【英语】陕西师范大学附属中学2016届高三下学期第十次模拟考试
精品：【全国百强校】山东省山东师范大学附属中学2016届高三下学期模拟考试文数试题(解析版)
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.设复数z 满足()2105z i i ∙+=-(i 虚数单位)，则z 的共轭复数z 为（ ）A ．34i -+B ．34i --C ．34i +D ．34i - 【答案】C 【解析】试题分析：由()2105z i i ∙+=-得()()()()10521051520342225i i i iz i i i i ----====-++-，所以34z i =+，故选C.考点：复数的运算与共轭复数的概念.2.已知集合{}|13M x x =-≤<，集合{|N x y ==，则MN =（ ）A ．MB ．NC ．{}|12x x -≤≤D ．{}|33x x -≤< 【答案】D考点：集合的运算.3.某校高三（1）班共有48人，学号依次为1，2，3，…，48，现用系统抽样的办法抽取一个容量为6的样本.已知学号为3，11，19，35，43的同学在样本中，那么还有一个同学的学号应为（ ） A ．27 B ．26 C ．25 D ．24 【答案】A 【解析】试题分析：根据系统抽样的规则——“等距离”抽取，也就抽取的号码差相等，根据抽出的序号可知学号之间的差为8，所以在19与35之间还有27，故选A.考点：随机抽样.4.已知直线1ax by +=经过点()1,2，则24a b +的最小值为（ ）AB．．4 D． 【答案】B考点：基本不等式.5.设,m n 是两条不同的直线，,αβ是两个不同的平面，给出下列四个命题： ①若//,m n m β⊥，则n β⊥；②若//,//m m αβ，则//αβ； ③若//,//m n m β，则//n β；④若//,m m αβ⊥，则αβ⊥； 其中真命题的个数为（ ）A ．1B ．2C ．3D ．4 【答案】B 【解析】试题分析：①因为“如果两条平行线中的一条垂直于一个平面，那么另一条也垂直于这个平面”，所以①正确；②当m 平行于两个相交平面,αβ的交线l 时，也有//,//m m αβ，所以②错误；③若//,//m n m β，则//n β或n β⊂内，所以③错误；④平面,αβ与直线m 的关系如下图所示，必有αβ⊥，故④正确.考点：空间中直线与平面平行与垂直关系的判断. 6.已知命题0:p x R ∃∈，使0sin x =:0,2q x π⎛⎫∀∈ ⎪⎝⎭，sin x x >，则下列判断正确的是（ ） βαmA ．p 为真B ．q ⌝为假C ．p q ∧为真D ．p q ∨为假 【答案】B考点：复合命题真假性判断.7.函数()()2sin 0,2f x x πωϕωϕ⎛⎫=+><⎪⎝⎭的部分图象如图所示，则()17012f f π⎛⎫+⎪⎝⎭的值为（ ）A ．2-B ．2C ．1D ．1+【答案】A考点：正弦函数的图象与性质.8.已知,x y 满足约束条件2025020x y x y y --≤⎧⎪+-≥⎨⎪-≤⎩，则11y z x +=+的范围是（ ）A ．1,23⎡⎤⎢⎥⎣⎦B ．11,22⎡⎤-⎢⎥⎣⎦C ．13,22⎡⎤⎢⎥⎣⎦ D ．35,22⎡⎤⎢⎥⎣⎦【答案】C考点：线性规划.【方法点晴】本题主要考查了简单的线性规划，考查了数形结合的思想方法，属于中档题.线性规划问题是统考和高考中常见的题型，解题的基本策略是作出约束条件表示的可行域，根据目标函数的几何意义来探索最优解，从而求得最值.探索目标函数的几何意义时，应充分联想学过的公式形式，最常见的是直线的斜截式方程、斜率公式及两点间的距离公式等，本题11y z x +=+与斜率公式形式一致，表示可行域内的点(),x y 与定点()1,1P --连线的斜率，结合图形即可求得目标函数的范围.9.已知函数()321132f x ax bx x =-+，连续抛掷两颗骰子得到点数分别是,a b ，则函数()f x '在1x =处取得最值的概率是（ ） A ．136 B ．118 C ．112 D ．16【答案】C考点：古典概型.【方法点晴】本题主要考查了古典概型、二次函数的最值及导数的运算问题，属于中档题.本题先通过求导得到要研究的二次函数，结合二次函数的性质找到1x =处取得最值,a b 满足的条件.因为连续抛掷两颗骰子，研究得到的点数情况满足有限性和等可能性，所以属于古典概型，列举出所有可能的基本事件空间，找出满足条件的基本事件，即得所求的概率.10.已知抛物线()220,y px p ABC =>∆的三个顶点都在抛物线上，O 为坐标原点，设ABC ∆三条边,,AB BC AC 的中点分别为,,M N Q ，且,,M N Q 的纵坐标分别为123,,y y y .若直线,,AB BC AC 的斜率之和为-1，则123111y y y ++的值为（ ） A ．12p -B ．1p -C ．1pD ．12p【答案】B 【解析】试题分析：设,,A B C 三点的坐标分别为()()(),,,,,A A B B C C x y x y x y ，则有222,2,A A B B y px y px ==22,C C y px =所以()()2222A B A B A B A B y y y y y y px px -=-+=-()2A B p x x =-，所以11222A B AB A B A B y y p p p k x x y y y y -====-+,同理可得23,BC AC p pk k y y ==，又因为AB k BC k +1AC k +=-，所以1231p p p y y y ++=-，所以1231111y y y p++=-，故选B. 考点：抛物线方程的应用.【方法点晴】本题主要考查了抛物线方程的应用，属于中档题.本题解答的关键是利用已知条件“ABC ∆的三个顶点都在抛物线上”，把,,A B C 三点坐标代入抛物线方程，通过两个方程相减得到经过两点的直线的斜率表达式，进而得到弦的斜率与中点坐标的关系，这种方法我们称为“平方差法”，主要就是来解决二次曲线弦的斜率问题，通常给出中点坐标时，考虑这种方法.第Ⅱ卷（非选择题共100分）二、填空题（本大题共5小题，每题5分，满分25分．）11.设ln 3,ln 7a b ==，则abe e +=__________.（其中e 为自然对数的底数） 【答案】10 【解析】试题分析：ln3ln 73710abe e e e +=+=+=.考点：对数恒等式.12.已知向量,a b 3,2a b ==，且()a b a -⊥，则向量a 和b 的夹角是__________． 【答案】6π考点：平面向量的数量积运算.13.已知过点()2,4的直线l 被圆22:2450C x y x y +---=截得的弦长为6，则直线l 的方程为________.【答案】20x -=或34100x y -+= 【解析】试题分析：圆22:2450C x y x y +---=的标准方程为()()221210x y -+-=，圆心为()1,2C ，半径r =.当直线l 的斜率不存在时，方程为2x =，圆心为()1,2C 到直线l 的距离为1d =，弦长为6=，满足题意；当直线l 的斜率存在时，设直线l 方程为()24y k x =-+即420kx y k -+-=，圆心为()1,2C 到直线l的距离为1d ，解得34k =，此时直线l 方程为34100x y -+=，综上所述，满足被圆截得的弦长为6的直线方程为20x -= 或34100x y -+=. 考点：直线与圆的位置关系.14.公元263年左右，我国数学家刘徽发现当圆内接正多边形的边数无限增加时，多边形面积可无限逼近圆的面积，并创立了“割圆术”.利用“割圆术”刘徽得到了圆周率精确到小数点后两位的近似值3.14.这就是著名的“徽率”.如图是利用刘徽的“割圆术”思想设计的一个程序框图，则输出n 的值为____________.1.732,sin150.2588,sin 7.50.1305≈≈≈）【答案】24考点：程序框图.【方法点晴】本题主要考查了程序框图中的循环结构，考查了两角差的正弦公式，属于基础题.解答程序框图问题的基本策略就是按照给出的程序一步一步运行，直到找出满足判断框内容的变量值，退出循环，得到问题的答案.运算时需严格按照程序框图的顺序计算，不能随意更改，否则极易出现错误.15.已知函数()()(),1,11,1x e x f x g x kx f x x ⎧≤⎪==+⎨->⎪⎩，若方程()()0f x g x -=有两个不同实根，则实数k的取值范围为___________. 【答案】(]1,11,12e e -⎛⎫-⎪⎝⎭考点：函数的零点.【方法点晴】本题主要考查了函数的问题，属于中档题.把函数的零点转化为两个基本初等函数的交点，通过数形结合来解决.本题中函数()(),11,1xe xf x f x x ⎧≤⎪=⎨->⎪⎩在()1,+∞上是以1为周期的周期函数，与()0,1上的图象相同，这样作出分段函数()f x 的图象，并求出()xf x e =在()0,1的切线方程1y x =+，把直线1y x =+旋转即可找到满足条件的斜率k 的范围.三、解答题（本大题共6小题，共75分.解答应写出文字说明、证明过程或演算步骤.）16.（本小题满分12分）近日，济南楼市迎来去库存一系列新政，其中房产税收中的契税和营业税双双下调，对住房市场持续增 长和去库存产生积极影响.某房地产公司从两种户型中各拿出9套进行促销活动，其中A 户型每套面积为 100平方米，均价1.1万元/平方米，B 户型每套面积80平方米，均价1.2万元/平方米.下表是这18套 住宅每平方米的销售价格：（单位：万元/平方米）：（1）求,a b 的值；（2）张先生想为自己和父母买两套售价小于100万元的房子，求至少有一套面积为100平方米的概率. 【答案】（1） 1.16, 1.17a b ==；（2）35.令事件A 为“至少有一套面积为100平方米住房”， 则A 中所含基本事件有{}{}{}{}{}{}{}{}{}121112131421222324,,,,,,,,,,,,,,,,,A A A B A B A B A B A B A B A B A B 共9个…………………………11分 ∴()93155P A ==即所买两套房中至少有一套面积为100平方米的概率为35………………………12分 考点：样本平均数与古典概型中某事件发生的概率. 17.(本小题满分12分)在ABC ∆中，内角,,A B C 的对边为,,a b c ，已知2cos 2c A a b +=. （1）求角C 的值；（2）若2c =，且ABC ∆,a b . 【答案】（1）3C π=；（2）2a b ==.考点：正余弦定理解三角形.18.（本小题满分12分）如图，四棱锥P ABCD -的底面为正方形，侧面PAD ⊥底面,,,,ABCD PA AD E F H ⊥分别为,,AB PC BC 的中点.（1）求证：//EF 平面PAD ；（2）求证：平面PAH ⊥平面DEF .【答案】（1）证明见解析；（2）证明见解析.试题解析：（1）方法一：取PD 中点M ，连接,FM AM .∵在PCD ∆中，,F M 为中点，∴//FM CD 且12FM CD =， ∵正方形ABCD 中，//AE CD 且12AE CD =，∴//AE FM 且AE FM =，……………………2分 则四边形AEFM 为平行四边形，∴//AM EF ，………………………………4分∵ EF ⊄平面,PAD AM ⊂平面PAD ，∴//EF 平面PAD ，…………………………………6分则BAH ADE ∠=∠，∴090BAH AED ∠+∠=，则DE AH ⊥，…………………………………8分∵PA ⊂平面,PAH AH ⊂平面,PAH PA AH A ⋂=∴DE ⊥平面PAH ，……………………………10分 ∵DE ⊂平面EFD ∴平面PAH ⊥平面DEF ，………………………………12分考点：空间中直线与平面的平行、垂直关系.19.（本小题满分12分）已知数列{}n a 是公差不为零的等差数列，其前n 项和为n S .满足52225S a -=，且1413,,a a a 恰为等比数 列{}n b 的前三项.（1）求数列{}{},n n a b 的通项公式；（2）设n T 是数列11n n a a +⎧⎫⎨⎬⎩⎭的前n 项和.是否存在*k N ∈，使得等式112k k T b -=成立，若存在，求出k 的值；若不存在，说明理由.【答案】（1）21n a n =+，3n n b =；（2）不存在*k N ∈，使得等式112k kT b -=成立.所以11111111112355721232323n T n n n ⎡⎤⎛⎫⎛⎫⎛⎫⎛⎫=-+-++-=- ⎪ ⎪ ⎪ ⎪⎢⎥+++⎝⎭⎝⎭⎝⎭⎝⎭⎣⎦，…………………9分 所以21112,32323k T k k ⎧⎫-=+⎨⎬++⎩⎭单调递减，得21312315k T <-≤，而1110,33k k b ⎛⎤=∈ ⎥⎝⎦， 所以不存在*k N ∈，使得等式112k kT b -=成立……………………………………12分 考点：等差、等比数列的通项公式及数列求和.20.（本小题满分13分）设椭圆()2222:10x y C a b a b +=>>，定义椭圆C 的“相关圆”方程为222222a b x y a b+=+.若抛物线24y x = 的焦点与椭圆C 的一个焦点重合，且椭圆C 短轴的一个端点和其两个焦点构成直角三角形.（1）求椭圆C 的方程和“相关圆”E 的方程；（2）过“相关圆”E 上任意一点P 的直线:l y kx m =+与椭圆C 交于,A B 两点. O 为坐标原点，若 OA OB ⊥，证明原点O 到直线AB 的距离是定值，并求m 的取值范围.【答案】（1）椭圆C 的方程为2212x y +=，“相关圆”E 的方程为2223x y +=；（2）m ≥或m ≤考点：椭圆的方程及直线与椭圆的位置关系.【方法点晴】本题主要考查了椭圆、圆的方程及直线与椭圆的位置关系，考查了圆锥曲线中的定值为题，属于中档题.求椭圆和圆的方程，只要根据条件建立基本量,,a b c 之间的关系，问题即可得解；定值问题也是直线与圆锥曲线位置关系的综合应用中的常见题型，解答的基本策略是把要证为定值量用参数表示，根据韦达定理、判别式及其它一些已知条件建立交点坐标与参数间的关系进行消元、运算，即可证得结论.21.（本小题满分14分）设函数()()()()221ln ,12f x ax b x xg x x b x =+-=-+-.已知曲线()y f x =在点()()1,1f 处的切线 与直线10x y -+=垂直.（1）求a 的值；（2）求函数()f x 的极值点；（3）若对于任意()1,b ∈+∞，总存在[]12,1,x x b ∈，使得()()()()12121f x f x g x g x m -->-+成立， 求实数m 的取值范围.【答案】（1）12a =-；（2）当4b <-时，函数()f x 和一个极大值点，当40b -≤≤时，函数()f x 在()0,+∞上有无极值点，当0b >时，函数()f x 有唯一的，无极小值点；（3）1m ≤-.（2）()()21ln 2f x x b x x =-+-，其定义域为()0,+∞， ()211x bx b f x x b x x --+⎛⎫'=-+-= ⎪⎝⎭，令()()2,0,h x x bx b x =--+∈+∞， 24b b ∆=+综上可知，当4b <-时，函数()f x . 当40b -≤≤时，函数()f x 在()0,+∞上有无极值点；当0b >时，函数()f x ，无极小值点……………………………8分 （3）令()()()F x f x g x =-，[]1,x b ∈，考点：导数的几何意义，利用导数研究函数的单调性和极值、最值等.【方法点晴】本题主要考查了导数的几何意义，利用导数研究函数的单调性和极值、最值等，考查了分类讨论的数学思想和转化的数学思想，属于难题.求曲线上某点的切线关键是根据导数的几何意义求得切线斜率，研究函数的极值就是研究导数的变号零点，本题中由于定义域为()0,x ∈+∞，所以转化为讨论二次函数在给定区间上的零点问题；本题的难点是第三问，通过构造函数，把问题转化为求新函数在给定区间上的最大值和最小值，充分体现了导数在研究函数中的工具作用.。
山东师范大学附属中学2016届高三上学期第三次模拟考试英语试题(含答案)
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1．What does the woman want the man to do?A．Come back soon．B．Pick up her friends．C．Return with information about the buses．2．Why was the woman late?A．She missed the bus． B. The traffic was really bad．C．Her car broke down．3．What does the man care about most?A．The car’s color．B．The car’s style．C．The car’s function．4. How did the woman learn about her new job?A．From a friend．B．From the paper．C．From the TV5．What is true about the man?A．He doesn’t work anywhere now．B．He will work for Tom’s company．C．He was fired by his boss．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。
陕西省师范大学附属中学2016届高三下学期第八次模拟理综物理试卷
陕西师大附中2016届高考理综模拟试题物理部分二、选择题（本题共8小题，每小题6分，在每小题给出的四个选项中，其中14-18题只有一项符合题目要求，第19-21题有的有多项符合题目要求。
全部选对的得6分，选对但不全的得3分，有选错的得0分）14．如图所示，固定的半球面右侧是光滑的，左侧是粗糙的，O 点为球心，A 、B 为两个完全相同的小物块（可视为质点），小物块A 静止在球面的左侧，受到的摩擦力大小为F 1，对球面的压力大小为N 1；小物块B 在水平力F 2作用下静止在球面的右侧，对球面的压力大小为N 2，已知两小物块与球心连线和竖直方向的夹角均为θ，则 A ．F 1：F 2=sin θ：1 B ．F 1：F 2＝sin θ：1 C ．N 1：N 2＝cos 2θ：1 D.N 1：N 2＝sin 2θ：115．如图所示，三维坐标系O-xyz 的z 轴方向竖直向上，所在空间存在沿y 轴正方向的匀强电场。
