上海市嘉定、长宁区2015年高三(二模)数学(理科)及答案

2023-2024学年上海市长宁区、嘉定区高三第二次模拟考试历史试卷注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗．一．选择题(12小题，每小题4分，共计48分。

在每小题列出的四个选项中，只有一项是最符合题目要求的。

) 1．抗战时期，根据地所有政权均以自然村为基础，部分恢复了乡里商议的古风，还创作了一批颂扬正直、勤劳、廉洁等传统美德的文艺作品。

这些举措A．旨在增强民族凝聚力B．缓和了根据地的阶级矛盾C．是对民主的成功探索D．扩大了抗日民族统一战线2．1946年1月，《申报》登载了一则律师陈庆丰代表余桂林、钱毓娥声明协议离婚的启事：“我俩结婚已逾五载，以双方意志不恰，难偕白首，两方愿协议离婚。

以后男婚女嫁，各听自由，互不干涉，除已立据各执外，再委登报声明等语。

”据此可知，这时的上海A．传统婚姻观念已经消除B．政府保护个人民主权利C．男女社会地位实现平等D．民众自由法治意识增强3．“为了正确地组织国民经济，为了根除银行投机……决定：国家垄断银行事业；现有的一切私人股份银行和银行办事处同国家银行合并；国家银行接收被取消企业的资产和负债；充分保障小额存户的利益。

”此法令颁布于A．统一之后的德意志帝国B．拿破仑统治时代的法国C．十月革命胜利后的苏俄D．罗斯福新政时期的美国4．演讲是时代的见证。

下表的演讲内容反映出当时的主流思潮是A．理性主义B．浪漫主义C．自由主义D．社会主义5．1861年，英国驻华公使馆参赞巴夏礼照会天国政府，以维护英国在华商务利益为由，要求太平军不得进入上海、九江等地一百里之内，对此，天国声明：“我军肩负重任，为上帝光复全国，不能弃寸土于不顾。

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2014 年上海市各区县初三数学二模压轴题 24 题及 25 题
25． （本题满分 14 分） 在△ ABC 中，已知 BA=BC，点 P 在边 AB 上，联结 CP，以 PA、PC 为邻边作平行四边 形 APCD，AC 与 PD 交于点 E，∠ABC=∠AEP= 0 90 . (1) 如图（1） ，求证:∠EAP=∠EPA； (2) 如图 （2） ， 若点 F 是 BC 中点， 点 M、 N 分别在 PA、 FP 延长线上， 且∠MEN=∠AEP， 判断 EM 和 EN 之间的数量关系，并说明理由. (3) 如图（3） ，若 DC=1，CP=3，在线段 CP 上任取一点 Q，联结 DQ，将△ DCQ 沿直线 DQ 翻折，点 C 落在四边形 APCD 外的点 C’处，设 CQ=x，△ DC’Q 与四边形 APCD 重合部 分的面积为 y，写出 y 与 x 的函数关系式及定义域.
2014 年上海市各区县初三数学二模压轴题 24 题及 25 题
黄浦区 24. （本题满分 12 分，第（1）小题满分 3 分，第（2）小题满分 4 分，第（3）小题 满分 5 分） 在平面直角坐标系 xOy 中，已知顶点为 P（0, 2）的二次函数图像与 x 轴交于 A、B 两点， A 点坐标为（2, 0）. （1）求该二次函数的解析式，并写出点 B 坐标； （2） 点 C 在该二次函数的图像上， 且在第四象限， 当△ABC 的面积为 12 时， 求点 C 坐标； （3）在（2）的条件下，点 D 在 y 轴上，且△APD 与△ABC 相似，求点 D 坐标.
25． （本题满分 14 分，第（1）小题 3 分，第（2）小题 5 分，第（3）小题 6 分） 在 ABC 中，AC=25， AB 35 ， tan A

2020年上海市长宁区中考数学二模试卷一．选择题（共6小题）1．下列实数中，无理数是（）A．0B．C．﹣3D．2．下列单项式中，与xy2是同类项的是（）A．x2y B．x2y2C．2xy2D．3xy3．关于反比例函数y＝，下列说法不正确的是（）A．点（﹣2，﹣1）在它的图象上B．它的图象在第一、三象限C．它的图象关于原点中心对称D．y的值随着x的值的增大而减小4．如图是关于某班同学一周体育锻炼情况的统计图，那么该班学生这一周参加体育锻炼时间的众数、中位数分别是（）A．8、9B．8、8.5C．16、8.5D．16、145．如果两圆的半径长分别为5和3，圆心距为7，那么这两个圆的位置关系是（）A．内切B．外离C．相交D．外切6．▱ABCD中，E，F是对角线BD上不同的两点．下列条件中，不能得出四边形AECF一定为平行四边形的是（）A．BE＝DF B．AE＝CF C．AF∥CE D．∠BAE＝∠DCF 二．填空题（共12小题）7．计算：（x3）2÷（﹣x）2＝．8．方程＝2的根是．9．不等式组的解集是．10．已知正三角形的边心距为1，那么它的边长为．11．如果抛物线y＝（a﹣1）x2﹣1（a为常数）不经过第二象限，那么a的取值范围是．12．如果关于x的多项式x2﹣2x+k在实数范围内能分解因式，那么k的取值范围是．13．从1，2，3，4四个数中任意取出2个数做加法，其和为偶数的概率是．14．我国古代数学著作《九章算术》中有一道阐述“盈不足术”的问题，原文是“今有人共买物，人出八，盈三；人出七，不足四，问人数、物价各几何？”大致意思是：“现有几个人共同购买一个物品，每人出8元，则多3元；每人出7元，则差4元．问人数、物品的价格各是多少？”如果设共有x人，物品的价格为y元，那么根据题意可列出方程组为．15．甲乙两位运动员在一次射击训练中各打五发，成绩的平均环数相同，甲的方差为1.6；乙的成绩（环）为：7，8，10，6，9，那么这两位运动员中的成绩较稳定．16．如图，已知在△ABC中，点D在边AC上，AD＝2DC，＝，＝，那么＝．（用含向量，的式子表示）17．如果一个四边形有且只有三个顶点在圆上，那么称这个四边形是该圆的“联络四边形”，已知圆的半径长为5，这个圆的一个联络四边形是边长为2的菱形，那么这个菱形不在圆上的顶点与圆心的距离是．18．如图，已知在△ABC中，∠C＝90°，BC＝2，点D是边BC的中点，∠ABC＝∠CAD，将ACD沿直线AD翻折，点C落在点E处，连结BE，那么线段BE的长为．三．解答题（共5小题）19．如图，在梯形ABCD中，AD∥BC，AD＝2，BC＝5，∠BAC＝45°，cos∠ACB＝（1）求线段AC的长；（2）联结BD，交对角线AC于点O，求∠ADO的余切值．20．如图，反映了甲、乙两名自行车爱好者同时骑车从A地到B地进行训练时行驶路程y （千米）和行驶时间x（小时）之间关系的部分图象，根据图象提供的信息，解答下列问题：（1）求乙的行驶路程y和行驶时间x（1≤x≤3）之间的函数解析式；（2）如果甲的速度一直保持不变，乙在骑行3小时之后又以第1小时的速度骑行，结果两人同时到达B地，求A、B两地之间的距离．21．如图，已知四边形ABCD是矩形，点E在对角线AC上，点F在边CD上（点F与点C、D不重合），BE⊥EF，且∠ABE+∠CEF＝45°．（1）求证：四边形ABCD是正方形；（2）连结BD，交EF于点Q，求证：DQ⋅BC＝CE⋅DF．22．如图，在平面直角坐标系xOy中，已知抛物线y＝x2+mx+n经过点A（2，﹣2），对称轴是直线x＝1，顶点为点B，抛物线与y轴交于点C．（1）求抛物线的表达式和点B的坐标；（2）将上述抛物线向下平移1个单位，平移后的抛物线与x轴正半轴交于点D，求△BCD 的面积；（3）如果点P在原抛物线上，且在对称轴的右侧，联结BP交线段OA于点Q，＝，求点P的坐标．23．已知AB是⊙O的一条弦，点C在⊙O上，联结CO并延长，交弦AB于点D，且CD ＝CB．（1）如图1，如果BO平分∠ABC，求证：AB＝BC；（2）如图2，如果AO⊥OB，求AD：DB的值；（3）延长线段AO交弦BC于点E，如果△EOB是等腰三角形，且⊙O的半径长等于2，求弦BC的长．参考答案与试题解析一．选择题（共6小题）1．下列实数中，无理数是（）A．0B．C．﹣3D．【分析】无理数就是无限不循环小数．理解无理数的概念，一定要同时理解有理数的概念，有理数是整数与分数的统称．即有限小数和无限循环小数是有理数，而无限不循环小数是无理数．由此即可判定选择项．【解答】解：A．0是整数，属于有理数；B.是无理数；C．﹣3是整数，属于有理数；D.，是整数，属于有理数．故选：B．2．下列单项式中，与xy2是同类项的是（）A．x2y B．x2y2C．2xy2D．3xy【分析】根据同类项的定义，所含字母相同且相同字母的指数也相同的项是同类项，同类项与字母的顺序无关，与系数无关．【解答】解：A．x2y与xy2所含字母的指数不同，所以不是同类项；B．x2y2与xy2所含字母的指数不尽相同，所以不是同类项；C.2xy2与xy2所含字母相同且相同字母的指数也相同的项是同类项；D.3xy与xy2所含字母的指数不尽相同，所以不是同类项．故选：C．3．关于反比例函数y＝，下列说法不正确的是（）A．点（﹣2，﹣1）在它的图象上B．它的图象在第一、三象限C．它的图象关于原点中心对称D．y的值随着x的值的增大而减小【分析】根据反比例函数y＝和反比例函数的性质，可以判断各个选项中的说法是否正确，从而可以解答本题．