上海交大中15学年度高三开学摸底考试卷
2021届上海市上海交通大学附属中学高三上学期开学摸底数学试题(解析版)
2021届上海市上海交通大学附属中学高三上学期开学摸底数学试题一、单选题1．函数y =x cos x +sin x 在区间[–π，π]的图象大致为（ ）A ．B ．C ．D ．【答案】A【解析】首先确定函数的奇偶性，然后结合函数在x π=处的函数值排除错误选项即可确定函数的图象. 【详解】因为()cos sin f x x x x =+，则()()cos sin f x x x x f x -=--=-， 即题中所给的函数为奇函数，函数图象关于坐标原点对称， 据此可知选项CD 错误；且x π=时，cos sin 0y ππππ=+=-<，据此可知选项B 错误. 故选：A. 【点睛】函数图象的识辨可从以下方面入手：(1)从函数的定义域，判断图象的左右位置；从函数的值域，判断图象的上下位置．(2)从函数的单调性，判断图象的变化趋势．(3)从函数的奇偶性，判断图象的对称性．(4)从函数的特征点，排除不合要求的图象．利用上述方法排除、筛选选项．2．已知,,A B C 为球O 的球面上的三个点，⊙1O 为ABC 的外接圆，若⊙1O 的面积为4π，1AB BC AC OO ===，则球O 的表面积为（ ） A ．64π B ．48πC ．36πD ．32π【答案】A【解析】由已知可得等边ABC 的外接圆半径，进而求出其边长，得出1OO 的值，根据球的截面性质，求出球的半径，即可得出结论. 【详解】设圆1O 半径为r ，球的半径为R ，依题意， 得24,2r r ππ=∴=，ABC 为等边三角形，由正弦定理可得2sin 6023AB r =︒=，123OO AB ∴==，根据球的截面性质1OO ⊥平面ABC ，222211111,4OO O A R OA OO O A OO r ∴⊥==+=+=， ∴球O 的表面积2464S R ππ==.故选：A【点睛】本题考查球的表面积，应用球的截面性质是解题的关键，考查计算求解能力，属于基础题.3．若点00(,)P x y 00(0)x y ≠在函数()y f x =的图像上，1()y f x -=为函数()y f x =的反函数，设100(,)P y x 、200(,)P y x -、300(,)P y x -、400(,)P y x --，则有（ ） A ．点1234,,,P P P P 有可能都在函数1()y f x -=的图像上B ．只有点2P 不可能在函数1()y f x -=的图像上C ．只有点3P 不可能在函数1()y fx -=的图像上D ．点23,P P 都不可能在函数1()y f x -=的图像上 【答案】D【解析】根据反函数存在的条件是原函数必须是一一对应的，然后根据反函数的性质可判断点1234,,,P P P P 是否在函数1()y f x -=图像上.【详解】存在反函数的条件是原函数必须是一一对应的,根据点00(,)P x y 00(0)x y ≠在函数()y f x =的图象上， 则100(,)P y x 在反函数1()y fx -=的图象若点100(,)P y x 与点300(,)P y x -都在反函数1()y fx -=的图象上，则相同的横坐标对应两个函数值，不符合一一对应；若点200(,)P y x -在反函数图象上则点00(,)x y -在函数()y f x =的图象上， 则相同的横坐标对应两个函数值，不符合一一对应； 故点23,P P 都不可能在函数1()y f x -=的图象上故选：D ． 【点睛】本题考查反函数存在的条件和函数的性质，同时考查分析问题的能力，属于基础题. 4．设集合S ，T ，S ⊆N ，T ⊆N ，S ，T 中至少有两个元素，且S ，T 满足： ①对于任意x ，y ∈S ，若x ≠y ，都有xy ∈T ②对于任意x ，y ∈T ，若x <y ，则yx∈S ； 下列命题正确的是（ ）A ．若S 有4个元素，则S ∪T 有7个元素B ．若S 有4个元素，则S ∪T 有6个元素C ．若S 有3个元素，则S ∪T 有5个元素D ．若S 有3个元素，则S ∪T 有4个元素 【答案】A【解析】分别给出具体的集合S 和集合T ，利用排除法排除错误选项，然后证明剩余选项的正确性即可. 【详解】首先利用排除法：若取{}1,2,4S =，则{}2,4,8T =，此时{}1,2,4,8S T =，包含4个元素，排除选项 C ；若取{}2,4,8S =，则{}8,16,32T =，此时{}2,4,8,16,32S T =，包含5个元素，排除选项D ；若取{}2,4,8,16S =，则{}8,16,32,64,128T =，此时{}2,4,8,16,32,64,128S T =，包含7个元素，排除选项B ； 下面来说明选项A 的正确性：设集合{}1234,,,S p p p p =，且1234p p p p <<<，*1234,,,p p p p N ∈，则1224p p p p <，且1224,p p p p T ∈，则41p S p ∈， 同理42p S p ∈，43p S p ∈，32p S p ∈，31p S p ∈，21p S p ∈， 若11p =，则22p ≥，则332p p p <，故322p p p =即232p p =， 又444231p p p p p >>>，故442232p p p p p ==，所以342p p =， 故{}232221,,,S p p p =，此时522,p T p T ∈∈，故42p S ∈，矛盾，舍.若12p ≥，则32311p p p p p <<，故322111,p pp p p p ==即323121,p p p p ==， 又44441231p p p p p p p >>>>，故441331p p p p p ==，所以441p p =， 故{}2341111,,,S p p p p =，此时{}3456711111,,,,p p p p p T ⊆. 若q T ∈， 则31q S p ∈，故131,1,2,3,4i q p i p ==，故31,1,2,3,4i q p i +==， 即{}3456711111,,,,q p p p p p ∈，故{}3456711111,,,,p p p p p T =， 此时{}234456711111111,,,,,,,S T p p p p p p p p ⋃=即S T 中有7个元素.故A 正确. 故选：A . 【点睛】“新定义”主要是指即时定义新概念、新公式、新定理、新法则、新运算五种，然后根据此新定义去解决问题，有时还需要用类比的方法去理解新的定义，这样有助于对新定义的透彻理解.但是，透过现象看本质，它们考查的还是基础数学知识，所以说“新题”不一定是“难题”，掌握好三基，以不变应万变才是制胜法宝.二、填空题5．已知集合{1,0,1,2},{0,2,3}A B =-=，则A B =_____.【答案】{}0,2【解析】根据集合的交集即可计算. 【详解】∵{}1,0,1,2A =-,{}0,2,3B = ∴{}0,2AB =故答案为：{}0,2. 【点睛】本题考查了交集及其运算，是基础题型．6．已知i 是虚数单位，则复数()()12z i i =+-的虚部是________ 【答案】1【解析】利用复数的乘法运算，化简复数3i z =+,即可得答案； 【详解】2213z i i i =-++=+，∴复数z 的虚部是1，故答案为：1. 【点睛】本题考查复数虚部的概念，属于基础题.7．已知一组数据4,2,3,5,6a a -的平均数为4，则a 的值是_____. 【答案】2【解析】根据平均数的公式进行求解即可． 【详解】∵数据4,2,3,5,6a a -的平均数为4∴4235620a a ++-++=，即2a =. 故答案为：2. 【点睛】本题主要考查平均数的计算和应用，比较基础．8．将一颗质地均匀的正方体骰子先后抛掷2次，观察向上的点数，则点数和为5的概率是_____. 【答案】19【解析】分别求出基本事件总数，点数和为5的种数，再根据概率公式解答即可． 【详解】根据题意可得基本事件数总为6636⨯=个.点数和为5的基本事件有()1,4，()4,1，()2,3，()3,2共4个. ∴出现向上的点数和为5的概率为41369P ==. 故答案为：19. 【点睛】本题考查概率的求法，考查古典概型、列举法等基础知识，考查运算求解能力，是基础题．9．25()()x x y xy ++的展开式中33x y 的系数为________【答案】15【解析】先把条件整理转化为求225()()x y x y ++展开式中43x y 的系数，再结合二项式的展开式的特点即可求解． 【详解】解：因为22255()()()()y x y x y x x y x x++++=； 要求展开式中33x y 的系数即为求225()()x y x y ++展开式中43x y 的系数；展开式含43x y 的项为：2223244435515x C x y y C x y x y +=；故25()()y x x y x++的展开式中33x y 的系数为15；故答案为：15.【点睛】本题主要考查二项式定理的应用，二项式展开式的通项公式，二项式系数的性质，属基础题．10．如果方程2lg (lg 6)lg lg 2lg 30x x ++⋅=的两个根为1x 、2x ，那么12x x ⋅的值为________ 【答案】16【解析】先对方程进行因式分解变形得(lg lg 2)(lg lg3)0x x ++=，求出12,x x 的值，即可得答案； 【详解】(lg lg 2)(lg lg3)0x x ++=， ∴lg lg 2x =-或lg lg3x =-，∴121123x x ==，，∴1216x x =，故答案为：16.【点睛】本题考查对数的运算，考查运算求解能力，属于基础题.11．设{a n }是公差为d 的等差数列，{b n }是公比为q 的等比数列．已知数列{a n +b n }的前n 项和221()n n S n n n +=-+-∈N ，则d +q 的值是_______． 【答案】4【解析】结合等差数列和等比数列前n 项和公式的特点，分别求得{}{},n n a b 的公差和公比，由此求得d q +. 【详解】设等差数列{}n a 的公差为d ，等比数列{}n b 的公比为q ，根据题意1q ≠. 等差数列{}n a 的前n 项和公式为()2111222n n n d d P na d n a n -⎛⎫=+=+- ⎪⎝⎭， 等比数列{}n b 的前n 项和公式为()1111111n n n b q b bQ q qq q-==-+---，依题意nn n S P Q =+，即22111212211nn b b d d n n n a n q q q ⎛⎫-+-=+--+ ⎪--⎝⎭， 通过对比系数可知111212211dd a q b q⎧=⎪⎪⎪-=-⎪⎨⎪=⎪⎪=-⎪-⎩⇒112021d a q b =⎧⎪=⎪⎨=⎪⎪=⎩，故4d q +=. 故答案为：4 【点睛】本小题主要考查等差数列和等比数列的前n 项和公式，属于中档题.12．如图，六角螺帽毛坯是由一个正六棱柱挖去一个圆柱所构成的．已知螺帽的底面正六边形边长为2 cm ，高为2 cm ，内孔半径为0.5 cm ，则此六角螺帽毛坯的体积是____cm.【答案】1232π【解析】先求正六棱柱体积，再求圆柱体积，相减得结果. 【详解】正六棱柱体积为23622=1234⨯⨯ 圆柱体积为21()222ππ⋅=所求几何体体积为1232π故答案为： 1232π【点睛】本题考查正六棱柱体积、圆柱体积，考查基本分析求解能力，属基础题.13．将函数y =πsin(2)43x ﹢的图象向右平移π6个单位长度，则平移后的图象中与y 轴最近的对称轴的方程是____. 【答案】524x π=-【解析】先根据图象变换得解析式，再求对称轴方程，最后确定结果. 【详解】3sin[2()]3sin(2)6412y x x πππ=-+=-72()()122242k x k k Z x k Z πππππ-=+∈∴=+∈当1k =-时524x π=-故答案为：524x π=-【点睛】本题考查三角函数图象变换、正弦函数对称轴，考查基本分析求解能力，属基础题.14．已知22451x y y +=（,x y R ∈），则22xy +的最小值是________【答案】45【解析】由已知求得2x ，代入所求式子，整理后，运用基本不等式可得所求最小值； 【详解】解：由22451x y y +=，可得42215y x y -=，由20x ，可得2(0y ∈，1]，则44222222211411(4)555y y x y y y y y y-++=+==+ 221142455y y =，当且仅当212y =，2310x =，可得22xy +的最小值为45； 故答案为：45. 【点睛】本题考查基本不等式的运用：求最值，考查转化思想和化简运算能力，属于中档题. 15．在△ABC 中，43=90AB AC BAC ==︒，，∠，D 在边BC 上，延长AD 到P ，使得AP =9，若3()2PA mPB m PC =+-（m 为常数），则CD 的长度是________．【答案】185【解析】根据题设条件可设()0PA PD λλ=>，结合32PA mPB m PC ⎛⎫=+- ⎪⎝⎭与,,B D C 三点共线，可求得λ，再根据勾股定理求出BC ，然后根据余弦定理即可求解. 【详解】∵,,A D P 三点共线， ∴可设()0PA PD λλ=>， ∵32PA mPB m PC ⎛⎫=+- ⎪⎝⎭，∴32PD mPB m PC λ⎛⎫=+- ⎪⎝⎭，即32m m PD PB PC λλ⎛⎫- ⎪⎝⎭=+， 若0m ≠且32m ≠，则,,B D C 三点共线， ∴321m m λλ⎛⎫-⎪⎝⎭+=，即32λ=， ∵9AP =，∴3AD =，∵4AB =,3AC =,90BAC ∠=︒， ∴5BC =，设CD x =，CDA θ∠=，则5BD x =-，BDA πθ∠=-. ∴根据余弦定理可得222cos 26AD CD AC xAD CD θ+-==⋅，()()()222257cos 265x AD BD AB AD BD x πθ--+--==⋅-，∵()cos cos 0θπθ+-=，∴()()2570665x x x --+=-，解得185x =，∴CD 的长度为185. 当0m =时， 32PA PC =，,C D 重合，此时CD 的长度为0， 当32m =时，32PA PB =，,B D 重合，此时12PA =，不合题意，舍去.故答案为：0或185.【点睛】本题考查了平面向量知识的应用、余弦定理的应用以及求解运算能力，解答本题的关键是设出()0PA PD λλ=>．16．在平面直角坐标系xOy 中，已知0)P ，,A B 是221:()362C x y +-=上的两个不同的动点，满足PA PB =，且PA PB a ⋅<恒成立，则实数a 最小值是________ 【答案】49【解析】因为PA PB =，可知PC 是AB 的垂直平分线，1PC =，设CE x =，PA 、PB 、AB 的长即可用x 表示，再利用余弦定理表示cos APB ∠，利用数量积的定义将PA PB ⋅用x 表示，()maxa PA PB>⋅，利用函数求出()max6PA PB⋅<，即得a 最小值.【详解】如图圆心10,2C ⎛⎫⎪⎝⎭，1PC =，因为PA PB =，所以PC 是AB 的垂直平分线，设PC 与AB 相交于点E ，则点E 是AB 的中点， 设CE x =，则2236AE x =-，()22436AB x=-，()2222221237AP BP AE EP AE x x ==+=++=+PA PB a ⋅<恒成立，所以()maxa PA PB>⋅cos PA PB PA PB APB ⋅=∠，在APB △中，由余弦定理得：222222cos 22AP BP AB AP AB APB AP BP AP BP +--∠==⨯⨯， 所以222222cos 22AP AB AP AB PA PB PA PB APB PA PB AP BP --⋅=∠=⨯=⨯， ()()22222323743652x x x x +--==+-，因为06x <<，所以6x =时，22235236123549x x +-<⨯+-=， 即()max49PA PB⋅<所以6a ≥，故实数a 最小值是49，故答案为：49【点睛】本题主要考查了平面向量数量积的定义，余弦定理，勾股定理，恒成立问题，求二次函数的最值，属于综合性题目，属于中档题.三、解答题17．在三棱锥A—BCD中，已知CB=CD=5,BD=2，O为BD的中点，AO⊥平面BCD，AO=2，E为AC的中点．（1）求直线AB与DE所成角的余弦值；（2）若点F在BC上，满足BF=14BC，设二面角F—DE—C的大小为θ，求sinθ的值．【答案】（115（2239【解析】（1）建立空间直角坐标系，利用向量数量积求直线向量夹角，即得结果；（2）先求两个平面法向量，根据向量数量积求法向量夹角，最后根据二面角与向量夹角关系得结果.