【考试必备】2018-2019年最新广东华南师范大学附属中学初升高自主招生化学模拟精品试卷【含解析】【4套】

2019年广东广州中考华南师大附中高中招生问答华南师大附中2019年高中招生问答问答目录1.华附今年的招生计划是怎样的？2.华附的“大学先修实验班”培养目标是怎样的？3.今年华附的招生开放日安排在什么时候？有哪些相关内容？4.华附高一新生设不设重点班？5.广州市的初中毕业生报考华附要有怎样的学业水平？6.报考华附应如何填志愿？7．学校住宿条件如何？填报志愿时填写“申请住宿”对录取有没有影响？8．华附高中如何收费？9．华附今年面向全省的创新班如何招生？10．什么样的学生适合报读华附？11．各地市都有创建示范性高中的名校，为什么华附还要办创新班与大学先修实验班？12．有的家长担心孩子入读华附后会有压力，孩子会不会难以承受？13．华附应对新高考综合改革有什么新举措？14.华附今年首次创办海军航空实验班（简称“海航班”），有哪些特点？15.今年广州实施50%指标到校的招生政策，会对考华附有什么影响？16.华附今年面向广州自主招生方案有什么内容？1.华附今年的招生计划是怎样的？高中招收12个班共564人：1.两个奥林匹克特长班共92人（面向全省）；2.两个创新人才实验班共100人（面向深圳、汕头、韶关、河源、梅州、惠州、汕尾、东莞、清远、潮州、揭阳等十一市）3.一个大学先修实验班共60人（面向全省）；4.一个海军航空班50人（面向全省）；5.六个班面向广州市生源共262人（其中包括纳入广州市自主招生30人，编为另一个大学先修实验班）。

2.华附的“大学先修实验班”培养目标是怎样的？华附“大学先修实验班”是经广东省教育厅批准开设的高中拔尖创新人才培养特色班。

该班通过引进大学先修课程与中学课程优化整合，探索中学与大学联合培养拔尖创新人才的模式，为拔尖创新人才成长提速。

该班为公办公费性质，单独编班，特色培养。

该班坚持立德树人，致力于提升学生的人文素养、科学素养、适应能力及创新实践能力等为核心的综合素质，为培养高层次的复合型创新人才奠基，为建设创新型国家培养各行各业领军人才的后备军。

广东省华南师范大学附属中学初三物理自主招生试题一、选择题1．如图所示，物体沿光滑斜面从顶端下滑至底端．在这个过程中，物体的速度v、通过的距离s、机械能E和动能k E随时间t的变化如图所示，则错误的是（）A．B．C．D．2．如图展示了我国古代劳动人民的智慧成果，其中所涉及的物理知识，下列说法中不正确的是（）A．古人冬天在路面上泼水成冰运送巨石，这是通过增大压力来增大摩擦B．日晷利用了光的直线传播C．古代捣谷工具利用了杠杆原理D．司南能够指南北是受地磁场的作用3．水平台面上有两个同规格烧杯,分别盛有甲、乙两种液体将两个完全相同的物体A、B分别放入两杯中静止时如图所示,甲、乙液面刚好相平此时,设A物体受到的浮力为F浮A甲液体对烧杯底部的压强为p甲;B物体受到的浮力为F浮B,乙液体对烧杯底部的压强为p乙,则A．F浮A=F浮B, p甲>p乙B．F浮A=F浮B, p甲<p乙C．F浮A <F浮B, p甲>p乙D．F浮A<F浮B, p甲<p乙4．如图所示的现象，物态变化类型相同的一组是（）① 露珠的形成②壶嘴里冒出的“白气”③正在消融的冰④寒冬，冰冻衣服晾干A．①②B．①③C．②③D．②④5．如图所示，关于生活中的一些物理现象，下列表述不正确的是（）A．鞋底印有花纹是为了增大摩擦B．吸盘“吸”在玻璃上，利用大气压的作用C．人离平面镜越近，所成的像越大D．伞被吹翻是因为伞上表面风速大，压强小6．下列实际应用中，主要从弹性的角度考虑的是（）A．用橡胶作为汽车轮胎的材料B．用液体氢作为发射火箭的燃料C．用塑料作为插座外壳的材料D．用胶木作为制作热水壶手柄的材料7．关于内能，下列说法中正确的是（）A．0℃的物体没有内能B．物体具有内能，也可以同时具有机械能C．具有机械能的物体不一定具有内能D．物体内能大小与温度无关8．下列关于热现象的一些说法，你认为正确的是（）A．破镜不能重圆，说明分子间有斥力B ．在寒冷的北方不用水银温度计测量气温，是因为水银的凝固点较高C ．两物体相互接触时，热量总是从内能大的物体转移到内能小的物体D ．夏天在室内洒水降温，利用了水的比热容较大的性质9．小华在实验操作中连接了如图所示的电路，闭合开关，发现灯泡1L 亮、2L 不亮，调节变阻器滑片P ，灯泡1L 的亮度发生变化，但灯泡2L 始终不亮，出现这一现象的原因可能是（ ）A ．灯泡2L 灯丝断了B ．灯泡2L 的灯座上两接线柱直接相连C ．滑动变阻器接触不良D ．滑动变阻器短路了10．今年入夏，市政部门组织高压冲洗作业车辆，对我市长虹路高架的隔离墩进行冲洗养护，高架上某一水平路段上，一辆高压冲洗作业车装满水后，一边消耗大量的水对隔离墩进行高压冲洗。

