:a 的2倍与3的和，下列表示正确的是（ ）A.2a-3B.2a ＋3C.2（a-3）D.2（a ＋3）2.某商店举办促销活动，促销的方法是将原价x 元的衣服以（54x-10）元出售，则下列说法中，能正确表达该商店促销方法的是（ ）A.原价减去10元后再打8折B.原价打8折后再减去10元C.原价减去10元后再打2折D.原价打2折后再减去10元3.用一根长为a （单位:cm ）的铁丝，首尾相接围成一个正方形，要将它按图的方式向外等距扩1（单位:cm ）得到新的正方形，则这根铁丝需增加（ ）A.4 cmB. 8 cmC.（a ＋4）cmD.（a ＋8）cm考点二 求代数式的值典例2 已知x 2＋2x ＝-1，则代数式5＋x （x ＋2）的值为___________.思路导引先根据整式的乘法去括号化简代数式，再将已知式子的值代入求值即可.点拨本题考查了代数式的化简求值，利用整式的乘法对代数式进行化简是解题关键. 跟踪训练 21.已知a ＋b ＝4，则代数式1＋2a ＋2b 的值为（ ）A.3B.1C.0D.-12.观察如图所示的程序计算，若输出的结果为3，则输入的值m 为__________.A.1B.2C.-1D.-23.已知x ＋2y ＝3，则1＋2x ＋4y ＝____________.考点三 同类项合并同类项典例3 若x a ＋1y 3与21x 4y 3是同类项，则a 的值是_____________. 思路导引所含字母相同，并且相同字母的指数也相同，这样的项叫做同类项，据此可得a 的值. 跟踪训练 31.如果3ab 2m-1与9ab m ＋1是同类项，那么m 等于（ ）A.2B.1C.-1D.02.若8x m y 与6x 3y n 的和是单项式，则（m ＋n ）3的平方根为（ ）A.4B.8C.±4D.±83.若单项式2x m-1y 2与单项式31x 2y n ＋1是同类项，则m ＋n ＝___________. 考点四 规律的探索典例4 如图所示各图形是由大小相同的黑点组成，图1中有2个点，图2中有7个点，图3中有14个点，…，按此规律，第10个图中黑点的个数是:____________.思路导引根据题意，找出图形的规律，得到第n 个图形的黑点数为n(n+1)+(n-1)=(n+1)2-2，即可求出答案.跟踪训练 41.如图所示，正方形ABCD 的边长为1，以对角线AC 为边作第二个正方形ACEF ，再以对角线AE 为边作第三个正方形AEGH ，依次下去，第n 个正方形的面积为（ ）A.（2）n-1B.2n-1C.（2）nD.2n2.按一定规律排列的一列数:3，32，3-1,33，3-4，37，3-11，318，…，若a，b，c表示这列数中的连续三个数，猜想a，b，c满足的关系式是____________.考点五整式的加减运算典例5计算2a-3a，结果正确的是（）A.-1B.1C.-aD.a思路导引根据合并同类项法则合并即可.点拨整式的加减计算，能熟练掌握去括号及合并同类项法则的内容是解题的关键.跟踪训练 51.下列运算正确的是（）A. 2a＋3b＝5abB. a3·a2＝a5C.（a＋b）2＝a2＋b2D.（a2b）3＝a6b2.计算x＋7x-5x的结果等于___________.3.合并同类项:4a2＋6a2-a2＝_____________.考点六整式的乘、除、乘方运算典例6若3m＝9n＝2.则3m＋2n＝_____________.思路导引首先根据幂的乘方的运算方法，求出32n的值；然后根据同底数幂乘法的运算方法，求出3m＋2n的值为多少即可.点拨此题考查幂的乘方与积的乘方，关键是根据幂的乘方与积的乘方解答.跟踪训练 61.计算a·a2结果正确的是（）A.aB.a2C.a3D.a42.下列运算正确的是（ ）A.3x 3·x 2＝3x 5B.（2x 2）3＝6x 6C.（x ＋y ）2＝x 2＋y 2D.x 2＋x 3＝x 53.若关于x 的二次三项式x2＋ax ＋41是完全平方式，则a 的值是__________. 考点七 整式的混合运算及化简求值典例7 先化简，再求值:（a-1）2＋a （a ＋2），其中a ＝2.思路导引先利用完全平方公式、单项式乘多项式法则展开，再去括号、合并同类项即可化简原式，继而将x 的值代入计算可得答案.点拨整式的混合运算化简求值，解题的关键是掌握平方差公式、完全平方公式、单项式乘多项式法则、去括号法则、合并同类项法则.跟踪训练 71.化简:（x-1）2-x （x ＋7）.2.化简:（a ＋2）（a-2）-a （a ＋1）.3.化简求值:（2x ＋3）（2x-3）-（x ＋2）2＋4（x ＋3），其中x ＝2.中考真题1.（2020·聊城）下列计算正确的是（ ）A.a 2·a 3＝a 6B.a 6÷a -2＝a -3C.（-2ab 2）3＝-8a 3b 6D.（2a ＋b ）2＝4a 2＋b 22.下列计算正确的是（ ）A. 2x ＋3y ＝5xyB.（x ＋1）（x-2）＝x 2-x-2C.a 2·a 3＝a 6D.（a-2）2＝a 2-43.计算（-2a 3）2÷a 2的结果是（ ）A.-2a 3B.-2a 4C.4a 3D.4a 44.（2020·攀枝花）下列式子中正确的是（ ）A.a 2-a 3＝a 5B.（-a ）-1＝aC.（-3a ）2＝3a 2D.a 3＋2a 3＝3a 35.（2020·遂宁）下列计算正确的是（ ）A.7ab-5a ＝2bB.（a ＋a 1）2＝a 2＋21aC.（-3a 2b ）2＝6a 4b 2D.3a 2b ÷b ＝3a 2 6.（2020·达州）如图所示，正方体的每条棱上放置相同数目的小球，设每条棱上的小球数为m ，下列代数式表示正方体上小球总数，则表达错误的是（ ）A.12（m-1）B.4m ＋8（m-2）C.12（m-2）＋8D.12m-167.（2020·枣庄）图1是一个长为2a ，宽为2b （a ＞b ）的长方形，用剪刀沿图中虚线（对称轴）剪开，把它分成四块形状和大小都一样的小长方形，然后按图2那样拼成一个正方形，则中间空余的部分的面积是（ ）A.abB.(a+b)2C.(a-b)2D.a 2-b 28.（2020·乐山）已知3m ＝4，32m-4n ＝2.若9n ＝x ，则x 的值为（ ） A.8 B.4 C.22 D.29.（2020·青海）下面是某同学在一次测试中的计算:①3m 2n-5mn 2＝-2mn ；②2a 3b ·（-2a 2b ）＝-4a 6b ；③（a 3）2＝a5；④（-a 3）÷（-a ）＝a 2.其中运算正确的个数为（ ）A.4个B.3个C.2个D.1个10.（2020·潍坊）若m 2＋2m ＝1，则4m 2＋8m-3的值是（ ）A.4B.3C.2D.1 11.（2020·盐城）把1-9这9个数填入3×3的方格中，使其任意一行，任意一列及两条对角线上的数之和都相等，这样便构成了一个“九宫格”.它源于我国古代的“洛书”（图1），是世界上最早的“幻方”.图2是仅可以看到部分数值的“九宫格”，则其中x的值为（）A.1B.3C.4D.612.（2020·牡丹江）一列数1，5，11，19，…，按此规律排列，第7个数是（）A.37B.41C.55D.7113.（2020·重庆B）下列图形都是由同样大小的实心圆点按一定规律组成的，其中第①个图形一共有5个实心圆点，第②个图形一共有8个实心圆点，第③个图形一共有11个实心圆点，…，按此规律排列下去，第⑥个图形中实心圆点的个数为（）A.18B.19C.20D.2114.（2020·安顺）化简x（x-1）＋x的结果是_____________.15.（2020·黔西南）若7a x b2与-a3b y的和为单项式，则y x＝___________.16.（2020·临沂）若a＋b＝1，则a2-b2＋2b-2＝____________.17.（2020·宜昌）数学讲究记忆方法，如计算（a5）2时若忘记了法则，可以借助（a5）2＝a5×a5＝a5＋5＝a10，得到正确答案.你计算（a2）5-a3×a7的结果是____________.18.（2020·北京）如图所示是某剧场第一排座位分布图.甲、乙、丙、丁四人购票，所购票数分别为2，3，4，5.每人选座购票时，只购买第一排的座位相邻的票，同时使自己所选的座位号之和最小，如果按“甲、乙、丙、丁”的先后顺序购票，那么甲购买1，2号座位的票，乙购买3，5，7号座位的票，丙选座购票后，丁无法购买到第一排座位的票.若丙第一个购票，要使其他三人都能购买到第一排座位的票，写出一种满足条件的购票的先后顺序_______________.19.（2020·黔西南）如图所示，是一个运算程序的示意图，若开始输入x 的值为625，则第2020次输出的结果为_____________.20.（2020·宁波）计算:（a ＋1）2＋a （2-a ）.21.（2020·攀枝花）已知x ＝3，将下面代数式先化简，再求值:（x-1）2＋（x ＋2）（x-2）＋（x-3）（x-1）.22.（2020·济宁）先化简，再求值:（x ＋1）（x-1）＋x （2-x ），其中x ＝21.23.（2020·常州）先化简，再求值:（x ＋1）2-x （x ＋1），其中x ＝2.24.（2020·广东）先化简，再求值:（x ＋y ）2＋（x ＋y ）（x-y ）-2x 2，其中x ＝2，y ＝3.25.（2020·荆门）先化简，再求值:（2x＋y）2＋（x＋2y）2-x（x＋y）-2（x＋2y）（2x＋y），其中x＝2＋1，y＝2-1.26.（2020·北京）已知5x2-x-1＝0，求代数式（3x＋2）·（3x-2）＋x（x-2）的值.27.（2020·河北）有一电脑程序:每按一次按键，屏幕的A区就会自动加上a2，同时B 区就会自动减去3a，且均显示化简后的结果.已知A，B两区初始显示的分别是25和-16，如图所示.如，第一次按键后，A，B两区分别显示:（1）从初始状态按2次后，分别求A，B两区显示的结果；（2）从初始状态按4次后，计算A，B两区代数式的和，请判断这个和能为负数吗？说明理由.参考答案考点突破典例1 B跟踪练习1 1.B 2.B 3.B典例2 4跟踪练习2 1.A 2.C 3.7典例3 3跟踪练习3 1.A 2.D 3.4典例4 119跟踪练习4 1.B 2.bc=a典例5 C跟踪练习5 1.B 2.3x 3.9a 2典例6 4跟踪练习6 1.C 2.A 3.±1典例7 解:原式＝a 2-2a ＋1＋a 2＋2a ＝2a 2＋1，当a ＝2时，原式＝5.跟踪训练71.解:原式＝x 2-2x ＋1-x 2-7x ＝-9x ＋1.2.解:原式＝a 2-4-a 2-a ＝-4-a3.解:原式＝4x 2-9-（x 2＋4x ＋4）＋4x ＋12＝4x 2-9-x 2-4x-4＋4x ＋12＝3x 2-1， 当x ＝2时，原式＝3×（2）2-1＝3×2-1＝6-1＝5.中考真题1.C2.B3.D4.D5.D6.A7.C8.C9.D10.D 11.A 12.C 13.C 14.x 2 15.8 16.-117.0 18.丙，丁，甲，乙 19.120.解:原式＝a 2＋2a ＋1＋2a-a 2＝4a ＋1.21.解:原式＝x 2＋1-2x ＋x 2-4＋x 2-x-3x ＋3＝3x 2-6x ，将x ＝3代入，原式＝27-18＝9.22.解:原式＝x 2-1＋2x-x 2＝2x-1，当x ＝21时，原式＝2×21-1＝0. 23.解:原式＝x 2＋2x ＋1-x 2-x ＝x ＋1，当x ＝2时，原式＝2＋1＝3.24.解:原式＝x 2＋2xy ＋y 2＋x 2-y 2-2x 2＝2xy ，当x ＝2，y ＝3时，原式＝2×2×3＝26.25.解:原式＝[(2x ＋y)-(x ＋2y)]2-x 2- xy ＝（x-y ）2-x 2-xy ＝x 2-2xy ＋y 2-x 2-xy ＝y 2-3xy.当x＝2＋1，y＝2-1时，原式＝(2-1)2-3(2＋1)(2-1)＝3-22-3＝-22.26.解:原式＝9x2-4＋x2-2x＝10x2-2x-4，∵5x2-x-1＝0，∴5x2-x＝1.∴原式＝2（5x2-x）-4＝-2.27.解:（1）A区显示的结果为:25＋2a2，B区显示的结果为:-16-6a；（2）这个和不能为负数，理由:根据题意得，25＋4a2＋（-16-12a）＝25＋4a2-16-12a＝4a2-12a＋9＝（2a-3）2，∵（2a-3）2≥0，∴这个和不能为负数.。

