江苏省南京市金陵中学河西分校2024-2025学年九年级上学期数学期中复习试卷一、单选题1．已知一组数据3，7，5，3，2，这组数据的众数为（）A ．2B ．3C ．4D ．52．已知⊙O 的直径为10cm ，圆心O 到直线l 的距离为10cm ，直线l 与圆O 的位置关系为（）A ．相交B ．相切C ．相离D ．无法确定3．用配方法解方程241x x -=时，配方所得的方程为（）A ．()221x +=B ．()221x -=C ．()225x +=D ．()225x -=4．下列说法中，正确的有（）（1）长度相等的弧是等弧；（2）三点确定一个圆；（3）平分弦的直径垂直于弦；（4）三角形的内心到三角形三边的距离相等A ．4个B ．3个C ．2个D ．1个5．如图，从一块直径为2m 的圆形铁皮上剪出一个圆心角为90°的扇形，则此扇形的面积为（）A ．2πB ．πC ．12πD 6．如图，ABCD 中，AD BC ，8,4,60AD CD B ==∠=︒，若点P 在线段BC 上，且ADP 为直角三角形，则符合要求的点P 的个数有（）A ．4个B ．3个C ．2个D ．1个二、填空题7．某招聘考试分笔试和面试两项，笔试成绩和面试成绩按3：2计算平均成绩．若小明笔试成绩为85分，面试成绩为90分，则他的平均成绩是分．8．设12,x x 是方程240x x m -+=的两个根，且12x x +－21x x ＝1,则m=.9．若一个圆锥的底面半径为2，母线长为6，则该圆锥侧面展开图的圆心角是°．10．如图，在扇形OAB 中，C 为 AB 上的点，连接AC 、BC ，若∠ACB ＝2∠O ，则∠O 的度数为°．11．如图，AB 是⊙O 的弦，点C 在过点B 的切线上，OC ⊥OA ，OC 交AB 于点D ．若∠BDC ＝68°，则∠ABC 的度数为°．12．如图，在O 的内接五边形ABCDE 中，210B E ∠+∠=︒，则CAD ∠=°．13．⊙O 是△ABC 的外接圆，连接OB ，∠ABO ＝38°，则∠C 的度数为.14．如图，AB BC CD DA 、、、都是O 的切线，2,8AD AB CD =+=，则BC =．15．若关于x 的一元二次方程20ax bx c ++=（a 、b 、c 都为有理数）的一个解是14x =-，则方程的另一个解是．16．如图，在矩形ABCD 中，4,6AD AB ==，P 为CD 的中点，连接BP ．在矩形ABCD 内部找一点E ，使得BEC BPC ∠=∠，则线段DE 的最小值为．三、解答题17．解下列方程：（1）x 2﹣6x ﹣5＝0；（2）3x （x ＋2）＝2x ＋418．某品牌汽车2月份至6月份销售的月增量（单位：万辆）折线统计图如下．注：月增量＝当月的销售量一上月的销售量，月增长率100⨯且的销售量＝上月的销售量%，例如，8月份的销售量为2万辆，9月份的销售量为2.4万辆，那么9月份销售的月增量为2.420.4-=（万辆），月增长率为20%．(1)下列说法正确的是（）A .2月份的销售量为0.4万辆B .2月份至6月份销售的月增量的平均数为0.26万辆C .5月份的销售量最大D .5月份销售的月增长率最大(2)6月份的销售量比1月份增加了多少万辆？(3)2月份至4月份的月销售量持续减少，你同意这种观点吗？说明理由．19．如图，AB 是⊙O 的直径，AC 、BC 分别交⊙O 于点D 、E ，连DE ，AD =BE ．求证：（1）DE ∥AB ；（2）DC =EC ．20．如图，在一个长16m ，宽12m 的矩形花圃外围铺设等宽的小路，且铺设小路的面积为花圃面积的三分之二，求小路的宽度．21．如图，ABC V 中，AB AC =，以A 为直径的O 交BC 于D ，交AC 于E ．(1)求证：BD CD =；(2)若50BAC ∠=︒，求EBC ∠和EDC ∠的度数．22．已知关于x 的一元二次方程22240x x k ++-=有两个不相等的实数根．（1）求k 的取值范围；（2）若k 为正整数，且该方程的根都是整数，求k 的值．23．已知：BC 是O 的直径，A 是O 上一点，AD BC ⊥，垂足为D ， AB AE =，BE 交A 的延长线于点F ，延长BE AC 、交于点G ．求证：BF FG =．24．如图，AB 是⊙O 的直径，BC 与⊙O 相切于点B ，AD 是⊙O 的弦，AD ∥OC ，延长CD 、BA 相交于点E ．（1）求证CE 是⊙O 的切线；（2）若A 恰好是OE 的中点，AD ＝3，则阴影部分的面积为．25．某商店经销的某种商品，每件成本价为40元，经市场调研，售价为50元/件，可销售150件；销售单价每提高1元，销售量将减少5件．如果商店将一批这种商品全部售完，盈利了1500元，问：该商店销售了这种商品多少件？每件售价多少元？26．已知点A 在O 上．(1)在图①中，点B 在O 上，用尺规作图：在AB上找点C ，使得ABC 为等腰三角形；(2)用无刻度的直尺在O 上画出B 、C 两点，分别满足下列要求：①在图②中，使得ABC 为直角三角形；②在图③中，使得ABC 为等腰三角形，且AB AC =．27．在一次数学探究活动中，王老师设计了一份活动单：“追梦”学习小组通过操作、观察、讨论后汇报：点A 的位置不唯一，它在以BC 为弦的圆弧上（点B 、C 除外），…小华画出了符合要求的一条圆弧（如图1）．(1)小华同学提出了下列问题，请你帮助解决：①该弧所在的圆的半径长为_____；②ABC V 面积的最大值为_____．(2)经过比对发现，小明同学所画的角的顶点不在小华所画的圆弧上，而在如图1所示的弓形的外部，我们记为P ，请你利用图1证明45BPC ∠<︒；(3)请你运用所学知识，结合以上活动经验，解决问题：如图2，已知矩形ABCD 的边长4AB =，BC =M 在直线CD 的左侧，且30DMC ∠=︒．①用尺规作出点M 的运动路径，并求线段MB 长的最小值；②过点M 作MH CD ⊥，垂足为H ，若MCD S △不小于，则DH 长的范围是．。
沪教版-九年级(初三)数学上册-期中考试复习试卷试题及答案(Word版)AC51.将抛物线y=x^2向右平移1个单位长度，再向上平移2个单位长度所得的抛物线解析式为哪一个？A。
y=(x-1)^2+2B。
y=(x+1)^2+2C。
y=(x-1)^2-2D。
y=(x+1)^2-22.已知二次函数y=ax^2-1的图象经过点(1,-2)，那么a的值为多少？A。
a=-2B。
a=2C。
a=1D。
a=-13.对于非零向量a、b，如果2|a|=3|b|，且它们的方向相同，那么用向量a表示向量b正确的是哪一个？A。
b=a*(3/2)B。
b=a*(2/3)C。
b=-a*(3/2)D。
b=-a*(2/3)4.在四边形ABCD中，若AB=a，AD=b，BC=c，则CD等于哪一个？A。
a-b-cB。
-a+b-cC。
a-b+cD。
-a+b+c5.在直角三角形ABC中，∠C=90°，如果∠A=α，AB=3，那么AC等于哪一个？A。
3sinαB。
3cosαC。
sinα/3D。
cosα/36.在直角三角形ABC中，∠C=90°，如果AC=4，BC=3，那么∠A的正切值为多少？A。
3/4B。
4/3C。
5/3D。
3/57.在直角三角形ABC中，∠ACB=90°，BC=1，AC=2，则下列结论正确的是哪一个？A。
