2018届长春外国语学校高三上学期期末考试英语试题及答案

长春外国语学校2023-2024学年第一学期第二次月考高一年级数学试卷本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共4页.考试结束后，将答题卡交回.注意事项：1.答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区.2.选择题必须使用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚.3.请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效.4.作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑.5.保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀.第Ⅰ卷一、单项选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的．1. 函数()ln(12)f x x =-的定义域为（ ）A. 1,2⎛⎤-∞ ⎥⎝⎦B. 1,2⎛⎫-∞ ⎪⎝⎭C. 10,2⎛⎫ ⎪⎝⎭D. 1,2⎛⎫+∞⎪⎝⎭2. 实数0.2,a b c ===的大小关系正确的是（）A. a c b<< B. a b c<< C. b a c<< D. b<c<a 3. 已知对数函数()log a f x x =是增函数，则函数()1fx +的图象大致是（）.A.B.C. D.4. 已知函数2log ,0()91,0x x x f x x ->⎧=⎨+≤⎩，则31((1))(log )2f f f +的值是A. 2B. 3C. 5D. 75. 设()e ,0ln ,0x x g x x x ⎧≤=⎨>⎩，则关于x 的不等式()1g x ≤的解集是（ ）A. (],e -∞ B. (],1-∞ C. []0,e D. []0,16. 已知点(1,2)在α终边上，则cos α=（ ）A.B.C.23D.137. 已知α锐角，且cos 6πα⎛⎫+= ⎪⎝⎭，则tan 3πα⎛⎫-= ⎪⎝⎭（ ）A.B.C.D.8. 把物体放在冷空气中冷却，如果物体原来的温度为1θC ，空气的温度是0θC ，那么t 分钟后物体的温度θ（单位C ）可由公式：()010kteθθθθ-=+-求得，其中k 是一个随着物体与空气的接触状况而定的正常数.现有100℃的物体，放在20C 的空气中冷却，4分钟后物体的温度是60C ，则再经过（ ）分钟，物体的温度是40C （假设空气的温度保持不变）.A. 2B. 4C. 6D. 8二、多项选择题：本题共4小题，每小题5分，共20分．在每小题给出的选项中，有多项符合题目要求，全部选对的得5分，部分选对的得2分，有选错的得0分．9．下列选项中正确的是（ ）9. 下列选项中正确的是（ ）A. ()sin 3sin απα-= B. 7cos sin 2απα⎛⎫-=- ⎪⎝⎭C. ()tan tan απα--=- D. 5sin cos 2παα⎛⎫-= ⎪⎝⎭的为10. 下列所给函数中值域为()0,∞+的是（ ）A. ()23f x x-= B.()1xf x e=C. ()()23log 1f x x =+ D. ()15,01,0x x f x x x ⎧⎪>=⎨⎪-+≤⎩11. 若105a =，1020b =，则（ ）A. 4a b += B. lg 4b a -= C. 22lg 5ab < D. lg 5b a ->12. 下列正确的命题是（ ）A 5πlg sin 02⎛⎫⎛⎫=⎪ ⎪⎝⎭⎝⎭B 若()cos cos 2f x x =，则()sin 30f ︒=C. 若()1sin π2α+=-，则()1sin 4π2α-=-D. 若()tan π2α+=，则()()()()sin πcos π3sin πcos παααα-+-=+--第Ⅱ卷三、填空题：本题共4小题，每小题5分，共20分．13. 半径为2，面积等于45π的扇形的圆心角的大小是_________．14. 若函数5()log f x x =（0x >），则方程(1)(3)1f x f x ++-=的解x =________.15. 设函数()2222x x f x x x ⎧<=⎨≥⎩，，，若()()121f a f a +≤-，则实数a 的取值范围是__________.16. 已知定义在R 上的函数()f x 图像关于点1(,0)2中心对称，且当12x >时，1()f x x m x=++，若()f x 的值域为R ，则实数m 的取值范围为________．四、解答题：本题共6小题，共70分．第17题10分，其他每题12分，解答应写出文字说明、证明过程或演算步骤．17. （1）3log 2832lg 2lg 253log 9log 64+++⨯（2）2102329272()(3)(()483----++..18. 已知角α的终边落在直线4y x =-上，且0x ≤，求sin α，cos α，tan α的值．19. 已知1sin cos 5θθ+=，(0,)θπ∈，求下列各式的值．（1）sin cos θθ⋅；（2）sin cos θθ-．20. 已知函数3sin cos tan()22()cos()sin(3)x x x f x x x πππππ⎛⎫⎛⎫-+-- ⎪ ⎪⎝⎭⎝⎭=+-，且1()3f α=.（1）求2sin cos sin 2cos αααα-+的值；（2）求222sin sin cos cos αααα--的值.21. 已知定义在R 上的函数2()51x f x m =-+（1）判断并证明函数()f x 的单调性；（2）若()f x 是奇函数，求m 的值；（3）若()f x 的值域为D ，且[3,1]D ⊆-，求m 的取值范围．22. 已知函数()1lg 1xf x x -=+.（1）求不等式()()()lg20ff x f +>解集；（2）函数()()30,1xg x a a a =->≠，若存在[)12,0,1x x ∈，使得()()12f x g x =成立，求实数a 的取值范围.的长春外国语学校2023-2024学年第一学期第二次月考高一年级数学试卷出题人 ：赵宇审题人：王骏牧本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共4页.考试结束后，将答题卡交回.注意事项：1.答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区.2.选择题必须使用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚.3.请按照题号顺序在各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试题卷上答题无效.4.作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑.5.保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀.第Ⅰ卷一、单项选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题目要求的．1. 函数()ln(12)f x x =-的定义域为（ ）A. 1,2⎛⎤-∞ ⎥⎝⎦B. 1,2⎛⎫-∞ ⎪⎝⎭C. 10,2⎛⎫ ⎪⎝⎭D. 1,2⎛⎫+∞⎪⎝⎭【答案】B 【解析】【分析】使得式子有意义，列出不等式即可求解.【详解】定义域要求120x ->，即12x <.故选：B ．2. 实数0.2,a b c ===的大小关系正确的是（）A. a c b <<B. a b c<< C. b a c<< D. b<c<a【答案】C【解析】【分析】利用指数函数、对数函数的单调性可得到a b c 、、的范围从而得到答案.【详解】000.21a <=<=，0.20b =<=，1c =>=，所以b a c <<，故选：C.3. 已知对数函数()log a f x x =是增函数，则函数()1fx +图象大致是（）.A.B.C. D.【答案】B 【解析】【分析】利用代特殊点和对数函数的图像性质排除选项即可.【详解】由题意，1a >，()()1log 1afx x +=+，()()11f x f x -+=+，所以函数()1f x +是偶函数，当0x =时，()()01log 010af+=+=，故排除选项C 、D ，当0x >时，由对数函数的单调性，对数函数增长越来越慢，可排除选项A.故选：B【点睛】本题主要考查函数图像的识别和判断，利用函数的奇偶性和带入特殊值排除法是解题的关键，属于基础题.4. 已知函数2log ,0()91,0x x x f x x ->⎧=⎨+≤⎩，则31((1))(log )2f f f +的值是A. 2B. 3C. 5D. 7【答案】D 【解析】的【分析】根据给定的分段函数，按条件分段计算即可作答.