2017上海中学高一周练8

上海中学高一周练数学卷2016.12.22一. 填空题1. 函数()f x x =--(0)x ≤的反函数是1()f x -=2. 若4log 124x =，则x = 3. 函数2()lg(23)f x x x =--的递减区间是4. 函数21()12f x x =+(2)x <-的反函数是1()f x -= 5. 若函数6,2()3log ,2a x x f x x x -+≤⎧=⎨+>⎩(0a >且1)a ≠的值域是[4,)+∞，则实数a 的取值范 围是6. 若函数()8x f x =的图像经过点1(,)3a ，则1(2)f a -+=7. 若函数24,3()(1)1,3x x f x a x x ⎧-≥=⎨-+<⎩存在反函数，则实数a 的取值范围为8. 如果log 41a b =-，则a b +的最小值为9. 若实数t 满足()f t t =-，则称t 是函数()f x 的一个次不动点，设函数()ln f x x =与反函 数的所有次不动点之和为m ，则m =10. 设lg lg lg 111()121418x x x f x =+++++，则1()()f x f x+= 11. 设方程24x x +=的根为m ，方程2log 4x x +=的根为n ，则m n +=12. 对区间I 上有定义的函数()g x ，记(){|(),}g I y y g x x I ==∈，已知定义域为[0,3]的 函数()y f x =有反函数1()y f x -=，且1([0,1))[1,2)f -=，1((2,4])[0,1)f -=，若方程 ()0f x x -=有解0x ，则0x =二. 选择题13. 如果23499log 3log 4log 5log 100x =⋅⋅⋅⋅⋅⋅⋅，则x ∈（ ）A. (1,2)B. (2,3)C. (5,6)D. (6,7)14. 函数2x xe e y --=的反函数是（ ）15. 已知函数()f x 为R 上的单调函数，1()f x -是它的反函数，点(1,3)A -和点(1,1)B 均在函数()f x 的图像上，则不等式1|(2)|1x f -<的解集为（ ）A. (1,1)-B. (1,3)C. 2(0,log 3)D. 2(1,log 3)16. 设,,0x y z >，且12xyz y z ++=，则422log log log x y z ++的最大值为（ ）A. 3B. 4C. 5D. 6三. 解答题17. 已知910390x x -⨯+≤，求函数111()4()242x x y -=-+的最大值和最小值；18. 给定实数a ，0a ≠且1a ≠，设函数11x y ax -=-； （1）求证：经过这个函数图像上的任意两个不同的点的直线不平行于x 轴；（2）判断此函数的图像是否关于直线y x =对称，说明你的理由；19. 作出下列函数的大致图像；（1）3|log |||y x =；（2）12log (24)y x =+；20. 设a 是实数，函数()4|2|x xf x a =+-；（1）求证：()f x 不是奇函数；（2）当0a >时，求()f x 的值域；21. 设函数()n n f x x bx c =++，*n N ∈，b 、c R ∈； （1）设2n ≥，1b =，1c =-，证明：()n f x 在区间1(,1)2内存在唯一的零点； （2）设2n =，若对任意12,[1,1]x x ∈-，有2122|()()|4f x f x -≤，求b 的取值范围；参考答案一. 填空题1. 2x -(0)x ≤2.116 3. (,1)-∞- 4. (3)x > 5. (1,2] 6. 237. (1,2] 8. 1 9. 0 10. 3 11. 4 12. 2二. 选择题13. D 14. C 15. C 16. A三. 解答题17. max ()(0)2f x f ==，min ()(1)1f x f ==；18.（1）略；（2）1()()f x f x -=，是； 19. 略；20.（1）略；（2）当102a <<，值域为2[,)a +∞；当12a ≥，值域为1[,)4a -+∞； 21.（1）单调递增，1()02n f <，(1)0n f >；（2）[2,2]-；。

上海中学高一周练数学卷2016.10.13一. 填空题1. 下列不等式的解为：①2560x x -+< ，②2560x x -++<2. 写出命题：若2017x y +≠，则2016x ≠或1y ≠的等价命题3. 已知：11a b -≤+≤，且13a b ≤-≤，则3a b -的取值范围为4. 不等式20ax bx a ++<(0)ab >的解集是空集，则222a b b +-的取值范围是5. 不等式20ax bx c ++>的解集是1(,3)2-，则不等式20cx bx a ++<的解集为 6. 已知12a ≥，22()f x a x ax c =-++，对于任意[0,1]x ∈，()1f x ≤恒成立，则实数c 的 取值范围是7. 已知实数,x y 满足2241x y xy ++=，则2x y +的最大值为8. 若不等式2051x px ≤++≤恰好有一个实数值为解，则p =9. 若下列三个方程：24430x ax a +-+=，22(1)0x a x a +-+=，2220x ax a +-=中 至少有一个方程有实根，则a 的取值范围是10. 已知,,a b c 为互不相等的整数，则22224()()a b c a b c ++-++的最小值为11. 已知,a b R ∈，关于x 的方程432210x ax x bx ++++=存在一个实根，则22a b +的最 小值为二. 选择题1. 集合{|41,}A x x k k Z ==+∈，{|42,}B x x k k Z ==+∈，{|43,}C x x k k Z ==+∈ 若a A ∈，b B ∈，c C ∈，则（ ）A. abc A ∈B. abc B ∈C. abc C ∈D. abc A B C ∉2. 设a 和b 都是非零实数，则不等式a b >和11a b>同时成立的充要条件是（ ） A. 0a b >> B. 0a b >> C. 0a b >> D. 以上答案均不对3. 假设n 是不小于3的正整数，n 个给定的实数12,,,n x x x ⋅⋅⋅具有如下性质：对任意一个二 次函数()y f x =，数12(),(),,()n f x f x f x ⋅⋅⋅中至少有三个数相同，则下列对于12,,,n x x x ⋅⋅⋅ 的判断中，正确的是（ ）A. 至少有三个数是相同的B. 至少有两个数是相同的C. 至多有三个数是相同的D. 至多有两个数是相同的4. 当一个非空数集F 满足“如果,a b F ∈，则,,a b a b ab F +-∈，且0b ≠时，a F b∈” 时，我们称F 就是一个数域，以下四个关于数域的命题：① 0是任何数域的元素；② 若数 域F 有非零元素，则2016F ∈；③ 集合{|3,}P x x k k Z ==∈是一个数域；④ 有理数集 是一个数域；其中真命题有（ ）个A. 0B. 1C. 2D. 3三. 解答题1. 解关于x 的不等式[(3)1](1)0m x x +-+>()m R ∈；2.（1）是否存在实数p ，使得40x p +<是220x x -->成立的充分不必要条件？如果存在，求出p 的取值范围，如果不存在，说明理由；（2）是否存在实数p ，使得40x p +<是220x x -->成立的必要不充分条件？如果存在，求出p 的取值范围，如果不存在，说明理由；3. 已知集合22{|410813,,}A t t a ab b a b a Z b Z ==++--+∈∈，对于任意的x A ∈，y A ∈，判断元素xy 与集合A 的关系，并证明你的结论；4. 已知二次函数()y f x =的二次项系数是1，并且一次项系数和常数项都是整数，若(())0f f x =有四个不同的实数根，并且在数轴上四个根成等距排列，试求二次函数()y f x =的解析式，使得其所有项的系数和最小；参考答案一. 填空题1. (2,3)、(,1)(6,)-∞-+∞2. 若2016x =且1y =，则2017x y +=3. [1,7]4. 4[,)5-+∞5. 1(2,)3-6. 34c ≤ 8. 4p =± 9. 32a ≤-或1a ≥- 10. 2 11. 8二. 选择题1. B2. A3. B4. D。

上海市2016-2017学年高一数学上学期周练06一。

填空题1。

写出下列不等式（组）的解集：（1）2654x x +< ；（2）23(1)(2)(3)(4)0x x x x ----≥ ；（3）3||1||22x x -≥- ；(4)||11x x x x-≥++ ； （5）|21|2|2|2x x +--> ；（6）25|21|x x x -->- ；(7）2112||x x ≤- ;（1< ; （9）2680321x x x x ⎧-+>⎪⎨+>⎪-⎩ ；（10）032||32x x x x x >⎧⎪--⎨>⎪++⎩ ; 2. 不等式20ax bx c ++>的解为m x n <<(0)m n <<，用,m n 表示20cx bx a -+<的 解为3. 已知函数2()f x x =，()1g x x =-，若存在x R ∈,使()()f x bg x <成立，则实数b 的 取值范围为4.满足1100<的最小正整数x 是 5. 已知三个不等式：（1）|24|5x x -<-；（2）22132x x x +≥-+；（3)2210x nx +-<; 同时满足（1）、(2)的x 也满足（3），则n 的最大值为6。

