2016北京市东城区高三(二模)

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2016东城高三二模数学理

北京市东城区2015-2016学年度第二学期高三综合练习（二）数学（理科）学校_____________班级_______________姓名______________考号___________ 本试卷分第Ⅰ卷和第Ⅱ卷两部分，第Ⅰ卷1至2页，第Ⅱ卷3至5页，共150分。

考试时长120分钟。

考生务必将答案答在答题卡上，在试卷上作答无效。

考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷（选择题共40分）一、选择题(本大题共8小题，每小题5分，共40分.在每小题列出的四个选项中，选出符合题目要求的一项)1．集合{1234}A =，，，，{|3}B x R x =∈≤，则=A B I A.{1234}，，， B. {123}，， C. {23}， D.{14}， 2．已知命题p ：∃x ∈R 有sinx ≥1，则﹁p 为A. sin 1x R x ∀∈≤，B.sin 1x R x ∃∈<，C. sin 1x R x ∀∈<，D.,sin 1x R x ∃∈≤3．如图，ABC V 为正三角形，111////AA BB CC ，1CC ⊥底面ABC V ，若1122BB AA ==，113AB CC AA ==，则多面体111ABC A B C -在平面11A ABB 上的投影的面积为A. 274B. 92C. 9D. 2724．若向量=(1,0)a ，=(2,1)b ，=(,1)x c 满足条件3a -b 与c 共线，则x 的值A. 1B. -3C. -2D. -1 5．成等差数列的三个正数的和等于6，并且这三个数分别加上3、6、13后成为等比数列{}n b 中的b 、b 、b ，则数列{}n b 的通项公式为A.12n n b -= B. 13n n b -= C. 22n n b -=D. 23n n b -=6．一名顾客计划到商场购物，他有三张优惠劵，每张优惠券只能购买一件商品。

根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠劵1：若标价超过50元，则付款时减免标价的10%；优惠劵2：若标价超过100元，则付款时减免20元；优惠劵3：若标价超过100元，则超过100元的部分减免18%。

2016年北京市东城区高考数学二模试卷(理科)(解析版)

