上海市二模试卷a卷

2023学年第二学期初三年级学业质量调研语文试卷（考试时间100分钟，满分150分）考生注意：1.本试卷含四个大题，共22题。

答题时，考生务必按答题要求在答题纸规定的位置上作答，在草稿纸、本试卷上答题一律无效。

一、古诗文（35分）（一）默写与运用（13分）1默写.（1）念天地之悠悠，____________！（陈子昂《登幽州台歌》）（2）____________，留取丹心照汗青。

（文天祥《过零丁洋》）（3）锦帽貂裘，____________。

（苏轼《江城子·密州出猎》）（4）面对难题，我们有时会在反复尝试中自我怀疑，但再坚持一会儿，或许就能如《游山西村》中所言，迎来“____________，____________”的那一刻。

【答案】①. 独怆然而涕下②. 人生自古谁无死③. 千骑卷平冈④. 山重水复疑无路⑤. 柳暗花明又一村【解析】【详解】本题考查名句名篇默写。

注意本题中的易错字：独、怆、涕、骑、冈、疑、柳。

（二）（22分）阅读下面文言文，完成各题【甲】初，权谓吕蒙曰：“卿今当涂掌事，不可不学！”蒙辞以军中多务。

权曰：“孤岂欲卿治经为博士邪！但当涉猎，见往事耳。

卿言多务，孰若孤？孤常读书，自以为大有所益。

”蒙乃始就学。

及鲁肃过寻阳，与蒙论议，大惊曰：“卿今者才略，非复吴下阿蒙！”蒙曰：“士别三日，即更刮目相待，大兄何见事之晚乎！”肃遂拜蒙母，结友而别。

【乙】鲁哀公问于孔子曰：“当今之时，君子谁贤？”对曰：“卫灵公。

臣观于朝廷。

灵公之弟曰公子梁牟，其知足以治千乘之国，其信足以守之，而灵公爱之；又有士曰王林，国有贤人必进而任之。

无不达也；不能达，退而与分其禄，而灵公尊之；又有士曰庆足，国有大事，则进而治之，无不济也，而灵公说之；史①去卫，灵公邸舍②三月，琴瑟不御③，待史之入也而后入。

臣是以知其贤也。

”【注释】①史：史鰌，卫国大夫，以正直闻名于世。

②邸舍：客栈。

③御：用，古代君王所用称“御用”。

2024年上海市松江区高三数学4月二模考试卷（满分150分，完卷时间120分钟）2024.4考生注意:1.本考试设试卷和答题纸两部分，试卷包括试题与答题要求，所有答题必须涂（选择题）或写（非选择题）在答题纸上，做在试卷上一律不得分.2.答题前，务必在答题纸上填写学校、班级、姓名和考号.3.答题纸与试卷在试题编号上是一一对应的，答题时应特别注意，不能错位.一、填空题（本大题满分54分）本大题共有12题，第1~6题每个空格填对得4分，第7~12题每个空格填对得5分，否则一律得零分.1．函数lg(2)y x =-的定义域为2．在复平面内，复数z 对应的点的坐标是(1,2)，则i z ⋅=.3．已知随机变量X 服从正态分布()23,N σ，且(35)0.3P X ≤≤=，则(5)P X >=.4．已知点A 的坐标为13,22⎛⎫ ⎪ ⎪⎝⎭，将OA 绕坐标原点O 逆时针旋转π2至OP ，则点P 的坐标为.5．已知7270127(1)(1)(1)x a a x a x a x =+-+-++- ，则5a =．6．若一个圆锥的侧面展开图是面积为2π的半圆面，则此圆锥的体积为.（结果中保留π）7．已知等差数列{}n a 的公差为2，前n 项和为n S ，若35a S =，则使得n n S a <成立的n 的最大值为.8．已知函数()2log f x x =，若()()()1212f x f x x x =≠，则124x x +的最小值为．9．12,F F 是双曲线()222210,0x ya b a b-=>>的左、右焦点，过1F 的直线l 与双曲线的左、右两支分别交于A 、B 两点，若22::3:4:5AB BF AF =，则双曲线的离心率为10．已知正三角形ABC 的边长为2，点D 满足CD mCA nCB =+，且0m >，0n >，21m n +=，则||CD 的取值范围是.11．已知02a <<，函数()1241,22,2x a x a x y a x -⎧-++≤=⎨>⎩，若该函数存在最小值，则实数a 的取值范围是.12．某校高一数学兴趣小组一共有30名学生，学号分别为1，2，3，…，30，老师要随机挑选三名学生参加某项活动，要求任意两人的学号之差绝对值大于等于5，则有种不同的选择方法.二、选择题（本大题满分18分）本大题共有4题，每题有且只有一个正确答案，第13、14题选对得4分，第15、16题选对得5分，否则一律得零分.13．已知集合{|04}A x x =≤≤，{|2,Z}B x x n n ==∈，则A B = （）A ．{1,2}B ．{2,4}C ．{0,1,2}D ．{0,2,4}14．垃圾分类是保护环境，改善人居环境､促进城市精细化管理､保障可持续发展的重要举措.某小区为了倡导居民对生活垃圾进行分类，对垃圾分类后处理垃圾x （千克）所需的费用y （角）的情况作了调研，并统计得到下表中几组对应数据，同时用最小二乘法得到y 关于x 的线性回归方程为0.70.4y x =+，则下列说法错误的是（）x2345y22.33.4mA ．变量x 、y 之间呈正相关关系B ．可以预测当8x =时，y 的值为6C ． 3.9m =D ．由表格中数据知样本中心点为()3.5,2.8515．已知某个三角形的三边长为a 、b 及c ，其中a b <.若a ，b 是函数2y ax bx c =-+的两个零点，则a 的取值范围是（）A ．1,12⎛⎫ ⎪⎝⎭B ．15122⎛⎫ ⎪⎝⎭C ．10,2⎛⎫⎪ ⎪⎝⎭D ．51,12⎛⎫ ⎪ ⎪⎝⎭16．设n S 为数列{}n a 的前n 项和，有以下两个命题：①若{}n a 是公差不为零的等差数列且N k ∈，2k ≥，则12210k S S S -⋅= 是120k a a a ⋅= 的必要非充分条件；②若{}n a 是等比数列且N k ∈，2k ≥，则120k S S S ⋅= 的充要条件是10k k a a ++=.那么（）A ．①是真命题，②是假命题B ．①是假命题，①是真命题C ．①、②都是真命题D ．①、②都是假命题三、解答题（本大题满分78分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤.17．设2()sinsin(0)222f x x x x ωωωω=>，函数()y f x =图象的两条相邻对称轴之间的距离为π．(1)求函数()y f x =的解析式；(2)在ABC 中，设角A 、B 及C 所对边的边长分别为a、b 及c ，若a =b ，3()2f A =，求角C ．18．如图，在四棱锥P ABCD -中，底面ABCD 为菱形，PD ⊥平面ABCD ，E 为PD 的中点.(1)设平面ABE 与直线PC 相交于点F ，求证：//EF CD ；(2)若2AB =，60DAB ∠=︒，PD =，求直线BE 与平面PAD 所成角的大小.19．某素质训练营设计了一项闯关比赛.规定：三人组队参赛，每次只派一个人，且每人只派一次：如果一个人闯关失败，再派下一个人重新闯关；三人中只要有人闯关成功即视作比赛胜利，无需继续闯关.现有甲、乙、丙三人组队参赛，他们各自闯关成功的概率分别为1p 、2p 、3p ，假定1p 、2p 、3p 互不相等，且每人能否闯关成功的事件相互独立.(1)计划依次派甲乙丙进行闯关，若13p 4=，223p =，312p =，求该小组比赛胜利的概率；(2)若依次派甲乙丙进行闯关，则写出所需派出的人员数目X 的分布，并求X 的期望()E X ；(3)已知1231p p p >>>，若乙只能安排在第二个派出，要使派出人员数目的期望较小，试确定甲、丙谁先派出.20．如图，椭圆22:12y x Γ+=的上、下焦点分别为1F 、2F ，过上焦点1F 与y 轴垂直的直线交椭圆于M 、N两点，动点P 、Q 分别在直线MN 与椭圆Γ上.(1)求线段MN 的长；(2)若线段PQ 的中点在x 轴上，求2F PQ △的面积；(3)是否存在以2F Q 、2F P 为邻边的矩形2F QEP ，使得点E 在椭圆Γ上？若存在，求出所有满足条件的点Q 的纵坐标；若不存在，请说明理由.21．已知函数ln y x x a =⋅+（a 为常数），记()()y f x x g x ==⋅.(1)若函数()y g x =在1x =处的切线过原点，求实数a 的值；(2)对于正实数t ，求证：()()()ln 2f x f t x f t t a +-≥-+；(3)当1a =时，求证：e ()cos xg x x x +<.1．2+∞（，）【详解】要使函数lg(2)y x =-有意义，则202x x ->⇒>，所以函数lg(2)y x =-的定义域为2+∞（，），故答案为2+∞（，）.2．2i -+##i-2【分析】根据复数的乘法运算求解即可.【详解】由题意知，12z i =+，则i i (12i)2i z ⋅=⋅+=-+，故答案为：2i -+3．0.2##15【分析】根据题意，结合正态分布的对称性，即可求解.【详解】因为随机变量X 服从正态分布()23,N σ，且(35)0.3P X ≤≤=，可得(5)0.5(35)0.50.30.2P X P X >=-≤≤=-=.故答案为：0.2.4．21⎛⎫ ⎪ ⎪⎝⎭【分析】由题意可求π3xOA ∠=，5π326ππxOP ∠=+=，利用任意角的三角函数的定义即可求解．【详解】因为点A 的坐标为12⎛ ⎝⎭，可得π3xOA ∠=，所以5π326ππxOP ∠=+=，可得5πcos6P x ==，5π1sin 62P y ==，所以点P 的坐标为12⎛⎫⎪ ⎪⎝⎭，故答案为：12⎛⎫ ⎪ ⎪⎝⎭.5．21【分析】先将7x 变形为7[1(1)]x +-的形式，再应用二项式定理求解即可.【详解】77[1(1)]x x =+-，由二项式定理得：5567C (1)T x =-，所以5257776C C 2121a ⨯====⨯.故答案为：21.6【分析】通过侧面展开图的面积．求出圆锥的母线，底面的半径，求出圆锥的体积即可．【详解】由题意一个圆锥的侧面展开图是面积为2π的半圆面，设圆锥的母线长为l ，底面半径为r ，则212ππ2l =，所以2l =，则半圆的弧长为2π，所有圆锥的底面半径为2π2πr =，1r =，所以圆锥的体积为：21π1π33⨯⨯=．．7．5【分析】根据题意，列出方程求得14a =-，得到25n S n n =-且26n a n =-，结合n n S a <，列出不等式，即可求解.【详解】由等差数列{}n a 的公差为2，前n 项和为n S ，若35a S =，可得115422522a a ⨯+=+⨯⨯，解得14a =-，所以2(1)4252n n n S n n n -=-+⨯=-，且3(1)226n a n n =-+-⨯=-，因为n n S a <，即2526n n n -<-，整理得27+60n n -<，解得16n <<，因为N n *∈，所以使得n n S a <成立的n 的最大值为5.故答案为：5.8．4【分析】由题意及对数的运算与对数函数的性质可得121x x ⋅=，利用基本不等式即可求解．【详解】()222log ,01log log ,1x x f x x x x -<<⎧==⎨≥⎩，若()()()1212f x f x x x =≠，不妨设1201x x <<≤，则2122log log x x -=，所以2122212log log log 0x x x x +=⋅=，即121x x ⋅=，所以1244x x +≥=，当且仅当112x =，22x =时，等号成立．故答案为：4．9【分析】根据双曲线的定义可求得1a =，290ABF ∠=︒，再利用勾股定理可求得122||c F F =，从而可求得双曲线的离心率．【详解】解：22||:||:||3:4:5AB BF AF = ，不妨令||3AB =，2||4BF =，2||5AF =，22222||||||AB BF AF += ，290ABF ∴∠=︒，又由双曲线的定义得：12||||2BF BF a -=，21||||2AF AF a -=，11||345||AF AF ∴+-=-，1||3AF ∴=．12||||3342BF BF a ∴-=+-=，1a ∴=．在Rt △12BF F 中，222221212||||||6452F F BF BF =+=+=，2212||4F F c = ，2452c ∴=，13c ∴=．∴双曲线的离心率13c e a==．故答案为：13．10．()1,2【分析】取AC 的中点E ，由题意可得2CD mCE nCB =+，从而推得,,B D E 三点共线，进而得出CE CD CB <<，即可得出答案.【详解】取AC 的中点E ，则2CA CE =，又2CD mCA nCB mCE nCB =+=+，又因为21m n +=，故,,B D E 三点共线，即点D 在中线BE 上运动，在正三角形ABC 中，BE AC ⊥，又0m >，0n >，则CE CD CB <<，故()1,2CD ∈ .故答案为：()1,211．1{|02a a <≤或1}a =【分析】令()(2)41g x a x a =-++，(],2x ∞∈-，1()2x h x a -=，(2,)x ∈+∞，分类讨论a 的取值范围，判断()g x ，()h x 的单调性，结合()f x 存在最小值，列出相应不等式，综合可得答案．【详解】由题意，令()(2)41g x a x a =-++，(],2x ∞∈-，1()2x h x a -=，(2,)x ∈+∞，当01a <<时，()g x 在(],2-∞上单调递减，()h x 在(2,)+∞上单调递减，则()h x 在(2,)+∞上的值域为(0,2)a ，因为()f x 存在最小值，故需()2(2)2410g a a =-⨯++≤，解得12a ≤，结合01a <<，此时102a <≤；当12a <<时，()g x 在(],2-∞上单调递减，()h x 在(2,)+∞上单调递增，则()h x 在(2,)+∞上的值域为(2,)a +∞，因为()f x 存在最小值，故需()22g a ≤，即(2)2412a a a -⨯++≤，解得34a ≤，这与12a <<矛盾；当1a =时，()5g x x =-+在(],2-∞上单调递减，且在(],2-∞上的值域为[)3,+∞，()2h x =，此时存在最小值2；则实数a 的取值范围为1{|02a a <≤或1}a =．故答案为：1{|02a a <≤或1}a =．12．1540【分析】根据题意，设挑选出的三名学生的学号分别为x ，y ，z ，不妨设x y z <<，结合题意转化为()()()443123x y x z y z +--+--+-=，进而转化为四个正整数的和为23，结合隔板法，即可求解.【详解】设挑选出的三名学生的学号分别为x ，y ，z ，不妨设x y z <<，则有恒等式()()()()3030*x y x z y z +-+-+-=，其中1x ≥，5y x -≥，5z y -≥，300z -≥，即1x ≥，41y x --≥，41z y --≥，311z -≥，故()*式为()()()443123x y x z y z +--+--+-=，上式四个正整数的和为23，相当于23个1分成四组，运用隔板法，在22个空中放3块板，故有322C 1540=种方法．故答案为：1540．13．D【分析】直接根据交集概念求解.【详解】因为集合{|04}A x x =≤≤，{|2,Z}B x x n n ==∈，所以{0,2,4}A B = .故选：D.14．C【分析】利用回归直线方程可判断A 选项；将8x =代入回归直线方程可判断B 选项；计算出样本的中心点坐标，结合平均数公式可判断CD 选项.【详解】对于A 选项，因为回归直线方程0.70.4y x =+，故变量x 、y 之间呈正相关关系，A 对；对于B 选项，当8x =时，0.780.46y =⨯+=，B 对；对于CD 选项，23453.54x +++== ，则0.7 3.50.4 2.85y =⨯+=，故样本的中心点的坐标为()3.5,2.85，另一方面，2 2.3 3.4 2.854my +++==，解得 3.7m =，C 错D 对.故选：C.15．B【分析】由a ，b 为函数2()f x ax bx c =-+的两个零点可得()222ax a a b x a b ax bx c -++=-+，即可得21a b a =-、41a c a =-，由两边之和大于第三边，结合题意可得15122a <<.【详解】由,ab 为函数2()f x ax bxc =-+的两个零点，故有()()2a x a xb ax bxc --=-+，即()222ax a a b x a b ax bx c -++=-+恒成立，故()a a b b +=，2a b c =，则21a b a =-，242211a a c a b a a a==⨯=--，由a ，b ，c 为某三角形的三边长，且a b <，故10a ->，且21a a a<-，则112a <<，因为b c a +>必然成立，所以a c b a b c +>⎧⎨+>⎩，即42241111a a a a a a a a a a⎧+>⎪⎪--⎨⎪+>⎪--⎩，解得10201a a ⎧<<⎪⎨⎪<<⎩，所以1122a <<，故a的取值范围是：11,22⎛⎫ ⎪ ⎪⎝⎭.故选：B.16．C【分析】根据题意，由等差数列和等差数列的前n 项和性质分析①的真假，由等比数列和等比数列的前n 项和性质分析②的真假，综合可得答案.【详解】根据题意，对于命题①，{}n a 是公差不为零的等差数列，若120k a a a ⋅= ，则在12,,,k a a a 中，至少有一项为0，假设()0,1m a m k =≤≤，则()()()12121212102m m m m a a S m a ---+==-=，必有12210k S S S -⋅= ，反之，在等差数列{}n a 中，若23n a n =-，则121,1a a =-=，有20S =，则120k S S S ⋅= 成立，但120k a a a ⋅= 不成立，故12210k S S S -⋅= 是120k a a a ⋅= 的必要非充分条件，故①正确；对于命题②，若{}n a 是等比数列，设其公比为q ，若N k ∈，2k ≥时，有120k S S S ⋅= ，则12,,,k S S S 中，至少有一项为0，则1q ≠，假设0,m S =则有()110,1mm a q S q-==-必有1mq=，又由1q ≠，必有m 为偶数且1q =-，故10k k a a ++=，反之，若10k k a a ++=，则1q =-，必有20S =，则有N k ∈，2k ≥，则120k S S S ⋅= ，若{}n a 是等比数列且N k ∈，2k ≥，则120k S S S ⋅= 的充要条件是10k k a a ++=，故②正确.故选：C.【点睛】关键点点睛：本题解决的关键点是，熟练掌握等差数列与等比数列的通项公式与求和公式，从而分析得解.17．(1)π1()sin(62f x x =-+(2)π12【分析】（1）根据降幂公式，二倍角公式及辅助角公式化简()f x ，再根据()y f x =图象的两条相邻对称轴之间的距离为π求出ω即可；（2）由3()2f A =得出2π3A =，过点C 作AB CD ⊥于点D ，得出π6ACD ∠=，分别求出,AD CD 的长，结合AB即可得出BD CD =，进而得出BCD ∠，根据ACB BCD ACD ∠=∠-∠即可求得答案．【详解】（1）1cos 3π1()sin sin()2262x f x x x ωωω-=+=-+，因为函数()y f x =图象的两条相邻对称轴之间的距离为π，所以π2T =,则2π2πT ω==，解得1ω=，所以π1()sin()62f x x =-+．（2）由3()2f A =得，π13ππ()sin(2π,Z 62262f A A A k k =-+=⇒-=+∈，因为(0,π)A ∈，所以ππ62A -=，即2π3A =，22221cos22b c a A bc +-===-，解得622c =(舍负)，过点C 作AB CD ⊥于点D ，如图所示，由π2π,23D BAC ∠=∠=得，π6ACD ∠=，则1π,cos 2262AD AC CD AC ===⨯=，所以BD AB AD =+=BD CD =，所以π4BCD ∠=，则πππ4612ACB BCD ACD ∠=∠-∠=-=．18．(1)证明见解析(2)π6【分析】（1）根据线面平行的判定定理，证出//AB 平面PCD ，然后根据平面ABE ⋂平面PCD EF =，利用线面平行的性质定理证出//EF CD ；（2）连接BD ，取AD 中点H ，连接BH 、EH ，根据线面垂直的判定定理，证出BH ⊥平面PAD ，可得BEH ∠是直线BE 与平面PAD 的所成角，然后在Rt BEH △中利用锐角三角函数的定义算出答案．【详解】（1）证明： 平面ABE 与直线PC 相交于点F ，∴平面ABE ⋂平面PCD EF =，四边形ABCD 是菱形，//AB CD ∴，AB ⊄ 平面PCD ，CD ⊂平面PCD ，//AB ∴平面PCD ，AB ⊂ 平面ABE ，平面ABE ⋂平面PCD EF =，//EF CD ∴；（2）连接BD ，取AD 中点H ，连接BH 、EH ，菱形ABCD 中，AB AD =，60DAB ∠=︒，ABD ∴ 是等边三角形，H 是AD 中点，BH AD ∴⊥，PD ⊥ 平面ABCD ，BH ⊂平面ABCD ，BH PD ∴⊥，PD 、AD ⊂平面PAD ，PD AD D = ，BH ∴⊥平面PAD ．BEH ∴∠是直线BE 与平面PAD 的所成角，E 是PD 中点，PD =12DE PD ∴==PD ⊥ 平面ABCD ，AD ⊂平面ABCD ，PD AD ∴⊥，H 为AD 中点，112DH AD ∴==，Rt DEH △中，3EH =，等边ABD △中，高BH AD ==Rt BEH ∴ 中，tan BH BEH EH ∠=可得π6BEH ∠=，即直线BE 与平面PAD 的所成角等于π6．19．(1)2324(2)121223p p p p --+(3)先派出甲【分析】（1）利用独立事件的概率乘法公式求解；（2）由题意可知，X 的所有可能取值为1，2，3，利用独立事件的概率乘法公式求出相应的概率，进而得到X 的分布，再结合期望公式求解；（3）分别计算出依次派甲乙丙进行闯关和依次派丙乙甲进行闯关，所派出人员数目的期望，再利用作差法比较大小即可．【详解】（1）设事件A 表示“该小组比赛胜利”，则()3121112344343224P A =+⨯+⨯⨯=；（2）由题意可知，X 的所有可能取值为1，2，3，则1(1)P X p ==，12(2)(1)P X p p ==-，12(3)(1)(1)P X p p ==--，所以X 的分布为：X123P 1p 12(1)p p -12(1)(1)p p --所以112121212()2(1)3(1)(1)23E X p p p p p p p p p =+-+--=--+；（3）若依次派甲乙丙进行闯关，设派出人员数目的期望为1E ，由（2）可知，1121223E p p p p =--+，若依次派丙乙甲进行闯关，设派出人员数目的期望为2E ，则2323223E p p p p =--+，则1212123232121323(23)(23)22E E p p p p p p p p p p p p p p -=--+---+=--+21313132()2()()(2)p p p p p p p p =---=--，因为1231p p p >>>，所以130p p ->，220p -<，所以120E E -<，即12E E <，所以要使派出人员数目的期望较小，先派出甲．20．(1)MN =22(3)2-1-.【分析】（1）根据已知求出点N 的横坐标，根据对称性可得线段MN 的长；；（2）线段PQ 的中点在x 轴上，得Q 点纵坐标，代入椭圆方程得Q 点横坐标，此时1QF x ⊥轴，易得其面积；（3）假设存在2F Q ，2F P 为邻边的矩形2F QEP ，使得点E 在椭圆C 上，设0(,1)P x ，11(,)Q x y ，22(,)E x y ，由平行四边形对角线互相平分把E 点坐标用,P Q 点坐标表示，然后把,Q E 坐标代入椭圆方程，利用垂直得向量的数量积为0，得出110,,x y x 的关系，结合起来可得00x =或01x x =-，再分别代入求得1y ，得结论．【详解】（1）由22:12y x Γ+=可得：a =1b =，从而1c ==，所以令1y =，则2112x +=，解得：22x =±，所以MN =（2）线段PQ 的中点在x 轴上，则1P y =，所以1Q y =-，即2QF y ⊥轴，所以令1y =-，则2112x +=，解得：x =所以221211222POF S F Q F F =⋅==（3）22121122222POF S F Q F F =⋅=⨯= ，假设存在以2F Q ，2F P 为邻边的矩形2F QEP ，使得点E 在椭圆C 上，设0(,1)P x ，11(,)Q x y ，22(,)E x y ，2(0,1)F -，因为四边形2F QEP 是矩形，一定为平行四边形，所以222F P F Q F E +=，则021x x x =+，212y y =+，所以011(,2)E x x y ++，,Q E 都在椭圆上，()()22112211012212y x y x x ⎧+=⎪⎪⎨+⎪++=⎪⎩，变形得201012220x x x y +++=①，又22QF PF ⊥，所以220F Q F P ⋅=，即110110(,1)(,2)2(1)0x y x y x x +⋅=++=，则11022y x x +=-②，②代入①得20010x x x +=，解得：00x =或01x x =-，若00x =时，11y =-，122x =±，此时P 与1F 重合，Q 点坐标为2(,1)2±-；若01x x =-时，联立()()22112211012212y x y x x ⎧+=⎪⎪⎨+⎪++=⎪⎩，消去1x 可得：211420y y ++=，解得：12y =-因为1y ⎡∈⎣，所以12y =-所以存在满足题意的Q点，其纵坐标为2-1-..【点睛】思路点睛：对于圆锥曲线中探索性问题，求解步骤如下：第一步：假设结论存在；第二步：结合已知条件进行推理求解；第三步：若能推出合理结果，经验证成立即可肯定正确；若推出矛盾，即否定假设；第四步：反思回顾，查看关键点、易错点及解题规范．21．(1)12(2)证明见解析(3)证明见解析【分析】（1）根据题以，得到()ln ,0a g x x x x=+>，求得2()x a g x x -'=，结合导数的几何意义，求得切线方程，将原点代入切线方程，即可求解；（2）设函数()()(),0h x f x f t x t =+->，求得()lnx h x t x '=-，求得函数()h x 的单调性和最小值为(2t h ，得到()(2t h x h ≥，即可得证；（3）根据题意，得到1e ln cos xx x x x +<-，结合cos [1,1]x ∈-，把转化为1e ln 1x x x x +<-，设()1e ln 1,0x k x x x x x=+-+>，利用导数求得()k x 的单调性和最大值()12e k =-，即可得证.【详解】（1）解：由题意，函数ln y x x a =⋅+，且()()y f x x g x ==⋅，可得()()ln ,0f x a g x x x x x ==+>，则221()a x a g x x x x-'=-=，所以(1)1g a '=-，又因为(1)ln1g a a =+=，所以()g x 在1x =处的切线方程为(1)(1)y a x a =--+，又因为函数()y g x =在1x =处的切线过原点，可得0(1)(01)a a =-⋅-+，解得12a =.（2）解：设函数()()(),0h x f x f t x t =+->，可得()ln ()ln()2h x x x t x t x a =+--+，其中0x t <<，则()ln 1ln()1lnx h x x t x t x'=+---=-，令()0h x '>，可得1x t x >-，即20x t t x ->-，即20x t x t-<-，解得2t x t <<，令()0h x '<，可得01x t x <<-，解得02t x <<，所以()h x 在(,)2t t 上单调递增，在(0,)2t 上单调递减，可得()h x 的最小值为(2t h ，所以()(2t h x h ≥，又由()()()(ln 2ln 22222t t t t h f f t t a f t t a =+-=+=-+，所以()()()ln 2f x f t x f t t a +-≥-+.（3）解：当1a =时，即证1e ln cos xx x x x+<-，由于cos [1,1]x ∈-，所以e e cos 1x x x x x -≥-，只需证1e ln 1xx x x+<-，令()1e ln 1,0xk x x x x x=+-+>，只需证明()0k x <，又由()22211e (1)(1e )(1)x x x x k x x x x x ---'=--=，因为0x >，可得1e 0x -<，令()0k x '>，解得01x <<；令()0k x '<，解得1x >，所以()k x 在(0,1)上单调递增，在(1,)+∞上单调递减，所以()k x 在1x =处取得极大值，也时最大值，所以()()max 12e 0k x k ==-<，即()0k x <，即1a =时，不等式e ()cos x g x x x +<恒成立.【点睛】方法技巧：对于利用导数研究不等式的恒成立与有解问题的求解策略：1、通常要构造新函数，利用导数研究函数的单调性，求出最值，从而求出参数的取值范围；2、利用可分离变量，构造新函数，直接把问题转化为函数的最值问题．3、根据恒成立或有解求解参数的取值时，一般涉及分离参数法，但压轴试题中很少碰到分离参数后构造的新函数能直接求出最值点的情况，进行求解，若参变分离不易求解问题，就要考虑利用分类讨论法和放缩法，注意恒成立与存在性问题的区别．。

