2019.6二模试卷讲评及评分标准(仅限于海淀区内部使用)

北京海淀区2019年中考语文二模试题及答案北京海淀区2019年中考语文二模试题及答案内容预览：海淀区九年级第二学期期末练习语文参考答案及评分标准2019.6一、选择（每小题2分，共12分）1.A2.D3.B4.B5.C6.A二、填空（共8分）7．（1）长风破浪会有时（2）何事长向别时圆（3）断肠人在天涯（4）阡陌交通鸡犬相闻（5）乱花渐欲迷人眼浅草才能没马蹄（共5分。

共5小题，每小题1分，有错该小题不得分）8．①学思结合②鱼我所欲也③舍生取义（共3分。

共3空，每空1分）三、综合性学习（共11分）9．特点：答案示例：（1）近年来，北京市民整体阅读率逐年增长。

（2）近年来，北京市民数字化方式阅读率增长幅度远高于传统方式阅读率的增长幅度。

（或：近年来，北京市民数字化方式阅读率增长迅速，但是传统的阅读方式始终占主要地位。

或：北京市民传统方式阅读率与数字化方式阅读率三年来均逐年增长）（3）北京市民最喜欢阅读中国古代四大名着。

（或：中国古代四大名着最受北京市民欢迎）优势：答案示例：（1）信息量大（2）时间利用率高（或：零碎时间可用）（3）方便阅读（或：阅读便捷（4）降低阅读成本（或：省了买书钱）〔共5分。

“特点”3分；“优势”2分〕10．答案示例：（1）中学生：放松神经，调整心情，更好地投入学习。

（2）大学生：让自己的专业知识更扎实，人生方向更明确。

（或：为将来的工作和生活打下良好的基础）（3）老年人：使晚年生活更加丰富多彩。

（或：排遣退休生活的空虚乏味，找到乐趣）（共3分。

共3类人群，每类人群1分）11．答案示例：人物：《水浒传》中的鲁达点评：他好打抱不平，疾恶如仇，粗中有细。

情节：鲁提辖拳打镇关西（共3分。

共3项内容，每项内容1分）四、文言文阅读（共8分）12．（1）停，过（2）更加（3）特意（4）通“剂”（共2分。

共4小题，每小题0.5分）13．（1）医生喜欢给没病（的人）治“病”，以此显示自己的本领。

北京市海淀区2019年中考语文二模试题及答案内容预览：北京市海淀区九年级第二学期期末练习(二模)语文(2019.6)整理录入：青峰弦月一、选择。

下面各题均有四个选项，其中只有一个符合题意，选出答案后在答题纸上用铅笔把对应题目的选项字母涂黑涂满。

(共12分，每小题2分)1.下列词语中加点字的读音完全正确的一项是A.粗犷(guǎng)哺育(bǔ)呜咽(yè)牵强附会(qiǎng)B.暂时(zàn)细菌(jǔn)琐屑(xiè)厚此薄彼(bó)C.广袤(mào)炫耀(xuàn)狭隘(ài)轩然大波(pō)D.恣意(zì)脸颊(xiá)嗤笑(chī)断壁残垣(yuán)2.依据对下列各组词语中加点字的解释，判断词语意思都不正确的一项是A.和蔼--心平气和解释：“和”有“平和、和缓”的意思。