2016年北京市东城区高考数学二模试卷（理科）一、选择题（本大题共8小题，每小题5分，共40分.在每小题列出的四个选项中，选出符合题目要求的一项）1．（5分）集合A＝{1，2，3，4}，B＝{x∈R|x≤3}，则A∩B＝（）A．{1，2，3，4}B．{1，2，3}C．{2，3}D．{1，4} 2．（5分）若命题p：∃x∈R，sin x≥1，则￢p为（）A．∀x∈R，sin x≤1B．∀x∈R，sin x＜1C．∃x∈R，sin x＜1D．∃x∈R，sin x≤13．（5分）如图，△ABC为正三角形，AA1∥BB1∥CC1，CC1⊥底面△ABC，若BB1＝2AA1＝2，AB＝CC1＝3AA1，则多面体ABC﹣A1B1C1在平面A1ABB1上的投影的面积为（）A．B．C．9D．4．（5分）若向量＝（1，0），＝（2，1），＝（x，1）满足条件3﹣与共线，则x的值（）A．1B．﹣3C．﹣2D．﹣15．（5分）成等差数列的三个正数的和等于6，并且这三个数分别加上3、6、13后成为等比数列{b n}中的b3、b4、b5，则数列{b n}的通项公式为（）A．b n＝2n﹣1B．b n＝3n﹣1C．b n＝2n﹣2D．b n＝3n﹣2 6．（5分）一名顾客计划到商场购物，他有三张优惠券，每张优惠券只能购买一件商品．根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠券1：若标价超过50元，则付款时减免标价的10%；优惠券2：若标价超过100元，则付款时减免20元；优惠券3：若标价超过100元，则超过100元的部分减免18%．若顾客购买某商品后，使用优惠券1比优惠券2、优惠券3减免的都多，则他购买的商品的标价可能为（）A．179元B．199元C．219元D．239元7．（5分）已知函数f（x）＝，则f（2+log23）的值为（）A．24B．16C．12D．88．（5分）集合A＝{（x，y）|x，y∈R}，若x，y∈A，已知x＝（x1，y1），y＝（x2，y2），定义集合A中元素间的运算x*y，称为“*”运算，此运算满足以下运算规律：①任意x，y∈A有x*y＝y*x②任意x，y，z∈A有（x+y）*z＝x*z+y*z（其中x+y＝（x1+x2，y1+y2））③任意x，y∈A，a∈R有（ax）*y＝a（x*y）④任意x∈A有x*x≥0，且x*x＝0成立的充分必要条件是x＝（0，0）为向量，如果x＝（x1，y1），y＝（x2，y2），那么下列运算属于“*”正确运算的是（）A．x*y＝x1y1+2x2y2B．x*y＝x1y1﹣x2y2C．x*y＝x1y1+x2y2+1D．x*y＝2x1x2+y1y2二、填空题（本大题共6小题，每小题5分，共30分）9．（5分）设i是虚数单位，复数所对应的点在第一象限，则实数a的取值范围为．10．（5分）设变量x，y满足约束条件，则目标函数z＝2x+y的最大值为．11．（5分）（坐标系与参数方程选做题）已知直线（t为参数）与直线l2：2x﹣4y＝5相交于点B，又点A（1，2），则|AB|＝．12．（5分）为了调查某厂工人生产某种产品的能力，随机抽查了20位工人某天生产该产品的数量．产品数量的分组区间为[45，55），[55，65），[65，75），[75，85），[85，95）由此得到频率分布直方图如图．则产品数量位于[55，65）范围内的频率为；这20名工人中一天生产该产品数量在[55，75）的人数是．13．（5分）若点O和点F2（﹣，0）分别为双曲线＝1（a＞0）的中心和左焦点，点P为双曲线右支上的任意一点，则的取值范围为．14．（5分）已知函数f n（x）＝（n∈N*），关于此函数的说法正确的序号是①f n（x）（n∈N*）为周期函数；②f n（x）（n∈N*）有对称轴；③（，0）为f n（x）（n∈N*）的对称中心：④|f n（x）|≤n（n∈N*）．三、解答题（本大题共6小题，共80分.解答应写出文字说明，演算步骤或证明过程）15．（13分）已知函数f（x）＝2sin（ωx）•cos（ωx）+2cos2（ωx）（ω＞0），且函数f（x）的最小正周期为π．（Ⅰ）求ω的值；（Ⅱ）求f（x）在区间上的最大值和最小值．16．（14分）如图1，△ABC是等腰直角三角形∠CAB＝90°，AC＝2a，E，F 分别为AC，BC的中点，沿EF将△CEF折起，得到如图2所示的四棱锥C′﹣ABFE（Ⅰ）求证：AB⊥平面AEC′；（Ⅱ）当四棱锥C′﹣ABFE体积取最大值时，（i）若G为BC′中点，求异面直线GF与AC′所成角；（ii）在C′﹣ABFE中AE交BF于C，求二面角A﹣CC′﹣B的余弦值．17．（13分）在2015﹣2016赛季CBA联赛中，某队甲、乙两名球员在前10场比赛中投篮命中情况统计如下表（注：表中分数，N表示投篮次数，n表示命中次数），假设各场比赛相互独立．根据统计表的信息：（Ⅰ）从上述比赛中等可能随机选择一场，求甲球员在该场比赛中投篮命中率大于0.5的概率；（Ⅱ）试估计甲、乙两名运动员在下一场比赛中恰有一人命中率超过0.5的概率；（Ⅲ）在接下来的3场比赛中，用X表示这3场比赛中乙球员命中率超过0.5的场次，试写出X的分布列，并求X的数学期望．18．（14分）已知f（x）＝2ln（x+2）﹣（x+1）2，g（x）＝k（x+1）．（Ⅰ）求f（x）的单调区间；（Ⅱ）当k＝2时，求证：对于∀x＞﹣1，f（x）＜g（x）恒成立；（Ⅲ）若存在x0＞﹣1，使得当x∈（﹣1，x0）时，恒有f（x）＞g（x）成立，试求k的取值范围．19．（13分）已知椭圆C：＝1（a＞b＞0）过点（，1），且以椭圆短轴的两个端点和一个焦点为顶点的三角形是等腰直角三角形．（Ⅰ）求椭圆的标准方程；（Ⅱ）设M（x，y）是椭圆C上的动点，P（p，0）是x轴上的定点，求|MP|的最小值及取最小值时点M的坐标．20．（13分）数列{a n}中，定义：d n＝a n+2+a n﹣2a n+1（n≥1），a1＝1．（Ⅰ）若d n＝a n，a2＝2，求a n；（Ⅱ）若a2＝﹣2，d n≥1，求证此数列满足a n≥﹣5（n∈N*）；（Ⅲ）若|d n|＝1，a2＝1且数列{a n}的周期为4，即a n+4＝a n（n≥1），写出所有符合条件的{d n}．2016年北京市东城区高考数学二模试卷（理科）参考答案与试题解析一、选择题（本大题共8小题，每小题5分，共40分.在每小题列出的四个选项中，选出符合题目要求的一项）1．（5分）集合A＝{1，2，3，4}，B＝{x∈R|x≤3}，则A∩B＝（）A．{1，2，3，4}B．{1，2，3}C．{2，3}D．{1，4}【考点】1E：交集及其运算．【解答】解：∵A＝{1，2，3，4}，B＝{x∈R|x≤3}，∴A∩B＝{1，2，3}，故选：B．2．（5分）若命题p：∃x∈R，sin x≥1，则￢p为（）A．∀x∈R，sin x≤1B．∀x∈R，sin x＜1C．∃x∈R，sin x＜1D．∃x∈R，sin x≤1【考点】2J：命题的否定．【解答】解：∵命题p：∃x∈R，sin x≥1，则﹣p为：∀x∈R，sin x＜1，故选：B．3．（5分）如图，△ABC为正三角形，AA1∥BB1∥CC1，CC1⊥底面△ABC，若BB1＝2AA1＝2，AB＝CC1＝3AA1，则多面体ABC﹣A1B1C1在平面A1ABB1上的投影的面积为（）A．B．C．9D．【考点】LA：平行投影及平行投影作图法．【解答】解：根据题意，多面体ABC﹣A1B1C1在平面A1ABB1上的投影是几何体的正视图，如图所示；所以该投影面的面积为3×3﹣×2×1.5﹣×1×1.5＝．故选：A．4．（5分）若向量＝（1，0），＝（2，1），＝（x，1）满足条件3﹣与共线，则x的值（）A．1B．﹣3C．﹣2D．﹣1【考点】96：平行向量（共线）．【解答】解：∵向量＝（1，0），＝（2，1），＝（x，1），∴3﹣＝（1，﹣1），又3﹣与共线，∴x•（﹣1）﹣1×1＝0，解得x＝﹣1．故选：D．5．（5分）成等差数列的三个正数的和等于6，并且这三个数分别加上3、6、13后成为等比数列{b n}中的b3、b4、b5，则数列{b n}的通项公式为（）A．b n＝2n﹣1B．b n＝3n﹣1C．b n＝2n﹣2D．b n＝3n﹣2【考点】8M：等差数列与等比数列的综合．【解答】解：设成等差数列的三个正数为a﹣d，a，a+d，即有3a＝6，解得a＝2，由题意可得2﹣d+3，2+6，2+d+13成等比数列，即为5﹣d，8，15+d成等比数列，即有（5﹣d）（15+d）＝64，解得d＝1（﹣11舍去），即有4，8，16成等比数列，可得公比为2，则数列{b n}的通项公式为b n＝b3•2n﹣3＝4•2n﹣3＝2n﹣1．故选：A．6．（5分）一名顾客计划到商场购物，他有三张优惠券，每张优惠券只能购买一件商品．根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠券1：若标价超过50元，则付款时减免标价的10%；优惠券2：若标价超过100元，则付款时减免20元；优惠券3：若标价超过100元，则超过100元的部分减免18%．若顾客购买某商品后，使用优惠券1比优惠券2、优惠券3减免的都多，则他购买的商品的标价可能为（）A．179元B．199元C．219元D．239元【考点】5C：根据实际问题选择函数类型．【解答】解：由题意，优惠劵1比优惠劵2减免的多，所以他购买的商品的标价超过200元．他购买的商品的标价为219元，优惠劵1减免21.9元；优惠劵2减免20元；优惠劵3减免21.42元；标价为239元，优惠劵1减免23.9元；优惠劵2减免20元；优惠劵3减免25.02元；故选：C．7．（5分）已知函数f（x）＝，则f（2+log23）的值为（）A．24B．16C．12D．8【考点】3P：抽象函数及其应用．【解答】解：由f（x）＝，由2+log23＜4，可得f（2+log23）＝f（3+log23），由3+log23＞4，可得f（3+log23）＝＝23•2log23＝8•3＝24．故选：A．8．（5分）集合A＝{（x，y）|x，y∈R}，若x，y∈A，已知x＝（x1，y1），y＝（x2，y2），定义集合A中元素间的运算x*y，称为“*”运算，此运算满足以下运算规律：①任意x，y∈A有x*y＝y*x②任意x，y，z∈A有（x+y）*z＝x*z+y*z（其中x+y＝（x1+x2，y1+y2））③任意x，y∈A，a∈R有（ax）*y＝a（x*y）④任意x∈A有x*x≥0，且x*x＝0成立的充分必要条件是x＝（0，0）为向量，如果x＝（x1，y1），y＝（x2，y2），那么下列运算属于“*”正确运算的是（）A．x*y＝x1y1+2x2y2B．x*y＝x1y1﹣x2y2C．x*y＝x1y1+x2y2+1D．x*y＝2x1x2+y1y2【考点】2K：命题的真假判断与应用．【解答】解：由题意，若x＝（2，﹣2），y＝（1，1），A，x*y＝﹣2，y*x＝﹣7，不满足①；B，x*y＝﹣5，y*x＝5，不满足①；C，x*x＝﹣7，不满足④；D中运算均适合．故选：D．二、填空题（本大题共6小题，每小题5分，共30分）9．（5分）设i是虚数单位，复数所对应的点在第一象限，则实数a的取值范围为．．【考点】A4：复数的代数表示法及其几何意义．【解答】解：∵复数＝＝+i又∵z在复平面内所对应的点位于第一象限，∴＞0且＞0解得．故答案为：．10．（5分）设变量x，y满足约束条件，则目标函数z＝2x+y的最大值为5．【考点】7C：简单线性规划．【解答】解：画出满足条件的平面区域，如图示：，由，解得A（3，﹣1），由z＝2x+y得：y＝﹣2x+z，平移直线y＝﹣2x，结合图象直线过A（3，﹣1）时，z最大，z的最大值是5，故答案为：5．11．（5分）（坐标系与参数方程选做题）已知直线（t为参数）与直线l2：2x﹣4y＝5相交于点B，又点A（1，2），则|AB|＝．【考点】IR：两点间的距离公式；QH：参数方程化成普通方程．【解答】解：由，得4x+3y﹣10＝0，由解得，即B（，0），所以|AB|＝＝，故答案为：．12．（5分）为了调查某厂工人生产某种产品的能力，随机抽查了20位工人某天生产该产品的数量．产品数量的分组区间为[45，55），[55，65），[65，75），[75，85），[85，95）由此得到频率分布直方图如图．则产品数量位于[55，65）范围内的频率为0.4；这20名工人中一天生产该产品数量在[55，75）的人数是13．【考点】B8：频率分布直方图．【解答】解：由直方图可知：生产该产品数量在[55，65）的频率＝1﹣（0.005+0.0100+0.020+0.025）×10＝0.4∴生产该产品数量在[55，75）的人数＝20×（0.04+0.025）×10＝13，故答案为：0.4 1313．（5分）若点O和点F2（﹣，0）分别为双曲线＝1（a＞0）的中心和左焦点，点P为双曲线右支上的任意一点，则的取值范围为（1，+]．【考点】KC：双曲线的性质．【解答】解：∵点O和点F2（﹣，0）分别为双曲线＝1（a＞0）的中心和左焦点，∴c＝，则c2＝a2+1＝2，则a2＝1，即双曲线方程为x2﹣y2＝1，设P（x，y），则x≥1，则＝＝＝＝1++•（）2，则x≥1，∴1++•（）2＞1，又1++•（）2＝•（+）2，∵x≥1，∴0＜≤1，即当＝1时，1++•（）2＝•（+）2取得最大值为•（1+）2＝+，故的取值范围为（1，+]，故答案为：（1，+]，14．（5分）已知函数f n（x）＝（n∈N*），关于此函数的说法正确的序号是①②④①f n（x）（n∈N*）为周期函数；②f n（x）（n∈N*）有对称轴；③（，0）为f n（x）（n∈N*）的对称中心：④|f n（x）|≤n（n∈N*）．【考点】2K：命题的真假判断与应用．【解答】解：∵函数f n（x）＝（n∈N*），∴①f n（x+2π）＝f n（x）（n∈N*），f n（x）为周期函数，正确；②f n（﹣x）＝＝，f n（x）＝（n∈N*）是偶函数，∴f n（x）＝（n∈N*）有对称轴，正确；③n为偶数时，f n（）＝＝0，∴（，0）为f n（x）（n∈N*）的对称中心，不正确；④∵|sin nx|≤|n sin x|，∴|f n（x）|≤n（n∈N*），正确．故答案为：①②④．三、解答题（本大题共6小题，共80分.解答应写出文字说明，演算步骤或证明过程）15．（13分）已知函数f（x）＝2sin（ωx）•cos（ωx）+2cos2（ωx）（ω＞0），且函数f（x）的最小正周期为π．（Ⅰ）求ω的值；（Ⅱ）求f（x）在区间上的最大值和最小值．【考点】GL：三角函数中的恒等变换应用；HW：三角函数的最值．【解答】解：（Ⅰ）因为函数f（x）＝2sin（ωx）•cos（ωx）+2cos2（ωx），所以，又f（x）的最小正周期为，所以＝，即＝2．﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣6分（Ⅱ）由（Ⅰ）可知，因为，所以．由正弦函数的性质可知，当，即时，函数f（x）取得最大值，最大值为f（）＝3；当时，即时，函数f（x）取得最小值，最小值为f（）＝0．﹣﹣﹣﹣﹣﹣13分16．（14分）如图1，△ABC是等腰直角三角形∠CAB＝90°，AC＝2a，E，F 分别为AC，BC的中点，沿EF将△CEF折起，得到如图2所示的四棱锥C′﹣ABFE（Ⅰ）求证：AB⊥平面AEC′；（Ⅱ）当四棱锥C′﹣ABFE体积取最大值时，（i）若G为BC′中点，求异面直线GF与AC′所成角；（ii）在C′﹣ABFE中AE交BF于C，求二面角A﹣CC′﹣B的余弦值．【考点】LF：棱柱、棱锥、棱台的体积；LM：异面直线及其所成的角；MJ：二面角的平面角及求法．【解答】证明：（Ⅰ）因为△ABC是等腰直角三角形，∠CAB＝90°，E，F分别为AC，BC的中点，所以EF⊥AE，EF⊥C'E．又因为AE∩C'E＝E，所以EF⊥平面AEC'．由于EF∥AB，所以有AB⊥平面AEC'．4分解：（Ⅱ）（i）取AC'中点D，连接DE，EF，FG，GD，由于GD为△ABC'中位线，以及EF为△ABC中位线，所以四边形DEFG为平行四边形．直线GF与AC'所成角就是DE与AC'所成角．所以四棱锥C'﹣ABFE体积取最大值时，C'E垂直于底面ABFE．此时△AEC'为等腰直角三角形，ED为中线，所以直线ED⊥AC'．又因为ED∥GF，所以直线GF与AC'所成角为．10分（ii）因为四棱锥C'﹣ABFE体积取最大值，分别以EA、EF、EC'所在直线为x轴、y轴、z轴，建立空间直角坐标系如图，则C'（0，0，a），B（a，2a，0），F（0，a，0），C'B（a，2a，﹣a），C'F（0，a，﹣a）．设平面C'BF的一个法向量为＝（x，y，z），由得，取y＝1，得＝（﹣1，1，1）．平面C'AE的一个法向量＝（0，1，0）．所以cos ＜＞＝＝，故平面C'AE与平面C'BF 的平面角的夹角的余弦值为．14分17．（13分）在2015﹣2016赛季CBA联赛中，某队甲、乙两名球员在前10场比赛中投篮命中情况统计如下表（注：表中分数，N表示投篮次数，n表示命中次数），假设各场比赛相互独立．根据统计表的信息：（Ⅰ）从上述比赛中等可能随机选择一场，求甲球员在该场比赛中投篮命中率大于0.5的概率；（Ⅱ）试估计甲、乙两名运动员在下一场比赛中恰有一人命中率超过0.5的概率；（Ⅲ）在接下来的3场比赛中，用X表示这3场比赛中乙球员命中率超过0.5的场次，试写出X的分布列，并求X的数学期望．【考点】CB：古典概型及其概率计算公式；CH：离散型随机变量的期望与方差．【解答】解：（Ⅰ）根据投篮统计数据，在10场比赛中，甲球员投篮命中率超过0.5的场次有5场，分别是4，5，6，7，10，所以在随机选择的一场比赛中，甲球员的投篮命中率超过0.5的概率是．在10场比赛中，乙球员投篮命中率超过0.5的场次有4场，分别是3，6，8，10，所以在随机选择的一场比赛中，乙球员的投篮命中率超过0.5的概率是．3分（Ⅱ）设在一场比赛中，甲、乙两名运动员恰有一人命中率超过0.5为事件A，甲队员命中率超过0.5且乙队员命中率不超过0.5为事件B1，乙队员命中率超过0.5且甲队员命中率不超过0.5为事件B2．则P（A）＝P（B1）+P（B2）＝＝．7分（Ⅲ）X的可能取值为0，1，2，3．P（X＝0）＝＝，P（X＝1）＝，P（X＝2）＝＝，P（X＝3）＝＝，X的分布列如下表：∵X～B（3，），∴EX＝3×＝．18．（14分）已知f（x）＝2ln（x+2）﹣（x+1）2，g（x）＝k（x+1）．（Ⅰ）求f（x）的单调区间；（Ⅱ）当k＝2时，求证：对于∀x＞﹣1，f（x）＜g（x）恒成立；（Ⅲ）若存在x0＞﹣1，使得当x∈（﹣1，x0）时，恒有f（x）＞g（x）成立，试求k的取值范围．【考点】3R：函数恒成立问题；6B：利用导数研究函数的单调性．【解答】解：（Ⅰ），当f′（x）＞0 时，所以x2+3x+1＜0，解得﹣2＜x，当f′（x）＜0时，解得，所以f（x）单调增区间为，递减区间是（，+∞）；（Ⅱ）当k＝2时，g（x）＝2（x+1）．令H（x）＝f（x）﹣g（x）＝2ln（x+2）﹣（x+1）2﹣2（x+1）．H′（x）＝，令H′（x）＝0，即﹣2x2﹣8x﹣6＝0，解得x＝﹣1或x＝﹣3（舍）．∴当x＞﹣1时，H′（x）＜0，H（x）在（﹣1，+∞）上单调递减．∴H max（x）＝H（﹣1）＝0，∴对于∀x＞﹣1，H（x）＜0，即f（x）＜g（x）．（Ⅲ）由（II）知，当k＝2时，f（x）＜g（x）恒成立，即对于“x＞﹣1，2 ln（x+2）﹣（x+1）2＜2 （x+1），不存在满足条件的x0；当k＞2时，对于“x＞﹣1，x+1＞0，此时2 （x+1）＜k（x+1）．∴2 ln（x+2）﹣（x+1）2＜2 （x+1）＜k（x+1），即f（x）＜g（x）恒成立，不存在满足条件的x0；令h（x）＝f（x）﹣g（x）＝2ln（x+2）﹣（x+1）2﹣k（x+1），h′（x）＝，当k＜2时，令t（x）＝﹣2x2﹣（k+6）x﹣（2k+2），可知t（x）与h′（x）符号相同，当x∈（x0，+∞）时，t（x）＜0，h′（x）＜0，h（x）单调递减，当x∈（﹣1，x0）时，h（x）＞h（﹣1）＝0，即f（x）﹣g（x）＞0恒成立，综上，k的取值范围为（﹣∞，2）．19．（13分）已知椭圆C：＝1（a＞b＞0）过点（，1），且以椭圆短轴的两个端点和一个焦点为顶点的三角形是等腰直角三角形．（Ⅰ）求椭圆的标准方程；（Ⅱ）设M（x，y）是椭圆C上的动点，P（p，0）是x轴上的定点，求|MP|的最小值及取最小值时点M的坐标．【考点】K3：椭圆的标准方程；KL：直线与椭圆的综合．【解答】解：（Ⅰ）由题意，以椭圆短轴的两个端点和一个焦点为顶点的三角形是等腰直角三角形，所以b＝c，a2＝2b2，则椭圆C的方程为．又因为椭圆C：过点A（，1），所以，故a＝2，b＝.所以椭圆的标准方程为．﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣﹣4分（Ⅱ）|MP|2＝（x﹣p）2+y2．因为M（x，y）是椭圆C上的动点，所以，故．所以．因为M（x，y）是椭圆C上的动点，所以|x|≤2．（1）若|2p|≤2，即|p|≤1，则当x＝2p时，|MP|取最小值，此时M．（2）若p＞1，则当x＝2 时，|MP|取最小值|p﹣2|，此时M（2，0）．（3）若p＜﹣1，则当x＝﹣2 时，|MP|取最小值|p+2|，此时M（﹣2，0）．﹣﹣﹣﹣﹣﹣﹣13分20．（13分）数列{a n}中，定义：d n＝a n+2+a n﹣2a n+1（n≥1），a1＝1．（Ⅰ）若d n＝a n，a2＝2，求a n；（Ⅱ）若a2＝﹣2，d n≥1，求证此数列满足a n≥﹣5（n∈N*）；（Ⅲ）若|d n|＝1，a2＝1且数列{a n}的周期为4，即a n+4＝a n（n≥1），写出所有符合条件的{d n}．【考点】8H：数列递推式．【解答】解：（Ⅰ）∵a n＝d n＝a n+2+a n﹣2a n+1（n≥1），∴a n+2﹣2a n+1＝0（n≥1）；又∵a1＝1，a2＝2，∴数列是以1为首项，2为公比的等比数列，故数列{a n}的通项公式为；（Ⅱ）证明：∵d n≥1，∴a n+2+a n﹣2a n+1≥1，令c n＝a n+1﹣a n，则c n+1﹣c n≥1，叠加得，c n≥n﹣4；即a n+1﹣a n≥n﹣4，叠加可得，≥﹣5．（Ⅲ）由于|d n|＝1，a1＝1，a2＝1，若d1＝1，则可得a3＝2，若d1＝﹣1可得a3＝0；同理，若d2＝1可得a4＝4或a4＝2，若d2＝﹣1可得a4＝0或a4＝﹣2；具体如下表所示，1，1，；所以{a n}可以为1，1，2，2；1，1，2，2；1，1，2，2；…或1，1，0，0；1，1，0，0；1，1，0，0；…此时相应的{d n}为1，﹣1，﹣1，1，1，﹣1，﹣1，1，…或﹣1，1，1，﹣1，﹣1，1，1，﹣1，…．。

2016年北京市东城区高三二模政治试卷含答案

北京市东城区2016届高三下学期综合练习（二）文科综合能力测试政治试题2016.5 为纪念联合国成立70周年，中国政府向联合国赠送一座“和平尊”，回答24、25题。

24. “和平尊”以景泰蓝工艺制成。

尊体以中国传统吉祥纹饰，辅以丝绸之路等元素，这一工艺源于古代西域文化，在中国得到完善发展。

这体现了A. 不同文化在相互交流中逐渐趋同B. 不同文化可以交流互鉴、兼容并蓄C. 中国传统文化的独特魅力和价值D. 历史情怀与时代精神的有机融合25.“和平尊”以中国古代青铜器中的“尊”为原型，“尊”取敬重之义，在中国传统文化中是十分隆重的礼器，以“尊”为礼表达中国对联合国的重视和支持，也承载了中国人民对联合国的美好祝福。

这说明我国A.致力于促进世界政治经济一体化B.注重大国形象，承担国际责任C.积极参与联合国的各项工作D.遵循联合国的宗旨和原则26. 新修订的《中小学生守则》保留了原有仍具时代价值、体现中华传统美德的内容，补充了一些具体行为规范，如主动分担家务、自觉礼让排队等；增加了新时期学生成长发展中需要高度关注的内容，如养成阅读习惯、低碳环保生活等。

