浙江省杭州师大附中2012届高三第四次月考试题(英语)
湖南师大附中2025届高三月考数学(三)试卷及答案
大联考湖南师大附中2025届高三月考试卷(三)数学时量:120分钟满分:150分一、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的.1.集合{}0,1,2,3的真子集个数是()A .7B .8C .15D .162.“11x -<”是“240x x -<”的()A .充分不必要条件B .必要不充分条件C .充要条件D .既不充分也不必要条件3.已知角α的终边上有一点P 的坐标是)4,3(a a ,其中0a ≠,则sin2α=()A .43B .725C .2425D .2425-4.设向量a,b 满足+=-=a b a b ,则⋅a b 等于()A .B .2C .5D .85.若无论θ为何值,直线sin cos 10y x θθ⋅+⋅+=与双曲线2215x y m -=总有公共点,则m的取值范围是()A.1m ≥B .01m <≤C .05m <<,且1m ≠D .1m ≥,且5m ≠6.已知函数()2f x 的图象关于原点对称,且满足()()130f x f x ++-=,且当()2,4x ∈时,()()12log 2f x x m =--+,若()()2025112f f -=-,则m 等于()A .13B .23C .23-D .13-7.已知正三棱台111ABC A B C -所有顶点均在半径为5的半球球面上,且AB =11A B =()A .1B .4C .7D .1或78.北宋数学家沈括博学多才、善于观察.据说有一天,他走进一家酒馆,看见一层层垒起的酒坛,不禁想到:“怎么求这些酒坛的总数呢?”经过反复尝试,沈括提出对于上底有ab 个,下底有cd 个,共n 层的堆积物(如图所示),可以用公式()()()2266n nS b d a b d c c a ⎡⎤=++++-⎣⎦求出物体的总数,这就是所谓的“隙积术”,相当于求数列()()(),11,2ab a b a +++.()()()2,,11b a n b n cd ++-+-= 的和.若由小球堆成的上述垛积共7层,小球总个数为238,则该垛积最上层的小球个数为()A .2B .6C .12D .20二、选择题:本题共3小题,每小题6分,共18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6分,部分选对的得部分分,有选错的得0分.9.若()202422024012202412x a a x a x a x +=++++ ,则下列正确的是()A .02024a =B .20240120243a a a +++= C .012320241a a a a a -+-++= D .12320242320242024a a a a -+--=- 10.对于函数()sin cos f x x x =+和()sin cos 22g x x x ππ⎛⎫⎛⎫=--- ⎪ ⎪⎝⎭⎝⎭,下列说法中正确的有()A .()f x 与()g x 有相同的零点B .()f x 与()g x 有相同的最大值点C .()f x 与()g x 有相同的最小正周期D .()f x 与()g x 的图象有相同的对称轴11.过点()0,2P 的直线与抛物线2:4C x y =交于()()1122,,,A x y B x y 两点,抛物线C 在点A 处的切线与直线2y =-交于点N ,作NM AP ⊥交AB 于点M ,则()A .5OA OB ⋅=-B .直线MN 恒过定点C .点M 的轨迹方程是()()22110y x y -+=≠D .AB MN选择题答题卡题号1234567891011得分答案三、填空题:本题共3小题,每小题5分,共15分.12.已知复数12,z z 的模长为1,且21111z z +=,则12z z +=_____.13.在ABC 中,角,,A B C 所对的边分别为,,a b c 已知5,4a b ==,()31cos 32A B -=,则sin B =_____.14.若正实数1x 是函数()2e e x f x x x =--的一个零点,2x 是函数()g x =()()3e ln 1e x x ---的一个大于e 的零点,则()122e ex x -的值为_____.四、解答题:本题共5小题,共77分.解答应写出文字说明、证明过程或演算步骤.15.(本小题满分13分)现有某企业计划用10年的时间进行技术革新,有两种方案:贷款利润A 方案一次性向银行贷款10万元第1年利润1万元,以后每年比前一年增加25%的利润B 方案每年初向银行贷款1万元第1年利润1万元,以后每年比前一年增加利润3000元两方案使用期都是10年,贷款10年后一次性还本付息(年末结息),若银行贷款利息均按10%的复利计算.(1)计算10年后,A 方案到期一次性需要付银行多少本息?(2)试比较A B 、两方案的优劣.(结果精确到万元,参考数据:10101.1 2.594,1.259.313≈≈)如图,四棱锥P ABCD -中,底面ABCD 为等腰梯形,22AD AB BC ==2=.点P 在底面的射影点Q 在线段AC 上.(1)在图中过A 作平面PCD 的垂线段,H 为垂足,并给出严谨的作图过程;(2)若2PA PD ==.求平面PAB 与平面PCD 所成锐二面角的余弦值.已知函数()()e sin cos ,x f x x x f x =+-'为()f x 的导数.(1)证明:当0x ≥时,()2f x '≥;(2)设()()21g x f x x =--,证明:()g x 有且仅有2个零点.在平面直角坐标系xOy 中,已知椭圆()2222:10x y C a b a b +=>>的两个焦点为12,F F P、为椭圆C 上一动点,设12F PF ∠θ=,当23πθ=时,12F PF ∆.(1)求椭圆C 的标准方程.(2)过点()0,2B 的直线l 与椭圆交于不同的两点(M N M 、在,B N 之间),若Q 为椭圆C上一点,且OQ OM ON =+,①求OBM OBNSS ∆∆的取值范围;②求四边形OMQN 的面积.飞行棋是大家熟悉的棋类游戏,玩家通过投掷骰子来决定飞机起飞与飞行的步数.当且仅当玩家投掷出6点时,飞机才能起飞.并且掷得6点的游戏者可以连续投掷骰子,直至显示点数不是6点.飞机起飞后,飞行步数即骰子向上的点数.(1)求甲玩家第一轮投掷中,投掷次数X 的均值()()1(k E X kP k ∞===∑()1lim n n k kP k ∞→=⎫⎛⎫⎪ ⎪⎝⎭⎭∑;(2)对于两个离散型随机变量,ξη,我们将其可能出现的结果作为一个有序数对,类似于离散型随机变量的分布列,我们可以用如下表格来表示这个有序数对的概率分布:(记()()()()()(1211,,mni i i j j j i j i p x p x p x y p y p y p x ξη========∑∑,)j y .)ξη1x 2x ...n X 1y ()11,p x y ()21,p x y ...()1,n p x y ()21p y 2y ()12,p x y ()22,p x y ...()2,n p x y ()22p y ...⋯⋯...⋯...my ()1,m p x y ()2,m p x y ...(),n m p x y ()2m p y ()11p x ()12p x ...()1n p x 1若已知i x ξ=,则事件{}j y η=的条件概率为{}j i P y x ηξ===∣{}{}()()1,,j i i j i i P y x p x y P x p x ηξξ====.可以发现i x ηξ=∣依然是一个随机变量,可以对其求期望{}{}()111mi j j i j i E x y P y x p x ηξηξ===⋅===∑∣∣.()1,mj i j j y p x y =∑(i )上述期望依旧是一个随机变量(ξ取值不同时,期望也不同),不妨记为{}E ηξ∣,求{}E E ηξ⎡⎤⎣⎦∣;(ii )若修改游戏规则,需连续掷出两次6点飞机才能起飞,记0ξ=表示“甲第一次未能掷出6点”,1ξ=表示“甲第一次掷出6点且第二次未能掷出6点”,2ξ=表示“甲第一次第二次均掷出6点”,η为甲首次使得飞机起飞时抛掷骰子的次数,求E η.炎德・英才大联考湖南师大附中2025届高三月考试卷(三)数学参考答案题号1234567891011答案C A C B B D A B BC ACD BC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的.1.C 【解析】集合{}0,1,2,3共有42115-=(个)真子集.故选C .2.A 【解析】解不等式240x x -<,得04x <<,解不等式11x -<,得02x <<,所以“11x -<”是“240x x -<”的充分不必要条件.3.C 【解析】根据三角函数的概念,2442sin cos 2tan 24tan ,sin23311tan 25y a x a αααααα======+,故选C .4.B 【解析】()()()22111911244⎡⎤⋅=+--=-=⎣⎦a b a b a b .5.B 【解析】易得原点到直线的距离1d ==,故直线为单位圆的切线,由于直线与双曲线2215x y m -=总有公共点,所以点()1,0±必在双曲线内或双曲线上,则01m <≤.6.D 【解析】依题意函数()f x 的图象关于原点对称,所以()f x 为奇函数,因为()()()133f x f x f x +=--=-,故函数()f x 的周期为4,则()()20251f f =,而()()11f f -=-,所以由()()2025112f f -=-可得()113f =,而()()13f f =-,所以()121log 323m --=,解得13m =-.7.A 【解析】上下底面所在外接圆的半径分别为123,4r r ==,过点112,,,A A O O 的截面如图:22222121534,543,1OO OO h OO OO =-==-∴=-=,故选A .8.B 【解析】由题意,得6,6c a d b =+=+,则由()()()772223866b d a b d c c a ⎡⎤++++-=⎣⎦得()()7[26212(6b b a b b a ++++++6)]()762386a a ++-=,整理得()321ab a b ++=,所以773aba b +=-<.因为,a b 为正整数,所以3ab =或6.因此有6,3a b ab +=⎧⎨=⎩或5,6.a b ab +=⎧⎨=⎩而63a b ab +=⎧⎨=⎩无整数解,因此6ab =.故选B .二、选择题:本题共3小题,每小题6分,共18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6分,部分选对的得部分分,有选错的得0分.9.BC 【解析】对于A :令0x =,则01a =,故A 错误;对于B :令1x =,则20240120243a a a +++= ,故B 正确;对于C :令1x =-,则012320241a a a a a -+-++= ,故C 正确;对于D ,由()202422024012202412x a a x a x a x +=++++ ,两边同时求导得()20232202312320242024212232024x a a x a x a x ⨯⨯+=++++ ,令1x =-,则12320242320244048a a a a -++-=- ,故D 错误.故选BC .10.ACD 【解析】()()32sin ,2sin 2sin 4244f x x g x x x ππππ⎛⎫⎛⎫⎛⎫=+=--=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭.令()0f x =,则,4x k k ππ=-+∈Z ;令()0g x =,则3,4x k k ππ=+∈Z ,两个函数的零点是相同的,故选项A 正确.()f x 的最大值点是()2,,4k k g x ππ+∈Z 的最大值点是32,4k k ππ-+∈Z ,两个函数的最大值虽然是相同的,但最大值点是不同的,故选项B 不正确.由正弦型函数的最小正周期为2πω可知()f x 与()g x 有相同的最小正周期2π,故选项C 正确.曲线()y f x =的对称轴为,4x k k ππ=+∈Z ,曲线()y g x =的对称轴为5,4x k k ππ=+∈Z ,两个函数的图象有相同的对称轴,故选项D 正确.故选ACD.设直线AB 的方程为2y tx =+(斜率显然存在),221212,,,44x x A x B x ⎛⎫⎛⎫ ⎪ ⎪⎝⎭⎝⎭,联立22,4,y tx x y =+⎧⎨=⎩消去x 整理可得2480x tx --=,由韦达定理得12124,8x x t x x +==-,A .22121212124,84444x x y y OA OB x x y y =⋅=⋅=+=-+=- ,故A 错误;B .抛物线C 在点A 处的切线为21124x x x y ⎛⎫=+ ⎪⎝⎭,当2y =-时,11121244282222x x x x x t x x =-=-=+=-,即()2,2N t -,直线MN 的方程为()122y x t t +=--,整理得xy t=-,直线MN 恒过定点(0,0),故B 正确;C .由选项B 可得点M 在以线段OP 为直径的圆上,点O 除外,故点M 的轨迹方程是()()22110y x y -+=≠,故C 正确;D.222t MN +==,AB =则()2221412222t AB MNt +⎫==+,,m m =≥则12ABm MN m ⎛⎫=- ⎪⎝⎭,设()1,f m m m m =-≥,则()2110f m m=+>',当m ≥,()f m 单调递增,所以()min f m f==,故D 错误.故选BC .三、填空题:本题共3小题,每小题5分,共15分.12.1【解析】设()()12i ,,i ,z a b a b z c d c d =+∈=+∈R R ,因为21111z z +=,所以2122111z zz z z z +=.因为11221,1z z z z ==,所以121z z +=,所以()()i i i 1a b c d a c b d -+-=+-+=,所以1,0a c b d +=+=,所以()()12i 1z z a c b d +=+++=.13.74【解析】在ABC 中,因为a b >,所以A B >.又()31cos 32A B -=,可知A B-为锐角且()sin 32A B -=.由正弦定理,sin 5sin 4A aB b ==,于是()()()5sin sin sin sin cos cos sin 4B A A B B A B B A B B ⎡⎤==-+=-+-⎣⎦.将()cos A B -及()sin AB -的值代入可得3sin B B =,平方得2229sin 7cos 77sin B B B ==-,故7sin 4B =.14.e 【解析】依题意得,1211e e 0x x x --=,即()()12311122e e ,0,e ln 1e 0x x x x x x -=>---=,即()()3222e ln 1e ,e x x x --=>,()()()131122e e e e ln 1x x x x x ∴-==--,()()()()()()211ln 111112212e e ln 1e ,e e ln 1e e x x x x x x x x -+++⎡⎤∴-=--∴-=--⎣⎦,又22ln 1,ln 10,x x >->∴ 同构函数:()()1e e ,0x F x x x +=->,则()()312ln 1e F x F x =-=,又()()111e e e e e 1e x x x x F x x x +++=-+=-+',00,e e 1,e 10x x x >∴>=∴-> ,又()()1e 0,0,x x F x F x +>'>∴单调递增,()()()3122212222e ln 1e e ln 1,e e e ex x x x x x ---∴=-∴===.四、解答题:本题共5小题,共77分.解答应写出文字说明、证明过程或演算步骤.15.【解析】(1)A 方案到期时银行贷款本息为()1010110%26⨯+≈(万元).……(3分)(2)A 方案10年共获利:()()1091.2511125%125%33.31.251-+++++=≈- (万元),……(5分)到期时银行贷款本息为()1010110%25.9⨯+≈(万元),所以A 方案净收益为:33.325.97-≈(万元),……(7分)B 方案10年共获利:()()101010.31 1.3190.310123.52⨯-⨯++++⨯=⨯+= (万元),……(9分)到期时银行贷款本息为()()()()101091.11.11110%110%110%17.51.11-++++++=≈- (万元),……(11分)所以B 方案净收益为:23.517.56-≈(万元),……(12分)由比较知A 方案比B 方案更优.……(13分)16.【解析】(1)连接PQ ,有PQ ⊥平面ABCD ,所以PQ CD ⊥.在ACD 中,2222cos 54cos AC AD CD AD CD ADC ADC ∠∠=+-⋅⋅=-.同理,在ABC 中,有222cos AC ABC ∠=-.又因为180ABC ADC ∠∠+= ,所以()1cos ,0,1802ADC ADC ∠∠=∈ ,所以60ADC ∠= ,3AC =故222AC CD AD +=,即AC CD ⊥.又因为,,PQ AC Q PQ AC ⋂=⊂平面PAC ,所以CD ⊥平面PAC .CD ⊂平面PCD ,所以平面PCD ⊥平面PAC .……(5分)过A 作AH 垂直PC 于点H ,因为平面PCD ⊥平面PAC ,平面PCD ⋂平面PAC PC =,且AH ⊂平面PAC ,有AH ⊥平面PCD .……(7分)(2)依题意,22AQ PA PQ DQ =-=.故Q 为,AC BD 的交点,且2AQ ADCQ BC==.所以2222326,333AQ AC PQ PA AQ ===-.过C 作直线PQ 的平行线l ,则,,l AC CD 两两垂直,以C 为原点建立如图所示空间直角坐标系,则:()()36131,0,0,0,,0,3,0,,,03322D P A B ⎛⎫⎛⎫- ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭,所以()326232613261,0,0,0,,0,,,,,3333263CD CP AP BP ⎛⎛⎛===-=- ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭ .设平面PCD 的法向量为(),,x y z =m ,则()0,0,3CD x CP y ⎧⋅==⎪⎨⋅=+=⎪⎩m m取()0,=-m .同理,平面PAB的法向量)1=-n ,1cos<,3⋅>==m n m n m n ……(14分)故所求锐二面角余弦值为13.……(15分)17.【解析】(1)由()e cos sin x f x x x =++',设()e cos sin x h x x x =++,则()e sin cos x h x x x '=-+,当0x ≥时,设()()e 1,sin x p x x q x x x =--=-,()()e 10,1cos 0x p x q x x ''=-≥=-≥ ,()p x ∴和()q x 在[)0,∞+上单调递增,()()()()00,00p x p q x q ∴≥=≥=,∴当0x ≥时,e 1,sin x x x x ≥+≥,则()()()e sin cos 1sin cos sin 1cos 0x h x x x x x x x x x '=-+≥+-+=-++≥,∴函数()e cos sin x h x x x =++在[)0,∞+上单调递增,()()02h x h ∴≥=,即当0x ≥时,()2f x '≥.……(7分)(2)由已知得()e sin cos 21x g x x x x =+---.①当0x ≥时,()()()e cos sin 220,x g x x x f x g x ≥''=++-=-∴ 在[)0,∞+上单调递增,又()()010,e 20g g πππ=-<=->∴ 由零点存在定理可知,()g x 在[)0,∞+上仅有一个零点.……(10分)②当0x <时,设()()2sin cos 0e x x xm x x --=<,则()()2sin 10exx m x '-=≤,()m x ∴在(),0∞-上单调递减,()()01m x m ∴>=,()e cos sin 20,e cos sin 20x x x x g x x x '∴++-<∴=++-<,()g x ∴在(),0∞-上单调递减,又()()010,e 20g g πππ-=-<-=+> ,∴由零点存在定理可知()g x 在(),0∞-上仅有一个零点,综上所述,()g x 有且仅有2个零点.……(15分)18.【解析】(1)设()00,,P x y c 为椭圆C 的焦半距,12122F PF p S c y ∆=⋅⋅,00y b <≤ ,当0y b =时,12F PF S 最大,此时()0,P b 或()0,P b -,不妨设()0,P b ,当23πθ=时,得213OPF OPF π∠∠==,所以c =,又因为12F PF S bc ∆==,所以1,b c ==从而2,a =∴椭圆C 的标准方程为2214x y +=.……(3分)(2)由题意,直线l 的斜率显然存在.设()()1122: 2.,,,l y kx M x y N x y =+.……(4分)1112OBM S OB x x ∆∴=⋅=,同理,2OBN S x ∆=.12OBM OBN S xS x ∆∆∴= (6))联立()22222,141612044y kx k x kx x y =+⎧⇒+++=⎨+=⎩,……(8分)()()()22223164121416430,4k k k k ∴∆=-⨯⨯+=->∴>.……(9分)又121212221612,0,,1414k x x x x x x k k-+==>∴++ 同号.()()2222122121212216641421231414k x x x x k k x x x x kk-⎛⎫ ⎪++⎝⎭∴===+++.()22212122364641616,4,,42143331434x x k k x x k k ⎛⎫>∴=∈∴<++< ⎪⎛⎫+⎝⎭+ ⎪⎝⎭ .令()120x x λλ=≠,则116423λλ<++<,解得()()11,11,3,,11,333OBM OBN S S λ∆∆⎛⎫⎛⎫∈∴∈ ⎪ ⎪⎝⎭⎝⎭ .……(12分)(3)()1212,,OQ OM ON Q x x y y =+∴++.且四边形OMQN 为平行四边形.由(2)知()12121222164,41414k x x y y k x x k k-+=∴+=++=++,22164,1414kQ k k -⎛⎫∴ ⎪++⎝⎭.而Q 在椭圆C 上,2222164441414k k k -⎛⎫⎛⎫∴+⨯= ⎪ ⎪++⎝⎭⎝⎭.化简得2154k =.……(14分)∴线段161219357115224MN ==⋅+,……(15分)O到直线MN的距离d == (16))OMQN 574S MN d ∴=⋅=四边形.……(17分)19.【解析】(1)()115,1,2,3,66k P X k k -⎛⎫==⨯= ⎪⎝⎭ ,所以()()215111,1,2,3,,5126666nk n k k k P X k k kP k n =⎛⎫⋅====⨯+⨯+⨯ ⎪⎝⎭∑ ,记211112666n n S n =⨯+⨯++⨯ ,则2311111126666n n S n +=⨯+⨯++⨯ .作差得:1211111511111111661666666556616nn n n n n n S n n ++⎛⎫- ⎪⎛⎫⎛⎫⎝⎭=+++-⨯=-⨯=-+ ⎪⎪⎝⎭⎝⎭- ,所以()16111661,555566556n nn n n k n S kP k S n =⎡⎤⎛⎫⎛⎫⎛⎫⎛⎫=⋅-+==-+⎢⎥ ⎪⎪ ⎪⎪⎝⎭⎝⎭⎝⎭⎝⎭⎢⎥⎣⎦∑.故()()()116616lim lim 5565nn n n k k E X kP k kP k n ∞∞∞→→==⎡⎤⎛⎫⎛⎫⎛⎫===-+=⎢⎥ ⎪ ⎪⎪⎝⎭⎝⎭⎝⎭⎢⎥⎣⎦∑∑.……(6分)(2)(i ){}E ηξ∣所有可能的取值为:{},1,2,,i E x i n ηξ== ∣.且对应的概率{}{}()()()1,1,2,,i i i p E E x p x p x i n ηξηξξ====== ∣∣.所以{}{}()()()()()111111111,,,nnmn m i i j i j i j i j i i j i j i E E E x p x y p x y p x y p x y p x ηξηξ=====⎛⎫⎡⎤==⋅=⋅= ⎪⎣⎦ ⎪⎝⎭∑∑∑∑∑∣∣又()()()()21111111,,,nmmnmn mj i j j i j j i j j j i j j i j i j y p x y y p x y y p x y y p y E η=======⎛⎫⋅=⋅==⋅= ⎪⎝⎭∑∑∑∑∑∑∑,所以{}E E E ηξη⎡⎤=⎣⎦∣.……(12分)(ii ){}{}{}12355101,;12,;22,63636E E p E E p E p ηξηηξηη==+===+====∣∣,{}()()5513542122636363636E E E E E ηηξηηη⎡⎤==++++⨯=+⎣⎦∣,故42E η=.……(17分)。
师大附中高三月考试题
2010—2011哈师大附中高三月考语文试卷本试卷分第I卷（阅读题）和第Ⅱ卷（表达题）两部分，其中第I卷第三、四题为选考题，其它题为必考题。
考生作答时，将答案答丰答题卡上，在本试卷上答题无效。
第Ⅰ卷阅读题甲必考题一、现代文阅读（9分）汉服运动：文化焦虑与认同危机面对悄然兴起的“汉服运动”，我心情异常复杂。
这一运动的个体性或小团体性，使得他们的行为在消费时代显得有些尴尬，甚至会引来颇多人的误解。
无论如何，它都不可能像超女那样引来广泛的参与，不管是支持还是反对。
每个时代有每个时代的文化焦虑，而我们这个时代最大的焦虑则在于对文化存在的忘却和对焦虑的失语。
我们既承续了上个世纪自觉的传统断裂形成的文化失序、异域接续的文化混乱，又面临着日益紧张的全球化造成的文化同一。
“历史形成的各种文明与文化开始同自己的根源相脱离，它们融合到技术、经济的世界中，融合到一种空洞的理智主义中。
”（卡尔•雅斯贝斯）然而，这种趋势几乎是不可抗拒的。
全球化首先是资本的全球化，然后，文化舶来品依靠资本的流动和输出广泛传播。
资本处于强势的，其文化也会自然处于一种主动的强势地位，以美国为最显著的例子。
“肯德基”、“麦当劳”、“可口可乐”……首先是一种资本和商业行为，然后成为一种具体的、渗透性的文化行为。
这种文化的殖民化不再倚重于武装侵略，但是其影响却显然更大。
中国面对这样的环境已经有一百多年了，让我们痛心的是，当我们回首这充满动荡和文化嬗变的百年时，传统文化的流失和歧变触目惊心。
事实上，和“汉服运动”的动机一样，早在“五四”就有文化保守主义反对全盘西化，有“国剧运动”，有“新格律诗”，进入当代也有新儒家和文化“寻根”，有重倡“读经”，有弘扬“京剧”，但是他们都没能阻挡资本输出带来的文化传播，也有人叫做文化侵略，或者后殖民。
满眼望去，“一个民族的全部生活方式，从出生到走进坟墓，从清早到夜晚，甚至在睡梦之中”（艾略特）都被一种区别于中国传统文化的多重异质文化所覆盖。
2024届湖南师范大学附属中学高三上学期月考卷(四)语文及答案
湖南师大附中2024届高三月考试卷(四)语文试卷讲评稿本试卷共四道大题,23 道小题，满分150分一、现代文阅读(35 分)(-)现代文阅读I(本题共5小题,19 分)阅读下面的文字,完成 1~5 题。
材料一①一碗苏式汤面，浇头数以百计，精工细作汇聚万千风味;一曲吴语《声声慢》轻柔婉转,引得青年男女排起长龙,叶红花，夜晚清净优雅依旧光影斑斓②以全国 0.09%的土地创造全国约2%名列国家创新型城市创新能力前十强③苏州等城市恰如苏作“双面绣”:一城双面，面面精彩。
千百年来人文与经济的莫定了城市发展的风格特质。
精致、创新、内涵等文化特质,也是苏州等地经济发展的一贯坚持和内在追求。
文化影响人的创造,将腔调注入，融成独特的物质和精神发展成果。
遗存、城市精神,更使得丝绸纺织等经济业态长盛不衰。
历史证明，独特的文化中心更代化进程中充分展现。
(摘编自新华网·)中国美术学院象②③《新周刊》:或许因为文化上的厚重④王澍：杭州直到20世纪7020世纪初;西湖边的新新饭店只6界是 80 年代末,西湖边上出现了第一栋 50 米高的高层建筑。
突破这个高度之后,几十湖山一半城”的结构里活动,出了这个范围,对我来说就相当于出差,去了一个不知道什么样的地方。
⑦《新周刊》挖掘历史身份的做法贯穿了许多城市，大家韵。
⑧王澍因为宋朝对中国的艺术来说可以,要有更高更远的认识;只是单纯地模仿上特别发达,过来,⑨这个时代的城市风貌是不是有可能重现一千年前的美感B.“优美乐章”实际上是指城市人文风貌与经济发展协调共生而带来的良好状态。
C.“冷眼”D.“再次装裱”【关键能力】重点考查学生理解关键词语的能力。
【答案】 D【解析】“实质是复刻历史，缺乏新时代的创意”在文中找不到依据。
建筑家王澍和《分)展的过程中起着十分重要的作用。
B.,那么它在秉承自身独特人文基因、促成C.“-半湖山一半城”的城市结构,对于现在的城市结构特点并不上分认可。
师大附中2025届高三第四次月考物理答案(公众号：昆明师说)
物理参考答案·第1页（共5页）物理参考答案选择题：共10小题，共43分。
在每小题给出的四个选项中，第1~7题只有一项符合题目要求，每小题4分；第8~10题有多项符合题目要求，每小题5分，全部选对的给5分，选对但不全的给3分，有选错的给0分。
题号 1 2 3 4 5 6 7 8 9 10 答案 CBCABADADBDAC【解析】1．根据功的定义式cos W Fx α= 可知J N m = ，则有J N m N m m== ，因N 是力的单位，故单位为J/m 的物理量是力。
故选C 。
2．第一宇宙速度是所有绕地球做圆周运动的卫星的最大环绕速度，则“夸父一号”的速度小于7.9km/s ，故A 错误，B 正确。
“夸父一号”绕地球转动的轨道半径小于同步卫星的轨道半径，“夸父一号”的运行周期小于24小时，故C 错误。
根据2MmGma r =可知“夸父一号”绕地球做圆周运动的向心加速度小于地球表面的重力加速度，故D 错误。
3．因绳B 较长，若A B h h =，则B 的重心较低，故A B W W >，故A 错误。
若A B h h >，则一定是B 的重心低，那A B W W >，故B 错误。
若A B h h <，不能确定两根绳子重心的高低，可能A B W W <，也可能A B W W >，还可能A B W W =，故C 正确，D 错误。
4．设月球半径为R ，质量为M ，对嫦娥六号，根据万有引力提供向心力2224π()Mm Gm kR kR T=，月球的体积34π3V R =，月球的平均密度M V ρ=，联立可得323πk GT ρ=，故选A 。
5．橡皮参与了水平向右和竖直向上的分运动，水平方向匀速，竖直向上的分速度与沿绳方向的分速度1v 大小相同，把笔尖的水平速度沿绳及垂直绳方向分解，1sin θ=v v ，1v 增大，所以橡皮做曲线运动，速度大小及方向都改变，故选B 。
浙江省杭州师范大学附属中学2011届高三上学期第一次月考英语试题