判断：“和蔼”指态度温和，容易接近;“心平气和”指心里平和，不急躁，不生气。

B.举措--举一反三解释：“举”有“举动;提出”的意思。

判断：“举措”指举动、措施;“举一反三”指举出一件事情就可类推而知其他许多事理。

C.当之无愧--锐不可当解释：“当”有“承当、承受;阻挡、抵挡”的意思。

判断：“当之无愧”指承当某种称号或荣誉，能够当得起，不用感到惭愧;“锐不可当”指来势凶猛，不可阻挡。

D.左顾右盼--三顾茅庐解释：“顾”有“拜访;转过头看、看”的意思。

判断：“左顾右盼”指拜访朋友时，盼望早点见到;“三顾茅庐”指三次到草庐中去看望他，比喻诚心诚意地邀请。

3.下列句子中加点词语使用有误的一项是A.这个年轻人，因为生活阅历浅，思想不够成熟，作品难免幼稚，可能会贻笑大方;但其中蕴涵的朝气却是最宝贵的。

B.端午节，我国南方盛行赛龙舟。

竞赛时，各个竞赛队在浪花里随波逐流，奋勇前进。

C.胡锦涛总书记在纪念共青团成立90周年大会上发表讲话，激励优秀青年要百尺竿头，更进一步。

2019年北京市海淀区高考数学二模试卷（理科）一、选择题（共8小题，每小题5分，满分40分）1．已知全集U=R，M={x|x≤1}，P={x|x≥2}，则∁U（M∪P）=（）A．{x|1＜x＜2}B．{x|x≥1} C．{x|x≤2} D．{x|x≤1或x≥2}2．数列{a n}的首项a1=2，且（n+1）a n=na n+1，则a3的值为（）A．5 B．6 C．7 D．83．若点P（2，4）在直线l：（t为参数）上，则a的值为（）A．3 B．2 C．1 D．﹣14．在△ABC中，cosA=，cosB=，则sin（A﹣B）=（）A．﹣B．C．﹣D．5．在（x+a）5（其中a≠0）的展开式中，x2的系数与x3的系数相同，则a的值为（）A．﹣2 B．﹣1 C．1 D．26．函数f（x）=lnx﹣x+1的零点个数是（）A．1 B．2 C．3 D．47．如图，在等腰梯形ABCD中，AB=8，BC=4，CD=4，点P在线段AD上运动，则|+|的取值范围是（）A．[6，4+4]B．[4，8]C．[4，8]D．[6，12]8．直线l：ax+y﹣1=0与x，y轴的交点分别为A，B，直线l与圆O：x2+y2=1的交点为C，D，给出下面三个结论：①∀a≥1，S△AOB=；②∃a≥1，|AB|＜|CD|；③∃a≥1，S△COD＜．其中，所有正确结论的序号是（）A．①②B．②③C．①③D．①②③二、填空题（共6小题，每小题5分，满分30分）9．已知=1﹣i，其中i为虚数单位，a∈R，则a=．10．某校为了解全校高中学生五一小长假参加实践活动的情况，抽查了100名学生，统计他们假期参加实践活动的实践，绘成的频率分布直方图如图所示，这100名学生中参加实践活动时间在6﹣10小时内的人数为．11．如图，A，B，C是⊙O上的三点，点D是劣弧的中点，过点B的切线交弦CD的延长线于点E．若∠BAC=80°，则∠BED=．12．若点P（a，b）在不等式组所表示的平面区域内，则原点O到直线ax+by﹣1=0的距离的取值范围是．13．已知点A（，），B（，1），C（，0），若这三个点中有且仅有两个点在函数f（x）=sinωx的图象上，则正数ω的最小值为．14．正方体ABCD﹣A1B1C1D1的棱长为1，点P，Q，R分别是棱A1A，A1B1，A1D1的中点，以△PQR为底面作正三棱柱．若此三棱柱另一底面的三个顶点也都在该正方体的表面上，则这个正三棱柱的高h=．三、解答题（共6小题，满分80分）15．已知函数f（x）=﹣2sinx﹣cos2x．（1）比较f（），f（）的大小；（2）求函数f（x）的最大值．16．某空调专卖店试销A、B、C三种新型空调，销售情况如表所示：第一周第二周第三周第四周第五周A型数量（台）11 10 15 A4A5B型数量（台）10 12 13 B4B5C型数量（台）15 8 12 C4C5（1）求A型空调前三周的平均周销售量；（2）根据C型空调前三周的销售情况，预估C型空调五周的平均周销售量为10台，当C 型空调周销售量的方差最小时，求C4，C5的值；（注：方差s2= [x1﹣）2+（x）2+…+（x n﹣）2]，其中为x1，x2，…，x n的平均数）（3）为跟踪调查空调的使用情况，根据销售记录，从第二周和第三周售出的空调中分别随机抽取一台，求抽取的两台空调中A型空调台数X的分布列及数学期望．17．如图，等腰梯形ABCD中，AB∥CD，DE⊥AB于E，CF⊥AB于F，且AE=BF=EF=2，DE=CF=2．将△AED和△BFC分别沿DE，CF折起，使A，B两点重合，记为点M，得到一个四棱锥M﹣CDEF，点G，N，H分别是MC，MD，EF的中点．（1）求证：GH∥平面DEM；（2）求证：EM⊥CN；（3）求直线GH与平面NFC所成角的大小．18．已知函数f（x）=e x（x2+ax+a）．（1）当a=1时，求函数f（x）的单调区间；（2）若关于x的不等式f（x）≤e a在[a，+∞）上有解，求实数a的取值范围；（3）若曲线y=f（x）存在两条互相垂直的切线，求实数a的取值范围．（只需直接写出结果）19．