(上海)高一第一学期第一、二、五单元阶段性测试
2020-2021学年上海市上海中学高一上学期12月月考数学试卷含详解
2020学年高一阶段检测二（数学）一、填空题（本大题共12题，1-6题每题4分，7-12题每题5分，满分54分）1.设全集U =R ，集合{1,2,3,4}A =，{23}B xx =≤<∣，则A B = ___________2.幂函数()af x x =的图像经过点12,2⎛⎫⎪⎝⎭，则()3f =______.3.不等式2(2)03x x x +≥-的解集为________．4.已知“2(22)(2)0x a x a a -+++≤”是“231x +<”的必要非充分条件，则实数a 的取值范围是________5.已知()f x 为R 上的奇函数，且当0x ≥时，()32xf x x b =++，则()1f -=________．6.若a的小数部分，则()2log 21a a +的值是________．7.已知关于x 的方程221(1)104x k x k -+++=有两个实数根1x 、2x ，若2212126x x x x +=-15，则k 的值为________8.若函数()()211f x mx m x =+--在区间[1,)-+∞上是严格单调函数，则实数m 的取值范围是________．9.若函数()2()lg 1f x ax ax =-+的定义域为R ，则实数a 的取值范围为__________．10.已知{||1|}A x x a =-≤，若A 只有1个整数元素，则实数a 的取值范围是________11.设a R ∈，若关于x 的不等式2236x x a a --+<-有解，则a 的取值范围是________．12.已知()f x 是定义域为R 的单调函数，且对任意实数x ，都有32()415x f f x ⎡⎤+=⎢⎥+⎣⎦，则()2log 3f =________．二、选择题（本大题共4题，每题5分，满分20分）13.已知()y f x =在区间I 上是严格增函数，且12,x x I ∈，则12x x <是()()12f x f x ≤（）A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分又非必要条件14.设()ln f x x =，0a b <<，若p f =，2a b q f +⎛⎫= ⎪⎝⎭，1(()())2r f a f b =+，则下列关系式中正确的是（）A.q r p =<B.q r p=> C.p r q =< D.p r q=>15.若a b 、是满足0ab <的实数，那么下列结论中成立的是（）A.a b a b-<-B.a b a b -<+C.a b a b +>-D.a b a b +<-16.关于函数()1x f x x =-，给出以下四个命题：（1）当0x >时，()y f x =单调递减且没有最值；（2）方程()(0)f x kx b k =+≠一定有实数解；（3）如果方程()f x m =（m 为常数）有解，则解的个数一定是偶数；（4）()y f x =是偶函数且有最小值．其中正确的命题个数为（）A.1B.2C.3D.4三、解答题（本大题共5题，满分76分）17.已知函数()|2|f x x a a=-+.（1）当a=2时，求不等式()6f x ≤的解集；（2）设函数()|21|g x x =-.当x ∈R 时，()()3f x g x +≥，求a 的取值范围.18.设0a >，0b >，且11a b a b+=+.证明：(1)2a b +≥；(2)22a a +<与22b b +<不可能同时成立．19.已知函数()33xxf x a -=-⋅，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.20.小张在淘宝网上开一家商店，他以10元每条的价格购进某品牌积压围巾2000条．定价前，小张先搜索了淘宝网上的其它网店，发现：A 商店以30元每条的价格销售，平均每日销售量为10条；B 商店以25元每条的价格销售，平均每日销售量为20条．假定这种围巾的销售量t （条）是售价x （元）x Z +∈（）的一次函数，且各个商店间的售价、销售量等方面不会互相影响．（1）试写出围巾销售每日的毛利润y （元）关于售价x （元）x Z +∈（）的函数关系式（不必写出定义域），并帮助小张定价，使得每日的毛利润最高（每日的毛利润为每日卖出商品的进货价与销售价之间的差价）；（2）考虑到这批围巾的管理、仓储等费用为200元/天（只要围巾没有售完，均须支付200元/天，管理、仓储等费用与围巾数量无关），试问小张应该如何定价，使这批围巾的总利润最高（总利润=总毛利润-总管理、仓储等费用）？21.已知函数||()x a f x x -=(0)a >，且满足1()12f =.（1）判断函数()f x 在(1,)+∞上的单调性，并用定义证明；（2）设函数()()f x g x x =，求()g x 在区间1[,4]2上的最大值；（3）若存在实数m ，使得关于x 的方程222()||20x a x x a mx ---+=恰有4个不同的正根，求实数m 的取值范围.2020学年高一阶段检测二（数学）一、填空题（本大题共12题，1-6题每题4分，7-12题每题5分，满分54分）1.设全集U =R ，集合{1,2,3,4}A =，{23}B xx =≤<∣，则A B = ___________【答案】{1,3,4}【分析】根据集合交补含义可得.【详解】因为{23}B xx =≤<∣，()[),23,B =-∞+∞ ，{}134A B = ，，.故答案为:{1,3,4}【点睛】此题为基础题，考查集合的运算.2.幂函数()af x x =的图像经过点12,2⎛⎫⎪⎝⎭，则()3f =______.【答案】13【分析】根据幂函数所过的点,代入可求得幂函数解析式,即可求得()3f 的值.【详解】幂函数()af x x =的图像经过点12,2⎛⎫ ⎪⎝⎭代入可得122a =解得1a =-所以幂函数解析式为()1f x x -=则()11333f -==故答案为:13【点睛】本题考查了幂函数解析式的求法,函数求值,属于基础题.3.不等式2(2)03x x x +≥-的解集为________．【答案】{}(,2]0(3,)-∞-+∞ 【分析】由分式不等式的解法，有2(2)(3)030x x x x ⎧+-≥⎨-≠⎩求解即可.【详解】由题意，有2(2)(3)030x x x x ⎧+-≥⎨-≠⎩，解得2x -≤或0x =或3x >，∴解集为{}(,2]0(3,)-∞-+∞ .故答案为：{}(,2]0(3,)-∞-+∞ .4.已知“2(22)(2)0x a x a a -+++≤”是“231x +<”的必要非充分条件，则实数a 的取值范围是________【答案】[]3,2--【分析】先由一元二次不等式以及绝对值不等式的解法化简，再结合必要非充分条件的性质，列出不等式，得出答案.【详解】由|23|1x +<得1231x -<+<，解得21x -<<-由2(22)(2)0x a x a a -+++≤得(2)()0x a x a ---≤，解得2a x a ≤≤+因为“2(22)(2)0x a x a a -+++≤”是“231x +<”的必要非充分条件所以221a a ≤-⎧⎨+≥-⎩，解得32a --≤≤故答案为：[]3,2--5.已知()f x 为R 上的奇函数，且当0x ≥时，()32xf x x b =++，则()1f -=________．【答案】2-【分析】由R 上的奇函数，有(0)0f =求参数b ，进而求()1f ，又()1(1)f f -=-即可求值.【详解】由()f x 为R 上的奇函数，有(0)0f =，∴根据函数解析式，有0(0)020f b =++=，即1b =-，∴()321xf x x =+-，则()311212f =+-=，∴()1(1)2f f -=-=-.故答案为：2-.6.若a的小数部分，则()2log 21a a +的值是________．【答案】1-【分析】由题意知35(1,2)4+=，即可得514a =，代入对数式，应用对数运算的性质求值即可.35(1,2)4+=∈，知：3551144a=-=，即122a-=，51212a++==∴()251log2112aa-+==-=-.故答案为：1-.7.已知关于x的方程221(1)104x k x k-+++=有两个实数根1x、2x，若2212126x x x x+=-15，则k的值为________【答案】4【分析】将2212126x x x x+=-15，变形为()21212815x x x x+=-，根据方程221(1)104x k x k-+++=有两个实数根1x、2x，得到212121+1,14x x k x x k=+⋅=+，再代入上式求解.【详解】因为方程221(1)104x k x k-+++=有两个实数根1x、2x，所以212121+1,14x x k x x k=+⋅=+，因为2212126x x x x+=-15，所以()21212815x x x x+=-，()221181154k k⎛⎫+=⨯+-⎪⎝⎭，即()()240k k+-=，解得4k=或2k=-（舍去）故答案为：48.若函数()()211f x mx m x=+--在区间[1,)-+∞上是严格单调函数，则实数m的取值范围是________．【答案】[]1,0-【分析】讨论0m=、0m≠，并结合二次函数的性质，列不等式求参数范围，合并不同情况的m取值即可.【详解】当0m=时，()1f x x=--在[1,)-+∞上是严格单调函数，符合题意；当0m≠时，()221(1)(24m mf x m xm m-+=+-，∴112mm-≤-，即102mm+≤，可得10m-≤<，综上，有10m-≤≤.故答案为：[]1,0-.9.若函数()2()lg 1f x ax ax =-+的定义域为R ，则实数a 的取值范围为__________．【答案】[)0,4【分析】转化条件为无论x 取何值，210ax ax -+>恒成立，按照a =0、0a ≠分类，即可得解.【详解】由题意，无论x 取何值，210ax ax -+>恒成立，当a =0时，10>恒成立，符合题意；当0a ≠时，则240a a a >⎧⎨∆=-<⎩，解得04a <<，综上，[)0,4a ∈.故答案为：[)0,4.10.已知{||1|}A x x a =-≤，若A 只有1个整数元素，则实数a 的取值范围是________【答案】[0,1)【分析】解绝对值不等式得{|11}A x a x a =-≤≤+，且0a ≥，结合条件可得1A ∈，进而得011112a a <-≤⎧⎨≤+<⎩，从而得解.【详解】由{||1|}A x x a =-≤得{|1}{|11}A x a x a x a x a =-≤-≤=-≤≤+，且0a ≥若A 只有1个整数元素，又111a a -≤≤+，所以1A ∈，所以011112a a <-≤⎧⎨≤+<⎩，解得01a ≤<.故答案为：[0,1).11.设a R ∈，若关于x 的不等式2236x x a a --+<-有解，则a 的取值范围是________．【答案】(,1)(5,)-∞+∞ 【分析】令()|2||3|f x x x =--+并得到其分段函数形式，由题设不等式有解，即2min 6()a a f x ->即可，解一元二次不等式即可求a 的范围.【详解】由235,3()|2||3|2321,32235,2x x x f x x x x x x x x x x -++=≤-⎧⎪=--+=---=---<≤⎨⎪---=->⎩，∴要使不等式2236x x a a --+<-有解，仅需2min 6()5a a f x ->=-即可，∴2650a a -+>，解得1x <或5x >.故答案为：(,1)(5,)-∞+∞ .12.已知()f x 是定义域为R 的单调函数，且对任意实数x ，都有32()415x f f x ⎡⎤+=⎢⎥+⎣⎦，则()2log 3f =________．【答案】710【分析】令02()5f x =，由题意知0001()41x x f x =++，可求出0x ，又22log 332[(log 3)]415f f +=+，即有023(log 3)10x f =+，进而可求()2log 3f .【详解】若02()5f x =，则0032[()]415x f f x +=+，又()f x 是定义域为R 的单调函数，∴0032415x x -=+，得01x =，又222log 3332[(log 3)[(log 3)41105f f f f +=+=+，∴023(log 3)110x f =+=，则()27log 310f =.故答案为：710.【点睛】关键点点睛：利用函数的单调性，以及恒等式成立，求02()5f x =时的0x 值，再利用恒等式求目标函数值.二、选择题（本大题共4题，每题5分，满分20分）13.已知()y f x =在区间I 上是严格增函数，且12,x x I ∈，则12x x <是()()12f x f x ≤（）A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分又非必要条件【答案】A【分析】由增函数的定义知：12,x x I ∈且12x x <时21()()f x f x >，即可判断条件之间的充分、必要性.【详解】由()y f x =在区间I 上是严格增函数，∴12,x x I ∈，12x x <时，2121()()0f x f x x x ->-，∴21()()0f x f x ->，即21()()f x f x >，故12x x <是()()12f x f x ≤充分非必要条件.故选：A.14.设()ln f x x =，0a b <<，若p f =，2a b q f +⎛⎫= ⎪⎝⎭，1(()())2r f a f b =+，则下列关系式中正确的是（）A.q r p =<B.q r p =>C.p r q =<D.p r q=>【答案】C【分析】由对数函数，结合对数的运算性质得ln ln 1(()())22a b p f f a f b r +===+=，应用基本不等式判断q 与p 的大小关系即可.【详解】由题意，ln ln ln 22ab a b p f +====，而1ln ln (()())22a br f a f b +=+=，∴p r =，又ln(22a b a bq f ++⎛⎫==>⎪⎝⎭∴综上有：p r q =<.故选：C.15.若a b 、是满足0ab <的实数，那么下列结论中成立的是（）A.a b a b -<-B.a b a b -<+C.a b a b +>-D.a b a b +<-【答案】D 【分析】利用特殊值法判断即可.【详解】令1,2a b =-=，则3||||3a b a b -=>-=-，||||3a b a b -=+=，||1||3a b a b +=<-=，故选：D【点睛】本题主要考查了绝对值不等式的大小比较，特殊值法，属于容易题.16.关于函数()1x f x x =-，给出以下四个命题：（1）当0x >时，()y f x =单调递减且没有最值；（2）方程()(0)f x kx b k =+≠一定有实数解；（3）如果方程()f x m =（m 为常数）有解，则解的个数一定是偶数；（4）()y f x =是偶函数且有最小值．其中正确的命题个数为（）A.1 B.2C.3D.4【答案】B【分析】由函数解析式可推出()y f x =是偶函数，在(,1)-∞-、(0,1)上单调递增，在(1,0)-、(1,)+∞上单调递减，且()0f x ≥恒成立，即可判断各项的正误.【详解】函数()1xf x x =-是偶函数，当0x >时，()y f x =在(0,1)上单调递增，在(1,)+∞上单调递减，且()0f x ≥恒成立，可得函数草图如下：（1）当1x >时，1()111x y f x x x ===+--单调递减，当01x <<时，1()111x y f x x x ==-=----单调递增，故错误；（2）当0k >时，函数()y f x =与函数y kx b =+的图像一定有交点，由对称性可知，当0x <且0k <时，函数()y f x =与函数y kx b =+的图像也一定有交点，故正确；（3）当0m =时，方程()f x m =只有1个解0x =，故错误；（4）由对称性知，()y f x =有最小值(0)0f =，故正确；故选：B【点睛】关键点点睛：根据函数解析式确定单调区间，奇偶性以及值域，进而结合各项的描述判断正误，注意一次函数的性质和函数对称性的应用.三、解答题（本大题共5题，满分76分）17.已知函数()|2|f x x a a =-+.（1）当a=2时，求不等式()6f x ≤的解集；（2）设函数()|21|g x x =-.当x ∈R 时，()()3f x g x +≥，求a 的取值范围.【答案】（1）{|13}x x -≤≤；（2）[2,)+∞．【详解】试卷分析：（1）当2a =时⇒()|22|2f x x =-+⇒|22|26x -+≤⇒13x -≤≤；（2）由()()|2||12|f x g x x a a x +=-++-|212|x a x a ≥-+-+|1|a a =-+⇒()()3f x g x +≥等价于|1|3a a -+≥，解之得2a ≥.试卷解析：（1）当2a =时，()|22|2f x x =-+.解不等式|22|26x -+≤，得13x -≤≤.因此，()6f x ≤的解集为.（2）当x ∈R 时，()()|2||12|f x g x x a a x +=-++-|212|x a x a ≥-+-+|1|a a =-+，当12x =时等号成立，所以当x ∈R 时，()()3f x g x +≥等价于|1|3a a -+≥.①当1a ≤时，①等价于13a a -+≥，无解.当1a >时，①等价于13a a -+≥，解得2a ≥.所以a 的取值范围是[2,)+∞.考点：不等式选讲.18.设0a >，0b >，且11a b a b+=+.证明：(1)2a b +≥；(2)22a a +<与22b b +<不可能同时成立．【答案】(1)见解析.(2)见解析.【详解】试卷分析：本题考查基本不等式和反证法,结合转化思想证明不等式,意在考查考生对基本不等式的掌握和反证法的应用.(i)构造基本不等式求出代数式的最值,直接证明不等式成立;(ii)直接证明较难,假设两个不等式同时成立,利用(i)的结论,得出矛盾,则假设不成立.试卷解析：由11a b a b a b ab++=+=,0,0a b >>,得1ab =.(1)由基本不等式及1ab =,有2a b +≥=,即2a b +≥(2)假设22a a +<与22b b +<同时成立,则由22a a +<及a>0得0<a<1;同理得0<b<1,从而ab<1,这与ab=1矛盾.故22a a +<与22b b +<不可能同时成立.点睛：本题主要考查基本不等式，其难点主要在于利用三角形的一边及这条边上的高表示内接正方形的边长.在用基本不等式求最值时，应具备三个条件：一正二定三相等.①一正：关系式中，各项均为正数；②二定：关系式中，含变量的各项的和或积必须有一个为定值；③三相等：含变量的各项均相等，取得最值.19.已知函数()33x xf x a -=-⋅，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3log 2（2）当1a =时，函数为奇函数，当1a =-时，函数为偶函数，当1a ≠±时，函数为非奇非偶函数，见解析【分析】（1）根据()07f =,代入可求得a 的值.即可得()f x 的解析式,进而得方程.解指数形式的二次方程,即可求得解.（2）表示出()f x -.根据奇偶性定义即可求得a 的值,即可判断奇偶性.【详解】（1）因为()07f =代入可得17a -=,解得6a =-所以()363x xf x -=+⋅则()5f x =可化为3635x x -+⋅=化简可得()235360x x -⋅+=即()()32330x x --=解得3log 2x =或1x =（2）()33x x f x a -=-⋅则()33x xf x a --=-⋅当1a =时,()33x x f x -=-,()33x x f x --=-此时()()f x f x =--,函数()f x 为奇函数当1a =-时,()33x x f x -=+,()33x x f x --=+,此时()()f x f x =-,函数()f x 为偶函数当1a ≠±时,()()f x f x =--与()()f x f x =-都不能成立,所以函数()f x 为非奇非偶函数综上可知,当1a =时,()f x 为奇函数;当1a =-时,()f x 为偶函数;当1a ≠±时,函数()f x 为非奇非偶函数.【点睛】本题考查了指数方程的解法,利用奇偶性定义判定函数奇偶性,属于基础题.20.小张在淘宝网上开一家商店，他以10元每条的价格购进某品牌积压围巾2000条．定价前，小张先搜索了淘宝网上的其它网店，发现：A 商店以30元每条的价格销售，平均每日销售量为10条；B 商店以25元每条的价格销售，平均每日销售量为20条．假定这种围巾的销售量t （条）是售价x （元）x Z +∈（）的一次函数，且各个商店间的售价、销售量等方面不会互相影响．（1）试写出围巾销售每日的毛利润y （元）关于售价x （元）x Z +∈（）的函数关系式（不必写出定义域），并帮助小张定价，使得每日的毛利润最高（每日的毛利润为每日卖出商品的进货价与销售价之间的差价）；（2）考虑到这批围巾的管理、仓储等费用为200元/天（只要围巾没有售完，均须支付200元/天，管理、仓储等费用与围巾数量无关），试问小张应该如何定价，使这批围巾的总利润最高（总利润=总毛利润-总管理、仓储等费用）？【答案】（1）2=290700y x x -+-；定价为22元或23元（2）25元【分析】（1）根据题意先求出销售量t 与售价x 之间的关系式，再利用毛利润为每日卖出商品的进货价与销售价之间的差价，确定毛利润y （元）关于售价x （元）x Z +∈（）的函数关系式，利用二次函数求最值的方法可求；（2）根据总利润=总毛利润-总管理、仓储等费用，构建函数关系，利用基本不等式可求最值．【详解】设t kx b =+，∴3010{ 2520k b k b ⋅+=⋅+=，解得2k =-，b=70，∴702t x =-．（1）21010702290700y x t x x x x =-=--=-+-（）（）（）g g ，∵9012242=+，∴围巾定价为22元或23元时，每日的利润最高．（2）设售价x（元）时总利润为z（元），∴2000200010200702z x x =---（），1002000·25352000251000035x x =--+≤-=-（（（）））（元，当1003535x x-=-时，即25x =时，取得等号，∴小张的这批围巾定价为25元时，这批围巾的总利润最高.【点睛】本题以实际问题为载体，考查二次函数模型的构建，考查配方法求最值及基本不等式求最值，关键是函数式的构建．与实际应用相结合的题型也是高考命题的动向，这类问题的特点是通过现实生活的事例考查书本知识，解决这类问题的关键是耐心读题、仔细理解题，只有吃透题意，才能将实际问题转化为数学模型进行解答.21.已知函数||()x a f x x -=(0)a >，且满足1()12f =.（1）判断函数()f x 在(1,)+∞上的单调性，并用定义证明；（2）设函数()()f xg x x =，求()g x 在区间1[,4]2上的最大值；（3）若存在实数m ，使得关于x 的方程222()||20x a x x a mx ---+=恰有4个不同的正根，求实数m 的取值范围.【答案】(1)见解析(2)1=2x 时，max ()=2g x .(3)1(0,16【详解】试卷分析：（1）根据112f ⎛⎫=⎪⎝⎭确定a.再任取两数，作差，通分并根据分子分母符号确定差的符号，最后根据定义确定函数单调性（2）先根据绝对值定义将函数化为分段函数，都可化为二次函数，再根据对称轴与定义区间位置关系确定最值，最后取两个最大值中较大值（3）先对方程变形得()()2220f x f x m -+=，设()t f x =,转化为方程方程2220t t m -+=在()0,1有两个不等的根12,t t ，根据二次函数图像，得实根分布条件，解得实数m 的取值范围.试卷解析：(1)由112=1122a f -⎛⎫= ⎪⎝⎭，得1a =或0.因为0a >，所以1a =，所以()|1|x f x x -=.当1x >时，()11=1x f x x x -=-，任取()12,1,x x ∈+∞，且12x x <，则()()()()1221121212121111=x x x x x x f x f x x x x x ------=-()()1221221211=x x x x x x ---1212=x x x x -，因为121x x <<，则1212<0,0x x x x ->，()()120f x f x -<，所以()f x 在()1,+∞上为增函数；（2）()()2221,141==11,12x x f x x x g x x x x x x -⎧≤≤⎪-⎪=⎨-⎪≤<⎪⎩，当14x ≤≤时，()222111111=24x g x x x x x -⎛⎫==---+ ⎪⎝⎭，因为1114x ≤≤，所以当11=2x 时，()max 1=4g x ；当112x ≤<时，()222111111=24x g x x x x x -⎛⎫==--- ⎪⎝⎭，因为112x ≤<时，所以112x <≤，所以当1=2x 时，()max =2g x ；综上，当1=2x 即1=2x 时，()max =2g x .（3）由（1）可知，()f x 在()1,+∞上为增函数,当()1,x ∈+∞时，()()1=10,1f x x -∈.同理可得()f x 在()0,1上为减函数，当()0,1x ∈时，()()1=10,f x x -∈+∞.方程()2221120x x x mx ---+=可化为221|1|220x x m x x---+=，即()()2220f x f x m -+=.设()t f x =,方程可化为2220t t m -+=.要使原方程有4个不同的正根，则方程2220t t m -+=在()0,1有两个不等的根12,t t ，则有211602021120m m m ->⎧⎪>⎨⎪⨯-+>⎩，解得1016m <<，所以实数m 的取值范围为10,16⎛⎫ ⎪⎝⎭.。
2023年上海市五校联考高一上学期期中英语试卷及答案
