2010年8所大学自主招生试题

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2010复旦交大清华北大自主招生数学试题

O x O xO x则该多面体的体积为______________A. 32个；B. 30个；C.28个；D.26个7、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；8、在直角坐标系Oxy 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 9、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.10、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/12.11、设复数βαβαcos sin ,sin cos i w i z +=+=满足z w =3/2，则sin(β−α)=______. A.±3/2;B.3/2，−1/2;C. ±1/2;D.1/2,−3/2.12、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 213、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2aπ的周期函数D ．周期为2π的周期函数.14、将同时满足不等式x−ky−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=2;D.k=1.15、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.16、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17、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≠1D ．1<a≤218、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)19、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- 20、已知x x x x f 2cos 3cos sin )(+=，定义域⎥⎦⎤⎢⎣⎡=ππ127,121)(f D ，则=-)(1x f_____A ．π12123arccos 21+⎪⎪⎭⎫ ⎝⎛-xB ．π6123arccos 21-⎪⎪⎭⎫ ⎝⎛-x C ．π12123arcsin 21+⎪⎪⎭⎫ ⎝⎛--x D ．π6123arcsin 21-⎪⎪⎭⎫ ⎝⎛-x 21、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2l D ．存在与1l 和2l 都相交的直线与l 平行22、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 ．21 B ．43 C ．814 D ．82323、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24、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 25、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,,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 26、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 n B ．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−i C ．1+i D ．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=±by 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k ; B. m,n 的最大公因子整除k ; C. m,n,k 两两互素; D. m,n,k 除1外没有其它共因子2010年五校合作自主选拔通用基础测试数学试题适用高校:清华大学、上海交通大学等五校一、选择题1．设复数2()1a i w i+=+，其中a 为实数，若w 的实部为2，则w 的虚部为( ) (A)32- (B)12- (C)12 (D)322．设向量,a b ，满足||||1,==⋅=a b a b m ，则||+a tb ()t R ∈的最小值为( ) (A)2(C)13. 无试题4. 无试题5．在ABC ∆中，三边长,,a b c ，满足3a c b +=，则tan tan 22A C的值为( ) (A)15 (B)14 (C)12 (D)236．如图，ABC ∆的两条高线,AD BE 交于H ，其外接圆圆心为O ，过O 作OF 垂直BC 于F ，OH 与AF 相交于G ，则OFG ∆与GAH ∆面积之比为( )(A)1:4 (B)1:3 (C)2:5 (D)1:2O H G FEDCBA7．设()e (0)axf x a =>．过点(,0)P a 且平行于y 轴的直线与曲线:()C y f x =的交点为Q ，曲线C 过点Q 的切线交x 轴于点R ，则PQR ∆的面积的最小值是( )(A)1 (C)e2(D)2e 48．设双曲线2212:(2,0)4x y C k a k a -=>>，椭圆2222:14x y C a +=．若2C 的短轴长与1C 的实轴长的比值等于2C 的离心率，则1C 在2C 的一条准线上截得线段的长为( )(A) (B)2 (C) (D)49．欲将正六边形的各边和各条对角线都染为n 种颜色之一，使得以正六边形的任何3个顶点作为顶点的三角形有3种不同颜色的边，并且不同的三角形使用不同的3色组合，则n 的最小值为( )(A)6 (B)7 (C)8 (D)910．设定点A B C D 、、、是以O 点为中心的正四面体的顶点，用σ表示空间以直线OA 为轴满足条件()B C σ=的旋转，用τ表示空间关于OCD 所在平面的镜面反射，设l 为过AB 中点与CD 中点的直线，用ω表示空间以l 为轴的180°旋转．设στ表示变换的复合，先作τ，再作σ.则ω可以表示为( )(A)στστσ (B)στστστ (C)τστστ (D)στσστσ 二、解答题11．在ABC ∆中，已知22sin cos 212A BC ++=，外接圆半径2R =． (Ⅰ)求角C 的大小；(Ⅱ)求ABC ∆面积的最大值．12．设A B C D 、、、为抛物线24x y =上不同的四点，,A D 关于该抛物线的对称轴对称，BC 平行于该抛物线在点D 处的切线l ．设D 到直线AB ，直线AC 的距离分别为12,d d ，已知12d d +=．(Ⅰ)判断ABC ∆是锐角三角形、直角三角形、钝角三角形中的哪一种三角形，并说明理由；(Ⅱ)若ABC ∆的面积为240，求点A 的坐标及直线BC 的方程．O(Ⅱ)一般地，设正n 棱锥的体积V 为定值，试给出不依赖于n 的一个充分必要条件，使得正n 棱锥的表面积取得最小值．14．假定亲本总体中三种基因型式：,,AA Aa aa 的比例为:2:u v w (0,0,0,21)u v w u v w >>>++=且数量充分多，参与交配的亲本是该总体中随机的两个．(Ⅰ)求子一代中，三种基因型式的比例；(Ⅱ)子二代的三种基因型式的比例与子一代的三种基因型式的比例相同吗？并说明理由．15．设函数()1x m f x x +=+，且存在函数()1(,0)2s t at b t a ϕ==+>≠，满足2121()t s f t s-+=． (Ⅰ)证明：存在函数()(0),t s cs d s ψ==+>满足2121()s t f s t +-=； (Ⅱ)设113,(),1,2,.n n x x f x n +===证明：1123n n x --≤．2010年名牌大学自主招生考试试题(3)适用高校：清华大学、上海交通大学等五校(样题)一、选择题(每题5分，共25分)1.函数y=32cos sin cos x x x +-的最大值为 (A)2827 (B)3227 (C)43 (D)40272．已知a 、b 、c 、d 是实数,az bcz dω+=+, 且当Imz>0时，In ω＞0．则 (A)ad+bc>0; (B)ad+bc ＜0; (C)ad−bc ＞0; (D)ad−bc<0.3．甲、乙、丙、丁等七人排成一排，若要求甲在中间，乙丙相邻,且丁不在两端，则不同的排法共有( )(A)24种； (B)48种; (C)96种; (D)120种4．己知F 为抛物线y 2＝2px 的焦点，过点F 的直线l 与该抛物线交于A 、B 两点,l 1、l 2分别是该抛物线在A 、B 两点处的切线，l 1、l 2相交于点C ，设|AF|=a ，|BF|=b ，则|CF|=(C)2a b+;5．设θ是三次多项式f(x)＝x 3−3x ＋10的一个根，且α=222θθ+-,若h(x)是一个有理系数的二次多项式，满足条件()h αθ=．则h(0)= (A)−2; (B)2; (C)12-; (D)12二、解答题(本大题共55分)1.(本题15分)己知f(x)是定义在R 上的奇函数，且当x ＜0时,f(x)单调递增，f(−1)=0．设函数()2sin cos 2x x m x m ϕ=+-,集合M=()|0,,02m x x πϕ⎧⎫⎡⎤∈<⎨⎬⎢⎥⎣⎦⎩⎭对任意的,N=()|0,,[]02m x f x πϕ⎧⎫⎡⎤∈<⎨⎬⎢⎥⎣⎦⎩⎭对任意的,求MN.2.(本题20分)甲、乙、丙、丁等4人相互传球，第一次由甲将球传出，每次传球时，传球者将球等可能地传给另外3人中的任何1人．(l)经过2次传球后，球在甲乙两人手中的概率各是多少？(2)经过n 次传球后，球在甲手中的概率记为p n (n=1,2,…) ,试求1n P +与n P 的关系式,并求n P 的表达式及lim n n P →∞3.(本题20分)设p 、q 是一元二次方程x 2+2ax−1=0(a>0)的两个根．其中p ＞0，令y 1=p−q,yn+1=2n y −2,n=1,2，…，证明：11212111lim ......n n y y y y y y →∞⎛⎫+++⎪⎝⎭=p. 2010年北京大学、香港大学、北京航空航天大学三校联合自主招生考试试题(数学部分)1．(仅文科做)02απ<<，求证：sin tan ααα<<．(25分) 2．AB 为边长为1的正五边形边上的点．证明：AB(25分)3．AB 为21y x =-上在y 轴两侧的点，求过AB 的切线与x 轴围成面积的最小值．(25分)4．向量OA 与OB 已知夹角，1OA =，2OB =，(1)OP t OA =-，OQ tOB =，01t ≤≤．PQ 在0t 时取得最小值，问当0105t <<时，夹角的取值范围．(25分)5．(仅理科做)存不存在02x π<<，使得sin ,cos ,tan ,cot x x x x 为等差数列．(25分)。

北京大学 2010 年自主招生试题

北京大学2010 年自主招生试题1.Ca 在空气中燃烧的固体产物溶于水，放热，放出有臭味的气体，写出方程式。

2.同样浓度下，醋酸和氨水的电离程度相同，但氢氧化铝可以完全溶于醋酸，却不能溶于氨水，问这能说明氢氧化铝的什么性质？3.和水一样，酯也可以在氨中发生氨解反应，写出RCOOR'的氨解反应方程式。

4.不同于水溶液，在液氨的环境中，"不活泼"金属可以将"活泼"金属置换出来，如Mg+NaI =MgI+Na，解释为什么可以发生这样的反应。

5.5．Fe，Cu 溶于稀硝酸，剩余固体为以下情况时，溶液中可能的阳离子：（1）不剩余固体（2）剩余固体为Cu （3）剩余固体为Fe，Cu （4）可不可能剩余的固体只有Fe，为什么？6.6．已知C（s），氢气（g），乙醇（l）的燃烧热为394kJ/mol，286kJ/mol，1367kJ/mol，由这些可以知道哪些数据？7.7．在发烟硝酸H2SO4·SO3 中，2molI2 和3molI2O5 生成I2（SO4）3，I2（SO4）3溶于水生成I2 和I2O4，写出以上两个方程式。

8.8.测定溶液中I¯的方法，当I¯太少时可用增大倍数的方法，第一种：用氯气将I¯氧化为HIO3，后除去多余氯气，用KI 还原HIO3 后测定I¯的量；第二种：用IO4¯将I¯氧化为IO3¯，加入一种物质阻止IO4¯和I¯反应，用KI 还原IO3¯后测定I¯的量。

