2016-2017学年度上学期高三12月联考试题

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精选高三数学上学期12月月考试卷理

2016—2017学年度上学期12月阶段测试高三（17届）数学理科试题命题：高三数学备课组说明：1、测试时间：120分钟总分：150分2、客观题涂在答题卡上，主观题答在答题纸上第Ⅰ卷（60分）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.设集合}log ,3{2a P =，{}b a Q ,=，若}0{=Q P ，则=Q P （） A.{}0,3 B.{}2,0,3 C.{}1,0,3 D.{}2,1,0,32．若奇函数f （x ）的定义域为R ，则有（）A ．f （x ）＞f （-x ） C ．f （x ）≤f （-x ） C ．f （x ）·f （-x ）≤0 D ．f （x ）·f （-x ）＞03．若a,b 是异面直线，且a ∥平面，那么b 与平面的位置关系是（）A ．b ∥B ．b 与相交C ．b ⊂D ．以上三种情况都有可能4.下列函数中，图象的一部分如右图所示的是（）（A ）sin 6y x π⎛⎫=+⎪⎝⎭ （B ）sin 26y x π⎛⎫=- ⎪⎝⎭（C ）cos 43y x π⎛⎫=- ⎪⎝⎭ （D ）cos 26y x π⎛⎫=- ⎪⎝⎭5.已知等比数列{n a }的前n 项和12-=n n S ，则++2221a a …2n a +等于（）A ．2)12(-nB ．)12(31-nC ．14-nD ．)14(31-n6．若两个非零向量，满足|+|=|﹣|=2||，则向量+与﹣的夹角是（）A ．B ．C ．D ．7．设变量x ，y 满足约束条件，则z=﹣2x+y 的最小值为（）A ． ﹣7B ． ﹣6C ． ﹣1D ． 28．下列函数中在上为减函数的是（）A ．y=﹣tanx B．C ．y=sin2x+cos2xD ．y=2cos 2x ﹣19.圆柱被一个平面截去一部分后与半球（半径为r ）组成一个几何体，该几何体的三视图中的正视图和俯视图如图所示，若该几何体的表面积为1620π+，则r =( ) （A ）1 （B ）2 （C ）4 （D ）810.已知三个互不重合的平面γβα、、，且c b a ===γβγαβα ,,，给出下列命题：①若c a b a ⊥⊥,，则c b ⊥；②若P b a = ，则P c a = ；③若c a b a ⊥⊥,，则γα⊥；④若b a //，则c a //．其中正确命题个数为（）A ．1个B ．2个C ．3个D ．4个11．已知点P 为函数f （x ）=lnx 的图象上任意一点，点Q 为圆[x ﹣（e+）]2+y 2=1任意一点，则线段PQ 的长度的最小值为（） A．B．C．D ．e+﹣112．已知f （x ）=x （1+lnx ），若k ∈Z ，且k （x ﹣2）＜f （x ）对任意x ＞2恒成立，则k 的最大值为（）A ． 3 B. 4 C ． 5 D ． 6 第Ⅱ卷（90分）二．填空题（本大题共4小题，每小题5分，共20分）_____)1()10()0(2)0)(1(log )(.13123=-+⎪⎩⎪⎨⎧≤>-=+f f x x x x f x ，则14.,0,5a b a b >+=若________15．正三角形ABC 的边长为2，将它沿高AD 翻折，使点B 与点C间的距离为，此时四面体ABCD 外接球表面积为______． 16．过双曲线=1（a ＞0，b ＞0）的左焦点F （﹣c ，0）作圆x 2+y 2=a 2的切线，切点为E ，延长FE 交抛物线y 2=4cx 于点P ，O 为原点，若，则双曲线的离心率为．三．解答题（本大题共6小题,满分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12分）已知函数)0(2sin 2)sin(3)(2>+-=ωωωm xx x f 的最小正周期为π3，当[0,]x π∈时，函数()f x 的最小值为0. （Ⅰ）求函数)(x f 的表达式；（Ⅱ）在△ABC ，若A C A B B C f sin ),cos(cos sin 2,1)(2求且-+==的值 18. （本小题满分12分）设各项均为正数的数列{}n a 的前n 项和为n S ,满足21441,,n n S a n n N *+=--∈且2514,,a a a 构成等比数列. (1) 证明:2a =(2) 求数列{}n a 的通项公式; (3) 证明:对一切正整数n ,有1223111112n n a a a a a a ++++<. 19. （本小题满分12分）如图，四棱锥S —ABCD 的底面是正方形，SD ⊥平面ABCD ，SD=2a ，AD =点E 是SD 上的点，且(02)DE a λλ=<≤（Ⅰ）求证：对任意的(0,2]λ∈，都有AC BE ⊥ （Ⅱ）设二面角C —AE —D 的大小为θ，直线BE 与平面ABCD 所成的角为ϕ，若tan tan 1θϕ=g ，求λ的值. 20. （本小题满分12分）已知点F 为抛物线2:4C y x =的焦点，点P 是准线l 上的动点，直线PF 交抛物线C 于,A B 两点，若点P 的纵坐标为(0)m m ≠，点D 为准线l 与x 轴的交点．（1）求直线PF 的方程；（2）求DAB ∆的面积S 范围；（3）设AF FB λ=，AP PB μ=，求证λμ+为定值 21. （本小题满分12分）设函数()1xf x e -=-.(Ⅰ)证明:当x ＞-1时,()1x f x x ≥+; (Ⅱ)设当0x ≥时,()1xf x ax ≤+,求a 的取值范围.请考生在第22、23题中任选一题作答，如果多做，则按所做的第一题计分。

2017届高三数学12月联考试题理

行唐县第三中学、正定县第三中学、正定县第七中学2016—2017学年第一学期12月联考试卷高三数学（理科）时间:120分钟满分:150分第Ⅰ卷一、选择题：共12小题，每小题5分，共60分．在每个小题给出的四个选项中，只有一项是符合题目要求的一项．1．已知集合A ＝{x |x 2－2x －3≥0}，B ＝{x |－2≤x ＜2}，则A ∩B ＝( )A ．[－2，－1]B ．[－1,2)C ．[－1,1]D ．[1,2) 2．设z ＝11＋i＋i ，则|z |＝( )A.12B.22C.32D ．2 3．设向量a ，b 满足|a ＋b |＝10，|a －b |＝6，则a ·b ＝( )A ．1B ．2C ．3D ．5 4．抛物线y 2＝8x 的焦点到直线x －3y ＝0的距离是( )A ．2 3B ．2C.3D ．15．设m ，n 是两条不同的直线，α，β是两个不同的平面( )A ．若m⊥n，n ∥α，则m⊥αB ．若m∥β，β⊥α，则m⊥αC ．若 m⊥β，n ⊥β，n ⊥α，则 m⊥αD ．若 m⊥n，n ⊥β，β⊥α，则m⊥α6．4位同学各自在周六、周日两天中任选一天参加公益活动，则周六、周日都有同学参加公益活动的概率为( ) A.18B.38 C.58D.787．若变量x ，y 满足约束条件⎩⎪⎨⎪⎧x ＋y≤8，2y －x≤4，x ≥0，y ≥0，且z ＝5y －x 的最大值为a ，最小值为b ，则a －b 的值是( )A ．48B ．30C ．24D ．168．将函数y ＝3sin ⎝⎛⎭⎪⎫2x ＋π3的图象向右平移π2个单位长度，所得图象对应的函数( ) A ．在区间⎣⎢⎡⎦⎥⎤π12，7π12上单调递减B ．在区间⎣⎢⎡⎦⎥⎤π12，7π12上单调递增C ．在区间⎣⎢⎡⎦⎥⎤－π6，π3上单调递减D ．在区间⎣⎢⎡⎦⎥⎤－π6，π3上单调递增 9．设等差数列{a n }的前n 项和为S n ，若S m －1＝－2，S m ＝0，S m ＋1＝3，则m ＝( )A ．3B ．4C ．5D ．6 10．由曲线y ＝x ，直线y ＝x －2及y 轴所围成的图形的面积为( )A.103B ．4 C.163D ．6 11．已知抛物线C ：y 2＝8x 的焦点为F ，准线为l ，P 是l 上一点，Q 是直线PF 与C 的一个交点，若，则|QF |＝( )A.72B.52C ．3D ．2 12．已知函数f (x )＝ax 3－3x 2＋1，若f (x )存在唯一的零点x 0，且x 0＞0，则a 的取值范围为( )A ．(2，＋∞) B．(－∞，－2) C ．(1，＋∞) D．(－∞，－1)第Ⅱ卷二、填空题：本大题共4小题，每小题5分．13．直线x ＋2y －5＋5＝0被圆x 2＋y 2－2x －4y ＝0截得的弦长为________． 14．在△ABC 中，内角A ，B ，C 所对的边分别是a ，b ，c.已知b －c ＝14a ，2sin B ＝3sin C ，则cos A 的值为________．15．若数列{a n }的前n 项和 S n ＝23a n ＋13，则{a n }的通项公式是a n ＝ .16．已知三棱锥S －ABC 的所有顶点都在球O 的球面上，△ABC 是边长为1的正三角形，SC 为球O 的直径，且SC ＝2，则此棱锥的体积为______________ .三、解答题：解答应写出文字说明，证明过程或演算步骤．17．(12分)C ∆AB 的内角，，所对的边分别为，，．向量(),3m a b = 与()cos ,sin n =A B 平行．（I ）求；（II ）若a =2b =求C ∆AB 的面积．18. (12分)如图，四棱锥PABCD 中，底面ABCD 为矩形，PA ⊥平面ABCD ，E 为PD 的中点．(1)证明：PB∥平面AEC ；(2)设二面角D AEC 为60°，AP ＝1，AD ＝3，求三棱锥E ACD 的体积．19. (12分)端午节吃粽子是我国的传统习俗，设一盘中装有10个粽子，其中豆沙粽2个，肉粽3个，白粽5个，这三种粽子的外观完全相同，从中任意选取3个。

【月考试卷】安徽省滁州2017届高三上学期12月月考英语试卷 Word版含答案

滁州中学2016—2017学年度第一学期半月考高三英语试卷（满分：150分用时：120分钟命题：高三英语备课组）注意事项：1. 答题前，务必在试题卷、答题卡规定的地方填写自己的姓名、座位号。

2. 答第Ⅰ卷时，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。

3. 答第Ⅱ卷时，请在答题卷上．．．．书写，要求认真审题、仔细作答、字体工整、笔迹清晰。

第Ⅰ卷第一部分听力（共两节，满分30分）第一节听下面5段对话，每段对话后有一个小题。

从题中所给的A,B,C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1.What are the speakers talking about?A. Having a birthday party.B. Doing some exercise.C. Getting Lydia a gift2.What is the woman going to do?A. Help the man.B. Take a bus.C. Get a camera.3.What does the woman suggest the man do?A. Tell Kate to stopB. Call Kate’s friendsC.Stay away Kate4.Where does the conversation probably take place?A. In a wine shopB. In a supermarketC.In a restaurant.5.What does the woman mean?A. Keep the window closed.B. Go out for fresh air.C. Turn on the fan.第二节听下面5段对话或独白。