上海市2024年黄浦区中考数学二模试卷考生注意：1.本试卷含三个大题，共25题；2.答题时，考生务必按答题要求在答题纸规定的位置上作答，在草稿纸、本试卷上答题一律无效；3.除第一、二大题外，其余各题如无特别说明，都必须在答题纸的相应位置上写出证明或计算的主要步骤。

一、选择题：(本大题共6题，每题4分，满分24分)【下列各题的四个选项中，有且只有一个是正确的，选择正确项的代号并填涂在答题纸的相应位置上】1.多项式的因式分解与整式乘法是互逆的.在整式乘法中，“单项式乘以多项式”所对应的互逆因式分解方法是(▲)(A)提取公因式法：(B)公式法;(C)十字相乘法;(D)分组分解法.2.已知第二象限内点P到x轴的距离为2，到y轴的距离为3，那么点P的坐标是(▲)(A)(-2,3);(B)(-3,2);(C)(2,-3);(D)(3,-2).3.如图1，一个3×5的网格，其中的12个单位正方形已经被2张“L”型和1张“田字”型纸片互不重叠地占据了.下列有4个均由4个单位正方形所组成的纸片，依次记为型号1、型号2、型号3和型号4.将这4个型号的纸片做平移、旋转，恰能将图1中3个未被占据的单位正方形占据，并且与已有的3张纸片不重叠的是(▲)(A)型号1;(B)型号2;(C)型号3;(D)型号4.4.对于数据:2、2、2、4、5、6、8、8、9、100,能较好反映这组数据平均水平的是(▲)(A)这组数据的平均数；(B)这组数据的中位数；(C)这组数据的众数；(D)这组数据的标准差.5.反比例函数=1的图像有下述特征：图像与x轴没有公共点且与x轴无限接近.下列说明这一特征的理由中，正确的是(▲)(A)自变量x≠0且x的值可以无限接近0；(B)自变量x≠0且函数值y可以无限接近0；(C)函数值y≠0且x的值可以无限接近0；(D)函数值y≠0且函数值y可以无限接近0.6.小明在研究梯形的相似分割问题，即如何用一条直线将一个梯形分割成两个相似的图形.他先从等腰梯形开始进行探究，得到下面两个结论.结论1：存在与上、下底边相交的直线，能将等腰梯形分割成两个相似的图形；结论2：不存在与两腰相交的直线，能将等腰梯形分割成两个相似的图形.对这两个结论，你认为(▲)(A)结论1、结论2都正确;(B)结论1正确、结论2不正确；(C)结论1不正确、结论2正确;(D)结论1、结论2都不正确.二、填空题：(本大题共12题，每题4分，满分48分)7.100的平方根是▲.8.计算:−X²=.9.方程=+2的解是▲.10.已知关于x的方程.W+B−1=0,判断该方程的根的情况是▲.11.将直线y=2x向上平移2个单位，所得直线与x轴、y轴所围成的三角形面积是▲.12.一副52张的扑克牌(无大、小王)被任意打乱后背面朝上放在桌上，小华先从中抽取1张，取得的是黑桃A.然后小王从剩下的牌中再任意抽取1张，他恰好抽到A的概率是▲.13.小黄对学校提供午餐中的主食、荤菜、蔬菜和汤，开展了一次满意度调查.他利用中午休息时间，随机对学校中50名学生做了问卷调查，汇总数据如下表.如果学校共有1400名学生，那么全校对午餐中主食满意的学生约有▲名.类别主食荤菜蔬菜汤满意人数16520814.现有一张矩形纸片，其周长为36厘米，将纸片的四个角各剪下一个边长为2厘米的正方形，然后沿虚线(如图2所示)将纸片折成一个无盖的长方体.如果所得的长方体的体积是48立方厘米，设原矩形纸片的长是x厘米，那么可列出方程为▲.15.如图3,D、E分别是△ABC边AB、AC上点,满足,A=2A,∠A=∠Bu记B = ,B = ,那么向量B =¯(用向量a、b表示).16.如图4,正六边形MNPQRS位于正方形ABCD内,它们的中心重合于点O,且.M‖B.已知正方形ABCD的边长为a,正六边形MNPQRS的边长为b,那么点P到边CD的距离为▲.(用a、b 的代数式表示)17.如图5，由4个全等的直角三角形拼成一个大正方形ABCD，内部形成一个小正方形MNPQ.如果正方形MNPQ的面积是正方形ABCD面积的一半，那么.∠ABM的正切值是▲.18.如图6,D是等边△ABC边BC上点,BD:CD=2:3,作AD的垂线交AB、AC分别于点E、F,那么AE:AF=▲.三、解答题：(本大题共7题，满分78分)19.(本题满分10分)+2024−20240.计算：|1−tan60∘|20.(本题满分10分)解不等式组：−5≤0,+1−23<021.(本题满分10分).如图7,D是△ABC边AB上点,已知∠BCD=∠A,AD=5,BD=4.(1)求边BC的长;(2)如果△ACD∽△CBD(点A、C、D对应点C、B、D),求∠ACB的度数.网络平台上有一款代金券，主打的广告语是“满80团1张”.规则如下：在平台可以花75元团购一张80元代金券，一张代金券在平台商城内可以抵80元消费额，每笔消费可用于抵扣的代金券数量不限，但不找零.(1)在平台商城一笔375元的消费，如果使用4张代金券，实际共支付了多少元?(2)在充分使用代金券的情况下，在平台商城一笔x元的消费与实际总支付y元间存在着依赖关系,当320<x<375时,写出y关于x的函数关系式;(3)广告语是“满80团1张”.如果在平台商城一笔消费未满80元，那么是不是就一定没必要“团”哪?说说你的理由.23.(本题满分12分)如图8,M、N分别是平行四边形ABCD边AD、BC的中点,对角线BD交AN、CM分别于点P、Q.(1)求证:P=13A;(2)当四边形ANCM是正方形时，试从内角大小和邻边的数量关系的角度探究平行四边形ABCD的形状特征.问题：已知抛物线L：=W−2u抛物线W的顶点在抛物线L上(非抛物线L的顶点)且经过抛物线L的顶点.请求出一个满足条件的抛物线W的表达式.(1)解这个问题的思路如下：先在抛物线L上任取一点(非顶点)，你所取的点是①；再将该点作为抛物线W的顶点，可设抛物线W的表达式是②；然后求出抛物线L的顶点是③；再将抛物线L的顶点代入所设抛物线W的表达式，求得其中待定系数的值为④；最后写出抛物线W的表达式是⑤.(2)用同样的方法，你还可以获得其他满足条件的抛物线W，请再写出一个抛物线W的表达式.(3)如果问题中抛物线L和W在x轴上所截得的线段长相等，求抛物线W的表达式.25.(本题满分14分)的中点分别为M、N，MN与AB、OA、已知:如图10,△B是圆O的内接三角形，B=B,弧B、BAC分别交于点P、T、Q.(1)求证:B⊥M;(2)当△B是等边三角形时，求A A的值；(3)如果圆心O到弦BC、MN的距离分别为7和15，求线段PQ的长.。

2024年上海市黄浦区中考物理二模试卷一、选择题（本大题共6题，每题2分，共12分。

每题只有一个正确选项）1．（2分）原子中带负电的粒子是（）A．电子B．中子C．质子D．核子2．（2分）下列属于三原色光的是（）A．黄光B．紫光C．绿光D．白光3．（2分）如图所示的编钟展现了我国灿烂的文化，用相同的力敲击大小不同的编钟，发出的声音有不同的（）A．响度B．音调C．音色D．振幅4．（2分）书本静止在水平桌面上，下列属于平衡力的是（）A．桌子所受重力和书本对桌面的压力B．桌子所受重力和地面对桌子的支持力C．书本所受重力和书本对桌面的压力D．书本所受重力和桌面对书本的支持力5．（2分）已知某物体透过凸透镜，在距离透镜20厘米的光屏上成缩小的像，若将物体移动到距焦点10厘米处，则此时成的像（）A．一定是放大的虚像B．可能是放大的实像C．一定是等大的实像D．可能是缩小的实像6．（2分）甲、乙两小车沿同一直线同向而行，甲车的s﹣t图像如图所示。

P、Q是直线上的两点，当甲经过P点时，乙刚好经过Q点。

已知PQ相距5米，再过2秒，甲、乙两车相距3米，则乙车的速度可能是（）A．2米/秒B．4米/秒C．6米/秒D．8米/秒二、填空题（本大题共7题，共24分）7．（3分）家用空调正常工作时两端电压为伏；发电站通过输电线路将电能输送至远方的变电站（选填“高压”或“低压”）；导体通电一段时间后温度会升高，这是通过的方式改变了其内能（选填“热传递”或“做功”）。

8．（3分）物理知识在生活有广泛的应用：用吸管吸饮料，利用了的作用；图中，开瓶盖时，开瓶器可看作杠杆；汽车的四冲程汽油机工作时，通过做功冲程将部分内能转化为能。

9．（3分）“池水映明月”，水中的明月是光的现象形成的（选填“反射”或“折射”）；“潭清疑水浅”是由于光从水斜射入空气时，折射角入射角而形成的（选填“大于”“等于”或“小于”）；“飞流直下三千尺”，水下落过程中重力势能（选填“增大”“减小”或“不变”）。

上海市闵行区2024届高考二模考试数学试卷（考试时间120分钟，满分150分）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） 考生应在答题纸相应位置直接填写结果．1.集合{|210}A x x =+≤，{2,1,0}B =--，则A B = ________.2.复数z 满足(2)z +i 34=+i （i 为虚数单位），则z =_________.3.始边与x 轴的正半轴重合的角α的终边过点(3,4)-，则sin()απ+=_________.4.在6(21)x -的二项展开式中，3x 项的系数为_________. 5.正实数a b 、满足21a b +=，则ab 的最大值为_________.6.等比数列{}n a 的前n 项和为n S ，若23a =，581a =，则5S =_________.7.现有5个工程队承建某工程的5个不同项目，每个工程队承建一个项目，其中甲工程队不能承建A 项目，则不同的承建方案有_________种.（用数字作答） 8. 函数2y x x=-在1x =处的切线方程为_________. 9.已知a 、b 是空间中两个互相垂直的单位向量，向量c 满足3c = ，且1c a c b ⋅=⋅=，当λ取任意实数时，()c a b λ-+的最小值为_________.10.双曲线22:16y x Γ-=的左右焦点分别为12F F 、，过坐标原点的直线与Γ相交于A B 、两点，若112F B F A =，则22F A F B ⋅=_________.11.对于任意的12x x ∈R 、,且20x >，不等式1122ln x e x x x a -+->恒成立，则实数a 的取值范围为_________.12.已知空间中有2个相异的点，现每增加一个点使得其与原有的点连接成尽可能多的等边三角形.例如,空间中3个点最多可连接成1个等边三角形，空间中4个点最多可连接成4个等边三角形.当增加到8个点时，空间中这8个点最多可连接成________个等边三角形.二、选择题（本大题共有4题，满分18分，第13-14题每题4分，第15-16题每题5分）每题有且只有一个正确选项．考生应在答题纸的相应位置，将代表正确选项的小方格涂黑．13.设a ∈R ，则“21a >”是“31a >”的（ ）（A ）充分非必要条件 （B ）必要非充分条件（C ）充要条件 （D ）既非充分又非必要条件 14.已知()y f x =，x ∈R 为奇函数，当0x >时，2()log 1f x x =-， 则集合{|()()0}x f x f x --<可表示为（ ）（A ）(2,)+∞ （B ）(,2)-∞- （C ）(,2)(2,)-∞-+∞ （D ）(2,0)(2,)-+∞15.某疾病预防中心随机调查了339名50岁以上的公民，研究吸烟习惯与慢性气管炎患病的关系，调查数据如下表：不吸烟者 吸烟者 总计 不患慢性气管炎者 121 162 283 患慢性气管炎者13 43 56 总计134205339假设0H ：患慢性气管炎与吸烟没有关系，即它们相互独立. 通过计算统计量2χ，得27.468χ≈，根据2χ分布概率表:2( 6.635)0.01P χ≥≈,2( 5.024)0.025P χ≥≈, 2( 3.841)0.05P χ≥≈,2( 2.706)0.1P χ≥≈.给出下列3个命题，其中正确的个数是（ ）①“患慢性气管炎与吸烟没有关系”成立的可能性小于5%； ②有99%的把握认为患慢性气管炎与吸烟有关； ③2χ分布概率表中的0.05、0.01等小概率值在统计上称为显著性水平，小概率事件一般认为不太可能发生.（A ）0个 （B ）1个 （C ）2个 （D ）3个 16.已知()sin f x x =，集合[,]22D ππ=-，(){},2()()0,,x y f x f y x y D Γ=+=∈， {(,)|2()()0,,}x y f x f y x y D Ω=+≥∈.关于下列两个命题的判断，说法正确的是（ ） 命题①：集合Γ表示的平面图形是中心对称图形；命题②：集合Ω表示的平面图形的面积不大于2512π.（A ）①真命题；②假命题 （B ）①假命题；②真命题（C ）①真命题；②真命题 （D ）①假命题；②假命题三、解答题（本大题共有5题，满分78分）解答下列各题必须在答题纸的相应位置写出必要的步骤．17.（本题满分14分，第1小题满分6分，第2小题满分8分）在锐角ABC △中，角A B C 、、所对边的边长分别为a b c 、、，且2sin 0b A =.（1）求角B ；（2）求sin sin A C +的取值范围.18.（本题满分14分，第1小题满分6分，第2小题满分8分）如图，已知ABCD 为等腰梯形, //AD BC ,120BAD ∠=︒,PA ⊥平面ABCD ,2AB AD AP ===.（1）求证：PC AB ⊥； （2）求二面角C BP A --的大小.19.（本题满分14分，第1小题满分4分，第2小题满分4分，第3小题满分6分）ChatGPT 是OpenAI 研发的一款聊天机器人程序，是人工智能技术驱动的自然语言处理工具，它能够基于在预训练阶段所见的模式和统计规律来生成回答，但它的回答可能会受到训练数据信息的影响，不一定完全正确.某科技公司在使用ChatGPT 对某一类问题进行测试时发现，如果输入的问题没有语法错误，它回答正确的概率为0.98；如果出现语法错误，它回答正确的概率为0.18. 假设每次输入的问题出现语法错误的概率为0.1，且每次输入问题，ChatGPT 的回答是否正确相互独立.该公司科技人员小张想挑战一下ChatGPT ，小张和ChatGPT 各自从给定的10个问题中随机抽取9个作答，已知在这10个问题中，小张能正确作答其中的9个.（1）求小张能全部回答正确的概率；（2）求一个问题能被ChatGPT 回答正确的概率；（3）在这轮挑战中，分别求出小张和ChatGPT 答对题数的期望与方差.20.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）如图，已知椭圆221:14x C y +=和抛物线()22:20C x py p =>，2C 的焦点F 是1C 的上顶点，过F 的直线交2C 于M 、N 两点，连接NO 、MO 并延长之，分别交1C 于A 、B 两点，连接AB ，设OMN △、△（1）求p 的值；（2）求OM ON ⋅的值；（3）求OMNOABS S △△的取值范围.21.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）已知定义在∞（0,+）上的函数()y f x =的表达式为()sin cos f x x x x =-,其所有的零点按从小到大的顺序组成数列{}n x （1,n n ≥∈N ）.（1）求函数()y f x =在区间()0,π上的值域；（2）求证：函数()y f x =在区间()(),1n n ππ+（1,n n ≥∈N ）上有且仅有一个零点；（3）求证：()11n n n x x nππ++<-<.参考答案与评分标准一. 填空题 1．{2,1}--； 2； 3．45； 4．160-； 5．18； 6．121；7．96；8．340x y +-=；9．； 10．4； 11．(),2-∞；12．20. 二. 选择题 13．B ； 14．D ； 15．D ； 16．A ． 三. 解答题17．[解] （1）2sin 0b A =,2sin sin 0A B A ∴=,……………4分 又 sin 0A ≠,sin 2B ∴=,∴3B π=. ………………………………6分（2） ABC △为锐角三角形，A ∴(,62ππ∈,则2sin sin sin sin()3A C A A π+=+-3sin cos 22A A =+6A π=+，…10分 sin sin A C ∴+3(2∈. ………………………………14分18．[解] （1）连接AC ,ABCD 为等腰梯形，//AD BC ,120BAD ∠=︒,2AB AD ==；4,BC AC ∴==，90BAC ∠=︒，………………2分 PA ⊥ 平面ABCD ,所以由三垂线定理得PC AB ⊥. ……………………6分 （2）取BP 的中点H ，连接CH AH 、，则AH PB ⊥，因为4PC BC ===，所以CH BP ⊥,所以CHA ∠为二面角C BP A --的平面角，…………………8分 因为,PA AC AC AB ⊥⊥，PA AB A = ，所以AC ⊥平面ABP ,所以AC ⊥AH ……………………10分 在Rt AHC △中，CA =AH =所以tan CHA ∠=所以二面角C BP A --的大小为.……………………14分19．[解] （1）设小张答对的题数为X ，则999101(9)10C P X C ===. ………4分 （2）设事件A 表示“输入的问题没有语法错误”， 事件B 表示“一个问题能被ChatGPT 正确回答”，由题意知()0.1P A =，()0.98P B A =，()0.18P B A =，则()1()0.9P A P A =-=， ………………………………6分()()()()()()()P B P B A P B A P B A P A P B A P A =+=+0.980.90.180.10.9=⨯+⨯= ………………………………8分 （3）设小张答对的题数为X ，则X 的可能取值是89、，且8191910C C 9(8)C 10P X ===，99910C 1(9)C 10P X ===，………………………………10分设ChatGPT 答对的题数为Y ，则Y 服从二项分布9(9,10B ， 91()898.11010E X =⨯+⨯=，()90.98.1E Y np ==⨯=，……………………12分 22819811()(8(9)0.0910101001D X =-⨯+-⨯=，()90.90.10.81D Y npq ==⨯⨯=. ……………………14分20．[解] （1）抛物线2C 的焦点为()0,1F ，故2p =. ……………………4分 （2）若直线MN 与y 轴重合，则该直线与抛物线2C 只有一个公共点，不合乎题意， 所以，直线MN 的斜率存在，设直线MN 的方程为1y kx =+，点()11,M x y 、()22,N x y ， 联立214y kx x y=+⎧⎨=⎩可得2440x kx --=， 216160k ∆=+>恒成立，则124x x =-, ……………………………6分221212121241344x x OM ON x x y y x x ⋅=+=+=-+=- . ……………………10分（3）设直线NO 、MO 的斜率分别为1k 、2k ，其中10k >，20k <，联立12244y k x x y =⎧⎨+=⎩可得()221414k x +=，解得x =，………………12分 点A在第三象限，则A x =，点B在第四象限，同理可得B x =， ……………………………14分且121212121164y y x x k k x x ===-1222OMN OAB OM ON x x S S OB OA⋅⋅==⋅ △……………………………16分==2≥=，当且仅当112k=时，等号成立. …………18分21．[解] （1）由)()cos cos sin sinf x x x x x x x'=--=，………………2分当()0,xπ∈时，()0f x'>，即函数()y f x=在区间()0,π上是严格增函数，且()00f=，()fππ=，所以()f x在区间()0,π上的值域为()0,π. ……………………………4分（2）当()(),1x n nππ∈+时，①当n是偶数时，()0f x'>，函数()y f x=在区间()(),1n nππ+上是严格增函数；…………………6分②当n是奇数时，()0f x'<，函数()y f x=在区间()(),1n nππ+上是严格减函数；…………………8分且()()11nf n nππ-=-，故()()()()2110f n f n n nπππ⋅+=-+<，所以由零点存在定理可知，函数()y f x=在区间()(),1n nππ+上有且仅有一个零点. …………………10分（3）由（2）可知函数()f x在()(),1n nππ+上有且仅有一个零点nx，且满足()sin cos0n n n nf x x x x=-=，即tann nx x=（几何意义：nx是y tan x=与y x=交点的横坐标）…………………………12分又因为()12nf nππ⎛⎫+=-⎪⎝⎭，故()02f n f n nππππ⎛⎫⋅+=-<⎪⎝⎭，所以由零点存在性定理可知，函数()y f x=在,2n nπππ⎛⎫+⎪⎝⎭上有且仅有一个零点nx，于是()()1,1,12n nx x n nππππ+⎛⎫+∈+++⎪⎝⎭，()1,22n nx xπππ+⎛⎫-+∈- ⎪⎝⎭()()()111111tan tantan tan1tan tan1n n n nn n n nn n n nx x x xx x x xx x x xπ++++++---+=-==+⋅+⋅ (14)分①因为10n nx x+->，得()()1tan0n nx xπ+-+>所以()1n nx xπ+-+>，即1n nx xπ+<-；（或者()111tan tan tan tan0n n n n n nx x x x x xπ+++-+=-=->()1tan tann nx xπ+⇒>+1n nx xπ+⇒->） (16)分② 因为()()112222133322tan 12n n n n n n n x x x x x x x n n n ππππππ+++--+=<<=<+⋅ 由（1）可知，当0,2x π⎛⎫∈ ⎪⎝⎭时，有tan x x < 故()()()11tan n n n n x x x x n πππ++-+<-+<，所以1n n x x nππ+-<+；由①②可知()11n nn x x nππ++<-<. ………………………………18分。