【详解】函数2log ,0()91,0xx x f x x ->⎧=⎨+≤⎩，则2(1)log 10f ==，0((1))(0)912f f f ==+=，而331log log 202=-<，因此，33log 2log 222331(log )(log 2)91(3)12152f f =-=+=+=+=，所以31((1))(log 2572f f f +=+=故选：D5. 设()e ,0ln ,0x x g x x x ⎧≤=⎨>⎩，则关于x 不等式()1g x ≤的解集是（ ）A. (],e -∞B. (],1-∞C. []0,eD. []0,1【答案】A 【解析】【分析】分0x ≤、0x >解不等式()1g x ≤，综合可得出原不等式的解集.【详解】当0x ≤时，由()e 1xg x =≤可得0x ≤；当0x >时，由()ln 1g x x =≤可得0e x <≤.综上所述，不等式()g x 的解集为(],e -∞.故选：A.6. 已知点(1,2)在α的终边上，则cos α=（ ）A.B.C.23D.13【答案】B 【解析】【分析】根据终边上点，结合三角函数的定义求余弦值即可.【详解】由题设cos α==.故选：B7. 已知α为锐角，且cos 6πα⎛⎫+= ⎪⎝⎭，则tan 3πα⎛⎫-= ⎪⎝⎭（ ）A.B.C.D.的的【答案】D 【解析】【分析】注意到πππ632αα⎛⎫⎛⎫++-= ⎪ ⎪⎝⎭⎝⎭，利用同角三角函数的关系求角π6α+的正弦，再利用诱导公式求角π3α-的正弦、余弦，从而得到π3α-的正切.【详解】因为α为锐角，所以ππ2π,663α⎛⎫+∈ ⎪⎝⎭且πcos 6α⎛⎫+= ⎪⎝⎭，所以22πsin 06ππsin cos 166ααα⎧⎛⎫+> ⎪⎪⎪⎝⎭⎨⎛⎫⎛⎫⎪+++= ⎪ ⎪⎪⎝⎭⎝⎭⎩得πsin 6α⎛⎫+= ⎪⎝⎭由诱导公式得ππππsin sin cos 3266ααα⎡⎤⎛⎫⎛⎫⎛⎫-=-+=+=⎪ ⎪ ⎪⎢⎥⎝⎭⎝⎭⎝⎭⎣⎦，ππcos sin 36αα⎛⎫⎛⎫-=+=⎪ ⎪⎝⎭⎝⎭.所以πsin π3tan π3cos 3ααα⎛⎫- ⎪⎛⎫⎝⎭-=== ⎪⎛⎫⎝⎭- ⎪⎝⎭.故选:D8. 把物体放在冷空气中冷却，如果物体原来的温度为1θC ，空气的温度是0θC ，那么t 分钟后物体的温度θ（单位C ）可由公式：()010kteθθθθ-=+-求得，其中k 是一个随着物体与空气的接触状况而定的正常数.现有100℃的物体，放在20C 的空气中冷却，4分钟后物体的温度是60C ，则再经过（ ）分钟，物体的温度是40C （假设空气的温度保持不变）.A. 2 B. 4 C. 6 D. 8【答案】B 【解析】【分析】根据题意将数据120θ=o，0100θ= ，60θ= ，4t =代入()010kte θθθθ-=+-，可得1412k e -⎛⎫= ⎪⎝⎭，再将40θ =代入即可得8t =，即可得答案.【详解】由题意知：120θ=o，0100θ= ，60θ= ，4t =代入()010kte θθθθ-=+-得：()4602010020ke-=+-，解得1412k e -⎛⎫= ⎪⎝⎭所以当40θ =时，()1440201002012t ⎛⎫ -⎪⎭=+⎝，解得：124114212t ⎛⎫== ⎛⎫ ⎝⎪⎭⎪⎭⎝，所以8t =，所以再经过4分钟物体的温度是40C ， 故选：B【点睛】本题主要考查了指数函数的综合题，关键是弄清楚每个字母的含义，属于中档题.二、多项选择题：本题共4小题，每小题5分，共20分．在每小题给出的选项中，有多项符合题目要求，全部选对的得5分，部分选对的得2分，有选错的得0分．9．下列选项中正确的是（ ）9. 下列选项中正确的是（ ）A. ()sin 3sin απα-= B. 7cos sin 2απα⎛⎫-=- ⎪⎝⎭C. ()tan tan απα--=- D. 5sin cos 2παα⎛⎫-= ⎪⎝⎭【答案】BCD 【解析】【分析】利用诱导公式一一验证即可；【详解】解：sin(3)sin()sin()sin απαππαα-=-=--=-，故A 不正确；71cos cos sin 22απαπα⎛⎫⎛⎫-=+=- ⎪ ⎪⎝⎭⎝⎭，故B 正确；tan()tan()tan απαα--=-=-，故C 正确；51sin sin cos 22παπαα⎛⎫⎛⎫-=-= ⎪ ⎪⎝⎭⎝⎭，故D 正确.故选：BCD10. 下列所给函数中值域为()0,∞+的是（）A. ()23f x x-= B.()1xf x e=C. ()()23log 1f x x =+ D. ()15,01,0x x f x x x ⎧⎪>=⎨⎪-+≤⎩【答案】AD 【解析】【分析】A. 利用幂函数的性质判断；B.令 ()()1,00,t x=∈-∞⋃+∞，转化为指数函数判断；C. 令211t x =+≥，转化为对数函数判断；D. 分0x >和 0x ≤讨论求解判断.【详解】A. 因为()23f x x -=的定义域为{}|0x x ≠，因为函数在()0,∞+上是减函数且为偶函数，所以其值域是()0,∞+，故正确；B.令 ()()1,00,t x=∈-∞⋃+∞，则()()()10,11,x f x e =∈⋃+∞，故错误；C. 令211t x =+≥，则()()23log 1[0,)f x x =+∈+∞，故错误；D. 当0x >时，()()0,f x ∈+∞，当 0x ≤时，()[1,)f x ∈+∞，综上：()()0,f x ∈+∞，故正确；故选：AD11. 若105a =，1020b =，则（ ）A. 4a b += B. lg 4b a -= C. 22lg 5ab < D. lg 5b a ->【答案】BC 【解析】【分析】由105,1020a b ==，得lg 5,lg 20a b ==，再利用对数运算公式对,a b 进行a b +，b a -，ab 运算，从而可判断各选项.【详解】由105,1020a b ==，得lg 5,lg 20a b ==，则()lg 5lg 20lg 520lg1002a b +=+=⨯==，选项A 错误；20lg 20lg 5lglg 4lg 55b a -=-==<，选项B 正确，选项D 错误；()2lg 5lg 20lg 5lg 4lg 5lg 5lg 4lg 5ab =⨯=⨯+=⨯+，lg 4lg 5<Q ，222lg 5lg 4lg 5lg 5lg 5lg 52lg 5⨯+<⨯+=∴，22lg 5ab <∴ ，选项C 正确.故选：BC.12. 下列正确的命题是（ ）A. 5πlg sin 02⎛⎫⎛⎫= ⎪ ⎪⎝⎭⎝⎭B. 若()cos cos 2f x x =，则()sin 30f ︒=C. 若()1sin π2α+=-，则()1sin 4π2α-=-D. 若()tan π2α+=，则()()()()sin πcos π3sin πcos παααα-+-=+--【答案】ACD【解析】【分析】运用诱导公式、特殊角的三角函数值及同角三角函数的商数关系即可求得各个选项.【详解】对于A 项，5ππlg sin lg sin lg1022⎛⎫⎛⎫⎛⎫⎛⎫=== ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭⎝⎭，故A 项正确；对于B 项，因为()cos cos 2f x x =，所以1(sin 30)(cos 60)cos1202f f ︒︒︒===-，故B 项错误；对于C 项，因为()1sin πsin 2αα+=-=-，所以1sin 2α=，所以()1sin 4πsin()sin 2ααα-=-=-=-，故C 项正确；对于D 项，因为()tan πtan 2αα+==，所以()()()()sin πcos πsin cos sin cos tan 1213sin πcos πsin cos sin cos tan 121αααααααααααααα-+---+++=====+---+---，故D 项正确.故选：ACD.第Ⅱ卷三、填空题：本题共4小题，每小题5分，共20分．13. 半径为2，面积等于45π的扇形的圆心角的大小是_________．【答案】25π【解析】【分析】根据扇形面积公式即可求出．【详解】设扇形的圆心角的大小为α，由212S r α=可得，241252πα=⨯⨯，解得25πα=．故答案为：25π．14. 若函数5()log f x x =（0x >），则方程(1)(3)1f x f x ++-=的解x =________.【答案】4.【解析】【分析】根据对数的运算性质，可得(1)(3)5x x +-=，解得答案．【详解】解：因为5()log f x x =，所以()()555(1)(3)log 1log 3log (1)(3)f x f x x x x x ++-=++-=+-，5(1)(3)log (1)(3)1f x f x x x ++-=+-= 即(1)(3)5x x +-=，所以4x =或2x =-（舍去），故答案为：4．【点睛】本题考查对数函数的图象和性质，二次函数的图象和性质，属于基础题．15. 设函数()2222x x f x x x ⎧<=⎨≥⎩，，，若()()121f a f a +≤-，则实数a 的取值范围是__________.