2016-2017学年河北省沧州市高三12月联考文数(详细答案版)

2016-2017学年河北省沧州市高三12月联考文数一、选择题：共12题1．已知全集,集合,则A. B. C. D.【答案】A【解析】本题主要考查集合的基本运算.,则.2．设是虚数单位,复数为纯虚数,则实数为A. B. C. D.【答案】C【解析】本题主要考查复数的四则运算、纯虚数. 复数为纯虚数,所以且，所以a=2.3．已知,则A. B. C. D.【答案】B【解析】本题主要考查二倍角公式、同角三角函数关系式.4．若正方形边长为为边上任意一点,则的长度大于的概率等于A. B. C. D.【答案】B【解析】本题主要考查几何概型.如图所示，当M、N分别是BC、DC的中点，且|AM|=|AN|=,当点E在折线段MCN上时，的长度大于，所以的长度大于的概率等于5．某几何体的三视图如图所示,则此几何体的外接球的表面积为A. B. C. D.【答案】C【解析】本题主要考查空间几何体的三视图、球的表面积与体积，考查了空间想象能力与逻辑推理能力.由三视图可知，该几何体是由一个长、宽、高分别为3,2,2的长方体截下的一个三棱锥，所以该几何体的外接球的直径的平方(2R)2=17,所以此几何体的外接球的表面积为6．已知命题,命题,则下列命题中为真命题的是A. B. C. D.【答案】B【解析】本题主要考查全称命题与特称命题、逻辑联结词，考查了逻辑推理能力.令x=4，则，故命题p是假命题；当时，成立，故命题q是真命题，因此是真命题，是假命题，所以答案为B.7．执行如图所示的程序框图,若输出的值为,则判断框内可填入的条件是A. B. C. D.【答案】D【解析】本题主要考查当型循环结构程序框图，考查了逻辑推理能力.运行程序：k=10，S=1;S=,k=11;S=,k=12;S=,k=13;S=,k=14;S=,k=15;S=,k=16,此时不满足条件，循环结束，输出k=16，所以判断框内可填入条件是8．若实数满足则只在点处取得最大值,则的取值范围为A. B.C. D.【答案】D【解析】本题主要考查线性规划问题，考查了数形结合思想与逻辑失推理能力.作出不等式组所表示的平面区域，如图所示，只在点处取得最大值,当a>0时，由目标函数z与直线在y轴上的截距之间的关系可知，,则0<a<1(如图中红线)；当a<0时，由目标函数z与直线在y轴上的截距之间的关系可知，只在点处取得最大值(如图中蓝线)；当a=0时，满足题意，因此，的取值范围是9．如图,在三棱锥中,,平面平面是的中点,则与所成角的余弦值为A. B. C. D.【答案】B【解析】本题主要考查线面、面面垂直的判定与性质、异面直线所成的角，考查了逻辑推理能力与空间想象能力.取AD的中点F，因为是的中点,所以EF//AC,则是与所成的角或补角，令，则AC=，EF=，由面面垂直的性质定理易得，则BE=，又BF=，在三角形BEF中，由余弦定理可得10．已知,函数在上单调递减,则的取值范围是A. B. C. D.【答案】A【解析】本题主要考查三角函数的图像与性质，考查了逻辑推理能力.因为，所以，因为函数在上单调递减,所以由正弦函数的单调性可得,即,当k=0时可得的取值范围是11．已知偶函数的定义域为,且是奇函数,则下面结论一定成立的是A.是偶函数B.是非奇非偶函数C. D.是奇函数【答案】D【解析】本题主要考查函数的图像与性质，考查了逻辑推理能力.因为偶函数的定义域为,所以函数的图像关于直线x=0对称，又因为是奇函数,所以函数的图像关于点对称，所以函数的对称轴为x=2n，n是整数，对称点为(2n+1,0),n是整数，则(3,0)是函数图像的对称点，将函数的图像向左平移3个单位可得函数，即对称点为(0,0),所以函数是奇函数，故答案为D.12．数列满足,则的前项和为A. B. C. D.【答案】C【解析】本题主要考查递推公式的应用、数列求和、等差数列求和，考查了逻辑推理能力与计算能力.，，，，，，，，，，所以，，，，，，，所以的前项和为项项二、填空题：共4题13．已知向量,向量的夹角为,则等于__________.【答案】【解析】本题主要考查平面向量的坐标表示与数量积，考查了计算能力.因为，向量的夹角为则,所以14．若,则的最小值是__________.【答案】【解析】本题主要考查基本不等式、对数的运算性质，考查了计算能力.由可得2xy=1，且x、y均为正数，则，当且仅当，即，时，等号成立.15．在中,．若以为焦点的椭圆经过点,则该椭圆的离心率为__________.【答案】【解析】本题主要考查椭圆的定义与性质、余弦定理，考查了逻辑推理能力与计算能力.令,由题意可得2c=4,由余弦定理可得,所以2a=，则该椭圆的离心率16．已知奇函数是定义在上的连续函数,满足,且在上的导函数,则不等式的解集为__________.【答案】【解析】本题主要考查导数、函数的性质，考查了转化思想与逻辑推理能力.令，因为奇函数是定义在上的连续函数,所以函数是定义在上的连续函数,则,所以函数在上是减函数，又，所以不等式的解集为三、解答题：共7题17．在等差数列中,,其前项和为,若为公差是的等差数列.(Ⅰ)求数列的通项公式;(Ⅱ)设数列,求数列的前项和．【答案】(Ⅰ)设的公差为,由,.当时,(Ⅱ)由(Ⅰ)知:.)【解析】本题主要考查等差数列的通项公式与前项和公式，考查了裂项相消法与计算能力.(1) 设的公差为,由题意得出通项公式，再利用等差数列的前项和公式，化简可得，由为公差是的等差数列，即可求出d，则可得结论；(2) 由(Ⅰ)知:，利用裂项相消法求和即可.18．如图,在四边形中,,将沿折起,得到三棱锥为的中点,为的中点,点在线段上,满足．(Ⅰ)证明:平面;(Ⅱ)若,求点到平面的距离.【答案】(Ⅰ)过点作的平行线,交直线于点,过点作的平行线,交直线于点,因为,所以,且,所以四边形为平行四边形,所以,且平面平面,所以平面.(Ⅱ)因为,所以,且,所以平面.由:,,所求点到平面的距离.【解析】本题主要考查折叠问题、线面、面面平行与垂直的判定与性质、点到平面的距离、空间几何体的体积，考查了转化思想、逻辑推理能力与空间想象能力.(1) 过点作的平行线,交直线于点,过点作的平行线,交直线于点,根据题意，证明四边形为平行四边形,则结论易得；(2)易证平面，由求解易得结论.19．某学校为了制定治理学校门口上学、放学期间家长接送孩子乱停车现象的措施,对全校学生家长进行了问卷调查.根据从其中随机抽取的份调查问卷,得到了如下的列联表:已知在抽取的份调查问卷中随机抽取一份,抽到不同意限定区域停车问卷的概率为．(Ⅰ)请将上面的列联表补充完整;(Ⅱ)是否有的把握认为是否同意限定区域停车与家长的性别有关?请说明理由; (Ⅲ)学校计划在同意限定区域停车的家长中,按照性别分层抽样选取人,在上学、放学期间在学校门口维持秩序．已知在抽取的男性家长中,恰有位日常开车接送孩子．现从抽取的男性家长中再选取人召开座谈会,求这两人中至少有一人日常开车接送孩子的概率．附临界值表及参考公式:,其中.【答案】(Ⅰ)列联表补充如下:(Ⅱ)因为,所以我们有的把握认为是否同意限定区域停车与家长的性别有关.(Ⅲ)男性家长人数,女性家长人数,所以,按照性别分层抽样,需从男性家长中选取人,女性家长中选取人.记位男性家长中不开车的为,开车的为.则从人中抽取人,有,共有种,其中至少有一人日常开车接送孩子的有,共种.则这两人中至少有一人日常开车接送孩子的概率为.【解析】本题主要考查独立性检验及其应用、古典概型、分层抽样，考查了分析问题与解决问题的能力.(1)由在抽取的份调查问卷中随机抽取一份,抽到不同意限定区域停车问卷的概率为，即可得出结论；(2)将表中的数据代入公式求出k2的观测值，再对照临界值表，即可得出结论；(3)由题意可知，按照性别分层抽样,需从男性家长中选取人,女性家长中选取人，记位男性家长中不开车的为,开车的为，从人中抽取人,列出所有的基本事件，再从中找出所求事件所包含的基本事件，利用古典概型的概率公式求解即可.20．已知抛物线,过动点作抛物线的两条切线,切点分别为,且. (Ⅰ)求点的轨迹方程;(Ⅱ)试问直线是否恒过定点?若恒过定点,请求出定点坐标;若不恒过定点,请说明理由. 【答案】(Ⅰ)设,则直线,代入抛物线方程:,因为直线与抛物线相切,所以,同理,有,所以分别为方程:的两个不同的实数根,,所以,所以点的轨迹方程为.(Ⅱ)设,由,所以抛物线在点的切线方程分别为,又都过点,所以所以直线的方程为,所以直线恒过定点.【解析】本题主要考查抛物线的方程与性质、导数的几何意义、直线方程、点的轨迹方程，考查了方程思想与逻辑推理能力.(1) 设,则直线,代入抛物线方程，由直线与抛物线相切可得,同理可得,则分别为方程:的两个不同的实数根, 结论易得；(2) 设,由导数可得过两点的切线方程, 又都过点,则直线AB的方程为,则可得结论.21．已知函数(Ⅰ)讨论函数的单调性;(Ⅱ)若函数存在两个极值点,且,若恒成立,求实数的取值范围．【答案】(Ⅰ),令,对应,若,即时,,此时函数在上单调递增.若时,即或时,当时,对应方程的根分别为,且由根与系数的关系可知:所以两根均为负数,此时函数在上单调递增.当时,对应方程的两根均为正数,且,此时函数在上单调递增,上单调递减,上单调递增.综上:当时,在上单调递增,当时,在上单调递增;在上单调递减;在上单调递增.(Ⅱ)由(Ⅰ)知,若函数有两个极值点,则,且即:,解得.,.,即函数在上单调递增,,即．综上可得:.【解析】本题主要考查导数、函数的性质与极点，考查了恒成立问题、分类讨论思想与转化思想、逻辑推理能力与计算能力.(1), 令,分、两种情况讨论求解即可；(2)由(Ⅰ)知,若函数有两个极值点,则,由易得，,求导，判断函数的单调性，并求出最大值，即可得出结论.22．在平面直角坐标系中,曲线的参数方程为为参数)若以坐标系原点为极点,轴正半轴为极轴建立极坐标系,曲线的极坐标方程为).(Ⅰ)求曲线的普通方程和曲线的直角坐标方程;(Ⅱ)将曲线向下平移)个单位后得到的曲线恰与曲线有两个公共点,求实数的取值范围.【答案】(Ⅰ)由已知,得),.(Ⅱ)将曲线向下平移)个单位后得到的曲线对应方程为,则当直线与圆相切时,,即,又直线恰过点时,,结合图象,可得.【解析】本题主要考查参数方程与极坐标，考查了参直与极直互化、图像变换、点到直线的距离公式.(1)消去参数可得曲线的普通方程)；由题意易得曲线的直角坐标方程；(2) 将曲线向下平移)个单位后得到的曲线对应方程为, 当直线与圆相切时,,求解，结合图象,可得结论.23．设函数.(Ⅰ)求函数的最小值;(Ⅱ)若有解,求实数的取值范围.【答案】(Ⅰ)由不等式的性质,可得,所以当且仅当时函数的最小值为.(Ⅱ)又函数恒过定点,结合函数图象,可得或.【解析】本题主要考查含绝对值不等式的解法、绝对值三角不等式，考查了逻辑推理能力.(1)利用绝对值三角不等式求解即可；(2)恒过定点, 结合函数图象,可得结论.。