2018-2019年最新华师大附中自主招生考试英语模拟精品试卷（第一套）考试时间：120分钟总分：150分第I卷（选择题，共100分）第一节：单项填空（共25小题，每小题1分，满分25分）1. —When did the terrible earthquake in YaNan happen?—It happened ________ the morning of April 20, 2013.A. onB. atC. inD. /2. Our teacher told us ________ too much noise in class.A. to makeB. makeC. not to makeD. not make3. Here is your hat. Don’t forget______ when you __________.A. to put it on, leaveB. to wear it, leaveC. to wear it, will leaveD. putting it on, will leave4. The baby is sleeping. You _____ make so much noise.A. won’tB. mustn’tC. may notD. needn’t5. Since you are _____ trouble, why not ask _________ help?A. in, forB. in, toC. with, forD. with, to6. It’s about___________kilometers from Nanchong to Chengdu.A. two hundredsB. two hundreds ofC. two hundredD. two hundred of7. It is six years since my dear uncle ________China.A. leftB. has leftC. is leftD. had left8. —How long _______ you _______ the bicycle?—About two weeks.A. have, hadB. have, boughtC. did, buyD. have, have9. The Yellow River is not so ________ as the Yangtze River.A. longerB. longC. longestD. a long10. Mrs.Green usually goes shopping with ________ umbrella in ________ summer. A. a；theB. an； /C. the； aD. /；/11. At first, I was not too sure if he could answer the question. However, ____,he worked it out at last with the help of his friend.A. to my angerB. to my surpriseC. in other wordsD. in a word12. —Must I stay here with you?—No, you ______.You may go home, but you _____ go to the net bar (网吧).A. mustn't; needn'tB. needn't; mustn'tC. must; needD. need; must13. I ______ the newspaper while my mother _____TV plays yesterday evening.A. was reading; was watchingB. was reading; watchedC. read; was watchingD. read; would watch14. It's a rule in my class that our classroom ________ before 6：00 p. m.every day.A. be able to cleanB. should be cleaningC. must cleanD. must be cleaned15. —Tom wants to know if you ________ a picnic next Sunday.—Yes. But if it ________， we'll visit the museum instead.A. will have; will rainB. have; rainsC. have; will rainD. will have; rains16.—Would you mind looking after my dog while I'm on holiday?—________.A. Of course notB. Yes. I'd be happy toC. Not at all. I've no timeD. Yes, please17. Many students didn’t realize the importance of study _______they left school.A. whenB. untilC. afterD. unless18. My father _______ to Shanghai. He _______ for over 2 months.A. has been, has leftB. has gone, has goneC. has gone, has been awayD. has been, has gone19. They are your skirts. Please __________.A. put it awayB. put out itC. put them awayD. put them out20. —Please read every sentence carefully. you are, mistakes you’ll make.—Thank you for your advice.A. The more carefully; the fewerB. The more careful; the lessC. The more carefully; the lessD. The more careful; the fewer21. My friend is coming today but he didn’t tell me _______.A. when did the train arriveB. how did the train arriveC. when the train arrivedD. how the train arrived22. I felt it hard to keep up with my classmate s. But whenever Iwant to _______, my teacher always encourages me to work harder.A. go onB. give upC. run awayD. give back23. —________ fine weather it is today!—Let's go for a picnic.A. WhatB. HowC. What aD. How a24. — Mary, you’re going to buy an apartment here, aren’t you?—Yes, but I can’t_______an expensive one.A. spendB. costC. payD. afford25. —Would you like to drink coffee or milk?—_________. Please give me some tea.A. NeitherB. BothC. EitherD. None第二节：完形填空（共20小题，每小题1分，满分20分）(A)Big schoolbags have been a serious problem for students for a long time.Maybe your schoolbag is too __26__ to carry, and it troubles you a lot __27__ you want to find a book out to read. Now an e­textbook will __28__ you.It is said that e­textbooks are going to be __29__ in Chinese middle schools.An e­textbook, in fact, is a small __30__ for students.It is much __31__ than a usual schoolbag and easy to carry. Though it is as small as a book, it can __32__ all the materials (材料) for study.The students can read the text page by page on the __33__， take notes with the pointer (屏写笔). Or even “__34__” their homework to their teachers by sending e­mails. All they have to do is to press a button.Some people say e­textbooks are good, but some say they may be __35__ for the students' eyes. What do you think of it?26.A.light B. heavy C. useful D. comfortable27.A.till B. after C. before D. when28.A.trouble B. prevent C. help D. understanded B. kept C. invented D. lent B. radio C. pen D. computer31.A.heavier B. lighter C. cheaper D. brighter32.A.hold B. build C. discover D. practice33.A.blackboard B. desk C. screen D. card34.A.find out B. hand in C. get back D. give back35.A.helpful B. famous C. good D. bad(B)。

广东省华南师范大学附属中学高一分班考试题化学卷_图文一、选择题1．有一包固体粉末，可能由CaCO3、Na2SO4、KNO3、FeSO4、BaCl2中的一种或几种组成，做实验得以下结果：⑴ 将此固体粉末加到水中，得到白色沉淀，且上层清液为无色；⑵ 该白色沉淀部分溶于稀硝酸，并有无色气体产生。

据此实验，得出的下列判断中正确的是A．粉末中一定含有CaCO3、FeSO4、BaCl2 B．该粉末中一定不含有KNO3、FeSO4C．该粉末的组成中可能含有KNO3 D．该粉末中一定含有Na2SO4、KNO3、BaCl22．除去下列各物质中混有少量杂质，所用试剂正确的是选项物质杂质所用试剂A镁粉铁粉稀硫酸B N2O2灼热的铜网C稀盐酸MgCl2KOH溶液D NaCl Na2SO4Ba(NO3)2溶液A．A B．B C．C D．D3．现有表面被氧化的镁条样品6g,加入到盛有73g质量分数为19%的稀盐酸的烧杯中恰好完全反应，得到0.2g气体。

則原镁条样品中镁元素的质量分数为（ )A．48% B．60% C．76% D．84%4．下列四个图像中，能正确反映对应关系的是A．一定温度下，向一定量水中加入KNO3固体B．加热一定量的高锰酸钾固体C．向一定量的硫酸铜溶液中加入铁粉D．向一定量的MnO2中加入H2O2溶液5．甲、乙两种固体物质（不含结晶水）的溶解度曲线如图所示。

下列说法正确的是A．t1℃时，甲溶液中溶质的质量分数一定等于乙溶液B．降低温度，可使甲的饱和溶液变为不饱和溶液C．t2℃时，分别在100 g水中加入50 g 甲、乙，同时降温至t1℃，甲、乙溶液均为饱和溶液D．将t2℃时甲的饱和溶液降温至t1℃，溶液质量不变6．下列除杂方案中（括号中物质是杂质），正确的是（）A．N2（O 2）：通过红热的木炭 B．烧碱（纯碱）：加适量稀盐酸、蒸发C．Cu（CuO）：加过量的盐酸溶液并过滤 D．NaHCO3（Na2CO3）：高温煅烧7．下列曲线能正确表达对应的反应或过程的是A．向一定量的盐酸中逐滴加水稀释B．某温度下将一定量接近饱和的KNO3溶液恒温蒸发水分C．金属与一定量的稀硫酸反应，由图像可知，金属N比金属M活泼D．将a、b、c三种物质的饱和溶液分别由t1℃升温至t2℃时，所得溶液中溶质质量分数大小关系是：a＞b＞c8．下列图象中，能正确反映其对应变化关系的是（）A．服用胃舒平[主要成分是Al（OH）3]治疗胃酸过多，胃液pH的变化B．向一定质量的稀盐酸和氯化铜的混合溶液中加入氢氧化钠溶液C．将等质量的镁和铁分别投入到盛有足量同种稀硫酸的两个容器中D．浓盐酸敞口放置9．除去下列物质中所含的杂质，选用的试剂（括号内的物质）正确的是：（）A．CaO中混有少量CaCO3（盐酸） B．CO2中混有HCl气体（NaOH溶液）C．Cu(NO3)2溶液中混有AgNO3（铜粉） D．CO2中混有少量CO（氧气）10．中和一定质量的稀硫酸，需用m克氢氧化钠，若改用m克氢氧化钾，反应后溶液的PH 应当是（）A．<7 B．>7 C．=7 D．无法确定11．下列从左到右依次代表ABCD四个图像中，能正确表示对应变化关系的是（）A．向氢氧化钠和碳酸钠的混合溶液中滴加盐酸 B．向一定量稀硫酸中加水稀释C．加热等质量的氯酸钾制取氧气 D．向饱和氢氧化钙溶液中加入CaO12．除去物质中的少量杂质，下列方法不能达到目的的是（）选项物质杂质除去杂质的方法A CaO CaCO3高温充分煅烧B KCl溶液CaCl2通入足量的CO2，过滤C CO2CO通过足量的灼热氧化铜D H2HCl依次通过足量的NaOH溶液和浓硫酸A．A B．B C．C D．D13．除去下列各组物质中的杂质，所用试剂和方法均正确的是物质杂质除杂所用的试剂和方法A CaO CaCO3加入适量的稀盐酸，蒸发B H2HCl依次通过NaOH溶液、浓硫酸C NaOH溶液Ca(OH)2先加入过量的Na2CO3溶液，再过滤D KCl溶液CuCl2加入氢氧化钠溶液至不再产生沉淀，过滤A．A B．B C．C D．D14．实验室有一包含有少量氯化钠杂质的硝酸钾固体，为提纯硝酸钾，设计如下图所示操作，有关分析中正确的是A．操作Ⅰ～Ⅲ分别是加热浓缩、蒸发结晶、过滤B．操作Ⅰ是过滤，将氯化钠固体从溶液中分离除去C．操作Ⅱ是加热浓缩，趁热过滤，除去杂质氯化钠D．操作Ⅲ是过滤，将硝酸钾晶体从溶液中分离出来15．将一定质量的铜锌合金的粉末加入到一定量的硝酸银溶液中充分反应后过滤，向滤渣中滴加少量的稀盐酸，有气泡产生，下列说法正确的是（）A．滤液中的溶质一定含有硝酸铜 B．滤液中溶质一定不含硝酸银C．滤渣中可能含有银和锌 D．滤渣中一定没有铜16．下列表中除杂方法与试剂错误的是（）选项物质杂质除去杂质的方法及试剂A KCl MnO2加入足量水溶解，过滤，蒸发B NaOH Na2CO3加入适量的盐酸，至恰好无气体C CO2CO通过灼热的氧化铜粉末D FeCl2CuCl2加入过量的铁粉，充分反应后过滤A．A B．B C．C D．D17．黄铜渣中约含Zn 7%、ZnO 31%、Cu 50%、CuO 5%，其余为杂质。

