上海市行知中学2017-2018学年高二上学期第一次月考数学试卷 Word版含答案

上海中学高二期中试卷2017.11一. 填空题1.直线350x --=的倾斜角大小为2. 过点(2,1)A -与(1,2)B 半径最小的圆的方程为3. 若由矩阵2222a x a a y a +⎛⎫⎛⎫⎛⎫= ⎪⎪ ⎪⎝⎭⎝⎭⎝⎭表示x 、y 的二元一次方程组无解，则实数a = 4. 一条直线经过直线230x y +-=，310x y -+=的交点，并且与直线2350x y +-=垂 直，则这条直线方程为5. 行列式351236724---中，元素6-的代数余子式的值为6. 过点(2017,2017)P 且在两坐标轴上截距相等的直线方程为7.4=上的点到原点的最短距离为8. 已知圆22:(4)(3)4C x y -+-=和两点(,0)A m -，(,0)B m (0)m >，若圆C 上至少存在 一点P ，使得90APB ︒∠=，则m 的取值范围是9. 平面直角坐标系中，O 为坐标原点，已知两点(6,0)A ，(2,6)B -，若点C 满足 OC OA OB αβ=+，其中21αβ+=，则点C 的轨迹方程为10. 当实数x 、y 满足221x y +=时，|2||32|x y a x y +++--的取值大小与x 、y 均无关， 则实数a 的取值范围是11. 已知OA a =，OB b =，若13OC a =，34OD b =，且AD 与BC 交于E 点，则OE = （用a 、b 表示）12. 已知正三角形的三个顶点(0,0)A 、(2,0)B、C ，一质点从AB 的中点0P 沿与 AB 夹角为θ的方向射到BC 边上的点1P 后，依次反射到CA 和AB 边上的点2P 、3P ，若 1P 、2P 、3P 是三个不同的点，则tan θ的取值范围为二. 选择题13. 已知向量(1,2)a =，(2,3)b x =-，若a //b ，则x =（ ）A. 3B. 34C. 3-D. 34-14. 若不等式组2022020x y x y x y m +-≤⎧⎪+-≥⎨⎪-+≥⎩表示的平面区域为三角形，且其面积等于43，则m =（ ） A. 3- B. 1 C. 43D. 3 15. 动点P 满足1[(1)(1)(12)]3OP OA OB OC λλλ=-+-++()λ∈R ，动点P 一定会过 △ABC 的（ ）A. 内心B. 垂心C. 重心D. 外心16. 在平面直角坐标系xOy 中，已知向量a 、b ，||||1a b ==，0a b ⋅=，点Q 满足 2()OQ a b =+，曲线{|cos sin ,02}C P OP a b θθθπ==+≤<，区域{|0P r Ω=<≤ ||,}PQ R r R ≤<，若C Ω为两段分离的曲线，则（ ）A. 13r R <<<B. 13r R <<≤C. 13r R ≤<<D. 13r R <<< 三. 解答题17. 若a 与b 是夹角为120°的两个单位向量. （1）若2a b -与a kb +垂直，求k ； （2）求2a b +与a b -的夹角.18. 运用行列式讨论关于x 、y 的方程组22(1)(1)1(1)(1)2a x a y a x a y ⎧---=⎪⎨-+-=⎪⎩解的个数，并解出此方程组.19. 设集合1{(,)||2|}2A x y y x =≥-，{(,)|||}B x y y x b =≤-+，A B ≠∅.（1）求b 的取值范围；（2）若(,)x y A B ∈，且x y +的最大值为9，求b 的值；（3）当12b <≤时，若(,)x y AB ∈，求kx y +的最大值.20. 过点(2,1)P -的直线l 分别交12y x =(0)x ≥与2y x =-(0)x ≥于A 、B 两点. （1）设△AOB 的面积为245，求直线l 的方程； （2）当||||PA PB ⋅最小时，求直线l 的方程.21. 已知圆222:O x y r +=（O 为原点），与x 轴不重合的动直线l 过定点(,0)D m(0)m r >>，且与圆O 交于P 、Q 两点（允许P 、Q 重合），点S 为点P 关于x 轴的对称点. （1）若2m =，1r =，P 、Q 重合，求直线SQ 与x 轴的交点坐标；（2）求△OSQ 面积的最大值.参考答案一. 填空题 1. 3π 2. 22315()()222x y -+-= 3. 2- 4. 2114170x y -+=5. 296. 4034x y +=或y x =7.8. 3m ≥9. 65180x y +-= 10. a ≥11. 1293a b + 12.二. 选择题13. D 14. B 15. C 16. A三. 解答题17.（1）54；（2）3π. 18. 当1a =时，无解；当1a ≠时，223(1)(22)a x a a a +=-++，21(1)(22)a y a a a -=-++. 19.（1）1b ≥；（2）9b =；（3）当(,1)k ∈-∞-，最大值2223k kb b -++； 当[1,1]k ∈-，最大值b ； 当(1,)k ∈+∞，最大值222kb k b -+-.20.（1）11122y x =-；（2）37y x =-.21.（1）1(,0)2；（2）当r m <≤，2max 2r S =；当m >，max 2r S m =.。