若不等式20ax bx c ++>的解集为(1,2)-，则不等式2||a b c b x x++>的解为 二。

选择题7。

设2()()()f x x a x bx c =+++，2()(1)(1)g x ax cx bx =+++，其中,,a b c R ∈，记集合 {|()0,}S x f x x R ==∈,{|()0,}T x g x x R ==∈，若||S 、||T 分别为集合S 、T 的元 素个数，则下列结论中不可能的是( )A. ||1S =且||0T = B 。

上海中学高一周练数学卷2016.09.18一. 填空题1. 已知{|2,}E x x x R =≥∈，{|8,}F x x x R =<∈，{|06,}G x x x R =≤≤∈，则 E F = ； F G = ； R C E F = ； R R C E C G = ；F CG = ； ()F C GE = ； 2. 用列举法表示集合*12{|,}5a N a Z a∈∈=- 3. 若“x a ≥”是“||2x ≤”的必要条件，则实数a 的取值集合是4. 命题“若x A ∈或x B ∈，则x A B ∈”的否命题是5. 某校一年级的200人中，爱好数学的有95人，爱好体育的有156人，则数学体育都爱好 的人数的最小值是6. 集合2{|(1)0}A x k x x k =++-=有且仅有两个子集，则实数k 的值为7. 非空集合{|121}A x a x a =+≤<-，{|25}B x x =-≤≤，若A A B ⊆，则a 的取值 范围是8. 关于x 的方程26(2)50x a x b ++++=的解集是N ，关于x 的方程220x ax b -+=的 解集是M ，1{}2M N =，则集合M 为 9. 集合*{|2,,50}A m m k k N k ==∈≤，集合{|,,,}B n n i j i j i A j A ==+<∈∈，则B中元素的个数是10. 若“存在{|12}x x x ∈≤≤使得310x a ++≥”是真命题，则a 的取值范围是11. 设A 是整数集的一个非空子集，对于k A ∈，若1k A -∉且1k A +∉，则称k 是A 的 一个“孤立元”，给定{1,2,3,4,5,6}S =，在S 的所有3元子集中，含“孤立元”的集合共 有 个12. 若集合{,,,}{1,2,3,4}a b c d =，且下列四个关系：①1a =；②1b ≠；③2c =；④4d ≠； 有且只有一个是正确的，则符合条件的有序数组(,,,)a b c d 的个数是13. 非空集合{|2}A x x a =-≤≤，{|23,}B y y x x A ==+∈，2{|,}C z z x x A ==∈， 若C B ⊆，则a 的取值范围是二. 选择题14. 对于集合A 和B ，令{|,,}A B x x a ba Ab B +==+∈∈，如果{|2,}S x x k k Z ==∈， {|21,}T x x k k Z ==+∈，则S T +=（ ）A. 整数集ZB. SC. TD. {|41,}x x k k Z =+∈15. 已知真命题“a b c d ≥⇒>”和“a b e f <⇒≤”，则“c d ≥”是“e f ≤”的（ ）A. 充分条件B. 必要条件C. 充要条件D. 既不充分也不必要条件16. 在下面的三个命题中，正确的个数是（ ）①“△ABC 和△111A B C 都是直角三角形”的否定形式是“△ABC 和△111A B C 都不是直角 三角形”；② 命题“若0xyz <，则,,x y z 中至少有两个负数”的逆否命题是“若,,x y z 中 至多有一个负数，则0xyz ≥”；③ 命题“两个无理数的积仍是无理数”的逆命题是“乘 积为无理数的两数都为无理数”；A. 0B. 1C. 2D. 317. 设Q 是有理数集，集合{|2,,,0}X x x a b a b Q x ==+∈≠，在下列集合中：①{2|x }x X ∈；②{}2x X ∈；③1{|}x X x ∈；④2{|}x x X ∈；与X 相同的集合有（ ） A. ①② B. ②③ C. ①②④ D. ①②③18. 设集合0123{,,,}S A A A A =，在S 上定义运算⊕为：i j k A A A ⊕=，其中k 为i j +被4 除的余数，,{0,1,2,3}i j ∈，则满足关系式20()x x A A ⊕⊕=的x ()x S ∈的个数为（ ）A. 4B. 3C. 2D. 1三. 解答题19. 设2()f x x ax b =++，{|()}{}A x f x x a ===，求a 、b 的值；20. 求证：222()()()a b b c c a -=-=-的充要条件是a b c ==；参考答案一. 填空题1. {|28}x x ≤<、{|8}x x <、{|8}x x <、{|2x x <或6}x >、{|68x x <<或0}x <、 {|2x x <或68}x <<2. {7,1,1,2,3,4}--3. {|2}a a ≤-4. 若x A ∉且x B ∉，则x A B ∉5. 516. 1-或12- 7. 23a <≤ 8. 1{,4}2- 9. 97 10. 7a ≥-11. 16 12. 6 13.132a ≤≤二. 选择题14. C 15. A 16. C 17. D 18. C三. 解答题 19. 13a =，19b =； 20. 略；。

上海中学高一数学周练卷2017.6.1一. 填空题1. 设234212121212333333n n n S -=-+-+⋅⋅⋅+-，则lim n n S →∞=2. n →∞=3. 用数学归纳法证明123(21)(1)(21)n n n +++⋅⋅⋅++=++时，从“n k =到1n k =+”时，左边需增加的代数式是4. 数列2211,(12),(122),,(1222),n -+++⋅⋅⋅+++⋅⋅⋅+⋅⋅⋅的前n 项和是5.计算：3lim(log n →∞= 6. 数列{}n a 按以下条件给出：11122,2,n n n n a a a n a a n ++=⎧⎪=+⎨⎪=⎩当为奇数时当为偶数时，则2015a =7. 若通项公式1(1)()32n n a nλ=-++的数列{}n a 的各项都是正数，则λ的取值范围是8. 设各项皆为非零实数实数的数列{}n a 的前n 项和是n S ，且11a =，对任意*n N ∈都有 112n n n S a a +=，则n a = 9. 设数列{}n a 的前n 项和1lg n n S a b =+，则使得lim 1n n S →∞=成立的实数b 的取值范围是10. 如图，一个粒子的起始位置为原点，在第一象限内于两正半轴上运动，第一秒运动到(0,1)，而后它接着按图示在x 轴、y 轴的垂直方向来回运动，且每秒移动一个单位长度，那么经过2015秒时，这个粒子所处位置的坐标是11. 若在由正整数构成的无穷数列{}n a 中，对任意的正整数n ，都有1n n a a +≤，且对任意的 正整数k ，该数列中恰有21k -个k ，则2015a =12. 有五只猴子摘了一些桃子，打算隔天早上起来分了吃，晚上的时候，第一只猴子偷偷起来把桃子分成五堆，还多了一个，就把多了的那个吃掉，并拿走了一堆，第二只猴子也偷偷起来将桃子分成了五堆，还是又多了一个，同样吃掉了这一颗桃子，并拿走了其中一堆，第三只、第四只、第五只猴子都做了同样的事情，则这堆桃子最少有 个二. 选择题13. 某个命题与自然数n 有关，如果n k =时命题成立，可以推得1n k =+时该命题也成立，现知道15n =时该命题不成立，则（ ）A. 16n =时该命题不成立B. 16n =时该命题成立C. 14n =时该命题不成立D. 14n =时该命题成立14. 已知1lim 1nnn a b a →∞-=+（b 为常数），则a 的取值范围是（ ） A. a R ∈且1a ≠ B. ||1a > C. 11a -<≤ D. 0a =或1a =15. 等差数列{}n a 中，n n S m =，m m S n=（m n ≠，*,,m n N ∈），则m n S +的值（ ） A. 大于4 B. 等于4 C. 小于4 D. 大于2或小于416. 已知A 、B 为ABC ∆的内角，tan A 是以4-为第三项，4为第七项的等差数列的公差，tan B 是以13为第三项，9为第六项的等比数列的公比，则此三角形为（ ） A. 钝角三角形 B. 锐角三角形C. 等腰直角三角形D. 非等腰的直角三角形三. 简答题17. 求11sin cos lim sin cos n n n n n θθθθ++→∞-+，其中3(0,)4πθ∈；18. 已知数列{}n a 是公差为d 的等差数列，证明：数列{}n a 的通项公式是1(1)n a a n d =+-；19. 用哪个数学归纳法证明：223521n n n +⋅++（*n N ∈）能被25整除；20. 我们将分母为正整数，分子为1的分数叫做单位分数，如果两个单位分数的分母是两个连续正整数，就称这两个单位分数为连续单位分数，证明：对任意不小于2的正整数n ，111111234212n n-+-+⋅⋅⋅+--可以写成n 个连续单位分数的和；参考答案一. 填空题 1. 182. 13. (22)(23)k k +++4. 122n n +--5. 16. 1007624⋅-7. 5[3,)2- 8. n 9. b < 10. (9,44)11. 45 12. 3121二. 选择题13. C14. C 15. A 16. B。

