华伦中学试题

福建省福州市台江区华伦中学2023-2024学年七年级上学期
期末数学试题
学校:___________姓名：___________班级：___________考号：___________
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二、填空题
11．11-的相反数是．
12．已知2230m x -+=是关于x 的一元一次方程，则m =．
13．841的算术平方根是．
14．若一个角的补角是其余角的3倍，则这个角的度数为．
15．如图，点C 是线段AB 上一点，点M 是线段AB 的中点，点N 是线段 AC 的中点． 若线段MN 的长为4，则线段BC 的长度是．
16．“幻方”最早记载于春秋时期的《大戴礼》中，现将1、2、3、4、5、7、8、9这8个数字填入如图1所示的“幻方”中，使得每个三角形的三个顶点上的数字之和都与中间
正方形四个顶点上的数字之和相等．现有如图2所示的“幻方”，则()m n x y --的值是．
1。

福建省福州市台江区福州华伦中学2023-2024学年八年级下学期月考数学考试试题一、单选题1．下列图形中，既是轴对称图形又是中心对称图形的是（ ）A ．B ．C ．D ．2．关于x 的一元二次方程20ax bx c ++=，若420a b c -+=，则该方程必有一个根是（ ） A ．2x =- B ．2x = C ．12x =- D ．12x = 3．某种芯片实现国产化后，经过两次降价，每块芯片单价由128元降为88元.若两次降价的百分率相同，设每次降价的百分率为x ，根据题意，可列方程A ．128（1 - x 2）= 88B ．88（1 + x )2 = 128C ．128（1 - 2x ）= 88D ．128（1 - x )2 = 884．如图，44⨯方格中的ABC EFD △∽△，则相似比为（ ）．A ．12 B C ．25 D 5．某兴趣小组有5名成员，身高（厘米）分别为：161,165,169,163,167．增加一名身高为165厘米的成员后，现兴趣小组成员的身高与原来相比，下列说法正确的是（ ） A ．平均数不变，方差不变B ．平均数不变，方差变小C ．平均数不变，方差变大D ．平均数变小，方差不变．6．在如图所示的正方形网格中，以点O 为位似中心，作△ABC 的位似图形，若点D 是点C 的对应点，则点A 的对应点是（ ）A ．EB ．FC ．GD ．H7．某校学生期末操行评定奉行五育并举，五方面按32212∶∶∶∶确定最终成绩．王林同学本学期五方面得分如图所示，则王林期末操行最终得分为（ ）A ．9.2B ．9.1C ．9.3D ．9.48．在平面直角坐标系中，抛物线22y x =保持不动，将x 轴向上平移1个单位（y 轴不动），则在新坐标系下抛物线的解析式是（ ）A ．221y x =+B ．221y x =-C ．()221y x =-D ．()221y x =+ 9．如图，在ABC V 中，135BAC ∠=︒，将ABC V 绕点C 逆时针旋转得到DEC V ，点A ，B 的对应点分别为D ，E ．当点A 、D 、E 在同一条直线上时，下列结论不正确．．．的是（ ）A ．ABC DEC ≌△△B ． AE AB CD =+C ． AD = D ． AB AE ⊥10．如图，在Rt ABC △中，90,BAC AD BC ∠=︒⊥于点,D ACB ∠的平分线CE 交AB 于点E ，交AD 于点F ．若,,BD a DF b DC c ===，则关于x 的一元二次方程240ax bx c ++=的根的情况（ ）.A ．有两个相等的实数根B ．有两个不相等的实数根C ．只有一个实数根 D ．无实数根二、填空题11．如果2x =是一元二次方程210ax bx ++=的一个解，则2a b +的值是．12．如图，五线谱是由等距离、等长度的五条平行横线组成的，同一条直线上的三个点 ,,A B C 都在横线上，若线段4AB =，则线段BC 的长为．13．如图，△COD 是△AOB 绕点O 顺时针旋转38︒所得到的图形，点C 恰好在AB 上，AOD 90∠=︒，则B ∠的度数是．14．小明用()()()22221210133310S x x x ⎡⎤=-+-++-⎣⎦L 计算一组数据的方差，那么12310x x x x ++++=L ．15．如图，在ABCD Y 中，23AE AD =，连接BE ，交AC 于点F ，10AC =，则CF 的长为．16．如图，抛物线y ＝ax 2与直线y ＝bx ＋c 的两个交点坐标分别为A （﹣4，8），B （2，2），则关于x 的方程ax 2﹣bx ﹣c ＝0的解为．三、解答题17．解方程：(1)22x x =；(2)2220x x --=．18．已知关于x 的一元二次方程226910x mx m -+-=．(1)求证：方程有两个不相等的实数根；(2)设此方程的两个根分别为1x ，2x ，且12x x <．若2123x x =-，求m 的值．19．如图，已知在四边形ABCD 中，ADB ACB ∠=∠，延长AD 、BC 相交于点E ．求证：AC DE BD CE ⋅=⋅20．我市某校为了解九年级学生体育备考情况，对全校九年级240名男生进行了体育测试，并随机抽取甲、乙两个班（两班男生人数相同）各10名男生的跳绳测试成绩并整理、描述、分析．【收集数据】甲、乙两班10名男生的跳绳成绩（单位：次）如下：甲：135 149 198 150 160 123 155 160 137 186乙：100 132 133 146 146 152 164 173 197 210【分析数据】根据以上数据，得到以下统计量．根据以上信息，回答下列问题：(1)表格中的=a ，b =，c =；(2)综合上表中的统计量，你认为哪一个班的男生成绩较好，并说明理由：(3)洛阳市2024年中招体育考试九年级终结性评价评分标准规定：跳绳男子满分标准为150次，估计该校本次测试成绩满分的男生人数．21．直播带货新平台“西方甄选”所推销的大米成本为每袋40元，当售价为每袋80元时，每分钟可销售100袋，为了吸引更多顾客，“西方甄选”采取降价措施，据市场调查反映：销售单价每降1元，则每分钟可多销售5袋，设每袋大米的售价为x 元（x 为正整数），每分钟的销售量为y 袋．(1)求出y 与x 的函数关系式；(2)设“西方甄选”每分钟获得的利润为w 元，当销售单价为多少元时，每分钟获得的利润最大，最大利润是多少？22．在ABC V 中，90C ∠=︒，()045CAB αα∠=︒<<︒，将ABC V 绕点A 逆时针旋转，旋转角为()0180ββ︒<<︒，记点B ，C 的对应点分别为D ，E ．(1)若ABC V 和线段AD 如图所示，请在图中作出ADE V （要求；尺规作图，不写作法，保留作图痕迹）；(2)M 是AB 的中点，N 是点M 旋转后的对应点，连接MN ，CD ，BD ，则是否存在β与α的某种数量关系，使得无论α取何值时，都有MN CD =？若存在，请说明理由，并直接写出此时BC 与BD 的数量关系；若不存在，也请说明理由．23．为了加强视力保护意识，欢欢想在书房里挂一张测试距离为5m 的视力表，但两面墙的距离只有3m .在一次课题学习课上，欢欢向全班同学征集“解决空间过小，如何放置视力表问题”的方案，其中甲、乙两位同学设计方案新颖，构思巧妙． 图例(1)甲生的方案中如果大视力表中“E ”的高是3.5cm ，那么小视力表中相应“E ”的高是多少？(2)乙生的方案中如果视力表的全长为0.8m ，请计算出镜长至少为多少米．24．如图1，在ABC V 中，90,,BAC AB AC D ∠=︒=是AB 边上不与,A B 重合的一个定点．AO BC ⊥于点O ，交CD 于点E ．DF 是由线段DC 绕点D 顺时针旋转90︒得到的，,FD CA 的延长线相交于点M ．(1)求证：ADE FMC △∽△；(2)求ABF ∠的度数；(3)若N 是AF 的中点，如图2．求证：ND NO =． 25．已知抛物线2y x mx n =++，其中m ，n 为实数．(1)若抛物线经过点(),9m n ，请判断抛物线与x 轴的交点个数：(2)抛物线经过点()1,0x ，()2,0x ，()1,a ，()3,b ． ①若211x x -=时，求a b +的取值范围；②若1213x x <≤<，当ab 取得最大值时，求抛物线的解析式．。