已知点A（x1，y1），D（x2，y2）（其中x1＜x2）是曲线y2=4x（y≥0）上的两点，A，D两点在x轴上的射影分别为点B，C，且|BC|=2．（Ⅰ）当点B的坐标为（1，0）时，求直线AD的斜率；（Ⅱ）记△OAD的面积为S1，梯形ABCD的面积为S2，求证：＜．20．已知集合Ωn={X|X=（x1，x2，…，x i，…，x n），x i∈{0，1}，i=1，2，…，n}，其中n ≥3．∀X={x1，x2，…，x i，…，x n}∈Ωn，称x i为X的第i个坐标分量．若S⊆Ωn，且满足如下两条性质：①S中元素个数不少于4个；②∀X，Y，Z∈S，存在m∈{1，2，…，n}，使得X，Y，Z的第m个坐标分量是1；则称S为Ωn的一个好子集．（1）S={X，Y，Z，W}为Ω3的一个好子集，且X=（1，1，0），Y=（1，0，1），写出Z，W；（2）若S为Ωn的一个好子集，求证：S中元素个数不超过2n﹣1；（3）若S为Ωn的一个好子集，且S中恰有2n﹣1个元素，求证：一定存在唯一一个k∈{1，2，…，n}，使得S中所有元素的第k个坐标分量都是1．2019年北京市海淀区高考数学二模试卷（理科）参考答案与试题解析一、选择题（共8小题，每小题5分，满分40分）1．已知全集U=R，M={x|x≤1}，P={x|x≥2}，则∁U（M∪P）=（）A．{x|1＜x＜2}B．{x|x≥1} C．{x|x≤2} D．{x|x≤1或x≥2}【考点】交、并、补集的混合运算．【分析】求出M∪P，从而求出其补集即可．【解答】解：M={x|x≤1}，P={x|x≥2}，∴M∪P={x|x≤1或x≥2}，∁U（M∪P）={x|1＜x＜2}，故选：A．2．数列{a n}的首项a1=2，且（n+1）a n=na n+1，则a3的值为（）A．5 B．6 C．7 D．8【考点】数列递推式．【分析】由题意可得a n+1=a n，分别代值计算即可．【解答】解：数列{a n}的首项a1=2，且（n+1）a n=na n+1，∴a n+1=a n，∴a2=a1=2×2=4，∴a3=×a2=×4=6，故选：B．3．若点P（2，4）在直线l：（t为参数）上，则a的值为（）A．3 B．2 C．1 D．﹣1【考点】参数方程化成普通方程．【分析】由题意可得：，解得a即可得出．【解答】解：∵，解得a=﹣1．故选：D．4．在△ABC中，cosA=，cosB=，则sin（A﹣B）=（）A．﹣B．C．﹣D．【考点】两角和与差的正弦函数．【分析】根据同角三角函数得到sinA，sinB的值；然后将其代入两角和与差的正弦函数中求值即可．【解答】解：∵0＜A＜π，0＜B＜π，cosA=，cosB=，∴sinA=，sinB=，∴sin（A﹣B）=sinAcosB﹣cosAsinB=×﹣×=．故选：B．5．在（x+a）5（其中a≠0）的展开式中，x2的系数与x3的系数相同，则a的值为（）A．﹣2 B．﹣1 C．1 D．2【考点】二项式系数的性质．【分析】通过二项式定理，写出（x+a）5（其中a≠0）的展开式中通项T k+1=x5﹣k a k，利用x2的系数与x3的系数相同可得到关于a的方程，进而计算可得结论．【解答】解：在（x+a）5（其中a≠0）的展开式中，通项T k+1=x5﹣k a k，∵x2的系数与x3的系数相同，∴a3=a2，又∵a≠0，∴a=1，故选：C．6．函数f（x）=lnx﹣x+1的零点个数是（）A．1 B．2 C．3 D．4【考点】函数零点的判定定理．【分析】利用导数求出函数的最大值，即可判断出零点的个数．【解答】解：f′（x）=﹣1=，∴当x=1时，函数f（x）取得最大值，f（1）=0﹣1+1=0，因此函数f（x）有且仅有一个零点1．故选：A．7．如图，在等腰梯形ABCD中，AB=8，BC=4，CD=4，点P在线段AD上运动，则|+|的取值范围是（）A．[6，4+4]B．[4，8]C．[4，8]D．[6，12]【考点】平面向量数量积的运算．【分析】可过D作AB的垂线，且垂足为E，这样可分别以EB，ED为x轴，y轴，建立平面直角坐标系，根据条件即可求出A，B，D的坐标，从而可以得出直线AD的方程为，从而可设，且﹣2≤x≤0，从而可以求出向量的坐标，从而得出，而配方即可求出函数y=16（x2+2x+4）在[﹣2，0]上的值域，即得出的取值范围，从而得出的取值范围．【解答】解：如图，过D作AB的垂线，垂足为E，分别以EB，ED为x，y轴，建立平面直角坐标系；根据条件可得，AE=2，EB=6，DE=；∴；∴直线AD方程为：；∴设，（﹣2≤x≤0）；∴，；∴；∴=16（x2+2x+4）=16（x+1）2+48；∵﹣2≤x≤0；∴48≤16（x+1）2+48≤64；即；∴；∴的范围为．故选：C．8．直线l：ax+y﹣1=0与x，y轴的交点分别为A，B，直线l与圆O：x2+y2=1的交点为C，D，给出下面三个结论：①∀a≥1，S△AOB=；②∃a≥1，|AB|＜|CD|；③∃a≥1，S△COD＜．其中，所有正确结论的序号是（）A．①②B．②③C．①③D．①②③【考点】直线与圆的位置关系．【分析】①当a≥1时，分别可得直线的截距，由三角形的面积公式易得结论①正确；②当a≥1时，反证法可得结论②错误；③由三角形的面积公式可得S△COD=sin∠AOC≤，可得结论③正确．