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基础题与中考新考法·七年级·上·数学微专题8利用一元一次方程的概念或解求字母的值76考建议用时：20分钟题型分类练6.已知关于x的一元一次方程2(x-1)=4m+8类型一利用方程的概念求字母的值与}(6-3)+5(3x-2)=m的解互为相反1.已知关于x的方程x2m3+1=12是一元一次数，求m的值.方程，则m=2.已知关于x的方程(a-1)x3a-21+4=5是元一次方程，求a的值.类型四利用方程的错解求字母的值类型二利用方程的解求字母的值7.小玥在解关于x的方程5x-7m=14-2x时，3.已知x=2是方程3x-9m=2x-8的解，则m误将“-2x”看成“+2x”,得到方程的解为x=7,则原方程正确的解为4.已知关于x的一元一次方程2m+9x=5x+438小林在解方程8-3，去分母时，方4的解为x=1,求关于x的方程5x-6=2(1程右边的-3忘记乘8，因而得到方程的错解2m)的解。x=2.(1)求a的值；(2)求出该方程正确的解类型三利用两个方程的解的关系求字母的值5.已知关于x的一元一次方程3x+12=6a与x-0=x+a的解相同，则a的值为4872

1111-)++（20+1-2+P402+140S≤8+(2+12+)+2+12+131.1320.(1)球队参加两场比赛后积分X的取值为0,1,2,3,4,6，4*4i6,PX=)=x)+x=11111.111则P(X=0)=二×二=4224411111PX2号×)=4，PX3=X+744448,1.1.1111.11P(X=4)=×5+×=42244,P(X=6)=4X4161所以随机变量X的分布列为：X0234611P16416随机变量X的数学期望：1(2)由于小组赛共打6场比赛，每场比赛两个球队共积2分或者3分；6场比赛总积分的所有情况为12分，13分，14分，15分，16分，17分，18分共7种情况，要使四支球队积分相同，则总积分被4整除，所以每只球队总积分为3分或者4分.若每支球队得3分：则6场比赛都出现平局，其概率为：B=2:1若每支球队得4分：则每支球队3场比赛结果均为1胜1平1负，1.1.1.1.1.1其概率为：B=4×2X4*4*2*465×4x6=所以四支球队积分相同的概率为P=B+B=2+年=5121.61121.（1)解：由题意得e=S-5a 2.5a2=4c2=4a2+b2）,.a2=4b2,点(4,5)在C上，31会亲解得b2=1,.a2=4,

M:Don't worry.It's nothing serious.You're not running a high temperature.W:What should I do?Should I take some medicine?M:I should say you've been working too hard.You'd better take a good rest for a cou-ple of days.I'll give you some pills.Take one of them,3 times a day after meals.Drink plenty of water and avoid fried food.W:Thank you for your advice.M:I hope you'll feel better soon.(Text 10)W:Bob,can we really afford a holiday?M:Now listen.You work hard and I work hard.We're not talking about whether wecan have a holiday.We can talk about where and when.W:Shall we go to Sweden?M:Sweden's colder than Sheffield.I'd rather not go to Sweden.W:What about Florida?Florida's warmer than Sheffield.M:You are right,but it's a long way.How long does it take to get from here to Flori-da?W:All right.Let's go to Hawaii.M:You must be joking.How much would it cost for the two of us?W:But the brochure says the problem of money will disappear.Bob,where do you re-ally want to go?M:I'm thinking of Wales or Scotland.Do you know why?W:Yes,they're right on our doorstep and so close to our home.参考答案第一部分听力1-5 ACABA 6-10 CBACB 11-15 CBCAC 16-20 BBACB第二部分阅读理解第一节21-23CCD24-27DBBA28-31DACA32-35CDBB第二节36-40 ECAGF第三部分英语知识运用第一节完形填空41-45 DBACB46-50 CDACB 51-55 AACDB 56-60 DBDAC第二节61.excellent62.0n63.held64.receiving65.the66.rose67.recognition68.and69.who/that70.to save第四部分写作短文改错1.noticed前加been2.a改成the3.because改成that4.burying改成buried5.are改成is6.Therefore改成However7.that改成which8.opinions改成opinion9.efficiently改成efficient高三英语答案第3页（共4页）