2017-2018学年高二上学期第一次月考数学（理）试题第Ⅰ卷（共50分）一、选择题：本大题共10个小题,每小题5分,共50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.在ABC ∆中，4a b B π===，则A 等于（ ）A ．6π B ．3π C ．6π或56π D ．3π或23π 2.已知等差数列{}n a 满足24354,10a a a a +=+=,则它的前10项的和n S =（ ） A ．23 B ．85 C ．95 D ．135 3.数列{}n a 满足：11221,2,n n n a a a a a --===(3n ≥且*n N ∈)，则8a =（ ） A ．12B ．1C ．2D ．20132- 4.等差数列{}n a 是递减数列，且23423448,12a a a a a a =++=，则数列{}n a 通项公式是（ ） A ．210n a n =+ B ．212n a n =- C ．24n a n =+ D ．212n a n =+ 5.已知{}n a 是等差数列，且23101148a a a a +++=，则67a a +=（ ） A ．12 B ．24 C ．20 D ．166.在ABC ∆中，已知222sin sin sin A B C =+，且sin 2sin cos A B C =，则ABC ∆的形状是 A.等腰三角形B.直角三角形C.等腰直角三角形D.等边三角形7．已知A 船在灯塔C 北偏东85︒且A 到C 的距离为2km ，B 船在灯塔C 西偏北25︒且B 到C 的，则,A B 两船的距离为（ ）ABC． D． 8.ABC ∆中，2,3BC B π==，当ABC ∆时，sin C =（ ） ABD ．129.已知等差数列{}n a 中，n S 是它的前n 项和，若160S >，且170S <，则当n S 取最大值时的n 值为（ ）A ．7B ．8C ．9D ．1610.已知ABC ∆中，()sin sin sin cos cos A B C A B +=+，则ABC ∆的形状是（ ） A.直角三角形B.锐角三角形C.钝角三角形D.等腰三角形第Ⅱ卷（共90分）二、填空题（每题5分，满分25分，将答案填在答题纸上） 13.ABC ∆中，已知2,45a b B ==︒，则A 为 ．12.在ABC ∆中，角,,A B C 所对应的边分别为,,a b c ，已知c o s c o s2b C c B b +=，则ab= ． 13.在数列{}n a 中，已知其前n 项和为23n n S =+，则n a = ． 14.设n S 是等差数列{}n a 的前n 项和，若4813S S =，则1216SS = ．15.将正奇数如下分组：（1）()3,5 ()7,9,11 ()13,15,17,19则第n 组的所有数的和为 ．三、解答题 （本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤.） 16. 如图，在ABC ∆中，4AB B π=∠=，D 是BC 边上一点，且3ADB π∠=.（1）求AD 的长；（2）若10CD =，求AC 的长及ACD ∆的面积.17.在锐角ABC ∆中，,,a b c 分别为角,,A B C2sin c A =. （1）确定角C 的大小；（2）若c ABC ∆，求a b +的值. 18.数列{}n a 的通项()()*10111nn a n n N ⎛⎫=+∈ ⎪⎝⎭，试问该数列{}n a 有没有最大项？若有，求出最大项；若没有，说明理由.19.在等差数列{}n a 中，131,3a a ==-. （1）求数列{}n a 的通项公式；（2）若数列{}n a 的前k 项和35k S =-，求k 的值. 20.在ABC ∆中，222a c b ac +-=. （1）求角B 的大小； （2）求sin sin A C ⋅的最大值.21.已知数列{}n a 中，148,2a a ==，且满足 2120n n n a a a ++-+= （1）求{}n a 的通项公式 （2）设123n n S a a a a =++++，求n S .试卷答案一、选择题1-5: DCCAB 6-10: CADBA 二、填空题11.6π 12. 2 13.()()15122n n n a n -=⎧⎪=⎨≥⎪⎩ 14.3515.3n三、解答题16.解：（1）在ABD ∆中，由sin sin AD ABB ADB=∠=∴6AD = （2）∵3ADB π∠=，∴23ADC π∠=由余弦定理知：22222cos 3AC AD DC AD DC π=+-⋅⋅ ∴213610026101962AC ⎛⎫=+-⨯⨯⨯-= ⎪⎝⎭∴14AC = ∵12sin23S AD DC π=⋅⋅，∴16102S =⨯⨯=17.解：（1）在锐角ABC ∆中2sin c A =2sin sin A C A =⋅ ∵sin 0A ≠，∴sin C = ∴3C π=（2）∵2222cos c a b ab C =+-⋅ ∴()22273a b ab a b ab =+-=+-又∵1sin 2S ab C === ∴6ab =∴()225a b += ∴5a b +=18. 解：设n a 是该数列的最大项，则11n n nn a a a a +-≥⎧⎨≥⎩∴()()()111010121111101011111n n n n n n n n +-⎧⎛⎫⎛⎫+≥+⎪ ⎪ ⎪⎪⎝⎭⎝⎭⎨⎪⎛⎫⎛⎫+≥ ⎪ ⎪⎪⎝⎭⎝⎭⎩∴910n ≤≤∴最大项为1091091011a a ==19. 解：（1）设等差数列{}n a 的公差为d ，则()11n a a n d =+-. 由131,3a a ==-，可得123d +=-.解得2d =-.从而，()()11232n a n n =+-⨯-=-. （2）由（1）可知32n a n =-.所以()213222n n n S n n +-⎡⎤⎣⎦==-.进而由35k S =-可得2235k k -=-. 即22350k k --=，解得7k =或5-. 又*k N ∈，故7k =为所求.20. 解：（1）∵2221cos 222a cb ac B ac ac +-===∴3B π=（2）∵3B π=∴23A C π+=∵23C A π=-∴21sin sin sin sin sin sin 32A C A A A A A π⎫⎛⎫⋅=⋅-=+⎪ ⎪⎪⎝⎭⎝⎭ 11sin 2264A π⎛⎫=-+ ⎪⎝⎭ ∵203A π<<，∴7666A πππ-<2-< 当62A ππ2-=时，sin sin A C ⋅最大为34. 21. 解：（1）∵22n n n a a a ++=，∴{}n a 是等差数列 由148,2a a ==知2d =-∴210n a n =-+ （2）当5n ≤时，0n a ≥ 12312n n n S a a a a a a a =++++=+++210n =-+当5n >时，n a <0 ()()1212567n n n S a a a a a a a a a =+++=+++-+++()()125122n a a a a a a =+++-+++2940n n =++综上：229,5940,5n n n n S n n n ⎧-+≤⎪=⎨++>⎪⎩。

行知中学高二月考数学试卷2018.10一. 填空题1. 已知向量(4,1)OA =，(1,5)OB =，则向量AB 的单位向量是2. 若三点(2,2)A 、(,0)B a 、(0,4)C ，若存在实数λ，使得AB BC λ=，则实数a =3. 已知向量(2,1)m =-，(1,1)n =，若(2)()m n am n -⊥+，则实数a =4. 等差数列{}n a 的前n 项和为n S ，12lim (32)nn n nS n S →∞+=+5. 已知数列{}n a 满足10a =，1n a +=（*n ∈N ），则10a 的值为6. 求值：()1123122114⎡--⎤⎛⎫⎛⎫⋅+⋅=⎢⎥ ⎪ ⎪-⎝⎭⎝⎭⎣⎦ 7. 已知||||2a b ==，a 与b 的夹角为3π，则()a b +在a 上的投影为 8. 各项均为正数的无穷等比数列{}n a ，满足2a m =，4a t =，且x my t =⎧⎨=⎩是增广矩阵为3122012-⎛⎫⎪⎝⎭的线性方程组1112121222a x a y c a x a y c +=⎧⎨+=⎩的解，则无穷等比数列{}n a 各项和的数值是9. 函数2sin(2)y x =的图像按a 平移后得到的图像解析式是2sin(2)13y x π=++，则当||a 取得最小时，a =10. 已知数列{}n a 的通项公式是23n a n =+（*n ∈N ），数列{}n b 满足1n n b b a +=（*n ∈N ）且11b a =，则数列{}n b 的通项公式为11. 如图，在同一个平面内，向量OA 、OB 、OC 的模分别 为1，OA 与OC 的夹角为α，且tan 7α=，OA 与OB 的夹角为135°，若OC mOA nOB =+（,m n ∈R ），则m n +=12. 已知数列{}n a 的首项1a a =，其前n 项和为n S ，且满足213n n S S n -+=（2n ≥），若对任意的*n ∈N ，1n n a a +<恒成立，则a 的取值范围是二. 选择题13. 用数学归纳法证明等式(3)(4)123(3)2n n n +++++⋅⋅⋅++=（*n ∈N ）时，第一步验证1n =时，左边应取的项是（ ）A. 1B. 12+C. 123++D. 1234+++ 14. 有命题：（1）三阶行列式的任一元素的代数余子式的值和其余子式的值互为相反数； （2）三阶行列式可以按其任意一行展开成该行 元素与其对应的代数余子式的乘积之和； （3）如果将三阶行列式的某一列的元素与另一 列的元素的代数余子式对应相乘，那么它们的 乘积之和等于零；其中所有正确命题的序号是（ ） A.（1）（2） B.（1）（3） C.（2）（3） D.（1）（2）（3） 15. 当向量(2,2)a c ==-，(1,0)b =时，执行如 图所示的程序框图，输出的i 值为（ ） A. 5 B. 4 C. 3 D. 216. 已知数列{}n a 中，12a =，点列n P （1,2,n =⋅⋅⋅）在△ABC 内部，且△n P AB 与△n P AC 的面积比为2:1，若对*n ∈N 都存在数列{}n b 满足11(32)02n n n n n n b P A a P B a P C ++++=， 则4a 的值为（ ）A. 54B. 68C. 76D. 80三. 解答题17. 已知(1,2)A -、(2,1)B 、(3,2)C 、(2,3)D -. （1）求23AD BD BC +-；（2）若非零向量AM 满足：AM BC ⊥且||22AM =，求点M 的坐标.18. 用行列式解关于x 、y 的方程组：12ax y a x ay a+=+⎧⎨+=⎩（a ∈R ）.19. 如图，平行四边形ABCD 中，4AB =，3AD =，AB a =，AD b =，23BM BC =，34AN AB =. （1）试用a 、b 来表示DN 、AM ；（2）若60DAB ∠=︒，求AD DN DN NA ⋅+⋅的值； （3）若0AD DB ⋅=，求DN AB ⋅.20. 已知数列{}n a 和{}n b 满足：111a b ==，且1a 、22a 、44a 成等比数列，24b 、32b 、4b 成等差数列.（1）行列式21111213234234111n n n a a a M M M ++-=-++（*n ∈N ），且1113M M =， 求证：数列{}n a 是等差数列；（2）在（1）的条件下，若{}n a 不是常数列，{}n b 是等比数列， ① 求{}n a 和{}n b 的通项公式；② 设m 、n 是正整数，若存在正整数i 、j 、k （i j k <<），使得m j a b ⋅，m n i a a b ⋅⋅，n k a b ⋅成等差数列，求m n +的最小值.21. 设函数2()(32)32k k f x x k x k =-++⋅，x ∈R . （1）若(1)0f ≤，求实数k 的取值范围；（2）若k 为正整数，设()0f x ≤的解集为212{,}k k a a -，求1234a a a a +++及数列{}n a 的前2n 项和2n S ；（3）对于（2）中的数列{}n a ，设212(1)nn n nb a a --=⋅，求数列{}n b 的前n 项和n T 的最大值.参考答案一. 填空题1. 34(,)55-2. 43.574. 25. 06. 57. 38. 329. (,1)6π- 10. 323n n b +=- 11. 3 12. 39(,)22二. 选择题13. D 14. B 15. B 16. D三. 解答题17.（1）(14,6)-；（2）(3,4)-或(1,0)-.18. ①1a ≠±时，唯一解1211a x a a y a ⎧=⎪⎪+⎨+⎪=⎪+⎩；②1a =时，无穷多解2x t y t =⎧⎨=-⎩（t ∈R ）；③1a =-时，无解.19.（1）34DN a b =-，23AM a b =+；（2）9-；（3）3. 20.（1）略；（2）①n a n =，12n n b -=；② 6.21.（1）1(,0][,)3-∞+∞；（2）123415a a a a +++=，21233=2222n n S n n ++-+；（3）max 21()8n T T ==-.。

