江苏省常州市2023届高三上学期期中考试英语试题含答案

常州市2023-2024学年上学期期中学业水平监测高三数学注意事项：1．答卷前，考生务必将自己的姓名、考生号等填写在答题卡指定位置上．2．回答选择题时，选出每小题答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑如需改动，用橡皮擦干净后，再选涂其他答案标号．回答非选择题时，将答案写在答题卡上，写在本试卷上无效．3．考试结束后，将答题卡交回．一、单项选择题：本题共8小题，每小题5分，共40分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．已知集合{}310,1A x x B xx ⎧⎫=-≥=≤⎨⎬⎩⎭，则()RA B =ð（ ）A ．()1,3B ．(]1,3C ．[)1,3D ．[]1,32．i 是虚数单位，复数i1i+在复平面内的对应点位于（ ） A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限 3．函数()()22ln 1f x x x =-的部分图象为（ ）A ．B ．C ．D ．4．某学生社团举办数学史知识竞赛，经海选，甲、乙、丙、丁四位同学参加最后一轮的现场决赛，角逐唯一的冠军．有四位观赛同学对冠军的预测如下：“甲或乙是冠军”、“甲是冠军”、“丁是冠军”、“乙、丙两人都不是冠军”．若赛后发现，这四位同学中有且只有两位预测正确，则冠军是（ ） A ．甲 B ．乙 C ．丙 D ．丁 5．已知0,2πα⎛⎫∈ ⎪⎝⎭，且3cos2sin 1αα+=，则（ ） A ．()2sin 3πα-=B ．()2cos 3πα-=-C ．sin 2πα⎛⎫+=⎪⎝⎭ D ．cos 2πα⎛⎫+= ⎪⎝⎭6．已知四棱台1111ABCD A B C D -的两底面均为长方形，且上下底面中心的连线与底面垂直若119,6,3AB AD A B ===，棱台的体积为 ）A ．60B ．C ．60D ．60+7．已知函数()cos (0)f x x ωω=>，点,A B 分别为()f x 图象在y 轴右侧的第一个最高点和第一个最低点，O 为坐标原点，若OAB △为锐角三角形，则ω的取值范围为（ ）A ．⎛ ⎝⎭ В．⎫⎪⎝⎭ C ．()D ．⎫+∞⎪⎝⎭8.．居民的某疾病发病率为1%，现进行普查化验，医学研究表明，化验结果是可能存有误差的．已知患有该疾病的人其化验结果99%呈阳性，而没有患该疾病的人其化验结果1%呈阳性．现有某人的化验结果呈阳性，则他真的患该疾病的概率是（ ）A ．0.99B ．0.9C ．0.5D ．0.1二、多项选择题：本题共4小题，每小题5分，共20分．在每小题给出的选项中，有多项符合题目要求．全部选对的得5分，部分选对的得2分，有选错的得0分．9．已知函数()32f x x ax bx c =+++，且()()()31120f f f -<-==≤，则（ ） A ．2a =- B ．1b = C ．03c <≤ D ．12c -<≤10．某高校有在校学生9000人，其中男生4000人，女生5000人，为了解学生每天自主学习中国古典文学的时间，随机调查了40名男生和50名女生，其中每天自主学习中国古典文学的时间超过3小时的学生称为“古文迷”，否则为“非古文迷”，调查结果如下表，则（ ）参考公式：()()()()22()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++．参考数据：A ．该校某位学生为古文迷的概率的估计值为0.6B ．随机调查的男女生人数符合分层抽样的抽样方法C ．有99%的把握认为学生是否为“古文迷”与性别有关系D ．没有99%的把握认为学生是否为“古文迷”与性别有关系11．设ABC △内角,,A B C 所对的边为,,a b c ，则下列说法正确的有（ ） A ．若2sin sin sin A B C ⋅>，则3C π<B ．若sin sin 2sin A BC +>，则3C π<C ．若2C π>，则可能有444a b c += D ．若2C π<，则可能有112a b c +<12．已知AB 为圆柱的母线，BD 为圆柱底面圆的直径，且4AB BD O ==,为AD 的中点，点C 在底面圆周上运动（不与点,B D 重合），则（ ） A ．平面ABC ⊥平面OCDB ．当BC CD =时，点A 沿圆柱表面到点C C ．三棱锥D OBC -的体积最大值是163D ．AC 与平面ABD 所成角的正切值的最大值是12三、填空题：本题共4小题，每小题5分，共20分．13．将5本不同的书分发给4位同学，其中甲、乙两本书不能同时发给某一位同学，每位同学都发到书，每本书只能给一位同学，则不同的分配方案数为_________（用数字作答） 14．在提醒ABCD 中，已知,2,1,60AB DC AB AD BC ABC ===∠=︒∥，点,E F 分别在线段BC 和CD 上，则AE AF ⋅的最大值为_________． 15．若关于x 的方程ln 2xt x =-有两个不相等的实数根，则实数t 的取值范围是_________．16．在平面凸四边形ABCD 中，CB CD AB AD ===，且60,90B A D BCD ∠=︒∠=︒，将四边形ABCD 沿对角线BD 折起，使点A 到达点E 的位置．若二面角E BD C --的大小范围是5,36ππ⎡⎤⎢⎥⎣⎦，则三棱锥E BCD -的外接球表面积的取值范围是_________．四、解答题：本题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤．17．（10分）某校数学建模学生社团进行了一项实验研究，采集了x y 、的一组数据如下表所示：该社团对上述数据进行了分析，发现y 与x 之间具有线性相关关系．附：在线性回归方程y a bx =+中，1221ˆˆˆ,()niii nii x ynxybay bx xn x ==-==--∑∑，其中,x y 为样本平均值． （1）画出表中数据的散点图，并指出y 与x 之间的相关系数r 是正还是负； （2）求出y 关于x 的线性回归方程，并写出当9x =时，预测数据y 的值．18．（12分）已知ABC △中，90BAC ∠=︒，点,M N 在边BC 上，,AM AN 三等分BAC ∠，M 靠近,B N 靠近C ．（1）若2AN MN =，且4AB =，求BM ； （2）若11BC BM =，求BNBM． 19．（12分）已知函数()()2212ln ,2a f x x a x x a =+--∈R ． （1）讨论()f x 的单调性；（2）对于[][)1,e ,2,x b ∀∈∃∈+∞，使得()f x b ≥，求实数a 的取值范围．20．（12分）盒子里放着三张卡片，一张卡片两面都是红色，一张卡片两面都是黑色，剩下的一张卡片一面是红色一面是黑色．（1）随机抽出一张卡片并随机展示它一面的颜色．假设展示的这一面的颜色是红色，那么剩下一面的颜色也是红色的概率是多少？（2）随机抽出一张卡片并随机展示它一面的颜色，放回后，再随机抽出一张卡片并随机展示它一面的颜色．两次展示的颜色中，黑色的次数记为X ，求随机变量X 的分布和数学期望．21．（12分）已知三棱柱111ABC A B C -，2AB AC ==，111360AA A AB A AC BAC =∠=∠=∠=︒，,M N 为线段11,AC BA 上的点，且满足11(01)AM BNt t AC BA ==<<．（1）求证：MN ∥平面ABC ； （2）求证：1BB BC ⊥；（3）设平面MNA 平面ABC l =，已知二面角M l C --t 的值． 22．（12分）已知函数()()sin 0,02f x A x πωϕωϕ⎛⎫=+><<⎪⎝⎭的部分图象如图所示．将函数()f x 的图象向左平移6π个单位长度得到函数()g x 的图象，再将图象上所有点的横坐标伸长到原来的2倍（纵坐标不变），得到函数()h x 的图象．（1）求函数()f x 的解析式，并直接写出函数()(),g x h x 的解析式； （2）若()()2F x g x ah x π⎛⎫=++ ⎪⎝⎭在()()*0,n n π∈N 内恰有2023个零点，求实数a 与正整数n 的值．参考答案一、单项选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的．.1．【答案】C【解析】{}{}{}R 1,03,03A x x B x x x B x x =≥=<≥=≤<或ð，{}R 13A B x x =≤<ð，选C ．2．【答案】A【解析】()2i 1i i i i 1i 1i 222--+===+位于第一象限，选A ． 3．【答案】D【解析】()f x 为奇函数关于原点对称，排除BC ，12x <<时，()0f x <，排除A ，选D ． 4．【答案】D【解析】若甲是冠军，则三位预测正确，A 错． 若乙是冠军，则一位预测正确，B 错． 若丙是冠军，则没人预测正确，C 错． 若丁是冠军，则两人预测正确，D 对，选D ． 5．【答案】A【解析】3cos2sin 1αα+=，则()2312sinsin 1αα-+=，则()22sin sin 33απα=-=，A 对．()cos cos 3παα-=-=-，В错．sin cos 2παα⎛⎫+== ⎪⎝⎭，C 错，2cos sin 23παα⎛⎫+=-=- ⎪⎝⎭，D 错，选A ．6．【答案】D【解析】54S =上，326S =⨯=下，(15463V h =++=，h ∴=侧棱14AA ==，()11111393ABB A CDD C S S =+==， ()11111622ADD A BCC B S S =+⋅==，60S =+底D ． 7．【答案】B【解析】2,1,,1,A B AOB ππωω⎛⎫⎛⎫-⎪ ⎪⎝⎭⎝⎭△为锐角三角形，2220,10OA OB πω⋅>∴->，20,202AO AB πωω><⋅⋅∴+>恒成立；0BO BA ⋅>，2220πω∴-+>，2ω∴>，选B ． 8．【答案】C【解析】记“阳性”为A ，记“患病”为B ，()99%P A B =，()1%P B A =，()()()()1%99%1%P AB P AB P B P B ===，()99%1%P AB ∴=⨯，()()()1%99%1%P A P A P AB B =+=+⨯，()()()99%1%0.51%99%1%P AB P B A P A ⨯===+⨯， 选C ．二、多项选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合 题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分．9．【答案】AD【解析】()()()()112f x x x x m =+--+，30m -<≤，2c m =+，12c -<≤，D 对，C 错．112,2a a -++=-∴=-，A 对．()111212,1b b -⨯+-⨯+⨯=∴=-，B 错．本题考查知识点：三次函数韦达定理：()32f x ax bx cx d =+++有三个零点123,,x x x ，则123bx x x a++=-， 121323123,c dx x x x x x x x x a a++==-． 10．【答案】BC 【解析】6010.69000150=≠，A 错． 4000:500040:50=，B 对．2290(20102040)9 6.63560304050K ⨯-⨯==>⨯⨯⨯，C 对，D 错，选BC ．11．【答案】ABD【解析】2sin sin sin A B C >，则2ab c >，2222221cos ,22223a b c a b ab ab ab C C ab ab ab π+-+--=>≥=∴<，A对．sin sin 2sin ,2,2a bA B C a b c c ++>∴+><， ()2222222222()4424cos 228a b a b a b a ab b a b c C ab ab ab ++-+-+++-=>=22332621,8823a b ab ab ab C ab ab π+--=≥=∴<，B 对．2C π>，则2220a b c +-<，即222a b c +<，则442242a b a b c ++<与444a b c +>矛盾，C 错．2C π<，则222a b c +>，不妨设2,1a b c ===，则122+<，D 对．选ABD ．12．【答案】AB【解析】C 在以BD 为直径的圆上，CD CB ∴⊥，又,AB CD CD ⊥∴⊥面ABC ，∴面ABC ⊥面OCD ，A 对．BC CD =时，C 为半圆中点，展开后BC π=，min AC ∴=B 对．O 到面BCD 的距离为2，14242BCD S ≤⨯⨯=△，184233O BCD V -∴≤⨯⨯=，C 错． BD 为直径作EF BD ⊥为另一条直径，EF 为面ABD 的直径，以BD 中点建系，面ABD 的法向量的()1,0,0n =，()0,2,4A -，()4cos ,4sin ,0C θθ，()4cos ,4sin 2,4AC θθ=+-设AC 与面ABD 所成的角为α，sin cos ,16cos AC n α=〈〉====，[]4sin 9,5,13,sin t t θα⎡+=∈=⎢⎣，max 1sin 2α=，tan α最大值不是12，D 错，选AB ． 三、填空题：本题共4小题，每小题5分，共20分．13．【答案】216【解析】5本书送4人共有2454C A 240=，甲，乙送一人有44A 24=个结果，24024216-=． 14．【答案】3【解析】如图建系，()12,0,2B BM AN ==，32C ⎛∴ ⎝⎭，设13,,22E m m ⎛⎡⎤∈ ⎢⎥⎣⎦⎝⎭，令BF BC λ=，[]2,0,12F λλ⎛⎫-∈ ⎪⎝⎭， 3333322224424224m m AE AF m m m m λλλ⎛⎫⎛⎫⋅=-+=+-≤+-=+ ⎪ ⎪⎝⎭⎝⎭93344≤+=．15．【答案】()0,+∞【解析】()()()22122ln 1ln ln ,2(2)(2)x x x x x x f x f x x x x '----===---， ()()2222121ln ,0,2xg x x g x x x x x x-=--=-==='， ()g x 在()0,2，()2,+∞，()max ()211ln20g x g ==--<，()0f x ∴'<． ()f x ∴在()0,2，()2,+∞，01x <<时，()0f x >；2x >时，()0f x >；12x <<，()0f x <，()f x t ∴=有两个根0t ⇔>．16．【答案】1628,33ππ⎡⎤⎢⎥⎣⎦【解析】90,2CB CD BCD BD AB AD ==∠=︒∴===，利用双距离单交线公式，EBD △外心1O 到BD的距离123m =⨯⨯= BCD △的外心2O 到BD 的距离0,n E BD C =--交线2l BD ==，设二面角E BD C --平面角为θ，外接球半径为R ，22222212cos 531,,sin 4sin 36m n mn l R θππθθθ+-⎡⎤∴=+=+∈⎢⎥⎣⎦， 22147sin 1,433R θ∴≤≤∴≤≤， ∴三棱锥E BCD -外接球的表面积216284,33S R πππ⎡⎤=∈⎢⎥⎣⎦表． 应填：1628,33ππ⎡⎤⎢⎥⎣⎦注：第16题考得是进阶班第二讲外接球的公式，双距离单交线公式的运用．四、解答题：本题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤．17．【解析】（1）r 是负．（2）23456752.54540302517.54.5,3566x y ++++++++++==== 66211882.5,139ii i i i x y x ====∑∑ 61622216822.56 4.535ˆ71396 4.56ii i i i x y xy b xx ==--⨯⨯∴===--⨯-∑∑ˆˆ35(7) 4.566.5ay bx =-=--⨯=，∴关于x 线性回归方程为66.57y x =-当9x =时， 3.5y =．18．【解析】（1）30BAM MAN NAC ∠︒∠=∠==，在AMN △中，,2sin sin30AN MN AN MN AMN ==∠︒，sin 1,90,4sin302AMN AMN BM ∴∠=∴∠=︒∴=︒=．（2）设BM t =，1111BC BM t ∴==，故10CM t =，在ACM △中，由正弦定理()sin 90sin 60AM CM B ⇒=︒-︒10cos AM t B B ⇒==， 在ABM △中，由正弦定理2sin sin sin30AM BM AM t B B =⇒=︒⇒，2sin ,tan t B B =∴= 在AMN △中，()sin sin 30sin 120sin 30AM MN AM MN ANM B =⇒=∠︒︒-︒2013t MN ∴==， 20331313t t BN BM t +∴==． 19．【解析】（1）()()()()221212221ax a x ax x f x ax a x x x+---'+=+--==， ①当0a ≤时，()()0f x f x '<，在()0,+∞上；②当0a >时，令()10f x x a=⇒='． 且当10x a <<时，()()0,f x f x <'；当1x a >时，()()0,f x f x >'．（2）()min 2f x b ≥=对[]1,e x ∀∈恒成立．①当1a <时，()51122a f =-<，舍去． ②当1a ≥时，()()0f x f x '≥，在[]1,e 上，故只需()5611225a f a =-≥⇒≥符合． 综上：65a ≥． 20．【解析】（1）记事件A 为展示的一面颜色是红色，事件B 为剩下一面的颜色也是红色 ()()()()()11111,,33223P AB P B A P A P AB P A ∴==+⨯==， ()123132P B A ∴==． （2）随机抽出一张卡片，颜色是黑色的概率为()112P A -=， 12,2X B ⎛⎫∴~ ⎪⎝⎭的二项分布X 的所有可能取值为0，1，2 ()211024P X ⎛⎫=== ⎪⎝⎭，()212111C 22P X ⎛⎫=== ⎪⎝⎭，()124P X ==， X 的分布列如下：()11122E X =+=或由()1212E X nP ==⨯=． 21．【解析】（1）过,M N 分别作1ME CC ∥交AC 于点1,E NF A A ∥交AB 于点F ， 11ME AM CC AC ∴=且111111,,NF BN AM BN ME NF AA BA AC BA CC AA ==∴=， ME NF ∴∥，∴四边形MEFN 为平行四边形，MN EF MN ∴∴∥，∥平面ABC ．（2）11113,2,BB BC B C AC AB AC AB AA ===-=--， 2111144922222322313222B C ∴=++-⨯⨯⨯-⨯⨯⨯+⨯⨯⨯=， 1B C ∴=22211BB BC B C ∴+=，1BB BC ∴⊥．（3）取BC 中点D ，连接1,,A D AD ABC △为等边三角形且2AB =，AD ∴=在1A AB △中，1A B ==111,A AB A AC AC ∴=△≌△在1AAC △中，D 为BC 中点，1A D BC ∴⊥，1A D ∴== 222111,A D AD AAA D AD ∴+=∴⊥如图，分别以1,,DA DB DA 为,,x y z 轴建立空间直角坐标系．)()()((11,0,1,0,0,1,0,,A B C A C ∴--．()13,AM t AC M t =⇒--，又1BN tBA=，()0,1N t ∴-， ()()233,1,0,2,MN t AM t ∴=-=--，设平面AMN 的一个法向量(),,n x y z =，(101,30x y n ty ⎧-+=⎛⎫⎪∴⇒=- ⎪⎨⎝⎭⎪--+=⎩ 而平面ABC 的一个法向量()122120,0,1n n n n n ⋅==，3==，12t =或722． 22．【解析】（1）由图象知()f x 周期2,2T ππωπ=∴==，且52,12k k πϕπ⨯+=∈Z 5,0,,626k πππϕπϕϕ⎛⎫⇒=-∈∴= ⎪⎝⎭． 再由()()01sin 12,2sin 26f A A f x x πϕ⎛⎫=⇒=⇒=∴=+ ⎪⎝⎭， ()()2sin 22sin 22cos2,2cos 662g x x x x h x x πππ⎡⎤⎛⎫⎛⎫=++=+== ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎦． （2）()()22cos22cos 212sin 2sin 02F x x a x x a x π⎛⎫=+⋅=--= ⎪⎝⎭22sin sin 10x a x ⇒+-=令2sin ,210x t t at =∴+-=两根记为12,t t ，其中120t t <<， 作出sin y x =在()0,x n π∈上的大致图象如下：显然12,t t 中有一个为1-或1．①当11t =-时1a =，此时212t =，当n 为偶数时，1sin 2t =有n 个交点，sin 1t =-有2n 个交点，此时2023,2n n n +=∈Z 舍去． 当n 为奇数时，1sin 2t =有1n +个解，sin 1t =-有12n -个解，有3120232n n +=⇒∈Z ，舍去． ②当21t =时，1a =-，此时112t =-． 当n 为偶数时，sin 1t =有2n 个交点，1sin 2t =-有n 个交点，此时32023,2n n =∈Z 舍去． 当n 为奇数时，sin 1t =有12n +个解，1sin 2t =-有1n -个解． 11202313492n n n +∴+-=⇒=，故1,1349a n =-=．。