8已知双曲线尽-芳1。>0,6>0)的离心率为，直线1的斜率为-号，且过点M(。b),直线1与x轴交于点C,点D在E的右支上，且满足MD=AM元，则入=cD.二、选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分9,在我们发布的各类统计数据中，同比和环比都是反映增长速度的核心数据指标.如图是某专业机构统计的2022年1一12月中国校车销量走势图，则下列结论正确的是增长率250%241.6%同比增长案环比增长率150%704%86,9%50%14,8%-50%3.09g2896」-33.9%9.5%12.7%2833%199%-36.532.058,9%-51.6%68.59%-6689652.5%5799%44.49%-35.5%37.6%-150%1月2月3月4月5月6月7月8月9月10月11月2月月份A.8月校车销量的同比增长率与环比增长率都是全年最高B.1一12月校车销量的同比增长率的平均数小于环比增长率的平均数C.1一12月校车销量的环比增长率的极差大于同比增长率的极差D.1一12月校车销量的环比增长率的方差小于同比增长率的方差10.已知-T0的左右焦点分别为R.尽.M是C上的动点，△FB的面积的真我realme3,Sho均o真我吓Neo5SE2023082722:16数学第2页（共4页）

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高三第一轮复习周渊来教学10.(17扎记【答案BC二、填空题：本题共2小题，每小题6分，共12分已知清e·海豆少S事中7明四专3￥8身(1)习7则摸出的球中至少有一个黑球的概率为(2)习5【解题分析】记摸出的球中至少有一个黑球为事件A,则P(A)=8-281【解放PA)=1-P(A-器则C【答案器8一顶“过关游戏”规定：在第n关要抛掷一颗般子”次，如果这”次所出现的点数之和大于2，则雕过关.则某人连过前三关的概率是【解题分析】通过第一关时抛掷一次餐子，点数大于2的概率为香=，第二关掬骰子两次，基本事件有=363个，不能过关的有(1,1)、1,2)、(1,3)、(2,1)、(2,2)、(3,1)，共6个，所以过关概率为36,6=536，第三关掬殷子三次本事件有6个，不能过天的基本事件有G于C十C十C=C20个，所以过关概串为1一得-智所以美人前三关的率为号×音×-48611.【答案)三、解答题：本题共3小题，共52分.解答应写出文字说明、证明过程或演算步骤.9.(17分)某学校高二学生参加信息技术学分认定考试，从参赛的学生中随机选取100人的成绩作为样本，得到如图所示的频率分布直方图.(1)求频率分布直方图中α的值，并估计该校此次参赛学生成绩的中位数；(2)在该样本中，若采用分层随机抽样方法从成绩在[45,55)，[85,95)的学生中随机抽取6人调查他们的答题情况，再从这6人中随机抽取3人进行深人调研，求这3人中至少有2人的成绩在[85,95)内的概率.【解题分析】(1)根据频率分布直方图可得(0.005十0.025×2十0.01十a)◆频率×10=1,组距解得a=0.035.由(0.005+0.025)×10=0.3，(0.005+0.025+0.035)×10=0.65，可得0.025中位数位于[65,75).设中位数为x,(0.005+0.025)×10+(x-65)×0.035=0.0100.5,可得x=4950.0057’0455565758595成绩/份所以参赛学生成绩的中位数约为495，7(2)根据频率分布直方图得到，成绩在[45,55)，[85,95)内的频率分别为0.05,0.1，所以在采用分层随机抽样的方法从样本中抽取的6人中，成绩在[45,55)内的有2人，记为A,B,成绩在[85,95)内的有4人，分别记为a,b,c,d,从这6人中随机抽取3人，所有可能的结果为ABa,ABb,ABc,ABd,Aab,Aac,Aad,Abc,Abd,Acd,Bab,Bac,Bad,Bbc,Bbd,Bcd,abc,abd,acd,bcd,共20种.这3人中至少有2人的成绩在[85,95)内的有Aab,Aac,Aad,Abc,Abd,Acd,Bab,Bac,Bad,Bbc,Bbd,Bcd,abc,abd,acd,bcd,共16种.所以这3人中至少有2人的成续在[85,95)内的福率为8-号102(24·G3ZCJ(新高考)数学-XJB-必考-QG】