【解答】解：①当a≥1时，把x=0代入直线方程可得y=a，把y=0代入直线方程可得x=，∴S△AOB=×a×=，故结论①正确；②当a≥1时，|AB|=，故|AB|2=a2+，直线l可化为a2x+y﹣a=0，圆心O到l的距离d===，故|CD|2=4（1﹣d2）=4[1﹣（a2+）]，假设|AB|＜|CD|，则|AB|2＜|CD|2，即a2+＜4（1﹣），整理可得（a2+）2﹣4（a2+）+4＜0，即（a2+﹣2）2＜0，显然矛盾，故结论②错误；S△COD=|OA||OC|sin∠AOC=sin∠AOC≤，故∃a≥1，使得S△COD＜，结论③正确．故选：C．二、填空题（共6小题，每小题5分，满分30分）9．已知=1﹣i，其中i为虚数单位，a∈R，则a=1．【考点】复数代数形式的乘除运算．【分析】根据复数的代数运算性质，求出a的值即可．【解答】解：∵=1﹣i，∴a+i=∴a=﹣i=﹣i=1．故答案为：1．10．某校为了解全校高中学生五一小长假参加实践活动的情况，抽查了100名学生，统计他们假期参加实践活动的实践，绘成的频率分布直方图如图所示，这100名学生中参加实践活动时间在6﹣10小时内的人数为58．【考点】频率分布直方图．【分析】利用频率分布直方图中，频率等于纵坐标乘以组距，求出在6﹣10小时外的频率；利用频率和为1，求出在6﹣10小时内的频率；利用频数等于频率乘以样本容量，求出这100名同学中学习时间在6﹣10小时内的同学的人数．【解答】解：由频率分布直方图知：（0.04+0.12+a+b+0.05）×2=1，∴a+b=0.29，∴参加实践活动时间在6﹣10小时内的频率为0.29×2=0.58，∴这100名学生中参加实践活动时间在6﹣10小时内的人数为100×0.58=58．故答案为：5811．如图，A，B，C是⊙O上的三点，点D是劣弧的中点，过点B的切线交弦CD的延长线于点E．若∠BAC=80°，则∠BED=60°．【考点】与圆有关的比例线段．【分析】由弦切角定理可得∠EBC=∠A，再由圆的圆周角定理，可得∠BCE=∠A，在△BCE中，运用三角形的内角和定理，计算即可得到所求值．【解答】解：由BE为圆的切线，由弦切角定理可得∠EBC=∠A=80°，由D是劣弧的中点，可得∠BCE=∠A=40°，在△BCE中，∠BEC=180°﹣∠EBC﹣∠BCE=180°﹣80°﹣40°=60°．故答案为：60°．12．若点P（a，b）在不等式组所表示的平面区域内，则原点O到直线ax+by﹣1=0的距离的取值范围是[，1]．【考点】简单线性规划．【分析】由约束条件作出可行域，由点到直线的距离公式求出原点O到直线ax+by﹣1=0的距离为，结合的几何意义得答案．【解答】解：由约束条件作出可行域如图，原点O到直线ax+by﹣1=0的距离为，由图可知的最小值为|OA|=1，最大值为|OB|=2，∴原点O到直线ax+by﹣1=0的距离的取值范围是[，1]．故答案为：[，1]．13．已知点A（，），B（，1），C（，0），若这三个点中有且仅有两个点在函数f（x）=sinωx的图象上，则正数ω的最小值为4．【考点】正弦函数的图象．【分析】由条件利用正弦函数的图象特征，分类讨论，求得每种情况下正数ω的最小值，从而得出结论．【解答】解：①若只有A、B两点在函数f（x）=sinωx的图象上，则有sin（ω•）=，sin（ω•）=1，sinω•≠0，则，即，求得ω无解．②若只有点A（，），C（，0）在函数f（x）=sin（ωx）的图象上，则有sin（ω•）=，sin（ω•）=0，sin（ω•）≠1，故有，即，求得ω的最小值为4．③若只有点B（，1）、C（，0）在函数f（x）=sinωx的图象上，则有sinω•≠，sinω=1，sinω=0，故有，即，求得ω的最小正值为10，综上可得，ω的最小正值为4，故答案为：4．14．正方体ABCD﹣A1B1C1D1的棱长为1，点P，Q，R分别是棱A1A，A1B1，A1D1的中点，以△PQR为底面作正三棱柱．若此三棱柱另一底面的三个顶点也都在该正方体的表面上，则这个正三棱柱的高h=．【考点】棱柱、棱锥、棱台的体积．【分析】分别取过C点的三条面对角线的中点，则此三点为棱柱的另一个底面的三个顶点，利用中位线定理证明．于是三棱柱的高为正方体体对角线的一半．【解答】解：连结A1C，AC，B1C，D1C，分别取AC，B1C，D1C的中点E，F，G，连结EF，EG，FG．由中位线定理可得PE A1C，QF A1C，RG A1C．又A1C⊥平面PQR，∴三棱柱PQR﹣EFG是正三棱柱．∴三棱柱的高h=PE=A1C=．故答案为．三、解答题（共6小题，满分80分）15．已知函数f（x）=﹣2sinx﹣cos2x．（1）比较f（），f（）的大小；（2）求函数f（x）的最大值．【考点】三角函数中的恒等变换应用．【分析】（1）将f（），f（）求出大小后比较即可．（2）将f（x）化简，由此得到最大值．【解答】解：（1）f（）=﹣，f（）=﹣，∵﹣＞﹣，∴f（）＞f（），（2）∵f（x）=﹣2sinx﹣cos2x．=﹣2sinx﹣1+2sin2x，=2（sinx﹣）2﹣，∴函数f（x）的最大值为3．16．