2023～2024学年度第一学期期中质量调研九年级英语试题2023.11（考试范围：至牛津初中英语9上Unit4）注意事项：1．本试卷共10页，满分100分。

考试时间90分钟。

2．请将答案全部填写在第8—10页的答题纸上，在1—7页上答题无效。

第一卷（共74分）一、听力（共20小题；每小题1分，满分20分）A）听下面10段对话。

每段对话后有1个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话读两遍。

1．What is the animal sign of the boyA．B．C．2．How does Tom learn about the worldA．B．C．3．What's David's problemA．B．C．4．What does the boy think of the storybookA．B．C．5．What does the man meanA．Someone else will take the seat. B．The woman can take the seat.C．The man will take the seat himself.6．What does Jack want to doA．Go riding. B．Go swimming. C．Watch TV.7．How much money does the woman haveA．12 yuan. B．10 yuan. C．2 yuan.8．How long does Peter do sports every dayA．For two hours. B．For an hour. C．For half an hour. 9．Where are they talkingA．In the school. B．In the hospital. C．In a restaurant. 10．How often does Daniel go to the English ClubA．Twice a week. B．Once a week. C．Twice a month.B）听对话或独白。

2023年秋学期高一期中质量调研英语试卷（答案在最后）第一部分听力(共两节，满分30分)第一节(共5小题：每小题1.5分，共7.5分)听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What is the woman selling?A.Her car.B.Her house.C.Her bicycle.2.Which group does the woman’s charity probably support?A.Children.B.Old people.C.Animals.3.Where did the man go yesterday?A.To a book shop.B.To an art museum.C.To a writers’meeting.4.What is the woman’s problem?A.She got a wrong e-mail.B.She took a wrong course.C.She couldn’t find her class.5.What is the man probably going to do next?A.Speak to the teacher.B.Lend the woman a pen.C.Borrow the woman’s note.第二节(共15小题：每小题1.5分，满分22.5分)听下面5段对话或独白。

每段对话或独白后有几个小题,从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟;听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，回答第6、7题。

6.Where does the conversation probably take place?A.On a busB.In a museum.C.In a supermarket.7.Why is the man lost?A.This city has changed a lot.B.It’s his first time visiting here.C.He takes different transport this time.听第7段材料,回答第8至10题。

2022-2023高三上英语期末模拟试卷注意事项：1．答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0．5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