sinA=3/2B。
tanA=1/2C。
cosB=3/2D。
tanB=3/48.抛物线y=-3x^2+2x-1的图象与x轴交点的个数是多少？A。
没有交点B。
只有一个交点C。
有且只有两个交点D。
有且只有三个交点9.关于二次函数y=(x+1)^2的图象，下列说法正确的是哪一个？A。
开口向下B。
经过原点C。
对称轴右侧的部分是下降的D。
顶点坐标是(-1,0)10.在三角形ABC中，点D、E分别在AB、AC上，如果AD=2，BD=3，那么由下列条件能够判定DE//BC的是哪一个？A。
DE^2/BC^2=3/2B。
2024人教版九年级英语上期期中单项选择专题复习练习题1．—Annie’s voice is so beautiful.—Yes. She is born with the ________ to sing.A．head B．ability C．pride D．courage2．—________ do you make so many friends—________ helping others.A．How; By B．How; With C．What; By D．What; With3．— You must spend money ________ or you will be poor at the end of the month.— OK, Dad. I will.A．wisely B．heavily C．completely D．differently4．—Is there a fast train to Shanghai today I wonder if you could ________ for me—Sorry, the last train left 15 minutes ago.A．pick it up B．give it up C．take it up D．look it up 5．—Will you attend the meeting in person—I decided to go there as a (n) _________ of support. A．expression B．conversation C．pronunciation D．attention 6．—I don’t want you to _________ a word of this to anyone. —OK! Just trust me. I will keep my mouth tightly shut.A．show B．review C．spell D．repeat7．The 13-year-old artist ________ more than 50 paintings so far.A．has created B．will create C．is creating D．creates8．The music is too ________, so I have to speak ________. A．loud; aloud B．aloud; loud C．loudly; loudly D．aloud; aloud 9．Chinese scientists have ________ a kind of special flower. It is so “shy” that it closes quickly after you touch it.A．invented B．discovered C．repeated D．created10．No matter what Liu Xiang does, he never _________.A．sets it up B．gives it up C．picks it up D．looks it up 11．Mary often goes ________ on business. She went to England last year.A．aloud B．abroad C．instead D．inside12．Li Ming, do you know who ________ the first computer A．invented B．discovered C．found D．found out13．— Do you like your new English teacher— Yes, I like her. She is always _________ with us when we make mistakes.A．careful B．shocked C．patient D．honest14．He never shows off and he is ________ enough to keep everything in good order.A．serious B．organized C．curious D．patient15．A new railway will be built to ________ Yangzhou ________the others in Changjiang Delta (长江三角洲) in the following years.A．connect; to B．connected; with C．connects; to D．connecting; with16．—What is the ________ to your excellent spoken English —Practice makes perfect.A．result B．habit C．excuse D．secret17．—Alice, you shouldn’t buy things ________ because they are on sale.—Sorry, I won’t.A．certainly B．simply C．wisely D．clearly18．With a basic ________ of cooking, teenagers can’t go hungry when their parents are out.A．knowledge B．tool C．adventure D．will19．We’ll ________ the English play “Snow White” until next week because of the bad weather.A．put up B．put out C．put off D．put on20．—Listen! Someone is playing the piano.—Wow. ________ beautiful music it is!A．How a B．How C．What a D．What21．They are talking about ________ they can borrow some money from their friends.A．if B．that C．whether D．who22．Don’t eat too much junk foo d, or you will ________ weight.A．put away B．put up C．put on D．put off23．