藏躲市安详阳光实验学校考能专项突破(七)重点题型——⑦育种归纳类[题型特点] 以新成果、新情景为背景，综合考查杂交育种、诱变育种、单倍体育种和基因工程育种等原理、过程、特点及应用，是该类题型的重要特点，该题型是近几年来高考的热点，应重点把握。

如图所示，科研小组用60Co照射棉花种子，诱变当代获得棕色(纤维颜色)新性状，诱变Ⅰ代获得低酚(棉酚含量)新性状。

已知棉花的纤维颜色由一对等位基因(A、a)控制，棉酚含量由另一对等位基因(B、b)控制，两对基因遗传。

(1)两个新性状中，棕色是________性状，低酚是________性状。

(2)诱变当代中，棕色、高酚的棉花植株基因型是________，白色、高酚的棉花植株基因型是____________。

(3)棕色棉抗虫能力强，低酚棉产量高。

为获得抗虫高产棉花新品种，研究人员将诱变Ⅰ代中棕色、高酚植株自交，每株自交后代种植在一个单独的区域，从__________________的区域中得到纯合棕色、高酚植株。

请你利用该纯合子作为一个亲本，再从诱变Ⅰ代中选择另一个亲本，设计一方案，尽快选育出抗虫高产(棕色、低酚)的纯合棉花新品种(用遗传图解和必要的文字表示)。

答案(1)显性隐性(2)AaBB aaBb(3)不发生性状分离(或全为棕色棉，或没有出现白色棉)表现为棕色、低酚(AAbb)性状的植株即为需要选育的新品种。

解析(1)由图中突变当代自交后发生性状分离可知，棕色性状是显性性状，低酚是隐性性状。

(2)因为棕色性状是显性性状，低酚是隐性性状，所以突变当代棕色、高酚的棉花植株基因型是AaBB，白色、高酚的棉花植株基因型是aaBb。

(3)突变当代棕色、高酚的棉花植株(AaBB)自交，得到诱变Ⅰ代中棕色、高酚植株基因型有两种：AABB和AaBB。

它们分别自交，后代种植在一个单独的区域，AaBB出现性状分离，而AABB不出现性状分离(全为棕色棉，没有出现白色棉)，可以获得纯合棕色、高酚植株。

2023年中考英语一轮复习语法知识专项突破-时间状语从句一、选择题Aunt Lucy will tell us something about her trip to Australia when she _____ back. A．came B．comes C．would come D．will comeHe is going to be a scientist when he _____.A．grows up B．grow upC．is going to grow up D．grew upShe _____ a math teacher when she grows up.A．is B．be C．am D．is going to be—Please tell Jim to call me as soon as he _____ back.—All right. I will.A．came B．come C．will come D．comes—Our new teacher has _____ to Beijing. How can I get in touch with her —Don't worry. She will phone you as soon as she _____ there.A．been; will get B．been; gets C．gone; will get D．gone; getsI will do some cleaning as soon as I _____ my homework.A．finish B．will finish C．has finished D．finishedYou can play computer games as soon as you _____ doing the housework. A．will finish B．finish C．finishes D．finishedHenry will give us a report as soon as he _____.A．arrives B．arrived C．is arriving D．will arriveI _____ Tim the news as soon as I see him tomorrow.A．tell B．told C．will tell D．have toldHenry will give us a report as soon as he _____ time.A．has B．had C．will arrive D．haveAs soon as he _____ here, we will give him the ticket.A．arrive B．arrives C．will arrive D．arrived—Dad, I'm wondering when Mum _____ home. I miss her very much.—She will get back when she _____ her work.A．returns; finishes B．returns; will finishC．will return; finishes D．will return; will finish—I'm afraid the class has begun.—Don't worry. It _____ until the bell _____.A．doesn't begin; rings B．won't begin; will ringC．won't begin; rings D．doesn't begin; will ringI will call you as soon as he _____ back. You can go home now.A．come B．came C．comes D．will comeI will go home for the vacation as soon as I _____ my exam.A．will finish B．finish C．finishing D．finishedAfter we pass the exams,we _____ by having a party next week. A．celebrated B．celebrate C．have celebrated D．will celebrateTony _____ a new motorcycle as soon as he gets his salary (薪水) tomorrow. A．buys B．bought C．has bought D．will buy—I will go to Guangdong for my summer holidays, mom.—I will meet you when you _____ the airport.A．will reach B．reaches C．reached D．reachMy brother wants to be a pilot when he _____.A．will grow up B．grew up C．is growing up D．grows upWhen he _____, he is going to be an excellent engineer like his father.A．gets up B．grows up C．will get up D．wu grow up—Linda has _____ to Paris. How can I get in touch with her—Don't worry. She will call you as soon as she _____ there.A．been; will get B．been; gets C．gone; will get D．gone; gets—I don't know when _____ tomorrow.—I will call you as soon as he _____.A．he will come; will arrive B．he will come; arrivesC．will he come; arrivesI _____ you as soon as I arrive in Beijing.A．call B．called C．will call D．is callingWe will go on with the match as soon as it _____.A．will stop raining B．stops rainingC．stop to rain D．isn't rainI will telephone you when he _____ back.A．comes B．will come C．come D．cameThe police _____ whether there is anyone injured when they arrive at the scene of an accident.A．checked B．will check C．are checking D．have checked根据语境，选出最佳选项。

2023年中考英语一轮复习语法知识专项突破-形容词、一、选择题、1.The hotel is the best here. It has _____ rooms.A．the worse B．most comfortableC．best D．the most comfortable2.The little Johnny sweeps the floor very often to make the house _____.A．cool B．warm C．clean D．large3.The Amazon Rainforest is one of _____ wettest places in the world.A．a B．an C．the D．/4.The population of Shenzhen is _____ than that of many other cities in China.A．large B．larger C．largest D．the largest5.—It's _____ for you to play football on the street.—Sorry, we won't. Thank you.A．wonderful B．dangerous C．understanding6.Now Huawei mobile phones made in China are very popular. They look _____ and sell _____.A．good; well B．good; good C．well; good D．well; well7.—John got an "A" in the physics exam.—I'm not _____ to hear that. He worked really hard this term.A．sorry B．excited C．happy D．surprised8.—What a pity! I didn't get full marks in the physics test.—Come on! Nobody can make everything _____.A．perfect B．useful C．natural D．active9.The boy didn't work _____ the exam.A．enough hard to pass B．hard enough to pastC．hard enough to pass D．hard enough passing10.Jason's has _____ quality clothes _____ Trendy Teen's.A．more; than B．better; than C．the best; than D．best; of11.In the reading class, the _____ you are, the _____ you can find answer in the passage.A．careful; easily B．more careful; more easilyC．carefuler: easier D．more careful: easier12.Always doing the same thing is really very _____. I don't like it.A．interesting B．relaxing C．boring D．exciting13.Susan never gets upset when she has to wait in line. She is very .A．shy B．honest C．funny D．patient14.—I think it's necessary to learn how to work in groups.—I quite agree. Sometimes it's even _____ than grades.A．less important B．more importantC．importanter D．the most important15.—The doctor told me not to eat too much, but I find it difficult.—The doctor is right. _____ you eat, _____ you will be.A．The less; the healthier B．The less; the more healthierC．The more; the healthier D．The more; the more healthier16.Red lanterns are _____ things at Spring Festival.A．funny B．traditional C．interesting D．special17.—Come here and have a look, Andy! What about the sweater?—Its style is very _____. I'll take it.A．expensive B．popular C．smooth D．comfortable18.—Do you like these books?—No, I don't. I think they are _____.A．boring B．free C．fun D．relaxing19.—Tina, can you lend me _____ money for this book?—Sorry, I don't have _____ money for that.A．some; enough B．some; some C．any; any D．any; enough20.—How much does your new dress cost?—It's not _____. It's only 80 yuan.A．good B．high C．cheap D．expensive21.—Do you think the old machine is _____, grandma?—Yes, it is _____ for carrying water.A．use; using B．useful; used C．use; used D．useful; use22.The man is _____ and he has _____.A．enough old; enough money B．old enough; enough moneyC．old enough; money enough D．enough old; money enough23.In most countries, people usually eat _____ food on special holidays.A．cheap B．creative C．salty D．traditional24.Maths is one of Peter's _____.A．the worst subjects B．worst subjectC．worse subject D．worst subjects25.—What do you think of the new English teacher?—I think no one is _____. She is a very kind person.A．good B．better C．bad D．worse26.The telephone is _____. I can call my friends with it.A．healthy B．difficult C．useful D．relaxing27.—Why would you like to go to Wanda Cinema IMAX to watch the new movie?—Because it has _____ seats and we can sit _____.A．the biggest; most comfortably B．biggest; the more comfortablyC．bigger; more comfortable28.My father has _____ eating habits, and he eats _____ every day.A．good; good B．good; well C．well; well D．well; good29.—Let's go to the school library, Alice.—I am very _____ now. What about this afternoon?A．busy B．happy C．tidy D．healthy30.I love Kung fu Panda very much. It's _____.A．difficult B．boring C．interesting D．free 31.—You know what? This year we have 3 P.E. lessons every week.—Great! It's really _____ for us students to have a strong body.A．important B．interesting C．special D．different32.—I heard people can't eat or drink on the subway in Hefei.—Yes. In order to have a more _____ space, we need to do that.A．personal B．relaxing C．exciting D．comfortable33.Kevin is really a _____ boy. His room is always in a mess, and he never tidies it up.A．wise B．lazy C．powerful D．magical34.I think history is very _____, and I like it.A．boring B．interesting C．favorite D．difficult35.It's so _____. How about having a cold drink with me in the coffee shop?A．late B．cool C．hot D．wet36.—Hi, Lucy. Are you _____ now?—Yes. I have a lot of things to do.A．busy B．free C．easy D．great37.I don't believe that this _____ boy can paint such a nice picture.A．five years old B．five-years-old C．five-year-old D．five year old38.I like the silence in the countryside. The city is too _____ for me.A．boring B．large C．noisy D．crowded39.—Sonia's English is very _____.—Yeah! And she speaks French (法语) very _____.A．good; well B．well; good C．good; good D．well; well40._____ exercise you take, _____ you'll be.A．The fewer, the heavier B．The less, the heavierC．The less, the much heavier41.We went to the _____ restaurant in town last night. The menu had only ten dishes and the service wasnot good at all.A．bad B．worse C．worst42.—How are you today?—I am much _____. I think this medicine is good for me.A．well B．better C．worse43.Jet sings _____ and he is a _____ singer (歌手).A．good; good B．good; well C．well; good44.If there is _____ pollution, the air in our city will be _____ dirtier.A．more; much B．less; more C．more; more45.Dumpling House is _____ restaurant in the city. You can get a big plate of dumplings for only five yuan.A．cheaper B．cheapest C．the cheapest46.I often fail in English tests, but have a good result in Maths tests. So I think English is _____ Maths.A．as easy as B．as difficult asC．not so difficult as D．not so easy as47.The _____ took on the young man's face made us _____.A．surprised; surprised B．surprising; surprisedC．surprising; surprising D．surprised; surprising48._____ useful information she got yesterday! She seemed _____ when she got it.A．What a, to be happy B．What, happyC．How, happy49.The little girl is _____ to go to school, but her father doesn't have _____ for her study.A．old enough, enough money B．enough old, money enoughC．old enough, enough moneys50.Happiness is very important. _____ you live, _____ you are. So try your best to make yourself happy everyday.A．The happier, the healthierB．The more happily, the more healthilyC．The more happily, the healthier答案一、选择题（共50题）1. 【答案】D【解析】句意：这家旅馆是这儿最好的，它有最舒适的房间。