某空调专卖店试销A、B、C三种新型空调，销售情况如表所示：第一周第二周第三周第四周第五周A型数量（台）11 10 15 A4A5B型数量（台）10 12 13 B4B5C型数量（台）15 8 12 C4C5（1）求A型空调前三周的平均周销售量；（2）根据C型空调前三周的销售情况，预估C型空调五周的平均周销售量为10台，当C 型空调周销售量的方差最小时，求C4，C5的值；（注：方差s2= [x1﹣）2+（x）2+…+（x n﹣）2]，其中为x1，x2，…，x n的平均数）（3）为跟踪调查空调的使用情况，根据销售记录，从第二周和第三周售出的空调中分别随机抽取一台，求抽取的两台空调中A型空调台数X的分布列及数学期望．【考点】极差、方差与标准差．【分析】（1）根据平均数公式计算即可，（2）根据方差的定义可得S2= [2（c4﹣）+]，根据二次函数性质求出c4=7或c4=8时，S2取得最小值，（3）依题意，随机变量的可能取值为0，1，2，求出P，列出分布表，求出数学期望．【解答】解：（1）A型空调前三周的平均周销售量=（11+10+15）=12台，（2）因为C型空调平均周销量为10台，所以c4+c5=10×15﹣15﹣8﹣12=15，又S2= [（15﹣10）2+（8﹣10）2+（12﹣10）2+（c4﹣10）2+（c5﹣10）2]，化简得到S2= [2（c4﹣）+]，因为c4∈N，所以c4=7或c4=8时，S2取得最小值，此时C5=8或C5=7，（3）依题意，随机变量的可能取值为0，1，2，P（X=0）=×=，P（X=1）=×+×=，P（X=2）=×=，随机变量的X的分布列，X 0 1 2P随机变量的期望E（X）=0×+1×+2×=．17．如图，等腰梯形ABCD中，AB∥CD，DE⊥AB于E，CF⊥AB于F，且AE=BF=EF=2，DE=CF=2．将△AED和△BFC分别沿DE，CF折起，使A，B两点重合，记为点M，得到一个四棱锥M﹣CDEF，点G，N，H分别是MC，MD，EF的中点．（1）求证：GH∥平面DEM；（2）求证：EM⊥CN；（3）求直线GH与平面NFC所成角的大小．【考点】直线与平面所成的角；直线与平面平行的判定．【分析】（1）连结NG，EN，则可证四边形ENGH是平行四边形，于是GH∥EN，于是GH ∥平面DEM；（2）取CD的中点P，连结PH，则可证明PH⊥平面MEF，以H为原点建立坐标系，求出和的坐标，通过计算=0得出EM⊥CN；（3）求出和平面NFC的法向量，则直线GH与平面NFC所成角的正弦值为|cos＜＞|，从而得出所求线面角的大小．【解答】证明：（1）连结NG，EN，∵N，G分别是MD，MC的中点，∴NG∥CD，NG=CD．∵H是EF的中点，EF∥CD，EF=CD，∴EH∥CD，EH=CD，∴NG∥EH，NG=EH，∴四边形ENGH是平行四边形，∴GH∥EN，又GH⊄平面DEM，EN⊂平面DEM，∴GH∥平面DEM．（2）∵ME=EF=MF，∴△MEF是等边三角形，∴MH⊥EF，取CD的中点P，连结PH，则PH∥DE，∵DE⊥ME，DE⊥EF，ME∩EF=E，∴DE⊥平面MEF，∴PH⊥平面MEF．以H为原点，以HM，HF，HP为坐标轴建立空间直角坐标系，如图所示：则E（0，﹣1，0），M（，0，0），C（0，1，2），N（，﹣，1）．∴=（，1，0），=（﹣，，1）．∴=+1×+0×1=0．∴．∴EM⊥NC．（3）F（0，1，0），H（0，0，0），G（，，1），∴=（，，1），=（0，0，2），=（﹣，，1），设平面NFC的法向量为=（x，y，z），则，即．令y=1得=（，1，0），∴cos＜＞==．∴直线GH与平面NFC所成角的正弦值为，∴直线GH与平面NFC所成角为．18．已知函数f（x）=e x（x2+ax+a）．（1）当a=1时，求函数f（x）的单调区间；（2）若关于x的不等式f（x）≤e a在[a，+∞）上有解，求实数a的取值范围；（3）若曲线y=f（x）存在两条互相垂直的切线，求实数a的取值范围．（只需直接写出结果）【考点】利用导数研究函数的单调性；利用导数研究曲线上某点切线方程．【分析】（1）当a=1时，f（x）=e x（x2+x+1），求出其导数，利用导数即可解出单调区间；（2）若关于x的不等式f（x）≤e a在[a，+∞）上有解，即x2+ax+a≤e a﹣x，在[a，+∞）上有解，构造两个函数r（x）=x2+ax+a，t（x）=e a﹣x，研究两个函数的在[a，+∞）上的单调性，即可转化出关于a的不等式，从而求得a的范围；（3）由f（x）的导数f′（x）=e x（x+2）（x+a），当a≠﹣2时，函数y=f′（x）的图象与x 轴有两个交点，故f（x）图象上存在两条互相垂直的切线．【解答】解：（1）当a=1时，f（x）=e x（x2+x+1），则f′（x）=e x（x2+3x+2），令f′（x）＞0得x＞﹣1或x＜﹣2；令f′（x）＜0得﹣2＜x＜﹣1．