一质量为m 、电荷量为+q 的小球从z 轴上的A 点以速度v 沿x 轴正方向水平抛出，A 点坐标为（0，0，L ），重力加速度为g ，场强q mg E /=。
则下列说法中正确的是（ ）A ．小球运动的轨迹为抛物线B ．小球在xOz 平面内的分运动为非平抛运动C ．小球到达xOy 平面时的速度大小为gL v 22+D ．小球的运动轨迹与xOy 平面交点的坐标为（g L v /，L ，0）16．一平行板电容器的电容为C ，两板间的距离为d ，上板带正电，电量为Q ，下板带负电，电量也为Q ，它们产生的电场在很远处的电势为零．两个带异号电荷的小球用一绝缘刚性杆相连，小球的电量都为q ，杆长为l ，且l ＜d ．现将它们从很远处移到电容器内两板之间，处于图示的静止状态（杆与板面垂直），在此过程中电场力对两个小球所做总功的大小等于多少？（设两球移动过程中极板上电荷分布不变）（ ） A ．B ．0C ．D ．17．如图所示为某住宅区的应急供电系统，由交流发电机和副线圈匝数可调的理想降压变压器组成．发电机中矩形线圈所围的面积为S ，匝数为N ，电阻不计，它可绕水平轴OO '在磁感应强度为B 的水平匀强磁场中以角速度ω匀速转动．矩形线圈通过滑环连接降压变压器，滑动触头P 上下移动时可改变输出电压，0R 表示输电线的电阻．以线圈平面与磁场平行时为计时起点，下列判断正确的是（ ） A ．若发电机线圈某时刻处于图示位置，变压器原线圈的电流瞬时值为零 B ．发电机线圈感应电动势的瞬时值表达式为 sin e NBS t ωω= C ．当滑动触头P 向下移动时，变压器原线圈两端的电压将升高D ．当用户数目增多时，为使用户电压保持不变，滑动触头P 应向上滑动 18．如图所示，半径为1R 的导体球，外套一个与它同心的导体球壳，球壳的内外半径分别为2R 和3R ，当内球带电量为Q 时，在带电球与球壳内表面之间的区域存在电场，若用K 表示静电常量，你可能不会计算电场的能量，但你可根据其他方法判断下列电场能量E 的表达式中正确的是A.1211()2Q E K R R =- B.21211()2Q E K R R =-C.1211()2Q E K R R =+ D.21211()2Q E K R R =+19．甲、乙两车某时刻由同一地点，沿同一方向开始做直线运动，若以该时刻作为计时起点，得到两车的位移﹣时间图象，即x ﹣t 图象如图所示，甲图象过O 点的切线与AB 平行，过C 点的切线与OA 平行，则下列说法中正确的是（ ）A ．在两车相遇前，t 1时刻两车相距最远B ．t 3时刻甲车在乙车的前方C ．0﹣t 2时间内甲车的瞬时速度始终大于乙车的瞬时速度D ．甲车的初速度等于乙车在t 3时刻的速度20．如图所示，在倾斜的滑杆上套一个质量为m 的圆环，圆环通过轻绳拉着一个质量为M 的物体，在圆环沿滑杆向下滑动的过程中，悬挂物体的轻绳始终处于竖直方向。
(解析版)陕西师大附中2016年高考数学模拟试卷(文科)(
陕西师大附中2016年高考数学模拟试卷（文科）（十）（解析版）一、选择题（本题共12小题，每小题5分，共60分）1．若集合A={y|y=lgx}，B={x|y=}，则A∩B为（）A．[0，1]B．（0，1]C．[0，∞）D．（﹣∞，1]2．（5分）（2016陕西校级模拟）复数z1=cosx﹣isinx，z2=sinx﹣icosx，则|z1z2|=（）A．1B．2C．3D．43．（5分）（2012菏泽一模）命题“∀x∈[1，2]，x2﹣a≤0”为真命题的一个充分不必要条件是（）A．a≥4B．a≤4C．a≥5D．a≤54．（5分）（2016山东模拟）2016年2月，为保障春节期间的食品安全，某市质量监督局对超市进行食品检查，如图所示是某品牌食品中微量元素含量数据的茎叶图，已知该组数据的平均数为11.5，则的最小值为（）A．9B．C．8D．45．（5分）（2016陕西校级模拟）从圆x2﹣2x+y2﹣2y+1=0外一点P（3，2）向这个圆作两条切线，则两切线夹角的余弦值为（）A．B．C．D．06．（5分）（2016陕西校级模拟）在数列{a n}中，a1=﹣，a n=1﹣（n≥2，n∈N*），则a2016的值为（）A．B．5C．D．7．（5分）（2016陕西校级模拟）如图为某几何体的三视图，求该几何体的内切球的表面积为（）A．B．3πC．4πD．8．（5分）（2016陕西校级模拟）在平面直角坐标系中，点P是由不等式组所确定的平面区域内的动点，M，N是圆x2+y2=1的一条直径的两端点，则的最小值为（）A．4B．C．D．79．（5分）（2016陕西校级模拟）已知函数，则关于a的不等式f （a﹣2）+f（a2﹣4）＜0的解集是（）A．B．（﹣3，2）C．（1，2）D．10．（5分）（2016陕西校级模拟）函数f（x）=﹣2sin2x+sin2x+1，给出下列四个命题：①在区间[]上是减函数；②直线x=是函数图象的一条对称轴；③函数f（x）的图象可由函数y=sin2x的图象向左平移个单位得到；④若x∈[0，]，则f（x）的值域是[0，]．其中，正确的命题的序号是（）A．①②B．②③C．①④D．③④11．（5分）（2014福建模拟）若双曲线（a＞b＞0）的左右焦点分别为F1、F2，线段F1F2被抛物线y2=2bx的焦点分成7：5的两段，则此双曲线的离心率为（）A．B．C．D．12．（5分）（2014浙江模拟）对于函数f（x）和g（x），设α∈{x∈R|f（x）=0}，β∈{x∈R|g （x）=0}，若存在α、β，使得|α﹣β|≤1，则称f（x）与g（x）互为“零点关联函数”．若函数f（x）=e x﹣1+x﹣2与g（x）=x2﹣ax﹣a+3互为“零点关联函数”，则实数a的取值范围为（）A．B．C．[2，3]D．[2，4]二、填空题（本题共4小题，每小题5分，共20分.把答案填写在题中的横线上）13．（5分）（2016陕西校级模拟）在等比数列{a n}中，已知a1+a2+…+a n=2n﹣1，则a12+a22+…+a n2=．14．（5分）（2013西安三模）连掷两次骰子得到的点数分别为m和n，若记向量=（m，n）与向量的夹角为θ，则θ为锐角的概率是．15．（5分）（2016陕西校级模拟）已知程序框图如图所示，其功能是求一个数列{a n}的前10项和，则数列{a n}的一个通项公式a n=，数列{a n a n+1}的前2016项和为．16．（5分）（2016陕西校级模拟）已知a＞0，函数f（x）=，若f（t﹣）＞﹣，则实数t的取值范围为．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）（2015衡阳三模）在△ABC中，角A、B、C所对的边为a、b、c，且满足cos2A﹣cos2B=（1）求角B的值；（2）若且b≤a，求的取值范围．18．（12分）（2016陕西校级模拟）某学校为调查高三年学生的身高情况，按随机抽样的方法抽取80名学生，得到男生身高情况的频率分布直方图（图（1））和女生身高情况的频率分布直方图（图（2））．已知图（1）中身高在170～175cm的男生人数有16人．（Ⅰ）试问在抽取的学生中，男、女生各有多少人？（Ⅱ）根据频率分布直方图，完成下列的2×2列联表，并判断能有多大（百分几）的把握认为“身高与性别有关”？（Ⅲ）在上述80名学生中，从身高在170～175cm之间的学生中按男、女性别分层抽样的方法，抽出5人，从这5人中选派3人当旗手，求3人中恰好有一名女生的概率．参考公式：K2=参考数据：19．（12分）（2016陕西校级模拟）如图，在底面为梯形的四棱锥S﹣ABCD中，已知AD∥BC，∠ASC=60°，AD=DC=，SA=SC=SD=2．（Ⅰ）求证：AC⊥SD；（Ⅱ）求三棱锥B﹣SAD的体积．20．（12分）（2016陕西校级模拟）已知椭圆C：=1（a＞b＞0）的离心率为，以原点为圆心，椭圆的短半轴长为半径的圆与直线x﹣y+=0相切．A、B是椭圆C的右顶点与上顶点，直线y=kx（k＞0）与椭圆相交于E、F两点．（1）求椭圆C的方程；（2）当四边形AEBF面积取最大值时，求k的值．21．（12分）（2014东城区二模）已知a∈R，函数f（x）=x3+（a﹣2）x2+b，g（x）=2alnx．（Ⅰ）若曲线y=f（x）与曲线y=g（x）在它们的交点（1，c）处的切线互相垂直，求a，b 的值；（Ⅱ）设F（x）=f′（x）﹣g（x），若对任意的x1，x2∈（0，+∞），且x1≠x2，都有F（x2）﹣F（x1）＞a（x2﹣x1），求a的取值范围．请考生在第22，23，24题中任选一题作答，如果多做，则按所做的第一题计分，作答时请写清题号．[选修4-1：几何证明选讲]22．（10分）（2015吉林三模）如图，在△ABC中，∠B=90°，以AB为直径的⊙O交AC 于D，过点D作⊙O的切线交BC于E，AE交⊙O于点F．（1）证明：E是BC的中点；（2）证明：ADAC=AEAF．[选修4-4：坐标系与参数方程]23．（2016永州模拟）选修4﹣4：坐标系与参数方程．极坐标系与直角坐标系xoy有相同的长度单位，以原点为极点，以x轴正半轴为极轴，已知曲线C1的极坐标方程为ρ=4cosθ，曲线C2的参数方程为（t为参数，0≤α＜π），射线θ=φ，θ=φ+，θ=φ﹣与曲线C1交于（不包括极点O）三点A、B、C．（I）求证：|OB|+|OC|=|OA|；（Ⅱ）当φ=时，B，C两点在曲线C2上，求m与α的值．[选修4-5：不等式选讲]24．（2013新课标Ⅰ）（选修4﹣5：不等式选讲）已知函数f（x）=|2x﹣1|+|2x+a|，g（x）=x+3．（Ⅰ）当a=﹣2时，求不等式f（x）＜g（x）的解集；（Ⅱ）设a＞﹣1，且当时，f（x）≤g（x），求a的取值范围．2016年陕西师大附中高考数学模拟试卷（文科）（十）参考答案与试题解析一、选择题（本题共12小题，每小题5分，共60分）1．若集合A={y|y=lgx}，B={x|y=}，则A∩B为（）A．[0，1]B．（0，1]C．[0，∞）D．（﹣∞，1]【分析】由A={y|y=lgx}={y|y∈R}，B={x|y=}={x|1﹣x≥0}={x|x≤1}，能求出A∩B．【解答】解：∵A={y|y=lgx}={y|y∈R}，B={x|y=}={x|1﹣x≥0}={x|x≤1}，∴A∩B={x|x≤1}=（﹣∞，1]．故选D．【点评】本题考查交集的定义和运算，是基础题．解题时要认真审题，仔细解答．2．（5分）（2016陕西校级模拟）复数z1=cosx﹣isinx，z2=sinx﹣icosx，则|z1z2|=（）A．1B．2C．3D．4【分析】直接利用复数的乘法以及三角函数的运算法则化简复数，然后求解复数的模．【解答】解：复数z1=cosx﹣isinx，z2=sinx﹣icosx，则z1z2=cosxsinx﹣cosxsinx+i（﹣cos2x ﹣sin2x）=﹣i．则|z1z2|=1．故选：A．【点评】本题考查复数的代数形式混合运算，复数的模的求法，考查计算能力．3．（5分）（2012菏泽一模）命题“∀x∈[1，2]，x2﹣a≤0”为真命题的一个充分不必要条件是（）A．a≥4B．a≤4C．a≥5D．a≤5【分析】本题先要找出命题为真命题的充要条件{a|a≥4}，从集合的角度充分不必要条件应为{a|a≥4}的真子集，由选择项不难得出答案．【解答】解：命题“∀x∈[1，2]，x2﹣a≤0”为真命题，可化为∀x∈[1，2]，a≥x2，恒成立即只需a≥（x2）max=4，即“∀x∈[1，2]，x2﹣a≤0”为真命题的充要条件为a≥4，而要找的一个充分不必要条件即为集合{a|a≥4}的真子集，由选择项可知C符合题意．故选C【点评】本题为找命题一个充分不必要条件，还涉及恒成立问题，属基础题．4．（5分）（2016山东模拟）2016年2月，为保障春节期间的食品安全，某市质量监督局对超市进行食品检查，如图所示是某品牌食品中微量元素含量数据的茎叶图，已知该组数据的平均数为11.5，则的最小值为（）A．9B．C．8D．4【分析】根据平均数的定义求出a+b=2，再利用基本不等式求出的最小值即可．【解答】解：根据茎叶图中的数据，该组数据的平均数为=（a+11+13+20+b）=11.5，∴a+b=2；∴=+=2+++≥2+=，当且仅当a=2b，即a=，b=时取“=”；∴+的最小值为．故选：B．【点评】本题考查了平均数的定义与基本不等式的应用问题，是基础题目．5．（5分）（2016陕西校级模拟）从圆x2﹣2x+y2﹣2y+1=0外一点P（3，2）向这个圆作两条切线，则两切线夹角的余弦值为（）A．B．C．D．0【分析】先求圆心到P的距离，再求两切线夹角一半的三角函数值，然后求出结果．【解答】解：圆x2﹣2x+y2﹣2y+1=0的圆心为M（1，1），半径为1，从外一点P（3，2）向这个圆作两条切线，则点P到圆心M的距离等于，每条切线与PM的夹角的正切值等于，所以两切线夹角的正切值为，该角的余弦值等于，故选B．【点评】本题考查圆的切线方程，两点间的距离公式，是基础题．6．（5分）（2016陕西校级模拟）在数列{a n}中，a1=﹣，a n=1﹣（n≥2，n∈N*），则a2016的值为（）A．B．5C．D．【分析】由a1=﹣，a n=1﹣（n≥2，n∈N*），利用递推思想求出数列的前4项，从而得到{a n}是以3为周期的周期数列，由此能求出a2016．【解答】解：∵在数列{a n}中，a1=﹣，a n=1﹣（n≥2，n∈N*），∴=5，=，=﹣，∴{a n}是以3为周期的周期数列，∵2016=672×3，∴a2016=a3=．故选：C．【点评】本题考查数列的递推公式的求法，是中档题，解题时要认真审题，解题的关键是推导出{a n}是以3为周期的周期数列．7．（5分）（2016陕西校级模拟）如图为某几何体的三视图，求该几何体的内切球的表面积为（ ）A ．B ．3πC ．4πD ．【分析】球心到棱锥各表面的距离等于球的半径，求出棱锥的各面面积，使用体积法求出内切球半径．【解答】解：由三视图可知几何体为四棱锥，作出直观图如图所示： 其中SA ⊥底面ABCD ，底面ABCD 是边长为3的正方形，SA=4．∴SB=SD==5，∴S △SAB =S △SAD =，S △SBC =S △SCD =．S 底面=32=9．V 棱锥==12．S 表面积=6×2+7.5×2+9=36．设内切球半径为r ，则球心到棱锥各面的距离均为r ．∴S 表面积r=V 棱锥．∴r=1． ∴内切球的表面积为4πr 2=4π． 故选C ．【点评】本题考查多面体的内切球的运算，解题时注意体积法的应用．8．（5分）（2016陕西校级模拟）在平面直角坐标系中，点P是由不等式组所确定的平面区域内的动点，M，N是圆x2+y2=1的一条直径的两端点，则的最小值为（）A．4B．C．D．7【分析】设出M，N，P的坐标，根据向量数量积的公式进行转化，利用数形结合转化为线性规划进行求解即可．【解答】解：∵M，N是圆x2+y2=1的一条直径的两端点，∴设M（a，b），N（﹣a，﹣b），则满足a2+b2=1，设P（x，y），则=（a﹣x，b﹣y）（﹣a﹣x，﹣b﹣y）=﹣（a﹣x）（a+x）﹣（b﹣y）（b+y）=﹣a2+x2﹣b2+y2=x2+y2﹣（a2+b2）=x2+y2﹣1，设z=x2+y2，则z的几何意义是区域内的点到原点距离的平方，作出不等式组对应的平面区域如图：则原点到直线x+y﹣4=0的距离最小，此时d==2，则z=d2=（2）2=8，则=x2+y2﹣1=8﹣1=7，故选：D．【点评】本题主要考查向量数量积以及线性规划的应用，利用坐标系结合斜率数量积的公式转化为线性规划问题是解决本题的关键．考查学生的转化能力．9．（5分）（2016陕西校级模拟）已知函数，则关于a的不等式f （a﹣2）+f（a2﹣4）＜0的解集是（）A．B．（﹣3，2）C．（1，2）D．【分析】根据已知中的函数解析式，先分析函数的单调性和奇偶性，进而根据函数的性质及定义域，可将不等式f（a﹣2）+f（a2﹣4）＜0化为1＞a﹣2＞4﹣a2＞﹣1，解不等式组可得答案．【解答】解：函数的定义域为（﹣1，1）∵f（﹣x）=﹣sinx=﹣f（x）∴函数f（x）为奇函数又∵f′（x）=+cosx＞0，∴函数在区间（﹣1，1）上为减函数，则不等式f（a﹣2）+f（a2﹣4）＜0可化为：f（a﹣2）＜﹣f（a2﹣4）即f（a﹣2）＜f（4﹣a2），即1＞a﹣2＞4﹣a2＞﹣1解得＜a＜2故关于a的不等式f（a﹣2）+f（a2﹣4）＜0的解集是（，2）．故选：A．【点评】本题考查的知识点是函数的单调性和奇偶性的性质，解不等式，是函数图象和性质与不等式的综合应用，属于中档题．10．（5分）（2016陕西校级模拟）函数f（x）=﹣2sin2x+sin2x+1，给出下列四个命题：①在区间[]上是减函数；②直线x=是函数图象的一条对称轴；③函数f（x）的图象可由函数y=sin2x的图象向左平移个单位得到；④若x∈[0，]，则f（x）的值域是[0，]．其中，正确的命题的序号是（）A．①②B．②③C．①④D．③④【分析】将函数进行化简，结合三角函数的图象和性质即可求函数y=f（x）图象的单调区间、对称轴、平移、值域．【解答】解：①求函数的单调减区间：∴，∴①正确；②求函数的对称轴为：2x=∴∴②正确；③由y=向左平移个单位后得到，∴③不正确；④当时，∴∴∴④不正确．故正确的是①②，故选：A．【点评】本题考查了三角函数图象和性质，属于易考题．11．（5分）（2014福建模拟）若双曲线（a＞b＞0）的左右焦点分别为F1、F2，线段F1F2被抛物线y2=2bx的焦点分成7：5的两段，则此双曲线的离心率为（）A．B．C．D．【分析】依题意，抛物线y2=2bx 的焦点F（，0），由=可求得c=3b，结合双曲线的性质即可求得此双曲线的离心率．【解答】解：∵抛物线y2=2bx 的焦点F（，0），线段F1F2被抛物线y2=2bx 的焦点分成7：5的两段，∴=，∴c=3b，∴c2=a2+b2=a2+c2，∴=．∴此双曲线的离心率e=．故选C．【点评】本题考查双曲线的简单性质与抛物线的简单性质，求得c=3b是关键，考查分析与运算能力，属于中档题．12．（5分）（2014浙江模拟）对于函数f（x）和g（x），设α∈{x∈R|f（x）=0}，β∈{x∈R|g （x）=0}，若存在α、β，使得|α﹣β|≤1，则称f（x）与g（x）互为“零点关联函数”．若函数f（x）=e x﹣1+x﹣2与g（x）=x2﹣ax﹣a+3互为“零点关联函数”，则实数a的取值范围为（）A．B．C．[2，3]D．[2，4]【分析】先得出函数f（x）=e x﹣1+x﹣2的零点为x=1．再设g（x）=x2﹣ax﹣a+3的零点为β，根据函数f（x）=e x﹣1+x﹣2与g（x）=x2﹣ax﹣a+3互为“零点关联函数”，及新定义的零点关联函数，有|1﹣β|≤1，从而得出g（x）=x2﹣ax﹣a+3的零点所在的范围，最后利用数形结合法求解即可．