可见《中小学生守则》的修订①坚持辩证否定观，解放思想，与时俱进②树立正确价值观，消除价值判断差异③抓住矛盾主要方面，防止矛盾转化④坚持知行统一原则，树立实践第一的观点A. ①②B. ②③C. ①④D. ③④27. 高中生小华家里有闲置现金50万元，欲用于理财。

下表是小华父母分别列出的投资理财计划对父母的理财计划，小华利用所学经济知识给出了合理建议，包括①投资理财项目越多，收益就越大②存款储蓄虽然收益低，，但没风险③组合投资，分散风险④投资理财应该综合考虑多种因素A.①③B.②④C.①④D.③④28.“互联网+”为人大代表与人民群众的联系铺设了“信息快轨”，送来了“网络直通车”。

某市人大网站的首页醒目位置设置了“市民论坛”“建言献策”“立法在线”3个栏目市民不需登陆注册就可以自由发表意见建议。

2016年北京市东城区高三二模英语试题及答案

2016年北京市东城区高三二模英语试题及答案2016年北京市东城区高三二模英语试题及答案1. What as the oman disappointed about?A. The eather.B. The hotel.C. The food.2. What kind of pet does the man ant? 东城区2016 2016学年度第二学期教学统一检测高三英语2016.5本试卷共14页，共150分。

考试时长120分钟。

考生务必将答案答在答题卡上，在试卷上作答无效。

考试结束后，将本试卷和答题卡一并交回。

第一部分：听力理解（共三节，30分）第一节（共5小题；每小题1.5分，共7.5分）听下面5段对话或独白。

每段对话或独白后有一道小题，从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话或独白后，你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话或独白你将听一遍。

例：What is the man going to read?A．A nespaper.B．A magazine.C．A book.答案是A。

1. What as the oman disappointed about?A. The eather.B. The hotel.C. The food.2. What kind of pet does the man ant?A. A parrot.B. A dog.C. A rabbit.3. Who is ill in hospital?A. George.B. Mary.C. Lucy.4. What does the oman think the film ill be like?A. Sad.B. Terrible.C. Funny.5. What are the speakers talking about?A. Saving money.B. Writing s.C. Working arrangements.第二节（共10小题；每小题1.5分，共15分）听下面4段对话。

试卷_2016东城区高三英语二模

北京市东城区2015—2016学年度第二学期高三综合练习（二）2016.5第一部分：听力理解（共三节，30分）第一节（共5小题；每小题1.5分，共7.5分）1. Which subject does the boy like best?A. Science.B. Maths.C. History.2. Who is the boy with glasses?A. Ben.B. Mike.C. Tom.3. What’s the date of Lisa’s birthday party?A. 21st June.B. 20th July.C. 21st July.4. Where are the speakers?A. In a garage.B. In a parking lot.C. In a factory.5. What present will the man probably choose?A. Flowers.B. Chocolates.C. Wine.第二节（共10小题;每小题1.5分，共15分）听第6段材料，回答第6至7题。

6. What does the woman like to be?A. A journalist.B. A teacher.C. A doctor.7. What are they talking about?A. Why they should study.B. Where they should work.C. What subjects they should take.听第7段材料，回答第8至10题。

8. Where does the woman plan to go?A. Italy.B. England.C. Austria.9. Where did the man buy his walking shoes?A. At a market.B. In a supermarket.C. In a shoe shop.10. What does the man advise the woman to take?A. A jacket.B. A sweater.C. T-shirts.听第8段材料，回答第11至13题。

2016年北京市东城区高三二模英语试卷【解析版】

2016年北京市东城区高三二模英语试卷一、单选题（共15小题）21．The ceiling’s low，_____ you need to be careful not to hit your head．A．so B．but C．for D．or 22．Nigel sent the girl a nice little note _____ her for a drink．A．invited B．invitingC．to be inviting D．invite23．George decided it was such a rare car that he _____ it only for a few exhibitions．A．used B．was usingC．had used D．would use24．She read a poem by Carver _____ describes his life in the countryside．A．who B．which C．what D．whose 25．A team of scientists _____ the effects of acid rain over the last twenty-year period．A．studied B．had studiedC．is studying D．has been studying26．That knife’s extremely sharp! _____ you don't cut yourself．A．Mind B．MindingC．To mind D．Minded27．Finally I found my handbag，which _____ under a pile of old newspapers．A．has buried B．had buriedC．has been buried D．had been buried28．My mum’s letters really encouraged me _____ my illness．A．over B．forC．throughout D．within29．The Centre became a place _____ many came to talk about their hope and fears．A．which B．that C．where D．when 30．I always check the prices of different brands _____ I make a major purchase．A．before B．becauseC．although D．where31．Fresh milk _____ in the fridge，or it will go bad．A．may keep B．may be keptC．must keep D．must be kept32．Since there is only one laboratory in the school，it is important to check _____ the students can use it．A．which B．what C．when D．where33．_____ myself enough time to catch the train，I set my alarm for five in the morning．A．Give B．Being givenC．To give D．Given34．If Julia had practised hard enough last night，she _____ more confident on the stage now．A．is B．would beC．had been D．would have been35．_____ with two over-packed suitcases，I arrived at the airport just in time for my flight．A．Arming B．Armed C．To arm D．Arm二、完形填空（共1小题）.阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

2016年北京市东城区高三二模历史试题及答案分析

北京市东城区2016届高三下学期综合练习（二）文科综合能力测试历史试题2016．5 12．下列是史籍上对一些官职的描述：序号描述出处①有两丞，秩千石。

一曰中丞，在殿中兰台，掌图籍秘书……受公卿奏事，举劾（劾：揭发）按章。

《汉书·百官公卿表》②掌经度一路财赋，而察其登耗有无，以足上供及郡县之费。

岁行所部，检察储积，稽考帐籍，凡吏蠹民瘼，悉条以上达。

《宋史·职官七》③不过文学侍从，而其重亦止于票拟。

其委任之权力，与前代宰相绝不相同《明神宗实录·卷五》A．①丞相②三司使③军机大臣B．①丞相②转运使③枢密使C．①御史大夫②转运使③内阁大学士D．①御史大夫②通判③内阁大学士13．有学者认为，“平均地权、节制资本”的思想并非孙中山所首创，在一定程度上是受中国古代传统经济政策的影响。

下列各项能为此观点提供论据的是①奖励耕织②盐铁官营③方田均税④闭关锁国A．①④B．②③C．①②D．③④14．图6为中国人龚容（1538～1603，福建人，移居菲律宾，是当时最著名的从事印刷出版业的华侨）在马尼拉出版的汉文木刻本《无极天主正教真传实录》。

它可用于研究①中国文化对东南亚地区的影响②印刷术对欧洲宗教改革的推动③中西之间的文化交流④英国在东南亚的殖民统治A．②④B．①③C．①②D．③④15．近代思想家严复在他的译作《群己权界论》（今译为《论自由》）中指出：“穆勒此篇，本为英民说法，然其所论，理通他制。

使其事宜任小己之自由，则无间君上贵族社会，皆不得干涉者也。

”由此可见他主张A．尊重个人权利B．倡导民主共和C．学习西方科技D．提高国民素养16．读图7，判断下列各项表述正确的是A．在④诞生了中国最早的一批民族资本主义企业B．在②出现了中国第一个具有资本主义性质的改革方案C．在①建立了中国第一家近代军用企业D．在③开办了中国第一个使用机械开采的煤矿17．有观点认为：中美关系发展史跌宕起伏，以曲折和波动为主其特征始终难以“正常”二字来形容。

高考专题北京市东城区-16第二学期高三综合练习(二).docx

高中数学学习材料马鸣风萧萧*整理制作北京市东城区2015-2016学年度第二学期高三综合练习（二）数学（理科）学校_____________班级_______________姓名______________考号___________ 本试卷分第Ⅰ卷和第Ⅱ卷两部分，第Ⅰ卷1至2页，第Ⅱ卷3至5页，共150分。

考试时长120分钟。

考生务必将答案答在答题卡上，在试卷上作答无效。

考试结束后，将本试卷和答题卡一并交回。

第Ⅰ卷（选择题共40分）一、选择题(本大题共8小题，每小题5分，共40分.在每小题列出的四个选项中，选出符合题目要求的一项)1．集合{1234}A =，，，，{|3}B x R x =∈≤，则=A B I A.{1234}，，， B. {123}，， C. {23}， D.{14}， 2．已知命题p ：∃x ∈R 有sinx ≥1，则﹁p 为A. sin 1x R x ∀∈≤，B.sin 1x R x ∃∈<，C. sin 1x R x ∀∈<，D.,sin 1x R x ∃∈≤3．如图，ABC V 为正三角形，111////AA BB CC ，1CC ⊥底面ABC V ，若1122BB AA ==，113AB CC AA ==，则多面体111ABC A B C -在平面11A ABB 上的投影的面积为A.274 B. 92 C. 9 D. 2724．若向量=(1,0)a ，=(2,1)b ，=(,1)x c 满足条件3a -b 与c 共线，则x 的值A. 1B. -3C. -2D. -15．成等差数列的三个正数的和等于6，并且这三个数分别加上3、6、13后成为等比数列{}n b 中的b 、b 、b ，则数列{}n b 的通项公式为A. 12n n b -= B. 13n n b -= C. 22n n b -=D. 23n n b -=6．一名顾客计划到商场购物，他有三张优惠劵，每张优惠券只能购买一件商品。

2016年北京市东城区高考数学二模试卷(文科)(解析版)

