哈工大附中入学考试

黑龙江省哈尔滨市工业大学附属中学2022-2023学年九年级下学期开学考试数学试题学校:___________姓名：___________班级：___________考号：___________A．B．C．D．A．B．C．D．BD BE EF CF AD BD DE AC二、填空题三、解答题(1)在图中画出以AB为对角线的正方形AEBF，点E和点F均在小正方形的顶点上，其中点E在AB的左侧；Y，点G和点H均在小正方形的顶点上，连接DH，(2)在图中画出以CD为边的CDGHY的面积为15，连接HF，请直接写出线段HF的长．CDH△为等腰三角形，且CDGH23．为了了解同学们线上听课时所用的电子设备类型，某中学开展了一项调查活动，围绕“电脑、平板、学习机、手机四种电子产品中，你使用的是哪一类？（必选且只选一类）”的问题，在全校范围内随机抽取部分学生进行问卷调查，将调查结果整理后绘制成如图所示的不完整的条形统计图和扇形统计图，请你根据图中提供的信息回答下列问题：(1)在这次调查中，一共抽取了多少名学生？(2)请通过计算补全条形统计图；(3)若这所中学共有2500名学生，请你估计该中学不使用电脑上课的学生有多少名．24．已知：如图，在矩形ABCD中，对角线AC、BD相交于点O，OE BD⊥交AD边于点E，连接BE．∠；（1）如图1，求证：BD平分EBC2=，求d与t之⊥于点F，EF交线段AB于点G，EF BDEF OB=，设OD t=，EG d间的函数关系式（不要求写出自变量t的取值范围）；∥，OM交线段AG点M，连接EM并(3)如图3，在（2）的条件下，过点O作OM CE∠=∠，求点N的坐标．延长交x轴于点N，若BOM ANM。

黑龙江省哈尔滨市工大附中2020-2021学年九年级上学期数学开学考试试卷一、单选题1.﹣5的倒数是（）A. ﹣5B. 5C. 15D. −152.下列计算，正确的是（）A. a2⋅a3=a6B. 2a2−a=aC. a6÷a2=a3D. (a2)3=a63.下列四个图案中，是轴对称图形的是（）A. B. C. D.4.如图是由6个相同的小正方体搭成的几何体，那么这个几何体的俯视图是（）A. B. C. D.5.如图，已知⊙O的直径AB与弦AC的夹角为35∘，过C点的切线PC与AB的延长线交于点P，则∠P等于（）A. 15∘B. 20∘C. 25∘D. 30∘6.一块面积为900平方米的矩形绿地，长比宽多10米，设绿地的长为x米，根据题意，可列方程为（）A. x(x−10)=900B. x(x+10)=900C. 10(x+10)=900D. 2[x+(x+10)]=9007.如图是某商场一楼与二楼之间的手扶电梯示意图．其中AB、CD分别表示一楼、二楼地面的水平线，∠ABC＝150°，BC的长是8m，则乘电梯从点B到点C上升的高度h是（）A. 83√3m B. 4 m C. 4 √3m D. 8 m8.⊙O是△ABC的外接圆，则点O是△ABC的（）A. 三条边的垂直平分线的交点B. 三条角平分线的交点C. 三条中线的交点D. 三条高的交点9.如图，已知△ABC的三个顶点均在格点上，则cosA的值为（）A. √33B. √55C. 2√33D. 2√5510.如图，在△ABC中，点D在边AB上，DE⁄⁄BC，DF⁄⁄AC，联结BE，BE与DF相交于点G，则下列结论一定正确的是（）A. ADDB=DEBC B.AEAC=BFBC C.BDAD=BFDE D.DGGF=BFFC二、填空题11.地球与月球的平均距离大约384000km，用科学记数法表示这个距离为________km．12.若式子x+ √x−1在实数范围内有意义，则x的取值范围是________．13.计算√7−√28的结果是 .14.分解因式：3x2−27= ．15.如图，四边形ABCD内接于⊙O，连接OB,OD,∠BOD=136°．延长BC至点E，则∠DCE的度数为．16.不等式组{x2⩽−1−x+7>4的解集是________.17.某扇形的圆心角是45°，面积为18π，该扇形的半径是________．18.如图，AB是半⊙O的直径，点C,D均在半⊙O上，OD⊥AC于点E，若BC=3DE，则ACDE的值为．19.矩形ABCD中，连接BD,cos∠ADB=2√55，点E为AD中点，点F为BC上一点，连接EF，若CD=2,EF=√5，EF与BD交于点G，则BG的长为．20.如图，在正方形ABCD中，点E为BC边上一点，且CE=2BE，点F为对角线BD上一点，且BF=2DF，连接AE交BD于点G，过点F作FH⊥AE于点H，若HG=2cm，则正方形ABCD的边长为 cm．三、解答题21.先化简，再求代数式(1−3x+2)÷x2−1x+2的值，其中x=4sin45°﹣2cos60°．22.如图，在每个小正方形的边长均为1的方格纸中，有线段AB，点A、B均在小正方形的顶点上．（1）.在方格纸中画出以AB为一边的直角三角形ABC，点C在小正方形的顶点上，且三角形ABC的面积为15 2；（2）.在方格纸中画出以AB为一边的菱形ABDE，点D、E均在小正方形的顶点上，且菱形ABDE的面积为3；（3）.连接CE，请直接写出线段CE的长．23.为评估九年级学生的学习状况，某中学抽取了部分参加考试的学生的成绩作为样本分析，绘制成了如下两幅不完整的统计图，请根据图中提供的信息解答下列问题：（1）.求该中学抽取了多少名学生的成绩进行调查；（2）.求样本中成绩类别为“中”的人数，并将条形统计图补充完整；（3）.该校九年级共有1000人参加了这次考试，请估算该校九年级共有多少名学生的成绩达到优秀？24.已知：BD是△ABC的角平分线，点E，F分别在BC，AB上，且DE∥AB，BE=AF.（1）.如图1，求证：四边形ADEF是平行四边形；（2）.如图2，若AB=AC，∠A=36°，不添加辅助线，请你直接写出与DE相等的所有线段（AF除外）. 25.禹驰商店决定购进A、B两种纪念品．若购进A种纪念品8件，B种纪念品3件，需950元；若购进A 种纪念品5件，B种纪念品6件，需800元。