【解答】解：函数f（x）=e x﹣1+x﹣2的零点为x=1．设g（x）=x2﹣ax﹣a+3的零点为β，若函数f（x）=e x﹣1+x﹣2与g（x）=x2﹣ax﹣a+3互为“零点关联函数”，根据零点关联函数，则|1﹣β|≤1，∴0≤β≤2，如图．由于g（x）=x2﹣ax﹣a+3必过点A（﹣1，4），故要使其零点在区间[0，2]上，则g（0）×g（2）≤0或，解得2≤a≤3，故选C．【点评】本题主要考查了函数的零点，考查了新定义，主要采用了转化为判断函数的图象的零点的取值范围问题，解题中注意体会数形结合思想与转化思想在解题中的应用．二、填空题（本题共4小题，每小题5分，共20分.把答案填写在题中的横线上）13．（5分）（2016陕西校级模拟）在等比数列{a n}中，已知a1+a2+…+a n=2n﹣1，则a12+a22+…+a n2=．【分析】根据条件等比数列{a n}中，已知a1+a2+…+a n=2n﹣1，可知a1=1，公比为2，从而有{a n2}是以1为首项，4为公比的等比数列，故可求．【解答】解：由等比数列{a n}中，已知a1+a2+…+a n=2n﹣1，可知a1=1，公比为2∴{a n2}是以1为首项，4为公比的等比数列∴a12+a22+…+a n2==故答案为：．【点评】本题的考点是数列的求和，主要考查等比数列的求和，关键是判断出{a n2}是以1为首项，4为公比的等比数列，从而利用等比数列的求和公式．14．（5分）（2013西安三模）连掷两次骰子得到的点数分别为m和n，若记向量=（m，n）与向量的夹角为θ，则θ为锐角的概率是．【分析】设连掷两次骰子得到的点数记为（m n），其结果有36种情况，若向量与向量的夹角θ为锐角，则，满足这个条件的有6种情况，由此求得θ为锐角的概率．【解答】解：设连掷两次骰子得到的点数记为（m n），其结果有36种情况，若向量=（m，n）与向量的夹角θ为锐角，则，满足这个条件的有6种情况，所以θ为锐角的概率是，故答案为．【点评】本题主要考查用数量积表示两个向量的夹角，古典概型及其概率计算公式的应用，属于中档题．15．（5分）（2016陕西校级模拟）已知程序框图如图所示，其功能是求一个数列{a n}的前10项和，则数列{a n}的一个通项公式a n=，数列{a n a n+1}的前2016项和为．【分析】执行程序框图，写出每次循环得到的S，n，k的值，观察数列{a n}的前n项和的变化规律，即可求解．利用裂项法即可求和．【解答】解：执行程序框图，有 S=0．n=2，k=1不满足k ≤10第1次执行循环体，S=，n=4，k=2不满足k ≤10第2次执行循环体，S=+，n=6，k=3不满足k ≤10第3次执行循环体，S=++，n=8，k=4不满足k ≤10第3次执行循环体，S=+++，n=10，k=5 …综上可知，程序框图的功能是求一个数列{a n }的前10项和，S=++++…+故数列{a n }的一个通项公式a n =．则a n a n+1==（﹣），则数列{a n a n+1}的前2016项和S=（1﹣+…+﹣）=（1﹣）==故答案为：，．【点评】本题主要考察了程序框图和算法，数列通项公式和和的求法，根据程序框图求出通项公式以及利用裂项法进行求和是解决本题的关键．16．（5分）（2016陕西校级模拟）已知a ＞0，函数f （x ）=，若f （t ﹣）＞﹣，则实数t 的取值范围为 （0，+∞） ．【分析】根据分段函数的表达式判断函数的单调性，根据函数的单调性将不等式进行转化即可得到结论．【解答】解：当x ∈[﹣1，0）时，函数f （x ）=sin单调递增，且f （x ）∈[﹣1，0），当x ∈[0，+∞）时，函数f （x ）=ax 2+ax+1的对称轴为x=﹣，此时函数f （x ）单调递增且f （x ）≥1，综上当x ∈[﹣1，+∞）时，函数单调递增，由f （x ）=sin =得=，解得x=，则不等式f （t ﹣）＞﹣，等价为f （t ﹣）＞f （﹣）， ∵函数f （x ）是增函数，∴t ﹣＞﹣， 即t ＞0，故答案为：（0，+∞）【点评】本题主要考查不等式的求解，根据条件判断分段函数的单调性是解决本题的关键．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）（2015衡阳三模）在△ABC 中，角A 、B 、C 所对的边为a 、b 、c ，且满足cos2A ﹣cos2B=（1）求角B 的值；（2）若且b ≤a ，求的取值范围．【分析】（1）由条件利用三角恒等变换化简可得 2﹣2sin 2A ﹣2cos 2B=﹣2sin 2A ，求得cos 2B 的值，可得cosB 的值，从而求得B 的值．（2）由b=≤a ，可得B=60°．再由正弦定理可得．【解答】解：（1）在△ABC 中，∵cos2A ﹣cos2B==2（cosA+sinA ）（cosA ﹣sinA ）=2（cos 2A ﹣sin 2A ）=cos 2A ﹣sin 2A=﹣2sin 2A ．又因为 cos2A ﹣cos2B=1﹣2sin 2A ﹣（2cos 2B ﹣1）=2﹣2sin 2A ﹣2cos 2B ，∴2﹣2sin 2A ﹣2cos 2B=﹣2sin 2A ，∴cos 2B=，∴cosB=±，∴B=或．（2）∵b=≤a ，∴B=，由正弦====2，得a=2sinA ，c=2sinC ，故a ﹣c=2sinA ﹣sinC=2sinA ﹣sin （﹣A ）=sinA ﹣cosA=sin （A ﹣），因为b ≤a ，所以≤A ＜，≤A ﹣＜，所以a ﹣c=sin （A ﹣）∈[，）．【点评】本题主要考查正弦定理、余弦定理的应用，三角恒等变换，属于中档题．18．（12分）（2016陕西校级模拟）某学校为调查高三年学生的身高情况，按随机抽样的方法抽取80名学生，得到男生身高情况的频率分布直方图（图（1））和女生身高情况的频率分布直方图（图（2））．已知图（1）中身高在170～175cm 的男生人数有16人．（Ⅰ）试问在抽取的学生中，男、女生各有多少人？（Ⅱ）根据频率分布直方图，完成下列的2×2列联表，并判断能有多大（百分几）的把握认为“身高与性别有关”？（Ⅲ）在上述80名学生中，从身高在170～175cm之间的学生中按男、女性别分层抽样的方法，抽出5人，从这5人中选派3人当旗手，求3人中恰好有一名女生的概率．参考公式：K2=参考数据：【分析】（Ⅰ）由直方图中身高在170～175cm的男生的频率为0.08×5=0.4，可得男生数为40．由男生的人数为40，得女生的人数为80﹣40=40；（Ⅱ）求出男生身高≥170cm的人数，女生身高≥170cm的人数，得到2×2列联表，求出k2，则答案可求；（Ⅲ）求出在170～175cm之间的男生有16人，女生人数有4人．再由分层抽样的方法抽出5人，得到男生占4人，女生占1人．然后利用枚举法得到选派3人的方法种数，求出3人中恰好有一名女生的种数，利用古典概率模型计算公式得答案．【解答】解：（Ⅰ）直方图中，∵身高在170～175cm的男生的频率为0.08×5=0.4，设男生数为n1，则，得n1=40．由男生的人数为40，得女生的人数为80﹣40=40．（Ⅱ）男生身高≥170cm的人数=（0.08+0.04+0.02+0.01）×5×40=30，女生身高≥170cm的人数0.02×5×40=4，所以可得到下列列联表：，∴能有99.9%的把握认为身高与性别有关；（Ⅲ）在170～175cm之间的男生有16人，女生人数有4人．按分层抽样的方法抽出5人，则男生占4人，女生占1人．设男生为A1，A2，A3，A4，女生为B．从5人任选3名有：（A1，A2，A3），（A1，A2，A4），（A1，A2，B），（A1，A3，A4），（A1，A3，B），（A1，A4，B），（A2，A3，A4），（A2，A3，B），（A2，A4，B），（A3，A4，B），共10种可能，3人中恰好有一名女生有：（A1，A2，B），（A1，A3，B），（A1，A4，B），（A2，A3，B），（A2，A4，B），（A3，A4，B），共6种可能，故所求概率为．【点评】本小题主要考查频率分布直方图、2×2列联表和概率等基础知识，考查数据处理能力、运算求解能力以及应用用意识，考查必然与或然思想、分类与整合思想等，是中档题．19．（12分）（2016陕西校级模拟）如图，在底面为梯形的四棱锥S﹣ABCD中，已知AD∥BC，∠ASC=60°，AD=DC=，SA=SC=SD=2．（Ⅰ）求证：AC⊥SD；（Ⅱ）求三棱锥B﹣SAD的体积．【分析】（1）取AC中点O，连结OD，SO，由等腰三角形的性质可知AC⊥SO，AC⊥OD，故AC⊥平面SOD，于是AC⊥SD；（2）由△ASC是等边三角形可求得SO，AC，利用勾股定理的逆定理可证明AD⊥CD，SO⊥OD，故而SO⊥平面ABCD，代入体积公式计算即可．【解答】证明：（1）取AC中点O，连结OD，SO，∵SA=SC，∴SO⊥AC，∵AD=CD，∴OD⊥AC，又∵OS⊂平面SOD，OD⊂平面SOD，OS∩OD=O，∴AC⊥平面SOD，∵SD⊂平面SOD，∴AC⊥SD．（2）∵SA=SC=2，∠ASC=60°，∴△ASC 是等边三角形，∴AC=2，OS=，∵AD=CD=，∴AD 2+CD 2=AC 2，∴∠ADC=90°，OD==1．∵SD=2，∴SO 2+OD 2=SD 2，∴SO ⊥OD ，又∵SO ⊥AC ，AC ⊂平面ABCD ，OD ⊂平面ABCD ，AC ∩OD=O ， ∴SO ⊥平面ABCD ，∴V 棱锥B ﹣SAD =V 棱锥S ﹣ABD =S △ABD SO==．【点评】本题考查了线面垂直的判定与性质，棱锥的体积计算，属于中档题．20．（12分）（2016陕西校级模拟）已知椭圆C ： =1（a ＞b ＞0）的离心率为，以原点为圆心，椭圆的短半轴长为半径的圆与直线x ﹣y+=0相切．A 、B 是椭圆C 的右顶点与上顶点，直线y=kx （k ＞0）与椭圆相交于E 、F 两点． （1）求椭圆C 的方程；（2）当四边形AEBF 面积取最大值时，求k 的值．【分析】（1）通过椭圆的离心率，直线与圆相切，求出a ，b 即可求出椭圆的方程．（2）设E （x 1，kx 1），F （x 2，kx 2），其中x 1＜x 2，将y=kx 代入椭圆的方程，利用韦达定理，结合点E ，F 到直线AB 的距离分别，表示出四边形AEBF 的面积，利用基本不等式求出四边形AEBF 面积的最大值时的k 值即可．【解答】解：（1）由题意知：=∴=，∴a2=4b2．…（2分）又∵圆x2+y2=b2与直线相切，∴b=1，∴a2=4，…（3分）故所求椭圆C的方程为…（4分）（2）设E（x1，kx1），F（x2，kx2），其中x1＜x2，将y=kx代入椭圆的方程整理得：（k2+4）x2=4，故．①…（5分）又点E，F到直线AB的距离分别为，．…（7分）所以四边形AEBF的面积为==…（9分）===，…（11分）当k2=4（k＞0），即当k=2时，上式取等号．所以当四边形AEBF面积的最大值时，k=2．…（12分）【点评】本题考查直线与椭圆的位置关系，圆锥曲线的综合应用，考查分析问题解决问题的能力，转化思想以及计算能力．21．（12分）（2014东城区二模）已知a∈R，函数f（x）=x3+（a﹣2）x2+b，g（x）=2alnx．（Ⅰ）若曲线y=f（x）与曲线y=g（x）在它们的交点（1，c）处的切线互相垂直，求a，b 的值；（Ⅱ）设F（x）=f′（x）﹣g（x），若对任意的x1，x2∈（0，+∞），且x1≠x2，都有F（x2）﹣F（x1）＞a（x2﹣x1），求a的取值范围．【分析】（Ⅰ）求出曲线y=f（x）和y=g（x）的导数，利用导数的几何意义，建立方程关系即可得到结论；（Ⅱ）求出F（x）表达式，利用函数的单调性即可得到结论．【解答】解：（Ⅰ），．，g'（1）=2a．依题意有f'（1）g'（1）=﹣1，可得，解得a=1，或．当a=1时，f（x）=x3﹣x2+b，g（x）=2lnx．由，解得c=0．b=，当a=时，f（x）=x3﹣x2+b，g（x）=lnx．由，解得c=0．b=．（Ⅱ）．不妨设x1＜x2，则等价于F（x2）﹣F（x1）＞a（x2﹣x1），即F（x2）﹣ax2＞F（x1）﹣ax1．设G（x）=F（x）﹣ax，则对任意的x1，x2∈（0，+∞），且x1≠x2，都有，等价于G（x）=F（x）﹣ax在（0，+∞）是增函数．，可得，依题意有，对任意x＞0，有x2﹣2x﹣2a≥0．由2a≤x2﹣2x=（x﹣1）2﹣1，可得．【点评】本题主要考查导数的几何意义，以及利用导数研究函数的单调性，考查学生的运算能力．请考生在第22，23，24题中任选一题作答，如果多做，则按所做的第一题计分，作答时请写清题号．[选修4-1：几何证明选讲]22．（10分）（2015吉林三模）如图，在△ABC中，∠B=90°，以AB为直径的⊙O交AC 于D，过点D作⊙O的切线交BC于E，AE交⊙O于点F．（1）证明：E是BC的中点；（2）证明：ADAC=AEAF．【分析】（1）欲证明E是BC的中点，即证EB=EC，即要证ED=EC，这个可通过证明∠CDE=∠C得到；（2）因由相似三角形可得：AB2=AEAF，AB2=ADAC，故欲证ADAC=AEAF，只要由AB=AB 得到即可．【解答】证明：（Ⅰ）证明：连接BD，因为AB为⊙O的直径，所以BD⊥AC，又∠B=90°，所以CB切⊙O于点B，且ED切于⊙O于点E，因此EB=ED，∠EBD=∠EDB，∠CDE+∠EDB=90°=∠EBD+∠C，所以∠CDE=∠C，得ED=EC，因此EB=EC，即E是BC的中点（Ⅱ）证明：连接BF，显然BF是R t△ABE斜边上的高，可得△ABE∽△AAFB，于是有，即AB2=AEAF，同理可得AB2=ADAC，所以ADAC=AEAF【点评】本题主要考查了相似三角形的判定，与圆有关的比例线段．属于基础题．[选修4-4：坐标系与参数方程]23．（2016永州模拟）选修4﹣4：坐标系与参数方程．极坐标系与直角坐标系xoy有相同的长度单位，以原点为极点，以x轴正半轴为极轴，已知曲线C1的极坐标方程为ρ=4cosθ，曲线C2的参数方程为（t为参数，0≤α＜π），射线θ=φ，θ=φ+，θ=φ﹣与曲线C1交于（不包括极点O）三点A、B、C．（I）求证：|OB|+|OC|=|OA|；（Ⅱ）当φ=时，B，C两点在曲线C2上，求m与α的值．【分析】（Ⅰ）依题意，|OA|=4cosφ，|OB|=4cos（φ+），|OC|=4cos（φ﹣），利用三角恒等变换化简|OB|+|OC|为4cosφ，=|OA|，命题得证．（Ⅱ）当φ=时，B，C两点的极坐标分别为（2，），（2，﹣）．再把它们化为直角坐标，根据C2是经过点（m，0），倾斜角为α的直线，又经过点B，C的直线方程为y=﹣（x﹣2），由此可得m及直线的斜率，从而求得α的值．【解答】解：（Ⅰ）依题意，|OA|=4cosφ，|OB|=4cos（φ+），|OC|=4cos（φ﹣），…（2分）则|OB|+|OC|=4cos（φ+）+4cos（φ﹣）=2（cosφ﹣sinφ）+2（cosφ+sinφ）=4 cosφ，=|OA|．…（5分）（Ⅱ）当φ=时，B，C两点的极坐标分别为（2，），（2，﹣）．化为直角坐标为B（1，），C（3，﹣）．…（7分）C2是经过点（m，0），倾斜角为α的直线，又经过点B，C的直线方程为y=﹣（x﹣2），故直线的斜率为﹣，…（9分）所以m=2，α=．…（10分）【点评】本题主要考查把参数方程化为直角坐标方程，把点的极坐标化为直角坐标，直线的倾斜角和斜率，属于基础题．[选修4-5：不等式选讲]24．（2013新课标Ⅰ）（选修4﹣5：不等式选讲）已知函数f（x）=|2x﹣1|+|2x+a|，g（x）=x+3．（Ⅰ）当a=﹣2时，求不等式f（x）＜g（x）的解集；（Ⅱ）设a＞﹣1，且当时，f（x）≤g（x），求a的取值范围．【分析】（Ⅰ）当a=﹣2时，求不等式f（x）＜g（x）化为|2x﹣1|+|2x﹣2|﹣x﹣3＜0．设y=|2x﹣1|+|2x﹣2|﹣x﹣3，画出函数y的图象，数形结合可得结论．（Ⅱ）不等式化即1+a≤x+3，故x≥a﹣2对都成立．故﹣≥a﹣2，由此解得a的取值范围．【解答】解：（Ⅰ）当a=﹣2时，求不等式f（x）＜g（x）化为|2x﹣1|+|2x﹣2|﹣x﹣3＜0．设y=|2x﹣1|+|2x﹣2|﹣x﹣3，则y=，它的图象如图所示：结合图象可得，y＜0的解集为（0，2），故原不等式的解集为（0，2）．（Ⅱ）设a＞﹣1，且当时，f（x）=1+a，不等式化为1+a≤x+3，故x≥a﹣2对都成立．故﹣≥a﹣2，解得a≤，故a的取值范围为（﹣1，]．【点评】本题主要考查绝对值不等式的解法，函数的恒成立问题，函数的单调性的应用，体现了数形结合以及转化的数学思想，属于中档题．。
2023届陕西省西安市雁塔区陕西师范大学附属中学三模英语试题