议论文专题复习（二）【精准突破】一、信息提取筛选二、材料衔接题三、议论文语言特色三、议论文语言特色四、标题与词句的含义五、语段作用分析六、谈感受、评价等开放性试题【精讲精练】一、阅读下面的文章，回答以下各题。

独处是生命的良田韩青①我一直认为，群居往往是肤浅的、浮躁的、表象的，而独处往往是深刻的、安静的、本质的。

要知道，人多的时候，唇枪舌剑，熙熙攘攘，人心难以安静，而心不能安静，就不能深入地思考、探究，这样一来，自然不会把事做好；而独处的时候，人是安静的、自由的，可以思考、探究自己喜欢的事情，这样一来，就会遇到很多的奇迹或是意想不到的美好。

②再说，世间的任何一种美好，都有它自己的规律和节奏，一般来说，它需要我们的安静、沉思、专心和孤独，没有这些元素，我们就难以遇见它，而这些元素也只有在我们独处的时候才有。

就是说，独处的时候，就是我们与美好相逢的时候。

比如，牛顿发现万有引力定律，爱因斯坦发现相对论，爱迪生发明电灯，马克思写《资本论》，司马迁写《史记》，曹雪芹写《红楼梦》等等，他们的“作品”都是独处时结出的硕果。

③俗话说，热闹的大街不长草。

热闹之所，连草都不长了，还能长什么好东西呢？能长的，只能是浮躁、杂乱、庸俗之类的东西。

而一个人如果被这些东西主宰了，那么他就不可能还有追求和梦想；一个没有追求和梦想的人，就会变得日益庸俗乃至低俗。

这样的人就像小水洼，一有什么风吹草动，他就会躁动不安。

显而易见，这样的人没有定力，而没有定力的人，往往就没有恒心；没有恒心的人，就很难做成大事。

④美国女诗人艾米莉•狄金森深谙此道。

她不喜欢热闹、喧哗，深爱独处，在她的一生中，除了年轻时有一次长途旅行外，几乎都在乡间隐居。

在那期间，她写了近两千首的诗，而且，诗歌结集出版后引起轰动，人们因此誉她为二十世纪现代主义诗歌的先驱之一。

如果她不喜欢独处，常常跟人在一起嬉戏玩耍、虚掷光阴，那么她就不会有这样的成就，更可怕的是，如果她交上了坏朋友或染上了坏习气，那么她的品质就可能开始变坏。

2023年中考英语一轮复习语法知识专项突破-非谓语动词一、选择题—Mr Lee is an animal-lover. He always does everything he can _____ animals.—Oh, he is a true friend of animals'.A．to hunt B．hunting C．to protect D．protecting—Do you know why he left so early The show was so wonderful.—_____ for the English test, I guess.A．Study B．Studied C．To study D．StudyingHe tried different ways he could think of _____ English well.A．learns B．to learn C．learning D．learned—Did the book give you all the information you wanted—Yes, but _____ it, I had to read the whole book.A．find B．found C．finding D．to find—Why do you come to school so early —_____ the classroom. I'm on duty (值日) today.A．Clean B．Cleaning C．To clean D．Cleaned_____ other students, Li Wei did a better job in this competition.A．Compare with B．Compared with C．Compare to—Your English has improved a lot. How did you do it—I promised Ms Wang to practice English every day and I _____ my words.A．got lost B．stuck to C．listenedTony is new here. He doesn't know _____ .A．how to get to the bank B．how can he get to the bankC．where is the bank—Look, Linda looks worried.—Yes, She didn't know French, but she was made _____ to sing a French song in two days.A．mention B．learn C．to mention D．to learn—We can use WeChat (微信) to talk with each other.—Really Would you show me _____ itA．what to use B．how to useC．what can I use D．how can I use—Boys and girls, I have something exciting _____ you.—Really What's itA．tell B．telling C．to tell D．toldI got up early this morning _____ my best friend at the train station.A．to meet B．meeting C．met D．meet—Mom, I need a special pen to draw this picture.—OK. Let's go to the supermarket _____ one.A．buy B．buys C．buying D．to buyMr. Li is a kind-hearted man. He does everything he can _____ homeless people. A．helped B．helping C．help D．to help—As a new student, Jack doesn't know _____ in our class.—Let's go and help him.A．what to expect B．when to expect C．how to expect D．who to expectCan you tell me _____ to do nextA．when B．why C．what D．how—Could you tell me _____—Sorry, I have no idea.A．that there is a bank nearby B．what's the shirt made ofC．how to deal with the problem D．how soon he would come back—Could you help me with my English—Yes, of course. I'll do what I can _____ you.A．help B．to help C．helpingAs volunteers, we could do something we can _____ those sick kids. A．encourage B．to encourage C．encouraging—Could you tell me _____ to meet Miss Li—Please fill in this form and call her to meet you.A．how B．where C．when—Excuse me. Could you please tell me _____ my car—Sure. Park it right here.A．how to stop B．where to park C．where to stop D．when to parkEddie is hungry and too weak _____ any further.A．walk B．to walk C．walked D．walkingAs a new student, Jack doesn't know _____ in our class.A．what to expect B．when to expect C．how to expect D．who to expect_____ from the moon, our earth, with water _____ seven percent of its surface, appears as "blue ball".A．Seen; covered B．Seeing; coveringC．Seen; covering D．To see; to cover—Mum, the flowers are so beautiful. Let's pick some.—Oh, dear. We shouldn't pick flowers in the park. Just leave them _____.A．to grow B．growing C．grow D．grownCan you find a new way _____ out this Maths problemA．to work B．worked C．working D．to workingMy sister is a book lover and she enjoys _____ very much.A．read B．reading C．to read D．to readingLucy has few close friends, so she really doesn't know _____ about her problems. A．who to speak B．who to talk withC．who to say D．what to talk_____ water is easy to _____.A．Drinking polluted; get ill B．To drink pollution; get illC．To drink polluted; make ill D．Drinking pollution; make ill_____ is a great way _____ English.A．Note; to learn B．To note; learnC．Noting; learn D．Noting; to learn从下面各题所给选项中，选择最佳选项。

2023新考案一轮复习第八章专项突破6电场中的力电综合问题精炼一、多选题1.如图甲所示，一绝缘的圆环上均匀分布着正电荷，一光滑细杆过圆心且垂直于圆环平面，杆上套有带正电的小球。