上海中学高一周练数学卷2016.12.01一. 填空题1. 函数3()8f x x =-的零点为2. 设函数(1)()()x x a f x x++=为奇函数，则a = 3. 若函数()y f x =的值域是1[,3]2，则函数1()()()F x f x f x =+的值域是 4. 命题“若()f x 是奇函数，则()f x -是奇函数”的否命题是5. 函数,0()1,0x a x f x x x -+≥⎧=⎨--<⎩是R 上的减函数，则实数a 的取值范围是6. 函数y =的最大值为7. 设()f x ()x R ∈为奇函数，1(1)2f =，(2)()(2)f x f x f +=+，则(5)f = 8. 若()f x 是定义在R 上的偶函数，在(,0]-∞上是减函数，且(2)0f =，则使()0f x <的 x 的取值范围是9. 已知2()y f x x =+是奇函数，且(1)1f =，若()()2g x f x =+，则(1)g -=10. 已知函数1()42x f x =+，若函数1()4y f x m =+-为奇函数，则实数m =11. 已知函数()f x =(1)a ≠，若()f x 在区间(0,1]上是减函数，则实数a 的取值 范围是 12. 对于函数1()42x x f x m +=-⋅，若存在实数0x ，使得00()()f x f x -=-，则实数m 的取值范围是二. 选择题 13. 已知函数()f x 、()g x 定义在R 上，()()()h x f x g x =⋅，则“()f x 、()g x 均为奇函 数”是“()h x 为偶函数”的（ ）条件A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件14. 若函数1()21x f x =+，则该函数在R 上（ ） A. 单调递减无最小值 B. 单调递减有最小值C. 单调递增无最大值D. 单调递增有最大值15. 设奇函数()f x 在(0,)+∞上为增函数且(1)0f =，则不等式()()0f x f x x --<的解集 为（ ）A. (1,0)(1,)-+∞B. (,1)(0,1)-∞-C. (,1)(1,)-∞-+∞D.(1,0)(0,1)-16. 设()f x 是偶函数，且当0x ≥时，()f x 是单调函数，则满足3()()4x f x f x +=+的所有 x 之和为（ ）A. 3-B. 3C. 8-D. 8三. 解答题17. 根据函数单调性的定义，证明：函数31y x =-是R 上的递减函数；18. 已知a 是实数，函数2()223f x ax x a =+--，如果函数()y f x =在区间[1,1]-上有零点，求a 的取值范围；19. 已知函数2()4x f x x =-； （1）指出函数()f x 的单调性，并予以证明；（2）画出函数()f x 的大致图像；20. 已知2()a f x x x=+()a R ∈； （1）判断函数()f x 的奇偶性，说明理由；（2）若()f x 在区间[1,)+∞上是增函数，求实数a 的取值范围；21. 设函数()f x =，其中2k <-；（1）求函数()f x 的定义域；（2）写出()f x 的单调区间；参考答案一. 填空题1. 22. 1-3. 10[2,]34. 若()f x 不是奇函数，则()f x -不是奇函数5. 1a ≤-52 8. (2,2)- 9. 1- 10. 12 11. (,0)(1,3]-∞ 12. 12m ≥二. 选择题 13. A 14. A 15. D 16. C三. 解答题17. 略；18. ([1,)-∞+∞； 19.（1）在(,2)-∞-、(2,2)-和(2,)+∞上单调递减，证明略；（2）略；20.（1）当0a =，偶函数，当0a ≠，非奇非偶函数；（2）2a ≤；21.（1）(,1(12,1)(1,12)(12,)k k k -∞--------+---+-+∞；（2）在(,1-∞-上单调递增，在(11)--单调递减，在(1,1--上单调递增，在(1)-+∞单调递减；。

上海中学2019届高一数学周练十二2016.12.08一. 填空题1. 幂函数23y x -=的定义域为 ，值域为2. 定义在[4,4]-上的偶函数()g x 满足：当0x ≤时，()g x 单调递增，若(1)()g m g m -<， 则m 的取值范围是3. 若函数2()|21|f x x x a a =++-+的图像关于y 轴对称，则实数a =4. 若函数()y f x =是定义在(0,)+∞上的减函数，则函数2(2)y f x x =-的单调递增区间 是5. 已知点(,)A a b ()a b ≠位于直角坐标平面的第一象限，点A 以及点A 关于直线y x =的 对称点B 都在一个幂函数()y f x =的图像上，则()f x =6. 设函数()y f x =对一切实数x 均满足(5)(5)f x f x +=-，且方程()0f x =恰有7个不 同的实根，则这7个实根的和为7. 已知函数()||f x x a x b =-+，给出下列命题：（1）当0a =时，()f x 的图像关于点(0,)b 成中心对称；（2）当(,)x a ∈+∞时，()f x 是递增函数；（3）当0x a ≤≤时，()f x 的最大值为24a b +，其中正确的序号是 8. 已知函数()y f x =是R 上的增函数，则0a b +>是()()()()f a f b f a f b +>-+-的 条件9. 函数(2)y f x =+的图像过点(1,3)-，则函数()y f x =的图像关于x 轴对称的图像一定 经过点10. 函数122010()1232011x x x x f x x x x x +++=+++⋅⋅⋅+++++的图像的对称中心为 11. 设函数1()f x x x =+的图像为1C ，1C 关于点(2,1)A 对称的图像为2C ，2C 对应的函数 为()g x ，则()g x 的解析式为12. 若函数()f x 满足(||)|()|f x f x =，则称()f x 为对等函数，给出以下三个命题：（1）定义域为R 的对等函数，其图像一定过原点（2）两个定义域相同的对等函数的乘积一定是对等函数（3）若定义域是D 的函数()y f x =是对等函数，则{|(),}{|0}y y f x x D y y =∈⊆≥其中真命题的个数是二. 选择题13. 幂函数223()(1)m m f x m m x +-=--在(0,)+∞上是减函数，则实数m =（ ）A. 2或1-B. 1-C. 2D. 2-或114. 已知函数:f R R →，则对所有实数x ，满足221()(())4f x f x -≥，且对不同的x ， ()f x 也不同，这样的函数()f x （ ）A. 不存在B. 有限多个C. 唯一存在D. 无穷多个15. 函数()y f x =的定义域和值域都是(,0)-∞，则()y f x =-的图像一定位于（ ）A. 第一象限B. 第二象限C. 第三象限D. 第四象限16. 已知集合{()|()A f x f x =是幂函数且为奇函数}，集合{()|()B f x f x =是幂函数且 在R 上单调递增}，集合{()|()C f x f x =是幂函数且图像过原点}，则（ ）A. A B C =B. B A C =C. C A B =D. A B C =17. 定义域和值域均为[,]a a -（常数0a >）的函数()y f x =和()y g x =的图像如图所示，给出下列四个命题：（1）方程(())0f g x =有且仅有三个解；（2）方程(())0g f x =有且仅 有三个解；（3）方程(())0f f x =有且仅有九个解；（4）方程(())0g g x =有且仅有一个解； 那么，其中正确命题的个数是（ ）A. 4B. 3C. 2D. 1三. 解答题18. 画出下列函数图像：（1）34y x =；（2）2y x -=；19. 若函数34220()(42)(1)f x mx x m x mx -=++++-+的定义域为R ，求实数m 的范围；20. 已知函数22()k k f x x -++=()k Z ∈满足(2)(3)f f <；（1）求k 的值并求出相应的()f x 的解析式；（2）对于（1）中的()f x ，试判断是否存在q (0)q >，使函数()1()(21)g x qf x q x =-+- 在区间[1,2]-上的值域为17[4,]8-？若存在，求出q ；若不存在，请说明理由；21. 已知函数()f x = （1）求函数()f x 的定义域和值域；（2）若00()f x x =，求0x 的值；参考答案一. 填空题1. (,0)(0,)-∞+∞，(0,)+∞ 2. 1[3,)2- 3. 12 4. (,0)-∞ 5. 1x - 6. 35 7. （1）（3） 8. 充要 9. (1,3)-10. (1006,2011)- 11. 1()24g x x x =-+- 12. 1二. 选择题13. B 14. A 15. D 16. B 17. C三. 解答题18. 略；19. 1,2)；20.（1）0k =或1，2()f x x =；（2）2q =；21.（1）定义域[1,0)[1,)-+∞，值域[0,)+∞；（2；。