2023届陕西省西安市雁塔区陕西师范大学附属中学三模英语试题学校:___________姓名：___________班级：___________考号：___________一、阅读理解One of the best ways to pay for college is to find work that helps pay part of the school fee. Here are four part-time jobs that provide students with extra income.Library ClerkThis is a part-time position with the Saratoga Springs Library for approximately twenty-three to thirty-one hours per week. You must be able to read and write in English.SCHEDULES:Monday 8:30 AM-2:30 PM.Wednesday 3:15 PM-8:15 PM.Friday 1:15 PM-6:15 PM.Saturday 9:45 AM-6:15 PM, half an hour lunch break.Customer Service RepresentativeCMG (California Marketing Group) is currently seeking motivated On-Call employees to work from home.Technical Requirements:PC running Windows 10 Pro or Windows 10 HomeHigh Speed Wired Internet (10 Mbps or more download/10 Mbps or more upload)Special Requirements:Must have a quiet space free of background noise while working.Pay: US$11.00 per hour.E-mail:******************.Telephone OperatorA Telephone Operator for Waldorf Astoria Hotel is responsible for answering and responding to internal and external calls in the hotel’s continuing effort to deliver outstanding guest service and financial profitability. Specifically, you would be responsible for performing the following tasks to the highest standards:Respond to guest inquiries and requests in a timely, friendly and efficient manner.Provide information about the hotel facilities and services.We will pay you US$15.00 per hour. Please send e-************************.Please contact the Human Resources Department at 979-3187 if you have any questions.Executive AssistantThis is a 1099-Independent Contractor position and does not include benefits.Executive Assistants are available from Monday to Friday, at least 10 hours per week and up to 15 hours per week.Executive Assistants are available to respond to new messages and requests from their executives within one hour of receiving them during business hours.Hourly compensation starts at US$22.00 per hour and increases based on your years of relevant experience.Please send e-********************************************-3609 to contact us.1．Which is the best choice if you want to work at home?A．Library Clerk.B．Customer Service Representative.C．Telephone Operator.D．Executive Assistant.2．What should you do if you work for the Waldorf Astoria Hotel?A．Answer customer calls only from inside the hotel.B．Work for twenty-three to thirty-one hours per week.C．Respond to guest requests timely, kindly and efficiently.D．Have a quiet space free of background noise while working.3．How much can an Executive Assistant earn at least per month?A．US$220.B．US$330.C．US$880.D．US$1,320.Kurth Reis of San Francisco, California, has been through many hard times in his life. In 2018, Reis had a serious motorcycle accident and spent time in a hospital. The accident affected him deeply, body and spirit. He had several medical operations. Reis said he felt like he was “reborn” each time he woke after an operation. Following 88 days in the hospital, Reis was released and felt ready to change his ways.Lately, he says he just wants to make people happy by making bubbles. You can watch him perform his bubble art for hours at a time around the city’s streets and in its parks.Sometimes he puts out a glass container called a tip jar. People who watch his show can drop money into it if they want to.If the weather is good for bubbles, Reis makes a special mixture that can make bubbles the size of a small car. Humidity, or the amount of water in the air, is good for bubbles. So, he does not perform on very dry days. To make his large bubble, he puts a small rope hanging from two long sticks into the bubble mixture. As he removes it, he opens his arms wide and the bubbles begin to form. Once enough air is inside the bubble, he moves his arms back together to set the bubble free. Some people feel it looks like a bubble “ballet.”While Reis may seem like a bubble-making expert, he only got started in April 2020. Reis can support himself with donations from crowds that watch him perform. But money is not what stirs him to make bubbles. He feels his art is useful in more important ways. Not long ago, a woman told Reis after a performance that his bubbles had lifted her spirit when her dad died.Reis can see smiles rise from under the face covers worn by those watching him perform. Children cheer and clap their hands. Reis said such reactions make him feel like an essential worker whose job is to spread joy during the health crisis.“I’m just trying to put a smile on somebody’s face by doing some bubbles.” said Reis. 4．What can we know about Kurth Reis from Paragraph 1?A．He had to repay his operation fees.B．He intended to do something different.C．He suffered a minor motorcycle accident.D．He gave up his career as a motorcyclist.5．What may people do when they watch Reis’ performances?A．Put some money into a tip jar near him.B．Give him a hand when he sets a bubble free.C．Grasp a small rope hanging from two long sticks.D．Add a special mixture to help him make large bubbles.6．What does the underlined word “stirs” mean in Paragraph 4?A．forces B．determines C．stops D．encourages 7．What is the best title for the text?A．Lost Time Is Never Found AgainB．Ups and Downs Make One StrongC．Everything Comes to Him Who WaitsD．Small Actions Have a Big ImpactActivities such as art classes could be recommended as an alternative to medication for patients in England as part of a major initiative to reduce the number of people becoming dependent on prescription drugs.The Times newspaper quotes figures showing that in the past 12 months,8.4 million adults in England were taking antidepressants(抗抑郁药)，which is 8 percent higher than 2019,which has resulted in the new advice.Around 23 percent of women are on antidepressants, and 12 percent of men.“Medicines offer a fantastic range of tools for NHS staff to provide care that can be positively life-changing,” said Tony Avery, the national clinical director for prescribing at NHS England. “However, we need to be alert to the risks of some medicines, and the framework we are publishing today empowers local services to work with people to ensure they are being effectively supported when a medicine is no longer providing overall benefit.”The NHS report drew particular attention to projects carried out in the county ofGlouc-ester shire. One service, called Art on Prescription, was described as “a form of social prescription and is a non-clinical intervention delivered by art practitioners for therapeutic benefit”. Another, a course called Artlift, begins with “a personalized ‘What Matters To You’ conversation prior to the start of the program and (we) agree a personalized support plan and goals with each participant”. They all reported improvement in participants’ mentalwell-being.Actually, as long ago as September 2018, then health secretary Matt Hancock said, “The evidence increasingly shows that activities like social clubs, art, ballroom dancing, and gardening can be more effective than medicines for some people and I want to see an increase in that sort of social prescribing.”8．Why does activities such as art classes are recommended for patients in England? A．Because they are more effective than medicines.B．Because people in England prefer to attend art classes.C．Because they can replace medication for patients in England.D．Because they may help reduce the people’s dependence on certain drugs.9．What can we learn from Tony Avery’s words?A．Medicines can provide life-changing effects all the time.B．We need to be cautious about the dangers of some medicines.C．The framework published is greatly supported by the local people.D．Local services can work with patients to provide them with overall benefit.10．What do you know about the projects carried out in the county of Gloucester-shire? A．The two projects were carried out in the rural areas of Gloucester-shire.B．Art on Prescription was a clinical intervention delivered by art practitioners.C．The patients’ mental health in the two projects were both reported to be improved.D．A personalized “What Matters To You” conversation started after the start of the program Artlift.11．What’s the purpose of the passage?A．To persuade people to stop taking medicine.B．To introduce a new kind of life-changing medicine.C．To appeal to the government to organize more social activities.D．