尸0时刻把小球从。

点由静止释放后，小球沿细杆运动经过仄C两点，小球运动的Lf图像如图乙所示。

下列判断正确的是（）A.小球从。

点运动到点的过程中电势能增大B.圆环在圆心处产生的电场强度为0C.。

点的电场强度大于b点的电场强度D. a、Z?两点电势差4,小于氏C,两点电势差Ubr二、单选题2.如图所示，在绝缘水平面上方存在着足够大的水平向右的匀强电场，带正电的小金属块以一定初速度从A点开始沿水平面向左做直线运动，经L长度到达2B点，速度变为零.此过程中，金属块损失的动能有M转化为电势能.金属块继续运动到某点C （图中未标出）时的动能和A点时的动能相同，则金属块从A 开始运动到C整个过程中经过的总路程为（）A. 1.5LB.2LC.3LD.4L三、多选题3.在电场方向水平向右的匀强电场中，一带电小球从A点竖直向上抛出，其运动的轨迹如图所示，小球运动的轨迹上A、8两点在同一水平线上，M为轨迹的最高点，小球抛出时的动能为8 J,在M点的动能为6 J,不计空气阻力，则下列判断正确的是（）A.小球水平位移汨与尼的比值为1 ： 3B.小球水平位移汨与电的比值为1 ： 4C.小球落到B点时的动能为32 JD,小球落到8点时的动能为14 J四、单选题4.如图所示，一半径为R的绝缘圆形轨道竖直放置，圆轨道最低点与一条水平轨道相连，轨道都是光滑的。

轨道所在空间存在水平向右的匀强电场。

从水平轨道上的A点由静止释放一质量为的带正电的小球，已知小球受到的电场力3大小等于小球重力的4倍。

为使小球刚好在圆轨道内做圆周运动，则释放点A 距圆轨道最低点B的距离S为（）五、多选题5.如图所示，一平行板电容器的电容为C,带有等量异种电荷的两极板A、B倾斜放置，质量为m带电荷量为-q的油滴，从极板A上的小孔P以初速度V。

2024年中考英语一轮复习语法知识专项突破突破17 主谓一致(there be)【知识突破】主谓一致主谓一致包括语法一致、意义一致和就近原则。

语法一致，即用作主语的名词中心词和谓语动词在单、复数形式上一致。

意义一致，即主语和谓语的一致关系取决于主语的单、复数意义。

就近原则，即谓语动词的单复形式取决于最靠近它的词语。

一、语法一致原则主语采用单数形式时，谓语动词也要采用单数形式；主语采用复数形式时，谓语动词也要采用复数形式。

1．当and连接两个或多个名词，或both，．and．连接两个名词作主语时，谓语动词用复数形式。

Tom and Mike are good friends．汤姆和麦克是好朋友。

2．不定代词either，neither，anybody，anyone，anything，someone, somebody, something, everyone, everybody．nobody, no one，nothing等作主语时，谓语动词要用单数形式。

Everyone is waiting for the coming sports meeting．每个人都等待着即将到来的运动会。

3．由each, each…and each…,every, every．．．and every…，one of．．．等作主语时，谓语动词用单数形式。

Each boy and each girl was given a flower．每个男生女生都领了一朵花。

4．主语后接有with, along with．together with，as well as，no less than, more than, including, besides, like, except, but等词或短语时，谓语动词的单复数形式由主语的单复数形式决定。

Mr．White with two friends is leaving for Beijing．怀特先生和两个朋友将动身去北京。

专项突破二元素及其化合物综合题的突破方法类型一信息提供型元素及其化合物综合题此类题目往往起点高、落点低,考查的是对信息的获取与问题解决能力,解题的关键是理解新信息。

当遇到这一类题目时,第一步是读题,陌生度较高的信息应逐字逐句阅读,挖掘关键字,排除定式思维的影响;第二步是联想,在读题的基础上结合题目的问题联想和分析考查的知识模块,提取出已学的相关化学知识;第三步是解题,按要求填好相应的问题答案。

典例1工业上氰化物的用途广泛,在电镀、油漆、燃料、橡胶等行业都会用到。

(1)氢氰酸(HCN)是一种酸性很弱的酸,其中碳元素的化合价为,氢氰酸分子的结构式为。

(2)氰化钠(NaCN)溶液显强碱性,原因是(用离子方程式表示)。

已知Na2CO3溶液能和HCN反应:Na2CO3+HCN NaHCO3+NaCN,则向NaCN溶液中通入少量CO2时反应的离子方程式为。

(3)双氧水可消除氰化物(如NaCN)污染:NaCN+H2O2+H2O A+NH3↑,则生成物A的化学式为,H2O2常被称为“绿色氧化剂”的理由是。

(4)在氯氧化法处理含CN的废水过程中,液氯在碱性条件下可以将氰化物氧化成氰酸盐(其毒性仅为氰化物的千分之一),氰酸盐进一步被氧化为无毒物质。

某厂废水中含KCN,其浓度为650mg·L1。

现用氯氧化法处理,发生如下反应:KCN+2KOH+Cl2KOCN+2KCl+H2O,投入过量液氯,可将氰酸盐进一步氧化为氮气:2KOCN+4KOH+3Cl22CO2+N2+6KCl+2H2O。

若处理上述废水20L,使KCN完全转化为无毒物质,至少需液氯g。

答案(1)+2(2)CN+H2O HCN+OH CN+H2O+CO2HC O3-+HCN(3)NaHCO3还原产物H2O没有污染解析(1)根据价键规律,可知C、N之间以三键结合,H、C之间以单键结合。

H显+1价,N的非金属性比C强,N显3价,则C显+2价。

(2)NaCN是强碱弱酸盐,CN水解使溶液显碱性。

2023新考案一轮复习第三章专项突破2牛顿运动定律的四类问题(wd无答案)一、多选题(★★★) 1. 水平面上有一质量M=51kg的小车D，其上有一轻质定滑轮C。

通过绳在滑轮两侧分别连有质量m1=5kg和m2=4kg的物体A和B，其中物体A在小车的水平台面上，物体B被绳悬挂。

各接触面和滑轮轴均光滑。

系统处于静止时，各物体的位置关系如图所示。

为保证物体A与小车之间不出现相对滑动，现对小车施加一水平向右的恒力F，使各物体保持相对静止向右做匀加速直线运动，重力加速度g=10m/s 2，则（）A．绳的拉力大小为NB．绳与竖直方向夹角为53°C．水平恒力F大小为480ND．系统的加速度大小为8m/s2(★★★) 2. 我国高铁技术处于世界领先水平，和谐号动车组是由动车和拖车编组而成，提供动力的车厢叫动车，不提供动力的车厢叫拖车。

假设动车组各车厢质量均相等，动车的额定功率都相同，动车组在水平直轨道上运行过程中阻力与车重成正比。

某列动车组由8节车厢组成，其中第1、5节车厢为动车，其余为拖车，则该动车组（）A．启动时乘客受到车厢作用力的方向与车运动的方向相反B．做匀加速运动时，第5、6节与第6、7节车厢间的作用力之比为3：2C．与改为4节动车带4节拖车的动车组最大速度之比为1：2D．与改为4节动车带4节拖车的动车组最大速度之比为1：4二、解答题(★★★) 3. 如图所示，物体甲与物体丙通过不可伸长的轻绳跨过光滑的轻质定滑轮连接，物体丙离地面的高度为H。