2017届高三12月份联考英语试题(附答案)

考生注意：1.本试卷分第I（选择题）和第II卷（非选择题）两部分，共150分。

考试时间120分钟。

2.请将各题答案填在试卷后面的答题卡上。

3.本试卷主要考试内容：必修1――必修4第I 卷第一部分：听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A. ￡19.15B. ￡9.18C. ￡9.151. What sport does the man like at present?A. BasketballB. FootballC. Table tennis2. What is the woman going to do?A. Watch TVB. Go shoppingC. Stay at home3. What gift should the woman first buy in the man’s opinion?A. Olympic FuwaB. A pictureC. A CD4. What did the man see last night?A. A strange and noisy birdB. A red-colored birdC. A bird that flew very quietly5. Why does the woman ask for help?A. She is unable to read her mapB. She has lost her city mapC. She can’t find the museum in map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。

2016-2017度高三文科数学12月月考试卷 (教师用卷)资料讲解

2016-2017学年度高三文科数学12月月考试卷(教师用卷)九月教育2016-2017学年度11月月考试卷高三数学（文）考试范围：高考总复习内容；考试时间：120分钟；总分：150分；命题人：郑周立学生姓名：___________班级：___________注意事项：第I 卷（选择题）评卷人得分一、选择题（本题共12道小题，每小题0分，共0分）已知集合A={1,2,3}，B={x|x 2＜9}，则A∩B= （A ）{-2,-1,0,1,2,3}（B ）{-2,-1,0,1,2}（C ）{1,2,3} （D ）{1,2}答案及解析：1.D由x 2＜9得，-3＜x ＜3，所以B={x|-3＜x ＜3}，所以A∩B={1,2}，故选D. 2.设复数z 满足z +i =3-i ，则z =（A ）-1+2i （B ）1-2i （C ）3+2i （D ）3-2i答案及解析：2.C由z +i =3-i 得，z =3-2i ，故选C.3.已知向量()2,4a =，()1,1b =-，则2a b -=（） A.()5,7 B.()5,9 C.()3,7 D.()3,9答案及解析：3.A4.右图是由圆柱与圆锥组合而成的几何体的三视图，则该几何体的表面积为（A ）20π （B ）24π （C ）28π （D ）32π答案及解析：4.C几何体是圆锥与圆柱的组合体，设圆柱底面圆半径为r ，周长为c ，圆锥母线长为l ，圆柱高为h ．由图得2r =，2π4πc r ==，由勾股定理得：()222234l =+，S 表=πr 2+ch +21cl =4π+16π+8π=28π. 5.下列函数中，其定义域和值域分别与函数y=10lg x 的定义域和值域相同的是（A ）y =x （B ）y =lg x （C ）y =2x （D ）y x=答案及解析：5.Dy=10lg x =x ，定义域与值域均为(0,+∞)，只有D 满足，故选D ．6.过点P ）（1,3--的直线l 与圆122=+y x 有公共点，则直线l 的倾斜角的取值范围是（）(A)]60π，（ (B)]30π，（ (C)]60[π， (D)]30[π，答案及解析：6.D7.设x，y满足的约束条件1010330x yx yx y+-≥⎧⎪--≤⎨⎪-+≥⎩，则2z x y=+的最大值为（A）8 （B）7 （C）2 （D）1答案及解析：7.B..7,2).1,0(),2,3(),0,1(.Byxz故选则最大值为代入两两求解，得三点坐标，可以代值画可行区域知为三角形+=8.为了得到函数xxy3cos3sin+=的图象，可以将函数xy3sin2=的图象（）A.向右平移12π个单位长 B.向右平移4π个单位长C.向左平移12π个单位长 D.向左平移4π个单位长答案及解析：8.C9.执行如图所示的程序框图，输出的S值为（）A.1B.3C.7D.15开始输出结束是否答案及解析：9.C10.设等比数列{a n}的前n项和为S n，若S2=3，S4=15，则S6=( )A. 31B. 32C. 63D. 64答案及解析：10.C11.设F为抛物线C：y2=4x的焦点，曲线y=kx（k>0）与C交于点P，PF⊥x轴，则k= （A）12（B）1 （C）32（D）2答案及解析：11.D焦点F(1,0)，又因为曲线(0)ky kx=>与C交于点P，PF⊥x轴，所以21k=，所以k=2，选D.12.设函数()f x的定义域为R，(1)2f-=，对于任意的x R∈，()2f x'>，则不等式()24f x x>+的解集为（）A．(1,1)- B．()1,-+∞ C．(,1)-∞- D．(,)-∞+∞答案及解析：12.B第II 卷（非选择题）二、填空题（本题共4道小题，每小题0分，共0分）3种颜色的运动服中选择1种，则他们选择相同颜色运动服的概率为_______.答案及解析： 13.31.313131313131313131.3131=•+•+•••率为他们选择相同颜色的概色的概率也是同理，均选择红、或蓝为甲乙均选择红色的概率14.2.在等差数列{}n a 中，若a 1+ a 2+ a 3+ a 4=30，则a 2+ a 3= .答案及解析：14.1515.一个六棱锥的体积为2的正六边形，侧棱长都相等，则该六棱锥的侧面积为。