To recommend a way to reduce patients’ dependence on prescribed drugs.Building good transportation is a good idea. To have environmental value, new transportation has to sufficiently replace or eliminate driving to cut energy consumption overall. That means that a new traffic system has to be supported by reduction in car use. Traffic lanes should be eliminated or converted into bike or bus lanes. Ideally, these should be combined with higher fuel taxes, and parking fees. Needless to say, I have to struggle to make myself extensively understood. But they’re necessary, because you can’t make people drive less, in the long run, by taking steps that make driving more pleasant, economical, and productive.Lengthy commuting (通勤) time is a forceful factor which can slow the growth of suburbs. The farther people live away from cities, the longer commuting time they need, which means more pollution their cars produce. If, in a misguided effort to do something of environmental value, governments take steps that make long-distance car commuting faster or more convenient—by adding lanes, building bypass, employing traffic-control measures that make it possible for existing roads to accommodate more cars with fewer delays—we are actually encouraging people to live still farther from their jobs, stores, and schools. As a result, governments are forced to further extend road networks, water lines, and other facilities. Ifyou cut commuting time by 10 percent, people who now drive fifty miles each way to work can find reason to move five miles farther out, because their travel time won’t change.Traffic congestion (拥堵) isn’t an environmental problem; traffic is. Relieving congestion without doing anything to reduce the total volume of cars can only make the real problem worse. Highway engineers have known for a long time that building new car lanes only temporarily reduces congestion, because the new lanes add additional driving. Widening roads makes traffic move faster in the short term, but the improved conditions eventually attract additional drivers, and congestion reappears. With more car on the roads, people think about widening roads again. Moving drivers out of cars and into other forms of transportation can have the same effect, if existing traffic lanes are kept in service: road space stimulates road use.One of the arguments that cities inevitably make in promoting transportation plans is that the new system, by relieving automobile congestion, will improve the lives of those who continue to drive. No one ever promotes a transportation system by arguing that it would make travelling less convenient—even though, from an environmental perspective, inconvenient travel is a worthy goal.12．In the first paragraph, the author gives us the hint that his recommendations are ______. A．not widely supported B．costly to carry outC．generally recognized D．temporarily beneficial 13．According to the passage, what will happen if commuting time for drivers is reduced? A．Drivers will become more productive employees.B．Mass transportation will be extended farther into suburban areas.C．Drivers will be more willing to live farther from their working place.D．Mass transportation will carry fewer passengers and receive less government funding. 14．Which of the following can be inferred about the author’s attitude towards the measures to improve traffic?A．They are environmentally beneficial and should be carried out immediately.B．They are well intentioned but ultimately lead to environmental harm.C．They will definitely arouse people’s awareness of environmental protection.D．They will only work if they can make driving more economical and productive. 15．The author wrote this massage mainly to ______.A．support the claim that efforts to reduce traffic actually increase traffic.B．oppose the belief that improving mass transportation systems is good for the environment. C．provide a balance between suburban expansion and traffic congestion.D．indicate that making driving less agreeable is a way to reduce negative effects of traffic.二、七选五Does gardening leave you feeling happy and relaxed? Your brain might be telling youhow gardening can have many physical benefits. But research shows that these benefits can also affect our minds as well!In Japan, there is a growing trend called forest bathing, where people immerse themselves in the outdoors as a way to relax and improve concentration. Why has this caught on? ____17____Studies have shown that forest bathing forces people to disconnect from distractions and be more mindful of their immediate surroundings. This can also happen while gardening. If you’ve ever weeded a garden bed, you will know that it requires a high degree of focus in order to identify unwanted plants. ____18____Another important aspect of gardening is getting your hands dirty, and research show that this can improve your mental health. Scientists have discovered that the mycobacterium (分枝杆菌) found in soil can improve brain function. The micro bacteria found in the soil increases serotonin produced in the brain (also known as the “happy” chemical). ____19____ There’s also the sentimental (情感的) attachment to your garden. Gardening takes effort and because of this, a natural responsibility for the survival of your plants starts to rise with you. Sometimes you see them from seed to plant. Other times you forget to water them and they die.____20____In addition, the hard work will provide you with delicious little vegetables.A．Because it is effective.B．Because you don’t have a backyard.C．You should look for areas to put planters.D．By getting your hands dirty, you are also making your brain happy.E．Gardening is a useful way of improving your physical and mental health.F．By noticing the smallest details, you are also improving your concentration. G．Regardless, caring for something other than yourself can be satisfying and purposeful.三、完形填空“When we feel love and kindness toward others, it not only makes others feel loved and cared23．A．thoroughly B．smoothly C．barely D．actually 24．A．observed B．witnessed C．inspected D．accompanied 25．A．hanging out B．checking out C．setting out D．working out 26．A．expectation B．hesitation C．assumption D．intention 27．A．deal with B．take in C．make up D．cut down 28．A．much B．enough C．little D．awful 29．A．urgent B．absurd C．hopeless D．embarrassing 30．A．roughly B．clearly C．correctly D．dimly 31．A．brightens B．ruins C．begins D．influences 32．A．undertook B．tried C．promised D．failed 33．A．dynamic B．appealing C．friendly D．merciful 34．A．neither B．either C．no D．another 35．A．limited B．vital C．necessary D．countless 36．A．deserve B．charge C．determine D．cost 37．A．efforts B．achievements C．returns D．consequences 38．A．assist B．remind C．permit D．persuade 39．A．similar B．beneficial C．fundamental D．appropriate 40．A．admit B．prefer C．recommend D．consider四、用单词的适当形式完成短文including ambergris (龙涎香) and those featuring the scents of rose and lily. Yang also makes sure his products move with the times, ____48____(roll) out thousands of incense products with a modern appeal. To date, he has innovated ____49____traditional craft by making smokeless incense and developing a legendary product which, after burning, displays promising patterns and characters. They have won him multiple national ____50____(patent).五、短文改错51．文中共有10处语言错误，每句中最多有两处。
高三英语月考试题及答案-陕西西安市长安区第十中学2016届高三下学期第三次月考