问以上两种方法分别将I¯扩大了多少倍？2009 北京大学自主招生语数外物化试题（理科）化学1 填充题（1）在NaCl 的溶液里有Mg2+（NaOH），SO42-（BaCl2），Ca2+（Na2CO3）等杂质离子，括号中是除杂的试剂，加入试剂的顺序为（2）电解熔融LiCl，得到Li 和Cl2。

2010年全国部分高校自主招生语文试题辑录

2010年全国部分高校自主招生语文试题辑录.h1{FONT-WEIGHT:bold;TEXT-JUSTIFY:inter-ideograph;FONT-SIZE:22pt; MARGIN:17pt0cm16.5pt;LINE-HEIGHT:240%;TEXT-ALIGN:justify}.h2{FONT-WEI GHT:bold;TEXT-JUSTIFY:inter-ideograph;FONT-SIZE:16pt;MARGIN:13pt0cm;L INE-HEIGHT:173%;TEXT-ALIGN:justify}.h3{FONT-WEIGHT:bold;TEXT-JUSTIFY: inter-ideograph;FONT-SIZE:16pt;MARGIN:13pt0cm;LINE-HEIGHT:173%;TEXT-A LIGN:justify} 由于今年武大重新调整了笔试分值，因此试卷未出现大-想象作文题，语文卷只有一道小-想象作文，要求学生依“×季的情趣”为题，从“春夏秋冬”四季中任选一篇短文素胚勾勒出青花笔锋浓转淡，瓶身描绘的牡丹一如你初妆……有什么语法错误？”近日，在北大自主招生试题中，周杰伦这首《青花瓷》中的歌词被作为错误的语法版本，成为一道纠错题语文考试的-想象作文给出一段腐败官员对腐败行为的辩解，称腐败可以促进消费、拉动经济、促进人员之间的感情、有利于社会和谐，要求考生驳斥这种言论，至少要引用5句古诗词。

有一道语文题让考生曲解成语，给出的例子是“度日如年”，曲解为日子过得快乐得和过年一样，让考生再想两个曲解成语的例子有一题出上联“博雅塔前人博雅”，叫学生以北大的景物对下联，着实难倒了不少考生从“酷”“粉丝”“小众化”“媒体”等十个流行名词中选择5个，来解释其含义。

清华大学：《汉书·艺文志》中有“小说家者流，盖处于稗官，街谈巷语，道听途说者之所造也……”先用中文解释其含义，再用英文概括其大意，并用英文评论其观点。

清华大学等自主招生

2010年北大清华浙大复旦等8所名校自主招生试题（word版）2010年清华大学自主招生试题语文：语文题量很大，包括两篇现代文阅读、古诗词鉴赏、古文翻译、古文断句等。

两篇现代文阅读，一篇为“科学与人文”摘自杨叔子《融则利而育全人》一书，所选段落涉及DNA知识、《红楼梦》、《老子》、《大学》等诸多内容。

另一篇是俄国作家蒲宁的文章《山口》。

此外有一篇古代诗文阅读《寻陆鸿渐不遇》。

两篇文言文阅读，断句，以及将《论语·泰伯》、《世说新语·汰侈》部分段落译为现代汉语。

作文是材料作文，有五十分，题目为“网瘾”。

卫生部日前发出通知称：“电击治疗网瘾”技术的安全性尚不确切，暂不宜应用于临床。

《中国青年报》：在过去三年里，已有近3000名网瘾少年在某网瘾戒治中心接受过电击治疗。

《亚太经济时报》：从电击疗法寿终正寝推及其他对青少年的教育方法，问题的根本在于教育已到了革故鼎新的时刻。

《东方早报》：当孩子网络成瘾后，学校除了把孩子当作“差生”、“问题生”推给家长之外，并没有针对这些孩子开展相应的教育。

《新民晚报》：治疗网瘾已成为迫切需要解决的时代课题，有效的治疗手段，一定会带来巨大的利润。

新浪网：一旦网瘾确实能被电击治愈，那么如烟瘾、酒瘾等好多棘手问题都将成为科学实验室的目标。

请联系社会实际，选择一个角度进行探讨，发表你的见解。

写一篇不少于800字的论述文。

文科综合特色测试有关国庆阅兵的军事知识，还考了经济学、心理学知识、蝴蝶效应、东盟自由贸易区、有关澳门回归的《七子之歌》等，此外，还有《哈姆雷特》、《双城记》等英文原著的经典语句以及国际组织的英文缩写等。

其中写作题还出自一位境外学者之手，要求考生以梁漱溟的一段话，结合自己的实际生活，撰写短文阐述中国人是权利本位还是责任本位。

另外考察了“猪肉价格下降的原因”、“三农问题含义”等与农村考生联系密切的知识点。

选择出维吾尔族的特征：题干部分涉及藏族建筑(碉房)，维吾尔族的地方舞蹈(十二木卡姆)，维吾尔族的日常饮食(馕)和维吾尔族的历史(回鹘)等。

江苏地区2010年普通高校单独招生统一试卷机电专业综合理论试卷

绝密★启用前江苏省2010年普通高校单独招生统一试卷机电专业综合理论试卷本试卷分第Ⅰ卷（客观题）和第Ⅱ卷（主观题）两部分。

第Ⅰ卷1页至4页，第Ⅱ卷5页至14页。

两卷满分300分。

考试时间150分钟。

第I卷( 共85分)注意事项：1．答第Ⅰ卷前，考生务必按规定要求填涂答题卡上的姓名、准考证号等项目。

2．用2B铅笔把答题卡上相应题号中正确答案的标号涂黑。

答案不涂写在答题卡上无效。

一、判断题（本大题共14小题，每小题2分，共28分。

下列每小题表述正确的在答题卡上将A涂黑，错误的将B涂黑。

）1．当电路处于开路状态时，电源端电压和负载上的电压都等于0。

2．虽然电路中某点电位的高低与参考点的选择有关，但两点间的电压是这两点的电位之差，所以两点间电压的大小与参考点的选择无关。

3．用万用表R×1 k挡判别一只10 μF电容器的性能。

测量时发现，指针偏转后稳定在刻度盘的中部。

这说明该电容器的质量是好的。

4．只要穿过线圈中的磁通发生改变，就必然产生电磁感应，但不一定产生感应电流。

5．额定电压为220 V的交流电磁铁，在直流220 V下使用时，会有因过流而烧毁线圈的危险。

6．在日光灯电路两端并联一个容量适当的电容器后，电路的功率因数提高了，灯管亮度增强了。

7．在题7图中，列举了三眼插座的4种接法，其中只有第4种接法是正确的。

LN1243题7图8．改变三相异步电动机转向的方法是改变电源相序，即任意交换两根电源相线的位置，而改变电容分相式单相异步电动机转向的方法是交换电源相线与零线的位置。

9．单相半波整流电路中，如把晶体二极管反接，则电路将发生短路事故。

10．正负逻辑体制是人为规定的，其选择不影响电路本身的逻辑功能。

11．摩擦轮传动中若阻力矩小于摩擦力矩，两轮接触处将出现“打滑”现象。

12．在柱体凸轮机构中，从动件可以通过直径不大的圆柱凸轮或端面凸轮获得较大的行程。

13．降低空气温度可以降低空气中水蒸气的含量。

2010年自主招生考试样题_数学

数学试题一、选择题：本大题共12个小题，每小题3分，共36分．在每小题给出的四个选项中，只有一项是符合题目要求的．1.4的算术平方根是 ( )A ．±2B ．2C ．2D ．±2．旱魃肆虐，河流干涸，大地荒芜，近期西南旱情时时牵动着人们的心，截至3月30日，兰州市三县五区受旱农田面积已经达到176.81万亩，将176.81万亩用科学记数法表示为（）A ．176.81×104亩B ．1.77×106亩C ．1.7681×104亩D ．1.7681×106亩 3．从小明、小凡、小丽、小红四人中用抽签的方式，选取两人为上海世博会的志愿者，那么能选中小明、小丽两人同时为上海世博会志愿者的概率为（）A ．14B ．112C ．12D ．164．某物体的三个视图如图所示，该物体的直观图是（） 5．如图4，边长为1的正方形ABCD 绕点A 逆时针旋转300，得到正方形A ＇B ＇C ＇D ＇，则图中阴影部分的面积为（） A ．12 B ． C ．1- D ．1- 6．据报道，在4月22日世界地球日来临之际，世界各地呼吁人们关注地球，热爱地球，珍爱生命，创建和谐世界大型庆祝活动中，四个大城市参加庆祝活动人数统计如下表：A ．27，28B ．27.5，28C ．28，27D ．26.5，27A ．B ．C ．D ． A 第5题图7．如图，正方形ABCD 的边长为2，点E 在AB 边上．四边形EFGB 也为正方形，设△AFC 的面积为S ，则 ( ) A ．S=2 B ．S=2.4 C ．S=4 D ．S 与BE 长度有关8．连接边长为1的正方形对边中点，可将一个正方形分成２个大小相同的长方形，选右边的长方形进行第二次操作，又可将这个长方形分成２个更小的正方形……重复这样的操作，经过仔细地观察与思考，猜想n n )21()21()21()21(21132+++++- 的值等于（） A ．1 B ．n)21(C .1)21(1--nD ．n)21(1-9．如图，在四边形ABCD 中，动点P 从点A开始沿A B CD 的路径匀速前进到D 为止。

复旦大学自主招生试题2010

复旦大学自主招生试题（2009.2）(2009-02-21 10:50:56)分类：自主招生标签：求职教育复旦金融晰杨晓倩上海杂谈核心提示：为期两天的复旦大学上海学生面试招生昨天结束，复旦的几位资深面试专家在接受早报记者采访时称，面试题目并不像笔试题目一样有标准的出题模式，面试题目出题时，面试专家有很大的自主权，每位专家独自出题。