上海市十二校2017届高三12月联考英语试题

2016学年第一学期十二校联考英语试卷I. Listening ComprehensionPart A Short ConversationsDirections: In Part 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. Lend the man some money.B. Take the man to the bank.C. Ask the man when he’ll be paid.D. Help the man to draw some cash.2. A. She broke her mobile phone.B. She forgot to reply to the man.C. She didn’t get the man’s messages.D. She couldn’t remember the man’s phone number.3. A. He received permission to carry on an extra bag.B. He doesn’t know the woman ahead of him.C. He’s carrying someone else’s suitcase.D. He’d like some help with his luggage.4. A. Go to the city on another day.B. Avoid driving after taking her medicine.C. Pick up her medicine before they leave.D. Wait to take her medicine until after their trip.5. A. The air will be cleaner if they go to a different city.B. It’ll soon be too late to control the pollution.C. Society will not pay attention to the new laws.D. The situation will improve if changes are made.6. A. He didn’t have time to look for his jacket.B. He misunderstood the weather report.C. He didn’t know it would be cold.D. He forgot where his jacket was.7. A. Attend a conference with her.B. Mail her the paper after the deadline.C. Hand in a handwritten draft of the paper.D. Complete the course without handing in the paper.8. A. He saw Mary earlier.B. Someone else saw Mary.C. He can’t help the woman.D. Mary asked for directions to the office.9. A. She fell asleep before the program ended.B. She especially enjoyed the end of the program.C. She missed the beginning of the program.D. She wishes she had gone to sleep earlier.10. A. He may feel better soon.B. He doesn’t like to take pills.C. He may not be able to wake up.D. He may want to take the pills without food.Section BDirections: In Section B, you will hear several short passages and longer conversations, and you will be asked three questions on each of the passages and the conversations. The passages and the conversations will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. They couldn’t fall asleep there.B. There was no empty room available.C. The melting snow blocked their view.D. Their room was taken up by someone else.12. A. Skiing. B. Shopping. C. Bowling. D. Jogging. Questions 14 through 16 are based on the following passage.14. A. The scientific evidence that those who are good at sports make more money.B. The scientific evidence that the length of our fingers isn’t inherited from parents.C. Whether there is connection between numbers-based skills or words-based ones.D. Whether there is link between people’s talents and the length of their fingers.15. A. They are more likely to do well in sports.B. They are more likely to be interested in literature.C. They are less likely to be good at maths.D. They are less likely to make a big fortune.16. A. Cambridge scientists’ study challenged some established theories.B. Cambridge scientists’ study had chosen the improper subjects.C. Cambridge scientists’ findings may not be true to the fact.D. Cambridge scientists’ findings were the same as theirs.Questions 17 through 20 are based on the following conversation.17. A. The man’s terrible experience on the day.B. The woman’s unlucky first day at work.C. The woman’s boss, who is hard to deal with.D. The man’s daughter, who failed in the job interview.18. A. He feeds on vegetables alone.B. He seldom talks to his employees.C. He didn’t go to the meeting that day.D. He has decided to fire the woman.19. A. A cup of coffee. B. A salad.C. A hammer.D. A stone.20. A. Take a break. B. Apologise to her boss.C. Call her friends.D. Leave the company.II. Grammar and VocabularySection ADirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Lightning BoltUsain Bolt is the world’s fastest man. He first came to the public’s attention at the Beijing Olympics in 2008, where he won three gold medals. During that race, he reached a top speed of 43.9 kmph. So, we ask, how does the man (21)_____ nickname is “Lightning Bolt” run so fast?Usain Bolt was born in Jamaica on 21 August 1986. He was running around at primary school, when a teacher noticed (22)_____ talent for sprinting(短跑). He became one of the best sprinters at his high school even though he didn’t train very hard. At the age of fifteen, Bolt was 196 cm tall and he dominated the 2002 World Junior Championships, becoming the youngest person ever (23)_____ (win) the 200 metres. He turned professional when he left high school, (24)_____ (age) seventeen. During the first couple of years of Bolt’s professional life, he got a few injuries, but his health soon improved and he began to win all the major championships. He went from strength to strength, (25)_____ (amaze) the world with his speed.So, how does he do it? Bolt says that he is naturally fast—just something he was born (26)_____. He’s also got a number of people looking after him and one of the main reasons for his success is Norman Peart, his manager. Peart (27)_____ (look) after Bolt since he was fifteen, working hard to keep him focused.(28)_____ you explain it, Bolt’s performances in Beijing were truly marvellous. What’s more marvellous is (29)_____, since then, he has continued to get even faster. In August 2009, he broke his own record by running the 100 metres in 9.58 seconds. At the (30)_____ (fast) point in this race, he ran at an astonishing 44.9 kmph.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.Columbus: Myth and RealityEveryone knows the name of Christopher Columbus, and, as with any historical icon, there are as many myths as truths about the man. Take, for example, the disagreement about his 31 . The Spanish say he was from Spain, and the Italians claim he was from Italy. There is, in fact, some 32 that he was born in 1451 in Genoa, which is now part of Italy.Columbus became a sailor at an early age and had made journeys as far as Iceland and Guinea before he made his famous voyage in 1482. Contrary to popular 33 , Columbus didn’t sail to the Americas in order to find out whether the Earth was round: at the end of the 15th century almost everyone knew it was round. We do know that he sailed in part to fulfill a religious quest: he saw his journeys as a fulfillment of a divine (神圣的) plan for his life.Of course, the other 34 known reason for this voyage was that Columbus was looking for a new route to the Spice Islands (now part of Indonesia), and he believed he could reach them by sailing west rather than east. The discovery of the New World was therefore a(n) 35 case of “serendipity (机缘凑巧)”. In 1492, when he unexpectedly discovered the Americas, he had been traveling for five weeks and had sailed for 3,000 miles. He thought he had arrived in the East Indies.Columbus left on the voyage of discovery from the south of Spain, with a(n) 36 made up mainly of experienced sailors from the area. He made two 37 voyages before the end of the century, taking Europeans across to the new lands. On his third voyage in 1498, he also took women to the New World.This third voyage was not a happy one for Columbus. The settlers 38 against him, and he was unable to send a lot of gold back, so he was arrested and returned to Spain in chains. However, the King and Queen soon apologized, saying there had been a mistake, and Columbus was freed. By this time, 1500, Columbus was not a well man and he died quietly at the age of 55 in Valladolid, Spain, on May 20, 1506, in his own apartment 39 by family and friends. He was a(n) 40 rich man at the time of his death.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.Agree to DisagreeIn a world of 6.5 million opinionated people, arguments are sure to happen. Many people seearguments as an inevitable and negative part of life. Inevitable, yes; 41 , maybe not. Arguments can often lead to positive change—if you argue 42 .Arguing “well”“There 43 is such a thing as a ‘healthy argument’,” says Marian Donahue, a human relations professional, San Diego. “In a healthy argument, one’s own goal should be to explain the issues in detail, to communicate the upset behind the issues, and to really seek to move forward towarda 44 ,” she says. “The minimum goal should be to preserve the relationship well enough to keep45 alive.”What not to doNothing 46 a healthy argument like a personal attack, and personal attacks are a big no-no if you want an argument to end positively. Dina Connolly, a graduate student at Northwestern University, Illinois, says that when professional relationships start amassing (积累) personal baggage, 47 arguments are just around the corner.“The structure or wall of professionalism collapses,” Connolly says, “taking down any filters as well. 48 , after an individual interrupted and then corrected me while making a public speech, I later ended up in an argument where I completely lost my temper and raised my voice. I was embarrassed, and because my relationship with that person was already so deconstructed and unprofessional, I 49 with that person directly and unprofessionally in an unf iltered attack.”Don’t be 50 the heatDonahue 51 that personal issues must be left at the door—but that doesn’t mean arguments won’t get heated. “Passion and conflict are 52 in an argument as long as you keep to the issue,” she says. “Attacki ng the other person is not useful. That kind of argument closes down the 53 on both sides to keep talking.”By actively listening, many arguments can be 54 altogether. If you do find yourself in the thick of one, listening with an open mind can bring about a swift 55 to the argument and perhaps a positive resolution.41. A. sure B. argumentative C. negative D. changing42. A. confidently B. correctly C. heatedly D. hesitantly43. A. definitely B. barely C. accidentally D. clearly44. A. tendency B. destination C. purpose D. solution45. A. explanation B. communication C. cooperation D. negotiation46. A. kills B. helps C. keeps D. starts47. A. heated B. healthy C. nasty D. fresh48. A. For instance B. In addition C. As a result D. On the other hand49. A. stayed B. fought C. chatted D. argued50. A. keen on B. bored with C. afraid of D. eager for51. A. agrees B. denies C. orders D. recalls52. A. dependable B. invisible C. acceptable D. accessible53. A. gratitude B. impression C. influence D. willingness54. A. tracked B. avoided C. undertook D. grasped55. A. pace B. end C. movement D. decisionSection 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)Things changed for Ben Southall when the Australian state of Queensland advertised a job for someone to look after Hamilton Island in the Great Barrier Reef. They knew it sounded like the best job in the world, but they were surprised when over 35,000 people applied for the job. Then they had to make a difficult decision—which person to choose from so many candidates? After a lot of testing and interviewing, they announced 34-year-old Ben Southall from England as the winner. Ben now works for the Queensland Tourist Board and his job is to look after the island and to promote tourism there. Because of the unique nature of the job, the Tourist Board wanted a unique person, with a range of skills and qualities. It was a long interview process, involving a variety of tasks to find out about each candidate.Fitness was very important; swimming ability was particularly essential. Ben can swim very well and he also likes running, climbing, diving and mountain biking. It is clear that, physically, he can do almost anything. The ability to communicate was as important as fitness. For the last part of the interview process, the final sixteen andidates did various tests and tasks, including talking to TV and radio reporters. The competition was touch and the candidates needed to show what they could do. The interviewers were interested in how the candidates performed in the tasks, how they handled the press attention and their ability to write about their adventures in a daily log. The candidates did their best to impress the interviewers and they knew they couldn’t make any mistakes at this final stage.Before he went, Ben was confident about his abilities to handle the challenge. He couldn’t do everything they asked him in the interview, as he can’t speak any other languages, but he felt that his other skills and his personality were impressive. He made a huge effort during the interview process and he was able to convince the interviewers that he was the best person for the job. Even so, he says he was amazed when he got the job; he couldn’t believe it! He hopes to do a good job and promote the island successfully: he has to get to know every part of the island and tell the world about it in numerous media interviews. When you read Ben’s blogs from his interview tasks, it is easy to see why they chose him. He is funny and easy-going and he will certainly get the attention of any potential tourist to this beautiful place.56. According to the passage, Ben’s job includes all of the following EXCEPT _____.A. knowing Hamilton Island very wellB. going to Hamilton Island once a dayC. being interviewed in different mediaD. drawing travellers’ attention to the island57. During the interview process, the candidates were asked to_____.A. go through a fitness trainingB. take part in various TV showsC. write about their own interviewsD. communicate with the press58. Why was Ben chosen for the job?A. He is easy to get along with.B. He kept his personal blog very well.C. He used to be a swimming champion.D. He can speak several foreign languages.59. Which of the following might be the best title of the passage?A. Hamilton Island gets well protectedB. The funniest job in the worldC. Ben gets dream jobD. Tourism in Australia(B)60. The passage is most probably found in _____.A. a magazineB. a newspaperC. a textbookD. a guidebook61. In which section is a reader most likely to find what a person thinks of a historical event?A. Main IdeaB. Why It Matters NowC. Terms & NamesD. One American’s Story62. Heads are presented in different colours in order to _____.A. give readers a whole picture of the sectionB. help readers find different kinds of topicsC. attract readers’ attention, especially young readersD. get readers to identify most important points(C)In 1851, Auguste Comte, the French philosopher and father of sociology, coined the new word altruism as part of a drive to create a non-religious religion based on scientific principles. He defined it as “intentional action for the welfare of others that involves at least the possibility of either no benefit or a loss to the actor”. At that time, studies of animal behavior and phrenology (颅相学) led him to locate egotistical (自我本位的) instincts at the back of the brain, altruistic ones at the front.Today, we have a far more sophisticated knowledge of the neurological (神经学的) and biochemical factors that underpin kind behavior. And this science forms the bases of two books aimed at general readers—but also at those who, despite the research, still doubt the existence of altruism.However, the books may end up providing more information for those who are doubtful. Take The Altruistic Brain by neuroscientist Donald Pfaff. On solid scientific ground, he builds a five-step theory of how altruism occurs, which depends on an idea that is unconvincing and may achieve the opposite result. Pfaff argues that to act altruistically you should first visualize the receiver of your good will, then mentally tr ansform their image into your own, “from angle to angle and curve to curve”. Does it really work?At the core of evolutionary biologist David Sloan Wilson’s Does Altruism Exist?is another contentious (有争议的) idea: altruism has evolved as the result of group selection. But Wilson argues his corner masterfully, providing a clever reply to the belief that natural selection occurs only at the level of the selfish gene: “Selfishness beats altruism within groups. Altruistic groups beat selfish groups,” he says.In other words, we cooperate when doing so gives our team the advantage. That doesn’t sound very selfless either.Wilson acknowledges this, but argues that thoughts and feelings are less important than actions. According to evolutionary theory, pure altr uists do exist, but it doesn’t matter why people choose to help others—their reasons may be difficult even for themselves to understand. What matters is that humans can coordinate their activities in just the right way to achieve common goals. Other animals do this too, but we are masters. “Teamwork is the signature adaptation of our species,” he says.Pfaff goes further, insisting that our brain biology “urges us to be kind”. He believes this knowledge alone will inspire individuals to be more altruistic. His desire to create a better world is admirable and some of his ideas are interesting, but Wilson’s analysis is clearer.While it is in our nature to be altruistic, Wilson says, we also have a healthy regard for self-interest and a resistance to being pushed around. Which one comes to the fore depends on the environment in which we find ourselves. Ethics, he says, cannot be taught at individual level, but are “a property of the whole system”.63. Which of the following can be considered an altruistic beh aviour according to Comte’s definition?A. A person offers to donate his liver to another who needs one.B. A clerk returns the umbrella to his colleague which he has kept for a long time.C. A student volunteers to work in the orphanage to collect data for his research.D. A police officer spots a car parking in the no-parking area, finding a child in the trunk.64. What does Donald Pfaff think people should do in order to behave altruistically?A. Draw a picture of the person they are going to help.B. Transform the receiver into a kind person.C. Visualize what they are going to do in mind first.D. Imagine they themselves are to be helped.65. Which of the following statements is David Sloan most likely to agree with in his book?A. Being kind is not something people are born with.B. People in groups are less likely to be selfish.C. People may well act selflessly because of where they are.D. Most people know clearly why they are ready to help others.66. What can be concluded from the passage?A. Figuring out what makes us behave selflessly is a tricky business.B. Unlike Donald Pfaff’s book, David Sloan’s book aims at professional readers.C. Comte’s definition of altruism proves to be impractical in modern times.D. Both Donald Pfaff and David Sloan lay emphasis on team work.Section CDirections: Complete the following passage by using the sentences given below. Each sentence can be used only once. Note that there are two more sentences than you need.I owe it all to my community collegeIn 1974, I graduated from Skyline High School in Oakland, California, an underachieving student with poor SA T scores. I couldn’t afford tuition for college anyway. 67 .For thousands of commuting students like me, Chabot was our Harvard, offering course in physics, stenography, automechanics, certified public accounting, foreign language, journalism and so on. Classmates included veterans(老兵) back from Vietnam, married women returning to school, middle-aged men wanting to improve their employment prospects and paychecks. We could get our general education requirements out of the way at Chabot—credits we could transfer to a university—which made those two years an invaluable head start.Classes I took at Chabot have rippled(起涟漪) through my professional pond. I produced the HBO mini-series John Adams with an outline format I learned from a pipe-smoking historian, James Coovelis, whose lectures were interesting. Mary Lou Fitzgerald’s “Studies in Shakespeare” taught me how the five-act structures of Richard III, The Tempest, and Othello focused their themes.In Herb Kennedy’s “Drama in Performance,” I read plays like The Hot L Baltimore and Desire Under the Elms, then saw their productions. I got to see the plays he taught, through student rush tickets at the American Conservatory Theater in San Francisco and the Berkeley Repertory Theatre.68 I got an A. Some hours I stayed in the huge library, where I first read the New York Times, frustrated by its lack of comics.If Chabot’s library still has its collection of vinyl records (黑胶唱片), you will find my name repeatedly on the takeout slip of Jason Robards’s performance of the monologue of Eugene O’Neill.69Chabot College is still in Hayward, though Mr. Coovelis, Ms. Fitzgerald, and Mr. Kennedy are no longer there. I drove past the campus a few years ago with one of my kids and summed up my two years there this way: “70 ”A. I listened to it 20 times at least.B. That place made me what I am today.C. Community colleges have improved a lot these years.D. Those plays filled my head with expanded dreams.E. Of course, I enjoyed the pleasure of eating French fries between classes.F. So I sent my test results to Chabot, a community college in nearby Hayward, California, which accepted everyone and was free.IV．Summary WritingDirections: Read the following passage. Summarize in no more than 60 words the main idea of the passage and how it is illustrated. Use your own words as far as possible.Learn from mistakesThe best way to learn something is to make mistakes first. Thomas Edison, who invented the light bulb, told his colleagues: “Of the 200 light bulbs that didn’t work, every failure told me something I was able to incorporate i nto the next attempt.” Benjamin Franklin, the US statesman and scientist once said: “I haven’t failed. I have had 10,000 ideas that didn’t work.”Both these people understood that failures and false starts are the condition of success. In fact, a surprising number of everyday objects had their beginnings in a mistake or a misunderstanding. Post-it notes, packets of crisps and even bread are all unexpected inventions. In 2600 BC, a tired Egyptian slave invented bread when the dough rose during his sleep. And crisps were first cooked by a chef in the USA when a customer complained that his fried potatoes were not thin enough.In 1968 Spencer Silver was trying to develop a strong adhesive when he accidentally invented a very weak glue instead. His colleague, Art Fry, decided to use it six years later, in 1974, to hold his bookmarks in his books and the post-it note was invented.Successful businesspeople have often made big, expensive mistakes in their past. When anemployee of IBM made a mistake that cost the company $600,000, Thomos Watson, the chairman, was asked if he would fire the man. “Of course not,” he replied. “I have just spent $600,000 training him. I am not going to let another company benefit from experience.”The important thing to remember is that you need to learn from your mistakes. If you don’t, then there is no sense in making them.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 熬夜会大大消耗你的体力。