2018-2019学年上海市行知中学高二上学期第一次月考数学试题一、单选题1．用数学归纳法证明等式时，第一步验证时，左边应取的项是( )A ．1B ．C ．D ．【答案】D【解析】由数学归纳法的证明步骤可知：当时，等式的左边是，应选答案D 。

2．有命题：（1）三阶行列式的任一元素的代数余子式的值和其余子式的值互为相反数；（2）三阶行列式可以按其任意一行展开成该行元素与其对应的代数余子式的乘积之和；（3）如果将三阶行列式的某一列的元素与另一列的元素的代数余子式对应相乘，那么它们的乘积之和等于零，其中所有正确命题的序号是（ ）．A ．（1）（2）B ．（1）（3）C ．（2）（3）D ．（1）（2）（3）【答案】C【解析】根据代数余子式的意义,进行判断即可得出结论.【详解】(1)三阶行列式的任一元素的代数余子式的值和其余子式的值互为相反数或相等,故(1)不正确;(2)根据代数余子式的意义,可知三阶行列式可以按其任意一行展开成该行元素与其对应的代数余子式的乘积之和,故(2)正确;(3)根据代数余子式与该行的该行的元素值无关,可得如果将三阶行列式的某一列的元素与另一列的元素的代数余子式对应相乘，那么它们的乘积之和等于零,故(3)正确.故选:C.【点睛】本题考查了代数余子式的意义,属于基础题.3．当向量，时，执行如图所示的程序框图，输出的值为（ ）．(2,2)a c ==-(1,0)b = iB ．C ．D ．5432【答案】B【解析】时， ，时，，i 0=22(2)28a c ⋅=-+= i 1=(2)(1)226a c ⋅=-⨯-+⨯= 时，，时，，(2)0224a c ⋅=-⨯+⨯= i 3=(2)1222a c ⋅=-⨯+⨯=时，，此时，所以输出．故选．(2)2220a c ⋅=-⨯+⨯= 0a c ⋅= i 4=B :本题考查的是算法与流程图,对算法与流程图的考查，侧重于对流程图循环结构的考查.要先明晰算法及流程图的相关概念，包括选择结构、循环结构、伪代码，其次要重视循环起点条件、循环次数、循环终止条件，更要通过循环规律，明确流程图研究的数学问题，是求和还是求项.交于,因为与的面积比为,所以点,到的距离之比为2:1,nBC D n n 2:1B C n所以点到的距离之比为2:1,,B C n P D与的面积比为,n P D△B n P D△C 2:1,即 ,:2:1BD DC =2BD DC =,11(32)02n n n n n n b P A a P B a P C ++++=11(32)2n n n n n na BPb AP a CP +-=++ ()n BP BA - (32)()n n a BP BC ++- ,11(32)(32)2n n n n n n a b a BP b BA a BC +----=--+ 3(32)2n n b BA a BD=--+ 3二、填空题．已知向量，则与向量同向的单位向量是________．(4,1),(1,5)OA OB == AB 【答案】34(,)55-【解析】先求出，再求出，然后代入即可求出答案。

理科数学试题 第1页（共4页） 理科数学试题 第2页（共4页）………………○………………内………………○………………装………………○………………订………………○………………线………………○………………………………○………………外………………○………………装………………○………………订………………○………………线………………○………………… 学校：______________姓名：_____________班级：_______________考号：______________________2017-2018学年上学期第一次月考（9月）原创卷A 卷高二理科数学（考试时间：120分钟 试卷满分：150分）注意事项：1．本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

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5．考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷一、选择题（本题共12小题，每小题5分，共60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．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，已知1b =，4B π=，1cos 3A =，则a =A ．43 B 2 C ．34D 22．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，若222a b c bc =++，则A =A ．3π B ．6π C ．23πD ．3π或32π3．在等比数列{}n a 中，若12a =，416a =，则数列{}n a 的前5项和5S 等于 A ．30 B ．31 C ．62D ．644．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，若8b =，3c =，60A =︒，则此三角形外接圆的半径R = A ．823B ．33C ．73D 735．某观察站C 与两灯塔A ，B 的距离分别为a 米和b 米，测得灯塔A 在观察站C 北偏西60︒，灯塔B 在观察站C 北偏东60︒，则两灯塔A ，B 间的距离为 A 22a b +B 22a b ab +-米C 22a b ab ++D 223a b ab +-6．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，若60C =︒，4a b =，13c =，则ABC △的面积为 A 3B 13C ．23D 137．大衍数列，来源于《乾坤普》中对易传“大衍之数五十”的推论，主要用于解释中国传统文化中太极衍生原理．数列中的每一项，都代表太极衍生过程中，曾经经历过的两翼数量总和，是中国传统文化中隐藏着的世界数学史上第一道数列题．其前10项依次是0，2，4，8，12，18，24，32，40，50，……则此数列的第20项为 A ．180 B ．200 C ．128D ．1628．已知等差数列{}n a 的前n 项和为n S ，若80S >且90S <，则当n S 最大时n 的值为 A ．8 B ．5 C ．4D ．39．在等差数列{}n a 中，已知22383829a a a a ++=，且0n a <，则数列{}n a 的前10项和10S =A ．9-B ．11-C ．13-D ．15-10．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，已知cos cos cos a A b B c C +=，则ABC △是A ．直角三角形B ．等腰三角形C ．等腰直角三角形D ．等边三角形11．已知1a ，2a ，1b ，2b 为实数，且1-，1a ，2a ，4-成等差数列，1-，1b ，2b ，8-成等比数列，则211a ab -的值为理科数学试题 第3页（共4页） 理科数学试题 第4页（共4页）………………○………………内………………○………………装………………○………………订………………○………………线………………○………………此卷只装订不密封………………○………………外………………○………………装………………○………………订………………○………………线………………○………………A ．14- B ．12 C ．14或14-D ．12或12-12．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，已知3a =，11sin 6B =，32C ππ<<sin 2sin sin 2b Ca b A C=--，则b 等于 A 3 B ．2 C 5D ．3第Ⅱ卷二、填空题（本题共4小题，每小题5分，共20分）13．在等差数列{}n a 中，已知12a =，3510a a +=，则7a =________________．14．设等比数列{}n a 的公比为q ，其前n 项和为n S ，若2232S a =+，4432S a =+，则q =________________．15．在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，若sin :sin :sin 3:2:4A B C =，则sin C 的值为________________．16．已知各项均为正数的数列{}n a 满足：2123n a a a n n +=+，则12231n a a an +++=+________________．三、解答题（本大题共6小题，共70分．解答应写出文字说明、证明过程或演算步骤） 17．（本小题满分10分）已知公差不为零的等差数列{}n a 的前n 项和为n S ，若10110S =，且1a ，2a ，4a 成等比数列． （1）求数列{}n a 的通项公式；（2）若1(1)(1)n n n b a a =-+，求数列{}n b 的前n 项和n T ．18．（本小题满分12分）如图所示，在四边形ABCD 中，2D B =，且2AD =，6CD =，3cos B =． （1）求ACD △的面积；（2）若43BC =，求AB 的长．19．（本小题满分12分）在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，已知232cos cos a c bA B-=． （1）若35sin b B =，求a 的值； （2）若5a =，ABC △的面积为5，求b c +的值．20．（本小题满分12分）已知数列{}n a 的前n 项和为n S ，点(,)n n S 在抛物线23122y x x =+上，各项都为正数的等比数列{}n b 满足214b =，4116b =． （1）求数列{}n a ，{}n b 的通项公式；（2）记n n n a a C a b =+，求数列{}n C 的前n 项和n T ． 21．（本小题满分12分）已知数列{}n a 满足11a =，11021n n n a a a +++=-．（1）证明：数列1{}na 是等差数列； （2）若数列{}nb 满足12b =，112n nn n b a b a ++=，求数列{}n b 的前n 项和n S ． 22．（本小题满分12分）在ABC △中，角A ，B ，C 的对边分别为a ，b ，c ，已知向量(sin ,sin sin )A B C =-m ，=n (3,)a b b c -+，且⊥m n ．（1）求角C 的值；（2）若ABC △为锐角三角形，且1c =3a b -的取值范围．。