2024届福建省福州市华伦中学中考联考英语试卷含答案注意事项1．考生要认真填写考场号和座位序号。

2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。

第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。

3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。

Ⅰ. 单项选择1、— Excuse me, could you tell me ?— Sorry, sir. I wasn't there at that time yesterday.A．how the accident happens B．how does the accident happenC．how the accident happened D．how did the accident happen2、–– I am so glad that you are safe now.––Thank you! When I realized I couldn’t ______ the fire, I ran at once.A．give out B．put out C．clear out3、—Are you clear about the job of a policeman, Ben?—Yes, to keep people ________ and the society in good order.A．busy B．safeC．lucky D．healthy4、—What kind of books do you like?—I like funny storybooks. They're very_.A．boring B．lazy C．quiet D．interesting5、A walk every day is enough to keep you healthy and in good shape．A．30-minute B．30-minutes C．30 minute's D．30-minutes'6、—What do you think of the movie you saw last night?—I think it is worth ________.A．seeing B．sees C．to see7、Mike looked the girl up and down．He wondered ______.A．where does he meet her B．where had he met herC．where he meets her D．where he had met her8、— How often do I need to feed my pet dog, Mr Henry?—Once or twice a day.A．go for a walk with B．give food to C．take care of9、It’s very hot. But I think it’s impolite to _____ your clothes in public.A．set off B．turn offC．take off D．get off10、―WeChat has made a great difference to people's life.―. We can use it to communicate with others easily.A．Completely B．Possibly C．Probably D．ExactlyⅡ. 完形填空11、It’s 12 o’clock. A man goes into a fast food restaurant for 1 . “Hi!” a waiter says. “Can I 2 you?” “I’d like some French fries, a 3 and a medium Coke,” says the man. “What 4 foods would you like? ” asks the waiter. “No,” the man answers. “That’s 5 .” “For here or to go?” asks the waiter. “To go, please,” says the man.The man 6 his lunch and the waiter puts the food into a bag. Then the man goes away 7 the bag. He goes out of the restaurant. He looks 8 and finds a beautiful park over there. So he walks to the park. He sits down and opens the bag to enjoy his delicious food. Suddenly(突然) he stops eating. He finds that there is also some9 in the bag. “Oh! That’s the money for my lunch,” says the man. Then he goes back to the restaurant because he doesn’t want to 10 his lunch for free.1．A．breakfast B．lunch C．dessert D．dinner2．A．ask B．call C．help D．answer3．A．bread B．meat C．dumpling D．hamburger4．A．other B．the other C．another D．any5．A．all B．her C．them D．me6．A．cuts down B．looks at C．eats out D．pays for7．A．of B．with C．from D．on8．A．for B．at C．like D．around9．A．money B．apples C．soup D．pancake10．A．play B．give C．get D．bringⅢ. 语法填空12、One sunny afternoon Bernard Shaw was having a walk in the quiet field. The air was fresh and the view was beautiful. While he 1．(walk), a bike rider ran into him. Mr Shaw 2．(fall) to the ground. The rider was very sorry. He got off his bike 3．(help) Mr Shaw get up. Luckily, Mr Shaw 4．(not hurt). "I'm so sorry!" said the rider. "Oh, no," said Bernard Shaw. "I should 5．(say) sorry. I'm sorry for not 6．(give) luck to you." Mr Shaw looked at the puzzled rider and added, "If you killed me, you know, you would be famous all over the world."Ⅳ. 阅读理解A13、Several days ago, Brend a had a car accident that led to one of her legs being cut off. Since then she didn’t talk to anyone.“I wish I could bring her friends to visit her,” said Brenda’s mother. “But it’s a long bus trip.” The nurse smiled, “Don’t worry. We have a plan.”Later that day, the nurse had taken Brenda to another room. “Here’s your new roommate, Annie Wiggle-Do,” the nurse introduced a dark-hair teenager on the other bed.As soon as the nurse left, she jumped out of her bed with her only foot and sat at the other end of Brenda’s bed, “I lost my leg from bone cancer,” she said. “What happened to yours?” Brenda was so shocked that she couldn’t say a word. “You’re lucky.” Annie continued. “You’ve still got your knee. They had to take mine.”“I’d like to have a chat with you, but my friends are coming any time now, so I have to get ready.” Annie said when she took off her hair! Her head was completely bald(秃头的).“Oh, I forgot to tell you, the medicine they gave me to kill the cancer also killed my hair.” Annie looked out he r wigs(假发), brown and yellow, short and long, straight and curly.“That’s why I thought up ‘Annie Wiggle-Do’.” Annie smiled. “Get it? Any wig will do? Annie Wiggle-Do?” “When Annie’s friends came, she introduced Brenda to them all. Before long, Brenda star ted chatting with Annie and her friends. They didn’t make her feel like a strange person at all!The girls shared their names with each other. When it was time to go to bed, Brenda said, “Good night,Annie-Wiggle-Do. Can’t wait till morning.”1．We can infer that no friends visited Brenda because ________.A．she had no friends at school B．she didn’t want to see her friendsC．her friends were very busy D．her friends knew she had an accident2．In order to cheer Brenda up, the nurse planned to ________.A．introduce some healthy friends to herB．let her share the same room with AnnieC．show her some more seriously injuredD．move her to a room filled with light and music3．When Brenda first saw Annie, she ________.A．discovered that Annie’s head was baldB．t hought up “Annie-Wiggle-Do”C．was too surprised to say anythingD．shared her dream with Annie4．Which of the following about Annie is true?A．She has different kinds of wigs. B．She thinks she is strange.C．Her sin cancer killed her hair. D．She lost both her legs.5．Which of the following words can best describe Annie?A．Patient. B．Careful C．Polite D．BraveB14、Do you enjoy visiting a museum? Did you ever make a plan before a visit? Every museum must have something that attracts you. And there are many possible ways to enjoy yourself in a museum.If you follow these steps below, you'll know what is worth seeing and doing, so that you can make the most of your time at the museum.Decide what museum you will visit. There are so many different kinds of museum and you first need to find one that you like. It's easy for you to choose one and start an enjoyable visit!Do some research online. Every museum now has a website which allows you to look through the information about it. On the website, you may look for such things as:The exhibits.See what is on show at the museum at all times, and what special exhibitions are held for a short time.The history of the museum—There will often be very interesting stories about the exhibits and the benefactors(捐赠者).That can make your visit more interesting.Activities—See whether there are talks, tours or special activities on the day when you visit. Many museums hold some activities that meet the interests of all age groups.Cost, food and storage—It’s impo rtant to know how much the visit will cost. Y ou hate to decide whether or not you can eat there. You might also need to find out about our transportation needs, as well as storage for coats, bags etc.. Learn at least one thing on your visit. It’s always go od to take away something new from your visit.Plan breaks into your visit.When you walk around, standing here and studying exhibits there, you may become very tired. So it’s important to take breaks. A break is a good opportunity for you to think of what you have seen and what else you might want to do in the museum.Take a friend of two. Visiting museums is always a lot more fun when you are with someone else. You can talk over what you’re seeing. A friend also brings another way of thinking when you talk about the exhibits.1．According to the passage, we should first ________.A．do some research online B．make a plan for lunchC．decide on a museum to visit D．choose a friend to go with2．To make our visit more interesting, we can ________.A．organize activities like special shows and talksB．read the stories about exhibits and benefactorsC．learn about the interests of all age groupsD．walk around the museum without breaks3．If we visits museum with friends, we can ________.A．share the experience with them B．come up with strange ideasC．cut down the cost of the visit D．discuss the next visit plan4．What does the passage mainly talk about?A．What to do in a museum. B．When to visit a museum.C．Where to find a museum. D．How to enjoy a museum.C15、When I was in primary school, I got into a major argument(争论) with a boy named Michael in my class. I have forgotten what the argument was about, but I have never forgotten the lesson I learned that day.I was convinced that I was right and he was wrong, and Michael was just as convinced that I was wrong and he was right. The teacher decided to teach us a very important lesson. She brought us up to the front of the class, placed Michael on one side of her desk and me on the other. In the middle of her desk was a large, round object. I could clearly see that it was black. And she asked Michael what color the object was, “White,” he answered.I couldn’t believe he said the object was white, when it was obviously black! Another argument started between Michael and me, this time about the color of the object.The teacher told me to go stand where Michael was standing and told him to come and stand where I had been. We changed places, and now she asked me what the color of the object was. I had to answer, “White.” It was an ob ject with two differently colored sides, and from his viewpoint（视角）it was white. Only from my side it was black.My teacher taught me a very important lesson that day. You must stand in the other person’s shoes and look at the situation through their eyes in order to truly understand their perspective.1．What was the argument about between the author(作者) and Michael at first?A．The color of the object. B．The answer of a math question.C．The author was not sure. D．The time of beginning class.2．The author fe el ________ when he heard Michael’s answer.A．happy B．unbelievable C．tired D．helpless3．What’s the meaning of the word underlined in Paragraph 2?A．确信B．辩解C．怀疑D．猜测4．What did the teacher put in the middle of her desk?A．A round and colorful object. B．A white and black bottle.C．An object with two mirrors D．An object with two colors.5．What’s the best title for the passage?A．An Argument B．My School LifeC．My Friend-Michael D．Different ViewpointsD16、Last week, Chicago became the first ci ty in the US to join the “Lights Out Plan”. People turned off the lights in the city’s tallest buildings, so that thousands of birds could get to their winter homes. Every year in autumn, some birds fly over Chicago on their way to the south, and come back the next spring．Lights mean danger to birds. Birds find their way by looking at the stars in the sky. Lights in tall buildings are so bright that birds may mistake them as stars. This means they can not find the right way to go home．This month, about 300 types of birds are flying over Chicago to go back to the south to live through the cold winter. Birds fly to warmer places for a few reasons. Many birds cannot live in the cold, so they fly to warmer places. But there are other reasons，too. Birds need to look for food in the south. Another reason is that they want to have baby birds. Many birds like to have their baby birds in the same “house” they lived in last year, so they fly back there.There are about 9,000 kinds of birds in the world, and about 600 kinds of birds migrate（迁徙）. Some birds can fly a very long way. Sometimes they fly to other countries. We have fewer birds today because there are fewer places for birds．1．Why did people in Chicago turn off their lights last week?A．Because people wanted to save money．B．Because people liked the dark night．C．Because people were afraid that birds would make much noise．D．Because people were afraid that birds would lose their way．2．Today we have fewer birds because __________．A．lots of birds are often ill B．people kill lots of birdsC．there are fewer places for birds D．other animals eat them3．Which of the following statements is NOT true?A．All birds fly to warmer places every year．B．Some birds have to fly to warmer places in autumn．C．Some birds can fly a long way to other countries．D．About 600 kinds of birds migrate in the world．E17、Most people may think that people who write computer code (代码) must be good at Maths and logical (逻辑的) thinking. However, people who write computer code say that creativity is also important for writting code.Software developers (开发者) in the USA have created a game called Osmo Coding Jam. The game is designed to help children use the creative side of their minds when learning to code. Children can play the game on iPads.Tanya Dodge is the mother of two children who play the game. According to her, these activities give her children important skills for the future. “It’s an analytical (分析的) skill,” said Dodge.But the developers believe writing code is not just an analytical skill. “We want to explore the creative side of coding that I think is often not as explored,” said Felix Hu, an Osmo engineer. Hu added, “The coolest part is that we’re teaching kids how to be creative with code and that’s a really important thing that kids should get comfortable with because coding is creative.”Hu also sees many parents who feel that software code is a second language that children need to learn to succeed in future jobs. Tanya Dodge agrees. She said, “l think you’re going to have to understand the idea of coding will work well in the future.” Hu also explains that very often kids grow up not understanding how a computer works. He says by breaking it down to a lower level, kids can understand that the computer isn’t as smart as they think it is.1．What is Osmo Coding Jam designed for?A．Training kids’ logical thinking.B．Helping kids learn to code fast.C．Helping children learn Maths well. D．Helping kids become more creative.2．What does Tanya Dodge think of Osmo Coding Jam?A．It needs to be improved. B．It can help kids play well.C．It is of great help to today’s kids.D．It is not perfect in training kids’ analytical skills.3．What can we learn from the passage?A．If someone doesn’t learn Maths well, he or she can’t write code.B．Creativity comes from writing code in daily life.C．Writing code is just a skill which helps kids to analyze things well.D．A lot of parents agree that software code will be useful for their kids’ future jobs.4．The writer wrote this passage __________.A．to tell how to learn to code well B．to tell about a new game for kidsC．to encourage kids to learn to study well D．to show the importance of creativityF18、Mails, games, music, news, chat rooms and shopping ! The Internet is part of the way we live to day. It’s very useful and it's easy to get onto the Internet. The only thing we need to do is to use a modem which is used for connecting a computer to a telephone line. The Internet is changing and growing all the time.More and more people have computers or cellphones(手机) and use the Internet. Using the Internet means using the World Wide Web (That’s “www”you always hear about.) The Web (网) has a lot of websites in it. They are the places you go to get information and do things.Where do these websites come from ? They are made by web designers(设计者). What happens when you click on a word or a picture ? You are sent to another page. It’s all because of the web designer. Web designers do a lot of work by using a computer programming language.Is Web design a ll about computer programming ? No. It’s about making something new. Web designers must imagine a lot when they are making a website. It must look good and be fun to use. A big part of Web design is art. They choose the best pictures and colors to make the website look good. They also write the things that you see on the website. An important part of their job is to share ideas with the website manager about how to design the website well. 1．This passage is mainly about ___________ .A．computer programming language B．the web designers’ workC．the website manager’s work D．the way to get onto the Internet2．More and more people are using the Internet because it’s _________ .A．easy and useful B．beautiful and funnyC．colorful and hopeful D．changing and growing3．Which of the following is wrong?A．“www” means “World Wide Web”.B．There’re a few websites on the web.C．The Internet has changed people’s lives.D．We can do things like shopping on the Internet.4．The web designers do a lot of work except _______.A．making the websites new and beautiful B．writing things on the InternetC．doing the computer programming D．following the manager’s ideasⅤ.书面表达19、书面表达：假定你是李华，你的英国朋友Mike得知你们开展了“做生态小公民，建设美丽家乡”的活动，他来信表示很感兴趣并想了解具体细节，请给Mike写一封回信向他描述你（们）曾经做过的一件事或参与的一次活动。