2月11日，两名参加复旦大学自主招生面试的考生展示自己的考生报到证。

早报记者鲁海涛图“我算出来了，我算出来了。

”昨天(2月12日，下同)，沪上一间写字楼的办公室内，几个白领用笔在会议桌上比画，把“=”号移动到“-”号处，“62=63-1”的等式出现了，办公室里爆发出掌声。

白领们如此热衷的游戏是复旦大学今年自主招生面试的一道试题，面试官问学生，如何通过移动一根火柴，使得“62-63=1”的等式成立。

为期两天的复旦大学上海学生面试招生昨天结束，堪比“十万个为什么”的考题也成了白领间讨论的话题。

千奇百怪的题目究竟是如何出炉的？复旦的几位资深面试专家在接受早报记者采访时称，面试题目并不像笔试题目一样有标准的出题模式，面试题目出题时，面试专家有很大的自主权，每位专家独自出题。

252位专家准备数千题据了解，今年有252位专家参与面试，专家准备好的问题超过了数千条，专家出题时，会结合自己的专业背景，但也不囿于专业限制，还会结合考生的材料，以及考生的现场回答深入追问。

每一位考生会接受五位专家的面试，五位专家组成的面试组会在面试前一个小时就自己事先准备的题目进行统筹，去掉重复的，“不过，在面试中，不同的专家出同样的问题也有可能，但是同样的问题提问的角度肯定不一样。

”复旦的一位连续四年参加过面试的面试官表示。

复旦面试专家也提醒，那些提前进行应试程式的准备，到了面试现场背诵的考生，不会得高分，对于极个别“背诵”答案、力求回答正确的考生，考官反而要扣分，“一旦发现考生在"背"，我们就会马上跳过，所以考前集训没有用。

2010年各大学自主招生面试题

上海交大2010年自主招生面试题：面试时5名考生一组，每人先用1分钟时间阐述同一个问题，然后在余下的半个小时里，小组成员一起讨论另一问题。

如果进入交大，交大能为你带来什么?你能为交大带来什么?对于谷歌退出中国，你们怎么看?你对火车票实名制的看法。

请对海地地震、汶川地震发表自己的看法。

2009自主招生面试题：三国演义中谁的名字是双名?你眼中的…90后‟是什么样的?浙江大学2010年房价是涨还是跌?佛山优势有哪些?奥巴马获诺贝尔和平奖。

上海迪斯尼的利与弊。

真小人还是伪君子。

正说历史与戏说历史。

高学历与高素质。

天空为什么是蓝色?干净的海水为什么是绿色?如何杜绝大头娃娃、三鹿等类似事件?近期温家宝总理在剑桥大学演讲被打断，你如何看待?妈妈做的哪些事对你产生很大影响?假如你是中学校长，为实施素质教育你将首先做哪几件事?北京奥运会有什么负面影响?2008年发生了什么大事?明年上海将举行世博会，口号是什么?你觉得你将在其中扮演什么角色?此次金融危机是金融还是经济先开始出现问题?对衢州人懒、经济落后的说法有什么看法?成绩考差了怎么办?对大学有什么期望?如果发现不符合期望怎么办?找工作时，看重薪水还是专业对口?"范跑跑"现象你如何看待?如何看待"人肉搜索"现象?某医生在工作了一年后转行到了银行，对此有何看法?如果你是老板，有200名员工，在金融危机下，你会怎样裁员?一个铺好地板的房间水管铺错了，在不弄坏地板的情况下，如何确定水道走向?大学毕业后，你面临两份工作：一份专业对口而工资很低，一份专业不对口而工资较高，你怎么选择?中山大学你怎么看待开心农场的…偷菜‟行为?”如何看待“偷菜”改为“摘菜”?假如没有光纤会怎样?谈谈太空旅游。

你准备选择什么专业?为什么?你最喜欢中国的哪个节日?人民币应该升值吗?”设想一种自主招生的模式。

你怎么看chimerica(中美国)这个单词?孔子、苏东坡名言有哪些?谈谈对孔子“己欲立而立人，己欲达而达人”这句话的理解。

2008-2010年清华大学自主招生试卷

2008年清华大学考题1.求()x e f x x=的单调区间及极值.2.设正三角形1T 边长为a ，1n T +是n T 的中点三角形，n A 为n T 除去1n T +后剩下三个三角形内切圆面积之和.求1lim nk n k A →∞=∑.3.已知某音响设备由五个部件组成，A 电视机，B 影碟机，C 线路，D 左声道和E 右声道，其中每个部件工作的概率如下图所示.能听到声音，当且仅当A 与B 中有一工作，C 工作，D 与E 中有一工作；且若D 和E 同时工作则有立体声效果.求：（1）能听到立体声效果的概率；（2）听不到声音的概率.4.(1)求三直线60x y+=，1 2y x=，0y=所围成三角形上的整点个数；(2)求方程组21260y xy xx y<⎧⎪⎪>⎨⎪+=⎪⎩的整数解个数.5.已知(1,1)A--，△ABC是正三角形，且B、C在双曲线1(0)xy x=>一支上.(1)求证B 、C 关于直线y x =对称；(2)求△ABC 的周长.6.对于集合2M R ⊆，称M 为开集，当且仅当0P M ∀∈，0r ∃>，使得20{}P R PP r M ∈<⊆.判断集合{(,)4250}x y x y +->与{(,)0,0}x y x y ≥>是否为开集，并证明你的结论.2009年清华大学自主招生数学试题第一天（共11题，艺术生做1－7，10－11，其他考生1－9题）1.求公差是8、由三个质数组成的数列。

2.证明：一个2n+1项的整数数列，它们全部相等的充分必要条件是满足条件p ，条件p 为任意取出2n 个数，都存在一种划分方法，使得两堆数每堆含有n 个数，并且这两堆数的和相等。

3.四面体ABCD,AB=CD,AC=BD,AD=BC 。

（1）求证：这个四面体的四个面都是锐角三角形。

（2）设底面为BCD ，设另外三个面与面BCD 所形成的二面角为α，β，γ。

同济大学_自主招生_数学_真题

同济大学2010年暨保送生考试数学试题一、填空题1．f (x )是周期为2的函数，在区间[-1,1]上，f (x )=|x |，则3(2)2f m +=___(m 为整数)． 2．函数y =cos2x -2cos x ,x ∈[0,2π]的单调区间是__________________． 3．函数2y =__________________．4．5．函数y ＝f (x )，f (x +1)-f (x )称为f (x )在x 处的一阶差分，记作△y ，对于△y 在x 处的一阶差分，称为f (x )在x 处的二阶差分△2y ，则y ＝f (x )＝3x ·x 在x 处的二阶差分△2y =____________． 6．7．从1～100这100个自然数中取2个数，它们的和小于等于50的概率是__________． 8．正四面体ABCD ，如图建立直角坐标系，O 为A 在底面的投影，则M 点坐标是_________，CN 与DM 所成角是_________． 9．双曲线x 2-y 2＝1上一点P 与左右焦点所围成三角形的面积___________．10．椭圆22143x y +=在第一象限上一点P (x 0,y 0)，若过P 的切线与坐标轴所围成的三角形的面积是_________．二、解答题11．不等式22222log 0364x kx kx x ++<++对于任意x ∈R 都成立，求k 的取值范围． 12．不动点，()bx c f x x a +=+．(1) 12,3为不动点，求a ,b ,c 的关系；(2) 若1(1)2f =，求f (x )的解析式；(3) 13．已知sin cos ([0,2))2sin cos y θθθπθθ⋅=∈++，(1) 求y 的最小值；(2) 求取得最小值时的θ．14．正三棱柱ABC －A 1B 1C 1，|AA 1|=h ，|BB 1|=a ，点E 从A 1出发沿棱A 1A 运动，后沿AD 运动，∠A 1D 1E =θ，求过EB 1C 1的平面截三棱柱所得的截面面积S 与θ的函数关系式． 15．已知数列{a n }满足112n n n a a a -++=． (1) 若b n ＝a n -a n -1(n=2,3,…)，求b n ；(2) 求1ni i b =∑；(3) 求lim nn a→∞．16．抛物线y 2＝2px ，(1) 过焦点的直线斜率为k ，交抛物线与A ,B ，求|AB |．(2) 是否存在正方形ABCD ，使C 在抛物线上，D 在抛物线内，若存在，求这样的k ，正方形ABCD 有什么特点？同济大学2010年自主招生优秀考生文化测试数学试卷BAC D A 1D 1 C 1 B1一、填空题（本大题共有8题，只要求直接填写结果，每题答对得5分，否则一律得零分，本大题满分40分） 1．函数12()log (sin cos )f x x x =+的单调递增区间是_______________________．2．如图所示，为某质点在20秒内作直线运动时，速度函数()v v t =的图象，则该质点运动的总路程s =_____（厘米）．3．设a 与b 是两条非相互垂直的异面直线，α与β分别是过直线a 与b 的平面，有以下4个结论：(1) b //α，(2) b ⊥α，(3) β//α，(4) β⊥α，则其中不可能出现的结论的序号为__________．4．设某地于某日午后2时达到最高水位，为3.20米，下一个最高水位恰在12小时后达到，而最低水位为0.20米。