【答案】[2,)+∞【解析】【分析】根据指数函数和幂函数的性质可得()f x 在R 上为增函数，利用函数的单调性解不等式即可得解.【详解】由于当2x <时，()2xf x =为增函数，且()()24f x f <=，由于当2x ≥时，()2f x x =为增函数，且()()24f x f ≥=，∴()f x 在R 上为增函数，∵()()121f a f a +≤-，∴121a a +≤-，解得2a ≥，所以实数a 的取值范围为[2,)+∞，故答案为：[2,)+∞．16. 已知定义在R 上的函数()f x 图像关于点1(,0)2中心对称，且当12x >时，1()f x x m x =++，若()f x 的值域为R ，则实数m 的取值范围为________．【答案】(,2]-∞-【解析】【分析】由题可得函数()f x 关于点1,02⎛⎫⎪⎝⎭对称，进而可得当12x >时，1()0f x x m x =++≤有解，利用基本不等式即得.【详解】∵定义在R 上的函数()f x 满足1122f x f x ⎛⎫⎛⎫-=-+ ⎪ ⎪⎝⎭⎝⎭，∴函数()f x 关于点1,02⎛⎫⎪⎝⎭对称，又当12x >时，1()f x x m x =++，在1,12x ⎛⎫∈ ⎪⎝⎭，()f x 单调递减，当()1,x ∈+∞，()f x 单调递增，要使函数()f x 的值域为R ，则当12x >时，1()0f x x m x=++≤有解，又当12x >时，12x m m m x ++≥=+，当且仅当1x x =，即1x =取等号，∴20m +≤，即实数m 的取值范围为(,2]-∞-.故答案为：(,2]-∞-.四、解答题：本题共6小题，共70分．第17题10分，其他每题12分，解答应写出文字说明、证明过程或演算步骤．17. （1）3log 2832lg 2lg 253log 9log 64+++⨯（2）2102329272()(3)(()483----++【答案】（1）8 ；（2）132【解析】【分析】（1）利用对数运算性质化简即可得出答案（2）利用指数运算性质化简即可得到答案.【详解】(1)原式6232=lg 4lg 252log 3log 23+++⨯2lg100263=++⨯2248=++=；(2)原式34413162992=--++=18. 已知角α的终边落在直线4y x =-上，且0x ≤，求sin α，cos α，tan α的值．【答案】sin α=，cos α=tan 4α=-.【解析】【分析】根据给定条件，求出角α的终边上一个点的坐标，再利用三角函数定义求解即得.【详解】角α的终边落在直线4y x =-上，且0x ≤，取角α的终边上的点(1,4)P -，则||r OP ===，所以sin α==cos α==；4tan 41α==--.19. 已知1sin cos 5θθ+=，(0,)θπ∈，求下列各式的值．（1）sin cos θθ⋅；（2）sin cos θθ-．【答案】（1）1225-；（2）75．【解析】【分析】（1）由1sin cos ,(0,)5θθθπ+=∈，利用三角函数的基本关系式，即可求解；（2）由（1）知sin cos 0θθ⋅<，得出可得sin θcos θ0->，结合三角函数的基本关系式，即可求解.【详解】（1）由题意知1sin cos ,(0,)5θθθπ+=∈，可得21(sin cos )12sin cos 25θθθθ+=+⋅=，解得12sin cos 25θθ⋅=-．（2）由（1）知12sin cos 025θθ⋅=-<，所以sin 0,cos 0θθ><，可得sin θcos θ0->，所以sin cos θθ-===75=．20. 已知函数3sin cos tan()22()cos()sin(3)x x x f x x x πππππ⎛⎫⎛⎫-+-- ⎪ ⎪⎝⎭⎝⎭=+-，且1()3f α=.（1）求2sin cos sin 2cos αααα-+的值；（2）求222sin sin cos cos αααα--的值.【答案】（1）17-；（2）-1.【解析】【分析】（1）用诱导公式化简函数得()tan f x x =，已知条件为1tan 3α=，然后求值式利用弦化切法化为正切的函数，再求值；（2）由“1”的代换得2222222sin sin cos cos 2sin sin cos cos sin cos αααααααααα----=+，然后分子分母同除以2cos αtan α的函数再代入求值．【详解】（1）cos sin (tan )()tan cos sin x x x f x x x x -==- ∵1()3f α=，∴1tan 3α= 2sin cos 2tan 1sin 2cos tan 2αααααα--=++121131723⨯-==-+（2）2222222sin sin cos cos 2sin sin cos cos sin cos αααααααααα----=+2211212tan tan 19311tan 119ααα⨯----===-++．【点睛】本题考查诱导公式，考查同角间三角函数关系，齐次式求值问题．关于sin ,cos αα的齐次分式均可化为关于tan α的函数求值．21. 已知定义在R 上的函数2()51x f x m =-+（1）判断并证明函数()f x 的单调性；的（2）若()f x 是奇函数，求m 的值；（3）若()f x 的值域为D ，且[3,1]D ⊆-，求m 的取值范围．【答案】（1）见解析；（2）1；（3）[1,1]-【解析】【分析】（1）利用函数单调性的定义进行证明即可；（2）利用函数奇偶性的定义求解即可；（3）求出函数的值域，利用子集关系求解即可.【小问1详解】证明：设12x x <且12,x x R∈则()()()()()121212122552251515151x x x x x x f x f x m m -⎛⎫-=---= ⎪++++⎝⎭121212510,510,550x x x x x x <∴+>+>-< ()()120f x f x -<即()()12f x f x <()f x 在R 上单调递增【小问2详解】()f x 是R 上的奇函数，22()()05151x x f x f x m m -+-=-+-=++即225202205151x x x m m ⎛⎫⨯-+=⇒-= ⎪++⎝⎭1m =【小问3详解】由22500225151x x x m m m >⇒<<⇒-<-<++(2,)D m m =-，[3,1]D ⊆-23111m m m -≥-⎧⇒-≤≤⎨≤⎩m 的取值范围是[1,1]-22. 已知函数()1lg1x f x x -=+.（1）求不等式()()()lg20f f x f +>的解集；（2）函数()()30,1x g x aa a =->≠，若存在[)12,0,1x x ∈，使得()()12f x g x =成立，求实数a 的取值范围.【答案】（1）19,311⎛⎫ ⎪⎝⎭（2）()3,+∞【解析】【分析】（1）求得()f x 的定义域和值域及函数的单调性，得1111012x x -<<+，解不等式即可得到所求范围；（2）求得当01x ≤<时，()f x 的值域；以及讨论1a >，01a <<时()g x 的值域，由题意可得()f x 和()g x 的值域存在交集，即可得到所求范围；【小问1详解】由101x x ->+，可得11x -<<，故函数定义域为()1,1-，关于原点对称，又()()11lg lg 11x x f x f x x x +--==-=--+，即()f x 为奇函数.又()()1212lg lg lg 1111x x f x x x x -++-⎛⎫===-+ ⎪+++⎝⎭，函数211y x =-++在()1,1-上单调递减，值域()0,∞+.由复合函数的单调性质知()f x 在()1,1-上单调递减，且()f x 的值域为R ，不等式()()()lg20f f x f +>，转化为()()()lg2f f x f >-，因为()f x 为奇函数，所以()()()()lg2lg2ff x f f >-=-，因为()f x 在()1,1-上单调递减，所以()1lg2f x -<<-，即11lg lg21x x --<<-+，即1111012x x -<<+，即111102x x x ++<-<，解得19311x <<，为则原不等式的解集为19,311⎛⎫ ⎪⎝⎭.【小问2详解】因为存在[)12,0,1x x ∈，使得()()12f x g x =成立，所以[)0,1x ∈时，()f x 的值域与()g x 的值域有交集.因为()2lg 11f x x ⎛⎫=-+ ⎪+⎝⎭在[)0,1上是减函数，()01f =，所以()f x 的值域为(],0-∞，当1a >时，()3xg x a =-在[)0,1上单调递减，故()g x 的值域为(]3,2a -，所以30a -<即3a >，当01a <<时，()3xg x a =-在[)0,1上单调递增，故()g x 的值域为[)2,3a -，不符.综上所述，实数a 的取值范围为()3,+∞.。