上海市地区2023高考数学二模试卷一、填空题1．已知集合A =(1，3) B =[2，+∞) 则A ∩B = ． 2．不等式 xx−1<0 的解集为3．若幂函数的图象经过点 (3,√33) 则该函数的解析式为4．已知复数(m 2−3m −1)+(m 2−5m −6)i =3（其中i 为虚数单位） 则实数m = ．5．已知数列{a n }的递推公式为{a n =2a n−1+1(n ≥2)a 1=2则该数列的通项公式a n = ．6．在 (x +2x)6的展开式中常数项为 (用数字作答).7．从装有3个红球和4个蓝球的袋中 每次不放回地随机摸出一球．记“第一次摸球时摸到红球”为A“第二次摸球时摸到蓝球”为B 则P(B|A)= ．8．若数列{a n }为等差数列 且a 2=2 S 5=20 则该数列的前n 项和为S n = ． 9．已知△ABC 的内角A B C 的对边分别为a b c 已知asinA+C2=bsinA 则B = . 10．如图是某班一次数学测试成绩的茎叶图（图中仅列出[50，60) [90，100)的数据）和频率分布直方图 则x −y = ．11．已知函数f(x)=1a x +1−12（a >0且a ≠1） 若关于x 的不等式f(ax 2+bx +c)>0的解集为(1，2) 其中b ∈(−6，1) 则实数a 的取值范围是 ．12．已知非零平面向量 a ⃗ ,b ⃗ 不共线 且满足 a ⃗ ⋅b ⃗ =a ⃗ 2=4 记 c ⃗ =34a ⃗ +14b ⃗ 当 b ⃗ ,c ⃗ 的夹角取得最大值时 |a −b⃗ | 的值为 ． 二、单选题13．若α：x 2=4 β：x =2 则α是β的（ ）A ．充分非必要条件B ．必要非充分条件C ．充要条件D ．既非充分又非必要条件14．已知定义在R上的偶函数f(x)=|x−m+1|−2若正实数a、b满足f(a)+f(2b)=m则1a+2b的最小值为（）A．95B．9C．85D．815．将正整数n分解为两个正整数k1、k2的积即n=k1⋅k2当k1、k2两数差的绝对值最小时我们称其为最优分解．如20=1×20=2×10=4×5其中4×5即为20的最优分解当k1、k2是n的最优分解时定义f(n)=|k1−k2|则数列{f(5n)}的前2023项的和为（）A．51012B．51012−1C．52023D．52023−116．在空间直角坐标系O−xyz中已知定点A(2，1，0)B(0，2，0)和动点C(0，t，t+2)(t≥0).若△OAC的面积为S以O，A，B，C为顶点的锥体的体积为V则V S的最大值为() A．215√5B．15√5C．415√5D．45√5三、解答题17．已知函数f(x)=sinxcosx−√3cos2x+√32．（1）求函数y=f(x)的最小正周期和单调区间；（2）若关于x的方程f(x)−m=0在x∈[0，π2]上有两个不同的实数解求实数m的取值范围．18．四棱锥P−ABCD的底面是边长为2的菱形∠DAB=60°对角线AC与BD相交于点O PO⊥底面ABCD PB与底面ABCD所成的角为60° E是PB的中点．（1）求异面直线DE与PA所成角的大小（结果用反三角函数值表示）；（2）证明：OE∥平面PAD 并求点E到平面PAD的距离．19．下表是某工厂每月生产的一种核心产品的产量x(4≤x≤20，x∈Z)（件）与相应的生产成本y （万元）的四组对照数据．（1）试建立x与y的线性回归方程；（2）研究人员进一步统计历年的销售数据发现．在供销平衡的条件下 市场销售价格会波动变化．经分析 每件产品的销售价格q （万元）是一个与产量x 相关的随机变量 分布为假设产品月利润=月销售量×销售价格−成本．（其中月销售量=生产量） 根据（1）进行计算 当产量x 为何值时．月利润的期望值最大？最大值为多少？20．已知抛物线Γ：y 2=4x ．（1）求抛物线Γ的焦点F 的坐标和准线l 的方程；（2）过焦点F 且斜率为12的直线与抛物线Γ交于两个不同的点A 、B 求线段AB 的长；（3）已知点P(1，2) 是否存在定点Q 使得过点Q 的直线与抛物线Γ交于两个不同的点M 、N （均不与点Р重合） 且以线段MN 为直径的圆恒过点P ？若存在 求出点Q 的坐标；若不存在 请说明理由．21．直线族是指具有某种共同性质的直线的全体．如：方程y =kx +1中 当k 取给定的实数时 表示一条直线；当k 在实数范围内变化时 表示过点(0，1)的直线族（不含y 轴）．记直线族2(a −2)x +4y −4a +a 2=0（其中a ∈R ）为Ψ 直线族y =3t 2x −2t 3（其中t >0）为Ω． （1）分别判断点A(0，1) B(1，2)是否在Ψ的某条直线上 并说明理由；（2）对于给定的正实数x 0 点P(x 0，y 0)不在Ω的任意一条直线上 求y 0的取值范围（用x 0表示）； （3）直线族的包络被定义为这样一条曲线：直线族中的每一条直线都是该曲线上某点处的切线 且该曲线上每一点处的切线都是该直线族中的某条直线．求Ω的包络和Ψ的包络．答案解析部分1．【答案】[2，3) 2．【答案】（0,1） 3．【答案】4．【答案】-15．【答案】3×2n−1−1 6．【答案】160 7．【答案】238．【答案】n(n −1) 9．【答案】π3 10．【答案】0.004 11．【答案】(1，2) 12．【答案】4 13．【答案】B 14．【答案】A 15．【答案】B 16．【答案】C17．【答案】（1）解：f(x)=sinxcosx −√3cos 2x +√32=12sin2x −√32cos2x =sin(2x −π3)则函数y =f(x)的最小正周期T =2π2=π； 令2kπ−π2≤2x −π3≤2kπ+π2(k ∈Z) 解得 kπ−π12≤x ≤kπ+5π12(k ∈Z)可得函数y =f(x)的单调递增区间为[kπ−π12，kπ+5π12](k ∈Z)· 令 2kπ+π2≤2x −π3≤2kπ+3π2(k ∈Z) 解得 kπ+5π12≤x ≤kπ+11π12(k ∈Z) 可得因数y =f(x)的单调递减区间为[kπ+5π12，kπ+11π12](k ∈Z) ； （2）解：由（1）可知 x ∈[0，π2]时 y =f(x)在[0，5π12]上单调递增 在[5π12，π2]上单调递减当x ∈[0，5π12] 2x −π3∈[−π3，π2] f(x)由−√32增大到1当x ∈[5π12，π2] 2x −π3∈[π2，2π3] f(x)由1减小到√32若关于x 的方程f(x)−m =0在x ∈[0，π2]上有两个不同的实数解 则实数m 的取值范围为[√32，1)18．【答案】（1）解：由题意 PO ，OC ，OB 两两互相垂直 以O 为坐标原点 射线OB 、OC 、OP 分别为x 轴、y 轴、z 轴的正半轴建立空间直角坐标系 如图菱形ABCD 中 ∠DAB =60° 所以BD =2OB =2 在Rt △AOB 中OA =√AB 2−OB 2=√3因为PO ⊥底面ABCD 所以PB 与底面ABCD 所成的角为∠PBO =60° 所以PO =OB ⋅tan60°=√3则点A 、B 、D 、P 的坐标分别是A(0，−√3，0)，B(1，0，0)，D(−1，0，0)，P(0，0，√3)E 是PB 的中点 则E(12，0，√32) 于是DE ⃗⃗⃗⃗⃗⃗ =(32，0，√32) AP ⃗⃗⃗⃗⃗ =(0，√3，√3). 设DE ⃗⃗⃗⃗⃗⃗ ，AP ⃗⃗⃗⃗⃗ 的夹角为θ 则有cosθ=32√94+34√3+3=√24故θ=arccos √24∴异面直线DE 与PA 所成角的大小是arccos √24.（2）证明：连接OE∵E ，O 分别是PB ，BD 的中点 ∴EO//PD∵EO ⊄平面PAD PD ⊂平面PAD ∴EO//平面PAD.因为AP ⃗⃗⃗⃗⃗ =(0，√3，√3) AD →=(−1，√3，0) 设平面PAD 的法向量n →=(x ，y ，z)则{n⃗ ⋅AD ⃗⃗⃗⃗⃗⃗ =−x +√3y =0n⃗ ⋅AP ⃗⃗⃗⃗⃗ =√3y +√3z =0 令x =√3 则y =1，z =−1 所以n →=(√3，1，−1) 又DE⃗⃗⃗⃗⃗⃗ =(32，0，√32) 则点E 到平面PAD 的距离d =|DE ⃗⃗⃗⃗⃗⃗⃗ ⋅n →||n →|=|3√32−√32|√3+1+1=√3√5=√155. 19．【答案】（1）解：设x 与y 的回归方程为y ∧=b ∧x +a ∧ 则b ∧=∑x i y i4i=1−4x ̅y̅∑x i 2−4x̅24i=1又∑x i y i 4i=1=48+120+224+840=1232 x ̅=14(4+6+8+10)=7y ̅=14(12+20+28+84)=36 ∑x i 24i=1=16+36+64+100=216. 则b ∧=∑x i y i 4i=1−4x ̅y̅∑x i 2−4x̅24i=1=1232−4×7×36216−4×49=565.a ∧=y ̅−b ∧x ̅=36−565×7=−2125则回归方程为：y ∧=565x −2125(x ∈[4，20]，x ∈Z). （2）解：设月利润的期望值为f(x) 则由题可得：f(x)=14(100−x)x +12(90−x)x +14(80−x)x −(14+12+14)(565x −2125)=−x 2+3945x +5125=−(x −1975)2+4136925 则f(x)在[4，20]上单调递增则当x =20时 f(x)最大 f(x)max =f(20)=63925. 即x =20件时 月利润的期望值最大 最大值为63925万元20．【答案】（1）解：∵抛物线Γ：y 2=4x 则p =2 且焦点在x 轴正半轴故抛物线Γ的焦点F(1，0) 准线l ：x =−1.（2）解：由（1）可得：F(1，0) 可得直线AB ：y =12(x −1)设A(x 1，y 1)，B(x 2，y 2)联立方程{y =12(x −1)y 2=4x消去y 得x 2−18x +1=0 可得Δ=(−18)2−4×1×1=320>0，x 1+x 2=18 故|AB|=x 1+x 2+p =20. （3）解：存在 理由如下：设直线MN ：x =my +n ，M(x 3，y 3)，N(x 4，y 4) 联立方程{x =my +ny 2=4x 消去x 得y 2−4my −4n =0 则Δ=16(m 2+n)>0，y 3+y 4=4m ，y 3y 4=−4n可得PM ⃗⃗⃗⃗⃗⃗ =(x 3−1，y 3−2)，PN ⃗⃗⃗⃗⃗⃗ =(x 4−1，y 4−2) 若以线段MN 为直径的圆恒过点P 则PM ⃗⃗⃗⃗⃗⃗ ⊥PN⃗⃗⃗⃗⃗⃗ 可得PM ⃗⃗⃗⃗⃗⃗ ⋅PN ⃗⃗⃗⃗⃗⃗ =(x 3−1)(x 4−1)+(y 3−2)(y 4−2)=(my 3+n −1)(my 4+n −1)+(y 3−2)(y 4−2)=(m 2+1)y 3y 4+(mn −m −2)(y 3+y 4)+(n −1)2+4 =(m 2+1)⋅(−4n)+(mn −m −2)⋅(4m)+(n −1)2+4=−4(m +1)2+(n −3)2=(n +2m −1)(n −2m −5)=0 可得n +2m −1=0或n −2m −5=0若n +2m −1=0 则n =1−2m 可得直线MN ：x =my +1−2m =m(y −2)+1 过定点(1，2) 与点P 重合 不合题意；若n −2m −5=0 则n =2m +5 此时Δ=16(m 2+n)=16(m 2+2m +5)=16[(m +1)2+4]>0 可得直线MN ：x =my +2m +5=m(y +2)+5 过定点(5，−2)； 综上所述：直线MN 过定点Q(5，−2).21．【答案】（1）解：把点A(0，1)代入直线族Ψ的方程2(a −2)x +4y −4a +a 2=0得：4−4a +a 2=0因为Δ=16−4×4=0 所以方程4−4a +a 2=0有实数根 所以点A(0，1)在Ψ的某条直线上.把点B(1，2)代入直线族Ψ的方程2(a −2)x +4y −4a +a 2=0 得：a 2−2a +4=0因为Δ=4−4×4<0 所以方程a 2−2a +4=0无实数根 所以点B(1，2)不在Ψ的某条直线上.（2）解：因为点P(x 0，y 0)不在Ω的任意一条直线上 所以方程y 0=3t 2x 0−2t 3在t ∈(0，+∞)上无实数解即方程2t 3−3x 0t 2+y 0=0在t ∈(0，+∞)上无实数解. 令ℎ(t)=2t 3−3x 0t 2+y 0，t ∈(0，+∞) 则ℎ′(t)=6t 2−6x 0t因为x 0为正实数 所以当ℎ′(t)>0时 解得t >x 0；当ℎ′(t)<0时 解得0<t <x 0； 所以ℎ(t)在(0，x 0)上单调递减 在(x 0，+∞)上单调递增 所以ℎ(x 0)=2x 03−3x 0⋅x 02+y 0>0 解得y 0>x 03所以y 0的取值范围为(x 03，+∞).（3）解：由(2)的结论猜测Ω的包络是曲线y =x 3(x >0).(x 3)′=3x 2 解3x 2=3t 2得x =t .在曲线y =x 3(x >0)上任取一点(t ，t 3)(t >0)则过该点的切线方程是y −t 3=3t 2(x −t)即y =3t 2x −2t 3. 而对任意的t >0 y =3t 2x −2t 3的确为曲线y =x 3(x >0)的切线.故Ω的包络是曲线y =x 3(x >0). 将2(a −2)x +4y −4a +a 2=0整理为关于a 的方程 a 2+2(x −2)a +4(−x +y)=0若该方程无解 则Δ=4(x −2)2−16(−x +y)<0 整理得y >x 24+1.猜测Ψ的包络是抛物线y =x 24+1.(x 24+1)′=x 2 解x 2=−2(a−2)4得x =2−a . 在抛物线y =x 24+1上任取一点(2−a ，(2−a)24+1)则过该点的切线方程是2(a −2)x +4y −4a +a 2=0而对任意的a ∈R 2(a −2)x +4y −4a +a 2=0确为抛物线y =x 24+1的切线.故Ψ的包络是抛物线y =x 24+1.。

2023年上海市徐汇区初三二模英语试卷(考试时间90分钟满分140分)Part 1 Listening (第一部分听力)L. Listening Comprehension (听力理解}: (共25分)A. Listen and choose the right picture (根据你听到的内容，选出相应的图片): (5 分)B. Listen to the dialogue and choose the best answer to the question you hear (根据你听到的对话和问题，选出最恰当的答案): (5分)6. A. In China.B. In Singapore.C. In Japan.D. In France.7. A. 6 months oldB. 7 months old.C. 12 months old.D. 18 months old.8. A. An E-dictionary.B. Sports shoes.C. Tickets for Shanghai Disney.D. Dinner with friends.9. A. The reading club.B. The racing club.C. The language club.D. The cooking club.10. A. The change for a new flat.B. The share of housework.C. The decoration of the bedroomD. The design of the garden.C. Listen to the conversation and tell whether the following statements are true or false (判断下列句子是否符合你听到的内容,符合的用“下表示，不符合的用“F”表示): (5 分)11. The conversation is about an interview with a journalist in a studio.12. David's first ambition was to be a scientist when he was young.13. Because of a special radio program, David became a student journalist.14. It was easy for David to get a first job of being a journalist at AFP.15. Today's broadcast is to help the audience learn from David's experience.D. Listen to the passe and complete the flow sentences (听短文，完成下列内容，每空格限填一词): (10分)16. The speaker is introducing ________ ________ in the world to the audience.17. Though the Clock Tower was renamed, tourists will call it "Big Ben” ________ ________.18. The Shanghai Iv Tower got the nickname "Pearl of the East" from its ________ ________.19. The eleven balls of the Oriental Pear! Tower are of ________ ________.20. Besides offices the Petronas Towers house a museum, an art gallery and a ________ ________.Part 2 Grammar and Vocabulary (第二部分词汇和语法)II. Choose the best answer (选择最恰当的答案) (共15分)21. Our monitor is kind and always gives me ______ hand when I have trouble.A. aB. anC. theD./22. The movie on TV yesterday made me think of an experience of ______ own.A. IB. meC. myD. mine23. Picasso, a famous European artist, had a great influence on art ______ the 20th century.A. atB. inC. onD. from24. The headmaster was very pleased ______ the performance by the talent boy.A. ofB. inC. withD. for25. Besides the main character, can you name some ______ little monsters in the cartoon?A. othersB. anotherC. the otherD. other26. In Shanghai, PE lessons at school ______ more and more interesting since 2018.A. becomeB. becameC. have becomeD. will become27. There's nothing left in the fridge, and we'd better ______ some food in the market.A. buyB. to buyC. buyingD. bought28. Counting penguins in Antarctic (南极洲) was one of ______ jobs in the world.A. strangeB. strangerC. strangestD. the strangest29. When you wear a smile on your face, you look ______ to customers.A. warmlyB. happilyC. correctlyD. friendly30. ______ kids have smartphones, they may get calls from strangers and get cheated.A. IfB. UntilC. ThoughD. Unless31. Merle first ______ the world record for swimming 10 kilometers in 2019.A. setsB. setC. was settingD. has set32. The amazing walking tools ______ allow you to walk up to I kilometers an hour.A. needB. canC. mustD. should33. Follow the instructions carefully, ______ you will operate the machine easily.A. andB. butC. forD. or34. ______ shining the little girl is in her traditional Chinese dress on the stage!A. WhatB. What aC. HowD. How an35. -______ does your brother go cycling after work?-Once a week.A. How farB. How soonC. Hong longD. How oftenIII. Complete the following passage with the words or phrases in the box. Each one can only be used once. (选择最恰当的选项填入空格。

上海市2024年杨浦区中考语文二模试卷一、古诗文（35分）（一）默写与运用（13分）1.默写。

（1）古今多少事，__________。

（陈与义《临江仙·夜登小阁，忆洛中旧游》）（2）__________，任尔东西南北风。

（郑燮《竹石》）（3）__________，不可知其源。

（柳宗元《小石潭记》）（4）小语在电视剧《三国演义》中看到两军激战的场面时，不禁想起了《破阵子·为陈同甫赋壮词以寄之》中的诗句：“__________，__________”。

（二）（22分）阅读下面选文,完成下面小题。

【甲】①先帝创业未半而中道崩，今天下三分，益州疲弊，此诚危急存亡之秋也。

然侍卫之臣不懈于内，忠志之士忘身于外者，盖追先帝之殊遇，欲报之于陛下也。

……②亲贤臣，远小人，此先汉所以兴隆也；亲小人，远贤臣，此后汉所以倾颓也。

先帝在时，每与臣论此事，未尝不叹息痛恨于桓、灵也。

侍中、尚书、长史、参军，此悉贞良死节之臣，愿陛下亲之信之，则汉室之隆，可计日而待也。

【乙】①当余之从师也，负箧曳屣行深山巨谷中，穷冬烈风，大雪深数尺，足肤皲裂而不知。

至舍，四支僵劲不能动，媵人持汤沃灌，以衾拥覆，久而乃和。

……②今诸生学于太学，县官日有廪稍之供，父母岁有裘葛之遗，无冻馁之患矣；坐大厦之下而诵诗书，无奔走之劳矣；有司业、博士为之师，未有问而不告，求而不得者也；凡所宜有之书，皆集于此，不必若余之手录，假诸人而后见也。