—Does the child need any help—No, he is old enough to _________ himself.A．put on B．wear C．dress D．take care24．—The sick man ________ in bed ________ to the doctor again. —Yes, he said he had already taken the pill ________ on the table by the nurse a moment ago.A．lying; lied; laid B．laying; lay; lain C．lying; laid; lay D．laying; lied; lair25．—Her paintings were much ________ across the country. —Right! So many people expected to get one as their collection. A．reviewed B．noted C．compared D．admired 26．—Wow, here is still some cake left!—Come on, you can eat ________ cake and leave the other for________ comes later.A．any; who B．any; whoever C．both; who D．either; whoever 27．—Every student is expected to ________ a sporting activity for a healthy life.—I couldn’t agree more. Health matters a lot.A．deal with B．take up C．end up D．run after28．The young man in yellow ________ his keys in his office. He is forgetful and can’t enter the house.A．left B．forgot C．has left D．has forgotten29．—Do you know the buzzword (流行语) “lying flat”—Yes. It’s often used by Chinese young people to ________ their feelings under much stress.A．express B．support C．protect D．manage 30．—Confucius (孔子) was a great Chinese educator and philosopher (哲学家).—His thoughts and ideas have had a deep ________ both in China and beyond.A．attention B．influence C．chance D．choice 31．Recently, the “Guochao” trend has driven an increasing need for ________ products and brands in China instead of foreign ones. A．awful B．local C．expensive D．international 32．—Kate’s never late for school, ________—________. She’s always the first to go to school.A．is she, Yes B．isn’t she, Yes C．is she, No D．isn’t she, No 33．—I don’t have a par tner to practice my oral English ________. —Why not join an English club to practice it more to avoid ________ mistakesA．/, making B．with, to make C．/, to make D．with, making 34．You will fail your next exam ________ you start to work at your studies now.A．because B．unless C．if D．so35．________ careful you are, ________ mistakes you will make. A．The more, the more B．The less, the lessC．The more, the fewer D．The less, the fewer36．—I tried to make Alice ________ her mind, but I found it difficult. —Well, I saw you ________ that when I went past.A．to change; do B．change; doing C．change; do D．to change; doing37．—Tell us something about your survey Homework after Double Reduction (双减)—Well, most students tell us that it ________ takes them one hour, and sometimes even shorter.A．normally B．exactly C．directly D．naturally38．The film The Battle at Lake Changjin（长津湖）________ very popular since it was on show.A．become B．became C．will become D．has become 39．—Thank you for helping me with my lessons. I’ll work ha rder to make greater progress.—________. Wish you a better future.A．With pleasure B．It doesn’t matter C．Don’t mention it D．Never mind40．— Can you guess if they ________ to play basketball with us—I think they’ll come if they _________.A．come; invite B．will come; will be invitedC．will come; will invite D．will come; are invited41．— Besides eating regularly, what else should I pay attention to ________ my body— You should pay attention to ________ exercise regularly.A．