3．请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效。

4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀。

第一部分（共20小题，每小题1.5分，满分30分）1．Sorry I’m s o late, but you cannot imagine ________ great trouble I took to find your house.A．which B．howC．what D．that2．Mr. Wilson is a man of patience and kindness, and his good temper never ______ him. A．fails B．disappointsC．controls D．worries3．—Do you really plan to drop out of the football team?—________ It’s time for me to concentrate on my study.A．I’m just kidding.B．Definitely not.C．I mean it D．What a pity!4．volleyball is her main focus, she is also great at basketball.A．Since B．OnceC．Unless D．While5．In fact，most of us would the consequences of stupid decisions taken by others.A．handle B．solve C．follow D．suffer6．The dining room is clean and tidy, with a table already ______for a big meal．A. being laid B．laying C．to lay D．laid7．This book is said to be the special one, which ________ many events that cannot be found in other history books.A．covers B．writesC．prints D．reads8．Owing to The Chinese Poetry Competition, publications on classical Chinese literature are __________ a significant share of storage space at the bookstore.A．taking up B．dividing up C．breaking up D．putting up9．----What happened to the young trees we planted last week？---The trees_____________ well，but I didn't water them.A．might grow B．needn't have grownC．would grow D．would have grown10．Sympathy for the rebels, the government claimed, is beginning to ______because of more and more harm they did to common people.A．fade B．decline C．fail D．collapse11．Sometimes, the kind of food we serve a person suggests ________ we show our gratitude.A．when B．whatC．why D．how12．—Tony _______ what I did annoying though he didn’t say anything.—So you think you will have to make an apology?A．could find B．should have foundC．might find D．must have found13．Frankly speaking, I am not sure whether I ________ this in the old days with that kind of equipment, which looks quite odd and ridiculous.A．should have done B．need have done C．would have done D．must have done14．Our boss is too strict with us. I can’t _____ in with the work situation here.A．fit B．get C．make D．take15．The artist is said during the production and thus a pirated video was sold in every part of Kenya.A．to be cheated B．being cheatedC．to have been cheated D．having been cheated16．Pele had bags of natural talent, but he ______ without the determination to deal with all the problems life threw in his path.A．would never succeed B．never succeededC．would never have succeeded D．have never succeeded17．Between the two generations, it is often not their age, _________ their education that causes misunderstanding.A．like B．as C．or D．but18．The wide spread of super hybrid rice around the world ______ the lives of millions and millions of people suffering from hunger to a great level.A．has improved B．is improving C．improved D．has been improving19．— I am just wondering which team, Chicago Bulls or Washington Wizards, won the game last night?—________ I don’t really like either team.A．Don’t mention it. B．No problem.C．Who cares? D．Why bother?20．________ and open to various interpretations, the terms of the new proposal need improving based on the interests of both sides.A．Accessible B．ApparentC．Ambiguous D．Aggressive第二部分阅读理解（满分40分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。

2023-2024学年第一学期常州市高三期中教学情况调研语文试题参考答案及评分建议一、现代文阅读（35分）（一）1．D（3分）2．B（3分）3．A（3分）4．指的是《阮玲玉》中三条叙事线不断在现实和虚拟之间转换，（1分）使所有叙述停留在知与不可知、信与不确信之间。

（2分）激发观众探求自己对人物及其经历的理解与判断。

（1分）5．比较《奥本海默》与《阮玲玉》的不同叙事策略（前者严丝合缝，灌输观众唯一权威解读，后者充满不确定性，鼓励观众怀疑和探究），突出诺兰在表现历史人物时的传统态度。

（3分）比较《奥本海默》与《奇幻核子战》对核爆危害的不同处理方式（前者对核辐射影像进行转述性展示，后者虚构核弹砸在纽约街头的画面），批评诺兰对历史灾难的回避态度。

（3分）（二）6．B（3分）（A项，两句话流露出的是鲁迅特有的悲观与自嘲；C项，由下文“有置身农贸市场的感觉”可知“衬托”错，应该是破坏了“庄严肃穆感”；D项，主要原因是我认为大陆新村的管理者没有真正尽到保护故居和宣传鲁迅精神的责任） 7．A（3分）（“轻快”不准确，作者的心情是崇敬与追怀）8．①营造萧瑟、清冷的氛围，衬托我对鲁迅先生的追思和哀悼，增强文章的感染力；②风声“海潮般的轰鸣”，象征鲁迅先生与黑暗斗争、启蒙大众、震撼人心的一生；③风吹走“我”献给鲁迅先生的玉兰叶，寓示鲁迅先生不务虚名的冷峻孤高；④隐喻鲁迅先生在不同时代声誉和评价的起落，暗示“我”的立场和态度。

（4分，答出一点给2分。

其他合理答案酌情给分）9．“真正的郁积”是指鲁迅先生心中对中国人、中国社会的忧思与批判。

（3分）阐述举例：①虚伪冷酷的鲁四老爷、赵太爷等人物，体现了鲁迅对辛亥革命前后依旧顽固猖狂的封建势力的痛恨；②勤劳驯顺的祥林嫂和自欺欺人的阿Q，寄寓了鲁迅对底层民众充满奴性、愚昧麻木的“国民性”的忧思；③《祝福》中面对现实徘徊、逃避的“我”，表现了启蒙者在自我困境中的彷徨和苦闷。

（3分。

2023～2024学年度江苏省常州市第二学期期初调研高三年级英语试题考试时间：120分钟试题总分：150分注意事项1.答题前，考生务必将自己的姓名、准考证号、班级、学校在答题卡上填写清楚。

2.每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号。

在试卷上作答无效。

3.考试结束后，请将答题卡交回，试卷自行保存。

满分150分，考试用时120分钟。

第一部分听力（共两节，满分30分）略第二部分阅读（共两节，满分50分）第一节（共15小题；每小题2.5分，满分37.5分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项。

AThe State of Colorado has four of the best parks out of the 58 national parks in the United States. The parks have some of the best scenery of all the national parks.Black Canyon (峡谷) of Gunnison National ParkThis park offers the most breathtaking views from up in the mountains into the canyons below. While exploring the canyons, you will find thatthe walls drop nearly straight down into the narrow valleys of the snake-like rivers below. Visitors are offered more than 100 camping sites, and a lot of bird species and many animals are native to the area. Rocky Mountain National ParkIt is the only national park in the north central region in the state of Colorado. Elevations in this park are anywhere from 8,000 feet to 14,259 feet at the top of Longs Peak. While traveling throughout this park you will notice two very different climates because of the difference the upper peaks of the Rocky Mountains make. You can enjoy 359 miles of hiking trails, a lot of places for camping, horse-back riding and beautiful scenery.Mesa Verde National ParkThis is probably the most interesting national park, offering a fascinating trip back in time to 600 AD up to 1300 AD．This park was declared a protected national park in 1906 because of the cliff dwellings(住所) that were found throughout the area, which were once home to American Indians. Many of these dwellings can be walked through, while you imagine what each room may have been used for so many years ago. Great Sand Dunes (沙丘) National ParkThe Great Sand Dunes National Park lies in south central Colorado, about 127 miles from Pueblo. This park has the tallest sand dunes in all of North America and has trails for hiking. The natural sandy beachesaround the small rivers and lakes are good for swimmers. 21．What’s the most breathtaking thing in the Black Canyon of Gunnison National ParkA．The animals. B．The walls.C．The hiking trails. D．The camping sites.22．If you are interested in history, you are advised to visit________. A．the Mesa Verde National ParkB．the Rocky Mountain National ParkC．the Great Sand Dunes National ParkD．the Black Canyon of Gunnison National Park23．What’s the author’s purpose in writing this passageA．Telling people some traveling information in Colorado. B．Persuading people to visit Colorado when in America. C．Introducing the best four parks in Colorado to people. D．Showing people which park is the best of the four in Colorado.BGoffin’s cockatoos, a kind of small parrot native to Australasi a, have been shown to have similar shape-recognition abilities to a humantwo-year-old. Though not known to use tools in the wild, the birds have proved skilful at tool use while kept in the cage. In a recent experiment, cockatoos were presented with a box with a nut inside it. The clear front of the box had a “keyhole” in a geometric shape, and the birds weregiven five differently shaped “keys” to choose from. Inserting the correct “key” would let out the nut.In humans, babies can put a round shape in a round hole from around one year of age, but it will be another year before they are able to do the same with less symmetrical (对称的) shapes. This ability to recognize that a shape will need to be turned in a specific direction before it will fit is called a n “allocentric frame of reference”. In the experiment, Goffin’s cockatoos were able to select the right tool for the job, in most cases, by visual recognition alone. Where trial-and-error was used, the cockatoos did better than monkeys in similar tests. Th is indicates that Goffin’s cockatoos do indeed possess an allocentric frame of reference when moving objects in space, similar to two-year-old babies.The next step, according to the researchers, is to try and work out whether the cockatoos rely entirely on visual clues (线索), or also use a sense of touch in making their shape selections.24. How did the cockatoos get the nut from the box in the experimentA. By following instructions.B. By using a tool.C. By turning the box around.D. By removing the lid.25. Which task can human one-year-olds most likely complete according to the textA. Using a key to unlock a door.B. Telling parrots from other birds.C. Putting a ball into a round hole.D. Grouping toys of different shapes.26. What does the follow-up test aim to find out about the cockatoosA. How far they are able to see.B. How they track moving objects.C. Whether they are smarter than monkeys.D. Whether they use a sense of touch in the test.27. Which can be a suitable title for the textA. Cockatoos: Quick Error CheckersB. Cockatoos: Independent LearnersC. Cockatoos: Clever Signal-ReadersD. Cockatoos: Skillful Shape-Sorters CCherie Burns is author of Diving for Starfish—The Jeweler, The Actress, The Heiress and One of the World’s Most Alluring Pieces of Jewelry, a stylish detective story with a piece of glittering French vintage jewelry at its heart was published by St. Martin’s Press on February 27, 2018. Her previous book, Searching for Beauty—The Life of Millicent Rogers was the first comprehensive biography of Standard Oil heiress and fashion icon Millicent Rogers. It is now also available from St Martin’s Griffin softcover under the slightly amended title, Searching for Beauty — The Life of Millicent Rogers, the American Heiress Who Taught the World About Style.The author’s previous book, The Great Hurricane: 1938, was published by Grove/Atlantic (2005) in soft and hardcover. Jonathan Yardley of The Washington Post wrote: “Her own very good book is sure to help keepthe terrible storm in it s proper place in New England’s memory...”, and Liz Smith wrote in her column in The Daily News that the book was “A must if you care about brilliant reporting...” “Before there was the Perfect Storm, there was the Great Hurricane of 1938. Cherie Bums’ new book is not only a riveting and wonderfully written account of one of the worst storms of the century, it is a marvelous portrait of an era and a region. A must for all New Englanders and lovers of the sea,” said National Book Award winner Nathaniel Philbrick, author of Sea of Glory. Burns’ first book, Stepmotherhood—How to Survive Without Feeling Frustrated, Left Out or Wicked (Times Books) has been reprinted by HarperCollins and Three Rivers and has sold over 40,000 copies in the U. S., England and Germany. It has remained in print for 20 years. Ms. Burns’ work has also appeared in The New York Times Magazine, People, Glamour, New York, Sports Illustrated, The Wall Street Journal and other publications. She currently lives in Taos, New Mexico. See more about the author and the above titles at www..28．How many books does this article mentionA．2 B．3 C．4 D．529．Where can you probably find this articleA．A book-selling website B．A science magazineC．A travel brochure D．A book review30．Which word can replace the underlined word “amended” in thearticleA．official B．improved C．various D．orderly31．What is the article mainly aboutA．The author Cherie Burns and her books. B．The book review about Diving for Starfish.C．The information about Cherie Burns’ books. D．A promotion for Cherie Burns’ new books.DWhen New York City asked residents to stay home due to the pandemic, Jesse Means figured he wasn’t going to have any visitors anytime soon, so he might as well turn his living room into a studio.Means, a Broadway actor turned elementary school music teacher, uses that studio to record weekly lessons that he said seek to not only educate but uplift and encourage. “My job is teaching, but my ultimate work is building up people and making sure their spirits are all right,” he said. “I became the modern-day Mr. Rogers, as some have referred to me.”Mr. Means Music, his YouTube series, teaches rhythm, songs and vocabulary, but also includes assignments like asking students to write down something kind they did recently or a fond memory with a parent. And because his lessons are public, he said he’s received fan mails from as far as the United Kingdom and Kenya. “These little kids really need tohave some normalcy(常态),” he said. “They’re used to seeing specific faces eve ry day, mine being one of them.”While Means said he works almost straight through every weekend on new 10-to 20-minute episodes, he said seeing video reactions showing strengthened bonds between parent and child has made the extra work worthwhile. One father, for example, regularly submitted videos of his daughter, sitting alone and responding to Means’ weekly questions. Halfway through the school year, the videos changed. “There was this very burly (魁梧的) man who is now in the video with his daughtersingi ng ‘the bell on the buoy goes ding ding ding!’ and touching his nose,” Means said. “You can see how much he loves his daughter. That’s what keeps me going in those moments when I can barely keep my eyes open.”32．Why did Means start his series on the Internet during the pandemic A．To remember his days at Broadway. B．To become famous and popular online.C．To cheer people up by teaching music. D．To follow Mr. Rogers’ path to success.33．What is a special feature of Means’ music seriesA．It requires learners to share their lives. B．It shows specific faces on a daily basis.C．It aims to attract kids in foreign countries. D．It is specially designed for pupils in New York.34．How does Means feel about his work on the seriesA．It is funny and attractive. B．It is boring and needs improvement. C．It is tiring and demanding. D．It is meaningful and worth the effort. 35．According to the last paragraph, what does Means’ series remind people ofA．Connection with friends. B．Importance of music. C．Enthusiasm for their careers. D．Love for their family.第二节（共5小题；每小题2.5分，满分12.5分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。

