吉林省长春市东北师大逐梦芳华2019年初中毕业生考前冲刺卷(四)图片版 含答案
【20套精选试卷合集】吉林省长春市东北师大附中明珠学校2019-2020学年中考数学模拟试卷含答案
吉林省长春市朝阳区东北师大附中2024年初中英语毕业考试模拟冲刺卷含答案
吉林省长春市朝阳区东北师大附中2024年初中英语毕业考试模拟冲刺卷含答案注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
回答非选择题时，将答案写在答题卡上，写在本试卷上无效。
3．考试结束后，将本试卷和答题卡一并交回。
Ⅰ. 单项选择1、—I always get nervous when I start a(an) with others?—Take it easy. Believe in yourself.A．education B．introduction C．communication D．exhibition2、—Why did you come to discuss the question？—Because it was a question which was worth ______ consideration.A．nervous B．serious C．anxious D．strict3、Jack __________ his father, because they are both easygoing.A．looks after B．looks likeC．takes after D．looks up4、It’s a /bæd/ habit to put off today’s work till tomorrow.A．bad B．bag C．bat D．bed5、The world’s longest cross-sea bridge, the 55-km-long Hong Kong-Zhuhai-Macao Bridge (HZMB) ________ on Oct 24. The HZMB will make it much easier to travel between the three areas.A．opens B．was open C．opened6、Both of them had the same opinion. They reached a(n) ______ quickly.A．organization B．victory C．situation D．agreement7、— ________ work it is!— But we will try our best to finish it on time.A．What easy B．How easy C．What hard D．How hard8、一“Food Safety”problem is becoming______these days．﹣I think so．The government must do something to deal with it．A．smaller and smaller B．worse and worseC．better and better D．nicer and nicer9、Linda, you need to talk to my grandma loudly, she is a bit __.A．deaf B．blind C．clever D．kind10、--He seems _____ ill. Shall we take him to the hospital right now?--I don’t think it matters. Maybe he’s caught a bit of a cold.A．terrible B．terribly C．even D．to be terribleⅡ. 完形填空11、Life in the 22nd century will be different from life in the 2lth century, because many changes will take place in the new century. But what will the changes be?The population(人口) is 1 fast. There will be more and more people in the world, and most of them will live 2 than before. 3 will be much smaller and more useful, and there will be at least one in every home, And computer studies will be one of the important subjects at 4 .People will work fewer hours than they did in the 21th century, and they will have more free time for sports, 5 TV and traveling. Traveling will be more 6 . And many more people will go to other countries for holidays.More land(土地) will be used for building new towns and houses, Then there will be less room for cows and sheep, so 7 will be more expensive, Maybe no one will eat it every day, instead they eat 8 vegetables and fruit. Maybe people will be healthier.Work in the future will be 9 , too. Dangerous and hard work will be done by robots(机器人). 10 of this, many people will not have enough work to do. This will be a problem.1．A．making B．growing C．running D．doing2．A．longer B．shorter C．faster D．taller3．A．Trains B．Cars C．Computers D．Houses4．A．factory B．hospital C．farm D．school5．A．watching B．seeing C．looking D．buying6．A．interesting B．convenient（方便）C．expensive D．difficult7．A．fruit B．milk C．meat D．bread8．A．more B．fewer C．less D．much9．A．dangerous B．difficult C．heavy D．different10．A．One B．Some C．Because D．AllⅢ. 语法填空12、Millie :Have you heard about the pop star Nancy? It's said that she has got cancer.Sandy:I 1．(hear) about it last week. It's very sad because she 2．(be) so kind.Millie: I heard that Nancy once donated ~100,000 to people who 3．(suffer) great loss in the earthquake in Wenchuan. Sandy: Yes. She is a generous girl.Millie: Now Nancy 4．(receive) medical treatment in Belling. An operation5．(do) on her yesterday and it was a success.Sandy . That's great. I really hope Nancy 6．(get) well again soon.Ⅳ. 阅读理解A13、A Girl or A Boy, A Woman or A man?A lot of boys and girls in America are wearing the same clothes and many of them have long hair. So it is often difficult to tell whether they are boys or girls.One day an old man went for a walk in a park in Washington, and he was tired, he sat down on a bench(长凳). A young person was standing on the other side of the pond(水池)."Excuse me," the old man said to the person next to him on the bench, "Do you see the person with the red trousers and long hair? Is it a boy or a girl?" "A girl," said his neighbor, "She is my daughter.""Oh," the old man said quickly, "I am sorry, but I didn't know that you were her mother." "I'm not," said the other person. "I'm her father."1．It isn't often easy to tell whether many of American children are boys or girl ____.A．because they all look like each otherB．because they are wearing the same kinds of caps and shoesC．because they have long hair and wear the same clothes2．One day an old man went for a walk in ____.A．the street in WashingtonB．the Washington Park in AmericaC．in a park in Washington3．There were ____ persons beside the pond, they are ____.A．three ... a man, a woman and a girlB．three ... two men and a girlC．two ... a man and a girl4．The young person wore ____.A．a pair of red trousersB．