2016年北京市东城区高考数学二模试卷（文科）一、选择题（共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项）1．（5分）已知集合A＝{x∈N|x≤4}，B＝{x∈N|x＞2}，那么A∩B＝（）A．{3，4}B．{0，1，2，3，4}C．N D．R 2．（5分）如图，根据样本的频率分布直方图，估计样本的中位数是（）A．10B．12C．13D．163．（5分）执行如图所示程序框图，则输出的结果是（）A．B．C．D．4．（5分）已知A，B为圆x2+（y﹣1）2＝4上关于点P（1，2）对称的两点，则直线AB的方程为（）A．x+y﹣3＝0B．x﹣y+3＝0C．x+3y﹣7＝0D．3x﹣y﹣1＝0 5．（5分）若a、b为实数，则“ab＜1”是“”的（）A．充分而不必要条件B．必要而不充分条件C．充分条件D．既不充分也不必要条件6．（5分）已知函数g（x）＝f（x）﹣x是偶函数，且f（3）＝4，则f（﹣3）＝（）A．﹣4B．﹣2C．0D．47．（5分）已知向量＝（cosβ，sinβ），将向量绕坐标原点O逆时针旋转θ角得到向量（0＜θ＜90°），则下列说法不正确的是（）A．||+||＞|﹣|B．||＜C．|+|＝|﹣|D．（+）⊥（﹣）8．（5分）如图，边长为a的正方形组成的网格中，设椭圆C1、C2、C3的离心率分别为e1、e2、e3，则（）A．e1＝e2＜e3B．e2＝e3＜e1C．e1＝e2＞e3D．e2＝e3＞e1二、填空题共6小题，每小题5分，共30分．9．（5分）如图所示，在复平面内，点A对应的复数为z，则复数z＝．10．（5分）若函数y＝a+sin x在区间[π，2π]上有且只有一个零点，则a＝．11．（5分）已知双曲线x2﹣＝1（b＞0）的虚轴长是实轴长的2倍，则实数b ＝．12．（5分）已知一个三棱锥的三视图如图所示，其中俯视图是等腰直角三角形，则该三棱锥的四个面中，最大面积为．13．（5分）已知数列{a n}满足a1＝1，a2＝﹣2，且a n+1＝a n+a n+2，n∈N*，则a5＝；数列{a n}的前2016项和为．14．（5分）一名顾客计划到某商场购物，他有三张商场的优惠劵，商场规定每购买一件商品只能使用一张优惠券．根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠劵A：若商品标价超过50元，则付款时减免标价的10%；优惠劵B：若商品标价超过100元，则付款时减免20元；优惠劵C：若商品标价超过100元，则付款时减免超过100元部分的18%．某顾客想购买一件标价为150元的商品，若想减免钱款最多，则应该使用优惠劵（填A，B，C）；若顾客想使用优惠券C，并希望比优惠券A和B减免的钱款都多，则他购买的商品的标价应高于元．三、解答题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程．15．（13分）在△ABC中，角A，B，C所对的边分别是a，b，c，且a2＝3bc．（Ⅰ）若sin A＝sin C，求cos A；（Ⅱ）若A＝，且a＝3，求△ABC的面积．16．（13分）已知等差数列{a n}满足a3＝7，a5+a7＝26，其前n项和为S n．（Ⅰ）求{a n}的通项公式及S n；（Ⅱ）令b n＝（n∈N*），求数列{b n}的前8项和．17．（14分）在梯形ABCD中，AB∥CD，AD＝DC＝CB＝a，∠ABC＝60°．平面ACEF⊥平面ABCD，四边形ACEF是矩形，AF＝a，点M在线段EF上．（Ⅰ）求证：BC⊥AM；（Ⅱ）试问当AM为何值时，AM∥平面BDE？证明你的结论．（Ⅲ）求三棱锥A﹣BFD的体积．18．（13分）某出租车公司响应国家节能减排的号召，已陆续购买了140辆纯电动汽车作为运营车辆．目前我国主流纯电动汽车按续航里程数R（单位：公里）分为3类，即A类：80≤R＜150，B类：150≤R＜250，C类：R≥250．该公司对这140辆车的行驶总里程进行统计，结果如表：（Ⅰ）从这140辆汽车中任取一辆，求该车行驶总里程超过10万公里的概率；（Ⅱ）公司为了了解这些车的工作状况，决定抽取14辆车进行车况分析，按表中描述的六种情况进行分层抽样，设从C类车中抽取了n辆车．（ⅰ）求n的值；（ⅱ）如果从这n辆车中随机选取两辆车，求恰有一辆车行驶总里程超过10万公里的概率．19．（13分）已知椭圆C：+＝1（a＞b＞0）与y轴交于B1，B2两点，F1为椭圆C的左焦点，且△F1B1B2是边长为2的等边三角形．（1）求椭圆C的方程；（2）设直线x＝my+1与椭圆C交于P，Q两点，点P关于x轴的对称点为P1（P1与Q不重合），则直线P1Q与x轴是否交于一个定点？若是，请写出定点坐标，并证明你的结论；若不是，请说明理由．20．（14分）设函数f（x）＝﹣x，a∈R．（Ⅰ）若a＝﹣1，求f（x）在区间[，3]上的最大值；（Ⅱ）设b≠0，求证：当a＝﹣1时，过点P（b，﹣b）有且只有一条直线与曲线y＝f（x）相切；（Ⅲ）若对任意的x∈[，2]，均有f（x）|x﹣1|≤1成立，求a的取值范围．2016年北京市东城区高考数学二模试卷（文科）参考答案与试题解析一、选择题（共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项）1．（5分）已知集合A＝{x∈N|x≤4}，B＝{x∈N|x＞2}，那么A∩B＝（）A．{3，4}B．{0，1，2，3，4}C．N D．R【考点】1E：交集及其运算．【解答】解：∵A＝{x∈N|x≤4}，B＝{x∈N|x＞2}，∴A∩B＝{x∈N|2＜x≤4}＝{3，4}，故选：A．2．（5分）如图，根据样本的频率分布直方图，估计样本的中位数是（）A．10B．12C．13D．16【考点】BB：众数、中位数、平均数．【解答】解：由样本的频率分布直方图，得：[5，10）区间内的频率为0.04×5＝0.2，[10，15）区间内的频率为0.1×5＝0.5，∴估计样本的中位数为：10+＝13．故选：C．3．（5分）执行如图所示程序框图，则输出的结果是（）A．B．C．D．【考点】EF：程序框图．【解答】解：模拟执行程序，可得s＝0，n＝2满足条件n＜8，执行循环体，s＝，n＝4满足条件n＜8，执行循环体，s＝+，n＝6满足条件n＜8，执行循环体，s＝++，n＝8不满足条件n＜8，退出循环，输出s＝++＝．故选：D．4．（5分）已知A，B为圆x2+（y﹣1）2＝4上关于点P（1，2）对称的两点，则直线AB的方程为（）A．x+y﹣3＝0B．x﹣y+3＝0C．x+3y﹣7＝0D．3x﹣y﹣1＝0【考点】J8：直线与圆相交的性质．【解答】解：由题意，圆x2+（y﹣1）2＝4的圆心坐标为C（0，1），∵圆x2+（y﹣1）2＝4上存在A，B两点关于点P（1，2）成中心对称，∴CP⊥AB，P为AB的中点，∵k CP＝＝1，∴k AB＝﹣1，∴直线AB的方程为y﹣2＝﹣（x﹣1），即x+y﹣3＝0．故选：A．5．（5分）若a、b为实数，则“ab＜1”是“”的（）A．充分而不必要条件B．必要而不充分条件C．充分条件D．既不充分也不必要条件【考点】29：充分条件、必要条件、充要条件．【解答】解：若a、b为实数，ab＜1，令a＝﹣1，b＝1，ab＝﹣1＜1，推不出，若，可得b＞0，∴0＜ab＜1，⇒ab＜1，∴ab＜1”是“必要不充分条件，故选：B．6．（5分）已知函数g（x）＝f（x）﹣x是偶函数，且f（3）＝4，则f（﹣3）＝（）A．﹣4B．﹣2C．0D．4【考点】3K：函数奇偶性的性质与判断．【解答】解：函数g（x）＝f（x）﹣x是偶函数，可知g（3）＝g（﹣3），可得f（3）﹣3＝f（﹣3）+3，即4﹣3＝f（﹣3）+3，f（﹣3）＝﹣2．故选：B．7．（5分）已知向量＝（cosβ，sinβ），将向量绕坐标原点O逆时针旋转θ角得到向量（0＜θ＜90°），则下列说法不正确的是（）A．||+||＞|﹣|B．||＜C．|+|＝|﹣|D．（+）⊥（﹣）【考点】91：向量的概念与向量的模．【解答】解：以OA，OB为邻边作平行四边形OACB则AB＝||，∵OA+OB＞AB，∴||+||＞|﹣|，故A正确．∵OA＝OB＝1，∠AOB＜90°，∴AB＝＝，故B正确．∵|+|2＝++2，|﹣|2＝+﹣2，，∴|+|≠|﹣|．故C错误．∵OA＝OB，∴四边形ABCD是菱形，∴OC⊥AB，即（+）⊥（﹣），故D正确．故选：C．8．（5分）如图，边长为a的正方形组成的网格中，设椭圆C1、C2、C3的离心率分别为e1、e2、e3，则（）A．e1＝e2＜e3B．e2＝e3＜e1C．e1＝e2＞e3D．e2＝e3＞e1【考点】K4：椭圆的性质．【解答】解：由图形可知，椭圆C1的长半轴长为2a，短半轴长为1.5a，则e1＝＝椭圆C2的长半轴长为4a，短半轴长为2a，则e2＝＝椭圆C3的长半轴长为6a，短半轴长为3a，则e2＝＝∴e2＝e3＞e1，故选：D．二、填空题共6小题，每小题5分，共30分．9．（5分）如图所示，在复平面内，点A对应的复数为z，则复数z＝2﹣i．【考点】A4：复数的代数表示法及其几何意义．【解答】解：由图可知：点A对应的点为（2，﹣1），∴z＝2﹣i．故答案为：2﹣i．10．（5分）若函数y＝a+sin x在区间[π，2π]上有且只有一个零点，则a＝1．【考点】52：函数零点的判定定理．【解答】解：作函数y＝sin x在区间[π，2π]上的图象如下，，结合图象可知，若函数y＝a+sin x在区间[π，2π]上有且只有一个零点，则a﹣1＝0，故a＝1；故答案为：1．11．（5分）已知双曲线x2﹣＝1（b＞0）的虚轴长是实轴长的2倍，则实数b＝2．【考点】KC：双曲线的性质．【解答】解：双曲线x2﹣＝1（b＞0）的虚轴长是2b，实轴长：2，虚轴长是实轴长的2倍，可得2b＝4，解得b＝2．故答案为：2．12．（5分）已知一个三棱锥的三视图如图所示，其中俯视图是等腰直角三角形，则该三棱锥的四个面中，最大面积为2．【考点】L!：由三视图求面积、体积．【解答】解：由三视图可知：该几何体为如图所示的三棱锥其中底面ABC是等腰直角三角形，PC⊥底面ABC．∴该三棱锥的四个面中，最大面积为侧面△P AB．∴其面积S＝＝2．故答案为：213．（5分）已知数列{a n}满足a1＝1，a2＝﹣2，且a n+1＝a n+a n+2，n∈N*，则a5＝2；数列{a n}的前2016项和为0．【考点】8E：数列的求和．【解答】解：∵a n+1＝a n+a n+2，∴a n+2＝a n+1﹣a n，∵a1＝1，a2＝﹣2，∴a3＝a2﹣a1＝﹣3，a4＝a3﹣a2＝﹣3+2＝﹣1，a5＝a4﹣a3＝﹣1+3＝2，a6＝a5﹣a4＝2+1＝3，a7＝a6﹣a5＝3﹣2＝1，a8＝a7﹣a6＝1﹣3＝﹣2，∴a n+6＝a n．则S2016＝336（a1+a2+a3+a4+a5+a6）＝336×（1﹣2﹣3﹣1+2+3）＝0，故答案为：2，0．14．（5分）一名顾客计划到某商场购物，他有三张商场的优惠劵，商场规定每购买一件商品只能使用一张优惠券．根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠劵A：若商品标价超过50元，则付款时减免标价的10%；优惠劵B：若商品标价超过100元，则付款时减免20元；优惠劵C：若商品标价超过100元，则付款时减免超过100元部分的18%．某顾客想购买一件标价为150元的商品，若想减免钱款最多，则应该使用B优惠劵（填A，B，C）；若顾客想使用优惠券C，并希望比优惠券A和B减免的钱款都多，则他购买的商品的标价应高于225元．【考点】5C：根据实际问题选择函数类型．【解答】解：标价为150元的商品，使用优惠劵A，付款时减免15元；使用优惠劵B，付款时减免20元；使用优惠劵C，付款时减免9元，故想减免钱款最多，则应该使用优惠劵B．设标价为x元，则（x﹣100）×18%＞x×10%且（x﹣100）×18%＞20，∴x＞225，即他购买的商品的标价应高于225元．故答案为：B；225．三、解答题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程．15．（13分）在△ABC中，角A，B，C所对的边分别是a，b，c，且a2＝3bc．（Ⅰ）若sin A＝sin C，求cos A；（Ⅱ）若A＝，且a＝3，求△ABC的面积．【考点】HP：正弦定理；HR：余弦定理．【解答】（本题满分为13分）解：（Ⅰ）在△ABC中，由sin A＝sin C，利用正弦定理可得a＝c．又a2＝3bc，所以：c＝3b．所以：由余弦定理可得．…6分（Ⅱ）由已知a2＝3bc，且a＝3，所以bc＝3．故△ABC的面积．…13分16．（13分）已知等差数列{a n}满足a3＝7，a5+a7＝26，其前n项和为S n．（Ⅰ）求{a n}的通项公式及S n；（Ⅱ）令b n＝（n∈N*），求数列{b n}的前8项和．【考点】8E：数列的求和．【解答】解：（Ⅰ）设等差数列{a n} 的公差为d，由a5+a7＝26，得a6＝13，又a6﹣a3＝3d＝6，解得d＝2．∴a n＝a3+（n﹣3）d＝7+2（n﹣3）＝2n+1．∴以．（Ⅱ）由，得．设{b n} 的前n项和为T n，则．故数列{b n} 的前8项和为．17．（14分）在梯形ABCD中，AB∥CD，AD＝DC＝CB＝a，∠ABC＝60°．平面ACEF⊥平面ABCD，四边形ACEF是矩形，AF＝a，点M在线段EF上．（Ⅰ）求证：BC⊥AM；（Ⅱ）试问当AM为何值时，AM∥平面BDE？证明你的结论．（Ⅲ）求三棱锥A﹣BFD的体积．【考点】LF：棱柱、棱锥、棱台的体积；LS：直线与平面平行；LW：直线与平面垂直．【解答】（Ⅰ）证明：由题意知，梯形ABCD为等腰梯形，且AB＝2a，，由AB2+BC2＝AC2，可知AC⊥BC．又平面ACEF⊥平面ABCD，且平面ACEF∩平面ABCD＝AC，BC⊂平面ABCD，所以BC⊥平面ACEF．又AM⊂平面ACEF，所以BC⊥AM．…5分（Ⅱ）解：当时，平面BDE．证明如下：当，可得，故在梯形ABCD中，设AC∩BD＝N，连结EN，由已知可得CN：NA＝1：2，所以．所以EM＝AN．又EM∥AN，所以四边形ANEM为平行四边形．所以AM∥NE．又NE⊂平面BDE，AM⊄平面BDE，所以平面BDE．当时，平面BDE．…11分（Ⅲ）解：由已知可得△ABD 的面积，故．…14分18．（13分）某出租车公司响应国家节能减排的号召，已陆续购买了140辆纯电动汽车作为运营车辆．目前我国主流纯电动汽车按续航里程数R（单位：公里）分为3类，即A类：80≤R＜150，B类：150≤R＜250，C类：R≥250．该公司对这140辆车的行驶总里程进行统计，结果如表：（Ⅰ）从这140辆汽车中任取一辆，求该车行驶总里程超过10万公里的概率；（Ⅱ）公司为了了解这些车的工作状况，决定抽取14辆车进行车况分析，按表中描述的六种情况进行分层抽样，设从C类车中抽取了n辆车．（ⅰ）求n的值；（ⅱ）如果从这n辆车中随机选取两辆车，求恰有一辆车行驶总里程超过10万公里的概率．【考点】B3：分层抽样方法；CC：列举法计算基本事件数及事件发生的概率．【解答】解：（Ⅰ）从这140辆汽车中任取一辆，则该车行驶总里程超过10 万公里的概率为．（Ⅱ）（ⅰ）依题意．（ⅱ）5 辆车中已行驶总里程不超过10 万公里的车有3 辆，记为a，b，c；5 辆车中已行驶总里程超过10 万公里的车有2 辆，记为m，n．“从5 辆车中随机选取两辆车”的所有选法共10 种：ab，ac，am，an，bc，bm，bn，cm，cn，mn．从5 辆车中随机选取两辆车，恰有一辆车行驶里程超过10 万公里”的选法共6 种：am，an，bm，bn，cm，cn．则选取两辆车中恰有一辆车行驶里程超过10 万公里的概率．19．（13分）已知椭圆C：+＝1（a＞b＞0）与y轴交于B1，B2两点，F1为椭圆C的左焦点，且△F1B1B2是边长为2的等边三角形．（1）求椭圆C的方程；（2）设直线x＝my+1与椭圆C交于P，Q两点，点P关于x轴的对称点为P1（P1与Q不重合），则直线P1Q与x轴是否交于一个定点？若是，请写出定点坐标，并证明你的结论；若不是，请说明理由．【考点】K4：椭圆的性质．【解答】解：（1）由题意可得B1（0，b），B2（0，﹣b），F1（﹣c，0），|F1B1|＝＝a，由△F1B1B2是边长为2的等边三角形，可得a＝2，2b＝2，即b＝1，则有椭圆的方程为+y2＝1；（2）由，得（my+1）2+4y2＝4，即（m2+4）y2+2my﹣3＝0，m≠0，设P（x1，y1），Q（x2，y2）则P1（x1，﹣y1），且y1+y2＝﹣，y1y2＝﹣，经过点P1（x1，﹣y1），Q（x2，y2）的直线方程为＝，令y＝0，则x＝•y1+x1＝，又x1＝my1+1，x2＝my2+1．当y＝0时，x＝＝+1＝+1＝3+1＝4．这说明，直线P1Q与x轴交于定点（4，0）．20．（14分）设函数f（x）＝﹣x，a∈R．（Ⅰ）若a＝﹣1，求f（x）在区间[，3]上的最大值；（Ⅱ）设b≠0，求证：当a＝﹣1时，过点P（b，﹣b）有且只有一条直线与曲线y＝f（x）相切；（Ⅲ）若对任意的x∈[，2]，均有f（x）|x﹣1|≤1成立，求a的取值范围．【考点】6E：利用导数研究函数的最值；6H：利用导数研究曲线上某点切线方程．【解答】（I）解：a＝﹣1，f（x）＝﹣x，f′（x）＝﹣1＝．∴当时，f′（x）＞0，此时函数f（x）单调递增；当1＜x≤3时，f′（x）＜0，此时函数f（x）单调递减．∴在区间[，3]上，当x＝1时，函数f（x）取得最大值，f（1）＝﹣2．（II）证明：当a＝﹣1时，f（x）＝﹣x，f′（x）＝﹣1＞﹣1，设过点P（b，﹣b）与函数f（x）相切于点Q，切线斜率＝，化为：b＝2x0．切线方程为：y+2x0＝（x﹣2x0），与联立可得：化为：x2﹣2x0x+＝0，解得x＝x0，因此切线与曲线有且只有一个公共点Q．当x0＞0时，切点Q位于第四象限，因此只有一条切线；当x0＜0时，切点Q位于第二象限，因此只有一条切线．（III）当x＝1时，∀a∈R，均有f（x）|x﹣1|≤1成立．当x≠1时，不等式等价于a≤x2+．当x∈时，f（x）|x﹣1|≤1等价于：a≤x2+，令g（x）＝x2+，x∈，g′（x）＝2x+＞0，函数g（x）在x∈单调递增，∴当x＝时，函数g（x）取得最小值＝．∴a≤．当1＜x≤2时，f（x）|x﹣1|≤1等价于：a≤x2+，令h（x）＝x2+，则h（x）＝x2+1+＞2，∴a≤，不等式a≤x2+对于x∈（1，2]恒成立．综上可得：实数a的求值范围是．。