长春外国语学校2021-2022学年第一学期期末考试高一年级英语试卷本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

考试结束后，将答题卡交回。

注意事项：1.答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2.选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

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

4.作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。

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

第Ⅰ卷第一部分: 听力（共20小题，满分30 分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一小题，从题中所给的A、B、C 三个选项选出最佳答案。

每段对话仅读一遍。

1. When can the woman have her hair cut?A. On Thursday morning.B. On Thursday afternoon.C. On Friday afternoon.2. What color does the man prefer?A. Orange.B. Pink.C. Yellow.3. Where will the speakers take Jerry for lunch?A. In a cafe.B. In a bar.C. In a restaurant.4. What does the woman think is the most important to friendship?A. Understanding.B. Similarity.C. Honesty.5. What did the man think of the festival?A. Most of it was great.B. Everything about it was excellent.C. The dance music was better than last year.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。

绝密★启用前吉林省长春市外国语学校2020-2021学年八年级下学期期末英语试题试卷副标题注意事项：1．答题前填写好自己的姓名、班级、考号等信息 2．请将答案正确填写在答题卡上第I 卷（选择题）请点击修改第I 卷的文字说明一、单项选择 1．I enjoy having ________ breakfast with my family at home. It makes me feel relaxed. A ．aB ．anC ．theD ．/2．The little kids ran to their parents with ________ at the school gate after school. A ．excitementB ．progressC ．experienceD ．development3．He won’t borrow money from his friends ________ he really has to. A ．whenB ．sinceC ．becauseD ．unless4．As soon as he ________ in Guangzhou next Monday, he will call me. A ．will arrive B ．arrives C ．is arrivingD ．arrived5．—I never thought she would ________ my invitation to the concert. —What a pity! She would feel sorry for missing the concert some day. A ．remindB ．refuseC ．supposeD ．accept6．One of the oldest museums in the small town ________ here for over twenty years. A ．has beenB ．have beenC ．has goneD ．have gone7．—I haven't been to the Palace Museum. What about you? — I am planning to go there this weekend. A ．Me tooB ．Me neitherC ．So did ID ．Neither did I8．---I don't want to ______ my old friends.---You can still communicate with them after going to a new school. A ．clear outB ．check outC ．help withD ．part with9．—________ is the population of Changchun City? —It’s over nine million. A ．How manyB ．How muchC ．WhatD ．How10．How long have you .here? For two days. I ________ here the day before yesterday. A ．been; cameB ．come; cameC ．came; cameD ．come; was11．________ wonderful music Lang Lang and Gina played just now! A ．WhatB ．What aC ．HowD ．How a12．________ a job you love, and you’ll never work a day in your life. A ．FindB ．FindingC ．To findD ．Found13．No ocean in the world is as ________ as the Pacific Ocean. A ．bigB ．biggerC ．biggestD ．the biggest14．—What else did Tina ask you about the trip to Nanjing? —She asked me ______. A ．who was the guide of the tripB ．when they will visit the Presidential PalaceC ．how long would they stay at Nanjing MuseumD ．if she can go to Nanjing University alone on the second day 15．—Shall we make a cake for Tina as a birthday gift? —________. It will give her a big surprise. A ．It’s a pityB ．Good ideaC ．You’re welcomeD ．Never mind二、补全对话6选5 根据对话内容，运用方框中所给的句子补全对话。

长春外国语学校2018届高三数学上学期期末试卷（文科带答案）长春外国语学校2017-2018学年第一学期期末考试高三年级数学试卷（文科）出题人：姜海军审题人：于海君本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，共6页。

考试结束后，将答题卡交回。

注意事项：1.答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

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

4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。

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

第Ⅰ卷一、选择题：本题共12小题，每小题5分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1.已知集合()A.B.C.D.2.已知复数满足,则对应的点位于（）A.第一象限B.第二象限C.第三象限D.第四象限3.已知且与的夹角为,则为（）A.B.C.D.4.某几何体的三视图如图所示,则该几何体的表面积为（）A.B.C.D.5.已知命题:,使得，命题:,，则下列命题为真命题的是（）A.B.C.D.6.运行如图所示的程序框图，若输出的是，则①应为A.B．C．D．7.若实数满足求的最大值()A.B.C.D.8.已知,则的值为（）A.B.C.D.9.已知抛物线上点到焦点的距离为3,则点到轴的距离是（）A.B.1C.D.210.若函数的零点为，若,则的值满足（）A.B.C.D.的符号不确定11.已知是双曲线的左右焦点,点是上一点,若,且的最小内角为,则双曲线的离心率为（）A.B.C.D.12.已知函数,若函数有唯一零点,则下列说法错误的是（）A.B.函数在处的切线与直线平行C.函数在上的最大值为D.函数在上单调递减第Ⅱ卷二、填空题：本题共4小题，每小题5分。

吉林长春外国语学校18-19学度高二下学期3月抽考-英语2017—2018学年第二学期第一次月考考试高二年级英语试卷出题人：卢春红审题人：许艳君代春梅〔说明：考试时间：100分钟总分值：110分〕第一部分：听力〔共15小题，总分值15分〕听下面几段材料，回答第1至5题。

1.Whatdoesthemanwanttobuy?A.Asuit.B.Ashirt.C.Atie2.Wheredoestheconversationprobablytakeplace?A. Inadoctor’soffice.B. Inahotel.C. Inashoeshop.3.Whenwillthelecturebegin?A.At8:15.B.At7:45.C.At8:00.4.Whatarethespeakerstalkingabout?A.Theboy’sholiday.B.Theboy’swork.C.Theboy’sChineselessons.5.Howmuchdoesthewomanhavetopayforthetickets?A.100yuan.B.200yuan.C.300yuan.听第6段材料，回答第6,7题。

6.Whatwillthemanbuyforhissister?A.Anecklace.B.Awatch.C.Apairofearrings.7.Howmuchwillthemanpay?A.$3,500.B.$3,150.C.$3,850.听第7段材料，回答第8,9题。

8.Howmuchisaguitarlesson?A.30poundsperhour.B.26.5poundsperhour.C.17.5poundsperhour.9.Wheredoesthemanhavehisguitarlessons?A.Attheteacher’shouse.B.Athisownhouse.C.AttheChildren’sPalace.听第8段材料，回答第10至12题。

长春外国语学校2022-2023学年第一学期第一次月考初三年级英语试卷本试卷包括共五道大题，共10页。

全卷满分120分。

考试时间为100分钟。

考试结束后，将答题卡交回。

注意事项：1. 答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在考生信息条形码粘贴区。

2．选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整、笔迹清楚。

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

4．保持卡面清洁，不要折叠，不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀听力部分（共25分）I.听句子，根据所听内容选择合适的应答语。

句子读两遍。

（5分）1. A. Thank you. B. No problem. C. It’s nothing.2. A. Have fun. B. Never mind. C. Not yet.3. A. It’s done. B. It’s over there. C. No way.4. A. Me neither. B. So are you. C. I’m fine.5. A. Good idea. B. No big deal. C. That’s right.II. 听对话和问题，根据所听内容选择最佳答案。

对话和问题读两遍。

（5分）6.A. It’s noisy. B. It’s big. C. It’s great.7. A. In the library. B. In the office. C. In the morning.8. A. Tall with a hat. B. Short with glasses. C. Tall with glasses.9. A. A pair of socks. B. A baseball team. C. A basketball team.10. A. In his father’s car. B. By bike. C. By school bus. III.听描述，选出与其相符的图片，其中有一幅图片是多余的。