a pair of black trousersC．a pair of red sunglasses5．The old man thought his neighbor was the girl's ____.A．mother B．father C．brotherB14、I have a neighbor we call “Happy”. I have never seen her angry at anything and never heard her say a mean word to anyone or about anyone.Happy and her husband Ben have a huge garden. They spent many happy hours together working on it. Most of theneighbors watched interestingly as Ben doubled the size of their garden. As the cost of food climbed faster than Ben’s beans, we all wished we also had such a large garden. As the rest of us spent our dollars at the market, Happy could be seen picking beans in her back yard.Last month, Happy and Ben invited most of the neighborhood over for an “all-day food fest”. We were told to bring gloves and arrive very early in the morning. We didn’t know what was about to take place.By 9:00 am, there were nine of us in the garden picking tomatoes, beans, peppers, and cucumbers. By 10:00 am, there was lots of laughter. We shared a lot of stories. By five o’clock, everyone was a little drunk from the wine and beer. After dinner, we played games. As we were leaving, Happy and Ben handed each of us a shopping bag filled with the vegetables of the day, already packaged and frozen. What a delightful gift!Well, the point wasn’t so much about the food. The true gift was a day of friends enjoying one another’s company. None of it would have happened if it had been for Happy and Ben’s garden. Now they have a blog about gardening in case we decided to plant a garden. And I am so proud of my tomato plants!1．We can infer that Happy and her husband Ben_______.A．don’t like spending time with othersB．sometimes quarrel with each otherC．live on the food they grow in their gardenD．are a generous and warm-hearted couple2．According to paragraph 2, people wish they also had a garden so that_______.A．they didn’t have to spend so much money on foodB．they could grow vegetables and sell at the marketC．they could invite their neighbors and hold parties in itD．they could spend happy times together with their family in it3．For what purpose did Happy and Ben invite the neighbors to their garden?A．To ask them to attend a birthday partyB．To help them get to know each other.C．To let them enjoy what they grew in the garden.D．To ask them to share some interesting stories.4．What did the writer most probably think of the time he spent in the garden?A．It was too long B．It was wonderful.C．It was not as good as he thought. D．It was too terrible.C15、It was a dark and stormy night. I was about to go to bed when I heard a tapping sound on my window. “Who’s there?” I sho uted. Suddenly there was a flash of lighting; I saw a face at the window. It looked like an alien that I have seen on the television show.I felt very scared. I ran to my bed and pulled my blanket(毛毯) over my head. I started to shout for my parents but there was no reply. Then I remembered that they were at a dress party.After a while my head showed up out of my blanket but it was too dark to see anything. Then I heard footsteps. They were getting louder and louder. It was dark but I knew the way to drawer where I kept my camera. I ran there and took out my camera and started to take pictures in the direction of the window. Soon the footsteps____, maybe because of my taking picture.The grandfather clock struck…It was 12 midnight. I went back to my bed and tried to sleep. But I couldn’t sleep. I felt too frightened. I sat up; my mind was full of thoughts. Time passed, one o’clock, two o’clock, ... Finally, I fell asleep.I woke up only after eight and decided to find out the truth. I found some footprints outside my bedroom window. I measured them with a tape(卷尺) and found them to be exactly the same size as my father’s shoes. The footprints ended at the door of my house. I then went to town to get the film developed(洗胶片). But when I saw the photos, they were black and I could hardly see anything. Then I remembered that I did not use the flash.When I reached home, I told my father the whole matter and he started to laugh. I also started laughing when he told me that he had dressed up as an alien for the party.1．The writer ______ when a face appeared at the window.A．was tapping the windowB．was watching a flash of lightingC．was about to go to bedD．was watching TV2．What’s the right order during the night?a. shouted for parentsb. sat up on the bedc. heard the footstepsd. took the picturese. covered the headA．bcaed B．eacdbC．bacde D．ecbad3．What does the underlined phrase “died off” mean?A．逃跑B．死掉C．消失D．重现4．Why did the writer’s father laugh?A．He had heard a strange dream for the kid.B．He thought the writer was a coward (胆小的) kid.C．He thought he dressed up as an alien successfully.D．He found out the truth about the alien last night.5．What’s the best title for this passage?A．A Terrifying DreamB．A Scary NightC．The Frightened KidD．