2018年复旦大学自主招生试题(部分) + 参考答案
2018年复旦大学自主招生试题（部分）解析
2018年复旦大学自主招生试题（部分）解析
题目的解答都是本人独立完成，如需转载，请说明转自《阿叶数学》，谢谢!
前端时间就发现有公众号转载我那篇中科大自主招生的解析，但是把我文章里面所有关于《阿叶数学》的痕迹都抹掉了，甚至于把文章中我的名字给抹掉了，给读者造成一种错觉，题目的编辑和解答都是“他”完成的，后面与微信公众号的作者联系，了解了一下情况，大家都是站在相互理解角度上解决了这个事情，鉴于前车之鉴，本来想给自己后面的文章加水印，但是考虑到会影响读者的阅读感受，水印最终还是没有加上去，所以真心的希望读者在转载的时候，请说明一下转自《阿叶数学》，毕竟题目的解答和编辑花费一些时间，谢谢！
题目中的图形来自于赵海洋老师
说明：第五题根据条件，应该是中线，不是角平分线。
复旦自主招生试题及答案
复旦自主招生试题及答案一、语文部分阅读理解：1. 阅读下面短文，回答问题。
（1）张謇（1854-1926）是中国现代教育家、政治家、社会活动家和思想家。
张謇曾于光绪十九年（1893年）中策划创办私立南洋公学，为中国留学生出国深造提供了机会，也为中国教育事业的发展做出了巨大贡献。
（2）南洋公学的创建者张謇，生于一般家庭，自小勤奋好学。
他上学时就常常帮助同学，与人为善，仗义疏财。
他在学习中总是能将分散的学习知识联系起来，形成系统地知识体系，且能应用灵活。
在上学期间，他还考取了举人资格。
（3）1875年，张謇考入了南洋公学，他将自己多年的积累展示了出来，并在广大师生的面前，发表了知名的《自力更生》演讲。
这个演讲使他备受赞誉，也为他未来的事业奠定了基础。
（4）张謇毕业后曾出任江西体育局局长，任内积极推行体育运动，提倡健身，改变了当时青年学生体育锻炼不足的状况。
后来，他还出任过官员、教育家等多个职位，努力改革中国教育制度，致力于提高教育的普及率和质量。
（5）张謇还通过创办南京高级工业学堂（复旦大学前身），来培养工科人才。
这一举措对中国的现代工业化进程起到了积极作用。
张謇还参与了辛亥革命，成为众多反清护国的活动家之一。
问题：（1）张謇是中国的哪位教育家和思想家？（2）张謇曾任职的机构有哪些？（3）南京高级工业学堂现在的名称是什么？答案：（1）张謇是中国现代教育家、政治家、社会活动家和思想家。
（2）张謇曾任江西体育局局长，官员和教育家等多个职位。
（3）南京高级工业学堂现在的名称是复旦大学。
二、数学部分选择题：1. 已知函数 f(x) = 2x + 3，求 f(4) 的值。
A. 7B. 9C. 11D. 132. 若 a + b = 20，且 a:b = 2:3，则 a 的值为多少？A. 8B. 10C. 12D. 16填空题：1. C = πd 的公式中，若 d = 10cm，则 C = ______ cm。
(复旦大学)自主招生与三位一体面试真题及答案分析
复旦大学自主招生与三位一体面试真题及答案分析1.你对当前房价上涨有何看法？【参考答案】现在的房子不是用来住的，是用来炒的。
真正想住房子的人住不上房子，房子只是那些商家用来赚钱的工具。
中国楼市这样下去总有一天崩盘。
投机倒把，没有任何理性，房价显示出人性最丑陋的一面，正确认识这些问题，对症下药、加大力度，遏制房价上涨势头，这既是广大群众的强烈呼声，也是关乎国民经济又好又快发展的重大问题。
还有人认为改革开放以来居民收入增加是房价上涨的首要原因，其次宽松的信贷政策是房价上涨的重要支撑，所以房价上涨也是理所当然的。
当然，每个人的年龄和他所处的环境不同，对房价上涨都会有不同的看法。
【专家点评】考查学生对时事现象的关注和思考情况，言之有理自圆其说即可。
2.金融危机对农村有何影响？【参考答案】金融危机不断向各国各个领域蔓延。
目前已经对农村和农民也有了非常直接的影响。
首先是由于出口需求的缩减，导致相关企业经营不景气，首当其冲的就是农民工失去就业机会，造成农民工返乡潮，既影响农民收入，也影响农村稳定，造成一些混乱局面；其次是以农副产品为原材料的加工业也很不景气，从而导致对农副产品需求的减少和价格回落，直接影响农民收入；第三，由于整体上预期收入和购买力增长的不协调，导致农产品价格合理上涨的势头受到抑制，甚至可能出现一定程度的价格回落；第四，由于各级财政收入可能因金融危机的影响而增幅减缓，而用于涉农的财政支出必将受到较大的影响，而直接影响农村基础设施和公共品的供给。
这些问题应当引起相关部门的重视。
换言之，应对金融危机，农村经济和农民生活是不可忽视的一个重要领域，国家要大力重视这个问题。
【专家点评】考查学生对于社会热点问题的理解。
3.如何对待文理分科？【参考答案】现在的社会是一个讲求专业人才、讲究分工协作的社会，人们主要从各自的专长和兴趣出发进行工作。
经过初中以及高一的文理科学习，相信大部分学生已经能够发现自己的能力和兴趣所在，此时进行文理分科有利于各类专才的早日培养，因为到了高中阶段学生的学习特长、兴趣倾向已经呈现，要根据自身的特长和今后的发展方向，自主选择侧重文科还是理科，有利于他们集中精力，为今后的发展奠定基础。
最新复旦大学历年自主招生---语文真题及答案
复旦大学自主招生---语文真题071．[唐]韩愈《进学解》：“业精于勤，荒于嬉；行成于思，毁于随。
”这一句子中“于”的意思是____________。
A．在 B.从 C.由 D.对于2．［当］王充《论衡·量知篇》：“人之学问，知能成就，犹骨象玉石，切磋琢磨。
”其中“磋”字的准确含义是____________。
A．搓弄 B.商量讨论 C.摘取 D.把象牙加工成器物3．《左传·宣公十五年》：“我无尔诈，尔无我虞。
”句中前一个“尔”的意思是。
A．如此 B.而已 C.你 D.那样4．“苦口老师归寂日，知恩弟子庆生辰。
”（［宋］惠洪《石门文字禅·云庵生辰》）其中“苦口”一词的含义是_____。
A.佛口B.说话太多口变苦C.口气沉重D.不辞烦劳、反复恳切地说5．当代小说家毕淑敏在《提醒幸福》中写道：“幸福有时会同我们开一个玩笑，乔装打扮而来。
机遇、友情、成功、团圆……它们都酷似幸福，但它们并不等同于幸福。
”与这里的“乔装打扮”一语的意思最远的一顶是_______。
A.涂脂沫粉B.改头换面C.庐山面目D.面目全非6．韩小蕙在《悠悠心会》中写道：“有的夫妻一个屋檐下厮守一辈子，有的同事一个办公室对坐几十年，就是没话，心灵始终隔膜着一片寸草不生的荒漠。
”与这里的“寸草不生”一语的意思最近的一项是______。
A. 赤地千里B.天府之国C.鱼米之乡D.山穷水尽7.2004情，通过中国国际救援队队员等多方救助后情况就得到了改善。
句中方框应填入的字是_________。
A.防B.措C.猝D.促8．［清］刘熙载《艺论》：“是其苦心孤诣，且不欲徇非常人意，况肯徇非常人之意乎？”句中“苦心孤诣”一语的结构属于____。
A.并列式B.偏正式C.补充式D.主谓式9．蒋子龙在《乔厂长上任记》中写道：“但是，他相信生活不是命运，也不是赶机会，而是需要智慧和斗争的无情逻辑！因此他要采取大会战孤注一掷。
”这里的“孤注一掷”在句中作________。
2018年复旦大学自主招生试题解析
2018年复旦大学自主招生试题1.设x ∈R ，求函数f x =16x +41-x +4⋅2x +14x +21-x的最小值.【答案】103.【考点】求函数最小值问题.【解析】f x =2x 4+22x 2+4⋅2x +12x 2+22x =2x 2+22x 2+12x 2+22x =2x 2+22x +12x 2+22x，令t =2x 2+22x =2x 2+12x +12x ≥3，则f x ≥103. 当x =0时，函数f x 的最小值为103. 2.设f x =4x +2x +1−8，求A =x ∈−6,6 |f x >0 的区间长度.【答案】5【考点】函数定义域的应用.【解析】f x =4x +2x +1-8=2x -2 2x +4 >0⇒x >1，所以A 的区间长度为5.3.求能放入一个半径为r 的球体的圆锥体积最小值.【答案】8πr 23【考点】立体几何问题.【解析】如图所示，设圆锥的底面半径为R ，圆锥的顶点A 到球体的球心距离为m ，所以△ABO 1∼△AOD , 所以OD AD =BO 1AO 1，即R m +r =r m 2-r 2⇒R 2=r 2m +r m -r ，则V ABC =πr 23 m +r 2m -r =πr 23 m -r +4r 2m -r +4r≥8πr 23 . 4.极坐标系中，曲线C :ρ2-6ρcos θ-8ρsin θ+16=0上一点与曲线D :ρ2-2ρcos θ-4ρsin θ+4=0上一点的距离最大值是多少？【答案】4+22 .【考点】圆的参数方程的问题.【解析】C :x -3 2+y -4 2=9,D :x -1 2+y -2 2=1，则两个动点的距离最大值为圆心距加两个半径，即为4+22 .5.△ABC 中，D 为BC 上一点，AB =c ,AC =b ,AD =h ,BD =x ,CD =y ,则x 2+y 2+2h 2=b 2+c 2是AD 为中线的什么条件？【答案】必要不充分条件【考点】三角函数问题和余弦定理的应用.【解析】△ADB 中，由余弦定理cos ∠ADB =x 2+h 2-c 22xh, 在△ADC 中，由余弦定理cos ∠ADC =y 2+h 2-b 22yh,AB C DOO 1博观而约取 厚积而薄发由∠ADB +∠ADC =π，所以x 2+h 2-c 22xh +y 2+h 2-b 22yh=0，考虑到x 2+y 2+2h 2=b 2+c 2，所以x 2+h 2-c 2=b 2-y 2-h 2=0，此时x 不一定等于y ，此时AD 不一定为中线，而当x =y 时x 2+y 2+2h 2=b 2+c 2，所以x 2+y 2+2h 2=b 2+c 2是AD 为中线的必要不充分条件.6.求最小正整数k ，使得4725k 为完全平方数.【答案】21【考点】初等数论问题.【解析】4725k =152⋅21k , 又因为m 是正整数，所以k min =21.7.1900年，数学家_______在巴黎国际数学家大会上提出了23个未解决的问题.【答案】希尔伯特.【考点】数学史问题.【解析】希尔伯特.8.记正方体的六个面中心为A ,B ,C ,D ,E ,F , 先在这6个点中任取两点连线，再在这6个点中任取两点连线，则两条线段平行但不重合的概率是多少？【答案】475.【考点】立体几何问题.【解析】已知这个六面体是两个正四棱锥结合在一起，中间正方形的平行有两对，上下两个正四棱锥侧棱平行有四对，则所求概率为P =12C 26C 26=475 . 9.直线l 1:mx +y -1=0,l 2:x -my +2+m =0分别过定点A ,B ，若两直线交于点P ，求P A +PB 的取值范围.【答案】P A +PB ∈2,22 .【考点】直线和三角函数问题.【解析】直线l 1⊥l 2, 所以P A ⊥PB ，而A 0,1 ,B -2,1 满足P A 2+PB 2=4,令P A =2cos α,PB =2sin α,α∈0,π2 ,则P A +PB =22 sin α+π4 ，所以P A +PB ∈2,22 .10.在单位正方体ABCD -EFGH 中，M ,N 分别为棱CG ,AE 的中点，P 为平面BFGC 上一点，并满足EP 平行平面BMN ，求EP 长度的取值范围.【答案】30 5≤EP ≤2 .【考点】立体几何问题.【解析】取BF 中点，连接EK ，GK 与EG ，则平面EKG 平行于平面NBM ，所以点P 在线段KG 上运动，在△EKG 中，cos ∠EKG =54 +54 -22⋅54 =15 ,则EP min =EK sin ∠EKG =5 2 26 5 =30 5,所以305 ≤EP ≤2 . 11.已知在△ABC 中，A (3,2)，B (4,3)，C (6,7)，求△ABC 的面积.【答案】1【考点】解三角形问题.【解析】S △ABC =12 AB ×AC =12 (1,1)×(3,5) =1. 12.在△ABC 中，AD =2DB ,BE =2EC ，设直线CD 和AE 交于点P ，若AP =mAB +nAC , 求m ,n .【答案】m =27,n =47 .【考点】平面向量问题.【解析】过点D 作DF 平行于BC 交AE 于点F ，所以△ADF ∼△ABE ，则DF BE =AD AB =23 , 所以DF =23 BE =43 EC , △DFP ∼△CEP ，所以DF CE =FP PE =43 ，而AF FE =21 ，则AP =67 AE , 所以AP =27 AB +47 AC ，m =27,n =47 . 13. 令f x =sin nx sin x n ∈ℕ* ，下列结论正确的是_______.(1)f x 是周期函数；(2)f x 有对称轴；(3)f x 关于π2,0 对称；(4)f x ≤n 【答案】（1）（2）（4）【考点】三角函性质的应用.【解析】显然（1）对; f x 是偶函数，（2）对；（3）由f x +π +f -x =0,n 偶数≠0，n 奇数 ，（3）错；（4）由数学归纳法可以证明sin nx ≤n sin x ，所以（4）正确. 答案（1）（2）（4）.14.若函数f x 满足f 1x +1x f -x =2x x ≠1 ，求f 2 .【答案】f 2 =92.【考点】赋值法的应用.【解析】赋值法. 令x =12 ,f 2 +2f -12=1, 令x =-2,f -12 -12f 2 =-4,解得f 2 =92. 15.已知A 0,1 ,B 1,-1 ，直线ax +by =1与线段AB 有公共点，求a 2+b 2的最小值.【答案】12.【考点】直线与距离的应用.【解析】将直线ax +by =1看成关于变量a ,b 的直线，则a 2+b 2表示直线上一点到原点距离的平方，则a 2+b 2≥1x 2+y 2 ，又0≤x ≤1,-1≤y ≤1，则a 2+b 2≥112+12 =12 .博观而约取 厚积而薄发16.设方程log 3x 3+log 273x =-43 的两个根为a 和b ，求a +b 的值.【答案】1081.【考点】对数方程问题和换元法的应用.【解析】记log 33x =t ，则1t +t 3 =-43⇒t =-1,-3，所以a =19 ,b =181 ,则a +b =1081. 17.已知方程x 4+ax 3+bx 2-3x -2=0有两个实根x 1=2,x 2=-1，则其余两根为______.A.相同的实根B.不同的实根C.共轭复根D.以上都不对【答案】C【考点】方程复数根的问题.【解析】x 1=2,x 2=-1⇒b +2a =-2b -a =-2 ⇒a =0,b =-2.则x 4+0⋅x 3-2x 2-3x -2=x +1 x -2 x 2+x +1 ，所以另外两个复根为x =-1±3 i 2，答案C .18.定义x ⊕y =log x y +2，解方程x ⊕4 ⊕4=0.【答案】x =2-43.【考点】对数方程的问题.【解析】记log x 4+2=t ，则方程即log t 4+4=0⇒t =12 ⇒x =2-43 . 19.已知a >0，设f x =4x -1-2x +a -1, 若x 1x 2=a 2，且x 2>x 1>0，试比较f x 2 和f x 1 的大小.【答案】f x 2 >f x 1 .【考点】指数函数问题.【解析】记t =2x -1，则f x =g t =t 2-2a t ,t 1=2x 1-1,t 2=2x 2-1, 因为x 1x 2=a 2，且x 2>x 1>0，所以x 2>a >x 1⇒2x 2-1>2a -1>2x 1-1，另一方面，2x 2-1+2x 1-1>22x 1+x 2-1-1 >222x 1x 2 -1-1 =2a ,所以f x 2 >f x 1 .20.已知x 4-ax 3-bx 2+12x +36=0有二重根，求a 2+b +1 2的值.【答案】1440【考点】方程根的问题.【解析】x 4-ax 3-bx 2+12x +36=x 2x 2-ax -b +1 +x 2+12x +36=0,方程有二重根，所以-a =12,-b +1 =-36⇒a =12,b =35⇒ a 2+b +1 2=1440.21.在1，2，3 ，⋯,10中等概率的取出两个数a ,b ，使得x +1 2+3y 2+1=a b +1 x 2+4b a +2 y +3 2 是抛物线的概率为_______.【答案】P =9+2C 210=1145 .【考点】解析几何和概率问题.【解析】①当a b +1=1时，此时有9个；②当4b a +2 =3时a ,b =2,3 ,6,6 ,10,9 但是a ,b =10,9 与①中重复出现，所以此时只有2个，则所求概率P =9+2C 210=1145 . 22.已知正数a ,b ，则log a b =log b a 是a =b 的_______条件.【答案】既不必要也不充分条件【考点】逻辑关系问题.【解析】既不必要也不充分条件. 考虑到log 22-1=log 2-12=-1和a =b =1情形.23.设A ,B ,C ,P 是平面上不同的点，则P A +PB +PC =0 是P 为△ABC 的重心的______条件.【答案】充要条件【考点】逻辑关系问题.【解析】充要条件，平面奔驰定理直接推论.。
2018复旦附中自招英语卷(3).pdf