其业有不精，德有不成者，非天质之卑，则心不若余之专耳，岂他人之过哉！【丙】景公信用谗佞，赏无功，罚不辜。

晏子谏曰：“臣闻明君望圣人而信其教，不闻听谗佞以诛赏。

今与左右相说颂①也，曰：‘比死者勉②为乐乎！吾安能为仁而愈黥民③耳矣！’故内宠之妾，迫夺于国，外宠之臣，矫夺于鄙，执法之吏，并荷百姓。

民愁苦约病④，而奸驱尤佚⑥，隐情奄恶，蔽谄其上，故虽有至圣大贤，岂能胜若谗哉！是以忠臣之常有灾伤也。

臣闻古者之士，可与得之，不可与失之；可与进之，不可与退之。

上海市闵行区2024届高考二模考试英语试卷(考试时间120分钟，试卷满分140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 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. A fridge. B. An electric cooker. C. Laundry machines. D. Dishes.2. A. $450. B. $500. C. $550. D. $510.3. A. Flowers. B. A gardening tool. C. Cooking appliances. D. A cookbook.4. A. Disappointed. B. Proud. C. Confident. D. Encouraged.5. A. The man. B. The woman. C. Their boss. D. Sarah.6. A. At a concert venue. B. At a movie theater.C. At a hotel reception.D. At a restaurant.7. A. Keep playing video games. B. Get more sleep.C. Buy a comfortable bed.D. Establish a regular bedtime.8. A. She is confused about the software program as well.B. She understands the software program completely.C. She doesn’t care about the software program.D. She has lost the software password.9. A. He wants more recognition for his volunteer work.B. He prefers to keep his volunteer work private.C. He regrets volunteering at the animal shelter.D. He wants to discuss his volunteer work further.10. A. The students were interested in sharing.B. The students were eager to learn knowledge.C. The students were amazed at the learning material.D. The students were respectful towards the teacher.Section BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages andthe conversation 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 talk.11. A. In her arm. B. In her lung. C. On her shoulder. D. In her back.12. A. Over five years. B. About three months.C. Less than two weeks.D. A few months.13. A. To find ways to help Mrs. Smith’s family.B. To hear an update on Mrs. Smith’s situation.C. To figure out what’s wrong with Mrs. Smith.D. To discuss the company’s helping policies.Questions 14 through 16 are based on the following talk.14. A. Improving artistic theory. B. Putting forward flow theory.C. Holding attractive activities.D. Studying business matters.15. A. To promote the painters’ spirit. B. To discover the exception to the theory.C. To study the way to get the flow state.D. To discover the best flow quality.16. A. When they consider nothing seems to matter.B. When they began to learn new skills.C. When they work in different professions.D. When they are engaged in their pursuits.Questions 17 through 20 are based on the following conversation.17. A. It was stolen. B. It was involved in an accident.C. It ran out of gas.D. It was parked illegally and pulled away.18. A. It’s only for loading purposes. B. It’s reserved for motorcycles.C. It’s free for anyone to park there.D. It’s for library use only.19. A. The parking services office. B. The main entrance of the library.C. The vehicle storage facility.D. The campus gymnasium.20. A. $10 B. $50 C. $75 D. $85II. Grammar and VocabularySection 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.By day, Robert Titterton is a lawyer. In his spare time, he goes on stage beside pianist Maria Raspopova—not as a musician but as her page-turner. “(21)________ not being a trained musician, I’ve learned to read music to assist Maria in her performance.”Mr Titterton is chairman of the Omega Ensemble but (22)________(act) as the group’s official page-turner for the past four years. His job is to sit beside the pianist and turn the pages of the score. In this way, the musicians don’t have to break the flow of sound by doing it (23)________. He said he became just as nervous as those playing instruments on stage.Being a page-turner requires plenty of practice. Some pieces of music (24)________ go for 40 minutes and require up to 50 pages of turns, including back turns for repeat passages.(25)________ matters is onstage communication. Each pianist has their own style of “nodding”(26)________( indicate) a page turn that they need to practise with their page-turner.But like all performances, there are moments (27)________ things go wrong. “I was turning the page to get ready for the next page, but the draft wind from the turn caused the spare pages to fall off the stand,” Mr Titterton said, “Luckily, I was able to catch them and put them back.”(28)________ most page-turners are piano students or up-and-coming concert pianists, Ms Raspopova has once asked her husband to help her out on stage.“Sometimes my husband is not an attentive page-turner. He’s interested in the music,(29)________(feel) every note, but I have to say: ‘Turn, turn!’ ” she laughed. “But Robert is(30)________ (qualified) page-turner I’ve had in my entire life.”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.contrastB.instructedC.concentratingD.potentialE. touchingF.playedG.betterH.specializedI.spotJ.followK.tracingUnfamiliar Music May Help People Chat at PartiesIf you want your guests to be particularly sociable at an upcoming party, make sure you play music they probably haven’t heard before.To explore how background music affects the way we 31 conversations, researchers Jane Brown and Gavin Bidelman conducted a study analyzing the brain activity of 31 individualsaged 21 and 33. During the experiment, participants listened to 72 minutes of an audiobook (有声读物), which the pair used as a replacement for 32 on someone talking, while background music was accompanied by the audiobook for most of the time.For half of the experiment, the participants were asked to focus on 2-minute parts of an unfamiliar audiobook read by a man. The rest of the time, they were told to focus on four background songs, which were similarly 33 for 2 minutes at a time. This 34 in voices aimed to assess participants’ ability to shift attention between two distinctly different voices.During the experiment, all the participants wore 35 caps to monitor the electrical activity taking place in their brains. This 36 of electrical activity was the key. It allowed Brown and Bidelman to discover how efficiently these individuals could focus on either the audiobook or the music when 37 to do so. The finding revealed that the participants could 38 turn their attention to the audiobook if the background music was unfamiliar to them.Following the task, the participants completed a music perception survey evaluating their musical skills, such as the capacity to 39 whether a pair of similar-sounding tunes are the same. Notably, those with lower musical scores demonstrated slower attentional shifts between songs and audiobooks, suggesting a(n) 40 link between musical ability and attention management skills.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.In Favour of Simple WritingDo you edit text messages carefully before sending them? If so, you may be the kind of person who takes pride in 41 even the simplest message. If you do not, you may see yourself as a go-getter, one who values excitement and speed over42 : get it done decently now rather than perfectly later.People are constantly receiving messages, from the mailbox to the inbox to the text-message alert. What to read, what to skim (略读) and what to ignore are decisions that nearly everyone has to make dozens of times a day. A new book titled All Readers are Busy Nowadays makes the argument for being the careful kind of 43 , even in informal lines. The authors also present well-established 44 that have long been prized in guides to writing.Take “less is more”. Most books on writing well advocate the advice to 45 needless words. The authors, however, have 46 the idea. In an email to thousands of school-board members asking them to take a survey, cutting the count from 127 to 49 words almost 47 the response rate.Keeping messages to a 48 idea—or as few as absolutely needed—helps ensure that they will be read, remembered and acted on. 49 the number of the available options has thesame effect, too. A link in an email, 50 , attracted 50% more clicks when presented alone than when it was sent alongside a second additional link.Syntax(句法) and 51 matter, too. It is more 52 to adopt short and active sentences, with common words familiar to everyone. From Facebook posts to online-travel reviews, even brief, informal pieces of writing that follow these rules get more likes and shares.If everyone is a busy reader, everyone is a busy writer, too. That may make it tempting to sent as many messages as 53 as possible and hope for the best. But from essays to text messages organizing dinner plans, devoting time to the needs of readers has provable 54 . If you are so busy that you write an undisciplined message which readers scan, ignore and delete, then you might as well have not 55 it at all.41.A. conveying B. understanding C. crafting D. sending42.A. care B. quantity C. simplicity D. technology43.A. reader B. poster C. learner D. writer44.A. structures B. principles C. aims D. alternatives45.A. remove B. ignore C. reconsider D. interpret46.A. conveyed B. translated C. tested D. shaped47.A. lowered B. affected C. doubled D. maintained48.A. basic B. positive C. definite D. single49.A. Recording B. Reducing C. Counting D. Estimating50.A. in comparison B. after all C. for instance D. in particular51.A. word-choice B. pattern-design C. target-setting D. platform-selection52.A. difficult B. suitable C. challenging D. common53.A. carefully B. often C. politely D. quickly54.A. outcomes B. points C. figures D. benefits55.A. received B. written C. read D. answeredSection 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 read.(A)Growing up in Ukraine, Vadim didn’t know what it was like to live in a safe, stable home. His parents were alcoholics who would often beat him. They’d even stuff him into a wine container, breaking his little body and leaving only a small opening at the top so he could breathe and see—but only just a little.By the time Vadim turned 9, he was living in an orphanage (孤儿院). Unfortunately, as is the case with far too many little ones, his life only got worse there. Not only was he hurt, but he was placed in a room on the third floor, making it impossible to get downstairs in a wheelchair.This left Vadim crawling up and down the stairs, an activity that was both physically and mentally exhausting. He’d often be late for meals. If the food wasn’t already gone by the time he arrived, other kids would steal from him.Then, a chain effec t began when some special folks visited the orphanage. They told him a story about a spiritual figure who advocated love and forgiveness. This conv ersation helped the 14-year-old find his faith and, in turn, he had more hope than he ever had before.Today, Vadim is on longer the boy subject to fate. He is a father to his own kids, and his life couldn’t be more different or better. Over the years, he’s discovered a gift for expressing himself through art. This inspired Tim Tebow Foundation, an organization fighting for the most vulnerable (脆弱的) people around the world, to ask if he’d like to create a piece that representedwhat it looked and felt like for him to havegone from “darkness to light.”The result? A truly remarkable paintingthat features Vadim, in his wheelchair, leavingbehind his old home, including the winecontainer his parents stuffed him into. His newdirection includes a beautiful forest full of fallleaves and bright light, showing the hope he issaid to have found in the inspiring story.56. According to the passage, Vadim’s parents treated him ________.A. abusivelyB. forgivinglyC. thoughtfullyD. strictly57. Why did Vadim crawl up and down the stairs when living in the orphanage?A. Because his little roommates often did damage to his wheelchair.B. Because other children would take his meal without permission.C. Because he couldn’t use the wheelchair to go downstairs from a high floor.D. Because getting downstairs was demanding for him physically and mentally.58. The phrase “a chain effec t ” in paragraph 4 refers to _________.A. an effective treatment for Vadim’s disabilityB. a series of positive changes occurring in Vadim’s lifeC. a sense of hope from the story of a spiritual figureD. a helping hand from Tim Tebow Foundation59. What is the message that Vadim wants to convey in his remarkable painting?A. He admires the beauty and harmony of nature.B. He leads a miserable life with his own kids.C. He excels in delicate painting techniques.D. He says farewell to the past and harvests happiness.(B)The Role of Crowdfunding in Business GrowthCrowdfunding is a fundraising method that makes use of the power of the Internet and social networks. It involves raising small amounts of money from a large number of individuals or investors, typically through online platforms. These platforms connect entrepreneurs(创业者) with potential backers who contribute funds to support a specific project, business, or idea.Types of Crowdfunding●Reward-Based Crowdfunding—Backers get a reward, such as a product sample or easy access, in exchange for their contribution. This model is popular for startups and creative projects.●Equity(股权) Crowdfunding—Investors receive shares or equity in the business in exchange for their funding. This model is ideal for small businesses looking to raise substantial capital and is subject to specific regulations.●Debt Crowdfunding—Entrepreneurs borrow money from backers and agree to repay it with interest over time. This model is similar to a loan and is suitable for businesses with a clear repayment plan.Tips for a Successful Crowdfunding Campaign●Set clear goals: Define your funding goal, the purpose of the funds, and how you’ll use the money.●Persuasive story: Make an appealing and genuine story about your business. Explain why it matters and how backers’ contributions will make a difference.●Engage your network: Mobilize your existing network of friends, family, and professional contacts to support your campaign. Their initial contributions can build momentum (动力).●Transparency: Be transparent and honest about your project’s progress and any challenges you encounter. Backers appreciate honesty.●Fulfill promise s: Once your campaign is successful, fulfill your promises to backers timely and communicate regularly.60. According to the passage, which of the following is accurate about crowdfunding?A. Reward-Based Crowdfunding is the most popular type of crowdfunding.B. Backers can get the same kinds of rewards in the three types of crowdfunding.C. Crowdfunding is a fundraising technique that relies on offline platforms.D. Debt Crowdfunding is fit for businesses with a specific repayment schedule.61. The 4th tip “Transparency” probably means “________”.A. carefulnessB. perseveranceC. franknessD. optimism62. The owners of Exploding Kittens, a card game corporation established six years ago, plan toraise a large sum of capital to start a promotion campaign. They are highly recommended to ________.A. prefer Reward-Based Crowdfunding to Equity CrowdfundingB. draft an attractive story about the campaign based on real informationC. realize their promises to backers on time even if the campaign is a failureD. compare the initial support provided by different existing contacts(C)Hundreds of people die at sea every year due to ship and airplane accidents. Emergency teams have little time to rescue those in the water because the probability of finding a person alive falls dramatically after six hours. Beyond tides and challenging weather conditions, unsteady coastal currents often make search and rescue operations extremely difficult.New insight into coastal flows gained by an international research team led by George Haller, Professor of Nonlinear Dynamics at ETH Zurich, promises to enhance the search and rescue techniques currently in use. Using tools from dynamical systems theory and ocean data, the team has developed an algorithm (算法) to predict where objects and people floating in water will go. “Our work has a clear potential to save lives,” says Mattia Serra, the first author of a study recently published in Nature Communications.In today’s rescue operations at sea, complicated models of ocean dynamics and weather forecasting are used to predict the path of floating objects. For fast-changing coastal waters, however, such predictions are often inaccurate due to uncertain boundaries and missing data. As a result, a search may be launched in the wrong location, causing a loss of precious time.Haller’s research team obtained mathematical results predicting that objects floating on the ocean’s surface should gather along a few special curves (曲线) which they call TRansient Attracting Profiles (TRAPs). These curves can’t be seen with our eyes but can be tracked frominstant ocean surface current data using recent mathematical methods developed by the ETH team. This enables quick and precise planning of search paths that are less sensitive to uncertainties in the time and place of the accident.In cooperation with a team from MIT, the ETH team tested their new, TRAP-based search algorithm in two separate ocean experiments near Martha’s Vineyard, which is on the northeastern coast of the United States. Working from the same real-time data available to the Coast Guard, the team successfully identified TRAPs in the region in real-time. They found that buoys and manikins (浮标和人体模型) thrown in the water indeed quickly gathered along these emerging curves. “Of several competing approaches tested in this project, this was the only algorithm that consistently found the right location”, says Haller.“Our results are rapidly obtained, easy to interpret, and cheap to perform,” points out Serra. Haller stresses: “Our hope is that this method will become a standard part of the tool kit of coast guards everywhere.”63.In a search and rescue operation, ________.A. the survival rate drops to almost zero after six hoursB. the use of dynamics leads to the wrong locationC. weather conditions are a determining factorD. changing currents present a challenge64. The main significance of the new algorithm is ________.A. accurately predicting weather conditions during rescue operationsB. dependence on satellite technology to locate distressed individuals at seaC. cost-effective, efficient tracking of objects and individuals in coastal watersD. predicting the exact time and location of ocean accidents65. Paragraph 5 mainly talks about ________.A. the collection of dataB. the testing of the algorithmC. the identification of the TRAPsD. the cooperation of two research teams66. Which of the following is the best title for the passage?A. How Mathematics Can Save Lives at SeaB. How Coastal Waters Affect Saving LivesC. Why Algorithms Are Popular in Rescue OperationsD. Why Success Rates of Rescue Operations Have FallenSection 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. Such media doesn’t just entertain.B. You can easily pick out the differences among your siblings.C. As we journey through adulthood, it’s crucial to reflect on its impact.D. Media exposure during childhood impacts each child in distinct ways.E. Additionally, media have proven to have long-term effects on individuals.F. However, our mental and physical states may not be adequately equipped to handle it.Childhood Media Shaping FuturesMuch of the media we consume during our formative years shapes us into the people we are today. Reflect on a particular piece of media from our childhood—perhaps it’s the TV show we eagerly awaited every weekend during visits to our grandmother’s house. 67 It shapes our dreams and fears and even drives us to future careers.68 Older children may have had a lot more restrictions, like TV shows, movies, and social media access. And because of these, they were able to be a child for longer compared to their siblings (兄弟姐妹). Children who have older siblings tend to show more mature tendencies and can appear to “grow up quicker” than other children their age.While they might have been restricted from social media accounts until a certain age, once given access, they tend to be more prepared. The media exposure of our generation has undoubtedly led to an increased maturation at younger ages. 69 9Simply looking back at previous generations and the rate of consumption and processing of information that we experience every day, the effects of such are only beginning.As soon-to-be or current adults, we are already facing issues such as depression, anxiety, and delays in certain learning and social skills, just to name a few. Are we “more mature?” or are we overexposed and at risk for exceptional mental, physical, and emotional consequences?In conclusion, childhood media consumption significantly influences our lives. 70 Striking a balance between media exposure and mental well-being is essential for our growth in today’s media-rich world.IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point (s) of the passage in no more than 60 words. Use your own words as far as possible.Have You Got Success Amnesia?Have you heard yourself say “it was nothing really” when someone congratulates you on a job well done? Or have you drawn a blank when you are asked to make a list of what you have achieved? If so, you have suffered success amnesia. Failing to acknowledge your hard work is often a sign of success amnesia. It signals that there might be a gap between how others view your achievements and how you see them.People who have success amnesia often have a strong track record at work or get it sorted for family members. They are people who others would describe as successful and yet they find it difficult to acknowledge and own their results. They don’t hold their achievements in their memory bank.This particular type of memory loss robs them of the satisfaction and pleasure that can follow in achieving a goal. And, perhaps more importantly, it robs them of confidence. Confidence does not guarantee success, but it does increase the chance of success. Why not try some practical methods?Ask for feedback about the impact you’ve had and then listen carefully. Watch out for anything that you begin to tell yourself “It wasn’t that big a deal.” Try to absorb what you hear. You can also look back over the past 6 or 12 months, capture every success you can think of, whether large or small, and write them down clearly. Purposefully acknowledging and admitting your achievements can help to bring them into more realistic focus. Besides, be mindful that you have a tendency to forget or minimize your achievements. A sticky note on your laptop screen might help: my strengths and achievements are bigger than they appear to me.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 这种新产品防水耐高温，卖得很好。

上海市2024初中英语二模试卷Shanghai City 2024 Junior High School English Second Mock Exam PaperSection A: Reading Comprehension1. Read the following passage and answer the questions.The Great Wall of China is one of the most famous landmarks in the world. It was built over 2,000 years ago to protect China from invasions by nomadic tribes. The Great Wall is over 13,000 miles long and is made of stone, brick, and wood.Question 1: Why was the Great Wall of China built?Question 2: How long is the Great Wall of China?Question 3: What materials were used to build the Great Wall?2. Read the passage below and fill in the blanks with the correct words from the box.A panda's diet is mainly made up of bamboo, which makes up 99% of its food intake. Pandas spend up to 12 hours a day eating bamboo. They also eat small animals and fish occasionally.Question 1: What is the main food of pandas?Question 2: How many hours a day do pandas spend eating bamboo?Question 3: What other types of food do pandas eat?Section B: WritingWrite a short essay (200-250 words) on the importance of learning English in today's world. Include examples of how English is used in different fields and how it can benefit individuals in their personal and professional lives.Section C: Listening ComprehensionListen to the following audio clips and answer the questions below.Clip 1: A weather report for Shanghai for the coming week.Question 1: What is the weather forecast for Shanghai for the next Monday?Question 2: What is the expected temperature for Tuesday in Shanghai?Clip 2: An interview with a famous author about his latest book.Question 1: What is the title of the author's latest book? Question 2: What inspired the author to write the book? Section D: Grammar and VocabularyChoose the correct answer to complete each sentence.1. We ____________ to the beach tomorrow.A) goingB) goC) goes2. Can you ____________ me a favor?A) doB) doesC) did3. My brother ____________ his homework last night.A) finishB) finishesC) finished4. The concert was ____________ exciting.A) veryB) tooC) so5. She ____________ to the zoo every Sunday.A) goesB) goingC) goSection E: Error CorrectionIdentify and correct the errors in the following sentences.1. He don't like vegetables.2. My mother is cook dinner right now.3. There are three book on the shelf.4. I have went to France last year.5. The childrens are playing in the park.Good luck on your exam!。