【详解】（1）连,CO BC CD BO OD CO BD ==∴⊥以,,OB OC OA 为,,x y z 轴建立空间直角坐标系，则(0,0,2),(1,0,0),(0,2,0),(1,0,0)(0,1,1)A B C D E -∴15(1,0,2),(1,1,1)cos ,1553AB DE AB DE ∴=-=∴<>==- 从而直线AB 与DE 所成角的余弦值为1515（2）设平面DEC 一个法向量为1(,,),n x y z =11200(1,2,0),00x y n DC DC x y z n DE ⎧+=⋅=⎧⎪=∴⎨⎨++=⋅=⎪⎩⎩令112,1(2,1,1)y x z n =∴=-=∴=- 设平面DEF 一个法向量为2111(,,),n x y z =11221117100171(,,0),4244200x y n DF DF DB BF DB BC n DE x y z ⎧⎧+=⋅=⎪⎪=+=+=∴⎨⎨⋅=⎪⎩⎪++=⎩令111272,5(2,7,5)y x z n =-∴==∴=-12cos ,67813n n ∴<>== 因此12239sin 13θ== 【点睛】本题考查利用向量求线线角与二面角，考查基本分析求解能力，属中档题.18．在锐角△ABC 中，角A ，B ，C 的对边分别为a ，b ，c，且2sin 0b A =． （I ）求角B 的大小；（II ）求cos A +cos B +cos C 的取值范围．【答案】（I ）3B π=；（II）32⎤⎥⎝⎦【解析】（I ）首先利用正弦定理边化角，然后结合特殊角的三角函数值即可确定∠B 的大小；（II ）结合(1)的结论将含有三个角的三角函数式化简为只含有∠A 的三角函数式，然后由三角形为锐角三角形确定∠A 的取值范围，最后结合三角函数的性质即可求得cos cos cos A B C ++的取值范围.【详解】（I）由2sin b A =结合正弦定理可得：2sin sin ,sin 2B A A B =∴= △ABC 为锐角三角形，故3B π=.（II ）结合(1)的结论有：12cos cos cos cos cos 23A B C A A π⎛⎫++=++- ⎪⎝⎭11cos cos sin 222A A A =-++11cos 222A A =++ 1sin 62A π⎛⎫=++ ⎪⎝⎭.由203202A A πππ⎧<-<⎪⎪⎨⎪<<⎪⎩可得：62A ππ<<，2363A πππ<+<，则sin 32A π⎛⎤⎛⎫+∈ ⎥ ⎪ ⎝⎭⎝⎦，113sin ,2232A π⎛⎤⎛⎫++∈ ⎥ ⎪ ⎝⎭⎝⎦. 即cos cos cos A B C ++的取值范围是13,22⎛⎤⎥ ⎝⎦.【点睛】解三角形的基本策略：一是利用正弦定理实现“边化角”，二是利用余弦定理实现“角化边”；求最值也是一种常见类型，主要方法有两类，一是找到边之间的关系，利用基本不等式求最值，二是转化为关于某个角的函数，利用函数思想求最值.19．已知函数()|31|2|1|f x x x=+--.（1）画出()y f x=的图像；（2）求不等式()(1)f x f x>+的解集；（3）若不等式22()3f x t at≥-+-，对于任意的x∈R，任意的[1,1]a∈-恒成立，求实数t的取值范围.【答案】（1）图像见解析；（2）7(,)6-∞-；（3）2t≤-或2t≥.【解析】（1）根据绝对值定义去掉绝对值符号化函数为函数形式，然后可分段作出函数图象；（2）把函数()y f x=的图像向左平移1个单位长度后得到函数(1)y f x=+的图像，由图象可得不等式的解；（3）首先由()f x图象得()f x的最小值83-，然后问题转化为282,33t at-≥-+-对任意[]1,1a∈-恒成立，引入函数()g a=223t at-+-，这是关于a的一次函数，由一次函数性质易得结论．【详解】（1）由题设知13,,31()51,1,33, 1.x xf x x xx x⎧--≤-⎪⎪⎪=--<≤⎨⎪+>⎪⎪⎩()y f x=的图像如图所示.（2）函数()y f x =的图像向左平移1个单位长度后得到函数(1)y f x =+的图像，()y f x =的图像与(1)y f x =+的图像的交点坐标为711(,)66--，由图像可知当且仅当76x <-时，()y f x =的图像在(1)y f x =+的图像上方， ∴不等式()(1)f x f x >+的解集为7(,)6-∞-．（3）由函数图像性质可知，当13x =-时，()f x 取得最小值83-， 则原问题转化为282,33t at -≥-+- 对任意[]1,1a ∈-恒成立，即220t at --≥对任意[]1,1a ∈-恒成立，记函数()22g a ta t =-+-，要使()0g a ≥对任意[]1,1a ∈-恒成立，只需()()1010g g ⎧≥⎪⎨-≥⎪⎩，即222020t t t a ⎧--≥⎨+-≥⎩，解得：2,t ≤-或2t ≥.【点睛】本题考查作含绝对值函数图象，用图象解不等式，考查不等式恒成立问题，不等式恒成立问题的关键是转化，一是转化为求出函数的最小值，二是转化为与一次函数有关的不等关系．20．在平面直角坐标系xOy 中，已知椭圆22:143x y E +=的左、右焦点分别为1F 、2F ，点A 在椭圆E 上且在第一象限内，212AF F F ⊥，直线1AF 与椭圆E 相交于另一点B .（1）求12AF F ∆的周长；（2）在x 轴上任取一点P ，直线AP 与椭圆E 的右准线相交于点Q ，求OP QP ⋅的最小值；（3）设点M 在椭圆E 上，记OAB 与MAB △的面积分别为12,S S ，若213S S =，求点M 的坐标.【答案】（1）6；（2）4- ；（3）M 点坐标为(2,0)或212(,)77-- .【解析】（1）由椭圆标准方程可知a ，b ，c 的值，根据椭圆的定义可得12AF F △的周长22a c =+，代入计算即可．（2）由椭圆方程得3(1,)2A ，设(,0)P t ，进而由点斜式写出直线AP 方程，再结合椭圆的右准线为：4x =，得点Q 为34(4,)21tt--，再由向量数量积计算最小值即可．（3）在计算OAB ∆与MAB ∆的面积时，AB 可以最为同底，所以若213S S =，则O 到直线AB 距离1d 与M 到直线AB 距离2d ，之间的关系为213d d =，根据点到直线距离公式可得135d =，295d =，所以题意可以转化为M 点应为与直线AB 平行且距离为95的直线与椭圆的交点，设平行于AB 的直线l 为340x y m -+=，与直线AB 的距离为95，根据两平行直线距离公式可得，6m =-或12，然后在分两种情况算出M 点的坐标即可． 【详解】（1）由椭圆的标准方程可知，24a =，23b =，2221c a b =-=， 所以△12AF F 的周长226a c =+=．（2）由椭圆方程得3(1,)2A ，设(,0)P t ，则直线AP 方程为32()1y x t t=--，椭圆的右准线为：24a x c==，所以直线AP 与右准线的交点为34(4,)21tQ t--，(OP QP t =，0)(4t -，22340)4(2)4421tt t t t--=-=----，当2t =时，()4min OP QP =-．（3）若213S S =，设O 到直线AB 距离1d ，M 到直线AB 距离2d ，则2111||||22AB d AB d ⨯⨯=⨯⨯，即213d d =， 3(1,)2A ，1(1,0)F -，可得直线AB 方程为3(1)4y x =+，即3430x y -+=，所以135d =，295d =，由题意得，M 点应为与直线AB 平行且距离为95的直线与椭圆的交点，设平行于AB的直线l 为340x y m -+=，与直线AB 的距离为95，95=，即6m =-或12，当6m =-时，直线l 为3460x y --=，即3(2)4y x =-， 联立223(2)4143y x x y ⎧=-⎪⎪⎨⎪+=⎪⎩，可得(2)(72)0x x -+=，即20M N x y =⎧⎨=⎩或27127M Mx y ⎧=-⎪⎪⎨⎪=-⎪⎩， 所以(2,0)M 或2(7-，12)7-．当12m =时，直线l 为34120x y -+=，即3(4)4y x =+， 联立223(4)4143y x x y ⎧=+⎪⎪⎨⎪+=⎪⎩，可得221182404x x ++=，△9(3656)0=⨯-<，所以无解， 综上所述，M 点坐标为(2,0)或2(7-，12)7-．【点睛】本题考查椭圆的定义，向量的数量积，直线与椭圆相交问题，解题过程中注意转化思想的应用，属于中档题．21．已知数列{}n a （*n ∈N ）的首项11a =，前n 项和为n S ，设λ与k 是常数，若对一切正整数n ，均有11111k k k n n n S S a λ++-=成立，则称此数列为“~k λ”数列.（1）若等差数列{}n a 是“~1λ”数列，求λ的值； （2）若数列{}n a 是”数列，且0n a >，求数列{}n a 的通项公式；（3）对于给定的λ，是否存在三个不同的数列{}n a 为“~3λ”数列，且0n a ≥？若存在，求λ的取值范围；若不存在，说明理由.【答案】（1）1λ=；（2）()()211342n n n a n -⎧=⎪=⎨⨯≥⎪⎩；（3）存在，01λ<<. 【解析】（1）根据新定义，即由11n n n S S a λ++-=，求λ，此式变形为1(1)0n a λ+-=，分析后可得．（2=11n n n a S S ++=-转化为{}n S 的递推关系，令n b =，得{}n b 的递推关系，求得n b ，从而可得n S ，n a ．（3）类似（2）的转化，令n c，则1 1)n n c c -=≥，即333(1)(1)( 1)n n n c c c λ-=-≥．（），分析此式中n c 的解的情况，注意到321(1)(1)n n n n c c c c -=-++，210n n c c ++>，在0λ≤或1λ=时，（）只有一解1n c =，对应{}n a 只有一个， 在1λ>时，同样得出{}n a 只有一个，在01λ<<时，（）有三个解，一个在(0,1)上，一个是1，一个在(1,)+∞上，即有两个不小于1的解，设在(1,)+∞上的解为t ，则1n n S S +=或31n n S t S +=，这样对数列{}n S ，由其中任一项n S 求其后一项1n S +时都有两种个解，这样所得数列{}n S 会有无数个，从而得{}n a 有无数个．由此可得结论． 【详解】（1）∵等差数列{}n a 是“λ～1”数列，则11n n n S S a λ++-=，即11n n a a λ++=， 也即1(1)0n a λ+-=，此式对一切正整数n 均成立，若1λ≠，则10n a +=恒成立，∴320a a -=，而211a a -=-，这与{}n a 是等差数列矛盾，∴1λ=．（此时，任意首项为1的等差数列都是“1～1”数列） （2）∵数列*{}()n a n ∈N 是”数列，∵0n a >，∴10n n S S +>>1=，n b =，则1n b -=221(1)(1)(1)3n n n b b b -=->， 解得：2n b =2=，也即14n nS S +=，∴数列{}n S 是公比为4的等比数列， ∵111S a ==，∴14n n S -=．2n ≥时，12214434n n n n n n a S S ----=-=-=⨯，∴21(1),34(2).n n n a n -=⎧=⎨⨯≥⎩（3）设各项非负的数列*{}()n a n ∈N 为“~3λ”数列， 则11133311n n n S S a λ++-== ∵0n a ≥，而11a =，∴10n n S S +≥>1=n c，则1 1)n n c c -=≥，即333(1)(1)( 1)n n n c c c λ-=-≥．（） ①若0λ≤或=1λ，则（）只有一解为=1n c ，即符合条件的数列{}n a 只有一个；（此数列为1，0，0，0，…）②若1λ>，则（）化为3232(1)(1)01n nnc c c λλ+-++=-， ∵1n c ≥，∴3232101n nc c λλ+++>-，则（）只有一解为=1n c ， 即符合条件的数列{}n a 只有一个；（此数列为1，0，0，0，…）③若01λ<<，则3232101nnc c λλ+++=-的两根分别在（0，1）与（1，+∞）内， 则方程（）有两个大于或等于1的解：其中一个为1，另一个大于1（记此解为t ）， ∴1n n S S +=或31n n S t S +=，由于数列{}n S 从任何一项求其后一项均有两种不同结果，努力的你，未来可期!精品 ∴这样的数列{}n S 有无数多个，则对应的{}n a 有无数多个； 综上：能存在三个各项非负的数列{}n a 为“~3λ”数列，λ的取值范围是01λ<<．【点睛】本题考查数列新定义，解题是把新定义进行转化，本题就是转化为已知11111k k k n n n S S a λ++-=求n a ，这样只要利用n S 与n a 的关系进行转化．考查了学生分析问题、解决问题的能力，转化与化归能力，本题属于难题．。
上海交通大学附属中学2014-2015学年上学期高三数学摸底考试卷
上海交通大学附属中学2014-2015学年高三上学期数学摸底考试卷（满分150分，120分钟完成，答案一律写在答题纸上）一、填空题（本大题共14题，每题4分，满分56分）1．函数的反函数________________．答案：解：∵，∴，由得，故2. 函数的最小值_________答案：3. 若，则的取值范围是___________答案：4．若对任意正实数，不等式恒成立，则实数的最小值为．答案：-1解：因为对任意正实数，不等式恒成立，所以，因此5．同时满足（1）答案：156．集合，．若“a＝1”是“”的充分条件，则实数b的取值范围是．答案：解：“a＝1”是“”的充分条件的意思是说当时，，现在，，由得或，即或，所以的范围是. 7．已知，则．答案：解：由可得，所以8．方程有解，则________答案：9. 如果答案：10．函数图像的对称中心是．答案：解：因为函数为奇函数，对称中心是，因此函数图像的对称中心是.11.答案：12.答案：13. 关于函数必定是的整数倍；（2）的表达式可改写为；（4）____________答案：（2），（3）14.已知等比数列的首项为，公比为，其前项和记为，又设，的所有非空子集中的最小元素的和为，则的最小正整数为．答案:45解：由题意有，对于和，我们首先把中的元素按从小到大顺序排列，当时，，对于中的任一元素，比它大的有个，这个元素组成的集合的所有子集有个，把加进这些子集形成新的集合，每个都是以为最小元素的的子集，而最小元素为的的子集也只有这些，故在中出现次，所以，时，适合上式，时，．当，不成立，当时，，，由于，，，所以，最小的为．二、选择题（本大题共4题，每题5分，满分20分）15．下列说法正确的是（）A．命题“若，则”的否命题是“若，则”B．“”是“”的必要不充分条件C．命题“若，则”的逆否命题是真命题D．“”是“”的充分不必要条件答案：C解：中，否命题应该是“若，则”，错；中时，有，故至少是充分的，错；中“若，则”是真命题，因此其逆否命题也是真命题，选，而应该是必要不充分条件．16. 若是的最小值，则的取值范围为（）.(A)[-1,2] (B)[-1，0] (C)[1，2] (D)答案：D解：由于当时，在时取得最小值，由题意当时，应该是递减的，则，此时最小值为，因此，解得，选D．17.如果的三个内角的余弦值分别等于的三个内角的正弦值，则（）A ．和都是锐角三角形B ．和都是钝角三角形C ．是钝角三角形，是锐角三角形D ．是锐角三角形，是钝角三角形答案：D解： 是锐角三角形如果是锐角三角形，则，，，不可能成立；如果是直角三角形，不妨设，则，A 1=0不合题意；所以是钝角三角形。
2022届上海市交通大学附属中学高三上学期开学摸底考数学试题(word版)
①若 为锐角三角形，且满足 ，则
②在 的二项展开式中， 项的系数为
③函数 与函数 关于直线 对称
④设等差数列 前n项和为 ，若 ，则
⑤函数 的最小值为2
11.已知有限集 ，如果A中元素 满足： ，就称A为n元“均衡集”．若 是二元“均衡集”，则 的取值范围是__．
【答案】（1） ；（2） ；（3）存在， .
（1）∵函数y＝f（x）满足f（3x）＝3f（x），
又∵当x∈[1，3]时，函数y＝f（x）的图象与x轴所围成的图形面积：
，
∴当x∈[31，32]时，函数y＝f（x）的图象与x轴所围成的图形面积：
，
当x∈[32，33]时，函数y＝f（x）的图象与x轴所围成的图形面积：
，…
当x∈[3n﹣1，3n]时，函数y＝f（x）的图象与x轴所围成的图形面积：
，
此时函数y＝f（x）的图象与x轴所围成的图形面积S＝S1+S2+S3+…+Sn﹣1＝ ；
（2）当 时， ， ，
由 可得，
当 时， 时取 ，
当 时， 时取 ，
当 ， 时取 ，
经计算可知 ，且 ，
所以当 时，函数 的最大值为：
【答案】（1） ；（2）不存在，理由见解析.