2018-2019年最新广东华南师范大学附属中学自主招生语文模拟精品试卷（第一套）（满分：100分考试时间：90分钟）一、语文基础知识（18分，每小题3分）1．下列词语中加点的字，读音全都正确的一组是（）A．连累(lěi) 角(jué)色河间相(xiàng) 冠冕(miǎn)堂皇B专横(hèng) 忖(cǔn)度涮(shuàn) 羊肉妄加揣(chuāi)测C．笑靥(yè) 顷(qīng)刻汗涔(cén)涔休戚(qì)相关D慨叹(kǎi) 俨(yǎn)然刽子手(kuàì) 刎(wěn)颈之交2、下列各项中字形全对的是（）A、橘子州偌大急躁光阴荏苒B、蒙敝犄角慰籍书生意气C、敷衍磕绊笔竿艰难跋涉D、翱翔斑斓屏蔽自怨自艾3、依次填入下列各句横线上的词语，最恰当．．的一项是（）⑴虽然他尽了最大的努力，还是没能住对方凌厉的攻势，痛失奖杯。

⑵那些见利忘义，损人利己的人，不仅为正人君子所，还很可能滑向犯罪的深渊。

⑶我认为，真正的阅读有灵魂的参与，它是一种个人化的精神行为。

A.遏制不耻必需B.遏止不耻必需C.遏制不齿必须D.遏止不齿必须4、下列句中加点的成语，使用恰当的一句是（）A、故宫博物院的珍宝馆里，陈列着各种奇珍异宝、古玩文物，令人应接不暇。

B、任何研究工作都必须从积累资料做起，如果不掌握第一手资料，研究工作只能是空中楼阁．．．．。

C、电影中几处看来是闲笔，实际上却是独树一帜之处。

D、这部精彩的电视剧播出时，几乎万人空巷，人们在家里守着荧屏，街上显得静悄悄的。

5、下列句子中，没有语病的一项是（）A 大学毕业选择工作那年，我瞒着父母和姑姑毅然去了西藏支援边疆教育。

B北京奥运会火炬接力的主题是“和谐之旅”，它向世界表达了中国人民对内致力于构建和谐社会，对外努力建设和平繁荣的美好世界。

C他不仅是社会的一员，同时还是宇宙的一员。

华师一附中2019年自主招生（理科实验班）预录考试化学训练试题总分：50分可能用到的相对原子质量H=1 O=16 S=32 C=12 Cu=64 Mg=24 Ca=40 Fe=56一、选择题。

（每小题只有1个答案共20分）化学部分9、核外电子数相同、所显电性和所带电量也相同的微粒称为等电子等质子体。

下列各组内的两种微粒不属于等电子等质子体的是（）A．Cl- 和HS- B．Na＋和NH4＋C．F－和OH－D．O2－和S2－10、海洋中有丰富的食品、矿产、能源、药物和水产资源等(如下图所示)下列有关说法不．正确的是()A．从能量转换角度来看，框图中的氯碱工业是一个将电能转化为化学能的过程B．过程②中结晶出的MgCl2·6H2O要在HCl氛围中加热脱水制得无水MgCl2C．在过程③⑤中溴元素均被氧化D．过程①中除去粗盐中的SO2－4、Ca2＋、Mg2＋、Fe3＋等杂质，加入的药品顺序为：Na2CO3溶液→NaOH溶液→BaCl2溶液→过滤后加盐酸11、化学是以实验为基础的学科，化学实验设计和操作中必须十分重视师生安全问题和环境保护问题。

下列操作方法不．正确的是()A．制氧气时排水法收集氧气后出现倒吸现象，立即松开试管上的橡皮塞B．在气体发生装置上直接点燃乙炔气体时，必须先检验乙炔气体的纯度C．实验结束后将所有的废液倒入下水道排出实验室，以免污染实验室D．给试管中的液体加热时不停移动试管或加入碎瓷片，以免暴沸伤人12、取4份等质量的KClO3，向其中3份中分别加入少量等质量的KMnO4、MnO2和Mn，分别在某温度下加热至质量不再改变，测定产生氧气的质量。

然后将剩余固体溶于足量水已知m 1＞m 2＞m 3，下列关于此实验的说法一定不正确的是（ ）。

A ．3种物质的加入都有利于KClO 3分解放出氧气B ．残留不溶物的质量关系为w 1＜w 2＜w 3C ． 三种催化效果的比较是 KMnO4＞MnO 2＞MnD ．不加入其他物质时，KClO 3也可以发生分解反应13、右下图中连线两端的物质在通常情况下可以相互反应。