上海复旦附中自主招生英语试题(3)1.A.increasinglyB.loweringmonD.solutionsE.individuallyF. callingG.dependent H.shortcomings I.consumption J.introduced K.sensesA United Nations panel on climate change says global warming is causing extreme weather all over the world and is__41__on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants,scientists in Denmark are trying to lower their nation’s energy needs with new types of smart streetlights.Our__42__industrialized world needs huge amounts of electrical energy,but our power plants still rely mostly on technology__43__as early as the19th century—coal—powered plants, hydroelectric dams or somewhat never nuclear energy,all of which have their own__44__.But scientists say we can slow down global warming by__45__energy demands for street lights.These__46__features of the world’s urban areas require a lot of electricity.The U.S.Energy Information Administration estimates that in2012,lighting for buildings, streets and highways in the ed about274billion kilowatt hours.In a bid to make Copenhagen the world’s first carbon-neutral city by2025,scientists in the Danish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We have installed nine kilometers of streets,we have280masts placed here,we have50 different__47__,we have10different management systems,and we have a lot of different sensors and things out in the open area,”said Brostrom.Chief science officer Jakob Andersen says the lights can be managed__48__from a tablet computer or a smart phone.The main goal is to lower energy__49__when the light is not needed.So the lamp brightens up only when it__50__an approaching pedestrian,cyclist or vehicle.Some of them even have a backup wind generator or a solar cell.2.Diet Coke,diet Pepsi,diet pills,on-fat diet,vegetable diet…We are__51__by the word “diet”everywhere we look and listen.We have so easily been attracted by the promise and__52__ of diet products that we have stopped thinking about what diet products are doing to us.We are paying for products that__53__us psychologically and physically(身体上).Diet products significantly weaken us psychologically.On one level,we are not allowing our brain to__54__that our weight problems lie not in actually losing the weight,but in controlling the__55__of fatty,high-calorie,unhealthy foods.Diet products allow us to jump over the thinking stage and go straight for the scale(秤)instead.All we have to do is to swallow or__56__ the word“diet”in food labels.On another level,diet products have greater psychological effects.Every time we have azero-calorie drink,we are telling ourselves without our__57__that we don’t have to work to get results.Diet products make people believe that gain comes without pain,and that life can be without resistance a(n)__58__.The danger of diet products lies not only in the psychological effects they have on us,but also in the physical harm that they cause.Diet foods can__59__harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having__60__ nutrients(营养成分).Diet foods and diet pills__61__zero calorie only because the diet industry has created chemicals to produce these wonder products.Diet products may not be__62__,and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us,it is time to__63__think about buying them.Losing weight lies in the power of minds,not in the power of chemicals. __64__we realize this,we will be much better able to resist diet products,and__65__prevent the psychological harm that comes from using them.51. A.confused B.surrounded C.mixed D.fascinated52. A.potential B.affection C.obligation D.calculation53. A.weaken B.harm C.enforce D.inspire54. A.admire B.argue C.deny D.admit55. A.assumption B.digestion C.dissolution D.consumption56. A.recognize B.foresee C.overlook D.research57. A.frustration B.ignorance C.awareness D.emphasis58. A.maintenance B.efficiency C.struggle D.setback59. A.indirectly B.inevitably C.incredibly D.innocently60. A.extra B.basic anic D.delicate61. A.contain B.persist C.exclude D.melt62. A.nutritional B.poisonous C.ridiculous D.sensitive63. A.strongly B.enthusiastically C.eagerly D.seriously64. A.Unless B.While C.Though D.Once65. A.therefore B.otherwise C.meanwhile D.furthermore 3.It was a bitter cold evening in northern Virginia many years ago.The old man’s beard was glazed by winter’s frost while he waited for a ride across the river.The wait seemed endless.His body became numb and stiff from the frigid north wind.It was long before he heard the faint,steady rhythm of hooves(马蹄)along the frozen path. Anxiously watching several horsemen coming up,he let the first one pass by without any effort to get his attention,then another passed by,and another.Finally,the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said,“Sir,would you mind giving an old man a ride to the other side?”Stopping his horse,the rider replied,“Sure!Jump aboard.”Seeing the old man unable to lift his half-frozen body from the ground,the horseman got down to help him.The horseman took him not just across the river,but to his destination just a few miles away.As they approached the tiny but cozy cottage,the horseman’s curiosity caused him to inquire,“Sir,I noticed you let several other riders pass by without making an effort to secure a ride.Then I came up and you immediately asked me for a ride.I am curious why,on such a bitter night,you would wait and ask the last rider.What if I had refused and left you here?”The old man looked the rider straight in the eyes and replied,“I reckon I know people pretty good.I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride.But when I looked into your eyes,your gentle spirit would welcome the opportunity to give me assistance in my time of need.”Those heart-warming comments touched the horseman deeply.“I’m so grateful for what you have said,”he told the old man.“May I never get too busy in my own affairs that I fail to respond to the needs of others with kindness and compassion.”With that,Thomas Jefferson turned his horse around and made his way back to the White House.66.Why didn’t the old man ask the previous riders for a ride?A.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?A.The old man’s poor situation.B.The old man’s warm comments.C.His own affairs.D.Kindness and sympathy.68.What do you know about the old man?A.He judged people by looking into their eyes.B.He lived in a cozy cottage a few miles away.C.He gave the last rider an opportunity to help.D.He recognized the president at first.69.Which can be the best title of this text?A.Look into your eyes.passion of a great man.C.The last rider to help.D.Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post?Here at the International Book Club,we already have many members buying books from us by mail. Immediate benefits：●As a special offer,you may choose any reduced price books from our new members’book list,to the value of$6in total(plus postage and packing).By doing this,you will save pounds on the publishers’prices.●Tick the box on your form to order a free watch.●If you reply within seven days,we will send you another free gift carefully chosen from ourbook list by our staff.●Order a DVD from the many on offer in our list,at half the recommended retail price.When you’ve joined：As a member,you’ll enjoy savings of between30%and50%off the publisher’s price onevery book you buy,and what’s more,they’ll come straight to your door.Your free club magazine arrives once a month,to keep you up to date with the latest bestsellers.This means that every year we offer over1,000books to choose from.On the Internet,you can find all our titles for the year on our exclusive members’website.Being a member：All we are asking you to do while you are a member is to choose four books during your first year.After that,you can decide on the number of books you wish to take.In each of our monthly club magazines,our experienced staff choose a Club Choice book—a work of fiction or a reference title which they feel is particularly worth buying,and which is offered at an extra special price.However,if you do not want this book,just say so in the space provided on the form.We will always send the book if we do not receive this.So,return your application form today,but hurry—it’s not every day we can make you an offer like this.To apply to become a member,all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.Before you know it,your books will be with you.Please don’t send any money now,as we will send you your bill with the books.And remember,you have up to a fortnight to decide if you wish to keep the books you have ordered.You should then either return the books or send your payment.70.Which of the following doesn’t belong to the benefits of being a club member?A.Get four books for free in the first year.B.Order a free watch.C.Get a gift for nothing.D.Order a DVD at a low price.71.Every month the club provides a free club magazine in order to_______.A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksC.make readers know the club’s developmentD.attract more and more readers to join the club72.If a book is worth$100,how much will a member probably save if he buys one?A.