杭师大附中2010学年高三年级第一次月考英语试卷第Ⅰ卷（共80分）第一部分英语知识运用（共两节，满分30）第一节单项填空（共20小题；每小题0.5分，满分10分）1. ---I hear that Mary won the prize of the biology contest.---______ She was not interested in it at all.A. You’re kidding!B. So what?C. Why not?D. Not really.2. ---What do you remember Alexander Graham Bell as?--- ______ inventor of ______ telephone.A. an; /B. the; aC. the; theD. /; the3. Was it in 1969______ the American astronaut succeeded ______ landing on the moon?A. when; onB. that; onC. when; inD. that; in4. ---Do you have ______ for the party, Mary?---No, we still have to get another five chairs and some fresh flowers.A. somethingB. everythingC. anythingD. nothing5. A survey was carried out on the sleep time of students in middle schools, ______ weresurprising.A. its resultsB. whose resultC. the results of whichD. of which results6. The building around the corner caught fire last night. The police are now ______ the matter.A. getting throughB. working outC. looking intoD. watching over7. One of the best ways for people to keep fit is to ______ healthy eating habits.A. growB. developC. increaseD. raise8. When ______ comes to research into heart disease and its effects on the body, we do not haveadequate substitutes for the use of animals.A. thatB. itC. thisD. what9. ---Mary has been trained hard for the last two years.---______ she did so well at the track and field meet yesterday.A. No doubtB. No questionC. No wonderD. No problem10. I won’t give you such help ______ you tell me the truth. It’s beyond my ability.A. whenB. sinceC. ifD. even if11. ---Mr. Smith, ______ he have all these letters typed for you right away?---He ______. They should be ready by 10 o’clock this morning.A. will; mustB. shall; has toC. need; willD. would; ought to12. ---Have the police found the parents of the baby found by the road?---Not yet. His identity ______.A. would be found outB. has been found outC. is being found outD. had been found out13. ---How often do you eat out?---______, but usually once a week.A. Have no ideaB. As usualC. It dependsD. Generally speaking14. Since David ______ downloaded a virus into his computer, he can not open the file now.A. readilyB. accidentallyC. horriblyD. irregularly15. ---It’s getting dark, but Mr. Johnson is still at his office.---No surprise. Who else can ______ he does?A. do less work thanB. work as hardly asC. work as hard asD. be working hardly like16. Most birds find it safe to sleep in the trees, but ______ they have eggs or young chicks, theydon’t use a nest.A. whyB. howC. whereD. unless17. Many new______ will be opened up in the future for those with a university degree.A. realitiesB. necessitiesC. probabilitiesD. opportunities18. We were all surprised when he made it clear that he ______ office soon.A. leavesB. leftC. would leaveD. had left19. ---May I take your order now?---______.A. Yes, two hamburgersB. No, my affairs are in orderC. Yes, we must obey ordersD. No, it isn’t my order20. Exciting as its special effects are ______, there is too much violence in the film.A. to watchB. to be watchedC. watchingD. being watched第二节：完形填空（共20小题；每小题1分，满分20分）Born in America, I spoke English, not Chinese, the language of my ancestors. When I was three, my parents flashed cards with Chinese 21 at my face, but I pushed them 22 . My mom believed I would learn 23 I was ready. But the 24 never came.On a Chinese New Year’s Eve, my uncle spoke to me in Chinese, but all I could do was 25 at him, confused, scratching my head. “Still can’t speak Chinese?” He 26 me , “You can’t even buy a fish in Chinatown .”“Hey,this is America, not China. I’ll get some 27 with or without Chinese.” I replied and turned to my mom for 28 .“Remember to ask for fresh fish, Xin Xian Yu,” she said, handing over a $20 bill. I 29 the words, running downstairs into the streets of Chinatown.I found the fish 30 surrounded in a sea of customers. “I’d like to buy some fresh fish,” I shouted to the fisherman. But he 31 my English words and turned to serve the next customer. The laugh of the people behind increased 32 their impatience. With every 33 ,the breath of the dragons on my back grew stronger—my blood boiling—34 me to cry out. “ Xian Sheng Yu, please.” “Very Xian Shen ,” I repeated. The crowd erupted into laughter. My face turned 35 and I ran back home 36 , except for the $20 bill I held tightly in my pocket.Should I laugh or cry? They’re Chinese. I should feel right at 37 . Instead, I was the joke , a disgrace (丢脸)to the language.Sometimes, I laugh at my fish 38 , but, in the end, the joke is on 39 . Every laugh is a culture 40 ; every laugh is my heritage (传统) fading away.21.A. custom B. games C .characters D. language22.A. ahead B. around C. along D. aside23.A. when B. before C. unless D. until24.A. success B. study C. time D. attempt25.A. aim B. joke C. nod D. stare26.A. cared about B. laughed at C. argued with D. asked after27.A. right now B. from now C. at times D. in time28.A. decision B. permission C. information D. preparation29.A. repeated B. reviewed C. spelled D. kept30.A. farm B. stand C. pond D. market31.A. guessed B. forget C. doubted D. ignored32.A. byB. asC. withD. from33.A. second B. effort C. desire D. movement34.A. forcing B. allowing C. persuading D. leading35.A. bright B. blank C. pale D. red36.A. open-mouthed B. tongue-tied C. empty-handed D. broken-hearted37.A. service B. home C. risk D. root38.A. trade B. deed C. challenge D. incident39.A. it B. us C. me D. them40.A. thrown B. lost C. divided D. reflected第二部分：阅读理解(第一节20小题，第二节5小题；每小题2分，满分50分)第一节：阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。
湖南师大附中2024四届高三月考试卷三英语
湖南师大附中2024四届高三月考试卷三英语一、选择题（每题2分，共24分）1. The teacher asked the students to _______ their composition books.A. take outB. take upC. take offD. take away2. It was only when he reached the tea house _______ he realized he had left his wallet at home.A. thatB. whichC. whereD. what3. — How much did you pay for the new smartphone?— I paid _______ my old one.A. as much as twiceB. twice as much asC. much as twiceD. as twice much as4. — Have you decided where to go for your summer vacation?— Not yet. But it will be _______ the sea.A. somewhereB. anywhereC. everywhereD. nowhere5. — How was your interview yesterday?— Oh, it couldn't have been _______! I'm sure I'll get the job.A. worseB. betterC. so badD. the worst6. — Excuse me, could you please tell me where the nearest post office is? — Sure, it's just _______ the bank and the supermarket.A. betweenB. amongC. acrossD. opposite7. — What do you think of the new movie?— It's _______ interesting _______ I want to see it again.A. so; thatB. such; thatC. too; toD. enough; to8. — How did you find your visit to the museum?— _______.A. It was really boringB. Oh, yes, it was interestingC. I went there by busD. It was a fine day9. — Would you like to have another cup of coffee?— _______, but I'm afraid I have to finish my report first.A. I'd love toB. Not at allC. Never mindD. It doesn't matter10. — Can I help you with anything?— _______, please. I'm looking for a pair of shoes.A. Yes, you canB. You'd better notC. Yes, pleaseD. No, thanks11. — How many languages can you speak?— I can speak _______ English _______ Chinese.A. not only; but alsoB. either; orC. both; andD. neither; nor12. — _______ do you usually go to the library?— Twice a week.A. How oftenB. How longC. How many timesD. How much二、填空题（每题2分，共24分）1. The teacher asked the students to write an essay on the topic "The _______ (importance) of Education".2. The _______ (discover) of the new planet was a major scientific breakthrough.3. After a long journey, the travelers finally arrived at their _______ (destinate).4. The book is divided into three _______ (part).5. The _______ (suggest) made by the professor was highly valuable.6. She _______ (determine) to become a doctor after seeing her sick mother suffer so much.7. The _______ (develop) of technology has greatly changed our lives.8. We should always remain _______ (optimistic) in the face of challenges.9. The students were _______ (amaze) at the _______ (amaze) scientific exhibition.10. The _______ (predict) for tomorrow's weather is sunny.11. She has a great passion for _______ (write) and wants to be a writer in the future.12. The _______ (major) of the university is engineering.三、作文题（15分）Title: The Impact of Technology on Our Daily LivesDirections: Write an essay discussing the positive and negative impacts of technology on our daily lives. Use specific。
2024-2025学年湖南师范大学附属中学高三上学期月考(一)语文试题及答案
湖南师大附中2025届高三月考试卷（一）语文本试卷共四道大题，23道小题，满分150分。
时量150分钟。
一、现代文阅读（35分）（一）现代文阅读Ⅰ（本题共5小题，19分）阅读下面的文字，完成下面小题。
科学中的对称对称既然在人类历史上占有非常重要、非常基本的地位，哲学家和科学家很自然会想广泛地加以运用。
1595年的时候，天文学家开普勒就曾经想用一些几何的对称来解释太阳系各行星轨道的直径的比例。
他希望在一个球里面放一个内接的正方体，在这个正方体里面放一个内接的正三角体，希望用这些正多面体的大小比例来解释太阳系各行星轨道的大小比例。
我们知道许多早期用到科学上的对称原理，并没有很大的成果，可是它们说明了科学家很早就对对称发生兴趣了。
对称在科学界开始产生重要的影响始于19世纪。
发展到近代，我们已经知道这个观念是晶体学、分子学、原子学、原子核物理学、化学、粒子物理学等现代科学的中心观念。
近年来，对称更变成了决定物质间相互作用的中心思想。
（所谓相互作用，是物理学的一个术语，意思就是力量，质点跟质点之间的力量。
）20世纪物理学的作用。
我准备分下列几节来讨论：①、②、“群”与对称、守恒定律与对称、宇称守恒与左右对称、规范对称。
最后，我想跟大家谈一下未来的发展。
①1871年麦克斯韦发表了一篇题为《物理量的数学分类》的文章。
麦克斯韦以及比他更早的一个数学家兼物理学家哈密顿，了解到物理里面所讲的量不止一种，有的叫作标量，有的叫作向量。
标量没有方向，向量除了大小外，还有方向。
这篇文章非常有意思，因为今天物理学常用的一些观念，这篇文章已经非常清楚地用一些几何图像表示了出来。
比如麦克斯韦称为“内向”的观念，今天我们常把这个量叫作“散度”（即向外发散的程度），这是一个重要观念。
另一个重要的观念叫作“旋度”。
这些观念的引进都有赖哈密顿跟麦克斯韦的努力。
在另外一篇文章里，麦克斯韦把电学跟磁学的基本公式写了下来。
这是19世纪最重要的物理学工作，麦克斯韦写这篇文章的时候，对于向量的观念虽然已经非常了解，却没有引进向量的符号。
高中英语 2023-2024学年浙江省杭州市四校联考高一(上)月考英语试卷(10月份)
2023-2024学年浙江省杭州市四校联考高一（上）月考英语试卷（10月份）Ⅰ.单词拼写1．They started strolling down the（满是灰尘的） road in the moonlight．2．They are likely to （响应） positively to the President's request for aid．3．He had the complete support of hospital（职员）．4．He（怀疑） that the woman staying in the flat above was using heroin．5．Mr．Smith said he was（辱骂） by the judge's remarks．6．Later she（责骂） her daughter for having talked to her father like that．7．The（醉的） man was kicked out of the bar．8．The passengers went through immigration control and collected their（行李）．9．The workers'（要求） for better conditions was a catalyst for social change．10．The seven-year-old boy was found crying with（抓） on his face and neck．Ⅱ.阅读理解11．We are always told that blue is for boys and pink is for girls． But does this rule result from born differen ce between sexes or are they culturally constructed？In 1918 a trade magazine for baby clothes companies said although opinions varied on this subject， there was a generally accepted rule-pink for the boy and blue for the girl，because pink being a more decided and stronger color is more suitable for the boy；while blue which is more delicate and elegant is prettier for the girl．Unluckily，this attempt at setting the rule for sellers and producers clearly did not work． A 1927 chart i n Time Magazine contacted department stores in various cities and asked what colors they used for boys and girls． The result was all over the map． It wasn't until after the Second World War that the modern standard started to become popular and even so，it didn't get rooted until the 1980s．As for why today's strict color standard set in at all， a sociologist at the University of Maryland thinks the y are basically the outcome of a marketing technique． If salesmen can convince you of following the standard， you will buy a certain product，which makes sense in promoting its sales． Another historian from the sa me university argues that the rule we use today may reflect the influence of French fashion． Traditional Fren ch culture paired pink with girls and blue with boys and because France set the fashion in the 20th century，t heir tradition ruled the world．So do girls prefer pink and boys prefer blue from birth？ It depends on whom you ask． The debate abou t how we got to the point will probably continue． After all， a century ago a magazine firmly declared the o pposite rule．（1）When did today's strict standard set in people's mind？A．Until the 1980s．B．In 1927．C．In 1918．D．After 1945．（2）What made the generally accepted rule change to today's standard？A．The fast changing society．B．The functions of colors．C．The success of marketing techniques．D．The purpose of French businessmen．（3）The underlined part"all over the map" in the third paragraph probably refers to ""．A．in a messB．in the mapC．in agreementD．in order（4）Today's strict color standard may contribute to．A．making products more beautifulB．attracting more visitors to FranceC．bringing in more sales profitsD．understanding boys and girls easily12．When her five daughters were young，Helene An always told them that there was strength in unity（团结）．To show this，she held up one chopstick，representing one person．Then she easily broke it into two p ieces．Next，she tied several chopsticks together，representing a family．She showed the girls it was hard t o break the tied chopsticks．This lesson about family unity stayed with the daughters as they grew up．Helene An and her family own a large restaurant business in California．However，when Helene and her hu sband Danny left their home in Vietnam in 1975，they didn't have much money．They moved their family to S an Francisco．There they joined Danny's mother，Diana，who owned a small Italian sandwich shop．Soon aft erwards，Helene and Diana changed the sandwich shop into a small Vietnamese restaurant．The five daughte rs helped in the restaurant when they were young．However，Helene did not want her daughters to always w ork in the family business because she thought it was too hard．Eventually the girls all graduated from college and went away to work for themselves，but one by one，th e daughters returned to work in the family business．They opened new restaurants in San Francisco and Lo s Angeles．Even though family members sometimes disagreed with each other，they worked together to mak e the business successful．Daughter Elizabeth explains，"Our mother taught us that to succeed we must hav e unity，and to have unity we must have peace．Without the strength of the family，there is no business．" Their expanding business became a large corporation in 1996，with three generations of Ans working toge ther．Now the Ans' corporation makes more than ＄20 million each year．Although they began with a small r estaurant，they had big dreams，and they worked together．Now they are a big success．（1）Helene tied several chopsticks together to show．A．the strength of family unityB．the difficulty of growing up。
上海市华东师范大学第二附属中学2024-2025学年高三上学英语9月月考试卷(无答案)
华东师大二附中2024学年第一学期9月英语试卷高三英语考试时间：120分钟满分：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. 145 minutes. B. 120 minutes. C 130 minutes. D. 160 minutes2. A. Teacher and student B. Eye doctor and patient.C. Salesman and customer D Interviewer and applicant.3. A. On Saturday. B. On Monday C. On Thursday. D. On Friday.4. A. Neither of them knows the composer of the music.B. The style of the music is not familiar to the man.C. The woman is as good a composer as the man.D. They share the same opinion of the odd music.5. A. They should talk about the apartment later.B. The apartment is still available to customers.C. The apartment had already been sold.D. It is not a suitable time to buy the apartment6. A. The customer's feedback. B. The responsibilities of her jobC. The prospects of her job.D. The manager's opinion of her7. A. The woman should think of giving up the subject.B. The woman should seek help from the tutoring service.C. The woman should work as a tutor to help others.D. The woman should major in accounting8. A. He is rejected for lack of experience. B. He quit his job not long agoC. He doesn't care about his appearanceD. He shaves himself every day.9. A. The woman had violated traffic regulationsB. The woman had been fined many times beforeC. The woman knows how to deal with the situation.D. The woman crossed the traffic light for poor eyesight.10. A. He is too busy to attend the lecture on Friday.B. Professor Simpson's lecture is not interestingC. He might miss the lecture if he was not reminded.D. The lecture has an opposite effect on himSection 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 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 would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. Aluminum (铝) cans. B. Plastic bags.C. Glass bottles.D. Cigarette-related litter.12. A. By 60 million. B. By 500 per cent. C. By 500 million. D. By 120 per cent.13. A. Simply leaving rubbish where it belongs is all that we can do.B. Littering is a more pressing problem than people might think.C. Only measuring the harm of rubbish by its lifetime is not enough.D. A large sum of money has been spent in order to keep streets clean.Questions 14 through 16 are based on the following passage.14. A. The rise of sea level. B. Flooding. C. High temperature. D. Bad light.15. 