数学周刊参考答案第1期苏科八年级3版∠DFE,∠EHJ=∠HJF=90°.所以△EHM≌△FJM.BD=12×8×10=40.所以甲、乙二人的土地面积不变15.证明：(1)因为AB∥DE,所以∠B=∠E.因为AC∥FD,拓展训练所以∠BCA=∠EFD.因为FB=CE,所以BC=EF.证明：(1)因为△ABC和△DBE是等腰直角三角形，所以在△ABC和△DEF中，∠B=∠E,BC=EF,∠BCA=∠EFD,AB=BC,BD=BE所以△ABC≌△DEF(ASA).因为LABC=∠DBE=90°，所以ABC-∠DBC=LDBE-∠DBC,(2)因为△ABC≌△DEF,所以AC=DF即∠ABD=∠CBE.在△AC0和△DF0中，∠AOC=∠DOF,∠ACO=∠DF0,在△ABD和△CBE中，AB=CB,∠ABD=∠CBE,BD=BE,所AC=DF,所以△ACO≌△DFO(AAS).所以AO=DO.以△ABD≌△CBE(SAS).16.(1)解：在△ABC和△ADC中，AB=AD,CB=CD,AC=所以AD=CE.AC,所以△ABC≌△ADC(SSS).所以∠ACB=∠ACD.(2)延长AD分别交BC和CE于点G因为∠BCD=80°，所以∠ACB=∠ACD=40°.和F,如图所示(2)证明：在△COD和△COB中，CD=CB,∠DCO=∠BCO,因为△ABD≌△CBE,所以∠BAD=∠BCE.DCO=CO,所以△COD≌△COB(SAS).因为∠BAD+∠ABC+∠BGA=∠BCE+G(3)解：因为△COD≌△COB,所以LDOC=∠BOC=90°，∠AFC+∠CGF=180°，∠BGA=∠CGF,所以所以S形w=Sam+Sa0=2AC~D0+2AC~B0=)AC:∠AFC=∠ABC=90°.所以AD⊥CE.

4.very much;Me too5.Many of6.is good at swimmingIⅡ.1-5 EBGDASection CI.1-5 DSDSS6-10 SDSSDII.1.Of course .2.hero3.swimming4.drawing5.matches6.team7.talk aboutlⅢ.l.a member of2.my favourite3.make me happy4.open the box5.play volleyball with6.feel great。

that it has a collection of roughly 400 thousands art works,paintings and sculptures included.thousandIn front of the museum is a glass pyramid designed by leoh Ming Pei.Who makes LouvreWhatworld-famous is Da Vinci's Mona Lisa.It is a pity that not all the collections are openly to the public,and Louvre is very worth aopenwellvisit.书面表达One possible version:Dear Tom,As you are very interested in Chinese kung fu,I am very excited to invite you to attendthe Martial Arts Festival.It will be held next weekend in my city.When being there,we can visit an exhibit,from which we can learn the history and signif-icance of Martial Arts Festival.Besides,we can watch many martial arts competitions and enjoy some wonderful shows.At the same time,we can also taste some delicious local snacks.Ibelieve you will really enjoy itLooking forward to your early reply.Yours,Li Hua附：听力部分录音材料(Text 1)W:Excuse me,sir,didn't you see the red light?M:Oh,I thought I could make a right turn on red here as I am hurrying back to work afterdinner.(Text 2)W:What can I do for you?M:I want a ticket to New York.How can I get there as soon as possible?W:This afternoon there's a flight leaving at 3:30.You'll get there 3 hours later.Is that OK?M:OK,thank you.(Text 3)W:So when are you going to Sweden,tomorrow or the day after tomorrow?M:Neither.Don't you see I'm packing now?My train leaves in just five hours.W:I thought you were just going to do your laundry.(Text 4)W:Hey Kevin,where are you going?M:I'm heading over to the gym.I've been studying all day at the library and I feel an hour ofexercise would do me good.·33·【24·G3DY·英语·参考答案一R-必考-QG