2018-2019年最新华南师范大学附属中学自主招生考试英语模拟精品试卷（第一套）考试时间：120分钟总分：150分第I卷（选择题，共100分）第一节：单项填空（共25小题，每小题1分，满分25分）1. —When did the terrible earthquake in YaNan happen?—It happened ________ the morning of April 20, 2013.A. onB. atC. inD. /2. Our teacher told us ________ too much noise in class.A. to makeB. makeC. not to makeD. not make3. Here is your hat. Don’t forget______ when you __________.A. to put it on, leaveB. to wear it, leaveC. to wear it, will leaveD. putting it on, will leave4. The baby is sleeping. You _____ make so much noise.A. won’tB. mustn’tC. may notD. needn’t5. Since you are _____ trouble, why not ask _________ help?A. in, forB. in, toC. with, forD. with, to6. It’s about___________kilometers from Nanchong to Chengdu.A. two hundredsB. two hundreds ofC. two hundredD. two hundred of7. It is six years since my dear uncle ________China.A. leftB. has leftC. is leftD. had left8. —How long _______ you _______ the bicycle?—About two weeks.A. have, hadB. have, boughtC. did, buyD. have, have9. The Yellow River is not so ________ as the Yangtze River.A. longerB. longC. longestD. a long10. Mrs.Green usually goes shopping with ________ umbrella in ________ summer.A. a；theB. an； /C. the； aD. /；/11. At first, I was not too sure if he could answer the question. However, ____,he worked it out at last with the help of his friend.A. to my angerB. to my surpriseC. in other wordsD. ina word12. —Must I stay here with you?—No, you ______.You may go home, but you _____ go to the net bar (网吧).A. mustn't; needn'tB. needn't; mustn'tC. must; needD. need; must13. I ______ the newspaper while my mother _____TV plays yesterday evening.A. was reading; was watchingB. was reading; watchedC. read; was watchingD. read; would watch14. It's a rule in my class that our classroom ________ before 6：00 p. m.every day.A. be able to cleanB. should be cleaningC. must cleanD. must be cleaned15. —Tom wants to know if you ________ a picnic next Sunday.—Yes. But if it ________， we'll visit the museum instead.A. will have; will rainB. have; rainsC. have; will rainD. will have; rains16.—Would you mind looking after my dog while I'm on holiday?—________.A. Of course notB. Yes. I'd be happy toC. Not at all. I've no timeD. Yes, please17. Many students didn’t realize the importance of study _______they left school.A. whenB. untilC. afterD. unless18. My father _______ to Shanghai. He _______ for over 2 months.A. has been, has leftB. has gone, has goneC. has gone, has been awayD. has been, has gone19. They are your skirts. Please __________.A. put it awayB. put out itC. put them awayD. put them out20. —Please read every sentence carefully. you are,mistakes you’llmake.—Thank you for your advice.A. The more carefully; the fewerB. The more careful; the lessC. The more carefully; the lessD. The more careful; the fewer21. My friend is coming today but he didn’t tell me _______.A. when did the train arriveB. how did the train arriveC. when the train arrivedD. how the train arrived22. I felt it hard to keep up with my classmate s. But whenever I wantto _______, my teacher always encourages me to work harder.A. go onB. give upC. run awayD. give back23. —________ fine weather it is today!—Let's go for a picnic.A. WhatB. HowC. What aD. How a24.— Mary, you’re going to buy an apartment here, aren’t you?—Yes, but I can’t_______an expensive one.A. spendB. costC. payD. afford25. —Would you like to drink coffee or milk?—_________. Please give me some tea.A. NeitherB. BothC. EitherD. None第二节：完形填空（共20小题，每小题1分，满分20分）(A)Big schoolbags have been a serious problem for students for a long time.Maybe your schoolbag is too __26__ to carry, and it troubles you a lot __27__ you want to find a book out to read. Now an e­textbook will __28__ you.It is said that e­textbooks are going to be __29__ in Chinese middle schools.An e­textbook, in fact, is a small __30__ for students.It is much __31__ than a usual schoolbag and easy to carry. Though it is as small as a book, it can __32__ all the materials (材料) for study.The students can read the text page by page on the __33__， take notes with the pointer (屏写笔). Or even “__34__” their homework to their teachers by sending e­mails. All they have to do is to press a button.Some people say e­textbooks are good, but some say they may be __35__ for the students' eyes. What do you think of it?26.A.light B. heavy C. useful D. comfortable27.A.till B. after C. before D. when28.A.trouble B. prevent C. help D. understanded B. kept C. invented D. lent B. radio C. pen D. computer31.A.heavier B. lighter C. cheaper D. brighter32.A.hold B. build C. discover D. practice33.A.blackboard B. desk C. screen D. card34.A.find out B. hand in C. get back D. give back35.A.helpful B. famous C. good D. bad(B)Food is very important. Everyone needs to _36_ _well if he/she wants to have a strong body. Our minds also need a kind of food. This kind of food is__ 37 __.We begin to get a knowledge even when we are very young. Small children are __38__ in everything around them. They learn __39 __while they are watching and listening. When they are getting older, they begin to ___ 40__ story books, science books…anything they like. When they find something new, they have to ask questions and__41___ to find out the answers.What is the best ___42___to get knowledge? If we learn___43___ourselves, we will get the most knowledge, If we are__44___getting answers from others and don’t ask why, we will never learn more and understand___45_.36. A. sleep B. read C. drink D. eat37. A. sport B. exercise C. knowledge D. meat38. A. interested B. interesting C. weak D. meat39. A. everybody B. something C. nothing D. anything40. A. lend B. write C. think D. read41. A. try B. wait C. think D. need42. A. place B. school C. way D. road43. A. in B. always C. to D. by44. A. seldom B. always C. certainly D. sometimes45.A.harder B. much C. well D. better第三节：阅读理解（共25小题，每小题2分，满分50分）AFamous Museums_______ .A. BeijingB. LondonC. New YorkD. The USA47. New York Museum is America’s largest museum on American__________.A. areaB. historyC. collectionsD. buildings48. The Palace Museum. Which is in the center of Beijing, is also called“Forbidden City(紫禁城)” in China. It lies in __________.A.Chang’an StreetB. New Oxford StreetC. BerlingD. Chestnut Street49. According to the form, if you want to see ancient Chinese collections,you can visit ____ at most.A. one museumB. two museumsC. three museumsD. four museums50. Which of the following is TRUE according to the information above?A. Each ticket for the Palace Museum costs the same in the whole year.B. You don’t have to pay for tickets if you visit New York Museum on Monday.C. British Museum lies in Chestnut street, London.D. New York Museum is the largest in the world.BIn recent years, more and more people like to keep pets such as a dog, a cat, a monkey and other animals. But usually people would accept tame(温顺的) and loyal(忠诚的) animals as pets rather than dangerous ones such as a lion，a tiger or a snake.People love pets and take good care of them. The owners usually regard pets as good friends and some even consider them as members of the family. Although they are not human beings(人类), their behavior sometimes is better than human beings, for they are always loyal to their owners. There are always many stories about brave and smart pets. We often hear that a pet dog saved the owner's life or traveled thousands of miles to return home. Such stories often make pets more lovely.Some pets can also be trained to help people with some special work. For example, trained dogs can help the blind to walk and trained dogs and pigs can even help police to find where drugs are easily.But pets are sometimes trouble-makers. Some pets like dogs or snakes may hurt people without any warning. Some people may become