【解答】解：∵反比例函数y＝，∴当x＝﹣2时，y＝﹣1，即点（﹣2，﹣1）在它的图象上，故选项A正确；它的图象在第一、三象限，故选项B正确；它的图象关于原点中心对称，故选项C正确；在每个象限内，y的值随着x的值的增大而减小，故选项D不正确；故选：D．4．如图是关于某班同学一周体育锻炼情况的统计图，那么该班学生这一周参加体育锻炼时间的众数、中位数分别是（）A．8、9B．8、8.5C．16、8.5D．16、14【分析】根据中位数、众数的概念分别求得这组数据的中位数、众数．【解答】解：众数是一组数据中出现次数最多的数，即8；而将这组数据从小到大的顺序排列后，处于中间位置的那个数，由中位数的定义可知，这组数据的中位数是9；故选：A．5．如果两圆的半径长分别为5和3，圆心距为7，那么这两个圆的位置关系是（）A．内切B．外离C．相交D．外切【分析】求出两圆半径的和与差，再与圆心距比较大小，确定两圆位置关系．根据两圆的位置关系得到其数量关系．设两圆的半径分别为R和r，且R≥r，圆心距为d：外离，则d＞R+r；外切，则d＝R+r；相交，则R﹣r＜d＜R+r；内切，则d＝R﹣r；内含，则d＜R﹣r．【解答】解：设圆心距为d，因为5﹣3＝2，3+5＝8，圆心距为7cm，所以，2＜d＜8，根据两圆相交，圆心距的长度在两圆的半径的差与和之间，所以两圆相交．故选：C．6．▱ABCD中，E，F是对角线BD上不同的两点．下列条件中，不能得出四边形AECF一定为平行四边形的是（）A．BE＝DF B．AE＝CF C．AF∥CE D．∠BAE＝∠DCF 【分析】连接AC与BD相交于O，根据平行四边形的对角线互相平分可得OA＝OC，OB＝OD，再根据对角线互相平分的四边形是平行四边形，只要证明得到OE＝OF即可，然后根据各选项的条件分析判断即可得解．【解答】解：如图，连接AC与BD相交于O，在▱ABCD中，OA＝OC，OB＝OD，要使四边形AECF为平行四边形，只需证明得到OE＝OF即可；A、若BE＝DF，则OB﹣BE＝OD﹣DF，即OE＝OF，故本选项不符合题意；B、若AE＝CF，则无法判断OE＝OF，故本选项符合题意；C、AF∥CE能够利用“角角边”证明△AOF和△COE全等，从而得到OE＝OF，故本选项不符合题意；D、∠BAE＝∠DCF能够利用“角角边”证明△ABE和△CDF全等，从而得到DF＝BE，然后同A，故本选项不符合题意；故选：B．二．填空题（共12小题）7．计算：（x3）2÷（﹣x）2＝x4．【分析】直接利用幂的乘方运算法则以及同底数幂的除法运算法则计算得出答案．【解答】解：（x3）2÷（﹣x）2＝x6÷x2＝x4．故答案为：x4．8．方程＝2的根是x＝﹣1．【分析】此题需把方程两边平方去根号后求解，然后把求得的值进行检验即可．【解答】解：两边平方得：3﹣x＝4，x＝﹣1．检验：当x＝﹣1时，原方程的左边＝2，右边＝2，∴x＝﹣1是原方程的根．故答案为：x＝﹣1．9．不等式组的解集是﹣≤x≤6．【分析】分别求出每一个不等式的解集，根据口诀：同大取大、同小取小、大小小大中间找、大大小小无解了确定不等式组的解集．【解答】解：解不等式3x+4≥0，得：x≥﹣，解不等式x﹣2≤1，得：x≤6，则不等式组的解集为﹣≤x≤6，故答案为：﹣≤x≤6．10．已知正三角形的边心距为1，那么它的边长为2．【分析】根据题意，画出图形作AD⊥BC，BE⊥AC于点D和E，点O即为△ABC的外心，根据特殊角30度即可求出BD的值，进而可得三角形的边长．【解答】解：根据题意，画出图形，∵△ABC是正三角形，作AD⊥BC，BE⊥AC于点D和E，∴点O即为△ABC的外心，∴OD＝1，∠DBO＝30°，∴BD＝，∴BC＝2BD＝2．故答案为：2．11．如果抛物线y＝（a﹣1）x2﹣1（a为常数）不经过第二象限，那么a的取值范围是a ＜1．【分析】根据抛物线y＝（a﹣1）x2﹣1（a为常数）不经过第二象限可以确定不等式的开口方向，从而确定a的取值范围．【解答】解：∵抛物线y＝（a﹣1）x2﹣1（a为常数）不经过第二象限，且该抛物线与y 轴交于负半轴，∴a﹣1＜0，解得：a＜1．故答案为：a＜1．12．如果关于x的多项式x2﹣2x+k在实数范围内能分解因式，那么k的取值范围是k≤1．【分析】本题实际上求一元二次方程x2﹣2x+k在实数范围内有实数根时，k的取值范围．所以根据一元二次方程的根的判别式解答即可．【解答】解：∵二次三项式x2﹣2x+k在实数范围内能分解因式，∴一元二次方程x2﹣2x+k在实数范围内有实数根，∴△＝4﹣4k≥0，解得，k≤1．故答案为：k≤1．13．从1，2，3，4四个数中任意取出2个数做加法，其和为偶数的概率是．【分析】列举出所有情况，看和为偶数的情况数占总情况数的多少即可．【解答】解：共12种情况，和为偶数的情况数有4种，所以概率为．故答案为．14．我国古代数学著作《九章算术》中有一道阐述“盈不足术”的问题，原文是“今有人共买物，人出八，盈三；人出七，不足四，问人数、物价各几何？”大致意思是：“现有几个人共同购买一个物品，每人出8元，则多3元；每人出7元，则差4元．问人数、物品的价格各是多少？”如果设共有x人，物品的价格为y元，那么根据题意可列出方程组为．【分析】根据“8×人数﹣多出的钱数＝物品的价格和7×人数+差的钱数＝物品的价格”列方程即可得．【解答】解：设共有x人，物品的价格为y元，根据题意，可列方程组为，故答案为：．15．甲乙两位运动员在一次射击训练中各打五发，成绩的平均环数相同，甲的方差为1.6；乙的成绩（环）为：7，8，10，6，9，那么这两位运动员中甲的成绩较稳定．【分析】利用方差的公式求得乙的方差，与甲的方差比较，方差较小的成绩稳定．【解答】解：乙的平均成绩为（7+8+10+6+9）÷5＝8，方差为：[（7﹣8）2+（8﹣8）2+（10﹣8）2+（6﹣8）2+（9﹣8）2]＝2，∵甲的方差为1.6，∴甲的方差较小，∴成绩较稳定的是甲，故答案为：甲．16．如图，已知在△ABC中，点D在边AC上，AD＝2DC，＝，＝，那么＝﹣+．（用含向量，的式子表示）【分析】利用三角形法则可知：＝+，求出即可解决问题．【解答】解：∵AD＝2DC，∴AD＝AC，∴＝＝，∴＝+，∴＝﹣+，故答案为﹣+．17．如果一个四边形有且只有三个顶点在圆上，那么称这个四边形是该圆的“联络四边形”，已知圆的半径长为5，这个圆的一个联络四边形是边长为2的菱形，那么这个菱形不在圆上的顶点与圆心的距离是1．【分析】先根据题意画出图形，连接BD、OD，设AM＝x，根据AD2﹣AM2＝OD2﹣OM2，列出方程，求出x，再根据OC＝OA﹣AM﹣CM计算即可．【解答】解：根据题意画图如下：连接BD，与AC交与点M，∵四边形ABCD是菱形，∴∠AMD＝∠DMC＝90°，∠ACD＝∠ACB，CD＝CD，AM＝CM，∴DM2＝AD2﹣AM2，设AM＝x，则DM2＝（2）2﹣x2，连接OD、OB，在△OCD和△OCB中，，∴△OCD≌OCB（SSS），∴∠OCD＝∠OCB，∴∠ACD+∠OCD＝∠ACB+∠OCB＝180°，∴OC与AC在一条直线上，∴△OMD是一个直角三角形，OM＝OA﹣AM＝5﹣x，∴DM2＝OD2﹣OM2，＝52﹣（5﹣x）2，∴（2）2﹣x2＝52﹣（5﹣x）2，x＝2，∴AM＝CM＝2，∴OC＝OA﹣AM﹣CM＝5﹣2﹣2＝1．故答案为：1．18．如图，已知在△ABC中，∠C＝90°，BC＝2，点D是边BC的中点，∠ABC＝∠CAD，将ACD沿直线AD翻折，点C落在点E处，连结BE，那么线段BE的长为．【分析】证△ABC∽△DAC，得出AC2＝BC×CD＝2，AC＝，由勾股定理得出AD＝，由折叠的性质得ED＝CD＝1，∠ADE＝∠ADC，得出BD＝ED，作DF⊥BE于F，则BF＝EF，∠BDF＝∠EDF，证△BDF∽△DAC，求出BF＝，即可得出答案．【解答】解：如图所示：∵BC＝2，点D是边BC的中点，∴BD＝CD＝1，∵∠ABC＝∠CAD，∠C＝∠C，∴△ABC∽△DAC，∴AC：CD＝BC：AC，∴AC2＝BC×CD＝2×1＝2，∴AC＝，∴AD＝＝＝，由折叠的性质得：ED＝CD＝1，∠ADE＝∠ADC，∴BD＝ED，作DF⊥BE于F，则BF＝EF，∠BDF＝∠EDF，∴∠BDF+∠ADC＝×180°＝90°，∵∠ADC+∠DAC＝90°，∴∠BDF＝∠DAC，又∵∠DFB＝∠C＝90°，∴△BDF∽△DAC，∴＝，即＝，∴BF＝，∴BE＝2BF＝；故答案为：．三．解答题（共5小题）19．如图，在梯形ABCD中，AD∥BC，AD＝2，BC＝5，∠BAC＝45°，cos∠ACB＝（1）求线段AC的长；（2）联结BD，交对角线AC于点O，求∠ADO的余切值．【分析】（1）如图，过点B作BE⊥AC于点E，根据已知条件和cos∠ACB＝可得，CE ＝3，AE＝BE＝4，进而可求AC的长；（2）结合（1）和AD∥BC，可得＝，得AO和OC的长，从而可求OE的长，进而得∠ADO的余切值即为∠BOE的余切值．【解答】解：（1）如图，过点B作BE⊥AC于点E，∴∠AEB＝90°，∵∠BAC＝45°，∴AE＝BE，∵cos∠ACB＝，即＝，∵BC＝5，∴CE＝3，∴BE＝＝4，∴AE＝BE＝4，∴AC＝AE+EC＝4+3＝7．答：线段AC的长为7；（2）∵AD∥BC，∴＝，∴＝，解得AO＝2，∴OC＝5，∴OE＝OC﹣CE＝5﹣3＝2，∴＝＝，∵∠ADO＝∠BOE，∴cot∠ADO＝cot∠BOE＝．∴∠ADO的余切值即为∠BOE的余切值为．