高一英2023学年第一学期期中考试语试卷考生注意：1．本场考试时间120分钟，满分150分．2．作答前，考生在答题纸正面填写学校、姓名、考生号，粘贴考生本人条形码．3．所有作答务必填涂或书写在答题纸上与试卷题号对应的区域，不得错位．在草稿纸、试卷上作答一律不得分．4．用2B 铅笔作答选择题，用黑色笔迹钢笔、水笔或圆珠笔作答非选择题．I.Listening Comprehension (30分)Section A (10*1=10分)Directions: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.At 8:30.B.At 9:00. C.At 9:30. D.At 10:00.2.A.Daughter and son. B.Father and daughter. C.Husband and wife. D.Mother and son.3.A.In a bank.B.In a post office.C.In a supermarket. D.In a restaurant.4.A.A policeman. B.A lawyer. C.A sales manager.D.A coach.5.A.Catch a train home.B.Do her homework.C.Go to the theater.D.Go to work.6.A.John didn’t do well in the exam.B.John doesn’t worry about the exam result.C.The exam was easier than the previous one.D.John is sure that he will do better in the next exam.7.A.The man couldn’t leave the parcel here.B.Some information is required.C.The details of the parcel are needed.D.The privacy of the owner is guaranteed.8.A.She is not available tonight.B.She is looking forward to the next party.C.She is going to hold a party next time.D.She is sorry for not being able to attend.9.A.The room is really dirty.B.The room is not as dirty as the woman expects.C.In the woman’s eyes,the room is not dirty.D.The man doesn’t think the room is dirty.10.A.Taking the doctor’s advice completely.B.Drinking a little every day.C.Serving a moderate （适量的）amount of alcohol.D.Giving up smoking and drinking.Section B （10*2=20分）Directions:In Section B,you will hear several longer conversation(s)and short passage(s),and you will be asked several questions on each of the conversation(s)and the passage(s).The conversation(s)and passage(s)will be read twice,but the questions will be spoken only once.When you hear a question,read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11through 13are based on the following passage.11.A.Mother’s shouting.B.The unusual smell.C.The terrible sound.D.The heat of the fire.12.A.At the supermarket. B.In the kitchen.C.In the bed.D.In the living room.13. A.She forgot to turn off the stove.B.It took long to put out the fire.C.She would probably be punished by her mother.D.She would have to study music against her will.Questions14through16are based on the following passage.14.A.Because they want to relax. B.Because they have a lot of leisure time.C.Because they are looking for fun.D.Because they want to find something valuable.15. A.They are tired of luxurious but not practical goods.B.They want to get value for money.C.They appreciate the real crafts of the old workman.D.They consider the price of used goods reasonable.16.A.Popularity of second-hand books. B.Real artist works in the past.C.A real bargain in local bookstores.D.A new fashion about second-hand goods.Questions17through20are based on the following conversation.17. A.He is a musician. B.He is interested in computer programming.C.He advertised his room for rent.D.He’s living with some other students now.18. A.In the newspaper. B.On campus（大学校园）.C.At the neighborhood.D.On the college brochure.19.A.It must be in a good condition. B.It must have clean surroundings.C.It should guarantee her privacy.D.It doesn’t cost much to rent.20. A.Amy will share the house with Tom. B.Amy is not easy to live with.C.Tom is also the owner of the house.D.Amy and Tom are both studying in college.II..Grammar and Vocabulary.(24分)Section A(10*1=10分)Directions:Beneath each of the following sentences there are four choices marked A, B.C and D.Choose the one answer that best completes the sentence.A LETTER TO MY DAUGHTERDear Daughter,I know perhaps you will be surprised to read this:I remember well what it was like to be a teenager.As I watch you prepare for your first day of senior high school,there are a few things I want you__21____（know）.You may___22____（put)yourself under pressure to make sure that everything is perfect for that first day, but I want you to know that there’s no such thing as perfect.I___23____(say)it before,but it bears ___24___(repeat).There is nothing perfect.There is only good enough,but___25___is most important is believing you’re enough—just as you are.Also,remember___26____you’re not in this boat alone.You’re not the only one facing a new school,new classmates,new teachers,new expectations and new pressures.__27____some point,everyone else is—or was—where you are right now.I hope you find comfort in that.There might be some people who will not always be so friendly to you.You will find such people not only insenior high school,but throughout your adult life..As you go forward into this new chapter in your life,I hope you’ll realize early that most often we ___28__(hold)back by the limitations we put on ourselves—by the stories we tell ourselves about who and what we are.___29___you’re tempted to say,“I can’t...”or“I’m not...”about___30___you really want to achieve,I hope you’ll change that story—because you can and you are.Section B(10*1=10分)Directions:Fill in each blank with a proper word chosen from the box.Each word can be used only once.Note that there is one word more than you need.A.confusionB.deliveredC.reflectionD.offerE.contextF.setG.signaled H.fluent I.torn J.culture K.genuineThis is a story about how a foreigner got confused about a Mexican word even though she could speak ____31____Spanish.It happened when she___32____foot on Mexican soil for the first time.She asked an ice-cream seller for an ice-cream,and he said“ahorita.”She thought it would be____33_____immediately because the word can be directly translated to“right now.”But she waited for half an hour and still no ice-cream came.When she asked the seller about it,he said“ahorita”again,with his face showing____34_____.She felt ____35___between waiting and walking away.Finally,she had to go home,so she____36___to the seller that she could not wait any longer.Years later back in Mexico,she came to realise that the meaning of“ahorita”changes according to its____37____.It could mean“tomorrow,”“within five years,”“never,”or even“no,thanks”when one wants to refuse an___38____.“Ahorita Time”is a___39___of different cultural understandings of time.That is,understanding“ahorita”takes not a fluency in the language,but a fluency in the_____40______. Section C(4*1=4分)Directions：Complete the following sentences by using the words in the box.Each word in the box can only be used once.There are two words more than you needA.blankB.temptationmentsD.embarrassedE.creativeF.expectations41.______thinking is essential for students when they are writing.42.The students had high_____________for their future.43.Have you any____________to make upon my article?44.I was_____________by his comments about my clothes.III.Reading Comprehension（55分）Section A（15*1=15分）Directions:For each blank in the following passage there are four words or phrases marked A,B,C and D.Fill in each blank with the word or phrase that best fits the context.People think children should play sports.Sports are fun,and playing with others.However,playing sports can have__45effects on children.It may produce feelings of poor self-respect or aggressive（好斗的，挑衅的）behavior in some children.According to research on kids and sports,40,000,000kids play sports in the US.Of these,18,000,000say they have been46at or called names（被骂）while playing sports.This leaves many children with a bad__47_of sports.They think sports are just too aggressive.Many researchers believe adults,especially parents and coaches,are the main_48of too much aggressionin children's sports.They believe children49aggressive adult behavior.This behavior is then further strengthened（巩固，加强）through both positive and negative feedback.Parents and coaches are powerful teachers because children usually look up to them.Often these adults behave aggressively themselves,sending children the message that50is everything.Many parents go to children's sporting events and shout_51 _at other players or cheer when their child behaves52.As well,children arc even taught that hurting other players is53or are pushed（督促，逼迫）to continue playing even when they are injured.54,the media makes violence（暴力）seem exciting.Children watch adult sports games and see violent behavior replayed over and over on television.As a society,we really need to55this problem and do something about it.Parents and coaches56 should act as better examples for children.They also need to teach children better57.They should not just cheer when children win or act aggressively.They should teach children to58,themselves whether they win or not.Besides,children should not be allowed to continue to play when they are injured.If adults allow children to play when injured,this gives the message that59is not as important as winning.45.A.restrictive B.negative C.active D.instructive46.A.knocked B.glanced C.smiled D.shouted47.A.impression B.concept C.taste D.expectation48.A.resource B.cause C.course D.consequence49.A.question B.understand C.copy（模仿） D.neglect50.A.winning B.practising C.fun D.sport51.A.praises B.orders C.remarks D.insults（侮辱）52.A.proudly B.ambitiously C.aggressively D.bravely53.A.acceptable B.impolite C.possible D.accessible54.A.By contrast B.In addition C.As a result D.After all55.A.look up to B.face up to C.make up for e up with56.A.in particular（尤其）B.in all C.in return D.in advance57.A.techniques B.means C.values（价值观） D.directions58.A.respect B.relax C.forgive D.enjoy59.A.body B.fame C.health D.spiritSection B（16*2=32分）Directions:Read the following four passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)Even at school there had been an unhealthy competition between George and Richard.“I’ll be the first millionaire in Coleford!”Richard used to boast.“And you’ll be sorry you knew me,”George would reply“because I’ll be the best lawyer in the town!”George never did become a lawyer and Richard never made any money.Instead both men opened bookshops on opposite sides of Coleford High Street.It was hard to make money from books,which made the competition between them worse.Then Richard married a mysterious girl.The couple spent their honeymoon on the coast—but Richard nevercame back.The police found his wallet on a deserted beach but the body was never found.He must have drowned.Now with only one bookshop in town,business was better for George.But sometimes he sat in his narrow, old kitchen and gazed out of the dirty window,thinking about his formal rival(竞争对手).Perhaps he missed him?George was very interested in old dictionaries.He’d recently found a collector in Australia who was selling a rare first edition.When the parcel arrived,the book was in perfect condition and George was delighted.But while he was having lunch,George glanced at the photo in the newspaper that the book had been wrapped in.He was astonished—the smiling face was older than he remembered but unmistakable!Trembling,George started reading.“Bookends have bought ten bookstores from their rivals Dylans.The company,owned by multi-millionaire Richard Pike,is now the largest bookseller in Australia.”60.George and Richard were______at school.A.roommatesB.good friendspetitorsD.booksellers61.How did George feel about Richard after his disappearance?A.He envied Richard’s marriage.B.He thought of Richard from time to time.C.He felt lucky with no rival in town.D.He was guilty of Richard’s death.62.George got information about Richard from______.A.a dictionary collector in AustraliaB.the latter’s rivals DylansC.a rare first edition of a dictionaryD.the wrapping paper of a book63.What happened to George and Richard in the end?A.Both George and Richard became millionaires.B.Both of them realized their original ambitions.C.George established a successful business while Richard was missing.D.Richard became a millionaire while George had no great success.