2023-2024学年江苏省常州市前黄高级中学高三（上）期中数学试卷一、选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中只有一项是符合题目要求. 1．已知集合P ＝{y |y ＝x +1，x ∈R }，Q ＝{y |y ＝1﹣x ，x ∈R }，则P ∩Q ＝（ ） A ．∅B ．{1}C ．{（0，1）}D ．R2．已知i 是虚数单位，设复数z 满足（i ﹣1）z ＝|1+√3i |+3i ，则z 的共轭复数对应的点位于（ ） A ．第一象限B ．第二象限C ．第三象限D ．第四象限3．已知sin （π3−α）=14，则sin （π6−2α）＝（ ） A ．78B ．−78C ．±78D ．−184．设a →，b →是两个单位向量，若a →+b →在b →上的投影向量为23b →，则cos〈a →，b →〉=（ ） A ．−13B ．13C ．−2√23D ．2√235．为进一步在全市掀起全民健身热潮，兴义市于9月10日在万峰林举办半程马拉松比赛．已知本次比赛设有4个服务点，现将6名志愿者分配到4个服务点，要求每位志愿者都要到一个服务点服务，每个服务点都要安排志愿者，且最后一个服务点至少安排2名志愿者，有（ ）种分配方式 A ．540B ．660C ．980D ．12006．在△ABC 中，“tan B tan C ＞1”是“△ABC 为锐角三角形”的（ ） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件D ．既不充分也不必要条件7．设实数t ＞0，若不等式e 2tx −ln2+lnxt≥0对x ＞0恒成立，则t 的取值范围为（ ） A ．[12e，+∞) B ．[1e，+∞) C ．(0，1e]D ．(0，12e] 8．水平桌面上放置了4个半径为2的小球，4个小球的球心构成正方形，且相邻的两个小球相切．若用一个半球形的容器罩住四个小球，则半球形容器内壁的半径的最小值为（ ） A ．4B ．2√2+2C ．2√3+2D ．6二、选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分.9．已知事件A ，B 满足P （A ）＝0.5，P （B ）＝0.2，则（ ） A ．若B ⊆A ，则P （AB ）＝0.5B ．若A 与B 互斥，则P （A +B ）＝0.7C．若A与B相互独立，则P(AB)=0.9D．若P（B|A）＝0.2，则A与B相互独立10．如图，在正方体ABCD﹣A1B1C1D1中，E、F、G分别为BC、CC1、BB1的中点，则（）A．A1C⊥AB1B．A1B与AD1所成角为60°C．D1D⊥AF D．A1G∥平面AEF11．已知函数f（x）＝sin（cos x）+cos（sin x），则（）A．f（x）是奇函数B．f（x）的最大值大于√2C．∀x∈R，f（x﹣2π）＝f（x）D．∀x∈[0，π]，f（x+π）＞012．已知函数f（x）及其导函数f′（x）的定义域均为R，记g（x）＝f′（x）．若f（x）满足f（2x）＝f （2﹣2x），g（x+1）的图象关于直线x＝﹣1对称，且g（0）＝1，则（）A．g（1）＝0B．f（x）为奇函数C．g（x）＝g（x+4）D．∑2023k=1g(k2)=−1三、填空题：本题共4小题，每小题5分，共20分.13．若两个正实数x，y满足4x+y﹣xy＝0，且不等式xy≥m2﹣6m恒成立，则实数m的取值范围是．14．在锐角三角形ABC，AB＝2，且1tanA +1tanB=4tanC，则AB边上的中线长为．15．已知函数f(x)=xe x，过点（0，a）可作曲线f（x）的3条切线，则实数a的取值范围为．16．已知x0是函数f(x)=2a√x+b−e x2的一个零点，且x0∈[14，e]，则a2+b2的最小值为．四、解答题：本题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤.17．（10分）已知函数f(x)=2√3cos2(π2+x)−2sin(π+x)cosx−√3．（1）求f（x）的最小正周期和单调增区间；（2）若f(x0−π6)=1425，x0∈[3π4，π]，求sin2x0的值．18．（12分）已知函数f（x）＝x+1x−2．（1）若不等式f（2x）﹣k•2x≥0在x∈[﹣1，1]上恒成立，求实数k的取值范围；（2）若关于x的方程f（|2x﹣1|）+k•2|2x−1|−3k＝0有三个不同的实数解，求实数k的取值范围．19．（12分）如图，平面五边形ABCDE中，△ADE是边长为2的等边三角形，CD∥AE，CD＝AE，∠BAD=∠ABC=π2，将△ADE沿AD翻折，使点E翻折到点P．（Ⅰ）证明：PC⊥BC；（Ⅱ）若PC＝3，求直线PB与平面PCD所成角的正弦值．20．（12分）在△ABC中，角A，B，C所对的边分别为a，b，c，且√3bsin B+C2=asinB，边BC上有一动点D．（1）当D为边BC中点时，若AD=√3，b=2，求c的长度；（2）当AD为∠BAC的平分线时，若a＝4，求AD的最大值．21．（12分）为了解某市区高中学生的阅读时间，从该市区随机抽取了800名学生进行调查，得到了这800名学生一周的平均阅读时间（单位：小时），并将样本数据分成九组，绘制成如图所示的频率分布直方图．（1）求a的值；（2）为进一步了解这800名学生阅读时间的分配情况，从周平均阅读时间在（12，14]，（14，16]，（16，18]三组内的学生中，采用分层抽样的方法抽取了10人，现从这10人中随机抽取3人，记周平均阅读时间在（14，16]内的学生人数为X，求X的分布列和数学期望；（3）以样本的频率估计概率，从该市区学生周平均阅读时间在（8，14]内中随机抽取20名学生．这20名学生中，周平均阅读时间在（10，12]内的学生最可能有多少名？22．（12分）设a∈R，函数f（x）＝ax﹣1+e x的图象与直线2x﹣y＝0相切，其中e是自然对数的底数．（1）求实数a的值；（2）当x∈[0，π2)时，f（x）≥m sin2x恒成立，求实数m的取值范围．2023-2024学年江苏省常州市前黄高级中学高三（上）期中数学试卷参考答案与试题解析一、选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中只有一项是符合题目要求. 1．已知集合P ＝{y |y ＝x +1，x ∈R }，Q ＝{y |y ＝1﹣x ，x ∈R }，则P ∩Q ＝（ ） A ．∅B ．{1}C ．{（0，1）}D ．R解：x ∈R 时y ＝x +1∈R ，所以集合P ＝{y |y ∈R }，同理可得Q ＝{y |y ∈R }，故P ∩Q ＝R ． 故选：D ．2．已知i 是虚数单位，设复数z 满足（i ﹣1）z ＝|1+√3i |+3i ，则z 的共轭复数对应的点位于（ ） A ．第一象限B ．第二象限C ．第三象限D ．第四象限解：（i ﹣1）z ＝|1+√3i |+3i ＝2+3i ，则z =2+3i−1+i =(2+3i)(−1−i)(−1−i)(−1+i)=12−52i ，z =12+52i ， 故z 的共轭复数对应的点（12，52）位于第一象限．故选：A ．3．已知sin （π3−α）=14，则sin （π6−2α）＝（ ）A ．78B ．−78C ．±78D ．−18解：因为sin （π3−α）＝cos[π2−（π3−α）]＝cos （π6+α）=14，所以sin （π6−2α）＝cos[π2−（π6−2α）]＝cos2（π6+α）＝2cos 2（π6+α）﹣1＝2×（14）2﹣1=−78．故选：B ．4．设a →，b →是两个单位向量，若a →+b →在b →上的投影向量为23b →，则cos〈a →，b →〉=（ ）A ．−13B ．13C ．−2√23D ．2√23解：∵a →+b →在b →上的投影向量为23b →，∴(a →+b →)⋅b →|b →|⋅b→|b →|=23b →，∴a →⋅b →=−13， ∵|a →|=|b →|=1，∴由向量的夹角公式可知，cos〈a →，b →〉=a →⋅b→|a →||b →|=−13．故选：A ．5．为进一步在全市掀起全民健身热潮，兴义市于9月10日在万峰林举办半程马拉松比赛．已知本次比赛设有4个服务点，现将6名志愿者分配到4个服务点，要求每位志愿者都要到一个服务点服务，每个服务点都要安排志愿者，且最后一个服务点至少安排2名志愿者，有（ ）种分配方式 A ．540B ．660C ．980D ．1200解：根据题意，最后一个服务区有2名志愿者或3名志愿者， 分2种情况讨论：①最后一个服务区有2名志愿者，先为最后一个服务区选择2名志愿者，再将剩下4人分为3组，安排到前3个服务区即可，有C 62⋅C 42C 21C 11A 22A 33=540种安排方法；②最后一个服务区有3名志愿者，先为最后一个服务区选择3名志愿者，剩下3人全排列，安排到前3个服务器即可，有C 63C 31C 21C 11=120种安排方法，共有540+120＝660种安排方法． 故选：B ．6．在△ABC 中，“tan B tan C ＞1”是“△ABC 为锐角三角形”的（ ） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件D ．既不充分也不必要条件解：∵tan B tan C ＞1＞0，∴B 、C 为锐角，∴tan B ＞0，tan C ＞0， ∴tan （π﹣A ）＝tan （B +C ）=tanB+tanC1−tanBtanC ＜0 ∴tan A ＞0，∴A 为锐角，∴△ABC 为锐角三角形； ∵△ABC 为锐角三角形，∴A 、B 、C 为锐角， ∴B +C 为钝角，tan （B +C ）＜0，∴tanB+tanC 1−tanBtanC ＜0，∵tan B ＞0，tan C ＞0，∴1﹣tan B tan C ＜0， ∴tan B tan C ＞1．∴“tan B tan C ＞1”是“△ABC 为锐角三角形”的充要条件． 故选：C ．7．设实数t ＞0，若不等式e 2tx −ln2+lnxt≥0对x ＞0恒成立，则t 的取值范围为（ ） A ．[12e，+∞) B ．[1e，+∞) C ．(0，1e]D ．(0，12e] 解：e 2tx −ln2+lnx t≥0对x ＞0恒成立，即te 2tx ≥ln 2x ，即2txe 2tx ≥2xln 2x ＝ln 2x •e ln 2x， 令F （x ）＝xe x （x ＞0），则F '（x ）＝（x +1）e x ＞0， 故F （x ）在（0，+∞）单调递增，故2tx ＞ln 2x ，故t ≥ln2x 2x ，问题转化为t ≥(ln2x2x )max， 令H(m)=lnmm ，H ′(m)=1−lnmm 2，令H '（m ）＞0，解得0＜m ＜e ，令H '（m ）＜0，解得m ＞e ， 故H （m ）在（0，e ）单调递增，在（e ，+∞）单调递减， 故H （m ）max ＝H （e ）=1e ，故t ≥1e ． 