20．如图，反映了甲、乙两名自行车爱好者同时骑车从A地到B地进行训练时行驶路程y （千米）和行驶时间x（小时）之间关系的部分图象，根据图象提供的信息，解答下列问题：（1）求乙的行驶路程y和行驶时间x（1≤x≤3）之间的函数解析式；（2）如果甲的速度一直保持不变，乙在骑行3小时之后又以第1小时的速度骑行，结果两人同时到达B地，求A、B两地之间的距离．【分析】（1）根据函数图象中的数据，可以求得乙的行驶路程y和行驶时间x（1≤x≤3）之间的函数解析式；（2）根据函数图象中的数据，可以分别求得甲的速度和乙开始的速度，然后设出A、B 两地之间的距离，再根据甲的速度一直保持不变，乙在骑行3小时之后又以第1小时的速度骑行，结果两人同时到达B地，可以列出相应的方程，从而可以得到A、B两地之间的距离．【解答】解：（1）设乙的行驶路程y和行驶时间x（1≤x≤3）之间的函数解析式为y＝kx+b，，解得，，即乙的行驶路程y和行驶时间x（1≤x≤3）之间的函数解析式是y＝10x+20；（2）设A、B两地之间的距离为S千米，甲的速度为60÷3＝20（千米/时），乙开始的速度为30÷1＝30（千米/时），，解得，S＝80，答：A、B两地之间的距离是80千米．21．如图，已知四边形ABCD是矩形，点E在对角线AC上，点F在边CD上（点F与点C、D不重合），BE⊥EF，且∠ABE+∠CEF＝45°．（1）求证：四边形ABCD是正方形；（2）连结BD，交EF于点Q，求证：DQ⋅BC＝CE⋅DF．【分析】（1）作EM⊥BC于点M，可证EM∥AB，可得∠ABE＝∠BEM，∠BAC＝∠CEM，由角的数量关系可得∠CEM＝45°＝∠BAC，可证AB＝BC，可得结论；（2）通过证明△BCE∽△FDQ，可得，可得结论．【解答】证明：（1）如图，作EM⊥BC于点M，∵四边形ABCD是矩形，∴AB⊥BC，∴EM∥AB，∴∠ABE＝∠BEM，∠BAC＝∠CEM，∵∠ABE+∠CEF＝45°，∴∠BEM+∠CEF＝45°，∵BE⊥EF，∴∠CEM＝45°＝∠BAC，∴∠BAC＝∠ACB＝45°，∴AB＝BC，∴矩形ABCD是正方形；（2）如图，∵∠BEF+∠BCF+∠EFC+∠EBC＝360°，∴∠EBC+∠EFC＝180°，且∠EFC+∠QFD＝180°，∴∠DFQ＝∠EBC，∵四边形ABCD是正方形，∴∠ACB＝∠BDC＝45°，∴△BCE∽△FDQ，∴，∴BC•DQ＝CE•DF．22．如图，在平面直角坐标系xOy中，已知抛物线y＝x2+mx+n经过点A（2，﹣2），对称轴是直线x＝1，顶点为点B，抛物线与y轴交于点C．（1）求抛物线的表达式和点B的坐标；（2）将上述抛物线向下平移1个单位，平移后的抛物线与x轴正半轴交于点D，求△BCD 的面积；（3）如果点P在原抛物线上，且在对称轴的右侧，联结BP交线段OA于点Q，＝，求点P的坐标．【分析】（1）先根据对称轴求出m，再将点A坐标代入抛物线解析式中求出能，得出抛物线解析式，最后配成顶点式，即可得出结论；（2）先求出点D坐标，进而求出直线CD解析式，得出点E坐标，再用面积公式求解即可得出结论；（3）设出点P坐标，构造出△PMQ∽△PNB，得出＝，表示出QM＝（a2﹣2a+1），PM＝（a﹣1），进而表示出Q（a+，a2﹣a﹣），代入直线OA中，即可得出结论．【解答】解：（1）∵抛物线y＝x2+mx+n的对称轴是直线x＝1，∴﹣＝1，∴m＝﹣2，∴抛物线解析式为y＝x2﹣2x+n，∵抛物线过点（2，﹣2），∴4﹣2×2+n＝﹣2，∴n＝﹣2，∴抛物线的解析式为y＝x2﹣2x﹣2＝（x﹣1）2﹣3，∴顶点B的坐标为（1，﹣3）；（2）如图1，由平移知，平移后的抛物线解析式为y＝x2﹣2x﹣3，令y＝0，则x2﹣2x﹣3＝0，∴x＝﹣1或x＝3，∵点D在x正半轴上，∴D（3，0），针对于抛物线y＝x2﹣2x﹣2，令x＝0，则y＝﹣2，∴C（0，﹣2），∴直线CD的解析式为y＝x﹣2，记直线CD与直线x＝1的交点为E，则E（1，﹣），∴S△BCD＝BE•|x D﹣x C|＝×|﹣﹣（﹣3）|×3＝；（3）如图2，设P（a，a2﹣2a﹣2），过点P作PN垂直于直线x＝1于点N过点Q作QM⊥PN于M，∴QM∥NN，∴△PMQ∽△PNB，∴＝，∵，∴＝，∵PN＝a﹣1，BN＝a2﹣2a﹣2+3＝a2﹣2a+1，∴，∴QM＝（a2﹣2a+1），PM＝（a﹣1），∴MN＝PN﹣PM＝（a﹣1），点Q与点B的纵坐标之差的绝对值为（a2﹣2a+1），∴Q（a+，a2﹣a﹣），∵A（2，﹣2），∴直线OA的解析式为y＝﹣x，∵点Q在线段OA上，∴a++a2﹣a﹣＝0，∴a＝﹣3（舍）或a＝4，∴P（4，6）．23．已知AB是⊙O的一条弦，点C在⊙O上，联结CO并延长，交弦AB于点D，且CD ＝CB．（1）如图1，如果BO平分∠ABC，求证：AB＝BC；（2）如图2，如果AO⊥OB，求AD：DB的值；（3）延长线段AO交弦BC于点E，如果△EOB是等腰三角形，且⊙O的半径长等于2，求弦BC的长．【分析】（1）证明△OBA≌△OBC即可解决问题．（2）如图2中，作DM⊥OB于M，DN⊥OA于N，设OM＝a．首先证明∠CDB＝∠CBD ＝75°，解直角三角形求出AD，BD（用a表示）即可解决问题．（3）因为∠OEB＝∠C+∠COE＞∠OBE，推出OE≠OB，分两种情形：如图3﹣1中，当BO＝BE时，如图3﹣2中，当EO＝EB时，分别求解即可解决问题．【解答】（1）证明：如图1中，∵BO平分∠ABC，∴∠ABO＝∠CBO，∵OB＝OA＝OC，∴∠A＝∠ABO，∠C＝∠OBC，∴∠A＝∠C，∵OB＝OB，∴△OBA≌△OBC（AAS），∴AB＝BC．（2）解：如图2中，作DM⊥OB于M，DN⊥OA于N，设OM＝a．∵OA⊥OB，∴∠MON＝∠DMO＝∠DNO＝90°，∴四边形DMON是矩形，∴DN＝OM＝a，∵OA＝OB，∠AOB＝90°，∴∠A＝∠ABO＝45°，∵OC＝OB，CD＝CB，∴∠C＝∠OBC，∠CDB＝∠CBD，∵∠C+∠CDB+∠CBD＝180°，∴∠C＝30°，∴∠CDB＝∠CBD＝75°，∵∠DMB＝90°，∴∠MDB＝∠DBM＝45°，∴DM＝BM，∠ODM＝30°，∴DM＝OM＝a，DN＝DM＝a，AD＝DN＝a，∴＝＝．（3）解：如图3﹣1中，当BO＝BE时，∵CD＝CB，∴∠CDB＝∠CBD，∴∠A+∠AOD＝∠OBA+∠OBC，∵∠A＝∠ABO，∴∠AOD＝∠OBC＝∠C，∵AOD＝∠COE，∴∠C＝∠COE＝∠CBO，∵∠C＝∠C，∴△OCE∽△BCO，∴＝，∴＝，解得EC＝﹣1+或﹣1﹣（舍弃），∴BC＝+1．如图3﹣2中，当EO＝EB时，同法可证△OEB是等腰直角三角形，∴EO＝EB＝EC＝OB＝，∴BC＝2，∵∠OEB＝∠C+∠COE＞∠OBE，∴OE≠OB，综上所述，BC的值为+1或2．。

上海市长宁区、嘉定区2014届高三英语二模试卷（含答案及听力文字）2014年长宁区、嘉定区高三英语教学质量检测试卷第I卷（共103分）I. Listening ComprehensionSection ADirections:In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At a paint store. B. At a grocery store.C. At a drugstore.D. At a video game store.2. A. ￡40. B. ￡60. C. ￡120. D. ￡180.3. A. He left the door open. B. He broke the vase.C. He took the vase off the table.D. He turned out to be innocent.4. A. Judge and lawyer. B. Policeman and driver.C. Cleaner and walker.D. Teacher and student.5. A. She’s got a full time job at the university. B. She was surprised to get a full scholarship.C. Everything went just as had been expected.D. Brighton University is not her ideal school.6. A. The man has a serious sleep problem. B. Neither of them has finished the paper.C. They both had a hard time doing the paper.D. The woman thought the paper easy to do.7. A. Help the woman find the building. B. Follow the woman to the exhibit.C. Assist the woman to read the map.D. Show the woman where to get a new map.8. A. Mrs. Brown was unhappy this