工大附中：七年语文试卷一、积累与运用（共 50分）（一）六年级下知识回顾（35分）1.（2分）下列词语中加点字注音完全正确的一项是（ D ）A.分．外（fèn）徘徊．(huí) 无独有偶．(ǒu)B.间．断(jiàn) 剥削．(xiāo) 焉．知非福(yān)C.空虚．(xǖ) 依偎．(wēi) 重见．天日(jiàn)D.处．境(chǔ) 占据．(jù) 万象更．新(gēng)2、（2分）下列词语中的加下横线字注音全对的一项是（ C ）A.峡谷(xiá) 搜索(sōu) 笼罩(lǒng) 透露(lòu)B.挪移(nuó) 徘徊(pái) 觉察(chá) 蒸融(lóng)C.吞噬(shì) 初旬(xún) 演绎(yì) 恐吓（hè）D.栅栏(zhà) 敦厚(tún) 抛弃(pāo) 深重(zhòng)3.（2分）下列词语中没有错别字的一项是（C）A.通宵沸滕翻箱倒柜B.拨弄惊惶万不得以C.资格严峻司空见惯D.书籍奈何见微知箸4.（2分）选出下列字形完全正确的一项（ C ）A.伴奏梗概畏惧山涯B.碰到帐蓬木筏陆续C.凄凉潮水安慰水源D.防御简陋竟然寂莫5.（2分）对病句修改不正确的一项是（ D ）A.通过抗击新冠疫情，更多人加大了爱国意识。