2017-2018学年上学期第一次月考高二数学（理）试卷说明：本试卷满分150分，答题时间120分钟第Ⅰ卷（选择题，共60分）一、选择题（本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一项符合题目的要求）1．若直线l 过点A )3,2(-，B )2,3(-，则l 的斜率为（ ）A ．1B ．1-C ．2D ．2-2.某学校有教师160人,其中有高级职称的32人,中级职称的56人,初级职称的72人.现抽取一个容量为20的样本,用分层抽样法抽取的中级职称的教师人数应为( ) A.4 B.6 C.7 D.9 3．设α和β为不重合的两个平面， l 是一条直线，给出下列命题中正确的是( ) A. 若一条直线l 与α内的一条直线平行，则//l α B. 若平面α内有无数个点到平面β的距离相等，则//αβ C. 若l 与α内的无数条直线垂直，则l α⊥ D. 若直线l 在α内，且l β⊥，则αβ⊥4．梁才学校高中生共有2 400人，其中高一年级800人，高二年级900人，高三年级700人，现采用分层抽样抽取一个容量为48的样本，那么高一、高二、高三各年级抽取人数分别为（ ）A ．16，20，12B ．15，21，12C ．15，19，14D ．16，18，14 5．有五组变量：①汽车的重量和汽车每消耗1升汽油所行驶的平均路程； ②平均日学习时间和平均学习成绩； ③某人每日吸烟量和其身体健康情况； ④正方形的边长和面积； ⑤汽车的重量和百公里耗油量；其中两个变量成正相关的是 （ ） A ．①③ B ．②④ C ．②⑤ D ．④⑤6．已知等差数列{}n a 的前n 项和为n S ，若M N P 、、三点共线， O 为坐标原点，且156ON a OM a OP =+（直线MP 不过点O ），则20S 等于( ) A. 20 B. 10 C. 40 D. 15 7.右图是计算201614121++++ 的值的一个流程图，其中判断框内应填入的条件是A ．21≤iB ．11≤iC ．21≥iD ．11≥i 8．设l ，m 是两条不同的直线，α是一个平面，则下列命题正确的是（ ） A ．若l ∥α，m ⊥α，则l ⊥m B ．若l ⊥m ，m ∥α，则l ⊥α C ．若l ⊥m ，m ⊥α，则l ∥α D ．若l ∥α，m ∥α，则l ∥m9．执行如右图所示的程序框图，若输入32n =，则输出的结果为( ) A. 80 B. 84 C. 88 D. 9210．从装有2个红球和2个黑球的口袋内任取2个球，那么互斥而不对立的两个事件是（ ）A ．至少有一个黑球与都是黑球B ．至少有一个黑球与都是红球C ．至少有一个黑球与至少有1个红球D ．恰有1个黑球与恰有2个黑球11．矩形ABCD 中，3=AB ，1=BC ，将△ABC 与△ADC 沿AC 所在的直线进行随意翻折，在翻折过程中直线AD 与直线BC 成的角范围（包含初始状态）为（ ）A ．]6,0[πB ．]3,0[πC ．]2,0[πD ．]32,0[π12．记n 项正项数列为n a a a ,,,21⋅⋅⋅，其前n 项积为n T ，定义)lg(21n T T T ⋅⋅⋅⋅为“相对叠乘积”，如果有2013项的正项数列201321,,,a a a ⋅⋅⋅的“相对叠乘积”为2013，则有2014项的数列 201321,,,,10a a a ⋅⋅⋅的“相对叠乘积”为( )A.2014B.2016C.3042D.4027 二.填空题: （每小题5分，共20分）13.某校高中生共有900人，其中高一年级300人，高二年级200人，高三年级400人，现采用分层抽样法抽取一个容量为45的样本，那么从高一、高二、高三各年级抽取人数分别为 .14．一个四棱锥的三视图如右图所示，主视图为等腰直角三角形，俯视图中的四边形为正方形，则该四棱锥外接球的体积为__________．15．圆1)1()1(22=-+-y x 上的点到直线02=--y x 的距离最大值是 ．16.用“辗转相除法”求得459和357的最大公约数是 三、解答题(解答应写出文字说明，证明过程或演算步骤)17．(10分)已知,,a b c 分别是ABC ∆内角,,A B C 的对边， 2sin 2sin sin B A C =． (1)若a b =，求cos B ;(2)若90B =，且a =求ABC ∆的面积．18．已知以点)2,1(-A 为圆心的圆与直线0543:=++y x m 相切． （1）求圆A 的方程；（2）过点)1,0(-B 的动直线l 与圆A 相交于M 、N 两点，当32||=MN 时，求直线l 方程．19.（本小题满分12分）假设某种设备使用的年限x （年）与所支出的维修费用y （万元）有以下统计资料：若由资料知y 对x 呈线性相关关系。

上海市行知中学2018-2019学年高二上学期第一次月考数学试卷考试时间：100分钟 满分：100分一、填空题（每题3分）1．设n S 是数列{}n a 的前n 项和，且221n S n n =--，则n a =________. 2．在等比数列{}n a 中，51a =，116k a =，公比12q =-，k = . 3．平行四边形ABCD 中，已知顶点()()()21,32,13A B C --，，，，则顶点D 的坐标是_________.4．已知数列{}n a 中，12213,6,n n n a a a a a ++===-，则2015a =_________. 5．一个无穷等比数列，各项为正，已知12342a a a a +++≤ ，则公比q 的取值范围是______________.6．若(1,2)a =-，(3,1)b =-，0c 是与b a -平行的单位向量，则0c = . 7．已知}{n a 是首项为32的等比数列，n S 是其前n则数列|}log {|2n a 前10项和为_______________. 8．设数列{},{}n n a b 均为等差数列，lim4n n na b →∞=，则123lim nn n b b b na →∞+++ =________. 9．若5lim 3nn nn a →∞+存在，则实数a 的取值范围为10．等差数列{}n a 的通项公式为28n a n =-，下列四个命题，①数列{}n a 是递增数列；②数列{}n na 是递增数列；③数列n a n ⎧⎫⎨⎬⎩⎭是递增数列；④数列{}2n a 是递增数列.其中真命题的序号是___________.11．公差为d ，各项均为正整数的等差数列中，若11=a ，51=n a ，则d n +的最小值等于 .12．已知线段AB 上有9个确定的点（包括端点A 与B ）.现对这些点进行往返标数（从A →B →A →B →…进行标数，遇到同方向点不够数时就“调头”往回数）.如图：在点A 上标1称为点1，然后从点1开始数到第二个数，标上2，称为点2，再从点2开始数到第三个数，标上3，称为点3（标上数n 的点称为点n ），…，这样一直继续下去，直到1，2，3，…，2018都被标记到点上.则点2018上的所有标记的数中，最小的是____________.二、选择题（每题3分）13．若O E F ，，是不共线的任意三点，则以下各式中成立的是（ ）A ．EF OF OE =+B ．EF OF OE =-C ．EF OF OE =-+D ．EF OF OE =--14．执行如图所示的程序框图，如果输入的]2,2[-∈t ，则 输出的S 属于（ ） A ．]2,6[--B ．]1,5[--C ．]5,4[-D ．]6,3[-15．用数学归纳法说明：()111112321nn n ++++<>- ，在第二步证明从n k =到1n k =+成立时，左边增加的项数是（ ） A ．2k B ．21k - C ．12k - D ．21k +16．设等差数列{}n a 满足公差(1,0)d ∈-，当且仅当9n =时，数列{}n a 的前n 项和n S 取得最大值，求该数列首项1a 的取值范围（ ） ABCD三、解答题 17．（本大题满分8分）已知数列{}n a 中，12a =，1n n a a c +=+（c 是常数，n N +∈），且1a ，2a ，4a 成等比数列．求数列{}n a 的前n 项和n S18．（本大题满分8分，每小题4分）已知数列{}n b 满足：28b =，1011n nb b n n +=+-（1）求数列{}n b 的通项公式；（2）令()*n n b a n n N =+∈，是否存在非零常数,p q ，使得n a np q ⎧⎫⎨⎬+⎩⎭成为等差数列？说明理由.19．（本大题满分10分，每小题5分）某产品具有一定的时效性，在这个时效期内，由市场调查可知，在不做广告宣传且每件获利a 元的前提下，可卖出b 件；若做广告宣传，广告费为n 千元比广告费为()1n -千元时多卖出()*2n bn N ∈件。