绝密★启用前天一大联考安微专版2023一2024学年（上）高年级阶段性测试（一）英语考生注意：1.答题前，考生务必将自已的姓名、考生号填写在试卷和答题卡上，并将考生号条形鼎贴在答题卡上的指定位置。2回答选择题时，选出每小题答案后，用铅笔把答题卡对应题目的答案标号涂黑。男改动，用橡皮擦干净后，再选涂其他答案标号。回答非选择题时，将答案写在答卡上。写在本试卷上无效。obi3.考试结束后，将本试卷和答题卡一并交回。Do4907,m「f哭)io面人.“oo2第一部分听力（共两节，满分30分）rlO er oif norpiom odt biod wrtasl o ne3 ied做题时，先将答案标在试卷上。录音内容结束后，你将有2分钟的时间将试卷上的答案转涂到答题卡上。第一节（共5小题；每小题1.5分，满分7.5分）91roB91sdmu打Tsh9Wo179fo山听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。例：How much is the shirt?A.￡19.15答案是C。B..18.phin..￡9.15..0oP6·，月1.What does the man want the woman to do?(A)Work hard.B.Do her homework.2.Where does the conversation take place?Vork overtime.In a shop.B.In a plane.3.What does the woman want to do?In an office.(A.Enjoy a computer.B.Play computer games.4.What are the speakers talking about?Go to the computer store.(A.A speech.B)A clock.C.Their teacher.5.What does the man speaker think of his way of getting to South Korea?A.Boring.B.Expensive.第二节（共15小题；每小题1.5分，满分22.5分）CPleasant.听下面5段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题给出5秒钟的作答时间。每段对话或独白读两遍。听第6段材料，回答第6、7题。6 What did the woman do just now?A She restarted her computer.B.She typed a report.ewatched a film.英语试题第1页（共8页）

19.(12分)如图，在四棱锥P-ABCD中，PAL平面ABCD,PA=AD=2AB=2CD=4,∠BMD=∠CDA=号(I)求证：BC∥平面PAD;(Ⅱ)求直线PD与平面PBC所成角的正弦值.20.(12分)如图，已知平行六面体ABCD-AB,C,D1中，BC⊥DC,D,C⊥DC1,E为D1C,DC1的交点，且DC1⊥BE.(I)求证：平面CCDD⊥平面ABCD;(Ⅱ)若DD1⊥DC,AB=2BC=2,求二面角A-BE-D的余弦值.ED21.(12分)已知各项均不为0的数列{an}的前n项和为Sn,且2”an+1=nSn(I)若b=0,求数列+的前n项和T;aj)若62，求的最大值22.(12分)已知函数f(x)=2x-2(a+1)e+ae2(a∈R).(I)若f(x)单调递增，求a的值；(Ⅱ)设x1,x2(x12.数学试题第4页（共4页）

B.Interesting. C.Well-organized. 听第7段材料，回答第8至10题。 8.What do the speakers plan to do next? A.Rush to the store. B.See the girl's classmates. C.Visit the girl's grandparents. 9.What did the teacher ask the girl to do? A.Make a list. B.Get materials ready. C.Do some homework. 10.When does the girl need to have her materials ready? A.Later today.

第三部分 完形填空（共20小题；每小题1分，满分20分） 阅读下面短文，从短文后各题所给的A、B、C和D四个选项 中，选出可以填入空白处的最佳选项 My grandfather insists on getting me coffee.He is ninety- two years old,but he 15 my help and rolls his 16 over to the table in the corner,filling a cup with boiling black 17 His room at the nursing home is 18,nothing more than a bed and a bathroom.His walls are covered in 19 of his six children and nineteen grandchildren.I 20 my own face,sev- en years old and covered in chocolate.When I 21 the photo, he laughs."You were the fattest little kid.Your mom was so 22 99 My grandfather has many fine 23 and wisdom is one of

M:Good afternoon,this is Mike with Wash-N-Dry.How can I help you? W:Hello,I'm the manager at 909 Chestnut Street.A dryer here isn't working well. M:I'm sorry about that.We'll fix the problem right away.Be- fore I send someone out there,I'd like to ask you a few ques- tions.How long has the dryer been like this? W:For two weeks so far. M:Can you describe what's wrong with it? W:Yes.The clothes used to dry perfectly with $2.Last week, we had to use 3 for the same amount of clothes.This week, we have to use $4. M:Oh,that's bad!Do you know which dryer it is?