福建省福州市台江区福州华伦中学2023-2024 学年八年级下学期月考数学试题一、单选题1．如图标志既是轴对称图形又是中心对称图形的是（ ） A ．B ．C ．D ．2．端午前夕，学校食堂调查学生对豆沙粽、蛋黄粽、肉粽这三种粽子的喜爱程度，以决定最终的采购方案．下面统计量中，最值得关注的是（ ） A ．平均数B ．方差C ．中位数D ．众数3．如图，AD BE CF ∥∥，若2AB =，4BC =，5EF =，则DE 的长是（ ）A ．3B ．5C ．4D ．2.54．已知一组数据23，27，20，18，x ，12，若它们的中位数是21，那么数据x 是（ ） A ．23B ．22C ．21D ．20二、多选题5．如图，在平面直角坐标系中，AOB V 与COD △是以原点为位似中心的位似图形，若2OC OA =，点B 的坐标为()1,3，则点D 的坐标为（ ）A ．()2,6B ．()2,6--C ．()3,9D ．()3,9--三、单选题6．如图，在ABC V 中，30A ∠=︒，将ABC V 绕点C 逆时针旋转得到A B C ''△，点A ，B 的对应点分别是A '，B '，边A B ''经过点B ，若42BCA '∠=︒，则ABC ∠的大小为（ ）A ．62︒B ．65︒C ．70︒D ．72︒7．甲、乙、丙、丁四位学生进行“汉字拼写”训练，每位同学五次训练成绩的平均数均为90，方差分别为211.6S =甲，229.2S =乙，211.2S =丙，2 1.2S =丁．若要从中选择一名发挥稳定的学生参加比赛，应选择（ ） A ．甲B ．乙C ．丙D ．丁8．如图，在ABC V 中，E 、F 分别是AB 、AC 上的点，EF BC ∥，且12AE EB =，若AEF △的面积为2，则四边形EBCF 的面积为（ ）A ．16B ．14C ．12D ．89．如图，D 是ABC V 的边AB 上的一点，那么下列四个条件不能单独判定ABC ACD V V ∽的是（ ）A ．B ACD ∠=∠ B ．ADC ACB ∠=∠ C ．AC ABCD BC= D ．2AC AD AB =g10．小红从图所示的二次函数2y ax bx c =++的图象中．观察得出了下面五条信息：①0b >；②0abc >；③0a b c -+>；④230a b -=；⑤40c b ->，你认为其中正确信息的个数有（ ）A ．2个B ．3个C ．4个D ．5个四、填空题11．在平面直角坐标系中，点(1,2)-关于原点对称的点的坐标是．12．已知抛物线()220y ax ax c a =-+>，且经过点()12,y -，()23,y -，试比较1y 和2y 的大小：1y 2y （填“>”、“<”或“=”）．13．若一组数据1x ，2x ，3x ，…，n x 的平均数为4，方差为2，则122024x -，222024x -，322024x -，…，22024n x -的方差为．14．若m 是一元二次方程230x x --=的根，则325m m m +-的值为15．某种型号的小型飞行器着陆后滑行的距离(S 单位：米)关于滑行的时间(t 单位：秒)的函数解析式是2100.25S t t =-，此飞行器滑行的最大距离是米．16．如图，在正方形ABCD 中，点O 是对角线AC BD ，的交点，点E 在边CD 上，连接BE ，交OC 于点G ，过点C 作CF BE ⊥，垂足为点F ，连接OF ．现给出以下结论： ①45BFO ∠=︒； ②BE 平分CBD ∠； ③BOF BED V V ∽；④若2DE CE =，则点G 是OC 的中点． 其中正确的是 .（写出所有正确结论的序号）五、解答题 17．解方程： (1)220x x +=； (2)24410x x -+=．18．如图，有一池塘，要测池塘两端A B ，的距离，可先在平地上取一个点C ，从点C 不经过池塘可以直接到达点A 和B ，连结AC 并延长到点D ，使12CD AC =，连结BC 并延长到点E ，使12CE BC =，连结DE ．量得DE 的长为15米，求池塘两端A B ，的距离．19．已知关于x 的一元二次方程()2330x m x m -++=．(1)求证：无论m 取任何实数，方程总有实数根；(2)若一元二次方程的两根为1x ，2x ，且满足22121219x x x x +-=，求m 的值． 20．如图，在平面直角坐标系中，ABC V 的三个顶点坐标为(34)A -，，(42)B -，，(21)C -，，ABC V 绕原点逆时针旋转90︒，得到111A B C △，111A B C △向右平移6个单位，再向上平移2个单位得到222A B C △．(1)画出111A B C △和222A B C △；(2)(,)P a b 是ABC V 的AC 上一点，ABC V 经旋转、平移后点P 的对应点为2P ，则点2P 的坐标是．(3)若ABC V 直接旋转得到222A B C △，则旋转点M 坐标是．21．公安部门提醒市民，骑车出行必须严格遵守“一盔一带”的规定． 某头盔经销商统计了某品牌头盔4月份到6月份的销量，该品牌头盔4月份销售1500个，6月份销售2160个，且从4月份到6月份销售量的月增长率相同． (1)求该品牌头盔销售量的月增长率；(2)按照这个增长率，预计7月份该品牌头盔销售量是多少？22．青少年是国家的未来，他们的健康关系到国家富强和民族的昌盛，体育是学校培养全方面发展的社会主义建设者和接班人的一项主要教育内容，在新课程理念下，上好初中体育课至关重要．某校为了解学生体育运动的情况，对全校男生投掷铅球进行测试，测试结束后，随机抽取了30名男生的成绩（单位：米），并对成绩进行整理得到下表：请你根据统计表提供的信息解答下列问题：(1)表中=a ______，所抽取男生成绩的中位数落在______组； (2)求所抽取的这30名男生投掷铅球的平均成绩；(3)若该校有600名男生，请估计该校男生投掷铅球成绩不小于9米的学生人数． 23．根据以下素材，探索完成任务．1从喷水口喷出的喷水时的截面示意图，喷出的水柱在离喷水口水平距花坛是花坛，调整喷水口的高度，喷出的水柱形状与原来相24．如图1，矩形EBGF 和矩形ABCD 共顶点，且绕着点B 顺时针旋转，满足34BC BG AB BE ==．(1)DFAE的比值是否发生变化，若变化，说明理由；若不变，求出相应的值，并说明理由； (2)如图2，若点F 为CD 的中点，且8AB =，6AD =，连接CG ，求△FCG 的面积． 25．已知二次函数2y ax c =+的最小值为0，且其图象过点()2,1-． (1)求,a c 的值；(2)已知点()()0,1,0,0P O ．①若直线21733y t t ⎛⎫=≤≤ ⎪⎝⎭与抛物线2y axc =+相交于()()1122,,,A x y B x y 两点，求2124x x -的最大值；②已知点Q 是抛物线2y ax c =+上异于其顶点的任意一点，过Q 作QT 垂直x 轴于T ，OT 的中点为M ，请证明QM 平分PQT ∠．。