2013上海市中考语文质量测试（A）（满分150分考试时间100分钟）考生注意：1.本试卷共27题。

2.请将所有答案做在答题纸的指定位置上，做在试卷上一律不计分。

一、文言文（42分）（一）默写（18分）1．去年今日此门中，。

（《题都城南庄》）2．欲把西湖比西子，。

（《饮湖上初晴后雨》）3．青山横北郭，。

（《送友人》）4．，左牵黄，右擎苍。

（《江城子•密州出猎》）5．，不可知其源。

（《小石潭记》）6．沙鸥翔集，。

（《岳阳楼记》）（二）阅读下面的曲，完成第7—8题（4分）四块玉·别情关汉卿自送别，心难舍，一点相思几时绝。

凭阑袖拂扬花雪：溪又斜，山又遮，人去也。

7．曲中的“杨花雪”是指（2分）8．下列对这首曲理解不正确的一项是（2分）A.本曲描写了一个感情丰富且多情的女子。

B.“心难舍”句刻画了女子依依不舍的心理。

C.“拂”字流露出女子想见爱人的急切心情。

D.全曲表达了作者对自己爱人的相思之苦。

（三）阅读下文，完成第9—11题（8分）出师表亲贤臣，远小人，此先汉所以兴隆也；亲小人，远贤臣，此后汉所以倾颓也。

先帝在时，每与臣论此事，未尝不叹息痛恨于桓、灵也！侍中、尚书、长史、参军，此悉贞亮死节之臣也，愿陛下亲之、信之，则汉室之隆，可计日而待也。

臣本布衣，躬耕南阳，苟全性命于乱世，不求闻达于诸侯。

先帝不以臣卑鄙，猥自枉屈，三顾臣于草庐之中，谘臣以当世之事，由是感激，遂许先帝以驱驰。

后值倾覆，受任于败军之际，奉命于危难之间：尔来二十有一年矣。

先帝知臣谨慎，故临崩寄臣以大事也。

受命以来，夙夜忧虑，恐付托不效，以伤先帝之明；故五月渡泸，深入不毛。

今南方已定，甲兵已足，当奖帅三军，北定中原，庶竭驽钝，攘除奸凶，兴复汉室，还于旧都：此臣所以报先帝而忠陛下之职分也。

至于斟酌损益，进尽忠言，则攸之、依、允等之任也。

9．本文的作者是时期政治家、军事家（人名）（2分）10．用现代汉语翻译下面的句子，注意加点词的含义。

上海市中考数学二模试卷一、选择题（共6小题，每小题4分，满分24分）1．﹣8的立方根是（）A．2 B．﹣2 C．±2 D．2．下列属于最简二次根式的是（）A．B．C．D．3．下列方程中，有实数根的是（）A．=﹣2 B．x2+1=0 C．=1 D．x2+x+1=04．在△ABC中，DE∥BC，DE与边AB相交于点D，与边AC相交于点E．如果DE过重心G点，且DE=4，那么BC的长是（）A．5 B．6 C．7 D．85．饭店为某公司提供“白领午餐”，有12元、15元、18元三种价格的套餐可供选择，每人限购一份．本周销售套餐共计500份，其中12元的占总份数的20%，15元的卖出180份，其余均为18元的，那么所购买的盒饭费用的中位数和众数分别是（）A．15元和18元B．15元和15元C．18元和15元D．18元和18元6．如图，某水渠的横断面是等腰梯形，已知其斜坡AD和BC的坡度为1：0.6，现测得放水前的水面宽EF为1.2米，当水闸放水后，水渠内水面宽GH为2.1米．求放水后水面上升的高度是（）A．0.55 B．0.8 C．0.6 D．0.75二、填空题（共12小题，每小题4分，满分48分）7．计算：2﹣2= ．8．用科学记数法表示：3402000= ．9．化简分式：= ．10．不等式组的解集是．11．方程x+=0的解是．12．已知反比例函数y=（k≠0）图象过点（﹣1，﹣3），在每个象限内，自变量x的值逐渐增大时，y的值随着逐渐．（填“减小”或“增大”）13．文件夹里放了大小相同的试卷共12张，其中语文4张、数学2张、英语6张，随机从中抽出1张，抽出的试卷恰好是数学试卷的概率为．14．某品牌汽车经过两次连续的调价，先降价10%，后又提价10%，原价10万元的汽车，现售价万元．15．如图，在正方形ABCD中，如果AC=3，=，=，那么|﹣|= ．16．某公园正在举行郁金香花展，现从红、黄两种郁金香中，各抽出6株，测得它们离地面的高度分别如下（单位cm）：红：54、44、37、36、35、34；黄：48、35、38、36、43、40；已知它们的平均高度均是40cm，请判断哪种颜色的郁金香样本长得整齐？．（填“红”或“黄”）17．已知⊙O的直径是10，△ABC是⊙O的内接等腰三角形，且底边BC=6，求△ABC的面积是．18．如图，在Rt△ABC中，∠ACB=90°，将△ABC沿BD折叠，点C恰巧落在边AB上的C′处，折痕为BD，再将其沿DE折叠，使点A落在DC′的延长线上的A′处．若△BED与△ABC相似，则相似比= ．三、解答题（共7小题，满分78分）19．计算：﹣|cos45°﹣1|+（﹣2015）0+3．20．解方程组：．21．已知：如图，点E是矩形ABCD的边AD上一点，BE=AD，AE=8，现有甲乙两人同时从E点出发，分别沿EC，ED方向前进，甲的速度是乙的倍，甲到达目的地C点的同时乙恰好到达终点D处．（1）求tan∠ECD的值；（2）求线段AB及BC的长度．22．某公司的物流业务原来由A运输队承接，已知其收费标准y（元）与运输所跑路程x（公里）之间是某种函数关系．其中部分数据如表所示：x（公里）80 120 180 200 …y（元）200 300 450 500 …（1）写出y（元）关于x（公里）的函数解析式；（不需写出定义域）（2）由于行业竞争激烈，现B运输队表示：若公司每次支付200元的汽车租赁费，则可按每公里0.9元收费．请写出B运输队每次收费y（元）关于所跑路程x（公里）的函数解析式；（不需写出定义域）（3）如果该公司有一笔路程500公里的运输业务，请通过计算说明应该选择哪家运输队？23．已知：如图（1），在平行四边形ABCD中，点E、F分别在BC、CD上，且AE=AF，∠AEC=∠AFC．（1）求证：四边形ABCD是菱形；（2）如图（2），若AD=AF，延长AE、DC交于点G，求证：AF2=AG•DF；（3）在第（2）小题的条件下，连接BD，交AG于点H，若HE=4，EG=12，求AH的长．24．已知如图，二次函数图象经过点A（﹣6，0），B（0，6），对称轴为直线x=﹣2，顶点为点C，点B关于直线x=﹣2的对称点为点D．（1）求二次函数的解析式以及点C和点D的坐标；（2）联结AB、BC、CD、DA，点E在线段AB上，联结DE，若DE平分四边形ABCD的面积，求线段AE的长；（3）在二次函数的图象上是否存在点P，能够使∠PCA=∠BAC？如果存在，请求出点P的坐标；若不存在，请说明理由．25．已知：如图1，在△ABC中，已知AB=AC=6，BC=4，以点B为圆心所作的⊙B与线段AB、BC 都有交点，设⊙B的半径为x．（1）若⊙B与AB的交点为D，直线CD与⊙B相切，求x的值；（2）如图2，以AC为直径作⊙P，那么⊙B与⊙P存在哪些位置关系？并求出相应x的取值范围；（3）若以AC为直径的⊙P与⊙B的交点E在线段BC上（点E不与C点重合），求两圆公共弦EF的长．上海市中考数学二模试卷参考答案与试题解析一、选择题（共6小题，每小题4分，满分24分）1．﹣8的立方根是（）A．2 B．﹣2 C．±2 D．【考点】立方根．【分析】利用立方根的定义即可求解．【解答】解：∵（﹣2）3=﹣8，∴﹣8的立方根是﹣2．故选B【点评】本题主要考查了平方根和立方根的概念．如果一个数x的立方等于a，即x的三次方等于a（x3=a），那么这个数x就叫做a的立方根，也叫做三次方根．读作“三次根号a”其中，a叫做被开方数，3叫做根指数．2．下列属于最简二次根式的是（）A．B．C．D．【考点】最简二次根式．【分析】判断一个二次根式是否为最简二次根式主要方法是根据最简二次根式的定义进行，或直观地观察被开方数的每一个因数（或因式）的指数都小于根指数2，且被开方数中不含有分母，被开方数是多项式时要先因式分解后再观察．【解答】解：A、，无法化简，故是最简二次根式，故本选项正确；B、，被开方数中含有分母；故本选项错误；C、，被开方数中含有分母，故本选项错误；D、所以本二次根式的被开方数中含有没开的尽方的数；故本选项错误；故选：A．【点评】本题考查了最简二次根式的定义．在判断最简二次根式的过程中要注意：（1）在二次根式的被开方数中，只要含有分数或小数，就不是最简二次根式；（2）在二次根式的被开方数中的每一个因式（或因数），如果幂的指数大于或等于2，也不是最简二次根式．3．下列方程中，有实数根的是（）A．=﹣2 B．x2+1=0 C．=1 D．x2+x+1=0【考点】根的判别式；无理方程；分式方程的解．【专题】计算题．【分析】根据二次很式的性质可对A进行判断；根据判别式的意义对B、D进行判断；通过解分式方程对C进行判断．【解答】解：A、方程=﹣2没有实数解，所以A选项错误；B、△=0﹣4＜0，方程没有实数解，所以B选项错误；C、去分母得1=x+1，解得x=0，经检验x=0是原方程的解，所以C选项正确；D、△=14＜0，方程没有实数解，所以D选项错误．故选C．【点评】本题考查了根的判别式：一元二次方程ax2+bx+c=0（a≠0）的根与△=b2﹣4ac有如下关系：当△＞0时，方程有两个不相等的两个实数根；当△=0时，方程有两个相等的两个实数根；当△＜0时，方程无实数根．也考查了分式方程和无理方程．4．在△ABC中，DE∥BC，DE与边AB相交于点D，与边AC相交于点E．如果DE过重心G点，且DE=4，那么BC的长是（）A．5 B．6 C．7 D．8【考点】三角形的重心．【专题】计算题．【分析】如图，连结AG并延长交BC于F，根据三角形重心性质得=2，再证明△ADE∽△ABC，根据相似三角形的性质得=，然后利用比例的性质计算BC的长．【解答】解：如图，连结AG并延长交BC于F，如图，∵点G为△ABC的重心，∴=2，∵DE∥BC，∴△ADE∽△ABC，∴=，即=，∴BC=6．故选B．【点评】本题考查了三角形的重心：三角形的重心是三角形三边中线的交点；重心到顶点的距离与重心到对边中点的距离之比为2：1．也考查了相似三角形的判定与性质．5．饭店为某公司提供“白领午餐”，有12元、15元、18元三种价格的套餐可供选择，每人限购一份．本周销售套餐共计500份，其中12元的占总份数的20%，15元的卖出180份，其余均为18元的，那么所购买的盒饭费用的中位数和众数分别是（）A．15元和18元B．15元和15元C．18元和15元D．18元和18元【考点】众数；中位数．【分析】根据题意先计算出本周销售套餐12元和18元的份数，再根据中位数和众数的定义即可得出答案．【解答】解：12元的份数有500×20%=100（份），18元的份数有500﹣100﹣180=220（份），∵本周销售套餐共计500份，∴所购买的盒饭费用的中位数是第250和251个数的平均数，∴中位数是15元；18元出现的次数最多，则众数是18元；故选A．【点评】此题考查了众数与中位数，众数是一组数据中出现次数最多的数；中位数是将一组数据从小到大（或从大到小）重新排列后，最中间的那个数（最中间两个数的平均数），叫做这组数据的中位数，如果中位数的概念掌握得不好，不把数据按要求重新排列，就会出错．6．如图，某水渠的横断面是等腰梯形，已知其斜坡AD和BC的坡度为1：0.6，现测得放水前的水面宽EF为1.2米，当水闸放水后，水渠内水面宽GH为2.1米．求放水后水面上升的高度是（）A．0.55 B．0.8 C．0.6 D．0.75【考点】解直角三角形的应用-坡度坡角问题．【分析】先过点E作EM⊥GH于点M，根据水渠的横断面是等腰梯形，求出GM，再根据斜坡AD 的坡度为1：0.6，得出EM：GM=1：0.6，最后代入计算即可．【解答】解：如图；过点E作EM⊥GH于点M，∵水渠的横断面是等腰梯形，∴GM=×（GH﹣EF）=×（2.1﹣1.2）=0.45，∵斜坡AD的坡度为1：0.6，∴EM：GM=1：0.6，∴EM：0.45=1：0.6，∴EM=0.75，故选：D．【点评】此题考查了解直角三角形的应用，用到的知识点是坡度、等腰三角形的性质，关键是根据题意画出图形，作出辅助线，构造直角三角形．二、填空题（共12小题，每小题4分，满分48分）7．计算：2﹣2= ．【考点】负整数指数幂．【专题】计算题．【分析】根据负整数指数幂的定义求解：a﹣p=（a≠0，p为正整数）【解答】解：2﹣2==，故答案为．【点评】本题考查了负整数指数幂的定义，解题时牢记定义是关键，此题比较简单，易于掌握．8．用科学记数法表示：3402000= 3.402×106．【考点】科学记数法—表示较大的数．【分析】确定a×10n（1≤|a|＜10，n为整数）中n的值是易错点，由于3402000有7位，所以可以确定n=7﹣1=6．【解答】解：3402000=3.402×106．故答案为：3.402×106．【点评】此题考查科学记数法，用科学记数法表示一个数的方法是（1）确定a：a是只有一位整数的数；（2）确定n：当原数的绝对值≥10时，n为正整数，n等于原数的整数位数减1；当原数的绝对值＜1时，n为负整数，n的绝对值等于原数中左起第一个非零数前零的个数（含整数位数上的零）．9．化简分式：= ．【考点】约分．【专题】计算题．【分析】先把分母因式分解，然后进行约分即可．【解答】解：原式==．故答案为．【点评】本题考查了约分：约去分式的分子与分母的公因式，不改变分式的值，这样的分式变形叫做分式的约分．10．不等式组的解集是x≥3 ．【考点】解一元一次不等式组．【分析】根据不等式的性质求出不等式①和②的解集，根据找不等式组的解集的规律找出不等式组的解集即可．【解答】解：由①得：x＞﹣2，由②得：x≥3，∴不等式组的解集是x≥3．故答案为x≥3．【点评】本题主要考查对不等式的性质，解一元一次不等式，解一元一次不等式组等知识点的理解和掌握，能根据不等式的解集找出不等式组的解集是解此题的关键．11．方程x+=0的解是0 ．【考点】无理方程．【分析】本题含根号，计算比较不便，因此可先对方程两边平方，得到x=x2，再对方程进行因式分解即可解出本题．【解答】解：原方程变形为：x=x2即x2﹣x=0∴（x﹣1）x=0∴x=0或x=1∵x=1时不满足题意．∴x=0．故答案为：0．【点评】本题考查了一元二次方程的解法．解一元二次方程常用的方法有直接开平方法，配方法，公式法，因式分解法，要根据方程的提点灵活选用合适的方法．本题运用的是因式分解法和平方法．12．已知反比例函数y=（k≠0）图象过点（﹣1，﹣3），在每个象限内，自变量x的值逐渐增大时，y的值随着逐渐减小．（填“减小”或“增大”）【考点】反比例函数的性质．【分析】首先利用待定系数法确定反比例函数的比例系数，然后根据其符号确定其增减性即可．【解答】解：设反比例函数的解析式为y=（k≠0），∵反比例函数图象过点（﹣1，﹣3），∴把（﹣1，﹣3）代入得3=k＞0，根据反比例函数图象的性质可知它在每个象限内y随x的增大而减小，故答案为：减小；【点评】考查了反比例函数的性质，解答此题的关键是要熟知反比例函数图象的性质及用待定系数法求反比例函数的解析式．反比例函数图象的性质：（1）当k＞0时，反比例函数的图象位于一、三象限；（2）当k＜0时，反比例函数的图象位于二、四象限．13．文件夹里放了大小相同的试卷共12张，其中语文4张、数学2张、英语6张，随机从中抽出1张，抽出的试卷恰好是数学试卷的概率为．【考点】概率公式．【分析】由文件夹里放了大小相同的试卷共12张，其中语文4张、数学2张、英语6张，直接利用概率公式求解即可求得答案．【解答】解：∵文件夹里放了大小相同的试卷共12张，其中语文4张、数学2张、英语6张，∴随机从中抽出1张，抽出的试卷恰好是数学试卷的概率为：=．故答案为：．【点评】此题考查了概率公式的应用．用到的知识点为：概率=所求情况数与总情况数之比．14．某品牌汽车经过两次连续的调价，先降价10%，后又提价10%，原价10万元的汽车，现售价9.9 万元．【考点】有理数的混合运算．【专题】计算题．【分析】根据题意列出算式，计算即可得到结果．【解答】解：根据题意得：10×（1﹣10%）×（1+10%）=9.9（万元），则现售价为9.9万元．故答案为：9.9．【点评】此题考查了有理数的混合运算，熟练掌握运算法则是解本题的关键．15．如图，在正方形ABCD中，如果AC=3，=，=，那么|﹣|= 3 ．【考点】*平面向量．【分析】首先由在正方形ABCD中，如果AC=3，可求得BC的长，又由=，=，可得|﹣|=||=BC．【解答】解：∵在正方形ABCD中，AC=3，∴AB=BC=3，∵=，=，∴﹣=﹣=，∴|﹣|=||=BC=3．故答案为：3．【点评】此题考查了平面向量的知识．注意掌握三角形法则的应用．16．某公园正在举行郁金香花展，现从红、黄两种郁金香中，各抽出6株，测得它们离地面的高度分别如下（单位cm）：红：54、44、37、36、35、34；黄：48、35、38、36、43、40；已知它们的平均高度均是40cm，请判断哪种颜色的郁金香样本长得整齐？黄．（填“红”或“黄”）【考点】方差．【分析】先根据方差公式S2=[（x1﹣）2+（x2﹣）2+…+（x n﹣）2]分别求出红颜色和黄颜色的方差，然后进行比较，即可得出答案．【解答】解：红颜色的郁金香的方差是：[（54﹣40）2+（44﹣40）2+（37﹣40）2+（36﹣40）2+（35﹣40）2+（34﹣40）2]≈49.67，黄颜色的郁金香的方差是：[（48﹣40）2+（35﹣40）2+（38﹣40）2+（36﹣40）2+（43﹣40）2+（40﹣40）2]≈29.67，＞S2黄，∵S2红∴黄颜色的郁金香样本长得整齐；故答案为：黄．【点评】本题考查方差的定义与意义：一般地设n个数据，x1，x2，…x n的平均数为，则方差S2=[（x1﹣）2+（x2﹣）2+…+（x n﹣）2]，它反映了一组数据的波动大小，方差越大，波动性越大，反之也成立．17．已知⊙O的直径是10，△ABC是⊙O的内接等腰三角形，且底边BC=6，求△ABC的面积是3或27 ．【考点】垂径定理；等腰三角形的性质；勾股定理．【分析】从圆心在三角形内部和外部两种情况讨论，根据垂径定理和三角形的性质求出答案．【解答】解：当圆心在三角形内部时，0B=5，BD=3，根据勾股定理，OD=4，则AD=9，S△=×6×9=27，ABC当圆心在三角形外部时，0B=5，BD=3，根据勾股定理，OD=4，则AD=1，=×6×1=3，S△ABC故答案为：3或27．【点评】本题考查的是垂径定理、等腰三角形的性质和勾股定理，正确运用定理和性质是解题的关键，注意分情况讨论思想的运用．18．如图，在Rt△ABC中，∠ACB=90°，将△ABC沿BD折叠，点C恰巧落在边AB上的C′处，折痕为BD，再将其沿DE折叠，使点A落在DC′的延长线上的A′处．若△BED与△ABC相似，则相似比= ．【考点】相似三角形的性质；翻折变换（折叠问题）．【分析】根据△BED与△ABC相似和△ABC沿BD折叠，点C恰巧落在边AB上的C′处，求出∠A=∠DBA=∠DBC=30°，利用三角函数求出BD、AC的长，得到答案．【解答】解：△BED与△ABC相似，∴∠DBA=∠A，又∠DBA=∠DBC，∴∠A=∠DBA=∠DBC=30°，设BC为x，则AC=x，BD=x，=．故答案为：．【点评】本题考查的是相似三角形的性质和翻折变换的知识，掌握相似三角形的对应角相等和锐角三角函数的应用是解题的关键．三、解答题（共7小题，满分78分）19．计算：﹣|cos45°﹣1|+（﹣2015）0+3．【考点】二次根式的混合运算；分数指数幂；零指数幂；特殊角的三角函数值．【专题】计算题．【分析】根据零指数幂、分数指数幂和特殊角的三角函数值得到原式=﹣|﹣1|+1+，然后分母有理化和去绝对值后合并即可．【解答】解：原式=﹣|﹣1|+1+=2﹣+﹣1+1+=2+．【点评】本题考查了二次根式的计算：先把各二次根式化为最简二次根式，再进行二次根式的乘除运算，然后合并同类二次根式．也考查了零指数幂和分数指数幂．20．解方程组：．【考点】高次方程．【分析】把①化为x=±2y，把②化为x+y=±2，重新组成方程组，解二元一次方程组即可．【解答】解：，由①得，x=±2y，由②得，x+y=±2，则，，，解得，，，，．【点评】本题考查的是二元二次方程组的解法，把二元二次方程根据平方差公式和完全平方公式进行变形化为两个二元一次方程是解题的关键．21．已知：如图，点E是矩形ABCD的边AD上一点，BE=AD，AE=8，现有甲乙两人同时从E点出发，分别沿EC，ED方向前进，甲的速度是乙的倍，甲到达目的地C点的同时乙恰好到达终点D处．（1）求tan∠ECD的值；（2）求线段AB及BC的长度．【考点】勾股定理．【分析】（1）设ED=a，则EC=a，在Rt△EDC中根据勾股定理用a表示出DC的长，在Rt△ABE 中，根据BE2=AB2+AE2求出a的值，故可得出ED及CD的长，由锐角三角函数的定义即可得出结论；（2）由（1）中，DE=a，CD=3a，a=2可得出DE=2，CD=6，再根据四边形ABCD是矩形，BE=AD 即可得出结论．【解答】解：（1）设ED=a，则EC=a，在Rt△EDC中，∵DC===3a，∴BE=AE+ED=8+a．在Rt△ABE中，∵BE2=AB2+AE2，即（8+a）2=（3a）2+82，解得a=2，∴ED=2，CD=6，∴tan∠ECD===．（2）∵由（1）知，DE=a，CD=3a，a=2，∴DE=2，CD=6．∵四边形ABCD是矩形，BE=AD，AE=8，∴AB=CD=6，BC=AD=AE+DE=8+2=10．【点评】本题考查的是勾股定理，熟知在任何一个直角三角形中，两条直角边长的平方之和一定等于斜边长的平方是解答此题的关键．22．某公司的物流业务原来由A运输队承接，已知其收费标准y（元）与运输所跑路程x（公里）之间是某种函数关系．其中部分数据如表所示：x（公里）80 120 180 200 …y（元）200 300 450 500 …（1）写出y（元）关于x（公里）的函数解析式y A=2.5x ；（不需写出定义域）（2）由于行业竞争激烈，现B运输队表示：若公司每次支付200元的汽车租赁费，则可按每公里0.9元收费．请写出B运输队每次收费y（元）关于所跑路程x（公里）的函数解析式y B=200+0.9x ；（不需写出定义域）（3）如果该公司有一笔路程500公里的运输业务，请通过计算说明应该选择哪家运输队？【考点】一次函数的应用．【分析】（1）根据表可知：当运输路程跑80公里时，收费200元，所以每公里收费为2.5元，所以y A=2.5x．（2）根据题意得：y B=200+0.9x．（3）当x=500时，y A=2.5×500=1250，y B=2000+0.9×500=2450，因为y A＞y B，所以选择B运输队．【解答】解：（1）根据表可知：当运输路程跑80公里时，收费200元，∴每公里收费为2.5元，=2.5x．∴yA故答案为：y A=2.5x．（2）根据题意得：y B=200+0.9x．故答案为：y B=200+0.9x．（3）当x=500时，y A=2.5×500=1250，y B=200+0.9×500=650，＞y B，∴yA∴选择B运输队．【点评】本题考查了一次函数的应用，解决本题的关键是读懂题意，列出函数解析式．23．已知：如图（1），在平行四边形ABCD中，点E、F分别在BC、CD上，且AE=AF，∠AEC=∠AFC．（1）求证：四边形ABCD是菱形；（2）如图（2），若AD=AF，延长AE、DC交于点G，求证：AF2=AG•DF；（3）在第（2）小题的条件下，连接BD，交AG于点H，若HE=4，EG=12，求AH的长．【考点】相似形综合题．【分析】（1）通过AAS证得△AEB≌△AFD，则其对应边相等：AB=AD，所以“邻边相等的平行四边形是菱形”；（2）欲证明AF2=AG•DF，需要通过相似三角形△GAD∽△AFD的对应边成比例得到AD=AF，则AF2=AG•DF；（3）根据菱形的性质和平行线分线段成比例得到：AH：HG=BH：HD，BH：HD=EH：AH，故AH：HG=EH：AH．把相关线段的长度代入来求AH的长度即可．【解答】（1）证明：如图1，∵四边形ABCD是平行四边形，∴∠B=∠D．∵∠AEC=∠AFC，∠AEC+∠AEB=∠AFC+∠AFD=180°，∴∠AEB=∠AFD．在△AEB和△AFD中，，∴△AEB≌△AFD（AAS）∴AB=AD，∴平行四边形ABCD是菱形；（2）由（1）知，△AEB≌△AFD，则∠BAE=∠DAF．如图2，∵四边形ABCD是平行四边形，∴AB∥DG，∴∠BAE=∠G，∴∠G=∠DAF．又∵∠ADF=∠GDA，∴△GAD∽△AFD，∴DA：DF=DG：DA，∴DA2=DG•DF．∵DG：DA=AG：FA，且AD=AF，∴DG=AG．又∵AD=AF，∴AF2=AG•DF；（3）如图2，在菱形ABCD中，∵AB∥DC，AD∥BC，∴AH：HG=BH：HD，BH：HD=EH：AH，∴AH：HG=EH：AH．∵HE=4，EG=12，∴AH：16=4：AH，∴AH=8．【点评】本题考查了相似综合题．此题综合性比较强，其中涉及到了菱形的性质，平行线分线段成比例，相似三角形的判定与性质，解题时，需要弄清楚相似三角形的对应边与对应角，以防弄错．24．已知如图，二次函数图象经过点A（﹣6，0），B（0，6），对称轴为直线x=﹣2，顶点为点C，点B关于直线x=﹣2的对称点为点D．（1）求二次函数的解析式以及点C和点D的坐标；（2）联结AB、BC、CD、DA，点E在线段AB上，联结DE，若DE平分四边形ABCD的面积，求线段AE的长；（3）在二次函数的图象上是否存在点P，能够使∠PCA=∠BAC？如果存在，请求出点P的坐标；若不存在，请说明理由．【考点】二次函数综合题．【专题】综合题；二次函数图象及其性质；二次函数的应用．【分析】（1）由二次函数对称轴为直线x=2，根据A坐标确定出二次函数与x轴的另一个交点坐标，设出二次函数解析式为y=a（x+6）（x﹣2），把C坐标代入求出a的值，确定出二次函数解析式，进而确定出C与D坐标即可；（2）连接AB、BC、CD、DA，点E在线段AB上，连接DE，如图1所示，利用勾股定理求出AB，BC，CD与BD的长，根据直线CD与直线AB斜率相等，得到DC与AB平行，继而得到四边形ABCD 为直角梯形，若DE平分四边形ABCD的面积，可得直角梯形面积等于三角形ADE面积的2倍，求出AE的长即可；（3）在二次函数的图象上存在点P，能够使∠PCA=∠BAC，如图2所示，直线CP与AB交于点G，可得GA=GC，根据直线AB解析式设出G坐标（x，x+6），利用两点间的距离公式求出x的值，确定出G坐标，利用待定系数法求出直线CG解析式，与二次函数解析式联立求出P坐标；由（2）得到四边形ABCD为直角梯形，即DC与AB平行，利用两直线平行内错角相等，得到P 与D重合时，满足题意，确定出此时P的坐标即可．【解答】解：（1）∵二次函数经过A（﹣6，0），B（0，6），对称轴为直线x=2，∴二次函数图象经过（2，0），设二次函数解析式为y=a（x+6）（x﹣2），把B（0，6）代入得：6=﹣12a，即a=﹣，∴二次函数解析式为y=﹣（x+6）（x﹣2）=﹣x2﹣2x+6=﹣（x+2）2+8，则C（﹣2，8），D（﹣4，6）；（2）如图1所示，由题意得：AB=6，BC=CD=2，BD=4，∵BD2=CD2+BC2，∴∠DCB=90°，∵直线AB的解析式为y=x+6，直线DC解析式为y=x+10，∴DC∥AB，∴四边形ABCD为直角梯形，，即×2×（2+6）=2××2×AE，若S梯形ABCD=2S△ADE解得：AE=4；（3）如图2，在二次函数的图象上存在点P，使∠PCA=∠BAC，直线CP与AB交于点G，可得GA=GC，∵A（﹣6，0），C（﹣2，8），直线AB解析式为y=x+6，设G（x，x+6），∴=，解得：x=﹣，经检验是原方程的根且符合题意，∴G（﹣，），设直线CG解析式为y=kx+b，把C与G坐标代入得：，解得：，∴直线CG解析式为y=7x+22，联立得：，解得：或（经检验不合题意，舍去），∴P坐标为（﹣16，﹣90）；由（2）得到四边形ABCD为直角梯形，AB∥CD，∴∠DCA=∠BAC，此时P与D重合，即P（﹣4，6），综上，满足题意P的坐标为（﹣16，﹣90）或（﹣4，6）．【点评】此题属于二次函数综合题，涉及的知识有：待定系数法确定二次函数解析式，待定系数法确定一次函数解析式，直角梯形的判定，直线与二次函数的交点，坐标与图形性质，熟练掌握待定系数法是解本题的关键．25．已知：如图1，在△ABC中，已知AB=AC=6，BC=4，以点B为圆心所作的⊙B与线段AB、BC 都有交点，设⊙B的半径为x．（1）若⊙B与AB的交点为D，直线CD与⊙B相切，求x的值；（2）如图2，以AC为直径作⊙P，那么⊙B与⊙P存在哪些位置关系？并求出相应x的取值范围；（3）若以AC为直径的⊙P与⊙B的交点E在线段BC上（点E不与C点重合），求两圆公共弦EF的长．【考点】圆的综合题．【分析】（1）作AH⊥BC于点H，根据直线CD与⊙B相切，得到CD⊥AB，从而得到cos∠DBC=cos∠ACH，利用余弦的定义得到BD：BC=CH：CA，从而得到BD：4=2：6，求得BD 的长即可求得圆的半径；（2）作PK⊥BC于点K，求得两圆的圆心距，然后根据两圆的半径和圆心距的大小关系得到位置关系即可；（3）设EF与PB交于点G，BG=m，在△PBE中，PE2﹣PG2=BE2﹣BG2求得m的值，然后根据EG2﹣BG2=BE2求得EG的长即可求得EF的长．【解答】解：（1）如图1，作AH⊥BC于点H，∵AB=AC=6，BC=4，∴BH=2．∵直线CD与⊙B相切，∴CD⊥AB，∵∠DBC=∠ACH，∴cos∠DBC=cos∠ACH，∴BD：BC=CH：CA，∴BD：4=2：6，∴BD=．（2）如图1，作PK⊥BC于点K，∴PK∥AH．∵AH⊥BC，AB=AC=6，BC=4，∴BH=2，∴AH=4．∵以AC为直径作⊙P，∴AP=PC，∴PK=2，CK=BC=1，∴BK=3，∴在Rt△PBK中，PB===，∴当0＜x＜﹣3时，⊙B与⊙P外离，当x=﹣3时，⊙B与⊙P外切，当﹣3＜x≤4时，⊙B与⊙P相交；（3）如图2，点E即为BC边的中点H，∴PE=3．设EF与PB交于点G，BG=m，∴在△PBE中，PE2﹣PG2=BE2﹣BG2，∴32﹣（﹣m）2=22﹣m2，∴m=．∵EG2﹣BG2=BE2，∴EG2﹣（）2=22，∴EG=，∴EF=．【点评】本题考查了圆的综合知识，题目中还涉及到了勾股定理、两圆的位置关系等知识，知识点较多，难度较大，特别是最后一题中两次运用勾股定理求得EG的长更是解决本题的关键．。