40% English football league grounds will be flooded every year.B. Many more matches will be shortened because of bad weather.C. Ticket prices of football matches will continue to rise.D. The revenue from ticket sales will be reduced.16. A. Spectators should be banned from watching sporting matches.B. Players, teams and sponsors promote carbon neutralization.C. Sports leaders keep the venue's address secret from the public.D. The government may cancel all the matches to be carbon-neutral.Questions 17 through 20 are based on the following conversation.17. A. Computer programmer. B. General manager. C. Salesman. D. 6ales manager.18. A. Two years. B. Three years. C. Five years. D. Six years.19. A. Achieving the assigned sales revenue target.B. Managing 50 employees in the department.C. Cooperating with her colleagues efficiently.D. Dealing with angry customers' complaints.20. A. Because she saw no chance for further advancement.B. Because she couldn't stand the pressure of the job.C. Because she was not satisfied with the low pay.D. Because she didn't want to work extra hours.II. Grammar and vocabularySection ADirections: After reading the passage below, fil 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 otherblanks, use one word that best fits each blank.A Day in the Life of a Curator (馆长)What are some of the most enjoyable aspects of being senior curator at the National Gallery?Among the joys of being a curator are getting (21) _________ (know) thoroughly great works of art; working alongside and learning from expert colleagues in different departments; and feeling that one's work, (22)_________ that concerns new acquisitions, displays and exhibitions, lectures or publications, can help shed important new light on our paintings, (23) _________, in turn, offers new ways for visitors to engage with them. What are some of the challenges of your role?One particular challenge is having to accept the frustrating reality (24) _________ although the gallery is there to connect people with pictures, it sadly doesn't have the capacity or resources to reach everyone all the time. (25)_________ is simply finding the time, amidst a busy workload of daily museum tasks and an intensive shorter-term exhibition schedule, to undertake longer-term research projects, involving thorough investigation of the pictures themselves, secondary research (26) _________ (conduct) in libraries, and conversations with peers worldwide. Have you personally had any unusual experiences during your work for the National Gallery?I have had plenty of memorable and exciting experiences, (27) _________ _________ ascending scaffolding (脚手架) to see Bridget Riley's Messengers in progress or looking at technical images to detect fascinating under drawing lying beneath the visible painted surface of a painting. A particularly happy moment for me (28) _________ (occur) when an album of 200 drawings came to light, the work by Elizabeth, Lady Eastlake (1809-1893) , wife of the gallery's first director. They included her sketches of places she visited abroad with her husband, as well as her pencil copies of paintings they inspected during his search to find qualified masterpieces for the national collection.I (29) _________ (imagine) that Lady Eastlake's sketches were lost or destroyed, so it was an extraordinary moment when I realised they were staring me in the face-and were so well preserved! The generous owner soon donated the precious album to the National Gallery so that her drawings (30) _________ be reunited with her husband's working notebooks and accessible for others to enjoy.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.A. analyzedB. boundaryC. compoundD. detectE. orbitF. potentialG. primitive H. stretching I. subsequently J. tubular K. unquestionablyVisitors are hereIn 2017, when astronomers discovered the asteroid (小行星) 11/2017 U1, it soon dawned on them that they had a strange object on their hands. The calculated 31 showed this long and thin rock to be simply passing through the solar system, and therefore its origin not of this world, as they like to say in the movies. The object was 32 named 'Oumuamua (from the Hawaiian word for “a person sent ahead to get information about the enemy's position, strength, etc.”) , raising memories of an old Star Trek episode, “For the World is Hollow and I Have Touched the Sky,” in which a long, 33 asteroid proved to be an alien ship in disguise (伪装) .There's nothing surprising about interstellar objects passing through our neighborhood. Or there shouldn't be, at least. There's no magical barrier at the 34 of our solar system. Although we see a sky full of stars a and inor telescopes 35 hundreds of clusters a and nebulae (星云) , most of the space in a galaxy's disk is practically empty, save for the thin interstellar medium.This month, science journalist David Chandler delivers a fascinating look at the 36 for spacecraft missions to interstellar intruders. Catching up to Oumuamua now would be virtually impossible. This thin, cigar-shaped rock, 37 about 1, 300 feet long, is rushing along at about 16 miles per second and is already as far away as the average distance to Pluto.But there's no doubt that other visitors from other stars will come by again. This has 38 happened countless times in the 4. 6-billion-year history of our star and its planets- and now, astrophysics is in an advanced state. Every day we learn about 39 conditions long ago in the solar system by studying pieces of rock or metal from space that have landed on Earth and other objects. With the chemistry of materials from the origin days of other stars 40 , who knows what could be found from such priceless relics.That's another comforting thought to keep in mind as you read David's story and then gaze up into a dark sky full of wonder.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.Should period dramas reflect modern sensibilities?Simon Jenkins The most popular films of my youth were war films. They were about how Britain won a war—and that could be any war you cared to mention. In my opinion, they were great fun and, mostly, patriotic 41 .I'm a journalist and occasional historian, and something the two professions share is a respect for the 42of truth. Both are in the business of bringing events to life through the power of fact, not falsification. They may sometimes be 43 of distortion (歪曲) and thoughtless analysis, but to be plain wrong is unethical and unprofessional. The gap between fact and fiction is one that should not be crossed—or if crossed, should stand corrected.Many playwrights, filmmakers and novelists 44 . To them, history is a stimulus to artistic licence, material to be exploited and 45 for dramatic effect. Their considerations are audience appeal, profit and, often, politics. They leave it to historians to worry about 46 . This, to me, is lying.I have always found ‘ 47 ’ (in which facts are the basis for fiction) hard to stomach. I can appreciate‘docudrama’, which dramatises the events, or the novels of Hilary Mantel, as attempts to deepen our understanding of the past. Mantel insisted that her goal was always to be as 48 as the facts allowed. She did not 49 create false events. The same was not true of The Crown and its much-documented faking of stories. The fact the team behind the show took such pains to cast actors that 50 their real-life counterparts simply added a touch of reality to the made-up story. The result was an audience 51 of what was true or false.I appreciate that history—as with 52 —involves selection, and that selection itself can be motivated by a desire to twist the truth. Each age puts pressure on historians to select material in a manner that respects the 53 or bias (偏向) of nations, groups or individuals. The duty of the historian is to see behind such bias. The task is toreveal what happened, why and how.In an age of artificial intelligence and online ‘deep fakery’, the truth has never been more 54 . The world of fiction has no need to be a parasite (寄生虫) on history: it has all of human imagination to supply it with plots. Every work that claims to be ‘based on real events’ should, in my view, be identified as lies, and should display a large ‘T’ or ‘NT’ —true or not true. Artistic licence should not be a (n) 55 to deceive.41. A. honour B. instinct C. rubbish D. masterpiece42. A. victory B sacredness C. suspicion D. degree43. A. proud B typical C. desperate D. guilty44. A. disagree B. persist C. hesitate D. echo45. A. recorded B. publicized C. abused D. corrected46. A. plot B. artistry C. edition D. truth47. A faction B. profile C nonfiction D. social-drama48. A. awesome B. imaginative C. accurate D. comprehensive49. A. necessarily B deliberately C. merely D. duly50. A. adored B. falsified C. documented D. resembled51. A. conscious B ignorant C. clear D. insightful52. A. journalism B. literature C. politics D. patriotism53. A. literacy B. reason C. justice D. sensitivity54. A. immoral B. precious C. sufficient D. revolutionary55. A. instance B. tendency C. licence D submissionSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)“Who says it's Father's Day?” my son says to me, with the questioning angry look of someone who's been told they have extra tax to pay. “Well, the world does,” I tell him, suddenly self-conscious. “It's a special day for daddies.”Something about this—I can't think what—comes out sounding quite desperate and he looks at me as if I've just suggested he prove his love for me with a face tattoo (文身) . It's a look of suspicion, but also of tender concern for my mental state.This is his fifth Father's Day, so I can't help feeling slightly wounded that the concept hasn't stuck with him. I also can't help noting that he has never had any such issue with Mother's Day, which has always seemed to him like common sense.The event's nearness to his own birthday two weeks from now—is making things more difficult for him to tolerate. It would seem he finds it impolite that the run-up to his special day should be interrupted so close to the finish line by a day that celebrates me, the lesser of his two parents. In any case, if he's planning to make or gift me something, this conversation has been a masterstroke of expectation management“So, will all daddies get a Father's Day?” he asks. “Yes,” I reply, “and this isn't new-it's every year!” I attempt to regulate my voice/offence, but also make it very clear I haven't made this idea up on the spot by myself. “You've been doing it since you were born. And it's been around longer than that. I get things for Grandad every year, too.”At this he stirs himself up. He has never quite stopped being fascinated by the idea that his grandad is my dad, in the same way that I am his. I suppose it's the same thrill I feel when I see pictures of massive cranes (起重机) being built by other, even bigger cranes.“What do you get him?” he asks. “Well,” I say, “things like CDs or socks-and always a card.” At this he seems inspired. “I'll do a card!” he says, brightening.“You could buy me something, too. . .” I begin, but he is no longer listening, running to grab coloured paper and glittery pens. Not wishing to see this tribute to myself a whole week early, I smile and tell him I really shouldn't be watching and get up to leave him to it.“Yes,” he says, just in time for me to see he's actually writing “Dear Grandad” on the page. “Don't tell him!”56. How does the writer feel when explaining Father's Day?A. Suspicious.B. Embarrassed.C. Proud.D. Ridiculous.57. It can be inferred from the son's response that ________.A. the son feels hurt because the concept escapes himB. the writer looks relieved due to his son's tender heartC. a face tattoo is the way to prove a son's love for his fatherD. the son identifies with Mother's Day more than Father's Day58. The writer mentions Grandad in order to ________.A. justify the annual celebration of Father's DayB. practise skills of expectation managementC. narrow the gap between the three generationsD. link Father's Day to his son's birthday59. Which of the following best summarises the passage?A. When celebrating Father's Day, you should also send a DIY card to your grandpa.B. It is a universally acknowledged fact that Father's Day is a special day for daddies.C. Father's Day is a special time to celebrate Dad, but for my son that's a bit of a stretch.D. My son and father have agreed to keep the Father's Day greetings card secret from me.(B)611907Elizabeth Maconchy is born on 19 March in Broxbourne,Hertfordshire. Her parents are both Irish, and the family later move toHowth, close to Dublin on the east coast of Ireland.Edward VII opens the new Old Bailey criminal court building inLondon, its dome decorated by Lady Justice, a bronze sword-holdingsculpture.1930In the same year that her PianoConcerto receives its world premiere(首次公演) in Prague, her orchestralsuite (组曲) The Land enjoys greatpraise when Sir Henry Wood conductsit at the BBC Concerts.At London's Queen's Hall, Adrian Boult conducts the recently founded BBC Symphony Orchestra in its first ever concert, featuring works by Wagner, Brahms and Ravel.1947Married since 1930 toWilliam LeFanu, a librarian at theRoyal College of Surgeons, shegives birth to their seconddaughter, Nicola LeFanu, who will also go on to enjoy a career as a composer.An exceptionally harsh winter results firstly in power cuts due to difficulties in transporting coal and then, as the snow melts in March, the most damaging flooding of the River Thames for more than 100 years.1968Her Aristophanes-inspired operaThe Birds, one of a number of piecesthat she composes for children, isperformed for the first time atBishop's Stortford College for Boys.After his controversial ‘Riversof Blood’ speech about immigration,MP Enoch Powell is removed fromthe Shadow Cabinet by Conservativeleader Edward Heath.1994Seven years after receiving a Damehood for services to music, she dies in Norwich, aged 87. During the week of May 13-17, 2024, she is featured as Composer of the Week on BBC RadioAt a ceremony in Calais on 6 May, Queen Elizabeth II and French president Fran gois Mitterrand officially open the Channel Tunnel, six years after tunnelling began on Dec. 1st , 1987. 1983She composes ‘Quartetto Corto’, the 13th and last of her string quartets (弦乐四重奏) , a series that, begun some half-a-century earlier, she describes as‘my best and most deeply felt works’.Jenny Pitman becomes the first woman to train a winner of the Grand National when Corbiere, ridden by Ben De Haan, finishes three-quarters of a length ahead of Greasepaint at Aintree.60. Elizabeth Maconchy is probably ________.A. Lady JusticeB. a conductorC. a librarianD. a composer61. The best title (numbered 61 ) of the passage is probably ________.A MACONCHY Life &Times B. MACONCHY AchievementsC. Irish Lady's ContemporariesD. Uphill Battle for Recognition62. What happened in the 1930s?A. Adrian Boult conducted Maconchy's Piano Concerto.B. William LeFanu, a surgeon, got married to Maconchy.C. Maconchy began composing a series of string quartets.D. Sir Henry Wood composed an orchestral suite The Land.