解：（1）数列 为“ 数列”，则 ，
所以 ，两式相减得： ，又 时， ，所以 ，
故 对任意的 恒成立，即 ，故数列 为等比数列，其通项公式为 ．
（2）假设存在这样的数列 ，则有 ，故有 ，
两式相减得， ，则又 ．
同理，由 是“ 数列”可得， ，
所以 对任意的 恒成立，
（1）设 ，将y表示成 的函数关系式，并指出 的范围；
上海市交大附中2024学年数学高三上期末调研试题含解析
上海市交大附中2024学年数学高三上期末调研试题考生请注意：1．答题前请将考场、试室号、座位号、考生号、姓名写在试卷密封线内，不得在试卷上作任何标记。
2．第一部分选择题每小题选出答案后，需将答案写在试卷指定的括号内，第二部分非选择题答案写在试卷题目指定的位置上。
3．考生必须保证答题卡的整洁。
考试结束后，请将本试卷和答题卡一并交回。
一、选择题：本题共12小题，每小题5分，共60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．在正方体1111ABCD A B C D -中，点E ，F ，G 分别为棱11A D ，1D D ，11A B 的中点，给出下列命题：①1AC EG ⊥；②//GC ED ；③1B F ⊥平面1BGC ；④EF 和1BB 成角为4π.正确命题的个数是（ ） A ．0B ．1C ．2D ．32．设i 是虚数单位，若复数1z i =+，则22||z z z+=（ ）A ．1i +B ．1i -C ．1i --D ．1i -+3．在一个数列中，如果*n N ∀∈，都有12n n n a a a k ++=（k 为常数），那么这个数列叫做等积数列，k 叫做这个数列的公积.已知数列{}n a 是等积数列，且11a =，22a =，公积为8，则122020a a a ++⋅⋅⋅+=（ ） A ．4711B ．4712C ．4713D ．47154．已知集合2{|23}A x y x x ==-++，{}2|log 1B x x =>则全集U =R 则下列结论正确的是( ) A ．AB A =B ．A B B ⋃=C ．()UA B =∅ D ．UB A ⊆5．在平面直角坐标系xOy 中，已知角θ的顶点与原点O 重合，始边与x 轴的非负半轴重合，终边落在直线2y x =上，则3sin 22πθ⎛⎫+= ⎪⎝⎭（ ） A ．45 B ．45-C ．35D ．356．用数学归纳法证明，则当时，左端应在的基础上加上（ ）A ．B ．C ．D ．7．已知甲、乙两人独立出行，各租用共享单车一次（假定费用只可能为1、2、3元）．甲、乙租车费用为1元的概率分别是0.5、0.2，甲、乙租车费用为2元的概率分别是0.2、0.4，则甲、乙两人所扣租车费用相同的概率为（ ）A ．0.18B ．0.3C ．0.24D ．0.368．刘徽是我国魏晋时期伟大的数学家，他在《九章算术》中对勾股定理的证明如图所示.“勾自乘为朱方，股自乘为青方，令出入相补，各从其类，因就其余不移动也.合成弦方之幂，开方除之，即弦也”.已知图中网格纸上小正方形的边长为1，其中“正方形ABCD 为朱方，正方形BEFG 为青方”，则在五边形AGFID 内随机取一个点，此点取自朱方的概率为（ ）A ．1637B ．949C ．937D ．3119．已知四棱锥P ABCD -中，PA ⊥平面ABCD ，底面ABCD 是边长为2的正方形，5PA =E 为PC 的中点，则异面直线BE 与PD 所成角的余弦值为（ ） A ．13 B 13 C ．15D 15 10．已知实数0a >，1a ≠，函数()2,14ln ,1x a x f x x a x x x ⎧<⎪=⎨++≥⎪⎩在R 上单调递增，则实数a 的取值范围是（ ）A ．12a <≤B ．5a <C ．35a <<D ．25a ≤≤11．已知函数()ln f x x =，()()23g x m x n =++，若()0,x ∀∈+∞总有()()f x g x ≤恒成立.记()23m n +的最小值为(),F m n ，则(),F m n 的最大值为（ ）A ．1B ．1eC ．21eD ．31e 12．一个四棱锥的三视图如图所示（其中主视图也叫正视图，左视图也叫侧视图），则这个四棱锥中最最长棱的长度是（ ）．A ．26B ．4C ．23D ．22二、填空题：本题共4小题，每小题5分，共20分。
2015-2016年上海市交大附中高三下开学考
上海交大附中高三开学摸底考数学试卷2016.02一. 填空题1. 设集合{|||4}A x x =<，2{|430}B x x x =-+>，则集合{|x x A ∈且()}x A B ∉=； 2. 若10112z ii-=+，则复数z =；3. 函数22()log (1)f x x =+(0)x <的反函数1()f x -=；4. 2222lim (1)n n nn C C n -→∞+=+； 5. 设12322()log (1)2x e x f x x x -⎧<=⎨-≥⎩，则不等式()2f x >的解集为； 6. 已知平面向量α、β，||2α=，||3β=，α、β的夹角为60°，则|2|αβ-=； 7. 已知圆锥的母线长为5，侧面积为15π，则此圆锥的体积为；（结果保留π）8. 以双曲线221416x y -=的右焦点为圆心，且被其渐近线截得的弦长为6的圆的方程是； 9. 设抛物线24x y =的焦点为F ，经过点(1,4)P 的直线l 与抛物线相交于A 、B 两点，且点P 恰为AB 的中点，则||||AF BF +=；10. 某中学在高一年级开设了4门选修课，每名学生必须参加这4门选修课中的一门，对于该年级的甲乙2名学生，这2名学生选择的选修课相同的概率是； 11. 各项为正数的无穷等比数列{}n a 的前n 项和为n S ，若1l i m1nn n S S →∞+=，则其公比q 的取值 范围是；12. 已知实数x 、y 满足222log (23)1log log x y x y ++=++，则xy 的最小值是；13. 已知函数()||f x x x =，当[,1]x a a ∈+时，不等式(2)4()f x a f x +>恒成立，则实数a 的取值范围是；14.（理）对任意x R ∈，函数1(1)2f x +=，设2[()]()n a f n f n =-（*n N ∈），数列{}n a 的前15项的和为3116-，则(15)f =； （文）已知数列{}n a 满足1(22()nn n n n a a a a n a +⎧⎪=⎨⎪-⎩为偶数)为奇数，若31a =，则1a 的所有可能的取值为；二. 选择题 15.在24上的展开式中，x 的幂指数是整数的项共有（） A.3项 B.4项C.5项D. 6项16. 已知a 、b 为实数，命题甲：2ab b >，命题乙：110b a<<，则甲是乙的（） A.充分不必要条件 B.必要不充分条件 C.充要条件D.既不充分也不必要条件17. △ABC 外接圆的半径为1，圆心为O ，且20OA AB AC ++=，||||OA AB =，则CA CB ⋅等于（）A.3218.（理）下列命题：①函数3sin(25)y x θ=+的图像关于y 轴对称的充要条件是2510k ππθ=+，k Z ∈； ②已知n S 是等差数列{}n a 的前n 项和，若75S S >，则93S S >； ③函数(1)y f x =+与函数(1)y f x =-的图像关于直线1x =对称；④对于任意两条异面直线，都存在无穷多个平面与这两条异面直线所成的角相等； 其中正确的命题有（）A.1个B.2个C.3个D.4个（文）设()f x 和()g x 是定义在同一个区间[,]a b 上的两个函数，若对于任意的[,]x a b ∈， 都有|()()|1f x g x -≤，则称()f x 与()g x 是在[,]a b 上的“密切函数”，[,]a b 称为“密 切区间”，设2()34f x x x =-+与()23g x x =-是在[,]a b 上的“密切函数”，则它的密切 区间可以是（）A.[1,4]B.[2,3]C.[3,4]D.[2,4]三. 解答题19. 在△ABC 中，角A 、B 、C 的对边分别为a 、b 、c ，已知a 、b 、c 成等比数列，且3cos 4B =； （1）求cot cot AC +的值；（2）设32BA BC ⋅=，求a c +的值；20.（文）如图，设计一个正四棱锥形冷水塔，高是0.85米，底面的边长是1.5米；（1）求这个正四棱锥形冷水塔的容积； （2）制造这个水塔的侧面需要多少平方米钢板？ （结果精确到0.01米）（理）如图，直三棱柱111ABC A B C -中，90ABC ︒∠=，4AB BC ==，13BB =，M 、N 分别是11B C 和AC 的中点；（1）求异面直线1AB 与1C N 所成的角； （2）求三棱锥1M C CN -的体积；21. 已知函数()||()f x x x a =-，a 为实数；（1）讨论()f x 在R 上的奇偶性；（只要写出结论，不需要证明） （2）当0a ≤时，求函数()f x 的单调区间；（3）当2a ≤-时，求函数()y f x =在1[1,]2-上的最大值；22.（1）若动点P 到定点F 的距离与到定直线:l x = 证：动点P 的轨迹是椭圆；（2）设（1）中的椭圆短轴的上顶点为A ，试找出一个以点A 为直角顶点的等腰直角三角 形ABC ，并使得B 、C 两点也在椭圆上，并求出△ABC 的面积；（3）对于椭圆2221x y a+=（常数1a >），设椭圆短轴的上顶点为A ，试问：以点A 为直角顶点，且B 、C 两点也在椭圆上的等腰直角三角形ABC 有几个？23.（理）已知数列{}n a *()n N ∈的前n 项和为n S ，数列{}n S n 是首项为0，公差为12的等 差数列；（1）求数列{}n a 的通项公式； （2）设4(2)15n a n b =⋅-*()n N ∈，对任意的正整数k ，将集合21221{,,}k k k b b b -+中的三个元 素排成一个递增的等差数列，其公差为k d ，求证：数列{}k d 为等比数列； （3）对（2）中的k d ，求集合1{|,}k k x d x d x Z +<<∈的元素个数；（文）已知数列{}n a *()n N ∈的前n 项和为n S ，数列{}n S n 是首项为0，公差为12的等 差数列；（1）求数列{}n a 的通项公式；（2）设4(2)15n a n b =⋅-*()n N ∈，对任意的正整数k ，将集合21221{,,}k k k b b b -+中的三个元 素排成一个递增的等差数列，其公差为k d ，求k d ；（3）对（2）中的k d ，设1(1,5)A d ，2(2,5)B d ，动点M 、N 满足MN AB =，点N 的 轨迹是函数()y g x =的图像，其中()g x 是以3为周期的周期函数，且当(0,3]x ∈时，()lg g x x =，动点M 的轨迹是函数()f x 的图像，求()f x ；上海交大附中高三开学摸底考数学试卷参考答案2016.02一. 填空题1. (4,4)A =-，(,1)(3,)B =-∞+∞，∴答案[1,3]；2. (12)(1)z i i +=-，∴1131255i z i i -==--+； 3. 221y x =-，∵0x <，∴1()f x -=(0)x >；4. 22222233lim lim (1)(1)2n n n n n n C C C n n -→∞→∞+==++； 5. 分类讨论，解集为(1,2)(10,)+∞；6. 2|2|1691213αβ-=+-=，∴|2|13αβ-=7. 底面半径为3，高为4，12V π=；8. 圆心为，圆心到渐近线距离为4，∴半径为5，∴22(25x y -+=； 9. 12||||42210AF BF y y p +=++=⨯+=； 10. 41444P ==⨯； 11. 分类讨论，1q =符合，1q ≠时，111lim lim 11nn n n n n S q S q +→∞→∞+-==-，01q <<，∴(0,1]q ∈；12. 2323x y xy ++=≥3， 4.5xy ≥，即最小值为4.5； 13. 22x a x +>，2x a <恒成立，即12a a +<，∴1a >14.（理）根据已知条件得221()(1)()(1)4f x f x f x f x ++=+++，∴1215...a a a +++= 2731(15)(15)416f f --=-，解得3(15)4f =； （文）31a =，∴22a =或5，∴14a =或7或10；二. 选择题 15. 15112243622424()()rrrrr C x x C x---=，0,6,12,18,24r =，选C ；16. 选B ；17. 根据题意，1AB =，AC =2BC =，∴3CA CB ⋅=，选C ； 18.（理）②④正确，选B ；（文）2|()()|571f x g x x x -=-+≤，解得[2,3]x ∈，选B ；三. 解答题 19.（1）cos cos sin 1sin sin sin sin sin A C B A C A C B +===；（2）2ac =，223cos 24a c ac B ac +-==，∴3a c +=；20.（文）（1）2311511.50.853380V Sh m ==⨯⨯=；（2）2144 1.5 3.402S S m ∆==⨯⨯≈（理）（1）取11AC 中点E ，连AE 、1B E ，sin θ=θ=或（2）111132233M C CN N C CM V V Sh --===⨯⨯=；21.（1）0a =时，奇函数；0a ≠时，非奇非偶函数；（2）0a =时，()f x 递增；0a <时，在(,)2a-∞和(0,)+∞上递增，在(,0)2a 上递减； （3）结合单调性可知1()2f 或(1)f -最大，分类讨论；当5(,]2a ∈-∞-，max ()f x =(1)1f a -=--；当5(,2]2a ∈--，max 11()()242af x f ==-；22.（1）椭圆第二定义，证明略；（2）椭圆方程2219x y +=，(0,1)A ，设:1AB y kx =+，∴2221891(,)9191k k B k k --+++，根据题意，1B C y x -=，即22291181919k k k k -+-=++，解得1k =或4k =1k =，8125S =；4k =2211881(29140S k ==+；∴8125S =或8140； （3）椭圆方程2221x y a +=，(0,1)A ，设:1AB y kx =+，∴222222221(,)11a k a k B a k a k --+++，同 理，1B C y x -=，即22222221211a k a k a k a k-+-=++，解得1k =或22(1)10k a k +-+=；当22(1)40a ∆=-->时，即)a ∈+∞时，k 有三解，即这样的三角形有3个；当0∆≤时，即(1a ∈时，k 只有一解，即这样的三角形有1个； 23.（理）（1）1122n S n n =-，21122n S n n =-，1n a n =-； （2）45kk d =，为等比数列；（3）分奇偶找规律，k 为奇数，2169k k e e +=-；k 为偶数，2169k k e e +=+；待定系数法求出两种情况下的通项公式，综合为13[4(1)]5kk k e +=+-；（文）（1）1n a n =-；（2）45kk d =；（3）()lg(3)g x x k =-，(3,33]x k k ∈+；()lg(31)12f x x k =-+-，(31,32]x k k ∈-+；。
(交大附中)2021-2022学年上海新高三入学摸底英语测试卷十一(学生版)
2021-2022学年上海新高三入学摸底英语测试卷十一（模拟交大附中入学摸底卷）第I卷（选择题）一、完形填空（每小题1分，共20分）Mark is leaving, and I’m feeling kind of sad. He’s been the heart and soul of the office for a couple of years, 1 good professional skills with a sweet and 2 personality.And now he’s moving on to an exciting new professional 3 . It sounds like it could be the chance of a lifetime, and we’re 4 pleased for him. But that doesn’t make it any 5 to say goodbye to a dear friend and trusted 6 .Life has a way of throwing these curve (曲线) balls 7 us. Just when we start to get8 with a person, a place or a situation, something comes along to change the recipe.Our ability to cope with 9 determines happiness in life. But how do we do that? Afri end of mine reminds us that “survivability depends upon 10 .” And then there’s Chris the California surfer, who once told me that the answer to life’s problems can be summed up in four words: “Go with the flow.”I think life is a series of 11 - both good and bad. No matter how excellent your organizational skills, there will always be life-influencing factors over which you have no12 . The truly successful person is prepared to 13 adjustments should the need arise.That doesn’t mean you don’t keep trying to make all your 14 come true. It just means when things come up that aren’t 15 in your plan, you work around them - and then you move on.“Change, indeed, is painful, 16 ever needful.” said philosopher Thomas Carlyle. “And if memory has its force and worth, so has hope.” We’re going to 17 Mark. But rather than stay on the 18 of our parting, we’ll focus on our hopes for a brighter future - for him, and for us. And then we’ll go out and 19 everything we can to make that future happen 20 our plans change again.1．A．associating B．comparing C．combining D．replacing 2．A．fragile B．gentle C．special D．split 3．A．separation B．destination C．expectation D．opportunity4．A．sincerely B．ridiculously C．absolutely D．secretly 5．A．nobler B．ruder C．easier D．fairer 6．A．colleague B．roommate C．teacher D．leader7．A．on B．with C．in D．at 8．A．autonomous B．sunburnt C．comfortable D．dynamic 9．A．change B．challenge C．choice D．chance 10．A．adaptability B．confidence C．accommodation D．competence 11．A．accidents B．barriers C．events D．records 12．A．control B．access C．advantage D．priority 13．A．take B．make C．get D．have 14．A．decisions B．promises C．dreams D．solutions 15．A．mostly B．accidentally C．eventually D．exactly 16．A．yet B．also C．even D．still 17．A．assist B．accompany C．miss D．forgive 18．A．complaint B．attention C．sadness D．sympathy 19．A．do B．demand C．face D．seize20．A．if B．until C．when D．after第II卷（非选择题）二、选用适当的单词或短语补全短文（每小题2分，共10分）根据句意，选择单词或短语并以其适当形式填空。
2015届上海高三第一学期开学摸底考试化学试卷
2014学年第一学期高三开学摸底考试化学试卷（考试时间120分钟，试卷满分150分）相对原子质量：H-1 C-12 N-14 O-16 Na-23 Cu-64 Sn-119一、选择题（每题只有1个选项符合题意。
每小题2分，满分10分。
） 1．下列说法正确的是A ．质子数相同的粒子其化学性质相同B ．1s 、2s 、3s 、4s 原子能级不同，电子云轮廓图形状相同C ．轨道表示式，是对原子核外电子运动状态最完美的描述D ．所有元素原子的最外层电子数都等于该元素的最高化合价 2．长期放置的浓硝酸常显黄色，消除其中的黄色最好的方法是A ．在光亮处放置B ．加入足量水C ．通入适量的空气D ．加入漂白粉 3．下列叙述中，正确的是A ．在船舶的外壳装上铜块可防止其发生电化学腐蚀B ．FeCl 3溶液和Fe 2(SO 4)3溶液加热蒸干、灼烧都得到Fe 2O 3C ．电解法精炼粗铜，用纯铜作阴极；在镀件上电镀锌，用锌作阳极D ．用惰性电极分别电解CuCl 2溶液和MgCl 2溶液分别得到单质Cu 和Mg4．已知ZnO(s)+ H 2SO 4(aq)→ZnSO 4(aq)+ H 2O(g)＋Q kJ(Q ＞0，其中“aq ”表示“溶液”)，关于该反应的叙述错误的是A ．该反应的化学能可以直接转化为电能B ．反应物的总能量高于生成物的总能量C ．该反应的Q 值与实际反应中反应物用量无关D ．若其它条件不变，上述反应生成液态水时，放出的反应热将大于Q kJ5．Na 2O 2是一种淡黄色固体，常用作潜水艇的供氧剂。
下列关于Na 2O 2的描述正确的是 A ．Na 2O 2晶体中阴阳离子个数之比为1:1 B ．Na 2O 2晶体中既有离子键又有非极性共价键 C ．Na 2O 2在空气中加热可以得到更稳定的Na 2O D ．Na 2O 2长期露置于空气中最终转变成NaOH二、选择题（每题只有1个选项符合题意。
每小题3分，满分36分。
【VIP专享】上海市交大附中2015届高三上学期摸底考试数学试题 Word版含答案
上海交通大学附属中学2014-2015学年度一学期高三数学摸底考试卷（满分150分，120分钟完成，答案一律写在答题纸上）一、填空题（本大题共14题，每题4分，满分56分）1．函数的反函数________________．答案：解：∵，∴，由得，故2. 函数的最小值_________答案：3. 若，则的取值范围是___________答案：4．若对任意正实数，不等式恒成立，则实数的最小值为．答案：-1解：因为对任意正实数，不等式恒成立，所以，因此5．同时满足（1）答案：156．集合，．若“a＝1”是“”的充分条件，则实数b的取值范围是．答案：解：“a＝1”是“”的充分条件的意思是说当时，，现在，，由得或，即或，所以的范围是.7．已知，则．答案：解：由可得，所以8．方程有解，则________答案：9. 如果答案：10．函数图像的对称中心是．答案：解：因为函数为奇函数，对称中心是，因此函数图像的对称中心是.11.答案：12.答案：13. 关于函数必定是的整数倍；（2）的表达式可改写为；（4）____________答案：（2），（3）14.已知等比数列的首项为，公比为，其前项和记为，又设，的所有非空子集中的最小元素的和为，则的最小正整数为．答案:45解：由题意有，对于和，我们首先把中的元素按从小到大顺序排列，当时，，对于中的任一元素，比它大的有个，这个元素组成的集合的所有子集有个，把加进这些子集形成新的集合，每个都是以为最小元素的的子集，而最小元素为的的子集也只有这些，故在中出现次，所以，时，适合上式，时，．当，不成立，当时，，，由于，，，所以，最小的为．二、选择题（本大题共4题，每题5分，满分20分）15．下列说法正确的是（）A．命题“若，则”的否命题是“若，则”B．“”是“”的必要不充分条件C．命题“若，则”的逆否命题是真命题D．“”是“”的充分不必要条件答案：C解：中，否命题应该是“若，则”，错；中时，有，故至少是充分的，错；中“若，则”是真命题，因此其逆否命题也是真命题，选，而应该是必要不充分条件．16. 若是的最小值，则的取值范围为（）.(A)[-1,2] (B)[-1，0] (C)[1，2] (D)答案：D解：由于当时，在时取得最小值，由题意当时，应该是递减的，则，此时最小值为，因此，解得，选D．17.如果的三个内角的余弦值分别等于的三个内角的正弦值，则（）A ．和都是锐角三角形B ．和都是钝角三角形C ．是钝角三角形，是锐角三角形D ．是锐角三角形，是钝角三角形答案：D解： 是锐角三角形如果是锐角三角形，则，，，不可能成立；如果是直角三角形，不妨设，则，A 1=0不合题意；所以是钝角三角形。
2023-2024学年上海交大附中高三上10月月考英语试题及答案
上海交通大学附属中学2023-2024学年度第一学期高三英语十月月考试卷（满分150分，120分钟完成。
答案请写在答题纸上。
）I.Listening Comprehension(25’)Section ADirections:In Section A,you will hear ten short conversations between two speakers.At the end of each conversation,a question will be asked about what was said.The conversations and the questions will be spoken only once.After you hear a conversation and the question about it,read the four possible answers on your paper,and decide which one is the best answer to the question you have heard.1.A.Go to catch the next train. B.Listen to the traffic report.C.Go to the city by other transportation.D.Check the weekend schedule.2.A.It doesn’t take a long time to get there. B.The lectures have been put off.C.There is no need to hurry.D.The lectures have already started.3.A.The woman should have gone to Paris earlier.B.He studied French in a different way in high school.C.Life in Paris helped improve the woman’s language skills.D.The woman must have had a good teacher in Paris.4.A.She thinks the post office is nearby. B.She is also looking for the post office.C.She thinks the man’s guess is right.D.She doesn’t know where the post office is.5.A.Her coat is similar to the man’s. B.The man needn’t have brought the coat.C.Her sweater is not warm enough.D.The man shouldn’t have worn a sweater.6.A.Make sure the registration office didn’t make a mistake.B.Decide whether to drop the course in the first week.C.Find out if a place opens up in the course later.D.Take the course of the creative writing next year.7.A.He recently spent a month in New York. B.He can recommend many things to do.C.He suggests the woman extend her trip.D.He bets the woman will have fun there.8.A.Disappointed. B.Excited. C.Proud. D.Embarrassed.9.A.He talks less than he used to. B.He hasn’t had time to play tennis recently.C.He shouldn’t have behaved so proudly.D.He has never talked to her after the game.10.A.The man should have had his car inspected earlier.B.There are always a lot of people at the auto inspection center.C.She waited longer than the man did to have her car inspected.D.The auto inspection center will close at the end of the month.Section BDirections:In Section B,you will hear several longer conversation(s)and short passage(s),and you will be asked several questions on each of the conversation(s)and the passage(s).The conversation(s)and passage(s)will be read twice,but the questions will be spoken only once.When you hear a question,read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions11through13are based on the following passage.11.A.The truck’s over speeding. B.The truck’s heavy load.C.The terrible weather.D.The pedestrians’carelessness.12.A.The relocation of several factories. B.The company’s pay offer.C.The high rate of unemployment.D.The union’s demand.13.A.They will increase by a third this year.B.They have been rising in the last five years.C.The average price of a house in the UK is£255,900.D.They make it extremely difficult for those on the property ladder to buy a house. Questions14through16are based on the following passage.14.A.What causes fearfulness externally. B.Why mice are particularly fearful animals.C.Whether fearfulness is inherited or not.D.How animals react to frightening situations.15.A.They wandered around the box. B.They bred again and again.C.They couldn’t find a hiding place.D.They remained close to one wall.16.A.Some changes in the nervous system. B.The interference from human beings.C.The size of nerve cells in the brain.D.The existence of certain nerve cells. Questions17through20are based on the following conversation.17.A.In the woman’s hometown. B.In the man’s hometown.C.Outside their hometown.D.In a small town.18.A.Choose whichever friend can give the best toast.B.Choose whichever friend can plan the reception.C.Choose whichever friend knows all their in-laws.D.Choose whichever friend knows a lot about weddings.19.A.The bride’s family. B.A wedding planner.C.The groom’s family.D.The new couple.20.A.She doesn’t think it is a tradition.B.She thinks her mother-in-law can plan the wedding well.C.She thinks it will cost too much to have a wedding planner.D.She doesn’t want her wedding to be in the charge of someone unknown to her.II.Grammar and Vocabulary(20’)Section ADirections:After reading the passages below,fill in the blanks to make the passages coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form of the given word;for the other blanks,use one word that best fits each blank.(A)What is nirvana(涅槃、超脱)for a potato?To be sliced and bathed in boiling oil before ____21____(emerge)as a French fry?To have its weight matched in butter and cream and be transformed into glorious mounds of mash?No.The answer is found in a plastic bag.For a potato,there is no nobler fate than to end up in a packet of Tayto cheese-and-onion crisps.Taytos are the perfect crisps.The company was established in Ireland in1954by Joe Murphy.He was not the inventor of crisps,but he has been credited____22____ transforming them.Until then there was no way to flavour the individual crisps____23____. Instead,each bag came with a small blue packet of salt____24____(shake)over the contents.Murphy started with artificial flavours of cheese and onion.The pairing is a classic,and the flavour combines well with potatoes.