T he Allen’s footprintsD16、Around the world, a lot of people do not have homes, they often live in dangerous situations. Many people and organizations(Ei R)around the world are working to solve the problem. Mel Young and Harald Schmied are two such people. Young is from Scotland and Schmied is from Austria. In 2001, the two men attended an international conference (会议) about homelessness. At the conference, Y oung and Schmied began to wonder if football could help the homeless people. They knew that sport could bring people together and give them hope. So, they asked themselves—what would happen if homeless people could train for and compete in their own world Cup?In 2001, Young and Schmied started the Homeless World Cup organization. The first Homeless World Cup took place in Graz, Austria in 2003. More than 140 homeless people from 18 countries played. Austria won the competition.Today the Homeless World Cup organization works with more than 70 other non-profit (非营利的) organizations. Each organization helps choose and train local homeless people for the yearly football competition. Today, 500 people from almost 50 countries play in the Homeless World cup.The players say that the event changes their lives. David Duke was homeless and didn’t have a job. H e heard about the Homeless World Cup in 2003 and decided to join. He played for Scotland. After that, lots of good things happened to him. He went back to school. He found a home. His team won the Homeless World Cup in 2007.In addition, the organizers of the Homeless World Cup say that the event can change the way we see homeless people. More than 100,000 people watch the Homeless World Cup every year.1．Where do Mel Young and Harald Schmied come from?A．They both come from Scotland.B．They both come from Austria.C．Schmied is from Scotland and Young is from Austria.D．Schmied is from austria and Young is from Scotland.2．When did the homeless world Cup organization start?A．In 2001. B．In 2003. C．In 2007. D．In 2009.3．The writer uses David Duke as an example to show that ________.A．team spirit is very importantB．football is a sport that has no age requirement (要求)C．hard work is the key to successD．the Homeless World Cup helps change peoples’ lives4．Which of the following is TRUE according to the passage?A．Few people watch the Homeless World Cup.B．Austria won the Homeless World Cup in 2007.C．The Homeless World Cup works with many other organizations.D．500 homeless people took part in the first Homeless World Cup.5．What can we know from the passage?A．A homeless man can become the best football player.B．Many people and organizations are helping the homeless people.C．Mel Young and Harald Schmied set up 70 organizations.D．No one likes to watch the Homeless World Cup at first.E17、阅读理解。
(数学3份试卷)2019年吉林省名校中考二轮复习仿真化学冲刺卷
中考数学模拟试卷一、选择题（本题包括10个小题，每小题只有一个选项符合题意）1．如图，已知////AB CD EF，那么下列结论正确的是（）A．AD BCDF CE=B．BC DFCE AD=C．CD BCEF BE=D．CD ADEF AF=【答案】A【解析】已知AB∥CD∥EF，根据平行线分线段成比例定理，对各项进行分析即可．【详解】∵AB∥CD∥EF，∴AD BCDF CE=．故选A．【点睛】本题考查平行线分线段成比例定理，找准对应关系，避免错选其他答案．2．A、B两地相距180km，新修的高速公路开通后，在A、B两地间行驶的长途客车平均车速提高了50%，而从A地到B地的时间缩短了1h．若设原来的平均车速为xkm/h，则根据题意可列方程为A．1801801(150%)x x-=+B．1801801(150%)x x-=+C．1801801(150%)x x-=-D．1801801(150%)x x-=-【答案】A【解析】直接利用在A，B两地间行驶的长途客车平均车速提高了50%，而从A地到B地的时间缩短了1h，利用时间差值得出等式即可．【详解】解：设原来的平均车速为xkm/h，则根据题意可列方程为：180 x ﹣180150%x+（）=1．故选A．【点睛】本题主要考查了由实际问题抽象出分式方程，根据题意得出正确等量关系是解题的关键．3．下列计算或化简正确的是（）A．234265=B842=C2(3)3-=-D2733=【解析】解：A．不是同类二次根式，不能合并，故A错误；B．822=，故B错误；C．2(3)3-=，故C错误；D．27327393÷=÷==，正确．故选D．4．按如下方法，将△ABC的三边缩小的原来的12，如图，任取一点O，连AO、BO、CO，并取它们的中点D、E、F，得△DEF，则下列说法正确的个数是（）①△ABC与△DEF是位似图形②△ABC与△DEF是相似图形③△ABC与△DEF的周长比为1：2 ④△ABC与△DEF的面积比为4：1．A．1 B．2 C．3 D．4【答案】C【解析】根据位似图形的性质，得出①△ABC与△DEF是位似图形进而根据位似图形一定是相似图形得出②△ABC与△DEF是相似图形，再根据周长比等于位似比，以及根据面积比等于相似比的平方，即可得出答案．【详解】解：根据位似性质得出①△ABC与△DEF是位似图形，②△ABC与△DEF是相似图形，∵将△ABC的三边缩小的原来的12，∴△ABC与△DEF的周长比为2：1，故③选项错误，根据面积比等于相似比的平方，∴④△ABC与△DEF的面积比为4：1．故选C．【点睛】此题主要考查了位似图形的性质，中等难度,熟悉位似图形的性质是解决问题的关键．5．若分式11xx-+的值为零，则x的值是( )A．1 B．1-C．1±D．2【解析】试题解析：∵分式11x x -+的值为零，∴|x|﹣1=0，x+1≠0，解得：x=1．故选A ．6．关于x 的一元一次不等式≤﹣2的解集为x≥4，则m 的值为（ ）A ．14B ．7C ．﹣2D ．2【答案】D【解析】解不等式得到x≥12m+3，再列出关于m 的不等式求解.【详解】23m x-≤﹣1，m ﹣1x≤﹣6，﹣1x≤﹣m ﹣6，x≥12m+3，∵关于x 的一元一次不等式23m x-≤﹣1的解集为x≥4，∴12m+3=4，解得m=1．故选D ．考点：不等式的解集7．甲、乙两超市在1月至8月间的盈利情况统计图如图所示，下面结论不正确的是（）A ．甲超市的利润逐月减少B ．乙超市的利润在1月至4月间逐月增加C ．8月份两家超市利润相同D ．乙超市在9月份的利润必超过甲超市【答案】D【解析】根据折线图中各月的具体数据对四个选项逐一分析可得．【详解】A 、甲超市的利润逐月减少，此选项正确，不符合题意；B 、乙超市的利润在1月至4月间逐月增加，此选项正确，不符合题意；C 、8月份两家超市利润相同，此选项正确，不符合题意；D 、乙超市在9月份的利润不一定超过甲超市，此选项错误，符合题意，故选D ．【点睛】本题主要考查折线统计图，折线图是用一个单位表示一定的数量，根据数量的多少描出各点，然后把各点用线段依次连接起来．以折线的上升或下降来表示统计数量增减变化．8．实数a 、b 、c 在数轴上的位置如图所示，则代数式|c ﹣a|﹣|a+b|的值等于（ ）A ．c+bB ．b ﹣cC ．c ﹣2a+bD ．c ﹣2a ﹣b 【答案】A【解析】根据数轴得到b ＜a ＜0＜c ，根据有理数的加法法则，减法法则得到c-a ＞0，a+b ＜0，根据绝对值的性质化简计算．【详解】由数轴可知，b ＜a ＜0＜c ，∴c-a ＞0，a+b ＜0，则|c-a|-|a+b|=c-a+a+b=c+b ，故选A ．【点睛】本题考查的是实数与数轴，绝对值的性质，能够根据数轴比较实数的大小，掌握绝对值的性质是解题的关键．9．如图是二次函数2y ax bx c =++的图象，有下面四个结论：0abc >①；0a b c ②-+>； 230a b +>③；40c b ->④，其中正确的结论是( )A ．①②B ．①②③C ． ①③④D ． ①②④【答案】D 【解析】根据抛物线开口方向得到a 0>，根据对称轴02b x a=->得到b 0<，根据抛物线与y 轴的交点在x 轴下方得到c 0<，所以0abc >；1x =-时，由图像可知此时0y >，所以0a b c -+>；由对称轴123b x a =-=，可得230a b +=；当2x =时，由图像可知此时0y >，即420a bc ++>，将23a b =-代入可得40c b ->.【详解】①根据抛物线开口方向得到0a >，根据对称轴02b x a =->得到b 0<，根据抛物线与y 轴的交点在x 轴下方得到c 0<，所以0abc >，故①正确.②1x =-时，由图像可知此时0y >，即0a b c -+>，故②正确.③由对称轴123b x a =-=，可得230a b +=，所以230a b +>错误，故③错误； ④当2x =时，由图像可知此时0y >，即420a bc ++>，将③中230a b +=变形为23a b =-，代入可得40c b ->，故④正确.故答案选D.【点睛】本题考查了二次函数的图像与系数的关系，注意用数形结合的思想解决问题。