物体甲置于物体乙的最左端，甲与乙之间的动摩擦因数为μ（μ<1）。

桌面光滑，物体乙离定滑轮足够远。

开始时控制物体甲和乙，使三个物体均处于静止状态。

现撤去控制，物体丙从静止开始下落，直至落地，此过程中物体甲与乙始终接触。

已知物体甲、乙、丙的质量分别为m、2 m、3 m，重力加速度为g。

求：（1）撤去控制前，轻绳对滑轮作用力的大小；（2）撤去控制后，物体丙下落过程中，甲物体受到的拉力。

2023年中考英语一轮复习语法知识专项突破-情态动词一、选择题1.—Who took the book away?—It _____ be Jack. Nobody else entered the room except him.A．could B．can't C．must D．might2.Be careful on the stairs, or you _____ fall.A．can B．must C．need D．might3.—How nice the building is! What is it for?—It _____ a hotel. But I'm not sure.A．must be B．have to be C．may be D．can be4.These pears are too big. You should _____.A．cut it up B．cut up it C．cut up them D．cut them up5.The river is too deep. You _____ swim in it.A．could't B．mustn't C．needn't D．don't6.Could you please _____ off the radio? I'm listening to it.A．turn B．not turn C．to turn D．not to turn7.I _____ find my Chinese textbook. Where is it?A．can't B．am not C．can D．don't8.—Helen, who _____ fix up the computer in our class?—I think Jeff can.A．should B．would C．must D．can9.We should keep quiet in the cinema. We speak loudly.A．can B．must C．needn't D．mustn't10.The world _____ not be ready for me, but ready or not, I am here now.A．can B．may C．should D．must 11.—Who is the boy over there? Is it Jack?—It _____ be him. He is much taller.A．can't B．mustn't C．shouldn't D．won't12.—_____ you come to my party on Sunday?—Sorry, I'm not available. I _____ study for the math test.A．Can; must B．Must; can C．Need; may D．May; can13.—Are you going to the cinema tonight?—I don't know. I _____ go or I _____ stay at home.A．will; will B．must; must C．should; should D．might; might14.Please speak loudly, or students at the back _____ hear you.A．can't B．needn't C．shouldn't15.—I've told you many times you _____ put the scissors there. The kids may play with them.—Sorry, I won't do it again.A．wouldn't B．mustn't C．couldn't D．needn't16.—When will you come back from Shanghai?—We _____ come back the day after tomorrow.A．may B．maybe C．may be17.If you feel angry, you should _____ a deep breath.A．take B．taking C．to take18.— Listen! I think it _____ be Susan singing in the office.—No. It _____ be her. She left for London two days ago.A．must; can't B．may; mustn't C．must; mustn't19.Look at the "No Parking"sign. You _____ park your car here.A．should B．needn't C．mustn't20.His sister _____ speak any English two years ago, but now she _____ talk to Americans in English.A．couldn't; could B．couldn't; can C．can't; could D．can't; can21.Five hours' walk, and you _____ be tired. Now sit down and have a rest.A．can B．should C．must D．will22.I _____ ride a bike when I was six years old.A．could B．would C．should D．can23.We _____ respect the disabled and be kind to them.A．dare to B．ought to C．have to24.—Must we clean the classroom now?—No, you _____. You can do it after school.A．mustn't B．shouldn't C．needn't25.—Do I have to finish my homework before supper?—Yes, you _____, or you can't go to the theater with us.A．can B．must C．may26.He _____ like coffee. I see him drink a cup sometimes.A．can't B．must C．may D．mustn't27.—Look! Fireworks!—Wow! How beautiful! But people living in this area can't _____ fireworks.A．let off B．get off C．let out D．get out28.—What will the weather be like this afternoon, Anna?—It _____ be fine. But who knows? It's always changing quickly.A．must B．will C．may D．need29.—What's your plan for the winter holiday?—I _____ go back to my hometown with my parents. They haven't decided yet.A．must B．may C．need D．should30.Teachers should _____ their students to practice _____ English as much as possible.A．let; speaking B．encourage; speakingC．make; speak D．let; speak31.John _____ come to see us tonight, but he isn't very sure yet.A．may B．can C．has to D．must32.You _____ be afraid of that dog. Look. It's a toy.A．needn't B．can't C．mustn't D．don't 33.—Jeff, you _____ swim alone in the river. It's dangerous.—Sorry, I won't.A．can B．must C．should D．shouldn't34.—Must I get there on time?—No, you _____.A．can't B．mustn't C．needn't D．couldn't35.All the drivers _____ reduce speed when driving near the zebra crossing.A．may B．can C．must D．need36.—Tom, please tell Jack the good news.—I _____. His father has told him about it already.A．don't have to B．have to C．must D．mustn't37.The man can't _____ stories, but he can _____.A．tells; sings B．say; dance C．tell; swim38.Peter can't go to the party because he _____ look after his sister at home.A．can B．has to C．would like39.The girl was _____ scared that she _____ say a word.A．so; can't B．too; couldn't C．so; couldn't40.—_____?—I would like some ice cream, please.A．What kind do you want B．What size would you likeC．May I take your order D．Is there any ice cream41.—Where are you going to study?—I'm not sure. I _____ study in Beijing.A．might B．should C．must D．can42.You _____ drive so fast, for we have enough time to arrive at the station.A．can't B．mustn't C．needn't D．shouldn't43.A country has dreams. We teenagers _____ also have dreams. With dreams and hard work, anythingamazing can be created.A．may B．must C．should D．can44.—Can you come to my party on Thursday, Jenny?—Sorry, I can't. I _____ finish my homework first.A．may B．will C．have to D．can45.It is raining now, Jim can't _____ on the playground.A．do morning exercises B．does morning exercisesC．do morning exercise D．does morning exercise46.—Hurry up, Jeff! Let's cross the road as fast as possible.—No, you _____. Don't you see the light is still red?A．couldn't B．wouldn't C．mustn't D．needn't47.—Molly, can you swim?—Yes, I _____. I do it really well!A．can B．can't C．need D．must48.—Must I make a phone call to him now?—No, you _____. You _____ write an email.A．mustn't; may B．may not; mustC．shouldn't; must D．don't have to; may49.—I can't stop smoking, doctor.—For your health, I'm afraid you _____.A．may B．can C．have to D．need50.—Must I practice soccer every day?—No, you _____.A．must B．mustn't C．needn't D．can't答案一、选择题（共50题）1. 【答案】C【解析】——谁把书拿走了？——一定是杰克，除了他没人进房间。

高考题型专项突破有机综合推断(2022·全国乙卷节选)左旋米那普伦是治疗成人重度抑郁症的药物之一，以下是其盐酸盐(化合物K)的一种合成路线(部分反应条件已简化，忽略立体化学)：已知：化合物F不能与饱和碳酸氢钠溶液反应产生二氧化碳。

回答下列问题：(1)C的结构简式为______________。

(2)写出由E生成F反应的化学方程式______________________________。

(3)E中含氧官能团的名称为______________。

(4)由G生成H的反应类型为____________。

(5)I是一种有机物形成的盐，结构简式为__________________。

[解题思路分析]A发生氧化反应生成B，B与C在NaNH2、甲苯条件下反应生成D，对比B、D的结构简式，结合C的分子式C8H7N，可推知C的结构简式为；D与30% Na2CO3反应后再酸化生成E，E在浓硫酸、甲苯条件下反应生成F，F不能与饱和NaHCO3溶液反应产生CO2，说明不含羧基，再结合E的结构和F的分子式C11H10O2，推出E发生分子内酯化生成F，则F的结构简式为；F与(C2H5)2NH在AlCl3、甲苯条件下反应生成G，G与SOCl2在甲苯条件下反应生成H，H的分子式为C15H20ClNO，H与I反应生成J，结合G、J的结构简式知，H的结构简式为；I的分子式为C8H4KNO2，I是一种有机物形成的盐，则I的结构简式为。

[答案](1)(2)浓硫酸甲苯＋H2O(3)羟基、羧基(4)取代反应(5)1．通过物理特征突破有机化合物中各类代表物的状态、气味、溶解性、密度、熔点、沸点等往往各有特点，解题时可考虑通过物理特征找到题眼。

2．根据反应物、产物分子式特征推断有机物结构及反应类型分析反应物、产物的分子式特征，根据其差异，联想已有有机化学知识，猜想可能的有机反应类型，由此确定反应物、产物的结构特点，结合框图中的其他物质，确定具体的结构。

2023年中考英语一轮复习语法知识专项突破-条件状语从句一、选择题1.—Won't you go to the dinner tonight?—I will if my cousin _____.A．will go B．go C．goes2.—Won't you go to the dinner tonight?—I will if my cousin _____.A．will go B．go C．goes3.Stop smoking, Joe! You _____ yourself if you keep on doing it like that!A．will kill B．have killed C．kill4.If our government _____ pay attention to the safety of food, our health _____ in danger.A．doesn't; will be B．won't; isC．isn't; will be5.Stop smoking, Dick! You _____ yourself if you keep on doing it like that!A．kill B．will kill C．kills D．killed6.If you _____ careful, you will fall off the table.A．don't be B．will not be C．aren't D．are7.从下面各题所给选项中，选择最佳选项。