(C)A theme at this year's World Economic Forum (WEF) meeting in Switzerland was the perceived need to “speed up breakthroughs in research and technology.” Some of this framing was motivated by the climate emergency, some by the opportunities and challenges presented by generative artificial intelligence. Yet in various conversations, it seemed to be taken for granted that to address the world's problems, scientific research needs to move faster. The WEF mindset is similar to the Silicon Valley dictate—to move fast and break things. But what if the thing being broken is science? Or public trust?The WEF meeting took place just two weeks after Harvard University President Claudine Gay stepped down after complaints were made about her political science scholarship. In response, Gay requested corrections to several of her papers. Although it may be impossible to determine just how widespread such problems really are,it's hard to imagine that the scene of high-profile scholars correcting and retracting papers has not had a negative impact on public trust in science and perhaps in experts broadly.In recent years we've seen important papers, written by outstanding scientists and published in celebrated journals, retracted because of questionable data or methods, hence a question: Are scholars at supercompetitive places such as Harvard and Stanford rushing to publish rather than taking the time to do their work right?It's impossible to answer this question scientifically because there's no scientific definition of what constitutes "rushing. "But there's little doubt that we live in a culture where academics at leading universities are under tremendous pressure to produce results—and a lot of them—quickly.The problem is not unique to the U. S. In Europe, formal research assessments—which are used to allocate (分配) future funding—have for years judged academic departments largely on the quantity of their output. A recent reform urging an emphasis on quality over quantity allowed that the existing system had created “counterincentives. ”Good science takes time. More than 50 years elapsed between the 1543 publication of Copernicus's On the Revolutions of the Heavenly Spheres. And it took just about half a century for geologists and geophysicists to accept geophysicist Alfred Wegener's idea of continental drift.There's plenty of circumstantial evidence that scientists and other scholars are pushing results out far faster than they used to. Consider the sheer volume of academic papers being published these days. One recent study put the number at more than seven million a year, compared with fewer than a million as recently as 1980. Some of this growth is driven by more scientists and more co-authorship of papers, but the numbers also suggest that the research world has prioritized quantity over quality. Researchers may need to slow down if we are to produceknowledge worthy of trust.63. WEF meeting in Switzerland advocated that ________.A. researchers need to achieve breakthroughs more rapidlyB. public trust in science is not supposed to be easily brokenC. WEF and Silicon Valley reach an agreement to move fastD. climate emergency and AI push scientific research hard64. Which of the following examples fails to prove that good science takes time?A. Gay's correction and retraction of papers.B. Publication of Copernicus's theory.C. High-profile scholars' tremendous output.D. Acceptance of the idea of continental drift.65. The underlined word “counterincentives” in para. 5 probably means ________.A. measures to increase quantities of outputB. discouragements of high quality papersC. rewards for leading universities' researchD. contradictory motives for future funding66. Which of the following is best title of the passage?A. WEF Coincides with Silicon ValleyB. Collapse of Public TrustC. Dilemma between Quantity and QualityD. Trouble in the Fast LaneSection CDirections: Read the passage carefully. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.A. Brentford FC has taken a different approach.B. Statistics have helped the team win on the pitch, too.C. He applied his talent to identifying the underlying strength of football teams.D. Analytics underlay and supported a remarkably profitable buy-low-sell-high transfer strategy.E. They were told to focus not on how many goals a team was scoring, which was subject to too much randomness.F. Like “Moneyball” , a hit book about the use of statistics in baseball, “Smart Money” is both informative and entertaining.Football and dataA numbers gameAt most football clubs, the equation is simple: you put in vast amounts of money, and you get out star players and win victories. Take Manchester City, the Premier League's reigning champions. Before its takeover in 2008 by a Middle East plutocrats (财阀) , the club often struggled in the bottom half of the table; it has won English football's championship seven times since 2011.67. _________ The club was promoted into the Premier League in 2021 after striving for decades in the lower reaches of football. What makes its success surprising is not how much money its owner, Matthew Benham, has put into the team, but how little. In a new book “Smart Money”. Alex Duff, a lifelong Brentford fan, explains how a money-saving plan made profits.Mr Benham studied physics at Oxford University and then went to work in banking. In his early 30s, sensing correctly that bookmakers (赌注登记人) were inaccurate when setting odds for football matches, Mr Benham leftbanking to become a full-time gambler.He set up his own company, Smartodds, and competed with financial institutions to hire the best mathematicians. 68. _________ Instead, their focus should be the "goal-scoring opportunities it was creating. In time, he reckoned, the goals would comeThe approach was so efficient that when Brentford, going through one of its periodic financial crises, put out a general appeal for help in 2005, Mr Benham offered his services. Within a decade he owned the club and was applying his ideas to how the team was constructed. 69. _________There were plenty of doubters within football about Brentford's philosophy. But in time it worked. In their first season in the Premier League, Mr Benham's investment of around f100m in the club—a tiny sum compared with competitors—realised its first profit of £25m.70. _________ Mr Benham identifed ser pieces (定位球) as an important part of creating scoring opportunities, and hired Gianni Vio, an Italian coach with 4, 000 such plays in his career. Players are instructed to press the opposition and tackle players within ten seconds of them receiving the ball. Though Brentford is not competing for the title, in recent years the team has beaten several of football's plutocrats—including Manchester City. What were the odds?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.Build better boundariesDoing a good deed like helping your friend with their homework or sharing a snack can make you feel happy. Studies show that kindness is good for your wellbeing. However, if you often agree to things you don't want to do, or feel guilty saying no, you could be falling into a people-pleasing trap. It's not always easy to tell when this happens but one clue is that it's difficult to stop. Pleasing other people may feel good for a short while but the feeling doesn't last. This is why it's a good idea to set limits on what you'll do for others. These are called “boundaries”.Spending too much energy on someone else can stop you doing things you want or need to do. Research has found that trying to please others can leave us feeling stressed and uncomfortable. We can also feel angry and frustrated with ourselves and our friends. “There's nothing wrong with being kind to other people,” says Dr Toru Sato, an author and expert in thoughts and feelings, but we need to be sure we're doing it out of kindness, not because we're worried about what other people think.Taking on so much that you end up letting others down doesn't make you a better friend. The youth mental health charity YoungMinds says boundaries include taking time alone when you need it and being able to explain your needs. If saying no feels hard, practise with small things, like if someone offers a straw in a restaurant. This can help you feel more confident. Thinking about how to say no also helps, YoungMinds says, and allows you to communicate what you want clearly and calmly. Remember, you don't need an excuse to say no; you don't owe anyone an explanation. The good people in your life will respect this boundary.71. _________________________________________________________________________________________ V. Translation。
浙江省杭州市2023_2024学年高一上册12月月考英语模拟测试卷(附答案)
浙江省杭州市2023_2024学年高一上册12月月考英语模拟测试卷第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节（共5小题：每小题1.5分，满分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 man looking for?A. His penB. His bookC. His phone2: What does Carol's father ask her to do?A. Talk with her friendsB. Go out with himC. Put on warm clothes3. How man members are there in Alice's group now?A.TwoB.FourC.Six C.Six4. What are the speakers talking about?A. Ways of cookingB. Healthy food for kidsC. Kids helping in the kitchen5. What is the woman?A. She's a shop assistantB. She's a receptionistC.She's a secretary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，各小题给出5秒钟的作答时间。
每段对话或独白读两遍。
2024-2025学年湖南师范大学附属中学高三上学期月考(一)数学试题及答案
大联考湖南师大附中2025届高三月考试卷（一）数学命题人：高三数学备课组 审题人：高三数学备课组时量：120分钟 满分：150分一､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的，1. 已知{}()260,{lg 10}A x x xB x x =+-≤=-<∣∣，则A B = （ ）A. {}32x x -≤≤∣ B. {32}xx -≤<∣C. {12}xx <≤∣ D. {12}xx <<∣2. 若复数z 满足()1i 3i z +=-+（i 是虚数单位），则z 等于（ ）A.B.54C.D.3. 已知平面向量()()5,0,2,1a b ==- ，则向量a b + 在向量b 上投影向量为（ ）A. ()6,3- B. ()4,2- C. ()2,1- D. ()5,04. 记n S 为等差数列{}n a 的前n 项和，若396714,63a a a a +==，则7S =（ ）A. 21B. 19C. 12D. 425. 某校高二年级下学期期末考试数学试卷满分为150分，90分以上（含90分）为及格．阅卷结果显示，全年级1200名学生的数学成绩近似服从正态分布，试卷的难度系数（难度系数=平均分/满分）为0.49，标准差为22，则该次数学考试及格的人数约为（ ）附：若()2,X Nμσ~，记()()p k P k X k μσμσ=-≤≤+，则()()0.750.547,10.683p p ≈≈．A 136人B. 272人C. 328人D. 820人6. 已知()π5,0,,cos ,tan tan 426αβαβαβ⎛⎫∈-=⋅= ⎪⎝⎭，则αβ+=（ ）A.π6 B.π4C.π3D.2π37. 已知12,F F 是双曲线22221(0)x y a b a b-=>>的左､右焦点，以2F 为圆心，a 为半径的圆与双曲线的一条的.渐近线交于,A B 两点，若123AB F F >，则双曲线的离心率的取值范围是（ ）A. ⎛ ⎝B. ⎛ ⎝C. (D. (8. 已知函数()220log 0x a x f x x x ⎧⋅≤=⎨>⎩，，，，若关于x 的方程()()0f f x =有且仅有两个实数根，则实数a 的取值范围是（ ）A. ()0,1 B. ()(),00,1-∞⋃ C. [)1,+∞ D. ()()0,11,+∞ 二､多选题：本题共3小题，每小题6分，共18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6分，部分选对的得部分分，有选错的得0分9. 如图，在正方体111ABCD A B C D -中，E F M N ，，，分别为棱111AA A D AB DC ，，，的中点，点P 是面1B C 的中心，则下列结论正确的是（ ）A. E F M P ，，，四点共面B. 平面PEF 被正方体截得的截面是等腰梯形C. //EF 平面PMND. 平面MEF ⊥平面PMN10. 已知函数()5π24f x x ⎛⎫=+ ⎪⎝⎭，则（ ）A. ()f x 的一个对称中心为3π,08⎛⎫ ⎪⎝⎭B. ()f x 的图象向右平移3π8个单位长度后得到的是奇函数的图象C. ()f x 在区间5π7π,88⎡⎤⎢⎥⎣⎦上单调递增D. 若()y f x =在区间()0,m 上与1y =有且只有6个交点，则5π13π,24m ⎛⎤∈⎥⎝⎦11. 已知定义在R 上的偶函数()f x 和奇函数()g x 满足()()21f x g x ++-=，则（）A. ()f x 的图象关于点()2,1对称B. ()f x 是以8为周期的周期函数C. ()20240g =D.20241(42)2025k f k =-=∑三､填空题：本题共3小题，每小题5分，共15分.12. 6(31)x y +-的展开式中2x y 的系数为______．13. 已知函数()f x 是定义域为R 的奇函数，当0x >时，()()2f x f x '->，且()10f =，则不等式()0f x >的解集为__________.14. 已知点C 为扇形AOB 弧AB 上任意一点，且60AOB ∠=，若(),R OC OA OB λμλμ=+∈，则λμ+的取值范围是__________.四､解答题：本题共5小题，共77分.解答应写出文字说明､证明过程或演算步骤.15. ABC V 的内角,,A B C 的对边分别为,,a b c ，已知22cos a b c B +=．（1）求角C ；（2）若角C 的平分线CD 交AB于点,D AD DB ==CD 的长．16. 已知1ex =为函数()ln af x x x =的极值点．（1）求a 的值；（2）设函数()ex kxg x =，若对()120,,x x ∀∈+∞∃∈R ，使得()()120f x g x -≥，求k 的取值范围．17. 已知四棱锥P ABCD -中，平面PAB ⊥底面,ABCD AD∥,,,2,BC AB BC PA PB AB AB BC AD E ⊥====为AB 的中点，F 为棱PC 上异于,P C 的点．的（1）证明：BD EF ⊥；（2）试确定点F 的位置，使EF 与平面PCD18. 在平面直角坐标系xOy 中，抛物线21:2(0)C y px p =>的焦点到准线的距离等于椭圆222:161C x y +=的短轴长，点P 在抛物线1C 上，圆222:(2)E x y r -+=（其中01r <<）.（1）若1,2r Q =为圆E 上的动点，求线段PQ 长度的最小值；（2）设()1,D t 是抛物线1C 上位于第一象限的一点，过D 作圆E 的两条切线，分别交抛物线1C 于点,M N .证明：直线MN 经过定点.19. 龙泉游泳馆为给顾客更好的体验，推出了A 和B 两个套餐服务，顾客可选择A 和B 两个套餐之一，并在App 平台上推出了优惠券活动，下表是该游泳馆在App 平台10天销售优惠券情况．销售量千张经计算可得：10101021111 2.2,118.73,38510i i i i i i i y y t y t =======∑∑∑（1）因为优惠券购买火爆，App 平台在第10天时系统出现异常，导致当天顾客购买优惠券数量大幅减少，已知销售量y 和日期t 呈线性关系，现剔除第10天数据，求y 关于t 的经验回归方程结果中的数值用分数表示；（2）若购买优惠券的顾客选择A 套餐的概率为14，选择B 套餐的概率为34，并且A 套餐可以用一张优惠券，B 套餐可以用两张优惠券，记App 平台累计销售优惠券为n 张的概率为n P ，求n P ；（3）记（2）中所得概率n P 的值构成数列{}()N n P n *∈.①求n P 的最值；②数列收敛的定义：已知数列{}n a ，若对于任意给定的正数ε，总存在正整数0N ，使得当0n N >时，n a a ε-<，（a 是一个确定的实数），则称数列{}n a 收敛于a .根据数列收敛的定义证明数列{}n P 收敛．.参考公式：()()()1122211ˆˆ,n ni i i ii in ni ii ix x y y x y nx ya y bxx x x nx====---==---∑∑∑∑.大联考湖南师大附中2025届高三月考试卷（一）数学命题人：高三数学备课组 审题人：高三数学备课组时量：120分钟 满分：150分一､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的，1. 已知{}()260,{lg 10}A x x xB x x =+-≤=-<∣∣，则A B = （ ）A. {}32x x -≤≤∣ B. {32}xx -≤<∣C. {12}xx <≤∣ D. {12}xx <<∣【答案】D 【解析】【分析】通过解一元二次不等式和对数函数的定义域，求出集合,A B ，再求交集．【详解】集合{}()32,{lg 10}{12}A x x B x x x x =-≤≤=-<=<<∣∣∣，则{12}A B xx ⋂=<<∣，故选：D ．2. 若复数z 满足()1i 3i z +=-+（i 是虚数单位），则z 等于（ ）A.B.54C.D.【答案】C 【解析】【分析】由复数的除法运算计算可得12i z =-+，再由模长公式即可得出结果.【详解】依题意()1i 3i z +=-+可得()()()()3i 1i 3i 24i12i 1i 1i 1i 2z -+--+-+====-+++-，所以z ==.故选：C3. 已知平面向量()()5,0,2,1a b ==- ，则向量a b +在向量b 上的投影向量为（ ）A. ()6,3- B. ()4,2- C. ()2,1- D. ()5,0【答案】A 【解析】【分析】根据投影向量的计算公式即可求解.【详解】()()7,1,15,a b a b b b +=-+⋅=== 所以向量a b +在向量b 上的投影向量为()()236,3||a b b b b b +⋅==- .故选：A4. 记n S 为等差数列{}n a 的前n 项和，若396714,63a a a a +==，则7S =（ ）A. 21 B. 19C. 12D. 42【答案】A 【解析】【分析】根据等差数列的性质，即可求解公差和首项，进而由求和公式求解.【详解】{}n a 是等差数列，396214a a a ∴+==，即67a =，所以67769,a a a a ==故公差76162,53d a a a a d =-=∴=-=-，()767732212S ⨯∴=⨯-+⨯=，故选：A5. 某校高二年级下学期期末考试数学试卷满分为150分，90分以上（含90分）为及格．阅卷结果显示，全年级1200名学生的数学成绩近似服从正态分布，试卷的难度系数（难度系数=平均分/满分）为0.49，标准差为22，则该次数学考试及格的人数约为（ ）附：若()2,X Nμσ~，记()()p k P k X k μσμσ=-≤≤+，则()()0.750.547,10.683p p ≈≈．A. 136人B. 272人C. 328人D. 820人【答案】B 【解析】【分析】首先求出平均数，即可得到学生的数学成绩2~(73.5,22)X N ，再根据所给条件求出(5790)P X ≤≤，即可求出(90)P X ≥，即可估计人数．【详解】由题得0.4915073.5,22μσ=⨯==，()()(),0.750.547p k P k X k p μσμσ=-≤≤+≈ ，()5790P X ∴≤≤()0.750.547p =≈，()()900.510.5470.2265P X ≥=⨯-=，∴该校及格人数为0.22651200272⨯≈（人），故选：B ．6. 已知()π5,0,,cos ,tan tan 426αβαβαβ⎛⎫∈-=⋅= ⎪⎝⎭，则αβ+=（ ）A.π6 B.π4C.π3D.2π3【答案】D 【解析】【分析】利用两角差的余弦定理和同角三角函数的基本关系建立等式求解，再由两角和的余弦公式求解即可．【详解】由已知可得5cos cos sin sin 6sin sin 4cos cos αβαβαβαβ⎧⋅+⋅=⎪⎪⎨⋅⎪=⋅⎪⎩，解得1cos cos 62sin sin 3αβαβ⎧⋅=⎪⎪⎨⎪⋅=⎪⎩，，()1cos cos cos sin sin 2αβαβαβ∴+=⋅-⋅=-，π,0,2αβ⎛⎫∈ ⎪⎝⎭，()0,παβ∴+∈，2π,3αβ∴+=，故选：D ．7. 已知12,F F 是双曲线22221(0)x y a b a b-=>>的左､右焦点，以2F 为圆心，a 为半径的圆与双曲线的一条渐近线交于,A B 两点，若123AB F F >，则双曲线的离心率的取值范围是（ ）A. ⎛ ⎝B. ⎛ ⎝C. (D. (【答案】B 【解析】【分析】根据双曲线以及圆的方程可求得弦长AB =，再根据不等式123AB F F >整理可得2259c a <，即可求得双曲线的离心率的取值范围.【详解】设以()2,0F c 为圆心，a 为半径的圆与双曲线的一条渐近线0bx ay -=交于,A B 两点，则2F 到渐近线0bx ay -=的距离d b ==，所以AB =，因为123AB F F >，所以32c ⨯>，可得2222299a b c a b ->=+，即22224555a b c a >=-，可得2259c a <，所以2295c a <，所以e <，又1e >，所以双曲线的离心率的取值范围是⎛ ⎝.故选：B8. 已知函数()220log 0x a x f x x x ⎧⋅≤=⎨>⎩，，，，若关于x 的方程()()0f f x =有且仅有两个实数根，则实数a 的取值范围是（ ）A. ()0,1 B. ()(),00,1-∞⋃ C. [)1,+∞ D. ()()0,11,+∞ 【答案】C 【解析】【分析】利用换元法设()u f x =，则方程等价为()0f u =，根据指数函数和对数函数图象和性质求出1u =，利用数形结合进行求解即可．【详解】令()u f x =，则()0f u =．①当0a =时，若()0,0u f u ≤=；若0u >，由()2log 0f u u ==，得1u =．所以由()()0ff x =可得()0f x ≤或()1f x =．如图所示，满足()0f x ≤的x 有无数个，方程()1f x =只有一个解，不满足题意；②当0a ≠时，若0≤u ，则()20uf u a =⋅≠；若0u >，由()2log 0f u u ==，得1u =．所以由()()0ff x =可得()1f x =，当0x >时，由()2log 1f x x ==，可得2x =，因为关于x 的方程()()0f f x =有且仅有两个实数根，则方程()1f x =在(,0∞-]上有且仅有一个实数根，若0a >且()(]0,20,xx f x a a ≤=⋅∈，故1a ≥；若0a <且()0,20xx f x a ≤=⋅<，不满足题意．综上所述，实数a 的取值范围是[)1,+∞，故选：C ．二､多选题：本题共36分，共18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6分，部分选对的得部分分，有选错的得0分9. 如图，在正方体111ABCD A B C D -中，E F M N ，，，分别为棱111AA A D AB DC ，，，的中点，点P 是面1B C 的中心，则下列结论正确的是（ ）A. E F M P ，，，四点共面B. 平面PEF 被正方体截得的截面是等腰梯形C. //EF 平面PMND. 平面MEF ⊥平面PMN【答案】BD 【解析】【分析】可得过,,E F M 三点的平面为一个正六边形，判断A ；分别连接,E F 和1,B C ，截面1C BEF 是等腰梯形，判断B ；分别取11,BB CC 的中点,G Q ，易证EF 显然不平行平面QGMN ，可判断C ；EM ⊥平面PMN ，可判断D.