to shape; to do B．shaping; to doC．shaping; doing D．to shape; doing42．— Are all the students in your school from ________— No. Only a small number of them are ________. A．Germany; Germans B．German; GermanyC．Germany; Germen D．Germen; Germany43．The English Festival ________ every two years in our school. A．is taken place B．is taking place C．takes place D．holds 44．He told us a ________ story about the great ________ writer. A．live; living B．lively; living C．lively; alive D．live; alive 45．Dick ________ in the school now because in the school most of his time ________.A．used to live; is used to study B．is used to living; used to study C．is used to living; is used to studying D．is used to living; is used to study46．To ________ making some mistakes, he often writes the notesbeside it while doing homework.A．practice B．avoid C．suggest D．consider47．—I’m afraid Lucy can’t finish the project in such a short time.— Oh Can she finish it if she ________ two more daysA．will be given B．will give C．gives D．is given48．It is terrible that teenagers always ________ to their parents nowadays. It is bad for parent-child relationship.A．look up B．pay attention C．talk back D．look forward 49．—According to the ________ situation, we must change ourselves as the society develops rapidly.— Yeah, or we will be behind the times.A．present B．patient C．central D．humorous50．We each will be provided ________ to achieve our dreams. So, come on, everyone.A．chances B．expressions C．celebrations D．invitations 51．—Your ring looks nice. Is it made ________ silver—Yes. It’s made______ China.A．from; by B．from; in C．of; by D．of; in52．—Mr. Wu does most things ________ instead of depending on others.—So he does. That’s why he runs his business well.A．in public B．in person C．in total D．in fact53．—The Internet has made communication much more ________. —I agree. But we shouldn’t spend much time on it.A．difficult B．popular C．convenient D．important 54．—Why do you know a lot about our new classmate—She is my ________. My father is her uncle.A．stranger B．guide C．tradition D．relative55．—How can we manage to escape from the building if there is a fire—There’s a door at ________ end of the hallway.A．none B．either C．both D．all56．Lisa is a good girl. She always answers the phone _________ when I call her.A．politely B．suddenly C．easily D．luckily57．— I always get nervous when I give a (an) _________ in public. — Take it easy. Believe in yourself.A．speech B．celebration C．information D．communication 58．Now many Chinese people like to travel from one place to________ to enjoy the beauty of the country.A．other B．the other C．another D．others59．—Hey, Sam. What are you doing—I’m reading today’s news. It is said that the old newspapers can be ________ some beautiful and creative clothes. That sounds reallyinteresting.A．turned on B．turned offC．turned in D．turned into60．—What if you treat everyone with ________ and warmth—I’m sure you will feel happy.A．shyness B．illness C．business D．kindness 61．—Harry, why did you put off your trip to Hangzhou—I failed ________ on the plane in time because of the heavy traffic. A．