ill after being hurt because of the virus carried by the pets. If they are not taken good care of, they will become very dirty and easily get ill. So pets are helpful to us but keeping pets is not an easy job.51. What animals are thought to be dangerous as pets?A. Cats.B. Dogs.C. Snakes.D. Monkeys52. Which of the following statements is TRUE about pets?A. All the pets are considered as family members.B. Pets always behave better than human beings.C. Sometimes some pets can protect their owners.D. Pets like traveling far away from home.53. Why do people train pets according to the passage?A. To make them more clever.B. To make them more lovely.C. To find drugs for the blind.D. To do some special work.54. What can we learn from the last paragraph?A. Pets often hurt strange people.B. Pets can live well with the virus.C. Pets are dirty and dangerous.D. Pets should be looked after well.55. What is the best title for the passage?A. Training Pets.B. Keeping Pets.C. Cleaning Pets.D.Loving Pets.CFrom Feb. 8 to Mar. 1 is our winter holiday. I think everybody did a lot in the holiday. But it seems that I did nothing and it was my most unlucky holiday.I spent a lot of time on my homework. Every morning my mother woke me up early and I had breakfast in a hurry. Then I had to do my homework almost the whole day! I’m not a very slow person but the homework was too heavy!I was also unlucky when playing. During the Spring Festival, I played fireworks but my finger was hurt because I was careless to light the fireworks. I began to fear playing with fireworks from then.I was still unlucky on my friend’s party. On my friend’s birthday, unusually I woke up at 10:50 because my parents went to visit my grandmother early in the morning. The party would start in 10 minutes! So I hurried to my friend’s home without breakfast. I returned very late that day and when I got home, my parents were very angry with me.Another worrying thing was my weight. Last term, I was 46 kg but nowI am 51 kg! I have to consider losing weight!56. How long did the winter holiday last?A. two monthsB. one monthC. 4 weeksD. 22 days57. The writer got up early every day during the holiday because ______.A. he had to finish homeworkB. he had to have breakfastC. he was a very slow personD. his mother was in a hurry58. He hurt his finger because of ________.A. the Spring FestivalB. his carelessnessC. the light of fireworksD. his fear of playing59. Why were the writer’s parents angry with him?A. Because he got up too late.B. Because he missed breakfast.C. Because he was late for the party.D. Because he came back home too late.60. What did the writer want to tell us in the passage?A. He had an unlucky holiday.B. He had too much homework.C. His parents were very strict.D. He planned to lose weight.DSteven Jobs, the designer of Apple Computer, was not clever when he was in school.At that time, he was not a good student and he always made troubles with his schoolmates.When he went into college, he didn't change a lot.Then he dropped out.But he was full of new ideas.After he left college, Steven Jobs worked as a video game designer.He worked there for only se­veral months and then he went to India.He hoped that the trip would give him some new ideas and give him a change in life.Steven Jobs lived on a farm in California for a year after he returned from India.In 1975, he began to make a new type of computer.He designed the Apple Computer with his friend in his garage.He chose the name “Apple” just because it could help him to remember a happy summer he once spent in an apple tree garden.His Apple Computer was such a great success that Steven Jobs soon became famous all over the world.61.Steven Jobs was not a good student in school because he ________.A. never did his lessonsB. was full of new ideasC. always made troubles with his schoolmatesD. dropped out62.Did Steven Jobs finish college?A. Yes, he did.B. No, he didn't.C. No, he didn't go into college.D. We don't know.63.Steven Jobs designed his new computer ______.A. in IndiaB. with his friendC. in a pear tree gardenD. by himself64.Steven Jobs is famous for his ________ all over the world.A. new ideasB. appleC. Apple ComputerD. video games65.From this passage we know ________.A. Steven Jobs didn't finish his studies in the college because he hatedhis schoolmatesB. Steven Jobs liked traveling in India and CaliforniaC. Steven Jobs liked trying new things and making new ideas become trueD. Steven Jobs could only design video gamesEIf you go into the forest with friends, stay with them. If you don't, you may get lost. If you get lost, this is what you should do. Sit down and stay where you are. Don't try to find your friends. Let them find you. You can help them find you by staying in one place. There is another way to help your friends or other people to find you. You can shout or whistle (吹口哨) three times. Stop. Then shout or whistle three times again. Any signal given three times is a call for help.Keep up shouting or whistling. Always three times together. When people hear you, they will know that you are not just making a noise for fun. They will let you know that they have heard your signal. They will give you two shouts or two whistles. When a signal is given twice, it is an answer to a call for help.If you don't think that you will get help before night comes, try to make a little house with branches .Make yourself a bed with leaves and grass.When you need some water, you have to leave your little branch house to look for it. Don't just walk away .Pick off small branches and drop them as you walk in order to go back again easily.66.If you get lost in the forest, you should ________.A. walk around the forest to find your friendsB. stay in one place and give signalsC. climb up a tree and wait for your friends quietlyD. shout as loudly as possible67.Which signal is a call for help?A. Shouting one time as loudly as you can.B. Crying twice.C. Shouting or whistling three times together.D. Whistling everywhere in the forest.68.When you hear two shouts or two whistles, you know that ________.A. someone finds something interestingB. people will come and help youC. someone needs helpD. something terrible will happen69.Before night comes, you should try to make a little house with ________.A. stoneB. earthC. leaves and grassD. branches70.Which of the following is the best title?A. Getting Water in the ForestB. Spending the Night in the ForestC. Surviving (生存) in the ForestD. Calling for Help in the Forest 第四节：补全对话，从方框内7个选项中选择恰当的5个句子完成此对话(共5分)John: Hi, Karl. You were not here, in your class yesterday afternoon. What was wrong?Karl: 71________John: Sorry to hear that.72Karl: Much better. The fever is gone. But I still cough and I feel weak. John: 73Karl: Yes, I have. I went to the doctor’s yesterday afternoon. The doctor gave me some medicine and asked me to stay in bed for a few days. John: 74Karl: Because I’m afraid I’ll miss more lessons and I’ll be left behind. John: Don’t worry. Take care of yourself. 75第Ⅱ卷（非选择题,共50分）一、根据句意及所给提示，补全单词或用单词、固定短语、固定搭配的正确形式填空(10分)76. Many athletes won gold medals in the Olympics, they are our national h_____.77. Tom didn’t finish _____________( write) his test because he ran out of the time.78. The girl is making a model doll ___________ (care).79. The boy felt __________(困倦的) in class because he stayed up late last night.80. So Terrible! The airplane ______________(起飞) five minutes ago.81.I don't think students should be（允许）to bring mobile phones to school.82.I find it useless to spend much time（解释）it to him.83. She prefers keeping silent to（争吵）with others.84. It is important for us to be（有信心的）of doing everything.85. The doctor operated on the patient（成功）yesterday.二、汉译英, 一空一词（共5小题，每小题2分，计10分）86. 他默默地在雨中行走，浑身上下都被淋湿。