吉林省长春市朝阳区长春外国语学校2024-2025学年七年级上学期9月月考英语试题一、单词拼写1．Next week is f for me. I have lots of things to do.2．China is a great c . It has a great history of over 5000 years.3．Don’t be afraid of making m when you learn English.4．Jack has a t brother. They look the same.5．I am a t fan and Zheng Qinwen is my favorite star.6．The new book has many p . I can’t finish (完成) reading it on time.7．If you need, you can look for any i on the Internet.8．I like b best. It’s the color of sky.9．Please c from one to twenty in English.10．Good friends should always help each o in study.11．Look at the girl over there. (she) name is Lucy.12．There (be) a pair of shoes under the bed.13．My (hobby) are reading and running.14．Tim (not be) short now. He is growing taller and taller.15．Boys and girls, please (keep) the classroom tidy in school.16．What’s (these) in English?It’s a cap.17．My brother (like) sharing his toys with other children.18．Here is our school library. Let (I) show you around.19．After school, I’d like (go) home by bus.20．How many (potato) can you see in the picture?二、单项选择21．Lucy can play ________ violin, but she doesn’t like playing ________ chess.A．the, a B．/, the C．the, /D．a, the 22．—What are ________ over there?—________ are the school computers.A．these, These B．those, They C．they, These D．those, Those 23．Our new teacher comes ________ the UK and he lives in China ________ his parents now.A．in, with B．from, with C．for, in D．to, from24．I don’t want to eat ________ but my sister ________.A．chickens, does B．chicken, want C．chicken, does D．chickens, wants 25．Miss Wang and Miss Sun ________ me. They ________ very nice.A．both like, are both B．are all like, are both C．both like, both areD．all like, are both26．—Is this ________ family photo?—Yes, it is. And in the middle are their grandparents.A．Lily and Frank B．Lily’s and Frank’s C．Lily and Frank’s D．Lily’s and Frank 27．The film is very interesting and we like it ________.A．a lot B．a little C．very often D．every day 28．— We’re free this afternoon. Let’s ________ for a walk in the park.— OK! That sounds great.A．to go B．going C．goes D．go29．Tom is in Class One. His brother is in Class Two. They are in ________.A．the same class B．the same room C．different classes D．different class 30．—________ sweater is this?—Sarah’s.A．Who B．Whose C．What D．Where 31．—Mary, ________ is Li Lei. ________ is my good friend.—Nice to meet you, Li Lei.A．he, This B．this, He C．it, He D．she, It 32．—Are those your brothers?—________ They are my friends.A．Yes, they are.B．No, they aren’t.C．Yes, he is.D．No, he isn’t. 33．Be kind to the people around you, and ________ will be kind to you, too.A．he B．she C．they D．we34．I sit ________ Lily. She is in front of me.A．behind B．in front of C．next to D．between35．— Would you like something to eat?— ________ I’m full.A．Yes, please.B．No, thanks.C．Yes, I would.D．That’s OK.三、完形填空The Greens have two sons. Their 36 are Nick and Jack. Aunt Tina 37 them at 782-0910 now. Nick answers the phone. “Hello? This is Nick. 38 is that?”“This is Aunt Tina. Nick, can you tell me what your favorite color 39 ? I want to buy a 40 for you.” Aunt Tina says on the 41 . Nick says he likes 42 .“OK,” says Aunt Tina, “I see a jacket in the shop this morning, It’s 43 . I want to buy 44 . One is for you and one is for Jack. But I can’t decide the 45 . Now I know I will buy green ones.”“No, no, no...Aunt Tina, I like green but Jack 46 .” says Nick. “Oh? What color does he like?” 47 Aunt Tina. “Black.”“Oh, you are 48 , but you are 49 , I see! I will buy a green one and a black one. See you 50 afternoon!” says Aunt Tina.36．A．boxes B．names C．families D．pictures 37．A．calls B．sees C．e-mails D．finds 38．A．What B．How C．Who D．Where 39．A．be B．are C．am D．is40．A．book B．cup C．jacket D．hat 41．A．radio B．TV C．plane D．phone 42．A．green B．red C．black D．brown 43．A．everywhere B．English C．next D．nice44．A．two B．three C．four D．five45．A．set B．color C．day D．head 46．A．does B．doesn’t C．is D．isn’t 47．A．asks B．spells C．thinks D．speaks48．A．cousins B．friends C．brothers D．sisters 49．A．same B．difficult C．good D．different 50．A．today B．the C．this D．here四、阅读理解Hi, my name is Eric. There are four things in my room.51．What color is the cap?A．Yellow and blue.B．Yellow and black.C．Black and blue.D．Green and black.52．Where is the model plane now?A．In the bookcase.B．On the bed.C．In the schoolbag.D．On the chair.53．What are NOT in the schoolbag?A．The notebooks.B．The books.C．The pens.D．The pencils. 54．Which(哪一些) things are Eric’s?①The radio. ①The schoolbag.①The cap.①The model plane.A．①①①B．①①①C．①①①D．①①①55．From the above(上述的) information, we can know ________.A．Eric can use the radio B．Eric has a yellow schoolbagC．Eric is Anna’s brother D．the cap is in the bookcase① Hello, I’m Bob. I’m 12 years old. I am at school. I want to say something about me.① Playing soccer is my hobby. I like it very much. I always play soccer with my friends after school. It’s relaxing for me. I have five soccer balls. They are under my desk. And I like to watch soccer games on TV.① I like some food. I have eggs, milk and some fruit for breakfast. For lunch, I have hamburgers and some salad. For dinner, I have chicken and some vegetables. I don’t eat ice-cream. It’s not healthy. My favorite food is fruit and vegetables. I think they are good for our health.① I’m healthy because I like to play sports and eat healthy food. What about you? Can you tell me about your hobby and eating habits?阅读短文，根据短文内容选择最佳答案。