“Potatoes,”____25____(write)Seamus Heaney, one of Ireland’s greatest poets,“promise the taste of ground and root”.The ____26____(poetic)might describe them as a bit plain.Sprinkled with the salty umami(鲜味) of Murphy’s seasoning,however,they became a cut-price sensation.Taytos remain the classic Irish crisp,but now they are available elsewhere,____27____, of course,many other brands of flavoured crisps are.That is a mixed blessing.Once upon a time even industrially produced foods had a limited range.To travel was to discover not only the cooking in other places,but the snacks.Going to France was a chance to chug(一饮而尽)a bottle of Orangina,a fizzy drink.For me,Taytos were____28____once-a-year treat, to be eaten on a beach in south-west Ireland shivering after an icy swim or sweating at the top of a mountain.Thanks to a globalised food system and the appetites of homesick migrants,such items are now available far beyond their lands of origin.That shift results in the loss of a modest joy.At first glance a bag of Taytos is the opposite of a seasonal or local food.____29____(enclose)in their silvery plastic,they survive in all seasons and locales.And yet,for me at least,these potato snacks are entangled with their Irish roots.The ingenious seasoning should taste no different____30____I am in a London park or in Murphy’s homeland.But somehow it does.(B)Are you afraid of getting old?____31________31________31____we get past the age of25,many of us immediately feel the urge to stop the signs of ageing—especially the visible ones.Men and women are now using topical“anti-ageing”creams,spa treatments and medical procedures____32____(counter)many of them.____33____these methods can somewhat affect the way you look,ageing is an internal process.A new study has found exactly when during your lifetime this process peaks.A group of scientists based out of the Stanford University School of Medicine have discovered that____34________34____being a smooth,continuous process,ageing surges forward at three distinct stages of life:first,at the age of34,then at age60,and finally at78.The study,published in Nature Medicine,reveals that scientists can not only predict your age by studying the proteome(protein levels in the blood)but also determine which organs are ageing faster than____35________35____,and which age-related diseases your body is more likely to develop.The study measured plasma proteins(血浆蛋白) collected from4,263adults between the ages of18-95years and studied the changes in the proteome that occurred with age.Their ultimate goal was to understand how to identify the changes associated with cardiovascular issues and age-related diseases like Alzheimer's____36________36____ therapeutic treatments can be devised to counter their onset while there's still time.Dr Tony Wyss-Coray,one of the leading members of the study,told Stanford Medicine News Center,“We've known for a long time that____37____(measure)certain proteins can give you information about a person's health status—lipoproteins(脂蛋白)for cardiovascular(心血管的)health,for example.But it____38____(not appreciate)that so many different proteins'levels—roughly a third of all the ones we looked at—change markedly with advancing age.”This difference between the chronological(按时间计算的)and physiological(生理的) age,according to the scientists'“plasma-protein clock”,showed that a lot of people in the study seemed younger than they actually are.What's more,the study also confirmed that men and women,though equally____39____(represent)in the study,age differently.Does this mean medications and lifestyle methods,with further research,can also be devised to help____40____ages too rapidly and is at risk of contracting age-related diseases like hypertension and Alzheimer's?You never know.Section B:Directions:Complete the following passages by using the words in the box.Each word can only beIt launched an independent review of security after items including gold jewellery and gems of semiprecious stones and glass dating from the15th century BC to the19th century AD were found to be missing,stolen or damaged.Legal action against the____41____member of staff will be taken and the matter is also being investigated by the economic crime command of the Metropolitan police.George Osborne,the museum’s chair,said:“The trustees of the British Museum were extremely____42____when we learned earlier this year that items of the collection had been stolen.“The trustees have taken____43____action to deal with the situation,working with the team at the museum.We called in the police,imposed emergency measures to increase security,set up an independent review into what happened and lessons to learn,and used all the____44____powers available to us to deal with the individual we believe to be responsible.“Our priority is now threefold:first,to____45____the stolen items;second,to find out what,if anything,could have been done to stop this;and third,to do whatever it takes,with investment in security and collection records,to make sure this doesn’t happen again.“This incident only reinforces the____46____for the reimagination of the museum we have embarked upon.It’s a sad day for all who love our British Museum,but we’re determined to____47____the wrongs and use the experience to build a stronger museum.”Hartwig Fischer,the museum’s director,said:“This is a highly unusual incident.We take the safeguarding of all the items in our care____48____.The museum apologises for what has happened,but we have now brought an end to this–and we are determined to put things right.We have already tightened our security arrangements and we are working alongside outside experts to complete a definitive____49____of what is missing,damaged and stolen.This will allow us to____50____our efforts into our work to ensure the stolen items are returned to the museum.”III.Reading ComprehensionSection ADirections:For each blank in the following passage there are four words or phrases marked A,B,C and D.Fill in each blank with the word or phrase that best fits the context.I own a market research company,so I understand the importance of gathering data from your target audience and using that data in order to make product development.I also know that surveys can provide____51____information that's extremely valuable to our clients.But the quality of the data you get as an output from surveys is only as strong as how well you____52____the survey questions.One of the main pitfalls I see teams make is writing leading questions that might get the company results they want to hear,but those results are not always____53____.Below are common ways I've seen companies ask leading questions and how to avoid them:1.Don't make assumptions for your participants.“How well do you think we delivered on your project?”implies your team did a good job.To make it more objective,____54____to ask,“How did we deliver on your project?”It's a subtle change,but the second question takes out the implicit bias.2.Balance the options from which participants can choose.Let's say you want to know the level of satisfaction or dissatisfaction customers have with your product or service.If you ask this in a multiple-choice format,you need to ensure the____55____is balanced for both positive and negative responses.The following options, for example,would not work:•Extremely satisfied•Very satisfied•Satisfied•Somewhat unsatisfied•UnsatisfiedAs a rule of thumb,if you have“extremely”on the positive end,you should have “extremely”on the negative side as well,and give a(n)____56____option in the middle of the scale.3.Don't'lead the witness'(or participant).Again,if you're seeking____57____(and you should have started with knowing why you're conducting the survey in the first place),you don't want to put statements in front of a question that will lead participants to____58____in a certain way.____59____,my company works a lot with educational technology companies.We would never write a question such as this:“Most of the people who use this educational technology product say that the adaptive and personalized nature of the product is better than others on the market.What do you think?”This is because,now,the participant knows exactly what we want them to think.4.Avoid double-barrel questions.Be mindful about including two questions in one and____60____how a participant can respond.Say you ran an event for customers;you wouldn't want to ask,“What do you think about the location and the quality of the speakers?”and then have multiple choice options where they are really only able to respond to one question.They might have loved the venue but hated your presenters.The____61____of the data you gather is compromised when you put questions together.5.Don't write coercive questions.These questions don't sit well.In my experience,they tend to come up more in customer ____62____surveys and employee surveys when you really want to be able to highlight the positives.Examples of coercive questions include:"You'll leave us a positive Google Review,won't you?""You'll tell your friends to visit our restaurant,right?"Naturally,these are full of bias,so they should be avoided____63____.Know what the goals of your survey are.If you want to get data that____64____biases, yes,leading questions can help you get those data points.But the integrity of the data cannot be trusted when you're not writing questions in a(n)____65____way for your participants to answer.51. A.quantitative B.controversial C.mysterious D.proper52. A.craft B.pave C.tempt D.anchor53. A.delightful B.dominant C.accurate D.independent54. A.repeat B.rephrase C.restore D.refresh55. A.portion B.category C.thread D.scale56. A.random rmative C.sacred D.neutral57. A.instinct B.gratitude C.truth D.harmony58. A.reverse B.respond C.deny pete59. A.In addition B.For instance C.After all D.Above all60. A.limiting B.spilling C.inserting D.distracting61. A.integrity B.endurance C.exploitation D.highlight62. A.discrimination B.satisfaction C.transition D.perseverance63. A.on good terms B.by no means C.at all costs D.to some extent64. A.conserves B.entitles C.seals D.includes65. A.isolated B.objective C.selected D.reflectiveSection BDirections:Read the following three passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)In winter,Hammerfest is a thirty-hour ride by bus from Oslo,though why anyone would wantto go there in winter is a question worth considering.It is on the edge of the world,the northernmost town in Europe,a place of dark and fierce winters,where the sun sinks into the Arctic Ocean in November and does not rise again for ten weeks.I wanted to see the Northern Lights...but now as l picked my way through Oslo in late December.I was beginning to have my doubts.Things had not started well.I had overslept at the hotel,missing breakfast,and had to leap into my clothes.I couldn't find a taxi and had to drag my over-weighted bag eight blocks to the central bus station.I had had huge difficulty persuading the staff at the Kreditkassen Bank on Karl Johans Gate to cash sufficient traveller's cheques to pay the1,200-kroner bus fare------they simply could not be made to grasp that the William McGuire Bryson on my passport and the Bill Bryson on my traveller's cheques were both me-and now here l was arriving at the station two minutes before departure...and the girl at the ticket counter was telling me that she had no record of my reservation.'This isn't happening,'I said.'I'm still at home in England enjoying Christmas...'Actually,I said, 'There must be some mistake.Please look again.'The girl studied the passenger list.'No,Mr Bryson,your name is not here.'But I could see it,even upside-down.'There it is,second from the bottom.''No,'the girl decided,'that says Bernt Bjornson.That's a Norwegian name.''It doesn't say Bernt Bjorson.It says Bill Bryson.Look at the y,the two ls.Miss,please,’But she wouldn't have it.'If I miss this bus,when does the next one go?''Next week at the same time.'Oh,splendid.'Miss,believe me,it says Bill Bryson.''No,it doesn't.''Miss,look,I've come from England.I'm carrying some medicine that could save a child's life.' She didn't buy this.'l want to see the manager.''He's in Stavanger.''Listen,I made a reservation by telephone.If I don't get on this bus,I'm going to write a letter to your manager that will cast a shadow over your career prospects for the rest of this century.'This clearly did not alarm her.Then it struck me.'If this Bemt Bjorson doesn't show up,can l have this seat?''Sure.'Why don't I think of these things in the first place...?'Thank you,'I said...66.What can be learned from the passage about Hammerfest?A.It is located in the South of the city of Oslo.B.It is where the Northern Lights can be seen.C.It remains a town without sufficient power supply.D.It remains in the darkness from November till next March.67.The writer got to the station just two minutes before the train's departure because he spent much time_____.A.cashing his traveller's chequesB.finding a place to have breakfastC.waiting for a taxi to send him thereD.choosing suitable clothes to wear68.By“Oh,splendid”,the writer meant that he actually felt_____.A.puzzledB.amazedC.worriedD.relieved69.Why did the writer say he was carrying some medicine and he would write to the manager?A.To tell the girl what he really wanted to do.B.To show the girl how angry he was with her.C.To warn the girl of the potential consequences.D.To persuade the girl to give him a seat on the bus.(B)Care for a zoom-in observation of animals with no bars between you and the observed as opposed to ordinary zoos?Where to have close-up encounters with some of the world’s most rare animals？We are revealing for you：1.Right whales,Bay of Fundy,CanadaNorthern right whales are on the brink of extinction,but survivors arrive in the Bay of Fundy each summer(May through October)to feed east of Grand Manan Island.They are recognized by a broad back and no dorsal fin,which distinguish them from other whales entering the bay.Planning:Whale-watching tours operate out of Digby Neck peninsula on Nova Scotia and nearby islands,such as Brier Island.St.Andrews.Grand Manan Island.and Deer Island.2.Grizzly bears,AlaskaGrizzlies like salmon.In mid-July and again in mid-August,grizzlies make for Alaskan rivers to hook out the fish with their formidable claws.The bears gather in large numbers at rapids and pools,sometimes fighting for the best sites.Brooks Falls in Katmai National Park,and Fish Creek, near Hyder,have viewing platforms.Planning:Most fishing sites are reached by chartered light aircraft and a hike.Hyder is off the Swart-Cassiar Highway.3.Monarch butterflies,Sierra Chincua,MexicoEach fall,millions of North American monarch butterflies migrate thousands of miles to the oyalmel fir forests of the Transvolcanic Mountain Range,in the state of Mchoacdn.They flock intimately(closely)on tree trunks,bushes,and on the ground,fully showing their gregarious natureand occupy Sierra Chincua and four neighbouring hills that make up the Monarch Butterfly Biosphere Reserve.Planning:Chineua is one of two hills in the reserve open to the public from November through March.4.Komodo dragons,Komodo Island,IndonesiaLanding on Komodo,you would feel like stepping back to a time when dinosaurs ruled the Earth,as park maps reported,“Here be dragons!”This mountainous volcanic island is home to the world's largest living lizard---the Komodo dragon.Weighing79to91kg.the Komodo dragon has a tail as long as its body.You can hike to a viewpoint at Banugulung and watch as park rangers feed food to the lizards,some of which are more than10ft(3m)long.Planning:Komodo is reached solely by boat from Bima(on eastern Sumbawa)or Labuan Bajo (on western Flores).5.Wildebeest migration,Serengeti,TanzaniaUndoubtedly the world's most spectacular wildlife sight is the annual wildebeest migration, when1.4million wildebeest and200,000zebras and gazelles are on the move across the Serengeti plains.The animals are trekking to chase the clean water and fresh grass.Along the way,lions and hyenas stalk them,and crocodiles lie in wait.Planning:The herds migrate across Tanzania from December through July,and then pass through the Masai Mara in Kenya in August and September.70.The underlined word gregarious is closest in meaning to________________.A.being able to climbB.preferring