华南师大附中2018—2019学年第一学期期中考试初 二 数 学 试 题本试卷分选择题、填空题和解答题三部分，共4页，满分150分，考试用时120分钟。

注意事项：1．答卷前，考生务必用黑色字迹的钢笔或签字笔将自己的班别、姓名、学号填写在答题卷的密封线内。

必须用黑色字迹的钢笔或签字笔作答。

2．选择题每小题有且只有一个正确答案，选出答案后，将答案序号填写到另发的答题卷的相应表格中；填空题和解答题的答案必须写在另发的答题卷各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔（画图除外）和涂改液（涂改带）。

不按以上要求作答的答案无效。

3．考生必须保持答题卷的整洁，考试结束后，只上交答题卷，自行保存好试卷。

一、选择题（每小题3分，共30分）1. 下列各式从左到右的变形正确的是（▲）(A) 11++=x y x y (B) axayx y =(C) x a y a x y 22= (D) x a y a x y )1()1(22++= 2. 一次函数|1|y mx m =+-的图象过点（0，2）且y 随x 的增大而增大，则m =（▲）(A) 1- (B) 3(C) 1(D) 1-或33. 已知函数221+-=x y ，当11≤<-x 时，y 的取值范围是（▲） (A) 2325≤<-y (B) 2523<<y (C) 2523<≤y (D) 2523≤<y4. 已知关于x 的多项式x 2－kx ＋1是一个完全平方式，则一次函数(2)2y k x =-+ 经过的象限是（▲）(A) 第一、二、三象限 (B) 第一、二、四象限(C) 第二、三、四象限(D) 第一、三、四象限5. 如图，A 点坐标为（5，0），直线y = x + b （b ＞0）与y 轴交于点B ，连接AB ，∠α = 75︒，则b 的值为（▲）(A) 3 (B) (C) 4 (D) 6. 若11)1)(1(3-++=-+-x B x A x x x ，则A B A B=-＋（▲） (A) 3 (B) －3 (C) 13(D)－137. 甲、乙两人在直线跑道上同起点、同终点、同方向匀速跑步500米，先到终点的人原地休息．已知甲先出发2秒．在跑步过程中，甲、乙两人的距离y (米)与乙出发的时间t (秒)之间的关系如图所示，给出以下结论： ① a = 8； ② b = 92； ③ c = 123．其中正确的是（▲）(A) ①②③ (B) 仅有①② (C) 仅有①③ (D) 仅有②③8. 若0x y y z z xabc a b c---===<，则点P (ab ，bc ) 不可能在第（▲）象限 (A) 一 (B) 二 (C) 三 (D) 四 9. 如图，在□ABCD 中，AB = 6，AD = 9，∠BAD 的平分线交BC 于点E ，交DC 的延长线于点F ，BG ⊥AE ，垂足为G ，BG =24，则△CEF 的周长为（▲）(A) 8 (B) 9.5 (C) 10 (D) 11.5 10. 下面有四个命题： (1) 一组对边相等且一组对角相等的四边形是平行四边形；(2) 一组对边相等且一条对角线平分另一条对角线的四边形是平行四边形；(3) 一组对角相等，这一组对角的顶点所连接的对角线平分另一条对角线的四边形是平行四边形；(4) 一组对角相等，这一组对角的顶点所连接的对角线被另一条对角线平分的四边形是平行四边形.其中正确命题的个数有（▲）(A) 1个 (B) 2个 (C) 3个 (D) 4个二、填空题（每小题4分，共32分）11. 计算：112---x x x ＝ ▲ .12. 因式分解：22221a b a b --+= ▲ .13. 直线y = k 1x + b 1（k 1 > 0）与y = k 2x + b 2（k 2 < 0）相交于点（－2，0），且两直线与y 轴围城的三角形面积为4，那么b 1－b 2等于 ▲ ．14. 直线b x k y l +=11:与直线x k y l 22:=在同一平面直角坐标系中的图象相交，且交点的横坐标为1-，当0b >时，关于x 的不等式21k x k x b >+的解集为 ▲ ．15. 设()2f x x mx n =++（m 、n 为整数）既是多项式42+625x x +的因式，又是多项式4234285x x x +++的因式，则m n = ▲ .16. 已知2()4()()b c a b c a -=--，且a≠0，则b ca+= ▲ ． 17. R t △ABC 中，∠A = 3∠C = 90︒，AB = 3，点Q 在边AB 上且BQ=33-Q 作QF ∥BC 交AC 于点F ，点P 在线段QF 上，过P 作PD ∥AC 交AB 于点D ，PE ∥AB 交BC 于点E ，当P 到△ABC 的三边的距离之和为3时，PD + PE + PF = ▲ .18. 在面积为15的□ABCD 中，过点A 作AE 垂直于直线BC 于点E ，作AF 垂直于直线CD 于点F ，若AB ＝5，BC ＝6，则CE ＋CF 的值为 ▲ . 三、解答题（共88分）19. （6分）已知一次函数y = ax + b 的图象经过点A （2，0）与B （0，4）．求此一次函数的解析式，并在直角坐标系内画出这个函数的图象.20. （6分）先化简，再求值：第9题图x x x x x x x -++⎪⎪⎭⎫ ⎝⎛-+-+-÷144214222，其中x 为不等式x －3(x －2)≥2 的正整数解． 21. （8分）已知：244-=+b a a b ，求⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛+-⎪⎭⎫ ⎝⎛+---+÷÷224122222a b a b a b b a b a b a b a 的值.22. 把下列各式因式分解（每题6分，共18分）：（1）432126168x x x --（2）3235)32()23(2)32(a a a a a a -+-+- （3）333333333(2)()abc a b c abc a b b c c a ++++++23. （10分）某饮料厂生产一种饮料，经测算，用1吨水生产的饮料所获利润y （元）是1吨水的价格x （元）的一次函数．(1) 根据下表提供的数据，求y 与x 的函数关系式；当水价为每吨10元时，1吨水生产出的饮料所获的利润是多少？(2) 为节约用水，这个市规定：该厂日用水量不超过20吨时，水价为每吨4元；日用水量超过20吨时，超过部分按每吨40元收费．已知该厂日用水量不少于20吨，设该厂日用水量为t 吨，当日所获利润为W 元，求W 与t 的函数关系式；该厂加强管理，积极节水，使日用水量不超过25吨，但仍不少于20吨，求该厂的日利润的取值范围．24. （8分）如图，在等腰△ABC 中，∠ACB = 90︒，点D 为CB 延长线上一点，过A 作AE ⊥AD ，且AE = AD ，BE 与AC 的延长线交于点P ，求证：PB = PE .25. （8分）已知实数x 、y 满足22()32y x x x yx⎧-=-+⎨≥⎩，记93223yA x y -=+-，求当A 的值为整数时，整数y 的值．26. （12分）如图，一次函数y =+x 轴、y 轴分别交于点A 、B ，以线段AB 为直角边在第一象限内作Rt △ABC ，且使∠ABC ＝30︒. (1) 求△ABC 的面积；(2) 如果在第二象限内有一点P （m ，2），试用含m 的代数式表示四边形AOPB 的面积，并求当△APB 与△ABC 面积相等时m 的值；(3) 是否存在使△QAB 是等腰三角形并且在坐标轴上的点Q ？若存在，请写出Q 的所有可能的坐标；若不存在，请说明理由.27. （12分）一次函数(0)y ax b b =+≠与一次函数2y cx =-的图象的交点的纵坐标为a b +，222(1)(1)(1)3a b c bc ac ab ---++=． (1) 求ab bc ca ++的值；(2) 当1,1a b ≠≠ 时，求证：22(1)(1)b aa b =--．