∴函数f（x）的单调增区间（﹣∞，﹣2）与（﹣1，+∞），单调递减区间是（﹣2，﹣1）；（2）f（x）≤e a，即e x（x2+ax+a）≤e a，可变为x2+ax+a≤e a﹣x，令r（x）=x2+ax+a，t（x）=e a﹣x，当a＞0时，在[a，+∞）上，由于r（x）的对称轴为负，故r（x）在[a，+∞）上增，t（x）在[a，+∞）上减，欲使x2+ax+a≤e a﹣x有解，则只须r（a）≤t（a），即2a2+a≤1，解得﹣1≤a≤，故0＜a≤；当a≤0时，在[a，+∞）上，由于r（x）的对称轴为正，故r（x）在[a，+∞）上先减后增，t（x）在[a，+∞）上减，欲使x2+ax+a≤e a﹣x有解，只须r（﹣）≤t（﹣），即﹣+a≤e，当a≤0时，﹣+a≤e显然成立．综上知，a≤即为符合条件的实数a的取值范围；（3）a的取值范围是{a|a≠2，a∈R}．19．已知点A（x1，y1），D（x2，y2）（其中x1＜x2）是曲线y2=4x（y≥0）上的两点，A，D两点在x轴上的射影分别为点B，C，且|BC|=2．（Ⅰ）当点B的坐标为（1，0）时，求直线AD的斜率；（Ⅱ）记△OAD的面积为S1，梯形ABCD的面积为S2，求证：＜．【考点】抛物线的简单性质．【分析】（Ⅰ）由B的坐标，可得A的坐标，又|BC|=2，可得D的坐标（3，2），运用直线的斜率公式，即可得到所求值；（Ⅱ）法一：设直线AD的方程为y=kx+m．M（0，m），运用三角形的面积公式可得S1=|m|，将直线方程和抛物线的方程联立，运用判别式大于0和韦达定理，以及梯形的面积公式可得S2，进而得到所求范围；法二：设直线AD的方程为y=kx+m，代入抛物线的方程，运用韦达定理和弦长公式，点到直线的距离公式可得三角形的面积S1=|m|，梯形的面积公式可得S2，进而得到所求范围．【解答】解：（Ⅰ）由B（1，0），可得A（1，y1），代入y2=4x，得到y1=2，又|BC|=2，则x2﹣x1=2，可得x2=3，代入y2=4x，得到y2=2，则；（Ⅱ）证法一：设直线AD的方程为y=kx+m．M（0，m），则．由，得k2x2+（2km﹣4）x+m2=0，所以，又，又注意到，所以k＞0，m＞0，所以==，因为△=16﹣16km＞0，所以0＜km＜1，所以．证法二：设直线AD的方程为y=kx+m．由，得k2x2+（2km﹣4）x+m2=0，所以，，点O到直线AD的距离为，所以，又，又注意到，所以k＞0，m＞0，所以，因为△=16﹣16km＞0，所以0＜km＜1，所以．20．已知集合Ωn={X|X=（x1，x2，…，x i，…，x n），x i∈{0，1}，i=1，2，…，n}，其中n ≥3．∀X={x1，x2，…，x i，…，x n}∈Ωn，称x i为X的第i个坐标分量．若S⊆Ωn，且满足如下两条性质：①S中元素个数不少于4个；②∀X，Y，Z∈S，存在m∈{1，2，…，n}，使得X，Y，Z的第m个坐标分量是1；则称S为Ωn的一个好子集．（1）S={X，Y，Z，W}为Ω3的一个好子集，且X=（1，1，0），Y=（1，0，1），写出Z，W；（2）若S为Ωn的一个好子集，求证：S中元素个数不超过2n﹣1；（3）若S为Ωn的一个好子集，且S中恰有2n﹣1个元素，求证：一定存在唯一一个k∈{1，2，…，n}，使得S中所有元素的第k个坐标分量都是1．【考点】命题的真假判断与应用．【分析】（1）根据好子集的定义直接写出Z，W，（2）若S为Ωn的一个好子集，考虑元素X′=（1﹣x1，1﹣x2，…，1﹣x i，…，1﹣x n），进行判断证明即可．（3）根据好子集的定义，证明存在性和唯一性即可得到结论．【解答】解：（Ⅰ）Z=（1，0，0），W=（1，1，1），…2分（Ⅱ）对于X⊆Ω，考虑元素X′=（1﹣x1，1﹣x2，…，1﹣x i，…，1﹣x n），显然X′∈Ωn，∀X，Y，X′，对于任意的i∈{1，2，…，n}，x i，y i，1﹣x i不可能都为1，可得X，X′不可能都在好子集S中…4分又因为取定X，则X′一定存在且唯一，而且X≠X′，且由X的定义知道，∀X，Y∈Ω，X′=Y′⇔X=Y…6分这样，集合S中元素的个数一定小于或等于集合Ωn中元素个数的一半，而集合Ωn中元素个数为2n，所以S中元素个数不超过2n﹣1；…8分（Ⅲ）∀X={x1，x2，…，x i，…，x n}，．∀Y={y1，y2，…，y i，…，y n}∈Ωn，定义元素X，Y的乘积为：XY={x1y1，x2y2，…，x i y i，…，x n y n}，显然XY∈Ωn，．我们证明：“对任意的X={x1，x2，…，x i，…，x n}∈S，都有XY∈S．”假设存在X，Y∈S，使得XY∉S，则由（Ⅱ）知，（XY）′={1﹣x1y1，1﹣x2y2，…，1﹣x i y i，…1﹣x n﹣1y n﹣1，1﹣x n y n}∈S，此时，对于任意的k∈{1，2，…n}，x k，y k，1﹣x k y k不可能同时为1，矛盾，所以XS∈S．因为S中只有2n﹣1个元素，我们记Z={z1，z2，…，z i，…，z n}为S中所有元素的乘积，根据上面的结论，我们知道={z1，z2，…，z i，…，z n}∈S，显然这个元素的坐标分量不能都为0，不妨设z k=1，根据Z的定义，可以知道S中所有元素的k坐标分量都为1 …11分下面再证明k的唯一性：若还有z t=1，即S中所有元素的t坐标分量都为1，所以此时集合S中元素个数至多为2n﹣2个，矛盾．所以结论成立…13分2019年9月3日。