2016东城区高三二模英语试题

北京市东城区2015—2016学年度第二学期高三综合练习（二）第二部分：知识运用（共两节，45分）21. The ceiling’s low，_____you need to be careful not to hit your head.A. soB. butC. forD. or22. Nigel sent the girl a nice little note _____ her for a drink.A. invitedB. invitingC. to be invitingD. invite23. George decided it was such a rare car that he _____ it only for a few exhibitions.A. usedB. was usingC. had usedD. would use24. She read a poem by Carver _____ describes his life in the countryside.A. whomB. whichC. whatD. whose25. A team of scientists _____ the effects of acid rain over the last twenty-year period.A. studiedB. had studiedC. is studyingD. has been studying26. That knife’s extremely sharp! _____you don’t cut yourself.A. MindB. MindingC. To mindD. Minded27. Finally I found my handbag, which _____ under a pile of old newspapers.A. has buriedB. had buriedC. has been buriedD. had been buried28. My mum’s letters really encouraged me _____ my illness.A. fromB. forC. throughoutD. within29. The Centre became a place _____ many came to talk about their hopes and fears.A. whichB. thatC. whereD. when30. I always check the prices of different brands _____ I make a major purchase.A. beforeB. becauseC. althoughD. where31. Fresh milk _____ in the fridge, or it will go bad.A. may keepB. may be keptC. must keepD. must be kept32. Since there is only one laboratory in the school, it is important to check _____ the students can use it.A. whichB. whatC. whenD. where33. _____ myself enough time to catch the train, I set my alarm for five in the morning.A. GiveB. Being givenC. To giveD. Given34. If Julia had practised hard enough last night, she _____ more confident on the stage now.A. isB. would beC. h ad beenD. would have been35. _____ with two over-packed suitcases, I arrived at the airport just in time for my flight.A. ArmingB. ArmedC. To armD. Arm第二节完形填空（共20小题；每小题1.5分，共30分）My HeroWhat does it mean to be a hero? I think a hero is someone who goes out of his way to make others happy. My hero is Mr. Wright, my chorus（合唱队）teacher.When I was 12 years old, my grandparents passed away. I was really close to them, and losing them was the hardest thing I’ve ever had to36 through. I couldn’t eat, sleep, or think; I felt like I couldn’t even breathe. It was as if my whole world had fallen down from under me, and I 37 into this huge hole of depression（抑郁）.38 I was battling depression, I was determined to make my high school years the best of my life. It was difficult to be 39 , but I had t o try. I joined Women’s Choir. Mr. Wright was the choral director and he was so funny that the first day, I just knew I had made the best 40 of my life.As the year progressed, I loved chorus more and more. I began to smile again and really enjoy 41 .Then one day that all changed. My friends—or those that I thought were my friends—started talking about me behind my back. I was 42 , and I sat by myself. Mr. Wright came over and asked what was wrong. The look in his eyes told me that I could 43 him. Trying hard to 44 back tears, I told him the whole story.When I finished, he nodded and told me, “If you never learn anything from me, learn this：No one is worth 45 your joy. ” What Mr. Wright said really 46 a chord （心弦）in my heart. He 47 cared about me and what was going on. I’ll never be able to thank him enough, because he not only saved me but has 48 every day of my life since. Any time I feel like giving 49 , I remember Mr. Wright’s words and push forward.I’m proud to say that I 50 my depression, and I’m now a senior. I’m still a51 of chorus, and now I’m also in the best choir at my school.Mr. Wright is a hero 52 everyone he meets. He cares about every single person who walks through his door, and he loves what he does more than any other teacher I’ve known. That’s53 he deserves to be Educator of the Year. He deserves the 54 not just this year but every year.I’m glad I had the opportunity to meet you, Mr. Wright. You are an 55 teacher, and I hope your ealize that. You’re my hero.36. A. put B. walk C. run D. go37. A. looked B. broke C. fell D. turned38. A. If B. Although C. Because D. Once39. A. happy B. calm C. smart D. confident40. A. suggestion B. decision C. effort D. o ffer41. A. care B. nature C. health D. life42. A. refused B. forgotten C. hurt D. trapped43. A. trust B. impress C. respect D. satisfy44. A. set B. fight C. take D. call45. A. stealing B. sharing C. hiding D. feeling46. A. braked B. struck C. played D. shook47. A. cheerfully B. normally C. exactly D. truly48. A. made B. started C. understood D. influenced49. A. off B. out C. up D. away50. A. beat B. suffered C. developed D. saved51. A. leader B. part C. fan D. dancer52. A. about B. with C. to D. at53. A. when B. what C. where D. why54. A. title B. job C. help D. name55. A. amusing B. ambitious C. amazing D. advanced第三部分：阅读理解（共两节，40分）第一节（共15小题；每小题2分，共30分）AOur room was on the second floor but you could still hear the roar of the ocean and see the stars at night. I used to take long walks along the water. The food in town was wonderful and the people were very friendly. The area was very quiet and peaceful, and fairly deserted.The last evening of our vacation, however, we all heard strange footsteps following closely behind us as we were walking up to our room in the holiday centre. We turned around and noticed a fairly young man moving very rapidly across the beach and getting closer to us. He was tall and wore a baseball cap. We couldn’t see his face and he was approaching us very rapidly. The man’s actions made my dad very nervous. Dad warned us that we’d better try to make it to our hotel room as quickly as possible. I didn’t like my dad’s voice; I could hear fear in it. It was late and we were all alone. We didn’t have any cell phones on us. I never saw Dad as worried as he was then and I knew that something was terribly wrong. The sense of fear started to overwhelm Mom and me. We had had such a good time in town. Now, the night was rapidly turning into a dangerous situation.We could hear the man’s footsteps getting closer. Dad’s face was almost pale. The so-called intruder （侵入者）had moved nearer and nearer when all of a sudden, the nearby vending（自动售卖）machine started going crazy and spitting out cans of soda! The noise actually scared the intruder and he ran out of sight. My parents were shaking, but we all turned around to see who had put money into the vending machine downstairs, and actually saved us, but no one was around at all. Not a soul.It’s one vacation I will never forget.56. Where did the author spend the vacation?A. Near a lake.B. At the seaside.C. In a village.D. In a mountain.57. What happened on the last evening of their vacation?A. They were followed by a stranger.B. Their cell phones were missing.C. Their money was stolen.D. They lost their way.58. The underlined word “overwhelm” in Paragraph 2 means _____.A. controlB. moveC. exciteD. impress59. What helped them get out of the trouble?A. Their quick action.B. Other people’s kind help.C. The young man’s warning.D. The noise from the vending machine.BFor over 30 years, Rainbow Montessori in Addison has given children a place to grow and explore the world around them, and they’re still going strong today. With 20 years in the same location, the school is “not going anywhere,” says Dave Rodenborn, a son of the schoo l’s founders. As general director, Dave has overseen many improvements, including a new playground for the preschool and a complete modernization.The school serves families of children from 6 weeks to 6th grade. This allows them to have programs in baby care, preschool, kindergarten, and elementary（小学）. The curriculum has developed over the decades, most notably in the Elementary. At first somewhat jokingly referred to as “Monte-sorta”, due to its relaxed application of the Montessori Method, the school’s elementary now stresses a more traditional Montess environment. Montessori associates abstract concepts with concrete sensorial （感觉的）experiences, ensuring that children are involved in learning, not just memorization. Classrooms still have a creative, casual feel, with children having freedom of choice, but in keeping with Montessori principles, they work within a framework. This helps them learn about freedom within limits, maximizing their potential.The truly international Rainbow Montessori staff comes from a wide range of backgrounds, all Montessori-trained. “They are an energetic, devoted group,”says Dave. “They are loyal, caring and like what they do a lot. I’d say a good 30 to 40 percent of them have been here for almost a decade or more. ”Dave says that his favorite part of being at Rainbow Montessori is “making things grow”. By that, he doesn’t mean it in the sense of the organic, but by “coming up with good solutions to problems as they occur”. This is reflective of Montessori beliefs, in which each child learns to use the right tools and discover solutions for themselves. Dave credits a strong staff and great parents with lots of patience for helping to make Rainbow Montessori an ideal place for children to learn and grow.Rainbow Montessori790 East Duane Ave., Addison(408) 738－3261www. rainbowmontessori. com60. What do we know about Rainbow Montessori school?A. It was founded by Dave Rodenborn.B. It has stood at the same place for 20 years.C. Its students range from kindergarten to primary.D. Half of its staff have worked there for ten years.61. According to Paragraph 2, what is the characteristic of Rainbow Montessori?A. Students are expected to memorize concepts.B. Classroom regulations are highly stressed.C. Students are free to choose subjects.D. Active learning is encouraged.62. By saying “making things grow” in the last paragraph, Dave means the school _____.A. tries its best to prevent problems from occurringB. provides suitable learning tools for each single childC. creates a natural environment for the growth of studentsD. encourages students to find proper ways to solve problemsCResearchers continue to show the power behind our sense of smell. Recent studies have found, among other things, that the smell of foods like pizza can cause uncontrollable anger in drivers on roads.The review explains that smell is unique in its effects on the brain. According to Conrad King, the researcher who carried out the review, “more than any other senses, the sense of smell goes through the logical part of the brain and acts on the systems concerned with feelings. This is why the smell of baking bread can destroy the best intentions of a dieter. ”Smell, which dictates the unbelievable complexity of food tastes, has always been the least understood of our senses. Our noses are able to detect up to 10,000 distinct smells. Our ability to smell and taste this extremely large range of smells is controlled by something like 1,000 genes（基因）,which make up an amazing 3% of the human genome. Researchers Richard Axel and Linda Buck were together awarded a Nobel Prize in 2004 for their ground-breaking research on the nature of this extraordinary sense. These two scientists were the first to describe the family of 1,000 olfactory（嗅觉）genes and to explain how our olfactory system works.According to one study in the research review, smelling fresh pizza or even the packaging of fast foods can be enough to make drivers feel impatient with other road users. They are then more likely to speed and experience uncontrollable anger on roads. The most reasonable explanation is that these can all make drivers feel hungry, and therefore desperate to satisfy their appetites.In contrast, the smells of peppermint and cinnamon were shown to improve concentration levels as well as reduce drivers’ impatience. Similarly, the smells of lemon and coffee appeared to promote clear thinking and mental focus.However, the way genes regulate smell differs from person to person. A study by researchers in Israel has identified at least 50 olfactory genes which are switched on in some people and not in others. They believe this may explain why some of us love some smells and tastes while others hate them. The Israel researchers say their study shows that nearly every human being shows a different pattern of active and inactive smell-detecting receptors.63. What did Richard Axel and Linda Buck find out?A. The category of food smells.B. The logical part of human brain.C. The nature of human olfactory system.D. The relationship between food and feelings.64. Which of the following can help people concentrate?A. Bread.B. Fruits.C. Coffee.D. Fast food.65. What do we know from the last paragraph?A. Some people can recognize up to 50 smells.B. Every person has a different pattern of genes.C. Different people are sensitive to different smells.D. There are still some olfactory genes to be found out.66. What is the passage mainly about?A. Logic and behaviour.B. Smell and its influence.C. Sense ability and food tastes.D. Olfactory genes and its system.DCamaraderie over CompetenceThe importance of liking people is the subject of an article in the Harvard Business Review，which has carried out an experiment to find out who we’d rather work with. Hardly surprisingly, the people we want most as our workmates are both: brilliant at their jobs and delightful human beings. And the people we want least are both unpleasant and useless. More interestingly, the authors found that, given the choice between working with lovable fools and competent jerks（性情古怪的人），we irresistibly choose the former. Anyway, who likes those stupid men who annoy or hurt other people? We might insist that competence matters more，but our behavior shows we stay close to the people we like and sharing information with them.What companies should therefore do is to get people to like each other more. The trick here is apparently to make sure staffs come across each other as often as possible during the day. They also should be sent on bonding courses and so on to encourage friendliness and break down displeasure. However，more outdoor-activity weekends and shared coffee machines inspire no confidence at all.The reality is that people either like each other or they do n’t. You can’t force it. Possibly you can make offices friendlier by tolerating a lot of chat, but there is a productivity cost to that. In my experience, the question of lovable fool against competent jerk may not be the right one. The two are interrelated: we tend not to like our workmates when they are completely hopeless. I was once quite friendly with a woman whom I later worked with. I found her to be so outstandingly bad at her job that I lost respect for her and ended up not really liking her at all. Then is there anything that companies should be doing about it?By far the most effective strategy would be to hire people who are all pretty much the same，given that similarity is one of the main determinants of whether we like each other. I think this is a pretty good idea，but no one dares recommend this anymore without offending the diversity lobby group. There is only one acceptable view on this subject: teams of similar people are bad because they stop creativity. This may be true, though I have never seen any conclusive proof of it.Not only do we like similar people, we like people who like us. So if companies want to promote more liking, they should encourage a culture where we are all nice to each other. The trouble is that this needs to be done with some skill.67. According to the research, which kind of colleagues would most people tend to choose?A. Nice but unintelligent.B. Creative but unattractive.C. Competent but unfriendly.D. Humorous but unambitious.68. The author talks about her experience to show that _____.A. people respect outstanding leadersB. people tend to like optimistic workmatesC. a workmate’s working ability is importantD. talkative workmates make offices friendlier69. Some people think that similar people working together may _____.A. offend each otherB. c reate fewer new ideasC. talk more and work lessD. be likely to stick together70. To encourage workmates to like each other, companies could _____.A. arrange the training course for workers to study togetherB. organize team-building activities outside the officeC. encourage a diversity of opinions in workplaceD. employ staff who have a lot in common第二节（共5小题;每小题2分，共10分）HomeworkDo arithmetic problems 15 through 25. State the different forms of the verbs on page 50 of your French workbook. Read pages 12 through 20 of the Shakespeare play, and don’t forget to fill in the missing chemical symbols on the worksheet.Sound like a list of your homework for the next few nights—or maybe even just for tonight? 71 It’s your teachers’ way of evaluating how much you understand what’s going on in class. And it helps strengthen important concepts.72 It's inviting to start with the easy things to get them out of the way. However, you’ll have the most energy and focus when you begin, so it’s best to use this mental power on the subjects that are most challenging. Later, when you’re more tired, you can focus on the simpler things. If you get stuck on a problem, try to figure it out as well as you can—but don’t spend too much time on it because this can mess up your homework schedule for the rest of the night. 73 But don’t pick someone whom you’ll be up all night chatting with, or you’ll never get it done!Most people’s attention spans aren’t very long, so take some breaks while doing your homework. Sitting for too long without relaxing will make you less productive than if you stop every so often. Taking a 15-minute break every hour is a good idea for most people. 74_Once your homework is done, you can check over it if you have extra time. Be sure to put it safely away in your backpack—there’s nothing worse than having a completed assignment that you can’t find the next morning or that gets ruined by a careless brother or sister. 75 Now you’re free to hang out.A. Homework is a major part of going to school.B. Luckily, you can do a few things to do less homework.C. When you start your homework, deal with the hardest tasks first.D. But if you’re really concentrating, wait until it’s a good time to stop.E. If you need to, ask an adult for help or call or email a classmate for advice.F. And no teacher still believes that “chewed by the dog” line—even when it’s true!G. In conclusion, no one is expected to stay long, and people have very different learning styles.第四部分：书面表达（共两节，35分）第一节（15分）假设你是红星中学高三学生李华，将于七月赴美国参加游学夏令营。