2022年吉林省长春市南关区东北师大附中中考数学冲刺试卷(四)
2022年吉林省长春市南关区东北师大附中中考数学冲刺试卷（四）一、选择题（本大题共8小题，每小题3分，共24分）1．（3分）如图，数轴上被遮挡住的整数是（）A．1B．﹣3C．﹣1D．02．（3分）据长春海关统计数据显示，2020年一季度，全省出口总额为7 810 000 000元，7 810 000 000这个数用科学记数法表示为（）A．0.781×103B．7.81×109C．78.1×109D．7.81×1010 3．（3分）如图是由6个相同的小正方体组成的立体图形，这个立体图形的俯视图是（）A．B．C．D．4．（3分）a6可以表示为（）A．6a B．a2•a3C．（a3）2D．a12÷a25．（3分）《孙子算经》是中国古代重要的数学著作，其中第三卷中记载一题：今有兽，六首四足；禽，二首二足，上有七十六首，下有四十六足，问：禽、兽各几何？译文：今有一只怪兽，有6个头4只脚，一只怪鸟，有2个头2只脚，现在上面有76个头，下面有46只脚，问怪兽、怪鸟各有多少？设怪兽为x只，怪鸟为y只，可列方程组为（）A．B．C．D．6．（3分）小致利用测角仪和皮尺测量学校旗杆的高度，如图，小致在D处测得顶端P的仰角∠PDC＝α，D到旗杆的距离CD＝5米，测角仪BD的高度为1米，则旗杆P A的高度表示为（）米A．5tanα+1B．5sinα+1C．5cosα+1D．+1 7．（3分）如图，在△ABC中，按以下步骤作图：①以B为圆心，适当长度为半径作弧，交AB于点D，交BC于点E；②分别以D，E为圆心，以大于长为半径作弧，两弧交于点M；③作射线BM交AC于点N，若AB＝BN，∠A＝74°，则∠C的大小为（）A．32°B．42°C．37°D．40°8．（3分）如图，Rt△AOB的顶点A在第一象限，顶点B在x轴的正半轴，函数y＝（k ＞0，x＞0）的图象经过OA的中点D，与直角边AB交于点C，若点A的坐标为（4，3），则△AOC的面积为（）A．5B．3C．D．4.5二、填空题（本大题共6小题，每题3分，共18分）9．（3分）计算：×＝．10．（3分）把多项式a2b﹣2ab+b分解因式的结果是．11．（3分）如果关于x的方程2x2﹣3x+k＝0有两个相等的实数根，那么实数k的值是．12．（3分）把一块含有45°角的直角三角板与两条长边平行的直尺如图放置（直角顶点在直尺的一条长边上）．若∠1＝23°，则∠2＝°．13．（3分）如图，AB是⊙O的直径，C是⊙O上一点，∠ACB的平分线交⊙O于D，且AB ＝10，则AD的长为．14．（3分）抛物线y＝x2+bx+3的对称轴为直线x＝1，若关于x的一元二次方程x2+bx+3﹣t ＝0（t为实数）在﹣1＜x＜4的范围内有实数根，则t的取值范围是．三、解答题：（本大题共10小题，共78分）15．（6分）先化简，再求值：（2a﹣1）2+2a（3﹣2a），其中a＝2021．16．（6分）甲、乙两个不透明的袋子中分别装有三个标有数字的小球，小球除数字不同外，其余均相同，甲袋中三个小球上分别标有数字1、2、7，乙袋中三个小球上分别标有数字4、5、6，小明分别从甲、乙口袋中通随机摸出一个小球，用画树状图（或列表）的方法，求小明摸出两个小球上的数字之和为4的倍数的概率．17．（6分）为迎接五•一国际劳动节，某商店准备采购一批服装，经调查，用1000元采购A 种服装的件数与用800元采购B种服装的件数相等，A种服装每件的进价比B种服装多10元，求B种服装每件的进价．18．（7分）如图，AB为⊙O的直径，AC切⊙O于点A，连接BC交O于点D，E是⊙O上一点，且与点D在AB异侧，连接DE（1）求证：∠C＝∠BED；（2）若∠C＝50°，AB＝2，则的长为（结果保留π）19．（7分）为了了解同学们对垃圾分类知识的了解程度，增强同学们的环保意识某校数学兴趣小组设计了“垃圾分类知识及投放情况”问卷，并在本校随机抽取若干名同学进行了问卷测试，根据测试成绩分布情况，将测试成绩分成A、B、C、D四组，绘制了如下统计图表问卷测试成绩分组表组别分数/分A60＜x≤70B70＜x≤80C80＜x≤90D90＜x≤100（1）本次抽样调查的样本总量是；（2）样本中，测试成绩在B组的频数是，D组的频率是；（3）样本中，这次测试成绩的中位数落在组；（4）如果该校共有880名学生，请估计成绩在90＜x≤100的学生约有人．20．（7分）如图，在8×5的正方形网格中，每个小正方形的边长均为1，△ABC的三个顶点均在小正方形的顶点上．（1）在图1中画一个△ABD（点D在小正方形的顶点上），使△ABD的周长等于△ABC 的周长，且以A、B、C、D为顶点的四边形是轴对称图形；（2）在图2中画△ABF点E在小正方形的顶点上），使△ABE的周长等于△ABC的周长，且以A、B、C、E为顶点的四边形是中心对称图形．（3）直接写出图2中四边形的面积．21．（8分）端午节期间，甲、乙两人沿同一路线行驶，各自开车同时去离家560千米的景区游玩，甲先以每小时60千米的速度匀速行驶1小时，再以每小时m千米的速度匀速行驶，途中休息了一段时间后，仍按照每小时m千米的速度匀速行驶，两人同时到达目的地．图中折线（实线）、线段（虚线）分别表示甲、乙两人所走的路程y甲（km），y乙（km）与时间x（h）之间的函数关系．请根据图象提供的信息，回答下列问题：（1）图中点E的坐标是，题中m＝km/h，甲在途中休息了h；（2）求线段CD的解析式，并写出自变量x的取值范围；（3）两人第二次相遇后，又经过多长时间两人相距20km？22．（9分）如图，AD是△ABC的中线，过点C作直线CF∥AD．【问题】如图①，过点D作直线DG∥AB交直线CF于点E，连接AE，求证：AB＝DE．【探究】如图②，在线段AD上任取一点P，过点P作直线PG∥AB交直线CF于点E，连接AE、BP，探究四边形ABPE是哪类特殊四边形并加以证明．【应用】在探究的条件下，设PE交AC于点M．若点P是AD的中点，且△APM的面积为1，直接写出四边形ABPE的面积．23．（10分）如图，矩形ABCD中，AB＝4，AD＝3，∠DAB的平分线交边CD于点E，点P在射线AE上以每秒2个单位长度的速度沿射线AE方向从点A开始运动，过点P作PQ⊥AB于点Q，以PQ为边向右作平行四边形PQMN，点N在射线AE上，且AP＝PN．设点P的运动时间为t秒．（1）PQ＝（用含t的代数式表示）；（2）当点M落在BC上时，求t的值；（3）设平行四边形PQMN与矩形ABCD重合部分图形的面积为S，当点P在线段AE上运动时，求S与t的函数关系式；（4）直接写出在点P运动的过程中，整个图形中形成的三角形存在全等三角形时t的值（不添加任何辅助线）．24．（12分）对于某一函数给出如下定义：对于任意实数m，当自变量x≥m时，函数y关于x的函数图象为G1，将G沿直线x＝m翻折后得到的函数图象为G2，函数G的图象由G1和G2两部分共同组成，则函数G为原函数的“对折函数”如函数y＝x（x≥2）的对折函数为y＝（1）写出函数y＝﹣2x+1（x≥﹣1）的对折函数；（2）若函数y＝2x﹣2（x≥﹣）的对折函数与x轴交于点A，B（点A在点B的左侧），与y轴交于点C，求△ABC的周长；（3）若点P（m，5）在函数y＝（x﹣1）2﹣4（x≥﹣1）的对折函数的图象上，求m的值；（4）当函数y＝（x﹣1）2﹣4（x≥n）的对折函数与x轴有不同的交点个数时，直接写出n的取值范围．2022年吉林省长春市南关区东北师大附中中考数学冲刺试卷（四）参考答案与试题解析一、选择题（本大题共8小题，每小题3分，共24分）1．（3分）如图，数轴上被遮挡住的整数是（）A．1B．﹣3C．﹣1D．0【分析】根据数轴上的点表示的数以及实数的大小关系解决此题．【解答】解：设被挡住的数为x．由题意得，﹣2＜x＜0．∵﹣3＜﹣2＜﹣1＜0＜1，∴x＝﹣1．故选：C．【点评】本题主要考查数轴的点表示的数以及实数的大小关系，熟练掌握数轴上的点表示的数以及实数的大小关系是解决本题的关键．2．（3分）据长春海关统计数据显示，2020年一季度，全省出口总额为7 810 000 000元，7 810 000 000这个数用科学记数法表示为（）A．0.781×103B．7.81×109C．78.1×109D．7.81×1010【分析】科学记数法的表示形式为a×10n的形式，其中1≤|a|＜10，n为整数．确定n 的值时，要看把原数变成a时，小数点移动了多少位，n的绝对值与小数点移动的位数相同．当原数绝对值≥10时，n是正数；当原数的绝对值＜1时，n是负数．【解答】解：7 810 000 000＝7.81×109．故选：B．【点评】此题考查科学记数法的表示方法．科学记数法的表示形式为a×10n的形式，其中1≤|a|＜10，n为整数，表示时关键要正确确定a的值以及n的值．3．（3分）如图是由6个相同的小正方体组成的立体图形，这个立体图形的俯视图是（）A．B．C．D．【分析】根据从上边看得到的图形是俯视图，可得答案．【解答】解：这个立体图形的俯视图有两层，上层三个正方形，下层一个正方形，右齐．故选：D．【点评】本题考查了简单组合体的三视图，从上边看得到的图形是俯视图是解题关键．4．（3分）a6可以表示为（）A．6a B．a2•a3C．（a3）2D．a12÷a2【分析】根据同底数幂的乘法、幂的乘方、同底数幂的除法分别计算可得．【解答】解：A、6a表示6×a，此选项不符合题意；B、a2•a3＝a5，此选项不符合题意；C、（a3）2＝a6，此选项符合题意；D、a12÷a2＝a10，此选项不符合题意；故选：C．【点评】本题主要考查幂的运算，解题的关键是熟练掌握同底数幂的乘法、幂的乘方、同底数幂的除法的运算法则．5．（3分）《孙子算经》是中国古代重要的数学著作，其中第三卷中记载一题：今有兽，六首四足；禽，二首二足，上有七十六首，下有四十六足，问：禽、兽各几何？译文：今有一只怪兽，有6个头4只脚，一只怪鸟，有2个头2只脚，现在上面有76个头，下面有46只脚，问怪兽、怪鸟各有多少？设怪兽为x只，怪鸟为y只，可列方程组为（）A．B．C．D．【分析】根据怪兽和怪鸟的头数及脚数，即可得出关于x，y的二元一次方程，此题得解．【解答】解：依题意，得：．故选：C．【点评】本题考查了由实际问题抽象出二元一次方程组，找准等量关系，正确列出二元一次方程组是解题的关键．6．