group livingC.migrating in small numbersD.moderate in temper71.Which of the following statements is NOT TRUE according to the passage?A.Right whales are distinguished from other whales by unique appearance features.B.Viewing spots for grizzly bears are accessible by air and on foot.C.Komodo Island is located east of Flores and West of SumbawaD.Wildebeest herds travel to pursue favourable food conditions.72.Li Hua is an adventurous visitor longing for closer look at animals.He is taking a gap year and doing voluntary work now in Indonesia.He will go back to China and further his study next fall. Which of the following will be the most reasonable wildlife-watching route after he finishes his voluntary work this winter?A.Alaska→Bay of Fundy→Sierra Chincua→SerengetiB.Serengeti→Alaska→Bay of Fundy→Sierra ChincuaC.Bay of Fundy→Sierra Chincua→Serengeti→AlaskaD.Sierra Chincua→Serengeti→Alaska→Bay of Fundy(C)Many Americans harbor a false and exaggerated view of most of the risks surrounding food. Fergus Clydesdale,head of the department of food science and nutrition at the University of Massachusetts-Amherst,points out that if the dangers from bacterially polluted chicken were as great as some people believe,“the streets would be littered with people lying here and there.”Though the public increasingly demands no-risk food,there is no such thing.Bruce Ames, chairman of the biochemistry department at the University of California,Berkeley,points out that up to10%of a plant’s weight is made up of natural pesticides.Says he:“Since plants do not have jaws or teeth to protect themselves,they employ chemical warfare.”And many naturally produced chemicals,though occurring in tiny amounts,prove in laboratory tests to be strong carcinogens-a substance which can cause cancer.Mushrooms might be banned if they were judged by the same standards that apply to food additives.Declares Christina Stark,a nutritionist at Cornell University:“We’ve got far worse natural chemicals in the food supply than anything man-made.”Yet the issues are not that simple.While Americans have no reason to be terrified to sit down at the dinner table,they have every reason to demand significant improvements in food and water safety.They unconsciously and unwillingly take in too much of too many dangerous chemicals.If food already contains natural carcinogens,it does not make much sense to add dozens of new man-made ones.Though most people are subject to the small amounts of pollutants generally found in food and water,at least a few individuals will probably get cancer one day because of what they eat and drink.To make good food and water supplies even better,the Government needs to tighten its regulatory standards,enhance its inspection program and strengthen its enforcement policies.The food industry should modify some long-accepted practices or turn to less risky alternatives.Perhaps most important,consumers will have to do a better job of learning how to handle and cook food properly.The problems that need to be tackled exist all along the food-supply chain,from fields to processing plants to kitchens.73.What does the author think of the Americans’view of their food?A.They overstate the government’s interference with the food industry.B.They are overoptimistic about the safety of their food.C.They overestimate the risk of the food they eat.D.They overlook the potential danger caused by the food.74.The author considers it impossible to obtain no-risk food because________.A.no food is free from pollution in the environmentB.pesticides are widely used in agricultureC.many vegetables contain dangerous natural chemicalsD.almost all foods have hazardous additives75.By saying“they employ chemical warfare”(Para.2),Bruce Ames means“________”.A.plants produce certain chemicals to resist pests and diseasesB.plants absorb useful chemicals to promote their growthC.farmers use man-made chemicals to dissolve the natural chemicals in plantsD.farmers use chemicals to protect plants against pests and diseases76.What is the message the author wants to convey in the passage?A.Eating and drinking have become more dangerous than before due to additives.B.Sweeping measures must be taken immediately to ensure safety in food industry.C.Healthy food is a distant dream in the modern society,remaining to be realized.D.There is reason for caution but no cause for alarm with regard to food consumption.Section CDirections:Read the following passage.Fill in each blank with a proper sentence given in the box.Each sentence can be used only once.Note that there are two more sentences than you need.A.They differ in how they space the syllables in a sentence.B.Unlike other languages,English is unusually rich in consonant(辅音)clusters.C.French-speakers are familiar with a U.S.city called yoos-TON,not the English HYOO-ston.D.In“civilisation”the primary and secondary stress is on the4th and1st syllable respectively.E.There is much more to learning a foreign accent than the sounds that the letters on the page represent.F.As with chemistry,the important thing is not just how the elements behave in isolation,but how they cometogether.Why you have an accent in a foreign languageOpen a textbook for a foreign language,the first thing you see is an alphabet,listing the lettersand the sounds they represent.This is obviously crucial for unfamiliar systems,say those of Greek or Russian.But even for languages that rely on the Latin alphabet,the guide will explain how accentmarks change a letter’s pronunciation,and strange features such as the-gl-in Italian.And with that,it’s off to master greetings,vocabulary and so on,with little further thought for pronunciation.This is a shame.____87____To begin with,the rough equivalents given in Englishare often quite rough indeed.In French,the p in Paris sounds rather different from the p in English,a contrast often neglected in textbooks:the French version lacks the strong puff of air of the Englishone.Even when textbooks or instructors mention this sort of difference,the next step is often missing.____88____Each language has rules for these combinations,which native speakers generally grasp but don’t or can’t explain.。
2018-2019学年交大附中高三英语第一学期摸底考试卷,含答案及解析
2018-2019学年交大附中高三英语第一学期摸底考试卷I.Listening Comprehension(略)II.Grammar and Vocabulary(20分)Section ADirections:After reading the passage below,fill in the blanks to make the passage coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form of the given word;for the other blanks,use one word that best fits each blank.(A)Space is a dangerous place,not only because of meteors(流星)but also because of rays from the sun and other stars.The atmosphere again acts(21)our protective blanket on earth.Light gets through,and this is essential for plants(22)(make)the food which we eat.Heat,too,makes our environment endurable. Various kinds of rays come through the air from outer space,but enormous quantities of radiation from the sun(23) (screen)off.As soon as men leave the atmosphere,they are exposed to this radiation but their spacesuit or the walls of their spacecraft,(24)they are inside,do prevent a lot of radiation damage.Radiation is(25)(great)known danger to explorers in space.The unit of radiation is called"rem". Scientists have reason to think that a man can put up with far more than0.1rem without(26)(damage); the figure of60rems has been agreed on.The trouble is(27)it is extremely difficult to be sure about radiation damage-a person may feel perfectly well,but the cells of his or her sex organs may be damaged,and this will not be discovered(28)the birth of deformed children or even grandchildren.Missions of the Apollo flights have had to cross belts of high radiation and,during the outward and return journeys,the Apollo crew accumulated(积累)a large amount of rems.So far,no dangerous amounts of radiation have been reported,but the Apollo missions have been quite short.We simply don't know yet(29)men are going to get on when they spent weeks and months outside the protection of the atmosphere,working in a space laboratory.Drugs might help to decrease the damage(30)(do)by radiation,but no really effective ones have been found so far.(B)Living JewelsBefore I went to the British Koi Keepers Annual Show,I didn’t understand(31)people could take fish so seriously.However,the more I learned about koi,the more interested I became.As one expert told me, "Collecting koi is far more addictive than you might think.They’re as beautiful as butterflies and very calming to watch."Freddie Mercury,the lead singer of Queen,would have agreed the pool in his specially-built Japanese garden was home to89koi,(32)cost up to$10,000each.At the show I met koi enthusiast Jean Kelly.“Koi are getting more and more expensive,”she told me.“One recently sold for$250,000.”I was shocked that's almost as much as I paid for my house.Well,that was a record,(33)(admit)Jean.The normal price is nowhere near as high as that.Nevertheless,serious collectors can pay up to$15,000for a fully(34)(grow)koi,which is nearly as expensive as a new luxurious car,and the bigger they are,the more they cost.The cheapest I(35)find was$75each,but they were only about twice as big as my goldfish.Jean wasn’t impressed by one of the koi on sale either.“Actually,these koi aren’t any nicer than (36),”she commented.“(37)they are slightly bigger than the ones I’ve got,I paid considerable less than this.”I wasn’t quite as enthusiastic as Jean,but I did consider(38)(buy)one.Then I remembered that all but5of Freddie Mercury's koi died when someone accidentally turned off the electricity supply to their pool.Jean assured me that with all the new equipment available the survival rate was getting better and better,and that looking(39)koi was no harder than taking care of any other pet.However,in the end I decided to stick with my goldfish.They’re not nearly as beautiful as koi——but they’re a great deal cheaper(40) (replace)!Section B(10分)Directions:Complete the passage with the words in the box.Each word can only be used once.Note that there is one word more than you need.A.associatedB.likelyC.decreasesD.abstractE.limitF.funG.contributes H.consistently I.favorably J.reasoned K.averageThe Beatles sang that money can't buy you love.But what about happiness?Research(41)_____shows that the more money people have,the more likely they are to report being satisfied with their lives.And that makes sense:money buys you things that make life easier and more satisfying;the easier your life, the happier you tend to be.That relationship isn't entirely linear,since there's a(n)(42)_____to how much wealth can please you;the happiness benefit of an increasing income is especially powerful among people who don't have much money to start with,and(43)_____as wealth increases.But studies also reveal that as(44)_____income levels have risen over time—in the U.S.and European nations,for example—residents of those countries have not reported being any happier than people were30or40years ago.It's a paradox that while income and happiness may be(45)_____within a population at any given moment,overall economic growth does not appear to correspond to a boost in national satisfaction over time.(See a gallery of things money can buy.) To understand why,researchers at the University of Warwick and Cardiff University decided to break down how individual people evaluate their income.What does wealth mean to people?Previous work has suggested that people tend to value their own wealth more—and are happier—when it compares(46)_____to everyone else's. The so-called reference-income hypothesis holds that it's not simply how much money you make that(47)_____to satisfaction,but how much more money you make than,say,the national average.The higher your salary than the norm,the happier you tend to be.That could explain in part why populations as a whole do not experience sunnierdispositions with economic growth,since a majority of individuals may not fall above the national income average.But the reference-income hypothesis is rather(48)_____.The researchers wondered whether there was a more nuanced way to capture how people valued their income.They(49)_____that people tend to make specific comparisons of personal wealth,not only with the average income of the larger population,but with the individual incomes of their neighbors,colleagues at work or friends from college.And the higher their rank,the greater their sense of happiness and self-worth would(50)_____be."For example,people might care about whether they are the second most highly paid person,or the eighth most highly paid person,in their comparison set,"write the authors, Chris Boyce,a psychologist at the University of Warwick,and Simon Moore,a psychologist at Cardiff University.III.Reading Comprehension(45分）Section ADirections:For each blank in the following passage there are four words or phrases marked A,B,C and D.Fill in each blank with the word of phrase that best fits the context.The beauty,majesty,and timelessness of a primary rainforest are indescribable.It is impossible to(51)______ on film,to describe in words,or to explain to those who have never had the awe-inspiring experience of standing in the heart of a primary rainforest.Rainforests have(52)______over millions of years to turn into the incredibly complex environments they are today.Rainforests represent a store of living and(53)______renewable natural resources that for eons,by virtue of their richness in both animal and plant species,have(54)______a wealth of resources for the survival and well-being of humankind.These resources have included basic food supplies,clothing,shelter,fuel,spices, industrial raw materials,and medicine for all those who have lived in the majesty of the forest.(55)______,the inner dynamics of a tropical rainforest is an intricate and fragile system.Everything is so(56)______that upsetting one part can lead to unknown damage or even destruction of the whole.Sadly,it has taken only a century of human intervention to destroy what nature designed to(57)______forever.The scale of human(58)______on ecosystems everywhere has increased enormously in the last few decades. Since1980the global economy has tripled in size and the world population has increased by30percent. Consumption of everything on the planet has risen——at a cost to our(59)______.In2001,the World Resources Institute estimated that the demand for rice,wheat,and corn is expected to grow by40%by2020,increasing irrigation water demands by50%or more.They further reported that the demand for wood could double by the year2050;(60)______,it is still the tropical forests of the world that supply the bulk of the world's demand for wood.In1950,about15percent of the Earth's land surface was covered by rainforest.Today,more than half has already gone up in(61)______.In fewer than fifty years,more than half of the world's tropical rainforests have fallen(62)______to fire and the chain saw,and the rate of destruction is still accelerating.Unbelievably,more than 200,000acres of rainforest are burned every day.That is more than150acres lost every minute of every day,and 78million acres lost every year!More than20percent of the Amazon rainforest is already gone,and much more is severely threatened as the destruction continues.It is estimated that the Amazon alone is vanishing at a rate of 20,000square miles a year.If nothing is done to curb this(63)______,the entire Amazon could well be gone withinfifty years.Massive(64)______brings with it many ugly consequences-air and water pollution,soil erosion,malaria epidemics,the release of carbon dioxide into the atmosphere and the(65)______of biodiversity through extinction of plants and animals.Fewer rainforests mean less rain,less oxygen for us to breathe,and an increased threat from global warming.51.A.present B.capture C.claim D.prove52.A.changed B.evolved C.expanded D.existed53.A.energizing B.healing C.isolating D.breathing54.A.contributed B.stored C.reduced D.affected55.A.However B.Furthermore C.Therefore D.Otherwise56.A.active B.sensitive C.interdependent D.delicate57.A.restore B.support C.revive st58.A.pressure B.power C.concern D.strength59.A.existence B.ecosystem C.planet D.survival60.A.unfortunately B.consequently C.naturally D.similarly61.A.store B.food C.smoke D.wealth62.A.subject B.down C.apart D.victim63.A.trend B.practice C.decrease D.attitude64.A.destruction B.industrialization C.modernization D.deforestation65.A.appearance B.explosion C.loss D.increaseSection BDirections:Read