上海上海中学高一上学期周练英语试题集团标准化办公室：[VV986T-J682P28-JP266L8-68PNN]上海中学2017-2018学年第学期高一英语试题Choice21.The impact__________ high technology draws worldwide attention.A.onB.toC.ofD.in22.________________,the more expansive gestures you should employ when youdeliver a speech.A.The more audience there isB.The more the audience areC.As much audience as there isD.The larger the audience is23.John is really an independent boy and he tries his best to settle everyproblem_______.A.of his ownB.by his own C,for his own D.on his own24.The queen,__________ an old woman, made a poisonous apple and came tothe cottage to tempt Snow White to eat it.A,dressed in B.who was dressing like C.dressed like D.who had clotheson as25.It is reported that __________schools in the west of China are improvingtheir study environment.A.a great many ofB.the large number ofB..a great amount of D.a large number of26.Do you really mean_________a basketball player? Do you know thattraining to be a basketball player means_____________at least eight hoursevery day?A.being,practicingB.to be,practicingC.to be,to practiceD.being,topractice27.Balancing the workload of a _________job alongside a course of study can be difficult, so there is an increasing tendency for people to give up work and go back to school.A.demandingB.rewardingC.leadingD.outstanding28. I couldn’t re sist having another piece of cake ____________I was supposed to be on a diet and lose weight.A.untilB.wheneverC.asD.even if29. Your children will not follow your advice to ____________business management as his major if you ___________.A.take up,force him toB.take up,force himC.take on,force him toD.take on,force him30.The students of class 8____________a farewell party for their retired class teacher from then on.A.made a great decision to holdingB.made up their mind to holdC.were determined to holdD.decide to hold31.The machine is easy to___________，___________is shown in the pictures.A.operate on, whichB.be operated, whichC.be operated on, asD.operate, as32.Mary’s talent for music and acting led her into a(n)_________on the stage.A.workB.professionC.occupationD.career33.Although the old man insisted he ___________all right,his children all insisted he______________to hospital at once.A.was,would be sentB.was, be sentC.be,would be sentD.be,be sent34.It was the financial scandal that he was involved___________pushed him to give up his political career.A.that B，in what C.in that D. in whichans are parts of our body,____________a special function to perform.A.each of them has B,each has C.every of which has D.each of which has36.A;It will be the first time that I _____________the subject.B;Don’t worry.It will be a little difficult the first time you_________it.A.have taught,teachB.teach,have taughtC.will teach,will teachD.have taught,will teach37.Slipping off the bicycle an getting hurt,Jack asked a pass-by whether there was a drugstore around________he could buy the medicine for his broken knee,A.whereB.whenC.whichD.that38.I have a house,________ the southA.that window opensB.of which the window opens toC.whose window open toD.the windows of which opens39.E-mail is a convenient, highly informal medium for conveying message among people __________well satisfies human needs.A.what B,who C.that D.for which40.According to a report recently released by the US National Research Council,the amount of space junk flowing in Earth’s orbit has reached a critical lever_________future space mission may become too dangerous to fly.A.thatB.whereC.whose D of which41.Marco Polo,who was a great Italian traveler, traveled all the way to China,_________was then called Cathy.A.whereB.whichC.whenD.what42.He arrived in New York in 1986,____________some time later, he became a writer.A.whenB.whereC.thatD.which43.It was almost midnight_________the ceremony was over.A.thatB.sinceC.when D,till44.Jenny smiled________her mother did when she was Jenny’s age.A.whatB.whereC.thatD.which45._________did you use to do________you don’t do now?A.46._______glitters is not gold not all those__________wander are lost.A.What,whoB.All that,whoC.All,thatD.What,that47.Sparking Lake in Jiuzhaigou is so beautiful a place_________people can memorize forever even it no longer exists in real life.A.thatB.whichC.asD.what48.I sent invitation to 100people to the party,__________turned up.A.of whom only a thirdB.only 30 of theseC.almost all of themD.and none of them49.There is no difficulty___________we can overcome.A.whichB.thatC.whatD.but50.Could you lend me a knife________A.which to open the canB.with which to open a canC.with which I opened the canD.with which I can use to open a canVocabularyComplete 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.Prederic Mishikn, who’s been a professor at Columbia Business School for almost 30 years, is good at solving problems and expressing ideas. Whether he’s sending in front of a lecture hall or engaged in a ____51______ conversion, his hands are always waving and pointing. When he was in_____52_______school,one of his professors was so annoyed bythis____53_____gesturing that he made the young economist sit on his hands whenever he visited the professor’s office.It t urns out, however, that Mishikn’s professor had it exactly wrong. Gesture doesn’t prevent but ____54_____clear thought and speech.Research______55____that the movements we make with our hands when wetalk_______56_____a kind of second language, adding information that is____57_______from our words. It is learning’s_____58_______code;Gestures reveals what we know. It also reveals what we don’t know. What’s more, the agreement(or______59_______of agreement)between what our voices say and how our hands move offers a ___60________to our readiness to learn.III. Reading ComprehensionSection ADirections:For each blank in the following passage there are four wordsorphrasesmarked A,B,C and D. Fill in each blank with the word or phrase that best fits thecontext.One of the big excuses for not learning languages in Britain is that when you try them out abroad, the person you are speaking to responds in__61__ English, making you feel about two feet tall—or should that be 36 cm?English people are known for their reluctance to accept changes leading to closer union with us European partners. __62__ according to organizations promoting English business, ____63_____language learning is concerned, that simply doesn’t __53__ in that 21st century.Trade Section UK aims to help British companies trading overseas. Its chief executive, Sir David Wright, says: “Language __64__ are good for business, good for jobs and help people in their career. Although many people may speak English __65__, they will usually negotiate in their own language. If we are to compete on an equal basis, it’s decisive that business ______66____ the challenge and uses languages more effectively.”The Council of Europe __67__ language learning as an important tool to improve communication and mutual understanding between individuals. The Center for Information on Language Teaching says that being able to speak __68__ language is a “basic life skill” and that the “language deficit in the UK has become an urgent economic, __69__ and political question.”The department for Education and Skills wants to __70__ teaching of modern foreign languages (MFT) at an earlier stage in the future. Primary school children will get greater __71__to foreign language learning. Currently, about 20 percent of primary schools offer MFL teaching. The Department wants to increase this __72__ by 2012 every child has an entitlement to study a language at primary school.Education and Skills secretary Estelle Morris is very __73__ about more primary schools taking up the __74__ challenge. Children are just so much more responsive___75_____an earlier age.61. A. broken B. perfect C. natural D. simple62. A. And B. But C. So D. Besides63. A. whose B. where C. which D. that64. A. technology B. Learners C. skills D. teachers65. A. at home B. in school C aboard D. Overseas66. A. takes up B. takes off C. takes over D. takes in67. A. finds B. thinks C. regards D. believes68. A. native B. local C. another D. certain69. A. physical B. mental C. spiritual D. social70. A. permit B. encourage C. demand D. challenge71. A. admission B. access C. chance D. approach72. A. in that B. that C. now that D. so that73. A. worried B. concerned C. positive D. negative74. A. language B. business C. competition D. learning75. A. to B. on C. at D. ofReading comprehension(A)I made a pledge (发誓) to myself on the way down to the vacation beach cottage. For two weeks I would try to be a loving husband and father. Totally loving. No ifs, ands or buts.The idea had come to me as I listened to a talk on my car radio. The speaker was quoting a Biblical (圣经的) passage about husbands being thoughtful of their wives. Then he went on to say, "Love is an act ofwill.A person can choose to love." To myself, I had to admit that I had been a selfish husband. Well, for two weeks that would change.And it did. Right from the moment I kissed Evelyn at the door and said, "That new yellow sweater looks great on you."Oh, Tom, you noticed," she said, surprised and pleased, maybe a little puzzled.After the long drive, I wanted to sit and read. Evelyn suggested a walk on the beach. I started to refuse, but then I thought, "Evelyn's been alone here with the kids all the week and now she wants to stay with me." We walked on the beach while the children flew their kites.So it went. Two weeks of not calling the Wall Street firm where I am a director; a visit to the shell museum though I usually hate museums. Relaxed and happy, that's how the whole vacation passed. I made a new pledge to keep on remembering to choose love.There was one thing that went wrong with my experiment, however. Evelyn and I still laugh about it today.Last night at our cottage, preparing for bed, Evelyn stared at me with the saddest expression." What's the matter" I asked her."Tom," she said in a voice filled with distress, "do you know something I don't""What do you mean"" Well...that checkup (体检) I had several weeks ago...our doctor (i)he tell you something about meTom, you've been so good to me...am I dying"It took a moment for it all to sink in. Then I burst out laughing."No, honey," I said, wrapping her in my arms. "You're not dying; I'm just starting to live."76. In the first paragraph, "No ifs, ands or buts" probably means ____.A. UnnecessarilyB. unconditionallyC. impossiblyD. unexpectedly77. During the two weeks on the beach, Tom showed more love to his wife because _____.A. she looked lovely in her new clothesB. she was seriously illC. he was determined to be a good husbandD. he had made a lot of money in Wall Street78.By saying "I'm just starting to live", Tom means that _____.A. he is beginning to feel regretful for what he did to his wifeB. he lived an unhappy life before and is now starting to changeC. he is just beginning to understand the real meaning of lifeD. he is just beginning to enjoy his life as a loving husband(B)As I was thinking about language learning the other day, the image of baking bread came into my mind．I compared some of the exercises and drills that we put ourselves through in order to learn a language to the various ingredients (原料) that go into baking a loaf of fresh bread．Real language learning takes place in human relationships．No one sits down and eats a cup of flour, even if he is hungry and in a hurry．You don' t become bilingual (双语的) by learning lists of vocabulary．You don' tbecome a speaker of a language by memorizing grammatical rules．You become bilingual by entering a community that uses that other language as its basic means of communication．I am not suggesting that we can make bread without ingredients．Flour is necessary, as are yeast (酵母), salt, water and other ingredients．Vocabulary is part of any language and will have to be learned．Grammatical rules exist in every language and cannot be ignored．But merely combining the appropriate ingredients in the recommended proportions does not result in bread．At best, you only end up with a ball of dough (面团)．In order to get bread, you have to apply heat to the dough．And in language learning, that heat comes from the community．Anyone who has learned a second language has experienced that heat．It creeps up your neck when you ask the babysitter “Have you already been eaten” when you meant to say, ‘‘Have you already eaten” When you try to say something quite innocent and the whole room bursts into laughter, you are experiencing the heat that turns raw dough into good bread．Remember the old saying, “If you can' t stand the heat, get out of the kitchen"．This is where language learning often breaks down because we find the heat uncomfortable and we stop the baking process．In other words, we can' t stand the heat, so we get out of the kitchen．However, the language learner who stays in the kitchen－in the heat－until the combined ingredients are thoroughly transformed will enjoy the richness of a quality loaf of bread. He is glad that he did not "get out of the kitchen” at the important moment when the oven seemed too hot.The dedicated language learner knows that becoming bilingual cannot be achieved without the heat.79.According to the author, you can possibly become a speaker of a language by ________．A．bearing millions of words and expressions in your mindB．using the language to communicate with those around youC．Knowing verb conjugations and grammatical rulesD．saying something innocent to be laughed at by others80.'What’s the purpose of illustration of the example-you ask the babysitter,"Have you already been eaten"When you meant to say,"Have you already eaten"A. To verify that you are sure to make some mistakes when you enter a community.B.To show that you should combine the ingredients in the recommended proportions.C. To prove that you may experience"heat"from the community in language learning.D. To indicate that being bilingual calls for your courage, confidence and perseverance.81.According to the passage, which of the following is NOT the necessity of baking bread and learning language?A．Excellent Skills．B．Various ingredients．C．Appropriate proportions．D．Uncomfortable heat．(C)Like most people, I’ve long understood that I’ll be judged by my occupation, that my profession is used by people to see how talented I am. Recently, however, I was disappointed to see that it also decides how I’m treated as a person.Last year I left a professional position as a small-town reporter and took a job waiting tables. As someone paid to serve food to people, I had customers say and do things to me I suppose they’d never say or do to the people they know. One night a man talking on his cell phone waved me away,then called me back with his finger a minute later, saying angrily that he was ready to order and asking where I’d been.I had waited tables during summers in college and was treated like a peon（勤杂工） by plenty of people. But at 19 years old, I believed I deserved inferior（低等的）treatment from professional adults. Besides, people responded to me differently after I told them I was in college. Customers would joke that one day I’d be sitting at their table, waiting to be served.Once I graduated I took a job at a community newspaper. From my first day, I heard a respectful tone from everyone who called me. I assumed this was the way the professional world worked--- politely and formally.I soon found out differently. I sat several feet away from a person in advertising department with a similar name. Our calls would often get mixed up and someone asking for Kristen would be transferred to Christie. The mistake was immediately clear. Perhaps it was because of money, but people used a tone with Kristen that they never used with me.My job title made people treat me with courtesy. So it was a shock to return to be the restaurant industry.It’s no secret that there’s a lot to put up with when waiting tables, and fortunately, much of it can be easily forgotten when you pocket the tips. The service industry exists to meet others’ needs. Still, it seemed that many of my customers didn’t get the difference between server and servant.I’m now applying to graduate school, which means someday I’ll return to a profession where people need to be nice to me in order to get what they want. I think I’ll take them to dinner first, and see how they treat someone whose job is to serve them.82.The author was disappointed to find that_____________83.A. one’s position is used to measure one’s intelligence.B. Talented people like her should fail to get a respectable jobC. one’s occupation affects the way one is treated as a person.D. professionals tend to look down upon manual workers.83. What does the author intend to say by the example in Paragraph 2A. Waiting tables is a hard job.B. Some customers are difficult to deal with.C. The man making a phone call is absent-minded.D. Some customers show no respect to those who serve them.84.What does the author imply by saying"... Many of my customers didn’t get the difference between server and servant (Lines 3-4, Para. 7)A. Those who cater to others' needs are destined to be looked down upon.B. Those working in the service industry shouldn't be heated as servants.C. Those serving others have to put up with rough treatment to earn a living.D. The majority of customers tend to look on a servant as 4. server nowadays.85. The author says one day she’ll take her customers to dinner in order to _______.A. see what kind of person they areB. experience the feeling of being servedC. shoe her generosity towards people inferior to herD.arouse their sympathy for people living a humble life(D)In 1784, five years before he became president of the United States, George Washington, 52, was nearly toothless. So he hired a dentist to transplant nine teeth into his jaw—having extracted them from the mouths of his slaves.That's a far different image from the cherry-tree-chopping George most people remember from their history books. But recently, many historianshave begun to focus on the roles slavery played in the lives of thefounding generation. They have been spurred in part by DNA evidence made available in 1998, which almost certainly proved Thomas Jefferson had fathered at least one child with his slave Sally Hemings. And only over the past 30 years have scholars examined history from the bottom up. Works of several historians reveal the moral compromises made by the nation's early leaders and the fragile nature of the country's infancy. More significantly, they argue that many of the Founding Fathers knew slavery was wrong—andyet most did little to fight it.More than anything, the historians say, the founders were hampered bythe culture of their time. While Washington and Jefferson privately expressed distaste for slavery, they also understood that it was part ofthe political and economic bedrock of the country they helped to create.For one thing, the South could not afford to part with its slaves. Owning slaves was "like having a large bank account," says Wiencek, authorof An Imperfect God: George Washington, His Slaves, and the Creation of America. 'The southern states would not have signed the Constitutionwithout protections for the "peculiar institution," including a clause that counted a slave as three fifths of a man for purposes of congressional representation.And the statesmen's political lives depended on slavery. The three-fifths formula handed Jefferson his narrow victory in the presidential election of 1800 by inflating the votes of the southern states in the Electoral College. Once in office, Jefferson extended slavery with the Louisiana Purchase in 1803; the new land was carved into 13 states,including three slave states.Still, Jefferson freed Hemings' children—though not Hemings herself or his approximately 150 other slaves. Washington, who had begun to believethat all men were created equal after observing the bravery of the black soldiers during the Revolutionary War, overcame the strong opposition of his relatives to grant his slaves their freedom in his will. Only a decade earlier, such an act would have required legislative approval in Virginia.86. In Paragraph 1,George Washington's dental surgery is mentionedto__________A．show the poor medical practice in the past.B．demonstrate the great cruelty of slavery in his days.C．stress the important role of slaves in the entire U.S. history. D．reveal an unknown aspect of his life and introduce the topic87.We may infer from the second paragraph that_____________.A. DNA technology has been widely applied to history research.B. In its early day. s the U. S. was confronted with delicate situations.C. historians deliberately made up some stories of Jefferson's life.D.Political compromises are easily found throughout the U. S. history.88. What do we learn about Thomas Jefferson?A. His political view changed his attitude towards slavery.B. His status as a father made him free the child slaves.C. His attitude towards slavery was complex.D. His affair with a slave ruined his reputation.89.Which of the following is TRUE according to the text?A. Some founding fathers benefited politically from slavery.B. Slaves in the old days did not have the right to vote.C. Slave owners usually had large savings accounts.D. Washington decided to free slaves due to moral considerations. Translation1.社会上，年轻人赶时髦，穿时尚衣服是常有的事。