自主招生真题集萃

目录2010年华约自招——数学 (1)2011年华约自招——数学 (3)2011年卓越自招——数学 (5)2012年华约自招——数学 (7)2012年卓越自招——数学 (9)2013年北约自招——数学 (11)2013年华约自招——数学 (12)2013年卓越自招——数学 (13)2010年华约自招——物理 (15)2011年华约自招——物理 (18)2012年华约自招——物理 (21)2012年卓越自招——物理 (24)2013年北约自招——物理 (27)2013年华约自招——物理 (29)2013自招整体评析 (31)2013自主招生“北约”“华约”“卓越”数学试卷评析 (32)2013自主招生“北约”“华约”“卓越”物理试卷评析 (33)2013自主招生“北约”“华约”“卓越”语文试卷评析 (34)2013自主招生“华约”数学试卷解析 (35)2013自主招生“华约”数学试卷解析 (37)2013自主招生“北约”数学试卷解析 (38)2013自主招生“华约”物理试卷解析 (39)2013自主招生“北约”物理试卷解析 (41)2010年华约自招——数学即2010年五校合作自主选拔通用基础测试一、选择题：本大题共10小题，每小题3分，在每小题给出的四个选项中，只有一项是符合题目要求的．1．设复数21a i w i +⎛⎫= ⎪+⎝⎭，其中a 为实数，若w 的实部为2，则w 的虚部为A ．32-B ．12-C ．12D ．322．设向量a b ，满足1a b a b m ==⋅=，，则()a tb t +∈R 的最小值为A ．2 BC ．1 D3．如果平面αβ，，直线m n ，，点A B ，满足：m n A B αβαβαβ⊂⊂∈∈，，，，，∥且AB与α所成的角为π4m AB n ，，⊥与AB 所成的角为π3，那么m 与n 所成角的大小为A ．π3B ．π4C ．π6D ．π84．在四棱锥V ABCD -中，11B D ，分别为侧棱VB VD ，的中点，则四面体11AB CD 的体积与四棱锥V ABCD -的体积之比为 A ．1:6 B ．1:5 C ．1:4 D ．1:35．在ABC △中，三边长a b c ，，满足3a c b +=，则tan tan 22A C的值为A ．15B ．14C ．12D ．236．如图ABC △的两条高线AD BE ，交于H ，其外接圆圆心为O ，过O 作OF 垂直BC 于F ，OH 与AF 相交于G ，则OFG △与GAH △面积之比为A ．1:4B ．1:3C ．2:5D ．1:27．设()()0ax f x e a =>，过点()0P a ，且平行于y 轴的直线与曲线():C y f x =的交点为Q ，曲线C 过点Q 的切线交x 轴于点R ，则PQR △的面积的最小值是A ．1 BC ．2e D ．24e8．设双曲线()2212:204x y C k a k a -=>>，，椭圆2222:14x yC a +=，若2C 的短轴长与1C 的实轴长的比值等于2C 的离心率，则1C 在2C 的一条准线上截得线段的长为A． B ．2 C． D ．49．欲将正六边形的各边和各条对角线都染为n 种颜色之一，使得以正六边形的任何3个顶点作为顶点的三角形有3种不同颜色的边，并且不同的三角形使用不同的3色组合，则n 的最小值为 A ．6 B ．7 C ．8 D ．910．设定点A B C D 、、、是以o 点为中心的正四面体的顶点，用σ表示空间以直线OA 为轴满足条件()B C σ=的旋转，用τ表示空间关于OCD 所在平面的镜面反射，设l 为过AB 中点与CD 中点的直线，用ω表示空间以l 为轴的180旋转，设στ表示变换的复合，先作τ，再作σ，则ω可以表示为 A ．στστσ B ．στστστ C ．τστστ D ．στσστσFDBCOGH E A二、解答题：解答应写出文字说明，证明过程或演算步骤． 11．（本题满分14分）在ABC △中，已知22sin cos212A BC +==，外接圆半径2R =．⑴ 求角C 的大小；⑵ 求ABC △面积的最大值． 12．（本题满分14分）设A B C D ，，，为抛物线24x y =上不同的四点，A D ，关于该抛物线的对称轴对称，BC 平行于该抛物线在点D 处的切线l ．设D 到直线AB ，直线AC 的距离分别为12d d ，，已知12d d +=．⑴ 判断ABC △是锐角三角形、直角三角形、钝角三角形中的哪一种三角形，并说明理由； ⑵ 若ABC △的面积为240，求点A 的坐标及直线BC 的方程． 13．（本小题满分14分）⑴ 正四棱锥的体积3V =求正四棱锥的表面积的最小值；⑵ 一般地，设正n 棱锥的体积V 为定值，试给出不依赖于n 的一个充分必要条件，使得正n 棱锥的表面积取得最小值．14．（本小题满分14分）假定亲本总体中三种基因型式：AA Aa aa ，，的比例为:2:(0002u v w u v w u v >>>+，，， 1)w +=且数量充分多，参与交配的亲本是该总体中随机的两个． ⑴ 求子一代中，三种基因型式的比例；⑵ 子二代的三种基因型式的比例与子一代的三种基因型式的比例相同吗？并说明理由． 15．（本小题满分14分）设函数()1x m f x x +=+，且存在函数()102s t at b t a φ⎛⎫==+>≠ ⎪⎝⎭，，满足2121t s f t s -+⎛⎫=⎪⎝⎭． ⑴ 证明：存在函数()()0t s cs d s φ==+>，满足2121s t f s t +-⎛⎫=⎪⎝⎭； ⑵ 设()11312n n x x f x n +===，，，，，证明：1123n n x --≤．2011年华约自招——数学即2011年高水平大学自主选拔学业能力测试一、选择题1．设复数z 满足1z <且152z z +=则z =（） A ．45 B ．34 C ．23 D ．122．在正四棱锥P ABCD -中，M N 、分别为PA PB 、的中点，且侧面与底面所成二面角的正切为DM 与AN 所成角的余弦为（） A ．13 B ．16 C ．18D ．1123．过点（-1,1）的直线l 与曲线3221y x x x =--+相切，点（-1,1）不是切点，则直线l 的斜率是（） A ．2 B ．1 C ．-1 D ．-24．若2π3A B +=，则22cos cos A B +的最小值和最大值分别为（）A．312， B ．1322， C．11+ D．112+， 5．如图，1O 和2O 外切于点2C O ，又都和O 内切，切点分别为A B ，．设AOB ACB αβ∠=∠=，，则（）A ．cos sin02αβ+= B ．sin cos02αβ-=C ．sin 2sin 0βα+=D ．sin 2sin 0βα-=6．已知异面直线a b ，成60︒角．A 为空间一点则过A 与a b ，都成45︒角的平面（）A 有且只有一个B 有且只有两个C 有且只有三个D 有且只有四个7．已知向量()()313101112222a b c xa yb zc ⎛⎫⎛⎫==--=-++= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭，，，，，，，则222x y z ++的最小值为（）A ．1B ．43C ．32D ．28．AB 为过抛物线24y x =焦点F 的弦，O 为坐标原点，且135OFA ∠=︒，C 为抛物线准线与x 轴的交点，则ACB ∠的正切值为（）A ．BC D9．如图，已知ABC △的面积为2，D E ，分别为边AB ，边AC 上的点，F 为线段DE D 上一点，设ADAE DFx y z AB AC DE ===，，，且1y z x +-=，则BDF △面积的最大值为（） A ．827 B ．1027C ．1427D ．1627A D E F10．将一个正11边形用对角线划分为9个三角形，这些对角线在正11边形内两两不相交，则（）A ．存在某种分法，所分出的三角形都不是锐角三角形B ．存在某种分法，所分出的三角形恰有两个锐角三角形C ．存在某种分法，所分出的三有形至少有3个锐角三角形D ．任何一种分法所分出的三角形都恰有1个锐角三角形二、解答题11．已知ABC △不是直角三角形．⑴ 证明：tan tan tan tan tan tan A B C A B C ++=；⑵若tan tan 1tan B CC A+-=，且sin 2sin 2sin 2sin 2A B B C ，，，的倒数成等差数列，求cos 2A C-值． 12．已知圆柱形水杯质量为a 克，其重心在圆柱轴的中点处（杯底厚度及重量忽略不计，且水杯直立放置）．质量为b 克的水恰好装满水杯，装满水后的水杯的重心还有圆柱轴的中点处． ⑴ 若3b a =，求装入半杯水的水杯的重心到水杯底面的距离与水杯高的比值； ⑵ 水杯内装多少克水可以使装入水后的水杯的重心最低？为什么？13．已知函数()()2121123x f x f f ax b ⎛⎫=== ⎪+⎝⎭，，．令()1112n n x x f x +==，．⑴ 求数列{}n x 的通项公式； ⑵ 证明12112n x x x e +>． 14．已知双曲线()221222:100x y C a b F F a b -=>>，，，分别为C 的左右焦点．P 为C 右支上一点，且使12π3F PF ∠=，又12F PF △的面积为2．⑴ 求C 的离心率e ；⑵ 设A 为C 的左顶点，Q 为第一象限内C C 上的任意一点，问是否存在常数()0λλ>，使得22QF A QAF λ∠=∠恒成立．若存在，求出λ的值；若不存在，请说明理由．F 1F 2x2a 2cPE FP15．将一枚均匀的硬币连续抛掷n 次，以n p 表示未出现连续3次正面的概率．⑴ 求1234p p p p ，，，；⑵ 探究数列{}n p 的递推公式，并给出证明；⑶ 讨论数列{}n p 的单调性及其极限，并阐述该极限的概率意义．2011年卓越自招——数学一、选择题：本大题共10小题，每小题3分，在每小题给出的四个选项中，只有一项是符合题目要求的．1.向量,a b 均为非零向量，()2a b a -⊥，()2b a b -⊥，则,a b 的夹角为（） A ．6π B.3π C.23π D.56π 2.已知()sin 2sin 2n αγβ+=，则()()tan ()tan αβγαβγ++=-+A ．11n n -+ B. 1n n + C.1n n - D.11n n +- 3.在正方体1111ABCD A B C D -中，E 为棱1AA 的中点，F 是棱11A B 上的点，且11:1:3A F FB =，则异面直线EF 与1BC 所成角的正弦值为（）A ．153 B.155C.53D.554.已知抛物线的顶点在原点，焦点在x 轴上，ABC ∆三个顶点都在抛物线上，且ABC ∆的重心为抛物线的焦点，若BC 边所在直线的方程为4200x y +-=，则抛物线方程为（）A ．216y x = B.28y x =C. 216y x =-D. 28y x =-5.在三棱柱111ABC A B C -中，底面边长和侧棱长均等于2，且E 为1CC 的中点，则点1C 到平面1AB E 的距离是（） A ．3B.2C.32D.226.若关于x 的方程24xkx x =+有四个不同的实数解，则k 的取值范围是（）A ．()0,1 B.1,14⎛⎫ ⎪⎝⎭ C.1,4⎛⎫+∞ ⎪⎝⎭D.()1,+∞7.如图，ABC ∆内接于O ，过BC 中点D 作平行于AC 的直线l ，l 交AB 于E ，交O 于G ，F ，交O 在A 点处的切线于P ，若PE =3，ED =2，EF =3，则P A 的长为（）A ．5 B.6 C.7 D.228.数列{}n a 共有11项，11110,4,1,1,2,...,10k k a a a a k +==-==，满足这样的条件的不同数列的个数为（）A ．100 B. 120 C.140 D.1609. i 为虚数单位，设复数z 满足1z =，则2221z z z i-+-+的最大值为（）A 1 B. 2 C. 1 D. 2+10.设σ是坐标平面按照顺时针方向绕原点做角度为27π的旋转，τ表示坐标平面关于y 轴的镜面反射，用τσ表示变换的复合，先做τ，再做σ，用k σ表示连续k 次σ的变换，则234στστστσ是（） A ．4σ B. 5σ C. 2στ D. 2τσ二、解答题：解答应写出文字说明，证明过程或演算步骤． 11.（本题满分14分）设数列{}n a 满足1221,,2n n n a a a b a a a ++===+（1）设1n n n b a a +=-，证明：若a ≠b ，则{}n b 是等比数列；（2）若()12lim ...4n n a a a →∞+++=，求a 、b 的值12.（本题满分14分）在ABC ∆中，AB =2AC ，AD 是A 的角平分线，且AD =kAC 。