故选：B ．8．水平桌面上放置了4个半径为2的小球，4个小球的球心构成正方形，且相邻的两个小球相切．若用一个半球形的容器罩住四个小球，则半球形容器内壁的半径的最小值为（ ） A ．4B ．2√2+2C ．2√3+2D ．6解：要使半球形容器内壁的半径的最小，只需保证小球与18球各面（含球面部分）都相切，此时，如上图示，O 为半球的球心，A 为其中一个小球球心，则OA 是棱长为2的正方体的体对角线，且该小球与半球球面上的切点与O ，A 共线，所以半球形容器内壁的半径的最小值为小球半径与OA 长度之和，即2√3+2， 故选：C ．二、选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分.9．已知事件A ，B 满足P （A ）＝0.5，P （B ）＝0.2，则（ ） A ．若B ⊆A ，则P （AB ）＝0.5B ．若A 与B 互斥，则P （A +B ）＝0.7C ．若A 与B 相互独立，则P(AB)=0.9D ．若P （B |A ）＝0.2，则A 与B 相互独立解：对于A ，因为P （A ）＝0.5，P （B ）＝0.2，B ⊆A ，所以P （AB ）＝P （B ）＝0.2，故A 错误； 对于B ，因为A 与B 互斥，所以P （A +B ）＝P （A ）+P （B ）＝0.5+0.2＝0.7，故B 正确；对于C ，因为P （B ）＝0.2，所以P(B)=1−0.2=0.8，所以P(AB)=0.5×0.8=0.4，故C 错误； 对于D ，因为P （B |A ）＝0.2，即P(AB)P(A)=0.2，所以P(AB)=0.2×P(A)=0.1，又因为P(A)×P(B)=0.5×0.2=0.1， 所以P(AB)=P(A)⋅P(B)， 所以A 与B 相互独立，故D 正确． 故选：BD ．10．如图，在正方体ABCD ﹣A 1B 1C 1D 1中，E 、F 、G 分别为BC 、CC 1、BB 1的中点，则（ ）A ．A 1C ⊥AB 1 B ．A 1B 与AD 1所成角为60°C ．D 1D ⊥AFD ．A 1G ∥平面AEF解：以点D 为坐标原点，DA 、DC 、DD 1所在直线分别为x 、y 、z 轴建立如图所示的空间直角坐标系，设正方体ABCD ﹣A 1B 1C 1D 1的棱长为2，则A （2，0，0）、B （2，2，0）、C （0，2，0）、D （0，0，0）、E （1，2，0）、F （0，2，1）、G （2，2，1）、A 1（2，0，2）、B 1（2，2，2）、C 1（0，2，2）、D 1（0，0，2）．对于A ，AB 1→=(0，2，2)，A 1C →=(−2，2，−2)，AB 1→⋅A 1C →=4−4=0，所以A 1C ⊥AB 1，故A 正确；对于B ，A 1B →=(0，2，−2)，AD 1→=(−2，0，2)，cos〈A 1B →，AD 1→〉=A 1B →⋅AD 1→|A 1B →|⋅|AD 1→|=−422×22=−12，所以A 1B 与AD 1所成角为60°，故B 正确；对于C ，DD 1→=(0，0，2)，AF →=(−2，2，1)，则DD 1→⋅AF →=2≠0，故C 错误； 对于D ，设平面AEF 的法向量为m →=(x ，y ，z)，AE →=(−1，2，0)，EF →=(−1，0，1)， 则{m →⋅AE →=−x +2y =0m →⋅EF →=−x +z =0，取x ＝2，可得m →=(2，1，2)， 又A 1G →=(0，2，−1)，∵m →⋅A 1G →=2−2=0，∴m →⊥A 1G →，∵A 1G ⊄平面AEF ，∴A 1G ∥平面AEF ，故D 正确． 故选：ABD ．11．已知函数f （x ）＝sin （cos x ）+cos （sin x ），则（ ） A ．f （x ）是奇函数B ．f （x ）的最大值大于√2C ．∀x ∈R ，f （x ﹣2π）＝f （x ）D ．∀x ∈[0，π]，f （x +π）＞0解：f （x ）的定义域为R ，f （0）＝sin1+cos0＝sin1+1≠0，故选项A 错误；f （x ﹣2π）＝sin （cos （x ﹣2π））+cos （sin （x ﹣2π））＝sin （cos x ）+cos （sin x ）＝f （x ），故选项C 正确； f(0)=sin(cos0)+cos(sin0)=sin1+cos0=sin1+1＞√22+1＞√2，故选项B 正确；f （x +π）＝sin （cos （x +π））+cos （sin （x +π））＝sin （﹣cos x ）+cos （﹣sin x ）＝﹣sin （cos x ）+cos （sin x ）， ∵cosx +|sinx|≤√2＜π2，∴cosx ＜π2−|sinx|，当x ∈[0，π]时，cos x ∈[﹣1，1]，π2−|sinx|∈[π2−1，π2]，而y ＝sin x 在[−π2，π2]上单调递增， ∴sin(cosx)＜sin(π2−|sinx|)=cos(sinx)， ∴当x ∈[0，π]时，f （x +π）＞0，故选项D 正确， 故选：BCD ．12．已知函数f （x ）及其导函数f ′（x ）的定义域均为R ，记g （x ）＝f ′（x ）．若f （x ）满足f （2x ）＝f （2﹣2x ），g （x +1）的图象关于直线x ＝﹣1对称，且g （0）＝1，则（ ） A ．g （1）＝0B ．f （x ）为奇函数C ．g （x ）＝g （x +4）D ．∑ 2023k=1g(k2)=−1解：由f （2x ）＝f （2﹣2x ），得f （x ）＝f （2﹣x ），等式两边同时求导，得f ′（x ）＝﹣f ′（2﹣x ）， 即g （x ）+g （2﹣x ）＝0，故g （x ）的图象关于点（1，0）对称，故A 正确； 因为g （x +1）的图象关于直线x ＝﹣1对称，故g （x ）的图象关于直线x ＝0对称，即g （x ）为偶函数，则g （x ）＝g （﹣x ），所以f （x ）应满足f （x ）＝﹣f （﹣x ）+C （C 为常数）， 当C ≠0时，f （x ）不是奇函数，故B 错误；因为g （x ）＝g （﹣x ），g （x ）+g （2﹣x ）＝0，所以g （x ）＝g （x +4），故C 正确；因为g （x ）的图象关于点（1，0）对称，关于y 轴对称，且g （0）＝1，所以g （2）＝﹣1，g （3）＝0，g （4）＝1，在一个周期内，g （4）＝0，所以g （1012）＝﹣g （1012）＝﹣g （0）＝﹣1，故D 正确． 故选：ACD ．三、填空题：本题共4小题，每小题5分，共20分.13．若两个正实数x ，y 满足4x +y ﹣xy ＝0，且不等式xy ≥m 2﹣6m 恒成立，则实数m 的取值范围是 [﹣2，8] ．解：因为两个正实数x ，y 满足4x +y ﹣xy ＝0，所以xy ＝4x +y ≥2√4xy =4√xy ，当且仅当y ＝4x 且4x +y ﹣xy ＝0，即x ＝2，y ＝8时取等号， 所以xy ≥16，因为不等式xy ≥m 2﹣6m 恒成立， 所以m 2﹣6m ≤16，解得﹣2≤m ≤8． 故答案为：[﹣2，8]．14．在锐角三角形ABC ，AB ＝2，且1tanA+1tanB=4tanC，则AB 边上的中线长为 √2 ．解：三角形中，由1tanA+1tanB=4tanC ，可得cosA sinA+cosB sinB=4cosC sinC ，再由正弦定理和余弦定理可得：b 2+c 2−a 22abc +a 2+c 2−b 22abc=4(a 2+b 2−c 2)2abc，整理可得：a 2+b 2=32c 2，由余弦定理可得c 2＝a 2+b 2﹣2ab cos C ，可得2ab cos C ＝a 2+b 2﹣c 2=12c 2，设AB 边的中线CD ，则CD →=12（CB →+CA →），所以|CD →|2=14（CB →2+CA →2+2CB →•CA →）=14（a 2+b 2+2ab cos C ）=14（32c 2+12c 2）=12c 2，而c ＝AB ＝2，所以|CD |=√12×22=√2．故答案为：√2．15．已知函数f(x)=xe x ，过点（0，a ）可作曲线f （x ）的3条切线，则实数a 的取值范围为 (0，4e 2) ． 解：由f(x)=x e x ，得f ′（x ）=e x −xe x e 2x=1−xe x ，设切点为（t ，tet ），则过切点的切线方程为y −t e t =1−tet (x −t)， 把（0，a ）代入，可得a =t 2e t ，令g （t ）=t 2e t ，则g ′（t ）=t(2−t)e t，则当t ∈（﹣∞，0），（2，+∞）时，g （t ）单调递减，当t ∈（0，2）时，g （t ）单调递增， 又g （0）＝0，g （2）=4e 2， ∴要使过点（0，a ）可作曲线f （x ）的3条切线，则实数a 的取值范围为(0，4e 2)． 故答案为：(0，4e 2)． 16．已知x 0是函数f(x)=2a √x +b −e x 2的一个零点，且x 0∈[14，e ]，则a 2+b 2的最小值为e 344．解：由已知可得2a √x 0+b −e x 02=0，x 0∈[14，e ]，不妨设直线l ：2√x 0x +y −e x 02=0，则点A （a ，b ）是直线l 上的一点，原点O 到直线l 的距离d =e x 02√0，则|OA |=√a 2+b 2≥d =e x 02√0=√e x 04x 0+1，设g （x ）=e x4x+1，x ∈[14，e ]， g ′（x ）=(4x−3)e x (4x+1)2=0，得x =34，当14≤x ＜34时，g ′（x ）＜0，当34＜x ＜e 时，g ′（x ）＞0， ∴g （x ）在（14，34）上单调递减，在（34，e ）上单调递增，∴g （x ）min ＝g （34）=e 344，∴a 2+b 2的最小值为e 344．故答案为：e 344．四、解答题：本题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤. 17．（10分）已知函数f(x)=2√3cos 2(π2+x)−2sin(π+x)cosx −√3． （1）求f （x ）的最小正周期和单调增区间；（2）若f(x 0−π6)=1425，x 0∈[3π4，π]，求sin2x 0的值． 解：（1）f(x)=2√3[cos(π2+x)]2−2sin(π+x)⋅cosx −√3 =2√3sin 2x +2sinx ⋅cosx −√3=√3(1−cos2x)+sin2x −√3 =sin2x −√3cos2x =2sin(2x −π3)， 故周期为T =2π2=π， 令−π2+2kπ≤2x −π3≤π2+2kπ，k ∈Z ， −π12+kπ≤x ≤5π12+kπ，k ∈Z ， 所以f （x ）的增区间为[−π12+kπ，5π12+kπ]，k ∈Z ． （2）∵f(x 0−π6)=2sin[2(x 0−π6)−π3]=2sin(2x 0−2π3)=1425， ∴sin(2x 0−2π3)=725，∵3π4≤x 0≤π，∴5π6≤2x 0−2π3≤4π3， ∴cos(2x 0−2π3)=−√1−sin 2(2x 0−2π3)=−2425， 故sin2x 0=sin[(2x 0−2π3)+2π3] =sin(2x 0−2π3)cos 2π3+cos(2x 0−2π3)sin 2π3 =725×(−12)−2425×√32=−24√3+750． 