上海中学高一周练数学卷2016.09.18一. 填空题1. 已知{|2,}E x x x R =≥∈，{|8,}F x x x R =<∈，{|06,}G x x x R =≤≤∈，则 E F =I ； F G =U ； R C E F =U ； R R C E C G =U ； F C G = ； ()F C G E =I ；2. 用列举法表示集合*12{|,}5a N a Z a∈∈=- 3. 若“x a ≥”是“||2x ≤”的必要条件，则实数a 的取值集合是4. 命题“若x A ∈或x B ∈，则x A B ∈U ”的否命题是5. 某校一年级的200人中，爱好数学的有95人，爱好体育的有156人，则数学体育都爱好 的人数的最小值是6. 集合2{|(1)0}A x k x x k =++-=有且仅有两个子集，则实数k 的值为7. 非空集合{|121}A x a x a =+≤<-，{|25}B x x =-≤≤，若A A B ⊆I ，则a 的取值 范围是8. 关于x 的方程26(2)50x a x b ++++=的解集是N ，关于x 的方程220x ax b -+=的 解集是M ，1{}2M N =I ，则集合M 为9. 集合*{|2,,50}A m m k k N k ==∈≤，集合{|,,,}B n n i j i j i A j A ==+<∈∈，则B 中元素的个数是10. 若“存在{|12}x x x ∈≤≤使得310x a ++≥”是真命题，则a 的取值范围是11. 设A 是整数集的一个非空子集，对于k A ∈，若1k A -∉且1k A +∉，则称k 是A 的 一个“孤立元”，给定{1,2,3,4,5,6}S =，在S 的所有3元子集中，含“孤立元”的集合共 有 个12. 若集合{,,,}{1,2,3,4}a b c d =，且下列四个关系：①1a =；②1b ≠；③2c =；④4d ≠； 有且只有一个是正确的，则符合条件的有序数组(,,,)a b c d 的个数是13. 非空集合{|2}A x x a =-≤≤，{|23,}B y y x x A ==+∈，2{|,}C z z x x A ==∈， 若C B ⊆，则a 的取值范围是二. 选择题14. 对于集合A 和B ，令{|,,}A B x x a b a A b B +==+∈∈，如果{|2,}S x x k k Z ==∈， {|21,}T x x k k Z ==+∈，则S T +=（ ）A. 整数集ZB. SC. TD. {|41,}x x k k Z =+∈15. 已知真命题“a b c d ≥⇒>”和“a b e f <⇒≤”，则“c d ≥”是“e f ≤”的（ ）A. 充分条件B. 必要条件C. 充要条件D. 既不充分也不必要条件16. 在下面的三个命题中，正确的个数是（ ）①“△ABC 和△111A B C 都是直角三角形”的否定形式是“△ABC 和△111A B C 都不是直角 三角形”；② 命题“若0xyz <，则,,x y z 中至少有两个负数”的逆否命题是“若,,x y z 中 至多有一个负数，则0xyz ≥”；③ 命题“两个无理数的积仍是无理数”的逆命题是“乘 积为无理数的两数都为无理数”；A. 0B. 1C. 2D. 317. 设Q 是有理数集，集合{|,,0}X x x a a b Q x ==+∈≠，在下列集合中：①{2|x }x X ∈；②}x X ∈；③1{|}x X x ∈；④2{|}x x X ∈；与X 相同的集合有（ ） A. ①② B. ②③ C. ①②④ D. ①②③18. 设集合0123{,,,}S A A A A =，在S 上定义运算⊕为：i j k A A A ⊕=，其中k 为i j +被4 除的余数，,{0,1,2,3}i j ∈，则满足关系式20()x x A A ⊕⊕=的x ()x S ∈的个数为（ ）A. 4B. 3C. 2D. 1三. 解答题19. 设2()f x x ax b =++，{|()}{}A x f x x a ===，求a 、b 的值；20. 求证：222()()()a b b c c a -=-=-的充要条件是a b c ==；参考答案一. 填空题1. {|28}x x ≤<、{|8}x x <、{|8}x x <、{|2x x <或6}x >、{|68x x <<或0}x <、 {|2x x <或68}x <<2. {7,1,1,2,3,4}--3. {|2}a a ≤-4. 若x A ∉且x B ∉，则x A B ∉U5. 516. 1-或12- 7. 23a <≤ 8. 1{,4}2- 9. 97 10. 7a ≥-11. 16 12. 6 13.132a ≤≤二. 选择题14. C 15. A 16. C 17. D 18. C三. 解答题 19. 13a =，19b =； 20. 略；。