2017-2018学年吉林省长春外国语学校高一（上）期中数学试卷一、选择题：本题共12小题，每小题5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．（5分）设全集U={0，1，2，3，4}，集合A={1，2，3}，B={2，3，4}，则A ∩（∁U B）=（）A．{0}B．{1}C．{0，1}D．{0，1，2，3，4}2．（5分）已知集合A={x|x2﹣1=0}，则下列式子表示正确的有（）①1∈A②{1}∈A③∅⊆A④{1，﹣1}⊆A．A．1个 B．2个 C．3个 D．4个3．（5分）下列函数中，在区间（0，+∞）上为增函数的是（）A．f（x）=|x|﹣4 B．y=C．y= D．4．（5分）下列函数中，是同一函数的是（）A．B．y=x2与y=x|x|C．D．y=x2+1与y=t2+15．（5分）函数f（x）=（x﹣）0+的定义域为（）A．B．[﹣2，+∞）C．D．6．（5分）已知a=log20.3，b=20.3，c=0.30.2，则a，b，c三者的大小关系是（）A．a＞b＞c B．b＞a＞c C．b＞c＞a D．c＞b＞a7．（5分）已知函数f（x）=ax2+bx+3a+b是偶函数，且其定义域为[a﹣1，2a]，则（）A．，b=0 B．a=﹣1，b=0 C．a=1，b=1 D．a=，b=﹣18．（5分）已知f（x）=，则f（3）=（）A．3 B．2 C．4 D．59．（5分）若函数y=x2+（2a﹣1）x+1在区间（﹣∞，2]上是减函数，则实数a 的取值范围是（）A．[﹣，+∞）B．（﹣∞，﹣]C．[，+∞）D．（﹣∞，]10．（5分）函数y=（x＞0）的值域为（）A．（﹣，+∞）B．（﹣1，2）C．{y|y≠2}D．{y|y＞2}11．（5分）函数y=a x﹣a（a＞0，a≠1）的图象可能是（）A．B． C．D．12．（5分）设函数则使得f（﹣1）+f（m﹣1）=1成立的m的值为（）A．10 B．0，﹣2 C．0，﹣2，10 D．1，﹣1，11二、填空题：本题共4小题，每小题5分．13．（5分）已知f（2x+1）=x2﹣2x，则f（3）=．14．（5分）若x1，x2是方程2x2﹣4x+1=0的两个根，则=．15．（5分）若指数函数f（x）=（2a+1）x在R上的减函数，则a的取值范围是．16．（5分）设函数f（x）=是定义在（﹣∞，+∞）上是减函数，则a的取值范围是．三、解答题：共6小题，共70分.解答应写出必要证明过程或演算步骤.17．（10分）计算：（1）×．18．（12分）设全集为U={x|x≤4}，A={x|x2+x﹣2＜0}，B={x|x（x﹣1）≥0}．求：（1）A∩B；（2）A∪B；（3）∁U（A∩B）．19．（12分）已知函数f（x）是定义在R上的偶函数，且当x≤0时，f（x）=x2+2x．（1）现已画出函数f（x）在y轴左侧的图象，如图所示，请补出完整函数f（x）的图象，并根据图象写出函数f（x）的增区间；（2）写出函数f（x）的解析式和值域；（3）若方程f（x）﹣m=0有四个解，求m的范围．20．（12分）已知函数．（1）求函数f（x）的定义域；（2）求f（1），f（﹣1），f（2），f（﹣2）；（3）判断并证明f（x）的奇偶性．21．（12分）已知f（x）=16x﹣2×4x+5，x∈[﹣1，2]（1）若f（x）=4，求x；（2）求f（x）的最大值与最小值．22．（12分）若f（x）是定义在（0，+∞）上的函数，当x＞1时，f（x）＞0，且满足．（1）求f（1）的值；（2）判断并证明函数的单调性；（3）若f（2）=1，解不等式．2017-2018学年吉林省长春外国语学校高一（上）期中数学试卷参考答案与试题解析一、选择题：本题共12小题，每小题5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．（5分）设全集U={0，1，2，3，4}，集合A={1，2，3}，B={2，3，4}，则A ∩（∁U B）=（）A．{0}B．{1}C．{0，1}D．{0，1，2，3，4}【解答】解：全集U={0，1，2，3，4}，集合A={1，2，3}，B={2，3，4}，∴∁U B={0，1}，∴A∩（∁U B）={1}．故选：B．2．（5分）已知集合A={x|x2﹣1=0}，则下列式子表示正确的有（）①1∈A②{1}∈A③∅⊆A④{1，﹣1}⊆A．A．1个 B．2个 C．3个 D．4个【解答】解：因为A={x|x2﹣1=0}，∴A={﹣1，1}对于①1∈A显然正确；对于②{1}∈A，是集合与集合之间的关系，显然用∈不对；对③∅⊆A，根据集合与集合之间的关系易知正确；对④{1，﹣1}⊆A．同上可知正确．故选：C．3．（5分）下列函数中，在区间（0，+∞）上为增函数的是（）A．f（x）=|x|﹣4 B．y=C．y= D．【解答】解：在A中，f（x）=|x|﹣4在区间（0，+∞）上为增函数，故A正确；在B中，y=﹣在区间（0，+∞）上为减函数，故B错误；在C中，在区间（0，+∞）上为减函数，故C错误；在D中，在区间（0，1）上是减函数，在（1，+∞）上为增函数，故D 错误．故选：A．4．（5分）下列函数中，是同一函数的是（）A．B．y=x2与y=x|x|C．D．y=x2+1与y=t2+1【解答】解：∵=|x|，与y=x的对应关系不同，∴两函数不是同一函数，故A错误；∵y=x|x|=，与y=x2两函数对应关系不同，∴两函数不是同一函数，故B错误；∵（x≠1），与y=x+3的定义域不同，∴两函数不是同一函数，故C错误；y=x2+1与y=t2+1为相同函数，故D正确．故选：D．5．（5分）函数f（x）=（x﹣）0+的定义域为（）A．B．[﹣2，+∞）C．D．【解答】解：要使函数有意义，则，即，即x≥﹣2且x≠，即函数的定义域为，故选：C．6．（5分）已知a=log20.3，b=20.3，c=0.30.2，则a，b，c三者的大小关系是（）A．a＞b＞c B．b＞a＞c C．b＞c＞a D．c＞b＞a【解答】解：∵a=log20.3＜log21=0，b=20.3＞20=1，0＜c=0.30.2＜0.30=1，∴b＞c＞a．故选：C．7．（5分）已知函数f（x）=ax2+bx+3a+b是偶函数，且其定义域为[a﹣1，2a]，则（）A．，b=0 B．a=﹣1，b=0 C．a=1，b=1 D．a=，b=﹣1【解答】解：因为f（x）=ax2+bx+3a+b是偶函数，所以定义域关于原点对称，所以a﹣1+2a=0，解得a=．所以f（x）=x2+bx+1+b，因为函数为偶函数，所以f（﹣x）=f（x），即）x2﹣bx+1+b=x2+bx+1+b，所以2bx=0，解得b=0．