$20B.$40C.$60D.$7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with needed information and return it to the club.D.Apply for a membership card.5.In1789the ernment passed a law which said that the land of the American Indians could never be taken from them without their agreement.One hundred years later,however,the Indians only had a very small part of the land that originally belonged to them.How did this great injustice occur?After1812white settlers began to move west across North America.At first,the settlers and the Indians lived in peace.However,the number of settlers increased greatly every year,and slowly the Indians began to see the white settlers as a danger to their survival.To feed themselves,the settlers killed more and more wild animals.The Indians,who depended on these animals for food,had to struggle against starvation.The settlers also brought with them many diseases which were common in white society,but which were new for the Indians.Great numbers of Indians became sick and died.Between1843and1854the Indian population in one area of the country went down from100,000to30,000.More land was needed for the increasing number of white settlers.In Washington,the old respect for the rights of the Indians disappeared.The old promises to the Indians were broken;the government began to move groups of Indians from their original homelands to other poorer parts of the country.Some Indians reacted angrily and violently to this treatment.They began to attack white settlers,and the Indian war began.For30years,until the late1880s,different groups of Indians fought against the injustices of the white man.They had a few famous successes,but the result of the struggle was never in doubt.There were too many white soldiers,and they were too powerful.Many Indians were killed;the survivors were moved from their homelands to different area of the country.It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passage that______.A.in the U.S.there were many laws that provided the rights of American IndiansB.the law which was passed in1789by the ernment was not successfully carried outC.in the19th century no injustices were done against the Indians by the ernmentD.the majority of white settlers were openly opposed to the law passed in178975.According to the passage which of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the 19th century.C.Between1843and1854about70,000Indians were killed in the battle.D.The whites carried serious diseases into where the Indians lived.76.It is implied in the passage that______.A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’s opinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.B.He believed that the government can’t be criticized for its treatment to the Indians.C.He believed that the government treated the Indians unjustly.D.He believed that the government’s unfair treatment against the Indians was not on purpose.6.The question of whether our government should promote science and technology or the liberal arts in higher education isn’t an either/or proposition(命题),although the current emphasis on preparing young Americans for STEM(science,technology,engineering,maths)-related fields can make it seem that way.The latest congressional report acknowledges the critical importance of technical training,but also asserts that the study of the humanities(人文学科)and social sciences must remain central components of America’s educational system at all levels.Both are critical to producing citizens who can participate effectively in our democratic society,become innovative(创新的)leaders,and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’job prospects as technological advances and changes in domestic and global markets transform professions in ways that reduce wages and cut jobs.Under these circumstances,it’s natural to look for what may appear to be the most“practical”way out of the problem“Major in a subject designed to get you a job”seems the obvious answer to some,though this ignores the fact that many disciplines in the humanities characterized as“soft”often,in fact,lead to employment and success in the long run.Indeed,according to surveys,employers have expressed a preference for students who have received a broadly-based education that has taught them to write well,think critically,research creatively,and communicate easily.Moreover,students should be prepared not just for their first job,but for their4th and5th jobs, as there’s little reason to doubt that people entering the workforce today will be called upon to play many different roles over the course of their careers.The ones who will do the best in this new environment will be those whose educations have prepared them to be flexible.The ability to draw upon every available tool and insight—picked up from science,arts,and technology—to solve the problems of the future,and take advantage of the opportunities that present themselves, will be helpful to them and the United States.(Note:Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggests that________________________________.79.What is the main concern of students when they choose a major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶),a small piece of potato is cut into very thin pieces.These thin pieces are placed in a little glass container and covered with water.Then a little of the proper chemical is added.Immediately,because of the enzyme present in the potato,the chemical starts joining with the oxygen in the air above the water.If the container is entirely closed,a partial vacuum(真空)is framed inside.If the container is now connected with a fine tube which is dipped in water,the water is sucked part way up the tube because of the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time.The higher it is sucked,the more of that particular enzyme and evenabout the way in which it operates.And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?a.Whether enzyme is present in the potato.b.What particular enzyme there is in the potato.c.How much enzyme there is in the potato.d.How enzyme works in the potato.A.a and bB.c and dC.b and dD.a and c2.The proper title for the passage is______.A.How a Vacuum Is FormedB.How Enzyme Is StudiedC.How Enzyme Works in a PotatoD.How Much Enzyme There Is in the Potato3.Which of the following correctly shows how the experiment is done?A.Put very thin pieces or potato in a vacuum container.B.Connect the glass container with a tube through which oxygen is sent in.C.Add some chemical to the water before thin pieces of potato are put in.D.Place thin pieces of potato in a glass container,cover them with water and then close it.4.The result of the study shows that______.A.the higher water is sucked,the less of enzyme in the potato isB.the more water is put into,the more of enzyme in the potato isC.the higher water is sucked,the more of enzyme in the potato isD.the lower water is sucked,the more of enzyme in the potato is上海复旦附中自主招生英语试题(3)1.FAJHB CDEIK2.BABDD ACCAB AADDA3.CDAB4.ABBC5.BDDC6.78.The humanities and STEM subjects should be given equal importance.79.Their chances of getting a good job.80.Those who have received a well-rounded education.81.Preparing themselves to be flexible;achieving every available tool and insight.7.BBDC。
历年自主招生考试数学试题大全2018年上海复旦大学自主招生数学试题Word版