将“加大”改为“增强”。

B.是否具有创新精神，是民族兴旺的关键。

删去“是否”。

C.这篇阅读理解，我琢磨了整整一小时左右。

删去“左右”。

D.线上教学时，同学们通过小组合作讨论、解决、发现了学习中的一些问题。

将“发现”和“讨论”调换位置。

6.（2分）下列名著中表述正确的一项是（ B ）A.孙悟空大战流沙河，木叉奉法收悟净。

（《西游记》）B.《鲁滨逊漂流记》是英国作家丹尼尔·笛福的一部长篇历险小说作品,主要讲述了主人公鲁滨逊因出海遭遇灾难,并坚持在岛上生活了28年的故事。

黑龙江省哈尔滨市南岗区工业大学附属中学2023-2024学年九年级上学期开学考试数学（五四制）试题学校:___________姓名：___________班级：___________考号：___________一、单选题．．．．A ．EA EGBE EF=C ．AB BCAE CF=10．如图，ABC 与AEF △出下列结论：①C E ∠=∠中正确的结论有（）个A ．4B ．314．如图，抛物线y =或“<”）15．在综合与实践课上，老师组织同学们以矩形纸片ABCD 如图所示，点点记为点M ，若点M 恰好落在边是．16．在Rt ABC △中，90C ∠=17．如图，在ABC 中，ACB ∠为．5三、解答题21．先化简，再求代数式22．如图，方格纸中每个小正方形的边长均为点上．()1在图中画一个以AB为腰的等腰三角形'=；(1)如图1，求证：A F DF=，连接EC，请直接写出图中的正弦值为(2)如图2，若AB BC25．某果园有果树60棵，现准备多种一些果树提高果园产量，如果多种树，那么树之间的距离和每棵果树所受光照就会减少，每棵果树的平均产量随之降低，根据经验，增种10棵果树时，果园内的每棵果树平均产量为40kg的前提下，设增种果树x（0x>且x为整数）=+满足如图所示的图象．它们之间的函数关系y kx b(1)求y与x之间的函数关系式，并直接写出自变量(2)当增种果树多少棵时，果园的总产量w（kg(1)如图1，求证：2BP DE=；(2)如图2，连接AE并延长交BC于F，FC27．如图，在平面直角坐标系中，点O为坐标原点，抛物线点A、点B，与y轴交于点C，直线12 y x =(1)如图1，求拋物线的解析式；(2)如图2，点P在直线AC上方的抛物线上，横坐标为t，PQ的长为d，求d与t的函数关系式；(3)如图3，在（2）的条件下，点D在第一象限，。

2023-2024学年黑龙江省哈工大附中九年级（下）开学数学试卷（五四学制）一、选择题：本题共10小题，每小题3分，共30分。

在每小题给出的选项中，只有一项是符合题目要求的。

1.的绝对值是()A. B. C.7 D.2.下列运算一定正确的是()A. B. C. D.3.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.4.八个大小相同的正方体搭成的几何体如图所示，其主视图是()A.B.C.D.5.如图，AB是的直径，BC是的切线，点B为切点，若，，则BC的长为()A.8B.7C.10D.66.方程的解为()A. B. C. D.7.已知，，则在如图所示的平面直角坐标系中，小手盖住的点的坐标可能是()A.B.C.D.8.一个不透明的袋子中装有12个小球，其中8个红球、4个黄球，这些小球除颜色外无其它差别，从袋子中随机摸出一个小球，则摸出的小球是红球的概率是()A. B. C. D.9.如图，在中，，，，，则AE的长为()A.3B.4C.5D.610.周日，小辉从家步行到图书馆读书，读了一段时间后，小辉立刻按原路回家.在整个过程中，小辉离家的距离单位：与他所用的时间单位：之间的关系如图所示，则小辉从家去图书馆的速度和从图书馆回家的速度分别为()A.，B.，C.，D.，二、填空题：本题共10小题，每小题3分，共30分。

11.风能是一种清洁能源，我国风能储量很大，仅陆地上风能储量就有253000兆瓦，用科学记数法表示为______兆瓦．12.在函数中，自变量x的取值范围是______.13.9的算术平方根是______.14.把多项式分解因式的结果是______.15.不等式组的解集是______.16.二次函数的最大值是______.17.若双曲线的图象的一支位于第四象限，则k的取值范围是______.18.一个扇形的面积为，半径为6cm，则此扇形的圆心角是______度．19.在中，，，点D在AB边上，连接CD，若为直角三角形，则的度数为________度．20.如图，矩形ABCD的对角线BD的垂直平分线交AD于点E，交BC于点F，连接CE，的面积为，，则CD的长为______.三、解答题：本题共7小题，共60分。