上海中学2019届高一数学周练十二2016.12.08一. 填空题1. 幂函数23y x -=的定义域为 ，值域为2. 定义在[4,4]-上的偶函数()g x 满足：当0x ≤时，()g x 单调递增，若(1)()g m g m -<， 则m 的取值范围是3. 若函数2()|21|f x x x a a =++-+的图像关于y 轴对称，则实数a =4. 若函数()y f x =是定义在(0,)+∞上的减函数，则函数2(2)y f x x =-的单调递增区间 是5. 已知点(,)A a b ()a b ≠位于直角坐标平面的第一象限，点A 以及点A 关于直线y x =的 对称点B 都在一个幂函数()y f x =的图像上，则()f x =6. 设函数()y f x =对一切实数x 均满足(5)(5)f x f x +=-，且方程()0f x =恰有7个不 同的实根，则这7个实根的和为7. 已知函数()||f x x a x b =-+，给出下列命题：（1）当0a =时，()f x 的图像关于点(0,)b 成中心对称；（2）当(,)x a ∈+∞时，()f x 是递增函数；（3）当0x a ≤≤时，()f x 的最大值为24a b +，其中正确的序号是 8. 已知函数()y f x =是R 上的增函数，则0a b +>是()()()()f a f b f a f b +>-+-的 条件9. 函数(2)y f x =+的图像过点(1,3)-，则函数()y f x =的图像关于x 轴对称的图像一定 经过点10. 函数122010()1232011x x x x f x x x x x +++=+++⋅⋅⋅+++++的图像的对称中心为 11. 设函数1()f x x x =+的图像为1C ，1C 关于点(2,1)A 对称的图像为2C ，2C 对应的函数 为()g x ，则()g x 的解析式为12. 若函数()f x 满足(||)|()|f x f x =，则称()f x 为对等函数，给出以下三个命题：（1）定义域为R 的对等函数，其图像一定过原点（2）两个定义域相同的对等函数的乘积一定是对等函数（3）若定义域是D 的函数()y f x =是对等函数，则{|(),}{|0}y y f x x D y y =∈⊆≥其中真命题的个数是二. 选择题13. 幂函数223()(1)m m f x m m x +-=--在(0,)+∞上是减函数，则实数m =（ ）A. 2或1-B. 1-C. 2D. 2-或114. 已知函数:f R R →，则对所有实数x ，满足221()(())4f x f x -≥，且对不同的x ， ()f x 也不同，这样的函数()f x （ ）A. 不存在B. 有限多个C. 唯一存在D. 无穷多个15. 函数()y f x =的定义域和值域都是(,0)-∞，则()y f x =-的图像一定位于（ ）A. 第一象限B. 第二象限C. 第三象限D. 第四象限16. 已知集合{()|()A f x f x =是幂函数且为奇函数}，集合{()|()B f x f x =是幂函数且 在R 上单调递增}，集合{()|()C f x f x =是幂函数且图像过原点}，则（ ）A. A B C =B. B A C =C. C A B =D. A B C =17. 定义域和值域均为[,]a a -（常数0a >）的函数()y f x =和()y g x =的图像如图所示，给出下列四个命题：（1）方程(())0f g x =有且仅有三个解；（2）方程(())0g f x =有且仅 有三个解；（3）方程(())0f f x =有且仅有九个解；（4）方程(())0g g x =有且仅有一个解； 那么，其中正确命题的个数是（ ）A. 4B. 3C. 2D. 1三. 解答题18. 画出下列函数图像：（1）34y x =；（2）2y x -=；19. 若函数34220()(42)(1)f x mx x m x mx -=++++-+的定义域为R ，求实数m 的范围；20. 已知函数22()k k f x x -++=()k Z ∈满足(2)(3)f f <；（1）求k 的值并求出相应的()f x 的解析式；（2）对于（1）中的()f x ，试判断是否存在q (0)q >，使函数()1()(21)g x qf x q x =-+- 在区间[1,2]-上的值域为17[4,]8-？若存在，求出q ；若不存在，请说明理由；21. 已知函数()f x =； （1）求函数()f x 的定义域和值域；（2）若00()f x x =，求0x 的值；参考答案一. 填空题1. (,0)(0,)-∞+∞，(0,)+∞2. 1[3,)2-3. 124. (,0)-∞5. 1x -6. 357. （1）（3）8. 充要9. (1,3)-10. (1006,2011)- 11. 1()24g x x x =-+- 12. 1二. 选择题 13. B 14. A 15. D 16. B 17. C三. 解答题18. 略；19. 1,2)；20.（1）0k =或1，2()f x x =；（2）2q =；21.（1）定义域[1,0)[1,)-+∞，值域[0,)+∞；（2）12+；。