2015-2016学年下学期第三次月考高三英语试题I. 单项选择（共10小题; 每小题1分，满分10分）1. What ______ honest boy your son is and what __ fun he is!A. a; aB. a; /C. an; /D. an; a2. --You must obey every word of mine! -- I don’t?A. How aboutB. What ifC. So whatD. what about3. His suggestion _______ to have a picnic was supported by everyone in our class.A. that we goB. which we should goC. that we would goD. when we should go4. I can’t tell you the exact time when I’ll get there, maybe at eight or at nine or later. _____, I’ll be there as early as I can.A. AnyhowB. HoweverC. ThusD. Therefore5. On the top of the hill ______, ______ the old man once lived.A. a temple stands there; in whichB. a temple standing; on whichC. does a temple stand; whereD. stands a temple; where6. Paper produced every year is three times _______ the world’s production of vehicles.A. as heavier asB. more heavierC. of the weight ofD. the weight of7. --How beautiful her dress is!--Do you know that it was at the _______ of her whole month’s salary?A. priceB. payC. spendingD. cost8. --Do you like Jack?--Yes, Jack is good, kind, hard-working and int elligent; ______, I can’t speak too highly of him.A. as a resultB. in a wordC. by the wayD. on the contrary9. _____ is known to everybody, Taiwan is part of China. We must unify it.A. ItB. AsC. ThatD. What10. --I really appreciate ______ to spend holiday with you on this nice island.--It’s my pleasure.A. have timeB. having timeC. to have timeD. to having time II．完型填空（共20小题；每小题1分，满分20分）As darkness fell, hundreds of people in the Swiss village left their houses. They were starting _11 at the mountain top in the distance. It was covered with 12 beautiful and dangerous.The huge mountain is called Matter-horn. Mountain climbers had 13 the top, using the southern route. But no one had ever dared to try a winter climbing up the 14 side. But now one man was daring to try the 15 route. He was Walter Bonatti, a great mountain climber from Italy.For two days he had climbed. The village people had watched him 16 . Now they were waiting to see his 17 . If he planned to 18 the next day, he would light a green signal. A red light would mean that he was 19 .A tiny green light 20 high on the mountain side. Bonatti was not giving up! The people21 .The next day he continued his way upward. He was so lonely and so 22 ! But he would not give up. Again that night he lit the 23 light.In the morning, Bonatti 24 . He could not see the top, but he knew he was 25 there. Though the climb was painful, he moved up.Bonatti had spent months 26 for the climb. Was the training enough? Did he have the strength and 27 to climb to the top?He was finally at the top! News about his 28 was radioed to the world.The trip 29 the southern route was easy. He was warmly welcomed in the village. He had done the “ 30 ”, and would be well remembered as a climber of all time.11. A. back B. forward C. down D. up12. A. flowers B. ice and snow C. green trees D. rocks13. A. watched B. passed C. reached D. climbed14. A. western B. eastern C. southern D. northern15. A. difficult B. different C. same D. easy16. A. patiently B. carefully C. anxiously D. eagerly17. A. face B. figure C. flag D. signal18. A. return B. go on C. rest D. stop19 A. turning back B. moving up C. arriving D. in danger20. A. rose B. appeared C. turned on D. turned off21. A. cheered B. laughed C. jumped D. shouted22. A. sleepy B. excited C. tired D. happy23. A. yellow B. blue C. green D. red24. A. woke up B. turned up C. got up D. looked up25. A. already B. almost C. no longer D. surely26. A. training B. preparing C. planning D. asking27. A. courage B. skill C. money D. wish28. A. victory B. thing C. climb D. courage29. A. along B. up C. down D. to30. A. necessary B. important C. great D. impossibleIII．阅读理解（共20小题；每小题2分，满分40分）阅读下列短文，从每题所给的四个选项（A、B、C、D）中，选出最佳选项。
2016届黑龙江省哈尔滨师范大学附属中学高三下学期第四次模拟英语试题(图片版,含听力)
2016高三四模英语答案听力答案：1—5 BBACA 6—10 ACABA 11—15 ACBCB 16—20 CABCC阅读答案: 21—24 BADC 25—28 ACCB 29—31 CDB 32—35 ADCB36—40 CEADG完型填空：41—45 ABCAC 46—50 DDBAC 51—55 BDCA A 56—60 DBACD语法填空：61. flight 62. anxiously 63.for 64.held 65.How 66. has impressed / impresses 67. first68. to visit 69. a 70. but短文改错：Alice was a high school student. She didn’t have much money and her parents were not rich, andbutshe had an uncle who had been fortunate enough to collect great wealthy. He always gave herwealthvaluable Christmas and birthday present. With her uncle’s birthday come, Alice wanted to buy topresents cominghim something really special. But because he was so rich, she didn’t know how to get him.whatShe went into the best shop in her town and explained her problem to one of helpful assistants.theFinally he asked, “What do you have for someone who has already got everything he wants or sheneed?” The shop assistant sighed deeply and answer, “Envy, only envy.”needs answered书面表达参考范文:Dear Peter,I came to see you but you happened to be out. Spring is approaching, which makes us in good mood. As a result, several good friends and I have made a decision that we will have a gathering party in the Central Park. We would be very delighted if you could come.We plan to meet at the Central Park Gate at 8:00 on Saturday morning. Central Park is not hard to find. You can go straight on when you get out of the school gate and come to the street. Then turn right at the second crossing and you’ll find a hospital. Just opposite it is a No. 7 bus stop. Take a bus and get off at the fourth stop. Central park is just in front of it, where we’ll enjoy our time by climbing the hill, boating in the lake and having a picnic on the grass. What a beautiful day!Do come on time. We will wait for you at the park gate.Yours,Li Hua。
江西省师范大学附属中学2016届高三下学期第三次模拟考试英语试题 缺答案
江西师大附中高三年级英语三模试卷命题：高三英语备课组审题：徐耀军2016. 5本试卷分第I卷(选择题）和第II卷（非选择题)两部分。
第I卷注意事项：1. 答第I卷前,考生务必将自己的姓名、考生号填写在答题卡上。
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. ￡19.15。
B。
￡9.15。
C。
￡9。
16.答案是B。
1。
What does the man probably do？A. A salesman。
B. A librarian.C. An advertiser。
2. What do we know about the daughter？A。
She has been looking forward to the dance.B. She can do nothing but go to the dance。
C. She didn't plan to go to the dance at first。
3. How does the man like football?A。
He would like to play football now.B。
He does not like playing football now。
C。
He will never play football again.4. Which page was the woman talking about?A。
A page very close to the end。
精品：【全国百强校】山东省山东师范大学附属中学2016届高三下学期模拟考试文数试题(原卷版)
山东师范大学附属中学2016届高三下学期模拟考试文数试题一、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.设复数z 满足()2105z i i +=- (i 虚数单位)，则z 的共轭复数z 为（ ）A ．34i -+B ．34i --C ．34i +D ．34i -2.已知集合{}|13M x x =-≤<，集合{|N x y ==，则M N = （ ） A ．M B ．N C ．{}|12x x -≤≤ D ．{}|33x x -≤<3.某校高三（1）班共有48人，学号依次为1，2，3，…，48，现用系统抽样的办法抽取一个容量为6的样 本.已知学号为3，11，19，35，43的同学在样本中，那么还有一个同学的学号应为（ ）A ．27B ．26C ．25D ．244.已知直线1ax by +=经过点()1,2，则24a b+的最小值为（ ）A B ． C ．4 D ．5.设,m n 是两条不同的直线，,αβ是两个不同的平面，给出下列四个命题：①若//,m n m β⊥，则n β⊥；②若//,//m m αβ，则//αβ；③若//,//m n m β，则//n β；④若//,m m αβ⊥，则αβ⊥；其中真命题的个数为（ ）A ．1B ．2C ．3D ．46.已知命题0:p x R ∃∈，使0sin x =:0,2q x π⎛⎫∀∈ ⎪⎝⎭，sin x x >，则下列判断正确的是（ ） A ．p 为真 B ．q ⌝为假 C ．p q ∧为真 D ．p q ∨为假7.函数()()2sin 0,2f x x πωϕωϕ⎛⎫=+>< ⎪⎝⎭的部分图象如图所示，则()17012f f π⎛⎫+ ⎪⎝⎭的值为（ ）A．2- B．2 C．1-．1+8.已知,x y 满足约束条件2025020x y x y y --≤⎧⎪+-≥⎨⎪-≤⎩，则11y z x +=+的范围是（ ） A ．1,23⎡⎤⎢⎥⎣⎦ B ．11,22⎡⎤-⎢⎥⎣⎦ C ．13,22⎡⎤⎢⎥⎣⎦ D ．35,22⎡⎤⎢⎥⎣⎦ 9.已知函数()321132f x ax bx x =-+，连续抛掷两颗骰子得到点数分别是,a b ，则函数()f x '在1x =处取 得最值的概率是（ ）A ．136B ．118C ．112D ．1610.已知抛物线()220,y px p ABC =>∆的三个顶点都在抛物线上，O 为坐标原点，设ABC ∆三条边,,AB BC AC 的中点分别为,,M N Q ，且,,M N Q 的纵坐标分别为123,,y y y .若直线,,AB BC AC 的斜率 之和为-1，则123111y y y ++的值为（ ） A ．12p - B ．1p - C ．1p D ．12p第Ⅱ卷（非选择题共100分）二、填空题（本大题共5小题，每题5分，满分25分．）11.设ln 3,ln 7a b ==，则a be e +=__________.（其中e 为自然对数的底数）12.已知向量,a b2，且()a b a -⊥ ，则向量a 和b 的夹角是__________． 13.已知过点()2,4的直线l 被圆22:2450C x y x y +---=截得的弦长为6，则直线l 的方程为________. 14.公元263年左右，我国数学家刘徽发现当圆内接正多边形的边数无限增加时，多边形面积可无限逼近圆 的面积，并创立了“割圆术”.利用“割圆术”刘徽得到了圆周率精确到小数点后两位的近似值3.14.这 就是著名的“徽率”.如图是利用刘徽的“割圆术”思想设计的一个程序框图，则输出n 的值为___________.001.732,sin150.2588,sin 7.50.1305≈≈≈）15.已知函数()()(),1,11,1x e x f x g x kx f x x ⎧≤⎪==+⎨->⎪⎩，若方程()()0f x g x -=有两个不同实根，则实数k 的取值范围为___________.三、解答题（本大题共6小题，共75分.解答应写出文字说明、证明过程或演算步骤.）16.（本小题满分12分）近日，济南楼市迎来去库存一系列新政，其中房产税收中的契税和营业税双双下调，对住房市场持续增 长和去库存产生积极影响.某房地产公司从两种户型中各拿出9套进行促销活动，其中A 户型每套面积为 100平方米，均价1.1万元/平方米，B 户型每套面积80平方米，均价1.2万元/平方米.下表是这18套 住宅每平方米的销售价格：（单位：万元/平方米）：（1）求,a b 的值； （2）张先生想为自己和父母买两套售价小于100万元的房子，求至少有一套面积为100平方米的概率.17.(本小题满分12分)在ABC ∆中，内角,,A B C 的对边为,,a b c ，已知2cos 2c A a b +=.（1）求角C 的值；（2）若2c =，且ABC ∆,a b .18.（本小题满分12分）如图，四棱锥P ABCD -的底面为正方形，侧面PAD ⊥底面,,,,ABCD PA AD E F H ⊥分别为 ,,AB PC BC 的中点.（1）求证：//EF 平面PAD ；（2）求证：平面PAH ⊥平面DEF .19.（本小题满分12分）已知数列{}n a 是公差不为零的等差数列，其前n 项和为n S .满足52225S a -=，且1413,,a a a 恰为等比数列{}n b 的前三项.（1）求数列{}{},n n a b 的通项公式；（2）设n T 是数列11n n a a +⎧⎫⎨⎬⎩⎭的前n 项和.是否存在*k N ∈，使得等式112k k T b -=成立，若存在，求出k 的 值；若不存在，说明理由.20.（本小题满分13分）设椭圆()2222:10x y C a b a b +=>>，定义椭圆C 的“相关圆”方程为222222a b x y a b+=+.若抛物线24y x = 的焦点与椭圆C 的一个焦点重合，且椭圆C 短轴的一个端点和其两个焦点构成直角三角形.（1）求椭圆C 的方程和“相关圆”E 的方程；（2）过“相关圆”E 上任意一点P 的直线:l y kx m =+与椭圆C 交于,A B 两点. O 为坐标原点，若 OA OB ⊥，证明原点O 到直线AB 的距离是定值，并求m 的取值范围.21.（本小题满分14分）设函数()()()()221ln ,12f x ax b x xg x x b x =+-=-+-.已知曲线()y f x =在点()()1,1f 处的切线 与直线10x y -+=垂直.（1）求a 的值；（2）求函数()f x 的极值点；（3）若对于任意()1,b ∈+∞，总存在[]12,1,x x b ∈，使得()()()()12121f x f x g x g x m -->-+成立， 求实数m 的取值范围.。