2018年复旦大学自主招生考试数学试题选择题（每题5分，共150分，答对得5分，答错扣2分，不答得0分） 1．三边均为整数，且最大边长为11的三角形，共有 个． A ．20B ．26C ．30D ．362．若a>1，b>1且lg （a+b ）=lga+lgb ，则lg （a −1）+lg （b −1）= ． A ．lg2B ．1C ．不是与a 、b 无关的常数D ．03．已知z ∈C ，若∣z ∣＝2－4i ，则z1的值是 ． A ．3＋4i B ．i 5453+ C ．i 154153+ D ．i 254253-4．已知函数f （x ）=cos （x k 2316++π）+cos （x k 2316--）=23sin （x 23+π），其中x 为实数且k 为整数．则f （x ）的最小正周期为 ．A ．3πB ．2π C ．πD ．2π5．已知A ＝｛（x ，y ）∣y ≥x 2｝，B={（x ，y ）∣x 2+（y −a ）2≤1}．则使A∩B＝B 成立的充分必要条件为 ．A ．a=45B ．a≥45 C ．0<a<1 D ．a≥16．已知平面上三角形ABC 为等边三角形且每边边长为a ，在AB 和BC 上分别取D ，E 两点使得AD ＝BE ＝3a，连接A ，E 两点以及C ，D 两点．则AE 和CD 之间的最小夹角为 ． A ．9πa B ．3πa C ．3π D ．以上均不对7．已知数列｛a n ｝满足3a n+1+a n =4，（n≥1），且a 1=9， 其前n 项之和为S n ，则满足不等式∣S n −n −6∣<1251的最小整数是45． A ．6B ．7C ．8D ．98．将一个四棱锥的每个顶点染上一种颜色，并使用一条棱的两端点异色，若只有五种颜色可供使用，则不同的染色方法的总数为 ．A ．120B ．260C ．340D ．4209．设甲乙两个袋子中装有若干个均匀白球和红球，且甲乙两个袋子中的球数比为1∶3．已知从甲袋中摸到红球的概率为31，而将甲乙两个袋子中的球装在一起后，从中摸到红球的概率为32．则从乙袋中摸到红球率为 ． A ．97 B ． 4519C ．3013D ．4522 10．方程f （x ）=543423322212321---------x x x x x x x x x =0 的实根的个数是 ．A ．1个B ． 2个C ．3个D ．无实根11．已知a ，b 为实数，满足（a+b ）59=−1，（a −b ）60=1，则∑=-601)(n n nb a＝ ．A ．0121B ．−49C ．0D ．2312．a=21是“直线（a+2）x +3a y +1=0与直线（a −2）x +（a+2）y −3=0相互垂直”的 ． A ．充分必要条件B ．充分而不必要条件C ．必要而不充分条件D ．既不充分也不必要条件13．设函数y =f （x ）对一切实数x 均满足f （2+x ）=f （2−x ），且方程f （x ）=0恰好有7个不同的实根，则这7个不同实根的和为 ．A ．0B ．10C ．12D ．1414．已知α，β，γ分别为某三角形中的三个内角且满足tan 2βα+=sinγ，则下列四个表达式:（1）tanαtanβ=1 （2）0<sinα+sinβ≤2 （3）sin 2α+sin 2β=1 （4）cos 2α+cos 2β=sin 2γ中，恒成立的是 ．A ．（1）（3）B ．（10（4）C ．（2）（3）D ．（2）（4）15．设S n =1+2+…+n，n ∈N ．则∞→n lim1)32(2++n nS n nS ＝ ．A ．2B ．321C ．161 D ．6416．复数z =iia 212+-（a ∈R ，i=1-）在复平面上对应的点不可能位于 ． A ．第一象限B ．第二象限C ．第三象限D ．第四象限17．已知f （x ）=asin x +b 3x ＋4（a ，b 为实数）且f [lg （lg 310）]=5，则f [lg （lg3）]= ．A ．−5B ．−3C ．3D ．随a ，b 取不同值而取不同值18．已知四棱锥P －ABCD ，底面ABCD 是菱形，∠DAB ＝3π，PD ⊥平面ABCD ，线段PD ＝AD ，点E 是AB 的中点，点F 是PD 的中点，则二面角P －AB －F 的平面角的余弦值＝ ．A ．21 B ．552 C ．1475D ．1473 19．在（32-）50的展开式中有 项为有理数．A ．10B ．11C ．12D ．1320．棱长为a 的正方体内有两球互相外切，且两球各与正方体的三个面相切．则两球半径之和为为 ．A ．无法确定B ．aC ．a 233-D ．a 255- 21．在集合{1，2，…11}中任选两个作为椭圆方程12222=+by a x 中的a 和b ，则能组成落在矩形区域{（x ，y ）||x |<11，|y |<9}内的椭圆个数是 ．A ．70B ．72C ．80D ．8822．设a ，b ，c 为非负实数，且满足方程02562684495495=+⨯-++++cb a cb a ，则a+b+c的最大值和最小值 ．A ．互为倒数B ．其和为13C ．其乘积为4D ．均不存在23．给定正整数n 和正常数a ，对于满足不等式a 12+a n+12≤a 的所有等差数列a 1，a 2，a 3，…，和式∑++=1211n n i a的最大值＝ ．A ．)1(210+n aB ．n a210 C ．)1(25+n aD ．n a 2524．设z 0（z 0≠0）为复平面上一定点，z 1为复平面上的动点，其轨迹方程为|z 1−z 0|=|z 1|，z 为复平面上另一个动点满足z 1z =−1．则z 在复平面上的轨迹形状是 ．A ．一条直线B ．以01z -为圆心，01z 为半径的圆 C ．焦距为012z 的双曲线 D ．以上均不对25．一个球与正四面体的六条棱都相切，若正四面体的棱长为a ，则这个球的体积为 ．A ．3123a π B ．343a π C ．3242a π D ．3243a π 26．已知函数f （x ）的定义域为（0，2），则函数g （x ）=f （x +c ）+f （x −c ） 在 0＜21时的定义域为 ．A ．（1−c ，2+c ）B ．（c ，2−c ）C ．（1−c ，2−c ）D ．（c ，2+c ） 27．设函数f （x ）=sin （2x +ϕ），（−π<ϕ<0），y =f （x ）图象的一条直线x =8π．则ϕ的值为 ．A ．4πB ．43πC ．－43πD ．2π28．设f （x ）是定义在实数集上的周期为2的周期函数，且是偶函数．已知当x ∈[2，3]时，f （x ）=−x ，则当x ∈[－2，0］时，f （x ）的表达式为 ．A ．−3+|x +1|B ．2−|x +1|C ．3−|x +1|D ．2+|x +1|29．当a 和b 取遍所有实数时，则函数f （a ，b ）=（a+5−3|cosb|）2+（a −2）|sinb|）2所能达到的最小值为 ．A ．1B ．2C ．3D ．430．对任意实数x ，y ，定义运算x ºy 为x ºy ＝a x +b y +c xy ，其中a ，b ，c 为常数，且等式右端中的运算为通常的实数加法、乘法运算．已知1º2＝3，2º3＝4且有一个非零实数d ，使得对于任意实数x 均有x ºd=x ，则d= ．A ．－4B ．－2C ．1D ．4历年自主招生考试数学试题大全专题下载链接：/a760682.html链接打开方法：1、按住ctrl键单击链接即可打开专题链接2、复制链接到网页。
复旦大学自主招生考试数学试题及答案
1、设函数y=f（x）=e x+1，则反函数OyxOyxO x答案：A2、设f（x）是区间[a，b]f（x）是[a，b]上的递增函数，那么，f（xA．存在满足x<y的x，y∈[a，b]B．不存在x，y∈[a，b]满足x<y且fC．对任意满足x<y的x，y∈[a，b]D．存在满足x<y的x，y∈[a，b]答案：A3、设]2,2[,ππβα-∈，且满足sinαA． [−2，2] B． [答案：D4、设实数0,≥yx，且满足2=+yxA．97/8 B．答案：C5则该多面体的体积为______________。
A．2/3 B．3/4答案：D6、在一个底面半径为1/2，高为1的圆柱内放入一个直径为1的实心球后，在圆柱内空余的地方放入和实心球、侧面以及两个底面之一都相切的小球，最多可以放入这样的小球个数是___________。
A ．32个；B ．30个；C ．28个；D ．26个答案：B7、给定平面向量（1，1），那么，平面向量（231-，231+）是将向量（1，1）经过________． A ．顺时针旋转60°所得； B ．顺时针旋转120°所得； C ．逆时针旋转60°所得；D ．逆时针旋转120°所得；答案：C8、在直角坐标系O xy 中已知点A 1（1，0），A 2（1/2，3/2），A 4（−1，0），A 5（−1/2，−3/2）和A6（1/2， −3/2）．问在向量−−→−ji A A （i ，j=1，2，3，4，5，6，i≠j）中，不同向量的个数有_____． A ．9个； B ．15个； C ．18个； D ．30个答案：C9、对函数f:[0，1]→[0，1]，定义f 1（x ）=f （x ），……，f n（x ） =f （f n −1（x ）），n=1，2，3，……．满足f n （x ）=x 的点x ∈[0，1]称为f 的一个n −周期点．现设⎪⎪⎩⎪⎪⎨⎧≤≤-≤≤=121,22,210,2)(x x x x x f 问f 的n −周期点的个数是___________．A ．2n 个；B ．2n 2个；C ．2n个；D ．2（2n−1）个．答案：C10、已知复数z 1=1+3i ，z 2=−3+3i ，则复数z 1z 2的幅角__________． A ．13π/12 B ．11π/12 C ．−π/4 D ．−7π/12答案：A11、设复数βαβαcos sin ,sin cos i w i z +=+=满足z w =3/2，则sin （β−α）=______． A ．±3/2B ．3/2，−1/2C ．±1/2D ．1/2，−3/2答案：D12、已知常数k 1，k 2满足0<k 1<k 2，k 1k 2=1．设C 1和C 2分别是以y =±k 1（x −1）+1和y =±k 2（x −1）+1为渐近线且通过原点的双曲线．则C 1和C 2的离心率之比e 1/e 等于_______．A ．222111k k ++ B ．212211k k ++ C ．1 D ．k 1/k 2答案：C13、参数方程0,)cos 1()sin (>⎩⎨⎧-=-=a t a y t t a x 所表示的函数y=f （x ）是____________．A ．图像关于原点对称；B ．图像关于直线x =π对称；C ．周期为2a π的周期函数D ．周期为2π的周期函数．答案：C14、将同时满足不等式x −k y −2≤0，2x +3y −6≥0，x +6y −10≤0 （k>0）的点（x ，y ）组成集合D 称为可行域，将函数（y +1）/x 称为目标函数，所谓规划问题就是求解可行域中的点（x ，y ）使目标函数达到在可行域上的最小值．如果这个规划问题有无穷多个解（x ，y ），则k 的取值为_____．A ．k≥1;B ．k≤2C ．k=2D ．k=1．答案：C15、某校有一个班级，设变量x 是该班同学的姓名，变量y 是该班同学的学号，变量z 是该班同学的身高，变量w 是该班同学某一门课程的考试成绩．则下列选项中正确的是________．A ．y 是x 的函数；B ．z 是y 的函数；C ．w 是z 的函数；D ．w 是x 的函数．答案：B16、对于原命题“单调函数不是周期函数”，下列陈述正确的是________． A ．逆命题为“周期函数不是单调函数”； B ．否命题为“单调函数是周期函数”； C ．逆否命题为“周期函数是单调函数”； D ．以上三者都不正确 答案：D17、设集合A={（x ，y ）|log a x +log a y >0}，B={（x ，y ）|y +x <a}．如果A∩B=∅，则a 的取值范围是_______ A ．∅ B ．a>0，a≠1 C ．0<a≤2， a≠1 D ．1<a≤2答案：D18、设计和X 是实数集R 的子集，如果点x 0∈R 满足：对任意a>0，都存在x ∈X 使得0<|x −x 0|<a ，则称x 0为集合X 的聚点．用Z 表示整数集，则在下列集合（1）{n/（n+1）|n ∈Z ， n≥0}， （2） R\{0}， （3）{1/n|n ∈Z ， n≠0}， （4）整数集Z 中，以0为聚点的集合有_____． A ．（2），（3）B ．（1），（4）C ．（1），（3）D ．（1），（2），（4）答案：A19、已知点A （−2，0），B （1，0），C （0，1），如果直线kx y =将三角形△ABC 分割为两个部分，则当k =______时，这两个部分得面积之积最大？A ．23-B ．43-C ．34-D ．32-答案：A20、已知x x x x f 2cos 3cos sin )(+=，定义域⎥⎦⎤⎢⎣⎡=ππ127,121)(f D ，则=-)(1x f_____A ．π12123arccos 21+⎪⎪⎭⎫ ⎝⎛-x B ．π6123arccos 21-⎪⎪⎭⎫ ⎝⎛-x C ．π12123arcsin 21+⎪⎪⎭⎫ ⎝⎛--x D ．π6123arcsin 21-⎪⎪⎭⎫ ⎝⎛-x 答案：A21、设1l ，2l 是两条异面直线，则直线l 和1l ，2l 都垂直的必要不充分条件是______ A ．l 是过点11l P ∈和点22l P ∈的直线，这里21P P 等于直线1l 和2l 间的距离 B ．l 上的每一点到1l 和2l 的距离都相等 C ．垂直于l 的平面平行于1l 和2lD ．存在与1l 和2l 都相交的直线与l 平行 答案：D22、设ABC −A’B’C’是正三棱柱，底面边长和高都为1，P 是侧面ABB’A’的中心，则P 到侧面ACC’A’的对角线的距离是_____A ．21B ．43C ．814D ．823答案：C23、在一个球面上画一组三个互不相交的圆，成为球面上的一个三圆组．如果可以在球面上通过移动和缩放将一个三圆组移动到另外一个三圆组，并且在移动过程中三个圆保持互不相交，则称这两个三圆组有相同的位置关系，否则就称有不同的位置关系．那么，球面上具有不同的位置关系的三圆组有______A ．2种B ．3种C ．4种D ．5种 答案：A24、设非零向量()()()321321321,,,,,,,,c c c c b b b b a a a a ===为共面向量，),,(31x x x x x = 是未知向量，则满足0,0,0=⋅=⋅=⋅x c x b x a的向量x 的个数为_____A ．1个B ．无穷多个C ．0个D ．不能确定 答案：B25、在Oxy 坐标平面上给定点)1,2(),3,2(),2,1(C B A ，矩阵⎪⎪⎭⎫⎝⎛-112k 将向量OC OB OA ,,分别变换成向量,,，如果它们的终点',','C B A 连线构成直角三角形，斜边为''C B ，则k 的取值为______A ．2±B ．2C ．0D ．0，−2 答案：B26、设集合A ，B ，C ，D 是全集X 的子集，A∩B≠∅，A∩C≠∅．则下列选项中正确的是______． A ．如果B D ⊂或C D ⊂，则D∩A≠∅； B ．如果A D ⊂，则C x D∩B≠∅，C x D∩C≠∅； C ．如果A D ⊃，则C x D∩B=∅，C x D∩C=∅； D ．上述各项都不正确．27、已知数列{}n a 满足21=a 且n a n ⎧⎫⎨⎬⎩⎭是公比为2的等比数列，则∑==nk k a 1______A ．221-+n nB ．22)1(1+-+n n C ．)1(22-+n n n D ．n n n 22)1(+-28、复平面上圆周2211=+--iz z 的圆心是_______ A ．3+i B ．3−iC ．1+iD ．1−i29．已知C 是以O 为圆心、r 为半径的圆周，两点P 、P *在以O 为起点的射线上，且满足|OP|∙|OP *|=r 2，则称P 、P *关于圆周C 对称．那么，双曲线22x y -=1上的点P （x ，y ）关于单位圆周C':x 2＋y 2=1的对称点P *所满足的方程是（A ）2244x y x y -=+（B ）()22222x y x y-=+（C ）()22442x y x y-=+（D ）()222222x y x y-=+30、经过坐标变换⎩⎨⎧+-=+=θθθθcos sin 'sin cos 'y x y y x x 将二次曲线06532322=-+-y xy x 转化为形如1''2222=±b y a x 的标准方程，求θ的取值并判断二次曲线的类型_______ A ．)(6Z k k ∈+=ππθ，为椭圆 B ．)(62Z k k ∈+=ππθ，为椭圆C ．)(6Z k k ∈-=ππθ，为双曲线D ．)(62Z k k ∈-=ππθ，为双曲线31、设k ， m ， n 是整数，不定方程mx+ny=k 有整数解的必要条件是____________ A ．m ，n 都整除kB ．m ，n 的最大公因子整除kC ．m ，n ，k 两两互素D ．m ，n ，k 除1外没有其它共因子。
2018年上海市复旦附中自主招生物理真题及答案解析
正因为万有引力的存在，十九世纪四十年代 奥本 勒维耶 通过经典力学分析天王星轨
道的摄影后预测勒海王星的位置。十九世纪末天文学家根据对海王星的观察推测有其他行星 摄动天王星轨道。
我们相信，通过以上内容的阅读，你已经对匀速圆周运动有了一个初步的了解，接下来， 请回答以下问题：
二、问题：
1、判断以下说法是否正确：正确打“√”，错误打“ ” 1 360 2 ， 45 /4 ( )
2 匀速圆周运动的物体，周期越小，转的越快( ) 3 不同的匀速圆周运动中，相同时间内线速度大的物体一定比线速度小的物体转的圈 数多。( ) 4 对匀速圆周运动的物体进行受力分析的时候，向心力一定要画，因为它是客观存在 的。( ) 5 万有引力定律可以解释人造卫星绕地球做匀速圆周运动的原因，万有引力提供向心 力。( )
淋雨量问题涉及的主要因素有：单位体积降雨量 ，竖直雨速 v 雨，水平风速 v 风，人
的行走速度 v 人(当跑步时，v 人比较大)，行走的直线距离 L1 和人的淋浴面积。人可简化 为一个长方体模型，如图所示，可能被淋到的面为：S 顶，S 正(代表人的正面)，S 背 。若以 上条件均已知，则
(1) 在无风的情况下，即 v =0，人在雨中行走或跑步，S 顶，S 正，S 背三个面中，哪个面的 风
淋雨为 0？ (2) 请写出无风时，淋雨量不为 0 的各面的淋雨量的表达式。由此，在无风的情况，是 走还是跑才能被雨少淋？ (3) 若有风，且背面有风，求雨滴相对于地面的速度大小，并写出总淋雨量的表达式， 说明是走还是跑才能被雨少淋。
【例 4】
一、正文：
圆周运动
大家学习了有关物体运动的知识，但研究的基本都是直线运动，而直线运动是物体运动 的最简单形式，实际生活中，绝大部分物体的运动都不是直线运动，所以我们有必要对物体 运动的研究进行拓展，而今天我们要研究的是最简单曲线运动之一的圆周运动。 物体在以某点为圆心半径为 R 的圆周上运动，即物体运动时其轨迹是圆周的运动叫“圆周运 动”，它是一种最常见的曲线运动。例如吊扇、车轮、皮带轮等都做圆周运动。圆周运动分 为匀速圆周运动和变速圆周运动（如：竖直平面内绳/杆转动小球、竖直平面内的单摆运动）。 在圆周运动中，最常见和最简单的是匀速圆周运动（匀速圆周运动实际上是指速度大小始终 保持不变的圆周运动）
上海市复旦附中2018年初三自招考试英语真题(无听力部分)