2016年北京市东城区高考英语二模试卷

2016年北京市东城区高考英语二模试卷学校:___________姓名：___________班级：___________考号：___________I、单选题(本大题共15小题，共45.0分)1.The ceiling's low，_____you need to be careful not to hit your head．（）A.soB.butC.forD.or【答案】A【解析】答案A．B项"但是"；C项"为了，因为"；D项"或者，否则"；A项"因此"；根据前后两个分句的逻辑关系可知，因为天花板太低，所以（有可能撞到头）你需要小心．故选A．天花板太低，所以你需要小心而不要碰到你的头．本题考查连词的辨析．解答此类题目首先要读懂句意，理解每个选项中连词的意思，然后根据上下文语境锁定合适的连词．平时要加强连词的积累．2.Nigel sent the girl a nice little note_____her for a drink．（）A.invitedB.invitingC.to be invitingD.invite【答案】B【解析】答案：B分析句意可知，"_____her for a drink"在句中作后置定语，修饰a nice little note，其中动词invite与逻辑主语Nigel构成主谓关系，故应选动词的现在分词形式；C．to be inviting是动词不定式的进行时，表示正在进行的或与谓语动词同时发生的动作，用在此处不合句意；故选BNigel给那个女孩送了一张邀请她喝一杯的温馨的小便条．本题考查了动词的现在分词作定语的用法．做本题时，首先根据句意确定空缺处在句中所作的成分，找到动词与逻辑主语之间的关系；其次要正确区分现在分词，过去分词以及动词不定式的用法及区别．3.George decided it was such a rare car that he_____it only for a few exhibitions．（）edB.was usingC.had usedD.would use【答案】D【解析】答案：D根据主句中的decided使用了一般过去时以及句意（由于他认为这辆车非常罕见，所以将只用它做几次展览．）可知，从句应使用过去将来时，故选DGeorge认为这是一辆非常罕见的车，他将只用它做几次展览．本题考查了情态动词would的用法：在陈述语气中，通常用于第二、三人称，表示过去将来时，意为"将，会"．做本题时，需要根据句意，主句中时态的提示以及情态动词would的用法，选出正确答案．4.She read a poem by Carver_____describes his life in the countryside．（）A.whoB.whichC.whatD.whose【答案】B【解析】答案：B分析句意可知，"_____describes his life in the countryside"在句中做定语，修饰前面的名词a poem by Carver，因此本句是定语从句；由于a poem（一首诗）在从句中作主语，因此此处应选指物并且可以作主语的关系代词which；关系代词who可以作主语，但指人；whose的意思是"…的…"其后要加名词；what不是关系代词，不能用于定语从句；故选B她读了一首由雷蒙德．卡佛（Carver）写的诗，这首诗描述了他在乡下的生活．本题考查了定语从句中关系代词的用法．做本题时，首先根据句意判断本句为定语从句，其次根据先行词的意义及在从句中所作的成分，来选择相应的关系代词；另外还应熟练掌握各关系代词的用法及区别；最后要记住疑问代词what可以引导主语从句，表语从句，宾语从句等；但由于它不是关系代词，不能用于定语从句中．5.A team of scientists_____the effects of acid rain over the last twenty-year period．（）A.studiedB.had studiedC.is studyingD.has been studying【答案】D【解析】答案：D．根据时间状语over the last twenty-year period可知用现在完成进行时，表示从过去开始的动作持续到现在且一直还将进行下去，表达了他们的执着精神；故选D．一组科学家在过去20年里一直在研究酸雨的影响．分清楚不同时态的具体用法，尤其是现在完成进行时表达强烈的语气这一用法．6.That knife's extremely sharp!_____you don't cut yourself．（）A.MindB.MindingC.To mindD.Minded【答案】A【解析】答案：A空前为一个感叹句，故_____you don't cut yourself应为一个完整句子，故选A．句意为：这把刀子极其锋利！小心别伤着自己．考查此类试题，要分析句子结构，祈使句以动词原形开头，表建议，请求，命令等．7.Finally I found my handbag，which_____under a pile of old newspapers．（）A.has buriedB.had buriedC.has been buriedD.had been buried【答案】D【解析】答案：D．my handbag与bury之间应该是逻辑上的动宾关系，用被动语态，排除A和B；且被掩埋这个动作发生在我找到之前，即过去的过去，用过去完成时，排除C；故选D．最后我找到了我的包，它被埋在一堆旧报纸里．对于时态的题型要分析句子的具体语境，并且结合句子的内容综合分析方能得出答案．8.My mum's letters really encouraged me_____my illness．（）A.overB.forC.throughoutD.within【答案】C【解析】答案：Cover超过，在上方；for为了，因为；throughout自始至终，在…期间；within在…范围内．题干表示的是在我生病期间，故选C．在我生病期间，母亲的信给我带来了真正的鼓励．介词是比较灵活的一类词，平时学习时，要注意区分和掌握．9.The Centre became a place_____many came to talk about their hopes and fears．（）A.whichB.thatC.whereD.when【答案】C【解析】答案：C分析句子结构可知，"_____many came to talk about their hopes and fears．"在句中作定语，用来修饰前面的名词a place，因此本句是定语从句；由于从句中缺少地点状语，所以应选表示地点的关系副词where；A．B．是关系代词；D．是表示时间的关系副词；故选：C该中心成为许多人前来谈论他们的希望与恐惧的地方．本题考查了关系副词的用法．做本题时，首先应根据句意确定本句为定语从句；其次根据先行词在从句中所作的成分，选择相应的关系词；最后应牢固掌握关系词的意义及用法．例如：关系副词where在从句中作地点状语，when作时间状语；关系代词that（可以指人也可以指物），which（只能指物）在从句中作主语或宾语等．10.I always check the prices of different brands_____I make a major purchase．（）A.beforeB.becauseC.althoughD.where【答案】A【解析】答案A．before"在…之前；才…"，引导时间状语从句．because"因为"，引导原因状语从句．although"尽管，虽然"，引导让步状语从句．where"在…地方"，引导地点状语从句．分析可知前后两句话之间是逻辑上的"时间"关系，再结合句子所表达的意思可知答案选A．在我购买之前，我总是会检查不同品牌的价格．本题考查从属连词的用法．连词的用法辨析，要注意分析主从句之间的逻辑关系，再确定相应的连词，同时注意不同的连词的语义及用法区别．11.Fresh milk_____in the fridge，or it will go bad．（）A.may keepB.may be keptC.must keepD.must be kept【答案】D【解析】答案D．fresh milk与keep"保存"是被动关系，应该使用被动语态，可排除A和C；may意思是"可以"而must意思是"必须"，may比must的语气要弱很多，根据句意可知应该选用语气强的must，答案选D．鲜奶必须保存在冰箱里，否则会变质．本题考查情态动词的用法．情态动词表示说话人对某一动作或状态的态度，所以在做题时应该把握好说话人的情感态度．12.Since there is only one laboratory in the school，it is important to check_____the students can use it．（）A.whichB.whatC.whenD.where【答案】C【解析】答案C．check后面接的是宾语从句the students can use it．从句the students can use it不缺少主语与宾语，可排除答案A和B．因为which 引导宾语从句时，在从句中作主语、宾语、表语或定语，意为"哪一个"，表示在有限的范围内的某一个．what引导宾语从句时，在从句中作主语、宾语、表语．然后根据语境应是学生何时使用它，不是在哪里使用，故选C．因为学校里只有一个实验室，核实学生何时能使用它是很重要的．考查的是宾语从句，做此类题要理解句子的大意，以及连接词的用法．13._____myself enough time to catch the train，I set my alarm for five in the morning．（）A.GiveB.Being givenC.To giveD.Given【答案】C【解析】答案：C不等式作目的状语．题干所给句子中间有逗号分隔，没有连词，要用非谓语动词；give与句子的主语I之间构成主动关系．故选C．为了给自己足够的时间赶火车，我把闹钟调到了早上五点．不等式是非谓语动词的一种，用法灵活．按句子成分来划分有：主语（通常借助形式主语it）；宾语/表语；定语；状语；补语等．14.If Julia had practised hard enough last night，she_____more confident on the stage now．（）A.isB.would beC.had beenD.would have been【答案】B【解析】答案B．由语境可知：从句表示与过去事实相反的假设，主句则表示与现在事实相反．那么主句的结构为：would+do，故选B．如果朱丽亚昨晚练习够认真的话，那么她现在在舞台上更自信．在表示虚拟语气的句子中，条件从句表示的动作与主句表示的动作发生的时间并不一致，这时，谓语动词的形式要根据各自表示的时间来调整，这种现象叫作错综时间虚拟语气，也称作混合虚拟语气．例：If you had taken your medicine yesterday，you would be quite all right now．如果你昨天吃了药的话，现在就已经痊愈了．（从句表示与过去事实相反的假设，主句则表示与现在事实相反．）15._____with two over-packed suitcases，I arrived at the airport just in time for my flight．（）A.ArmingB.ArmedC.To armD.Arm【答案】B【解析】答案B前后两句用逗号隔开，前面做伴随状语表主语的状态，应用非谓语形式，行李箱是被手臂拉的，是被动的关系，应用armed，故选B．提着两个超负荷的行李箱，我到机场时刚刚好赶上我的航班．考查过去分词做状语，主要是根据语境与句意来选择合适的答案．II、完形填空(本大题共20小题，共3.0分)My HeroWhat does it mean to be a hero？I think a hero is someone who goes out of his way to make others happy．My hero is Mr．Wright，my chorus（合唱队）teacher．When I was 12years old，my grandparents passed away．I was really close to them，and losing them was the hardest thing I've ever had to (16) through．I couldn't eat，sleep，or think；I felt like I couldn't even breathe．It was as if my whole world had fallen down from under me，and I (17) into this huge hole of depression（抑郁）．(18) I was battling depression，I was determined to make my high school years the best of my life．It was difficult to be (19) ，but I had to try．I joined Women's Choir．Mr．Wright was the choral director and he was so funny that the first day，I just knew I had made the best (20) of my life．As the year progressed，I loved chorus more and more．I began to smile again and really enjoy (21) ．Then one day that all changed．My friends-or those that I thought were my friends-started talking about me behind my back．I was (22) ，and I sat by myself．Mr．Wright came over and asked what was wrong．The look in his eyes told me that I could (23) him．Trying hard to (24) back tears，I told him the whole story．When I finished，he nodded and told me，"If you never learn anything from me，learn this：No one is worth (25) your joy．"What Mr．Wright said really (26) a chord （心弦）in my heart．He (27) cared about me and what was going on．I'll never be able to thank him enough，because he not only saved me but has (28) every day of it since．Any time I feel like giving (29) ，I remember Mr．Wright's words and push forward．I'm proud to say that I (30) my depression，and I'm now a senior．I'm still a （51）of chorus，and now I'm also in the best choir at my school．Mr．Wright is a hero (31) everyone he meets．He cares about every single person who walks through his door，and he loves what he does more than any other teacher I've known．That's (32) he deserves to be Educator of the Year．He deserves the (33) not just this year but every year．I'm glad I had the opportunity to meet you，Mr．Wright．You are an (34) teacher，and I hope you realize that．You're my hero．16.A.put B.walk C.run D.go17.A.looked B.broke C.fell D.turned18.A.If B.Although C.Because D.Once19.A.happy B.calm C.smart D.confident20.A.suggestion B.decision C.effort D.offer21.A.care B.nature C.health D.life22.A.refused B.forgotten C.hurt D.trapped23.A.trust B.impress C.respect D.satisfy24.A.set B.fight C.take D.call25.A.stealing B.sharing C.hiding D.feeling26.A.braked B.struck C.played D.shook27.A.cheerfully B.normally C.exactly D.truly28.A.made B.started C.understood D.influenced29.A.off B.out C.up D.away30.A.beat B.suffered C.developed D.saved31.A.leader B.part C.fan D.dancer32.A.about B.with C.to D.at33.A.when B.what C.where D.why34.A.title B.job C.help 35.A.amusing B.ambitious C.amazing D.advanced．【答案】【小题1】D【小题2】C【小题3】B【小题4】A【小题5】B【小题6】D【小题7】C【小题8】A【小题9】B【小题10】A【小题11】B【小题12】D【小题13】D【小题14】C【小题15】A【小题16】C【小题17】D【小题18】A【小题19】C【小题20】略【解析】36．D考查动词短语，作者的祖父母去世了，那是作者经历的最艰难的时候，go through经历．根据语境可知，答案选D．37．C考查动词辨析，就好像整个世界都倒塌了，我坠入了巨大的沮丧的黑洞．根据语境可知，fall into坠入，落进．答案选C．38．B考查连词，尽管我在与抑郁作斗争，我还是要使我的学校生活变得美好．although尽管．根据语境可知，答案选B．39．A考查形容词，我很难高兴起来，但是我不得不尝试．根据语境可知，答案选A．40．B考查名词，我知道我做出了人生中最好的决定（decision），这个决定就是上句提到的I joined Women's Choir．根据语境可知，答案选B．41．D考查名词，我重新开始微笑，并真正享受生活．根据语境可知，答案选D．42．C考查动词，hurt伤害．Refuse拒绝；forget忘记；trap围困．我的朋友们开始背后议论我，这是我受到伤害．根据语境可知，答案选C．43．A考查动词，trust信任；impress留下印象；respect尊重；satisfy使满足，她的眼神告诉我我可以信任她．根据语境可知，答案选A．44．B考查动词搭配，极力抑制眼泪的同时，我把整个故事告诉了她．此处fight back 相当于hold back，意为"抑制"．根据语境可知，答案选B．45．A考查动词，世上没有人值得你为他流泪，根据语境可知，答案选A．46．B考查动词，Mr．Wright的所言扣动了我的心弦．brake．刹闸；strike打击，打动；shake摇晃．根据语境可知，答案选B．47．D考查副词，cheerfully鼓舞地；normally正常地；exactly确切地；truly真实地．他确实很关心我和正在发生的事情．根据语境可知，答案选D．48．D考查动词，他不仅拯救了我，也影响了从那以来我生活中的每一天．根据语境可知，答案选D．49．C考查介词，每当我想放弃的时候，我就会想起Mr．Wright的话，并继续前进．give up放弃．根据语境可知，答案选C．50．A考查动词，beat击败；suffer遭受；develop发展；save拯救，我很自豪地说我打败了抑郁．根据语境可知，答案选A．51．B根据上下文，我还是合唱团的一分子，并且我进入学校最棒合唱团．答案选B．52．C考查介词，Mr．Wright是他所遇到的每一个人的英雄．a…hero to…成为…的英雄．根据语境可知，答案选C．53．D考查名词性从句，这就是他应得今年年度教育工作者的原因．that's why…这就是为什么…．根据语境可知，答案选D．54．A考查名词title头衔，称号他不仅今年赢得这个头衔，每年他都应得到，答案选A．55．C考查形容词amusing 娱乐的；ambitious有抱负的；amazing令人惊异的advanced高级的．根据语境可知，答案选C．本文介绍了作者心目中的英雄-合唱队老师Mr．Wright．他不仅拯救了我，也影响了从那以来我生活中的每一天．完型填空，解题时首先需通读全文，理顺题意，找出信息词，建立语言的整体感．这是做好完型填空题的关键．其次细读首尾，推测意图，文章的首句是全文的"窗口"，尾句是文章的总结、结论或点睛之笔．这样，通过阅读首句和尾句，就可以了解背景知识，对于空格位置的词语进行大胆分析和判断，以便揣测作者的意图，理顺思路，为后面的答题做好铺垫．最后在通读全文的基础上，根据全文大意，展开逻辑思维，瞻前顾后，分析这一空格处在句中的地位，前后的关系和它所起的作用，认真观察选项，仔细推敲，确定最佳答案．III、阅读理解(本大题共15小题，共12.0分)AOur room was on the second floor but you could still hear the roar of the ocean and see the stars at night．I used to take long walks along the water．The food in town was wonderful and the people were very friendly．The area was very quiet and peaceful，and fairly deserted．The last evening of our vacation，however，we all heard strange footsteps following closely behind us as we were walking up to our room in the holiday centre．We turned around and noticed a fairly young man moving very rapidly across the beach and getting closer to us．He was tall and wore a baseball cap．We couldn't see his face and he was approaching us very rapidly．The man's actions made my dad very nervous．Dad warned us that we'd better try to make it to our hotel room as quickly as possible．I didn't like my dad's voice；I could hear fear in it．It was late and we were all alone．We didn't have any cell phones on us．I never saw Dad as worried as he was then and I knew that something was terribly wrong．The sense of fear started to overwhelm Mom and me．We had had such a good time in town．Now，the night was rapidly turning into a dangerous situation．We could hear the man's footsteps getting closer．Dad's face was almost pale．The so-called intruder （侵入者）had moved nearer and nearer when all of a sudden，the nearby vending（自动贩卖）machine started going crazy and spitting out cans of soda!The noise actually scared the intruder and he ran out of sight．My parents were shaking，but we all turned around to see who had put money into the vending machine downstairs，and actually saved us，but no one was around at all．Not a soul．It's one vacation I will never forget．36.Where did the author spend her vacation？______A.Near a lake．B.At the seaside．C.In a village．D.In a mountain．37.What happened on the last evening of their vacation？______A.They were followed by a stranger．B.Their cell phones were missing．C.Their money was stolen．D.They lost their way．38.The underlined word"overwhelm"in Paragraph 2 means ______ ．A.controlB.moveC.exciteD.impress39.What helped them get out of the trouble？______A.Their quick action．B.Other people's kind help．C.The young man's warning．D.The no ise from the vending machine．【答案】【小题1】B【小题2】A【小题3】A【小题4】D【解析】56．答案B 细节理解题；根据第一段中Our room was on the second floor but you could still hear the roarof the ocean and see the stars at night．可知作者在海边度过假期．故选项B正确．57．答案A 细节理解题；根据第二段The last evening of our vacation，however，we all heard strange footsteps following closely behind us一句，可知作者一家被陌生人跟踪，答案选A．58．答案A 细节理解题；根据第二段中Dad as worried as he was then and I knew that something was terriblywrong．The sense offear started to overwhelm Mom and me．可知母亲和作者被恐惧感所控制．故答案A正确．59．答案D 判断推理题；根据最后一段the nearby vending（自动贩卖）machine started going cra zy and spitting out cans of soda!Thenoise actually scared the intruder and heran out of sight．可知，故答案D正确．本文介绍了作者一次难忘的假期之旅．作者一家在海边度假时被陌生人跟踪，作者和母亲被恐惧感所控制，最终机智脱险．细节理解的解题技巧：1．扫题干2．抓关键词3．定位置4．