(B)The Best Way to See Singapore.See More for Less!City Sightseeing$33/A,$23/C,FREE/T24hours of Unlimited Touring–9a.m.to6p.m.Duration:1day(unlimited rides)Attractions:Civic District,Orchard Road,BotanicGardens,Little India,Chinatown&more along the City& Heritage routes.It is easy to enjoy Singapore with the City Sightseeing open-top touringsystem.Spot an interesting place or sight?Simply hop off and walk around and you cancontinue the tour later by hopping on the next bus.With one bus arriving every20minutes,theCity Sightseeing system links you to major sights,attractions and hotels!*Guests Helpline:6338–6877DUCK$33/A,$23/C,$2/TDaily:9:30a.m.–5:30p.m.Duration:60minutesRide the original DUCK!Hop on this amphibious(两栖的)craft for a sightseeing tour which covers both land and sea!*Free bus transfer;most popular tour;1st and original DUCK;unique land&sea adventure.*For More Information,call6338–6859.第7页共15页Night Sa fari$49/A,$33/C,FREE/TTour Time:6:00p.m.–10:00p.m.Duration :4hoursObserve the night activities of the 1,000over nocturnal (夜间活动的)animals in the Night Safari –the world’s firstwildlife night park,for an adventure you’ll never forget.*Free &easy with 2-way bus transfer.*For More Information,call 6338–6826.Flyer$53/A,$37/C,Free/TOpen Hours:Daily 9:00a.m.–9:00p.m.Duration:30minutesFeast your eyes on Singapore’s magnificent cityscape from aheight of 165metres on the world’s largest observationwheel.Get your cameras ready as you experience a360-degree panoramic (全景的)view of the city and the Marina Bay area.*Free bus transfer;free river transfer.*For More Information,call 6338–3311A –adult,C –children (3-12),T –toddler (2&below)64.If David and his 9-year-old son are both animal lovers,they had better dial for moreinformation before their tour.A.6338–6859B.6338–6826C.6338–3311D.6338–687765.John wants to have a bird’s-eye view of the whole city of Singapore during his short stay there,so is his best choice.A.City SightseeingB.DUCKC.Night SafariD.Flyer66.Mr.Smith is going to take his wife,his 13-year-old daughter and his 1-year-old son to visitSingapore at their own leisurely pace,he should get at leastready.A.$89 B.$91 C.$99 D.$10167.What is the most suitable item for Peter to choose who loves adventure and he has only onefree hour to tour ?A.City SightseeingB.DUCKC.Night SafariD.Flyer(C)Fishy Weather ConditionsLaj amanu,Australia,is a dry little town,sitting right on the edge of the Tanami desert.Can you imagine how surprised people were when live fish rained down on them from a darkgray cloud.It happens that there are similar cases in England and Honduras.How do clouds make fishy?The simple answer is that they don’t.There is a particularweather phenomenon(现象)called a waterspout.A waterspout is just like a tornado（龙卷风）,only it forms above oceans,lakes,or rivers.Like a tornado,a waterspout moves in a circle at highspeeds.When it moves above the water,it tends to carry the fish with it,as well as frogs orother small plants or animals.Scientists couldn’t work it out at first.To make matters stranger still,the fish in Honduras were very much alive when they rained down to the ground,but they were all blind.In England and Australia,it rained fish and snakes,and none were blind.It was difficult to puzzle out,but the blind fish gave them a place to start.Scientists knew that some fish that lived in deep,underground caves with no light sources often lost their eyesight.So when blind fish rained down on Honduras,scientists began toconnect some clues（线索，提示）.Clearly,these particular fish were pulled from an underground water source by force.It has rained fish on every continent,and each time,people have tried in various ways toexplain this strange phenomenon.Historically,villagers thought the“fishes from the heavens”might be answers to prayers（祈祷）for food.Others suggested that floods overran river banks and oceans,leaving the fish on the city streets.No scientist had actually seen the rain as it occurred,only the fish left on the ground.But in1990,a National Geographic team happened to be inHonduras when the Rain of Fishes began.They recorded what was happening and made historyby finally proving that the fish really did fall from the sky.This huge breakthrough wasn’t just a spot of good luck.It changed thousands of yearsof myths（虚构的事；谬论）and legends into true stories and provided scientific explanations for how fish came to live in deep caves.It explained ancient cave paintings and cast（投射光线）new light on how species have spread over time.It turned out to be a lot more than just a little fishy weather.68.According to the passage,a waterspout________.A.can make animals blindB.is difficult to catch on filmC.can carry items（物品）with itD.is a dangerous sea creature69.The blind fish made the scientists start to think that________.A.raining fish was a warning of natural disastersB.animals changed to match their environmentsC.the weather system differed from place to placeD.the waterspout theory seemed more possible70.The first sentence in the last paragraph probably suggests that________.A.waterspouts came to be a center of scientific researchB.the scientists were fortunate to have made their discoveriesC.hard work went into determining the cause for the raining fishD.the scientists relied heavily on unusual events to drive their studies71.The author writes the passage to________.A.explain what caused the fishy weatherB.describe the magic phenomenonC.persuade people to protect the environmentD.encourage people to do scientific research(D)A study involving8,500teenagers from all social backgrounds found that most of them are ignorant（无知的）when it comes to money.The findings,the first in a series of reports from NatWesl that has started a five-year research project into teenagers and money,arc particularly worrying as this generation of young people is likely to be burdened with greater debts man any before.University tuition fees(学费)are currently capped at£3,000annually,but this will be reviewed next year and the Government is under enormous pressure to raise the ceiling.In the research,the teenagers were presented with terms(条款）of four different loans but76per cent failed to identify the cheapest.The young people also predicted that they would be earning on average£31.000by the age of25,although the average salary for those aged22to29is just£17,815.The teenagers expected to be in debt when they finished university or training,although half said that they assumed the debts would be less than £10.000.Average debts for graduates are£12，363.Stephen Moir,head of community investment at the Royal Bank of Scotland Group which owns NatWest, said."The more exposed young people are to financial issues,and the younger they become aware of them,the more likely they arc to become responsible,forward-planning adults who manage their finances confidently and effectively."Ministers are deeply concerned about the financial pressures on teenagers and young people because of student loans and rising housing costs.They have just introduced new lessons in how to manage debts.Nikki Fairweathcr.aged15.from St Helens,said that she had benefited from lessons on personal finance,but admitted that she still had a lot to learn about money.72.Which of the following can be found from the five-year research project?A.Students understand personal finances differently.B.University tuition fees in England have been rising.C.Teenagers tend to overestimate their future earnings.D.The students'payback ability has become a major issue.73.The phrase"to raise the ceiling"in paragraph2probably means"______".A.to raise the student loansB.to improve the school facilitiesC.to increase the upper limit of the tuition（学费）D.to lift the school building roofs74.According to Stephen Moir,students_______.A.are too young to be exposed10financial issuesB.should learn to manage their finances wellC-should maintain a positive attitude when facing loansD.benefit a lot from lessons on personal finance75.What can we learn from the passage?A.Many British teenagers do not know money matters wellB.Teenagers in Britain are heavily burdened with debts.C.Financial planning is a required course at college.D.Young people should become responsible adults.Section C（8分）Directions:Read the following passage.Fill in each blank with a proper sentence given in the box.Each sentence can be used only once.Note that there are two more sentences than you need.A.Its goal is to have good,clean,fair food for all people.B.Today,there are great concerns about the way people grow and produce food.C.It should arrive on our plates in the cleanest and most environmentally responsible way.D.All people should be able to purchase healthy food.E.This event wasn’t the only thing that started the Slow Food Movement.F.Today the Slow Food Movement has already expanded out of Italy.The Slow Food Movement started in Rome,Italy in1986.When a new McDonalds wasopening near a beautiful historic place,some people stood outside the restaurant and shouted,“We do not want fast food.We want slow food!”(76)________One day Carlo Petrini went to a restaurant to eat a traditional meal.But thefood didn’t taste the same as he remembered.He learned that the peppers were shipped fromabroad because the prices were low.This deeply concerned Carlo.Carlo wanted people to care about where their foods came from and how their foods madetheir culture special.So he started a group to encourage this idea.It soon became the Slow Food Movement.(77)________First,what is good food?Good food is fresh.The vegetables are eaten close to the placewhere they are grown.The fish hasn’t been sitting for days before it is eaten.Good food isseasonable.It should be grown at the best time of the year for that food.Good food satisfies thesenses.It should look good,smell good and taste good.And finally,good food is cultural food.Each country has special foods that make it different.Second,food should be clean.(78)________Farmers use chemicals to kill insects andfeed plants.But the chemicals can also harm the natural environment around farms.Over time,they can cause health problems in people too.Clean food means food that does not harm ourbodies or the environment.And third,food should be fair.Food should not cost too much money.(79)________Thepeople who grow and make food should be paid fairly for their work.They should work in safe,Healthy conditions.第二卷I.Translation.(3+4+4+5=16分)80.作为学生，我们不应该无视校纪校规。
2022-2023学年周浦中学高一上10月月考化学试卷
2022学年周浦中学第一学期高一化学第一次阶段性测试可能用到的相对原子质量：H-1、O-16、N-14、Na-23、C-12、S-32一、选择题（每小题只有1个正确选项，共40分）1. 某地发布大雾橙色预警信号：预计未来6小时，将出现能见度小于200米的浓雾天气，请相关部门做好防雾工作。
雾属于下列分散系中的A．溶液 B. 悬浊液 C. 乳浊液 D. 胶体2．下列关于胶体的说法正确的是A. 胶体外观不均匀B．胶体不能通过滤纸C. 胶体都能产生丁达尔现象D. 胶体不稳定，静置后容易产生沉淀3．氯化铁溶液和氢氧化铁胶体具有的共同性质是A. 都能透过半透膜B. 都呈红褐色C．都是混合物 D. 都能产生丁达尔现象4．当皮肤表皮划破时，可用氯化铁溶液应急止血，其主要原因是A. 氯化铁溶液具有杀菌作用B. 氯化铁溶液能促进血液中胶粒聚沉C. 氯化铁溶液与血液产生了氢氧化铁沉淀D．氯化铁能氧化血红蛋白5. 下列应用或事实与胶体的性质无关的是A. 用明矾净化饮用水B. 在氯化铁溶液中滴加氢氧化钠溶液出现红褐色沉淀C. 用石膏或盐卤点制豆腐D. 清晨的阳光穿过茂密的林木枝叶所产生的美丽光线6. 在Fe(OH)3胶体中逐滴滴入下列某种溶液，出现的现象是先沉淀，后沉淀溶解。
这种溶液是A. CuSO4溶液B. 饱和MgSO4溶液C．稀盐酸 D. 氢氧化钠溶液7. 已知由硝酸银溶液和碘化钾溶液制得的碘化银胶体溶胶，当它与氢氧化铁溶胶相互混合后，析出碘化银和氢氧化铁的混合沉淀。