故选：A．8．（5分）已知f（x）=，则f（3）=（）A．3 B．2 C．4 D．5【解答】解：f（x）=，则f（3）=f（2+3）=f（5）=f（2+5）=f（7）=7﹣5=2．故选：B．9．（5分）若函数y=x2+（2a﹣1）x+1在区间（﹣∞，2]上是减函数，则实数a 的取值范围是（）A．[﹣，+∞）B．（﹣∞，﹣]C．[，+∞）D．（﹣∞，]【解答】解：∵函数y=x2+（2a﹣1）x+1的图象是方向朝上，以直线x=为对称轴的抛物线又∵函数在区间（﹣∞，2]上是减函数，故2≤解得a≤﹣故选：B．10．（5分）函数y=（x＞0）的值域为（）A．（﹣，+∞）B．（﹣1，2）C．{y|y≠2}D．{y|y＞2}【解答】解：y==2﹣．∵x＞0，∴x+1＞1，∴0＜＜1，∴﹣1＜2﹣＜2．∴函数y=（x＞0）的值域为（﹣1，2）．故选：B．11．（5分）函数y=a x﹣a（a＞0，a≠1）的图象可能是（）A．B． C．D．【解答】解：由于当x=1时，y=0，即函数y=a x﹣a 的图象过点（1，0），故排除A、B、D．故选：C．12．（5分）设函数则使得f（﹣1）+f（m﹣1）=1成立的m的值为（）A．10 B．0，﹣2 C．0，﹣2，10 D．1，﹣1，11【解答】解：∵函数∴f（﹣1）=（﹣1+1）2=0，∵f（﹣1）+f（m﹣1）=1，∴f（m﹣1）=1，当m﹣1＜1时，f（m﹣1）=m2=1，解得m=1或m=﹣1；当m﹣1≥1时，f（m﹣1）=4﹣=1，解得m=11．综上，m的值为1，﹣1，11．故选：D．二、填空题：本题共4小题，每小题5分．13．（5分）已知f（2x+1）=x2﹣2x，则f（3）=﹣1．【解答】解：【方法一】∵f（2x+1）=x2﹣2x，设2x+1=t，则x=，∴f（t）=﹣2×=t2﹣t+，∴f（3）=×32﹣×3+=﹣1．【方法二】∵f（2x+1）=x2﹣2x，令2x+1=3，解得x=1，∴f（3）=12﹣2×1=﹣1．故答案为：﹣1．14．（5分）若x1，x2是方程2x2﹣4x+1=0的两个根，则=4．【解答】解：∵x1，x2是方程2x2﹣4x+1=0的两个根，∴x1+x2=2，x1•x2=，∴===4，故答案为：415．（5分）若指数函数f（x）=（2a+1）x在R上的减函数，则a的取值范围是（，0）．【解答】解：因为指数函数f（x）=（2a+1）x在R上的减函数，则0＜2a+1＜1，解得＜a＜0．故答案为：（，0）．16．（5分）设函数f（x）=是定义在（﹣∞，+∞）上是减函数，则a的取值范围是[，）．【解答】解：由题意可得，求得≤a＜，故答案为：[，）．三、解答题：共6小题，共70分.解答应写出必要证明过程或演算步骤.17．（10分）计算：（1）×．【解答】解：1）×=﹣4﹣1+0.5×4=﹣3=lg5+lg2﹣lg0.1﹣2=1+﹣2=﹣．18．（12分）设全集为U={x|x≤4}，A={x|x2+x﹣2＜0}，B={x|x（x﹣1）≥0}．求：（1）A∩B；（2）A∪B；（3）∁U（A∩B）．【解答】解：全集为U={x|x≤4}，A={x|x2+x﹣2＜0}={x|﹣2＜x＜1}，B={x|x（x﹣1）≥0}={x|x≤0或x≥1}；（1）A∩B={x|﹣2＜x＜1}∩{x|x≤0或x≥1}={x|﹣2＜x≤0}；（2）A∪B={x|﹣2＜x＜1}∪{x|x≤0或x≥1}=R；（3）由A∩B={x|﹣2＜x≤0}，∴∁U（A∩B）={x|x≤﹣2或x＞0}．19．（12分）已知函数f（x）是定义在R上的偶函数，且当x≤0时，f（x）=x2+2x．（1）现已画出函数f（x）在y轴左侧的图象，如图所示，请补出完整函数f（x）的图象，并根据图象写出函数f（x）的增区间；（2）写出函数f（x）的解析式和值域；（3）若方程f（x）﹣m=0有四个解，求m的范围．【解答】解；（1）函数图象如右图所示：f（x）的递增区间是（﹣1，0），（1，+∞）．（2）根据图象可知解析式为：，值域为：{y|y≥﹣1}．（3）根据图象可知﹣1＜m＜0时y=f（x）与y=m有四个个交点∴方程f（x）﹣m=0有四个解，m的范围是：﹣1＜m＜0．20．（12分）已知函数．（1）求函数f（x）的定义域；（2）求f（1），f（﹣1），f（2），f（﹣2）；（3）判断并证明f（x）的奇偶性．【解答】解：（1）由2x﹣1≠0，解得x≠0．∴函数f（x）的定义域为（﹣∞，0）∪（0，+∞）；（2）f（1）=，f（﹣1）=，f（2）=，f（﹣2）==﹣；（3）函数为定义域内的奇函数．证明如下：函数f（x）的定义域为（﹣∞，0）∪（0，+∞）．∵=．f（﹣x）==﹣f（x）．∴函数为定义域内的奇函数．21．（12分）已知f（x）=16x﹣2×4x+5，x∈[﹣1，2]（1）若f（x）=4，求x；（2）求f（x）的最大值与最小值．【解答】解：（1）f（x）=16x﹣2×4x+5，x∈[﹣1，2]，由f（x）=4，即16x﹣2×4x+5=4，即有16x﹣2×4x+1=0，即（4x﹣1）2=0，可得4x﹣1=0，解得x=0；（2）设t=4x，x∈[﹣1，2]，可得t∈[，16]，则函数f（x）=16x﹣2×4x+5可化为g（t）=t2﹣2t+5=（t﹣1）2+4，t∈[，16]，当t=1，即x=0时，函数f（x）取得最小值，且为4；当t=时，g（t）=；当t=16，即x=2时，g（t）=229．则f（x）的最大值为229．综上可得，f（x）的最大值为229，最小值为4．22．（12分）若f（x）是定义在（0，+∞）上的函数，当x＞1时，f（x）＞0，且满足．（1）求f（1）的值；（2）判断并证明函数的单调性；（3）若f（2）=1，解不等式．【解答】解：（1）令x=y=1可得f（1）=f（1）﹣f（1）=0，（2）设x1＞x2＞0，则f（x1）﹣f（x2）=f（），∵x1＞x2＞0，∴＞1，∴f（）＞0，∴f（x1）﹣f（x2）＞0，即f（x1）＞f（x2），∴f（x）在（0，+∞）上是增函数．（3）∵f（2）=1，∴f（）=f（1）﹣f（2）=﹣1，∴f（4）=f（2）﹣f（）=2，∵，∴f（x2+3x）＜f（4）．∴，解得0＜x＜1．∴不等式的解集是（0，1）．赠送初中数学几何模型【模型五】垂直弦模型：图形特征：运用举例：1.已知A、B、C、D是⊙O上的四个点.(1)如图1，若∠ADC＝∠BCD＝90°，AD＝CD，求证AC⊥BD；(2)如图2，若AC⊥BD，垂足为E，AB＝2，DC＝4，求⊙O的半径.2.如图，已知四边形ABCD内接于⊙O，对角线AC⊥BD于P，设⊙O的半径是2。