2010年自主招生数学试题

北京大学：1.AB为y=1-x^2上在y轴两侧的点，求过AB的切线与x轴围成面积的最小值。

2.向量OA与OB已知夹角，|OA|=1，|OB|=2，OP=tOA，OQ=（1-t）OB，|PQ|在t0是取得最小值，问当0<t0<1/5时，夹角的取值范围。

3.存不存在0<x<π/2，使得sinx,cosx,tanx,cotx为等差数列。

上海交通大学：1．两个等差数列200，203，206，…和50，54，58…都有100项，它们共同的项的个数是__________．2．方程7x2 (k+13)x+k2 k 2＝0的两根分别在区间(0,1)和(1,2)内，则k的取值范围是__________．3．将3个相同的球放到4个盒子中，假设每个盒子能容纳的球数不限，而且各种不同的放法的出现是等可能的，则事件"有3个盒子各放一个球"的概率是________．4．若今天是星期二，则31998天之后是( )A．星期四B．星期三C．星期二D．星期一5．若一项数为偶数2m的等比数列的中间两项正好是方程x2+px+q＝0的两个根，则此数列各项的积是( )A．pm B．p2m C．qm D．q2m6．设f '(x0)＝2，则( )A．2 B．2 C．4 D．4）7．已知正数列a1，a2，…，an，且对大于1的n有，．试证：a1，a2，…，an中至少有一个小于1．8．设3次多项式f(x)满足：f(x+2)＝f( x)，f(0)＝1，f(3)＝4，试求f(x)．9．设在x＝0处可导，且原点到f(x)中直线的距离为，原点到f(x)中曲线部分的最短距离为3，试求b，c，l，m的值．(b,c>0)10．两名射手轮流向同一目标射击，射手甲和射手乙命中目标的概率都是．若射手甲先射，谁先命中目标谁就获胜，试求甲、乙两射手获胜的概率．。

2010年自主招生考试样题_英语

英语试卷本试卷分为第Ⅰ卷和第Ⅱ卷两部分，满分150分, 考试时间120分钟。

第Ⅰ卷（选择题，共100分）第一部分：英语知识运用（共两节，满分50分）第一节：单项填空（共20小题，每小题1分，满分20分）从（A、B、C、D）四个选项中，选出可以填入空白处的最佳选项.1. Harry Potter and the Sorcerer’s Stone was such _____ most interesting novel that many children want to read it _____ second time.A. a; aB. the; aC. the; theD. /; the2. Lucy tried her best to find a good job in the city , but she had no _______ .A. troubleB. ideaC. luckD. time3.—It’s not so difficult , Mr Green , I want ___________ .— Come on , please .A. tryB. a goC. startingD. to happen4.There are quite a few old books on the shelf , but _________ of them is useful to him .A. bothB. allC. neitherD. none5. —I don’t think it very expensive t o buy a family computer here .—Really ? I’ll buy _________ next week .A. itB. thisC. oneD. mine6._______ all the passengers are here , why don’t we start at once ?A. As soon asB.WhenC.Now thatD.After7. —I’m going to Hangzhou for a holiday this weekend .— _______ you are there , can you buy me some green tea ?A. BecauseB. WhileC. IfD. Though8. ----I _______his telephone number.----- I have his number,but I ___________to bring my phone book.A.forgot,forgetB.forget,forgetC.forget,forgotD. forgot,forgot9. _______ the night before Christmas Day , parents fill their children’s stocking with small presents .A. InB. AtC. ToD. On10.—Why do you like the music?—Because it reminds me __ my childhood..A. ofB. about.C.onD.for11.The coat bought last week is too big for me . I’d like to change it for a_______ one .A. smallB. largeC. nicerD. smaller12. Everyone except Bill and Jim ______there when the meeting began.A. wasB. isC. areD. were13. This kind of cloth________well.A．wash B．is washed C．washes D．washing14. He often helps the students _____ he thinks are not quick at their studies.A. whomB. whoC. whenD. because15. Some rules are almost the same _______in the world, but rules of etiquette can be different from place to place.A. somewhereB. anywhereC. nowhereD. everywhere16. ---Tom will take care of our cat while we're away.---_______________A. It doesn't matter.B. I'll do it myself.C. That's very kind of him.D.You are welcome17 The teacher explained the question again to make herself ________.A. understandB. to understandC. understandingD. understood18 The life we were used to __________ greatly since 1992.A. changeB. has changedC. changingD. have changed19. ---- How long do you think it is______ he arrived here?---- No more than half a year, I believe.A. whenB. thatC. beforeD. since20. Help! Tom ________ an accident.A. will haveB. has hadC. was havingD. had had第二节：完形填空（共15小题，每小题2分，满分30分）阅读下列短文，从短文后各题所给的(A、B、C、D)四个选项中选出能填入相应空白处的最佳选项。