（3分）小致利用测角仪和皮尺测量学校旗杆的高度，如图，小致在D处测得顶端P的仰角∠PDC＝α，D到旗杆的距离CD＝5米，测角仪BD的高度为1米，则旗杆P A的高度表示为（）米A．5tanα+1B．5sinα+1C．5cosα+1D．+1【分析】根据题意可得，四边形ABDC是矩形，根据锐角三角函数即可表示旗杆P A的高度．【解答】解：根据题意可知：四边形ABDC是矩形，∴∠PCD＝90°，AC＝BD＝1米，在Rt△PCD中，PC＝CD tanα＝5tanα，∴P A＝PC+AC＝（5tanα+1）米．答：旗杆P A的高度表示为（5tanα+1）米．故选：A．【点评】本题考查了解直角三角形的应用﹣仰角俯角问题，解决本题的关键是掌握仰角俯角定义．7．（3分）如图，在△ABC中，按以下步骤作图：①以B为圆心，适当长度为半径作弧，交AB于点D，交BC于点E；②分别以D，E为圆心，以大于长为半径作弧，两弧交于点M；③作射线BM交AC于点N，若AB＝BN，∠A＝74°，则∠C的大小为（）A．32°B．42°C．37°D．40°【分析】依据等腰三角形的性质即可得到∠ABN的度数，再根据角平分线的定义以及三角形内角和定理，即可得到∠C的度数．【解答】解：∵AB＝BN，∠A＝74°，∴∠ANB＝74°，∠ABN＝180°﹣2×74°＝32°，由作图痕迹可得，BN平分∠ABC，∴∠ABC＝2∠ABN＝64°，∴△ABC中，∠C＝180°﹣∠A﹣∠ABC＝180°﹣74°﹣64°＝42°，故选：B．【点评】本题主要考查了基本作图以及等腰三角形的性质，解题时注意：等腰三角形的两个底角相等．8．（3分）如图，Rt△AOB的顶点A在第一象限，顶点B在x轴的正半轴，函数y＝（k ＞0，x＞0）的图象经过OA的中点D，与直角边AB交于点C，若点A的坐标为（4，3），则△AOC的面积为（）A．5B．3C．D．4.5【分析】直接根据点D是OA的中点即可求出D点坐标，由D点坐标即可求出反比例函数的解析式，故可得出△OBC的面积，由S△AOC＝S△AOB﹣S△OBC即可得出结论．【解答】解：∵D是OA的中点，点A的坐标为（4，3），∴D（2，），把D（2，）代入反比例函数y＝的图象上，∴k＝2×＝3，∵点C在反比例函数y＝的图象上，∴S△OBC＝×3＝，∴S△AOC＝S△AOB﹣S△OBC＝×4×3﹣＝．故选：D．【点评】本题考查的是反比例函数综合题，熟知反比例函数中k＝xy的特点是解答此题的关键．二、填空题（本大题共6小题，每题3分，共18分）9．（3分）计算：×＝2．【分析】直接利用二次根式的乘法运算法则计算得出答案．【解答】解：×＝＝＝2．故答案为：2．【点评】此题主要考查了二次根式的乘除，正确掌握相关运算法则是解题关键．10．（3分）把多项式a2b﹣2ab+b分解因式的结果是b（a﹣1）2．【分析】直接提取公因式b，再利用完全平方公式分解因式即可．【解答】解：a2b﹣2ab+b＝b（a2﹣2a+1）＝b（a﹣1）2．故答案为：b（a﹣1）2．【点评】此题主要考查了提取公因式法以及公式法分解因式，正确应用公式是解题关键．11．（3分）如果关于x的方程2x2﹣3x+k＝0有两个相等的实数根，那么实数k的值是．【分析】根据方程的系数结合根的判别式Δ＝0，即可得出关于k的一元一次方程，解之即可得出结论．【解答】解：∵关于x的方程2x2﹣3x+k＝0有两个相等的实数根，∴Δ＝（﹣3）2﹣4×2×k＝9﹣8k＝0，解得：k＝．故答案为：．【点评】本题考查了根的判别式，牢记“当Δ＝0时，方程有两个相等的实数根”是解题的关键．12．（3分）把一块含有45°角的直角三角板与两条长边平行的直尺如图放置（直角顶点在直尺的一条长边上）．若∠1＝23°，则∠2＝68°．【分析】由等腰直角三角形的性质得出∠A＝∠C＝45°，由三角形的外角性质得出∠AGB ＝68°，再由平行线的性质即可得出∠2的度数．【解答】解：∵△ABC是含有45°角的直角三角板，∴∠A＝∠C＝45°，∵∠1＝23°，∴∠AGB＝∠C+∠1＝68°，∵EF∥BD，∴∠2＝∠AGB＝68°；故答案为：68．【点评】此题主要考查了等腰直角三角形的性质、平行线的性质以及三角形的外角性质，关键是掌握两直线平行，同位角相等．13．（3分）如图，AB是⊙O的直径，C是⊙O上一点，∠ACB的平分线交⊙O于D，且AB ＝10，则AD的长为5．【分析】根据圆周角定理得到∠ADB＝90°，再利用∠ACD＝∠BCD得到AD＝BD，于是可判断△ABD为等腰直角三角形，然后根据等腰直角三角形的性质求AD的长度．【解答】解：∵AB是⊙O的直径，∴∠ADB＝90°，∵∠ACB的平分线交⊙O于D，∴∠ACD＝∠BCD，∴＝，∴AD＝BD，∴△ABD为等腰直角三角形，∴AD＝AB＝10×＝5．故答案为5．【点评】本题考查了圆周角定理：在同圆或等圆中，同弧或等弧所对的圆周角相等，都等于这条弧所对的圆心角的一半．推论：半圆（或直径）所对的圆周角是直角，90°的圆周角所对的弦是直径．14．（3分）抛物线y＝x2+bx+3的对称轴为直线x＝1，若关于x的一元二次方程x2+bx+3﹣t ＝0（t为实数）在﹣1＜x＜4的范围内有实数根，则t的取值范围是2≤t＜11．【分析】根据抛物线y＝x2+bx+3的对称轴为直线x＝1，可以求得b的值，然后即可得到该函数的解析式，再根据二次函数的性质，即可得到当﹣1＜x＜4时，y的取值范围，然后令y＝t，即可转化为方程x2+bx+3﹣t＝0，从而可以得到t的取值范围．【解答】解：∵抛物线y＝x2+bx+3的对称轴为直线x＝1，∴﹣＝1，得b＝﹣2，∴y＝x2﹣2x+3＝（x﹣1）2+2，∴当﹣1＜x＜4时，y的取值范围是2≤y＜11，当y＝t时，t＝x2﹣2x+3，即x2+bx+3﹣t＝0，∵关于x的一元二次方程x2+bx+3﹣t＝0（t为实数）在﹣1＜x＜4的范围内有实数根，∴t的取值范围是2≤t＜11，故答案为：2≤t＜11．【点评】本题考查抛物线与x轴的交点、二次函数的性质，解答本题的关键是明确题意，利用二次函数的性质解答．三、解答题：（本大题共10小题，共78分）15．（6分）先化简，再求值：（2a﹣1）2+2a（3﹣2a），其中a＝2021．【分析】先根据完全平方公式和单项式乘多项式法则去括号，再合并同类项即可化简原式，最后将a的值代入计算即可．【解答】解：原式＝4a2﹣4a+1+6a﹣4a2＝2a+1，当a＝2021时，原式＝2×2021+1＝4042+1＝4043．【点评】本题主要考查整式的混合运算—化简求值，解题的关键是掌握完全平方公式和单项式乘多项式法则．16．（6分）甲、乙两个不透明的袋子中分别装有三个标有数字的小球，小球除数字不同外，其余均相同，甲袋中三个小球上分别标有数字1、2、7，乙袋中三个小球上分别标有数字4、5、6，小明分别从甲、乙口袋中通随机摸出一个小球，用画树状图（或列表）的方法，求小明摸出两个小球上的数字之和为4的倍数的概率．【分析】画树状图得出所有9种等可能的结果数，然后根据概率公式求解．【解答】解：如图所示：，P（小明摸出的两个小球上的数字之和为4的倍数）＝．【点评】本题考查了列表法与树状图法：利用列表法或树状图法展示所有等可能的结果n，再从中选出符合事件A或B的结果数目m，然后利用概率公式计算事件A或事件B的概率．17．（6分）为迎接五•一国际劳动节，某商店准备采购一批服装，经调查，用1000元采购A 种服装的件数与用800元采购B种服装的件数相等，A种服装每件的进价比B种服装多10元，求B种服装每件的进价．【分析】直接根据题意表示出采购A、B种服装的件数，进而得出等式求出答案．【解答】解：设B种服装每件的进价为x元，由题意可得：＝，解得：x＝40，经检验得：x＝40为原方程的解，且符合题意，答：B种服装每件的进价为40元．【点评】此题主要考查了分式方程的应用，正确得出等量关系是解题关键．18．（7分）如图，AB为⊙O的直径，AC切⊙O于点A，连接BC交O于点D，E是⊙O上一点，且与点D在AB异侧，连接DE（1）求证：∠C＝∠BED；（2）若∠C＝50°，AB＝2，则的长为（结果保留π）【分析】（1）连接AD，如图，根据圆周角定理得到∠ADB＝90°，根据切线的性质得到∠BAC＝90°，则利用等角的余角相等得到∠DAB＝∠C，然后根据圆周角定理和等量代换得到结论；（2）连接OD，如图，利用（1）中结论得到∠BED＝∠C＝50°，再利用圆周角定理得到∠BOD的度数，然后根据弧长公式计算的长度．【解答】（1）证明：连接AD，如图，∵AB为⊙O的直径，∴∠ADB＝90°，∵AC切⊙O于点A∴CA⊥AB，∴∠BAC＝90°，∴∠C+∠ABD＝90°，而∠DAB+∠ABD＝90°，∴∠DAB＝∠C，∵∠DAB＝∠BED，∴∠C＝∠BED；（2）解：连接OD，如图，∵∠BED＝∠C＝50°，∴∠BOD＝2∠BED＝100°，∴的长度＝＝π．【点评】本题考查了切线的性质：圆的切线垂直于经过切点的半径．若出现圆的切线，必连过切点的半径，构造定理图，得出垂直关系．也考查了圆周角定理和弧长公式．19．（7分）为了了解同学们对垃圾分类知识的了解程度，增强同学们的环保意识某校数学兴趣小组设计了“垃圾分类知识及投放情况”问卷，并在本校随机抽取若干名同学进行了问卷测试，根据测试成绩分布情况，将测试成绩分成A、B、C、D四组，绘制了如下统计图表问卷测试成绩分组表组别分数/分A60＜x≤70B70＜x≤80C80＜x≤90D90＜x≤100（1）本次抽样调查的样本总量是200；（2）样本中，测试成绩在B组的频数是0.15，D组的频率是B；（3）样本中，这次测试成绩的中位数落在132组；（4）如果该校共有880名学生，请估计成绩在90＜x≤100的学生约有132人．【分析】（1）根据C组的人数和所占的百分比可以求得本次抽样调查的样本总量；（2）根据（1）中的结果和统计图中的数据可以分别求得测试成绩在B组的频数和D组的频率；（3）根据统计图中的数据可以得到中位数落在那一组；（4）根据统计图中的数据可以计算出成绩在90＜x≤100的学生人数．【解答】解：（1）本次抽样调查的样本总量是：60÷30%＝200，故答案为：200；（2）样本中，测试成绩在B组的频数是20×36%＝72，在D组的频率是：30÷200＝0.15，故答案为：72，0.15；（3）样本中，这次测试成绩的中位数落在B组，故答案为：B；（4）880×＝132（人），故答案为：132．【点评】本题考查频数分布直方图、用样本估计总体、扇形统计图、中位数，解答本题的关键是明确题意，利用数形结合的思想解答．20．（7分）如图，在8×5的正方形网格中，每个小正方形的边长均为1，△ABC的三个顶点均在小正方形的顶点上．（1）在图1中画一个△ABD（点D在小正方形的顶点上），使△ABD的周长等于△ABC 的周长，且以A、B、C、D为顶点的四边形是轴对称图形；（2）在图2中画△ABF点E在小正方形的顶点上），使△ABE的周长等于△ABC的周长，且以A、B、C、E为顶点的四边形是中心对称图形．（3）直接写出图2中四边形的面积．【分析】（1）根据轴对称图形的性质作出图形即可．（2）根据中心对称图形的性质作出图形即可．（3）利用平行四边形的面积公式计算即可．【解答】解：（1）如图，△ABD即为所求．（2）如图，四边形ABEC即为所求．（3）四边形ABEC的面积＝4×2＝8．【点评】本题考查作图应用与设计，勾股定理，轴对称图形，中心对称图形等知识，解题的关键是理解题意，灵活运用所学知识解决问题．21．（8分）端午节期间，甲、乙两人沿同一路线行驶，各自开车同时去离家560千米的景区游玩，甲先以每小时60千米的速度匀速行驶1小时，再以每小时m千米的速度匀速行驶，途中休息了一段时间后，仍按照每小时m千米的速度匀速行驶，两人同时到达目的地．