18．（12分）已知函数f （x ）＝x +1x −2．（1）若不等式f （2x ）﹣k •2x ≥0在x ∈[﹣1，1]上恒成立，求实数k 的取值范围； （2）若关于x 的方程f （|2x﹣1|）+k •2|2x −1|−3k ＝0有三个不同的实数解，求实数k 的取值范围．解：（1）令t =2x ∈[12，2]，原不等式即为：t +1t −2−kt ≥0，t ∈[12，2]恒成立． 即k ≤1t 2−2t+1=(1t −1)2，t ∈[12，2]恒成立，易知，当t ＝1时，1t 2−2t+1取得最小值0，故k ≤0即为所求．（2）令t ＝|2x ﹣1|＞0，则原方程可化为：t +1t−2+2kt−3k =0，（t ＞0）， 整理得t 2﹣（2+3k ）t +2k +1＝0……（*），t ＞0，设方程（*）的根为t ，则由t ＝|2x ﹣1|，该方程的根为y ＝t 与y ＝|2x ﹣1|交点的横坐标．同一坐标系做出它们的图象：当y ＝t 在位置①时，有一个交点；当位于位置②时，有两个交点．所以要使原方程有三个根，只需一元二次方程（*）在（0，1）和[1，+∞）各有一个根． 令g （t ）＝t 2﹣（2+3k ）t +2k +1＝0，t ＞0，由题意得{g(0)＞0g(1)＜0，即{2k +1＞01−(2+3k)+2k +1＜0，解得k ＞0；特别的，当g （1）＝0时，k ＝0，此时方程（*）只有一个根1，不符合题意．综上可知，当k ＞0时，原方程有三个不同的实数解．19．（12分）如图，平面五边形ABCDE 中，△ADE 是边长为2的等边三角形，CD ∥AE ，CD ＝AE ，∠BAD =∠ABC =π2，将△ADE 沿AD 翻折，使点E 翻折到点P ．（Ⅰ）证明：PC ⊥BC ；（Ⅱ）若PC ＝3，求直线PB 与平面PCD 所成角的正弦值．解：（Ⅰ）证明：在平面图形中取AD 中点O ，连接OC ，OE ，∵△ADE是边长为2的等边三角形，∴OE⊥AD，OD＝1，故翻折后有OP⊥AD，又∵CD∥AE，∴∠CDO＝∠DAE=π3，∵CD＝AE＝2，∴OC⊥AD，且PO∩OC＝O，∴AD⊥平面POC，∵∠BAD=∠ABC=π2，∴AD∥BC，∴BC⊥平面POC，∵PC⊂平面POC，∴PC⊥BC；（Ⅱ）由（Ⅰ）得OP⊥AD，OC⊥AD，∴二面角P﹣AD﹣B的平面角为∠POC，在△POC中，OC＝OP=√3，PC＝3，由余弦定理得cos∠POC=−12，∴∠POC=2π3，二面角P﹣AD﹣B的大小是2π3，在平面POC内作OM⊥OC，交PC于M，∵AD⊥平面POC，∴以O为坐标原点，OA所在直线为x轴，OC所在直线为y轴，OM所在直线为z轴，建立空间直角坐标系，由（Ⅰ）得四边形OABC为矩形，∵∠POC=2π3，OP=√3，∴A （1，0，0），D （﹣1，0，0），B （1，√3，0），C （0，√3，0），P （0，−√32，32），∴PB →=（1，3√32，−32），PC →=（0，3√32，−32），DC →=（1，√3，0），设平面PCD 的法向量n →=（x ，y ，z ），则{n →⋅PC →=3√32y −32z =0n →⋅DC →=x +√3y =0，取y ＝1，得n →=（−√3，1，√3）， 设直线PB 与平面PCD 所成角为θ，则直线PB 与平面PCD 所成角的正弦值为：sin θ=|PB →⋅n →||PB →|⋅|n →|=√310⋅7=√21070．20．（12分）在△ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，且√3bsin B+C2=asinB ，边BC 上有一动点D ．（1）当D 为边BC 中点时，若AD =√3，b =2，求c 的长度； （2）当AD 为∠BAC 的平分线时，若a ＝4，求AD 的最大值． 解：（1）因为√3bsinB+C2=asinB ， 所以√3bsin π−A2=asinB ，即√3bcos A2=asinB ．由正弦定理，得√3sinB ⋅cos A2=sinA ⋅sinB ．因为sin B ≠0，所以√3cos A2=sinA =2sin A2cos A 2．因为cos A2≠0， 所以sinA 2=√32． 又因为0＜A 2＜π2， 所以A2=π3，所以A =2π3． 因为D 为边BC 中点，所以2AD →=AB →+AC →，则4|AD →|2=(AB →+AC →)2． 又AD =√3，b =2，A =2π3，所以12=c 2+4+4c ⋅cos2π3， 即c 2﹣2c ﹣8＝0，即（c ﹣4）（c +2）＝0， 所以c ＝4．（2）在△ABC 中，由余弦定理，得a 2＝b 2+c 2﹣2bc •cos ∠BAC ． 又a =4，∠BAC =2π3， 所以16＝b 2+c 2+bc ，所以16=(b +c)2−bc ≥(b +c)2−(b+c)24=34(b +c)2，当且仅当b ＝c 时取等号，所以(b +c)2≤643， 所以4＜b +c ≤8√33．因为S △ABC ＝S △ABD +S △ACD ，AD 平分∠BAC ，∠BAC =2π3， 所以12bc ⋅sin2π3=12b ⋅AD ⋅sinπ3+12c ⋅AD ⋅sin π3，所以bc ＝AD •（b +c ），所以AD =bc b+c =(b+c)2−16b+c =b +c −16b+c．令t ＝b +c ，则AD =t −16t ，4＜t ≤8√33． 因为y =t −16t 在(4，8√33]上单调递增， 所以当t =8√33即b =c =4√33时，y 取得最大值为2√33， 所以AD 的最大值为2√33． 21．（12分）为了解某市区高中学生的阅读时间，从该市区随机抽取了800名学生进行调查，得到了这800名学生一周的平均阅读时间（单位：小时），并将样本数据分成九组，绘制成如图所示的频率分布直方图．（1）求a的值；（2）为进一步了解这800名学生阅读时间的分配情况，从周平均阅读时间在（12，14]，（14，16]，（16，18]三组内的学生中，采用分层抽样的方法抽取了10人，现从这10人中随机抽取3人，记周平均阅读时间在（14，16]内的学生人数为X，求X的分布列和数学期望；（3）以样本的频率估计概率，从该市区学生周平均阅读时间在（8，14]内中随机抽取20名学生．这20名学生中，周平均阅读时间在（10，12]内的学生最可能有多少名？解：（1）由（0.02+0.03+0.05+0.05+0.15+a+0.05+0.04+0.01）×2＝1可得a＝0.1．（2）由频率分布直方图可得：周平均阅读时间在（12，14]，（14，16]，（16，18]三组的频率之比为0.05：0.04：0.01＝5：4：1，∴10人中，周平均阅读时间在（12，14]的人数为10×510=5人，在（14，16]的人数为10×410=4人，在（16，18]的人数为10×110=1人，则X所有可能的取值为0，1，2，3，∴P(X=0)=C63C103=20120=16，P(X=1)=C62C41C103=60120=12，P(X=2)=C61C42C103=36120=310，P(X=3)=C43C103=4120=130，∴X的分布列为：∴E(X)=0×16+1×12+2×310+3×130=65．（3）用频率估计概率，从该地区学生周平均阅读时间在（8，14]内中随机抽取20名学生，周平均阅读时间在（10，12]内的概率p=0.20.3+0.2+0.1=13，设周平均阅读时间在（10，12]内的学生有k 名， 则P(k)=C 20k p k (1−p)20−k=C 20k×(13)k ×(23)20−k =C 20k 220−k320，所以P(k+1)P(k)=C 20k+1219−k 320C 20k 220−k 320=12×20!(k+1)!(19−k)!20!k!(20−k)!=12×20−k k+1=12(−1+21k+1)，令P(k+1)P(k)=12(−1+21k+1)≥1，解得k ≤6，所以当k ＝6或k ＝7，P （k ）最大，所以，周平均阅读时间在（10，12]内的学生最可能有6名或7名．22．（12分）设a ∈R ，函数f （x ）＝ax ﹣1+e x 的图象与直线2x ﹣y ＝0相切，其中e 是自然对数的底数． （1）求实数a 的值；（2）当x ∈[0，π2)时，f （x ）≥m sin2x 恒成立，求实数m 的取值范围． 解：（1）由f （x ）＝ax ﹣1+e x ，得f ′（x ）＝a +e x ， 设切点为（x 0，y 0）， 则{a +e x 0=2ax 0−1+e x 0=2x 0， 消去a 得e x 0(x 0−1)+1=0，令g （x ）＝e x （x ﹣1）+1，g ′（x ）＝e x x ， 当x ＜0时，g ′（x ）＝e x x ＜0，g （x ）单调递减， 当x ＞0时，g ′（x ）＝e x x ＞0，g （x ）单调递增，所以g （x ）在（﹣∞，0）上单调递减，在（0，+∞）上单调递增， 且g （0）＝0，当x ≠0时，g （x ）＞0， 所以若g （x 0）＝0，则x 0＝0， 所以a ＝1；（2）由（1）得f （x ）＝x ﹣1+e x ，f （0）＝0， 且f ′（x ）＝1+e x ＞0，所以函数f （x ）在[0，π2)单调递增， 所以f （x ）≥f （0）＝0，对于当x ∈[0，π2)时，f （x ）≥m sin2x 恒成立，当m≤0时，m sin2x≤0，所以f（x）≥m sin2x恒成立；若当x∈[0，π2)时，f（x）≥m sin2x恒成立，则h（x）＝f（x）﹣m sin2x＝x﹣1+e x﹣m sin2x≥0在x∈[0，π2)恒成立，h′（x）＝1+e x﹣2m cos2x，x∈[0，π2)，当0＜m≤1时，x∈[0，π2)，h′（x）＝1+e x﹣2m cos2x≥1+e x﹣2m≥2﹣2m≥0，所以h（x）在x∈[0，π2)上单调递增，所以h（x）≥h（0）＝0，成立；当m＞1时，设F（x）＝1+e x﹣2m cos2x，x∈[0，π2 )，F′（x）＝e x+2m sin2x＞0在x∈[0，π2)上恒成立，所以h′（x）＝F（x）在[0，π2)上单调递增，因为h′（0）＝2﹣2m＜0，ℎ′(π4)=1+eπ4＞0，所以∃x1∈(0，π4)，使h′（x1）＝0，所以x∈（0，x1）时，h′（x）＜0，h（x）单调递减，x∈(x1，π2)时，h′（x）＞0，h（x）单调递增，所以当x∈（0，x1）时，h（x）＜h（0）＝0，即f（x）≤m sin2x，与题设矛盾，综上所述：m∈（﹣∞，1]．。