吉林省长春市朝阳区长春外国语学校2023-2024学年高三上学期11月期中英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解With the cost of living in the United States soaring, more and more people are setting their sights on an international destination.EcuadorFor real bargain hunters, Ecuador is cheap and safe with a very comfortable year-round climate. The cost of living for one person in the country is $750. Ecuador is geographically diverse with miles of endless beaches, hills and rainforests. Housing is economical with the average rent for one person costing around $307 per month.Costa RicaCosta Rica is the perfect place to live abroad without depleting(耗尽)your savings. The cost of living is around $893 and rent for one person runs approximately $406 per month. The tropical destination has cost-effective healthcare. The weather is gorgeous, the water is warm and the housing is highly affordable.UruguayThe country is exquisite(精美的), offering nearly 400 miles of coast, rolling mountains and four distinct seasons. The cost of living is nearly half of what it is in the states at $1,090 and you can find a nice apartment at the reasonable price of $500 per month.PanamaPanama could be a good option for anyone to live cheaply. The cost of living is under half of what it would cost in the U.S. at $1,040 for one person. Rent runs approximately $530 per month and food takes up another $353, but outside of that costs are minimal. The country has a mild climate and offers world-class beaches.1．Which country has economical healthcare?A．Ecuador.B．Costa Rica.C．Uruguay.D．Panama. 2．What makes Uruguay special?A．Its reasonable rent.B．Its good bargains.C．Its diverse climates.D．Its cheap apartments.3．How much is the cost of living in the United States?A．Close to $1,090.B．Around $750.C．Under $893.D．Above $2,080.At St. Francis High School in La Canada, Calif, there’s something to be said about math teacher Jim Connor.Truth is, Connor can be a bit of a drudge. But the 70-year-old Vietnam vet says he’s not here to entertain his students. “It drives me crazy when people say school should be fun,” he says. “I mean, it’s nice if it could be, but you can’t make school fun.”And for years, the kids thought that’s all there was to him — until last November, when senior Pat McGoldrick learned they didn’t know the half of him.Pat was in charge of a student blood drive and had just come to Children’s Hospital Los Angeles for a meeting. And he says it was weird: whenever he told someone he went to St. Francis High School, they all said, “Oh, you must know Jim Connor. Isn’t he wonderful? ”“It was disbelief, really,” Pat says. “It was almost kind of finding this alter ego (另一面) that he has.” Inside the blood donor center, Pat found a plaque listing all the top blood donors at the hospital, including the record holder, Jim Connor. Then he learned something even more unbelievable: that whenever Connor isn’t torturing kids with calculus (微积分), he’s on a whole other tangent-cuddling sick babies. Three days a week for the past 20 years, Jim has volunteered at the hospital, stepping in become involved in an activity when parents can’t, to hold, feed and comfort their children.“They tend to calm for him,” Nurse Erin says. “They tend to relax with him. They fall asleep with him.”“I just like them and relate to them somehow,” Connor says.Connor has never been married; he has no kids of his own. But he has fallen hard for these babies.“I’ve always respected him, but now it’s to an even different degree — really to the point where I try to emulate him,” Pat says. “He’s the epitome of a man of service.”4．What do we learn from paragraph 2?A．School can never be fun.B．Connor is highly demanding.C．Connor’s students drive him crazy.D．Connor thinks education is for all.5．What did Pat find out about Mr Connor?A．Mr Connor donated blood as well as his time.B．Mr Connor was awarded for his love toward babies.C．Mr Connor used to be a very strict teacher.D．Mr Connor had a unique teaching philosophy.6．Which of the following is true about Mr. Connor?A．He works two shifts every day for a living.B．He has his alter ego in the eyes of his students all the time.C．He has the ability to connect with those kids he holds.D．He falls hard for those sick kids so he decided not to have his own.7．Which expression can best replace the underlined word “epitome”?A．the best example B．the simplest oneC．the better man D．another candidateA new study found people growing up in rural areas have better navigation (导航) skills than those raised in cities and that people whose home cities have grid layouts (网格布局) are slightly better at navigating similarly organised streets, despite having poorer performance overall.The study involved nearly 4,000,000 participants from 38 countries who played Sea Hero Quest (SHQ), a game requiring them to navigate a boat in a virtual environment to find the places marked on a map. The researchers found that where people grew up influenced their performance in the game, while their present living place did not affect their scores.The researchers compared the home cities of the participants by analysing the “lack-of-order” state of the street networks, to measure the complexity of the layouts. People whose hometown’s street layouts were more ordered like New York were worse at playing SHQ. Those from cities with less ordered street layouts like Prague performed only slightly worse than those from rural areas. To test if people from cities could more effectively find the right direction in environments similar to where they grew up, the researchers developed a city-themed version of SHQ, called CHQ, requiring participants to drive down the streets in a virtual environment from simple grids to more winding street layouts. People growing up in cities with grid layouts were slightly better at navigating in similar environments, although the difference was not as significant as their performance in SHQ.The SHQ project was designed to aid Alzheimer’s research. Professor MichaelHornberger said, “Lack of spatial (空间的) navigation is a key Alzheimer’s symptom in the early stages of the disease. We are seeking to use the knowledge learned from SHQ to develop better disease monitoring tools.” Dr Susan Kohlhaas also said, “Thanks to the amazing response, we have been able to collect data from over four million players. If we’re to understand Alzheimer’s, it’s vital that we have participation from as many people as possible with diverse backgrounds and experiences.”8．What is the finding of the study?A．Street patterns in games are vital to one’s performance.B．People raised in cities have a good sense of direction.C．Growing up in rural areas improves navigation skills.D．One’s present living place affects their navigation skills.9．What did the participants do in the game?A．They drew their own maps of places in a virtual environment.B．They carried out a task of finding the marked place.C．They marked some places on a map to navigate a boat.D．They played games against each other to mark the map.10．What can be inferred about SHQ from Paragraph 3?A．It’s harder than CHQ for those from cities.B．Researchers developed it based on CHQ.C．It evaluates navigation skills better than CHQ.D．Players from New York did better than those from Prague.11．Why does Dr Susan Kohlhaas acknowledge the project?A．It helps Alzheimer’s patients play SHQ.B．It helps people gain navigation skills.C．It helps get a better knowledge of Alzheimer’s.D．It helps spot Alzheimer’s at an early stage.On Feb. 23, an environmental advocacy group “Grassroots” led by students hosted its monthly clothing exchange. The clothing exchange is a free activity on campus where students can donate clothes in exchange for new ones.“One of the key things about sustainability (可持续性) is to reuse,” Crystal Tynon, Co-president and Clothing Exchange Chair, said. “Instead of throwing away old clothes andbuying new clothes, you can donate them and give them a new purpose. You might be done with those clothing items, but someone else might not be.”According to Tynon, “Grassroots” is hoping to expand the activities to other schools. In order to do so, the team is brainstorming new ways to get the word out about donations, hours and events. Now, the clothing exchange is one of the club’s most well-known activities. “Throughout the semester when people realize we have these exchanges, they genuinely bring clothes and participate a lot more. So it does make a difference to clothing sustainability and it does create a community where everyone can share their clothes,” she added.As “Grassroots” is an initiative dedicated to sustainability, paper advertisement is not an option. Instead, the center relies mostly on word-of-mouth and e-mail announcements. It is bringing speakers to campus to talk about sustainability and environmental advocacy. It also has partnerships with local organizations such as “the Sunrise Rochester”, working together to have volunteers become more involved in local sustainability.Chloe Mendoza has been a volunteer since her freshman year. Not only does Mendoza appreciate the intended mission of promoting sustainability, but she also thinks the center has transformed into a safe and accepting community space for all students. Those who have come in looking for something practical often end up leaving with an armful of clothing and a heart full of warmth.“My favorite part about working there is that we get to help people find things that they need for free. Just providing a place for students to go where there isn’t pressure to spend money is really important. A lot of students love saving, so it’s something that students can relate and engage with easily, so I think it’s a really easy way to get students more involved in sustainability,” says Mendoza.12．Which of the following best describes Tynon’s feelings about their clothing exchange?A．Impressive.B．Innovative.C．Demanding.D．Rewarding.13．What can we learn about “Grassroots”?A．It relies heavily on paper advertisements.B．It cooperates with local institutions.C．It invites speakers to be volunteers.D．It earns instant fame in the community.14．What does Mendoza think is an additional benefit of the clothing exchange?A．It brings spiritual comfort.B．It widens the circle of friends.C．It reduces academic pressure.D．It gives a sense of achievement. 15．Which of the following could be the best title for the text?A．Saving Up Through Clothing ExchangeB．Engaging Students in “Grassroots” EventsC．Clothing Exchange Is the Only Way for SustainabilityD．Environmental Advocacy — “Grassroots” Catches On二、七选五your social circle and gain life-enriching benefits by becoming friends with someone younger or older than you. Having friends of different ages can greatly improve the quality of your life.Having older friends can change your attitude towards life because they have already gone through the challenges you are facing. They have been young parents, have survived a job loss, and can help you get through these changes in your own life. 17 Then you’ll feel more ready for what’s coming in future stages.When older people make friends with younger people, they get to share their experiences which can be very rewarding. 18 Giving your wisdom and attention makes you feel better. It gives you meaning and is good for your mental health. Having younger friends can also make you feel younger by including new ideas and energy in your life.19 While making new friends may seem frightening, it’s actually easier than you think. You can first think about your acquaintances or coworkers and see if any of them share your values and interests and would make a good friend. Then see if you can make a coffee date. Besides, you can consider joining in a class that your coworker or acquaintance participates in that you think you will enjoy. 20All in all making friends with people not your age can open your eyes to new ideas and new experiences that can be life-changing.A．For human beings, giving is good.B．Where to find friends sharing a common interest?C．Then how can you make intergenerational friends?D．Having friends at your own age is natural, of course.E．What’s more, younger friends can give you some fresh ideas.F．It’s believed that joining in activities like volunteering is also an effective way.G．An older friend also helps you “try on” certain life experiences before you get there.三、完形填空Every year I’d read over 2,000 college applications from students all over the world.It isrecommendations, one23 is always irresistible in a candidate：kindness.The most surprising 24 of kindness I’ve ever 25 came from a student who had excellent scores and a supportive recommendation from his college counselor(顾问).Even with these qualifications,he might not have 26 .But one letter of recommendation caught my eye.It was from a school security 27 .Letters of recommendation are typically written by people like former presidents,celebrities,and Olympic athletes.The security guard wrote that he supported this student’s admission because of his 28 . This young man was the only person in the school who knew the names of every member of the guard staff. He turned off lights in empty rooms,consistently 29 the hallway monitor each morning and tidied up the classroom after his peers left school 30 nobody was watching. This student, the security guard wrote, had a(n) 31 respect for every person at the school, regardless of position, popularity or power.It gave us a 32 onto a student’s life in the moments when nothing“counted”. That student was admitted by unanimous(一致的)vote of the admissions committee.Next year there might be a flood of security guard recommendations 33 this essay.But if it means students will start paying as much 34 to the people who clean their classrooms as they do to their principals and teachers,I’m happy to help start that 35 .21．A．decent B．difficult C．delicate D．desperate 22．A．However B．Otherwise C．Besides D．Therefore 23．A．ability B．quality C．limitation D．assumption 24．A．signal B．image C．appearance D．indication25．A．come out B．pick up C．come across D．bring up 26．A．stood up B．stood out C．given up D．given out 27．A．guard B．teacher C．principal D．counselor 28．A．wisdom B．bravery C．encouragement D．consideration 29．A．bothered B．answered C．visited D．thanked 30．A．as if B．now that C．even if D．in order that 31．A．demanding B．amusing C．refreshing D．puzzling 32．A．passion B．trouble C．method D．window 33．A．due to B．in need of C．except for D．along with 34．A．money B．notice C．attention D．curiosity 35．A．policy B．trend C．arrangement D．career四、用单词的适当形式完成短文阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。