2017-2018学年高二上学期第一次月考试题数学（文）第I 卷（选择题）一、选择题（本题共12道小题，每小题5分，共60分）1.如果a ＞b ，给出下列不等式：（1）＜；（2）a 3＞b 3；（3）a 2+1＞b 2+1；（4）2a ＞2b ．其中成立的不等式有（ ）A ．（3）（4）B ．（2）（3）C ．（2）（4）D ．（1）（3） 2.等比数列{a n }中，a 2+a 4=20，a 3+a 5=40，则a 6=（ ）A ．16B ．32C ．64D ．128 3.数列1，﹣3，5，﹣7，9，…的一个通项公式为（ ）A ．a n =2n ﹣1B ．a n =(﹣1)n(2n ﹣1)C ．a n =(﹣1)n+1(2n ﹣1)D ．a n =(﹣1)n (2n+1)4.已知{a n }是等比数列，且a n ＞0，a 2a 4+2a 3a 5+a 4a 6=25，那么a 3+a 5的值等于（ ）A ．5B ．10C ．15D ．205.已知x ＜，则函数y=4x ﹣2+的最大值是（ ）A ．2B ．3C ．1D ．6.两灯塔A 、B 与海洋观察站C 的距离都等于a km ，灯塔A 在C 北偏东300，B 在C 南偏东600，则A 、B 之间相距：A 、a kmB 、3a kmC 、2a kmD 、2a km7.在ABC ∆中，2,6a b B π===，则A 等于（ ）A ．4π B ．4π或34π C ．3π D ． 34π8.若a ，b 均为大于1的正数，且ab=100，则lga•lgb 的最大值是（ ）A ．0B ．1C ．2D ．9.若，则线性目标函数z=x+2y 的取值范围是（ ）A ．[2，5]B ．[2，6]C ．[3，5]D ．[3，6]10.ABC ∆的内角C B A ,,所对的边c b a ,,满足()422=-+c b a ，且C=60°，则ab 的值为（ ）A ．34 B ．348- C ． 1 D ．32 11.若数列{a n }的通项公式是a n =（﹣1）n（3n ﹣2），则a 1+a 2+…+a 20=（ ）A ．30B ．29C ．﹣30D ．﹣2912.设f n （x ）是等比数列1，﹣x ，x 2，…，（﹣x ）n 的各项和，则f 2016（2）等于（ ）A ．B ．C ．D ．II 卷（非选择题）二、填空题（本题共4道小题，每小题5分，共20分）13.已知x ＞0，y ＞0，x+y=1，则+的最小值为 ． 14.在数列{a n }中，a 1=1，a n+1=2a n +1，则其通项公式为a n = ．15.在△ABC 中，已知22,sin sin sin a b c A B C =+=，则△ABC 的形状为________.16.在等比数列{a n }中，若a 3，a 15是方程x 2﹣6x+8=0的根，则= ．评卷人得分三、解答题（本题共6道小题,第1题0分,第2题0分,第3题0分,第4题0分,第5题0分,第6题0分,共0分）17.正项数列{a n }的前n 项和为S n ，且2=a n+1．（1）试求数列{a n }的通项公式；（2）设b n =，{b n }的前n 项和为T n ，求证：T n ＜．18.在ABC ∆中，角,,A B C 的对边分别为,,,3a b c B π=，4cos ,5A b ==（1）求sin C 的值；（2）求ABC ∆的面积.19.如图，海上有A B ，两个小岛相距10km ，船O 将保持观望A 岛和B 岛所成的视角为60︒，现从船O 上派下一只小艇沿BO 方向驶至C 处进行作业，且OC BO =．设AC x =km 。

上海中学高二周练卷（一）一. 填空题1. 已知点(1,3)A 、(4,1)B -，则与AB方向相反的单位向量坐标为2. 设向量a 、b 不平行，向量a b λ+ 与2a b +平行，则实数λ=3. 设(1,2)a = ，(1,1)b =，c a kb =+ ，若b c ⊥ ，则实数k =4. 已知(1,3)a =- ，(2,1)b =，则a 在b 上的投影是5. 在平面直角坐标系xOy 中，已知四边形ABCD 是平行四边形，(1,2)AB =-，(2,1)AD =，则AD AC ⋅=6. 若向量a 、b 满足||||1a b == 及|32|3a b -= ，则|3|a b +=7. 已知23BAC π∠=，圆M 与AB 、AC 分别相切于点D 、E ，1AD =，点P 是圆M 及其 内部任意一点，且AP xAD yAE =+(,)x y ∈R ，则x y +的取值范围是8. 面积为1的△ABC 中，2AB AC BC ⋅+ 的最小值为9. 已知△ABC 为等边三角形，2AB =，设点P 、Q 满足AP AB λ= ，(1)AQ AC λ=-，λ∈R ，若32BQ CP ⋅=- ，则λ=10. 在△ABC 中，6AC =，7BC =，1cos 5A =，点O 是△ABC 的内心，若 OP xOA yOB =+，其中01x ≤≤，01y ≤≤，则动点P 的轨迹所覆盖的面积为11. 直角三角形ABC 中，3AB =，4AC =，5BC =，点M 是三角形ABC 外接圆上任意一点，则AB AM ⋅的最大值为12. 已知平面上三个不同的单位向量a 、b 、c 满足12a b b c ⋅=⋅= ，若e为平面内的任意单位向量，则||2||3||a e b e c e ⋅+⋅+⋅的最大值为二. 选择题13. 对任意向量a 、b，下列关系式中不恒成立的是（ ）A. ||||||a b a b ⋅≤B. ||||||||a b a b -≤-C. 22()||a b a b +=+ D. 22()()a b a b a b +-=-14. 若a 与b c - 都是非零向量，则“a b a c ⋅=⋅ ”是“()a b c ⊥-”的（ ）条件A. 充分不必要B. 必要不充分C. 充要D. 既不充分也不必要15. 设θ是两个非零向量a 、b 的夹角，若对任意实数t ，||a tb +的最小值为1，则下列判断正确的是（ ）A. 若||a 确定，则θ唯一确定B. 若||b确定，则θ唯一确定C. 若θ确定，则||b 唯一确定D. 若θ确定，则||a唯一确定16. 在平面上，12AB AB ⊥ ，12||||1OB OB == ，12AP AB AB =+ ，若1||2OP < ，则||OA的取值范围是（ ）A. B. C. D.三. 解答题17. 在平面直角坐标系xOy 中，已知向量(,22m =- ，(sin ,cos )n x x = ，(0,)2x π∈.（1）若m n ⊥ ，求tan x 的值；（2）若m 与n 的夹角为3π，求x 的值.18. 三角形ABC 内接于以O 为圆心，1为半径的圆，且3450OA OB OC ++=.（1）求OA OB ⋅；（2）求三角形ABC 的面积.19.（1）平面上给定四个点1P 、2P 、3P 、4P ，点H 满足12340HP HP HP HP +++=，现增加一点5P ，点1H 满足11121314150H P H P H P H P H P ++++= ，求151||:||H PH H； （2）平面上给定五个点1A 、2A 、3A 、4A 、5A ，若点A 满足12A A 、23A A 、34A A 、45A A 、5A A这五个向量中任意两个向量之和的模长等于其余三个向量之和的模长，证明：点A 与点1A 重合.参考答案一. 填空题1. 34(,)55-2.12 3. 32- 4.6. [4-+ 8. 1211. 12 12. 5二. 选择题13. B 14. C 15. D 16. D三. 解答题 17.（1）1；（2）512x π=. 18.（1）0；（2）65. 19.（1）4；（2）略.。