2018年上海复旦附中自主招生英语试题选择题31.They are fed up the old routine.A. withB. ofC. atD. on32.He is such a(n) teacher that has devoted all his and energy to his students.A. conscientiousB. consciousC. academicD. scientific33.We are looking for someone with a real sense of to the job.A. committeeB. commitmentC. communityD. commission34.Since you are to the seafood, you’d better avoid eating it.A. sensibleB. sentimentalC. sensitiveD. sensory35.During the celebration, fireworks have been at the bay.A. set outB. set aboutC. set upD. set off36.There are fewer working hours in the executive jobs, the job stress is comparatively higher.A. thatB. whereC. whichD.what37.They declared the war, for they believed that country had the weapons of mass destruction.A. liberatedB. counteredC. approvedD. proliferated38.The journalist reported the of children labors who had worked many days on end.A. expansionB. expeditionC. exploitationD. explorationWhat is the thing called happiness? For centuries, people were too busy pursuing it 39 much time analyzing it. Now a pioneering band of researchers has finally bagged the elusive quarry or at least taken its measure. Using such sophisticated new tools 40 the five-item Life Satisfaction Scale and the seven-point Delighted-terrible Scale (On a scale of one to seven, how do you feel about your life?), social psychologists have plumbed the heart of happiness. And their answer to the age-old 41 is that it all depends.Happiness, that is, 42 what makes you feel happy, which is why psychologists often call it “subjective well-being.” But from43 studies of various age and population groups in the United States and abroad, they have reached some 44 at the top of the charts is not, as many might expect, success, youth, good looks or any of those 45 assets. The clear winner is relationship, close ones, followed by happy marriage. Supportive, intimate connections with other people seem 46 important. Using simple survey questions, psychologist David Myers found that the 47 happy people are those in unhappy marriages. Happiest are those who married 48 their “best friend.”39. A. to spendB. spendingC. has spentD. have spent40. A. likeB. alikeC. asD. for instance41. A. psychologyB. mysteryC. solutionD. trick42. A. results inB. leans againstC. depends onD. arrives at43. A. realisticB. idealisticC. objectiveD. individualistic44. A. endlesslyB. contradictorilyC. harmoniouslyD. consistently45. A. enviableB. reliableC. inevitableD. endurable46. A. vastlyB. tremendouslyC. swiftlyD. basicallyD. D. off上海复旦附中自主招生英语试题(1)AABCD BDDAABCC DBBCB上海复旦附中自主招生英语试题(2)Sarah Alexander celebrated the start of her last year at Wells College the way many other seniors before her have. She ran across the picturesque to the shores of Cayuga Lake, where she jumped into the water.So did many of her fellow seniors. But dozens of students decided to stay away, especially the relatively few newly arrived male students.Wells College, which since 1868 had educated only women, began accepting men this year in hopes of bolstering its dwindling enrollment. For many students and alumnae, it was a crushing decision. After the college announced last October that it would go coeducational, about half of the students protested and two filed a lawsuit, which they later dropped.The students —33 men and 383 women – campus late month Both sexes are now trying to navigate new social landscape. Mr. Phillips said “You can’t do guy stuff. Every time you want to sit and watch sports or a game, it turns into a movie.” The women were “some what nasty.” I could see the dirty looks in their eyes,” he said. “But I was not going to let that stop me from coming.”Wells was a place where women did not have to fuss over their appearance or47. worstA. mostB. bestC. least 48. A. toB. withC. forfight to be taken seriously by their professors. They could enjoy the camaraderie of their campus sisters and their playful traditions. Besides jumping into the lake, the women dance around the maypole each May and kiss the feet of the statue of Minerva, the Roman goddess of wisdom, before exams.Ms. Alexander said, “People told us we wouldn’t notice a difference, but from the moment men arrived on campus not could notice a difference. Waking up early to put on makeup, and that’s odd,” she said.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college, when women were not considered capable of higher learning. “Give her the opportunity,” he wrote.Henry Wells, a founder of Wells Fargo and a friend of Cornell’s benefactor, Ezra Cornell established this college, when were not considered capable of higher learning. “Give her the opportunity,” he wrote.The great-great-great-great granddaughter of Henry Wells, Stephanie Redmond, 18, of Washington State, said that earlier this year a Wells student had tracked her down and asked her to support the protest. But Ms. Redmond said the move the move to admit men had encouraged her to enroll at Wells this year as a freshman. She plans on a career in engineering, a male-dominated field, and said attending an all-women’s college might have put her at a disadvantage.49.The primary reason for the Wells College to accept men is that .A.its enrollment rate is declineB.the campus is lack of vigor and vitalityC.it will face the destiny of being closed downD.all-women’s college might put a woman at a disadvantage50. A typical behavior for seniors to do is that .A.they jog along the picturesque campusB.they switch sports programs to a movieC.they celebrate their year by jumping into a lakeD.they swim in Cayuga Lake accompanied by friends51.The change after turning into a coed college is that .A.dirty looks in women’s eyes have disappearedB.women get up early to make upC.women are waking up early to studyD.women dance with men around the maypole52.The attitude of the author is that .A.she hares a tradition of all-women schoolsB.she calls on women in support the protestC.she dislikes the change and hopes to file a lawsuitD.she objectively describes the new and uneasy coeducation53.Which of the following statements is Not true?A.The enrollment of male students caused controversy,B.The grandchildren of the college founder benefited most.C.The current president of the college was also its graduate.D.The founder hoped to give women opportunities of higher education.But what is teacher quality? How can one measure it reliably?An analysis is issued a sample of data a Texas school district. Experts argue convincingly that teacher effectiveness should be measured by students’ gains on standardized tests: Mr. Smith is presumably a better teacher than Ms. Brown if his students consistently improve their test scores more than hers do.Though this approach is appealing, there are tricky issues. For example, what if Ms. Brown teaches in a school where students score so high there is little room for improvement?The authors try to correct for this problem, as well as other sorts of measurement issues, to generate a measurement of teacher effectiveness. The paper is primarily concerned with how this measure is related to other observable teacher characteristics.The first finding is that is a large variation in teacher effectiveness: some teachers consistently have a larger impact on their students’ achievement than others.Second, easily observable characteristics like having a master’s degree or a passing score on the teacher certification exam are not correlated with teacher effectiveness.Then what does matter? The most important single influence is experience: first-year teachers are much less effective than others. The second year is significantly better, and by the fourth year, most teachers hit their stride.It is not entirely clear whether this experience effect is learning by doing (the more you teach, the more effective you become) or survival of the fittest (those who are not good at teaching tend to drop out early).From my reading of the paper, both effects appear important and there is no simple answer. The data do suggest, however, that teacher effectiveness is pretty clear by the end of the second year, so the information to make an informed decision is available at that time.The authors also investigate the contentious issue of racial matching of students and teachers. Here they find strong evidence that minority teachers tend to be more effective with minority students. Again, it is unclear whether this is because of a role model effect (students respond better of their own race) or an empathy effect (teachers empathize better with students of their own race) or something