上海中学高一周练数学卷2016.11.03一. 填空题1. 求出下列不等式的解集：（1）||0a > （2）2103624x x ≤-+< （3）32x x<- （4）25||60x x -+>（5x < （6）22110x x x x--+≤（756x - 2. 已知集合8{|1}2A x x =>+，{|||}B x x a b =-≥，若A B R =，A B =∅，则 a = ，b =3. 若函数12y x b =+的图像与以(1,1)A 、(2,3)B 为端点的线段相交，则常数b 的取值范围 是4. 在maths 先生的数学班的所有学生中，对于问题“你喜欢数学吗？”在学年开始时，有 50%回答“是”，有50%回答“不”，学年结束时，有70%回答“是”，有30%回答“不”， 在全部学生中，有x %的学生在学年开始和结束时给出了不同的回答，则x 的最大值和最小 值的差是5. 对任意正数x 和y ，不等式1()()9ax y xy++≥恒成立，则常数a 的取值范围是 6. 令,,,a b c d 是集合{3,2,2,4}--中的不同的元素，则22()()a b c d +++的最大值与最小值之差为7. 关于x 的方程2(2)210x m x m +-+-=有一个根属于(0,1)，则m 取值范围是8. 若||2m ≤时不等式2210mx x m -+-<恒成立，则x 的取值范围是9. 若关于x 的不等式组22202(25)50x x x a x a ⎧--≥⎪⎨+++≤⎪⎩的解集中有且仅有两个整数，则a 的取值范围是10. 函数42321x y x =+的最小值是11. 若正实数a 和b 满足5a b +=+的最大值是二. 选择题1.“0.53k <<”是“关于x 的不等式4288(2)50x k x k +-+->的解集为R ”的（ ） A. 充分不必要条件 B. 必要不充分条件 C. 充要条件 D. 既不充分也不必要条件 2. 若面积为S 的正三角形其外接圆的半径是r ，则（ ）A. 2S =B. 2S =C. 2S =D. 2S = 3. 已知集合{|||1}A x x =<，对任意的a A ∈，B A ∈，则1a b ab ++和1a bab--（ ）A. 一定都属于AB.至少有一个属于AC. 至多有一个属于AD.是否属于A 不能确定三. 解答题1. 解关于x 的不等式2(1)10ax a x -++<；2.求函数y =的定义域和值域；3. 已知非空集合M R ⊆，定义域为R 的函数1,()0,M x Mf x x M∈⎧=⎨∉⎩，若A 、B 是R 的两个非空真子集，试求函数()1()()()1A B A B f x F x f x f x +=++的值域；4. 列车提速可以提高铁路运输量，但并非列车速度越大，列车的流量Q （单位时间内通过 观测点的列车数量）就越大，因为列车运行时，前后两车必须要保持一个“安全间隔”，“安 全间隔”与列车的速度v 的平方成正比（比例系数0k 为定值，00k >），假设所有的列车长 度均为l ，问：列车车速多大时，列车的流量Q 最大；5. 已知0x y >>y x >；参考答案一. 填空题 1.（1）(,1)(1,)-∞-+∞ （2）(3,1][4,6)-- （3）(2,)+∞ （4）(,3)(2,2)(3,)-∞--+∞ （5）R （6）{1} （7）36(,)25+∞ 2. 2a =，4b = 3. 1[,2]24. 605. [4,)+∞6. 607. 1(,62-8. 11(22-+ 9. (2,1][4,5)- 10. 011.二. 选择题1. A2. C3. A三. 解答题1. 当0a <，1(,)(1,)x a∈-∞+∞；当0a =，(1,)x ∈+∞；当01a <<，1(1,)x a∈；当1a =，x ∈∅；当1a >，1(,1)x a∈；2. 定义域：[1,2)(2,)+∞，值域：(,8](0,)-∞-+∞；3. 2{,1}3； 4. 20v Q l k v =+，v =Q 最大； 5. 略；。

上海中学高一周练数学卷2016.12.01一. 填空题1. 函数3()8f x x =-的零点为 2. 设函数(1)()()x x a f x x++=为奇函数，则a = 3. 若函数()y f x =的值域是1[,3]2，则函数1()()()F x f x f x =+的值域是 4. 命题“若()f x 是奇函数，则()f x -是奇函数”的否命题是5. 函数,0()1,0x a x f x x x -+≥⎧=⎨--<⎩是R 上的减函数，则实数a 的取值范围是6. 函数y =的最大值为7. 设()f x ()x R ∈为奇函数，1(1)2f =，(2)()(2)f x f x f +=+，则(5)f = 8. 若()f x 是定义在R 上的偶函数，在(,0]-∞上是减函数，且(2)0f =，则使()0f x <的 x 的取值范围是9. 已知2()y f x x =+是奇函数，且(1)1f =，若()()2g x f x =+，则(1)g -=10. 已知函数1()42x f x =+，若函数1()4y f x m =+-为奇函数，则实数m =11. 已知函数()f x =(1)a ≠，若()f x 在区间(0,1]上是减函数，则实数a 的取值 范围是12. 对于函数1()42x x f x m +=-⋅，若存在实数0x ，使得00()()f x f x -=-，则实数m 的取 值范围是二. 选择题13. 已知函数()f x 、()g x 定义在R 上，()()()h x f x g x =⋅，则“()f x 、()g x 均为奇函 数”是“()h x 为偶函数”的（ ）条件A. 充分不必要条件B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件14. 若函数1()21x f x =+，则该函数在R 上（ ） A. 单调递减无最小值 B. 单调递减有最小值C. 单调递增无最大值D. 单调递增有最大值15. 设奇函数()f x 在(0,)+∞上为增函数且(1)0f =，则不等式()()0f x f x x--<的解集 为（ ） A. (1,0)(1,)-+∞U B. (,1)(0,1)-∞-UC. (,1)(1,)-∞-+∞UD. (1,0)(0,1)-U16. 设()f x 是偶函数，且当0x ≥时，()f x 是单调函数，则满足3()()4x f x f x +=+的所有 x 之和为（ ）A. 3-B. 3C. 8-D. 8三. 解答题17. 根据函数单调性的定义，证明：函数31y x =-是R 上的递减函数；18. 已知a 是实数，函数2()223f x ax x a =+--，如果函数()y f x =在区间[1,1]-上有 零点，求a 的取值范围；19. 已知函数2()4x f x x =-； （1）指出函数()f x 的单调性，并予以证明；（2）画出函数()f x 的大致图像；20. 已知2()a f x x x=+()a R ∈； （1）判断函数()f x 的奇偶性，说明理由；（2）若()f x 在区间[1,)+∞上是增函数，求实数a 的取值范围；21. 设函数()f x =，其中2k <-；（1）求函数()f x 的定义域；（2）写出()f x 的单调区间；参考答案一. 填空题1. 22. 1-3. 10[2,]34. 若()f x 不是奇函数，则()f x -不是奇函数5. 1a ≤-6.7. 528. (2,2)-9. 1- 10. 1211. (,0)(1,3]-∞U 12. 12m ≥二. 选择题13. A 14. A 15. D 16. C三. 解答题17. 略；18. 3(,[1,)2-∞+∞U ； 19.（1）在(,2)-∞-、(2,2)-和(2,)+∞上单调递减，证明略；（2）略； 20.（1）当0a =，偶函数，当0a ≠，非奇非偶函数；（2）2a ≤；21.（1）(,1(11)(1,1(1)-∞-----+-++∞U U U ；（2）在(,1-∞-上单调递增，在(11)--单调递减，在(1,1--+上单调递增，在(1)-++∞单调递减；。

上海中学高一周练数学卷2016.12.22一. 填空题1.函数()f x =(0)x ≤的反函数是1()fx -= 2. 若4log 124x =，则x = 3. 函数2()lg(23)f x x x =--的递减区间是4. 函数21()12f x x =+(2)x <-的反函数是1()f x -= 5. 若函数6,2()3log ,2a x x f x x x -+≤⎧=⎨+>⎩(0a >且1)a ≠的值域是[4,)+∞，则实数a 的取值范 围是6. 若函数()8x f x =的图像经过点1(,)3a ，则1(2)f a -+= 7. 若函数24,3()(1)1,3x x f x a x x ⎧-≥=⎨-+<⎩存在反函数，则实数a 的取值范围为8. 如果log 41a b =-，则a b +的最小值为9. 若实数t 满足()f t t =-，则称t 是函数()f x 的一个次不动点，设函数()ln f x x =与反函 数的所有次不动点之和为m ，则m =10. 设lg lg lg 111()121418x x x f x =+++++，则1()()f x f x+= 11. 设方程24x x +=的根为m ，方程2log 4x x +=的根为n ，则m n +=12. 对区间I 上有定义的函数()g x ，记(){|(),}g I y y g x x I ==∈，已知定义域为[0,3]的 函数()y f x =有反函数1()y f x -=，且1([0,1))[1,2)f -=，1((2,4])[0,1)f -=，若方程 ()0f x x -=有解0x ，则0x =二. 选择题13. 如果23499log 3log 4log 5log 100x =⋅⋅⋅⋅⋅⋅⋅，则x ∈（ ）A. (1,2)B. (2,3)C. (5,6)D. (6,7)14. 函数2x xe e y --=的反函数是（ ） A. 奇函数，在(0,)+∞上是减函数 B. 偶函数，在(0,)+∞上是减函数C. 奇函数，在(0,)+∞上是增函数D. 偶函数，在(0,)+∞上是增函数15. 已知函数()f x 为R 上的单调函数，1()f x -是它的反函数，点(1,3)A -和点(1,1)B 均在函数()f x 的图像上，则不等式1|(2)|1x f -<的解集为（ ）A. (1,1)-B. (1,3)C. 2(0,log 3)D. 2(1,log 3)16. 设,,0x y z >，且12xyz y z ++=，则422log log log x y z ++的最大值为（ ）A. 3B. 4C. 5D. 6三. 解答题17. 已知910390x x -⨯+≤，求函数111()4()242x x y -=-+的最大值和最小值；18. 给定实数a ，0a ≠且1a ≠，设函数11x y ax -=-； （1）求证：经过这个函数图像上的任意两个不同的点的直线不平行于x 轴；（2）判断此函数的图像是否关于直线y x =对称，说明你的理由；19. 作出下列函数的大致图像；（1）3|log |||y x =；（2）12log (24)y x =+；20. 设a 是实数，函数()4|2|x xf x a =+-；（1）求证：()f x 不是奇函数；（2）当0a >时，求()f x 的值域；21. 设函数()n n f x x bx c =++，*n N ∈，b 、c R ∈； （1）设2n ≥，1b =，1c =-，证明：()n f x 在区间1(,1)2内存在唯一的零点； （2）设2n =，若对任意12,[1,1]x x ∈-，有2122|()()|4f x f x -≤，求b 的取值范围；参考答案一. 填空题1. 2x -(0)x ≤2.116 3. (,1)-∞- 4. (3)x > 5. (1,2] 6. 237. (1,2] 8. 1 9. 0 10. 3 11. 4 12. 2二. 选择题13. D 14. C 15. C 16. A三. 解答题17. max ()(0)2f x f ==，min ()(1)1f x f ==；18.（1）略；（2）1()()f x f x -=，是； 19. 略；20.（1）略；（2）当102a <<，值域为2[,)a +∞；当12a ≥，值域为1[,)4a -+∞； 21.（1）单调递增，1()02n f <，(1)0n f >；（2）[2,2]-；。