【月考试卷】辽宁省大连市2017届高三12月月考英语试题 Word版含答案

2016～2017学年度上学期12月月考试题高三英语试卷考试时间120分钟试题分数150卷I第一部分：听力（略）第二部分：阅读理解（共 2 节，满分40分）第一节（共15小题；每小题2分，满分30分）AOn one of her trips to New York several years ago, Eudora Welty decided to take a couple of New York friends out to dinner. They settled in at a comfortable East Side cafe and within minutes, another customer was approaching their table.“Hey, aren‟t you from Mississippi” the elegant, white-haired writer remembered being asked by the stranger. “I‟m from Mississippi too.”Without a second thought, the woman joined the Welty party. When her dinner partner showed up, she also pulled up a chair.“They began telling me all the news of Mississippi,” Welty said. “I didn‟t know what my New York friends were thinking.”Taxis on a rainy New York night are rarer than sunshine. By the time the group got up to leave, it was pouring outside. Welty‟s new friends immediately sent a waiter to fin d a cab. Heading back downtown toward her hotel, her big-city friends were amazed at the turn of events that had changed their Big Apple dinner into a Mississippi.“My friends said: …Now we believe your stories,‟” Welty added. “And I said: …Now you kno w. These are the people that make me write them.‟”Sitting on a sofa in her room, Welty, a slim figure in a simple gray dress, looked pleased with this explanation.“I don‟t make them up,” she said of the characters in her fiction these last 50 or so years. “I don‟t have to.”Welty‟s people come from afternoons spent visiting with old friends, from walks through the streets of her native land and from conversations overheard on a bus. It annoys Welty that, at 78, her left ear has now given out. Sometimes, sitting on a bus or a train, she hears only afragment(片段) of a particularly interesting story.21. What happened when Welty was with her friends at the café?A. Two strangers joined her.B. Her childhood friends came in.C. A heavy rain ruined the dinner.D. Some people held a party there.22. The underlined word “them” in Paragraph 6 refers to Welty‟s________ .A. readersB. partiesC. friendsD. stories23. What can we learn about the characters in Welty‟s fictio n?A. They live in big cities.B. They are mostly women.C. They come from real life.D. They are pleasure seekers.BAs Internet users become more dependent on the Internet to store information, are people remembering less? If you know your computer will save information, why store it in your own personal memory, your brain? Experts are wondering if the Internet is changing what we remember and how.In a recent study, Professor Betsy Sparrow conducted some experiments. She and her research team wanted to know the Internet was changing memory. In the first experiment, they gave people 40 unimportant facts to type into a computer. The first group of people understood that the computer would save the information. The second group understood that the computer would not save it. Later, the second group remembered the information better. People in the first group knew they could find the information again, so they did not try to remember it.In another experiment, the researchers gave people facts to remember, and told them where to find the information on the Internet. The information was in a specific computer folder (文件夹). Surprisingly, people later remembered the folder location better than the facts. When people used the Internet, they did not remember the information. Rather, they remembered how to find it. This is called "transactive memory (交互记忆)"According to Sparrow, we are not becoming people with poor memories as a result of the Internet. Instead, computer users are developing stronger transactive memories; that is, people are learning how to organize huge quantities of information so that they are able to access it at a later date. This doesn't mean we are becoming either more or less intelligent, but there is no doubt that the way we use memory is changing.24. The passage begins with two questions to ______.A. introduce the main topicB. show the author's altitudeC. describe how to use the Interne.D. explain how to store information25. What can we learn about the first experiment?A. Sparrow's team typed the information into a computer.B. The two groups remembered the information equally well.C. The first group did not try to remember the formation.D. The second group did not understand the information.26. In transactive memory, people ______.A. keep the information in mindB. change the quantity of informationC. organize information like a computerD. remember how to find the information27. What is the effect of the Internet according to Sparrow's research?A. We are using memory differently.B. We are becoming more intelligent.C. We have poorer memories than before.D. We need a better way to access information.CHow to Train Your Dragon by British author Cressida Cowell is one of the best pieces of children‟s literature. A child can make a whole alter native universe with a vivid imagination and Toothless, the hero‟s hunting dragon, thus turning a rainy day into an adventure of lifetime. However, if you have never read the book but instead choose to see the film version, you might think you were seeing a new-age war movie meant for adults rather than children.Let‟s look at Where the Wild Things Are for further discussion. The story centers around a lovely eight-year-old boy named Max, who sails away to an island. Creatures living there declare Max their king. What an amazing piece of children‟s literature! A treasure for every child‟s library. Yet, children were crying in the movie theatre. Owls were falling from the sky, chicken‟s arms were being torn off, and a child was running around a dark abandoned world, fighting evil as the only human. It was almost as if Hollywood could not imagine children enjoying a movie for its basic literature content. Hollywood might be right. But the audiences are complaining that there is more and more violence in ch ildren‟s stories today than in the past.While there appears to be a trend in our society to make more violence more accessible to younger children, books and literature are generally an exception. I truly believe that children‟sliterature has become more vivid and colorful. This is a great treasure for the children, and is certainly not violent. What has changed the children‟s stories of today is not the writers, but the film industry. In some way, children‟s literature is just being strangely twiste d. I wonder how much influence the author has over this.28. What can be inferred about the film Where the Wild Things Are?A. It is moving.B. It is frightening.C. It is interesting.D. It is amazing.29. Which of the following does the writer probably agree with?A. The film industry‟s treatment of children‟s literature is wrong.B. Writers should provide more colorful works for children.C. There is an increase in violence in children‟s literature.D. Children should read books rather than see films.30. How is the text mainly developed？A. By inferringB. By giving explanations.C. By providing examples.D. By making comparisons.31. What‟s the purpose of this passage?A. To make comments on two novels.B. To introduce two authors to children.C. To call for more attention to children‟s literature.D. To criticize some movies adapted from children‟s literature.DIt was reported last week that developers could take photos from Apple mobile and Google Android devices without the phone owners knowing that the images were being taken. In Apple‟s case, developers can also obtain the location information for each photo.Senator(参议员) Charles Schumer said in a telephone interview that his office had spoken with officials at both Apple and Google on Monday.“We asked them if they could find a way on their own to prevent Apple from having access to private information,” Mr. Schumer said. “They were friendly and open to the idea that this ought to be changed.”On Sunday, Mr. Schumer said that he planned to send a letter to the Federal Trade Commission asking the agency to investigate Apple and Google after the privacy concerns cameto light. Claudia Bourne Farrell, an F.T.C. spokeswoman, said the agency had received the letter but she could not comment further.“It worries people to think that one‟s personal photos, address book, and who knows what else, can be obtained an d even posted online without permission,” Mr. Schumer wrote in his letter to the F.T.C. “If the technology exists to open the door to this kind of privacy invasion, then surely technology exists to close it, and that‟s exactly what must happen.”Mr. Schumer said if Apple and Google could not come to an agreement to fix the problem, then he would be forced to take the issue further.He said other companies had been willing to work with his office to fix issues. “I‟m optimistic that we can get thi s changed without any regulation,” he said. “If it‟s not changed, then we‟ll turn to the F.T.C., and if that doesn‟t work , we‟ll consider legislative (法律的)approach.”The F.T.C. has warned companies to try to be more vigilant(警醒的) in their efforts to protect consumers when it comes to privacy.32. Which of the following statements is TRUE?A. Privacy invasion from Apple has existed for a long time.B. Mr. Schumer takes the privacy concerns caused by Apple and Google seriously.C. Privacy invasion from Google has existed for a long time.D. Apple and Google have decided to make a change.33. Mr. Schumer‟s letter to the F.T.C. mainly shows that the technology to open the door to privacy invasion___________.A. causes privacy invasion to happen frequentlyB. can be used if permittedC. causes people to worry about the safety of their personal informationD. causes personal information to be posted online without permission34. If the privacy concerns can‟t be solved with the help of the F.T.C., ___________.A. The senators will force the companies not to invade privacyB. The companies will be closedC. The companies will be finedD. The senators will turn to legislation35. Where can we read about the passage?A. In a newspaper.B. In a travel brochure.C. In a sci-fi magazineD. In a textbook.根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