【详解】对于A ：如图经过,,E F M 三点的平面为一个正六边形EFMHQK ，点P 在平面外，,,,E F M P ∴四点不共面，∴选项A 错误；对于B ：分别连接,E F 和1,B C ，则平面PEF 即平面1C BEF ，截面1C BEF 是等腰梯形，∴选项B 正确；对于C ：分别取11,BB CC 的中点,G Q ，则平面PMN 即为平面QGMN ，由正六边形EFMHQK ，可知HQ EF ，所以MQ 不平行于EF ，又,EF MQ ⊂平面EFMHQK ，所以EF MQ W = ，所以EF I 平面QGMN W =，所以EF 不平行于平面PMN ，故选项C 错误；对于D ：因为,AEM BMG 是等腰三角形，45AME BMG ∴∠=∠=︒，90EMG ∴∠=︒，EMMG ∴⊥，,M N 是,AB CD 的中点，易证MN AD ∥，由正方体可得AD ⊥平面11ABB A ，MN ∴⊥平面11ABB A ，又ME ⊂平面11ABB A ，EM MN ∴⊥，,MG MN ⊂ 平面PMN ，EM ∴⊥平面GMN ，EM ⊂ 平面MEF ，∴平面MEF ⊥平面,PMN 故选项D 正确．故选：BD ．10. 已知函数()5π24f x x ⎛⎫=+ ⎪⎝⎭，则（ ）A. ()f x 的一个对称中心为3π,08⎛⎫ ⎪⎝⎭B. ()f x 的图象向右平移3π8个单位长度后得到的是奇函数的图象C. ()f x 在区间5π7π,88⎡⎤⎢⎥⎣⎦上单调递增D. 若()y f x =在区间()0,m 上与1y =有且只有6个交点，则5π13π,24m ⎛⎤∈ ⎥⎝⎦【答案】BD 【解析】【分析】代入即可验证A ，根据平移可得函数图象，即可由正弦型函数的奇偶性求解B ，利用整体法即可判断C ，由5πcos 24x ⎛⎫+= ⎪⎝⎭求解所以根，即可求解D.【详解】对于A ，由35π3π2π0848f ⎛⎫⎛⎫=+⨯=≠⎪ ⎪⎝⎭⎝⎭，故A 错误；对于B ，()f x 的图象向右平移3π8个单位长度后得：3π3π5ππ228842y f x x x x ⎡⎤⎛⎫⎛⎫⎛⎫=-=-+=+= ⎪ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎝⎭⎣⎦，为奇函数，故B 正确；对于C ，当5π7π,88x ⎡⎤∈⎢⎥⎣⎦时，则5π5π2,3π42x ⎡⎤+∈⎢⎥⎣⎦，由余弦函数单调性知，()f x 在区间5π7π,88⎡⎤⎢⎥⎣⎦上单调递减，故C 错误；对于D ，由()1f x =，得5πcos 24x ⎛⎫+= ⎪⎝⎭ππ4x k =+或ππ,2k k +∈Z ，()y f x =在区间()0,m 上与1y =有且只有6个交点，其横坐标从小到大依次为：ππ5π3π9π5π,,,,,424242，而第7个交点的横坐标为13π4，5π13π24m ∴<≤，故D 正确.故选：BD11. 已知定义在R 上的偶函数()f x 和奇函数()g x 满足()()21f x g x ++-=，则（ ）A. ()f x 的图象关于点()2,1对称B. ()f x 是以8为周期的周期函数C. ()20240g =D.20241(42)2025k f k =-=∑【答案】ABC 【解析】【分析】根据函数奇偶性以及所满足的表达式构造方程组可得()()222f x f x ++-=，即可判断A 正确；利用对称中心表达式进行化简计算可得B 正确，可判断()g x 也是以8为周期的周期函数，即C 正确；根据周期性以及()()42f x f x ++=计算可得20241(42)2024k f k =-=∑，可得D 错误.【详解】由题意()()()(),f x f x g x g x -=-=-，且()()()00,21g f x g x =++-=，即()()21f x g x +-=①，用x -替换()()21f x g x ++-=中的x ，得()()21f x g x -+=②，由①+②得()()222f x f x ++-=所以()f x 的图象关于点(2,1)对称，且()21f =，故A 正确；由()()222f x f x ++-=，可得()()()()()42,422f x f x f x f x f x ++-=+=--=-，所以()()()()82422f x f x f x f x ⎡⎤+=-+=--=⎣⎦，所以()f x 是以8为周期的周期函数，故B 正确；由①知()()21g x f x =+-，则()()()()882121g x f x f x g x +=++-=+-=，故()()8g x g x +=，因此()g x 也是以8为周期的周期函数，所以()()202400g g ==，C 正确；又因为()()42f x f x ++-=，所以()()42f x f x ++=，令2x =，则有()()262f f +=，令10x =，则有()()10142,f f +=…，令8090x =，则有()()809080942f f +=，所以1012(2)(6)(10)(14)(8090)(8094)2222024f f f f f f ++++++=+++=个所以20241(42)(2)(6)(10)(14)(8090)(8094)2024k f k f f f f f f =-=++++++=∑ ，故D 错误.故选：ABC【点睛】方法点睛：求解函数奇偶性、对称性、周期性等函数性质综合问题时，经常利用其中两个性质推得第三个性质特征，再进行相关计算.三､填空题：本题共3小题，每小题5分，共15分.12. 6(31)x y +-的展开式中2x y 的系数为______．【答案】180-【解析】【分析】根据题意，由条件可得展开式中2x y 的系数为213643C C (1)⋅-，化简即可得到结果．【详解】在6(31)x y +-的展开式中，由()2213264C C 3(1)180x y x y ⋅⋅-=-，得2x y 的系数为180-.故答案为：180-．13. 已知函数()f x 是定义域为R 的奇函数，当0x >时，()()2f x f x '->，且()10f =，则不等式()0f x >的解集为__________.【答案】()()1,01,-⋃+∞【解析】【分析】根据函数奇偶性并求导可得()()f x f x ''-=，因此可得()()2f x f x '>，可构造函数()()2xf x h x =e并求得其单调性即可得()f x 在()1,+∞上大于零，在()0,1上小于零，即可得出结论.【详解】因为()f x 为奇函数，定义域为R ，所以()()f x f x -=-，两边同时求导可得()()f x f x ''--=-，即()()f x f x ''-=且()00f =，又因为当0x >时，()()2f x f x '->，所以()()2f x f x '>.构造函数()()2x f x h x =e ，则()()()22xf x f x h x '-'=e，所以当0x >时，()()0,h x h x '>在()0,∞+上单调递增，又因为()10f =，所以()()10,h h x =在()1,+∞上大于零，在()0,1上小于零，又因为2e 0x >，所以()f x 在()1,+∞上大于零，在()0,1上小于零，因为()f x 为奇函数，所以()f x 在(),1∞--上小于零，在()1,0-上大于零，综上所述，()0f x >的解集为()()1,01,-⋃+∞.故答案为：()()1,01,-⋃+∞14. 已知点C 为扇形AOB 的弧AB 上任意一点，且60AOB ∠=，若(),R OC OA OB λμλμ=+∈，则λμ+的取值范围是__________.【答案】⎡⎢⎣【解析】【分析】建系设点的坐标，再结合向量关系表示λμ+，最后应用三角恒等变换及三角函数值域求范围即可.【详解】方法一：设圆O 的半径为1，由已知可设OB 为x 轴的正半轴，O 为坐标原点，过O 点作x 轴垂线为y 轴建立直角坐标系，其中()()1,1,0,cos ,sin 2A B C θθ⎛ ⎝，其中π,0,3BOC θθ⎡⎤∠=∈⎢⎥⎣⎦，由(),R OC OA OB λμλμ=+∈，即()()1cos ,sin 1,02θθλμ⎛=+⎝，整理得1cos sin 2λμθθ+==，解得cos λμθ==，则ππcos cos ,0,33λμθθθθθ⎛⎫⎡⎤+==+=+∈ ⎪⎢⎥⎝⎭⎣⎦，ππ2ππ,,sin 3333θθ⎤⎡⎤⎛⎫+∈+∈⎥⎪⎢⎥⎣⎦⎝⎭⎦所以λμ⎡+∈⎢⎣.方法二：设k λμ+=，如图，当C 位于点A 或点B 时，,,A B C 三点共线，所以1k λμ=+=；当点C 运动到AB的中点时，k λμ=+==，所以λμ⎡+∈⎢⎣故答案为：⎡⎢⎣四､解答题：本题共5小题，共77分.解答应写出文字说明､证明过程或演算步骤.15. ABC V 的内角,,A B C 的对边分别为,,a b c ，已知22cos a b c B +=．（1）求角C ；（2）若角C 的平分线CD 交AB于点,D AD DB ==CD 的长．【答案】（1）2π3C = （2）3CD =【解析】【分析】（1）利用正弦定理及两角和的正弦定理整理得到()2cos 1sin 0C B +=，再利用三角形的内角及正弦函数的性质即可求解；（2）利用正弦定理得出3b a =，再由余弦定理求出4a =，12b =，再根据三角形的面积建立等式求解．【小问1详解】由22cos a b c B +=，根据正弦定理可得2sin sin 2sin cos A B C B +=，则()2sin sin 2sin cos B C B C B ++=，所以2sin cos 2cos sin sin 2sin cos B C B C B C B ++=，整理得()2cos 1sin 0C B +=，因为,B C 均为三角形内角，所以(),0,π,sin 0B C B ∈≠，因此1cos 2C =-，所以2π3C =．【小问2详解】因为CD 是角C的平分线，AD DB ==所以在ACD 和BCD △中，由正弦定理可得，,ππsin sin sin sin 33AD CD BD CDA B ==，因此sin 3sin B ADA BD==，即sin 3sin B A =，所以3b a =，又由余弦定理可得2222cos c a b ab C =+-，即222293a a a =++，解得4a =，所以12b =．又ABC ACD BCD S S S =+△△△，即111sin sin sin 222ab ACB b CD ACD a CD BCD ∠∠∠=⋅⋅+⋅⋅，即4816CD =，所以3CD =．16. 已知1ex =为函数()ln af x x x =的极值点．（1）求a 的值；（2）设函数()ex kxg x =，若对()120,,x x ∀∈+∞∃∈R ，使得()()120f x g x -≥，求k 的取值范围．【答案】（1）1a = （2）(]()10,-∞-+∞ ,【解析】【分析】（1）直接根据极值点求出a 的值；（2）先由（1）求出()f x 的最小值，由题意可得是求()g x 的最小值，小于等于()f x 的最小值，对()g x 求导，判断由最小值时的k 的范围，再求出最小值与()f x 最小值的关系式，进而求出k 的范围．【小问1详解】()()111ln ln 1a a f x ax x x x a x xα--=='+⋅+，由1111ln 10e e e a f a -⎛⎫⎛⎫⎛⎫=+= ⎪ ⎪⎪⎝⎭⎝⎭'⎭⎝，得1a =，当1a =时，()ln 1f x x ='+，函数()f x 在10,e ⎛⎫ ⎪⎝⎭上单调递减，在1,e∞⎛⎫+ ⎪⎝⎭上单调递增，所以1ex =为函数()ln af x x x =的极小值点，所以1a =．【小问2详解】由（1）知min 11()e e f x f ⎛⎫==- ⎪⎝⎭．函数()g x 的导函数()()1exg x k x -=-'①若0k >，对()1210,,x x k ∞∀∈+∃=-，使得()()12111e 1e k g x g f x k ⎛⎫=-=-<-<-≤ ⎪⎝⎭，即()()120f x g x -≥，符合题意．②若()0,0k g x ==，取11ex =，对2x ∀∈R ，有()()120f x g x -<，不符合题意．③若0k <，当1x <时，()()0,g x g x '<在(),1∞-上单调递减；当1x >时，()()0,g x g x '>在(1,+∞)上单调递增，所以()min ()1ek g x g ==，若对()120,,x x ∞∀∈+∃∈R ，使得()()120f x g x -≥，只需min min ()()g x f x ≤，即1e ek ≤-，解得1k ≤-．综上所述，k 的取值范围为(](),10,∞∞--⋃+．17. 已知四棱锥P ABCD -中，平面PAB ⊥底面,ABCD AD ∥,,,2,BC AB BC PA PB AB AB BC AD E ⊥====为AB 的中点，F 为棱PC 上异于,P C 的点．（1）证明：BD EF ⊥；（2）试确定点F 的位置，使EF 与平面PCD【答案】（1）证明见解析（2）F 位于棱PC 靠近P 的三等分点【解析】【分析】（1）连接,,PE EC EC 交BD 于点G ，利用面面垂直的性质定理和三角形全等，即可得证；（2）取DC 的中点H ，以E 为坐标原点，分别以,,EB EH EP 所在直线为,,x y z 轴建立，利用线面角公式代入即可求解．小问1详解】如图，连接,,PE EC EC 交BD 于点G ．因为E 为AB 的中点，PA PB =，所以PE AB ⊥．因为平面PAB ⊥平面ABCD ，平面PAB ⋂平面,ABCD AB PE =⊂平面PAB ，所以PE ⊥平面ABCD ，因为BD ⊂平面ABCD ，所以BD ⊥．因为ABD BCE ≅ ，所以CEB BDA ∠∠=，所以90CEB ABD ∠∠+= ，所以BD EC ⊥，因为,,PE EC E PE EC ⋂=⊂平面PEC ，所以BD ⊥平面PEC ．因为EF ⊂平面PEC ，所以BD EF ⊥．【小问2详解】如图，取DC 的中点H ，以E 为坐标原点，分别以,,EB EH EP 所在直线为,,x y z 轴建立空间直角坐标系，【设2AB =，则2,1,BC AD PA PB ====则()()()()0,0,1,1,2,0,1,1,0,0,0,0P C D E -，设(),,,(01)F x y z PF PC λλ=<<，所以()(),,11,2,1x y z λ-=-，所以,2,1x y z λλλ===-，即(),2,1F λλλ-．则()()()2,1,0,1,2,1,,2,1DC PC EF λλλ==-=-，设平面PCD 的法向量为(),,m a b c =，则00DC m PC m ⎧⋅=⎪⎨⋅=⎪⎩，，即2020a b a b c +=⎧⎨+-=⎩，，取()1,2,3m =--，设EF 与平面PCD 所成的角为θ，由cos θ=sin θ=．所以sin cos ,m EF m EF m EF θ⋅====整理得2620λλ-=，因为01λ<<，所以13λ=，即13PF PC = ，故当F 位于棱PC 靠近P 的三等分点时，EF 与平面PCD18. 在平面直角坐标系xOy 中，抛物线21:2(0)C y px p =>的焦点到准线的距离等于椭圆222:161C x y +=的短轴长，点P 在抛物线1C 上，圆222:(2)E x y r -+=（其中01r <<）.（1）若1,2r Q =为圆E 上的动点，求线段PQ长度的最小值；（2）设()1,D t 是抛物线1C 上位于第一象限的一点，过D 作圆E 的两条切线，分别交抛物线1C 于点,M N .证明：直线MN 经过定点.【答案】（1（2）证明见解析【解析】【分析】（1）根据椭圆的短轴可得抛物线方程2y x =，进而根据两点斜率公式，结合三角形的三边关系，即可由二次函数的性质求解，（2）根据两点坐标可得直线,MN DM 的直线方程，由直线与圆相切可得,a b 是方程()()()2222124240r x r x r -+-+-=的两个解，即可利用韦达定理代入化简求解定点.【小问1详解】由题意得椭圆的方程：221116y x +=，所以短半轴14b =所以112242p b ==⨯=，所以抛物线1C 的方程是2y x =.设点()2,P t t ，则111222PQ PE ≥-=-=≥，所以当232ι=时，线段PQ.【小问2详解】()1,D t 是抛物线1C 上位于第一象限的点，21t ∴=，且()0,1,1t D >∴设()()22,,,M a a N b b ，则：直线()222:b a MN y a x a b a --=--，即()21y a x a a b-=-+，即()0x a b y ab -++=.直线()21:111a DM y x a --=--，即()10x a y a -++=.由直线DMr =，即()()()2222124240r a r a r -+-+-=..同理，由直线DN 与圆相切得()()()2222124240r b r b r -+-+-=.所以,a b 是方程()()()2222124240r x r x r -+-+-=的两个解，22224224,11r r a b ab r r --∴+==--代入方程()0x a b y ab -++=得()()222440x y r x y +++---=，220,440,x y x y ++=⎧∴⎨++=⎩解得0,1.x y =⎧⎨=-⎩∴直线MN 恒过定点()0,1-.【点睛】圆锥曲线中定点问题的两种解法（1）引进参数法：先引进动点的坐标或动线中系数为参数表示变化量，再研究变化的量与参数何时没有关系，找到定点.（2）特殊到一般法：先根据动点或动线的特殊情况探索出定点，再证明该定点与变量无关.技巧：若直线方程为()00y y k x x -=-,则直线过定点()00,x y ;若直线方程为y kx b =+ (b 为定值),则直线过定点()0,.b 19. 龙泉游泳馆为给顾客更好的体验，推出了A 和B 两个套餐服务，顾客可选择A 和B 两个套餐之一，并在App 平台上推出了优惠券活动，下表是该游泳馆在App 平台10天销售优惠券情况．日期t 12345678910销售量千张 1.9 1.98 2.2 2.36 2.43259 2.682.76 2.70.4经计算可得：10101021111 2.2,118.73,38510i i i i i i i y y t y t =======∑∑∑.（1）因为优惠券购买火爆，App 平台在第10天时系统出现异常，导致当天顾客购买优惠券数量大幅减少，已知销售量y 和日期t 呈线性关系，现剔除第10天数据，求y 关于t 的经验回归方程结果中的数值用分数表示；..（2）若购买优惠券的顾客选择A 套餐的概率为14，选择B 套餐的概率为34，并且A 套餐可以用一张优惠券，B 套餐可以用两张优惠券，记App 平台累计销售优惠券为n 张的概率为n P ，求n P ；（3）记（2）中所得概率n P 的值构成数列{}()Nn P n *∈.①求n P 的最值；②数列收敛的定义：已知数列{}n a ，若对于任意给定的正数ε，总存在正整数0N ，使得当0n N >时，n a a ε-<，（a 是一个确定的实数），则称数列{}n a 收敛于a .根据数列收敛的定义证明数列{}n P 收敛．参考公式： ()()()1122211ˆˆ,n ni i i i i i n n ii i i x x y y x y nx y ay bx x x x nx ====---==---∑∑∑∑.【答案】（1）673220710001200y t =+ （2）433774n n P ⎛⎫=+⋅- ⎪⎝⎭（3）①最大值为1316，最小值为14；②证明见解析【解析】【分析】（1）计算出新数据的相关数值，代入公式求出 ,ab 的值，进而得到y 关于t 的回归方程；（2）由题意可知1213,(3)44n n n P P P n --=+≥，其中12113,416P P ==，构造等比数列，再利用等比数列的通项公式求解；（3）①分n 为偶数和n 为奇数两种情况讨论，结合指数函数的单调性求解；②利用数列收敛的定义，准确推理、运算，即可得证．【小问1详解】解：剔除第10天的数据，可得 2.2100.4 2.49y ⨯-==新，12345678959t ++++++++==新，则9922111119.73100.4114,73,38510285i i i i t y t ==⎛⎫⎛⎫=-⨯==-= ⎪ ⎪⎝⎭⎝⎭∑∑新新，所以912922119114,7395 2.4673ˆ2859560009i i i i t y t y b t t ==⎛⎫- ⎪-⨯⨯⎝⎭===-⨯⎛⎫- ⎪⎝⎭∑∑新新新新新，可得6732207ˆ 2.4560001200a =-⨯=，所以6732207ˆ60001200y t =+.【小问2详解】解：由题意知1213,(3)44n n n P P P n --=+≥，其中12111313,444416P P ==⨯+=，所以11233,(3)44n n n n P P P P n ---+=+≥，又由2131331141644P P +=+⨯=，所以134n n P P -⎧⎫+⎨⎬⎩⎭是首项为1的常数列，所以131,(2)4n n P P n -+=≥所以1434(2)747n n P P n --=--≥，又因为1414974728P -=-=-，所以数列47n P ⎧⎫-⎨⎬⎩⎭是首项为928-，公比为34-的等比数列，故143)74n n P --=-，所以1934433(()2847774n n n P -=--+=+-.【小问3详解】解：①当n 为偶数时，19344334()(28477747n n n P -=--+=+⋅>单调递减，最大值为21316P =；当n 为奇数时，19344334()(28477747n n n P -=--+=-⋅<单调递增，最小值为114P =，综上可得，数列{}n P 的最大值为1316，最小值为14.②证明：对任意0ε>总存在正整数0347[log ()]13N ε=+，其中 []x 表示取整函数，当 347[log ()]13n ε>+时，347log ()34333333()()()7747474n n n P εε-=⋅-=⋅<⋅=，所以数列{}n P 收敛.【点睛】知识方法点拨：与新定义有关的问题的求解策略：1、通过给出一个新的定义，或约定一种新的运算，或给出几个新模型来创设新问题的情景，要求在阅读理解的基础上，依据题目提供的信息，联系所学的知识和方法，实心信息的迁移，达到灵活解题的目的；2、遇到新定义问题，应耐心读题，分析新定义的特点，弄清新定义的性质，按新定义的要求，“照章办事”，逐条分析、运算、验证，使得问题得以解决.方法点拨：与数列有关的问题的求解策略：3、若新定义与数列有关，可得利用数列的递推关系式，结合数列的相关知识进行求解，多通过构造的分法转化为等差、等比数列问题求解，求解过程灵活运用数列的性质，准确应用相关的数列知识.。
浙江省杭师大附中高三月考英语试题
第Ⅰ卷（共80分）第一部分：英语知识运用（共两节，满分30）第一节：单项填空（共20小题；每小题0.5分，满分10分）1. —Let’s have a game of tennis; the loser has to treat the other to a hot do g.—_______.A. I’m afraid soB. It’s a dealC. My treatD. You’ve got a point2. What lessons China can draw from _______ global financial crisis has become_______hot topic among us students.A. the; aB. /; aC. a; theD. /; the3. She devoted herself _______ to her research and it earned her a good fame in her field.A. stronglyB. widelyC. entirelyD. freely4. —What did the shopkeeper say when you said the sweater was too expensive?—She said the sweater of this kind in other shops might be cheaper but _______.A. not so betterB. too worseC. not good asD. not as good5. _______ a mobile phone can you ring _______ you want to talk with anywhere .A. Using; whoeverB. By; whomeverC. Only on; whomeverD. With; whoever6. —_______was it that he managed to get the information?—Oh, a friend of his helped him.A. WhoB. WhatC. HowD. Why7. —Has Peter finished his graduation paper today?—I have no idea. He _______ it this afternoon.A. writesB. will writeC. had writtenD. was writing8. Jenny works hard as usual and it has_______. She got the first in the final exam again .A. showed offB. got backC. paid offD. turned up9. A road was closed off in Bedfordshire after a man was found _______ a serious headinjury.A. to suffer fromB. suffering fromC. suffer fromD. being sufferedfrom10. As it reported, it is 100 years _______Qinghua University was founded.A. whenB. beforeC. afterD. since11. She showed he visitors around the museum, _______ the construction has takenmore than three years.A. whoseB. in whichC. of whichD. to which12. It is still under discussion _______ the old bus station should be replaced with amodern hotel or not.A. whetherB. whenC. thatD. why13. Today we will begin ______ we stopped yesterday so that no point will be left out.A. whenB. whereC. howD. what14. Sarah pretended to be cheerful, _______ nothing about the argument.A. saysB. saidC. to sayD. saying15. —You _______ Tom the change of the schedule of trip.—Oh, my God! I forgot about it.A .must tell B. should tell C. must have told D. should havetold16. How many students in your school have been _______ to famous universities thisyear?A. enteredB. acceptedC. receivedD. admitted17. During that time about two thousand people went through the station, most of_______ on their way to work.A. themB. whoC. whomD. that18. The old engineer’s eyes still shone bright in the wrinkled brown face and his step as hecame across the room was________，though slow.A. shakyB. heavyC. casualD. steady19. Even if he has been a teacher for 20 years, he still has a good and serious _______towards his work.A. opinionB. attitudeC. viewD. principle20. We mustn’t waste anything. ________, you shouldn’t waste time.A. After allB. Above allC. At allD. In all第二节：完形填空（共20小题；每小题1分，满分20分）―Hi! John.‖ Mary ran towards me with a rare bright smile on her face, saying, ―I’m goin g to have a 21 performance tonight. I hope you’ll come. Here is the 22 . ‖ She left in a hurry, disappearing in the crowds of people 23 .―Is that true?‖ I asked myself. She was a quite 24 girl. I had never seen her making up or wearing attractive clothes, for she did not know how to 25 indeed.I arrived at the 26 with the ticket, and found my seat. Her performance was the seventh one. I knew I would 27 from a hard time before her turn, for I had no 28 of art, but her performance was 29 watching, no matter how long I would wait. Time went slowly. I 30 with myself not to fall asleep.―Let’ s welcome the next exciting dance—Latin‖31 filled the hall at once.I opened my eyes as large as possible, 32 to lose anything. Wearing a golden and shining skirt, Mary appeared on the stage. Dancing with a charming smile, she was fully 33 in the Latin music. At this moment, she looked like a pretty butterfly 34 on the splendid stage.After all the performance 35 , I waited for her at the gate.―Hi!‖ She stood in front of me with a bag and her crystal （水晶）high-heeled shoes in her hands, and 36 as she used to be, but the making-up still could be seen.―How do you feel?‖ There was not a little bit tired 37 on her face.―38 !‖ I answered.―Thank you! I knew it would be. ‖ She could not 39 her excitement, laughing like a child. Looking at the shining crystal high-heeled shoes in the wonderful starry night, I __40_ that every girl has a pair of special shoes which are like the crystal shoes of Cinderella.21. A. instrument B. dance C. music D. opera22. A. address B. number C. ticket D. invitation23. A. quickly B. completely C. quietly D. excitedly24. A. lovely B. popular C. confident D. ordinary25. A. cover up B. turn off C. dress up D. take in26. A. hall B. party C. theatre D. school27. A. relieve B. escape C. relax D. suffer28. A. interest B. ability C. sense D. touch29. A. proper B. worth C. good D. happy30. A. struggled B. knocked C. supported D. shouted31. A. Appreciation B. Attention C. Expectation D. Applause32. A. failing B. fearing C. forgetting D. regretting33. A. absorbed B. swallowed C. interested D. surrounded34. A. singing B. flying C. skipping D. staying35. A. stopped B. paused C. ended D. succeeded36. A. talked B. dressed C. laughed D. looked37. A. appearance B. excitement C. expression D. exhibition38. A. Sorry B. Congratulations C. Far from D. Fantastic39. A. hide B. prevent C. remove D. abandon40. A. doubted B. realized C. wondered D. suggested第二部分：阅读理解(第一节20小题，第二节5小题；每题2分，满分50分)第一节：阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。