morning.B. Mrs. Brown is a patient teacher.C. Susan must be poor at her studies.D. Susan might have been scolded by Mrs. Brown.9. A. She is going to try a new highway to the cinema.B. She wants to go early to avoid a traffic jam.C. She has no idea how to get to the cinema.D. She wants to leave the cinema before the movie is over.10. A. She loves going to work on foot. B. The firm she works in is not far away.C. She has to save money for her journey.D. It takes her too much time to go to work.Section BDirections:In Section B, you will hear two short passages, and you will be asked three questions on each of the passage. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. It is an important occasion of American cultural activities.B. They can have drinks and snacks while watching the game.C. Some companies offer viewers expensive sample products.D. The result of the game may be beyond people’s expectation.12. A. Exciting professional performances. B. Fancy advertisements of products.C. Pleasant atmosphere on the spot.D. Warm company of their family.13. A. Expensive and impressive TV commercials.B. Various ways of entertaining audience during intervals.C. An introduction to a popular ball game in America.D. Different sports people love to play in America.Questions 14 through 16 are based on the following passage.14. A. Introducing healthy genes into a virus. B. Removing faulty cells from patients.C. Providing emotional support to patients.D. Preventing patients from brain injuries.15. A. It still remains in an experimental stage at present.B. It has taken the place of surgery or medicine.C. It has only been tried on young patients so far.D. It helps patients to have a speedy and full recovery.16. A. Children are more likely to be infected by diseases.B. How to popularize gene therapy in different hospitals.C. A couple of successful examples of a new therapy.D. Genes rather than any other things are the master of our fortune.Section CDirections:In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Blanks 21 through 24 are based on the following conversation.II. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)A boy plays away from home and fights with others. He’s defeated, gets hurt and suffers shame. If he is strong-willed, he would clench (咬紧) his teeth, making a firm fist from (25) ______ (weep) in front of others. But as soon as he returns home he would burst out crying at the first sight of his close relatives. He would be all tears pouring out his sufferings.The same is true for a strong-willed grown-up. No matter what harm he suffers he would do his best (26) ______ (conceal) his feelings, trying not to let others know how he feels. He would swallow his bitter tears and show a smiling face at others (27) ______ ______ he didn’t care a bit. But however strong-willed he is, most probably he would cry as soon as he meets his close relative who loves him and to (28) ______ he can pour out his heart unreservedly. Not only would he weep but he’d cry his eyes out (29) ______ grief.If somebody weeps in your face —the person never of thetype doing this in front of others, you’d better sit by and let him cry to (30) ______ heart’s content, for it shows you are regarded as his dearest or (31) ______ (reliable) one.It’s much better to have someone crying in your face than be met exclusively by (32) ______ smiling face. Anyone can smile at you, but very few will weep in your face, because the latter is much harder for one to do than the former.