华南师大附中2018—2019学年第一学期期中考试初 二 数 学 详 答一、选择题(每题3分，共30分)二、填空题 (每题4分，共32分) 28.1x －1； 29. (1)(1)(1)(1)a a b b -+-+； 30. 4； 31. 1x <-； 32.125； 33. 2；34. 7-35. 11 +1132或 1＋ 32三、解答题（共88分） 36. （6分）解：依题意得：⎩⎨⎧2a ＋b ＝0b ＝4 ，解得：⎩⎨⎧a ＝－2b ＝4∴ 一次函数的解析式为 y = -2x + 4.过A （2，0），B （0，4）两点画直线AB ，则直线AB 为该函数的图象.37. （6分） 解：原式＝2)2(112+--+⋅x x x x ＝21+-x 解不等式 x －3(x －2)≥2 ，得x ≤2，正整数解为x ＝1，2， 当x ＝1时，原式无意义；当x ＝2时，原式＝－14．38. （8分） 【法1】：∵244-=+ba ab ∴ 22168b a ab +=-，即2(4)0a b +=，即4b a =-∴ 原式＝2224248416()[(1)]24244a a a a a a a a a a a a a a -+----++-÷÷ ＝1(3)[8(144)]3-+-++÷÷＝88()39-÷＝3- 【法2】：∵ 244-=+baa b∴ 22168b a ab +=-，即2(4)0a b +=，即4b a =-∴ 原式＝2282(2)(2)(2)4abb a b a b a b a a ⎡⎤-⎢⎥+-⎣⎦÷÷ ＝288(2)(2)(2)ab aba b a b a b +--÷ ＝22a b a b -+＝2424a aa a+-＝3-39. （每小题6分，共18分） 解：（1）原式＝6x 2 (2x 2－x －28) ＝6x 2 (2x ＋7)(x －4)（2）原式＝a 5(2－3a )＋2a 3(2－3a )2＋a (2－3a )3＝a (2－3a )[ a 4＋2a 2(2－3a )＋(2－3a )2 ] ＝a (2－3a )( a 2＋2－3a )2 ＝a (2－3a )(a －1)2(a －2)2（3）原式＝a 4bc + a 3(b 3 + c 3) + 2a 2b 2c 2 + abc (b 3+c 3) + b 3c 3 ＝bc (a 4 + 2a 2bc + b 2c 2) + a (b 3 + c 3)(a 2 + bc ) ＝bc (a 2 + bc )2 + a (b 3 + c 3)(a 2 + bc ) ＝(a 2 + bc )[bc (a 2 + bc ) + a (b 3 + c 3)] ＝(a 2 + bc )[(bca 2 + ab 3) + (b 2c 2 + ac 3)] ＝(a 2 + bc )[ab (ca + b 2) + c 2(b 2 + ac )] ＝(a 2 + bc )(b 2 + ac )(c 2 + ab )40. （10分）解：（1）设y 关于x 的一次函数式为：b kx y +=，根据题意得：⎩⎨⎧+=+=b k bk 61984200 解得：⎩⎨⎧=-=2041b k ∴ 所求一次函数关系式是：204+-=x y . 当x = 10时，y =－10 + 204 = 194（元）.（2）当1吨水的价格为40元时，所获利润是：y ＝－40＋204＝164（元）．∴ W 与t 的函数关系式是：164)20(20200⨯-+⨯=x w 即：720164+=t w ∵ 20 ≤ t ≤ 25， ∴ 4000≤W ≤4820.41. （8分）【法1】：过E 作EF ⊥AC ，垂足为F ，连接BF ，CE ∵ AE ⊥AD ，∠ACB = 90︒∴ ∠EAF + ∠CAD = 90︒，∠D + ∠CAD = 90︒∴∠EAF = ∠D又∵∠AFE = ∠ACB = 90︒，AE = AD ∴△AFE≌△DCA（AAS）∴EF = AC = BC∵BC⊥AC，EF⊥AC∴EF∥BC∴EF∥＝BC∴四边形BCEF为平行四边形∴PB = PE.【法2】：∵AD = AE且AD⊥AE∴可将△ADB绕点A逆时针旋转90︒至△AEH，由旋转性质得AH = AB且AH⊥AB∴△BAH为等腰直角三角形，∠ABH = 45︒又∵△ACB中，∠ACB = 90︒，AC = BC∴∠ABC = 45︒∴∠ABH = ∠ABC，则B、C、H三点共线∴AP垂直平分BH∴PH = PB∴∠PBH =∠PHB又由旋转性质得EH⊥BD，即EH⊥BH∴∠PHE = 90︒－∠PHB，∠PEH = 90︒－∠PBH，∴∠PEH =∠PHB∴PH=PE∴PB=PE42.（8分）解：由(y－x)2 =x2－3x + 2得(2y－3)x = y2－2∴x=y2－22y－3（∵2y－3≠0）∴A=2y2－3y+52y－3=y+52y－3∵A的值为整数，y为整数∴2y－3|5∴2y－3=±，±5∴y=1，2，4，－1当y=－1时，x=y2－22y－3=15，则y <x，不合题意，舍去；当y=1，2，4时，均满足y≥x ∴整数y的值是1，2，4．或者：由y≥x⇒y≥y2－22y－3⇒ (y－1)(y－2)≥0 ⇒y≤1或y≥2 ∴整数y的值是1，2，4．解：（1）由条件知：A （1，0），B （0，3 ） ∴ 在R t △ABO 中，AB ＝12+(3)2 ＝2 在R t △ABC 中，∵ ∠ABC ＝30° ∴ AC ＝AB 3＝233∴ S △ABC ＝12AC ·AB ＝233（2）S 四边形POAB ＝S △OBP ＋S △AOB∵ S △OBP ＝12·（-m ）·3 ＝－32mS △AOB ＝12·1·3 ＝32∴ S 四边形POAB ＝－32m + 32∵ S △AOP ＝12·1·32＝34∴ S △APB ＝S 四边形POAB －S △AOP ＝－32m + 34（m ＜0） 当S △APB ＝233时，－32m + 34＝233∴ m ＝－56（3）存在．有6个点：（3, 0），（－1, 0），（0, －3 ），（0, 3 +2），（0, 3 －2），（0, 33）.解：（1）依题意得：⎩⎨⎧a + b = ax + b ①a + b = 2－cx ②，且abc ≠0，由①得：x ＝1，代入②得：a + b + c = 2222(1)(1)(1)3a b c bc ac ab---++= ⇒ a 3 + b 3 + c 3－3abc －2(a 2 + b 2 + c 2) + (a + b + c ) = 0⇒ (a + b + c )(a 2 + b 2 + c 2－ab －bc －ca )－2(a 2 + b 2 + c 2) + (a + b + c ) = 0 ⇒ 2(a 2 + b 2 + c 2－ab －bc －ca )－2(a 2 + b 2 + c 2) + 2 = 0 ⇒ ab + bc + ca = 1（2）(a + b + c )2 = 22 = a 2 + b 2 + c 2 + 2(ab + bc + ca ) ⇒ a 2 + b 2 + c 2 = 4－2×1 = 2 当1,1a b ≠≠ 时，要证：22(1)(1)b aa b =--，只需证：b (1－b )2 = a (1－a )2 ⇔ b (1－b )2－a (1－a )2 = 0 ⇔ b －a －2(b 2－a 2) + (b 3－a 3) = 0⇔ (b －a )[1－2(a + b ) + (b 2 + a 2 + ab )] = 0 (*) i ）当a = b 时，(*)式显然成立； ii ）当a ≠b 时，∵ a + b + c = 2，a 2 + b 2 + c 2 = 2，ab + bc + ca = 1∴ a + b = 2－c ，a 2 + b 2 = 2－c 2，ab = 1－c (a + b ) = 1－c (2－c ) ∴ 1－2(a + b ) + (b 2 + a 2 + ab ) = 1－2(2－c ) + 2－c 2 + 1－c (2－c ) = 1－4＋2c ＋2－c 2＋1－2c ＋c 2 = 0 ∴ (*)式成立．综上，当1,1a b ≠≠ 时，均有22(1)(1)b aa b =--．。