哈工大附中入学条件哈工大附中是哈尔滨市的一所重点中学，其入学条件是非常严格和高要求的。

以下是哈工大附中入学条件的详细说明：1.年龄要求：学生应符合哈工大附中规定的年龄要求，一般为初中毕业后的14-15岁之间。

具体年龄要求可能会因学校政策而有所不同，请在报名前仔细查阅最新的入学要求。

2.入学考试：哈工大附中招生采取统一的入学考试。

考试内容包括语文、数学、英语等学科，主要测试学生的基础知识和学习能力。

通过考试的学生才有机会被录取。

3.成绩要求：考试成绩是决定录取的重要因素之一。

哈工大附中对学生的成绩要求非常高，一般要求学生在各科考试中取得优秀或良好的成绩。

具体的分数线可能会因年份和报考人数而有所浮动。

4.综合素质评价：除了考试成绩，哈工大附中还会综合考虑学生的综合素质评价。

这包括学生的学习态度、品德表现、社会实践经历等方面。

学生应在报名时提供详细的个人信息和相关证明材料。

5.面试环节：在综合素质评价的基础上，哈工大附中还会安排面试环节。

面试主要考察学生的口头表达能力、思维逻辑能力和综合素质等。

面试通常由学校的教师和管理人员组成的面试小组进行。

6.入学名额：哈工大附中每年的招生名额有限，竞争非常激烈。

根据学校规定，只有成绩优异、综合素质好的学生才有机会被录取。

因此，想要进入哈工大附中，学生需要在各方面都具备优秀的素质和能力。

总之，哈工大附中是一所对学生要求较高的中学。

只有在年龄要求、入学考试、成绩要求、综合素质评价和面试环节等方面都表现出色的学生，才有机会被录取进入这所优秀的学府。

希望所有报考哈工大附中的学生都能充分了解入学条件，并做好充分的准备，以期取得优异的成绩和综合素质评价，实现自己的入学愿望。

人教版小学数学哈工大附中入学数学真卷一、选择题（每小题3分，共12分）1．把3米的绳子对折两次，每一段的长度是（ ）米。

A.43 B.32 C.34 D.382．一个圆柱和一个圆锥的底面直径的比值是2:3，体积的比值是3:2，则圆柱与圆锥高的比值是（ ）。

A.1:1B.9:8C.8:9D.4:93．请你认真观察和分析图中数字变化的规律，由此得到图中所缺的数字应为（ ）。

A.1:1B.9:8C.8:9D.4:94．如图，四边形ABCD 、CEFG 均为正方形，已知正方形ABCD 的边长是5厘米，连接BD 、DF 、BF ，则△BDF 的面积是（ ）平方厘米。

A.llB.13.5C.12D.12.5二、填空题（每小题3分，共24分） 5．如果29＜1□＜23，那么在□中可填的自然数有 个。

6．甲数的35等于乙数的23，乙数与甲数的比值是 。

7．一个圆柱体的侧面积是9422cm ，体积是23552cm ，它的底面半径是 。

8．定义a*b ＝a ×b ＋a b ，则（3*2）*1的值是 。

9．一个教室长8米，宽6米，高3.5米，现需粉刷墙壁和天花板，门窗和黑板面积是22平方米，平均每平方米用乳胶漆0.25千克，那么粉刷面积 平方米，需乳胶漆 千克。

10．某玩具商店在一次买卖中卖出甲、乙两件玩具，每件都以240元的价格售出，但甲盈利20%，乙却亏本20%，则在这次买卖中，商店 （填“盈利”或“亏本”）了 元。

11．有一块铜重400克，有一块铁重600 克，现在从铜和铁上各挖一块重量相等的金属互换形成两块合金，结果这两块合金的铜铁重量比都相等，那么挖下的那块相等的重量是 克。

12．有甲、乙、丙三人同时同地出发，绕一个花园行走，乙、丙二人同方向行走，甲与乙、丙相背而行，甲每分钟走40米，乙每分钟走38米，丙每分钟走36米，出发后，甲和乙相遇后3分钟和丙相遇，则这个花园的周长是 米。