format.You will learn all about the history and trivia that sur- rounds Washington and visit the major monuments and attrac- tions DC has to offer. Please Note:Rates for this tour vary by day of the week. When you choose your specific date on the availability calendar, the rates for that date will be displayed. The Blossoms Tour Duration:3 hours Price:56 BEST WAY to experience the Cherry Blossoms!Each year from mid-March to mid-April,see the beautiful Cherry Blossoms in Washington DC and get great photos because you'll be led to all the best spots by the best guides.The annual spring bloom in

both gases.A final pair of rings was a control and received no added gases.The tests took place over two summers. During each field season,the scientists counted how many times insects visited the flowers in each ring. "The results were much more serious than we thought,' Ryalls says."Adding both the diesel exhaust and ozone pollution caused up to 90 percent less insects to be able to find the flowers that they need for food,he says.This was in comparison to the pollutant-free rings.In some cases,only some 30 percent of the polli nating insects even entered the circles with pollution. Many insect populations have been falling due to changes in land use,climate change and exposure to pesticides.This study focused on insects finding flowers.But insects also use smells for

C.Doing business. 3.What does the woman suggest doing? A.Studying harder. B.Spending more time learning English. C.Talking more with English speakers. 4.How does David probably feel? A.Happy. B.Disappointed. C.Surprised. 5.How long did the concert last? A.30 minutes. B.60 minutes. C.90 minutes.

【答案】 One possible version: Dear Mr Edward, I'd like to ask you to take part in "The differences between Chinese and Western Educational Systems"event to be organized by the Students'Union in our school. Scheduled from 8:00 am to 5:00 pm next Sunday,the event aims to help students learn more about the topic.There will be interesting lectures given by some experts and various forms of performances by students. We'd really appreciate it if you could offer some suggestions on how to improve the event.Looking forward to your reply. Thank you！ Yours sincerely, Li Hua

第三部分语言运用（共两节，满分30分） 第一节（共15小题；每小题1分，满分15分） 阅读下面短文，从每题所给的A、B、C、D四个选项中选出可以 填人空白处的最佳选项。 Having a job is great.It means I can have a place to 41 in.And with an above-average job,I can afford a car and over- seas vacations. However,I also understand how 42 it is to live with a below-average job,having had many jobs of this kind before.It's quite awful. I emailed my 43 to every company with an online careers page.I even printed my resume(简历)and 44 it out to hundreds of offices.

【答案】 One possible version: Paragraph 1: Justin walked in the headmaster's office.When the head- master asked Justin to explain his behavior,Justin broke into tears.He told the headmaster about his sadness of living without his parents.Then the headmaster said,"I see.I know you are having a hard time losing your parents and living with your aunt. But putting it on someone else is not a good way.Take one step at a time to show your kindness.The headmaster comforted Justin some more and told him that everything was going to be alright."If you feel like you need someone to talk to,you can find me here anytime.

25.Robert Winston's reaction on the train can be described as A.a way of returning good for evil B.a good example of stopping rudeness C.an answer to the call of the journalists D.an act of answering rudeness with rudeness 26.Being infected with rudeness can possibly lead to A.wiser decisions B.poorer work performance C.more destructive revenge D.more face-to-face communication

senior high school.Live away from my home for the first time,I found life there a bit difficult to get used.And the training officer was strict with her.I once thought I couldn't be stick to it.But anyway,I succeeded.The training made me much strong to adapt to life than before,but I think the difficulties have now become a precious memory in my life.In short,learning to regard the challenges of life as a stepping stone to future success and make a best of them.

【答案与解析】 本文介绍了The Dickens Exhibition这个展览的有关情况。 21.B 3By recreating the atmosphere of Victorian London through sound and projections可知，游客可以通过声音和影像 欣赏到维多利亚时代伦敦的城市景象。 22.D The great social problems of the 19th century will al- so be examined可知，l9世纪伦敦的重大社会问题也将被研 究，所有这些都为狄更斯的作品奠定了基础。 23.B根据最后一段第1句可知，游客可以在线预订行程，其中 The Dickens Exhibition下午的门票和酒店住宿的费用包括在 预订价格中。

reading a story,we are also imagining how the characters are feeling.We use our own experiences to imagine how we would feel in the same situation. Children who read do better at school.And they don't just do better at subjects like reading,English and history. 38 Reading is a great form of entertainment!A paperback book or an e-reader doesn't take up much space so you can take it any where and you'll never be lonely or bored if you have a book in your bag. 39 Reading relaxes the body and calms the mind. 40 The constant movement,flashing lights and noise are quite stressful for our brains.When we read in silence,the black print on a white page is much less stressful for our eyes and brains.

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