精品文档，欢迎下载如果你喜欢这份文档，欢迎下载，另祝您成绩进步，学习愉快！2019年北京市海淀区清华大学附中中考数学二模试卷一、选择题（本大题共10小题，共30.0分）1.下列计算正确的是（）A. a6÷a2=a3B. a2+a3=a5C. (a2)3=a6D. (a+a)2=a2+a22.计算（√2+1）2019•（√2-1）2018的结果是（）A. √2+1B. √2−1C. √2D. 13.以下说法正确的有（）①正八边形的每个内角都是135°②√27与√1是同类二次根式3③长度等于半径的弦所对的圆周角为30°，当x＜0时，y随x的增大而增大．④反比例函数y=-2aA. 1个B. 2个C. 3个D. 4个4.如图，数学兴趣小组的小颖想测量教学楼前的一棵树的树高，下午课外活动时她测得一根长为1m的竹竿的影长是0.8m，但当她马上测量树高时，发现树的影子不全落在地面上，有一部分影子落在教学楼的墙壁上（如图），他先测得留在墙壁上的影高为1.2m，又测得地面的影长为2.6m，请你帮她算一下，树高是（）A. 3.25aB. 4.25aC. 4.45aD. 4.75a5.某特警部队为了选拔“神枪手”，举行了1000米射击比赛，最后由甲、乙两名战士进入决赛，在相同条件下，两人各射靶10次，经过统计计算，甲、乙两名战士的总成绩都是99.68环，甲的方差是0.28，乙的方差是0.21，则下列说法中，正确的是（）A. 甲的成绩比乙的成绩稳定B. 乙的成绩比甲的成绩稳定C. 甲、乙两人成绩的稳定性相同D. 无法确定谁的成绩更稳定6.将两个大小完全相同的杯子（如图甲）叠放在一起（如图乙），则图乙中实物的俯视图是（）A.B.C.D.7. 某剧场为希望工程义演的文艺表演有60元和100元两种票价，某团体需购买140张，其中票价为100元的票数不少于票价为60元的票数的两倍，则购买这两种票最少共需要（ ） A. 12120元 B. 12140元 C. 12160元 D. 12200元 8. 若关于x 的方程a +a a −3+3a3−a =3的解为正数，则m 的取值范围是（ ）A. a <92 B. a <92且a ≠32 C. a >−94D. a >−94且a ≠−349. 如图所示，函数y 1=|x |和a 2=13a +43的图象相交于（-1，1），（2，2）两点．当y 1＞y 2时，x 的取值范围是（ ）A. a <−1B. −1<a <2C. a >2D. a <−1或a >210. 小明在超市帮妈妈买回一袋纸杯，他把纸杯整齐地叠放在一起，如图请你根据图中的信息，若小明把100个纸杯整齐叠放在一起时，它的高度约是（ ） A. 106cm B. 110cm C. 114cm D. 116cm 二、填空题（本大题共6小题，共18.0分）11. 中国的陆地面积约为9 600000km 2，把9 600 000用科学记数法表示为______． 12. 如图，已知零件的外径为25mm ，现用一个交叉卡钳（两条尺长AC 和BD 相等，OC =OD ）量零件的内孔直径AB ．若OC ：OA =1：2，量得CD =10mm ，则零件的厚度x =______mm ． 13. 在学校组织的义务植树活动中，甲、乙两组各四名同学的植树棵数如下，甲组：9，9，11，10；乙组：9，8，9，10；分别从甲、乙两组中随机选取一名同学，则这两名同学的植树总棵数为19的概率______．14. 已知：如图，O 为坐标原点，四边形OABC 为矩形，A （10，0），C （0，4），点D是OA 的中点，点P 在BC 上运动，当△ODP 是腰长为5的等腰三角形时，则P 点的坐标为______．15. 如图，在平面直角坐标系中，点O 为原点，菱形OABC 的对角线OB 在x 轴上，顶点A 在反比例函数y =2a 的图象上，则菱形的面积为______．16. 如图，已知圆锥的高为√3，高所在直线与母线的夹角为30°，圆锥的侧面积为______．三、解答题（本大题共7小题，共56.0分） 17. 解下列方程（组）：（1）（x +3）（x +1）=1；（2）aa −1-1=3(a −1)(a +2)； （3）{3a −5a =11.2a +a =3,18. 甲、乙两名学生练习计算机打字，甲打一篇1000字的文章与乙打一篇900字的文章所用的时间相同．已知甲每分钟比乙每分钟多打5个字，问：甲、乙两人每分钟各打多少个字？19. 如图，在平面直角坐标系xOy 中，点A （12，2），B （3，n ），在反比例函数y =aa （m为常数）的图象上，连接AO 并延长与图象的另一支有另一个交点为点C ，过点A 的直线l 与x 轴的交点为点D （1，0），过点C 作CE ∥x 轴交直线l 于点E ． （1）求m 的值，并求直线l 对应的函数解析式； （2）求点E 的坐标； （3）过点B 作射线BN ∥x 轴，与AE 的交于点M （补全图形），求证：tan ∠ABN =tan ∠CBN ．20. 荆门市是著名的“鱼米之乡”．某水产经销商在荆门市长湖养殖场批发购进草鱼和乌鱼（俗称黑鱼）共75千克，且乌鱼的进货量大于40千克．已知草鱼的批发单价为8元/千克，乌鱼的批发单价与进货量的函数关系如图所示．（1）请直接写出批发购进乌鱼所需总金额y （元）与进货量x （千克）之间的函数关系式；（2）若经销商将购进的这批鱼当日零售，草鱼和乌鱼分别可卖出89%、95%，要使总零售量不低于进货量的93%，问该经销商应怎样安排进货，才能使进货费用最低？