get B．got C．getting D．to get62．—I think we can’t find a nicer one!—Yeah! This house has 3 bedrooms, all with ________ bathrooms. A．helpful B．private C．available D．public63．—How is tea produced in China—________ I know, tea plants are grown on the sides of mountains. . A．as long as B．as soon as C．as far as D．as good as 64．—Jack, do you dare ________ bungee jumping (蹦极) —Completely not. I’m afraid of staying at high places.A．try B．trying C．to try D．tried65．—Why is Mike so popular in your class—Because he always tells jokes. He is ________.A．humorous B．silent C．honest D．lively66．You can’t go out unless your homework ________.A．finish B．will finish C．is finished D．will be finished 67．Her legs were hurt ________ badly ________ she had to see a doctor.A．so; that B．too; that C．such; that D．too; to68．You might ________ failing the exam unless you study hard. A．look up B．put up C．end up D．take up69．—Who is your hero in your heart—Yang Zhengning who won the Nobel Prize in science in 1957. I _________ him and dream of being a great scientist like him. A．look up B．look up to C．look for D．look forward to 70．—Tom, can you help me __________ the table Dinner is ready. —Sure, mom. I’m coming.A．give out B．put out C．take out D．lay out71．— The scarf is made of silk.— Oh, no wonder it ________ soft and comfortable.A．feels B．tastes C．smells D．sounds72．— Mr. Green ________ his son.— Yes. He likes talking about his son with any friend of his. A．takes care of B．takes up C．takes pride in D．takes after 73．—Would you like some coffee—No, thanks. I ________ drink coffee.A．seldom B．often C．sometimes D．only74．—________. I didn’t pay attention to your words.—OK. I’ll repeat them. Listen to me carefully this time.A．As far as I know B．To be honest C．In my opinion D．Pardon me 75．—The restaurant is always busy. I suggest ________ a little earlier to get a table.—OK. Thank you!A．come B．came C．coming D．to come76．— Will you ________ a school on your way home— Yes, the school is just beside my home.A．end up B．set up C．fix up D．pass by77．—I’m afraid to answer questions in English class because of my poor ________.—You’d better practice speaking more.A．introduction B．influence C．pronunciation D．information 78．Their father warned them _______ the mountain in such bad weather.A．climbing B．not climbing C．not to climb D．to climb 79．Many animals _______ the ability to swim, but humans must practice how to swim.A．part with B．agree with C．are good with D．are born with 80．—I found ________ very easy to learn English well if you put your heart into it.—I agree with you.A．that B．what C．it D．this81．—What’s the ________ of yesterday’s basketball game —Class Five 108 points to Class Seven 96.A．speed B．plan C．score D．record82．—Did Mike agree on the project—He kept ________ at the meeting, so I didn’t know whether he agreed or not.A．silent B．active C．busy D．proud83．—Do you want to play basketball tomorrow—It ________ the weather.A．looks at B．depends on C．believes in D．looks for 84．—To achieve a bright future, we should ________ study hard ________ keep in good health.—I agree with you.A．