2016届高三12月联考理综试卷

2016届高三第三次联考理综试题注意事项：1、本试卷分第I卷（选择题）和第II卷（非选择题）两部分。

答卷前、考生务必将自己的姓名、准考证号填写在答题卡上。

2、回答第I卷时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

写在本试卷上无效。

3、回答第II卷时，将答案写在答题卡上。

写在本试卷上无效。

4、考试结束后，将本试卷和答题卡一并交回。

可能用到的相对原子质量：Be—9 B—11 N—14 O—16 V—51 Mn—55第I卷一、选择题：本题共13小题，每小题6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.下列有关细胞中的元素和化合物的叙述，正确的是A．构成细胞的最基本元素是碳，这与其含量最高有关B．脂肪分子中氢的含量比糖类高，是细胞主要的能源物质C．细胞中的RNA分子一般是单链，且不含氢键D．细胞中的一个环状n肽分子被彻底水解需要破坏n个肽键2.下列关于真核细胞生物膜的叙述，正确的是A．构成生物膜的脂质主要有磷脂、胆固醇和脂肪B．抗体合成越旺盛的细胞，其高尔基体膜和细胞膜的成分更新速率越快C．细胞许多化学反应都在生物膜上进行，ATP分子都是在生物膜上合成的D．细胞在分化的过程中，其细胞膜的通透性稳定不变3.下图为甘蔗叶肉细胞内的一系列反应过程，下列说法错误的是A．过程①中叶绿体中的叶绿素主要吸收蓝紫光和红光B．过程②发生在叶绿体基质中，过程③发生在细胞质基质和线粒体中C．过程①产生[H]，过程②消耗[H]，过程③既产生也消耗[H]D．若过程②的速率大于过程③的速率，则甘蔗的干重会增加4.如图是某高等动物（基因型Bb）体内四个正在分裂的细胞，下列说法正确的是A．如果甲图7号上有B基因，则一般情况下2和6上有b基因B．卵巢会出现这四种细胞，乙图表示次级卵母细胞或第一极体C．丙图表示减数第一次分裂后期，细胞中有8条染色体D．含有同源染色体细胞有甲、乙和丙5.图中DNA分子含有5000个碱基对，其中腺嘌呤占全部碱基的20%。

2016-2017学年安徽省池州市东至县高三(上)12月联考数学试卷(理科)