图中折线（实线）、线段（虚线）分别表示甲、乙两人所走的路程y甲（km），y乙（km）与时间x（h）之间的函数关系．请根据图象提供的信息，回答下列问题：（1）图中点E的坐标是（2，160），题中m＝100km/h，甲在途中休息了1 h；（2）求线段CD的解析式，并写出自变量x的取值范围；（3）两人第二次相遇后，又经过多长时间两人相距20km？【分析】（1）根据速度和时间列方程：60×1+m＝160，可得m＝100，根据D的坐标可计算直线OD的解析式，从图中知E的横坐标为2，可得E的坐标，根据点E到D的时间差及速度可得休息的时间；（2）利用待定系数法求直线CD的解析式；（3）先计算第二次相遇的时间：y＝360时代入y＝80x可得x的值，再计算x＝5时乙行驶的路程，可得路程差为40km，所以存在两种情况：两人相距20km，列方程可得结论．【解答】解：（1）由图形得D（7，560），设OD的解析式为：y＝kx，把D（7，560）代入得：7k＝560，k＝80，∴OD：y＝80x，当x＝2时，y＝2×80＝160，∴E（2，160），由题意得：60×1+m＝160，m＝100，7﹣2﹣（560﹣160）÷100＝1，故答案为：（2，160），100，1；（2）∵A（1，60），E（2，160），∴直线AE：y＝100x﹣40，当x＝4时，y＝400﹣40＝360，∴B（4，360）∴C（5，360），∵D（7，560），∴设CD的解析式为：y＝kx+b，把C（5，360），D（7，560）代入得：，解得：，∴直线CD的解析式为：y＝100x﹣140（5≤x≤7）；（3）∵OD的解析式为：y＝80x（0≤x≤7），当x＝5时，y＝5×80＝400，400﹣360＝40，∴出发5h时两个相距40km，把y＝360代入y＝80x得：x＝4.5，∴出发4.5h时两人第二次相遇，①当4.5＜x＜5时，80x﹣360＝20，x＝4.75，4.75﹣4.5＝0.25（h），②当x＞5时，80x﹣（100x﹣140）＝20，x＝6，6﹣4.5＝1.5（h），答：两人第二次相遇后，又经过0.25时或1.5时两人相距20km．【点评】此题主要考查了一次函数的应用，读函数的图象时，首先要理解横纵坐标表示的含义，数形结合思想的应用是解题关键．22．（9分）如图，AD是△ABC的中线，过点C作直线CF∥AD．【问题】如图①，过点D作直线DG∥AB交直线CF于点E，连接AE，求证：AB＝DE．【探究】如图②，在线段AD上任取一点P，过点P作直线PG∥AB交直线CF于点E，连接AE、BP，探究四边形ABPE是哪类特殊四边形并加以证明．【应用】在探究的条件下，设PE交AC于点M．若点P是AD的中点，且△APM的面积为1，直接写出四边形ABPE的面积．【分析】【问题】如图①，过点D作直线DG∥AB交直线CF于点E，连接AE，只要证明△ABD≌△EDC即可；【探究】如图②，四边形ABPE是平行四边形，方法一，过点D作DN∥PE交直线CF 于点N，只要证明四边形PDNE是平行四边形，推出PE＝DN，由问题结论可得AB＝DN，推出PE＝AB，推出四边形ABPE是平行四边形；方法二，如图③中，延长BP交直线CF于点N，只要证明△ABP≌△EPN，即可解决问题；【应用】如图④，延长BP交CF于H．想办法求出△AEM的面积即可解决问题；【解答】【问题】证明：如图①∵DG∥AB，∴∠1＝∠2，∠B＝∠4，∵CF∥AD，∴∠2＝∠3，∴∠1＝∠3，∵AD是△ABC的中线，∴BD＝DC，∴△ABD≌△EDC，∴AB＝DE．（或证明四边形ABDE是平行四边形，从而得到AB＝DE．）【探究】四边形ABPE是平行四边形．方法一：如图②，证明：过点D作DN∥PE交直线CF于点N，∵CF∥AD，∴四边形PDNE是平行四边形，∴PE＝DN，∵由问题结论可得AB＝DN，∴PE＝AB，∴四边形ABPE是平行四边形．方法二：如图③，证明：延长BP交直线CF于点N，∵PG∥AB，∴∠1＝∠2，∠5＝∠4，∵CF∥AD，∴∠2＝∠3，∴∠1＝∠3，∵AD是△ABC的中线，CF∥AD，∴BP＝PN，∴△ABP≌△EPN，∴AB＝PE，∴四边形ABPE是平行四边形．【应用】如图④，延长BP交CF于H．由上面可知，四边形ABPE是平行四边形，∴AE∥BH，∴P A∥EH，∴四边形APHE是平行四边形，∴P A＝EH，∵BD＝DC，DP∥CH，∴BP＝PH，∴CH＝2PD，∵AP＝PD，∴EC＝3P A，∵P A∥EC，∴＝＝，∴S△AEM＝3S△APM＝3，∴S△ABP＝S△APE＝4，∴S平行四边形ABPE＝8．【点评】本题考查四边形综合题、全等三角形的判定和性质、平行线的性质、三角形的中位线定理等知识，解题的关键是学会添加常用辅助线，构造全等三角形解决问题，学会用转化的思想思考问题，属于中考压轴题．23．（10分）如图，矩形ABCD中，AB＝4，AD＝3，∠DAB的平分线交边CD于点E，点P在射线AE上以每秒2个单位长度的速度沿射线AE方向从点A开始运动，过点P作PQ⊥AB于点Q，以PQ为边向右作平行四边形PQMN，点N在射线AE上，且AP＝PN．设点P的运动时间为t秒．（1）PQ＝t（用含t的代数式表示）；（2）当点M落在BC上时，求t的值；（3）设平行四边形PQMN与矩形ABCD重合部分图形的面积为S，当点P在线段AE上运动时，求S与t的函数关系式；（4）直接写出在点P运动的过程中，整个图形中形成的三角形存在全等三角形时t的值（不添加任何辅助线）．【分析】（1）判断出△APQ是等腰直角三角形即可得出结论；（2）先判断出点Q是AB中点，进而求出AQ＝2，即可得出结论；（3）分三种情形讨论①如图4中，当0＜t≤时，重叠部分是平行四边形PQMN．②如图5中，当＜t≤2时，重叠部分是五边形PQMGE．③如图6中，当2＜t≤3时，重叠部分是五边形PQGCE，延长QP交CD于K．分别求解即可．（4）分三种情形讨论即可）①如图7中，当点Q是AB中点时，△APQ≌△QMB．②如图8中，当点P与点E重合时，△APQ≌△AED．③如图9中，当△PEK≌△QGB时，分别求解即可．【解答】解：（1）∵四边形ABCD是矩形，∴∠BAD＝90°，∵AE是∠BAD的角平分线，∴∠BAE＝∠BAD＝45°，∵PQ⊥AB，∴∠APQ＝45°＝∠BAE，∠AQP＝90°，即：△APQ是等腰直角三角形，由运动知，AP＝t，∴PQ＝t，故答案为：t；（2）如图1，∵四边形PQMN是平行四边形，∴PQ∥MN，∵点M在BC上，∴BN∥PQ，∵AP＝PN，∴AQ＝BQ＝AB＝2，在Rt△APQ中，∠P AQ＝45°，∴AP＝AQ＝2，由运动知，AP＝t，∴t＝2，∴t＝2；（3）①如图2中，当0＜t≤时，重叠部分是平行四边形PQMN，S＝t2，②如图3中，当＜t≤2时，重叠部分是五边形PQMGE，∴S＝S平行四边形PQMN﹣S△NGE＝t2﹣[]2＝﹣t2+6t﹣．③如图4中，当2＜t≤3时，重叠部分是五边形PQGCE，延长QP交CD于K．S＝S矩形QBCK﹣S△KPE﹣S△QBG＝3（4﹣t）﹣（）2﹣（4﹣t）2＝﹣t2+4t ﹣，综上所述，S＝．（4）①如图5中，当点Q是AB中点时，△APQ≌△QMB，此时t＝2．②如图6中，当点P与点E重合时，△APQ≌△AED，此时t＝3．③如图7中，当△PEK≌△QGB时，由EK＝BQ得到：＝4﹣t，解得t＝，综上所述，t＝2s或3s或s时，整个图形中形成的三角形存在全等三角形．【点评】本题考查四边形综合题、矩形的性质、等腰直角三角形的性质、平移变换、全等三角形的判定等知识，解题的关键是学会分类讨论，学会画好图形，学会利用分割法求面积，属于中考压轴题．24．（12分）对于某一函数给出如下定义：对于任意实数m，当自变量x≥m时，函数y关于x的函数图象为G1，将G沿直线x＝m翻折后得到的函数图象为G2，函数G的图象由G1和G2两部分共同组成，则函数G为原函数的“对折函数”如函数y＝x（x≥2）的对折函数为y＝（1）写出函数y＝﹣2x+1（x≥﹣1）的对折函数；（2）若函数y＝2x﹣2（x≥﹣）的对折函数与x轴交于点A，B（点A在点B的左侧），与y轴交于点C，求△ABC的周长；（3）若点P（m，5）在函数y＝（x﹣1）2﹣4（x≥﹣1）的对折函数的图象上，求m的值；（4）当函数y＝（x﹣1）2﹣4（x≥n）的对折函数与x轴有不同的交点个数时，直接写出n的取值范围．【分析】（1）当y＝﹣2x+1＝0时，x＝，即点B（，0），则点C（﹣，0），即可求解；（2）参考（1）求出对折后函数表达式即可求解；（3）求出对折函数，将点P（m，5）代入函数表达式，即可求解；（4）分当n＜﹣1、n＝﹣1、﹣1＜n＜3、n＝3、n＞3，分别求解即可．【解答】解：（1）如图1，设对折点为A，则点A（﹣1，3），设对折图象与x轴的交点为A、B，。
2019年吉林省长春市北师大附属学校中考四模英语试题(解析版)
2019年吉林省长春市北师大附属学校中考四模英语试本试卷包括四道大题。
共4页。
满分95分。
考试时间为100分钟。
考试结束后,将本试卷和答题卡一并交回。
注意事项:1.答题前,考生务必将自己的姓名、准考证号填写在各题卡上,并将条形码准确粘贴在条形码区域内。
2、答题时,考生务必按照考试要求在答题卡上的指定区域内作答,在草稿纸、试题卷上答题无效。
基础知识在下列各句的空白处填入一个适当的词,使句子意思完整、语法正确。
1. The 2018 Russia FIFA World Cup will start soon. It will last__________ June 14th to July 15th.2. The ninth-graders are_______ with their schoolwork and some even stay up late.3. Lucy had a toothache, and went to the__________. He said she ate too much candy.4. The students in Class 8 really want to____ the first place of the competition, so they practice a lot.5. Jenny's two brothers both work. One is a pilot and the__________ one is an engineer.【答案】1. from2. busy3. dentist4. win5. other【解析】【1题详解】句意：2018俄罗斯世界杯即将开幕。
它将从6月14日持续到7月15日。
根据句意可知，2018年俄罗斯世界杯从6月14日持续到7月15日，缺少一个介词from，构成“from…to…”从……到……。
吉林省长春市中考冲刺卷(Word版,有答案)
冰暖茶 2019 年长春市中考模拟试卷英语〔五〕〔冲刺卷〕本试卷包括四道大题 ,共8页 ,总分值95分 ,考试时间为100分钟。
考试结束后 ,将本试卷和答题卡一并交回。
考前须知：1. 答题前 ,考生务必将自己的姓名、准考证号填写在答题卡上 ,并将条形码准确粘贴在条形码区域内。
2. 答题时 ,考生务必按照考试要求在答题卡上的指定区域内作答 ,在草稿纸、试卷上答题无效。
一、根底知识〔共25分〕I. 在以下各句的空白处填入一个适当的词 ,使句子意思完整 ,语法正确。