2025届福建福州市台江区华伦中学七年级数学第一学期期末达标检测模拟试题注意事项：1． 答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B 铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。

一、选择题(每小题3分,共30分) 1．以下问题，适合用普查的是（ ） A ．调查某种灯泡的使用寿命 B ．调查中央电视台春节联欢会的收视率 C ．调查我国八年级学生的视力情况 D ．调查你们班学生早餐是否有喝牛奶的习惯2．下列方程变形中正确的是（ ） A ．2x-1=x+5移向得2x+x=5+1 B ．+=1去分母得3x+2x=1C ．(x+2)-2(x-1)=0,去括号得x+2-2x+2=0D ．-4x=2，系数化为1得 x=-2 3．2的绝对值是（ ）． A ．2B ．－2C ．－12D ．±24．有理数a ，b 在数轴上的位置如图所示，则下列式子错误的是（ ）A ．ab ＜0B ．a +b ＜0C ．|a |＜|b |D ．a ﹣b ＜|a |+|b |5．在数轴上，到表示5-的点的距离等于5个单位的点所表示的数是（ ） A ．10 B ．10-C ．0或10-D ．10-或106．已知12a b +=，则代数式223a b +﹣的值是( ) A ．2B ．-2C ．-4D ．132- 7．两根同样长的蜡烛，粗烛可燃4小时，细烛可燃3小时，一次停电，同时点燃两根蜡烛，来电后同时熄灭，发现粗烛的长是细烛的2倍，则停电的时间为（ ） A ．2小时B ．2小时20分C ．2小时24分D ．2小时40分8．2020年某市各级各类学校学生人数约为1 580 000人，将1 580 000 这个数用科学记数法表示为（ ） A ．0.158×107 B ．15.8×105 C ．1.58×106D ．1.58×1079．OB 是∠AOC 内部一条射线，OM 是∠AOB 平分线，ON 是∠AOC 平分线，OP 是∠NOA 平分线，OQ 是∠MOA 平分线，则∠POQ ∶∠BOC ＝（ ）A ．1∶2B ．1∶3C ．2∶5D ．1∶410．已知关于x 的方程250x m -+=的解是3x =-，则m 的值为（ ） A ．1B ．1-C ．11-D ．11二、填空题(本大题共有6小题，每小题3分，共18分)11．若关于x 的方程2x ＋a ＝1与方程3x －1＝2x ＋2的解相同，则a 的值为________． 12．如果+5表示收入5元．那么-1表示__________________．13．某书店把一本新书按标价的八折出售，仍获利30%，若该书的进价为40元，则标价为_____元． 14．当a =_________时，两方程232x a +=与22x a +=的解相同. 15．按一定顺序的一列数叫做数列，如数列：12，16，112，120，，则这个数列前2019个数的和为____．16．某校报名参加甲、乙、丙、丁四个兴趣小组的学生人数如图所示，那么报名参加甲组和丙组的人数之和占所有报名人数的百分比为 ．三、解下列各题(本大题共8小题，共72分)17．（8分）我们知道：若数轴上点A ，点B 表示的数分别为a ，b ，则A ，B 两点之间的距离ABa b ，如图1，数轴上点A 表示的数为10-，点B 表示的数为20，点P 从点A 出发，以每秒3个单位长度的速度沿数轴向右匀速运动，同时点Q 从点B 出发，以每秒2个单位长度的速度向右匀速运动，设运动时间为t 秒(0)t >（1）①A ，B 两点间的距离AB = ．②用含t 的代数式表示：t 秒后，点P 表示的数为 ，点Q 表示的数为 ． （2）求当t 为何值时，点P 追上点Q ，并写出追上点C 所表示的数； （3）求当t 为何值时，15PQ AB =拓展延伸：如图2，若点P 从点A 出发，点Q 从点M 出发，其它条件不变，在线段AB 上是否存在点M ，使点P 在线段AM 上运动且点Q 在线段MB 上运动的任意时刻，总有32PM BQ =？若存在，请求出点M 所表示的数；若不存在，请说明18．（8分）如图1，将一段长为60cm 绳子AB 拉直铺平后折叠（绳子无弹性，折叠处长度忽略不计），使绳子与自身一部分重叠．（1）若将绳子AB 沿M 、N 点折叠，点A 、B 分别落在A '、B '处． ①如图2，若A '、B '恰好重合于点О处，MN = cm ；②如图3，若点A '落在点B '的左侧，且20cm A B =''，求MN 的长度；③若cm A B n ''=，求MN 的长度．（用含n 的代数式表示）（2）如图4，若将绳子AB 沿N 点折叠后，点B 落在B '处，在重合部分B N '上沿绳子垂直方向剪断，将绳子分为三段，若这三段的长度由短到长的比为3：4：5，直接写出AN 所有可能的长度．19．（8分）下表是中国电信两种”4G 套餐”计费方式．（月基本费固定收，主叫不超过主叫时间，流量不超上网流量不再收费，主叫超时和上网超流量部分加收超时费和超流量费）月基本费/元主叫通话/分钟上网流量MB 接听主叫超时部分/（元/分钟）超出流量部分/（元/MB ）（1）若某月小萱主叫通话时间为220分钟，上网流量为800MB，则她按方式一计费需元，按方式二计费需元；若她按方式二计费需129元，主叫通话时间为240分钟，则上网流量为MB．（2）若上网流量为540MB，是否存在某主叫通话时间t（分钟），按方式一和方式二的计费相等？若存在，请求出t 的值；若不存在，请说明理由．（3）若上网流量为540MB，直接写出当月主叫通话时间t（分钟）满足什么条件时，选择方式一省钱；当每月主叫通话时间t（分钟）满足什么条件时，选择方式二省钱．20．（8分）某水果商店以每箱200元价格从市场上购进一批苹果共8箱，若以每箱苹果净重30千克为标准，超过千克数记为正数，不足千克数记为负数，称重后记录如下：1.5, 3.5,2,2.5, 1.5,4,2,1+-++---+（1）这8箱苹果一共中多少千克，购买这批苹果一共花了多少钱？（2）若把苹果的销售单价定为每千克x元，那么销售这批苹果（损耗忽略不计）获得的总销售金额为_____元，获得利润为____________元（用含字母x的式子表示）；32.75，请你通过列方程并求出x的值.（3）在（2）条件下，若水果商店计划共获利0021．（8分）一种商品按销售量分三部分制定销售单价，如表：（1）若买100件花元，买300件花元；买350件花元；（2）小明买这种商品花了338元，列方程求购买这种商品多少件？（3）若小明花了n元（n＞250），恰好购买0.45n件这种商品，求n的值．22．（10分）某铁路桥长1000米．现有一列火车从桥上匀速通过．测得火车从开始上桥到完全通过桥共用了1分钟（即从车头进入桥头到车尾离开桥尾），整个火车完全在桥上的时间为40秒．（1）如果设这列火车的长度为x米，填写下表（不需要化简）：（2）求这列火车的长度．23．（10分）已知M、N在数轴上，M对应的数是﹣3，点N在M的右边，且距M点4个单位长度，点P、Q是数轴上两个动点；（1）直接写出点N所对应的数；（2）当点P到点M、N的距离之和是5个单位时，点P所对应的数是多少？（3）如果P、Q分别从点M、N出发，均沿数轴向左运动，点P每秒走2个单位长度，先出发5秒钟，点Q每秒走3个单位长度，当P、Q两点相距2个单位长度时，点P、Q对应的数各是多少？24．（12分）解方程：(1) 5x－6＝3x－4 (2) 123173x x-+-=参考答案一、选择题(每小题3分,共30分)1、D【分析】根据被调查对象较小时，宜使用普查，可得答案．【详解】解：A、调查某种灯泡的使用寿命，不能使用普查，错误；B、调查中央电视台春节联欢会的收视率被调查的对象都较大，不能使用普查，错误；C、调查我国八年级学生的视力情况被调查的对象都较大，不能使用普查，错误；D、调查你们班学生早餐是否有喝牛奶的习惯被调查的对象较小，故D宜使用普查；故选：D．【点睛】本题考查了全面调查与抽样调查，被调查对象较小时宜使用普查．2、C【解析】将各项中方程变形得到结果，即可做出判断．【详解】A、2x-1=x+5，移项得：2x-x=5+1，错误；B 、+=1去分母得：3x+2x=6，错误；C 、（x+2）-2（x-1）=0去括号得：x+2-2x+2=0，正确；D 、-4x=2系数化为“1”得：x=-，错误． 故选C ． 