else entirely.The authors also look at teacher mobility. There is some evidence that teachers who quit teaching or switch schools tend to be below average in effectiveness. This is consistent with the survival-of-the-fittest model.54.The schoolmaster could decide wisely whether to further employ the teacher by the end of the .A. the first yearB. the second yearC. the third yearD. the fourth year55.The phrase “hit their stride” most probably means “”.A. reach their normal levelB. become confident1.A. increasinglyF.callingG.dependent senses B. lowering C. common D. solutions E. individually H. shortcomings I. consumption J. introduced K.C. walk with long stepsD. get bored56.The author of this passage holds the view that _ .A.teachers will perform better with time passingB.ineffective teachers should leave earlier rather than laterC.teacher’s effectiveness is apparent after a couple of yearsD.a master’s degree will improve teacher’s effectiveness57.Why do black teachers tend to be more effective with black students?A.Students feel secure, so they respond better.B.Teachers sympathize with students of their own race.C.There are entirely some other identified reasons.D.The reasons are far from clear and definite.58.Which of the following may serve as the best title?A.Tenure, Turnover and the Quality of TeachingB.Impact of Teacher Quality on Student LearningC.Different Sorts of Measurement IssuesD.Survival-of-the-fittest Model vs. Learning-by-doing Model上海复旦附中自主招生英语试题(2)ACBDCBACDA上海复旦附中自主招生英语试题(3)A United Nations panel on climate change says global warming is causing extreme weather all over the world and is 41 on governments to come up with new ideas to curb gas emissions. Since much of the air pollution comes from coal-fired power plants, scientists in Denmark are trying to lower their nation’s energy needs with new types of smart streetlights.Our 42 industrialized world needs huge amounts of electrical energy, but our power plants still rely mostly on technology 43 as early as the 19th century—coal—powered plants, hydroelectric dams or somewhat never nuclear energy, all of which have their own 44 .But scientists say we can slow down global warming by 45 energy demands for street lights.These 46 features of the world’s urban areas require a lot of electricity.The U.S. Energy Information Administration estimates that in 2012, lighting for buildings, streets and highways in the U.S. used about 274 billion kilowatt hours.In a bid to make Copenhagen the world’s first carbon-neutral city by 2025,scientists in the Danish capital are testing a variety of new street lighting technologies.Kim Brostrom is the chief technical officer at the Danish Outdoor Lighting Lab.“We have installed nine kilometers of streets, we have 280 masts placed here, we have 50 different 47 , we have 10 different management systems, and we have alot of different sensors and things out in the open area,” said Brostrom.Chief science officer Jakob Andersen says the lights can be managed 48 from a tablet computer or a smart phone.The main goal is to lower energy 49 when the light is not needed. So the lamp brightens up only when it 50 an approaching pedestrian, cyclist or vehicle. Some of them even have a backup wind generator or a solar cell.2.Diet Coke, diet Pepsi, diet pills, on-fat diet, vegetable diet… We are 51 by the word “diet” everywhere we look and listen. We have so easily been attracted bythe promise and 52 of diet products that we have stopped thinking about what diet products are doing to us. We are paying for products that 53 us psychologically and physically(身体上).Diet products significantly weaken us psychologically. On one level, we are not allowing our brain to 54 that our weight problems lie not in actually losing the weight, but in controlling the 55 of fatty, high-calorie, unhealthy foods. Diet products allow us to jump over the thinking stage and go straight for the scale( 秤) instead. All we have to do is to swallow or 56__ the word “diet” in food labels.On another level, diet products have greater psychological effects. Every time we have a zero-calorie drink, we are telling ourselves without our 57 that we do n’t have to work to get results. Diet products make people believe that gain comes without pain, and that life can be without resistance a(n) 58 .The danger of diet products lies not only in the psychological effects they have on us, but also in the physical harm that they cause. Diet foods can 59 harm our bodies because consuming them instead of healthy foods means we are preventing our bodies from having 60 nutrients( 营养成分). Diet foods and diet pills 61 zero calorie only because the diet industry has created chemicals to produce these wonder products. Diet products may not be 62 , and the chemical that go into diet products are potentially dangerous.Now that we are aware of the effects that diet products have on us, it is time to63 think about buying them. Losing weight lies in the power of minds, not in the power of chemicals. 64 we realize this, we will be much better able to resist diet products, and 65 prevent the psychological harm that comes from using them.51. A. confused B. surrounded C. mixed D. fascinated52. A. potential B. affection C. obligation D. calculation53. A. weaken B. harm C. enforce D. inspire54. A. admire B. argue C. deny D. admit55. A. assumption B. digestion C. dissolution D.consumption56. A. recognize B. foresee C. overlook D. research57. A. frustration B. ignorance C. awareness D. emphasis58. A. maintenance B. efficiency C. struggle D. setback59. A. indirectly B. inevitably C. incredibly D. innocently60. A. extra B. basic C. organic D. delicate61. A. contain B. persist C. exclude D. melt62. A. nutritional B. poisonous C. ridiculous D. sensitive63. A. strongly B. enthusiastically C. eagerly D. seriously64. A. Unless B. While C. Though D. Once65. A. therefore B. otherwise C. meanwhile D. furthermore3.It was a bitter cold evening in northern Virginia many years ago. The old man’s beard was glazed by winter’s frost while he waited for a ride across the river. The wait seemed endless. His body became numb and stiff from the frigid north wind.It was long before he heard the faint, steady rhythm of hooves (马蹄) along the frozen path. Anxiously watching several horsemen coming up, he let the first one pass by without any effort to get his attention, then another passed by, and another. Finally, the last rider drew near where the old man sat like a snow statue when old man caught his eyes and said, “Sir, would you mind giving an old man a ride to the other side?”Stopping his horse, the rider replied, “Sure! Jump aboard.” Seeing the old man unable to lift his half-frozen body from the ground, the horseman got down to help him. The horseman took him not just across the river, but to his destination just a few miles away.As they approached the tiny but c ozy cottage, the horseman’s curiosity caused him to inquire, “Sir, I noticed you let several other riders pass by without making an effort to secure a ride. Then I came up and you immediately asked me for a ride. I am curious why, on such a bitter night, you would wait and ask the last rider. What if I had refused and left you here?”The old man looked the rider straight in the eyes and replied, “I reckon I know people pretty good. I looked into the eyes of the other riders and immediately found no concern for my situation. It would have been useless even to ask them for a ride. But when I looked into your eyes, your gentle spirit would welcome the opportunity to give me assistance in my time of need.”Those heart-warming comments touched the horseman deeply. “I’m so grateful for what you have said,” he told the old man. “May I never get too busy in my own affairs that I fail to respond to the needs of others with kindness and compassion.”With that, Thomas Jefferson turned his horse around and made his way back to the White House.66.Why didn’t the old man ask the previous riders for a ride?A.Because he was waiting for the last rider.B.Because his efforts failed to get their attention.C.Because he assumed they had no concern for him.D.Because he was too numb to lift his half-frozen body.67.What caused the last rider to stop and help the old man?A. The old man’s poor situation.B. The old man’s warm comments.C. His own affairs.D. Kindness and sympathy.68.What do you know about the old man?A. He judged people by looking into their eyes.B. He lived in a cozy cottage a few miles away.C. He gave the last rider an opportunity to help.D. He recognized the president at first.69.Which can be the best title of this text?A. Look into your eyes.B. Compassion of a great man.C. The last rider to help.D. Return to the White House.4.International Book ClubHave you ever thought of joining a book club and buying new books through the post? Here at the International Book Club, we already have many members buying books from us by mail.Immediate benefits：●As a special offer, you may choose any reduced price books from our newmembers’ book list, to the value of $6 in total (plus postage and packing). By doing this, you will save pounds on the publishers’ prices.