2024年上海市静安区九年级中考语文二模试卷2024.04一、古诗文（35分）（一）默写与运用（13分）1.了却君王天下事，。

（《破阵子·为陈同甫赋壮词以寄之》）2.复行数十步，。

（《桃花源记》）3.，人皆有之，贤者能勿丧耳。

（《鱼我所欲也》）4.小明在演讲中引用《＜论语＞十二章》里的“，”来闸释兴趣对学习的重要性。

（二）阅读下面的文言文，完成第5-10题（22分）【甲】子曰：“贤哉，回也！一箪食，一瓢饮，在陋巷。

人不堪其忧，回也不改其乐。

贤哉，回也！”（《论语·雍也》）子曰：“饭疏食，饮水，曲肱而枕之，乐亦在其中矣。

不义而富且贵，于我如浮云。

”（《论语·述而》）【乙】当余之从师也，负箧曳屣行深山巨谷中。

穷冬烈风，大雪深数尺，足肤皲裂而不知。

至舍，四支僵劲不能动，媵人持汤沃灌，以衾拥覆，久而乃和。

寓逆旅，主人日再食，无鲜肥滋味之享。

同舍生皆被绮绣，戴朱缨宝饰之帽，腰白玉之环，左佩刀，右备容臭，烨然若神人；余则缊袍敝衣处其间，略无慕艳意，以中有足乐者，不知口体之奉不若人也。

盖余之勤且艰若此。

【丙】吕文懿勤学，至老不倦。

居秘阁①，图书左右，有得即识之，手录口诵，自晨至昃②不辍。

暮归，少暇，即为门人诵解书史。

退则吾伊③声复达于外，盖寝不移时④而起。

所修《宋元通鉴续编》，义例⑤精甚，有先儒所未到者。

书成，须发殆白。

[注释]①秘阁：古代宫中收藏珍贵图书之处。

②昃（zè）：指日西斜。

③吾伊：伊吾，咿吾。

读书声。

④不移时：不一会儿。

⑤义例：明义理的事例。

5.乙文作者，他是（朝代）文学家。

（2分）6.解释下列句子中加点词语的意思。

（4分）（1）穷冬烈风（）（2）有得即识之（）7.用现代汉语翻译乙文中的画线句。

（2分）盖余之勤且艰若此。

8.下列对甲文内容理解不当的一项是（）。

（2分）A.颜回没有因为物质条件的贫困而忧愁。

B.孔子反对用不正当的手段谋求富贵。

C.“贤哉，回也！”是倒装句，突出了孔子对颜回高尚品质的赞叹。

上海市初三语文质量测试（A）(满分150分考试时间100分钟)考生注意：1.本试卷共27题。

2.请将所有答案做在答题纸的指定位置上，做在试卷上一律不计分。

一、文言文（40分）（一）默写（15分）1．竹径通幽处，。

（常建《题破山寺后禅院》）2．，夕露沾我衣。

（陶渊明《归田园居》）3．月上柳梢头，。

（欧阳修《生查子•元夕》）4．，再而衰，三而竭。

（《左传•曹刿论战》）5．，虽鸡狗不得宁焉。

（柳宗元《捕蛇者说》（第四自然段）（二）阅读下面的诗，完成第6—7题（4分）蝶恋花宋柳永伫倚危楼风细细，望极春愁，黯黯生天际。

草色烟光残照里，无言谁会凭阑意。

拟把疏狂图一醉，对酒当歌，强乐还无味。

衣带渐宽终不悔，为伊消得人憔悴。

6.这首词围绕着“”来写景抒情。

（2分）（用文中语言回答）7．下列理解不正确．．．的一项是（2分）A．“残照”不仅点明时间，更增添了一层感伤的色彩。

B．“拟”写出词人想借酒浇愁、寻得欢乐的心理活动。

C．“终不悔”表现了主人公坚毅的性格和执着的态度。

D．“伊”是思念深爱的女子，也暗指人生的理想目标。

（三）阅读下文，完成第8—10题（9分）邹忌讽齐王纳谏（节选）①于是入朝见威王，曰：“臣诚知不如徐公美。

臣之妻私臣，臣之妾畏臣，臣之客欲有求于臣，皆以美于徐公。

今齐地方千里，百二十城。

宫妇左右莫不私王，朝廷之臣莫不畏王，四境之内莫不有求于王：由此．观之，王之蔽甚矣。

”②王曰：“善。

”乃下令：“群臣吏民能面刺寡人之过者，受上赏；上书谏寡人者，受中赏；能谤讥于市朝，闻寡人之耳者，受下赏。

”令初下，群臣进谏，门庭若市；数月之后，时时而间进；期年之后，虽欲言，无可进者。

8．《邹忌讽齐王纳谏》选自西汉（人名）编订的《》。

（2分）9.第①段加点词“此”指代的具体内容是（3分）10.联系上下文，说说对第②段王所说之“善”的理解。

（4分）（四）阅读下文，完成第11—13题（12分）孔子见罗雀者孔子见罗雀者①，所得皆黄口小雀。

上海市嘉定区2020-2022届（三年）高三二模英语试题分类汇编语法填空上海市嘉定区2022届高三二模英语试卷Section A (10分)Directions:After reading the passage 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.Will Robots Take Your Job in the Future?In 2013, researchers at Oxford University did a study on the future of work. They concluded that almost one in every two jobs have a high risk of (21) __________ (automate) by machines. Machine learning is the technology that’s responsible for most of this situation. It’s the most powerful branch of artificial intelligence. It allows machines to learn from data and imitate some of the things (22) __________humans can do.Machine learning started making its way into industry in the early 1990s. It started with relatively simple tasks. It started with things (23) __________ assessing credit risk from loan applications, sorting the mail by reading handwritten characters from zip codes. Over the past few years, we (24) __________(make)dramatic breakthroughs. Machine learning is now capable of far, far (25) __________ (complex) tasks. In 2012, Kaggle challenged its community (26) __________(build) an algorithm(算法) that could grade high-school essays. The winning algorithms were able to match the grades given by human teachers.Now, (27) __________ (give) the right data, machines are going to outperform humans at tasks like this. A teacher (28) __________ read 10,000 essays over a 40-year career. A machine can read millions of essays within minutes. We have no chance of competing against machines on frequent, high-volume tasks.But there are things we can do that machines c an’t do. (29) __________ machines have made very little progress is in dealing with novel situations. They can’t handle things they haven’t seen many times before. The fundamental limitation of machine learning is that it needs to learn from large volumes of past data. Now, humans don’t. We have the ability to connect seemingly different threads to solve problems we’ve never seen before. Machines cannot compete with us when it comes to dealing with novel situations, and this (30) __________ (put)a fundamental limit on the human tasks that machines will automate.上海市嘉定区2021届高三二模英语试卷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 from of the given word; for the other blanks, use one word that best fits each blank.Why Acting Is So Much More Than It Appears to BeFor many people, acting appears to be people talking while getting emotional, which is why so many people think they can do it. No one imagines (21) ______ waking up one day and being a professional singer or pianist. But for actors, they say, “Acting is hard only (22) ______ one has to memorize lines. If I could remember, I could be an actor, too.”But acting isn’t just about memorizing lines and talking in conversational reality. As Meisner said, “Acting is doing things truthfully under imaginary circumstances.” If (23) ______ (understand) correctly, this definition is an ambitious and remarkable thing to strive for.To do things truthfully, actors must acquire many challenging skills. (24) ______ these skills, the script will remain flat on the page, despite being recited out loud. To make a script come to life in a believable way, the actor (25) ______ make active choices.Imagine for a moment how many different ways there are (26) ______ (deliver) one single line. Even something as simple as “close the door” can mean so many different things and (27) ______ (express) in so many different ways. The wor ds are the writer’s, but the behavior ______ brings them to vivid life? That is the actor.The goal of great actors? That’s to act naturally. Good quality acting must always come down to kind of naturalness that makes those acting skills (29) ______ (visible) to the audience. In other words, a good actor must not appear to be acting at all.So do not be fooled into thinking that (30) ______ can read and speak can be an actor. The naturalness displayed by great actors is exactly what makes you think that way, but it took them years of training to get to this point. It is so much more than you know.上海市嘉定区2020届高三二模英语试卷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 from of the given word; for the other blanks, use one word that best fits each blank.Long-term low self-esteem can cause depressionLow self-esteem makes us feel bad about ourselves. But did you know that over time it also can cause the development of serious mental conditions such as depression?Self-esteem is, very si mply, the set of feelings you have about yourself. It’s developed by your experiences, thoughts, feelings, and relationships. ____1____ self-knowledge, which refers to how much you know about yourself, self-esteem is formed around whether you like yourself or not. Depression is much more than just feeling sad. It drains your energy and makes everyday activities difficult.Doctors use low self-esteem as one possible symptom ____2____ they diagnose the mentalcondition of major depressive disorder. They don’t necessarily care ____3____ low self-esteem causes the depression or vice versa. However, personality researchers have long wondered about the chicken-and-egg problem of self-esteem and depression. Certainly, if you dislike yourself, you’ll be more likely ____4____ (depress). On the other hand, if you’re depressed, you’ll be more likely to feel bad about yourself. The only way that ____5____ (employ) to explore the highly related concepts of self-esteem and depression is through continuous research, ___6___ people are followed up over time.A study on depression conducted by University of Basel researchers Julia Sowislo and Ulrich Orth, ____7____ (contrast) the competing directions of self-esteem to depression vs depression to self-esteem. The findings have revealed that over time low self-esteem is a risk factor for depression, regardless of who is tested and how. The study indicates that low self-esteem causes depression___8___ not vice versa.Therefore, if a person has low self-esteem, there’s a ___9___ (great) risk of developing depression. This is a very important discovery because it shows that ____10____ (improve) a person’s self-esteem can make him or her feel better.答案：上海市嘉定区2022届高三二模英语试卷21. being automated 22. that 23. like 24. have made 25. more complex 26. to build 27. given 28. may/might 29. Where 30. puts上海市嘉定区2021届高三二模英语试卷21. oneself/ himself/ themselves 22. because/ when/ if 23. understood 24. without25. must/ should 26. to deliver 27. be expressed 28. that/ which 29. less visible 30. whoever上海市嘉定区2020届高三二模英语试卷【答案】1. Unlike2. when3. whether4. to be depressed5. is employed6. in which7. contrasted8. but 9. greater10. improving【解析】【分析】这是一篇说明文。