【点睛】此题考查了解一元一次方程，其步骤为：去分母，去括号，移项合并，把未知数系数化为1，求出解． 3、A【解析】根据绝对值的含义指的是一个数在数轴上的点到距离，而正数的绝对植是一个正数，易找到2的绝对值． 【详解】A 选项根据正数的绝对值是它本身得∣2∣=2，正确；B 选项-2是2的相反数，错误；C 选项 12-是2的相反数的倒数，错误；D 选项既是2的本身也是2的相反数，错误． 故选：A ． 【点睛】本题考查的知识点是绝对值的概念，牢记绝对值的概念并能与相反数、倒数等概念加以区分是关键． 4、D【分析】根据图形可知0b a <<，且||||b a >，对每个选项对照判断即可． 【详解】解：由数轴可知b ＜0＜a ，且|b |＞|a |， ∴ab ＜0，答案A 正确； ∴a +b ＜0，答案B 正确； ∴|b |＞|a |，答案C 正确；而a ﹣b ＝|a |+|b |，所以答案D 错误； 故选：D ． 【点睛】本题考查的有理数及绝对值的大小比较，把握数形结合的思想是解题的关键． 5、C【分析】借助数轴可知这样的点在-5的左右两边各一个，分别讨论即可．【详解】若点在-5左边，此时到表示5-的点的距离等于5个单位的点所表示的数是-5-5=-10； 若点在-5右边，此时到表示5-的点的距离等于5个单位的点所表示的数是-5+5=0； 综上所述，到表示5-的点的距离等于5个单位的点所表示的数是-10或0 故选：C ． 【点睛】本题主要考查数轴与有理数，注意分情况讨论是解题的关键． 6、B【分析】把2a+2b 提取公因式2，然后把12a b +=代入计算即可. 【详解】∵()22323a b a b +-=+-， ∴将12a b +=代入得：12322⨯-=- 故选B ． 【点睛】本题考查了因式分解的应用，把一个多项式化成几个整式的乘积的形式，叫做因式分解.因式分解常用的方法有：①提公因式法；②公式法；③十字相乘法；④分组分解法. 7、C【分析】设停电x 小时．等量关系为：1-粗蜡烛x 小时的工作量=2×（1-细蜡烛x 小时的工作量），把相关数值代入即可求解．【详解】解：设停电x 小时． 由题意得：1﹣14x ＝2×（1﹣13x ）， 解得：x ＝2.1． 2.1h ＝2小时21分．答：停电的时间为2小时21分． 故选：C ． 【点睛】本题考查了一元一次方程的应用，把蜡烛长度看成1，得到两支蜡烛剩余长度的等量关系是解题的关键． 8、C【分析】将原数写成10n a ⨯的形式，a 是大于等于1小于10的数． 【详解】解：61580000 1.5810=⨯． 故选：C ． 【点睛】本题考查科学记数法，解题的关键是掌握科学记数法的表示方法． 9、D【分析】依据OM 是∠AOB 平分线，OQ 是∠MOA 平分线，可得∠AOQ=12∠AOM=14∠AOB ，依据ON 是∠AOC平分线，OP 是∠NOA 平分线，可得∠AOP=12∠AON=14∠AOC=14（∠AOB+∠BOC ），进而得出∠POQ ：∠BOC=1：1．【详解】解：∵OM 是∠AOB 平分线，OQ 是∠MOA 平分线，∴∠AOQ=12∠AOM=14∠AOB ， ∵ON 是∠AOC 平分线，OP 是∠NOA 平分线， ∴∠AOP=12∠AON=14∠AOC=14（∠AOB+∠BOC ）， ∴∠POQ=∠AOP-∠AOQ=14（∠AOB+∠BOC ）-14∠AOB ， =14∠BOC ， ∴∠POQ ：∠BOC=1：1， 故选D ． 【点睛】本题主要考查了角平分线的定义的运用，解决问题的关键是利用角的和差关系进行推算． 10、B【分析】根据一元一次方程的解定义，将3x =-代入已知方程列出关于m 的新方程，通过解新方程即可求得m 的值． 【详解】∵关于x 的方程250x m -+=的解是3x =- ∴()2350m ⨯--+= ∴1m =- 故选：B 【点睛】本题考查了一元一次方程的解．方程的解的定义，就是能够使方程左右两边相等的未知数的值．二、填空题(本大题共有6小题，每小题3分，共18分) 11、-5【解析】分别解出两方程的解，两解相等，就得到关于a 的方程，从而可以求出a 的值.【详解】解方程21x a +=，得12ax -=， 解方程3122x x -=+，得3x =，∴132a-=， 解得：5a =-. 故答案为：5-. 【点睛】此题考查同解方程的解答，解决的关键是能够求解关于x 的方程，同时正确理解“解相同”的含义. 12、支出1元【分析】此题主要用正负数来表示具有意义相反的两个量，根据正数与负数的意义即可得出． 【详解】收入与支出是具有相反意义的量， 若+5表示收入5元，则-1表示支出1元， 故答案为：支出1元． 【点睛】本题考查了正数与负数的意义，掌握与理解正数与负数的意义是解题的关键． 13、65【分析】根据题意，实际售价=进价+利润，八折即标价的80%；可得一元一次的等量关系式，求解可得答案． 【详解】设标价是x 元，根据题意有： 0.8x =40(1+30%)， 解得：x =65. 故标价为65元. 故答案为65. 【点睛】考查一元一次方程的应用，掌握利润=售价-进价是解题的关键. 14、53【分析】先求出每个方程的解，根据同解方程得出关于a 的方程，求出即可． 【详解】解2x+3=2a 得：232a x -=， 解2x+a=2得：22ax -=， ∵方程2x+3=2a 与2x+a=2的解相同，∴22322a a --=， 解得：53a = .【点睛】本题考查了一元一次方程相同解问题，根据两个方程的解相同建立关于a 的方程是解决本题的关键． 15、20192020【分析】根据数列得出第n 个数为()11n n +，据此可得前2019个数的和为111 (122320192020)+++⨯⨯⨯，再用裂项求和计算可得．【详解】解：由数列知第n 个数为()11n n +，则前2019个数的和为：11111...26122020192020+++++⨯ =111...122320192020+++⨯⨯⨯ =11111111...2233420192020-+-+-++-=112020-=20192020故答案为：20192020．【点睛】本题主要考查数字的变化类，解题的关键是根据数列得出第n 个数为()11n n +，并熟练掌握裂项求和的方法．16、40%【解析】试题分析：从条形统计图可知：甲、乙、丙、丁四个兴趣小组的总人数为200人，甲、丙两个小组的人数为80人，所以报名参加甲组和丙组的人数之和占所有报名人数的百分比为80÷200×100%=40%．三、解下列各题(本大题共8小题，共72分)17、（1）①30；②103t -+；202t +；（2）30()t s =；C 点表示的数是80；（3）24t s =或36s ；拓展延伸：存在；点M 所表示的数是8．【分析】（1）①利用题目中给出的距离公式计算即可；②利用代数式表示即可；（2）根据题意列方程，点P 追上点Q 时，多运动30个单位长度；（3）分类讨论，P 、Q 两点相距15AB 时，可能在相遇前也可能在相遇后； 拓展延伸：根据两点间距离公式，再找出等量关系列方程求解即可．【详解】解：（1）①=-10-20=30ABa b ， 故填：30；②点P 表示的数为：103t -+，点Q 表示的数为：202t +，故填：103t -+，202t +；（2）依题意得，3302t t =+解得：30t =此时，C 点表示的数是80（3）依题意得情况1：相遇前12303305t t +-=⨯ 解得，24t =情况2：相遇后13(230)305t t -+=⨯ 解得：36t =所以24t s =或36s 时，15PQ AB =拓展延伸： 32PM BQ = 3()2AM AP AB AM MQ -=-- 33(302)2AM t AM t -=-- 18AM =所以点M 所表示的数是8．【点睛】本题考查了数轴、绝对值与一元一次方程的应用，是一个综合问题，解题的关键是掌握点的移动与点所表示的数之间的关系，根据题目给出的条件，找出合适的等量关系列出方程，进而求解．18、（1）①30；②40cm ；③(30)2ncm +或(30)2n cm -；（2）AN 所有可能的长度为：25cm ，27.5cm ，32.5cm ，35cm ．【分析】（1）①根据折叠可得,AM OM BN ON ==，再利用线段的和差即可得出MN 的长度；②根据折叠可得,AM A M BN B N ''==，再利用线段的和差即可得出MN 的长度；③分点A '落在点B '的左侧时和点A '落在点B '的右侧两种情况讨论，利用线段的和差即可得出MN 的长度；（2）分别计算出三段绳子的长度，再分类讨论，利用线段的和差即可得出AN 的长度．