2024届湖南师范大学附属中学高三上学期月考卷(四)数学及答案
湖南师大附中2024届高三月考试卷（四）数学审题人：高三备课组时量：120分钟 满分：150分一、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的.1.已知复数12i z =+，其中i 为虚数单位，则复数2z 在复平面内对应的点的坐标为（ ）A.(4,5)- B.(4,3)C.(3,4)- D.(5,4)）2.若随机事件A ，B 满足1()3P A =，1()2P B =，3()4P A B = ，则(|)P A B =（ ）A.29B.23C.14D.168.设{}n a 是公比不为1的无穷等比数列，则“{}n a 为递减数列”是“存在正整数0N ，当0n N >时，1n a <”的（）A.充分而不必要条件B.必要而不充分条件C.充分必要条件D.既不充分也不必要条件4.设0,2πα⎛⎫∈ ⎪⎝⎭，0,2πβ⎛⎫∈ ⎪⎝⎭，且1tan tan cos αβα+=，则（ ）A.22παβ+=B.22παβ-=C.22πβα-=D.22πβα+=5.若52345012345(12)(1)(1)(1)(1)(1)x a a x a x a x a x a x -=+-+-+-+-+-，则下列结论中正确的是（ ）A.01a = B.480a =C.50123453a a a a a a +++++= D.()()10024135134a a a a a a -++++=6.函数1()2cos[(2023)]|1|f x x x π=++-在区间[3,5]-上所有零点的和等于（ ）A.2B.4C.6D.87.点M 是椭圆22221x y a b+=（0a b >>）上的点，以M 为圆心的圆与x 轴相切于椭圆的焦点F ，圆M 与y 轴相交于P ，Q ，若PQM △是钝角三角形，则椭圆离心率的取值范围是（）A.(0,2B.⎛ ⎝C.⎫⎪⎪⎭D.(2-8.已知函数22,0,()4|1|4,0,x x f x x x ⎧=⎨-++<⎩…若存在唯一的整数x ，使得()10f x x a -<-成立，则所有满足条件的整数a 的取值集合为（ ）A.{2,1,0,1}-- B.{2,1,0}-- C.{1,0,1}- D.{2,1}-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.知双曲线C过点且渐近线为y x =，则下列结论正确的是（ ）A.C 的方程为2213x y -= B.CC.曲线2e1x y -=-经过C 的一个焦点D.直线10x --=与C 有两个公共点10.已知向量a ，b满足|2|||a b a += ，20a b a ⋅+= 且||2a = ，则（ ）A.||8b = B.0a b += C.|2|6a b -=D.4a b ⋅= 11.如图、正方体1111ABCD A B C D -的棱长为2，点M 是其侧面11ADD A 上的一个动点（含边界），点P 是线段1CC 上的动点，则下列结论正确的是（）A.存在点P ，M ，使得二面角M DC P --大小为23πB.存在点P ，M ，使得平面11B D M 与平面PBD 平行C.当P 为棱1CC的中点且PM =时，则点M 的轨迹长度为23πD.当M 为1A D 中点时，四棱锥M ABCD -12.若存在实常数k 和b ，使得函数()F x 和()G x 对其公共定义域上的任意实数x 都满足：()F x kx b +…和()G x kx b +…恒成立，则称此直线y kx b =+为()F x 和()G x 的“隔离直线”.已知函数2()f x x =（x ∈R ），1()g x x=（0x <），()2eln h x x =（e 2.718≈），则下列选项正确的是（ ）A.()()()m x f x g x =-在x ⎛⎫∈ ⎪⎝⎭时单调递增B.()f x 和()g x 之间存在“隔离直线”，且b 的最小值为–4C.()f x 和()g x 之间存在“隔离直线”，且k 的取值范围是[4,1]-D.()f x 和()h x之间存在唯一的“隔离直线”ey =-三、填空题：本题共4小题，每小题5分，共20分.13.已知函数()y f x =的图象在点(1,(1))M f 处的切线方程是122y x =+，则(1)(1)f f +'=___________.14.如图，由3个全等的钝角三角形与中间一个小等边三角形DEF 拼成的一个较大的等边三角形ABC ，若3AF =，sin ACF ∠=，则DEF △的面积为___________.15.已知数列{}n a 的首项132a =，且满足1323n n n a a a +=+.若123111181n a a a a ++++< ，则n 的最大值为___________.16.在棱长为3的正方体1111ABCD A B C D -中，点E 满足112A E EB =，点F 在平面1BC D 内，则|1||A F EF +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2()2cos 2xf x x m ωω=++（0ω>）的最小值为–2.（1）求函数()f x 的最大值；（2）把函数()y f x =的图象向右平移6πω个单位长度，可得函数()y g x =的图象，且函数()y g x =在0,8π⎡⎤⎢⎥⎣⎦上单调递增，求ω的最大值.18.（12分）为了丰富在校学生的课余生活，某校举办了一次趣味运动会活动，学校设置项目A “毛毛虫旱地龙舟”和项目B “袋鼠接力跳”.甲、乙两班每班分成两组，每组参加一个项目，进行班级对抗赛.第一个比赛项目A 采取五局三胜制（即有一方先胜3局即获胜，比赛结束）；第二个比赛项目B 采取领先3局者获胜。
高中英语：2024届高三第二次学业质量评价(八省八校,T8联考)英语试题
广东实验中学东北育才中学石家庄二中华中师大一附中西南大学附中南京师大附中湖南师大附中福州一中2024届高三第二次学业质量评价（T8联考）英语试题考试时间:2024年3月21日上午8:00-10:00试卷满分:150分考试用时:120分钟注意事项:1.答卷前, 考生务必将自己的姓名、准考证号填写在答题卡上。
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.考试结束后将本试卷和答题卡一并交回。
第一部分听力（共两节, 满分3分）做题时,先将答案标在试卷上。
录音内后, 你将有两分钟的时间将试卷上的答案转涂到答题卡上。
第一节（共5小题；每小题1. 5分, 满分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。
例： How much is the shirt?A.£ 19. 15.B.£ 9. 18.C.£ 9. 15.答案是C。
1.Why is the man late for work?A.He repaired his clock.B.The clock didn’t ring.C.He experimented unsuccessfully.2.How will the woman get her health report?3. What does the man want to do?A. See a doctor.B. Deliver a speech.C. Keep a frog.4. Where can the woman get the bus information?A. From the apartment.B. From the bus stop.C. From the local library.5. When will the man leave?A. In the morning.B. In the afternoon.C. In the evening.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。
浙江省四校联考2023-2024学年高二下学期3月月考英语试卷(含答案)
浙江省四校联考2023-2024学年高二下学期3月月考英语试卷学校：___________姓名：___________班级：___________考号：___________ 一、阅读理解The Department of Labor's Employment and Training Administration (ETA) supports a wide variety of programs to ensure that all youth have the skills and training they need to successfully make the switch to adulthood and careers. These programs include: ApprenticeshipApprenticeship is a combination of on-the-job training and related classroom instruction in which workers learn the practical and theoretical aspects of a highly skilled occupation. Applicants for apprenticeship programs must be at least 16 years old and meet the program sponsor's qualifications.YouthBuildYouthBuild programs give at-risk youth ages 16-24 the opportunity to transform their lives by earning their high school certificate of graduation or an equally state-recognized degree, learning to be community leaders, and preparing for college and other post-secondary training opportunities.Job CorpsJob Corps is the nation's largest and most comprehensive residential, education, and job training program for at-risk youth, ages 16 through 24. Private companies, state agencies, federal agencies, and unions recruit(招募) young people to participate in Job Corps, where they can train for and be placed in jobs.Youth ConnectionsThe Workforce Innovation and Opportunity Act (WIOA) of 2014 is carrying out a comprehensive youth employment program for serving qualified youth, ages 14-24, who face barriers to education , training, and employment.For more information about youth programs, visit ETA's Division of Youth Services page. 1．What can participants do in the YouthBuild?A. Lead the state communities.B. Study theories of skilled work.C. Obtain a graduation certificate.D. Prepare for secondary training.2．Which program is suitable for teenagers aged 15?A. Apprenticeship.B. YouthBuild.C. Job Corps.D. Youth Connections.3．What is the author's purpose of writing the text?A. To improve youth training.B.To advertise for youth services.C. To transform youth development.D. To introduce ETA youth programs.In 2016, when I was on the graduate scheme (计划) at Deutsche Bank, Marie Inafidon, chief executive of Stemettes, who encourages girls to pursue careers in science, technology, engineering and maths (STEM) , was also working there. I didn't meet her at the time, but I did read an article about her and her career.Learning at 21 years old about the career of a young black woman' succeeding in a traditionally white male-dominated industry was one of the most influential things that ever happened to me. It gave me confidence that it was possible to do well in the office and work on personal external project at the same time.Role models can play a central role in shaping a young professional's career. They are especially important if you belong to an under-represented group for whom a lack of representation in the workplace can lead to feeling isolated and lacking in confidence. They can help those just starting out, whether or not they are a graduate as I was, to believe in their own abilities.There's a growing need to have accessible role models. Given the tendency to exaggerate (夸大) success stories, hearing from women who talk honestly about the challenges they have faced, either when starting a business or forming a new career path, is much more effective. A study revealed that 70 per cent of girls say they think differently about their futures after hearing from women role models.I'm frequently asked about what businesses could be doing to increase racial diversity in the workplace. A good starting point is to actively promote and support the voices of the people in the organisation that are leading positive change and inspiring others. This makes a real difference. Unlike the tokenism (装样子) I still come across, which results in individuals being made the lone representative for a group without real support from the organisation.Things came full circle for me when I interviewed Ms. Inafidon for my book in 2019. I was able to tell her of the incredible impact her passion and confidence had had on me as a graduate trainee and how grateful I would always be for that.4．What do we learn about Marie Inafidon?A. She became successful at 21.B. She was a trainee at Deutsche Bank.C. She encouraged girls to take up STEM-related work.D. She helped the author with her external project personally.5．Who can benefit most from role models in the work place according to the third paragraph?A. Experienced professionals.B. A graduate eager to succeed.C. People without special abilities.D. The young from an under-represented group. 6．What is effective in changing girls' mindset?A. Taking on challenging projects.B. Reading more made-up success stories.C. Starting their own business as early as possible.D. Listening to women role models share their experiences.7．What should businesses do to increase racial diversity in the workplace according to the author?A. Encourage positive opinions.B. Make more colored people authorities.C. Include more people of different races.D. Understand the true meaning of tokenism.New York University (NYU) surgeons have performed the world's first transplant of an entire human eye, an extraordinary addition to a face transplant, although it's far too soon to know if the man will ever see through his new left eye.An accident had destroyed most of Aaron James' face and one eye. His right eye still works. But the surgeons hoped replacing the missing one would produce better cosmetic (整容的) results for his new face. The NYU team is doing just that. James is recovering well from the dual (双重的) transplant last May and the donated eye looks remarkably healthy.Today, transplants of the cornea(眼角膜) are common to treat certain types of vision loss. But transplanting the whole eye—the eyeball, its blood supply, and the critical optic nerve(视神经) that must connect it to the brain-is considered a moonshot in the search to cure blindness.Whatever will happen next, James' surgery offers scientists a window into how the human eye tries to heal. "We're not claiming that we are going to restore sight," said Dr. Eduardo Rodriguez, who led the transplant. "But there's no doubt that we are one step closer."Some specialists had feared the eye would quickly become dry and wrinkled. However, when Rodriguez opened James' left eyelid, the donated eye was fat and full of liquid. Doctors see good blood flow and no sign of rejection.Now researchers have begun analyzing scans (扫描结果) of James' brain that detected some puzzling signals from that all-important but injured optic nerve. Dr. Jeffrey Goldberg, who has long studied how to make eye transplants a reality, called the surgery exciting. "It's an amazing confirmation of animal experiments that have kept transplanted eyes alive," he said. "The difficulty now is how to regrow the optic nerve, although animal studies are making progress." He praised the NYU team's "boldness" in even aiming for optic nerve repair and hopes the transplant will promote more research.8．What can be learnt from the first two paragraphs?A. James is fully content with the surgery result.B. The surgeons have transplanted the face and an eye to James.C. James can see through his transplanted eye pretty soon.D. The surgery to replace James' missing eye is underway.9．What does the underlined word “moonshot” in paragraph 3 probably mean?A. A task impossible to complete.B. A fantasy existing in the virtual world.C. A project extremely tough to accomplish.D. A mission probable to be complete without effort.10．What challenge are the researchers facing now?A. How to obtain better cosmetic results.B. How to stop the transplanted eye from shriveling(萎缩).C. How to make further progress in animal studies.D. How to grow the optic nerve of the transplanted eye again.11．What can be a suitable title for the text?A. James Received Transplanted Eye PerfectlyB. NYC Doctors Perform World's First Eye TransplantC. Various Methods to Treat Different Types of Vision LossD. Advances Made in Eye Transplant and Optic Nerve RepairCould you manage without the internet for four and a half years? That's exactly what the actress Selena Gomez has done in a bid to improve her mental health.She has spoken extensively about the relationship between her social media usage and mental well-being, recalling feeling like "an addict" as to becoming Instagram's most followed user in 2016. "Indeed, I regret quitting from social media that late", says she. "The unnecessary hate and comparisons went away once I put my phone down.”However, the increasing digitization (数字化) means that everything from paying a bill to even making a phone call is at the mercy of the internet. Actively opting (选择) out of the internet becomes a matter of privilege. Ms Gomez's multi-millionaire status has allowed her to take the "social” out of social media. The fact that she's still the second most-followed woman on Instagram suggests it's entirely possible to maintain a significant web profile to promote various projects by way of a dedicated team—without being exposed to the cruel comments.It goes without saying that this is fundamentally different from how the rest of us without beauty deals and films to publicize use the likes of Instagram and Twitter, but even the concept of a digital detox (戒瘾) requires having a device and connectivity to choose to disconnect from.The UK's digital divide has worsened over the past two years, leaving poorer families without broadband connections in their homes. Digital exclusion (数字隔绝) is a major threat to wider societal equality in the UK.Consequently, it's worth bearing in mind that while deleting all social media accounts will undoubtedly make some feel infinitely better, many other people benefit from the strong sense of community that sharing platforms can develop. Greater resources and initiatives are needed to provide the underprivileged with the connectivity they desperately need to learn, work and live. It's crucial that people feeling social media is harmful to their mental health are allowed to switch off and for those living in digital exclusion to be able to switch on primarily.12．What do we learn about the actress Selena Gomez in the past four and a half years?A. She has withdrawn from social media.B. She has won Instagram's most followers.C. She has had worsening mental problems.D. She has succeeded in a bid on the internet.13．Why does actively opting out of using the internet become a matter of privilege?A. Most people think that digital exclusion promotes societal equality in the UK.B. Most people can hardly abandon the web while avoiding hate and comparisons.C. Most people can hardly get by without the internet due to growing digitization.D. Most people have been seriously addicted to the web without being aware of it. 14．What is stressed concerning social media platforms in the last paragraph?A. They are beneficial to people's mental health.B. They create a virtual community on the internet.C. They help many people feel connected with others.D. They provide a necessary device for a digital detox.15．What is the author's attitude towards social media platforms?A. Subjective.B. Objective.C. Disapproving.D. Favorable.二、七选五16．In our fast-paced world, where speed and instant results often steal the spotlight, there's a quiet but great virtue that often goes unnoticed—the courage to go slow. It may sound abnormal, but instead of rushing to implement (实施), we need to slow down. This is particularly relevant when we start the journey of developing instructional strategies. ①_____●Start, add and abandon habits. Understand that habit formation takes time and requires testing, reflecting, and adapting. Set systems that focus you and your team and organization on the implementation and impact on a few key practices. ②_____●Push consistency over intensity. Focus on maintaining consistent effort rather than pushing for rapid, unsustainable changes. ③_____ This occurs because the lasting habits that are selected are implemented every day and reflected upon routinely.