2024-2025常州市正衡中学七年级上学期英语期中模拟试卷(7AU1-4) (2024.10)一、单词辩音（共4小题,每小题0.5分,满分2分）1. A. else B. enjoy C. tennis D. seldom2. A. thank B. English C. ant D. uncle3. A. juice B. music C. student D. usually4. A. term B. dinner C. her D. girl二、单项填空（共10小题,每小题1分,满分10分）5. My grandfather is ________ old man, but he likes playing ________ football very much.A. an; / B, an; the C. a; / D. a; the6. November 11 is coming. Suzy, ________ other girls, ________ shopping on Taobao.A. like; likesB. likes; likesC. likes; likeD. like; like7. --- Do you ________ the game called "Black Myth—WuKong"?--- Yes, but I don’t think everyone enjoys __________ it.A. watch; to playB. watch: playingC. look; playingD. look; to play8. I don't know how to ________ this word in English because I know ________ English.A. speak, only a littleB. say, only a littleC. speak, littleD. say, few9. --- ________ Mr Wang your teacher? --- Yes. He teaches ________ English.A. Is; youB. Does; ourC. Is; usD. Does; we10. The girl ________ glasses is our new classmate ________ from Shanghai.A. wears; comesB. with; comesC. wears; /D. with; /11. What ________ do you know about Mary?A. otherB. elseC. other'sD. others12. Shenzhou-16 was sent up into space ________ the morning of May 30 2023.A. inB. onC. atD. from13. I can't ________ early on weekdays. I think I need an alarm clock on my bedside table.A. give upB. get upC. put upD. stand up14. I hope you _________ fun learning English this term.A. to haveB. havingC. to havingD. will have三、完形填空（共10小题,每小题1分,满分10分）Jimmy loves games and he plays games every day. He likes all kinds of games like card games and sports games. Andhis favourite is winning ___15___. For Jimmy, winning is the happiest thing.Today Jimmy has a ___16___ game at school. He is in the blue team. When the game ___17___, Jimmy runs very fast. With bad luck, his leg hurts badly halfway. ___18___ he doesn't want to slow down. He says to himself, "I must win."Jimmy falls over ___19___. Many pairs of ___20___ run past him, but one pair stops."Come on! Let's finish together," says a boy. Jimmy looks ___21___. He is a big boy from the red team. The boy helps Jimmy ___21___ and they finish the game together. "___23___ do you help me?" Jimmy asks the boy. "You should help your red team win."The boy says, "Well, sometimes winning isn’t the most important thing. I just want to be a ___24___ boy first." Jimmy thinks and doesn't say anything. The boy teaches Jimmy a good lesson through the game.15. A. it B. them C. him D. that16. A. running B. jumping C. walking D. dancing17. A. shows B. finishes C. starts D. stops18. A. or B. but C. because D. so19. A. again B. just C. too D. soon20. A. eyes B. hands C. arms D. feet21. A. up B. down C. around D. behind22. A. hurry up B. pick up C. stand up D. get up23. A. How B. Why C. When D. Where24. A. nice B. right C. happy D. true四、阅读理解（共10小题,每小题1.5分,满分15分）ADavid lives in a small city. It’s a Monday morning. His boss Mr. Brown says to him, “David, I want you to go to London to see my friend. Here is the address (地址).”David goes to London by train. He goes out of the station and thinks, “The hospital is near the station. I can find it easily.” But after an hour, David is still looking for the hospital. He stops and asks an old woman. The woman says, “Go down Green Street, turn left at the end, and you will find it on your right.” David thanks her and soon he finds the hospital. It’s old but beautiful.A week later, David goes to London again, but again he can’t find that hospital. So he asks someone the way. He asks an old woman, too. It is the same woman! She is very surprised and asks, “Are you still looking for that place?”25. Why does David go to London?A. Find a job.B. Visit London.C. See the doctor.D. See his boss’s friend.26. Which of the following is the right place of the hospital?A. B. C. D.27. What does the underlined words “that place” in the last paragraph refer to?A. LondonB. the hospitalC. the small cityD. the train stationBWhen Mark Wellman was a 12-year-old boy, he began climbing mountains. He enjoyed outdoor activities very much and climbed many mountains. But in 1982 when Wellman was climbing a difficult mountain in North America he fell down from the mountain. He was only 21 at that time. After that, he couldn’t feel his legs and couldn’t walk. However, he didn’t give up his hobby. Seven years later, he got to the top of El Capitan—a famous mountain in Yosemite National Park.Wellman is still a mountain climber. He often takes part in different mountain climbing activities. Nothing can stop him, not even losing his legs.Wellman took part in two Paralympic Games(残奥会). He wrote his own story in a book called Climbing Back. The book gives hope and courage to thousands of people who cannot walk.Now, Mark Wellman lives in California and he has a company called “No Limits”. He often travels around America and gives speeches about his story. He talks to all kinds of people and he is warmly welcome. Wellman often tells his listeners that they can overcome any problems to make their dreams come true if they never give up. Everything is possible if you try your best to do it.28. When did Mark Wellman begin climbing mountains?A. When he was 11 years old.B. At the age of 21.C. In 1982.D. In 1973.29. What’s the correct order of the following events?① Mark Wellman wrote a book called Climbing Back.② Mark Wellman got to the top of El Capitan in Yosemite National Park.③ Mark Wellman climbed a difficult mountain in North America.④ Mark Wellman has a company called “No Limits”A. ③②①④B. ③②④①C. ②③①④D. ②①③④30. What’s the main idea of this passage?A. We should have a hobby and never give it up.B. Outdoor activities can make people healthier.C. Climbing mountains is exciting but dangerous.D. We should give hope and courage to healthy mountain climbers.C“What’s your favourite sport, Mike?” Ms. Smith asks.Nrok thinks for a moment. Everyone in the class is looking at him. He is nervous. He needs a good answer. “I like football.” Everyone smiles. A few students say, “I like football, too!”That is a safe answer. Mike really likes ice hockey, but no one else in the class likes it. He wishes he can be honest, but he worries about what they will say. They will say things like, “Ice hockey? Why?” or “What is that?” They don’t know about it.Mike comes from Maryland. All the kids there like hockey. But here in Florida, kids love football. He doesn’t really understand why they don’t like hockey.He asks his dad when he gets home. “Why don’t the kids here like ice hockey?”His dad smiles. “Their families grow up watching football. They like football. We grow up watching hockey, so we like hockey.”“They are so similar.”“Why don’t you invite some kids to the next game?” Dad asks. “We will take them with us.”Mike does that. He asks his friends Dave and Tommy. They do not know about ice hockey. They never watch a hockey game before. They are excited to see.At the game, they have hot dogs and cola. They watch the game. Dave and Tommy ask Mike many questions about the rules and the teams. They watch with great interest. All of them have fun.The next time at school when Ms. Smith asks Mike what his favourite sport is, he says, “Ice hockey.”Dave and Tommy smile and say, “We like hockey, too!”Mike is happy. He likes it when other people like the things he likes. He has friends who understand him.31. Which is the right order according to the story?①Mike is nervous in class. ② Mike is asking his dad for help.③ Mike's friends say they like hockey too. ④ Mike invites friends to watch the game.A. ④-②-③-①B. ④-③-②-①C. ①-③-②-④D. ①-②-④-③32. How do Dave and Tommy feel after watching the hockey game?A. Sad.B. Nervous.C. Happy.D. Angry.33. Why doesn’t Mike tell his true feeling at first?A. Because he likes football better than ice hockey.B. Because he is afraid other students don’t like him.C. Because he thinks football is a very popular sport.D. Because he thinks nobody likes football in his class.34. What’s the best title of the passage?A. A kind fatherB. A popular sportC. Mike and his friendsD. Mike’s favourite sport五、阅读下面短文,从短文后所给的六个选项中选出四个可以填入空白处的最佳选项。