(B)Some of young soldiers who had recently joined the army were being trained in modern ways of fighting. One of the lessons they should take was (33) ______ an unarmed man could trick an armed enemy, take his weapon away and have him (34) ______ (arrest). First one of their two instructors took a knife away from the other, using only his bare hands, and then he took a gun away from him in the same way.After the lesson, and before they went on to train the young soldiers to do these things themselves, the two instructors asked them a number of questions to see how well they had understood what (35) ______ (show). One of the questions was this, “Well, you now know (36) ______ an unarmed man can do against a man with a gun. Imagine that you (37) ______ (guard) a bridge at eight one night, and that you have a gun. Suddenly you see an unarmed enemy soldier (38) ______ (come) towards you, and what will you do?”The young soldier who (39) ______ ______ answer this question thought carefully for a few seconds (40) ______ he answered, and then said, “Well after what I have just seen, I think that the first thing I would do would be to get rid of my gun as quickly as I could so that the unarmed enemy soldier couldn’t take it from me and kill me with it!”Section BDirections: Complete the following passage by using the words in the box. Each word can onlyRain forests, found in Earth’s temperate and tropical(热带的) zones, are some of the most biologically varied ecosystems on the planet. All rain forests share certain ___41___ features, including a closed canopy, the dense vegetation of the top branches that forms a roof above the forest floor, a damp and warm climate, and ___42___ constant temperatures throughout the year. Most of the forest’s insect and animal life grows well in the cano py’s leafy and sunlit environment. The forest’s groundcover, by comparison, is small. Less than 2 percent of the sun’s light makes its way through the canopy and the darkness below. This darkness, along with the poor quality of the soils, ___43___ plant growth.Rain forests are a(n) ___44___ part of Earth’s total ecology. Huge amounts of water are absorbed into tree roots and ___45___ into the atmosphere from the tree leaves through a process called transpiration(蒸发). Tree roots also fix the soil in place and slow the runoff of rains into rivers and oceans. Through the process of photosynthesis(光合作用), rain forests absorb more carbon dioxide and give off more oxygen than any other ecosystem.The rain forests are ___46___ shrinking at a rapid rate as a result of the profitable ventures of farming, logging, and mining. When tropical rain forests are ___47___ in order to raise cattle and crops, the nutrient-poor soils are quickly ___48___. When farmers move on to new areas, heavy rains and baking sun leave the land fruitless and lifeless. Logging and mining cause similar damageto the land and destroy the territory of ___49___ millions of birds, insects and animals. By some ___50___, an area of tropical rain forest the size of the state of Delaware disappears in this way every month.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Archaeologists are scientists who search for clues that help form a clearer picture of the lives people led in the past. Archaeology is a modern science, but it has been ___51___ for centuries. More than 2,400 years ago, the Greek historian Herodotus described the Egyptian pyramids and other monuments. He may have been the first writer to consider that remains and ___52___ could provide information for ___53___ generations. For more than a thousand years, however, such ___54___ were observers rather than researchers.In the 1700s, scientists and adventurers from a variety of countries traveled ___55___ to explore ancient sites. Digs that are still ___56___ began in 1709 at Herculaneum, an Italian city buried in ash during the explosion of Mount Vesuvius in A. D. 79. The Danish scholar Carsten Niebuhr visited the ruins of Persepolis in the Middle East in 1765 to study cuneiform writing (楔形文字). ___57___, archaeology didn’t become a widely recognized science and schools didn’t recognize the subject as a scholarly pursuit until the 19th century. The term itself was ___58___ in 1837. It comes from a Latin word meaning “the study of antiquities(古物).”One of the first archaeologists to use a scientific approach to the discipline was Heinrich Schliemann