●④_____ Celebrate each little victory along the way. These moments of success, no matter how minor, are the building blocks of lasting change.●Seek support. Surround yourself with individuals who support your journey and value the importance of patience. Lean on their encouragement during challenging times.Admittedly, it takes courage to welcome the wisdom of going slow in this competitive world. ⑤_____ Taking it slow with patience enables individuals to travel along this journey with determination, as can be illustrated by the well-known story of the tortoise and the hare.A. Ask for suggestions.B. Applaud small wins.C. It's the slow and steady progress that leads to lasting habits.D. As we slow down, patience becomes our greatest companion.E. Protect these few practices by giving up other unsuitable ones.F. However, is it right for us common people to do so in such a way?G. The question then is, how do we go slow and develop and sustain a new habit?三、完形填空（15空）Adrienne Tully, an amateur photographer, went to the coast of a beach in Belmar, Newwhat he did.17．A. wildlife B. city C. fight D. sunrise18．A. launch B. anticipate C. shoot D. report19．A. cooperating B. forming C. arguing D. encountering20．A. hope B. charge C. absence D. face21．A. confused B. desperate C. anxious D. depressed22．A. fortunately B. however C. otherwise D. therefore23．A. defeated B. deserted C. stuck D. seated24．A. routines B. attempts C. excuses D. routes25．A. ruined B. interrupted C. canceled D. postponed26．A. purposely B. randomly C. elegantly D. heroically27．A. onlooker B. tourist C. surfer D. guide28．A. going B. washing C. thundering D. struggling29．A. ashamed B. mad C. amazed D. expert30．A. went off B. turned up C. settled down D. set out31．A. appreciated B. understood C. awarded D. supported四、短文填空32． The Qinghai Lake National Nature Reserve in northwest China's Qinghai Province has updated ①_____(it) list of protected wildlife, adding 10 species ②_____ the previoustotal of 72, according to a report by the Xinhua News Agency. The updated list, which was revised by experts, ③_____(include) 82 species of protected wildlife. The number of national first-level protected animals has increased from 19 to 22. Meanwhile, the number of second-level nationally protected animals has increased from 53 to 60. ④_____(additional), the number of wild plants under national protection has reached 12 species. According to the report, the ⑤_____(revise) of the wildlife list focused on optimizing (优化) ⑥_____ adjusting the bird list. Species with uncertain records were removed from the original list and new species that have been monitored in recent years were added, increasing the total number of bird species from 232 to 281.First ⑦_____(found) in 1975, the Qinghai Lake National Nature Reserve is located in the northeast of the Qinghai-Tibet Plateau, ⑧_____(cover) the entire water area of the Qinghai Lake and the islands, beaches and wetlands, ⑨_____ birds breed and nest. The reserve is the ⑩_____(early) of its kind in China to be listed in the List of Wetlands of International Importance in 1992, according to UNESCO.五、书面表达33．假定你是李华, 你的英国笔友Peter上周因为使用AI完成翻译作业而被中文老师批评, 心情非常低落。
浙江省杭州师大附中2015届高三第四次月考语文
浙江省杭州师大附中2015届高三第四次月考语文高三2012-05-18 14:54一、语言文字运用（共24分，其中选择题每小题3分）1．下列词语中加点字读音全都正确的一项是A 针砭（biān）鳏夫（guān）因噎废食(yē) 正当(dāng)防卫B 戏谑（xuâ）豢养（juàn）徇(xùn)私舞弊胼手胝（zhī）足C 木讷（nâ）莅临(lì)不稂不莠（láng）令人赧颜（nǎn）D 僭（jiàn）越蹊跷（qiào）剽悍少年（biāo）退避三舍(shě)2．下列各句中，没有错别字的一项是A．大学生一留学外国，便拾人牙慧。
/ 劳资谈判在秘密进行，双方仍是剑拔弩张。
/ 这是多么灵验的科学预言，多么宝贵的真知灼见。
（摘自网络新闻）B．发黄的照片，记载着峥嵘岁月。
/三年同窗情谊深，盼再聚渡假胜地——神仙居。
/ 追忆逝去的青葱岁月，捡拾失落的童年记忆。
（摘自毕业纪念册）C．您心连莘莘学子，情系祖国未来。
/ 您的胸怀像大海一样深邃，像天空一样辽阔。
/ 甘为人梯，沤心沥血，无私奉献。
（摘自教室板报）D．房地产过冬，政府当未雨绸缪。
/ 辽宁抚顺民警齐捐款，白内瘴患者重见光明。
/女童被碾引公众反思，见死不救显道德滑坡。
（摘自法制日报）3．下列各句中，加点的词语运用正确的一项是A．最新出炉的中国2050年空间科技发展路线图称，2030年前后，中国实现载人登月，建立有人长期逗留的空间站——月球基地。
B．按照康德的理论，道德品质和钱，似乎是完全不同的两个领域；不过康德说的是在思想上、原则上，而在实际上却仍是休戚相关的。
C．日前，中国科学院有多项科研成果被沿海地区的一些公司、企业引进，产生了很好的经济效益，真是“墙里开花墙外香”啊。
D．从明年起，浙江省将全面推行高中新课程改革，但是课程改革要依据地域自身实际，不能削足适履，一味照抄江苏、福建等地的经验。
2025届上师大附中高三数学上学期10月考试卷一附答案解析
2025届上师大附中高三10月月考数学试卷一一、填空题（1-6每题4分，7-12每题5分，共54分）1.函数()f x =的定义域为__．【答案】(0,1]．【解析】【分析】由函数有意义需要的条件，求解函数定义域【详解】函数的意义，有0110x x≠⎧⎪⎨-≥⎪⎩，解得01x <≤，即函数()f x =定义域为(0,1]．故答案为：(0,1]2. 已知0a >=________.【答案】34a 【解析】【分析】根式形式化为分数指数幂形式再由指数运算化简即可.1113322224a a a a ⎛⎫⎛⎫=⋅== ⎪ ⎪⎝⎭⎝⎭.故答案为：34a .3. 已知幂函数()f x 的图象经过点13,9⎛⎫ ⎪⎝⎭，求(3)f -=_________．【答案】19【解析】【分析】设幂函数为(),R f x x αα=∈，根据题意求得2α=-，得到2()f x x -=，代入即可求解.【详解】设幂函数为(),R f x x αα=∈，因为幂函数()f x 的图象经过点13,9⎛⎫ ⎪⎝⎭，可得139α=，解得2α=-，即2()f x x -=，所以21(3)(3)9f --=-=.故答案为：19.4. 若1sin 3α=，则cos(2)πα-=____.【答案】79-【解析】【分析】原式利用诱导公式化简后，再利用二倍角的余弦函数公式变形，将sin α的值代入计算即可求出值．【详解】因为1sin 3α=，所以()2227cos(2)cos 212sin12sin 199παααα-=-=--=-+=-+=-．故答案为： 79-5. 已知集合{|3sin ,}M y y x x =∈=R ，{|||}N x x a =<，若M N ⊆，则实数a 的取值范围是___________.【答案】(3,)+∞【解析】【分析】先求出集合M ，N ，再由M N ⊆可求出实数a 的取值范围【详解】解：由题意得{}{|3sin ,}33M y y x x y y ===-≤∈≤R ，{}{|||}N x x a x a x a =<=-<<，因为M N ⊆，所以3a >，故答案为：(3,)+∞6. 设a ，b ∈R ．已知关于x 的不等式250ax x b -+>的解集为21,34⎛⎫-⎪⎝⎭，则不等式250ax x b ++<的解集为__________．【答案】12,,43⎛⎫⎛⎫-∞-⋃+∞ ⎪ ⎪⎝⎭⎝⎭【解析】【分析】先由不等式250ax x b -+>的解集为21,34⎛⎫- ⎪⎝⎭求出实数a ，b 的值，再求不等式250ax x b ++<的解集.【详解】∵不等式250ax x b -+>的解集为21,34⎛⎫- ⎪⎝⎭，∴方程250ax x b -+=的两根分别为123x =-，214x =，且0a <∴由韦达定理可知，1212215342134x x a b x x a ⎧+=-+=⎪⎪⎨⎛⎫⎪=-⨯= ⎪⎪⎝⎭⎩解得122a b =-⎧⎨=⎩，∴将a ，b 代入不等式250ax x b ++<得212520x x -++<，即212520x x -->()()32410x x ⇔-+>∴不等式250ax x b ++<的解集为12,,43⎛⎫⎛⎫-∞-⋃+∞ ⎪ ⎪⎝⎭⎝⎭.故答案为：12,,43⎛⎫⎛⎫-∞-⋃+∞ ⎪ ⎪⎝⎭⎝⎭.7. 已知锐角α的顶点为原点，始边为x 轴的正半轴，将α的终边绕原点逆时针旋转π6后交单位圆于点1,3P y ⎛⎫- ⎪⎝⎭，则sin α的值为________．【解析】【分析】先求得ππcos ,sin 66αα⎛⎫⎛⎫++ ⎪ ⎪⎝⎭⎝⎭，然后利用三角恒等变换的知识求得sin α【详解】由于1,3P y ⎛⎫- ⎪⎝⎭在单位圆上，所以222181,39y y ⎛⎫-+== ⎪⎝⎭，由于α是锐角，所以289y y =⇒=13P ⎛- ⎝，所以π1πcos ,sin 636αα⎛⎫⎛⎫+=-+= ⎪ ⎪⎝⎭⎝⎭所以ππππππsin sin sin cos cos sin 666666αααα⎛⎫⎛⎫⎛⎫=+-=+-+ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭1132=⨯=.8. 已知()()()()1f x x x a x b =+++.若()y f x =为奇函数，则()0f '=__________.【答案】1-【解析】【分析】根据题意，求得()3f x x x =-，得到()231f x x ='-，即可求解.【详解】由函数()()()()321(1)()f x x x a x b x a b x a b ab x ab =+++=+++++++，可得()32(1)()f x x a b x a b ab x ab -=-+++-+++因为函数()f x 为R 上的奇函数，可得()()f x f x -=-，即3232(1)()(1)()x a b x a b ab x ab x a b x a b ab x ab -+++-+++=--++-++-，所以100a b ab ++=⎧⎨=⎩，解得01a b =⎧⎨=-⎩或10=-⎧⎨=⎩a b ，所以()3f x x x =-，可得()231f x x ='-，所以()01f '=-.故答案为：1-.9. 如图，某同学为测量鹳雀楼的高度MN ，在鹳雀楼的正东方向找到一座建筑物AB ，高约为37m ，在地面上点C 处（,,B C N 三点共线）测得建筑物顶部A ，鹳雀楼顶部M 的仰角分别为30o 和45 ，在A 处测得楼顶部M 的仰角为15 ，则鹳雀楼的高度约为___________m .【答案】74【解析】【分析】根据题意在Rt △ABC 中求出AC ，在△MCA 中利用正弦定理求出MC ，然后在Rt △MNC 中可求得结果.【详解】在Rt △ABC 中，274AC AB ==，在△MCA 中，105MCA ︒∠=，45MAC ︒∠=，则18030AMC MCA MAC ︒︒∠=-∠-∠=，由正弦定理得sin sin MC AC MAC AMC=∠∠，即74sin 45sin 30MC ︒︒=，解得MC =，在Rt △MNC中，74m MN ==.故答案：7410. 对于函数()f x 和()g x ，设(){}|0x f x α∈=，(){}|0x g x β∈=，若存在α，β，使得1αβ-<，则称()f x 与()g x 互为“零点相邻函数”.若函数()1e 2x f x x -=+-与()21g x x ax =-+互为“零点相邻函数”，则实数a 的取值范围是______.【答案】[2,)+∞【解析】【分析】由题知函数()f x 有唯一零点1，进而得210x ax -+=在(0,2)上有解，再根据二次函数零点分布求解即可.【详解】因为1()e 2-=+-x f x x ，所以()f x 在R 上为增函数，又0(1)e 120f =+-=，所以()f x 有唯一零点为1，令()g x 的零点为0x ，依题意知0||11x -<，即002x <<，即函数()g x 在(0,2)上有零点，令()0g x =，则210x ax -+=(0,2)上有解，即1x a x +=在(0,2)上有解，因为12x x +≥=，当且仅当1x x =，即1x =时，取等号，所以2a ≥，故答案为：[2,)+∞.为为在11. 若函数()y f x =的图像上存在不同的两点M (x 1,y 1)和N (x 2,y 2)，满足1212x x y y +≥()y f x =具有性质P ，给出下列函数：①()sin f x x =；②()x f x e =；③1(),(0,)f x x x x=+∈+∞；④()||1f x x =+．其中其有性质p 的函数为________（填上所有正确序号）．【答案】①②【解析】【分析】利用数量积性质得出过点O 的直线与函数图像存在至少两个不同的交点，结合函数图象可得．【详解】1212||||cos ,,|||OM ON x x y y OM ON OM ON OM ON ⋅=+=〈〉==所以1212cos ,1x x y y OM ON +≥⇔〈〉≥ ，即cos ,1OM ON 〈〉=± ．即O ，M ，N 三点共线，即过点O 的直线与函数图像存在至少两个不同的交点，由图可知，①②符合．故答案为：①②12. 已知函数()ln 1f x b x =--，若关于x 的方程()0f x =在2e,e ⎡⎤⎣⎦上有解，则22a b +的最小值为______．【答案】29e 【解析】【分析】设函数()f x 在2e,e ⎡⎤⎣⎦上的零点为m ，则由ln 10b m +--=，则(),P a b 在直线:ln 10l x y m +--=上，则22a b +可看作是O 到直线l 的距离的平方，利用导数求出其最小值即可得到答案【详解】解：设函数()f x 在2e,e ⎡⎤⎣⎦上的零点为m ，则ln 10b m --=，所以点(),P a b 在直线ln 10l x y m +--=上，设O 为坐标原点，则222||a b OP +=，其最小值就是O 到直线l 的距离的平方，，2e,eméùÎêúëû，设t⎤=⎦，设()2ln1tg tt+=，则()()212lntg t tt-⎤'=≤∈⎦，所以()g t在⎤⎦上单调递减，所以()()min3eeg t g==，3e≥即2229ea b+≥，所以22a b+的最小值为29e，故答案为：29e二、选择题（13-14每题4分，15-16每题5分，共18分）13. 已知a b∈R，且0ab≠，则“22a b>”是“11a b<”的（）A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件【答案】D【解析】【分析】结合指数函数单调性，根据充分必要条件的定义分别进行判断即可．【详解】22a b a b>⇔>Q，当0a b>>时，11a b<不成立，当11a b<<时，a b>不成立.所以a b>是11a b<的既不充分也不必要条件，即22a b>是11a b<的既不充分也不必要条件.故选：D.14. 设函数()sinf x x=，若对于任意5π2π,63α⎡⎤∈--⎢⎥⎣⎦，在区间[0,]m上总存在唯一确定的β，使得()()0f fαβ+=，则m的值可能是（）A.π6B.π3C.2π3D.5π6【答案】B【解析】的【分析】由等量关系找α与β的关系，由α的范围求出sin β的范围，从而得出m 的值.【详解】∵()()0f f αβ+=，∴sin sin 0αβ+=，即()sin sin sin βαα=-=-，∵5π2π,63α⎡⎤∈--⎢⎥⎣⎦，即2π5π,36α⎡⎤-∈⎢⎥⎣⎦，∴()1sin sin 2βα⎡=-∈⎢⎣，又∵[]0,m β∈，∴π3m =故选：B15. 已知在ABC V 中，0P 是边AB 上一定点，满足023P B AB = ，且对于边AB 上任意一点P ，都有00PB PC P B P C ⋅≥⋅ ，则ABC V 是（ ）A. 钝角三角形B. 直角三角形C. 锐角三角形D. 无法确定【答案】A【解析】【分析】取BC 的中点D ，DC 的中点E ，连接0P D ，AE ，根据向量的线性运算计算向量00,P B P C 并计算00P B P C ⋅ ，同理计算PB PC ⋅ ，根据不等关系可得出对于边AB 上任意一点P 都有0PD P D ≥ ，从而确定0P D AB ⊥，从而得到结果.【详解】取BC 的中点D ，DC 的中点E ，连接0P D ，AE （如图所示），则()()0000P B P C P D DB P D DC ⋅=+⋅+ ()()22000P D DB P D DB P D DB =+⋅-=- ，同理22PB PC PD DB ⋅=- ，因为00PB PC P B P C ⋅≥⋅ ，所以22220PD DB P D DB -≥- ，即220PD P D ≥ ，所以对于边AB 上任意一点P 都有0PD P D ≥ ，因此0P D AB ⊥，又023P B AB = ，D 为BC 中点，E 为DC 中点，所以023P B BD AB BE ==，所以0//P D AE ，即90BAE ∠=︒，所以90BAC ∠>︒，即ABC V 为钝角三角形.故选：A ．16. 设函数,()2,2x x P f x x x M x∈⎧⎪=⎨+∈⎪⎩其中,P M 是实数集R 的两个非空子集，又规定(){(),},(){(),}A P y y f x x P A M y y f x x M ==∈==∈∣∣，有下列命题：①对任意满足P M ⋃=R 的集合P 和M ，都有()()A P A M ⋃=R ；②对任意满足P M ⋃≠R 的集合P 和M ，都有()()A P A M ⋃≠R ，则对于两个命题真假判断正确的是（ ）A. ①和②都是真命题B. ①和②都是假命题C. ①是真命题，②是假命题D. ①是假命题，②是真命题【答案】B【解析】【分析】根据集合的新定义对两个命题进行分析，从而确定正确答案.【详解】对于①可举反例，(,0],(0,)P M =-∞=+∞此时()()()()(),0,2,,A P A M A P A M ∞∞⎤⎡=-=+⋃≠⎦⎣R ，故①是假命题；对于②，可举反例(,4],(4)P M =-∞=++∞，此时()(,4],()(4,),()()R A P A M A P A M =-∞=+∞= ，故②是假命题；故选：B【点睛】解新定义题型的步骤：(1)理解“新定义”——明确“新定义”的条件、原理、方法、步骤和结论.(2)重视“举例”,利用“举例”检验是否理解和正确运用“新定义”;归纳“举例”提供的解题方法.归纳“举例”提供的分类情况.(3)类比新定义中的概念、原理、方法，解决题中需要解决的问题.三、解答题（共5题，满分78分）17. 已知向量3sin ,,(cos ,1)4a x b x ⎛⎫==- ⎪⎝⎭ ．（1）当a b∥时，求tan 2x 的值；（2）设函数()2()f x a b b =+⋅ ，且π0,2x ⎛⎫∈ ⎪⎝⎭，求()f x 的值域．【答案】（1）247- （2）1322⎛⎤+ ⎥⎝⎦【解析】【分析】（1）根据向量平行列出等式，计算tan x 的值，二倍角公式即可计算tan 2x ；（2）计算()f x ，并用辅助角公式化简，根据角的范围可求出值域.【小问1详解】因为a b∥，所以3sin cos 4x x -=，因为cos 0x ≠，所以3tan 4x =-，所以22tan 24tan 21tan 7x x x ==--．【小问2详解】213π3()2()2sin cos 2cos sin 2cos 222242f x a b b x x x x x x ⎛⎫=+⋅=++=++=++ ⎪⎝⎭ ，因为π0,2x ⎛⎫∈ ⎪⎝⎭，所以ππ5π2,444x ⎛⎫+∈ ⎪⎝⎭，所以πsin 24x ⎛⎤⎛⎫+∈ ⎥ ⎪ ⎝⎭⎝⎦，所以()f x的值域为1322⎛⎤ ⎥⎝⎦．18. 已知函数()22x x a f x =+其中a 为实常数.（1）若()07f =,解关于x 的方程()5f x =;（2）判断函数()f x 的奇偶性,并说明理由.【答案】（1）1x =或2log 3（2）答案见解析【解析】【分析】（1）因为()22x x a f x =+,()07f =,可得6a =,故6()22x x f x =+,因为()5f x =,即6252x x+=,通过换元法,即可求得答案;（2）因为函数定义域为R ,分别讨论()f x 为奇函数和()f x 为偶函数,即可求得答案.【详解】（1） ()22x xa f x =+,∴()07f =,即17a +=解得:6a =可得:6()22x xf x =+ ()5f x =∴6252x x+=令2x t =(0t >)∴65t t+=,即:2560t t -+=解得:12t =或23t =即:122x =,223x =∴11x =或22log 3x =.（2）函数定义域为R ,①当()f x 为奇函数时,根据奇函数性质()()f x f x -=-可得2222x x x x a a --⎛⎫+=-+ ⎪⎝⎭恒成立即1(1)202x x a ⎛⎫+⋅+= ⎪⎝⎭恒成立,∴1a =-.②当()f x 为偶函数时,根据偶函数性质()()f x f x -=可得2222x x x x a a --+=+恒成立即1(1)202x x a ⎛⎫-⋅-= ⎪⎝⎭恒成立,∴1a =.③当1a ≠±时,函数为非奇非偶函数.【点睛】本题主要考查了解指数方程和根据奇偶性求参数,解题关键是掌握指数方程的解法和奇偶函数的定义,考查了分析能力和计算能力,属于中档题.19. 某创业投资公司拟投资开发某种新能源产品，估计能获得10万元～1000万元的投资收益.现准备制定一个对科研课题组的奖励方案：奖金y （万元）随投资收益x （万元）的增加而增加，且奖金不超过9万元，同时奖金不超过投资收益的20%.（1）若建立函数()f x 模型制定奖励方案，试用数学语言表述公司对奖励函数()f x 模型的基本要求；（2）现有两个奖励函数模型：①()2150x f x =+；②()ln 2f x x =-；问这两个函数模型是否符合公司要求，并说明理由？【答案】（1）答案见解析（2）()2150x f x =+不符合公司要求，()ln 2f x x =-符合公司要求，理由见解析【解析】【分析】（1）根据题意，用数学语言依次写出函数()f x 的要求即可；（2）判断两个函数模型的单调性，并判断()9f x ≤，()5x f x ≤是否成立得解.【小问1详解】设奖励函数模型为()y f x =，则公司对奖励函数模型基本要求是：当[]10,1000x ∈时，()f x 是严格增函数，()9f x ≤恒成立，()5x f x ≤恒成立.【小问2详解】①对于函数模型()2150x f x =+，易知当[]10,1000x ∈时，()f x 为增函数，且()()max 26100093f x f ==<，所以()9f x ≤恒成立，但是()101005f ->，不满足()5x f x ≤恒成立，所以()2150x f x =+不符合公司要求；②对于函数模型()ln 2f x x =-，的当[]10,1000x ∈时，()10f x x'=>，所以()f x 为增函数，且()max f x f =()100023ln109=-+<，所以()9f x ≤恒成立，令()()ln 255x x g x f x x =-=--，则()1105g x x '=-<，所以()()10ln1040g x g =-<≤，所以()5x f x ≤恒成立，所以()ln 2f x x =-符合公司要求.20. 已知函数()y f x =的定义域为区间D ，若对于给定的非零实数m ，存在0x ，使得()()00f f x x m =+，则称函数()y f x =在区间D 上具有性质()P m .（1）判断函数()2f x x =在区间[]1,1-上是否具有性质12P ⎛⎫ ⎪⎝⎭，并说明理由；（2）若函数()sin f x x =在区间()()0,0>n n 上具有性质4P π⎛⎫⎪⎝⎭，求n 的取值范围；（3）已知函数()y f x =的图像是连续不断的曲线，且()()02f f =，求证：函数()y f x =在区间[]0,2上具有性质13P ⎛⎫ ⎪⎝⎭.【答案】（1）具有性质12P ⎛⎫ ⎪⎝⎭，理由见解析 （2）5,8π⎛⎫+∞ ⎪⎝⎭（3）证明见解析【解析】【分析】（1）由题可得220012x x ⎛⎫=+ ⎪⎝⎭，则014x =-，结合条件即得；（2）由00sin sin 4x x π⎛⎫=+⎪⎝⎭，解得038x k ππ=+，()()050,N 48x k n k πππ+=+∈∈，可得58n π>，即得；（3）设()()13g x f x f x ⎛⎫=-+ ⎪⎝⎭，50,3x ⎡⎤∈⎢⎥⎣⎦，可得()()()1150200333k g g g g f f -⎛⎫⎛⎫⎛⎫++⋅⋅⋅++⋅⋅⋅+=-= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，当()0g 、13g ⎛⎫ ⎪⎝⎭、⋅⋅⋅、13k g -⎛⎫ ⎪⎝⎭、⋅⋅⋅、53g ⎛⎫ ⎪⎝⎭中有一个为0时，可得111333i i f f --⎛⎫⎛⎫=+ ⎪ ⎪⎝⎭⎝⎭，{}1,2,3,,6i ∈⋅⋅⋅，即证；当()0g 、13g ⎛⎫ ⎪⎝⎭、⋅⋅⋅、13n g -⎛⎫ ⎪⎝⎭、⋅⋅⋅、53g ⎛⎫ ⎪⎝⎭中均不为0时，由于其和为0，则其中必存在正数和负数，不妨设103i g -⎛⎫> ⎪⎝⎭，103j g -⎛⎫< ⎪⎝⎭，结合条件可知，存在0x ，()()000103g x f x f x ⎛⎫=-+= ⎪⎝⎭，即证.【小问1详解】函数()2f x x =在[]1,1-上具有性质12P ⎛⎫⎪⎝⎭.若220012x x ⎛⎫=+ ⎪⎝⎭，则014x =-，因为[]11,14-∈-，且[]1111,1424-+=∈-，所以函数()2f x x =在[]1,1-上具有性质12P ⎛⎫⎪⎝⎭.【小问2详解】解法1：由题意，存在()00,x n ∈，使得00sin sin 4x x π⎛⎫=+ ⎪⎝⎭，得0024x x k ππ+=+（舍）或0024x k x πππ+=+-()k ∈Z ，则得038x k ππ=+.因为0308x k ππ=+>，所以k ∈N .又因为()030,8x k n ππ=+∈且()()050,48x k n k πππ+=+∈∈N ，所以58n π>，即所求n 的取值范围是5,8π⎛⎫+∞ ⎪⎝⎭.解法2：当02n π<≤时，函数()sin f x x =，()0,x n ∈是增函数，所以不符合题意；当2n π>时，因为直线2x π=是函数()sin f x x =的一条对称轴，而函数()sin f x x =在区间()()0,0>n n 上具有性质4P π⎛⎫ ⎪⎝⎭，所以224n ππ⎛⎫-> ⎪⎝⎭，解得58n π>，即所求n 的取值范围是5,8π⎛⎫+∞ ⎪⎝⎭.【小问3详解】设()()13g x f x f x ⎛⎫=-+ ⎪⎝⎭，50,3x ⎡⎤∈⎢⎥⎣⎦.则有()()1003g f f ⎛⎫=- ⎪⎝⎭，112333g f f ⎛⎫⎛⎫⎛⎫=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，()22133g f f ⎛⎫⎛⎫=- ⎪ ⎪⎝⎭⎝⎭，⋅⋅⋅，11333k k k g f f --⎛⎫⎛⎫⎛⎫=- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，⋅⋅⋅，()55233g f f ⎛⎫⎛⎫=- ⎪ ⎪⎝⎭⎝⎭{}()1,2,3,,6k ∈⋅⋅⋅.以上各式相加得()()()115020333k g g g g f f -⎛⎫⎛⎫⎛⎫++⋅⋅⋅++⋅⋅⋅+=- ⎪⎪ ⎪⎝⎭⎝⎭⎝⎭即()11500333k g g g g -⎛⎫⎛⎫⎛⎫++⋅⋅⋅++⋅⋅⋅+= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，（ⅰ）当()0g 、13g ⎛⎫ ⎪⎝⎭、⋅⋅⋅、13k g -⎛⎫ ⎪⎝⎭、⋅⋅⋅、53g ⎛⎫ ⎪⎝⎭中有一个为0时，不妨设103i g -⎛⎫= ⎪⎝⎭，{}1,2,3,,6i ∈⋅⋅⋅，即110333i i i g f f --⎛⎫⎛⎫⎛⎫=-= ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭，即111333i i f f --⎛⎫⎛⎫=+ ⎪ ⎪⎝⎭⎝⎭，{}1,2,3,,6i ∈⋅⋅⋅，所以函数()y f x =在区间[]0,2上具有性质13P ⎛⎫⎪⎝⎭.（ⅱ）当()0g 、13g ⎛⎫ ⎪⎝⎭、⋅⋅⋅、13n g -⎛⎫ ⎪⎝⎭、⋅⋅⋅、53g ⎛⎫ ⎪⎝⎭中均不为0时，由于其和为0，则其中必存在正数和负数，不妨设103i g -⎛⎫>⎪⎝⎭，103j g -⎛⎫< ⎪⎝⎭，其中i j ≠，{}1,2,3,,6i j ∈⋅⋅⋅、.由于函数()y g x =的图像是连续不断的曲线，所以当i j <时，至少存在一个实数011,33i j x --⎛⎫∈ ⎪⎝⎭（当i j >时，至少存在一个实数011,33j i x --⎛⎫∈ ⎪⎝⎭），其中{}1,2,3,,6i j ∈⋅⋅⋅、，使得()00g x =，即()()000103g x f x f x ⎛⎫=-+= ⎪⎝⎭，即存在0x ，使得()0013f x f x ⎛⎫=+ ⎪⎝⎭，所以函数()y f x =在区间[]0,2上也具有性质13P ⎛⎫⎪⎝⎭.综上，函数()y f x =在区间[]0,2上具有性质13P ⎛⎫⎪⎝⎭.21. 已知函数()e (,1),()(,)k x f x x k k g x cx m c m =∈≥=+∈N R ，其中e 是自然对数的底数．（1）当1k =时，若曲线()y f x =在1x =处的切线恰好是直线()y g x =，求c 和m 的值；（2）当1k =，e m =-时，关于x 的方程()()f x g x =有正实数根，求c 的取值范围：（3）当2,1k m ==-时，关于x 的不等式2()e ()f x ax bx g x -≥+≥对于任意[1,)x ∈+∞恒成立（其中,a b ∈R ），当c 取得最大值时，求a 的最小值．【答案】（1）2e,e c m ==-（2）[2e,)+∞（3）1【解析】【分析】（1）利用导数求得()f x 在1x =处的切线方程，通过对比系数求得,c m .（2）由()()f x g x =分离c ，利用构造函数法，结合导数来求得c 的取值范围.（3）由恒成立的不等式得到e 1e xc x x-≤-恒成立，利用构造函数法，结合导数来求得c 的最大值，进而求得a 的最小值，并利用构造函数法，结合导数来判断a 的最小值符合题意.【小问1详解】当1k =时，()e x f x x =，所以()(1)e x f x x '=+，由(1)e,(1)2e f f '==，得曲线()y f x =在1x =处的切线方程为e 2e(1)y x -=-，即2e e y x =-，由题意，2e,e c m ==-．【小问2详解】当1k =，e m =-时，()e ,()e x f x x g x cx ==-，由题意，方程e e x x cx =-在(0,)+∞上有解，即e e x c x =+在(0,)+∞上有解，令e ()e (0)x h x x x =+>，则2e e ()x h x x'=-，由()0h x '=得1x =，()h x '在()0,∞+上严格递增，所以：当(0,1)x ∈时，()0h x '<，所以()h x 严格递减，当(1,)x ∈+∞时，()0h x '>，所以()h x 严格递增，所以min ()(1)2e h x h ==，又x →+∞时，()h x →+∞，所以()h x 的值域为[2e,)+∞，所以c 的取值范围为[2e,)+∞．【小问3详解】当2,1k m ==-时，2()e ,()1x f x x g x cx ==-，由题意，对于任意2[1,),()e ()x f x ax bx g x ∈+∞-≥+≥恒成立，即：22e e 1x x ax bx cx -≥+≥-（*）恒成立，那么，2e 1x x cx ≥-恒成立，所以e 1e xc x x-≤-恒成立，令e 1()e (1)x x x x x ϕ-=-≥，则2e 1()(1)e 0x x x x ϕ-'=++>在[1,)+∞上恒成立，所以()ϕx 在[1,)+∞上严格递增，所以min ()(1)1x ϕϕ==，从而1c ≤，即c 的最大值为1，1c =时，取1x =代入（*）式，得00a b ≥+≥，所以=-b a ，所以21ax ax x -≥-在[1,)+∞上恒成立，得1a ≥，即a 的最小值为1，当1a =时，记()222()()e e e (1)x F x f x x x x x x x =---=--+≥，则()2()2e 21x F x x x x '=+-+，设()()()()222e 21,42e 2x x x x x u u x x x x '+-+=++-=，因为()u x '在[1,)+∞上严格递增，所以()()17e 20u x u ''≥=->，所以()F x '在[1,)+∞上严格递增，所以()(1)3e 10F x F ''≥=->，所以()F x 在[1,)+∞上严格递增，所以()(1)0F x F ≥=，从而对于任意2[1,),()e ()x f x ax bx g x ∈+∞-≥+≥恒成立，综上，a 的最小值为1．【点睛】方法点睛：导函数中常用的两种常用的转化方法：一是利用导数研究含参函数的单调性，常化为不等式恒成立问题，注意分类讨论与数形结合思想的应用；二是函数的零点、不等式证明常转化为函数的单调性、极（最）值问题处理，。