〔5分〕1. If you have problems, don’t keep them ________ yourselves.2. There are four seasons in a year — spring, ________, autumn and winter.3. This weekend, I would like to eat ________ delicious and special.4. Do you often throw ________ things you don’t need any more?5. The Chinese people like red, because they believe that red can ________ them good luck.II. 用括号内所给单词的正确形式填空。
〔5分〕6. Never give up ________ (try) and you can achieve your dream.7. It’s ________ (luck) to eat the dumplings with coins in them on the Spring Festival.8. During the rain, the drivers must drive more ________ (careful) than usual.9. Lucy got a toy bear from her mother on her ________ (eight) birthday.10. It’s good for us to brush our ________ (tooth) twice a day.III. 单项选择。
吉林省长春市东北师范大附属中学2024届中考英语四模试卷含答案
吉林省长春市东北师范大附属中学2024届中考英语四模试卷含答案注意事项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．Ⅰ. 单项选择1、— ________do you have dinner with your family at restaurants?— Hardly ever.A．How long B．How oftenC．How many D．How much2、— What were you doing when we were playing basketball yesterday afternoon?— I ______ the classroom.A．was cleaning B．have cleanedC．will clean D．clean3、—Does the doctor live alone in his house?—Yes. He has a wife and two children. But ________ of them lives with him.A．both B．none C．all D．neither4、As a volunteer, the girl wants to visit sick kids in the hospital them up.A．cheered B．cheer C．cheering D．to cheer5、We are all encouraged to work hard and succeed life.A．on B．in C．out D．up6、China____great achievements in science and technology since 1978.A．make B．made C．will make D．has made7、China’s homegrown passenger plane C919 ________ on its first flight in Shanghai on May 5, 2017.A．took off B．took out C．took up D．took away8、-I prefer speaking to listening in English learning.-Oh. really? I think you should be good at of them.A．both B．neither C．some D．all9、—I love this painting. It ________the painter's love for nature.—I agree.A．plans B．expects C．shows D．depends10、good care of yourself when you are alone, or your parents will worry about you.A．Taking B．To take C．Taken D．TakeⅡ. 完形填空11、完形填空（10小题，每小题1分，共10分）Once, there lived a man in the mountains. He had a statue made by a famous master. But the statue was put at his door, ___to the ground, because he didn't like it at all.One day, a man from the city ________by his house. This man was full of Knowledge. When he saw the statue, he asked the owner _________ he would sell it.The owner laughed and said, "Who will like this dull and ____ stone?"The man from the city said, "I will give you five dollars ______ it."The owner was surprised and ____. Then the statue was moved to the city.A few months later, the man from the mountains visited ______. When he walked around the streets, he saw many people _______ in front of a shop, and a man was shouting in a loud voice, "Come in and see the most wonderful statue in the world. Only one dollar __________ this most great work of a master."The man from the mountains 1 one dollar and walked into the shop. He was shocked by the thing in the shop, because it was the stat-ue that he himself had sold for five dollars.1．A．facing B．faced C．looks D．looked2．A．past B．passed C．passes D．passing3．A．how B．when C．who D．if4．A．clean B．dirty C．interesting D．sad5．A．for B．on C．of D．with6．A．disagreed B．agreed C．left D．cried7．A．streats B．shop C．village D．city8．A．standing B．stand C．to stand D．stood9．A．to enjoy B．enjoying C．to buy D．buying10．A．sold B．spent C．cost D．paidⅢ. 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 fromkind 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、Here are two letters to George and his answers.1．According to the letters, we know that George is ______.A．a teacherB．a doctorC．a person who can give others adviceD．Bob and Alice’s friend2．The weight of Bob is ______ now.A．about 50 kg B．55 kgC．more than 55 kg D．less than 55 kg3．Alice is worrying about ______.A．her friends B．her marksC．her height D．her weight4．Bob should ______ according to George’s letter.A．take more exercise B．talk to his friendsC．join a basketball team D．learn some French5．George advises Alice to talk to ______ for help.A．her mother B．her teacherC．Bob’s teacher D．Bob’s friendsB14、Hello! I’m Ella! Let’s meet these famous pig stars! They come from stories and movies.Hello, I’m McDull. I have a birthmark on my right eye. I have a kind heart. I’m not clever buthappy, not rich but have many dreams. I want to visit Disneyland, and eat chicken at Christmas. Ihave a happy family and many good friends.Happy New Year, everyone! I’m Piglet! I like going on exciting experiences with Teddy Bear. I’m asmall but lovely pig. I live in the Hundred Wood with my friends. I wish my friends happiness andhealth.We’re Pig Brothers! We are good at building houses. We like to be called “Pig Engineers”. Wehelp others build houses in the countryside. Have you ever read our story? In the story, we build astone house and drive the wolf out.Long time no see! I’m Zhu Bajie, a very famous pig in a Chinese story Journey to the West. I’mgood at kungfu(功夫), but I don’t like working. In my spare time, I like eating and sleeping.1．. What does Piglet like doing?A．