the following three passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)The definition of the standard kilogram is fundamentally imperfect.Getting the definition right is a challenge that has tried the patience and intelligence of scientists for decades.Scientists use just seven basic units to define all the other quantities we use---quantities such as speed, density,or electric power.All of those basic units except the kilogram are themselves defined in terms of natural properties that are beyond human control.For example,the standard second(time)is defined as a specific number of vibration of a type of radiation released by atoms of a special metal.The standard meter(length),in turn,is defined as the length of the path light travels in a vacuum during a specific fraction of a second.Not so the kilogram.This orphan of the basic unit family is simply the mass of a small platinum-iridium alloy cylinder(铂-铱合金筒)locked away by the international Bureau of Weighs&Measures in France.Embarrassingly,the last time the copies were brought for a checkup in the1980s,officials found that some copies had gained about20parts per billion in weight compared to the master cylinder since the previous checkup in the1940s.This implies that the master cylinder itself may be an inconstant standard.No one knows what causes the weight changes.But the uncertainty can’t be tolerated when precision(精密度) in research and some manufacturing now demands accuracy to a few parts per billion.Several efforts in several different countries are under way to redefine the kilogram in terms of basic physical quantities such as counting the actual number of atoms of a specific substance in a kilogram or the electromagnetic force that balances a kilogram mass against gravity.A project of the latter type at the NIST laboratories in Gaithersburg hopes eventually to define mass in terms of electrical units.So far,none of these redefinition projects has borne fruit.They require precision of measurement and control of experimental conditions.The slightest pollution,tiny vibrations,or other influences---even changes in weather---can ruin results.You’ve got to hand it to scientists who are willing to devote many years to such painstaking but fundamentally important research.66.Which of the following best paraphrases the sentence“Not so the kilogram.”In paragraph4?A.The kilogram is not as accurate as the standard second.B.The kilogram is not universally accepted in the world.C.The kilogram is not defined in terms of natural properties.D.The kilogram is not well defined as time and length.67.Which of the following can NOT be concluded from the passage?A.Experiments are being carried out to redefine the kilogram.B.The uncertainty in the standard kilogram can seriously affect some research.C.The redefinition of the standard kilogram is quite complicated.D.Scientists will achieve success in redefining the kilogram in the near future.68.According to the passage,to define the weight of mass in terms of electrical units_______.A.is one of the best methods to redefine the kilogramB.has been accepted as the only possible redefinition projectC.is not as simple as what people can understandD.has been considered by some scientists as a better approach69.We can know from the passage that the redefinition of the kilogram is_________.A.more important in keeping market honestyB.worth years of scientists’painstaking researchC.the urgent requirement of business and manufacturing.D.bring about important and fruitful results(B)Stewart Island Ferry ServicesWhile most visitors spend at least one night on Stewart Island,it is also readily accessible by ferry as a day excursion from Invercargill and Bluff.Experience Foveaux Strait in comfort and style on board our express catamarans.During the one-hour crossing between Bluff and Stewart Island keep a lookout for wildlife,especially seabirds.Watching mollymawks (albatross)soaring behind the ferry is a fantastic sight.Interesting landmarks commonly seen include Dog Island Lighthouse,Ruapuke Island,Titi Islands and Mt Anglem-Stewart Island’s highest point.●Free tea and coffee on board●Interpretation handouts are available(English only).●Wheelchair access available●Personal baggage is carried free on the ferries-max.two bags per person(one stowed and onesmall carry-on).Additional baggage is by prior arrangement.●Vehicle parking available at Bluff(extra cost-reservations recommended)FERRY TO STEWART ISLAND Depart BluffAll year9:30amSep-May5:00pmOct–Apr11:00amJun–Aug4:30pmLate Dec–mid Jan8:00am FERRY TO BLUFF Depart Stewart IslandAll year8:00amSep–May3:30pmOct–Mar6:00pmApr5:00pmJun-Aug3:00pmLate Dec–mid Jan9:30amOther departures as locally advertisedDuration1hrCheck-in30minutes prior to the scheduleddeparture time.(Check-in and boarding gates are closed10minutes prior to times stated above.)“20%Multi-Purchase REWARD”on Return Ferry ServicesBuy2or more different excursions and SAVE20%off all lower priced!Kids Go FREE on selected departures during NZ School Holidays!Kids Go FREE for travel20April-5May2013.70.If a traveler plans to leave a car at Bluff,he had better________.A.refer to the handouts firste wheelchair accessC.make a reservationD.park it30minutes before departure time71.John,who went to Stewart Island on Dec.28th,got to the ferry dock at7:55am.When did he most probably leave Bluff？A.At8:00a.m.B.At9:30a.m.C.At11:00a.m.D.At3:00p.m.72.Which of the following is false about the ferry services？A.Tea and coffee are free for passengers.B.Children go free for travel for about15days.C.Travelers are sure to see some seabirds during the crossing.D.Passengers have to pay extra cost for extra pieces of luggage.（C）Like every dog,every disease now seems to have its day.World Tuberculosis(infections disease in which growths appear on the lungs)Day is on Saturday March24th.Tuberculosis was once terribly fashionable.Dying of"consumption"seems to have been a favorite activity of garret-dwelling19th-century artists,h has,however,been neglected of late.Researchers in the field never tire of pointing out that TB kills a lot of people.According to figures released earlier this week by the World Health Organization,1.6million people died of the disease in2005,compared with about3m for AIDS and l m for malaria. But it receives only a fraction of the research budget devoted to AIDS.America’s National Institutes of Health,for example,spends20times as much on AIDS as on TB.Nevertheless,everyone seems to getting in on the TB-day act this year.The Global Fund an international organization responsible fur fighting all three diseases but best known for its work on AIDS,has used the occasion to trumpet its tuberculosis projects.The fund claims that its anti-TB activities since it opened for business in2002have saved the lives of over1m people.The World Health Organization has issued a report that contains some good news.Although the number of TB cases is still rising,the rate of illness seems to have stabilized;the caseload,in other words,is growing only because the population itself is going up.Even drug companies are involved.In the nm-up to the day itself,Eli Lilly announced a$50m boost to its MDRTB Global Partnership.MDR stands for multi-drug resistance,and it is one of the reasons why TB is back in the limelight.Careless treatment has caused drug-resistant strains to evolve all over the world.The course of drugs needed to clear the disease completely takes six mouths,anti persuading people lo stay that course once their symptoms have gone is hard.Unfortunately,those infected with MDR have to be treated with less effective,more poisonous and more costly drugs.Naturally,these provoke still more.non-compliance and thus still more evolution.The other reason TB is back is its relationship to AIDS.The Global Fund’s joint responsibility for the diseases is no coincidence.AIDS does not kill directly.Rather,HIV,the virus that causes it,weakens the body’s immune system and exposes the sufferer to secondary infections.Of these,TB is one of the most serious.It kills200000 AIDS patients a year.However,some anti-TB drugs interfere with the effect of some anti-HIV drugs.Conversely, in about20%of cases where a patient has both diseases,anti-HIV drugs make the tuberculosis worse.The upshot is that125years after human beings worked out what caused TB,it is still a serious threat.73.The first sentence“Like every dog,every disease now seems to have its day.”means______.A.every dog enjoys good luck or success sooner or laterB.human beings can deal with problems caused by diseaseC.Tuberculosis becomes a serious infectious diseaseD.people attach importance to Tuberculosis recently74.By referring to AIDS in Paragraph2,the author intends to show______.A.the US government is reluctant to spend millions of dollars on TuberculosisB.the death rate of AIDS is higher than that of TuberculosisC.the officials did not pay much attention to the research of Tuberculosis in the pastpared with AIDS,Tuberculosis can be cured effectively75.Which of the following best defines the word“upshot”(Line6,Para5)?A.Outcome.B.Uphold.C.Achievement.D.Project76.Which of the following proverbs is closest in meaning to the message the passage tries to convey?A.Forgive and forget.B.Forgotten,but not gone.C.When the wound is healed,the pain is forgotten.D.Every dog is brave at his own door.Section CDirections:Read the passage carefully.Fill in each blank with a proper sentence given in the box. Each sentence can be used only once.Note that there are two more sentences than you need.A.The critical abilities are beginning to develop in adolescence.B.Their view on life usually falls in two extremes.C.Of all periods of life,this is what may best be called the plastic age.D.They are basically timid or self-conscious.E.Despite that,it is also in this period that strong ties between teachers and students develop.F.Fundamentally they want to be kept-busy but they refuse to admit it.Adolescents generally refer to boys and girls on the high-school level-more specifically,the second,third, and the fourth years of high school.In dealing with students at this level,we must bear in mind that to some degree they are at a difficult stage,generally called adolescence.Students at this level are likely to be confused mentally.They usually find it hard to concentrate on what they intend to do and often have romantic dreams.(77)They lack frankness and are usually very easily affected by their own emotions but hate to admit it.They are driven either by greater ambition,probably beyond their capability,or by extreme laziness caused by the fear of not succeeding or achieving their objectives.(78)They are willing to work,but they hate to work without obtaining the results they think they should obtain.Regarding school issues,although they seldom say so,they really want to be consulted and given an opportunity to direct their own affairs,but they need a good amount of guidance.They seldom admit that they need this guidance and they frequently rebel against it,but if it is intelligently offered they accept it with enthusiasm.As to persona]beliefs,most of adolescents are trying to form political ideas and they have a tendency to be sometimesextremely idealistic,and at other times conventional,blindly accepting what their fathers and grandfathers believed in.(79)On the one hand they are too modest,and on the other hand unreasonably boastful.They tend to be influenced more by a strong character than by great intelligence.(80)Having a better understanding of the characteristics and needs of young people at this age is a task that falls on both educators and the other people involved.It may also help the young go through this difficult and critical stage of life in a more constructive manner.【答案】77-80DFBC【解析】青春期的孩子要谨慎对待第一段引出话题，青春期是一个困难的时期to some degree...at a difficult stage...第二段描述了青春期的孩子们的各种纠结和扭吧77题的提示在后面，他们不愿坦诚，易受情绪影响又羞于承认，与这些描述相关就是they basically timid and self-conscious78题的提示也是在后面,they are willing to work,和前面的they want to be kept busy呼应第三段描述了青春期的孩子们还是很希望能参与到学校生活中并起主导作用，尽管他们不承认，他们需要良好的引导，需要一位强有力的人物的影响。
—度上海交通大学附中第一学期高三英语摸底考试试卷
上海交通大学附中2008—2009学年度第一学期高三摸底考试英语试卷（满分150分，150分钟完成，答案一律写在答题纸上）听力部分I．Listening Comprehension：（ 30% ）Part A Short ConversationsDirections: In Part A, you will hear ten short conversations between two speakers．At the end of each conversation, a question will be asked about what was said．The conversations and the questions will be spoken only once．After you hear a conversation and the question about it, read the four possible answers on your paper and decide which one is the best answer to the question you have heard．1． A．He doesn’t like the song．B．He doesn’t speak French．C．He is in no mood for singing．D．He can’t sing today．2． A．Peter has been fired．B．Peter has changed his job．C．Peter is still working in the company．D．Peter wants to leave the company．3． A．Stay in the office．B．Have her hair arranged．C．Buy some birthday presents．D．Go to Miss White’s home．4． A．The man doesn’t like her any more．B．The man never noticed her hairstyle before．C．The man is telling a lie．D．The man never praises her．5． A．12．B．6．C．24 D．186． A．Someone may enter the house through the open windows．B．There may be a strong wind and heavy rain tonight．C．The man may catch cold if he leaves the windows open．D．The windows may be broken during the night．7． A．She found it interesting．B．She found it enjoyable．C．She found it boring．D．She found it informative．8． A．To buy a piano．B．To play the music．C．To listen to her sing．D．To sing together with her．9． A．On a fishing boat．B．In an ocean park．C．In a gift shop．D．In a restaurant．10．A．In a hotel．B．In a school．C．In a hospital．D．In a police station．Part B PassagesDirections: In Part B, you will hear two short passages, and you will be asked three questions on each of the passages．The passages will be read twice, but the questions will be spoken once．When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard．Questions 11 through 13 are based on the following passage ．11．A．Boston．B．Vancouver．C．Canada．D．Teheran．12．A．Because he couldn’t refuse his friend．B．Because he was busy all evening．C．Because Mike’s line was busy．D．Because he preferred writing a letter．13．A．Some tapes．B．Some presents．C．His overseas friend．D．Nothing．Questions 14 through 16 are based on the following passage ．14．A．Fashion model．B．Film actress．C．Social activist．D．Cinema manager．15．A．In 1958．B．In 1960 C．In 1971．D．1978．16．A．Don’t They?B．Klute．C．Julia．D．Coming Home．Part C Longer ConversationsDirections: In Part C, you will hear two longer conversations．The conversations will be read twice．After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard．Write your answers on your answer sheet．17-24做在答题纸上。
上海交通大学附中—度第一学期高三英语摸底考试试卷
上海交通大学附中2008—2009学年度第一学期高三摸底考试英语试卷（满分150分，150分钟完成，答案一律写在答题纸上）听力部分I．Listening Comprehension：（30% ）Part A Short ConversationsDirections: In Part A, you will hear ten short conversations between two speakers．At the end of each conversation, a question will be asked about what was said．The conversations and the questions will be spoken only once．After you hear a conversation and the question about it, read the four possible answers on your paper and decide which one is the best answer to the question you have heard．1．A．He doesn’t like the song．B．He doesn’t speak French．C．He is in no mood for singing．D．He can’t sing today．2．A．Peter has been fired．B．Peter has changed his job．C．Peter is still working in the company．D．Peter wants to leave the company．3．A．Stay in the office．B．Have her hair arranged．C．Buy some birthday presents．D．Go to Miss White’s home．4．A．The man doesn’t like her any more．B．The man never noticed her hairstyle before．C．The man is telling a lie．D．The man never praises her．5．A．12．B．6．C．24 D．18 6．A．Someone may enter the house through the open windows．B．There may be a strong wind and heavy rain tonight．C．The man may catch cold if he leaves the windows open．D．The windows may be broken during the night．7．A．She found it interesting．B．She found it enjoyable．C．She found it boring．D．She found it informative．8．A．To buy a piano．B．To play the music．C．To listen to her sing．D．To sing together with her．9．A．On a fishing boat．B．In an ocean park．C．In a gift shop．D．In a restaurant．10．A．In a hotel．B．In a school．C．In a hospital．D．In a police station．Part B PassagesDirections: In Part B, you will hear two short passages, and you will be asked three questions on each of the passages．The passages will be read twice, but the questions will be spoken once．When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard．Questions 11 through 13 are based on the following passage ．11．A．Boston．B．Vancouver．C．Canada．D．Teheran．12．A．Because he couldn’t refuse his friend．B．Because he was busy all evening．C．Because Mike’s line was busy．D．Because he preferred writing a letter．13．A．Some tapes．B．Some presents．C．His overseas friend．D．Nothing．Questions 14 through 16 are based on the following passage ．14．A．Fashion model．B．Film actress．C．Social activist．D．Cinema manager．15．A．In 1958．B．In 1960 C．In 1971．D．1978．16．A．Don’t They?B．Klute．C．Julia．D．Coming Home．Part C Longer ConversationsDirections: In Part C, you will hear two longer conversations．The conversations will be read twice．After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard．Write your answers on your answer sheet．17-24做在答题纸上。