2010自主招生试题及答案

2010自主招生试题及答案【篇一：2010孝高英语自主招生试题及参考答案】参考)１．答题前，考生务必将自己所在县（市，区），毕业学校，考号，姓名填写在试卷上，答题卡上指定的位置．２．选择题选出答案后，用２Ｂ铅笔把答题卡上对应题目的答案标号涂黑；非选择题的答案必须写在答题卡的指定位置，在本试卷上答题无效．３．本试卷满分１２０分，考试时间９０分钟．第一部分：单项填空（共２０小题，每小题１分，满分２０分）从四个选择中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑．1.my father is ___university teacher. he always works very hard. aa. ab. anc. thed./2.jack,a friend of _______,keeps healthy by taking an activepart in sports and recreation. da. meb.ic. myd. mine3.there is still _____fish on the plate. please finish it off. ba. littleb .a little c. few d. a few.4.thanks to elaine. with her help, we finished the work an hour ______.ca. earlyb. earliestc. earlierd. the earliest5.he can hardly wait to hear the good news,__________? ba. can’t heb. can hec. does hed. doesn’t he6.since you are very tied, you ________finish the work today. you should go home earlier. aa. needn’tb. may notc. mustn’td. can’t7.try your best, ____you will make a great progress in your study. da. butb. ifc. ord .and8.let john ___milk and bread for breakfast himself. he’s ten years old now. aa. buyb. buysc. boughtd. is buying.9.a lot of workers set out to build the bridge _____a windy day. ba .inb .on c. atd. of10.after _____talk, they decided to go to beijing on holiday. da. two hourb. two hoursc. two-hoursd .two hours’11.---can we get together on saturday or sunday?---i’m afraid _______day is possible. da. eitherb. each c .bothd. neither12.”would you like me to show you the way?” the volunteersaid __to the tourist. da. lovelyb. likelyc. kindly d .friendly13.nowadays many people are too busy to ____a holiday with the family. ba. gob. affordc. offerd. cost.14.i _____vegetables to meat because they are good for my health. ca .produce b. prepare c. preferd. process15.i can’t ______the maths problem within an hour. it’s very difficult. ba. talk out b .work out c. put outd. look out16.many students have to ___their hobbies because of their busy school work. aa. give upb .put up c. stay upd .look up17.don’t forget to ____the lights and the tv in the sitting room before going to bed. ca. turn overb. turn onc. turn offd. turn up18.---have you read these books?---yes ,i _____them three days ago. aa .read b. have readc. have done d. did19.---_____will the astronaut be away from the earth? b---for about one month.a .how soon b. how long c. how oftend. how much20.---shall we make a pizza by ourselves instead of buying one? c---_______.a. the same to you .b. don’t worry. c .that’s a good idea.d .sodid i .第二部分:完形填空(共20小题;每小题1.5分,满分30分)阅读下列短文,从短文后所给各题的四个选项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑.on father’s day, i spent the day with my granddaughter emma. soon after i21my son’s home, emma told me that she 22to read me a story. emma has just finished kindergarten. she read meher 23 story the red rose. i was surprised24emma actuallyread the story, word25 word, from the book.it is a short story of a young boy who falls in love with a little girl who always26a small red rose on her head. they grow up and get married, and though he asks her27 she always wears the rose, she does not28 his question. finally in their 29 age, as she is lying on her death bed, she tells him to take off the rose. slowly and 30 he takes off the red rose and as he does, she31 and becomes a red rose.emma loves this story. she read it32 twice that day. then at bedtime, she told me the story again, this time in her own 33 .i wondered at how she 34 the story’s plot line, the vocabulary of the story, and the flow of the words. she did not try to 35the whole story word for word, but she used nearly the exact phrases she had read 36 .the point i want to make is that stories have a37 impact（作用）on the development of children. they help children understand the 38 around them and they also help children find39 for the way things are. storytelling helps them understand events, cause and effect, good and bad, and the list40 .21. a. look overb. arrived atc. went through d. set upb22. a. fearedb. pretended c. forgot d. wantedd23. a. favorite b. happy c. own d. boringa24. a. since b. as c. untild. beforeb25. a. with b. in c. for d. on c26. a. wears b. dressesc. puts d. takes a27. a. if b. becausec. why d. so c28. a. like b. repeat c. replyd. answerd29. a. middleb. colorful c. important d. oldd30. a. carefullyb. bravelyc. strangely d. casually a31. a. cries b. disappearsc. growsd. jumps b32. a. at last b. at mostc. at leastd. in anger c33. a. words b. bookc. voiced. experiencea34. a. lost b. understandc. read d. forgot b35. a. miss b. design c. writed. remember d36. a. betterb. louder c. earlier d. morea37. a. badb. great c. disappointing d. convincingb38. a. world b. danger c. character d. people d39. a. skillsb. newsc. reasons d. books Ｃ40. a. takes offb. turns up c. picks upd. goes ondand the list goes on数不胜数第三部分:阅读理解(共15小题,每小题2分,满分30分)阅读下列短文,从每篇短文后所给各题的四个选择中,选出最佳选项,并在答题卡上将该项涂黑.athere was once a king who had plenty of money and always bought beautiful clothes, but he was prouder of his boots than of anything else that he wore. the king had a very good servant(仆人), but he was old. one day, the old servant died and another man came to take his place.waited and waited, and then at last when he felt very hungry, he said, “please, yo ur majesty, you have not given me anything for my lunch yet.” “oh,” answered the king calmly, “it would be a waste of time to give you any food now, because you would only be hungry again in a few hours’ time.”41.what was the king proudest of according to the passage? _____ca. his old servantb. his beautiful clothesc. his bootsd. his money42.the king found a new servant because _____.ba. the new servant was young and clever.b. the old servant passed away.c. he needed the new servant to clean the boots for himd. the old servant was too old to serve him43.why did the king leave nothing for the servant to eat?____da. because the servant was not hungry.b. because the king was cruelc. because it would be a waste of time to give the servant something for his lunch.d. because he wanted to teach the lazy servant a lesson.bmany children use the internet to get useful knowledge and information, and to relax in their free time. but some of them are not using it in a good way. here are some rules to make sure you are safe and have fun on the internet.make rules for using the internet with your parents. for example, when you can go online, for how long and what activities you do online.don’t give your password（密码）to anyone else, and never leak out the following information: your real name, home address, age, school, phone number or other personal information. check with your parents before giving out a credit card (信用卡) number.never send a photo of yourself to someone in e-mail unless your parents say it’s ok.check with your parents before going into a chat room. different chat rooms have different rules and attract different kinds of people. you and your parents will want to make sure it’s a right place for you.never agree to meet anyone you meet on the internet without your parents’ permission（允许）. never meet anyone you meet online alone.always remember that people online may not be who they say they are. treat everyone online as if they were strangers.if something you see or read online makes you uncomfortable, leave the site. tell a parent or teacher right away.treat other people as you’d like to be treated. never use bad language.remember—not everything you read on the internet is true.44.it’s good for children to ____on the internet. ba. give password to othersb. get useful knowledge and informationc. give out a credit card numberd. go into a chat room as they’d like to45.the underlined phrase ”leak out ”in the third paragraph may mean ”_________”aa. make something knownb. to allow liquid or gas outc. hided. help out46.if your parents don’t ag ree never _____.ca. read anything on the internetb. relax in your free timec. have a face to face meeting with anyone you met onlined. treat other people as you’d like to be treated.47.this passage is mainly about ”_____”da. how to use computersb. surfing the internetc. information on the internetd. internet safety rulesＣmiss bailey taught me english in junior school. she cycled to school, and then when entering the school gate, she would give her bicycle to anyone of us to park it for her. it was a great honor when miss bailey gave her bicycle to you. one day shankar stood at the gate; shankar was a hunchback(驼背的人). we laughed and said, “move out of the way, shankar! miss bailey is going to enter!” miss bailey drov e in and we all rushed to offer our hands to her. but miss bailey looked past us all. “will you park it for me?”she asked. we looked back to see who it was and were surprised to see it was towards shankar. “i don’t think so, miss bailey!” stammered(结结巴巴地说) shankar. “why? you lazy fellow!”said miss bailey playfully. “you don’t want to help your teacher, do you?” “of course i want to, miss bailey!” whispered shankar. “but i might drop your cycle!” “if you drop it, you pick it up!”said the teacher with a smile.with that she gave her cycle to shankar and didn’t look to see how he’d manage. pretending she had confidence in his abilities, miss bailey turned and walked to class. we watched shankar as he held her bike. we held our breath as we thought it was goin g to fall. dinesh rushed to help. “leave it!” shankar said, and we all stopped. it seemed that his hump(驼背) disappeared as he drew himself up to his full height, and then with growing confidence, he pushed miss bailey’s cycle to the parking lot. the school bell rang, and we rushed to class. shankar was the last to enter, but we were surprised; it was a different boy who walked in.miss bailey didn’t even look at him as he walked to her and handed her the keys. fromthat day on, shankar was ready to answer the questions in class, his grades went up and a smile appeared on his face. 48. what does the underlined word “it” in the first paragraph probably refer to? ba) miss bailey’s bike b) parking the bike for miss bailey.c) going to school by bike. d) being a student of miss bailey.49.. from paragraph 2, we learn that _________.ca) miss bailey’s students disliked to help her. b) miss bailey didn’t like shankarc) shankar didn’t believe in his ability at first d) shankar didn’t want to help miss bailey50.. when shankar entered the classroom after parking the bike, _____.da)miss bailey praised him b)his classmates cheeredc)his hump disappeared d)he was full of confidence51. from the passage, we know that ____________.ca) shankar never stood at the school gateb) miss bailey pretended not to see shankar and walked to classc) parking the bike for miss bailey made shankar change himselfd) nobody wanted to help shankar park miss bailey’s bikedin canada you can find dogs, cats, horses, etc. in almost every family. these are their pets. people love these pets and have them as their good friends. before they keep them in their houses, they take them to animal hospitals to give them injections(注射)so that they wont carry disease. they have special animal food stores, though they can get animal food in almost every kind of store. some people spend around two hundred canadian dollars a month on animal food. when you visit peoples houses, they would be very glad to show you their pets and they are very proud of them. you will also find that almost every family has a feeding place for birds in their garden. all kinds of birds are welcomed to come and have a good meal. they are free to come and go and nobody is allowed to kill any animal in canada. they have a law against killing wild animals. if you killed an animal, you would be punished. if an animal happened to get run over by a car, people would be very sad about it.people in canada have many reasons to like animals. one of them might be that their family ties are not as close as ours. when children grow up, they leave their parents and start their own life. then the old will feel lonely, but pets can solve this problem. they can be good friends and never leave them alone.52.people can buy animal food for their pets_____. ba. only at the animal food storesb. in almost every storec. in the supermarkets d .in the pet shops53.when you visit people’s homes, _____.aa. people would be happy to show their animalsb .people would ask you to feed birdsc. you are not allowed to see their animalsd. it’s necessary for you to buy some animal food.54. when they grow up ____.ba. they dont love their parents any moreb. they don’t live together with their parentsc. they find jobs far from their parents【篇二：2010清华大学自主招生试题数学试题(带答案)】t>11．解：（Ⅰ）由得所以即因为所为内角，，（Ⅱ）又由余弦定理得即又所以，，有当且仅当即为等边三角形时，，的面积取得最大值12．解：（Ⅰ）设则由可知的斜率因此可以设直线方程为把所以因为所以直线代入，整理得都不平行于轴，斜率之和为可知直线所以作则由已知可得所以，所以为直角三角形可得，平分的倾角互补，而为垂足平行于轴，（Ⅱ）如图，根据的结果，可以设直线的方程分别为把分别代入，得【篇三：2010-2014年华约自主招生物理试题与答案】=txt>1.如图所示的传送带装置，与水平面的夹角为??，且????????=0.75。