第一套：满分120分2020-2021年华南师范大学附属中学初升高自主招生数学模拟卷一．选择题（共6小题，满分42分）1. （7分）货车和小汽车同时从甲地出发，以各自的速度匀速向乙地行驶，小汽车到达乙地后，立即以相同的速度沿原路返回甲地，已知甲、乙两地相距180千米，货车的速度为60千米/小时，小汽车的速度为90千米/小时，则下图中能分别反映出货车、小汽车离乙地的距离y （千米）与各自行驶时间t （小时）之间的函数图象是【 】A. B. C. D.2. （7分）在平面直角坐标系中，任意两点规定运算：①；②；③当x 1= x 2且y 1=y 2时，A =B.有下列四个命题：（1）若A (1，2)，B (2，–1)，则，； （2）若，则A =C ； （3）若，则A =C ；()()1122,,，A x y B x y ()1212,⊕=++A B x x y y 1212=⊗+A B x x y y (),31⊕= A B 0=⊗A B ⊕=⊕A B B C =⊗⊗A B B C（4）对任意点A 、B 、C ，均有成立. 其中正确命题的个数为（ ）A. 1个B. 2个C. 3个D. 4个 3．（7分）如图，AB 是半圆直径，半径OC ⊥AB 于点O ，AD 平分∠CAB 交弧BC 于点D ，连结CD 、OD ，给出以下四个结论：①AC ∥OD ；②CE=OE ；③△ODE ∽△ADO ；④2CD 2=CE •AB ．正确结论序号是（ ）A ．①②B ．③④C ．①③D ．①④ 4. （7分）如图，在△ABC 中，∠ACB =90º，AC =BC =1，E 、F 为线段AB 上两动点，且∠ECF =45°，过点E 、F 分别作BC 、AC 的垂线相交于点M ，垂足分别为H 、G ．现有以下结论：①；②当点E 与点B 重合时，；③；④MG •MH =，其中正确结论为（ ）A. ①②③B. ①③④C. ①②④D. ①②③④ 5.（7分）在数学活动课上，同学们利用如图的程序进行计算，发现无论x 取任何正整数，结果都会进入循环，下面选项一定不是该循环的是（ ）A. 4，2，1B. 2，1，4C. 1，4，2D. 2，4，1 6. （7分）如图，在矩形ABCD 中，AB =4，AD =5，AD 、AB 、BC 分别与⊙O 相切于E 、F 、G 三点，过点D()()⊕⊕=⊕⊕A B C A B C 2AB =12MH =AF BE EF +=12作⊙O 的切线交BC 于点M ，则DM 的长为（ ）A.B. C. D.二．填空题（每小题6分，满分30分）7.（6分）将边长分别为1、2、3、4……19、20的正方形置于直角坐标系第一象限，如图中方式叠放，则按图示规律排列的所有阴影部分的面积之和为 . 8.（6分）如图，三个半圆依次相外切，它们的圆心都在x 轴上，并与直线33y x =相切．设三个半圆的半径依次为r 1、r 2、r 3，则当r 1＝1时，r 3＝ ．9.（6分）如图，将一块直角三角板OAB 放在平面直角坐标系中，B （2，0），∠AOB=60°，点A 在第一象限，过点A 的双曲线为k y x=．在x 轴上取一点P ，过点P 作直线OA 的垂线l ，以直线l 为对称轴，线段OB 经轴对称变换后的像是O ´B ´．（1）当点O ´与点A 重合时，点P 的坐标是 ；（2）设P （t ，0），当O ´B ´与双曲线有交点时，t 的取值范围是 ．1339241332510.（6分）如图，正方形A 1B 1P 1P 2的顶点P 1、P 2在反 比例函数2(0)y x x=>的图象上，顶点A 1、B 1分别在x 轴、y 轴的正半轴上，再在其右侧作正方形P 2P 3A 2B 2，顶点P 3在反比例函数2(0)y x x=>的图象上，顶点A 2在x 轴的正半轴上，则点P 3的坐标为 ．11.（6分）如图，在⊙O 中，直径AB ⊥CD ，垂足为E ，点M 在OC 上，AM 的延长线交⊙O 于点G ，交过C 的直线于F ，∠1=∠2，连结CB 与DG 交于点N ．若点M 是CO 的中点，⊙O 的半径为4，cos ∠BOC=41，则BN= ．三．解答题（每小题12分，满分48分）12.（12分）先化简，再求值：， 其中.13.（12分）如图，点A （m ，m ＋1），B （m ＋3，m －1）都在反比例函数的图象上．（1）求m ，k 的值；32221052422x x x x x x x x --÷++--+-2022(tan 45cos30)21x =-+︒-︒-xky =xO yAB （2）如果M 为x 轴上一点，N 为y 轴上一点， 以点A ，B ，M ，N 为顶点的四边形是平行四边形，试求直线MN 的函数表达式． （3）将线段AB 沿直线进行对折得到线段，且点始终在直线OA 上，当线段与轴有交点时,则b 的取值范围为 （直接写出答案）14.（12分）如图，在Rt △ABC 中，∠ABC=90°，以AB 为直径作⊙O 交AC 于点D ，DE 是⊙O 的切线，连接DE ．（1）连接OC 交DE 于点F ，若OF=CF ，证明：四边形OECD 是平行四边形； （2）若=n ，求tan ∠ACO 的值b kx y +=11B A 1A 11B A x OFCF15.（12分）如图1，抛物线y ＝ax 2＋bx ＋c （a ≠0）的顶点为C （1，4），交x 轴于A 、B 两点，交y 轴于点D ，其中点B 的坐标为（3，0）。