交大附中高三第一学期英语阶段测试试卷
2015学年第一学期交大附中诊断测试高三年级英语(2015年10月23日)考生注意：1. 考试时间120分钟，试卷满分150分。
2. 本考试设答题卡和答题纸两部分。
答题卡题号(第1-16题，41-77题)必须和试卷题号一一对应，不要错位(答题卡题号17-40是空着的)。
第I卷(共103分)I. Listening ComprehensionSection ADirections:In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversation and the question will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At 10:30. B. At 10:50.C. A t 11:20.D. At 11:30.2. A. Having an interview. B. Filling out a form.C. Talking with his friend.D. Asking for information.3. A. A shop assistant. B. A telephone operator.C. A waitress.D. A clerk.4. A. At home. B. In an office.C. In a car.D. On the street.5. A. A railway porter. B. A telephone operator.C. A bus conductor.D. A postal clerk.6. A. A father and a son. B. A teacher and his student.C. A student and his classmate.D. A librarian and a student.7. A. A movie. B. A lecture.C. A play.D. A speech.8. A. The man won’t become a superstar. B. The man has no gift for table tennis.C. The man should find a new partner.D. The man should not give up.9. A. His injury kept him at home. B. He didn’t consider it necessary.C. He was too weak to see the doctor.D. He failed to make an appointment.10. A. He wants to get a new position. B. He is asking the woman for help.C. He has left the woman a good impression.D. He enjoys letter writing.Section B PassagesDirections:In Part B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. On Tuesdays and Wednesdays. B. On Tuesdays and Thursdays.C. On Wednesdays and Thursdays.D. On Tuesdays and Fridays.12. A. Once a week. B. Twice a week.C. Once a month.D. Twice a month.13. A. Classroom tests. B. Attendance rate.C. Research papers.D. Final exam.Questions 14 through 16 are based on the following passage.14. A. Music. B. Books.C. Films.D. Photographs.15. A. Poverty. B. Disasters.C. Racial injustice.D. Crime.16. A. He was the first director of Hollywood. B. He was born in Middle Eastern Africa.C. He lived a poor life in his childhood.D. He picked up photography in 1912.Section C Longer ConversationsComplete the form. Write ONE WORD for each answer.II. Grammar and VocabularySection ADirections: Read the following passage. For some blanks, there is a word given in the brackets. Fill in each of these blanks with the proper form of the given word. Fill in the other blanks with words that are correct in structure and proper in meaning.There is a picture in my living room that advises me to “Bloom where you are planted.” It reminds me of Dorothy. I got to know Dorothy in the early 1980s, (25) __________ I was teaching Early Childhood Development through a program with Union College in Barbourville, Kentucky. The job responsibilities required occasional visits (26) __________ the classroom of each teacher in the program. Dorothy stands out in my memory as one wh o “bloomed” in her remote area.Dorothy (27) __________ (teach) in a school In Harlan County, Kentucky, Appalachian Mountain area. To get to her school from the town of Harlan, I followed a road (28) __________ (wind) around the mountain. In the eight-mile journey, I crossed the same railroad track five times, giving (29) __________ possibility of getting caught by the same train five times. Rather than feeling excited by this drive through the mountains, I found it depressing. The poverty level was shocking and the small shabby houses gave me (30) __________ (great) feeling of hopelessness.From the moment of my arrival at the little school, all gloom disappeared. Upon arriving at Dorothy’s classroom, I (31) __________ (greet) with smiling faces and treated like a queen. The children had been prepared to show me their latest projects. Dorothy told me with a big smile (32) __________ they were servingpoke greens salad and cornbread for dinner. In case you don’t know, poke greens are a weed-type plant that grows wild, especially on poor ground.BIn W. H. Armstrong’s opinion, reading doesn’t just mean (33) __________ (recognize) each word on the page; it means taking in the information, digesting it and incorporating it into oneself just (34) __________ one digests a sandwich and makes it a part of himself. The goal is (35) __________ (bring) the information back to life, not just to treat it as dead facts on paper from dead trees. Reading and writing cannot be completely separated from each other; in fact, the aim of reading is to express the information you have got from the text. I’ve seen it again and again: (36) __________ who can’t express an idea after reading a text is just as ineffective as someone who hasn’t read it at all.Only a third of the book remains after that discussion, (37) __________ Armstrong devotes to specific tips for studying languages, math, science and history. Well, he was a history teacher — if (38) __________ (convey) only a tenth of his passion to his students, that was a hundred times more than my history teachers ever got across. To my disappointment, in this part of the book he ignores the arts. As a matter of fact, they demand all the concentration and study that math and science do, (39) __________ the study differs slightly in kind. Although it’s commonly believed that the arts (40) __________ only be naturally acquired, actually, learning the arts is no more natural than learning French or mathematics. My other comment is that the text aged. The first edition apparently dates to the 1960s —none of the references seem newer than the late 1950s. As a result, the discussion misses the entire computer age.Section BDirections:Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. academicB. interracialC. providedD. decreaseE. likelyF. liveG. surrounded H. resulting I. slowly J. interacted K. randomlySeveral recent studies have found that being randomly assigned to a roommate of another race can lead to increased tolerance but also to a greater likelihood of conflict. Recent reports found that lodging with a student of a different race might (41) __________ prejudice and compel students to engage in more ethnically diverse friendships.An Ohio State University study also found that black students living with a white roommate saw higher (42) __________ success throughout their college careers. Researchers believe this may be caused by social pressure. In a New York Times article, Sam Boakye, the only black student on his freshman year floor said that "if you're (43) __________ by whites, you have something to prove." Researchers also observed problems (44) __________ from pairing interracial students in residences.According to two recent studies, randomly assigned roommates of different races are more (45) __________ to experience conflicts so strained that one roommate will move out. An Indiana University study found that interracial roommates were three times as likely as two white roommates to no longer (46) __________ together by the end of the semester.Grace Kao, a professor at Penn said she was not surprised by the findings. "This may be the first time that some of these students have (47) __________, and lived, with someone of a different race," she said. At Penn, students are not asked to indicate race when applying for housing. "One of the great things about freshman housing is that, with some exceptions, the process throws you together (48) __________," said Undergraduate Assembly chairman Alec Webley. "This is the definition of integration.""I've experienced roommate conflicts between (49) __________ students that have both broken down stereotypes and reinforced stereotypes," said one Penn resident advisor (RA). The RA of two years added that while some conflicts (50) __________ more multicultural acceptance and mixing, there were also more culturalconfrontations. The RA said that these conflicts have also occurred among roommates of the same race.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.On Monday, nearly half a century after her life-changing quest began, Tu was awarded the Nobel Prize in medicine for her role in creating a drug that helped reduce malaria (疟疾) death rates in Africa and Asia, saving millions of lives. Yet for all her (51) __________, Tu, who is now 84, remains a little known figure, even in her native China where she had drifted into (52) __________ despite the achievements of her discovery.As news o f Tu’s victory reached her native land on Monday night, one fan wrote on Weibo, China’s Twitter: “(53) __________ at last!” Tu was born in Ningbo, a port city about 140 miles south of Shanghai, in 1930. She was named after a verse in the Book of Songs, a collection of ancient Chinese poetry that is believed to have been (54) __________ by Confucius. She enrolled at the Peking University School of Medicine and graduated from its Department of Pharmacology four years later. From university Tu moved to the Academy of Traditional Chinese Medicine. She married Li Tingzhao, a (55) __________ school classmate and factory worker with whom she would have two daughters, and (56) __________ down in Beijing. Then, in 1969, everything changed when Tu was (57) __________ to a medical research project so secret it was known only as “523”.Tu was tasked with searching in nature for a new malaria (58) __________ and was sent to Hainan, a tropical island off China’s southern coast that has long (59) __________ with its blight. There, in the hot rainforests of southern China, Tu witnessed up close the mosquito-borne disease’s devastating toll on the human body. “I saw a lot of children who were in the latest (60) __________ of malaria,” she told New Scientist in 2011. “Those kids died very quickly.” But it was in ancient Chinese (61) __________ that Tu found the key to beating the disease. Back in Beijing, Tu and her team searched books about traditional Chinese medicine for leads on (62) __________ that might help them defeat malaria.Tu’s team put it to the test. At first the results were (63) __________ but after much persistence the researchers identified an active compound in the plant that attacked malaria-causing parasites (寄生物) in the blood and would later become known as artemisinin(青蒿素). Not (64) __________ with identifying the remedy, which thus far had only been tested on animals, Tu took it upon herself to test it. “As the head of this research group, I had the (65) __________,” she said.51. A. ambitions B. dreams C. achievements D. beliefs52. A. obscurity B. community C. sincerity D. security53. A. Risked B. Spoken C. Agreed D. Recognised54. A. made B. compiled C. invented D. discovered55. A. former B. formal C. mature D. complicated56. A. maintained B. resolved C. adopted D. settled57. A. utilized B. created C. recruited D. cultivated58. A. treatment B. addition C. conclusion D. therapy59. A. contributed B. devoted C. fought D. struggled60. A. collections B. connections C. stages D. links61. A. compositions B. manuscripts C. preferences D. theories62. A. puzzles B. subjects C. substances D. matters63. A. combined B. interrupted C. mixed D. organized64. A. complex B. similar C. dependent D. content65. A. responsibility B. devotion C. creativity D. innovationSection BDirections: Read the following four passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Merchant and passenger ships are generally required to have a life preserver (救生衣) for every person aboard and in many cases, a certain percentage of smaller sizes for children. According to United States requirements, life preservers must be designed to be worn with either side of the cloth showing, capable of being quickly adjusted to fit the inexperienced individual, and must be so designed as to support the wearer in the water in an upright or slightly backward position.Sufficient buoyancy (浮力) to support the wearer should be retained by the life preserver after 48 hours in the water, and it should be reliable even after long period of storage. Thus it should be made of materials resistant to sunlight, gasoline, and oils, and it should be not easily set on fire? The position in which the life preserver will support a person who jumps or falls into the water is most important, as is its tendency to turn the wearer in the water from a face-down position to an upright or slightly backward position, with his face clear of the water, even when the wearer is exhausted or unconscious.The method of adjustment to the body should be simple, and self-evident to inexperienced persons even in the dark under the confused conditions, which follow a disaster. Thus, the life preserver should be reversible that it is nearly impossible to get it on wrong. Catches, straps, and ties should be kept to a minimum. In addition, the life preserver must be adjustable to the wide variety of shapes and sizes of wearers, since this greatly affects the position of floating and the self-righting qualities. A suitable life also be comfortable to wear at all times, in and out of the water, not so heavy as to encourage to take it off on shipboard while the ship is in danger, nor so burdensome that it hinders a person in the water while trying to swim.66. The passage is mainly about __________.A. the uses of life preserversB. the design of life preserversC. the materials for life preserversD. the buoyancy of life preservers67. According to the passage, a life preserver should be first of all __________.A. adjustableB. comfortableC. self-evidentD. self-righting68. United States Coast Guard does NOT require the life preserver to be made __________.A. with as few strings as possibleB. capable of being worn on both sidesC. according to each wearer's sizeD. comfortable and light to wear69. What would happen if a person were supported by the life preserver in a wrong position?A. The waves would move him backwards.B. The water would choke him.C. He would immediately sink to the bottom.D. He would be exhausted or unconscious.