【详解】解：（1）①因为A '、B '恰好重合于点О处，所以,AM OM BN ON ==， ∴11()3022MN OM ON OA OB AB =+=+==cm ， 故答案为：30； ②由题意得：,AM A M BN B N ''==，因为60AM A M A B B N BN AB ''''++++==cm,所以220260A M B N ''++=cm,即20A M B N ''+=cm ，所以40MN A M B N A B cm ''''=++=；③当点A '落在点B '的左侧时，由②得6060()22A B n A M B N cm ''--''+==， 60(30)22n n MN A M B N A B n cm -''''=++=+=+； 当点A '落在点B '的右侧时，如下图，可知2260A M B N A B cm ''''+-=，所以60()2n A M B N cm +''+=， 所以(30)2nMN A M B N A B cm ''''=+-=-，综上所述，MN 的长度是(30)2ncm +或(30)2n cm -； （2）根据题意，这三段长度分别为：3456015,6020,6025121212cm cm cm ⨯=⨯=⨯=， 所以AN 的长度可以为：2015252cm +=； 251527.52cm +=； 252032.52cm +=； 152027.52cm +=； 152532.52cm +=； 2025352cm +=； 故AN 所有可能的长度为：25cm ，27.5cm ，32.5cm ，35cm ．【点睛】本题考查线段的和差．掌握数形结合思想，能结合图形分析是解题关键．注意分情况讨论．19、（1）1；2；3;（2）见解析;（3）见解析.【解析】（1）根据表中数据分别计算两种计费方式，第三空求上网流量时，可设上网流量为xMB ，列方程求解即可； （2）分0≤t ＜200时，当200≤t≤250时，当t ＞250时，三种情况分别计算讨论即可；（3）本题结论可由（2）中结果直接得出．【详解】（1）方式一：49+0.2（220﹣200）+0.3（800﹣500）＝49+0.2×20+0.3×300 ＝49+4+901．方式二：69+0.2（800﹣600）＝69+0.2×200 ＝69+40＝2．设上网流量为xMB ，则69+0.2（x ﹣600）＝129解得x ＝3．故答案为1；2；3．（2）当0≤t ＜200时，49+0.3（540﹣500）＝61≠69∴此时不存在这样的t ．当200≤t ≤250时，49+0.2（t ﹣200）+0.3（540﹣500）＝69解得t ＝4．当t ＞250时，49+0.2（t ﹣200）+0.3（540﹣500）＝69+0.15（t ﹣250）解得t ＝210（舍）．故若上网流量为540MB ，当主叫通话时间为4分钟时，两种方式的计费相同．（3）由（2）可知，当t ＜4时方式一省钱；当t ＞4时，方式二省钱．【点睛】本题考查了一元一次方程的应用，找准等量关系，正确列出一元一次方程是解题的关键．本题难度中等偏大．20、 (1)这8箱苹果一共重236千克，购买这批苹果一共花了1600元.(2)236x ；2361600x -;(3) 若水果商店要获利0032.75，则销售单价应定为9元每千克.【分析】（1）将8筐苹果质量相加可得出购进苹果的总重量，再利用总价=每筐价格×8可得出购买这批苹果的总钱数； （2）根据销售总价=销售单价×数量，以及结合利润=销售总价-成本，即可得出结论；（3）由（2）的结论结合水果商店共获利0032.75，即可得出关于x 的一元一次方程，解之即可得出结论．【详解】解：（1）由题意得，8箱苹果一共重：830( 1.5 3.52 2.5 1.5421)⨯++-++---+=236（千克）购买这批苹果一共花了20081600⨯=（元）答：这8箱苹果一共重236千克，购买这批苹果一共花了1600元.（2）已知苹果的销售单价定为每千克x 元，依题意得销售金额为236x 元；获得利润为（2361600x -）元；（3）由题意得：002361600160032.75x -=⨯解得9x =（元）答：若水果商店要获利0032.75，则销售单价应定为9元每千克.【点睛】本题考查一元一次方程的应用以及列代数式，解题的关键是首先根据数量关系，列式计算；然后根据各数量之间的关系，利用含x的代数式表示出总销售金额及利润；最终找准等量关系，正确列出一元一次方程即可．21、（1）250；690；790；（2）140件；（3）1【分析】（1）根据总价=单价×数量结合表格中的数据，即可求出分别购买100件、300件、350件时花费的总钱数；（2）设小明购买这种商品x件，由250＜338＜690可得出100＜x＜300，根据100×2.5+（购买件数-100）×2.2=总钱数（338元），即可得出关于x的一元一次方程，解之即可得出结论；（3）分250＜n＜690及n＞690两种情况，找出关于n的一元一次方程，解之即可得出结论．【详解】（1）250；690；790（2）设小明购买这种商品x件∵250＜338＜690，∴100＜x＜300根据题意得100×2.5+（x﹣100）×2.2=338解得x=140答：小明购买这种商品140件（3）当250＜n＜690时，有250+2.2（0.45n﹣100）=n解得：n=3000（不合题意，舍去）当n＞690时，有690+2（0.45n﹣300）=n，解得：n=1．答：n的值为1【点睛】本题考查了一元一次方程的应用，解题的关键是：（1）根据总价=单价×数量结合表格中的数据，列式计算；（2）根据100×2.5+（购买件数-100）×2.2=总钱数，列出关于x的一元一次方程；（3）分250＜n＜690及n＞690两种情况，列出关于n的一元一次方程．22、（1）1000+x，100060x+，1000-x，100040x-；（2）200米【分析】（1）根据题意列出代数式即可．（2）通过理解题意可知本题存在两个等量关系，即整列火车过桥通过的路程=桥长+车长，整列火车在桥上通过的路程=桥长-车长，根据这两个等量关系可列出方程求解．【详解】解：（1）火车行驶过程 路程（米） 速度（米/秒） 完全通过桥 1000x + 100060x + 整列车在桥上1000x -100040x - （2）解：设这列火车的长度为x 米依题意得100010006040x x +-= 解得200x =答：这列火车的长度为200米．【点睛】本题考查了一元一次方程以及速度公式的应用．解题关键是弄清题意，合适的等量关系，列出方程．弄清桥长、车长以及整列火车过桥通过的路程，整列火车在桥上通过的路程之间的关系．23、（3）3；（2）﹣3.3或3.3．（3）P 对应的数﹣43，点Q 对应的数﹣2．【分析】(3)根据两点间的距离公式即可求解;(2) 分两种情况: ①点P 在点M 的左边; ②点P 在点N 的右边; 进行讨论即可求解;(3) 分两种情况: ①点P 在点Q 的左边;②点P 在点Q 的右边; 进行讨论即可求解.【详解】解：（3）﹣3+4=3．故点N 所对应的数是3；（2）（3﹣4）÷2=0.3，①﹣3﹣0.3=﹣3.3，②3+0.3=3.3．故点P 所对应的数是﹣3.3或3.3．（3）①（4+2×3﹣2）÷（3﹣2）=32÷3=32（秒），点P 对应的数是﹣3﹣3×2﹣32×2=﹣37，点Q 对应的数是﹣37+2=﹣33；②（4+2×3+2）÷（3﹣2）=36÷3=36（秒）；点P 对应的数是﹣3﹣3×2﹣36×2=﹣43，点Q 对应的数是﹣43﹣2=﹣2．【点睛】本题考查的是数轴，注意分类导论思想在解题中的应用.24、（1）x=1；（2）x=-1．【分析】（１）方程移项合并，把x 系数化为1，即可求出解；（2）方程去分母，去括号，移项合并，把x 系数化为1，即可求出解．【详解】(1) 5x －6＝1x －4解：5x －1x ＝－4+62x ＝2x ＝1 (2) 123173x x -+-= 解：()()3122173x x --=+3621721x x --=+6721213x x --=+-1339x -=3x =-【点睛】本题考查的是一元一次方程的解法，解题中注意移项要变号，去括号是要注意括号前的符号，去分母时防止漏乘是关键．。