陕西师范大学附属中学2025届高三第一次调研测试数学试卷含解析
陕西师范大学附属中学2025届高三第一次调研测试数学试卷注意事项：1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。
2．回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
回答非选择题时，将答案写在答题卡上，写在本试卷上无效。
3．考试结束后，将本试卷和答题卡一并交回。
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．存在点()00,M x y 在椭圆22221(0)x y a b a b+=>>上，且点M 在第一象限，使得过点M 且与椭圆在此点的切线00221x x y y a b +=垂直的直线经过点0,2b ⎛⎫- ⎪⎝⎭，则椭圆离心率的取值范围是（ ）A ．⎛ ⎝⎦B ．⎫⎪⎪⎝⎭C ．⎛ ⎝⎦D ．⎫⎪⎪⎝⎭2．关于圆周率π，数学发展史上出现过许多很有创意的求法，如著名的浦丰实验和查理斯实验．受其启发，我们也可以通过设计下面的实验来估计π的值：先请全校m 名同学每人随机写下一个都小于1的正实数对(),x y ；再统计两数能与1构成钝角三角形三边的数对(),x y 的个数a ；最后再根据统计数a 估计π的值，那么可以估计π的值约为（ ）A ．4a mB ．2a m +C ．2a m m +D ．42a m m+3．在ABC ∆中，角,,A B C 所对的边分别为,,a b c ，已知4cos sin b B C ，则B =（ ）A ．6π或56πB ．4πC ．3πD ．6π或3π 4．在ABC 中，D 为BC 边上的中点，且||1,|2,120AB AC BAC ==∠=︒，则||=AD （ ）A ．2B ．12C ．34D 5．已知定义在[)0,+∞上的函数()f x 满足1()(2)2f x f x =+，且当[)0,2x ∈时，2()2f x x x =-+.设()f x 在[)22,2n n -上的最大值为n a （*n N ∈），且数列{}n a 的前n 项的和为n S .若对于任意正整数n 不等式()129n k S n +≥-恒成立，则实数k 的取值范围为（ ）A ．[)0,+∞B ．1,32⎡⎫+∞⎪⎢⎣⎭C ．3,64⎡⎫+∞⎪⎢⎣⎭D ．7,64⎡⎫+∞⎪⎢⎣⎭6．如图，在底面边长为1，高为2的正四棱柱1111ABCD A BC D -中，点P 是平面1111D C B A 内一点，则三棱锥P BCD -的正视图与侧视图的面积之和为（ ）A ．2B ．3C ．4D ．57．阅读下侧程序框图，为使输出的数据为，则①处应填的数字为A ．B ．C ．D ．8．已知实数ln333,33ln3(n ),l 3a b c ==+=，则,,a b c 的大小关系是( )A ．c b a <<B ．c a b <<C ．b a c <<D ．a c b <<9．已知等差数列{}n a 的前n 项和为n S ，262,21a S ==，则5a =A ．3B ．4C ．5D ．6 10．已知i 是虚数单位，则（ ）A ．B ．C ．D ． 11．如下的程序框图的算法思路源于我国古代数学名著《九章算术》中的“更相减损术”．执行该程序框图，若输入的a ，b 分别为176，320，则输出的a 为（ ）A ．16B ．18C ．20D ．1512．()cos sin x e f x x =在原点附近的部分图象大概是（ ） A ． B ．C ．D ．二、填空题：本题共4小题，每小题5分，共20分。
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陕西师大附中高2016届高三第十次模拟考试高三年级英语试题本试分为第I卷和第II 卷两部分。
全卷共150分，考试时间120分钟。
第I 卷（选择题共100分）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 does the man say about the paintings?A. They are very expensive.B. They are very beautiful.C. They look like kids’ art.2. What does the man want to do?A. Look for a pet store.B. Buy something for dogs.C. Let the woman take care of his dogs.3. What are the speakers doing?A. Taking pictures.B. Doing exercise.C. Playing a video.4. What day is it today?A. Sunday.B. Saturday.C. Friday.5. Why does the woman want a later appointment?A. Her flight was delayed.B. She needs to pick up someone.C. She has to take her mother to the hospital.第二节听下面5段对话或独白。
每段对话或独白后有几个小题，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。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6、7题。
6. What are posted on the wall of the cafeteria?A. The food prices.B. Some pictures.C. The introduction to the cafeteria.7. What will the man probably have?A. Chicken.B. Fish.C. Noodles.听第7段材料，回答第8、9题。
8. According to the woman, what was the party like this year?A. It was very relaxed.B. It was too wild and crazy.C. It ended up a failure.9. What can we learn about the man?A. He has a secretary named Maggie.B. He had never been to an office party before.C. He wore a black suit to the party.听第8段材料，回答第10至12题。
10. What is bothering the man and his wife?A. The noise.B. The size of their room.C. The service of the elevator.11. What will the man do?A. Check out today.B. Wait in the hotel.C. Call the police.12. What did the woman promise to do?A. Repair the elevator.B. Cut down the price.C. Give the man a suite tomorrow.听第9段材料，回答第13至16题。
13. Why was the man so late?A. He was stuck in traffic.B. The bank opened late.C. He forgot about the time in the bank.14. Where is Henry from?A. America.B. Germany.C. France.15. What did Henry give the man?A. A guidebook.B. Some money.C. A map of the bus system.16. What is true of the speakers?A. They both work in a bank.B. They are traveling in Europe.C. They just came back from a holiday.听第10段材料，回答第17至20题。
17. When is the opening day?A. July 4.B. July 7.C. September 4.18. What do we find out about the America’s Cup?A. It is a boat race.B. It has been held in San Francisco before.C. The city spent one year preparing for it.19. Which team won the race last year?A. Italy.B. New Zealand.C. America.20. How many teams will be competing in the Challenger Series?A. Five.B. Four.C. Three.第二部分：阅读理解（共两节，满分40分）第一节（共15小题；毎小题2分，满分30分）阅读下列四篇短文，从每小题后所给的A、B、C、D四个选项中，选出最佳选项，并在答題卡上将该选项涂黑。
A.Homestay provides English language students with the opportunity to speak English outside the classroom and the experience of being part of a British home.What to ExpectThe host will provide accommodation and meals. Rooms will be cleaned and bedcovers changed at least once a week. You will be given the house key and the host is there to offer help and advice as well as to take an interest in your physical and mental health.Accommodation ZonesHomestays are located in London mainly in Zones 2, 3 and 4 of the transport system. Most hosts do not live in the town Centre as much of central London is commercial and not residential(居住的). Zones 3 and 4 often offer larger accommodation in a less crowded area. It is very convenient to travel in London by Underground.Meal Plans Available◇Continental Breakfast◇Breakfast and Dinner◇Breakfast, Packed Lunch and DinnerIt's important to note that few English families still provide a traditional cooked breakfast. Your accommodation includes Continental Breakfast which normally consists of fruit juice, cereal(谷物类食品), bread and tea or coffee. Cheese, fruit and cold meat are not normally part of a Continental Breakfast in England. Dinners usually consist of meat or fish with vegetables followed by dessert, fruit and coffee.FriendsIf you wish to invite a friend over to visit, you must first ask your host's permission. You have no right to entertain friends in a family home as some families feel it is an invasion of their privacy.Self-Catering (自助的)Accommodation in Private HomesAccommodation on a room only basis includes shared kitchen and bathroom facilities and often a main living room. This kind of accommodation offers an independent lifestyle and is more suitable for the long stay student. However, it does not provide the same family atmosphere as anordinary homestay and may not benefit those who need to practice English at home quite as much.21. The passage is probably written for________.A. hosts willing to receive foreign studentsB. foreigners hoping to build British cultureC. English learners applying to live in English homesD. travelers planning to visit families in London22. Which of the following will the host provide?A. Free transport.B. Medical care.C. Room cleaning.D. Physical training.23. What can be inferred from Paragraph 3?A. Zone 4 is more crowded than Zone 2.B. The business center of London is in Zone 1.C. Hosts dislike travelling to the city center.D. Accommodation in the city center is not provided.24. Why do some people choose self-catering accommodation?A. To enjoy much more freedom.B. To enrich their knowledge of English.C. To entertain friends as they like.D. To experience a warmer family atmosphere.B.Studies show that laughter is something that makes you feel calm or relaxed for both physical and psychological wounds though it may seem futile（无用的）to laugh in the face of pain and fear.When Dan Rather interviewed comedian Bill Cosby just one week after his son, Ennis, was killed, Cosby said, “I think it is time for me to tell people that we have to laugh. You can turn painful situations around through laughter. If you can find humor in anything, you can survive it.”Call it a flashlight for dark times: laughter just seems to adjust attitude better than anything else. Inspirational speaker Steve Rizzo recalls a TV interview with an injured firefighter a few days after 9.11．The man had fallen more than 30 stories in one of the towers and had broken a leg. Everyone was crying, and the reporter asked, “How is it that you’ve come out of this alive?” He looked at her and without missing a beat, said, “Look, lady, I’m from New York and I’m afirefighter; that’ all you need to know.”