(B)Women, drinking three or more cups of coffee a day, were 30 percent less likely to have memory decline at age 65 than those drinking one cup or less daily. And the benefit increased with age. Women over age 80 who drank three or more cups of coffee a day were about 70 percent less likely to have memory decline than thosewho drank one cup or less, the researchers said.Caffeinated tea had the same effect in the women，the study found, although more was needed to get the same caffeine boost. "Count roughly two cups of tea for a cup of coffee," said study leader Karen Ritchie of INSERM, the French National Institute for Health and Medical Research.But the researchers didn't find a similarly protective effect in men, although other studies have found a benefit to males.How might caffeine help ward off cognitive decline? "It is a cognitive stimulant." said Ritchie. It also helps to reduce levels of the protein called beta amyloid in the brain, she said, "whose accumulation is responsible for Alzheimer's disease but which also occurs in normal aging."Ritchie said she wasn't sure why men in the study didn't benefit from caffeine. "Our hypothesis is that either women metabolize caffeine differently than men, or there may be an interaction of the caffeine with the sex hormones, the estrogen-progesterone balance," she said.The French study confirms previous research, said William Scott, professor of medicine at the University of Miami Miller School of Medicine, who has researched caffeine's beneficial effects against Parkinson's disease, also a neurodegenerative disorder.As for caffeine only protecting women, Scott noted that just 2,800 of the 7,000 study participants were men, and the results might have differed if more men were included.A study published in February in the European Journal of Clinical Nutrition looked at 676 healthy men and found that regular coffee drinkers had a lower rate of cognitive decline over a 10-year follow-up than those who didn't drink coffee. Those who drank three cups daily had the least signs of decline.Both Scott and Ritchie agreed that more study is needed. Ritchie's research will next look at the relationship between caffeine and Alzheimer's.70. As it is indicated in the 1st paragraph, how does coffee influence women’s memory?A. The older the woman was, the more slowly her memory declined.B. The more coffee the woman drank, the more slowly her memory declined.C. The older the woman was, the more remarkable her memory was.D. The more coffee the woman drank, the more remarkable her memory was.71. What is true about caffeinated tea?A. It affected women’s memory in the same manner as coffee.B. It influenced women’s memory as effectively as coffee.C. It boosted women’s memory in the same rate as coffee.D. It contained the same amount of caffeine as coffee.72. According to Ritchie. Alzheimer's disease is resulted from __________.A. the lack of caffeine in the brainB. the accumulation of beta amyloidC. high level of proteins in the brainD. abnormal metabolism in normal aging73. William Scott would most probably agree that caffeine helped __________.A. reduce the risk of Alzheimer's diseaseB. protect both men and women from diseasesC. balance the production of female hormonesD. delay the process of cognitive decline(C)If our solar system has a Hell, it's Venus. The air is choked with foul and corrosive sulfur from ancient volcanoes and feeding acid clouds above. Although the second planet is a step farther from the sun than Mercury,a runaway greenhouse effect makes it hotter indeed. It's the hottest of the nine plants, a toasty 900 degrees Fahrenheit of baking rocky flats from equator to poles. All this under a crushing atmospheric pressure 90 times that of where you're sitting now. From the earthly perspective, it is a dead end. It must be lifeless."Venus has nothing," is the blunt word from planetologist Kevin Zahnle of NASA Ames Research Center in California's Silicon Valley. "We've written it off. "Yet a small group of advanced life-forms on Earth begs to differ, and theorizes that bizarre microbial ecosystems might have once populated Venus and, in fact, may be there still. Members of this loose band of researchers suggest that their colleagues have water too much on the brain, and are, in a sense, H2O chauvinists （盲目者）．"Astrobiologists are neglecting Venus due more to narrow thinking than actual knowledge of the environment, or environments, where life can thrive." says Dirk Schulze-Makuch, a geobiologist at the University of Texas at El Paso who recently co-authored a Venus-boosting paper in Astrobiology with colleague Louis Irwin.The bias against life on Venus is partly rooted in our own biology. Human experience instructs that liquid water, preferably lot of it, is essential for life. In search for extraterrestrial life, we obsess over small rivers in Mars' surface apparently carved by ancient gushes of water, and delight in hints of permafrost just underneath its surface. (By comparison, Venus isn't even that interesting to look at: A boring cue ball for backyard astronomers, its clouds reflects 75% of visible light.) Attention and then funding follow the water: Three more landers will depart for Mars this spring, and serious plans for sample-return missions hover in the midterm future."If you have limited resources, you base exploration on what you know." says Arizona State University planetary geologist Ronal Greeley. It's like losing your keys on the way home at night: The first place you look is under the streetlights not because they're more likely to be there, but because if they are. You’ll spot them. For astrobiologists, the streetlights are the spectral lines for water, and they've spotted that potential on Mars, Jupiter's moon Europa, even Neptune's moon Triton. Not on the baking rocky flats of Venus.74. Venus is the hottest of all the nine planets in the solar system because __________.A. it is not so close to the sun as MercuryB. greenhouse effect is uncontrollable on itC. it is covered by a thick layer of cloudD. many volcanoes spread the whole planet75. Some planetologists believed there had never been lives on Venus because __________.A. they couldn't find any trace of water on itB. they found Venus is too hot for any JivesC. Venus is covered by dirty and poisonous cloudD. Venus is the second nearest planet to the sun76. It can be inferred from the passage that the small group of advanced life forms on Earth believed that__________.A. life could exist in hot environmentB. life could exist without waterC. there are still lives on VenusD. there used to be lives on Mars77. What do we learn from the passage about Venus and Mars?A. The atmospheric pressure of Venus is stronger than that of Mars.B. Venus attracts more attention and funding than Mars.C. Venus is closer to the sun than Mars.D. Venus looks more beautiful than Mars.Section CDirections:Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.In fact, Chinese have been in the United States for almost two hundred years. The Chinese had business relations with Hawaii prior to relations with the mainland when Hawaii was not yet part of the United States. But United States investments controlled the capital of Hawaii at that time. In 1788,a ship sailed from Guangzhou to Hawaii. Most of the crewmen were Chinese. They were considered the pioneers of Hawaii. The Immigration Commission reported that the first Chinese arrived in the United States in 1820. eight in 1830 and seven hundred and eighty in 1850. The Chinese population gradually increased and reached 64,199 in 1870.For many years it was common in the United States to associate Chinese Americans with restaurants and laundries. People did not realize that the Chinese had been driven into these occupations by the prejudice and discrimination that faced them in this country.The First Chinese to reach the mainland United States came during the California Gold Rush of 1849. Like most of the other people there, they had come to search for gold. In that largely unoccupied land, the men staked a claim for themselves by placing markers in the ground. However, either because the Chinese were so different from the others or because they worked so patiently that they sometimes succeeded in turning a seemingly worthless mining claim into a profitable one, they became the scapegoats of their envious competitors. They were harassed in many ways. Often they were prevented from working their claims; some localities even passed regulations forbidding them to own claims. The Chinese therefore started to seek out other ways of earning a living. Some of them began to do the laundry for the white miners; others set up small restaurants. (There were almost no women in California in those days, and the Chinese filled a real need by doing this “woman's work”.) Some went to work as farmhands or as fishermen.In the early 1860's many more Chinese arrived in California. This time the men were imported as work crews to construct the first transcontinental railroad. They were sorely needed because the work was so strenuous and dangerous, and it was carried on in such a remote part of the country that the railroad company could not find other laborers for the job. As in the case of their predecessors, these Chinese were almost all males; and like them, too, they encountered a great deal of prejudice. The hostility grew especially strong after the railroad project was complete, and the imported laborers returned to California-thousands of them, all out of work. Because there were so many more of them this time, these Chinese drew even more attention than the earlier group did. They were so very different in every respect: in their physical appearance, including a long “pigtail”at the back of their otherwise shaved heads; in the strange, non-Western clothes they wore; in their speech (few had learned English since they planned to go back to China); and in their religion. They were contemptuously called “heathen Chinese” because there were many sacred images in their houses of worship.When times were hard, they were blamed for working for lower wages and taking jobs away from white men, who were in many cases recent immigrants themselves. Anti-Chinese riots broke out in several cities, culminating in arson and bloodshed. Chinese were barred from using the courts and also from becoming American citizens. Californians began to demand that no more Chinese be permitted to enter their state. Finally, in 1882, they persuaded Congress to pass the Chinese Exclusion Act, which stopped the immigration of Chinese laborers. Many Chinese returned to their homeland, and their numbers declined sharply in the early part of this century. However, during the World War II, when China was an ally of the United States, the Exclusion laws were ended; a small number of Chinese were allowed to immigrate each year, and Chinese could become American citizens. In 1965, in a general revision of our immigration laws, many more Chinese were permitted to settle here, as discrimination against Asian immigration was abolished.(Note: Answer the questions or complete the statements in NO MORE THAN 10 WORDS.)78.Most Chinese Americans worked in restaurants and laundries because of _______________________.79.In the early l860's, more Chinese were shipped to California to work as ________________________.80.Few Chinese learned English at that time because __________________________________________.81.The Immigration laws were at last revised so that __________________________________________.第II卷(共47分)I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.只要你不断努力，迟早会实现你做一名教师的理想。
2023-2024学年上海交大附中高三下学期数学模拟试卷及答案(2024.05)
1交大附中2023-2024学年第二学期高三年级数学阶段测二2024.05一、填空题（本大题共有12题,满分54分,第1-6题每题4分,第7-12题每题5分） 1．已知集合{}1,0A =−，集合{}2,B a =，若{}0A B = ，则a =________．2．已知方程22148x y k k+=−−表示的曲线是椭圆，则实数k 的取值范围是________．3．记等差数列{}n a 的前n 项和为n S ，76a =，则13S =________． 4．已知复数13z i =−，其中i 为虚数单位，则2z i +=________．5．在一次期末考试中某学校高三全部学生的数学成绩X 服从正态分布()2,N µσ，若()900.5P X ≥=，且()1100.2P X ≥=，则()7090P X ≤≤=________． 6．已知(a =，2a b ⋅= ，则b 在a 上的投影为________．7．已知ABC △的内角A 、B 、C 的对边分别为a 、b 、c，若cos C =a =，则cos A =________．8．已知样本1x ，…，2024x 的平均数为2，方差为2023，则21x ，22x ，…，22024x 的平均数为________．9．已知数列{}n a 满足3213223n n a a a a n++++=− （n 为正整数），则n a =________． 10．如图，在函数()sin y x =ω+ϕ的部分图像中，若TA AB = ，则点A 的纵坐标为________．211．波斯诗人奥马尔·海亚姆于十一世纪发现了一元三次方程32x a x b +=（0a ≠，0b >）的几何求解方法．在直角坐标系xOy 中，P 、Q 两点在x 轴上，以OP 为直径的圆与抛物线C ：2x ay =交于点R ，RQ OQ ⊥．已知x OQ =是方程32x a x b +=的一个解，则点P 的坐标为________．12．“布朗运动”是指微小颗粒永不停息地无规则随机运动，在如图所示的试验容器中，容器由三个仓组成，某粒子作布朗运动时每次运动会从所在仓的通道口中随机选择一个到达相邻仓或者容器外，一旦粒子到达容器外就会被外部捕获装置所捕获，此时试验结束．已知该粒子初始位置在1号仓，则试验结束时该粒子是从1号仓到达容器外的概率为________．二、选择题（共18分，第13、14题每题4分，第15、16题每题5分）．13．演讲比赛共有9位评委分别给出某选手的原始评分，评定该选手的成绩时，从9个原始评分中去掉1个最高分、1个最低分，得到7个有效评分．7个有效评分与9个原始评分相比，不变的数字特征是（ ） A ．中位数B ．平均数C ．方差D ．极差14．已知α、β是两个平面，m 、n 、l 是三条直线，则下列命题为真命题的是（ ） A ．若l ⊂β，m ⊂α，l m ⊥，则α⊥β B ．若∥l α，∥l β，m αβ= ，则∥l m C ．若m αβ= ，n βγ= ，l γα= ，则∥∥m n l D ．若m n ⊥，m ⊥α，则∥n α 15．已知直线l ：110ax y a+−=与圆O ：221x y +=相交于A 、B 两点，则下面结论中正确的是（ ）A ．线段AB 长度的最小值为1 B ．线段AB 长度的最大值为2C ．△OAB 的面积最小值为4D ．△OAB 的面积最大值为12316．已知函数()y f x =的定义域为R ．p ：存在a R ∈且0a ≠，对任意的x R ∈，有()()()f x a f x f a +<+恒成立．1q ：()y f x =为减函数，且()0f x >恒成立．2q ：()y f x =为增函数，且存在00x <使得()00f x =．则下列说法正确的是（ ） A ．只有1q 是p 的充分条件 B ．只有2q 是p 的充分条件 C ．1q 、2q 都是p 的充分条件D ．1q 、2q 都不是p 的充分条件三、解答题（共78分，第17、18、19题每题14分，第20、21题每题18分）． 17．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 已知()sin f x x =．（1）求4f x π−[]0,x ∈π上的解；（2）已知()()()()2πg x x f x f x f x π=+−+，若关于x 的方程()12g x m −=在0,2πx∈时有解，求实数m 的取值范围．418．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 如图（见答题卡），三棱柱111ABC A B C −中，侧面11BB C C ⊥底面ABC ，且AB AC =，11A B A C =．（1）证明：1AA ⊥平面ABC ；（2）若12AA BC ==，90BAC ∠=°，求平面1A BC 与平面11A BC 所成的二面角的余弦值．19．（本题满分14分）本题共有2个小题，第1小题满分7分，第2小题满分7分． 某大型企业准备把某型号的零件交给甲工厂或乙工厂生产．经过调研和试生产，质检人员抽样发现：甲工厂试生产的零件的合格品率为94%；乙工厂试生产的零件的合格品率为98%；将两个工厂生产的零件混合到一起后，合格品率为97%．（1）混合放在一起的零件有几万个，从中一次随机抽取3个，用抽样调查的频率估计概率，记这3个零件中来自甲工厂的个数为X ，求X 的分布和期望；（2）为了争取获得该零件的生产订单，甲工厂提高了生产该零件的质量指标．已知在甲工厂提高质量指标的条件下，该大型企业把零件交给甲工厂生产的概率，大于在甲工厂不提高质量指标的条件下，该大型企业把零件交给甲工厂生产的概率．设事件A 表示“甲工厂提高了生产该零件的质量指标”，事件B 表示“该大型企业把零件交给甲工厂生产”，已知()01P B <<，证明：()()||P A B P A B >．20．（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分．法国著名数学家加斯帕尔·蒙日在研究圆锥曲线时发现：椭圆的任意两条互相垂直的切线的交点Qa为椭圆的长半轴长，b为椭圆的短半轴长）为半径的圆，这个圆被称为蒙日圆．已知椭圆C：221 3x y+=．（1）求椭圆C的蒙日圆的方程；（2）若斜率为1的直线l与椭圆C相切，且与椭圆C的蒙日圆相交于M、N两点，求△OMN的面积（O为坐标原点）；（3）设Р为椭圆C的蒙日圆上的任意一点，过点Р作椭圆C的两条切线，切点分别为A、B，求△PAB面积的最小值．5621．（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分6分，第3小题满分8分．已知()sin f x x =，()g x kx b =+（0k ≠）． （1）若直线()y g x =是曲线()y f x =在(),0π处的切线，求()g x 的表达式；（2）若任取1x 、2x R ∈且12x x ≠，有()()()()()()()()21212g f x g f x k f g x f g x −≤−恒成立，求符合要求的数对(),k b 组成的集合．（3）当0b =时，方程()()()()f g x g f x =在区间[)0,2π上恰有1个解，求k 的取值范围．7参考答案一、填空题1.0;2.()()4,66,8∪;3.780.3; 6. a ; 7.13−;8.2027; 9.11,123,2n n n n −= ⋅≥; 10. ； 11.2,0b a12.1013 11．波斯诗人奥马尔·海亚姆于十一世纪发现了一元三次方程32x a x b +=（0a ≠，0b >）的几何求解方法．在直角坐标系xOy 中，P 、Q 两点在x 轴上，以OP 为直径的圆与抛物线C ：2x ay =交于点R ，RQ OQ ⊥．已知x OQ =是方程32x a x b +=的一个解，则点P 的坐标为________． 【答案】2,0b a【解析】设()0,P t,OP 的中点为02t ,,则以OP 为直径的圆的方程为22224t t x y −+=与抛物线2:C x ay =联立,可得22421,24t t x x a −+=化简可得4220x x tx a −+=, 由于RQ OQ ⊥,可得,R Q 的横坐标相等,则方程32x a x b +=和方程320x x t a−+=有相同的解,即有2b a t =,解得2b t a =,则20b P ,a. 12．“布朗运动”是指微小颗粒永不停息地无规则随机运动，在如图所示的试验容器中，容器由三个仓组成，某粒子作布朗运动时每次运动会从所在仓的通道口中随机选择一个到达相邻仓或者容器外，一旦粒子到达容器外就会被外部捕获装置所捕获，此时试验结束．已知该粒子初始位置在1号仓，则试验结束时该粒子是从1号仓到达容器外的概率为________．8【答案】1013【解析】设从i 出发, 最终从 1 号口出的概率为i P ,则122131232213311110333612P P P P P P P P P=+=++=+ =， 解得11013P =.故答案为:1013. 二、选择题13. A 14. B 15.D 16.C 15．已知直线l ：110ax y a+−=与圆O ：221x y +=相交于A 、B 两点，则下面结论中正确的是（ ）A ．线段AB 长度的最小值为1 B ．线段AB 长度的最大值为2C ．△OAB 的面积最小值为4D ．△OAB 的面积最大值为12【答案】D【解析】圆心O到直线距离d，弦长)AB ，所以A 、B错。
2022~2023年高三上半年摸底英语试卷完整版(上海市交大附中)
语法填空Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Space is a dangerous place, not only because of meteors (流星) but also because of rays from the sun and other stars. The atmosphere again acts 【1】our protective blanket on earth. Light gets through, and this is essential for plants 【2】(make) the food which we eat. Heat, too, makes our environment endurable. Various kinds of rays come through the air from outer space, but enormous quantities of radiation from the sun 【3】(screen) off. As soon as men leave the atmosphere, they are exposed to this radiation but their spacesuit or the walls of their spacecraft,【4】they are inside, do prevent a lot of radiation damage.Radiation is 【5】(great) known danger to explorers in space. The unit of radiation is called "rem". Scientists have reason to think that a man can put up with far more than 0.1 rem without 【6】(damage); the figure of 60 rems has been agreed on. The trouble is 【7】it is extremely difficultto be sure about radiation damage pared with AIDS, Tuberculosis can be cured effectively【3】Which of the following is best defines the word “upshot” (Para 5)?A.Outcome.B.Uphold.C.Achievement.D.Project.【4】Which of the following proverbs is closest in meaning to the message the passage tries to convey?A.Forgive and forget.B.Forgotten, but not gone.C.When the wound is healed, the pain is forgotten.D.Every dog is brave at his own door.【答案】【1】D【2】D【3】A【4】B【解析】本文是一篇说明文，介绍了结核病卷土重来的两个原因——被人们忽视以及它和艾滋病间的关系（抗艾滋病药物会使结核病恶化）。
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上海交通大学附属中学2014-2015学年度第一学期
高三数学开学摸底考试卷
（满分150分，120分钟完成）
一、填空题（本大题共14题，每题4分，满分56分）
1．函数的反函数________________．
2. 函数的最小值_________
3. 若，则的取值范围是___________
4．若对任意正实数，不等式恒成立，则实数的最小值为．
5．同时满足（1）
6．集合，．若“a＝1”是“”的充分条件，则实数b的取值范围是．
7．已知，则．
8．方程有解，则________
9. 如果
10．函数图像的对称中心是．
11.
12.
13. 关于函数必定是
的整数倍；（2）的表达式可改写为；
（4）
____________
14.已知等比数列的首项为，公比为，其前项和记为，又设
，的所有非空子集中的最小元素的和为，则的最小正整数为．二、选择题（本大题共4题，每题5分，满分20分）
15．下列说法正确的是（）
A．命题“若，则”的否命题是“若，则”
B．“”是“”的必要不充分条件
C．命题“若，则”的逆否命题是真命题
D．“”是“”的充分不必要条件
16. 若是的最小值，则的取值范围为（）.
(A)[-1,2] (B)[-1，0] (C)[1，2] (D)
17. 如果的三个内角的余弦值分别等于的三个内角的正弦值，则（）
A ．和都是锐角三角形
B ．和都是钝角三角形
C ．是钝角三角形，是锐角三角形
D ．是锐角三角形，是钝角三角形
18. 定义一种新运算：，已知函数，若函数
恰有两个零点，则的取值范围为（）.
A.(1,2]
B.．
C.
D.
三、解答题(本大题共5题，满分74分12’+14’+14’+16’+18’=74’)
19. 解关于x的不等式：
20．在中，角所对的边分别为，已知，（1）求的大小；
（2）若，求的取值范围.
21．数列的首项,
(1) 求数列的通项公式；
(2) 设的前项和为,若的最小值为，求的取值范围？
22．阅读：
已知、，，求的最小值.
解法如下：，
当且仅当，即时取到等号，
则的最小值为.
应用上述解法，求解下列问题：
（1）已知，，求的最小值；（2）已知，求函数的最小值；
（3）已知正数、、，，
求证：.
23．已知函数满足2+，对x≠0恒成立，在数列{a n}、{b n}中，a1=1，b1=1，对任意x∈N+，，。
（1）求函数解析式；
（2）求数列{a n}、{b n}的通项公式；
（3）若对任意实数,总存在自然数k,当n≥k时,恒成立，求k的最小值。