由此可知A. 该碘化银胶粒带正电荷B. 该碘化银胶粒不带电荷C. 该过程为胶体的渗析D. 该碘化银胶粒电泳时向阳极运动8．下列说法正确的是A. 1 mol任何物质中都约含有6.02×1023个原子B. 常温常压下，1 mol O2的质量是32gC. 1 mol H2的质量是2g，所占的体积约为22.4LD. 在标准状况下，气体摩尔体积约为22.4L9. 下列操作中，与物质的溶解性无关的是A. 蒸馏海水得到淡水B. 用装有水的洗气瓶，除去CO中的HClC. 用四氯化碳萃取碘水中的碘单质D. 热的硝酸钾饱和溶液冷却后析出硝酸钾晶体10. 1mol气体所占的体积取决于A. 微粒数目B. 微粒大小C．微粒间的距离 D. 以上皆有11．下列物质中，含水分子数最少的是A. 120g水B. 6.02×1024个水分子C. 8mol水D. 18mL水（ρ=1g·cm3）12．下列仪器中可直接加热的是A. 烧杯B. 试管C. 量筒D. 圆底烧瓶13．下列实验中，所采取的分离方法与对应原理都正确的是14. 下列实验操作中，正确的是A. 分液时，下层液体从下口中放出，上层液体从上口中倒出B. 蒸馏操作时，应使温度计水银球插入蒸馏烧瓶的溶液中C. 过滤操作中，为了加快过滤速度可用玻璃棒在漏斗中轻轻搅拌D. 萃取操作时，应选择有机萃取剂，且萃取剂的密度必须比水大15．下列混合物中，可用“溶解→过滤→蒸发”操作进行分离的是A. 混有泥沙的食盐B．混有水的酒精C．白糖与食盐的混合物 D. 铁粉与泥沙的混合物16．不能鉴别盐酸和NaOH溶液的是A．石蕊试液 B. 金属单质镁 C. 碳酸钠固体 D. 氯化钠固体17．淀粉溶液是一种胶体，已知淀粉遇碘变蓝色。
上海市高一第一学期期中考试物理试卷含答案(共5套)
上海市高一第一学期物理期中考试试卷满分：100 分 考试时间：60 分钟(注意：本卷 g 取 10 m/s 2)一．选择题（每题只有一个选项正确，1-25，每题2分，26-35每题3分，共80分）1. 下列物理量中属于矢量的是（ ）A.质量B.速度C.时间D.路程2.物理学中引入“质点”的概念，从科学方法来说，属于（ ）A.控制变量法B.观察、实验法C.建立模型法D.等效替代法3.下列关于位移和路程的说法，正确的是（ ） A.位移就是路程。
B.位移大小永远不等于路程。
C.位移是标量，而路程是矢量，有大小有方向。
D.若物体做单向、直线运动时，位移大小和路程相等。
4.下列各s-t 或v-t 图中，表示质点做匀速直线运动的是（ ）5.下列各位移-时间图像中，对实际运动的物体，不可能的是（ ）6.2006年7月12日，中国选手刘翔在2006年瑞士洛桑田径超级大奖赛男子110米栏的比赛中，以12.88秒的优异成绩获得冠军，打破了沉睡了13年之久、由英国名将科林—杰克逊创造的12.91的世界记录。
如果测定刘翔起跑时的速度为8.5m/s ，到达终点时速度为10.2m/s ，那么刘翔在全程的平均速度为（ ）A ．9.27m/s B.9.35 m/s C.8.54m/s D.10.2m/s7.有关瞬时速度、平均速度、平均速率说法正确的是（ ） A.瞬时速度是物体在某一时刻或某一位置时的速度。
B.匀速直线运动的物体的平均速度与任何时刻的瞬时速度只是大小相等。
C.做变速运动的物体，平均速率就是平均速度的大小。
D.变速运动的物体，平均速度就是物体通过的路程与所用时间的比值。
8.骑自行车的人沿着斜坡下行做变速运动，第1S 内通过1m ，第2s 内通过2m ，第3s 内通过3m ，第4S 内通过4m 。
则些列说法正确的是：（ ）A.第2S 内的平均速度是2m/s 。
B.第2S 末的瞬时速度为2 m/s 。
C.前2秒内的平均速度为2m/s 。
上海高一上英语月考卷
上海高一上英语月考卷一、听力部分（共30分）Section A（每小题1.5分，共15分）1. Listen to the dialogue and choose the best answer to each question.( ) 1. What does the man want to buy?A. A book.B. A pen.C. A ruler.( ) 2. Why does the woman refuse to go to the cinema?A. She is busy.B. She doesn't like movies.C. She has seen the movie.( ) 3. What time will the speakers meet?A. At 2:00 pm.B. At 3:00 pm.C. At 4:00 pm.Section B（每小题3分，共15分）4. Listen to the passage and choose the best answer to each question.( ) 4. What is the main topic of the passage?A. The benefits of exercise.B. The importance of healthy eating.C. The influence of sleep on health.( ) 5. According to the passage, which activity can help improve concentration?A. Reading.B. Running.C. Swimming.( ) 6. What is the author's attitude towards exercise?A. Negative.B. Indifferent.C. Positive.二、单项选择（共20分）710 CBAC1115 BCBB1620 CACA三、完形填空（共30分）2125 BDACA2630 ACBDB3135 DCBBA3640 ADBCA四、阅读理解（共40分）Passage 1（每小题3分，共15分）41. The main idea of the first paragraph is that ______.A. books are a good way to learn about the worldB. reading can improve people's imaginationC. reading is more beneficial than watching TV42. According to the author, which of the following is NOT a benefit of reading?A. Improving vocabulary.B. Enhancing concentration.C. Making friends.43. The author suggests that readers should ______.A. read books in a fixed orderB. choose books they are interested inPassage 2（每小题4分，共20分）44. What is the purpose of the passage?A. To introduce a new technology.B. To discuss the advantages of online education.C. To argue against traditional education.45. According to the passage, which of the following is a disadvantage of online education?A. Limited interaction between students and teachers.B. The need for highspeed internet.C. The lack of a formal classroom environment.46. The author believes that online education will ______ in the future.A. replace traditional educationC. face many challenges47. What is the author's attitude towards online education?A. Critical.B. Supportive.C. Neutral.五、书面表达（共20分）48. 假设你是李华，你的英国朋友Peter来信询问你所在城市的旅游景点。
上海市2021-2022年高一上学期1月阶段性检测物理试题
一月份月考高一物理卷一、单选题(每小题只有一个选项正确，每小题3分,共42分)1. 质点是理想化的物理模型，下列有关质点的说法中正确的是（）A. 研究车轮的转动时，车轮可看成质点B. 研究月球绕地球运动时，月球可看成质点C. 研究跳水运动员在空中的翻滚动作时，跳水运动员可看成质点D. 乒乓球很小，所以在任何情况下都可看成质点【答案】B【解析】研究车轮的转动时，车轮不可看成质点，A错误；研究月球绕地球运动时，月球可看成质点，B正确；研究跳水运动员在空中的翻滚动作时，跳水运动员不可看成质点，C错误；乒乓球很小，但是在研究乒乓球旋转的时候，就不可以看成质点，故D错误。
2. 以下说法正确的是（）A. 某时刻物体的速度为零，其一定处于静止状态B. 物体速度变化量为负值时，它的加速度可能为正值C. 物体速度变化很快，其加速度一定很大D. 物体加速度的大小不断变小，则速度大小也不断变小【答案】C【解析】试题分析：静止状态是速度为零，加速度也为零的状态，故A错。
有加速度的定义式可知，加速度方向与速度变化量的方向一致，物体速度变化量为负值时，它的加速度一定为负值，故B错。
加速度是表征速度变化快慢的物理量，速度变化很快，其加速度一定很大，故C对。
物体加速度的大小表速度变化快慢，加速度变小，表速度变化变慢，而速度可以增大，也可以减小。
故D错。
故选C。
考点：加速度概念的考查。
3. 下列说法正确的是( )A. 重力单位牛顿是国际制基本单位B. 时间是国际单位制中一个基本物理量C. 物理量质量是矢量D. 长度的国际制基本单位是千米【答案】B【解析】A项：牛顿是国际单位制的导出单位，不是基本单位，选项A错误；B项：力学中的基本物理量为质量、长度、时间，故B正确；C项：质量只有大小，没有方向，所以质量为标量，故C错误；D项：长度的国际制基本单位为米，故D错误。
4. 对于一些实际生活中的现象，某同学试图从惯性角度加以解释，其中正确的是（）A. 采用了大功率的发动机后，某些一级方程式赛车的速度甚至能超过某些老式螺旋桨飞机的速度，这表明：可以通过科学进步使小质量的物体获得大惯性B. “强弩之末势不能穿鲁缟”，这表明强弩的惯性减小了C. 货运列车运行到不同的车站时，经常要摘下或加挂一些车厢，这会改变它的惯性D. 自行车转弯时，车手一方面要适当的控制速度，另一方面要将身体稍微向里倾斜，这是为了通过调控人和车的惯性达到安全行驶的目的【答案】C【解析】惯性是物体的因有属性，大小与物体的质量有关，质量越大，惯性越大，与其它任何因素无关，AB错误；摘下或加挂一些车厢，改变了质量，从而改变惯性，C正确；人和车的质量不变，则其惯性不变，D错误．5. 如图所示，A、B两物体相距x＝7 m，物体A以v A＝4 m/s的速度向右匀速运动，而物体B 此时的速度v B＝10 m/s，只在摩擦力作用下向右做匀减速运动，加速度a＝－2 m/s2.那么物体A追上物体B所用的时间为( )A. 6 sB. 7 sC. 8 sD. 9 s【答案】C..................6. 如图所示，质量为m的小球用水平轻弹簧系住，并用倾角为30°的光滑木板AB托住，小球恰好处于静止状态．当木板AB突然向下撤离的瞬间，小球的加速度大小为 ( )A. 0B.C. gD.【答案】B【解析】撤离木板时，小球所受重力和弹簧弹力没变，二者合力的大小等于撤离木板前木板对小球的支持力F N，由于F N＝，所以撤离木板后，小球加速度大小为：a ＝.C项正确7. 有三个共点力F1、F2、F3作用于某一点，其合力为零．已知F3=5N，现将F3的方向沿逆时针方向绕作用点转动60°，同时其余两个力顺时针转动30°，则这三个力的合力大小变为（）A. B. 5N C. 10N D. 仍为零【答案】A点晴：三力的合力为零，则任意两力之和与第三力大小相等方向相反；由题意可知其他两力的合力大小及方向；利用平行四边形定则可求得转动之后的合力。
高一第一学期期中考试数学试卷含答案(共3套,上海市)
上海市高一第一学期期中考试数学一、 填空题(共42分，1-6每小题3分，7-12每小题4分) 1. 若82log 3x =-，则x = 2. 已知集合(){}(){}2,1,,1A x y y x B x y y x ==+==+，则AB =3. 若幂函数()f x 过)22,2(，则(8)f = 4. 不等式x x x 232)31()31(2<+-的解集为5. 若22xa=且0a >，则33x xxxa a a a --+=+ 6. 若关于x 的方程03422=-+x x 的两个根为21,x x ，则=+2221x x ______7. 若函数()21xy a =-在R 上是严格减函数，则实数a 的取值范围是___________8. 下列幂函数在区间(),0+∞上是严格增函数，且图像关于原点成中心对称的是（请填入全部正确的序号）(1) ;21x y =（2）;31x y = (3) ;32x y =(4) ;31-=xy (5) .3x y =9. 已知集合{}2(1)320A x a x x =-+-=的子集有且仅有2个，则a = 10. ＂2560x x ++≠＂是＂2x ≠-＂的 条件．11. 若关于x 的不等式组⎩⎨⎧>-≤+-00)23)(32(a x x x 的解集为φ，则实数a 的取值范围为12. 若x>0,y>0, x+2y=2，则11x y+的最小值为 二、选择题(共16分，每小题4分)13、若56789log 6log 7log 8log 9log 10p =⋅⋅⋅⋅，则 （ ） （A ）(0,1)p ∈；（B ）1p =；（C ）(1,2)p ∈;(D)2p =14、在同一平面直角坐标系中，指数函数(0xy a a =>且1)a ≠和一次函数(1)y a x =+的图像关系可能是 （ ）15、如果|a-c|<|b|，则一定有 （ ） A.a<b+c; B.|a|<|b|+|c|; C.a<c-b; D.|a|>|b|-|c|16、已知命题“非空集合M 中的元素都是集合P 中的元素”是假命题，现有下列命题： （1）M 中的元素都不是集合P 中的元素； （2）M 中一定有不属于P 的元素； （3）M 中一定有属于P 中的元素； （4）M 中的元素不都是集合P 中的元素。
2020-2021学年上海市行知中学高一上学期12月月考试卷英语 Word版含答案
上海市行知中学2020-2021学年高一年级第一学期第二次月考英语试卷考试时间：100分钟满分：100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. By bike. B. By car. C. By bus. D. On foot.2. A. The man’s violin. B. The man’s hobby.C. The man’s interview.D. The man’s job.3. A. P ositive. B. Interesting. C. Boring. D. Successful.4. A. He can’t get a room at the hotel at this ti me.B. He didn’t get the type of room he wanted.C. He expected the room to be more expensive.D. He thought he had already made a reservation.5. A. They should give Jessica some on-the-job training.B. They should offer Jessica some train tickets.C. They shouldn’t have taken Jessica into account.D. They should ask Jessica to get more qualification.6. A. The weather forecast says it will be fine.B. The weather will not affect their plan.C. They will not do as planned in case of rain.D. They will postpone their programme if it rains.7. A. She’s unable to finish her homework. B. She has to give up efforts.C. She has to remove the virus.D. She’s infected with some disease.8. A. He has to wait for someone else.B. He is concer ned about the woman’s safety.C. There is something wrong with the car.D. The woman must fasten the seat belt.9. A. She has been promoted to be the sales manager.B. She isn’t popular with the colleagues in the sales department.C. She enjoyed working in the sales department.D. She doesn’t like her new position very much.10. A. Few students meet Professor Brown’s requirements.B. Many students find Professor Brown’s lecture uninteresting.C. Few students understand Professor Brown’s lect ure.D. Many students have dropped Professor Brown’s class.Section BDirections:In Section B, you will hear two passages and one longer conversation. After each passage or conversation, you will be asked several questions. The passages and the conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one is the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. They use types of fuel that are not allowed on land.B. It takes more energy to move through water than over land.C. Their engines are not as powerful as those of other vehicles.D. They carry large numbers of passengers and vehicles as well.12. A. They are sometimes rude to other tourists.B. They don’t have meals in local restaurants.C. They fill up the restaurants and make noise.D. They complain when the city is too crowded.13. A. A new way of travelling. B. Reasons to ban cruise ships.C. Measures against pollution.D. Problems caused by cruise ships.Questions 14 through 16 are based on the following passage.14. A. To use an app to order meals.B. To know how to use a GPS signal.C. To communicate with the robot properly.D. To pay extra money for the delivery.15. A. It can move on its two feet at a very fast speed.B. It can identify the customers through its cameras.C. 3G technology enables it to find the customers’ houses.D. It was built by a European online take-away food company.16. A. The relationship between human and robot.B. The creative ways to use a robot.C. The world’s newest invention and technology.D. A self-driving food-delivery robot.Questions 17 through 20 are based on the following conversation.17. A. The approach to getting good scores.B. The effectiveness of cramming.C. The impact of a good night’s sleep on a test.D. The better way to prepare for a test.18. A. Join the woman in her study.B. Entertain himself and have fun.C. Memorize everything on his notes.D. Skip lunch and hurry to the cinema.19. A. Organize a study group and quiz herself.B. Get involved in the revision without rest.C. Review the materials earnestly as scheduled.D. Focus on the chapters assigned by the teacher.20. A. Hardworking and focused. B. Energetic but easily distracted.C. Score-oriented and efficient.D. Ambitious but readily discouraged. II. Grammar and VocabularySection ADirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.A Wrinkle in TimeTravelling faster than the speed of light is something that scientists and science-faction writers have dreamt about for a long time. In theory, if humans were able to do this, they could travel to distant planets in (21) ________ matter of minutes.In Madeleine L'Engle's novel, A Wrinkle in Time, the idea goes one step further: instead of travelling at great speeds, she processes a theory (22) ________ allows humans to travel through a fifth dimension（维度）. This means that you could get from Earth to another planet in a distant galaxy almost instantly.First (23) ________ (publish) in 1960, L' Engle's novel has captured the imaginations of young science-fiction fans all over the world for decades -- and now it (24) _______ (turn) into a film. The story follows 13-year-old Meg Murry, played by Storm Reid, who is seen by her classmates and teachers (25) ________ a troublesome pupil. She is the daughter of two world-famous physicists, but is saddened by the mysterious disappearance of her father. To help find her dad, three supernatural beings, Mrs. Who, Mrs. Whatist and Mrs. Which, transport Meg, her genius brother, Charles Wallace, and her classmate, Calvin, through the universe. (26) ________ (travel) through a wrinkling of time and space, also known as "tessering", they are soon transported to worlds that they never thought (27) ________ (exist).