of Germany, who in thelate 1800s ___59___ the ancient civilization of the city of Troy.Today, archaeologists uncover the past in many different ___60___, including deserts and jungles, at sites called digs. Ancient sources, folk tales, and landscape features can suggest where archaeologists should look. Surveys of the land help them choose sites ___61___ to provide artifacts, the objects that will unlock the story of a particular people —their daily lives, their beliefs, and their ties to other cultures. A site, however, does not have to be old to be interesting to an archaeologist. Some prefer to study more ___62___ settlements. One scientist, for instance, studies coal mining camps in California by examining the garbage that miners ___63___. Archaeologists may work for universities, museums or governments, and some of them are involved in educating the public about ___64___ ancient sites. Artifact hunters who are ___65___ history rob these places and sell what they find for a few dollars to immoral dealers in antiquities.51. A. adventuring B. changing C. digging D. evolving52. A. books B. history C. ruins D. science53. A. lost B. later C. older D. several54. A. inventors B. scholars C. visitors D. writers55. A. extensively B. nationwide C. regularly D. together56. A. in progress B. in good condition C. on display D. out of control57. A. Besides B. However C. Instead D. Meanwhile58. A. coined B. considered C. recognized D. used59. A. created B. developed C. established D. investigated60. A. countries B. fields C. locations D. ways61. A. certain B. likely C. ready D. necessary62. A. honorable B. peaceful C. rural D. recent63. A. gave away B. gave off C. left behind D. left out64. A. choosing B. examining C. studying D. protecting65. A. aware of B. fed up with C. ignorant of D. familiar withSection BDirections:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)When my old dog developed major health problems, I knew that watching him fail would be painful, but I wasn’t prepared for the powerful lessons he’d offer in the last year of his life.Chance was 14 when the problems started. First, he developed a cancer that left him whistling for breath. Then came cataracts (白内障) in both eyes, arthritis (关节炎) in his legs, and a series of ministrokes (小中风) that threw off his balance. Any one of these misfortunes would have left me begging for relief, but Chance became calmer as the disabilities piled up.When leg pain left him frozen on the floor, unable to rise for a quick pat as I came home, he didn’t complain. He just lay there patiently, signaling me with his hammering tail, each movement spelling out the value of waiting for the things you want. When his cataracts made steering impossible after dark, he’d stand calmly until I could guide him inside, proving how easy it is to find happiness if you let go of your pride and insecurities and learn to lean on those who love you. When ministrokes had him walk unsteadily like a drunk, he taught the value of persistence. For days after each attack, he’d fall as he moved about. Yet again and again he’d try to walk, each day moving a few more steps until finally he was able to get outside and back by himself.There were lessons in so much of what he did, but the key one surely was the importance of obtaining all the joy possible from each experience whether it’s a day lazing under a warm sun or a few minutes appreciating a favorite meal.For most of our life together, Chance was always rushing ahead, searching out new adventures, then circling back to let me know what lay around the next bend. As an old dog, he did the same thing, using his attitude, instead of his once-fast legs, to show the way.66. Chance suffered very much from all the diseases he had except for ______.A. having problem with breathB. walking around awkwardlyC. having trouble drinkingD. losing his eyesight in darkness67. ______ is the most important lesson the author learned from