2016-2017学年安徽省池州市东至县高三（上）12月联考数学试卷（理科）一、选择题：本大题共12个小题，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．（5分）已知集合A={x|（x﹣3）（x+1）≥0}，，则A∩B=（）A．{x|x≤﹣1}B．{x|x≥3}C．D．2．（5分）已知向量，，则向量的夹角为（）A．B．C． D．3．（5分）将函数的图象上的所有的点横坐标缩短为原来的（纵坐标不变），再将所得的图象向右平移个单位，则所得的函数图象对应的解析式为（）A． B．y=﹣sinx C．y=﹣cosx D．4．（5分）已知等比数列{a n}满足a1=3，a1+a3+a5=21，则a3+a5+a7=（）A．21 B．42 C．63 D．845．（5分）已知“x＞k”是“”的充分不必要条件，则k的取值范围为（）A．（﹣∞，﹣1]B．[1，+∞）C．[2，+∞）D．（2，+∞）6．（5分）《九章算术》是我国古代的数学名著，书中有如下问题：“今有五人分五钱，令上二人所得与下三人等．问各得几何．”其意思为“已知甲、乙、丙、丁、戊五人分5钱，甲、乙两人所得与丙、丁、戊三人所得相同，且甲、乙、丙、丁、戊所得依次成等差数列．问五人各得多少钱？”（“钱”是古代的一种重量单位）．这个问题中，甲所得为（）A．钱 B．钱 C．钱 D．钱7．（5分）如图可能是下列哪个函数的图象（）A．y=2x﹣x2﹣1 B．C．D．y=（x2﹣2x）e x8．（5分）已知函数，则关于x的不等式f（3x+1）+f（x）＞0的解集为（）A．（﹣∞，0）B．（0，+∞）C．D．9．（5分）在三角形ABC中，E，F分别为边AB，AC上的点，且=2，=，|AB|=3，|AC|=2，A=60°，则•等于（）A．B．C．D．10．（5分）已知S n是等差数列{a n}n∈N*的前n项和，且S6＞S7＞S5，给出下列五个命题：①d＜0；②S11＞0；③S12＜0；④数列{S n}中最大项为S11；⑤|a6|＞|a7|，其中正确命题的个数（）A．5 B．4 C．3 D．111．（5分）若x、y、z均为正实数，则的最大值为（）A．B．C．D．12．（5分）已知点P是△ABC的中位线EF上任意一点，且EF∥BC，实数x，y 满足，设△ABC，△PBC，△PCA，△PAB的面积分别为S，S 1，S2，S3，记，，，则λ2•λ3取最大值时，3x+y的值为（）A．B．C．1 D．2二、填空题（每题5分，满分20分，将答案填在答题纸上）13．（5分）已知幂函数y=f（x）的图象过点（4，2），则=．14．（5分）（2x+）dx=．15．（5分）设偶函数f（x）对任意x∈R，都有，且当x∈[﹣3，﹣2]时，f（x）=4x，则f（2018）=．16．（5分）在锐角三角形ABC中，若sinA=2sinBsinC，则tanAtanBtanC的最小值是．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．（10分）设函数f（x）=sin（2x+ϕ）（﹣π＜ϕ＜0），y=f（x）图象的一条对称轴是直线．（Ⅰ）求ϕ；（Ⅱ）求函数y=f（x）的单调增区间；（Ⅲ）证明直线5x﹣2y+c=0与函数y=f（x）的图象不相切．18．（12分）在△ABC中，2cos2cosB﹣sin（A﹣B）sinB+cos（A+C）=﹣．（1）求cosA的值；（2）若a=4，b=5，求在方向上的投影．19．（12分）设函数，m∈R．（1）当m=e（e为自然对数的底数）时，求f（x）的最小值；（2）讨论函数零点的个数．20．（12分）已知函数，若对于数列{a n}满足：a n+1=4f（a n）﹣a n﹣1+4（n∈N*，n≥2），且a1=﹣1，a2=2．（1）求证：数列{a n﹣a n}（n∈N*，n≥2）为等差数列，并求数列{a n}的通项﹣1公式；（2）设，若数列{b n}的前n项和为S n，求S n．21．（12分）设二次函数f（x）=ax2+bx+c（a＞0），方程f（x）﹣x=0的两个根x1，x2满足0＜x1＜x2＜．（1）当x∈（0，x1）时，证明x＜f （x）＜x1；（2）设函数f（x）的图象关于直线x=x0对称，证明x0＜．22．（12分）已知函数f（x）=（其中a为常数）．（Ⅰ）当a=0时，求函数的单调区间；（Ⅱ）当0＜a＜1时，设函数f（x）的3个极值点为x1，x2，x3，且x1＜x2＜x3．证明：x1+x3＞．2016-2017学年安徽省池州市东至县高三（上）12月联考数学试卷（理科）参考答案与试题解析一、选择题：本大题共12个小题，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．（5分）（2016秋•东至县月考）已知集合A={x|（x﹣3）（x+1）≥0}，，则A∩B=（）A．{x|x≤﹣1}B．{x|x≥3}C．D．【解答】解：A={x|（x﹣3）（x+1）≥0}={x|x≤﹣1或x≥3}，∵，∴A∩B={x|x≤﹣1}，故选A．2．（5分）（2016秋•东至县月考）已知向量，，则向量的夹角为（）A．B．C． D．【解答】解：向量，，∴+2•=0，即22+2×2×2×cos=0，解得cos=﹣，∴向量的夹角为．故选：C．3．（5分）（2016秋•东至县月考）将函数的图象上的所有的点横坐标缩短为原来的（纵坐标不变），再将所得的图象向右平移个单位，则所得的函数图象对应的解析式为（）A． B．y=﹣sinx C．y=﹣cosx D．【解答】解：将函数的图象上的所有的点横坐标缩短为原来的（纵坐标不变），所得的函数图象对应的解析式为y=sin（x﹣），再将所得的图象向右平移个单位，则所得的函数图象对应的解析式为y=sin（x ﹣﹣）=﹣cosx．故选：C．4．（5分）（2015•新课标Ⅱ）已知等比数列{a n}满足a1=3，a1+a3+a5=21，则a3+a5+a7=（）A．21 B．42 C．63 D．84【解答】解：∵a1=3，a1+a3+a5=21，∴，∴q4+q2+1=7，∴q4+q2﹣6=0，∴q2=2，∴a3+a5+a7==3×（2+4+8）=42．故选：B5．（5分）（2016秋•东至县月考）已知“x＞k”是“”的充分不必要条件，则k的取值范围为（）A．（﹣∞，﹣1]B．[1，+∞）C．[2，+∞）D．（2，+∞）【解答】解：由，化为：＞0，即（x+1）（x﹣2）＞0，解得x＞2，或x＜﹣1．∵x＞k”是“”的充分不必要条件，则k的取值范围为[2，+∞）．故选：C．6．（5分）（2017•南充三模）《九章算术》是我国古代的数学名著，书中有如下问题：“今有五人分五钱，令上二人所得与下三人等．问各得几何．”其意思为“已知甲、乙、丙、丁、戊五人分5钱，甲、乙两人所得与丙、丁、戊三人所得相同，且甲、乙、丙、丁、戊所得依次成等差数列．问五人各得多少钱？”（“钱”是古代的一种重量单位）．这个问题中，甲所得为（）A．钱 B．钱 C．钱 D．钱【解答】解：依题意设甲、乙、丙、丁、戊所得钱分别为a﹣2d，a﹣d，a，a+d，a+2d，则由题意可知，a﹣2d+a﹣d=a+a+d+a+2d，即a=﹣6d，又a﹣2d+a﹣d+a+a+d+a+2d=5a=5，∴a=1，则a﹣2d=a﹣2×=．故选：B．7．（5分）（2016秋•东至县月考）如图可能是下列哪个函数的图象（）A．y=2x﹣x2﹣1 B．C．D．y=（x2﹣2x）e x【解答】解：A中，∵y=2x﹣x2﹣1，当x趋向于﹣∞时，函数y=2x的值趋向于0，y=x2+1的值趋向+∞，∴函数y=2x﹣x2﹣1的值小于0，∴A中的函数不满足条件；B中，∵y=sinx是周期函数，∴函数y=的图象是以x轴为中心的波浪线，∴B中的函数不满足条件；C中，y=的定义域是（0，1）∪（1，+∞），且在x∈（0，1）时，lnx＜0，∴y=＜0，∴C中函数不满足条件；D中，∵函数y=x2﹣2x=（x﹣1）2﹣1，当x＜0或x＞2时，y＞0，当0＜x＜2时，y＜0；且y=e x＞0恒成立，∴y=（x2﹣2x）e x的图象在x趋向于﹣∞时，y＞0，0＜x＜2时，y＜0，在x趋向于+∞时，y趋向于+∞；∴D中的函数满足条件．故选：D．8．（5分）（2016秋•东至县月考）已知函数，则关于x的不等式f（3x+1）+f（x）＞0的解集为（）A．（﹣∞，0）B．（0，+∞）C．D．【解答】解：对于函数，其定义域为R，且=﹣f（x），为奇函数，分析易得函数在R上为增函数，则f（3x+1）+f（x）＞0⇔f（3x+1）＞﹣f（x）⇔f（3x+1）＞f（﹣x）⇔3x+1＞﹣x，解可得x＞﹣，即其解集为（﹣，+∞）；故选：D．9．（5分）（2014•东胜区校级二模）在三角形ABC中，E，F分别为边AB，AC上的点，且=2，=，|AB|=3，|AC|=2，A=60°，则•等于（）A．B．C．D．【解答】解：∵，．∴，．∴•=====．故选A．10．（5分）（2015春•龙海市期末）已知S n是等差数列{a n}n∈N*的前n项和，且S6＞S7＞S5，给出下列五个命题：①d＜0；②S11＞0；③S12＜0；④数列{S n}中最大项为S11；⑤|a6|＞|a7|，其中正确命题的个数（）A．5 B．4 C．3 D．1【解答】解：∵等差数列{a n}中，S6最大，且S6＞S7＞S5，∴a1＞0，d＜0，①正确；∵S6＞S7＞S5，∴a6＞0，a7＜0，∴a1+6d＜0，a1+5d＞0，S6最大，∴④不正确；S11=11a1+55d=11（a1+5d）＞0，S12=12a1+66d=12（a1+a12）=12（a6+a7）＞0，∴②⑤正确，③错误故选：C．11．（5分）（2010秋•皇姑区校级期末）若x、y、z均为正实数，则的最大值为（）A．B．C．D．【解答】解：法1、设恒成立，此不等式可化为x2+y2+z2﹣axy﹣ayz≥0即恒成立由于，故于是有≥故恒成立．法2、===，当且仅当当且仅当x=z=y，等号成立，∴的最大值为故选A12．（5分）（2016秋•东至县月考）已知点P是△ABC的中位线EF上任意一点，且EF∥BC，实数x，y满足，设△ABC，△PBC，△PCA，△PAB 的面积分别为S，S1，S2，S3，记，，，则λ2•λ3取最大值时，3x+y的值为（）A．B．C．1 D．2【解答】解：由题意可知：λ1+λ2+λ3=1，∵P是△ABC的中位线EF上任意一点，且EF∥BC，∴，∴，∴λ2λ3≤（）2=，当且仅当λ2=λ3=时取等号，∴λ2•λ3取最大值时P为EF的中点，延长AP交BC于M，则M为BC的中点，∴PA=PM，∴=﹣=﹣（），又∵，∴x=y=，∴3x+y=2．故选D．二、填空题（每题5分，满分20分，将答案填在答题纸上）13．（5分）（2016秋•东至县月考）已知幂函数y=f（x）的图象过点（4，2），则=﹣．【解答】解：设幂函数y=f（x）=xα，α∈R，其图象过点（4，2），∴4α=2，解得α=，∴f（x）=；∴f（2）=，∴==•=•=﹣．故答案为：﹣．14．（5分）（2015•德州一模）（2x+）dx=e2．【解答】解：∵（lnx）′=，（x2）′=2x，∴=x2|1e+lnx|1e=e2﹣1+lne﹣ln1=e2故答案为：e215．（5分）（2016秋•东至县月考）设偶函数f（x）对任意x∈R，都有，且当x∈[﹣3，﹣2]时，f（x）=4x，则f（2018）=﹣8．【解答】解：∵偶函数f（x）对任意x∈R，都有，∴f（x+6）=﹣=f（x），∵当x∈[﹣3，﹣2]时，f（x）=4x，∴当x∈[2，3]时，f（x）=f（﹣x），∴f（2018）=f（2）=f（﹣2）=4×（﹣2）=﹣8．故答案为：﹣8．16．（5分）（2016•江苏）在锐角三角形ABC中，若sinA=2sinBsinC，则tanAtanBtanC 的最小值是8．【解答】解：由sinA=sin（π﹣A）=sin（B+C）=sinBcosC+cosBsinC，sinA=2sinBsinC，可得sinBcosC+cosBsinC=2sinBsinC，①由三角形ABC为锐角三角形，则cosB＞0，cosC＞0，在①式两侧同时除以cosBcosC可得tanB+tanC=2tanBtanC，又tanA=﹣tan（π﹣A）=﹣tan（B+C）=﹣②，则tanAtanBtanC=﹣•tanBtanC，由tanB+tanC=2tanBtanC可得tanAtanBtanC=﹣，令tanBtanC=t，由A，B，C为锐角可得tanA＞0，tanB＞0，tanC＞0，由②式得1﹣tanBtanC＜0，解得t＞1，tanAtanBtanC=﹣=﹣，=（）2﹣，由t＞1得，﹣≤＜0，因此tanAtanBtanC的最小值为8，当且仅当t=2时取到等号，此时tanB+tanC=4，tanBtanC=2，解得tanB=2+，tanC=2﹣，tanA=4，（或tanB，tanC互换），此时A，B，C 均为锐角．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．（10分）（2005•安徽）设函数f（x）=sin（2x+ϕ）（﹣π＜ϕ＜0），y=f（x）图象的一条对称轴是直线．（Ⅰ）求ϕ；（Ⅱ）求函数y=f（x）的单调增区间；（Ⅲ）证明直线5x﹣2y+c=0与函数y=f（x）的图象不相切．【解答】解：（Ⅰ）∵x=是函数y=f（x）的图象的对称轴，∴，∴，k∈Z．∵﹣π＜ϕ＜0，ϕ=﹣．（Ⅱ）由（Ⅰ）知ϕ=﹣，因此．由题意得2kπ﹣，k∈Z．所以函数的单调增区间为．（Ⅲ）证明：∵|y'|==，所以曲线y=f（x）的切线斜率取值范围为[﹣2，2]，而直线5x﹣2y+c=0的斜率为＞2，所以直线5x﹣2y+c=0与函数的图象不相切．18．（12分）（2013•四川）在△ABC中，2cos2cosB﹣sin（A﹣B）sinB+cos（A+C）=﹣．（1）求cosA的值；（2）若a=4，b=5，求在方向上的投影．【解答】解：（Ⅰ）由可得，可得，即，即，（Ⅱ）由正弦定理，，所以=，由题意可知a＞b，即A＞B，所以B=，由余弦定理可知．解得c=1，c=﹣7（舍去）．向量在方向上的投影：=ccosB=．19．（12分）（2017春•田家庵区校级月考）设函数，m∈R．（1）当m=e（e为自然对数的底数）时，求f（x）的最小值；（2）讨论函数零点的个数．【解答】解：（1）当m=e时，，∴当x∈（0，e）时，f′（x）＜0，f（x）在x∈（0，e）上是减函数；当x∈（e，+∞）时，f′（x）＞0，f（x）在x∈（e，+∞）上是增函；∴当x=e时，f（x）取最小值．（2）∵函数，令g（x）=0，得；设，则φ′（x）=﹣x2+1=﹣（x﹣1）（x+1）当x∈（0，1）时，φ′（x）＞0，φ（x）在x∈（0，1）上是增函数；当x∈（1，+∞）时，φ′（x）＜0，φ（x）在x∈（1，+∞）上是减函数；当x=1是φ（x）的极值点，且是唯一极大值点，∴x=1是φ（x）的最大值点；∴φ（x）的最大值为，又φ（0）=0结合y=φ（x）的图象，可知：①当时，函数g（x）无零点；②当时，函数g（x）有且只有一个零点；③当时，函数g（x）有两个零点；④当m≤0时，函数g（x）有且只有一个零点；综上：当时，函数g（x）无零点；当或m≤0时，函数g（x）有且只有一个零点；当时，函数g（x）有且只有两个零点；20．（12分）（2016秋•东至县月考）已知函数，若对于数列{a n}满足：a n+1=4f（a n）﹣a n﹣1+4（n∈N*，n≥2），且a1=﹣1，a2=2．（1）求证：数列{a n﹣a n﹣1}（n∈N*，n≥2）为等差数列，并求数列{a n}的通项公式；（2）设，若数列{b n}的前n项和为S n，求S n．【解答】（1）证明：由题意，，即（a n+1﹣a n）﹣（a n﹣a n﹣1）=2（n≥2），∵a1=﹣1，a2=2，∴a2﹣a1=3，∴数列{a n+1﹣a n}是一个以3为首项，以2为公差的等差数列；则a n+1﹣a n=3+2（n﹣1）=2n+1，则a2﹣a1=2×1+1，a3﹣a2=2×2+1，…，a n﹣a n﹣1=2（n﹣1）+1（n≥2）．累加得．验证n=1时上式成立，∴；（2）解：，则，，两式作差得：．∴．21．（12分）（1997•全国）设二次函数f（x）=ax2+bx+c（a＞0），方程f（x）﹣x=0的两个根x1，x2满足0＜x1＜x2＜．（1）当x∈（0，x1）时，证明x＜f （x）＜x1；（2）设函数f（x）的图象关于直线x=x0对称，证明x0＜．【解答】证明：（1）令F（x）=f（x）﹣x．因为x1，x2是方程f（x）﹣x=0的根，所以F（x）=a（x﹣x1）（x﹣x2）．当x∈（0，x1）时，由于x1＜x2，得（x﹣x1）（x﹣x2）＞0，又a＞0，得F（x）=a（x﹣x1）（x﹣x2）＞0，即x＜f（x）．x1﹣f（x）=x1﹣[x+F（x）]=x1﹣x+a（x1﹣x）（x﹣x2）=（x1﹣x）[1+a（x﹣x2）]因为所以x1﹣x＞0，1+a（x﹣x2）=1+ax﹣ax2＞1﹣ax2＞0．得x1﹣f（x）＞0．由此得f（x）＜x1．（2）依题意知因为x1，x2是方程f（x）﹣x=0的根，即x1，x2是方程ax2+（b﹣1）x+c=0的根．∴，因为ax2＜1，所以．22．（12分）（2013•浙江二模）已知函数f（x）=（其中a为常数）．（Ⅰ）当a=0时，求函数的单调区间；（Ⅱ）当0＜a＜1时，设函数f（x）的3个极值点为x1，x2，x3，且x1＜x2＜x3．证明：x1+x3＞．【解答】解：（Ⅰ）令f'（x）=0可得．列表如下：单调减区间为（0，1），；增区间为．﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣（5分）（Ⅱ）由题，对于函数，有∴函数h（x）在上单调递减，在上单调递增∵函数f（x）有3个极值点x1＜x2＜x3，从而，所以，当0＜a＜1时，h（a）=2lna＜0，h（1）=a﹣1＜0，∴函数f（x）的递增区间有（x1，a）和（x3，+∞），递减区间有（0，x1），（a，1），（1，x3），此时，函数f（x）有3个极值点，且x2=a；∴当0＜a＜1时，x1，x3是函数的两个零点，﹣﹣﹣﹣（9分）即有，消去a有2x1lnx1﹣x1=2x3lnx3﹣x3令g（x）=2xlnx﹣x，g'（x）=2lnx+1有零点，且∴函数g（x）=2xlnx﹣x在上递减，在上递增要证明⇔⇔因为g（x1）=g（x3），所以即证构造函数，则只需要证明单调递增即可．而，，所F′（x）在上单调递增，所以F′（x）＜F′（）=0．∴当0＜a＜1时，．﹣﹣﹣﹣﹣﹣﹣﹣（15分）参与本试卷答题和审题的老师有：lcb001；742048；w3239003；吕静；沂蒙松；sxs123；danbo7801；刘长柏；394782；zhczcb；lily2011；zlzhan；ww方；qiss；刘老师；maths（排名不分先后）菁优网2017年5月9日。