(28) ________ the film follows the story of the book, not everything could be fitted in. One detail that fans of the book may notice is (29) ________ Meg's twin brothers have been written out of the script.Oprah Winfrey, who plays Mrs. Which, says the film is like The Wizard of Oz for a new generation. "It is a spaced-out Oz, with Meg as the new Dorothy, and I am Glinda [the Good Witch]," she says. "I think of it as a film for generations (30) ________ (come)."Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.The meaning of silence varies among cultural group. Silence may be 31 , or they may be empty when a person has nothing to say. A silence in a conversation may also show stubbornness, uneasiness, or worry. Silence may be viewed by some cultural groups as extremely uncomfortable; therefore attempts may be made to fill every 32 with conversation. Persons in other cultural groups value silence and view it as necessary for understanding a person’s needs. Many nati ve Americans value silence and feel it is a basic part of 33 among people, just as some traditional Chinese and Thai persons do. Therefore, when a person from one of theseculture is speaking and suddenly stops, what may be 34 is that the person wants the listener to consider what has been said before continuing. In these culture, silence is a call for 35 .Other cultures may use silence in other ways, particularly when dealing with 36 among people or in relationships of people with different amounts of power. For example, Russian, French, and Spanish persons may use silence to show 37 between parties about the topic under discussion. However, Mexicans may use silence when instructions are given by a person in authority rather than be rude to that person by arguing with him or her. In still another use, persons in Asian cultures may view silence as a sign of respect, particularly to an elder or a person in authority.Nurses and other care-givers need to be aware of the 38 meanings of silence when they come across the personal anxiety their patients may be experiencing. Nurses should recognize their own personal and cultural construction of silence so that a patient’s silence is not 39 too early or allowed to go on unnecessarily. A nurse who understands the healing 40 of silence can use this understanding to assist in the care of patients from their own and from other cultures.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.Animal RightsEvery conscious being has interests that should be respected. No being who is conscious of being alive should be devalued to thinghood, dominated, and used as a resource or ___41___. The key point of the idea known as animal rights is a movement to extend moral consideration to all ___42___ beings. Nobody should have to demonstrate a specific level of intelligence or be judged beautiful to be given moral consideration. No being should have to be useful to humanity or capable of accepting “duties” in order t o be extended moral consideration. ___43___, what other animals need from us is being free from duties to us.Animal rights is about letting animals live on their own terms. It can be written into our laws, but is not an actual list or bill of rights as we have for human society. It begins with our promises not to act like ___44___ of others. Animal rights is about justice ─ treating animals fairly.Why is animal rights ___45 ___? It is because we humans often act as though we are the only beings on the planet. Although we depend on other animals for our very survival, humans are the only animals that have upset the balance of nature. There are lots of ways that humans ___46___ animals. We domesticate them and use them for food, even though our nutritional needs can be completely supplied by a(n) ___47___ diet. Although other materials are available, we use animal’s skin and other body parts for clothing, furs, hats, boots, jewellery and even pet toys. Humans can talk about it but animals cannot. All animals wish to experience life in its fullness. Unlike many animals who have to kill to survive, humans do not. Why should humans cause ___48___ to other beings when it’s not necessary?As we do, animals protect their children; they feel fear; they warn each other of dangers; they play. We might differ from other animals in some ways, but that doesn’t give us the right to ___49___ them down, take their lands, pollute their waters, or use them for our conveniences. Animals also experience pain and it’s notdifficult to observe ___50___ of pain in the way a conscious being reacts to it. We take advantage, cause distress, and act ___51___ when we use animals for amusement. Lots of pets are ___52___ on the streets when their owners no longer find it convenient or affordable to keep or care for them.Whether we admit it or not, it’s a prejudice to think we are ___53___ to animals and that it is our right to control them, which can only make people act mean, hateful or neglectful. However, each of us has within us the power to ___54___. We can adopt a different attitude, one that reshape our destiny. This will have wonderful effects on the planet’s other communities, for life is ___55___ avoiding suffering. It is interacting, singing, pursuing joy. We humans can learn to live responsibly, with respect, kindness and love.41. A. companies B. goods C. insects D. providers42. A. active B. conscious C. intelligent D. strange43. A. Indeed B. Moreover C. Nevertheless D. Otherwise44. A. followers B. friends C. masters D. tutors45. A. necessary B. reflected C. respected D. revolutionary46. A. distinguish B. keep C. exploit D. raise47. A. animal-free B. eco-friendly C. low-salt D. well-balanced48. A. conflict B. confusion C. isolation D. misery49. A. calm B. chase C. pull D. put50. A. signs B. symbols C. symptoms D. performances51. A. differently B. similarly C. gently D. unfairly52. A. abandoned B. chosen C. oppressed D. spoiled53. A. accessible B. appealing C. reasonable D. superior54. A. change B. dominate C. persist D. proceed55. A. contrary to B. more than C. owing to D. rather thanSection BDirections:Read the following two passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C, D. Choose the one that fits best according to the information given in the passage you have read.(A)I used to think ants knew what they were doing. The ones marching across my kitchen counter looked so confident; I just figured they had a plan, knew where they were going and what needed to be done. How elsecould ants organize highways, build elaborate nests, launch impressive attacks, and do all the other things ants do?Turns out I was wrong. Ants aren’t clever little engineers, architects, or soldiers after all --- at least not as individuals. When it comes to deciding what to do next, most ants don’t have a clue. “If you watch an ant try to accomplish something, you’ll be impressed by how awkward it is,” says Deborah M.Gordon, a biologist at Stanford University.“Ants aren’t smart,” Gordon says. “Ant colonies are.” A colony can solve problemsunthinkable for individual ants, such as finding the shortest path to the best food source,assigning workers to different tasks, or defending a territory from neighbors. Asindividuals, ants might be tiny dummies, but as colonies they respond quickly andeffectively to their environment. They do it with something called collective intelligence.Where this intelligence comes from raises an essential question in nature: How do the simple actions of individual ants add up to the complex behavior of a group? How do hundreds of honey-bees make a critical decision about their hive (蜂巢)if many of them disagree? The collective abilities of such animals --- one of which grasps the big picture, but each of which contributes to the group’s success --- seem miraculous even to the biologists who know them best. Yet during the past few decades, researchers have come up with fascinating insights.56.The author’s former false impression about ants is that he thought them to be _______.A. smartB. awkwardC. elaborateD. creative57.Which of the following is TRUE according to the passage?A. Ants will function as a single body once a decision is made by the commander.B. Ants are the only species which developed collective intelligence.C. The ant queen plays a role in managing ant workers besides laying eggs.D. An individua l ant can’t comprehend the whole process of a big movement.58.The paragraph following the passage will most probably deal with _______.A. where we can observe such fantastic behavior of antsB. which is the leading ant in charge of the actionC. how the collective intelligence worksD. what inspiration can be drawn from the collective abilities(B)In spring, chickens start laying again, bringing a welcome source of protein at winter's end. So it's no surprise that cultures around the world celebrate spring by honoring the egg.Some traditions are simple, like the red eggs that get baked into Greek Easter breads. Others elevate the egg into a fancy art, like the heavily jewel-covered “eggs” that were favored by the Russians starting in the 19th century.One ancient form of egg art comes to us from Ukraine. For centuries, Ukrainians have been drawing complicated patterns on eggs. Contemporary artists have followed this tradition to create eggs that reflect the anxieties of our age: Life is precious, and delicate. Eggs are, too.“There’s something about their delicate nature that appeals to me,” says New Yorker cartoonist Roz Chast. Several years ago, she became interested in eggs and learned the traditional Ukrainian technique to draw her very modern character s. “I've broken eggs at every stage of the process一from the very beginning to the very, very end. ”But there’s an appeal in that vulnerability. “There’s part of this sickening horror of knowing you’re walking on the edge with this, that I kind of like, k nowing that it could all fall apart at any second.” Chast’s designs, such as a worried man alone in a tiny rowboat, reflect that delicateness.Traditional Ukrainian decorated eggs also reflect those fears. The elaborate patterns were believed to offer protection against evil.“There’s an ancient legend that as long as these eggs are made, evil will not prevail in the world,” says Joan Brander, a Canadian egg-painter who has been painting eggs for over 60 years, having learned the art from her Ukrainian relatives.The tradition, dating back to 300 B. C., was later incorporated into the Christian church. The old symbols, however, still endure. A decorated egg with a bird on it, given to a young married couple, is a wish for children. A decorated egg thrown into the field would be a wish for a good harvest.59. People in many cultures prize the egg because __________________.A. It can bring wealth and honor to them.B. It can easily be made into a work of art.C. It is their major source of protein in winter.D. It is a welcome sign of the coming of spring.60. What do we learn about the decorated “eggs” in Russia?A. They are cherished by the rich.B. They are favored as a form of art.C. They are shaped like jewel cases.D. They are heavily painted in red.61. Why have contemporary artists continued the egg art tradition?A. Eggs reflect the anxieties of people today.B. Eggs provide a unique surface to paint on.C. Eggs have an oval shape appealing to artists.D. Eggs serve as an enduring symbol of new life.62. Why does Chast enjoy the process of decorating eggs?A. Because she always gets great pleasure from designing something new.B. Because she is never sure what the final design will look like until the end.C. Because she can add multiple details to the design to communicate her idea.D. Because she never knows if the egg will break before the design is completed.Section CDirections:Read the passage carefully. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.A. In the upper parts of the atmosphere, it will burn up.B. There are also millions of smaller pieces of junk that we can’t see.C. Blowing up older satellites with a missile may create thousands of smaller pieces!D. One reason that it’s urgent is that countries are sending more and more objects into space.E. When two objects in space collide, the two objects break into many smaller pieces.F. Years of space exploration have left tons of “space junk” in orbit (轨道) around the planet.Many people know that trash is a big problem on planet Earth. What many people don’t know is that trash has become a problem in outer space too. (63) _________________________Statistically, there are more than 22,000 pieces of junk in space around the earth. And these are just the items that we can see from the surface of the earth by telescopes or radars. (64) ___________________Objects, like bits of old space rockets or satellites, move around the planet at very high speeds, so fast that even a very small piece can break important satellites or become dangerous to people, particularly astronauts. If the tiniest piece of junk crashed into a spacecraft, it could damage the vehicle. That’s because the faster an object moves, the greater the impact if the object collides with something else.To help minimize additional space junk, countries around the world have agreed to limit the time their space tools stay in orbit to 25 years. Each tool must be built to fall s afely into the earth’s atmosphere, or the mass of gases that surround the earth, after that. (65) ______________________Many scientists are also proposing different ways to clean up space junk. The Germans have been planning a space mission with robots that would collect pieces of space trash and bring them back to Earth so that they can be safely destroyed.“In our opinion the problem is very challenging, and it’s quite urgent as well,” said Marco Castronuovo, an Italian Space Agency researcher who is working to solve the problem. (66) _____________________ Many of these objects are tools that help people use their cell phones or computers.“The time to act is now; as we go farther in time we will need to remove more and more fragments,” he says.IV. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.67.父母应鼓励自己的孩子要有责任感。
高一上学期联考上海,附答案
快乐学习 > 高一 > 高一英语 > 高一试题 > 高一英语第一次月考卷附答案高一英语第一次月考卷附答案2012-08-02字体大小 T |T摘要：高一英语第一次月考，通过小测试帮助你回顾前面已经学过的内容，更好的掌握已经学过的内容。
第一卷（共115分）第一部分：听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）请听下面5段对话，选出最佳选项。
1. What will the man do this morning?A. Do some shopping.B. Go fishingtogether. C. Go skating.2. Why does the woman give a gift to Charlie?A. It is her birthday.B. It is hisbirthday. C. He is going abroad.3. What does the woman want the man to do?A. Read books.B. Wash hishands. C. Have dinner.4. What will the two speakers do?A. Cry for help.B. Find out what is happening in the room.C. Break the window and get inside the room. .5. Where are the two speakers now?A. In a hospital.B. In arestaurant. C. At home.第二节（共15小题; 每小题1.5分，满分22.5分）请听下面5段对话或独白，选出最佳选项。
请听第6段材料，回答第6、7题。
6. Who was badly hurt in the traffic accident?A. The bike rider.B. The truckdriver. C. The car driver.7. How do the two speakers get the news?A. On TV.B. On theradio. C. In a newspaper.请听第7段材料，回答第8至10题。
上海高一第一学期期中数学试卷及答案
上海高一第一学期期中数学试卷一、填空题（每题3分，共42分）1、已知全集U ＝{－2，－1,0,1,2}，集合A ＝{－1,0,1}，B ＝{－2，－1,0}，则U C AB ＝____________.2、“1m ”是“一元二次方程x 2＋x ＋m ＝0有实数解”的____________条件．3、不等式x>ax ＋32的解集是(4,b)，则b ＝________.4、若集合A ＝{x|(k-1)x 2＋x －k ＝0}有且仅有两个子集，则实数k 的值是________．5、函数232()23x x f x x的定义域是__________________.6、设函数f(x)＝－x ，x ≤0，x 2，x>0，若f(α)＝2，则实数α为________．7、不等式204x x的解集是___________________.8、不等式x 2－3>2|x|的解集是____________．9、已知0,0xy且2223,xy则212x y 的最大值是________________.10、下面几个不等式的证明过程：①若a 、,b R 则22;b a b a ab a b②xR 且0,x则4442;xxxxxx③若a 、,bR 0,ab 则()2 2.b a b a b a abab ab其中正确的序号是___________________.11、若实数x ，y 满足x 2＋y 2＋xy ＝1，则x ＋y 的最大值是________．12、某种商品将在某一段时间内进行提价，提价方案有三种：第一种：先提价%,m 再提价%;n 第二种：先提价%,2m n 再提价%;2m n 第三种：一次性提价()%.m n 已知0m n ，则提价最多的方案是第_________________种。
13、对a 、.bR 记,(),min ,,(),a ab a bb ab 函数1()min,12()2f x x x x R 的最大值为____________________.14、对,xR y R ,已知()()(),f x y f x f y 且(1)2,f 则(2)(3)(4)(1)(2)(3)f f f f f f (2015)(2016)(2014)(2015)f f f f 的值为____________________.二、选择题（每题3分，共12分）15、设0,xy 则下列各式中正确的是（）A ，2x y x xy y B ，2x y x xy y C ，2x yxyxyD ，2x yxyxy16、已知a 、b 、c 、d 为实数，且cd 则“ab ”是“ac bd ”的（）A ，充分而不必要条件B ，必要而不充分条件C ，充要条件D ，既不充分也不必要条件17、下列各对函数中，相同的是（）A ，2(),()1xx f x g x x xB ，()1,f x g x xC ，11(),()11u v f u g v uvD ，2(),()f x xg x x18、设,,a b c 为实数，2()()(),f x x a x bx c 2()(1)(1).g x ax cxbx 记集合()0,,Sx f x xR ()0,,Tx g x x R 若,S T 分别为集合S ，T 的元素个数，则下列结论不可能的是（）A ，10S T 且B ，11S T 且C ，22ST且D ，23ST且三、解答题19、（本题8分，每小题4分）解下列不等式组222116801233421815x x x x x x x x x 20、（本题8分，每小题4分）（1）已知1x，求27101xx yx 的最小值；（2）已知3412x y ，求xy 的最大值.21、（本题8分）已知适合不等式5|3||4|2x a x x的x 的最大值为3,求实数a 的值；并解该不等式.22、（本题12分，每小题4分）已知二次函数()yf x 满足条件1(0),(1)(1)42.2f m f x f x x m (m 为已知实数)（1）求函数()f x 的解析式；（2）如果函数()yf x 的图像与x 轴的两个不同交点在区间（0,4）内，求实数m 的取值范围；（3）当函数()yf x 的图像与x 轴有两个交点时，这两个交点能否在点1(,0)2的两旁？请说明理由.23、（本题10分，每小题5分）提高过江大桥的车辆通行能力可改善整个城市的交通状况.在一般情况下，大桥上的车流速度v （单位：千米/小时）是车流密度x （单位：辆/千米）的函数。
2023年上海高一上册数学月考试题沪教版好题
2022~2023学年度高一年级12月份月考数学全卷满分：150分；考试时间：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，并将条形码粘贴在答题卡上的指定位置。
2．回答选择题时，选出每小题答案后，用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收回。
4．本卷主要考查内容：必修第一册第一章～第五章5.3。
第I卷(选择题)一、单选题(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．已知函数y=f(x−2)的定义域是[−2,6]，则y=√x+3的定义域是()A．(-3,+∞)B．[-4,+∞)C．(−3,4]D．[−2,6]2．下列说法中正确的是()A．命题p:∀x∈R，x2>0为真命题B．若命题p:1x−1>0，则¬p:1x−1≤0C．若p是q的充分不必要条件，则¬q是¬p的必要不充分条件D．不等式x2+ax+a>0的解集为R的充要条件是a∈(0,4)3．若x<54，则4x−2+14x−5的最大值是()A．1B．5C．−1D．−5 4．函数f(x)=e x−e−xx−x3的图象的大致形状为()A．B．C ．D ．5．砖雕是我国古建筑雕刻中的重要艺术形式，传统砖雕精致细腻、气韵生动、极富书卷气.如图所示，一扇环形砖雕，可视为将扇形OCD 截去同心扇形OAB 所得图形，已知OA =0.2m ，AD =0.3m ，∠AOB =120°，则该扇环形砖雕的面积为( )A ．π5m 2B ．7π100m 2C ．π100m 2 D ．π10m 26．设a =−log 154,b =3lg2,c =0.5−0.2，则a,b,c 的大小关系是( )A ．a <b <cB ．b <a <cC ．c <b <aD ．c <a <b7．已知偶函数f (x )的定义域为R ，且对于任意x 1,x 2∈[0,+∞),(x 1≠x 2)均有f (x 2)−f (x 1)x 2−x 1>0成立，若f (1−a )>f (2a −1)，则实数a 的取值范围是( )A ．(−∞,0)∪(23,+∞) B ．(23,+∞)C ．(0,23)D ．(0,23]8． Logistic 函数是一种常见的S 形函数，它可以用来估计病毒的传播情况.忻州高级中学某学生对某地新冠肺炎爆发趋势用Logistic 函数建模研究后发现，从确诊第一名患者开始累计时间t (单位：天)与病情爆发系数f(t)之间，满足函数模型：f (t )=11+e 11−0.22t，据估算此时病情爆发系数为0.01，则此时t 约为( )(参考数据：e 4.6≈99)A ．28B ．40C ．29D ．30二、多选题(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．双曲函数是数学中一类非常重要的函数，其中就包括双曲正弦函数：f(x)=e x−e−x2，双曲余弦函数：g(x)=e x+e−x2(e≈2.71828⋯⋯，为自然对数的底数)．下列关于f(x)与g(x)说法正确的是()A．f(x)在R上单调递增B． g(x)>1恒成立C．∀x∈R，−1≤f(x)g(x)≤1D．∀x,y∈R，都有f(x+y)=f(x)g(y)+f(y)g(x)10．在下列所示电路图中，下列说法正确的是()A．如图①所示，开关L1闭合是灯泡M亮的必要不充分条件B．如图②所示，开关L1闭合是灯泡M亮的充分不必要条件C．如图③所示，开关L1闭合是灯泡M亮的充要条件D．如图④所示，开关L1闭合是灯泡M亮的既不充分也不必要条件11．已知θ∈(0,π),sinθ+cosθ=15，则下列结论正确的是()A．θ∈(0 ,π2)B．cosθ=−35C．tanθ=−34D．sin2θ+sinθcosθ=42512．定义在R上的函数f(x)满足f(2x)=2f2(x)−1，则下列结论正确的是() A．f(x)是偶函数B．f(x)≥−1恒成立C．f(x)是常数函数D．若存在a∈(1,+∞)，使得f(x)=a成立，则f(x)是单调递增函数第II卷(非选择题)三、填空题(本大题共4小题，每小题5分，共20分，把答案写在题中横线上)13．已知函数f(x)=x3+x2−x+1x2+1在[−2023,2023]上的最大值为5，则f(x)的最小值为______.14．已知角β的终边上有一点P(cos(3π2−α),sin(α−π2))，其中α满足{α|2kπ+π2<α <(2k+1)π,k∈Z}，则角β为第______象限角．15．已知p：x≤k，q：1x+1≤1，若p是q的充分不必要条件，则实数k的取值范围是______.16．已知f(x)=(e x−a−1)(ln(x+1)+a)，若f(x)只有一个零点，则实数a的取值范围是______.四、解答题(本大题共6小题，共70分，17题10分，其余各题12分)17．已知集合A={x|a−2＜x＜2a}，集合B={x|x2−5x+4<0}．(1)若A∩B=ϕ，求实数a的取值范围；(2)若A∪B=A，求实数a的取值范围．18．某单位购入了一种新型的空气消毒剂用于环境消毒，已知在一定范围内，每喷洒1个单位的消毒剂，空气中释放的浓度y(单位：毫克/立方米)随着时间x(单位：小时)变化如下图所示：当0≤x≤4时，y=a x−c；当4<x≤32时，y=5−log b x.若一次喷洒多个单位，则某一时刻空气中的消毒剂浓度为每次投放的消毒剂在相应时刻所释放的浓度之和.由实验知，当空气中消毒剂的浓度不低于4(毫克/立方米)时，它能起到杀灭空气中的病毒的作用.(精确到0.01，参考数据：log23≈1.58)(1)若喷洒1个单位的消毒剂，求空气中释放的浓度随着时间变化的关系式.(2)若一次喷洒2个单位的消毒剂，则有效杀灭时间可达几小时？19 ．已知函数f(x)=ax2−(a+3)x+3(a>0)．(1)若对任意的x∈R，f(x)≥−1恒成立，求实数a的范围；(2)求关于x的不等式f(x)<0的解集．20．已知函数f(x)=log2(2x+1)+kx(k∈R)是偶函数．(1)求k的值；(2)若函数g(x)=f(x)−b有两个零点，求b的取值范围．21．已知函数f(x)是定义域在R上的奇函数，且当x≥0时，f(x)=e x+x−1. (1)求函数f(x)的解析式；(2)若对任意的m∈[1,+∞),f(m2−mt)+f(tm +1m2)>0恒成立，求实数t的范围.22．对于函数f(x)，如果存在实数x0，使得f(x0)=m+x0成立，则称x0是函数f(x)关于参数m的不动点.(1) 若函数f(x)=lnx+4x−7有关于参数0的不动点x0∈[n,n+1),n∈Z，求n的值；(2) 当a∈(1,2)时，函数f(x)=log2(4x+a⋅2x+a−1)恒有关于参数m的不动点，求m的取值范围.。
上海高一上学期分考试数学试题(解析版)
一、填空题 1．关于x 的不等式的解集是___________. 23020x x -≤-【答案】(20,23]【分析】把给定不等式化成一元二次不等式求解即可. 【详解】不等式化为：，解得，23020x x -≤-200(23)(20)0x x x -≠⎧⎨--≤⎩2023x <≤所以不等式的解集是. 23020x x -≤-(20,23]故答案为：.(20,23]2．已知a 、，且，则ab 的最大值是____________. R b ∈2241a b +=【答案】##0.25 14【分析】利用基本不等式得，即可得到最大值. 22144a b ab =+≥ab 【详解】因为实数满足， ,a b 2241a b +=所以由基本不等式可得：221422a b a b =+≥⨯所以，当且仅当，即时等号成立， 14ab ≤22142a b ==a b ⎧=⎪⎪⎨⎪=⎪⎩a b ⎧=⎪⎪⎨⎪=⎪⎩即的最大值为.ab 14故答案为：.143．若点P (3，y )是角终边上一点，且，则y 的值是____________. α2sin 3=-a 【答案】【分析】利用三角函数值的定义，即可求解. 【详解】，解得s 32in α==-y =故答案为：4．已知.若是奇函数，则实数a 的值是____________.()11f x x x a =+-(1)=-y f x 【答案】2-【分析】利用已知函数的定义域，结合奇函数的定义计算作答即可. 【详解】函数的定义域为且， 11()f x x x a=+-{R |0x x ∈≠}x a ≠因为函数是奇函数，则当且时，恒成立， (1)=-y f x 1x ≠1x a ≠+(1)(1)0f x f x --+-=因此，整理得， 111101111x x a x x a+++=--------2221101(1)a x a x ++=-+-即，于是得，解得，22222(1)(1)(2)0(1)[(1)]a a a x x a x ++++--=-+-2(1)(1)020a a a ⎧+++=⎨--=⎩2a =-所以实数a 的值是. 2-故答案为：2-5．若函数的值域是，则函数的值域是____________.()y f x =1,42⎡⎤⎢⎥⎣⎦()()()12121F x f x f x =+++【答案】172,4⎡⎤⎢⎥⎣⎦【分析】由给定条件求出的值域，换元借助对勾函数性质即可得解.(21)f x +【详解】因函数的值域是，从而得函数值域为，()y f x =1,42⎡⎤⎢⎥⎣⎦(21)t f x =+1,42⎡⎤⎢⎥⎣⎦函数变为，，()F x 1y t t =+1,42t ⎡⎤∈⎢⎥⎣⎦由对勾函数的性质知在上递减，在上递增，1y t t =+1,12⎡⎤⎢⎥⎣⎦[1,4]时，，而时，，时，，即，1t =min 2y =12t =52y =4t =17y 4=max 174y =所以原函数值域是.172,4⎡⎤⎢⎥⎣⎦故答案为：.172,4⎡⎤⎢⎥⎣⎦6．已知里氏震级R 与地震释放的能量E 的关系为.那么里氏8.4级的地震释放的()2lg 11.43R E =-能量大约是里氏6.8级地震释放的能量的_____________倍.(精确到0.1) 【答案】251.2【分析】根据给定条件，作差并结合对数运算求解作答.【详解】令里氏8.4级的地震释放的能量为，里氏6.8级的地震释放的能量为，1E 2E 则，，两式相减并整理得，()12lg 11.48.43E -=()22lg 11.4 6.83E -=12lg lg 2.4E E -=即，因此. 12lg 2.4E E = 2.41210251.2EE =≈故答案为：251.27．若一个等腰三角形顶角的正弦值为，则其底角的余弦值为____________. 2425【答案】或.3545【分析】设顶角，则其底角的余弦值为，由半角公式求值即可. ()0,πα∈πcos sin 222ααæöç÷-=ç÷èø【详解】设顶角，则，∴或 ()0,πα∈247sin ,cos 2525αα==±3sin 25α=45则其底角的余弦值为或. π3cos sin 2225ααæöç÷-==ç÷èø45故答案为：或.35458．已知点A 的坐标为，将OA 绕坐标原点顺时针旋转至，则点的横坐标是(4,3)-3πOA 'A '____________.【分析】根据给定条件，利用三角函数定义，结合差角的余弦公式求解作答.【详解】以x 轴非负半轴为角的始边，令射线OA 为终边的角为，则射线为终边的角为αOA 'π3α-，显然，，5OA OA =='=34sin ,cos 55αα=-=因此，πππ413cos cos cos sin sin 333525ααα⎛⎫-=+=⨯- ⎪⎝⎭所以点A '5=9．方程的实数解为____________.9135x x+-=【答案】3log 2x =【分析】分、两种情况化简方程，求出的值，解之即可.0x ≤0x >9135x x+-=3x【详解】当时，则，由可得，可得；0x ≤31x ≤9135x x+-=()23340x x --=3x =当时，则，由可得，可得，解得.0x >31x >9135x x+-=()23360x x +-=32x =3log 2x =故答案为：.3log 2x =10．设，当时，恒成立，则实数m 的取值范围是()222x x f x --=R x ∈()()210f x mx f ++>____________. 【答案】()1,1-【分析】根据题意把不等式转化为即，结合函数的单调性2(2)(1)0f x mx f ++>2(2)(1)f x mx f +>-和奇偶性，得到在上恒成立，根据二次函数的性质，列出不等式，即可求解.2210x mx ++>R x ∈【详解】由函数，111(22)[2()]22222()2x x x x x x f x --=--=⋅-=均为在上的增函数，故函数是在上的单调递增函数，1212,2xxy y ⎛⎫==- ⎪⎝⎭R ()f x R 且满足，所以函数为奇函数， 1111()22()22()x x x x f x f x --------=-=-=-()f x 因为，即， 2(2)(1)0f x mx f ++>2(2)(1)(1)f x mx f f +>-=-可得恒成立，即在上恒成立， 221x mx +>-2210x mx ++>R x ∈则满足，即，解得， 2(2)40m -<244m <11m -<<所以实数的取值范围是. m (1,1)-故答案为：.(1,1)-11．已知，（是自然对数的底数），若对任意的，都存在唯一的()ln f x x =1,e D t ⎡⎤=⎢⎥⎣⎦e a D ∈b D∈，使得，则实数的取值范围是_____________.()()4f a f b +=t 【答案】{}5e 【分析】分析出函数在上单调递增，可得出，即可求得实数的值.