2021年上海市崇明区高考英语二模试卷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 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. （1分）A. In a bank.B. In a hotel.C. In a clinic.D. In a university.2. （1分）A.A toy designer.B.A shop assistant.C.A train conductor.D.A school teacher.3. （1分）A.Frank.B.Aggressive.C.Inconsiderate.D.Responsible.4. （1分）A.Their physics class.B.Correcting a mistake.C.The mid﹣term exam.D.Finding a private teacher.5. （1分）A.Take a later train.B.Go to the city on weekdays.C.Wait another 20 minutes.D.Check the weekend schedule.6. （1分）A.He doesn't like shopping.B.He doesn't want to attend the wedding.C.His suit fits James well.D.His suit is too old to wear.7. （1分）A.She can help the man tomorrow.B.The man should leave the library.C.The library will hire more people.D.It's normal for that period of time.8. （1分）A.Work as an adviser for the club.B.Ask the professor to head the club.C.Introduce the professor to the woman.D.Advise the woman to join the biology department.9. （1分）A.Her brother doesn't want to transfer.B.She doesn't think her brother should transfer.C.Her brother is trying to talk with her.D.She's talked to her brother since he transferred.10. （1分）A.The man likes Dr.White's lessons.B.The man has dropped the course.C.The woman can skip the experiments.D.The woman has to continue the course.Section BDirections: In Section B, you will hear two passages and one longer conversation.After each passage or conversation, you will be asked several questions.The passages and the conversation 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 is the best answer to the question you have heard.11. （4.5分）（1）A.Sixty﹣one percent of the world's food is wasted every year.B.Wasted food is mostly from stores and food service companies.C.Food waste is more serious in rich countries than in poor countries.ck of cold storage is the main cause of food waste in poor countries.（2）A.Cutting food prices.B.Stopping the destruction of nature.C.Eliminating starvation.D.Lessening carbon dioxide emissions.（3）A.Improper ways of manufacturing food.B.High frequency of food promotion.C.Unclear instructions on food containers.ck of deadlines for food consumption.12. （4.5分）（1）A.Reducing the working hours of food delivery riders.B.Classing food delivery riders as company﹣employed.C.Ensuring the use of new technology in food delivery.D.Defining the duties of food delivery companies and riders.（2）A.To ensure the riders' rights.B.To publicize the digital processes.C.To promote the digital economy.D.To improve food delivery service.（3）A.It lowers the riders' pay.B.It restricts customers' freedom.C.It reduces the number of riders.D.It harms intellectual property rights.13. （6分）（1）A.Their collections of albums.B.Their different habits of enjoying music.C.The living of musicians.D.The various means of streaming music.（2）A.They are shared too widely.B.They harm the rights of music lovers.C.They ignore the popular songs.D.They only focus on a part of an album.（3）A.To avoid advertisements.B.To listen to music of higher quality.C.To access better playlists.D.To save storage space on the phone.（4）A.To get free quality songs.B.To enjoy music conveniently.C.To value the work of musicians.D.To communicate with music fans.Ⅱ.Grammar and VocabularySection 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.14. （10分）Photographers Turn Their Cameras on PetsIn 2019 photographers Kendrick Brinson and David Walter Banks visited 14 countries on assignment.When the couple described the adventures （1）they had experienced when photographing, people invariably asked, "But who takes care of your four cats and dogs？" They joked that the pet sitter （临时看护宠物的人）made a lot of money.But 2020 couldn't have been（2）（different）.Due to COVID﹣19, Brinson and Banks never left the United States.Often, they didn't even leave their Los Angeles neighborhood.（3）spending long hours in airport security lines and waiting for the perfect lighting, the pair stayed along with dogs Tux and Tia and cats Rex and Kudzu."Our pets became emotional therapy animals, and our only friends we could safely hug in a world（4）（strike）by a deadly pandemic （大流行病）, " Banks said.As COVID﹣19 lockdowns swept across the world in March of 2020, the change made an especially great impact on photographers, who are accustomed to （5）（spend）long periods abroad.And so many cameras （6）（turn）on a domestic subject: the pet.Research suggests that pets have offered emotional support during the pandemic, helping （7）（make）the long days of isolation more bearable, says Emily McCobb, a clinical associate professor at Cummings School of Veterinary Medicine at Tufts University.In fact, the pandemic has sped up a trend, according to McCobb's and other scientists' observation, （8）the pet is becoming a member of the family."In the past 20 to 30 years, the role of the pet in the family （9）（take）on a whole new role, " says McCobb."It really hasn't been that long （10）these furry child substitutes gained this kind of importance in American society."Section BDirections: Fill in each blank with a proper word chosen from the box.Each word can be used only once.Note that there is one word more than you need.15. （10分）A.vacantB.raisedC.acknowledgesD.quotedE.alertsF.colonialG.housed H.former I.recommendations J.requests K.reviewsG. housed H. former I. recommendations J. requests K. reviewsMuseums Rethink What to Do with Their African Art Collections Recently, a discussion is happening in museums around the world over the volume of African art in their collections.Officials in Germany and the Netherlands have announced plans to return art and artifacts taken from Africa during the （1）period.And more museum staff are meeting on the topic across Europe.According to the most commonly （2）figures from UNESCO（United Nations Educational, Scientific and Cultural Organization）, 90% to 95% of sub﹣Saharan cultural artifacts are（3）outside Africa.Many were taken by force long ago and ended up in museums across Europe and North America.At the Africa Museum in Belgium, director Guido Gryseels says 85 percent of the museum's collection comes from the Congo ﹣the site of Belgium's（4）colony in Central Africa.For decades, Congolese leaders have asked for these objects to be returned.Most of their （5）and those by African countries to other museums, have been refused.But recent events in Europe have （6）the possibility of returns at a muchlarger scale.In addition to the plans announced in Germany, last year France conducteda study of how much African art French museums are holding and made （7）about what to do with itThe study recommended the return of a wide range of objects taken by force.The suggestion got mixed（8）in France, where there are at least 90, 000 African items in museums.In France, some people have suggested returns could leave shelves （9）in French museums.Gdeile Fromont, a French historian of Central African art, says that's not going to happen.One way of thinking about it, she says, is that more African art can go on display.However, Guido Gryseels of the Africa Museum in Belgium （10）that attitudes are changing.He says he's in discussion with the Congo to return works.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.16．（15分）Around 13, 000 years ago North America had a wider variety of mammals（哺乳动物）than modern Africa.There were multiple horse species, camels and some now ﹣extinct animals.And such （1）creatures were not just found in North America.On every continent mammals on average were a lot larger from around 2.5 million until about 11, 700 years ago.Scientists have long debated what caused all these large creatures to go extinct while many of the smaller ones （2）.A team of researchers led by biologist Felisa Smith analyzed evidence from millions of years' worth of mammalian extinctions and found that on each continent large mammals started to （3）around the same time humans first showed up.If the extinction trend continues, many more large mammals will soon disappear as well, as the primary threats from humans have （4）from overhunting to indirect processes such as habitat loss.In their new study Smith and her team analyzed a database of all land mammals that lived from 65 million years ago until today."We found（5）no effect of climate on mammalian extinction over 65 million years, " she says.But starting around 125, 000 years ago and continuing until today, large mammals have been more likely to go extinct than smaller ones, the researchers found.The average（6）of surviving mammals has decreased as a result.And those large﹣mammal extinctions are tightly coupled with the （7）of humans.For most of mammalian （8）history, an animal's size was not predictive of its extinction risk.That （9）only appeared once humans began to live alongside large mammals.This finding does not mean climate﹣related changes could not have（10）some wildlife populations, enabling humans to more easily bring about their eventual downfall, （11）it suggests the greater likelihood of large mammals going extinct is tied to human activities.The animals that evolved without the risk of hunting from humans were suddenly faced with a new（12）.They simply could not（13）fast enough to survive the invasion of humans.Smith says the lesson to be learned from the new findings is that our ancestors prepared us to be extremely skillful killers."What's（14）now，" she says，"is that some of us are comfortable enough，have a high enough standard of living，that we can start thinking about our use of die Earth." Rather than simply behaving as （15），many of us are now in a position to become environmental protectors.（1）A.smart B.massive C.marine D.ancient（2）A.survived B.shrank C.escaped D.returned（3）A.hide away B.make off C.breakup D.die out（4）A.faded B.restored C.improved D.expanded（5）A.absolutely B.predictably C.exclusively D.potentially（6）A.weight B.speed C.size D.appetite（7）A.production B.appearance C.exploration D.cruelty（8）A.recorded B.contemporary C.evolutionary D.ancient（9）A.link B.contact C.adaptation D.distinction（10）A.enlarged B.stressed C.impressed D.dominated（11）A.Moreover B.Otherwise C.Meanwhile D.Rather（12）A.species B.hope C.rule D.threat（13）A.grow B.digest C.withdraw D.adapt（14）A.instructive B.fashionable C.different D.marvelous（15）A.sponsors B.creators C.consumers D.designersSection 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 passageyou have just read.17. （8分）As the COVID﹣19 pandemic hit hard, fishermen watched their markets dryup.Restaurants ﹣normally major fish buyers ﹣closed or cut back orderssignificantly.Fishermen weren't sure if they were going to get paid for what they fished.Meanwhile as people lost jobs, food banks started to see a great demand for services.Things were getting desperate, with long lines for food assistance in many states.Out of these dual crises, a new idea was born.Food assistance programs across the country have started connecting with local fishermen to stock upon local seafood, many for the first time.And the arrangement seems to be helping the fishermen, the economy and those in need of healthy food.According to Catherine D'Amato, CEO of the Greater Boston Food Bank, the network usually keeps four or five weeks of food on hand in case of emergencies.The pandemic hit, and "we found ourselves below one week of stock and going down rapidly, " she says.That's because the food bank normally distributes about 1 million pounds of food a week, and that became 2.5 million pounds of food a week, D'Amato says.While Congress and the states have increased funding and donations for food banks during the pandemic, it hasn't been enough."For many years, we have been wanting to be able to work with organizations in the fishing industry, " D'Amato says.But it's complicated.Fishermen catch a lot of big fish, and food banks who might take it need the products to be cut small and easy to use for customers.It also has to be fish they know and recognize.The barriers have been too high in many places to make it work.But this spring, the state department of agriculture connected the food bank with some grant makers.They talked to some local fishermen about developing a traditional New England fish soup.The grants paid fishermen for their catch and provided money for a local manufacturer to process，freeze and deliver the soup to food banks in family﹣size servings.The soup is helping to feed families and keep fishermen fishing.The fishermen hope to sell it in stores soon，and D'Amato hopes to purchase more soup and expand into new seafood products for her customers.（1）The passage is mainly about.A.the food shortage during the COVID﹣19 pandemicB.the cooperation between fishermen and food banksC.the dramatic impact the pandemic had on fishermenD.the new seafood product manufactured for food banks（2）What do "dual crises" in paragraph 3 refer to？A.Fishermen's difficulty in storing seafood and the decline of the economy.B.Fishermen's difficulty in selling fish and food banks' need for more food.C.The closure of restaurants and food banks' great demand for food assistance.D.Many people's unemployment and many states' bad services in food industry.（3）According to paragraph 5, Catherine D'Amato thinks that.A.fishermen should start to process fishB.many fishes are unknown to customers.C.there's a gap between supply and needD.the fishing organizations are too independent（4）It can be learned from the passage that the fish soup.A.increases fishermen's productivityB.is commonly consumed by local fishermenC.makes food banks rethink their productsD.is produced by food banks in a traditional way18. （6分）Who we needWe are looking for talented and passionate people to work for health.WHO is committed to achieving workforce variety, aiming to achieve a broad representation of nationals of our member countries.Particular attention is paid to candidates from developing countries and gender filled in accordance with WHOs ability model.There are two key categories of staff at WHO：professionals（P）or directors（D）who are internationally recruited （招募）and general（G）or national professional（NPO）staff who are recruited locally for both fixed or short﹣term positions.We also run internship（实习）and opportunities for junior professional officers（JPOs）.There are two key categories of staff at WHO: professionals（P）or directors（D）who are internationally recruited （招募）and general（G）or national professional（NPO）staff who are recruited locally for both fixed or short﹣term positions. We also run internship （实习）and opportunities for junior professional officers（JPOs）.There are two key categories of staff at WHO：professionals（P）or directors（D）who are internationally recruited （招募）and general（G）or national professional（NPO）staff who are recruited locally for both fixed or short﹣term positions. We also run internship （实习）and opportunities for junior professional officers（JPOs）.Internationally recruited （P or D）Professional staff and directors are hired internationally and occupy leadership functions or positions that require a significant level of technical knowledge.P or D staff are mobile and are expected to work across the globe. Professional staff and directors are hired internationally and occupy leadership functions or positions that require a significant level of technical knowledge. P or D staff are mobile and are expected to work across the globe.Locally recruited （G orNPO）General Service staff arehired locally at the respectiveduty station.Their main roleis to work with and supportinternationally recruitedstaff in their roles and toassure the smoothfunctioning of alladministrative matters.National ProfessionalOfficers are nationals of thecountry in which they serveand perform functions of aprofessional nature requiringlocal knowledge,professional knowledge andexperience.National ProfessionalInternshipsWe offer internships forcurrent students witheducational background inpublic health, managementor administration fields.We offer internships forcurrent students witheducational background inpublic health，managementor administration fields.Officers are nationals of the country in which they serve and perform functions of a professional nature requiring local knowledge，professional knowledge and experience.Junior professional officer programmeThe Junior Professional Officer （JPO）Programme provides young professionals at an early stage in their career with practical experience in international technical cooperation.JPOs are sponsored by their respective governments.The Junior Professional Officer （JPO）Programme provides young professionals at an early stage in their career with practical experience in international technical cooperation. JPOs are sponsored by their respective governments.Recruitment restrictionsPlease note the following restrictions on recruitment: Relatives of WHO Staff：Except where another equally well qualified person cannot be recruited, appointment shall not be granted to a person who bears any of the following relationships to a staff member：father, mother, son, daughter, brother or sister.Candidates under the age of 20 and above the age of 62 will not be considered for any vacancy.Policy on Non﹣Recruitment of Smokers：WHO has a smoke﹣free environment and does not recruit smokers who do，not indicate a willingness to stop smoking.This policy underscores the Organization's commitment to promoting a smoke﹣free environment.Policy on Non﹣Recruitment of Smokers：WHO has a smoke﹣free environment and does not recruit smokers who do, not indicate a willingness to stop smoking. This policy underscores the Organization's commitment to promoting a smoke﹣free environment.Policy on Non﹣Recruitment of Smokers: WHO has a smoke﹣free environment and does not recruit smokers who do，not indicate a willingness to stop smoking. Thispolicy underscores the Organization's commitment topromoting a smoke﹣free environment.Policy on Non﹣Recruitment of Smokers：WHO has asmoke﹣free environment and does not recruit smokerswho do，not indicate a willingness to stop smoking. Thispolicy underscores the Organization's commitment topromoting a smoke﹣free environment.（1）The above webpage aims at.A.recruiting volunteers for WHOB.achieving a broad representation of nationalsC.explaining the functions of WHOD.providing information about WHO positions（2）What kind of applicants will definitely be turned down according to the restrictions？A.Males in their later 60s.B.People who have health problems.C.Children of WHO staff.D.Candidates with a smoking history.（3）What can be learned from the webpage？A.General Service staff are recruited all around the world.B.Junior Professional Officers work for local governments.C.Current students majoring in engineering can apply for internships.D.Professionals and directors are an internationally mobile workforce.19. （8分）A seismic （地震的；重大的）shift in climate science might be heating up.New research shows that sound waves produced by earthquakes can be used to measure temperatures in the ocean which traps 90% of the heat Earth absorbs from the sun, making long﹣term changes in ocean warmth, a major factor in how the world might respond to global warming.For years the main approach of measuring ocean temperature has been Argo，an array （阵列）of 4000 automatic floats，which drifts the globe，sampling ocean water and measuring its temperature.Yet Argo measurements stop at 2000 meters.The new technique called "Seismic Ocean Thermometry" would be especially useful in detecting long﹣term changes in ocean temperatures deeper than Argo's reach."Ocean Acoustic Tomography", the basis for the current research, was first tested nearly 30 years ago.The initial studies created sound waves artificially, basically increasing the volume on giant underwater speakers.Scientists measured the sound's travel time from the speakers to receivers thousands of kilometers away.Because ocean temperatures affect the speed of the waves, the researchers could calculate average temperatures along their paths.But some believed the noise was a threat to ocean life and the technique never took off.The new study instead uses a natural sound source for investigation: earthquakes making a low, continuous noise beneath the seafloor off the coast of Sumatra that drum up sound waves in the ocean.On the shores of the Chagos Islands in the East Indian Ocean, between 2005 and 2016 Seismic Station Diego Garcia recorded seismic waves produced by those earthquakes.Some of those waves created physical changes in land and sea as they traveled.Others were sound waves or T waves that moved through the deep ocean, delivering valuable data about ocean temperature.12 years of data coupled with mathematical models pointed to a temperature change of roughly 0.044 degrees per decade, a trend larger than those predicted by Argo.The findings suggest that Seismic Ocean Thermometry is a feasible method to measure changes in ocean temperature, Further data from other regions of the globe and other timeframes would help improve the warming models and predictions.And in future studies the researchers plan to listen directly for sound waves，using anetwork of hydrophones，microphones which detect sound waves under water.Sound waves set the tone for a deep dive into our warming oceans even if they fail to reach 60000 miles under the sea.（1）What disadvantage does Argo have？A.Its reach is limited.B.It takes long to collect samples.C.It doesn't work globally.D.Its prediction isn't reliable at all.（2）It can be learned that Ocean Acoustic Tomography.A.was tested many times but never succeededB.remained unpopular for fear of potential harmC.was assumed to be too complicated to be controllableD.measured ocean temperature just as the new research does（3）It can be inferred from the new findings that.A.some warming is working its way deeper into the oceanB.ocean temperature is rising faster owing to earthquakesC.sound travels faster in colder water than in hotter waterD.sound waves will slow down the warming of the ocean（4）Which is the best title for the passage？A.Sound Waves First Applied to Climate ScienceB.New Factors Found to Be Heating up the OceanC.A Natural Approach Holding Back Global WanningD.Ocean's Hidden Heat Measured with Earthquake SoundsSection CDirections: Complete the following passage by using the sentences in the box.Each sentence can only be used once.Note that there are two sentences more than you need.20. （8分）A.But the challenge is figuring out how to collect the energy from those winds.B.Kite power has the potential to greatly improve on current wind﹣power strategies.C.Wind at these altitudes （海拔高度）is stronger and steadier which increasesproductivity factors of the system to about 60%.D.Its plan is to build a kite power station using technology that can collectively generate（产生）large amounts of energy.E.Nevertheless, they successfully demonstrated that their kites could operateautomatically at an altitude of up to 700 meters.F.After the initial cost of designing and setting up the plant, little additional investmentwill be necessary, apart from standard maintenance.F.After the initial cost of designing and setting up the plant，little additional investmentwill be necessary，apart from standard maintenance.Kite PowerThe search for new, clean energy sources has occupied the attention of scientists and politicians for years.One common resource for green energy is the wind.A new twist on this old resource could cause the energy output of wind﹣power plants to rise dramatically.Standard wind﹣power plants rely on fixed support and generally can only reach a height of 200 meters or so.Higher than that, winds tend to be stronger and more persistent.（1）.Delft University of Technology in the Netherlands and Karlsruhe University of Applied Sciences in Germany have formed a kite﹣power research group.The group is working to develop kites with inflatable（可充气的）wings connected to electrical generators on the ground.The research group's goal is to design a kite that can operate on its own for 24 hours.Research has begun, but many challenges remain, including making the generators more efficient and perfecting the automatic flight control and the structure of the kites.（2）.Meanwhile, in Italy, researchers are working in a similar power generator that relies on kites.When the generator, called KiteGen, senses the wind blowing, kites are released from the ends of poles with high﹣resistance cables to control their height andangle.These cables are able to move the kites if the system senses incoming objects such as planes, helicopters or even individual birds.The kites themselves are light, tough and able to reach fairly high altitudes.They form a circular shape in the wind, which sets the core of the generator in motion, producing electric current.KiteGen has the potential to be very cost﹣effective in the long run.（3）.The plant also requires relatively little space, which makes it ideal for cities and means that multiple plants can be set up to provide even more energy.（4）.In the future，it may be an efficient，cost﹣effective addition to the other sources of energy we use，or even a replacement for some of them.Ⅳ.Summary Writing21. （10分）Directions: Read the following passage.Summarize the main idea and themain point（s）of the passage in no more than 60 e your own words as far aspossible.Robotic ExoskeletonsThanks to robotic exoskeletons, victims of spinal cord（脊椎）injury have a new reason to hope.Robotic exoskeletons, consisting of metal legs, motors, batteries, wiring, a controller and a set of strips, work together like the user's bones, muscles and nerves ﹣outside the body.Fastened into an exoskeleton and supported by sticks, users can direct the machinery to take them where they want to go.In addition to partly restoring mobility, robotic exoskeletons offer the significant mental and physical health benefits of standing up and moving.Just being able to get up from a wheelchair gives patients a more natural, positive view of the world.It also helps relieve pressure on patients' skin and reduces the danger of pressure sores.Standing upright strengthens a disabled person's muscles and bones, improves heart health, and reduces certain other health complications （并发症）.And it may actually result in partial nerve repair, something that can only happen when a patient is able to move.As promising as this technology is, however, it is no simple cure﹣all for paralysis （瘫痪）or its complications.The motion is not accurate compared with natural walking, and exoskeletons are not easy to use, especially on surfaces that are not smooth.They。