安徽省滁州高三上学期12月月考理科数学试卷 Word版含答案

滁州中学2016—2017学年度第一学期半月考高三数学（理科）试卷（满分：150分用时：120分钟命题：高三数学备课组）注意事项：1. 答题前，务必在试题卷、答题卡规定的地方填写自己的姓名、座位号。

2. 答第Ⅰ卷时，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。

3. 答第Ⅱ卷时，请在答题卷上．．．．书写，要求认真审题、仔细作答、字体工整、笔迹清晰。

第Ⅰ卷（选择题共60分）一、选择题（本题共有12小题，每小题5分，每小题只有一个选项正确）1. 已知集合{}1345A =，，，，集合{}2|450B x Z x x =∈--<，则A B ⋂的真子集个数为（） (A)5(B)6 (C)7 (D)8答案：C2. 设命题甲：2210ax ax ++>的解集是实数R .命题乙：01a <<.则命题乙是命题甲成立的（） (A)充分不必要条件 (B)充要条件(C)必要不充分条件 (D)既非充分条件又非必要条件答案：A3. 在各项均为正数的等比数列{}n a 中，12a =，且245,2,a a a +成等差数列，记n S 是数列{}n a 的前n 项和，则6S =（） (A)62(B)64(C)126(D)128答案：C4. ） (A)sin15cos15︒︒(B)22cossin 1212ππ-(C)1tan151tan15+︒-︒答案：C 5. 已知33cos ,4522πππαα⎛⎫+=≤≤ ⎪⎝⎭，则sin 2α=（）(A)45-(B)45(C)725-(D)725答案：D6. 一个四棱锥的底面是正方形，其三视图如图所示，则这个四棱锥的体积是（）(A)1 (B)2 (C)3 (D)4 答案：B7. 函数cos y x x =+的大致图象为（）(A)(B)(C)(D)答案：B8. 已知变量,x y 满足条件23033010x y x y y +-≤⎧⎪+-≥⎨⎪-≤⎩，若目标函数z ax y =+仅在点()3,0处取得最大值，则a 的取值范围是（） (A)1,2⎛⎫-∞-⎪⎝⎭(B)1,02⎛⎫-⎪⎝⎭(C)10,2⎛⎫ ⎪⎝⎭(D)1,2⎛⎫+∞⎪⎝⎭答案：D9. 已知定义在R 上的函数()f x 满足()()50f x f x +-=，且函数()1y f x =-的图象关于直线1x =对称，若()12f -=，则下列结论正确的是（）(A)()f x 为奇函数，且()20162f =- (B)()f x 为奇函数，且()20162f =(C)()f x 为偶函数，且()20162f =-(D)()f x 为偶函数，且()20162f = 答案：D10. 设直棱柱111ABC A B C -的体积为V ，点,P Q 分别在侧棱11,AA CC 上，且1PA QC =,则四棱锥B APQC -的体积为为（） (A)16V(B)14V(C)13V(D)12V答案：C 11. 若曲线212y x e=与曲线ln y a x =在他们的公共点(),P s t 处具有公共切线，则实数a =（）(A)1(B)2(C)3(D)4答案：A12. 棱长为1的正方体1111ABCD A BC D -中，M 为线段1A B 上的动点，则下列结论正确的是（）①三棱锥1M DCC -的体积为定值；②11DC D M ⊥③1AMD ∠的最大值为90°；④1AM MD +的最小值为2.(A)①② (B)②③(C)③④(D)①④答案：A二、填空题（本题共有4小题，每小题5分）13. 等边三角形ABC 的边长为1，如果,,BC a CA b AB c ===，则a b b c c a ⋅-⋅+⋅=____答案：12-14. 若直线4y π=被函数()()tan 0f x x ωω=>的图象的相邻两支截得的线段长为4π，则4f π⎛⎫= ⎪⎝⎭___________ 答案：015. 若高为2cm 的长方体木块的表面积为722cm ，体积为363cm ，则它的外接球的直径为__________ 答案：7cm16. 已知数列{}n a 是各项为正数且首项为1的等差数列，n S 为其前n 项和，若数列也为等差数列，则81n n S a ++的最小值是_____________ 答案：176三、解答题（本题共有6题，10+12+12+12+12+12=70分）17. 设{}{}2|3100,|121A x x x B x m x m =-++≥=+≤≤-，若B A ⊆.(1)求A ;（4分）(2)求实数m 的取值范围.（6分）答案：（1）{}|25A x x =-≤≤（2）3m ≤18. 已知函数()()21cos sin 2f x x x x x R =++∈. （1）当,46x ππ⎡⎤∈-⎢⎥⎣⎦时，求函数()f x 的最值；（6分）（2）设ABC ∆的内角,,A B C 所对的边分别为,,a b c，且()2c f C ==，若向量=m ()1,a 与向量n ()2,b =共线，求,a b 的值.（6分）答案：（1）最大值32，最小值0. （2）1,2a b ==19. 已知数列{}n a 满足2n n a qa +=()121,*,1,2q n N a a ≠∈==，且233445,,a a a a a a +++成等差数列.（1）求{}n a 的通项公式；（6分）（2）设2221log ,*nn n a b n N a -=∈,求数列{}n b 的前n 项和.（6分）答案：（1）1222,2,n n n n a n -⎧⎪=⎨⎪⎩为奇数为偶数（2）1242n n n S -+=-20. （1）已知一个圆柱的侧面展开图是边长为6π和8π的矩形，求该圆柱的表面积.（6分） (2) 如图，一个圆锥形的空杯子上面放着一个半球形的冰淇淋，如果冰淇淋融化了，冰淇淋会从被子溢出吗？请计算说明理由.（6分）答案：（1）（2）21. 已知函数()ln 1f x x x =-+，函数()4xg x axe x =-，其中a 为大于零的常数.（1）求函数()f x 的单调区间；（4分）（2）求证：()()()22ln ln 2g x f x a -≥-.（8分）答案：22. 如图所示，在四棱锥P ABCD -中，底面四边形ABCD 是菱形，AC BD O ⋂=,PAC ∆是边长为2的等边三角形，PB PD ==,4AP AF =.（1）求证：PO ⊥底面ABCD ;（2）求直线CP 与平面BDF 所成角的大小；（3）在线段PB 上是否存在一点M ，使得CM ∥平面BDF ？如果存在，求BMBP的值，如果不存在，请说明理由. 答案：。

辽宁省葫芦岛市高三数学12月月考试卷理

2016-2017学年度上学期高三12月联考试题高三数学（理科）试题时间：120分钟满分：150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，只有一项是符合题目要求的.1. 已知集合{|(3)0}A x Z x x =∈-≤，{|ln 1}B x x =<,则A B =I （）A ．{0,1,2}B ．{1,2,3}C ．{1,2}D ．{2,3}2. 设i 是虚数单位，复数z 满足()(12)|34|z i i i +-=+，则在复平面内，z 的共轭复数z 所对应的点的坐标为（）A ．(1,1)B ．(1,1)-C ．(1,1)-D ．(1,1)--3. 已知向量(1,)(3,2)a m b =-r r，=，且|||2|=+，则m = （）A.8-B. 6-C. 6D.84. 双曲线22212x y -=的渐近线与圆222210x y ay a +++-=相切,则正实数a 的值为（）A 5. 某公司为激励创新，计划逐年加大研发奖金投入。

若该公司2015年全年投入研发奖金130万元，在此基础上，每年投入的研发奖金比上一年增长12％，则该公司全年投入的研发奖金开始超过200万元的年份是( )(参考数据：lg1.120.05=，lg1.30.11=，lg 20.30=) A ．2018年 B ．2019年 C. 2020年 D ．2021年6. 若将函数y =2sin 2x 的图象向右平移π12个单位长度，则平移后图象的对称中心为（） A.))(0,62(Z k k ∈-ππ B. ))(0,62(Z k k ∈+ππC. ))(0,122(Z k k ∈-ππ D. ))(0,122(Z k k ∈+ππ 7. 一个棱锥的三视图如图，则该棱锥的全面积是( )正视图侧视图俯视图A.624+B.64+C.224+D.24+8. 若[]x 表示不超过x 的最大整数，执行如图所示的程序框图，则输出的S 值为（） A.4B.5C.7D.99. 《九章算术》是我国古代数学名著，在其中有道“竹九问题”“今有竹九节，下三节容量四升，上四节容量三升。

2016级高三上学期12月月考试卷_1

2016级高三上学期12月月考试卷本试卷分第1卷（选择题）和第Ⅱ卷（非选择题）。

共150分，考试时间120分钟。

注意事项：1．答第1卷前，考生务必将自己的姓名、考号填写在答题卡上。

2．选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。

如需改动，用橡皮擦干净后，再选涂其他答案标号。

不能答在本试卷上，否则无效。

第I卷（选择题共100分）第一部分听力（共两节，满分30分）做题时，先将答案标在试卷上，录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。

每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话仅读一遍。

1. Why is Ann so upset?A. She failed one of her exams.B. She is worrying about otherlessons.C. She has no time to do her math homework.2. What type of food does the woman eat?A. Junk food.B. Healthy food.C. Delivered food.3. What will the man probably do to stay warm?A. Use a blanket.B. Turn on the heater.C. Drink some hot chocolate.4. What are the speakers mainly talking about?A. The man’s career.B. The man’s travel plan.C. The man’s plan after graduating.5. What are the speakers’ opinions about the painting?A. It’s simple.B. It’s colorful.C. It’s complex.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。

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辽宁省葫芦岛市高三数学12月月考试卷理