—Please ask your father if he _____ time to talk with me tomorrow.—OK. I will let him call you if he _____ time.A．will have; will have B．has; will haveC．will have; has D．has; has8.单项选择，从下面各题所给的A、B、C、D四个选项中，选择可以填入空白处的最佳选项We won't go for a picnic if it _____ this Sunday.A．rained B．rains C．will rain D．is raining9.单项选择If we _____ take environmental problems seriously, the earth _____ worse and worse.A．don't; will be B．won't; isn'tC．won't; is D．don't; won't be10.单项选择The children will climb the hill if it _____ tomorrow.A．won't rain B．didn't rain C．isn't raining D．doesn't rain11.Shall we go to visit the Oriental Pearl TV Tower if it _____ tomorrow?A．will rain B．won't rain C．rains D．doesn't rain12.The air quality will be improved in Shanghai if more people _____ public transport.A．will take B．took C．take D．are taking13.The football team _____ warmly welcomed if it _____ to Shanghai.A．will be, comes B．is, comesC．is, will come D．will be, will come14.If you give a gift to a friend in the west, he or she _____ it in front of you.A．will open B．opens C．opened D．should open15.The restaurant _____ many customers if they don't improve the service.A．won't have B．don't have C．wouldn't have D．didn't have16.根据语境，选出最佳选项。