三、解答题（共7小题，共64分） 13.（15分）计算题（1）计算：121203(833-÷⨯1-0.625)(1.6+2)； （2）简便计算：183322+(4 1.68)2625555⨯+⨯+；（3）解方程：2123355x x +=-14.（7分）如图，正方形ABCD 的边长是4厘米，长方形DEFG 的长DG 是5厘米，两个图形如图放置，长方形的宽DE 是多少厘米？15.（7分）如图，两个圆的半径都是1厘米，圆心分别是1O 和2O ，并且图中两个阴影部分的面积相等，求图中长方形AB 1O 2O 的面积。

哈工大附中2021级九年级英语学科开学检测一、单项选择（每小题1分, 共30分）1. —If you don't take more exercise or eat less, you will___________ weight. It harms your health.—I agree.A. put upB. put offC. put on2. Nowadays, it's common to see people___________ daily things like soaps, cookers or clothes along the streets in the early morning for sale.A. find outB. lay outC. ran out3. Wang Chuqin and Sun Yingsha are so popular that all the Chinese people___________ them___________ winning the mixed doubles championship at the Pairs Olympics.A. admired, withB. look up, toC. admire, for4. —Do you know the man talking with your mother?—It's Mr. Zhang. He is one of our___________, my mother's cousin.A. relativesB. strangersC. patients5. He used to___________ a sweet tooth, but now he has been used to___________ all the desserts.A. have, dropB. having, give upC. have, giving up6. —___________ fun the Water Festival is!—___________much I wish I were a Thai!A. What, HowB. How, WhatC. What a, How7. —How do you learn a foreign language?—By___________ sentence patterns.A. memorizeB. memorizedC. memorizing8. To get the main idea of the passage quickly, it's not good for us to read___________.A. day by dayB. step by stepC. word by word9. —I always make mistakes when writing a composition.—Well, I think the writing method you are used to___________.A. need to be improvedB. needing to improveC. needs improving10. —Boy students are always naughty. But our teacher is patient___________ them.—You are___________ lucky because you have a good teacher.A. to, soB. with, soC. with, such11. A good student connects what he reads___________ what he sees around him.A. withB. forC. in12. Everyone should___________ their handwriting because it it very important.A. look forward toB. pay attention toC. lead to13. We talked about the problem and Tim___________ doing some research first.A. finishedB. practisedC. suggested14. On their way home, Lucy and her mother___________ by a big supermarket.A. pastB. passedC. will past15. —Excuse me, could you tell me___________?—Certainly. Go straight ahead and you'll see it on your left.A. where the post office wasB. which is the way to the post officeC. where is the post office16. —We are all proud___________ our hometown, Harbin. It's so beautiful and amazing.—I really agree with you. Wherever we go, we'll take pride___________ it in our hearts.A. in, ofB. of, ofC. of, in17. American English and British English are not___________ the same. There are some differences.A. exactlyB. generallyC. luckily18. Those who___________ English with others after school will never speak English well, because practice makes perfect.A. dare not to speakB. don't dare to speakC. doesn't dare speak19. My father is taking care of my sick grandfather___________. He doesn't want anyone else to help him.A. in personB. in totalC. in public20. It___________ about five years since since we___________ last. You look as young as before.So I can recognize you easily.A. is, have metB. is, metC. has been, has met21. —How could you___________ so many problems in one day?—With the help of Joe.A. deal withB. catch up withC. came up with22. People are often___________ to give an___________ in a job interview.A. require, attentionB. request, introductionC. required, introduction23. —Are the visitors all from___________?—No, there are only 5___________ in the group.A. Germany; GermanyB. Germany; GermansC. German; Germans24. —You will feel___________ relaxed after___________ a hard task with long-time effort.—I agree with you much.A. completely, completingB. competing, comparingC. completely, competing25. He went over the lessons as carefully as he could___________ the exam.A. avoid failingB. to avoid failingC. to avoid to fail26. Tea is popular in China. Tea plants___________ on the sides of mountains. When the leaves are ready, they are picked by hand.A. grewB. are growingC. are grown27. Wuchang of Harbin ___________ much great rice every year. People all like to eat rice grown there.A. makesB. producesC. product28. We should do our___________ homework carefully. That's what my mother tells me___________.A. everyday, everydayB. everyday, every dayC. every day, everyday29. I can't play basketball after school unless my homework___________.A. is finishedB. will be finishedC. finished30. If we don't protect the environment, we will be___________ by nature sooner or later.A. treatedB. punishedC. repeated二、完形填空（每小题1分, 共10分）Parents are taking care of you in daily life. They are your 31 people of all. Loving your parents is a part of life. Here are some ways to love them.Tell them you love them every morning. Without your parents, you might not become 32 . A gentle "good morning" and "I love you" will make them feel warm. Remember that they 33 you into this world. It's your turn to show love for them.Respect them and value these moments. It's OK to get angry when 34 bad happens. But these actions don't help you or your parents. Act 35 , listen to music, or talk to a friend After this, share your feelings with your parents. Use these moments to learn from them, 36 for the coming life on your own.Follow their requests. Sometimes you don't get 37 you want. It seems that you are going through hard times. Remember that your parents care for you on rainy or snowy days. Following their requests will help you get more respect 38 them.Spend time with them. Do things with your parents like watching TV, or going out for a walk. Listen to their old stories and learn from them. You will find they are your 39 in this way or another.Love is the key to a good 40 with your parents. It's a way to make you a better and happier person. Take action at once, my dear friends!根据短文内容选择最佳答案。