●Tick the box on your form to order a free watch.●If you reply within seven days, we will send you another free gift carefullychosen from our book list by our staff.●Order a DVD from the many on offer in our list, at half the recommended retailprice.When you’ve joined：As a member, you’ll enjoy savings of between 30% and 50% off the publisher’s price on every book you buy, and what’s more, they’ll come straight to your door. Your free club magazine arrives once a month, to keep you up to date with the latest bestsellers. This means that every year we offer over 1,000 books to choose from. On the Internet, you can find all our titles for the year on our exclusive members’ website. Being a member：All we are asking you to do while you are a member is to choose four books during your first year. After that, you can decide on the number of books you wish to take.In each of our monthly club magazines, our experienced staff choose a Club Choice book — a work of fiction or a reference title which they feel is particularlyworth buying, and which is offered at an extra special price. However, if you do not want this book, just say so in the space provided on the form. We will always send the book if we do not receive this.So, return your application form today, but hurry —it’s not every day we can make you an offer like this. To apply to become a member, all you need to do is simply fill in the enclosed form and return it in the postage paid envelope supplied.Before you know it, you r books will be with you. Please don’t send any money now, as we will send you your bill with the books. And remember, you have up to a fortnight to decide if you wish to keep the books you have ordered. You should then either return the books or send your payment.70.Which of the following doesn’t belong to the benefits of being a club member?A. Get four books for free in the first year.B. Order a free watch.C. Get a gift for nothing.D. Order a DVD at a low price.71.Every month the club provides a free club magazine in order to .A.let readers know the number of books to be soldB.keep readers well informed of recent bestselling booksC.make readers know the club’s developmentD.attract more and more readers to join the club72.If a book is worth $100, how much will a member probably save if he buys one?A. $20B. $40C. $60D. $7073.What should you do if you want to join the book club?A.Just fill in a form with personal information and send the club an email.B.Ask other club members to recommend you to the club.C.Fill in an application form with needed information and return it to the club.D.Apply for a membership card.5.In 1789 the U.S. government passed a law which said that the land of the American Indians could never be taken from them without their agreement. One hundred years later, however, the Indians only had a very small part of the land that originally belonged to them. How did this great injustice occur?After 1812 white settlers began to move west across North America. At first, the settlers and the Indians lived in peace. However, the number of settlers increased greatly every year, and slowly the Indians began to see the white settlers as a danger to their survival. To feed themselves, the settlers killed more and more wild animals. The Indians, who depended on these animals for food, had to struggle against starvation. The settlers also brought with them many diseases which were common in white society, but which were new for the Indians. Great numbers of Indians became sick and died. Between 1843 and 1854 the Indian population in one area of the country went down from 100,000 to 30,000.More land was needed for the increasing number of white settlers. In Washington, the old respect for the rights of the Indians disappeared. The old promises to the Indians were broken; the government began to move groups of Indians from theiroriginal homelands to other poorer parts of the country. Some Indians reacted angrily and violently to this treatment. They began to attack white settlers, and the Indian war began. For 30 years, until the late 1880s, different groups of Indians fought against the injustices of the white man. They had a few famous successes, but the result of the struggle was never in doubt. There were too many white soldiers, and they were too powerful. Many Indians were killed; the survivors were moved from their homelands to different area of the country. It was a terrible chapter in the history of a country that promised freedom and equality to everyone.74.It can be inferred from the passage that .A.in the U.S. there were many laws that provided the rights of American IndiansB.the law which was passed in 1789 by the U.S. government was not successfully carried outC.in the 19th century no injustices were done against the Indians by the U.S. governmentD.the majority of white settlers were openly opposed to the law passed in 178975.According to the passage which of the following is TRUE?A.The Indians believed that killing too many wild animals had disturbed the balance of nature.B.The government began to have a better understanding of the Indians in the fifties of the 19th century.C.Between 1843 and 1854 about 70,000 Indians were killed in the battle.D.The whites carried serious diseases into where the Indians lived.76.It is implied in the passage that .A.the Indians had many great successes in the Indians warsB.the Indians had no doubt that they would win the warsC.after the war the Indians stayed where they were beforeD.the Indians were too weak to win the struggle77.What is the writer’s opinion about the treatment that the Indians received from the U.S. government?A.He believed that the government always respected the rights of the Indians.B.He believed that the government can’t be criticized for its treatment to the Indians.C.He believed that the government treated the Indians unjustly.D.He believed that the government’s unfair treatment against the Indians was not on purpose.6.The question of whether our government should promote science and technology or the liberal arts in higher education isn’t an either/or proposition(命题), although the current emphasis on preparing young Americans for STEM(science, technology, engineering, maths)-related fields can make it seem that way.The latest congressional report acknowledges the critical importance of technical training, but also asserts that the study of the humanities(人文学科)and socialsciences must remain central components of America’s educational system at all levels. Both are critical to producing citizens who can participate effectively in our democratic society, become innovative(创新的)leaders, and benefit from the spiritual enrichment that the reflection on the great ideas of mankind over time provides.Parents and students who have invested heavily in higher education worry about graduates’ job prospects as technological advances and changes in domestic and global markets transform professions in ways that reduce wages and cut jobs. Under these circumstances, it’s natural to look for what may appear to be the most “practical” way out of the problem “Major in a subject designed to get you a job” seems the obvious answer to some, though this ignores the fact that many disciplines in the humanities characterized as “soft” often, in fact, lead to employment and success in the long run. Indeed, according to surveys, employers have expressed a preference for students who have received a broadly-based education that has taught them to write well, think critically, research creatively, and communicate easily.Moreover, students should be prepared not just for their first job, but for their 4th and 5th jobs, as there’s little reason to doubt that people entering the workforce today will be called upon to play many different roles over the course of their careers. The ones who will do the best in this new environment will be those whose educations have prepared them to be flexible. The ability to draw upon every available tool and insight—picked up from science, arts, and technology—to solve the problems of the future, and take advantage of the opportunities that present themselves, will be helpful to them and the United States.