2010自主招生考试真题

北京大学：1.中译英：与其诅咒黑暗，不如点亮蜡烛。

（better）能源危机对全球经济有消极作用，导致经济衰退。

（impact）复旦大学：1. In order to find ____ better job, he made up his mind to study ____ second foreign language.A. the; aB. a; aC. the; theD. a; the2. I like this house with a beautiful garden in front, but I don’t have enough money to buy___.A. oneB. itC. thisD. that3. The chemical factory is far away in the mountains. It is nearly ____ ride from the city.A. a six-hourB. a six hour’sC. six hour’sD. six hour4. —David promised to come round to have supper with us today.—But he ____. I’ve been alone for half an hour.A. won’tB. hadn’tC. hasn’tD. doesn’t5. This morning I went to school in such a hurry that I ____ the key to the classroom at home.A. forgotB. leftC. missedD. lost6. —I wonder if we could go skiing on the weekend.—______ good.A. SoundB. SoundedC. SoundingD. Sounds7. Mary spent her university life in London, where she ____ law for about four years.A. has studiedB. would studyC. is studyingD. studied8. — How about your journey to Mount Huangshan?— Everything was wonderful except that our car ____.A. slowed downB. broke downC. got downD. put down9. The water ____ cool when I jumped into the pool for morning exercise.A. was feltB. is feltC. feltD. feels10. If it is quite ____ to you, I’ll visit you next Tuesday.A. convenientB. fairC. easyD. comfortable11.Joe has joined the club ____ I was once trained in.A. whereB. whichC. whatD. when12. —It is very hot today, isn’t it?—Yes, ____.A. so it was yesterdayB. it was yesterdayC. so was it yesterdayD. neither was it yesterday13.—Could you be so kind as to close the window?—.A. With pleasureB. My pleasureC. Yes, pleaseD. That's OK14.The good chance that the young man has been looking forward to _____ at last.A. comingB. comesC. comeD. having come15. How much she looked without her glasses!A. wellB. goodC. bestD. better16. —Can the project be finished by the weekend?—Sure, ____ it in time, we’ll work two more hours a day.A. completesB. to completeC. completingD. complete17. What do you mean, there are only ten tickets? There be twelve.A. shouldB. wouldC. willD. shall18. The soldiers are sending ____ is badly needed to the earthquake-hit area by road.A. asB. thatC. whichD. what19. Peter was so excited ____ he received an invitation from his friend to visit the 2010Shanghai Expo.A. whereB. thatC. whyD. when20. The English teacher is very popular among his students as he always tries to make them____ in his lectures.A. interestedB. interestingC. interestD. to interestWhen I was in the seventh grade, I was a volunteer in a hospital. I spent most of the time there with Mr. Gillespie. He never had any 21 and nobody seemed to care about his life.I spent many days holding his hand, talking to him and 22 anything that needed to be done. He became my close friend even though he only responded (反应) with a weak smile.I left for a week to visit my parents. And when I came back, Mr. Gillespie was 23 . I didn’t have the 24 to ask the nurses where he was. I was afraid that they might 25 me that he had died.Several 26 later, I became a college student. One day, I noticed a familiar face at a gas station. When I 27 who it was, my eyes were filled with tears. He was 28 . He was Mr. Gillespie. With an uncertain look 29 his face, he replied “yes”. I 30 how I knew him, and that I had spent many hours talking with him in the hospital. His eyes were full of tears, and he gave me the warmest hug I had ever 31 .He began to tell me that 32 he lay there unconsciously(无意识地), he could hear me talking to him and could 33 me holding his hand all the time. He thought it was an angel, not a person, who was there with him.Mr. Gillespie 34 believed that it was my voice and touch that had kept him alive.Although I haven’t seen him after that, it fills my heart with 35 every day. I know that I made a difference between life and death and, more importantly, he made me an angel.21. A. visitors B. relatives C. patients D. doctors22. A. talking about B. looking after C. pointing out D. helping with23. A. killed B. lost C. gone D. changed24. A. energy B. chance C. courage D. time25. A. cheat B. tell C. remind D. warn26. A. days B. weeks C. months D. years27. A. recognized B. wondered C. heard D. asked28. A.well B.alive C.silent D.alone29. A.at B.on C. behind D. in30. A.apologized B.remembered C. explained D. understood31. A.dreamed B. seen C. wanted D. received32. A.because B. if C. unless D. although33. A.notice B. feel C. imagine D. watch34. A.hardly B.quickly C. strongly D. nearly35. A.joy B. regret C. respect D. sorrowAAre you sometimes a little tired and sleepy in the early afternoon? Many people feel this way after lunch. They may think that eating lunch is the cause of the sleepiness. Or, in summer, they may think it is the heat. However, the real reason lies inside their bodies. At that time—about eight hours after you wake up—your body temperature goes down. This is what makes you slow down and feel sleepy. Scientists have tested sleep habits in experiments where there was no night or day. The people in these experiments almost always followed a similar sleeping pattern (模式). They slept for one long period and then for one short period about eight hours later.In many parts of the world, people take naps (小睡) in the middle of the day. This is especially true in warmer climates, where the heat makes work difficult in the early afternoon. Researchers are now saying that naps are good for everyone in any climate. A daily nap gives one a more rested body and mind and therefore is good for health in general. In countries where naps are traditional, people often suffer less from problems such as heart disease.Many working people, unluckily, have no time to take naps. Though doctors may advise taking naps, employers(雇主) do not allow it! If you do have the chance, however, here are a few tips about making use of your nap. Remember that the best time to take a nap is about eight hours after you get up. A short sleep too late in the day may only make you feel more tired and sleepy afterward. This can also happen if you sleep for too long. If you do not have enough time, try a short nap – even ten minutes of sleep can be helpful.36. Why do people feel sleepy in the early afternoon according to the text?A. They eat too much for lunch.B. They sleep too little at night.C. Their body temperature becomes lower.D. The weather becomes a lot warmer.37. If you get up at 6:30 am, what is the best time for you to take a nap?A. About 12:30 pm.B. About 1:30 pm.C. About 2:30 pmD. About 3:30 pm38. What would be the best title for the text?A. Just for a RestB. All for a NapC. A Special Sleep Pattern.D.Taking Naps in Warmer Climate.BIn high school, George Lucas didn’t do much work because he spent all his time dreaming about racing cars.Just a few days before graduation, George was driving home from the library in his Fiat;he prepared for a left turn by glancing in the mirror. But as he started the turn, he heard the sound of another car, a blowing horn(喇叭), and then a speeding Ford hit the driver side of his car. The little Fiat turned four or five complete flips(空翻)before it stopped by a big tree. Luckily, George did not die in the accident, but his recovery was slow and he needed months of physical treatment. He would never be able to race cars now.The accident really changed George’s life. He thought there must be some reason why he survived, and made up his mind to get his act together and make something out of his life. He decided to go to university and he developed an interest in reading and writing. He did quite well in his studies. He didn’t quite forget about racing cars. At that time instead of driving racing cars, he began filming them.You may have seen one or all of George Lucas’most famous films from the Star Wars series to the Indiana Jones Trilogy(三部曲). Not only has George produced great movies, but also he has helped invent and develop new technologies to modernize the movie industy.Today, George Lucas is one of the American film industry’s most successful directors and producers, with a net worth of about 3.0 billion.39. What do we know about George Lucas when he was in high school?A. He was the worst car racer in his school.B. He showed a great interest in making movies.C. He was not so interested in studying.D. He was hated by all his teachers.40. We can infer from this passage that .A. George was seriously injured in the accidentB. The accident was by GeorgeC. George’s Fiat was not seriously damagedD. the driver of the Ford was not injured41. After the car accident, George Lucas .A. lost interest in racing carsB. lost interest in reading and writingC. lost heart and didn’t want to do anythingD. decided to achieve something in the future42. We can infer that as a film director and producer, George Lucas .A. doesn’t know how to make money out of making filmsB. played an important role in modernizing the movie industryC. hasn’t made any films about racing carsD. has made the most movies in AmericaCHi, everybody!Welcome to our newly-opened Richards Cinema Bookstore!Now let me introduce to you some of the new film books in our store.Are you Chinese film fans? OK, here comes the latest 25 New Takes about Chinese films. It is a collection of 25 fresh readings of different Chinese films from the 1930s to the present. In recent years, Chinese films are very popular in the States, such as Crouching Tiger and Hidden Dragon, Hero, and Flowers of Shanghai.Do you like French films? Well, here is The French Cinema Book. It covers French films from the 1890s to the beginning of the 21st century. It is written for all lovers of French cinema: students and teachers, specialists and fans, and so on.Maybe you are Indian film fans and star-chasers. Then here is Encyclopedia (百科全书) of Indian Cinema. The book is a complete introduction to all the best Indian films. It also offers afull list of names of the famous and successful film stars in the past ten years. You know, the Indian film industry is the largest in the world after our Hollywood.If you like British films, we have The British Cinema Book. It is a good review of British cinema. This book contains a good many nice pictures.In our bookstore, you can also find books about Mexican, Japanese, Australian, German and Italian films.Well, please help yourselves to some coffee or tea, and have a good time here!43. The speaker of the passage is most probably _______.A. the author of 25 New TakesB. a tourist in the cinema bookstoreC. the manager of the cinema bookstoreD. a reader of Encyclopedia of Indian Cinema44. How many Asian countries does the speaker mention when he talks about the film books?A. Two.B. Three.C. Four.D. Nine.45. Which of the following statements is NOT mentioned in the passage？A. Indian cinema is second only to Hollywood.B. The British Cinema Book includes a complete list of names of stars.C. Crouching Tiger and Hidden Dragon is well received in the States.D. The French Cinema Book covers over a century's French films.46. The purpose of the speaker is_______.A. to satisfy the customers' different kinds of tastesB. to keep the authors in the cinema bookstoreC. to offer the tourists chances to meet the film starsD. to develop the readers into film producersDSome people think that as more and more people have televisions in their homes, fewer and fewer people will buy books and newspapers. Why read an article in the newspaper, when the TV news can bring you the information in a few minutes and with pictures? Why read the life story of a famous man, when a short television program can tell you all that you want to know?Television has not killed reading, however. Today, newspapers sell in very large numbers. And books of every kind are sold more than ever before. Books are still a cheap way to get information and enjoyment. Although some books with hard covers are expensive, many books are printed today as paperbooks (平装本), which are quite cheap. A paperback collection of short stories, for example, is always cheaper than an evening at the cinema or the theater, and you can keep a book for ever and read it many times.Books are a wonderful provider of knowledge and pleasure and some types of books should be in every home. Every home should have a good dictionary. A good encyclopedia (百科全书), though expensive, is useful, too, because you can find information on any subject. Besides, you can have such books as history books, science textbook, cookbooks, and collections of stories and poems. Then from time to time you can take a book of poems off your shelves and read the thoughts and feelings of your favorite poets.47. It can be inferred from the passage that ____.A. TV programs are a chief provider of knowledgeB. cinemas are the best choice in getting informationC. reading is a cheap way of learning and having funD. newspapers are an expensive way to enjoy oneself48. What does the sentences “Television has not killed reading, however ” underlined in thesecond paragraph suggest?A. People only need reading, though.B. Reading is still necessary today.C. Reading is more fun than television.D. Watching television doesn’t help reading.49. Which of the following is mainly discussed in the last paragraph?A. Types of books.B. Kinds of dictionaries.C. Lists of history books.D. Collections of stories.50. What can we learn from the passage?A. Fewer and fewer people will buy books.B. A good dictionary should be kept in every home.C. Books with hard covers sell better than paperbooks.D. More people like TV programs about famous men.请阅读下列应用文及相关信息，并按照要求匹配信息。