上海中学高一周练数学卷2016.12.29一. 填空题1. 若2(25)6255x xx =，则x =2. 方程22333330x x x ++--+=的解是3. 若11(,)22a k k ∈-+，k Z ∈，则称k 是与a 最接近的整数，设30.618n =，则与n 最 接近的整数是4. 已知()f x 是定义在R 上的偶函数，且在区间(,0)-∞上单调递增，若实数a 满足 |1|(2)(2)a f f ->，则a 的取值范围是5. 不等式lg ||0x x >的解是6. 函数22()log log )f x x x =的最小值为7. 已知1a b >>，若5log log 2a b b a +=，b a a b =，则a = 8. 若函数()||f x x a b =--+与()||g x x c d =-+的图像相交于点(2,5)和(8,3)，则 a c +=9. 已知集合{(,)|lg()lg lg }A x y x y x y =+=+，集合{(,)|,}B x y x R y k =∈=，若 A B =∅，则常数k 的取值范围是10. 函数20()1log 0x x f x x x ⎧--≤⎪=⎨>⎪⎩，则使得00()()f x f x =-成立的实数0x 的个数是 11. 指出函数44y x x=+--的单调性： 12. 函数32()8331f x x x x =---的零点是二. 选择题1. 设集合{|2,}x A y y x R ==∈，2{|10}B x x =-<，则A B =A. (1,1)-B. (0,1)C. (1,)-+∞D. (0,)+∞2. 函数21()log (1)f x x =+（0x >）的反函数1()f x -=A. 121x -(0)x >B. 121x -()x R ∈ C. 21x -()x R ∈ D. 21x -(0)x > 3. 设a 、b 都是不等于1的正数，则“333a b >>”是“log 3log 3a b <”的A. 充要条件B. 充分不必要条件C. 必要不充分件D. 既不充分也不必要条件4. 函数()y f x =的图像与函数()y g x =的图像关于直线0x y +=对称，则()y f x =的反 函数是A. ()y g x =B. ()y g x =-C. ()y g x =-D. ()y g x =--5. 已知函数()f x （x R ∈）满足()2()f x f x -=-，若函数1x y x+=与()y f x =图像的 交点为1122(,),(,),,(,)m m x y x y x y ⋅⋅⋅，则1122()()()m m x y x y x y ++++⋅⋅⋅++=A. 0B. mC. 2mD. 4m6. 方程组2332x y x y ⎧=⎪⎨=⎪⎩ A. 无解 B. 有且仅有一组解C.有不止一组的有限组解D. 有无穷多组解7. 函数1()lg 1x f x x-=+是 A. 是奇函数且在定义域上单调递增B. 是奇函数且在定义域上单调递减C. 是非奇非偶函数且在定义域上单调递增D. 是非奇非偶函数且在定义域上单调递减8. 某公司为激励创新，计划逐年加大研发资金投入，若该公司2015年全年投入研发资金130 万元，在此基础上，每年投入的研发资金比上一年增长12%，则该公司全年投入的研发资 金开始超过200万元的年份是A. 2018年B. 2019年C. 2020年D. 2021年参考答案一. 填空题1. 2±2. 2-或13. 04. 13(,)225. (1,0)(1,)-+∞6. 14- 7. 4a =，2b = 8.10 9. 1k ≤ 10. 2 11. 在[4,0)-和(0,4]上单调递减二. 选择题1. C2. A3. B4. D5. B6. B7. B8. B。

上海中学高一周练数学卷2017.1.5一. 填空题 1. (3)(6)y a a =-+63a -≤≤）的最大值为2. 方程1313313x x -+=-的实数解为 3. 函数()f x 的图像向右平移1个单位长度，所得图像与x y e =关于y 轴对称，则()f x =4. 已知函数()x f x a b =+（0a >，1a ≠）的定义域和值域都是[1,0]-，则a b +=5. 若方程2||4x kx x =+有四个不同的实数解，则k 的取值范围为 6. 已知()|3||2||3|f x x x x =-+-++，当2(32)(1)f a a f a -+=-时，则a 的取值范围为7. 若函数22()(1)()f x x x ax b =-++的图像关于直线2x =-对称，则()f x 的最大值是8. 如图所示，函数()y f x =的图像由两条射线和三条线段组成，若任意x R ∈， ()(1)f x f x >-，则正实数a 的取值范围为9. 设函数21()ln(1||)1f x x x =+-+，则使得()(21)f x f x >-成立的x 的取值范围是10. 已知3()2log f x x =+，[1,9]x ∈，则22[()]()y f x f x =+的最大值为11. 已知函数2()f x x x k =++（12x ≥-）与它的反函数1()f x -的图像有两个不同的交点， 则实数k 的取值范围为 12. 若函数()f x 满足2229122()(56)(1)(2)(3)x x f x x f x x x x x x -+---+=---恒成立，则 ()f x =二. 选择题13. 已知函数()f x =a 为常数且*a N ∈），对于定义域内的任意两个实数1x 、 2x ，恒有12|()()|1f x f x -<成立，则正整数a 的取值有（ ）A. 4个B. 5个C. 6个D. 7个14. 定义域为R 的函数()f x 满足：对任意1x 、2x 有1212()()()1f x x f x f x +=++，则下 列说法一定正确的是（ ）A. ()f x 为奇函数B. ()f x 为偶函数C. ()1f x +为奇函数D. ()1f x +为偶函数15. 函数2()()ax b f x x c +=+的图像如图所示，则下列结论成立的是（ ）A. 0a >，0b >，0c <B. 0a <，0b >，0c >C. 0a <，0b >，0c <D. 0a <，0b <，0c <16. 若a b c <<，则函数()()()()()()()f x x a x b x b x c x c x a =--+--+--的两个零点 分别位于区间（ ）A. (,)a b 和(,)b c 内B. (,)a -∞和(,)a b 内C. (,)b c 和(,)c +∞内D. (,)a -∞和(,)c +∞内三. 解答题17. 已知函数2()log (424)x xf x b =+⋅+，()g x x =；（1）当5b =-时，求()f x 的定义域；（2）若()()f x g x >恒成立，求b 的取值范围；18. 某轮船公司的一艘轮船每小时花费的燃料费与轮船航行速度的平方成正比，比例系数为k ，轮船的最大速度为15海里/小时，当船速为10海里/小时，它的燃料费是每小时96元，其余航行运作费用（不论速度如何）总计是每小时150元，假定运行过程中轮船以速度v 匀 速航行；（1）求k 的值；（2）求该轮船航行100海里的总费用W （燃料费+航行运作费用）的最小值；19. 若函数22()(1)|1|f x x a x a =++++-的最小值()g a 大于5；（1）求()g a 的表达式；（2）求a 的取值范围；20. 已知()||f x x x a b =-+，x R ∈； （1）当1a =，1b =时，若5(2)4x f =，求x 的值； （2）若0b <，且对任何[0,1]x ∈不等式()0f x <恒成立，求实数a 的取值范围；参考答案一. 填空题 1.92 2. 3log 4x = 3. 11x e + 4. 32- 5. 1(,)4+∞ 6. [0,3] 7. 16 8. 1(0,)6 9. 1(,1)310. 13 11. 1[,0)4- 12. 1x二. 选择题13. B 14. C 15. C 16. A三. 解答题17.（1）(,0)(2,)-∞+∞；（2）3b >-； 18.（1）0.96k =；（2）12.5v =时，min 2400W =； 19. 1146((,)---∞+∞； 20.（1）1x =-，212log x +=（2）略；。