not only; but also B．not; but C．neither; nor D．either; or 85．—Where is he—He ________ France and he ________ France for two days. A．has gone to; has been to B．has gone to, has been in C．has been in, has gone to D．has been to; has been in 86．—I apologize that I broke the goods on the shelf, Mr. Yang. —Never mind. I’m sure you didn’t do it ________.A．on vacation B．on purpose C．on earth D．on business 87．—Are you going to the USA for vacation—Yes, I want you to ________ me with some information about it. A．give B．offer C．provide D．send88．—Hello, 110! A car was hit by a large truck. The ________ in Green Street is dangerous.—OK, we will be right away.A．situation B．development C．technology D．importance 89．— The doctors tried their best to do everything they can ______ the boy, but they failed.— What a pity! I am so sad to hear that.A．saving B．save C．to save D．saved90．—Peter's Chinese was very poor when he came to China, so he couldn't make himself ______.—So he did, but now he becomes better.A．understands B．understanding C．understand D．understood 91．—Could you tell me _________—Five minutes’ ride.A．how long is the post office B．how long the post office is C．how far is the post office D．how far the post office is 92．—How fast the dog is running!—Oh, hard to ________ one of its legs was once broken.A．know B．find C．imagine D．realize93．—Should we call them and make sure they have prepared for the party—T here’s no need to worry! Everything went ________ as planned. A．exactly B．wisely C．finally D．widely94．— Living and dealing with kids can be a difficult job these days. — I agree. It ________ a great deal of patience.A．requires B．includes C．draws D．requests95．—Who left the tap (水龙头) running The water began to________ across the floor.—Oh, I forgot to turn it off when the telephone rang.A．pass B．spread C．fill D．cover96．—How can I keep the food—It should be stored in a cool and dry places, away from ________ sunlight.A．normal B．active C．direct D．wide97．—What did your husband say—He asked why I couldn’t just forget about dieting and eat ________ instead.A．commonly B．exactly C．normally D．gradually98．—I really can’t tell which is the most exciting mov ie. What do you think—Exciting I think ________ of them is exciting. I almost left halfway. A．all B．any C．neither D．none99．—I wonder if I can improve my English in a week.—Be patient. _________. Rome was not built in a day.A．It’s a piece of cake B．It takes time C．You can’t be serious D．It’s up to you100．—Guess what! The farmers made Tian’anmen Square model with millions of corns.—Wow! There are always many ________ people around us! A．local B．creative C．tiny D．humorous答案1．B2．A3．A4．D5．A6．D7．A8．A9．B10．B11．B12．A13．C14．B15．A16．D17．B18．A19．C20．D21．C22．C23．C24．A25．D26．D27．B28．C29．A30．B31．B32．C33．D34．B35．C36．B37．A38．D39．C40．D41．D42．A43．C44．B45．D46．B47．D48．C49．A50．A51．D52．B53．C54．D55．B56．A57．A58．C59．D60．D61．D62．B63．C64．C65．A66．C67．A68．C69．B70．D71．A72．C73．A74．D75．C76．D77．C78．C79．D80．C81．C82．A83．B84．A85．B86．B87．C88．A89．C90．D91．D92．C93．A94．A95．B96．C97．C98．D99．B100．B。