Eating and sleeping. B．Building houses.C．Doing Chinese kungfu. D．Going on exciting experiences.2．. Which of the following can we use to describe “Pig brothers”?A．Shy. B．Lazy.C．Helpful. D．Dangerous.3．Which of the following about Zhu Bajie is true?A．He is from a Chinese story. B．He has no free time.C．He likes working. D．He is poor in kungfu.C15、One night in April, Corey Simmons got on the New York City subway, heading from Manhattan Brooklyn to pick up his son from the boy’s grandmother’s.Simmons knew he needed to open the green folder（文件夹）on his legs, becauseinside lay his son’s math homework that father and son were supposed to complete together.His son, who was in the third grade, had just failed a test on fractions（分数）.Simmons, 40, was never great at math. He remembered little about fractions. He opened the folder and started on a problem, but wasn’t sure if he was doing it correctly. That was when a man got on the subway and sat next to him.“He looked like a teacher or something,” Simmons thought. “He looked like he knew something about math.”Like most New Yorkers, Simmons . But this time, he shared his problem with the stranger. To his surprise, the man offered to help. The two men talked through the man problems. The stranger helped Simmons understand them, so he could later teach his son. The moment was captured by Denise Wilson, who was heading home from her job and saw the pair doing homework. She posted the photo online. “I really love seeing things like this especially in New York,” she wrote. “To be a dad…and put down his pride and learn from a complete stranger… it was really a moving moment.”The 20-minute subway lesson gave Simmons high hopes that his son would pass the next test. “He is going to surprise his teacher,” Simmons said.根据短文内容，选择最佳答案。
2019—2020学年度上学期东北师大附中初三第四次月考初中数学
2019—2020学年度上学期东北师大附中初三第四次月考初中数学数 学 试 题本试题卷包括七道大题，共26小题，共2页．全卷总分值120分．考试时刻为120分钟． 本卷须知：1．答题前，考生务必将自己的姓名、准考证号填写在答题卡上．2．答题时，考生务必按照考试要求在答题卡上的指定区域内作答，在草稿纸、试题卷上答题无效．一、选择题(每题3分，共24分)1．－6的倒数是〔 〕A ．－6B ．6C ．16-D ．162．方程260x x --=的解是 〔 〕A ．12x =-，23x =B ．12x =，23x =-C ．12x =-，23x =-D ．12x =，23x =3．某组数列排列如下：1，2，3，5，8，x ，21，那么x 的值为 〔 〕A ．10B ．12C ．13D ．17 4．点A 〔5,2〕向右平移2个单位后的坐标为〔 〕A ．〔3,2〕B ．〔7,2〕C ．〔5,4〕D ．〔5,0〕 5．线段AB=8cm ，⊙A 与⊙B 的半径均为4cm ．那么两圆的位置关系为 〔 〕A ．外离B ．外切C ．相交D ．内切 6．将一个立方体展开，错误的选项是〔 〕A ．B ．C ．D ．7．在某次实验中，测得两个变量x 与y 之间的4组对应数据如下表：x 1 2 3 4 y0.012.98.0315.1那么x 与y 之间的函数关系最接近．．以下关系式中的〔 〕A ．22y x =-B ．33y x =-C ．1y x =+D ．21y x =-8．如图，△ABC 内接于⊙O 中，∠BOC=100°，AB=AC ，那么∠ABC 的度数为〔 〕A ．75°B ．65°C ．55°D ．50°二、填空题〔每题3分，共18分〕 9．运算：4520+＝_________．10．二次函数5232+-=x x y 与y 轴的交点的坐标为 ．11．如图，⊙O 1与⊙O 2交于点A 、B ，过点A 、B 的直线分不交两圆于C 、D ，E 、F ，70ACE ∠=，那么∠ADF =__________°．12．如图，PC 为⊙O 的切线，C 为切点，连结PO 并延长，交⊙O 分不为A 、B 两点，且30P ∠=，PC=5cm ，那么BC 长为___________cm ．13．某超市进了一种方便面，销售价为一盒方便面3元，春节期间降价10%，每盒仍能够盈利0.3元，那么一盒方便面的进价为 元．14．如图，在扇形OAB 中，C 为OB 中点，∠AOB=120°，OA=6cm ，那么图中阴影部分的面积为________ _____cm 2． 三、解答题〔每题5分，共20分〕15．如图，在△ABC 中，AB=AC ，以AB 为直径的⊙O 交BC 于E ，过点E 作ED ⊥AC 于D ．图中共有多少个直角三角形？请直截了当把它们分不写出来〔不要求证明〕．OEDCBA16．运算：()131129tan 452-⎛⎫-+-+- ⎪⎝⎭．17．某商店在一次促销活动中规定：消费者消费满200元或者超过200元就可享受打折优待，一名同学为班级买奖品，预备买6本影集和假设干支钢笔，影集每本15元，钢笔每支8元，咨询他至少买多少支钢笔才能打折？18．一条抛物线32++=x mx y 与x 轴只有一个交点，求那个抛物线解析式． 四、解答题〔每题6分，共24分〕19．如图，要把一块三角形的蛋糕平均地分给四位小朋友，假如∠B=90°，∠C=30°，要使这四位小朋友所得蛋糕的大小、形状都相同，请在图①中画出分割方案〔要求：标出．．相应特点点的位置或角度〕；假如按上述条件，把蛋糕平均地分给三位小朋友，请在图②中画出分割方案〔要求：标出．．相应特点点的位置或角度〕．20．如图，周长为16的扇形，半径R 等于多少时，扇形的面积最大？最大的面积是多少？A21．阅读下面的文字，并应用其结论解题：〔1〕阅读1：如图①，：点P 是⊙O 外一点，PT 切⊙O 于点T ，P A 是⊙O 的割线，交⊙O于点A 、B ，那么有2PT PA PB =⋅．上面的结论，我们称为〝切割线定理〞，即：从圆外一点引圆的切线和割线，切线长是这点到割线与圆交点的两条线段长的比例中项．〔2〕阅读2：如图②，：点P 是⊙O ′外一点，P AB 、PCD 是⊙O ′的两条割线，分不交⊙O ′于点A 、B 和C 、D ，那么有PA PB PC PD ⋅=⋅．上面的结论，我们称为〝切割线定理的推论〞，即：从圆外一点引圆的两条割线，这一点到每条割线与圆的交点的两条线段的长的积相等．〔3〕应用上述结论解下面的题目：如图3，⊙O 和⊙O '都通过点A 、B ，点P 在BA 的延长线上，过P 作⊙O 的割线PCD 交⊙O 于C 、D 两点，作⊙O '的切线PE 切⊙O '于点E ．假设PC=4，CD=8，⊙O 的半径为5．〔1〕求PE 的长； 〔2〕求△COD 的面积．图1 图2 图322．某种爆竹点燃后，其上升的高度h 〔米〕和时刻t 〔秒〕符合关系式2012h v t gt =-〔0＜t ≤2＝，其中重力加速度g 以10米/秒2运算．这种爆竹点燃后以v 0=20米/秒的初速度上升．〔1〕这种爆竹在地面上点燃后，通过多长时刻离地面15米？〔2〕在爆竹点燃后1.5秒至1.8秒这段时刻内，判定爆竹是上升，或是下降，并讲明理由．五、解答题(每题7分，共14分)23．⊙O 1、⊙O 2相交于A 、B 两点，⊙O 1的半径r 1=4，⊙O 2的半径r 2=3，O 1O 2=6，将⊙O 2沿O 1O 2所在的直线向左或向右平移使其与⊙O 1相切，求平移方向〔左右〕和平移距离．21O O24．为了缓解〝停车难〞咨询题，某单位拟建筑地下停车库，建筑设计师提供了该地下停车库的设计示意图．按规定，地下停车库坡道口上方要张贴限高标志，以便告知停车人车辆能否安全驶入．为标明限高，请你依照该图运算CE ．〔sin18°=0.309，cos18°=0.951，tan18°=0.323，结果精确到0.1m 〕六、解答题〔每题10分，共20分〕25．如图，AB 是⊙O 的直径，AC 为弦，且平分∠BAD ，AD ⊥CD ，垂足为D ． 〔1〕求证：CD 是⊙O 的切线； 〔2〕求证：2AC AB AD =⋅；〔3〕假设⊙O 的直径为4，AD=3，求∠BAC 的度数．O DBA26．抛物线()221y a x t t =--+〔a 、t 是常数，且a ≠0，t ≠0〕的顶点是A ，抛物线y=x 2－2x+1的顶点为B ．〔1〕写出点A 的坐标〔用含t 的代数式表示〕，并判定点A 是否在抛物线y=x 2－2x+1上？〔2〕假如抛物线()221y a x t t =--+通过点B ．①求a 的值；②这条抛物线与x 轴的两个交点和它的顶点A 能否构成直角三角形，假设能，求出t 的值；假设不能，请讲明理由．。