Chance.A. Living in the present and enjoying what we haveB. Learning to depend on those who we love and trustC. That we should expect good things to happen patientlyD. That we should persevere in what we believe is worth trying68. It is implied in the passage that ______.A. people might suffer from different diseases when they grow oldB. people could face aging with courage and dignityC. pets would become calmer for lack of energy in their last daysD. pets and masters should stick together helping each other in difficulty69. Which of the following words best describes the author’s feelings to Chance?A. Bitter.B. Grateful.C. Proud.D. Sympathetic.* * * *70. To have a 1865 membership, guests need to ______.A. register at /doc/c83457229.htmlB. visit Langham three times in a yearC. have five stays in Langham yearlyD. stay in Langham properties once71. Which of the following is true according to the given information?A. Gateway members have 4pm late check-out priority any time they want.B. Members can get the benefits listed in the table at all Langham’s properties.C. The very first hotel of Langham collection was built in 1865 in Britain.D. Top 1% Voyagers with super residence record can apply for Destiny membership.72. Tony, on their honeymoon trip, wants to surprise his wife with a bunch of roses on arriving atthe hotel. Tony at least needs to have the membership of ______.A. EXPLORERB. GA TEW AYC. VOYAGERD. DESTINY73. What is the main purpose of the writing?A. To attract more potential guests.B. To share the history of Langham hotels.C. To introduce successful hotel management.D. To list Langham hotels’ exclusive benefits.(C)Charle s Dickens’ novel A Tale of Two Cities is set in the years before and during the French Revolution (1789 - 1799). During its course, French revolutionaries brought down the empire and established a republic of free and equal citizens.In reading the work, one sees that Dickens distorted some details of the French Revolution. At the beginning, Dickens notes that, in 1775, France was busy spending money. This mention of France’s spending touches briefly on what is perhaps the major cause of the French Revolution. Before the revolution, the government often borrowed money because it spent more than it raised in taxes. The increased spending and borrowing made many people’s blood boil, yet Dickens focused instead on the nobility’s oppression and exploitation of t he working class, including peasants, as the causes of the revolution.The Marquis, one of the book’s characters, ill-treats and kills many people. Thus, he represents the nobles who mistreat the lower classes. One reviewer criticized this picture as an unfair representation of French society in the mid-1700s. The reviewer pointed out that the government would have punished nobles who mistreated or murdered. Nobles may have been guilty of other evils, however, such as not feeding the starving masses after bad weather ruined crops in 1789.Dickens’ account of the storming of the Bastille fails to mention that the gang that stormed the prison was looking forbullets and bombs to use in defense against a possible attack by the kin g’s troops. Dickens does inclu de some accurate details, however, such as the crowd’s finding only seven prisoners and freeing them and the pack’s executing (处决) the prison administrator and sticking his head on a post. The scene that the women knit (编织) as they watch the executions may seem to be an odd detail, but actually many women did knit stockings for the war effort as they watched the killing machine at work.Dickens’ descriptions of the steady stream of sentenced people into prison and the carts taking them to their deaths give readers some idea of the frequency with which officials jailed and executed people during the Rule of T error, which lasted about a year. During the Terror, the government jailed about 250 thousand people, tried(审判) and killed about 17 thousand, and executed