福建省福州市华伦中学2024届物理九上期末学业水平测试模拟试题注意事项：1．答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

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一、单选题1．小强同学在探究串联电路电流规律的实验中，按下图连接好了电路，闭合开关S后，观察实验，两灯均不发光．为检测出电路故障，他做了以下操作：将电压表接到b、c两点，观察电压表、电流表均无示数．将电压表接到a、b两点，观察电压表有明显示数，而电流表示数几乎为零，则电路故障可能是A．灯L2断路B．灯L2短路C．电流表烧坏了D．灯L1断路2．如图所示，电源电压不变，小灯泡L标有“6V 3W”字样。

闭合开关S后，当滑片P移至某一位置时，小灯泡L 恰好正常发光，此时滑动变阻器R消耗的功率为P1；当滑片P移至某一端点时，电流表示数为0.3A，电压表示数变化了3V，此时滑动变阻器R消耗的功率为P2，且125 6PP，下列判断正确的是A．电源电压为12VB．滑动变阻器的最大阻值10ΩC．小灯泡L正常发光时，滑片P刚好位于滑动变阻器R的中点位置D．滑动变阻器R消耗的功率由P1变为P2的过程中，小灯泡L消耗的功率减少了2.1W 3．根据你所学的物理知识判断，下列说法中正确的是（）A．粗导线的电阻一定比细导线的电阻小B．用电器通电时间越长，它的电功率越小C．电流做功的过程就是消耗电能的过程D．并联电路的各支路电流是不可能相等的4．甲、乙两电热丝电阻之比为3:2，通电时间之比为3:5，它们产生的热量之比为18:5，则通过它们的电流之比为A．2:1 B．1:4 C．4:1 D．1:25．家庭每月用电量的计量单位是A．库仑B．瓦特C．焦耳D．千瓦时6．由欧姆定律公式I＝UR可变形得到R＝UI，对此，下列说法中正确的是A．通过导体的电流越大，则导体的电阻越小B．某段导体两端电压为0时，其电阻为0C．导体两端的电压跟通过导体电流的比值等于这段导体的电阻D．导体电阻的大小跟导体两端的电压成正比，跟通过导体的电流成反比7．通过大量实验研究得出电流与电压之间关系的科学家是A．安培B．伏特C．欧姆D．焦耳8．为了能自动记录跳绳的次数，某科技小组设计了一种自动计数器，其简化电路如图甲所示．R1是一种光敏元件，每当绳子挡住了射向R1的红外线时，R1的电阻会变大，自动计数器会计数一次，信号处理系统能记录AB间每一时刻的电压．若已知电源电压为12V，某一时段AB间的电压随时间变化的图象如图乙所示，则下列说法正确的是（）A．AB两端电压为6V时，跳绳自动计数器会计数一次B．绳子挡住了射向R1的红外线时，R1和R2的阻值相等C．绳子没有挡住射向R1的红外线时，R1的阻值是R2的3倍D．绳子挡住了射向R1的红外线时，R1的阻值会变为原来的5倍二、多选题9．在图所示的电路中，闭合开关后两个灯泡正常发光，则A．通过A点的电流大于通过B点的电流B．通过A点的电流等于通过C点的电流C．A、B两点间的电压一定小于A、C两点间的电压D．A、B两点间的电压一定等于B、C两点间的电压10．关于温度、热量和内能，下列说法正确的是（）A．物体的温度越高，所含热量越多B．物体的内能增大可能是吸收了热量C．用做功的方法可以改变物体的内能D．物体吸收热量时内能一定增加，但温度可能不变三、填空题11．某定值电阻两端电压由8V变为12V时，通过的电流增加了0.2A，该电阻的阻值为_______Ω；若它两端电压变为0V，则该电阻中电流为_______A，此时电阻为_______Ω。

2025年福建福州市台江区华伦中学学业水平考试英语试题试卷注意事项1．考生要认真填写考场号和座位序号。

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Ⅰ. 单项选择1、The number “23,456” can be read as “________”.A．twenty-three thousand, four hundred and fifty-sixB．twenty-three thousand and four hundred fifty-sixC．two three thousand and four five sixD．two three thousand, four and five six2、Both of them had the same opinion. They reached a(n) ______ quickly.A．organization B．victory C．situation D．agreement3、— Do you know our new manager?—Yes. He _______ to be a friend of my brother’s.A．turns up B．turns onC．turns off D．turns out4、Teenagers should ________ to take care of themselves from a young age.A．educate B．be educating C．have educated D．be educated5、Don't keep _________ when you are asked some questions in class.A．silent B．generous C．forgetful D．private6、—Susan has bought a large house with a swimming pool.—It ________ be very expensive. I never dream about it.A．must B．might C．can’t D．shouldn’t7、When I got into the room, Green was talking _________ the phone.A．on B．with C．to D．in8、—Now more and more people are paying attention to protecting the environment.—So we believe ________ there will be less pollution in the future.A．wrongly B．hardly C．strongly D．impossibly9、- excellent work you have done! -It's very kind of you to say so.A．What an B．How C．What D．How an10、--Could you tell me ?--Next Monday.A．when you will go to Beijing B．when will you go to BeijingC．how will you go to BeijingⅡ. 完形填空11、"Where is the university?" This is a question that many visitors to Cambridge(剑桥)ask. But no one can give thema 1 answer, for there is no wall to be found 2 the university. The university is the city. You can find classroom buildings, 3 , museums and offices of the university all over the city. And most of 4 members are the students and 5 of the thirty-one colleges.Cambridge was already a 6 town long before the first students and teachers arrived 800 years 7 .It grew up by the river Grant, and the river once 8 the Cam. A 9 was built over the river as early as 875. 10the town got its name "Cambridge".In the fourteenth and fifteenth centuries more and 11 land was used for college buildings. The town grew much 12 in the nineteenth century after the opening of the railway in 1845. Cambridge became a 13 in 1951 and now it has a population of over 100, 000.Many young students in 14 countries 15 to study at Cambridge. Thousands of people from all over the world come to visit the university town. It has become a famous place all around the world. 1．A．clean B．clear C．right D．real2．A．around B．in C．near D．by3．A．cinemas B．parks C．zoos D．libraries4．A．their B．his C．its D．my5．A．parents B．farmers C．workers D．teachers6．A．interesting B．usual C．developing D．common7．A．before B．ago C．later D．after8．A．said B．called C．spoken D．talked9．A．bridge B．building C．station D．house10．A．Because B．But C．And D．So11．A．less B．fewer C．more D．bigger12．A．smaller B．slower C．faster D．cleaner13．A．city B．college C．university D．country14．A．another B．other C．the other D．others15．A．stop B．hate C．hope D．needⅢ. 语法填空12、Mary is 1．eight-year-old girl. Every day she washes clothes, looks after2．(she) younger sister and works 3．(hardly) on the farm. Mary wants to go to school, but her mother needs her help at home. So Mary stays at home instead of 4．(go) to school.Do you want to help Mary? Well, join Save the Children, please! Just 6 yuan a day, you can 5．(helpful) a child like Mary. With your help, children like Mary will be able 6．(have) enough food and have chances to go to school.Save The Children is an organization to help poor children like Mary. It has been in service since 1932. The money from kind people will 7．(use) to build schools, hospitals and other necessary 8．(build)9．you are a volunteer, there are many wonderful things waiting for you — letters from the children, their photos and subject reports. Now, if you are interested10．the application form, and then you can donate some money. In this way, you can help a child like Mary!Ⅳ. 阅读理解A13、Rita stepped into the cool, moving water. She pushed a black inner tube in front of her. She had a worried look on her face because she had never floated down a river before.“Let me hold your tube while you climb on,” said her father. He smiled at her. “There’s not a cloud in the sky. It’s a great day to be in the river, isn’t it?”Rita looked out across the water. People were floating by on tubes. Some talked and laughed as they____easily down the river. Others leaned back with hats pulled over their faces. None of them looked terrified.“We’ll stay together,” said Rita’s father. “I’ll hold on to your rope.”“Will we go very fast?” Rita asked.“No,” said Dad. “We’ll move slowly for a while, and then it will get a little faster near the river’s bend. Don’t worry, Rita. You’ll be fine.”Rita looked at her tube. It gently moved up and down in the water. She saw a girl of her own age float by. The girl seemed to be having fun. Suddenly Rita’s worries disappeared.“I’m ready to climb on and ride, Dad,” she said.1．The underlined word “floated” in the reading means “________”.A．漂浮B．乘坐C．划船2．What is Rita’s problem in this story?A．She doesn’t like to be in cool water.B．She is afraid to try something new.C．She is worried that she will get sunburned .3．Wha t’s the weather like in the story?A．Cloudy. B．Rainy. C．Sunny.4．Which of these happened last in the story?A．Rita pushed her black tube.B．Rita saw a girl of her own age.C．Rita stepped into the water.5．What’s the best title for this passage?A．Rit a’s Ride.B．Rita’s Trip.C．Rita’s Visit.B14、Many Chinese students think American students enjoy more freedom than them at school. But American schools also have their rules. If the students break the rules, they will get punishment（惩罚）, too.On the first day of a new term, 128 students were sent home for wearing the wrong clothes. There are altogether l, 200 students in the school. Usually only 20 students break the school dress rule every day. So the headmaster Theresa Mayerik said it was the worst new term she had seen.At Morton High School, students' favorite clothing such as baggy（宽大）trousers, low-necked and tank tops（紧身短背心）are not allowed in classroom. Some students think they have the right to choose what to wear, but the headmaster doesn't think so. "I'm supportive if half the students were sent home because 99% will get the message that our school are for education." "Freedom" doesn't mean "free of restrictions（约束）".That is to say there is no total freedom in the world, no matter in the U.S.A or in China.1．Many Chinese students think that _______________.A．American students are very free at schoolB．American students are not so clever as themC．American students don't love their school at allD．American students obey their school rules2．128 Students of Morton High School were sent home for___________.A．not finishing their homework B．being late for schoolC．not wearing the right clothes D．not cleaning the classroom3．Some students in Morton High School think that they have the right to __________.A．decide when to go to school B．choose what to wearC．eat and drink in class D．do what they want4．What does the underlined word "supportive" mean in Chinese?A．高兴的B．支持的C．害怕的D．难过的5．What's the writer's attitude to the school dress rule?A．Agree. B．Disagree. C．Not sure. D．Not mentioned.C15、阅读下面的图表，做两个小题。