(Note: Answer the questions or complete the statements in NO MORE THAN TWELVE WORDS.)78.The latest congressional report suggests that.79.What is the main concern of students when they choose a major?80.What kind of job applicants do employers look for?81.What suggestions does the author give to college students?7.In order to study enzymes(酶), a small piece of potato is cut into very thin pieces. These thin pieces are placed in a little glass container and covered with water. Then a little of the proper chemical is added. Immediately, because of the enzyme present in the potato, the chemical starts joining with the oxygen in the air above the water. If the container is entirely closed, a partial vacuum(真空)is framed inside. If the container is now connected with a fine tube which is dipped in water, the water is sucked part way up the tube because of the vacuum.The scientists doing the experiment carefully notice how far up the tube is when water is sucked in a certain time. The higher it is sucked, the more of that particular enzyme and even about the way in which it operates. And all the time we are working with amounts far too small to see or weigh.1.What do the scientists want to find out in the experiment?。
2018年复旦大学自主招生试题(PDF)
2018年复旦大学自主招生试题（部分学生回忆）1.设R x ∈，求函数xx x x x x f --++⨯++=1124124416)(的最小值.2.设824)(1-+=+x x x f ，求}0)(|)6,6({>-∈=x f x A 的区间长度.3.求能放入一个半径为的球体的圆锥体积的最小值.4.极坐标系中，求曲线016sin 8cos 6:2=+--θρθρρC 上一点与曲线04sin 4cos 2:2=+--θρθρρD 上一点的距离的最大值.5.ABC ∆中，D 为边BC 上一点，,,,,,y CD x BD h AD b AC c AB =====则222222c b h y x +=++是AD 为角平分线的什么条件?6.求最小正整数k ，使得k 4725为完全平方数.7.1990年，数学家（）在巴黎国际数学大会上提出了23个未解问题.8.记正方体的六个面中心为F E D C B A ,,,,,，先在这6点中任取两点连线，再在这6点中任取两点连线，则两条线段平行但不重合的概率是多少？9.直线02:,01:21=++-=-+m my x l y mx l 分别过定点B A ,，若两条直线交于点P ，求PB PA +的取值范围.10.在单位正方体EFGH ABCD -中，N M ,分别为AE CG ,的中点，P 为平面BFGC 上一点，并满足||EP 面BMN ,求EP 长度的取值范围.11.已知在ABC ∆中，)7,6(),3,4(),2,3(C B A ，求ABC ∆的面积.12.在ABC ∆中EC BE DB AD 2,2==，设直线CD 和AE 交于点P ，若AC n AB m AP +=，求),(n m .13.令*∈=N n x nx x f ,sin sin )(，下列结论正确的是_________.(1))(x f 是周期函数；（2）)(x f 有对称轴；（3）)(x f 关于)0,2(π对称；（4）n x f ≤|)(|.14.若函数)(x f 满足)1(2)(1)1(≠=-+x x x f xx f ，求)2(f .15.已知)1,1(),1,0(-B A ，直线1=+by ax 与线段AB 有公共点，求22b a +的最小值.16.设方程343log 3log 273-=+x x 的两个根为a 和b ，求b a +的值.17.已知方程023234=--++x bx ax x 有两个实数根1,221-==x x ，则其余两根为_________.（1）相等实根;（2）不同实根;（3）共轭复根;（4）以上都不对.18.定义2log +=⊕y y x x ，解方程04)4(=⊕⊕x .19.已知0>a ，设1124)(-+++=a x x x f ，若221a x x =，且012>>x x ，比较)(1x f 和)(2x f 的大小.20.已知03612234=++--x bx ax x 有二重根，求22)1(++b a 的值.21.在10,3,2,1 中等概率的取出两个数b a ,，使得曲线2222)3(24113)1(++++=+++y a b x b a y x 是抛物线的概率为________.22.已知正数b a ,，则a b b a log log =是b a =的_________条件.23.设P C B A ,,,是平面上不同的点，则0=++PC PB PA 是P 为ABC ∆的重心的_________条件.。
2018年___自主招生数学试卷(含答案解析)
2018年___自主招生数学试卷(含答案解析)2018年___自主招生数学试卷一、选择题（本大题共6小题，共24.0分）1.√16的平方根是()A.4B.±4C.22.若√(1−x)2=x−1成立，则x满足()A.x≥1B.x≥C.x≤1D.±23.已知x=√5−1，则x2+2x的值是()A.2B.3C.4D.54.如图所示的四条直线a、b、c、d，直线a、b与水平线平行，以其中一条为x轴，d与水平线垂直，取向右为正方向；直线c、以其中一条为y轴，取向上为正方向．某同学在此坐标平面上画了二次函数x=xx2+2xx+2(x≠0)的图象如图，则下面结论正确的是()A.a为x轴，c为y轴B.a为x轴，d为y轴C.b为x轴，c 为y轴D.b为x轴，d为y轴5.如图，已知AB为圆的直径，C为半圆上一点，D为半圆的中点，xx⊥xx，垂足为H，HM平分∠xxx，HM交AB于x.若xx=3，xx=1，则MH长为()A.1B.1.5C.0.5D.0.76.如图，△xxx中，∠x=90°，D是BC边上一点，∠xxx=3∠xxx，xx=8，xx=7.则AB的值为()A.15B.20C.2√2+7D.2√2+√7二、填空题（本大题共10小题，共40.0分）7.已知实数x、y满足x+2x=5，则x−x=3.8.分解因式：x2+4xx+4x2+x+2x−2=(x+2x+1)2−3.9.在平面直角坐标系中，点A，B的坐标分别为(x,3)，(3x−1,3)，若线段AB与直线x=2x+1相交，则m的取值范围为(0,1)。
10.若一个圆锥的侧面展开图是半径为18cm，圆心角为240°的扇形，则这个圆锥的底面半径长是9cm。
11.如图，已知在矩形ABCD中，点E在边BC上，BE=2CE，将矩形沿着过点E的直线翻折后，点C、D、N处，B在同一直线上，分别落在M、F与BE交于点G.设AB=√3，那么△xxx的周长为4+4√3.12.如图，已知点x1，x2，…，xx均在直线x=x−1上，点x1，x2，…，xx均在双曲线x=−x上，x1x1⊥x并且满足：x1x2⊥x轴，x2x2⊥x轴，…，xx−1xx⊥x轴，xxxx⊥x轴，且x1x2=x2x3=…=xx−1xx，则n的最小值为2.1.由题意可知，点B在x轴负半轴，点A在x轴正半轴，且AB垂直于x轴，因此AB的斜率为0，即AB为x轴，所以B的纵坐标为0.又因为B在x轴负半轴，所以其横坐标为负数，设为-a。
复旦大学自主招生试题
复旦大学自主招生试题（正文）复旦大学自主招生试题自主招生，作为一种独特的选拔方式，给予了高中生更多展示自己的机会，而复旦大学作为一所顶尖的综合性大学，其自主招生试题更是备受考生关注。
本文将通过介绍复旦大学自主招生试题的一些例子，分析其考查内容和要求。
一、数学试题1. 已知函数f(x) = 2x^3 - 3x^2 - 12x + 5，求函数f(x)在区间[-2, 3]上的最小值和最大值。
分析：首先，我们需要先求出函数f(x)的导函数f'(x)，然后再通过导函数的零点来找出函数f(x)的极值点。
根据极值的定义，我们可以通过求解f'(x) = 0来得到。
2. 某商店商品价格打9折，然后再减去10元，最后的价格是原价的40%。
求该商品的原价。
分析：假设原价为x元，那么根据题意，我们可以得到以下等式：0.9x - 10 = 0.4x。
通过解这个方程，我们可以求出该商品的原价x。
二、英语试题1. 阅读下面短文，并根据短文内容完成后面的题目。
Most people know that exercise is good for their health. Regular physical activity can prevent a multitude of diseases and improve one’s overall well-being. However, it is essential to find an exercise routine that suits your lifestyle and preferences. In this regard, yoga is a great option for many.Yoga combines physical poses, breathing exercises, and meditation to promote a healthy mind and body. The slow and controlled movements help build flexibility, strength, and balance. Additionally, the focus on deep breathing and mindfulness promotes relaxation and stress reduction.Furthermore, yoga can be practiced by people of all ages and fitness levels. From beginner classes to advanced poses, there are variations suitable for everyone. It is a versatile practice that can be adapted to individual needs and goals.Based on the information provided in the passage, answer the following questions:a. What are the benefits of regular exercise?b. What aspects does yoga combine?c. Why is yoga suitable for people of all ages and fitness levels?三、文学试题阅读下面的《Active Learning》一文，根据文章内容回答问题。
XXX2018-2019年自招真题数学试卷(含答案)
XXX2018-2019年自招真题数学试卷(含答案)1.已知$a$、$b$、$c$是一个三角形的三边，则$a+b+c-2ab-2bc-2ca$的值是（）。
A。
恒正 B。
恒负 C。
可正可负 D。
非负答案：选B根据三角形两边之和大于第三边的性质，可得$a+b-c>0$，$a-b+c>0$，$a+b+c>0$，$-a+b+c>0$。
将其代入原式，得$(a-b+c)(a+b-c)(-a+b+c)(a+b+c-2ab-2bc-2ca)<0$，因此原式恒为负数，选B。
2.设$m$，$n$是正整数，满足$m+n>mn$，给出以下四个结论：①$m$，$n$都不等于1；②$m$，$n$都不等于2；③$m$，$n$都大于1；④$m$，$n$至少有一个等于1，其中正确的结论是（）。
A。
① B。
② C。
③ D。
④答案：选D将$m+n-mn>0$移项得$(m-1)(n-1)<1$。
因为$m$，$n$是正整数，所以只有$m=1$，$n=1$或$m=1$，$n=2$或$m=2$，$n=1$不满足条件，而$m=1$，$n$任意或$m$任意，$n=1$都满足条件，因此选D。
3.已知关于$x$的方程$2x+a=x+a$有一个根为1，则实数$a$的值为（）。
A。
$\frac{-1\pm\sqrt{5}}{2}$ B。
$0$ C。
$1$ D。
以上答案都不正确答案：选A将$x=1$代入方程，得$2+a=1+a$，解得$a= \frac{-1\pm\sqrt{5}}{2}$。
当$a=\frac{-1-\sqrt{5}}{2}$时，方程化简后为$2x^2+2x+(1+\sqrt{5})=0$，无实根，舍去；当$a=\frac{-1+\sqrt{5}}{2}$时，方程化简后为$x^2-x-(1+\sqrt{5})=0$，有一个根为1，因此选A。
4.已知$a$，$b$，$c$是不完全相等的任意实数，若$x=a-2b+c$，$y=a+b-2c$，$z=-2a+b+c$，则关于$x$，$y$，$z$的值，下列说法正确的是（）。
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2018-2019年最新复旦大学附属中学自主招生语文模拟精品试卷（第一套）（满分：100分考试时间：90分钟）③小屋在山的怀抱中，犹如在花蕊中一般，慢慢地花蕊绽开了一些，好像山后退了一些。
④当花瓣微微收拢，那就是夜晚来临了。
⑤小屋的光线既富于科学的时间性，也富于浪漫的文学性。
A．①③②④⑤ B．①④③②⑤ C．⑤③②①④ D．⑤③②④①二、阅读下面古诗文，完成7—14题。
（24分，7—12每题2分）勾践自会稽归七年，拊循其士民，欲用以报吴。
大夫逄同谏曰：“今夫吴兵加齐、晋，怨深于楚﹑越，名高天下，实害周室，德少而功多，必淫自矜。
为越计，莫若结齐，亲楚，附晋，以厚吴。
吴之志广，必轻战。
是我连其权，三国伐之，越承其弊，可克也。
”勾践曰：“善。
”其后四年。
吴士民罢弊，轻锐尽死于齐﹑晋。
而越大破吴，因而留围之三年，吴师败，越遂复栖吴王于姑苏之山。
吴王使公孙雄肉袒膝行而前，请成越王曰：“孤臣夫差敢布腹心，异日尝得罪于会稽，夫差不敢逆命，得与君王成以归。
今君王举玉趾而诛孤臣，孤臣惟命是听，意者亦欲如会稽之赦孤臣之罪乎？”勾践不忍，欲许之。
范蠡曰：“会稽之事，天以越赐吴，吴不取。
今天以吴赐越，越其可逆天乎？且夫君王蚤朝晏罢，非为吴邪？谋之二十二年，一旦而弃之，可乎？且夫天与弗取，反受其咎。
君忘会稽之厄乎？”勾践曰：“吾欲听子言，吾不忍其使者。
”范蠡乃鼓进兵，曰：“王已属政于执事，使者去，不者且得罪。
”吴使者泣而去。
勾践怜之，乃使人谓吴王曰：“吾置王甬东，君百家。
”吴王谢曰：“吾老矣，不能事君王！”遂自杀。
选自《史记·越王勾践世家》7．下列加点词语解释不正确的一项是（ ）A．越承其弊，可克也。
克：战胜 B．越遂复栖吴王于姑苏之山 栖：占领C．越其可逆天乎 逆：违背 D．吾老矣，不能事君王 事：侍奉8．下列加点词语古今意义相同的是（ ）A．今天以吴赐越 B．使者去，不者且得罪 C．谋臣与爪牙之士，不可不养而择也 D．微夫人之力不及此三、现代文阅读（14分） 大度读人 一个人就是一本书。