about 12thousand without a trial. Those executed included people who opposed the revolution, people who offended the revolutionaries, and even some revolutionaries. About 15 percent were members of the ministry or nobility.74. What does the word “distorted” in Paragraph 2 most probably mean?A. Discussed.B. Revealed.C. Provided.D. Twisted.75. Which of the following statements is true according to the passage?A. A wild crowd rushed into the Bastille to fight with the royal soldiers.B. The nobles’ m istreating and killing people is the maincause of the revolution.C. About thirty thousand people lost their lives in the course of the Rule of Terror.D. Women were forced to work for the war supplies while watching people killed.76. What can be inferred from the passage?A. Dickens was once among the revolutionaries storming the Bastille.B. There was an extreme disorder and horror during the revolution.C. Nobles of those days in France were loaded with heavy social responsibilities.D. Classic literary works may serve as history textbooks to a great degree.77. Which of the following might be the best title of the passage?A. The Collapse of the French EmpireB. Unknown Facts during the Rule of TerrorC. Dickens’ Description of the French Revolu tionD. A Critical View on A Tale of Two CitiesSection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.For decades, a small percentage of homeowners have been installing solar panels(嵌板) on their rooftops. Those panels collect solar energy and change it into electricity. Until recently, the panels were too expensive for average homeowners, and their designs were anything but appealing. Thanks to new advances, however, solar panels for homes are becoming cheaperand less awkward, causing more homeowners to consider installing them.Last fall furniture seller IKEA began selling solar panels in its U.K. stores. Of course, home improvement stores such as Home Depot have been selling panels for a while. But the initiative by IKEA is seen as a way to bring the Do It Yourself solar option to the masses. While shopping for inexpensive furniture, shoppers could add a box or two of solar panels to their carts. IKEA is partnering with a company that handles installation and servicing of the panels, making the switch to solar easy for customers. If all goes well, IKEA plans to begin selling the panels in other countries soon.SolTech, a Swedish tech company, offers a solar-power solution that is much more pleasing to the eye than traditional solar panels. Instead of flat panels, SolTech offers a glass tile (瓦片) solutionthat goes well with existing tiled roof designs. The see-through tiles have a silver-gray color to them, and their shape fits traditional tiled roof designs. SolTech currently offers the solar systems that heat the home’s air or water and one solar PV system that produces electricity.New Energy Technologies, Inc. is developing a solar application that won’t be installed on rooftop s. Instead, the first-of-its-kind SolarWindow TM technology enables see-through windows to produce electricity in the way of showering their glass surfaces with the company’s patent-pending (专利申请中的) electricity-producing coatings. Amazingly, SolarWindow TM can produce electricity in low-light conditions and can even turn indoor light into electricity! This product holds great promise for commercial buildings since about 60 percent of acommercial building’s surface is covered with windows.(Note: Answer the questions or complete the statements in NO MORE THAN EIGHT WORDS.)78. Solar panels on homeowners’ rooftops work by __________.79. What is IKEA doing to popularize their DIY solar option?80. SolTech’s solar panels are prettier because the see-through glass tiles are __________.81. How is SolarWindow TM technology used to produce electricity?第II卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 看，十年前种的那棵树现在长得多高了呀！(how)2. 你看上去很疲惫，为什么不回家好好睡一觉呢？(tired)3. 普遍认为在公共场合大声说话是粗鲁的，应该避免。