英语试卷考试时间：120分钟满分：140分第I卷（共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. In a supermarket. B. In a drug store.C. In a department store.D. In a car repair shop.2. A. 20 minutes. B. 45 minutes.C. 25 minutes.D. 65 minutes.3. A. Professor and student. B. Director and actor.C. Writer and advertiser.D. Hostess and guest.4. A. She picked up the book from the bus stop.B. She can help the man out.C. She’s also in need of a chemistry textbook.D. She will help the man to find the right person.5. A. Take the test in three weeks.B. Call to make inquiries about the test results.C. Be patient and wait for the test results.D. Inquire about the date when the results will be released.6. A. He set fire to the building.B. He parked his car beside the building.C. He was trying to clear the road with the help of some other people.D. He found out what was going on.7. A. He’s going to the theatre. B. He’s just returned from a job interview.C. He’s just visited his tailor.D. He’s dressed up to have his photo taken.8. A. Registering for courses. B. Studying engineering and art history.C. Buying literature books.D. Going to the registry office.9. A. The Jenkins made a wise investment.B. It is not sensible to make such an investment.C. The Jenkins should buy the stocks later.D. It is essential that the Jenkins should move out.10. A. It is not a good timing to build it. B. It should have been built earlier.C. She is curious about this plan.D. She doubts how long the plan will take.Section BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and the conversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one is the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. South Korean Women. B. American citizens.C. People in industrialized countries.D. People with economic improvements.12. A. High premature deaths.B. Overweight citizens.C. A lack of public health care.D. A shortage in new medical technologies.13. A. More facilities should be established.B. Additional pressure should be put on pensions.C. People should retire at an earlier age.D. People should be provided with more payments.Questions 14 through 16 are based on the following passage.14. A. Because of the security of the job.B. For a promotion to the Executive Director.C. To inspire the folks in the community.D. To enrich others and her own lives.15. A. The speaker graduated in law and used to earn generous salaries.B. Spelman is a non-profit institute which turns out social workers.C. The audiences are regarded as beautiful because they all belong to Spelman.D. Public service is rewarding both in a spiritual and material sense.16. A. Urging classmates to get involved in public service.B. Expressing gratitude to the audience for their volunteer work.C. Delivering a speech to the graduates from Spelman College.D. Illustrating how to help others as one climbs his career ladder.Questions 17 through 18 are based on the following conversation.17. A. May 19th. B. May 20th. C. May 23rd. D. May 16th.18. A. Three meals a day. B. Train fare.C. Competition entrance fee.D. Floor space.19. A. The entrance fee is 16 euros this year.B. College basket teams abroad can enter for the game by phone.C. It is the 80th anniversary of the Tampere Student Game.D. The game will end with a ceremony in the last evening.20. A. Students can enjoy a reduced rate during that period.B. All the basketball teams live in that hotel.C. It will provide three meals to the players living there.D. It is close to where all the matches are held.II. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages 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.Thoughts of a great mindTo you, Karl Marx (1818-1883) might be the man with a bushy face who watches over you in a frame in your classroom, usually alongside another bushy-faced man named Friedrich Engels (1820-1895). But ___21___ the world, Marx is a philosopher, economist, historian, and revolutionist. This year ___22___(mark) the 200th anniversary of Marx’s birth, so maybe it’s time for you to learn more about him. Indeed, he’s a man who helped us understand ___23___ the world works in more than one way.Marx was a philosopher. We use his theories all the time, even though we may not realize it. For example, he believed that a cause would always lead to a result, which urges us ___24___(think) twice before making a move. He also discovered the rule ___25___ when many small changes built up, they finally lead to a big one, good or bad, ___26___ reminds us of the importance of details even if they don’t seem to matter at the time. But Marx himself didn’t seem to think it was enough to simply be a philosopher. “The philosophers ___27___(interpret) the world, in various ways. The point, however, is to change it,” he once wrote. So he did.With his The Communist Manifesto (《共产党宣言》), ___28___(publish) in 1848 in London, Marx expressed his ideals on communism and how a fairer society could be built. He also delved into (探究) the fact that the world’s wealth wasn’t equally distributed, with 10 percent of the world’s population possessing most of it while the other 90 percent owned almost ___29___. Now that 150 years have passed, the world is still pretty much how Marx described it.But whether he was a philosopher, revolutionist or economist, all in all, Marx was a man who wanted to change the world for ___30___(good).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.Death of science iconThroughout modern history, there has perhaps never been a scientist as ___31___ as Stephen Hawking. Whether he was ___32___ the world with his knowledge of the universe, or making fun of himself in TV shows like The Simpsons, it’s hard to imagine what the world will be like now Hawking is no longer in it.On March 14, the British physicist passed away at his home in Cambridge, England. Since then, many people have ___33___ their condolences (哀悼) on social media, including British computer scientist Tim Berners-Lee, who invented the World Wide Web.Hawking was an icon for many reasons, but he will be best ___34___ for his work in the field of science. Building on German scientist Albert Einstein’s work, Hawking explained his belief that space started with the Big Bang, and will end with black holes. This ___35___ kicked off a series of investigations, including into the origin of the universe itself.His work in science aside, he also managed to overcome many difficulties in his personal life. While studying for a postgraduate degree in cosmology（宇宙学）at Cambridge University, he was ___36___ with motor neurone（运动神经元）disease at the age of 21. His illness left him paralyzed and he was told he only had a short time to live. However, as we all know, he went on to become one of the greatest minds the world has ever known. “I felt it was very unfair – why should this happen to me,” he wrote in his 2013 memoir（回忆录）. “At the time, I thought my life was over and that I would never realize the ___37___ I felt I had. But now, 50 years later, I can be quietly satisfied with my life.”Hawking leaves behind a great ___38___. His ___39___ book A Brief History of Time: From the Big Bang to Black Holes, published in 1988, became one of the world’s best-selling science publications. He may no longer be with us, but Hawking will continue ___40___ the world for generations to come. As he once said himself, “Look up at the stars and not down at your feet.”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.How important is a degree for a career? Do you need a degree in order to fulfill your dreams?There are some careers for which formal training and a degree is a(n) ___41___ must. Would you be willing to see a doctor who hadn’t ___42___ the mechanics of the human body? How about ___43___ an architect to build your house who had never seen a floor plan before? I didn’t think so. So if you want to become a doctor, and architect, an accountant, an engineer, a dentist or any of those jobs for which ___44___ skills are needed, then the answer to the question above is straightforward. It’s very important! But for most people, professional aspirations are ___45___ vague and many of us do a degree in a subject we are good at in the hope that all will become ___46___.A university degree can make you ___47___. Today, the job market is ___48___. There are lots of people competing for the jobs ___49___ and how is an employer to choose? If you have a university degree and have spent time learning and educating yourself, this is attractive to a potential ___50___. Furthermore, ___51___ enriching activities (particularly being involved in a team) while at university can show that you are a team player, which can be very important in the world of work.During your university degree you will learn much more than simple facts. You will learn about yourself, it can ___52___ you for situations in your future that could ___53___ be discouraging. You will need to learn to work and live with others, you will have access to world experts and be given the ___54___ to develop special skills and qualities you might never have known you had! It’s anopportunity for great personal ___55___ but it also teaches you discipline.41. A. relative B. various C. secondary D. absolute42. A. learnt B. taught C. managed D. suffered43. A. dismissing B. practicing C. employing D. persuading44. A. highly-paid B. highly-specializedC. highly-regardedD. highly- organized45. A. at least B. at large C. at most D. at best46. A. clear B. vague C. efficient D. convenient47. A. give out B. bring out C. stand out D. wear out48. A. necessary B. tough C. inspiring D. enormous49. A. accessible B. advisable C. sensible D. available50. A. competitor B. colleague C. employer D. advisor51. A. engaging in B. dropping in C. looking into D. running into52. A. allow B. prepare C. provide D. mistake53. A. furthermore B. hence C. otherwise D. therefore54. A. chance B. situation C. presentation D. method55. A. talent B. career C. dream D. growthSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Every April I am troubled by the same concern -- that spring might not occur this year. The landscape looks dull, with hills, sky and forest appearing gray. My spirits ebb, as they did during an April snowfall when I first came to Maine 15 years ago. “Just wait,”a neighbor advised. “You’ll wake up one morning and spring will just be here.”And look, on May 3 that year I awoke to a green so amazing as to be almost electric, as if spring were simply a matter of flipping a switch. Hills, sky and forest revealed their purples, blues and green. Leaves had unfolded and daffodils were fighting their way heavenward.Then there was the old apple tree. It sits on an undeveloped lot in my neighborhood. It belongs to no one and therefore to everyone. The tree’s dark twisted branches stretch out in unpruned（未经修剪的）abandon. Each spring it blossoms so freely that the air becomes filled with the scent of apple.Until last year, I thought I was the only one aware of this tree. And then one day, in a bit of spring madness, I set out with pruner to remove a few disorderly branches. No sooner had I arrived under the tree than neighbors opened their windows and stepped onto their porches. These were people I barely knew and seldom spoke to, but it was as if I had come uninvited into their personal gardens.My mobile-home neighbor was the first to speak. “You’re not cutting it down, are you?”sheasked anxiously. Another neighbor frowned as I cut off a branch. “Don’t kill it, now,” he warned.Soon half the neighborhood had joined me under the apple tree. It struck me that I had lived there for five years and only now was learning these people’s names, what they did for a living and how they passed the winter. It was as if the old apple tree was gathering us under its branches for the purpose of both acquaintanceship and shared wonder. I couldn’t help recalling Robert Frost’s words: The trees that have it in their pent-up budsTo darken nature and be summer woodsOne thing led to another. Just the other day I saw one of