2021年九年级数学中考一轮复习专题突破训练（选择题专项）：轴对称之线段最短问题（一）1．在平面直角坐标系中，长为2的线段CD（点D在点C右侧）在x轴上移动，A（0，2），B（0，4），连接AC，BD，则AC+BD的最小值为（）A．2B．2C．6D．32．如图，动点M在边长为2的正方形ABCD内，且AM⊥BM，P是CD边上的一个动点，E是AD边的中点，则线段PE+PM的最小值为（）A．﹣1B．+1C．D．+13．如图，正方形ABCD的边长为4，点E在AB上且BE＝1，F为对角线AC上一动点，则△BFE周长的最小值为（）A．5B．6C．7D．84．如图，在Rt△AOB中，∠AOB＝90°，OA＝3，OB＝4，以点O为圆心，2为半径的圆与OB交于点C，过点C作CD⊥OB交AB于点D，点P是边OA上的动点．当PC+PD 最小时，OP的长为（）A．B．C．1D．5．如图，在矩形ABCD中，AB＝6，AD＝3，动点P满足S△P AB ＝S矩形ABCD，则点P到A、B两点距离之和P A+PB的最小值为（）A．2B．2C．3D．6．如图，在Rt△ABO中，∠OBA＝90°，A（4，4），点C在边AB上，且＝，点D 为OB的中点，点P为边OA上的动点，当点P在OA上移动时，使四边形PDBC周长最小的点P的坐标为（）A．（2，2）B．（，）C．（，）D．（3，3）7．如图，点P是边长为1的菱形ABCD对角线AC上的一个动点，点M，N分别是AB，BC边上的中点，则MP+PN的最小值是（）A．B．1C．D．28．如图，在锐角三角形ABC中，BC＝4，∠ABC＝60°，BD平分∠ABC，交AC于点D，M，N分别是BD，BC上的动点，则CM+MN的最小值是（）A．B．2C．2D．49．如图，在菱形ABCD中，AC＝6，BD＝6，E是BC边的中点，P，M分别是AC，AB 上的动点，连接PE，PM，则PE+PM的最小值是（）A．6B．3C．2D．4.510．如图，∠AOB＝60°，点P是∠AOB内的定点且OP＝，若点M、N分别是射线OA、OB上异于点O的动点，则△PMN周长的最小值是（）A．B．C．6D．311．如图，在正方形ABCD中，E，F分别为AD，BC的中点，P为对角线BD上的一个动点，则下列线段的长等于AP+EP最小值的是（）A．AB B．DE C．BD D．AF12．如图，在正方形ABCD中，AB＝9，点E在CD边上，且DE＝2CE，点P是对角线AC 上的一个动点，则PE+PD的最小值是（）A ．3B ．10C ．9D ．913．如图，在Rt △ABC 中，∠ACB ＝90°，AC ＝6，BC ＝8，AD 平分∠CAB 交BC 于D 点，E ，F 分别是AD ，AC 上的动点，则CE +EF 的最小值为（ ）A ．B ．C ．D ．614．如图，在△ABC 中，AB ＝AC ，AD 、CE 是△ABC 的两条中线，P 是AD 上一个动点，则下列线段的长度等于BP +EP 最小值的是（ ）A ．BCB ．CEC ．AD D ．AC15．如图，在矩形ABCD 中，AB ＝5，AD ＝3，动点P 满足S △P AB ＝S 矩形ABCD ，则点P 到A 、B 两点距离之和P A +PB 的最小值为（ ）A ．B ．C ．5D ．16．如图，在△ABC 中，AC ＝BC ，∠ACB ＝90°，点D 在BC 上，BD ＝3，DC ＝1，点P 是AB 上的动点，则PC +PD 的最小值为（ ）A．4B．5C．6D．717．如图，在矩形ABCD中，AD＝4，∠DAC＝30°，点P、E分别在AC、AD上，则PE+PD 的最小值是（）A．2B．2C．4D．18．如图，矩形ABCD中，AB＝10，BC＝5，点E，F，G，H分别在矩形ABCD各边上，且AE＝CG，BF＝DH，则四边形EFGH周长的最小值为（）A．5B．10C．10D．1519．如图，矩形ABOC的顶点A的坐标为（﹣4，5），D是OB的中点，E是OC上的一点，当△ADE的周长最小时，点E的坐标是（）A．（0，）B．（0，）C．（0，2）D．（0，）20．如图，在Rt△ABC中，∠C＝90°，AC＝3，BC＝4，D、E分别是AB、BC边上的动点，则AE+DE的最小值为（）A．B．C．5D．参考答案1．解：设C（m，0），∵CD＝2，∴D（m+2，0），∵A（0，2），B（0，4），∴AC+BD＝+，∴要求AC+BD的最小值，相当于在x轴上找一点P（n，0），使得点P到M（0，2）和N（﹣2，4）的距离和最小，如图1中，作点M关于x轴的对称点Q，连接NQ交x轴于P′，连接MP′，此时P′M+P′N的值最小，∵N（﹣2，4），Q（0，﹣2）P′M+P′N的最小值＝P′N+P′Q＝NQ＝＝2，∴AC+BD的最小值为2．故选：B．2．解：作点E关于DC的对称点E'，设AB的中点为点O，连接OE'，交DC于点P，连接PE，如图：∵动点M在边长为2的正方形ABCD内，且AM⊥BM，∴点M在以AB为直径的圆上，OM＝AB＝1，∵正方形ABCD的边长为2，∴AD＝AB＝2，∠DAB＝90°，∵E是AD的中点，∴DE＝AD＝×2＝1，∵点E与点E'关于DC对称，∴DE'＝DE＝1，PE＝PE'，∴AE'＝AD+DE'＝2+1＝3，在Rt△AOE'中，OE'＝＝＝，∴线段PE+PM的最小值为：PE+PM＝PE'+PM＝ME'＝OE'﹣OM＝﹣1．故选：A．3．解：如图，连接ED交AC于一点F，连接BF，∵四边形ABCD是正方形，∴点B与点D关于AC对称，∴BF＝DF，∴△BFE的周长＝BF+EF+BE＝DE+BE，此时△BEF的周长最小，∵正方形ABCD的边长为4，∴AD＝AB＝4，∠DAB＝90°，∵点E在AB上且BE＝1，∴AE＝3，∴DE＝，∴△BFE的周长＝5+1＝6，故选：B．4．解：如图，延长CO交⊙O于点E，连接ED，交AO于点P，此时PC+PD的值最小．∵CD⊥OB，∴∠DCB＝90°，又∠AOB＝90°，∴∠DCB＝∠AOB，∴CD∥AO∴∵OC＝2，OB＝4，∴BC＝2，∴，解得，CD＝；∵CD∥AO，∴＝，即＝，解得，PO＝故选：B．5．解：设△ABP 中AB 边上的高是h ．