()f x D ()14e 1e f t f t ⎧⎛⎫+= ⎪⎪⎪⎝⎭⎨⎪>⎪⎩t 【详解】因为函数在上单调递增，()f x D 对任意的，都存在唯一的，使得，a D ∈b D ∈()()4f a f b +=则，解得.()1ln 14e 1ef t f t t ⎧⎛⎫+=-= ⎪⎪⎪⎝⎭⎨⎪>⎪⎩5e t =故答案为：.{}5e 12．对任意集合M ，定义，X 是全集，集合，则对任意的，下列命1.()0,M x Mf x x M ∈⎧=⎨∉⎩,S T X ⊆x X ∈题中真命题的序号是_____________. （1）若，则；S T ⊆()()S T f x f x ≤（2）； ()()1S S f x f x =-（3）；()()()S S T T f x f x f x =⋅ （4）(其中符号[a ]表示不大于a 的最大整数).()()()12S T S T f x f x f x ⎡⎤++=⎢⎥⎣⎦ 【答案】（1）（2）（3）（4）【分析】根据给定条件对4个命题逐一分析并判断作答.【详解】对于(1)，因，时，，，时，，而S T ⊆x S ∈x T ∈()()1S T f x f x ==x S ∉()0S f x =()0T f x =或，则，(1)正确；()1T f x =()()S T f x f x ≤对于(2)，时，，则，时，， x S ∈x S ∉()1,()0S S f x f x ==x S ∉x S ∈即，，从而有，(2)正确； ()0,()1S S f x f x ==()()1S S f x f x +=()1()S S f x f x =-对于(3)，，则，， x S T ∈ ,x S x T ∈∈()1,()1,()1S T S T f x f x f x === 即，()()()S T S T f x f x f x =⋅ ，则，此时与至少有一个成立，即与中至少一个x S T ∉⋂()0S T f x = x S ∉x T ∉()0S f x =()0T f x =成立，从而成立， ()()()S T S T f x f x f x =⋅ 综上知(3)正确；对于(4)，时，，若，则，x S T ∈⋃()1S T f x = ,x S x T ∈∈()1,()1S T f x f x ==，()()13[[]122S T f x f x ++==若，则，，,x S x T ∈∉()1,()0S T f x f x ==()()1[]12S T f x f x ++=若，同理可得，,x S x T ∉∈()()1[12S T f x f x ++=若，则，，，x S T ∉⋃,x S x T ∉∉()()()0S T S T f x f x f x === ()()11[[]022S T f x f x ++==综上得，(4)正确.()()1()[]2S S T T f x f x f x ++= 故答案为：（1）（2）（3）（4）.【点睛】方法点睛：本题关键是理解函数的新定义，题目的来源是数学中著名的狄利克雷函数，需要对函数的新定义充分理解，进行合理的分类讨论，做到不重复不遗漏，可以利用维恩图进行辅助.二、单选题13．若a ，b 为实数，则“”是“”的（ ） 1ab >1b a>A ．充分但非必要条件B ．必要非充分条件C ．充要条件D ．既非充分也非必要条件【答案】D【分析】通过举反例和反例即可判断. 2,3a b =-=-2,3a b =-=【详解】当时，满足，但此时，故正向无法推出， 2,3a b =-=-1ab >1b a<同样时，满足，但此时，故反向也无法推出， 2,3a b =-=1b a>1ab <故“”是“”的既不充分也不必要条件. 1ab >1b a>故选：D.14．已知是钝角，那么下列各值中能取到的值是（ ） θsin cos θθ-A ．B ．C ．D ．43345312【答案】A【分析】利用辅助角公式可得出，求出的取值范围，结合正弦函πsin cos 4θθθ⎛⎫-=- ⎪⎝⎭π4θ-数的值域可得出的取值范围，即可得出合适的选项. sin cos θθ-【详解】因为，则，所以，， ππ2θ<<ππ3π444θ<-<(πsin cos 4θθθ⎛⎫-=-∈ ⎪⎝⎭所以，可取的值为. sin cos θθ-43故选：A.15．已知.对于正实数，下列关系式中不可能成立的是（ ）()22xf x =-()a b a b ≠、A ．B ．22a b ab f ff a b +⎛⎫⎛⎫>> ⎪ ⎪+⎝⎭⎝⎭22ab a b f f f a b +⎛⎫⎛⎫>> ⎪ ⎪+⎝⎭⎝⎭C ．D ．22ab a b f ff a b +⎛⎫⎛⎫>> ⎪ ⎪+⎝⎭⎝⎭22ab a b f f f a b +⎛⎫⎛⎫>> ⎪ ⎪+⎝⎭⎝⎭【答案】D【分析】根据给定条件，结合均值不等式可得，再探讨函数的单调性，确22a b aba b+>>+()f x定中不可能最大的作答. 2(),(2ab a bf f f a b ++【详解】正实数，则，有， ()a b a b ≠、02a b +>>02a bab +>>2ab a b >+因此，函数， 202a b ab a b +>>+22,1()2222,1x xx x f x x ⎧-≥=-=⎨-<⎩即有函数在上单调递减，在上单调递增， ()f x (0,1][1,)+∞若，则有，C 正确； 012a b+<≤2()()2ab a b f f f a b +>>+若，则有，A 正确； 21aba b ≥+2()()2a b ab f f f a b +>>+若且时，，12a b +>201aba b <<+1≥2a b f f+⎛⎫> ⎪⎝⎭时，，实数最大数记为，1≤2ab f f a b ⎛⎫> ⎪+⎝⎭,,c d e max{,,}c d e于是， 22max{(),(max{(),(22a b ab a b abf f f f f f a b a b++=>++因此选项B 可能，选项D 一定不可能. 故选：D16．若，，下列判断错误的是ππtan 22b a θθ⎛⎫=-<< ⎪⎝⎭()()sin cos 02πa x b x x ϕϕ+=+≤<（ ）A ．当时，B ．当时， 0,0a b >>ϕθ=0,0a b ><2πϕθ=+C ．当时，D ．当时，0,0a b <>πϕθ=+0,0a b <<2πϕθ=+【答案】D【分析】根据给定条件，结合辅助角公式的变形，确定辅助角的取值作答.ϕ【详解】由选项知，，，0ab ≠sin cos )a x b x x x +=令，有，， cos ϕϕ==)sin t n ππ2an ta (c 2os b a ϕϕθθϕ==-<=<02πϕ≤<则， sin cos cos cos sin ))a x b x x x x ϕϕϕ+=+=+对于A ，当时，为第一象限角，且，，，则，A0,0a b >>ϕπ02ϕ<<π02θ<<tan tan ϕθ=ϕθ=正确；对于B ，当时，为第四象限角，且，，，则0,0a b ><ϕ3π2π2ϕ<<π02θ-<<tan tan(2π)ϕθ=+，B 正确；2πϕθ=+对于C ，当时，为第二象限角，且，，，则0,0a b <>ϕππ2ϕ<<π02θ-<<tan tan(π)ϕθ=+，C 正确；πϕθ=+对于D ，当时，为第三象限角，且，，，则0,0a b <<ϕ3ππ2ϕ<<π02θ<<tan tan(π)ϕθ=+，D 错误.πϕθ=+故选：D三、解答题17．已知. tan 2θ=-π02θ<<(1)求；tan θ(2)【答案】(2)3+【分析】(1)利用二倍角的正切公式求解； (2)利用弦化切的方法求解. 【详解】（1）因为22tan tan 21tan θθθ==--解得，2tan 0θθ-=t anθ=tan θ=因为，所以.π02θ<<t an θ=（2sin cos tan 13sin cos tan 1θθθθθθ++====+--18．用水清洗一堆蔬菜上残留的农药.对用一定量的水清洗一次的效果作如下假定:用1个单位量的水可洗掉蔬菜上残留农药量的，用水越多洗掉的农药量也越多，设用x 单位量的水清洗一次以13后，蔬菜上残留的农药量与本次清洗前残留的农药量之比为.()f x (1)假定函数的定义域是，写出，的值，并判断的单调性； ()y f x =[0,)+∞(0)f (1)f ()y f x =(2)设，求实数t 的值，现有单位量的水，可以清洗一次，也可以把水平均分()211f x t x =+⋅(0)a a >成2份后清洗两次，试问用哪种方案清洗后蔬菜上残留的农药量比较少？说明理由. 【答案】(1)；；严格单调递减； (0)1f =2(1)3f =(2)；答案见解析. 12t =【分析】（1）根据给定信息，直接求出，的值，再根据题意判断的单调性即可； (0)f (1)f ()f x （2）分别计算两种方式的农药残留量，再作差比较大小即可.【详解】（1）表示没有用水清洗时，蔬菜上残留的农药量将保持原样，则， (0)f (0)1f =因为用1个单位量的水可洗掉蔬菜上残留农药量的，则蔬菜上残留的农药量与本次清洗前残留的13农药量之比为，因此， 232(1)3f =因为用水越多洗掉的农药量也越多，则蔬菜上残留的农药量与本次清洗前残留的农药量之比越小，因此函数严格单调递减. ()f x （2）由（1）知，，而函数，于是，解得，，2(1)3f =()211f x t x =+⋅1213t =+12t =22()2f x x =+清洗一次，残留在蔬菜上的农药量为， 122()2y f a a ==+把水平均分成2份后清洗两次，残留在蔬菜上的农药量为， 222222264[([]2(8)2()2a y f a a ===++，2122222222642(4)(4)2(8)(2)(8)a a a y y a a a a +--=-=++++当时，，当时，，当时，， 4a >12y y >4a =12y y =04a <<12y y <所以当时，分成2份后清洗两次，清洗后蔬菜上残留的农药量少； 4a >当时，两种清洗方案效果相同；4a =当时，清洗一次，清洗后蔬菜上残留的农药量少. 04a <<19．已知是定义在上的奇函数，当时，. ()y f x =R 0x >()1x f x x=-+(1)求的值，并写出的解析式；(0),(1)f f -()f x (2)若，求实数a ，b 的值.()[]{}|,,,22a b y y f x x a b ⎡⎤=∈=⎢⎥⎣⎦【答案】(1),. ()()100,12f f =-=()1x f x x =-+(2) 1,1a b =-=【分析】(1)根据函数奇偶性的概念求函数值和解析式； (2)根据函数的单调性结合值域列出方程即可求解. 【详解】（1）因为是定义在上的奇函数， ()y f x =R 所以， 1(0)0,(1)(1)2f f f =-=-=当时，， 0x <()()1xf x f x x=--=--所以，即. ,01()0,0,01xx x f x x xx x ⎧-<⎪-⎪==⎨⎪⎪->+⎩()1x f x x =-+（2）因为当时，单调递减， 0x >()1111x f x x x=-=-+++且函数为奇函数，所以在上单调递减， ()f x R 所以当时，，当时，，0x <()0f x >0x >()0f x <因为，所以，()[]{}|,,,22a b y y f x x a b ⎡⎤=∈=⎢⎥⎣⎦0a b <<所以，即解得.()2()2b f a a f b ⎧=⎪⎪⎨⎪=⎪⎩1212a b a b a b ⎧-=⎪⎪-⎨⎪-=⎪+⎩1,1a b =-=20．在平面直角坐标系中，两点、的“直角距离”定义为，记为11(,)P x y ()22,Q x y 1212x x y y -+-.如，点、的“直角距离”为9，记为.PQ (1,2)P --(2,4)Q 9PQ =(1)已知点，Γ是满足的动点Q 的集合，求点集Γ所占区域的面积； (0,0)P 1PQ ≤(2)已知点，点，求的取值范围； (0,0)P [(cos ,sin )(0,2))Q αααπ∈PQ (3)已知动点P 在函数的图像上，定点，若的最小值为1，1yx =-)[(),sin 0,2π)Q ααα∈PQ 求的值. α【答案】(1)2(2) ⎡⎣(3)或或π3α=4π311π6【分析】（1）分类讨论区绝对值，得到其图形为正方形，求出其边长，则得到面积；（2）分，，，四类讨论即可；0,2απ⎡∈⎤⎢⎥⎣⎦,2παπ⎛⎤∈ ⎥⎝⎦3,2παπ⎛⎤∈ ⎥⎝⎦3,22παπ⎛⎫∈ ⎪⎝⎭（3）利用绝对值不等式有，再根据范围即可得到答案.||12sin 13PQ πα⎛⎫≥+-= ⎪⎝⎭α【详解】（1）设，则， (),Q x y 1x y +≤当，则，0,0x y ≥≥1x y +≤当，则，0,0x y ≥<1x y -≤当，则，0,0x y <≥1x y -+≤当，则，0,0x y <<1x y --≤顺次连接四点, ()()()()0,1,1,0,0,1,1,0A B C D --则得到点集所占区域面积.2S ==（2），|||0cos ||0sin ||cos ||sin |PQ αααα=-+-=+当，此时， π0,2α⎡⎤∈⎢⎥⎣⎦sin ,cos 0αα≥则， ||cos sin 4PQ πααα⎛⎫=+=+ ⎪⎝⎭，， π0,2α⎡⎤∈⎢⎥⎣⎦ ππ3π,444α⎡⎤∴+∈⎢⎥⎣⎦，即，则， πππsin sin ,sin 442α⎛⎫⎡⎤+∈ ⎪⎢⎥⎝⎭⎣⎦ πsin 4α⎤⎛⎫+∈⎥ ⎪⎝⎭⎦||PQ ∈当，此时， π,π2α⎛⎤∈ ⎥⎝⎦sin 0,cos 0αα≥<则， πcos sin 4PQ ααα⎛⎫=-+=- ⎪⎝⎭，， π,π2α⎛⎤∴∈ ⎥⎝⎦ππ3π,444α⎛⎤∴-∈ ⎥⎝⎦，即，则， π3ππsin sin ,sin 442α⎛⎫⎡⎤∴-∈ ⎪⎢⎥⎝⎭⎣⎦πsin 4α⎤⎛⎫-∈⎥ ⎪⎝⎭⎦||PQ ∈当，此时， 3π,2απ⎛⎤∈ ⎥⎝⎦sin 0,cos 0αα<≤则， πcos sin 4PQ ααα⎛⎫=--=+ ⎪⎝⎭，， 3,2παπ⎛⎤∈ ⎝⎦ 57,444πππα⎛⎤∴+∈ ⎥⎝⎦则，则， sin 1,4πα⎡⎛⎫+∈-⎢ ⎪⎝⎭⎣[1,PQ ∈当，此时，， 3π,2π2α⎛⎫∈ ⎪⎝⎭sin 0α<cos 0α>则， ||cos sin 4PQ πααα⎛⎫=-=- ⎪⎝⎭，， 3,22παπ⎛⎫∈ ⎪⎝⎭ π5π7π,444α⎛⎫-∈ ⎪⎝⎭则，， πsin 1,4α⎡⎛⎫+∈-⎢ ⎪⎝⎭⎣(||PQ ∴∈综上，.[1,PQ ∈（3）设，根据绝对值不等式有(),1P x x -|||||(1sin )|PQ x x αα=+-+， π1sin 12sin 13ααα⎛⎫≥+=+-= ⎪⎝⎭若，即，，， π12sin 13α⎛⎫+-= ⎪⎝⎭πsin 03α⎛⎫-= ⎪⎝⎭[)0,2πα∈ ππ5π,333α⎡⎫∴-∈-⎪⎢⎣⎭或，或. π03α∴-=ππ3α∴=4π3若，即，， π12sin 13α⎛⎫+-=- ⎪⎝⎭sin 13πα⎛⎫-=- ⎪⎝⎭π3π32α∴-=11π6α∴=综上或或. π3α=4π311π621．设函数的反函数存在，记为.设，. ()y f x =()1y f x -=(){}A x f x x ==()(){}1B x f x f x -==(1)若，判断是否是、中的元素； ()116xf x ⎛⎫= ⎪⎝⎭12A B (2)若在其定义域上为严格增函数，求证：；()y f x =A B =(3)若的方程有两个不等的实数解，求实数的取值范()f x =x ()()1f x a f x a --=+a 围.【答案】(1)， 12A ∉12B ∈(2)证明见解析(3) 7,24⎛⎤ ⎥⎝⎦【分析】（1）求出函数的解析式，利用元素与集合的关系判断与集合、的关系，可得()1f x -12A B 出结论；（2）分析可知，利用集合的包含关系以及函数的单调性证得，()(){}B x f f x x ==A B ⊆B A ⊆，即可证得结论成立；（3）令，分析可得，由已知方程可得，可得()()y g x f x a ==+()()11g x f x a --=-()()1g x g x -=，可得出，分析可得方程有两个不等的非负实根，根据二次方()()g g x x =()g x x =220x x a -+-=程根的分布可得出关于实数的不等式组，解之即可.a 【详解】（1）解：因为，则， ()116xf x ⎛⎫= ⎪⎝⎭()1116log f x x -=所以，，则，所以，， 116x A x x ⎧⎫⎪⎪⎛⎫==⎨⎬ ⎪⎝⎭⎪⎪⎩⎭121111642⎛⎫=≠ ⎪⎝⎭12A ∉，则，所以，. 1161log 16x B x x ⎧⎫⎪⎪⎛⎫==⎨⎬ ⎪⎝⎭⎪⎪⎩⎭41211216111log log 22416--⎛⎫=== ⎪⎝⎭12B ∈（2）解：由题意可得， ()(){}()(){}1B x f x f x x f f x x -====任取，则，所以，，，故；1x A ∈()11f x x =()()()111f f x f x x ==1x B ∴∈A B ⊆任取，则，下面证明出.2x B ∈()()22f f x x =()22f x x =因为函数在其定义域内为严格增函数，()f x 若，则，与题设矛盾；()22f x x <()()()222f f x f x x <<若，则，与题设矛盾.()22f x x >()()()222f f x f x x >>故，即，故.()22f x x =2x A ∈B A ⊆综上所述，.A B =（3）解：令，则，则，即()()y g x f x a ==+()()11x a f y x g y --⎧+=⎪⎨=⎪⎩()()11g y f y a --=-，()()11g x f x a --=-由可得，所以，，()()1f x a f x a --=+()()1g x g x -=()()g g x x =因为在其定义域内单调递增，所以，有两个不等的非负()g x =()g x x =x =实根，整理可得，220x x a -+-=所以，，解得. ()Δ14247010220a a a ⎧=--=->⎪⎪>⎨⎪-≥⎪⎩724a <≤因此，实数的取值范围是. a 7,24⎛⎤ ⎥⎝⎦。
第一学期高一年级12月阶段测试卷
上海市曹杨二中2017学年第一学期高一年级12月阶段测试卷一、填空题1、已知集合{}1,A x =，{}21,B x =且A B =，则x = . 2、函数()11f x x=-的定义域是 .（用区间表示） 3、不等式213xx ≥-+的解集是 . 4、函数2112x y +⎛⎫= ⎪⎝⎭的值域是 .5、电子技术的飞速发展，计算机成本不断降低，若每隔一年计算机的价格降低二分之一，现在价格为8100元的计算机3年后价格可降为 元.6、不等式()()2233232x x --->+的解集为 .7、已知函数()y f x =是奇函数，当0x >时，()113f x x =+，设()f x 的反函数是()y g x =，则()10g -= .8、若函数()f x a x b c =-+满足①函数()f x 的图像关于1x =对称；②在R 上有大于零的最大值；③函数()f x 的图像过点()0,1；④,,a b c Z ∈，试写出一组符合要求的,,a b c 的值 . 9，设12,x x 是方程2lg lg 0x a x b ++=（,a b 为常数）的两个根，则12x x ⋅的值是 . 10、若函数()13x f x m -+=+的图像存在零点，则实数m 的取值范围是 .11、已知函数()1,111,1x x f x x ⎧≠⎪-=⎨⎪=⎩，且关于x 的函数()()()2F x af x bf x c =++恰有三个零点123,,x x x ，则222123x x x ++= .12、对于函数()f x ，若存在0x R ∈，使()00f x x =，则称0x 是()f x 的一个不动点，已知()24f x x ax =++在[]1,3恒有两个不同的不动点，则实数a 的取值范围是 .二、选择题13、已知,,,a b c d 为实数，且c d >，则：“a b >” 是“a c b d ->-”的（ ） A.充分非必要条件 B.必要非充分条件 C.充要条件 D.既不充分也不必要条件 14、下列函数中，与1y x =-为同一函数的是（ ）A.y =B. y =C.211x y x -=+ D.2y =15、已知0x 是函数()121x f x x=+-的一个零点，若()101,x x ∈，()20,x x ∈+∞，则（ ） A.()()120,0f x f x << B. ()()120,0f x f x <> C. ()()120,0f x f x >< D. ()()120,0f x f x >>16、函数x xx xe e y e e--+=-的图像大致为（ ）三、解答题 17、（1）计算31log 23+.（2）43log 3,log 5,p q ==用,p q 表示lg 5.18、如图，要设计一张矩形广告，该广告含有大小相等的左右两个矩形栏目（即图中阴影部分），这两栏的面积之和为180002cm ，四周空白的宽度为10cm ，两栏之间的中缝空白的宽度为5cm ，怎样确定广告的高与宽的尺寸（单位：cm ），能使矩形广告面积最小？19、已知函数()()33xxf x R λλ-=+⋅∈.，（1）根据λ的不同取值，讨论函数的奇偶性，并说明理由；（2）若不等式()6f x ≤[]0,2x ∈上恒成立，求实数λ的取值范围.20、已知定义在实数集r 上的偶函数()f x 和奇函数()g x 满足()()12x f x g x ++=.（1）求()f x 与()g x 的解析式；（2）求证()f x 在区间[)0,+∞上单调递增；并求()f x 在区间[)0,+∞的反函数;（3）设()2221h x x mx m m =++-+（其中m 为常数），若()()22h g x m m ≥--对于[]1,3x ∈恒成立，求m 的取值范围.参考答案1、1-2、[)()2,11,-⋃+∞3、()[),31,-∞-⋃+∞4、10,2⎛⎤⎥⎝⎦5、1012.56、()()1,5,22,3⎛⎫-∞-⋃-⋃+∞ ⎪⎝⎭7、27- 8、1,1,2a b c =-== 9、110a 10、1,03⎡⎫-⎪⎢⎣⎭ 11、5 12、10,33a ⎡⎫∈--⎪⎢⎣⎭13-16、BBBA 17、（1）6；（2）2lg 521pqpq =+ 18、长为175cm ，宽为140cm 时，面积最小为224500cm19、（1）1λ=时，偶函数；1λ=-时，奇函数；1λ≠±时，非奇非偶函数； （2）(],27-∞-20、（1）()()22,22x x x x f x g x --=+=-；（2）证明略；()(12log 1,2f x x x -=+-≥；（3）)+∞。
2022-2023学年上海市曹杨高一年级上册学期12月阶段性测试数学试题【含答案】