2023年江苏省常州市中考英语模拟试卷（一）一、单选题（本大题共10小题，共10.0分）1. — Have you got________ticket to the second China international import Expo，Lisa？— Not yet.It is_______pity that I missed the chance.（ ）A. a；/B. the；/C. a：aD. the；a2. To spread our traditional culture，many teenagers came up with new .For example，Suansuan，a college student，has posted over 50 videos on Bilibili to show her love for our culture.（ ）A. methodsB. messagesC. meaningsD. medicines3. — Why did you buy such a small shelf？_______books_______shoes can be put on it.—But my blind boxes can，I guess.（ ）A. Both；andB. Neither；norC. Either；orD. Not only；but also4. —Is there anything special in today's newspaper？—Yes.The elevator in a tall flat went wrong and got trapped_______the floors.（ ）A. amongB. throughC. betweenD. across5. 一Hi，Jack!Surprised to see you here!一My father is here on a business trip.My family this city for 2 weeks.（ ）A. have gone toB. have been toC. have left forD. have been in6. Nowadays you are supposed not to miss taking your temperature_______you enter the school because of the spring flu.（ ）A. unlessB. untilC. afterD. before7. —Who_______be responsible（负责的）for this traffic accident？—It's not the right time to discuss that._______，we should send her to hospital.（ ）A. should；Above allB. must；In allC. can；At allD. may；Of all8. Mike only ________ work that excites him，even if it means turning down a lot of money.（ ）A. takes offB. takes onC. takes outD. takes up9. 一Though things are going smoothly now，I'm still in doubt .一Whatever the result is，don't be too hard on yourself.（ ）A. why are my parents strict with meB. if I can get high marks in the entrance examsC. how have I prepared for my entrance examsD. that I can enter my ideal senior high finally10. There is a famous old saying" ".Similarly，you may realize your dream only when you alwayswork hard.（ ）A. Many hands make light work.B. Great hope makes great man.C. Life is not all roses.D. No pain，no gain.二、完形填空（本大题共12小题，共12.0分）Every culture has set rules about how people should act.Ways of good behavior，or manners，show respect and care for others.Yet the details of（1）______ to express respect are so different.Greeting people（2）______ is almost always considered polite.But it's more important in some cultures than（3）______ .For example，when you enter a store in France，you should always greet the person working there.Other cultures also pay attention to greeting people.But of course the greetings are different as people speak different languages.When I was growing up in the United States，I once took part in a performance at my church.Afterwards，someone gave me compliment（恭维），but I felt like I had done a bad job.So I tried to（4）______ the compliment，saying "No，I didn't do that well."My mother stopped me and told me that was very （5）______ Later I learned that refusing a compliment is accepted in China.Some of the biggest cultural differences have to do with（6）______ .In North America，it's polite to eat as quietly as possible.That means chewing（咀嚼）with your mouth（7）______ and not slurping your soup.The same goes for burping（打嗝）.But in parts of Asia，slurping shows that you are enjoying your meal.And burping is a（8）______ of being full and content.There are also differences in how people eat across cultures.（9）______ ，in North America and Europe people use forks to bring food to their mouths.But in Thailand，a fork is only used to（10）______ food onto a spoon.In India and the Middle East，people eat with their hands.But eating with the left hand is frowned upon.This is because the left hand is considered（11）______ .Yet there are also similar points across cultures.Saying"please"and"thank you"is almost always polite.Ifyou show thanks and try to（12）______ local customs，people will generally respond well.Showing kindness can bring people together，no matter what culture they come from.11. A. what B. how C. when D. where12. A. cheerfully B. hurriedly C. excitedly D. silently13. A. the other B. other C. the others D. others14. A. accept B. achieve C. refuse D. continue15. A. rude B. simple C. common D. correct16. A. family parties B. table mannersC. fashion tastesD. instruction signs17. A. full B. closed C. open D. smiling18. A. symbol B. mark C. sign D. view19. A. What's more B. In short C. For example D. Above all20. A. push B. cut C. look D. pour21. A. unimportant B. uninteresting C. unusual D. unclean22. A. change B. develop C. follow D. mention三、补全对话-填空（本大题共1小题，共6.0分）23. Writing creatively is enjoyable and rewarding.It can be a hobby，a field of study，and even acareer.Anyone can be a creative writer.You just need a little inspiration（灵感）and some written language skills.By reading extensively（广泛地）and practicing your skills，you can become a talented writer.Reading extensively.All the best writers show great interest in reading.When you read a book，you should pay attention to the actual events in the book and the way the author created that piece of literature.By reading，you can also study how excellent authors use language in creative andinspiring ways.（1）______Thinking about pursuing（追求）writing in college.While you don't need to study writing incollege to become a writer，taking one or more writing courses can certain help.（2）______ And it may let you know more new authors and styles of literature that you have not explored before.Consider getting a Master of Fine Arts （MFA）degree.An MFA degree isn't necessary to practice writing.（3）______ You ' ll meet and study closely with a small group of like- minded individuals （个体）and you max end up becoming lifelong friends.（4）______ How you continue writing can decide whether it will remain your lifelong pursuit or something you never seem to pick back up.Even if you can only find an hour a day，spare that time and use it to write every day.A.Try to make and stick to a plan.B.Find a publishing market that is right for you.C.Therefore，reading with a purpose is also important.D.In some ways，your writing style can present your thoughts.E.This allows you to receive instruction and advice on your work.F.However，such a learning experience helps you build a sense of community(1)(2)(3)(4)四、阅读理解（本大题共14小题，共28.0分）ADo you want to make a difference to animals' lives？Become a volunteer at Irving Animal Services （IAS）.IAS depends on volunteers to help provide loving care and give animals a second chance to feel being loved and happiness.Here are several volunteer positions.OPPORTUNITIESAdoption Host：Helps the public at the shelter and off-site locations with questions，and helps to introduce possible adopters（收养人）and animals.Animal Care：Help staff with daily routines，such as cleaning animal houses，and preparing meet and greet rooms.Volunteers also work to socialize animals by reading to them，petting them or playing with them.Sometimes volunteers will perform bath services for animals.Supply Team：Helps provide daily supplies（供给）for basic needs for all the animals.This is very important for the health and well-being of the animals. Photographer：Photographs animals for adoption promotion and record keeping. Requirements：Volunteer application must be at least 18 years old and loveanimals.There is no cost to volunteers and no hours required.Interested people musthand in an application to the Volunteer Program.Volunteer Hours：9 a.m.to 6 p.m.Tuesday—Friday 8 a.m.to 5 p.m.Saturday—Monday Apply Today!Visit the IAS Volunteer Program portal（门户网站）and create an account.Fill out the basic information and hand in your application.We will check the application，and those accepted into the program will be contacted for training.The training must be finished before any volunteer task is carried out.For more information，please call （972）721-3582 or email the IAS Volunteer Coordinator（协调员）.24. What should volunteers in the Adoption Host position do______A. Play with animals.B. Provide necessary things for animals.C. Connect possible adopters with animals.D. Take photos of animals and their adopters.25. What is a requirement for an animal volunteer at IAS？______A. Being a young adult.B. Showing love for animals.C. Working for nine hours every day.D. Having experience of keeping animals.26. How can people apply for their favorite volunteer post at IAS？______A. By finishing practical training ahead of time.B. By offering personal information on a certain website.C. By sending an email to the IAS Volunteer Coordinator.D. By making a telephone call to ask for more information.BAmerica is a mobile society.Friendships between Americans can be close and real，yet disappear soon if situations change.Neither side feels hurt by this.Both may exchange Christmas greetings for a year or two，perhaps a few letters for a while - then no more.If the same two people meet again by chance，even years later，they pick up the friendship.This can be quite difficult for us Chinese to understand，because friendships between us flower more slowly but then may become lifelong feelings，extending（延伸）sometimes deeply into both families.Americans are ready to receive us foreigners at their homes，share their holidays，and their home life.They will enjoy welcoming us and be pleased if we accept their hospitality（好客）easily. Another difficult point for us Chinese to understand Americans is that although they include us warmly in their personal everyday lives，they don't show their politeness to us if it requires a great deal of time.This is usually the opposite of the practice in our country where we may be generous with our time.Sometimes，we，as hosts，will appear at airports even in the middle of the night to meet a friend.We may take days off to act as guides to our foreign friends.The Americans，however，express their welcome usually at homes，but truly cannot manage the time to do a great deal with a visitor outside their daily routine（事务）.They will be likely to expect us to get ourselves from the airport to our own hotel by bus.And they expect that we will phone them from there.Once we arrive at their homes，the welcome will be full，warm and real.We will find ourselves treated hospitably.For the Americans，it is often considered more friendly to invite a friend to their homes than to go to restaurants，except for purely business matters.So accept their hospitality at home!27. The writer of this passage must be ______ .A. an AmericanB. a ChineseC. a visitorD. a student28. Which of the following is true according to the passage______A. Americans will continue their friendships again even after a long break.B. Americans are usually more friendly than Chinese.C. Americans always show their warmth even if they are very busy.D. Friendships between Americans usually last for all their lives.29. From the last two paragraphs we can learn that when we arrive in America to visit an Americanfriend，we will be ______ .A. warmly welcomed at the airportB. offered a ride to his homeC. treated hospitably at his homeD. treated to dinner in a restaurant30. The underlined words "generous with our time" in Paragraph 3 mean ______ .A. strict with timeB. willing to spend timeC. careful with timeD. free with timeCEducation appears to protect older adults especially women，against memory loss，according to a study by researchers Georgetown University Medical Centre.The study tested declarative memory（陈述性记忆）in 704 older adults （58-98 years ofage）.Declarative memory refers to our ability to remember events，facts and words，such as where you put your keys or the name of that new neighbour.The researchers found that their memory performance became worse with aging.However，more years of early-life education countered these losses，especially in women.For example，the declarative memory abilities of an 80-year-old woman with a bachelor's degree（学士学位）would be as good as those of a 60-year-old woman with a high school education.So，four extra years of education make up for the memory losses from 20 years of aging."Simply said，learning brings about learning，"says the study's senior researcher，Michael Ullman."Since learning new information in declarative memory is easier if it is connected with knowledge we already have，more knowledge from more education should result in better memory abilities，even years later."adds the study's lead author，Jana Reifegerste."Evidence（证据）suggests that girls often have better declarative memory than boys，so educationmay lead to greater knowledge gains in girls，"says Ullman."Education may bring advantages to memory abilities in women，even years later in old age.""These findings may be important，especially considering the rapidly aging population，"Reifegerste says."The results argue for further efforts to increase chances of receiving education.""Education has also been found to slow down the beginning of Alzheimer's disease，"Ullman says."We believe that our findings may explain why this happens."31. The underlined " countered " in Paragraph 2 probably means ______ .A. cancelB. changeC. produceD. reduce32. What does the underlined word" it"in Paragraph 4 refer to？______A. New information.B. Declarative memory.C. More education.D. Better memory ability.33. The research findings may help ______ .A. slow down the process of agingB. push for the development of educationC. make progress in the study of Alzheimer diseaseD. fight for the equal rights of women's education34. The passage mainly talks about that ______ .A. declarative memory abilities fail with agingB. women should try to get a bachelor's degreeC. learning often helps improve old adults' memoryD. early-life education helps prevent memory loss in old ageDIs there a connection between music and language？According to recent studies，the answer is yes：music boosts certain language abilities in the brain.Here，we look at two examples.●Music and HearingA recent study by researcher Nina Kraus shows that playing a musical instrument can improve aperson's hearing ability.As a part of the study，two groups of people listened to a person talking in a noisy room.The people in the first group were musicians，while those in the second group had no musical training.The musicians were able to hear the talking person more clearly.Musicians hear better，says Kraus，because they learn to pay attention to certain sounds.Think about violinists in an orchestra.When the violinists play with the group，they hear their own instrument and many others，too.But the violinists must listen closely to what they are playing，and ignore（忽略）the other sounds.In this way，musicians are able to concentrate（集中注意力）on certain sounds，even in a room with lots of noise.●Music and SpeakingGottfried Schlaug，a doctor at Harvard Medical School，works with stroke patients.Because of their illness，these people cannot say their names，addresses，or other information normally.However，they can still sing.Dr.Schlaug was surprised to find that singing words helped his patients to eventually speak.Why does it work？Schaug isn't sure.Music seems to activate different parts of the brain，including the damaged parts.This somehow helps patients to use that part of brain again.●Understanding the ResultsMusic improves concentration，memory，listening skills and our overall language abilities.It can even help sick people get better.Playing an instrument or singing，says Nina Kraus，can help us do better in school and keep our brain sharp as we get older.Music，she adds，in not only enjoyable，it is also good for us in many other ways.35. What does the underlined word "stroke" mean in the passage？______A. lose abilities of movementB. hearing lossC. an illness of the brain for languageD. special talents of singing36. How does Gottfried Schlaug help stroke patients？______A. By repeating their name and address.B. By playing music for them.C. By asking them to sing.D. By getting them to play an instrument.37. Which type of improvement is NOT mentioned in the reading？______A. memoryB. school gradesC. language abilitiesD. sleep五、阅读填空（本大题共1小题，共10.0分）38. Rabbits are a courageous little species able to live everywhere，except Antarctica.Alongside the （1）______ （begin）of 2023，the New Year of the Rabbit is about to start!Maybe now is the best time（2）______ （talk）about this cute animal in the eyes of different cultures. Rabbits are quiet but agile（敏捷），which（3）______ （suit）traditional Chinese values of being gentle and cultivated.There is（4）______ view of rabbits in Chinese culture as being smart and gentle.This（5）______ （show）by the phrase"dongru tuotu"，a Chinese idiom praising people who are smart and agile like a rabbit.A Chinese legend tells that there is a Jade Rabbit（6）______ （live）on the moon which is the pet of Chang'e，a goddess（7）______ （wide）known in China.This can explain（8）______ rabbits are regarded as a special sign.Also，in ancient China，it was common sense that the more children you had，the（9）______ （lucky）and happier you would be.This belief made the rabbit a popular sign of good fortune，since rabbits are full（10）______ vitality and fertile in nature.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)六、完成句子（本大题共6小题，共9.0分）39. "一带一路"是东西之间交流的象征。

常州市联盟学校2023—2024学年度第一学期学情调研高三年级英语试卷（答案在最后）2023.12出卷老师审卷老师考试时间120分钟本试卷共四大题满分150分第一部分听力（共两节，满分30分）第一节：（共5小题；每小题1.5分，满分7.5）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What will Matthew do on the weekend?A.Attend an exhibition.B.Enter a contest.C.Visit China.2.Where do the speakers want to go?A.To a supermarket.B.To a bank.C.To a restaurant.3.When will the man see the film?A.At1:30p.m.B.At3:30p.m.C.At5:30p.m.4.What are the speakers mainly talking about?A.A noisy night.B.A place of living.C.Their sleeping habits.5.Why did the man call the woman last night?A.To give her fruits.B.To invite her to a party.C.To ask for her cousin's number.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。

每段对话或独白读两遍。