my neighbors at the local store. He remarked how this recent winter had been especially long and complained of not having seen or spoken at length to anyone in our neighborhood. And then, he looked at me and said, “We need to prune that apple tree again.”56. By saying that “my spirits ebb” (Para. 1), the author means that _________________.A.he feels relievedB. he feels blueC. he is surprisedD. he is tired57. The apple tree mentioned in the passage is most likely to _________________.A. be regarded as a delight in the neighborhoodB. have been abandoned by its original ownerC. have been neglected by everyone in the communityD. be appealing only to the author58. In Para. 4, “neighbors opened their windows and stepped onto their porches”probably because _____.A.they were surprised that someone unknown was pruning the treeB.they wanted to prevent the author from pruning the treeC.they were concerned about the safety of the treeD.they wanted to get to know the author59. It can be inferred that the author’s neighbor mentioned in the last paragraph most cared about __________.A.when spring would arriveB. how to pass the long winterC. the neighborhood gatheringD. the pruning of the apple tree(B)You probably know who Marie Curie was, but you may not have heard of Rachel Carson. Of the outstanding ladies listed below, who do you think was the most important woman of the past 100 years?Jane Addams (1860-1935)Anyone who has ever been helped by a social worker has Jane Addams to thank. Addams helped the poor and worked for peace. She encouraged a sense of community(社区)by creating shelters and promoting education and services for people in need. In 1931, Addams became the first American woman to win the Nobel Peace Prize.Rachel Carson (1907-1964)If it weren’t for Rachel Carson, the environmental movement might not exist today. Her popular 1962 book Silent Spring raised awareness of the dangers of pollution and the harmful effects of chemicals on humans and on the world’s lakes and oceans.Sandra Day O’Connor (1930-present)When Sandra Day O’Connor finished third in her class at Stanford Law School, in 1952, she could not find work at a law firm because she was a woman. She became an Arizona state senator(参议员) and, in 1981, the first woman to join the U. S. Supreme Court. O’Connor gave the deciding vote in many important cases during her 24 years on the top court.Rosa Parks (1913-2005)On December 1, 1955, in Montgomery, Alabama, Rasa Parks would not give up her seat on a bus to a passenger. Her simple act landed Parks in prison. But it also set off the Montgomery bus boycott. It lasted for more than a year, and kicked off the civil-rights movement. “The only tired I was, was tired of giving in,” said Parks.60. What is Jane Addams noted for in history?A. Her social work.B. Her teaching skills.C. Her efforts to win a prize.D. Her community background.61. Who made a great contribution to the civil-rights movement in the U.S.?A. Jane Addams.B. Rachel Carson.C. Sandra Day O’Connor.D. Ross Parks.62. What can we infer about the women mentioned in the text?A. They are highly educated.B. They are truly creative.C. They are pioneers.D. They are peace-lovers.(C)Does Fame Drive You Crazy?Although being famous might sound like a dream come true, today’s star, feeling like zoo animals, face pressures that few of us can imagine. They are at the center of much of the world’s attention. Paparazzi (狗仔队) camp outside their homes, cameras ready. Tabloids (小报) publish thrilling stories about their personal lives. Just imagine not being able to do anything without being photographed or interrupted for a signature.According to psychologist Christina Villareal, celebrities — famous people — worry constantly about their public appearance. Eventually, they start to lose track of who they really are, seeing themselves the way their fans imagine them, not as the people they were before everyone knew their names. “Over time,” Villareal says, “they feel separated and alone.”The phenomenon of tracking celebrities has been around for ages. In the 4th century B.C., painters followed Alexander the Great into battle, hoping to picture his victories for his admirers. When Charles Dickens visited America in the 19th century, his sold-out readings attracted thousandsof fans, leading him to complain about his lack of privacy. Tabloids of the 1920s and 1930s ran articles about film-stars in much the same way that modern tabloids and websites do.Being a public figure today, however, is a lot more difficult than it used to be. Superstars cannot move about without worrying about photographers with modern cameras. When they say something silly or do something ridiculous, there is always the Internet to spread the news in minutes and keep their “story” alive forever.If fame is so troublesome, why aren’t all celebrities running away from it? The answer is there are still ways to deal with it. Some stars stay calm by surrounding themselves with trusted friends and family or by escaping to remote places away from big cities. They focus not on how famous they are but on what they love to do or whatever made them famous in the first place.Sometimes a few celebrities can get a little justice. Still, even stars who enjoy full justice often complain about how hard their lives are. They are tired of being famous already.63. It can be learned from the passage that stars today______________.A. are often misunderstood by the publicB. can no longer have their privacy protectedC. spend too much on their public appearanceD. care little about how they have come into fame64. What is the main idea of Paragraph 3?A. Great heroes of the past were generally admired.B. The problem faced by celebrities has a long history.C. Well-known actors are usually targets of tabloids.D. Works of popular writers often have a lot of readers.65. What makes it much harder to be a celebrity today?A. Availability of modern media.B. Inadequate social recognition.C. Lack of favorable chances.D. Huge population of fans.66. What is the author’s attitude toward modern celebrity?A. Sincere.B. Skeptical.C. Disapproving.D. Sympathetic.(D)Old people are always saying that the young are not what they were. The same comment is made from generation to generation and it is always true. It has never been truer than it is today. The young are better educated. They have a lot more money to spend and enjoy more freedom. They grow up more quickly and are not so dependent on their parents. They think more for themselves and do not blindly accept the ideas of their elders. Events which the older generation remembers vividly are nothing more than past history. Every new generation is different from the older one and today the difference is very marked indeed.The old always assume that they know best for the simple reason that they have been around a bit longer. They don’t like to feel that their values are being questioned or threatened. And this is precisely what the young are doing. They take leave to doubt that the older generation has created thebest of all possible worlds. What they reject more than anything is conformity(一致性).Office hours, for instance, are nothing more than enforced slavery. Wouldn’t people work best if they were given complete freedom and responsibility? And what about clothing? Who said that all the men in the world should wear drab grey suits and convict haircuts? If we turn our minds to more serious matters, who said that human differences can best be solved through conventional politics or by violent means? Why have the older generation so often used violence to solve their problems? Why are they so unhappy and guilt-ridden in their personal lives, so obsessed with mean ambitions and the desire to amass(积聚) more and more material possessions? Haven’t the old lost touch with all that is important in life?These are not questions the older generation can shrug off lightly. Traditionally, the young have turned to their elders for guidance. Today, the situation might be reversed. The old could learn a thing or two from their children. One of the biggest lessons they could learn is that enjoyment is not ‘sinful’. It is surely not wrong to enjoy your work and enjoy your leisure. It is surely not wrong to live in the present rather than in the past or future. This emphasis on the present is only to be expected because the young have grown up under the shadow of the bomb: the constant threat of complete destruction.67. The old might be most displeased with the young generation’s ____________.A. Questioning their knowledge and valuesB. Looking at everything in a negative wayC. Spending money freelyD. Demanding too much freedom68. What do the young reject most?A. ValuesB. The assumption of the elders.C. Conformity.D. Conventional ideas.69. From the last paragraph, we know the author may support the idea that _____________.A. young people should show more respect to their eldersB. the old should not limit their children’s development a lotC. young people should always ask their elders for adviceD. the old should enjoy life70. What makes the young generation only want to emphasize the present?A. They are more realistic than the elders.B. They expect a life of pleasure.C. They think the past and future have nothing to do with them.D. They are faced with the threat of complete destruction frequently.71. The passage is mainly about __________________.A. the thing the old should learn from young generationsB. the difference between the young and the oldC. the reason that the old don’t like their values to be questionedD. the reason that young generations put emphasis on their presentSection CDirections: After reading the passage below, choose the best answers from the six statementsVoluntourismV olunteering to help people in need combined with travelling to faraway places is a new trend in the travel industry. It is called voluntourism. People travel to other countries, learn languages and gain new experiences. They find it is the best way to get the best of the world.Recent statistics show that in the past few years voluntourism has been one of the fastest-growing areas of tourism. More than 1.6 million people around the world are volunteers in other countries. They help build schools, assist in hospitals and do farming work in developing countries. 72 They keep in touch with their host families after they return home, and many return to vi sit.There are many reasons why people want to engage in voluntourism. When people choose to join a voluntourism program, they are joining a global network of volunteers who are living and working with diverse cultures on projects that have a positive effect. The volunteers come from all over the world, and they will share the passion for giving back and the desire to broaden horizons. Some students also see it as a gap year after school, while others simply want to take time out from a job and do something else. 73 However, many voluntourists do not see volunteering as what it is. They think it is a cheap way of travelling and don’t really want to get involved in hard work.While voluntourism has been around for over a century, modern volunteering started with the Peace Corps, a program that the US government started in the 1960s. From then on, voluntourism has become more and more popular. Many organizations start similar projects. 74 And they have hundreds of different types of programs for people to choose from in more than 30 developing countries. The programs run year round and each volunteer chooses when they want to start and the duration they would like to stay for.75 They say that if people really want to help those in need, there are many opportunities in their own community to do this. On the other side, volunteers are often not skilled enough for the tasks that they do. Travel experts point out that in some cases voluntourists are often taken advantage of by the organization that sets up the trips.第II卷（共40分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets. 1. 学生们为能够提前完成任务而自豪。