浙江省四校联盟2023-2024学年高三上学期12月联考英语试题
浙江省四校联盟2023-2024学年高三上学期12月联考英语试题一、听力选择题1．Where is the woman probably from?A．Peru.B．Britain.C．Mexico.2．What will the man do tonight?A．Attend a party.B．Reply to an invitation.C．Practise football.3．What does the woman think of her old roommate?A．Self-centered.B．Considerate.C．Cautious.4．What should the city do according to the woman?A．Create more jobs.B．Improve the air quality.C．Close some businesses.5．What are the speakers mainly talking about?A．Their insufficient sleep.B．Their pretty dormitory.C．The unusual weather.听下面一段较长对话，回答以下小题。
6．What time is it when the conversation happens?A．At 2:50 pm.B．At 3:20 pm.C．Around 3:10 pm7．What does the woman plan to do with the paper?A．To note down the solar eclipse (日食).B．To stop the birds singing.C．To protect her eyes.听下面一段较长对话，回答以下小题。
8．How does the woman feel now?A．Excited.B．Upset.C．Angry9．What did the woman do well?A．Driving uphill.B．Making turns.C．Parking10．Why did the woman hit a car?A．She failed to use the handbrake.B．She didn’t turn her head.C．She drove too fast.听下面一段较长对话，回答以下小题。
2024年杭州市高三年级教学质量检测英语
2024年杭州市高三年级教学质量检测英语The year 2024 marked a significant milestone for the education landscape in Hangzhou as the city's high school Grade 3 students underwent a comprehensive English teaching quality assessment. This evaluation aimed to gauge the effectiveness of the English language curriculum, teaching methodologies, and student learning outcomes, with the ultimate goal of enhancing the overall quality of English education in the city.The assessment process was meticulously planned and executed by a team of education experts, language specialists, and school administrators. The evaluation encompassed a multifaceted approach, including written examinations, oral proficiency tests, classroom observations, and student and teacher feedback surveys.The written examinations assessed the students' mastery of core English language skills, such as reading comprehension, grammar, vocabulary, and writing. The tests were designed to challenge the students' critical thinking abilities and their capacity to apply their knowledge in real-world scenarios. The results of these examinationsprovided valuable insights into the strengths and weaknesses of the students' English language proficiency.The oral proficiency tests, on the other hand, evaluated the students' ability to communicate effectively in English. These assessments involved one-on-one interviews, group discussions, and presentations, where students were required to demonstrate their fluency, pronunciation, and conversational skills. The objective was to gauge the students' comfort and confidence in using English as a means of expression and interaction.Classroom observations played a crucial role in the assessment process. Education experts and language specialists visited schools across Hangzhou, observing English language lessons and assessing the quality of teaching practices. They analyzed the teachers' instructional strategies, the use of educational resources, the engagement of students, and the overall learning environment.The student and teacher feedback surveys provided valuable insights into the perceptions and experiences of those directly involved in the English language education process. Students shared their perspectives on the relevance and effectiveness of the curriculum, the quality of instruction, and the availability of learning resources. Teachers, on the other hand, offered insights into the challenges they faced, the support they received, and their suggestions forimproving the English language education program.The results of the 2024 Hangzhou High School Grade 3 English Teaching Quality Assessment were comprehensive and insightful. The data collected from the various assessment components revealed both strengths and areas for improvement in the city's English language education system.One of the key strengths identified was the strong foundation in English language skills among the majority of the students. The written examinations demonstrated that a significant percentage of the students had achieved proficiency in core areas such as grammar, vocabulary, and reading comprehension. This was a testament to the dedication and hard work of both the students and the teaching staff.Another positive aspect was the overall enthusiasm and engagement of the students in English language learning. The classroom observations and feedback surveys revealed that students were generally motivated to learn and participate in English language activities. They expressed a keen interest in developing their communication skills and a desire to apply their knowledge in real-world contexts.However, the assessment also highlighted areas that required immediate attention and improvement. One of the primary concernswas the uneven distribution of English language proficiency among the students. While a substantial number of students excelled, there was also a significant portion who struggled to meet the expected learning outcomes. This disparity underscored the need for more targeted interventions and differentiated instructional approaches to cater to the diverse learning needs of the students.Another area of concern was the quality of English language instruction. The classroom observations revealed that while some teachers demonstrated exceptional teaching practices, there were also instances where the instructional methods lacked creativity, engagement, and alignment with the evolving language learning needs of the students. This finding emphasized the importance of ongoing professional development for teachers to enhance their pedagogical skills and stay abreast of the latest trends and best practices in English language education.The assessment also uncovered the need for a more comprehensive and well-resourced English language learning ecosystem. Students and teachers alike expressed the desire for increased access to authentic learning materials, technology-enabled resources, and opportunities for real-world language practice and application.Based on the findings of the 2024 Hangzhou High School Grade 3 English Teaching Quality Assessment, a comprehensive action planwas developed to address the identified areas of improvement. This plan involved a multi-pronged approach, including the implementation of targeted interventions, the enhancement of teacher professional development programs, the expansion of learning resources, and the fostering of collaboration between schools, families, and the broader community.One of the key initiatives was the introduction of personalized learning plans for students. These plans were designed to identify the specific learning needs of each student and provide them with tailored instructional support and resources to address their gaps and accelerate their progress. This approach aimed to ensure that every student had the opportunity to reach their full potential in English language proficiency.The professional development of teachers also became a top priority. The education authorities in Hangzhou invested in comprehensive training programs that focused on enhancing pedagogical skills, integrating technology in the classroom, and fostering innovative teaching methodologies. These initiatives were designed to empower teachers to deliver more engaging, effective, and student-centered English language instruction.Furthermore, the assessment led to the expansion of learning resources and partnerships. Schools collaborated with localbusinesses, cultural organizations, and international language institutions to provide students with authentic language-learning experiences, such as virtual exchanges, cultural immersion programs, and community-based projects. These initiatives aimed to bridge the gap between the classroom and the real world, enabling students to apply their English language skills in meaningful and practical contexts.The 2024 Hangzhou High School Grade 3 English Teaching Quality Assessment served as a pivotal moment in the city's educational landscape. It not only provided a comprehensive evaluation of the current state of English language education but also catalyzed a series of strategic interventions and innovations that have since transformed the way English is taught and learned in Hangzhou's high schools.As the city continues to evolve and its students prepare to navigate an increasingly globalized world, the lasting impact of this assessment will undoubtedly be felt for years to come. The commitment to excellence in English language education has become a cornerstone of Hangzhou's educational vision, ensuring that its students are equipped with the linguistic and intercultural skills necessary to thrive in the 21st century.。
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浙江省杭州师大附中2012届高三第四次月考试题（英语）第一部分：英语知识运用（共两节，满分30）第一节：单项填空（共20小题；每小题0.5分，满分10分）1. A Christmas tree is ______ sign that can only be understood as far as ______ certain cultural understanding is concerned.A. the, /B. a, theC. a, aD. the, a2. The accident happened at the crossroads but, fortunately, it has not done any ______ damage.A.practicalB.avoidableC.permanentD.beneficial3. Rock-climbing is a breathtaking activity, very popular nationwide among young people,______ cooperation as well as courage plays an important role.A. whoB. whichC. whereD. of which4. ---I’m sorry! I would have taken him to hospital if I had known he was seriously ill.--- But ______ .A.you didn'tB. you hadn'tC. he wasn'tD. you aren't5. People’s ______ for bicycles may reflect public dissatisfaction with bus service.A.insistenceB.allowanceC.preferenceD.reference6. Americans seldom sit down to a regular meal as they like things ______ immediately.A.doneB.being doneC.doingD.be done7. Though you’ve spent three days in drawing up the plan, you’ll still get______ with it.A.everywhereB.nowhereC.anywhereD.somewhere8. Anger makes you smaller, while forgiveness makes you grow what you were.A.withinB.behindC.withoutD.beyond9. Creating a Friends List on .allows you to______ your friends on the Internet.A.give way toB.keep track ofC.break away fromD.catch up with10. The world population______ 7 billion, which is a challenge to our resources.A.are reachingB.have reachedC.had reachedD.has reached11. Thank you for all your hard work last week. I don’t think we ______ it without you.A. can manageB. could have managedC. could manageD. can have managed12. ---I’ll take the iPhone.---You mean I have to use that old mobile phone? .A. Forget about it.B.That’s all right.C.I won’t let you.D.No, not at all.13. ______ criticize your roommate, why not find out if there’s something wrong with yourself?A.More thanB.Other thanC.Rather thanD.Except for14. "I would never advise anyone to ______ a great opportunity, "she said, "but going to the right school for you is the most important thing."A. set aboutB. deal withC. take afterD. turn down15. It is usually warm in my hometown in March, but it _______ be rather cold sometimes.A. mustB. canC. shouldD. must16. --- Our trip to Xinjiang is like tasting a thick book of Xinjiang history and culture.--- Absolutely! I’ve never had one before.A.a pleasantB. a more pleasantC. a most pleasantD. the most pleasant17. It's known to all that large quantities of TV and Radio programs in China were producedpeople’s concern over edible oil last year.A. to raiseB. raisingC. raisedD. having raised18. No matter ______ the CRH accident in Wenzhou, it had and will have much warningsignificance.A. how the investigators said causedB. what the investigators said causedC. why the investigators said causedD. the investigators said how caused19. ---Are you going to stay overnight?---Not______it’s absolutely necessary.A. unlessB.whenC.untilD.if20. --- Are you going to see The Flowers of War by Zhang Yimou?--- _______ It’s said to be too good a film to miss.A. No problem!B. Why bother?C. Why me?D. That’s for sure.第二节：完形填空（共20小题；每小题1分，满分20分）“Hi. Can I sit down?”I raised my head and there she was, with an irresistible smile on her round face.“What are you looking at?” she asked.“Ants.”“What are they doing?”“No 29 .”“I bet they’re playing games and making friends. Don’t you think so?”That was how our 30 started and it didn’t stop. We talked about everything under the sun—the ants, the clouds, my little niche (处境) — until it was sunset.Then suddenly, she saw my 31 . She just stared.My heart 32 . What I feared most had happened and I knew for sure she would 33 me now.She stood up, pointe d at my back and said, “I know 34 your back is hunched.”I closed my eyes like a criminal waiting to be 35 . I begged in my heart for her to36 , but she just kept on going. “I know what you’ve got in there. Do you?”“No,” I answered 37 .She bent and whispered in my ears.“Your back is hunched because you’ve got a pair of wings from the angels.”I was 38 . I looked into her eyes and her 39 touched my heart. From that day on, Istarted to learn to 40 myself because I have the wings of an angel and a kind-hearted friend.21. A. them B. it C. me D. her22. A. sadder B. shorter C. weaker D. slower23. A. looking B. smiling C. aiming D. glaring24. A. still B. alone C. straight D. together25. A. street B. sun C. corner D. mirror26. A. distant B. disappointed C. hopeless D. unlucky27. A. after B. while C. since D. until28. A. disturb B. seek C. comfort D. ignore29. A. wonder B. idea C. way D. problem30. A. games B. performance C. conversation D. competition31. A. face B. back C. eyes D. wings32. A. sank B. beat C. broke D. ached33. A. look up to B. catch up with C. look down upon D. put up with34. A. that B. how C. whether D. why35. A. tied B. arrested C. punished D. sentenced36. A. relax B. leave C. stop D. forbid37. A. shyly B. weakly C. proudly D. firmly38. A. astonished B. ashamed C. annoyed D. upset39. A. wisdom B. beauty C. honesty D. kindness40. A. control B. like C. forgive D. forget第二部分：阅读理解(第一节20小题，第二节5小题；每题2分，满分50分) 第一节：阅读下列短文，从每题所给的四个选项（A、B、C和D）中，选出最佳选项，并在答题纸上将该选项标号涂黑。