∵S △P AB ＝S 矩形ABCD ，∴AB •h ＝AB •AD ，∴h ＝AD ＝2，∴动点P 在与AB 平行且与AB 的距离是2的直线l 上，如图，作A 关于直线l 的对称点E ，连接AE ，BE ，则BE 的长就是所求的最短距离． 在Rt △ABE 中，∵AB ＝6，AE ＝2+2＝4，∴BE ＝＝＝2，即P A +PB 的最小值为2．故选：A ．6．解：∵在Rt △ABO 中，∠OBA ＝90°，A （4，4），∴AB ＝OB ＝4，∠AOB ＝45°，∵＝，点D 为OB 的中点， ∴BC ＝3，OD ＝BD ＝2，∴D （2，0），C （4，3），作D 关于直线OA 的对称点E ，连接EC 交OA 于P ，则此时，四边形PDBC 周长最小，E （0，2），∵直线OA的解析式为y＝x，设直线EC的解析式为y＝kx+b，∴，解得：，∴直线EC的解析式为y＝x+2，解得，，∴P（，），故选：C．7．解：如图，作点M关于AC的对称点M′，连接M′N交AC于P，此时MP+NP有最小值，最小值为M′N的长．∵菱形ABCD关于AC对称，M是AB边上的中点，∴M′是AD的中点，又∵N是BC边上的中点，∴AM′∥BN，AM′＝BN，∴四边形ABNM′是平行四边形，∴M′N＝AB＝1，∴MP+NP＝M′N＝1，即MP+NP的最小值为1，故选：B．8．解：如图，在BA上截取BE＝BN，因为∠ABC的平分线交AC于点D，所以∠EBM＝∠NBM，在△BME与△BMN中，所以△BME≌△BMN（SAS），所以ME＝MN．所以CM+MN＝CM+ME≥CE．因为CM+MN有最小值．当CE是点C到直线AB的距离时，即C到直线AB的垂线段时，CE取最小值为：4×sin60°＝．故选：C．9．解：如图，作点E关于AC的对称点E′，过点E′作E′M⊥AB于点M，交AC于点P，则点P、M即为使PE+PM取得最小值，其PE+PM＝PE′+PM＝E′M，∵四边形ABCD是菱形，∴点E′在CD上，∵AC＝6，BD＝6，∴AB＝＝3，＝AC•BD＝AB•E′M得×6×6＝3•E′M，由S菱形ABCD解得：E′M＝2，即PE+PM的最小值是2，故选：C．10．解：作P点分别关于OA、OB的对称点C、D，连接CD分别交OA、OB于M、N，如图，则MP＝MC，NP＝ND，OP＝OD＝OC＝，∠BOP＝∠BOD，∠AOP＝∠AOC，∴PN+PM+MN＝ND+MN+MC＝DC，∠COD＝∠BOP+∠BOD+∠AOP+∠AOC＝2∠AOB ＝120°，∴此时△PMN周长最小，作OH⊥CD于H，则CH＝DH，∵∠OCH＝30°，∴OH＝OC＝，CH＝OH＝，∴CD＝2CH＝3．故选：D．11．解：如图，连接CP，由AD＝CD，∠ADP＝∠CDP＝45°，DP＝DP，可得△ADP≌△CDP，∴AP＝CP，∴AP+PE＝CP+PE，∴当点E，P，C在同一直线上时，AP+PE的最小值为CE长，此时，由AB＝CD，∠ABF＝∠CDE，BF＝DE，可得△ABF≌△CDE，∴AF＝CE，∴AP+EP最小值等于线段AF的长，故选：D．12．解：如图，连接BE，设BE与AC交于点P′，∵四边形ABCD是正方形，∴点B与D关于AC对称，∴P′D＝P′B，∴P′D+P′E＝P′B+P′E＝BE最小．即P在AC与BE的交点上时，PD+PE最小，为BE的长度．∵直角△CBE中，∠BCE＝90°，BC＝9，CE＝CD＝3，∴BE＝＝3．故选：A．13．解：如图所示：在AB上取点F′，使AF′＝AF，过点C作CH⊥AB，垂足为H．在Rt△ABC中，依据勾股定理可知BA＝10．CH＝＝，∵EF+CE＝EF′+EC，∴当C、E、F′共线，且点F′与H重合时，FE+EC的值最小，最小值为故选：C．14．解：如图连接PC，∵AB＝AC，BD＝CD，∴AD⊥BC，∴PB＝PC，∴PB+PE＝PC+PE，∵PE+PC≥CE，∴P、C、E共线时，PB+PE的值最小，最小值为CE的长度，故选：B．15．解：设△ABP中AB边上的高是h．∵S △P AB ＝S 矩形ABCD ，∴AB •h ＝AB •AD ，∴h ＝AD ＝2，∴动点P 在与AB 平行且与AB 的距离是2的直线l 上，如图，作A 关于直线l 的对称点E ，连接AE ，连接BE ，则BE 的长就是所求的最短距离．在Rt △ABE 中，∵AB ＝5，AE ＝2+2＝4，∴BE ＝＝＝，即P A +PB 的最小值为．故选：D ．16．解：过点C 作CO ⊥AB 于O ，延长CO 到C ′，使OC ′＝OC ，连接DC ′，交AB 于P ，连接CP ．此时DP +CP ＝DP +PC ′＝DC ′的值最小．∵BD ＝3，DC ＝1∴BC ＝4，∴BD ＝3，连接BC ′，由对称性可知∠C ′BA ＝∠CBA ＝45°，∴∠CBC ′＝90°，∴BC′⊥BC，∠BCC′＝∠BC′C＝45°，∴BC＝BC′＝4，根据勾股定理可得DC′＝＝＝5．故选：B．17．解：作D关于直线AC的对称点D′，过D′作D′E⊥AD于E，则D′E＝PE+PD的最小值，∵四边形ABCD是矩形，∴∠ADC＝90°，∵AD＝4，∠DAC＝30°，∵DD′⊥AC，∴∠CDD′＝30°，∴∠ADD′＝60°，∴DD′＝4，∴D′E＝2，故选：B．18．解：作点E关于BC的对称点E′，连接E′G交BC于点F，此时四边形EFGH周长取最小值，过点G作GG′⊥AB于点G′，如图所示．∵AE＝CG，BE＝BE′，∴E′G′＝AB＝10，∵GG′＝AD＝5，∴E′G＝＝5，＝2E′G＝10．∴C四边形EFGH故选：B．19．解：作A关于y轴的对称点A′，连接A′D交y轴于E，则此时，△ADE的周长最小，∵四边形ABOC是矩形，∴AC∥OB，AC＝OB，∵A的坐标为（﹣4，5），∴A′（4，5），B（﹣4，0），∵D是OB的中点，∴D（﹣2，0），设直线DA′的解析式为y＝kx+b，∴，∴，∴直线DA′的解析式为y＝x+，当x＝0时，y＝，∴E（0，），故选：B．20．解：如图，作点A关于BC的对称点A′，过点A′作A′D⊥AB交BC、AB分别于点E、D，则A′D的长度即为AE+DE的最小值，AA′＝2AC＝2×3＝6，∵∠ACB＝90°，BC＝4，AC＝3，∴AB＝，∴sin∠BAC＝，∴A′D＝AA′•sin∠BAC＝6×＝，即AE+DE的最小值是．故选：B．。