高二上学期第一次月考数学试题含答案XXX高二第一次月考数学试题（2018.9）注意：本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，满分150分，时间120分钟。

每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

在试题卷上作答无效。

第Ⅰ卷一、选择题（本大题共12小题，每小题5分，共60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.已知数列1,3,5,7.92.则1,37是它的第（）A.第30项B.第31项C.第32项D.第33项2.一个各项为正数的等比数列，其每一项都等于它前面的相邻两项之和，则公比q=（）A.3/2B.5C.(5-1)/2D.(5+1)/23.已知三角形三边比为5:7:8，则最大角与最小角的和为（）A.90°B.120°C.135°D.150°4.已知锐角三角形ABC的面积为32，BC=4，CA=3，则角C的大小为（）A.75°B.60°C.45°D.30°5.设等差数列{an}的前n项和为Sn，若2a6=6+a7，则S9的值为（）A.27B.36C.45D.546.在△ABC中，若2cosBsinA=sinC，则△ABC一定是（）A.等腰直角三角形B.等腰三角形C.直角三角形D.等边三角形7.“远望巍巍塔七层，红光点点倍加增，共灯三百八十一，请问尖头几碗灯？”源自明代数学家XXX所著的《九章算术比类大全》，通过计算得到答案是（）A.2B.3C.4D.58.在△ABC中，若A=30°，a=6，b=4，则满足条件的△ABC（）A.有一个B.有两个C.不存在D.不能确定9.设等差数列{an}的前n项和为Sn，若Sm=2，S2m=10，则S3m=（）A.14B.24C.32D.4210.数列{(n+2)/(8/7)}的最大项为第k项，则k=（）A.5或6B.5C.6D.无法确定11.在坡度一定的山坡A处测得山顶上一建筑物CD的顶端C对于山坡的斜度为15°，向山顶前进100米到达B后，又测得C对于山坡的斜度为45°，若CD=50米，山坡对于地平面的坡角为θ，则cosθ=（）A.(23+1)/3B.(23-1)/3C.3-1D.3+112.已知数列{an}的通项公式为an=n^3-4n，则a10的值为（）A.596B.724C.900D.1024二、非选择题13.已知函数f(x)=2x^3-3x^2-12x+5，求f(-2)和f(3)的值。

2017—2018学年上学期第一次月考高二数学试卷命题人： 校对人：考试时间：120分钟 满分：150分本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。

第I 卷（选择题 共60分）一、选择题（本大题共12小题，每小题5分，共60分，在每小题给出的四个选项中，只有一项是最符合题目要求的。

）1．已知ABC ∆中4,30a b A === ，则B 等于（ ）A 、60°B ．60°或120°C ．30°D ．30°或150° 2．正项等比数列{}n a 中，312a =，23S =，则公比q 的值是（ ） A ．12 B ．12- C ．1或12- D ．-1或12- 3．已知△ABC 中，，则等于（ ）．C ．D ．4．已知等差数列}{n a 的前n 项和为n S ，且7218a a -=，=8S （ ）A ．18B ．36C ．54D ．72 5．已知，α∈（0，π），则sin2α=（ ） A ．﹣1 B ． C ．D ．16．△ABC 中，若，则△ABC 的形状为（ ）A. 直角三角形B. 等腰三角形C. 等边三角形D. 锐角三角形7．数列{}n a 满足1111,12n na a a +==-，则2010a 等于（ ）A 、12B 、-1C 、2D 、3 8．若△ABC 的内角A ，B ，C 满足6sinA=4sinB=3sinC ，则cosB=（ ）A. B. C.D.9．中国古代数学著作《算法统综》中有这样一个问题：“三百七十八里关，初步健步不为难，次日脚痛减一半，六朝才得到其关，要见次日行里数，请公仔仔细算相还”.其大意为：“有一个走378里路，第一天健步行走，从第二天起脚痛每天走的路程为前一天的一半，走了6天后到达目的地”.则该人第五天走的路程为（ ）A. 48里B. 24里C. 12里D. 6里 10．已知1322152,41,2,}{++++==n n n a a a a a a a a a 则是等比数列（ ） A.)41(16n -- B.)21(16n -- C.)41(332n -- D.)21(332n -- 11．要测量顶部不能到达的电视塔AB 的高度, 在C 点测得塔顶A 的仰角是45°,在D 点测得塔顶A 的仰角是30°,并测得水平面上的∠BCD=120°, CD=40m, 则电视塔的高度为（ ）A ．102mB ．20mC ．203mD ．40m 12．已知数列{}n a 满足：11a =，1(*)2n n n a a n N a +=∈+，若11()(1)(*)n nb n n N a λ+=-+∈，1b λ=-，且数列{}n b 的单调递增数列，则实数λ的取值范围为（ ）A ．2λ>B ．3λ>C ．2λ<D ．3λ<ABD第Ⅱ卷（非选择题 共90分）二、填空题（本大题共4小题， 每小题5分，共20分，把答案填在题中横线上）。