哈工大附中初四英语学科学情检测检测时间: 100分钟检测满分: 100分第I卷一、单项选择（本题共15分, 每小题1分）选择最佳答案。

1. Boys and girls, if you are careful enough, you are sure to make___________ amazing difference today.A. aB. anC. /2. —Look at the sign. It says "A house___________ sale"—I saw it. But it's too expensive for me to afford.A. forB. toC. in3. I came back from the supermarket with a bag of apples in the one hand and some vegetables in my___________ hand. Mum was very pleased with my help.A. otherB. the otherC. another4. —What___________ will you win after winning the competition in the program You Have Special Talents?—A set of English-Chinese dictionaries.A. prizeB. adviceC. attention5. —Today is my mother's___________ birthday.—I hope she can be happy and healthy.A. fourteenB. fortyC. fortieth6. —Which sport do you enjoy___________, running or playing soccer?—Neither. I like going hiking best.A. to keep healthyB. keeping healthyC. to keep healthily7. —There___________ a football match between Class 2 and Class 6 tomorrow.—That sounds great.A. will haveB. are going to beC. will be8. It's of great importance to manage your study well in the following four months. The better plans you make,the___________ your study will become.A. more easilyB. more easierC. easier9. Some resolutions___________ better planning, like making a weekly plan for schoolwork, but sometimes they may be too difficult for most students to keep.A. have to do withB. deal withC. is good with10. —___________I park my car here?—No, you mustn't. Don't you see the sign "NO PARKING"?A. WouldB. MayC. Must11. —Have you ever seen the film PEGASUS 2（飞驰人生2）?—Yes. I with my friend___________ it last Friday.A. will seeB. sawC. has seen12. —Could you please tell me___________?—In two weeks.A. when did he come backB. how long he come backC. how soon he will come back13. —Let's spend some time with our relatives and friends___________ we can get a better relation with them.—I couldn't agree with you more.A. in order toB. se thatC. even though14. Nowadays, some Chinese students___________ to do housework as part of their school tasks to learn life skills and prove they are growing up.A. will be askedB. are askedC. was asked15. —Do yo remember the beautiful teacher___________ you met on your first day?—Of course. She was kind to us, saying "Hello" with a smile in the hall.A. whenB. whoC. which二、完形填空（本题共25分, 每小题1分）（A）When I was 15 years old, something terrible happened 16 me. I fell down while walking and then my parents took me to a 17 . The doctors said I needed an operation（手术）on my head and I only had a 5% chance of living after that. Several doctors didn't want to perform（实施）the operation because it was too 18 .After my parents talked with me carefully, we made a decision to take a 19 . We found a doctor and he agreed to perform the operation. When I went into the operating room, no one knew if the operation would be successful. My parents, were very 20 outside.After the operation, I didn't remember anything for about two months. I 21 move. I didn't even open my eyes. More than once, the doctors advised my parents to give up on me. However, they didn't. Luckily, I finally22 .After being in hospital for nine months, I finally 23 home. Coming home was good for me. I could get up and try walking. After three weeks, I could walk around the house.Now I can 24 walk like a normal person. I 25 that I have to keep a positive（积极的）mind, because no one knows how something is going to be.根据短文内容选择最佳答案。