研选项（干扰项的特点）1）以偏概全与原句的内容相似，但在程度有变动2）无中生有明显不是文章的信息3）夸大/缩小是原文信息，但故意增加或减少细节4）偷梁换柱偷换文中细小信息5）半真半假信息部分正确，部分错误6）答非所问是原文信息，但不是题干要求的内容BFor over 30years，Rainbow Montessori in Addison has given children a place to grow and explore the world around them，and they're still going strong today．With 20years in the same location，the school is"not going anywhere，"says Dave Rodenborn，a son of the school's founders．As general director，Dave has overseen many improvements，including a new playground for the preschool and a complete modernization．The school serves families of children from 6weeks to 6th grade．This allows them to have programs in baby care，preschool，kindergarten，and elementary（小学）．The curriculum has developed over the decades，most notably in the Elementary．At first somewhat jokingly referred to as"Monte-sorta，"due to its relaxed application of the Montessori Method，the school's elementary now stresses a more traditional Montess environment．Montessori associates abstract concepts with concrete sensorial（感觉的）experiences，ensuring that children are involved in learning，not just memorization．Classrooms still have a creative，casual feel，with children having freedom of choice，but in keeping with Montessori principles，they work within a framework．This helps them learn about freedom within limits，maximizing their potential．The truly international Rainbow Montessori staff comes from a wide range of backgrounds，all Montessori-trained．"They are an energetic，devoted group，"says Dave．"They are loyal，caring and like what they do a lot．I'd say a good 30to 40percent of them have been here for almost a decade or more．"Dave says that his favorite part of being at Rainbow Montessori is"making things grow"．By that，he doesn't mean it in the sense of the organic，but by"coming up with good solutions to problems as they occur．"This is reflective of Montessori beliefs，in which each child learns to use the right tools and discover solutions for themselves．Dave credits a strong staff and great parents with lots of patience for helping to make Rainbow Montessori an ideal place for children to learn and grow．Rainbow Montessori790East Duane Ave，Addison（408）738-3261www．rainbow-montessori．com40.What do we know about Rainbow Montessori school？______A.It was founded by Dave Rodenborn．B.It has stood at the same place for 20years．C.Its students range from kindergarten to primary．D.Half of its staff have worked there for ten years．41.According to Paragraph 2，what is the characteristic of Rainbow Montessori？______A.Students are expected to memorize concepts．B.Classroom regulations are highly stressed．C.Students are free to choose subjects．D.Active learning is encouraged．42.By saying"making things grow"in the last paragraph，Dave means the school ______ ．A.tries its best to prevent problems from occurringB.provides suitable learning tools for each single childC.creates a natural environment for the growth of studentsD.encourages students to find proper ways to solve problems．【答案】【小题1】B【小题2】D【小题3】D【解析】60．B细节理解题．根据第一段With 20years in the same location，the school is"not going anywhere，"says Dave Rodenborn，a son of the school's founders．可知这所学校在20年里一直在同一个地方．故选B．61．D推理判断题．根据第二段Classrooms still have a creative，casual feel，with children having freedom of choice，可知Rainbow Montessori鼓励学生主动学习．故选D．62．D推理判断题．根据最后一段but by"coming up with good solutions to problems as they occur．可知该校鼓励学生寻找解决问题的适当方法．故选D．本文是一篇科教类阅读．文章主要介绍了Rainbow Montessori学校．这所学校鼓励学生主动学习，寻找解决问题的适当方法．本文考察学生的理解推断能力以及细心程度，只要抓住文章的关键词，采用寻读的方法查找细节，就能找到正确答案．CResearchers continue to show the power behind our sense of smell．Recent studies have found，among other things，that the smell of foods like pizza can cause uncontrollable anger in drivers on roads．The review explains that smell is unique in its effects on the brain．According to Conrad King，the researcher who carried out the review，"more than any other senses，the sense of smell goes through the logical part of the brain and acts on the systems concerned with feelings．This is why the smell of baking bread can destroy the best intentions of a dieter．" Smell，which dictates the unbelievable complexity of food tastes，has always been the least understood of our senses．Our noses are able to detect up to 10，000distinct smells．Our ability to smell and taste this extremely large range of smells is controlled by something like 1，000genes （基因），which make up an amazing 3% of the human genome．Researchers Richard Axel and Linda Buck were together awarded a Nobel Prize in 2004for their ground-breaking research on the nature of this extraordinary sense．These two scientists were the first to describe the family of 1，000olfactory （嗅觉）genes and to explain how our olfactory system works．According to one study in the research review，smelling fresh pizza or even the packaging of fast foods can be enough to make drivers feel impatient with other road users．They are thenmore likely to speed and experience uncontrollable anger on roads．The most reasonable explanation is that these can all make drivers feel hungry，and therefore desperate to satisfy their appetites．In contrast，the smells of peppermint and cinnamon were shown to improve concentration levels as well as reduce drivers'impatience．Similarly，the smells of lemon and coffee appeared to promote clear thinking and mental focus．However，the way genes regulate smell differs from person to person．A study by researchers in Israel has identified at least 50olfactory genes which are switched on in some people and not in others．They believe this may explain why some of us love some smells and tastes while others hate them．The Israel researchers say their study shows that nearly every human being shows a different pattern of active and inactive smell-detecting receptors．43.What did Richard Axel and Linda Buck find out？______A.The category of food smells．B.The logical part of human brain．C.The nature of human olfactory system．D.The relationship between food and feelings．44.Which of the following can help people concentrate？______A.Bread．B.Fruits．C.Coffee．D.Fast food．45.What do we know from the last paragraph？______A.Some people can recognize up to 50smells．B.Every person has a different pattern of genes．C.Different people are sensitive to different smells．D.There are still some olfactory genes to be found out．46.What is the passage mainly about？______A.Logic and behaviour．B.Smell and its influence．C.Sense ability and food tastes．D.Olfactory genes and its system．【答案】【小题1】C【小题2】C【小题3】C【小题4】B【解析】63．C细节理解题．根据第三段These two scientists were the first to describe the family of 1，000olfactory （嗅觉）genes and to explain how our olfactory system works．可知Richard Axel和Linda Buck这两位科学家首先描述了家族嗅觉基因并解释了我们的嗅觉系统的工作原理．由此推知，这俩位科学家揭示了人类嗅觉系统的本质．故选C．64．C细节理解题．根据第五段Similarly，the smells of lemon and coffee appeared to promote clear thinking and mental focus．可知喝咖啡有助于提高思考和注意力．故选C．65．C推理判断题．根据最后一段their study shows that nearly every human being shows a different pattern of active and inactive smell-detecting receptors．可知不同的人对不同的气味敏感．故选C．66．B主旨大意题．本文主要介绍了人类嗅觉的巨大能量及其对我们的影响．故选B．本文是一篇科教类阅读．文章主要介绍了人类嗅觉的巨大能量及其对我们的影响．不同的人对不同的气味敏感，喝咖啡有助于提高思考和注意力．本文考察学生的理解推断能力以及细心程度，只要抓住文章的关键词，采用寻读的方法查找细节，就能找到正确答案．DCamaraderie over CompetenceThe importance of liking people is the subject of an article in the Harvard Business Review，which has carried out an experiment to find out who we'd rather work with．Hardly surprisingly，the people we want most as our workmates are both：brilliant at their jobs and delightful human beings．And the people we want least are both unpleasant and useless．More interestingly，the authors found that，given the choice between working with lovable fools and competent jerks （性情古怪的人），we irresistibly choose the former．Anyway，who likes those stupid men who annoy or hurt other people？We might insist that competence matters more，but our behavior shows we stay close to the people we like and sharing information with them．What companies should therefore do is get people to like each other more．The trick here is apparently to make sure staffs come across each other as often as possible during the day．They also should be sent on bonding courses and so on to encourage friendliness and break down displeasure．However，more outdoor-activity weekends and shared coffee machines inspire no confidence at all．The reality is that people either like each other or they don't．You can't force it．Possibly you can make offices friendlier by tolerating a lot of chat，but there is a productivity cost to that．In my experience，the question of lovable fool against competent jerk may not be the right one．The two are interrelated：we tend not to like our workmates when they are completely hopeless．I was once quite friendly with a woman whom I later worked with．I found her to be so outstandingly bad at her job that I lost respect for her and ended up not really liking her at all．Then is there anything that companies should be doing about it？By far the most effective strategy would be to hire people who are all pretty much the same，given that similarity is one of the main determinants of whether we like each other．I think this is a pretty good idea，but no one dares recommend this anymore without offending the diversity lobby group．There is only one acceptable view on this subject：teams of similar people are bad because they stop creativity．This may be true，though I have never seen any conclusive proof of it．Not only do we like similar people，we like people who like us．So if companies want to promote more liking，they should encourage a culture where we are all nice to each other．The trouble is that this needs to be done with some skill．47.According to the research，which kind of colleagues would most people tend to choose？______A.Nice but unintelligent．B.Creative but unattractive．petent but unfriendly．D.Humorous but unambitious．48.The author talks about her experience to show that ______ ．A.people respect outstanding leadersB.people tend to like optimistic workmatesC.a workmate's working ability is importantD.talkative workmates makes offices friendlier49.Some people think that similar people working together may ______A.offend each otherB.create fewer new ideasC.talk more and work lessD.be likely to stick together50.To encourage workmates to like each other，companies could ______ ．A.arrange the training course for workers to study togetheranize team-building activities outside the officeC.encourage a diversity of opinions in workplaceD.employ staff who have a lot in common．【答案】【小题1】A【小题2】C【小题3】B【小题4】D【解析】67．答案A 细节理解题；根据第一段中the people we want most as our workmates are both：brilliant at their jobs anddelightful human beings．可知人们乐于与聪明且乐观的人一起共事，故选项A正确．68．答案C 细节理解题；根据第三段we tend not to like our workmates when they are completely hopeless．一句，可知同事的能力很重要．故答案选C．69．答案B 细节理解题；根据第四段中teams of similar people are bad because they stop creativity．可知相似的人在一起工作会阻碍创新能力．答案B正确．70．答案D 推理判断题；根据最后一段Not only do we like similar people，we like people who like us．So if companies want to promote more liking，they should encourage a culturewhere we are all nice to each other．可知，故答案D正确．本文通过调查发现人们乐于与聪明乐观，工作能力强的人一起工作，因为同事的能力很重要，相似的人在一起工作会阻碍创新能力，并据此为企业提供了一些建议．细节理解的解题技巧：1．扫题干2．抓关键词3．定位置4．研选项（干扰项的特点）1）以偏概全与原句的内容相似，但在程度有变动2）无中生有明显不是文章的信息3）夸大/缩小是原文信息，但故意增加或减少细节4）偷梁换柱偷换文中细小信息5）半真半假信息部分正确，部分错误6）答非所问是原文信息，但不是题干要求的内容IV、信息匹配(本大题共5小题，共3.0分)HomeworkDo arithmetic problems 15 through 25．State the different forms of the verbs on page 50of your French workbook．Read pages 12through 20of the Shakespeare play，and don't forget to fill in the missing chemical symbols on the worksheet．Sound like a list of your homework for the next few nights-or maybe even just for tonight？（71）It's your teachers'way of evaluating how much you understand what's going on in class．And it helps strengthen important concepts．（72）______ It's inviting to start with the easy things to get them out of the way．However，you'll have the most energy and focus when you begin，so it's best to use this mental power on the subjects that are most challenging．Later，when you're more tired，you can focus on the simpler things．If you get stuck on a problem，try to figure it out as well as you can-but don't spend too much time on it because this can mess up your homework schedule for the rest of the night．（73）______ But don't pick someone whom you'll be up all night chatting with，or you'll never get it done!Most people's attention spans aren't very long，so take some breaks while doing your homework．Sitting for too long without relaxing will make you less productive than if you stop every so often．Taking a 15-minute break every hour is a good idea for most。