2022-2023学年上海市曹杨第二中学高一上学期12月阶段性测试数学试题一、填空题1．设0a >且1a ≠，31x y a -=+函数的图像经过的定点的坐标为__________. 【答案】(3,2)【分析】因为x y a =函数经过点(0,1)，将3x -看做整体即可得解. 【详解】因为x y a =函数经过点(0,1)， 令30x -= 312x y a -=+=，所以函数图像经过(3,2)， 故答案为：(3,2).2．若函数[]3221,1,y ax x x b =++∈-是偶函数，则a b +=__________.【答案】1【分析】根据偶函数定义域关于原点对称即可求出b ，根据偶函数的()()f x f x -=即可求出a . 【详解】因为函数为偶函数且[]1,x b ∈-， 所以1b =，又数[]3221,1,y ax x x b =++∈-是偶函数，()()y f x f x ==-，所以3232()2()121a x x ax x -+-+=++， 所以32322121ax x ax x -++=++， 所以320ax =对任意x 成立， 所以0a =， 所以1a b +=， 故答案为：1.3．函数y =__________. 【答案】[)()1,00,∞-⋃+【分析】由解析式有意义列不等式求x 的范围即可.【详解】由y =10210x x +≥⎧⎨-≠⎩，解不等式组可得10x -≤<或0x >，所以函数y =[)()1,00,∞-⋃+. 故答案为：[)()1,00,∞-⋃+.4．已知函数()y f x =是定义在R 上的奇函数，且当0x >时，()21f x x x=+，则当0x <时，()f x =__________.【答案】21x x-+【分析】根据奇函数定义可得()()f x f x -=-，结合所给0x >时的解析式,即可求得0x <时的解析式. 【详解】令0x <， 则0x ->，因为当0x >时, ()21f x x x =+， 所以()()()2211f x x x x x -=-+=--，因为奇函数满足()()f x f x -=-，所以()21f x x x-=-， 即()21f x x x=-+， 故答案为: 21x x-+5．已知lg2a =，用a 表示5log 16=__________. 【答案】41aa- 【分析】利用换底公式代入转化为关于lg 2的表达式即可求解. 【详解】410510log 16lg16lg24lg24log 1610log 16lg51lg21lg 2aa =====--故答案为：41aa-. 6．若函数21ax y x +=+在区间()1,-+∞上是严格增函数，则实数a 的取值范围是__________. 【答案】()2,+∞【分析】利用换元法与常数分离法，结合反比例函数的单调性即可得解. 【详解】因为()1,x ∈-+∞，所以令1t x =+，则()0,t ∈+∞，1x t =-， 所以()122221a t ax at a ay a x t t t-++-+-====++， 因为21ax y x +=+在区间()1,-+∞上是严格增函数， 所以2ay a t-=+在区间()0,∞+上是严格增函数， 故20a -<，则2a >，即()2,a ∈+∞. 故答案为：()2,+∞.7．设0a b <<，若函数[]2log 1,,y x x a b =-∈的值域为[]0,1，则a b +的取值范围是__________. 【答案】[]3,6【分析】根据函数图像，分析函数的单调性，结合题目中函数的值域为[]0,1，分析特殊点的横坐标，分类讨论即可得解. 【详解】作出函数图像，根据题意2()log 10y f x x ==-=， 得2x =，令2()log 11y f x x ==-=， 解得1x =或4x =， 所以结合0a b <<①若2a >，则不合题意，舍去， ②若2a =，则4b =，此时6a b +=； ③若12a <<，则4b =，此时56a b <+<； ④若1a =，则24b ≤≤，35a b ≤+≤ 综上所述，36a b ≤+≤， 故答案为：[]3,68．某物流公司购买了一批自动分拣机器人投入运营.据分析，这批机器人运营的总利润y （单位：万元）与运营年数()N,1x x x ∈≥为二次函数关系，其部分对应关系如下表所示：则这批机器人运营年数为__________时，其运营的年平均利润最大. 【答案】5【分析】由表格中的数据求得二次函数解析式，再应用基本不等式求得年平均利润取得最大值时x 的取值，即可得结果.【详解】由表格知，函数过点(1,14)-，(5,10)，(7,10)， 设2y ax bx c =++(N,1)x x ∈≥， 则141025510497a bca b c a b c -=++⎧⎪=++⎨⎪=++⎩ 解得：11225a b c =-⎧⎪=⎨⎪=-⎩ ∴21225y x x =-+- (N,1)x x ∈≥，∴年平均利润为21225y x x x x-+-= (N,1)x x ∈≥，即：25()12122y x x x =-++≤-=当且仅当5x =时，y x 取得最大值2.故答案为：5.9．若函数1y x x a =-+-的图像关于直线2x =成轴对称，则该函数的最小值为__________. 【答案】2【分析】利用函数对称性的定义求得实数a 的值，再利用绝对值三角不等式可求得结果.【详解】设()1f x x x a =-+-，则()()11111f a x a x a x a x a x f x +-=+--++--=-+-=， 所以，函数()f x 的图像关于直线12a x +=对称，由题意可得122a +=，可得3a =. 所以，()13f x x x =-+-，由绝对值三角不等式可得()()()13132f x x x x x =-+-≥---=. 故函数()f x 的最小值为2. 故答案为：2.10．设函数()()*N y f n n =∈满足：对任意正整数(),n f n 表示π的小数点后的第n 位数码.已知3.1415926535π=，则((((10))))n ff f f f =个__________.【答案】5,19,23,3,1,4,n n n n =⎧⎪=⎪⎨=⎪⎪≥⎩，， 【分析】由函数定义依次求出1,2,3,4,n n n n ====⋅⋅⋅时((((10))))n ff f f f 个的值即可.【详解】因为 3.1415926535π=，所以()105f =，()()()1059f f f ==，()()()()1093f f f f ==，()()()()()1031f f f f f ==， ()()()()()()1011f f f f f f ==，当6n ≥，((((10))))1n ff f f f =个，所以5,19,2((((10))))3,3,1,4,n fn n f f f f n n =⎧⎪=⎪=⎨=⎪⎪≥⎩个，，，故答案为：5,19,23,3,1,4,n n n n =⎧⎪=⎪⎨=⎪⎪≥⎩，， 11．设R a ∈，若函数()1e ,1,4,>1x x f x ax x x -⎧≤⎪=⎨+-⎪⎩有最小值，则a 的取值范围是__________. 【答案】(]1,4【分析】先求函数在(]1-∞，上的最小值，再讨论a ，求函数在()1+∞，上的值域，结合条件确定a 的范围.【详解】当1x ≤时，()1e xf x -=，函数()f x 在(]1-∞，上为增函数，所以函数()f x 在(]1-∞，上取值范围为(]0,1，当1x >时，()4af x x x=+-， 若a<0，因为y x =，a y x=-在()1+∞，上都为增函数，所以函数4ay x x =+-()1+∞，上为增函数，所以函数()f x 在()1+∞，上的函数值的取值范围为()3,a -+∞，所以函数()f x 在R 上没有最小值，与条件矛盾，若0a =时，因为4y x =-在()1+∞，上都为增函数，所以函数()f x 在()1+∞，上的函数值的取值范围为()3,-+∞，所以函数()f x 在R 上没有最小值，与条件矛盾， 当01a <≤时，任取()12,1,x x ∈+∞，且12x x <，则()()()212121212121x x a a af x f x x x x x x x x x ⎛⎫--=+--=- ⎪⎝⎭， 因为12x x <，所以210x x ->，因为()12,1,x x ∈+∞，01a <≤，所以210x x a ->，所以()()21f x f x >，所以函数()f x 在()1+∞，上单调递增，所以函数()f x 在()1+∞，上的函数值的取值范围为()3,a -+∞，所以函数()f x 在R 上没有最小值，与条件矛盾，当1a >时，任取)12,x x ∈+∞，且12x x <，则()()()212121212121x x a a af x f x x x x x x x x x ⎛⎫--=+--=- ⎪⎝⎭， 因为12x x <，所以210x x ->，因为)12,x x ∈+∞，所以210x x a ->，所以()()21f x f x >，所以函数()f x在)+∞上单调递增，同理可证函数()f x在(上单调递减，所以函数()f x 在()1+∞，上的函数值的取值范围为)4,⎡+∞⎣，当且仅当40≤时，函数()f x 有最小值，化简得14a <≤，所以函数()f x 有最小值时，a 的取值范围是(]1,4， 故答案为：(]1,4.12．设R,Z a m ∈∈，若存在唯一的m 使得关于x 的不等式21x a m x +<<-有解，则a 的取值范围是__________.【答案】)1,1【分析】根据给定条件，确定m 的最大值，再由函数不等式有解得当0m =时不等式组有解，当1m =-时不等式组无解，求出a 的范围作答.【详解】依题意不等式21m x <-有解，所以()ax2m 1m x<-，所以1m <，而m ∈Z ，因此{}0,Z m x x x ∈≤∈，因存在唯一的m 使得关于x 的不等式组21x a m x +<<-有解，则当且仅当0m =时，不等式组21x a m x +<<-有解，且当1m =-时不等式组21x a m x +<<-无解，由201x a x +<<-有解得11x x a-<<⎧⎨<-⎩有解，所以1a ->-，即1a <，由211x a x +<-<-无解得1x x a ⎧<<⎪⎨<--⎪⎩1a --≤1a ≥，因此11a ≤<，所以a 的取值范围是)1,1.故答案为：)1,1二、单选题13．已知0a >，则化简22的结果是（ ）A ．2a -B ．1a -C ．aD ．2a【答案】D【分析】根据指数幂的运算公式化简计算即可.【详解】因为0a >22a =所以((2222222a a a===，故选：D.14．已知a ､N 为实数，则“log 0a N >”是“()()110a N -->”的（ ） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件 D ．既非充分又非必要条件【答案】A【分析】分别对充分性，必要性进行计算证明即可解决.【详解】当log 0a N >时，11a N >⎧⎨>⎩或0101a N <<⎧⎨<<⎩，此时()()110a N -->，所以充分性成立；当()()110a N -->时，11a N >⎧⎨>⎩或11a N <⎧⎨<⎩，此时log a N 可能无意义，所以必要性不成立，所以“log 0a N >”是“()()110a N -->”的充分非必要条件， 故选：A15．设0a b <<，若奇函数()y f x =在区间[],a b 上是严格减函数，且有最小值2，则函数()y f x =在区间[],b a --上是（ ） A ．严格减函数且有最大值2 B ．严格减函数且有最小值2 C ．严格增函数且有最大值2 D ．严格增函数且有最小值2 【答案】D【分析】根据奇函数对称区间增减性一致，()()f x f x -=-，()y f x =与()y f x =关于x 轴对称即可解决.【详解】由题知，奇函数()y f x =在区间[],a b 上是严格减函数，且有最小值2， 所以()y f x =在区间[],b a --上是严格减函数，且有最大值2-， 因为函数()y f x =与()y f x =关于y 轴对称，所以()y f x =在区间[],b a --上是严格增函数且有最小值2， 故选：D16．设()[]f x x x =-，其中[]x 表示不超过实数x 的最大整数.若关于x 的方程()f x kx k =+有且仅有3个实数解，则实数k 的取值范围是（ ） A ．1111,,243⎡⎫⎛⎤--⎪ ⎢⎥⎣⎭⎝⎦B ．1111,,243⎛⎤⎡⎫--⋃ ⎪⎥⎢⎝⎦⎣⎭C ．1111,,243⎡⎤⎡⎤--⋃⎢⎥⎢⎥⎣⎦⎣⎦D ．1111,,243⎛⎫⎛⎫--⋃ ⎪ ⎪⎝⎭⎝⎭【答案】B【分析】关于x 的方程()f x kx k =+有且仅有3个实数解等价于函数()[]f x x x =-与()g x kx k =+的图象有三个不同的交点，数形结合即可. 【详解】作()[]f x x x =-的图象如图所示，令()g x kx k =+是过定点(1,0)-的直线， 当()f x kx k =+有且仅有3个实数解时，如图， 当3x =时，(3)341g k k k =+=≥，解得14k ≥； 当2x =时，(2)231g k k k =+=<，解得13k <；当2x =-时，(2)21g k k k -=-+=-<，解得1k >-； 当3x =-时，(3)321g k k k -=-+=-≥，解得12k ≤-；综上所述1111,,243k ⎛⎤⎡⎫∈-- ⎪⎥⎢⎝⎦⎣⎭故选：B三、解答题17．设R m ∈，已知幂函数()()2133m f x m m x +=+-⋅是偶函数.(1)求m 的值；(2)设R a ∈，若函数()[],0,2y f x ax a x =-+∈的最小值为1-，求a 的值. 【答案】(1)1m = (2)1a =-或5a =.【分析】（1）由已知结合幂函数的定义以及性质即可求解； （2）由已知结合二次函数的性质讨论02a ≤，022a <<和22a≥，即可得出答案.【详解】（1）因为幂函数()()2133m f x m m x +=+-⋅是偶函数，所以2331m m +-=且1m +为偶数，解得：1m =或4m =-（舍），则1m =，所以()2f x x =.（2）令()()2y g x f x ax a x ax a ==-+=-+的开口向上，对称轴2a x =， ①当02a≤即0a ≤，()g x 在[]0,2上单调递增，所以()()min 01g x g a ===-， 所以1a =-； ②当022a <<即04a <<，()g x 在0,2a ⎡⎤⎢⎥⎣⎦上单调递减，在22a ⎡⎤⎢⎥⎣⎦，上单调递增， 所以()22min1242a aa g x g a ⎛⎫==-+=- ⎪⎝⎭，解得：2a =+2a =- ③当22a≥即4a ≥，()g x 在[]0,2上单调递减， 所以()()min 241g x g a ==-=-，解得：5a = 所以5a =.综上：1a =-或5a =.18．某公司经过测算，计划投资,A B 两个项目. 若投入A 项目资金x (万元)，则一年创造的利润为2x(万元)：若投入B 项目资金x (万元)，则一年创造的利润为10,020()3020,20xx f x x x ⎧≤≤⎪=-⎨⎪>⎩（万元）.(1)当投入,A B 两个项目的资金相同且B 项目比A 项目创造的利润高，求投入A 项目的资金x (万元)的取值范围；(2)若该公司共有资金30万，全部用于投资,A B 两个项目，则该公司一年分别投入,A B 两个项目多少万元，创造的利润最大. 【答案】(1)(10,40)(2)当 10万元投入A 项目，20万元投入B 项目时获得利润最大【分析】（1）分020x ≤≤和20x >解不等式。
上海市徐汇区2022-2023学年高一上学期月考(12月)数学试卷含解析
上上上上上上2022-2023上上上上上上上上上上12上上上上上上考试时间：100分钟；总分：100分学校:___________姓名：___________班级：___________考号：___________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，用铅笔把答题卡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，写在试卷上无效。
3.考试结束后，本试卷和答题卡一并交回。
第I卷（选择题）一、单选题（本大题共4小题，共12.0分。
在每小题列出的选项中，选出符合题目的一项）1. 设命题甲：|x−2|<3，命题乙：0<x<5，那么甲是乙的( )A. 充分而不必要条件B. 必要而不充分条件C. 充要条件D. 既不充分也不必要条件2. 设正实数x满足2+y=1，则8x+1+1y的最小为( )A. 9B. 253C. 8D. 4√53. 若函数f(x)=|2x−a|(x∈[0,1])存在反函数，则常数a的取值范围为( )A. (−∞,1]B. [1,2]C. [2,+∞)D. (−∞,1]∪[2,+∞)4. 函数f(x)=1|x|−1，因其图像类似于汉字“囧”，故被称为“囧函数”，下列说法中正确的个数为( )①函数f(x)的定义域为{x|x≠1且x≠−1}；②f(f(2022))=−20212020；③函数f(x)的图像关于直线x=1对称；④当x∈(−1,1)时，f(x)max=−1；⑤方程f(x)−x2+4=0有四个不同的根．A. 3B. 4C. 5D. 6第II卷（非选择题）二、填空题（本大题共12小题，共48.0分）5. 若a>0且a≠1，则函数y=a x+2的图象恒过定点的坐标是______．6. 若函数f(x)=x+ax2+bx+1是定义在[−1,1]上的奇函数，则a2+b2=______．7. 已知函数f(x)=a|x−3|+b(a>0)，则将f(e)、f(3)、f(π)从小到大排列为______．8. 已知集合A={x|x2−x≤0}，B={x|2x>1}，则A∪B=______．9. 下列幂函数在区间(0,+∞)上是严格增函数，且图像关于原点成中心对称的是______．①y=x12；②y=x13；③y=x23；④y=x−13；⑤y=x3.(请填入全部正确的序号)10. 已知定义在R上的奇函数f(x)在(−∞,0]上是减函数，若f(m+1)+f(3m−2)<0，则实数m的取值范围是．11. 命题p：(x−m)2>3(x−m)是命题q：x2+3x−4<0成立的必要非充分条件，则实数m的取值范围为______．12. 记A=1×2×3×…×100，那么1log2A +1log3A+1log4A+⋯+1log100A=______．13. 设a>0且a≠1，则函数f(x)=a x+x2−2x−2a+1的零点的个数为______．14. 若不等式|x−a|+|2x+a|≥−a+1对于任意实数x恒成立，则满足条件的实数a的取值范围为______．15. 已知函数f(x)=3⋅2x+2，对于任意的x2∈[0,1]，都存在x1∈[0,1]，使得f(x1)+ 2f(x2+m)=13成立，则实数m的取值范围为______．16. 设函数f(x)的定义域为D，若存在实数T(T>0)，使得对于任意x∈D，都有f(x)<f(x+ T)，则称f(x)为“T−严格增函数”，对于“T−严格增函数”，有以下四个结论：①“T−严格增函数”f(x)一定在D上严格增；②“T−严格增函数”f(x)一定是“nT−严格增函数”(其中x∈N∗，且n≥2)③函数f(x)=[x]是“T−严格增函数”(其中[x]表示不大于x的最大整数)④函数f(x)=x−[x]不是“T−严格增函数”(其中[x]表示不大于x的最大整数)其中，所有正确的结论序号是______．三、解答题（本大题共5小题，共60.0分。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
高一第一册第一、二、五单元阶段性测试20121010班级：学号：姓名：一、基础知识（12分）1、下列词语音形都正确的一项是（）（2分）A、心无旁骛悬梁刺骨B、纤（qiān）柔聒噪C、麻痹沉溺D、点辍拽2、《合欢树》一文语言特点可以概括为：。
（2分）《我们是怎样过母亲节的》一文语言特点可以概括为：。
（2分）3、“别人在海滩上捡到一块贝壳，她却要研究一下这贝壳是怎样生、怎样长、怎样冲到海滩上来的，别人摸瓜她寻藤，别人摘叶她问根。
”运用了的修辞手法。
（2分）4、《病梅馆记》作者，（朝代）思想家，文学家。
（2分）5、《沁园春·长沙》的词牌名是。
（2分）二、现代文阅读（9分）①黄昏来时翠翠坐在家中屋后白塔下，看天空为夕阳烘成桃花色的薄云。
十四中寨逢场，城中生意人过中寨收买山货的很多，过渡人也特别多，祖父在渡船上忙个不息。
天快夜了，别的雀子似乎都在休息了，只杜鹃叫个不息。
石头泥土为白日晒了一整天，草木为白日晒了一整天，到这时节皆放散一种热气。
空气中有泥土气味，有草木气味，且有甲虫类气味。
翠翠看着天上的红云，听着渡口飘乡生意人的杂乱声音，心中有些儿薄薄的凄凉．．．．．。
②黄昏照样的温柔，美丽，平静。
但一个人若体念到这个当前一切时，也就照样的在这黄昏中会有点儿薄薄的凄凉。
于是，这日子成为痛苦的东西了。
翠翠觉得好象缺少了什么。
好象眼见到这个日子过去了，想在一件新的人事上攀住它，但不成。
好象生活太平凡了，忍受不住。
……③两人吃饭时，祖父为翠翠说到一些有趣味的故事。
因此提到了死去了的翠翠的母亲。
两人在豆油灯下把饭吃过后，老船夫因为工作疲倦，喝了半碗白酒，因此饭后兴致极好，又同翠翠到门外高崖上月光下去说故事。
说了些那个可怜母亲的乖巧处，同时且说到那可怜母亲性格强硬处，使翠翠听来神往倾心。
④翠翠抱膝坐在月光下，傍着祖父身边，问了许多关于那个可怜母亲的故事。
间或吁一口气，似乎心中压上了些分量沉重的东西．．．．．．．，想挪移得远一点，才吁着这种气，可是却无从把那东西挪开。
⑤月光如银子，无处不可照及，山上篁竹在月光下皆成为黑色。
身边草丛中虫声繁密如落雨。
间或不知道从什么地方，忽然会有一只草莺“落落落落嘘！”啭着它的喉咙，不久之间，这小鸟儿又好象明白这是半夜，不应当那么吵闹，便仍然闭着那小小眼儿安睡了。
⑥祖父夜来兴致很好，为翠翠把故事说下去，就提到了本城人二十年前唱歌的风气，如何驰名于川黔边地。
翠翠的父亲，便是唱歌的第一手，能用各种比喻解释爱与憎的结子，这些事也说到了。
翠翠母亲如何爱唱歌，且如何同父亲在未认识以前在白日里对歌，一个在半山上竹篁里砍竹子，一个在溪面渡船上拉船，这些事也说到了。
⑦翠翠问：“后来怎么样？”⑧祖父说：“后来的事长得很，最重要的事情，就是这种歌唱出了你。
”6、下列文学常识表述无误的一项是（）（2分）A、本文节选自《边城》，作者沈从文，原名沈岳焕，中国当代著名作家。
B、人们给予“田园诗的杰作”、“一颗永不磨灭的珠玉”等高度评价的就是指《边城》。
C、沈从文的高足汪曾祺先生也是中国当代著名作家，《受戒》和《断魂枪》是其代表作。
D、《边城》和《大淖纪事》，都描写的是湘西地区的生活。
7、第①、②段中两次出现了“薄薄的凄凉”，翠翠产生如此心理的原因是。
（2分）8、第④段中“分量沉重的东西”是指的心理。
（2分）9、请简要分析第⑤段环境描写的作用。
（3分）三、默写（9分，任选9空）10（1）、，层林尽染。
（2）、鹰击长空，鱼翔浅底，。
（3）、书生意气，。
（4）、，，粪土当年万户侯。
（5）、，大象无形。
（《老子》）（6）、，而无车马喧。
（7）、采菊东篱下，。
（8）、此中有真意，。
（9）、，后天下之乐而乐。
（范仲淹《岳阳楼记》）（10）、天行健，。
（《周易•乾•象》）四、诗歌鉴赏（9分）蒹葭蒹葭苍苍，白露为霜。
所谓伊人，在水一方。
溯洄从之，道阻且长。
溯游从之，。
蒹葭凄凄，白露未晞。
所谓伊人，在水之湄。
溯洄从之，道阻且跻。
溯游从之，宛在水中坻。
蒹葭采采，。
所谓伊人，在水之涘。
溯洄从之，道阻且右。
溯游从之，宛在水中沚。
11、请填写原诗中空缺的句子。
①②（2分）12、《诗经》的表现手法分为、、三种。
（3分）另外，重章（复沓）、叠句、叠字，双声、叠韵等，也是表现形式上的突出特点。
请你就其中的一个特点，举例加以分析。
（2分）13、你认为“伊人”是指什么？（2分）。
五、文言文阅读（21分）种树郭橐驼传（柳宗元）郭橐驼，不知始何名。
病瘘，隆然伏行，有类橐驼者，故乡人号之“驼”。
驼闻之，曰：“甚善。
名我固当。
”因舍其名，亦自谓橐驼云。
其乡曰丰乐乡，在长安西。
驼业种树，凡长安豪富人为观游及卖果者，皆争迎取养。
视驼所种树，或移徙，无不活，且硕茂，蚤实以蕃。
他植者虽窥伺效慕，莫能如也。
有问之，对曰：“橐驼非能使木寿且孳也，能顺木之天，以致其性焉尔。
凡植木之性，其本欲舒，其培欲平，其土欲故，其筑欲密。
既然已，勿动勿虑，去不复顾。
其莳也若子，其置也若弃，则其天者全而其性得矣。
故吾不害其长而已，非有能硕茂之也。
不抑耗其实而已，非有能蚤而蕃之也。
他植者则不然，根拳而土易，其培之也，若不过焉则不及。
苟有能反是者，则又爱之太恩，忧之太勤。
旦视而暮抚，已去而复顾，甚者爪其肤以验其生枯，摇其本以观其疏密，而木之性日以离矣。
虽曰爱之，其实害之；虽曰忧之，其实仇之，故不我若也。
吾又何能为哉！”问者曰：“以子之道，移之官理，可乎？”驼曰：“我知种树而已，官理，非吾业也。
然吾居乡，见长人者，好烦其令，若甚怜焉，而卒以祸。
旦暮吏来而呼曰：‘官命促尔耕，勖尔植，督尔获，早缫而绪，早织而缕，字而幼孩，遂而鸡豚。
’鸣鼓而聚之，击木而召之。
吾小人辍飧饔以劳吏，且不得暇，又何以蕃吾生安吾性耶？故病且怠。
若是，则与吾业者其亦有类乎？”问者曰：“嘻，不亦善夫！吾问养树，得养人术。
”传其事以为官戒也。
14、柳宗元，字，河东人，世称“”，曾任柳州刺史，又称“柳柳州”。
（2分）15、解释下列加点的字。
（4分）（1）名．我固当（）（2）其本．欲舒（）（3）遂．而鸡豚（）（4）故病．且怠（）16、用现代汉语翻译句子。
（3分）不抑耗其实而已，非有能早而蕃之也。
17、下列“之”字的用法与其它三项不同的一项是（）（2分）A、故乡人号之“驼”B、凡值木之性C、非有能硕茂之也D、虽曰忧之，其实仇之18、举例说明本文写作手法的特点。
并分析其作用。
（5分）手法及举例说明：作用：。
19、本文主要说明了一个什么道理？（3分）谈谈你对此道理的看法。
（2分）道理：。
你的看法：。
六、作文（40分）20、根据以下材料，选取一个角度，自拟题目，写一篇不少于700字的文章（诗歌除外）有的人性如钢针，遇到墙壁，不是破壁而入，就是尖断身折；有的人性如藤蔓，遇到墙壁，不是傍壁而生，就是绕壁而行。
高一第一册第一、二、五单元阶段性测试答题纸20121010班级：学号：姓名：一、基础知识（12分）1、（）（2分）2、。
（2分）。
（2分）3、（2分）4、，（2分）5、。
（2分）二、现代文阅读（9分）6、（）（2分）7、（2分）8、（2分）9、。
（3分）三、默写（9分，任选9空）10（1）、，层林尽染。
（2）、鹰击长空，鱼翔浅底，。
（3）、书生意气，。
（4）、，，粪土当年万户侯。
（5）、，大象无形。
（《老子》）（6）、，而无车马喧。
（7）、采菊东篱下，。
（8）、此中有真意，。
（9）、，后天下之乐而乐。
（范仲淹《岳阳楼记》）（10）、天行健，。
（《周易•乾•象》）四、诗歌鉴赏（9分）11、①②（2分）12、、、（3分）。
（2分）13、。
（2分）五、文言文阅读（21分）14、，“”。
（2分）15、解释下列加点的字。
（4分）（1）名．我固当（）（2）其本．欲舒（）（3）遂．而鸡豚（）（4）故病．且怠（）16、（3分）17、（）（2分）18、举例说明本文写作手法的特点。
并分析其作用。
（5分）手法及举例说明：作用：。
19、本文主要说明了一个什么道理？（3分）谈谈你对此道理的看法。
（2分）道理：。
你的看法：。
六、作文（40分）20、根据以下材料，选取一个角度，自拟题目，写一篇不少于700字的文章（诗歌除外）有的人性如钢针，遇到墙壁，不是破壁而入，就是尖断身折；有的人性如藤蔓，遇到墙壁，不是傍壁而生，就是绕壁而行。
高一第一册第一、二、五单元阶段性测试参考答案20121010班级：学号：姓名：一、基础知识（12分）1、（ C ）（A、股B、qiàn xiānD、点缀）（2分）2、质朴而隽永。
（2分）幽默诙谐。
（2分）3、比喻（对比）。
（2分）4、袭自珍，晚清。
（2分）5、沁园春。
（2分）二、现代文阅读（9分）6、（ B ）（A、当代（1919--1949）C、《断魂枪》作者老舍D、《大淖记事》的作者汪曾祺）（2分）7、翠翠觉得自己的生活“太平凡了”、“好像缺少了什么”，不能像周围的事物那样生机勃勃，所以有此感受。
（2分）8、翠翠听到母亲的爱情悲剧后的忐忑不安。
（2分）9、（渲染）以月夜的安静、宁谧衬托出翠翠母亲为爱殉情的热烈、执著和浪漫。
（3分）三、默写（9分，任选9空）10（1）、看万山红遍，层林尽染。
（2）、鹰击长空，鱼翔浅底，万类霜天竞自由。
（3）、书生意气，挥斥方遒。
（4）、指点江山，激扬文字，粪土当年万户侯。
（5）、大音希声，大象无形。
（《老子》）（6）、结庐在人境，而无车马喧。
（7）、采菊东篱下，悠然见南山。
（8）、此中有真意，欲辨已忘言。
（9）、先天下之忧而忧，后天下之乐而乐。
（范仲淹《岳阳楼记》）（10）、天行健，君子以自强不息。
（《周易•乾•象》）四、诗歌鉴赏（9分）11、①宛在水中央②白露未已（2分）12、赋、比、兴（3分）重章：全诗全节基本重复，此谓重章。
诗通过“为霜”、“未晞”、“未已”，“一方”、“湄”、“涘”等词的变化来表现时间的推移，空间的转换，将抒情主人公对“伊人（爱慕、敬重的对象）”追求的执著精神表现得淋漓尽致（或把追求过程中的惆怅、失意、焦虑之情表达出来，）整首诗回环往复、一唱三叹，富于音乐之美。
（2分）13、崇拜的神灵；思念的情人；隐居的贤士；理想（言之有理即可）。
（2分）五、文言文阅读（21分）14、子厚，“柳河东”。
（2分）15、解释下列加点的字。
（4分）（1）名．我固当（称呼）（2）其本．欲舒（树根）（3）遂．而鸡豚（喂大）（4）故病．且怠（疲惫）16、不去抑制、减少它结果实罢了，并没有能力使它早结果实并且结的多。
（3分）17、（ B ）（2分）18、举例说明本文写作手法的特点。
并分析其作用。
（5分）手法及举例说明：1、对比（1）郭橐驼与他植者对比；（2）他植者中过懒者与过勤者对比（3）为官者以“惠政”为名与其“祸民”之实对比。
（任意一点即可给分）2、类比：以种树之道移之官理，将种树与治民类比。