福建省福州市台江区福州华伦中学2023-2024学年七下英语期末达标检测试题满分120分，时间90分钟一、单项选择（共10小题，满分10分）1、—It’s ________ today. Let’s go to the beach.—Sounds great! Don’t forget your sunglasses.A. rainyB. cloudyC. sunnyD. snowy2、The teachers often tell their students ________ their pen in class.A. not to playB. not to play withC. to playD. to play with3、—Linda, your phone is ringing all the time.—Oh, _________ from my friends on the Wechat.A. messagesB. newsC. noticesD. information4、—What __________ Mike __________?—He is tall and thin.A. does; likeB. does; look likeC. is; look likeD. is; look5、—Would you like some dumplings?—________. I’m hungry.A. Yes, pleaseB. No problemC. No, thanksD. Yes, I’d love to6、Listen! Someone ________ at the door of the meeting-room.A. knockedB. knocksC. is knockingD. was knocking7、Our science teacher often tells us it’s very ________ to leave much personal information on the Internet.A. helpfulB. excitingC. dangerousD. careless8、The dress is very nice, but it’s not ________.A. enough cheapB. cheap enoughC. enough cheaperD. cheaper enough9、A. sad B. shake C. travel D. happen10、— Wow, our head teacher is singing the song so beautifully.— Yes, I never heard her ________ like this before.A. singB. singingC. to singD. sang二、短文填空（10分）11、阅读下面短文，根据短文内容从方框中选出恰当的单词或短语填空，使语意通顺完整。

福建省福州市台江区福州华伦中学2024届中考数学模试卷注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗．一、选择题（每小题只有一个正确答案，每小题3分，满分30分）1．下列运算正确的是（）A．a﹣3a=2a B．（ab2）0=ab2C．8=22±D．3×27=92．2017上半年，四川货物贸易进出口总值为2 098.7亿元，较去年同期增长59.5%，远高于同期全国19.6%的整体进出口增幅．在“一带一路”倡议下，四川同期对以色列、埃及、罗马尼亚、伊拉克进出口均实现数倍增长．将2098.7亿元用科学记数法表示是（）A．2.098 7×103B．2.098 7×1010C．2.098 7×1011D．2.098 7×10123．已知x1、x2是关于x的方程x2﹣ax﹣2=0的两根，下列结论一定正确的是（）A．x1≠x2B．x1+x2＞0 C．x1•x2＞0 D．x1＜0，x2＜04．若a与5互为倒数，则a=（）A．15B．5 C．-5 D．15-5．如图，平行四边形ABCD中，E，F分别为AD，BC边上的一点，增加下列条件，不一定能得出BE∥DF的是（）A．AE＝CF B．BE＝DF C．∠EBF＝∠FDE D．∠BED＝∠BFD6．如图，田亮同学用剪刀沿直线将一片平整的树叶剪掉一部分，发现剩下树叶的周长比原树叶的周长要小，能正确解释这一现象的数学知识是（）A．垂线段最短B．经过一点有无数条直线C．两点之间，线段最短D．经过两点，有且仅有一条直线7．下列计算正确的是（）A．a2+a2=2a4B．（﹣a2b）3=﹣a6b3C．a2•a3=a6D．a8÷a2=a48．在一个不透明的口袋里有红、黄、蓝三种颜色的小球，这些球除颜色外都相同，其中有5个红球，4个蓝球．若随机摸出一个蓝球的概率为13，则随机摸出一个黄球的概率为（）A．14B．13C．512D．129．如图，已知点A在反比例函数y＝kx上，AC⊥x轴，垂足为点C，且△AOC的面积为4，则此反比例函数的表达式为（）A．y＝4xB．y＝2xC．y＝8xD．y＝﹣8x10．如果解关于x的分式方程2122m xx x-=--时出现增根，那么m的值为A．-2 B．2 C．4 D．-4二、填空题（共7小题，每小题3分，满分21分）11．已知一组数据1，2，x，2，3，3，5，7的众数是2，则这组数据的中位数是．12．二次函数y＝ax2+bx+c的图象如图所示，以下结论：①abc＞0；②4ac＜b2；③2a+b＞0；④其顶点坐标为（12，﹣2）；⑤当x＜12时，y随x的增大而减小；⑥a+b+c＞0中，正确的有______．（只填序号）13．如图，已知双曲线经过直角三角形OAB斜边OA的中点D，且与直角边AB相交于点C．若点A的坐标为（，4），则△AOC的面积为．14．如图，在⊙O中，点B为半径OA上一点，且OA＝13，AB＝1，若CD是一条过点B的动弦，则弦CD的最小值为_____．15．如图，身高是1.6m的某同学直立于旗杆影子的顶端处，测得同一时刻该同学和旗杆的影子长分别为1.2m和9m.则旗杆的高度为________m.16．已知A（0,3），B（2,3）是抛物线上两点，该抛物线的顶点坐标是_________.17．某商场将一款品牌时装按标价打九折出售，可获利80%，这款商品的标价为1000元，则进价为________元。

2025年福建省福州市台江区华伦中学初三下学期期末考试（第四次月考）英语试题考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。

2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。

3．考生必须保证答题卡的整洁。

考试结束后，请将本试卷和答题卡一并交回。

Ⅰ. 单项选择1、— Do you think that I can win the final?— ________. Everyone stands a chance.A．Y ou never know B．Y ou got itC．Y es, I do D．Y ou bet2、一Jim, is physics difficult to learn?一Sure, but all subjects can be learned well hard work.A．for B．from C．with D．through3、-- ________ coming earlier, we can easily find a good seat in the theater.-- You made a wise decision.A．Instead of B．Thanks to C．As for D．Except for4、— Should I give medicine to my baby as soon as it catches a cold?— Not really. Our bodies can ______ the cold, so sometimes we just give it some water to drink.A．fight B．hide C．cause D．keep5、Lily’s father often ________ newspapers after dinner.A．looks B．sees C．reads D．watches6、My father wants me to____ doing my homework as soon as I come home from school.A．win the heart of B．take care ofC．get into the habit of D．stay in touch with7、—Why don’t you like winter in Beijing?—Because it is __________ winter in Guangzhou.A．as cold as B．much colder thanC．not so clod as D．not colder than8、— Tom, which subject do you like ______, math or English?— Math.A．well B．better C．best D．the best9、At last his parents ___ him to move to the south alone for a job.A．agreed B．suggested C．hoped D．encouraged10、The lyrics（歌词）“If you care enough for ____ living, make it ___ better place for you and for me.” in the song Healing the World really touches me.A．the, a B．a, the C．the, the D．a, aⅡ. 完形填空11、One Saturday afternoon, Sarah went to buy something for her sister and herself. As Sarah was coming out of a 1 , a young lady walked towards her. She said she was Miss Green —a good friend of Sarah’s sister’s. Sarah 2 her. Then she called a taxi to send Sarah home. She told the driver where he should go. Sarah was 3 that it was not in the direction of her home.“Why?” Sarah asked. The lady smiled.When they came to a quiet road, a big rough man 4 on the road. He stopped the taxi driver, knocked him down, tied him and threw him out of the taxi. At the same time, Miss Green took out a knife and 5 Sarah. She asked Sarah to keep 6 . The man then started the taxi. “Oh, God! I’m being kidnapped (绑架),” Sarah said to herself.She tried to escape, but not succeeded. Suddenly an 7 came to her. She took out a lipstick (口红) from her pocket, wrote “SOS” on the windo w, and covered the word with her 8 . A few minutes later, a police car passed and the policemen saw the 9 . When the kidnappers saw the policemen, they stopped the taxi, jumped into the grass, and ran away.The policemen then picked up Sarah and sent her home. When her parents knew what had happened, they were greatly surprised. But they were also 10 because their daughter had finally come back safely.1．A．school B．taxi C．shop2．A．knew B．believed C．thanked3．A．pleased B．excited C．surprised4．A．drove B．climbed C．appeared5．A．frightened B．played C．helped6．A．healthy B．alive C．quiet7．A．idea B．answer C．interest8．A．fingers B．back C．dress9．A．picture B．map C．sign10．A．worried B．happy C．afraidⅢ. 语法填空12、阅读下面材料，在空白处填入适当的内容(1个单词) 或括号内单词的正确形式。