“Everyone laughed and though the laughter was only a couple of seconds,” says Rizzo.“Sometimes that’s all you need to catch your second breath. Laughter gives you that coupleof seconds. You’re sending a message to your brain, and the message is: If you can still laugh even a little among the pain, you are going to be OK.”Of course, there is a difference between laughing off a serious situation and laughing off the fear that results. The firefighter was doing the latter, states Rizzo, the author of Becoming a Humorous Being, and so should we. “If there is anything we have learnt from 9.11, it’s how precious life really is,” she says. “We have to send a message that our spirit won’t die. One important thing that unites us is our ability to laugh.”25. The writer uses the examples of the comedian and the firefighter to show______.A. it is your attitude that decides whether you can survive the pain or notB. laughter is the best way to cure psychological woundsC. laughter can make people feel calm or relaxedD. laughter is a good way to get rid of pain and fear26. We can infer from the passage that Steve Rizzo is __________.A. a reporterB. a soldierC. a firefighterD. a doctor27. From the passage, we can know that Americans are___________.A. really happy after 9.11B. greatly hurt by 9.11C. nearly surprised by 9.11D. hardly united after 9.11C.In my early 30s, I used an expired(过期的) student ID to buy discounted movie tickets. I’d tell myself, I’m buying a ticket I wouldn’t have otherwise bought. I think many people have done similar things; however, we still think of ourselves as honest citizens. Researchers who study these behaviours believe that character isn’t the real reason. We might break the rules under some conditions and in some mind-sets, but not in others.Years ago, Francesca Gino, a professor at Harvard, and Dan Ariel, a behavioural economist at Duke, wondered if people with highter IQs were more likely to cheat. They found that cleverness wasn’t closely connected to dishonesty, but creativity was. The more creative you are, the easier it is to retell the story of what happened when you behaved dishonestly.Harvard University psychologist Joshua Greene argues in his book Moral Tribe that we may be born without having a clear sense of right and wrong, but our culture sharpens it. If your tribe downloads pirated(盗版)music , you’re likely to go with the flow.Harvard researcher Leslie John, along with two colleagues conducted an experiment. They told volunteers that others in the room were making more money than they were for getting questions right on a test. Guess what happened? That group, which considered itself disadvantaged, cheated more than those who believed that everyone received an equal payment. The real threat is that rule breaking worsens over time. Behavioural psychology offers a few antidotes. Keep yourself fed and well-rested —we’re likelier to bebave badly when hungry or tied. Reflect on how your actions look through others’ eyes and see yourselves in a positive light. In a Stanford study, when researchers uesd the verb cheat —please don’t cheat —participants still cheated freely because they felt distanced (疏远)from the act. When the noun was used —don’t bea cheater —hardly anyone did.28. According to Francesca Gino, who are likeliest to break the rules in a company?A. Accountants.B. DesignersC. Cleaners.D. Typists.29. Why did volunteers in Leslie John’s experiment cheat more than others?A. Because they were not as smart as others.B. Because they thought others cheated too.C. Because they felt a sense of unfairness.D. Because they were tired and hungry.30. The underlined word “antidotes” in the last paragraph canbe replaced by _____.A. explanations.B. solutionsC. studiesD. novels.31. What’s the best title for the text?A. Why people break the rules.B. How people break the rules.C. The influence of breaking the rules.D. Different ways of breaking the rules.D.We all have our ways of marking time. My life is measured by taking pictures from one story to the next. My oldest son was born in the middle of a long story about endangered animals. Mydaughter came along with a pack of gray wolves.It's the story in Alaska that I'll remember best，though. It was the story about the loss of wild land，during which my wife Kathy got cancer. That's the one that made time stand still. With anxiety，I stopped taking pictures on the day when she found that tumor (肿瘤)．Cruelly，it was Thanksgiving Day. Early examination saves time. But ours was not early. By the time you can feel it yourself，it's often bigger than the doctor wants it to be.Cancer is a thief. It steals time. Our days are already short with worry. Then comes this terrible disease，unfair as storm at harvest time. But cancer also has the power to change us，for good. We learn to simplify it，enjoying what we have instead of feeling sorry for what we don't. Cancer even makes me a better father. My work has made me a stranger to my three kids. But now I pay attention to what really matters. This is a new way of life and a new way of seeing，all from the cancer.In the end each of us has so little time. We have less of it than we can possibly imagine. And even though it turns out that Kathy's cancer has not spread，and her prognosis (预断) is good. We try to make it all count(重要) now，enjoying every part of every day.I've picked up my camera again. I watch the sky，searching for beautiful light. When winter storms come，Kathy and I gather our children and take the time to catch snowflakes (雪花) on our tongues. After all，this is good. This is what we're living for.32．What is the writer?A．A sponsor. B．A photographer. C．A doctor. D．A director. 33．How did the writer feel after knowing Kathy's disease?A．Anxious. B．Innocent. C．Powerful. D．Optimistic. 34．What effect has the cancer had on the author?A．He focuses much more on his work. B．He spends more time with his family. C．He becomes a stranger to his children. D．He devotes much more to medical care. 35．What can be inferred from the passage?A．Cancer steals time.B．Kathy's cancer has spread.C．The author takes a different way of life.D．Snowflakes make the family feel cool.第二节（共5小题；毎小题2分，满分10分）Everyone is forgetful, but as we age, we start to feel like our brains are slowing down a bit —and that can be a very annoying thing._____36_____Read on for some techniques worth trying. 1.______37______People who regularly made plans and looked forward to upcoming events had a 50 percent reduced chance of Alzheimer's disease (早老性痴呆症), according to a recent study.______38_______Something as simple as setting a goal to have a weekly coffee date with a friend will do. There's evidence that people who have a purpose in life or who are working on long or short-term goals appear to do better. In other words, keep your brain looking forward.2. Go for a walk.Mildly raised glucose (葡萄糖) levels can harm the area of the brain that helps you form memories and physical activity can help get blood glucose down to normal levels. In fact, exercise produces chemicals that are good for your brain._______39_______3. Learn something new.Take a Spanish class online, join a drawing club, or learn to play cards. A study found that mental stimulation (刺激) limits the weakening effects of aging on memory and the mind. But the best thing for your brain is when you learn something new and are physically active at the same time. _____40______Or go dancing with your friends.A. Focus on the future.B. This can be especially harmful to the aged.C. It should be something like learning gardening.D. So take a few minutes each day to do some reading.E. But don't worry if your schedule isn't filled with life-changing events.F. Luckily, research shows there is a lot you can do to avoid those moments.G. In other words, when you take care of your body, you take care of your brain.第三部分英语知识运用（共两节，满分45分）第一节完形填空（共20小题；每题1. 5分，满分30分）阅读下面短文，从短文后各题所给的四个选项（A, B, C和D）中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。