2020年上海市高考英语二模试卷（A卷）II. Grammar and Vocabulary（20分）Section A（10分）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 withthe proper form of the given word； for the other blanks，use one word that best fits each blank.1. China’s leading online English learning brand 51Talk held （1）________ annual strategic conference in Beijing on Tuesday， with a focus on wider market access， more individual learning modes and AI technology applications．The brand，（2）________（bear） the idea of allowing more children to enjoy quality education， has announced strategic cooperation with partners including family early education brand Qiaohu， Aniworld TV and US publishing house TCM．Chinese singer and actor Wang Junkai， who boasts high popularity （3）________ younger Chinese，has been invited to be the brand’s latest spokesman．Huang Jiajia， founder and CEO of 51Talk，said at the press conference the brand’s users cover more than 500 cities nationwide， and the total amount of courses taken by learners has exceeded 3 million in a single month．Huang also believed 51Talk （4）________（dedicate）to promoting “universal education” since its establishment in 2011．"Enjoying qualified foreign teachers in language leaning （5）________ not be the exclusive privilege of children from wealthy families and of China’s first﹣tier cities． What 51Talk has been doing is making education resources accessible to more people，" the CEO added．To this end， 51Talk is ready to expand its appeal to more second﹣ and third﹣tier cities，and is expected （6）________（reach） more than 1，000 cities across the nation this year． Also， the English learning brand is poised to conduct （7）________ “one plus one” strategy by arranging foreign and Chinese teachers for learners．"Foreign teachers will continue to show off their professional teaching skills （8）________ Chinese teachers will act as the bridge to connect foreign teachers and students，" Huang said， adding the combination of foreign teachers and Chinese education can not only improve learning and communication efficiency， but also help students to achieve better results．（9）________， 51Talk will continue to follow the Belt and Road Initiative and introduce more Philippine foreign teachers to the teaching team．Huang said Philippine foreign teachers have a high﹣level English teaching ability，（10）________ plays an important role in improving Chinese students’ interest in learning English．【答案】its,bearing,among,has been dedicated,should,to reach,a,while,Besides,which【考点】说明文语法填空【解析】中国领先的在线英语学习品牌51Talk周二（1日）在北京举行年度战略会议，重点讨论更广泛的市场准入、更个性化的学习模式和人工智能技术应用．它对提高中国学生学习英语的兴趣起着重要作用．【解答】（1）its．考查代词．代指 51Talk ，做 annual strategic conference的定语，用形容词性物主代词its．（2）bearing．考查非谓语动词．做定语，和名词 The brand构成主动关系，表示“承载”，用现在分词bearing．（3）among．考查介词．修饰名词younger Chinese，表示“在…之中”，用介词among．（4）has been dedicated．考查谓语动词．根据时间状语since its establishment in 2011，可知谓语动词用现在完成时态，又因为dedicate和主语51Talk 是被动关系，所以谓语动词用has been dedicated．（5）should．考查情态动词．本句表示“在语言学习方面，享受合格的外籍教师不应该是富裕家庭和中国一线城市孩子的特权．”，所以表示“应该” 用情态动词should．（6）to reach．考查动词不定式．表示“被预料做某事”用be expected to do ，所以答案是to reach．（7）a．考查冠词．修饰名词“one plus one” strategy，表示“一个”，用不定冠词a．（8）while．考查连词．比较Foreign teachers 和Chinese teachers，用连词while．（9）Besides．考查句子之间的联系．本句表示“51谈话将继续遵循”一带一路“的倡议，引进更多的外国外籍教师到教学团队”，和上句是递进关系，用Besides．（10）which．考查非限制性定语从句．代指先行词a high﹣level English teaching ability，做非限制性定语从句plays an important role in improving Chinese students’ interest in learning English的主语，关系词用which．Section B（10分）Directions： Fill in each blank with a proper word chosen from the box. Each word can be used only once. Note that there is one word more than you need.For years people have recognized the power that writing something down has been able to anchor （固定） a thought or emotion in the brain． This （1）_______ of anchoring emotions and memories with physical touch is now well supported by studies and frequently used by those who practice Neuro﹣linguistic Programming （NLP）．Evidence that the mind and body connection exists in building and （2）_______ memories is abundant． More recently， however， researchers have been turning their attention to the （3）_______ between exercise and the brain． They are finding evidence that supports the belief that exercise can boost brain power．How can that happen？ U．S． researchers have found that exercise helps that brain develop new brain cells in an area of the brain called the dentate gyrus． This area is known to be involved with age﹣related memory loss． The studies performed （4）_______ mice and later humans supported the evidence found in those studies： there was increased blood flow to the memory center of the brain after exercise， which may help optimize the way the brain （5）_______． Basically， anything that helps the body to decrease stress hormones，which will improve attention span as well as mood and increase the body’s metabolism， will also help the brain． It helps by making the brain cells healthier and better able to link to other cells． This action is vital for learning and （6）_______ new information．The fact that exercise makes positive changes in the nervous system and boosts cognitive abilities has not gone （7）_______ by schools． Many states have now established minimum times and frequency for physical education． This type of action is supported bystudies that show how much better physically fit third graders and fifth graders performed on standardized tests than students who were still in their studies all the time． The evidence that （8）_______ obesity with lower levels of academic achievement in school children is starting to catch on everywhere．Walking （9）_______ at least three times a week was found to benefit your brain， for it will cease to grow for a lack of exercise． Creative writing benefits brain a lot as this type of activity is not mechanic and cause the brain to produce new （10）_______ which stimulate new dendrites and neurons to grow in the brain． Use one or more of your physical senses， involve your complete attention and break away from your routine in a significant way as dull brain is never ready for the unexpected．【答案】B,H,K,A,J,I,D,G,C,F【考点】选词填空【解析】多年来，人们已经意识到写下来的东西能够将思想或情感固定在大脑中的力量．本文主要介绍了运动与大脑的关系．【解答】1﹣5 BHKAJ 6﹣10 IDGCF（1） B．考查名词．句意：现在，这种通过身体接触来固定情绪和记忆的____得到了研究的充分支持．根据空前的指示代词This可知应用单数名词意为“过程”，故选B．（2） H．考查动词．句意：有大量证据表明，在建立和____记忆过程中存在着身心联系．结合句意可知此处意为“保持”，故选H．（3） K．考查名词．句意：然而，最近，研究人员将注意力转移到了运动与大脑的____上．根据空前的冠词the可知应用名词意为“关系”，故选K．（4） A．考查过去分词．句意：这些研究____到老鼠和后来的人类，支持了这些研究中发现的证据．结合句意可知此处意为“涉及”，故选A．（5） J．考查名词．句意：运动后大脑记忆中心的血液流量增加，这可能有助于优化大脑的____．结合句意可知此处意为“功能”，故选J．（6） I．考查动词．句意：这个动作对学习和____新信息至关重要．结合句意可知此处意为“传递”，故选I．（7） D．考查形容词．句意：运动能使神经系统发生积极的变化，提高认知能力，这一事实并没有被学校____．结合句意可知此处意为“忽视”，故选D．（8） G．考查动词．句意：肥胖与学龄儿童较低的学业成绩____的证据开始在世界各地流行起来．结合句意可知此处意为“有关”，故选G．（9） C．考查副词．句意：研究发现，每周至少____运动3次会有益于您的大脑．结合句意可知此处意为“高强度地”，故选C．（10） F．考查名词．句意：创造性写作使大脑受益匪浅，因为这种活动不是机械性的，它会导致大脑产生新的____，从而刺激新的树突和神经元在大脑中生长．结合句意可知此处意为“化学物质”，故选F．III. Reading Comprehension（45分）Section A（15分）Directions： 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.A college degree is, in most cases, the key to more money and a more comfortable standard of living． But that pathway to higher earnings is more （1）_______ to some than others: A lot of leading colleges do not enroll a lot of low﹣income students, and as aresult, they’re not （2）_______very many students from low﹣income households into the middle and upper classes．（3）_______, though strategies for enrolling and preserving low﹣income students are usually mentioned, they can be tough to （4）_______ at scale．Dozens of top colleges and universities have more students from the top 1 percent of the income scale than the （5）_______ 60 percent．And that’s a problem if colleges hope to escape the common （6）_______that they are little more than a finishing school for the elite （精英）．But there are institutions ﹣ a lot of them ﹣ that have strong track records of （7）_______ the socioeconomic fortunes of students． If higher education is supposed to be the great equalizer （平衡器）, these institutions ﹣ from community colleges to public regional four﹣year colleges ﹣ are the ones that are doing the most work．Colleges should be （8）_______ recruiting and enrolling low﹣income students ﹣ and that means more than targeting ads to （9）_______ students on social media． It means a commitment to going where they are ﹣ areas that a lot of schools do not typically recruit ﹣and publicize the process of going to college． Then they should be supporting students with （10）_______ when the students get to campus ﹣whether it’s writingcenters, generous financial aid packages, or simply sympathetic academic advisors who perhaps came from low﹣income backgrounds themselves． And it is also preparing students for jobs after college and building relationships with businesses that （11）_______ the process of finding post﹣graduation employment for students, especially for those whose parents don’t have their own professional （12）_______．Pace ranks first among private colleges in motivating its students from the lowest levels of the income scale and into the middle and upper class． There are a lot of ways in which people of privilege （特权）（13）_______ their college years or having unpaid internships （实习） or having the social capital to get certain jobs． But colleges can fill those （14）_______, particularly for low﹣income students, helping students get jobs, or sustaining them with programs that help them land paid internships with top companies． We can provide strong networks through faculty and staff as well to help a new generation, a new, socioeconomically （15）_______ generation, achieve the American dream．（1）A.significantB.necessaryC.availableD.realistic（2）A.evaluatingB.urgingC.refusingD.promoting（3）A.HoweverB.What’s moreC.By contrastD.On the whole（4）A.implementB.replaceC.overcomeD.track（5）A.minimumB.bottomC.mediumD.optimum（6）A.criticismmentC.practiceD.suspicion（7）A.worseningB.claimingC.improvingD.denying（8）A.directlyB.strictlyC.activelyD.cautiously（9）A.urbanB.nativeC.suburbanD.prospective（10）A.resourcesB.coachesC.skillsD.funds（11）A.pushB.easeC.slowD.affect（12）A.trainingsB.careersC.standardsworks（13）A.benefit fromB.invest inC.fit intoD.advance through（14）A.vacanciesB.gapsC.bottomsD.blanks（15）petitiveB.responsibleC.diverseD.dynamic【答案】CDBABACCDABDAC【考点】社会文化【解析】本文属于说明文阅读，作者通过这篇文章主要向我们描述了大学学位是获得更多金钱和更舒适生活水平的关键，但也并不绝对，当然提升教育是重要的．【解答】（1）C．考查形容词辨析．A． significant 重要的；B． necessary必要的；C． available 可用；D． realistic 现实的；但这条通往更高收入的途径对一些人来说更为有效：故选C（2）D．考查动词辨析．A． evaluating评估；B． urging 催促；C． refusing 拒绝；D． promoting 促进；很多名牌大学招收的低收入学生并不多，因此，他们并没有把很多低收入家庭的学生提升到中上阶层．故选D（3）B．考查副词辨析．A． However然而；B．What’s more更重要的是；C． By contrast 相比之下；D． On the whole总的来说；更重要的是，尽管人们经常提到招收和保护低收入学生的策略，但这些策略很难大规模实施．故选B（4）A．考查名词辨析．A． implement具；B． replace替换；C． overcome 克服；D． track 轨道；更重要的是，尽管人们经常提到招收和保护低收入学生的策略，但这些策略很难大规模实施．故选A（5）B．考查名词辨析．A． minimum最小值；B． bottom底部；C． medium 中等；D． optimum 最佳；几十所顶尖高校中，收入排名前1%的学生多于收入排名后60%的学生．故选B（6）A．考查名词辨析．A． criticism批评；B． comment 评论；C． practice 练习；D． suspicion 怀疑；如果大学希望摆脱人们的普遍批评，即他们只不过是精英的补习学校，那就是一个问题．故选A（7）C．考查动词辨析．A．worsening恶化；B．claiming索赔；C．improving改善；D． denying 否认；但也有一些机构﹣﹣其中很多机构﹣﹣在改善学生社会经济财富方面有着良好的记录．故选C（8）C．考查副词辨析．A． directly直接；B． strictly严格地；C． actively 积极的；D． cautiously谨慎地；高校应积极招收低收入学生；故选C（9）D．考查形容词辨析．A． urban城市；B． native 本地的；C． suburban 郊区；D． prospective 预期的；这意味着不仅仅是在社交媒体上针对未来学生的广告．故选D （10）A．考查名词辨析．A． resources资源；B． coaches教练；C． skills技能；D． funds基金；然后，他们应该在学生进入校园时为他们提供资源支持﹣﹣无论是写作中心、慷慨的经济援助，还是仅仅是同情那些可能来自低收入家庭的学术顾问．故选A（11）B．考查动词辨析．A． push推；B． ease 放松；C． slow 慢；D． affect 影响；此外，它还帮助学生为大学毕业后的工作做好准备，并与企业建立关系，以简化求职过程；故选B（12）D．考查名词辨析．A． trainings培训；B． careers 职业；C． standards 标准；D． networks网络；学生毕业就业，尤其是那些父母没有自己的专业网络的学生．故选D（13）A．考查短语辨析．A． benefit from受益于；B． invest in投资；C． fit into 融入；D． advance through 前进通过；享有特权的人有很多方式可以从他们的大学生活中受益，或者有无薪实习，或者有社会资本来获得某些工作．故选A（14）B．考查名词辨析．A． vacancies空缺；B． gaps 差距；C． bottoms底部；D． blanks 空白；但大学可以填补这些空白，特别是对低收入学生来说，帮助学生找到工作，或者通过帮助他们获得顶级公司的带薪实习机会的项目来维持他们的就业．故选B（15）C．考查形容词辨析．A． competitive竞争性；B． responsible负责的；C． diverse 多样性；D． dynamic动态的；我们可以通过教职工提供强大的网络，帮助新一代、新一代、社会经济多元化的一代实现美国梦．故选CSection B（22分）Directions： 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 round face, big eyes, soft fur and a quiet purr．It’s not easy to resist the company of an adorable cat． No wonder French﹣German philosopher Albert Schweitzer oncesaid, “There are two means of refuge f rom the miseries of life: music and cats．”Indeed, it’s no secret how much people around the world love cats．From China’s Sina Weibo to US video﹣sharing site YouTube, bloggers across the globe love to show off their cats．In September, a chari table activity called “Cat Month” was held in Beijing． It was meant to encourage more people to care for our furry friends, especially ________ cats．Cats become such a big part of pop culture in China that young people have come up with cat﹣related slang phrases, such as “cat slave” to refer to people who adore their cats, and “a daily dose of cats” to refer to having to watch a certain number of cat videos to get through the day．People in Japan are also huge fans of cats． As the birthplace of Hello Kitty and the “beckoning cat”,Japan made a “cat train” that was ridden around the country by 30 stray cats in 2017． Passengers could sit and play with the cats on the train, offering the animals plenty of care and warmth．Istanbul, a historic city in Turkey, is also friendly to cats． In the recent documentary film Kedi, which hit Chinese cinemas in September, director Ceyda Torun showed us the daily lives of seven street cats with vivid narration． Cats there are not afraid of people． They go in and out of almost everywhere ﹣ coffee shops, markets, universities, and even government buildings． If you sit on a park bench, a cat is likely to come and snuggle with you．Seeing how cats have become a worldwide addiction, you may wonder why some people prefer cats over dogs． This may be down to how they identify with themselves ﹣ modern young people see the independent attitude of cats as something they value more．“Unlike dogs, who look at us with their loving eyes, cats appear to show off their independence． They ask for attention in a way that tells us that they desire human companionship, but they don’t need it,” author Marie﹣Louise von Franz wrote in her book The Cat: A Tale of Feminine Redemption．（1）What’s probably the best title of this passage？________A. Time to End LonelinessB. Lovely CatsC.Loving Dogs， Loving CatsD. Cat Slaves．（2）The word “________” in the third paragraph most probably means “________”．A.disabledB. caringC. homelessD. restless．（3）Which of the following is NOT true according to the passage？________A.Japanese offer their care and love to stray cats and used to have a cat train．B.Kedi， a documentary film， tells us daily lives of seven street cats with attractive narration．C.Many people want to show off their cats on websites such as Sina Weibo．D.There are many cat﹣related slang phrases that people come up with around the world．．（4）Why do many people become addicted to cats？________A.Because they look at us with their loving eyes．B.Because cats are independent and sometimes will show off their characters．C.Because they ask for attention in a way that tells us that they need human companionship．D.Because people prefer cats to dogs．【答案】ACDB【考点】议论文阅读日常生活类阅读【解析】本文属于说明文阅读，作者通过这篇文章主要向我们描述了与猫有关的故事和俚语和猫的陪伴对人的作用【解答】（1）A．细节理解题．根据文章第一段 No wonder French﹣German philosopher Albert Schweitzer once said，“There are two means of refuge from the miseries of life： musicand cats．”难怪法德哲学家阿尔伯特•施韦策曾经说过：“有两种逃避生活苦难的方法：音乐和猫．”可知这篇文章最好的标题是结束孤独的时间到了；故选A．（2）C．推理判断题．根据文章第三段 It was meant to encourage more people to carefor our furry friends， especially stray cats．这是为了鼓励更多的人关心我们毛茸茸的朋友，特别是流浪猫．可知意为无家可归的；故选C．（3）D．细节理解题．根据文章第三段Cats become such a big part of pop culture in China that young people have come up with cat﹣related slang phrases，such as “cat slave” to refer to people who adore their cats，猫在中国成为流行文化的一个重要组成部分，以至于年轻人想出了一些与猫有关的俚语，可知并不是世界各地都有许多与猫有关的俚语；故选D．（4）B．推理判断题．根据文章倒数第二段This may be down to how they identify with themselves ﹣ modern young people see the independent attitude of cats as something they value more．你可能会想，为什么有些人更喜欢猫而不是狗，这可能是因为他们如何认同自己﹣﹣现代年轻人认为猫的独立态度是他们更看重的东西．可知很多人对猫上瘾因为猫是独立的，有时会炫耀自己的性格；故选B．Movies Not to MissIn 2019 there will be returns to classic movie characters and stories． FILE PHOTOSIn 2018, to which we’ve just said goodbye,we’ve seen blockbusters such as Black Panther, Crazy Rich Asians and A Star Is Born． And there are more exciting movies in the works for 2019． Below TEENS has picked three for you．Let’s take a look．Spider﹣Man: Far From Home, July 5, USTom Holland, the lead actor of 2017’s Spider﹣Man: Homecoming, returns to play Peter Parker, a high school student who gains superpowers after being bitten by a spider．When we see him again in theaters, Spider﹣Man will have a new red﹣and﹣black suit． The movie will take the famous wall﹣crawler on a global adventure outside of the US． According to Marvel Studios President Kevin Feige, Spider﹣Man will try a return to his “normal” self; he will try to find his old powers on his new journey．Hobbs and Shaw, July 26, USTo most people the Fast and Furious series is all about crazy drivers racing in sports cars． But in its spin﹣off, called Hobbs and Shaw, humor is added to the action﹣packed thrills．The new film will hit US theaters on July 26． Famous robust English actor Jason Statham will star alongside Dwayne Johnson, “The Rock”, as Deckard Shaw and Luke Hobbs respectively, as in their previous appearances in Fast and Furious films．When the pair fought face to face in Fast and Furious 8 （2017）, a confrontation was dubbed the “battle model for warriors”． The action and chemistry really stimulated their audience．But the new action scenes between an MI6 agent Hobbs and the killer Shaw will have to be good to beat their stand﹣off in the 2017 movie．The Lion King, July 19, USThis is a brand﹣new version of the classic children’s film． The story of wide﹣eyed young lion Simba still remains in hearts of world audiences even after 25 years． In this re﹣telling, Simba again begins the difficult journey to become the King of the Pride Lands, a vast African prairie．The favorite part of the story for many has always been the friendship between Simba, the meerkat called Timon and the warthog Pumbaa． The last two sacrifice all they have to help Simba to his throne． How will the new movie re﹣imagine their famous relationship?（1）Where might this passage come from？________A.An report in a newspaper．B. A notice in the window of a cinema．C.A magazine about fashion．D. A advertisement distributed by a cinema．．（2）Which film is filled with adventure and humor？________A.Spider﹣Man： Far From HomeB. The Lion KingC. Hobbs and ShawD. The Fast and Furious．（3）Which of the following statement is true according to the article？________A.In Spider﹣man： Far From Home， Tom Holland， the lead director will return to play Peter Parker．B.In The Lion King wide﹣eyed young lion Simba eventually becomes the King of the Pride Lands， a vast African prairie．C.The new action scenes in Hobbs and Shaw is a confrontation which is dubbed the “battle model for warriors”．D.In 2019， there will be three classic movies to be released in the US in all．【答案】ACB【考点】广告布告类阅读说明文阅读【解析】本文属于说明文阅读，作者通过这篇文章主要向我们描述了一些2019年即将上演的精彩的电影．【解答】（1）A．细节理解题．根据文章第一段And there are more exciting movies in the works for 2019． Below TEENS has picked three for you．Let’s ta ke a look．2019年还有更多激动人心的电影在制作中．以下青少年为您挑选了三部．让我们来看看．可知文章最可能来自报纸上的报道；故选A．（2）C．推理判断题．根据文章第二部分 To most people the Fast and Furious series is all about crazy drivers racing in sports cars． But in its spin﹣off， called Hobbs and Shaw，humor is added to the action﹣packed thrills．对大多数人来说，《快速与激情》系列都是关于疯狂的赛车手在跑车上的比赛，但是在它的衍生产品《霍布斯与肖》中，幽默被加入到了充满动作的刺激中．可知电影 Hobbs and Shaw充满了冒险和幽默；故选C．（3）B．细节理解题．根据文章倒数第二段The story of wide﹣eyed young lion Simba still remains in hearts of world audiences even after 25 years． In this re﹣telling， Simba again begins the difficult journey to become the King of the Pride Lands， a vast African prairie．大眼睛小狮子辛巴的故事依然留在世界观众的心中，辛巴再次踏上了成为非洲大草原骄傲之王的艰难征程．可知在狮子王大眼睛的年轻狮子辛巴最终成为骄傲之地一个广阔的非洲大草原的国王；故选B．A radio report caught my attention the other day, as it spoke straight to my heart: Cadets （学员） at the US Naval Academy are now required to revisit and potentially revive the ancient skill of steering a ship by the stars．By the stars﹣imagine that: looking up at the sky, not down at a screen, so many years after the heavens’ critical role in guiding mariners has fallen by the wayside, first displaced by radio waves, then by modern GPS． Much is gained﹣but something also lost﹣in such progress, I think．It reminded me of my love of 18th﹣ and 19th﹣century seafaring （航海的） tales （reading them is one of my coping mechanisms for life in the landlocked Midwest）, when sailors had only celestial （天空的） maps for navigation and still miraculously managed to sail the planet’s vast oceans and even circum navigate the globe．Recent cyber security concerns have triggered renewed interest in backup navigational strategies such as stargazing, and simple hand﹣held technologies like the sextant, so often invoked in Richard Henry Dana’s Two Years Before the Mast, a tale that chronicles a mid﹣19th﹣century merchant ship’s endlessly harrowing voyage from Boston to California andback．I wouldn’t wish the harsh conditions of that trip on modern sailors, but I am all for anything that gets people clued in to their compass bearings （方位） and travel trajectories without high﹣tech and often mindless guidance．“Is that north or south of here? ” I’ve asked motel clerks and gas station attendants abouta particular address I’m seeking in my GPS﹣less travels．“Well,it’s that way,” comes the most frequent reply, accompanied by a pointedfinger, and I realize that north, south, east, and west are not familiar coordinates （坐标）to many people otherwise thoroughly attuned to the local lay of their land．To be fair, I haven’t always been attuned to compass points either． In fact it was not until I was a young adult, lazing on a float in my parents’ pool on a late summer’s visit home, and watching the sun dip below the roofline, that I first realized that my childhood home faced due west．I was shocked that I’d been ________ this simple fact,especially since I’d begun to be schooled in geology and certainly in compass work． But like so many, I’d grown up thinking and navigating in terms of other coordinates, based on familiar streets, rights and lefts, and reference points such as my school, the homes of friends, the nearest playground, and the local shopping plaza．I’ve long since become accustomed to finding my bearings on travels in unfamiliar territory by the sun’s position．And now I’d love to sit in on a class at the academy to learn to navigate by the moon and stars．It’s a skill I’ll likely never need to draw upon． Yet just knowing how it would connect me, in a new and profound way, to the historical arc of human experience on this planet．As for modern sailors, it might just bring them safely home one day, if all else fails．（1）What kind of role do 18th and 19th century seafaring tales play in the author’s life？________A.Enriching his dull inland life．B.Triggering his concern for cyber security．C.Arousing his interest in modern navigational strategies．D.Strengthening his resolve to revive an ancient skill．．（2）The author mentions his experience of seeking an address in paragraph 6 and 7 to illustrate________．A.The importance of modern technology such as GPS in travels．B.That it’s essential to learn geography and compass work well at work．C.That many people don’t navigate in terms of coordinates such as north and south．D.The convenience of navigating based on familiar streets， rights and lefts and reference points．．（3）The underlined phrase “oblivious to” in paragraph 8 is closest in meani ng to________．A.obvious toB. familiar withC. unconcerned aboutD. unaware of．（4）Why does the author plan to learn to navigate by the moon and stars？________A.Because he expects to experience the harsh conditions on the voyage in the past．B.Because he is required to revisit this ancient skill as a cadet at the U．S． Naval Academy．C.Because the skill can make his feel connected to the historical heritage of human beings．D.Because the skill can bring sailors home， safe and sound， if modern technology fails．【答案】ACDC【考点】议论文阅读社会文化类阅读【解析】这是一篇记叙文．主要记叙了作者能够根据太阳的位置在陌生的地域里寻找方向，以及作者计划学习通过月亮和星星导航，因为这种技能可以让他感到与人类的历史遗迹有联系．【解答】（1）A．细节理解题．根据第三段中It reminded me of my love of 18th and 19th century seafaring tales （reading them is oneof my coping mechanisms for uneventful life in the landlocked Midwest）（这让我想起了我对18、19世纪航海故事的热爱（阅读这些故事是我在内陆的中西部平淡生活的应对机制之一））可知18、19世纪的航海故事扮演者丰富作者沉闷的内陆生活的角色．故选A．（2）C．推理判断题．根据第七段中“Well，it’s that way，” comes the most frequent reply， accompanied by a pointed finger， andI realize that north， south， east， and west are not familiar coordinates to many people．（“嗯，是这样的，”是最常见的回答，并伴随着一根手指，我意识到，对许多人来说并不熟悉东西南北坐标．）可知作者在第6段和第7段中提到了他寻找地址的经历，以此来说明很多人并不是按照南北坐标来导航的．故选C．（3）D．词义猜测题．结合上文In fact it was not until I was a young adult， lying on a float in my parents’ pool on a latesummer’s visit home， and watching the sun set belowthe roofline， that I first realized that my childhood home faced duewest．可知事实上，直到作者年轻的时候，才第一次意识到儿时的家是正西方的．说明之前作者一直忽视了这个简单的事实，因此在意识到之后感到很震惊．故划线短语意思为“忽视”，故选D．（4）C．细节理解题．根据倒数第二段中And now I’d love to sit in on a dlass at the academy to learn to navigate by the moonand stars．It’s a skill I’ll probably never need to draw upon． Yet it feels good to know how it would connect me， in a new andprofound way， to the historical trace of human experience on this planet．（现在我想去学院上课，学习如何通过月亮和星星导航．这是一种我可能永远都不会用到的技能．然而，知道它将如何以一种全新而深刻的方式把我与人类在这个星球上的历史痕迹联系起来，让我感觉很好．）可知作者计划学习通过月亮和星星导航，因为这种技能可以让他感到与人类的历史遗迹有联系Section C（8分）Directions： Read the following passages. Fill in each blank witha proper sentence given in the box. Each sentence can be used only once. Notethat there are two more sentences than you need.Children born today may be the last generation to see coral reefs in all their glory． T hat’s a warning from a marine biologist who is coordinating efforts to monitor the decline of the world’s most colorful ecosystem．Global heating and ocean acidification（酸化） have already taken a heavy toll on the world’s coral reefs． Some 16 to 33 percent of all warm﹣water reefs have been severely bleached（漂白）， and the remaining reefs are vulnerable to even a fraction of a degree more warming， said the marine biologist， David Obura． He chairs the Coral Specialist Group in the International Union for the Conservation of Nature．“It will be like lots of lights blinking off，” he told the Observer． "（1）________Between now and 2 degrees Celsius， we will see more reefs dropping off the map．"Today’s reefs have a history going back 25 million to 50 million years． They have survived collisions between the Earth’s tectonic plates（地壳板块）， such as that of Africa into Europe， and India into Asia． Yet in five decades， Obura said， mankind has undermined the global climate so fundamentally that the globally connected reef system could be lost in the next generation．The warning follows a landmark UN climate report．（2）________Scientists warned thatif warming reached 2℃， which now appears very likely in the next 50 years， there would be a more than 99% chance that tropical coral reefs would be wiped out．（3）________The UN report also warned of severe knock﹣on impacts to fisheries and millions of people living in coastal communities， who will lose vital sources of income andbe less protected from storms．Coral reefs are often described as undersea forests， but they are declining far more quickly than the Amazon rainforests．（4）________ A temperature rise of just 1 to 2 degrees Celsius can cause the algae（藻类） upon which corals（珊瑚虫） depend to leave． That would drain the coral reefs of colour and make the structure more easily broken． These bleaching events can be temporary if waters cool， but the more frequent they are and the longer they last， the greater the risk of irreparable damage．【答案】B,D,E,C【考点】说明文七选五【解析】本文是一篇选句填空，文章主要介绍了今天出生的孩子可能是最后一代看到珊瑚礁的人．这是一位海洋生物学家发出的警告，他正在协调各方力量，监控世界上最丰富多彩的生态系统的衰退．【解答】1﹣4 BDEC1．B．细节理解题．根据前文“It will be like lots of lights blinking off，” he told the Observer就像很多灯在闪烁，“他告诉《观察家报》”．可知此处应填“它不会马上发生，。