2022-2023学年冀教新版九年级上册数学期中复习试卷一．选择题（共16小题，满分32分，每小题2分）1．某班要推选学生参加学校的“诗词达人”比赛，有7名学生报名参加班级选拔赛，他们的选拔赛成绩各不相同，现取其中前3名参加学校比赛．小红要判断自己能否参加学校比赛，在知道自己成绩的情况下，还需要知道这7名学生成绩的（）A．众数B．中位数C．平均数D．方差2．方程x（x﹣6）＝0的解是（）A．x＝6B．x1＝0，x2＝6C．x＝﹣6D．x1＝0，x2＝﹣63．如图，点A、B、C、D、E、F分别是小正方形的顶点，在△ABC与△DEF中，下列结论成立的是（）A．∠BAC＝∠EDFB．∠DFE＝∠ACBC．∠ACB＝∠EDFD．这两个三角形中没有相等的角4．用配方法解方程x2﹣8x+9＝0，变形后的结果正确的是（）A．（x﹣4）2＝7B．（x﹣4）2＝﹣7C．（x﹣4）2＝25D．（x﹣4）2＝﹣255．重庆由于丘陵、山地的特殊地势，被网友们称为”3D魔幻城市”．在重庆，你有时会看到马路上面是房屋、马路下面也是房屋；你从底楼出来，看到门口是一条公路，等你坐电梯上到顶楼，发现还是公路．小王家就在这样的一栋楼里：他从家里底楼出来会看到一条斜坡公路DC，已知∠DCE＝30°，他从楼底B 出发，沿着公路到达C处后继续沿着斜坡前进到达D处，共走了27米，然后他又沿着斜坡DA 前进到达了顶楼A处，已知DA与水平线夹角为30°，大楼AB高米，假设BC、CD、AD、AB在同一平面内，则斜坡CD的长度约为（）（已知：≈1.73）A．10.3B．10.4C．9D．9.26．小刚身高180cm，他站立在阳光下的影子长为90cm，他把手臂竖直举起，此时影子长为115cm，那么小刚的手臂超出头顶（）A．35cm B．50cm C．25cm D．45cm7．下列四组线段中，是成比例线段的是（）A．2cm，3cm，4cm，5cm B．3cm，6cm，0.2dm，5cmC．2cm，4cm，6cm，8cm D．12cm，8cm，15cm，10cm8．已知x＝2是一元二次方程x2+bx﹣c＝0的解，则﹣4b+2c＝（）A．8B．﹣8C．4D．﹣49．一艘轮船和一艘渔船同时沿各自的航向从港口O出发，如图所示，轮船从港口O沿北偏西20°的方向航行60海里到达点M处，同一时刻渔船已航行到与港口O相距80海里的点N处．若M，N两点相距100海里，则∠NOF的度数为（）A．50°B．60°C．70°D．90°10．若一元二次方程x2﹣2x﹣m＝0无实数根，则一次函数y＝（m+1）x+m2+2的图象经过第（）A．二、三、四象限B．一、三、四象限C．一、二、四象限D．一、二、三象限11．如图，每个小正方形的边长均为1，则下列图形中的三角形（阴影部分）与△A1B1C1相似的是（）A．B．C．D．12．某商店销售富硒农产品，今年1月开始盈利，2月份盈利240000元，4月份盈利290400元，且从2月份到4月份，每月盈利的平均增长率相同，则每月盈利的平均增长率是（）A．8%B．9%C．10%D．11%13．为了宣传垃圾分类，小明写了一篇倡议书，决定用微博转发的方式传播．他设计了如下的传播规则：将倡议书发表在自己的微博上，再邀请n个好友转发，每个好友转发之后，又邀请n个互不相同的好友转发，依此类推．已知经过两轮转发后，共有111个人参与了宣传活动，则n的值为（）A．9B．10C．11D．1214．某校“研学”活动小组在一次野外实践时，发现一种植物的主干长出若干数目的枝干，每个枝干又长出同样数目的小分支，主干、枝干和小分支的总数是43，则这种植物每个枝干长出的小分支个数是（）A．4B．5C．6D．715．如图，在▱ABCD中，AB＝6，AD＝8，∠BAD的平分线与对角线BD交于点O，与DC的延长线交于点E．则△AOD与△DOE的面积比为（）A．3：4B．9：16C．2：3D．1：316．对于两个不相等的实数a，b，我们规定符号max{a，b}表示a、b中的较大的数，如：max{2，4}＝4，按照这个规定，方程max{x，﹣x}＝x2﹣x﹣1的解为（）A．1+或1﹣B．1或﹣1C．1﹣或1D．1+或﹣1二．填空题（共4小题，满分13分）17．（3分）如果地图上A、B两处的图距是4cm，表示这两地实际的距离是20km，那么实际距离是700km 的两地在地图上的距离是cm．18．（3分）如图，在△ABC中，点D在AC边上，AD：DC＝1：2，点E是BD的中点，连接AE并延长交BC于点F，BC＝12，则BF＝．19．（3分）如图，在Rt△ABC中，∠C＝90°，点E在AC边上．将∠A沿直线BE翻折，点A落在点A'处，连接A'B，交AC于点F．若A'E⊥AE，cos A＝，则＝．20．（4分）如图，一等腰三角形，底边长是21厘米，底边上的高是21厘米，现在沿底边依次从下往上画宽度均为3厘米的矩形，画出的矩形是正方形时停止，则这个矩形是第个．三．解答题（共6小题，满分55分）21．（16分）（1）解方程：x2+4x＝﹣3；（2）解方程：a2+3a+1＝0（用公式法）；（3）计算：sin45°•cos45°+tan30°；（4）计算：2﹣1﹣tan60°+（﹣1）0+|﹣|．22．（7分）本学期开学初，某学校体育组对2021届九年级某班50名学生进行了跳绳项目的测试，根据测试成绩制作了两个统计图．（1）在扇形统计图中，得3分学生的测试成绩所占扇形的圆心角度数为；（2）本次测试的中位数、众数分别是多少？（3）本次测试成绩的平均分是多少分？23．（7分）已知：△ABC三个顶点的坐标分别为A（﹣4，﹣4），B（0，﹣2），C（﹣6，0），（1）以点O为位似中心，将△ABC缩小为原来的倍，得到△A′B′C′，请在网格的第一象限中画出△A′B′C′，并写出点A′的坐标．（2）若AA'与BC相交于点D，求出sin∠CDA的值．24．（7分）小花和小明周末去大雁塔游玩，两人在A处测得大雁塔在北偏东60°方向C处，当小花和小明沿着正东方向走了1200米到达B处时，测得大雁塔在北偏东15°的方向上，求此时他们与大雁塔的距离BC约是多少？（结果保留整数，参考数据：≈1.4，≈1.7）25．（7分）一批发市场某服装批发价为240元/件．为拉动消费，该批发市场规定：当批发数量超过10件时，给予降价优惠，但批发价不得低于150元/件．经市场调查发现，优惠时批发价y（元/件）与x（件）之间成一次函数关系，当批发数量为15件时，批发价为210元/件；当批发数量为22件时，批发价为168元/件．（1）求批发价y（元/件）与x（件）之间的一次函数表达式；（2）在该市场降价优惠期间，某顾客一次性支付了3600元，求该顾客批发了多少件服装？26．（11分）如图，在平面直角坐标系中，点O为坐标原点，点A的坐标为（0，4），点B在x的负半轴上，△AOB的面积为8，作△AOB关于y轴的对称图形，点B的对应点为C．（1）求线段OC的长；（2）点D从A点出发，沿线段AO向终点O运动，同时点E从点C出发，沿x轴的正方向运动，且CE ＝AD，连接DE交AC于点G，判断DG和EG的数量关系，并说明理由．（3）在（2）的条件下，当∠CEG＝∠ABD时，求点G点坐标．参考答案与试题解析一．选择题（共16小题，满分32分，每小题2分）1．解：由于总共有7个人，且他们的成绩互不相同，第4的成绩是中位数，要判断自己能否参加学校比赛，故应知道中位数的多少．故选：B．2．解：x（x﹣6）＝0x＝0或x﹣6＝0解得x1＝0，x2＝6．故选：B．3．