2010年北京大学自主招生数学试题(含详细答案)

2010年北京大学、香港大学、北京航空航天大学三校联合自主招生考试试题（数学部分）1．（仅文科做）02απ<<，求证：sin tan ααα<<．（25分）【解析】不妨设()sin f x x x =-，则(0)0f =，且当02x π<<时，()1cos 0f x x '=->．于是()f x 在02x π<<上单调增．∴()(0)0f x f >=．即有sin x x >．同理可证()tan 0g x x x =->． (0)0g =，当02x π<<时，21()10cos g x x '=->．于是()g x 在02x π<<上单调增． ∴在02x π<<上有()(0)0g x g >=．即tan x x >．注记：也可用三角函数线的方法求解．2．AB 为边长为1的正五边形边上的点．证明：AB．（25分）【解析】以正五边形一条边上的中点为原点，此边所在的直线为x 轴，建立如图所示的平面直角坐标系．⑴当,A B 中有一点位于P 点时，知另一点位于1R 或者2R 时有最大值为1PR ；当有一点位于O 点时，1max AB OP PR =<；⑵当,A B 均不在y 轴上时，知,A B 必在y 轴的异侧方可能取到最大值（否则取A 点关于y 轴的对称点A '，有AB A B '<）．不妨设A 位于线段2OR 上（由正五边形的中心对称性，知这样的假设是合理的），则使AB 最大的B 点必位于线段PQ 上．且当B 从P 向Q 移动时，AB 先减小后增大，于是max AB AP AQ =或；对于线段PQ 上任意一点B ，都有2BR BA ≥．于是22max AB R P R Q ==由⑴，⑵知2max AB R P =．不妨设为x ．下面研究正五边形对角线的长．如右图．做EFG ∠的角平分线FH 交EG 于H ．易知5EFH HFG GFI IGF FGH π∠=∠=∠=∠=∠=．于是四边形HGIF 为平行四边形．∴1HG =．由角平分线定理知111EF EH x FGx HG===-．解得x =．3．AB 为21y x =-上在y 轴两侧的点，求过AB 的切线与x 轴围成面积的最小值．（25分）【解析】不妨设过A 点的切线交x 轴于点C ，过B 点的切线交x 轴于点D ，直线AC 与直线BD 相交于点E ．如图．设1122(,),(,)B x y A x y ，且有222211121,1,0y x y x x x =-=->>．由于2y x '=-，于是AC 的方程为2222x x y y =--；① BD 的方程为1122x x y y =--． ②联立,AC BD 的方程，解得121221(,1)2()y y E x x x x ---．对于①，令0y =，得222(,0)2y C x -；对于②，令0y =，得112(,0)2y D x -．于是221212121222112222y y x x CD x x x x --++=-=-． 121(1)2ECD S CD x x ∆=-．不妨设10x a =>，20x b -=>，则2222111111()(1)(22)44ECD a b S ab a b a b ab a b a b ∆++=++=+++++1111()(2)(2)44a b ab ab ab ab =+++⋅++≥ ③0s >，则有331111111(2)(.....)223399ECD S s s s s s s s s ∆=++=++++++6个 9个1243691616111116)]8()2393s s s ⋅⋅[⋅(⋅()=⋅≥3218)3=⋅(= ④又由当12x a x b s ===-==③，④处的等号均可取到．∴min ()ECD S ∆=I H GFE 1111x x-1注记：不妨设311()(2)2g s s s s=++，事实上，其最小值也可用导函数的方法求解．由2211()(32)2g s s s '=+-知当2103s <<时()0g s '<；当213s <时()0g s '>．则()g s 在(0,上单调减，在)+∞上单调增．于是当s =时()g s 取得最小值．4．向量OA 与OB 已知夹角，1OA =，2OB =，(1)OP t OA =-，OQ tOB =，01t ≤≤．PQ在0t 时取得最小值，问当0105t <<时，夹角的取值范围．（25分）【解析】不妨设OA ，OB 夹角为α，则1,2OP t OQ t =-=，令222()(1)42(1)2cos g t PQ t t t t α==-+-⋅-⋅2(54cos )(24cos )1t t αα=++--+．其对称轴为12cos 54cos t αα+=+．而12()54x f x x +=+在5(,)4-+∞上单调增，故12cos 1154cos 3αα+-+≤≤．当12cos 1054cos 3αα++≤≤时，012cos 1(0,)54cos 5t αα+=∈+，解得223αππ<<．当12cos 1054cos αα+-<+≤时，()g t 在[0,1]上单调增，于是00t =．不合题意．于是夹角的范围为2[,]23ππ．5．（仅理科做）存不存在02x π<<，使得sin ,cos ,tan ,cot x x x x 为等差数列．（25分）【解析】不存在；否则有(cos sin )(cos sin )cos sin cot tan sin cos x x x x x x x x x x-+-=-=，则cos sin 0x x -=或者cos sin 1sin cos x xx x+=．若cos sin 0x x -=，有4x π=1,1不成等差数列；若cos sin 1sin cos x x x x+=，有2(sin cos )12sin cos x x x x =+．解得有sin cos 1x x =而11sin cos sin 2(0,]22x x x =∈，矛盾！。

2010北京大学自主招生考试语文试卷

2010年北大自主招生试题语文试题（A卷）亲爱的同学，欢迎你参加北京大学自主招生语文测试。

本试卷侧重考察你的真实语文能力，希望你突破日常训练的局限，发挥出实际的语文潜力。

祝你成功！一、选择正确的或最好的表达形式（ 10分）1 只要你不再做坏事，我们就____。

A既往不咎 B继往不究 C，既往不究 ( )2．地震引发的瘟疫正在____。

A曼延 B漫延 C蔓延 ( )3．享受美好的事物，____其中的趣味。

A领略 B领会 C领悟 ( )4豆腐作为营养保健食品____受推崇。

A备 B倍 C，辈 ( )5．公元6年，罗马帝国____犹太傀儡王，犹太国从此灭了。

A废除 B废黜 C废出 ( )6．战略管理的过程一般包括战略设计和选择、政策____、指导战略实施等重要阶段。

A．制定 B．制订 C．制作 ( )7．他们对出线信心很足，却____无一点懈怠和轻视对手的思想。

A诀 B决 c绝 ( )8．两人观点____，难以协调。

A．方纳圆凿 B方枘蚓凿 C．圆凿方汭 ( )9动物性蛋白含有人体____的氨基酸。

A必需 B必须 C．须要 ( )10．其震动____这一个国家，世界文化的发展也深受影响。

A不仅局限于 B不限于 c不仅限于 ( )二、语言运用题（10分）最近网上流行一首80后歌曲，其中有一段绕口令式的歌词是：历史长河向前淌岸上睡着一只羊河里漂着一条狼狼要拿羊当口粮羊要认狼当爹娘羊要救狼，狼要吃羊不知是那羊救狼还是狼吃羊请仔细阅读这段歌词后，完成下列二题：1．找出所有押韵的字，用其中至少4个字写成一个单句。

（4）【简答】狼心狗肺的儿子用他娘唯一的羊皮坎肩换成了自己的口粮。

狼他娘以羊为粮2 找出所有的动词，并用其中笔画最少的两个字，写一句适合大学校园的宣传用标语。

（6分）【注】其中笔画最少的两个字是“认”和“吃”三．将下段古文翻译为现代汉语（20分）法者，天下之度量，而人主之准绳也。

县法者，法不法也；设赏者，赏当赏也。

2010年清华大学自主招生试题

语文第一题：科技说明文杨叔子《融则利而育全人》一书中的选段。

第二题：现代文阅读没时间了，就没怎么看。

山口蒲宁 <俄>夜幕已垂下很久，可我仍举步维艰地在崇岭中朝山口走去，朔风扑面而来，四周寒雾弥漫，我对于能否走至山口已失却信心，可我牵在身后的那匹浑身湿淋淋的、疲惫的马，却驯顺地跟随着我亦步亦趋，空荡荡的马蹬叮叮当当地碰响着。

在迷蒙的夜色中，我走到了松林脚下，过了松林便是这条通往山巅的光秃秃的荒凉的山路了。

我在松林外歇息了一会儿，眺望着山下宽阔的谷地，心中漾起一阵奇异的自豪感和力量感，这样的感觉，人们在居高临下时往往都会有的。

我遥遥望见山下很远的地方，那渐渐昏暗下去的谷地紧傍着狭窄的海湾，岸边点点灯火犹依稀可辨。

那条海湾越往东去就越开阔，最终形成一堵烟霞空蒙的暗蓝色障壁，围住了半壁天空。

但在深山中已是黑夜了。

夜色迅速地浓重起来，我向前走去，离松林越来越近。

只觉得山岭变得越来越阴郁，越来越森严，由高空呼啸而下的寒风，驱赶着浓雾，将其撕扯成一条条长长的斜云，使之穿过山峰间的空隙，迅疾地排空而去。

高处的台地上缭绕着大团大团松软的雾。

半山腰中的雾就是由那儿刮下来的。

雾的坠落使得群山间的万仍深渊看上去更显阴郁，更显幽深。

雾使松林仿佛冒起了白烟，并随同喑哑、深沉、凄冷的松涛声向我袭来。

周遭弥漫着冬天清新的气息，寒风卷来了雪珠……夜已经很深了，我低下头避着烈风，久久地在山林构成的黑咕隆咚的拱道中冒着浓雾向前行去，耳际回响着隆隆的松涛声。

“马上就可以到山口了，”我宽慰自己说。

“马上就可以翻过山岭到没有风雪而有人烟的明亮的屋子里去休息了……”但是半个小时过去了，一个小时过去了……每分钟我都以为再走两步就可到达山口，可是那光秃秃的石头坡道却怎么也走不到尽头。

松林早已落在半山腰，低矮的歪脖子灌木丛也早已走过，我开始觉得累了，直打寒颤。

我记起了离山口不远的松树间有好几座孤坟，那里埋葬着被冬天的暴风雪刮下山的樵夫。