2016年北京东城区高三二模物理(试题及详解)

2016年东城二模高中物理试卷解析一、选择题13.已知阿伏伽德罗常数为N a ，油酸的摩尔质量为M,密度为ρ。

则一个油酸分子的质量可表示为 A. B..C. .D...答案：A解析：分子的质量等于摩尔质量除以阿伏伽德罗常数，则m=AN M,故A 正确，B 、C 、D 错14.一束单色光在某种介质中的传播速度是其在真空中传播速度的0.5倍，则 A.该介质对于这束单色光的折射率为0.5B.这束单色光由该介质射向真空时的临界角为60°C.这束单色光在该介质中的频率为其在真空中频率的0.5倍D.这束单色光在该介质中的波长为其在真空中波长的0.5倍答案：D解析：根据光在介质中的传播速度公式V=n c 得，折射率n=c5.0c ,n=2,故A 错。

由临界角公式sinC=n1,得C=300,故B 错。

光的频率与介质无关，因此在不同介质中光的频率不变，故C 错。

根据波速公式v=λf 得，光在介质中波长为真空中波长的0.5倍，故D 对。

15.如图所示，两竖直杆顶端M 、N 位于等高处，将一根不可伸长的轻绳两端分别固定在M 、 N 两点，物体通过轻质光滑桂钩挂在轻绳中间，静止时轻绳所成夹角为120°。

若保持绳长不变，只适当增加两竖直杆之间的水平距离，则此时A.轻绳的弹力比物体的重力小B.轻绳的弹力与物体的重力相等C.轻绳的弹力比物体的重力大D.轻绳的弾力大小与物体的重力无关答案：C解析：设两杆间的距离为S ，细绳的总长度为L ，静止时轻绳两端夹角为1200，根据矢量的合成可知，三个力的大小相等，故轻绳的弹力大小为mg 。

若增加两竖直杆之间的水平距离，绳长不变，则重物静止后两根绳子之间的夹角大于1200，两个分力的夹角变大，而合力不变，所以两分力增大，即绳的拉力大于mg.16.关于静止在地球表面（两极除外）随地球自转的物体，下列说法正确的是 A.物体所受重力等于地球对它的万有引力 B.物体的加速度方向可能不指向地球中心 C.物体所受合外力等于地球对它的万有引力 D.物体在地球表面不同处角速度可能不同答案:B解析：物体所受重力只有在两极等于它的万有引力，A 错。

北京市东城区2016高三二模理综word版

东城区2015-2016学年第二学期期末综合练习(二)高三理科综合 2016.5可能用到的相对原子质量：H 1 C 12 N 14 O 161. 下列过程在生物膜上进行的是A.解旋酶的合成B.葡萄糖分解成丙酮酸C.光反应产生氧气D.大肠杆菌质粒的复制2．在一个细胞周期中，下列变化可能发生在同一时期的是A．核膜、核仁的消失和纺锤体的消失B．染色单体的形成和细胞板的形成C．DNA数目加倍和染色体数目加倍D．DNA的复制和中心粒的复制3. 2006年，日本学者山中伸弥成功将人体皮肤细胞诱导形成多能干细胞——“iPS细胞”，iPS细胞可以分裂、分化为神经元、心肌、肝等多种细胞。

下列叙述不正确．．．的是A. iPS细胞分化为多种细胞的过程体现了iPS细胞的全能性B．iPS细胞分化形成的心肌细胞和肝细胞中的RNA存在差异C．人体皮肤细胞诱导产生iPS细胞属于一种脱分化过程D．若在实际中应用该过程中的技术可提高器官移植的成功率4．下图表示健康人和Graves病人激素分泌的调节机制，A、B、C为三种激素。

下列叙述不正确．．．的是A. 图中C随血液运送至全身作用于靶器官或靶细胞B. 图中抗体的作用与促甲状腺激素释放激素的作用相似C. 甲状腺细胞释放的C对下丘脑具有反馈调节作用D. 由图分析可推知Graves病是一种自身免疫病5.水体富营养化是由于水体中氮、磷等营养物质含量过多导致的水质污染现象。

科研人员为找到水体富营养化的治理方法，对某淡水生态系统进行研究。

下面为此淡水生态系统的营养结构。

下列叙述不正确．．．的是A. 水体富营养化可能造成水中的鱼类由于缺氧大量死亡B. 图中所示的所有生物构成了该淡水生态系统的生物群落C. 图中浮游动物、低栖动物和鱼类都可作为第二营养级D. 可通过选择性地控制藻类竞争者和捕食者的数量来治理水体6.下列生活中常见的过程或现象不属于．．．化学变化的是A. NaOH 、Al——电解质B.C2H4、O2——易燃气体C.CaC2、K——遇湿易燃物品D.KMnO4、KClO3——还原剂8.下列说法不正确．．．的是A．麦芽糖和蔗糖的水解产物相同B．用新制的氢氧化铜可区分乙醇、乙醛C．用高锰酸钾酸性溶液可以区分苯、甲苯D．用饱和溴水可区分苯酚溶液、己烷、1-己烯9.下列做法不符合．．．．．．．．．．．绿色化学思想的是A. 开发氢能替代化石燃料B. 工业含氮废水经处理达标后排放C. 农作物秸秆等露天焚烧制肥料D. 金属、塑料、玻璃、纸类等制品应分类回收处理10.对下列各组实验所作的解释正确的是N11．下列事实或实验可以表明H 2SO 3的酸性强于H 2CO 3的是A.硫的非金属性比碳强B. SO 2气体依次通过NaHCO 3溶液、澄清石灰水，澄清石灰水变浑浊C. SO 2和CO 2气体分别通入水中至饱和，测定两溶液的pH ，前者小于后者D.室温下测定均为0.1mol/L 的NaHSO 3和NaHCO 3溶液的pH ，前者小于后者12.已知：2NO(g) +O 2(g)2NO 2(g)，其他条件相同时，分别测得NO 的平衡转化率在不同压强（p 1、p 2）下随温度变化的曲线（如右图）,下列说法不正确．．．的是 A.p 1＜p 2B.该反应的△H ＜0C.A 、B 两点的平衡常数：K (A)＜K (B)D.A 、B 两点的化学反应速率：v (A)＜v (B)13．已知阿伏伽德罗常数为N A ，油酸的摩尔质量为M ，密度为ρ。

2016年北京市东城高三二模数学(文科)试题及答案解析(word版)

北京市东城区 2015-2016学年度第二学期高三综合练习(二) 数学 (文科)一、单选题（共8小题）1．已知集合，，那么（）A．B．C．D．2．如图，根据样本的频率分布直方图，估计样本的中位数是（）A ．B．C．D．3．执行如图所示程序框图，则输出的结果是（）A．B．C．D．4．已知，为圆上关于点对称的两点，则直线的方程为（）A．B．C．D．5．设，为实数，则“”是“”的（）A．充分而不必要条件B．必要而不充分条件C．充分必要条件D．既不充分也不必要条件6．已知函数是偶函数,且，则（）A ．B．C．D．7．已知向量，将向量绕坐标原点逆时针旋转角得到向量，则下列说法不正确的是（）A．B．C．D．8．如图，在边长为的正方形组成的网格中，有椭圆，，，它们的离心率分别为，，，则（）A．B．C．D．二、填空题（共6小题）9.如图所示，在复平面内，点A对应的复数为，则复数_____________．10.若函数在区间上有且只有一个零点，则实数_______．11.已知双曲线的虚轴长是实轴长的倍，则实数_______.12.已知一个三棱锥的三视图如图所示，其中俯视图是等腰直角三角形，则该三棱锥的四个面中，最大面积为________.13.已知数列满足,，且，，则；数列的前项的和为________．14.一名顾客计划到某商场购物，他有三张商场的优惠劵，商场规定每购买一件商品只能使用一张优惠券．根据购买商品的标价，三张优惠券的优惠方式不同，具体如下：优惠劵A：若商品标价超过元，则付款时减免标价的；优惠劵B：若商品标价超过元，则付款时减免元；优惠劵C：若商品标价超过元，则付款时减免超过元部分的．某顾客想购买一件标价为元的商品，若想减免钱款最多，则应该使用优惠劵（填A,B,C）；若顾客想使用优惠券C，并希望比优惠券A和B减免的钱款都多，则他购买的商品的标价应高于________元．三、解答题（共6小题）15.在△中，角，，所对的边分别是，，，且．（Ⅰ）若，求；（Ⅱ）若，且，求△的面积．16.已知等差数列满足，，其前项和为.（Ⅰ）求的通项公式及；（Ⅱ）令，求数列的前项和.17.在梯形中，，，.平面⊥平面，四边形是矩形，，点在线段上．（Ⅰ）求证：；（Ⅱ）试问当为何值时，AM//平面？证明你的结论．（Ⅲ）求三棱锥的体积.18.某出租车公司响应国家节能减排的号召，已陆续购买了辆纯电动汽车作为运营车辆．目前我国主流纯电动汽车按续航里程数（单位：公里）分为类，即类：，类：，类：．该公司对这辆车的行驶总里程进行统计，结果如下表：（Ⅰ）从这辆汽车中任取一辆，求该车行驶总里程超过万公里的概率；（Ⅱ）公司为了了解这些车的工作状况，决定抽取辆车进行车况分析，按表中描述的六种情况进行分层抽样，设从类车中抽取了辆车．（ⅰ）求的值；（ⅱ）如果从这辆车中随机选取两辆车，求恰有一辆车行驶总里程超过万公里的概率．19.已知椭圆与轴交于两点，为椭圆的左焦点，且△是边长为等边三角形．（Ⅰ）求椭圆的方程；（Ⅱ）设直线与椭圆交于，两点，点关于轴的对称点为（与不重合），则直线与轴是否交于一个定点？若是，请写出定点坐标，并证明你的结论；若不是，请说明理由．20.设函数，．（Ⅰ）若，求在区间上的最大值；（Ⅱ）设，求证：当时，过点有且只有一条直线与曲线相切；（Ⅲ）若对任意的，均有成立，求的取值范围．北京市东城区 2015-2016学年度第二学期高三综合练习(二) 数学 (文科)答案1.考点：集合的运算试题解析：所以。