解：A、如图，易得tan∠BAC＝，tan∠EDF＝＝，那么两个角相等，故A成立；B、∠DFE＝45°，∠ACB小于45°，那么两个角不相等，故B不成立；C、∠ACB＝45°﹣正切值为的角，∠EDF＝45°﹣正切值为的角，那么两个角不相等，故C不成立；B、C、D均不成立，故选：A．4．解：方程移项得：x2﹣8x＝﹣9，配方得：x2﹣8x+16＝7，即（x﹣4）2＝7，故选：A．5．解：作DH⊥AB于H，CK⊥DH于K．设CD＝x米，则BC＝KH＝（27﹣x）米，CK＝BH＝x米，DK＝x米，在Rt△ADH中，∵∠ADH＝30°，∴tan30°＝，∴＝解得x＝6≈10.4，∴CD＝10.4米．故选：B．6．解：设小刚的手臂超出头顶xm，则＝，解得x＝50cm．故选：B．7．解：A、3×4≠5×2，故选项错误；B、0.2dm＝2cm，3×5≠6×2，故选项错误；C、2×8≠4×6，故选项错误；D、12×10＝8×15，故选项正确．故选：D．8．解：由题意得：把x＝2代入方程x2+bx﹣c＝0中，22+2b﹣c＝0，∴2b﹣c＝﹣4，∴﹣4b+2c＝﹣2（2b﹣c）＝﹣2×（﹣4）＝8，故选：A．9．解：∵OM＝60海里，ON＝80海里，MN＝100海里，∴OM2+ON2＝MN2，∴∠MON＝90°，∵∠EOM＝20°，∴∠NOF＝180°﹣20°﹣90°＝70°，故选：C．10．解：由已知得：Δ＝b2﹣4ac＝（﹣2）2﹣4×1×（﹣m）＝4+4m＜0，解得：m＜﹣1．∵一次函数y＝（m+1）x+m2+2中，k＝m+1＜0，b＝m2+2＞0，∴该一次函数图象一、二、四象限．故选：C．11．解：因为△A1B1C1中有一个角是135°，选项中，有135°角的三角形只有B，且满足两边成比例夹角相等，故选：B．12．解：设该商店的每月盈利的平均增长率为x，根据题意得：240000（1+x）2＝290400，解得：x1＝10%，x2＝﹣2.1（舍去）．故选：C．13．解：依题意，得：1+n+n2＝111，解得：n1＝10，n2＝﹣11．故选：B．14．解：设这种植物每个枝干长出x个小分支，依题意，得：1+x+x2＝43，解得：x1＝﹣7（舍去），x2＝6．故选：C．15．解：∵四边形ABCD是平行四边形，∴AB∥CD，∴∠DEA＝∠BAE，∵AE平分∠BAD，∴∠DAE＝∠BAE，∴∠DAE＝∠DEA，∴DE＝AD＝8，∵AB∥CD，∴△BOA∽△DOE，∴＝＝＝，∴△AOD的面积：△DOE的面积＝OA：OE＝3：4，故选：A．16．解：①当x≥﹣x，即x≥0时，∵max{x，﹣x}＝x2﹣x﹣1，∴x＝x2﹣x﹣1，解得：x＝1+（1﹣不符合舍去）；②当﹣x＞x，即x＜0时，﹣x＝x2﹣x﹣1，解得：x＝﹣1（1不符合舍去），即方程max{x，﹣x}＝x2﹣x﹣1的解为1+或﹣1，故选：D．二．填空题（共4小题，满分13分）17．解：设实际距离700km的两地在地图上的图距是xcm，则4：2000000＝x：70000000，解得x＝140．故答案是140．18．解：过E作EG∥BC，交AC于G，∵EG∥BC，E为BD中点，∴DG＝CG，＝，又∵AD：DC＝1：2，∴＝＝，∴BF：FC＝1：3，∵BC＝12，∴BF＝3；故答案为：3．19．解：∵∠C＝90°，cos A＝，∴，设AC＝4x，AB＝5x，则BC＝3x，∵AE⊥AE′，∴∠AEA′＝90°，A′E∥BC，由于折叠，∴∠A′EB＝∠AEB＝（360﹣90）÷2＝135°，A∵∠′EF＝90°，∴∠BEC＝45°，即△BCE为等腰直角三角形，∴EC＝3x，∴AE＝AC﹣EC＝x＝A′E，∵∠A′EF＝∠C＝90°，∠EFA′＝∠BFC，∴△A′EF∽△BCF，∴，故答案为：．20．解：已知剪得的纸条中有一张是正方形，则正方形中平行于底边的边是3，所以根据相似三角形的性质可设从顶点到这个正方形的线段为x，则，解得x＝3，所以另一段长为21﹣3＝18，因为18÷3＝6，所以是第6个．故答案为：6三．解答题（共6小题，满分55分）21．解：（1）x2+4x＝﹣3，x2+4x+3＝0，（x+1）（x+3）＝0，∴x+1＝0或x+3＝0，∴x1＝﹣1，x2＝﹣3；（2）a2+3a+1＝0，∵Δ＝32﹣4×1×1＝5＞0，∴a＝，∴a1＝，a2＝；（3）sin45°•cos45°+tan30°＝×+＝+；（4）2﹣1﹣tan60°+（﹣1）0+|﹣|＝﹣+1+＝．22．解：（1）360°×10%＝36°，故答案为：36°；（2）将这组数据从小到大排列处在中间位置的两个数都是4分，因此中位数是4分，这组数据出现次数最多的数是4分，共出现25次，因此众数是4分，答：中位数是4分，众数是4分；（3）这组数据的平均数为＝3.7（分），答：这组数据的平均数为3.7分．23．解：（1）如图所示，△A′B′C′即为所求，点A′的坐标为（2，2）．（2）由位似图形的性质知BC∥B′C′，取格点P、Q，连接OP、PQ、A′P，∴OP∥B′C′，∴BC∥OP，则∠ADC＝∠BDO＝∠A′OP，∵OP＝A′P＝，∴△A′OP是等腰三角形，∵Q是A′O中点，∴∠PQO＝90°，∴sin∠ADC＝sin∠A′OP＝＝＝．24．解：过点B作BD⊥AC于D，如图所示：由题意得：∠CAB＝90°﹣60°＝30°，∠ABC＝90°+15°＝105°，AB＝1200米，∴∠C＝180°﹣30°﹣105°＝45°，在Rt△ABD中，∠CAB＝30°，∴BD＝AB＝×1200＝600（米），在Rt△CBD中，∠C＝45°，∴BC＝＝＝600≈840（米），答：此时他们与大雁塔的距离BC约是840米．25．解：（1）设批发价y（元/件）与x（件）之间的一次函数表达式为y＝kx+b（k≠0），将（15，210），（22，168）代入y＝kx+b，得：，解得：．当y＝150时，﹣6x+300＝150，解得：x＝25．∴批发价y（元/件）与x（件）之间的一次函数表达式为y＝．（2）240×10＝2400（元），150×25＝37500（元），∵2400＜3600＜37500，∴10＜x＜25．依题意，得：x（﹣6x+300）＝3600，整理，得：x2﹣50x+600＝0，解得：x1＝20，x2＝30（不合题意，舍去）．答：该顾客批发了20件服装．26．解：（1）如图1中，∵A（0，4），∴OA＝4，＝×OB×OA＝8，∵S△AOB∴OB＝4，∵△AOB与△AOC关于y轴对称，∴OC＝OB＝4．（2）如图2中，结论：DG＝GE．理由：作DH∥EC交AC于H．∵OA＝OC，∠AOC＝90°，∴∠DAH＝∠ACO＝45°，∵DH∥OC，∴∠AHD＝∠ACO＝45°，∴∠DAH＝∠AHD，∴AD＝DH，∵AD＝EC，∴DH＝EC，∵∠DHG＝∠GCE，∠DGH＝∠CGE，∴△DGH≌△EGC（AAS），∴DG＝EG．（3）如图3中，以AC为斜边向上作等腰直角三角形ACT，则T（4，4），连接TE．∵TA＝TC，∠TAD＝∠TCE＝90°，AD＝CE，∴△TAD≌△TCE（SAS），∴DT＝TE，∠ATD＝∠CTE，∴∠DTE＝∠ATC＝90°，∴△TDE是等腰直角三角形，∵∠ABD＝∠CEG，∠ABD+∠DBO＝45°，∴∠DBO+∠CEG＝45°，∴∠BDE＝180°﹣45°＝135°，∴B，D，E共线时，满足条件，此时直线BT的解析式为y＝x+2，∴D（0，2），∴E（6，0），∵DG＝GE，∴G（3，1）．。