最低费用是多少？21. 学习了统计知识后，班主任王老师叫班长就本班同学的上学方式进行了一次调查统计，图1和图2是他通过收集数据后，绘制的两幅不完整的统计图，请你根据图中提供的信息，解答以下问题：（1）在扇形统计图中，计算出“步行”部分所对应的圆心角的度数；（2）求该班共有多少名学生；（3）在图1中，将表示“乘车”的部分补充完整．22.在△ABC中，AB=AC，CG⊥BA交BA的延长线于点G．一等腰直角三角尺按如图1所示的位置摆放，该三角尺的直角顶点为F，一条直角边与AC边在一条直线上，另一条直角边恰好经过点B．（1）在图1中请你通过观察、测量BF与CG的长度，猜想并写出BF与CG满足的数量关系，然后证明你的猜想；（2）当三角尺沿AC方向平移到图2所示的位置时，一条直角边仍与AC边在同一直线上，另一条直角边交BC边于点D，过点D作DE⊥BA于点E．此时请你通过观察、测量DE、DF与CG的长度，猜想并写出DE+DF与CG之间满足的数量关系，然后证明你的猜想；（3）当三角尺在（2）的基础上沿AC方向继续平移到图3所示的位置（点F在线段AC上，且点F与点C不重合）时，（2）中的猜想是否仍然成立（不用说明理由）．23.如图1，若抛物线L1的顶点A在抛物线L2上，抛物线L2的顶点B也在抛物线L1上（点A与点B不重合）我们把这样的两抛物线L1、L2互称为“友好”抛物线，可见一条抛物线的“友好”抛物线可以有很多条．（1）如图2，已知抛物线L3：y=2x2-8x+4与y轴交于点C，试求出点C关于该抛物线对称轴对称的对称点D的坐标；（2）请求出以点D为顶点的L3的“友好”抛物线L4的解析式，并指出L3与L4中y 同时随x增大而增大的自变量的取值范围；（3）若抛物y=a1（x-m）2+n的任意一条“友好”抛物线的解析式为y=a2（x-h）2+k，请写出a1与a2的关系式，并说明理由．答案和解析1.【答案】C【解析】解：A、应为a6÷a2=a4，故本选项错误；B、a2与a3，不是同类项不能合并，故本选项错误；C、（a2）3=a6，正确；D、应为（a+b）2=a2+2ab+b2，故本选项错误；故选：C．根据同底数幂的除法，底数不变，指数想减；幂的乘方，底数不变指数相乘；完全平方公式，对各选项分析判断后利用排除法求解．主要考查同底数幂的除法，幂的乘方的性质，完全平方公式，熟练掌握各种运算的法则是解题的关键．2.【答案】A【解析】解：原式=[（+1）（-1）]2018•（+1）=（2-1）2018•（+1）=+1．故选：A．先利用积的乘方得到原式=[（+1）（-1）]2018•（+1），然后利用平方差公式计算．本题考查了二次根式的混合运算：先把二次根式化为最简二次根式，然后合并同类二次根式即可．在二次根式的混合运算中，如能结合题目特点，灵活运用二次根式的性质，选择恰当的解题途径，往往能事半功倍．3.【答案】C【解析】解：①正八边形的每个内角都是：=135°，故①正确；②∵=3，=，∴与是同类二次根式；故②正确；③如图：∵OA=OB=AB，∴∠AOB=60°，∴∠C=∠AOB=30°，∴∠D=180°-∠C=150°，∴长度等于半径的弦所对的圆周角为：30°或150°；故③错误；④反比例函数y=-，当x＜0时，y随x的增大而增大．故④正确．故正确的有①②④，共3个．故选：C．①由正多边形的性质，即可求得正八边形的每个内角的度数；②首先化简，则可求得与是同类二次根式；③可求得长度等于半径的弦所对的圆周角为30°或150°；④由反比例函数的性质，可得反比例函数y=-，当x＜0时，y随x的增大而增大．此题考查了圆周角定理、正多边形的性质、同类二次根式以及反比例函数的性质．此题难度不大，注意掌握数形结合思想的应用．4.【答案】C【解析】【分析】解题的关键要知道竹竿的高与其影子的比值和树高与其影子的比值相同．此题首先要知道在同一时刻任何物体的高与其影子的比值是相同的，所以竹竿的高与其影子的比值和树高与其影子的比值相同，利用这个结论可以求出树高．【解答】解：如图，设BD是BC在地面的影子，树高为x，根据竹竿的高与其影子的比值和树高与其影子的比值相同得而CB=1.2，∴BD=0.96，∴树在地面的实际影子长是0.96+2.6=3.56，再竹竿的高与其影子的比值和树高与其影子的比值相同得，∴x=4.45，∴树高是4.45m．故选C．5.【答案】B【解析】解：∵甲的方差是0.28，乙的方差是0.21，∴S甲2＞S乙2，∴乙的成绩比甲的成绩稳定；故选：B．根据方差的意义可作出判断．方差是用来衡量一组数据波动大小的量，方差越小，表明这组数据分布比较集中，各数据偏离平均数越小，即波动越小，数据越稳定．本题考查方差的意义，方差是用来衡量一组数据波动大小的量，方差越大，表明这组数据偏离平均数越大，即波动越大，数据越不稳定；反之，方差越小，表明这组数据分布比较集中，各数据偏离平均数越小，即波动越小，数据越稳定．6.【答案】C【解析】【分析】此题主要考查了三视图的知识，俯视图是从物体的上面看得到的视图．俯视图是从上面看，可以看到上面杯子的底，是圆形，可以看到两杯子的口，也是圆形．【解答】解：从上面看，看到两个圆形，故选C．7.【答案】C【解析】解：设票价为60元的票数为x张，票价为100元的票数为y张，故可得：x≤由题意可知：x，y为正整数，故x=46，y=94，∴购买这两种票最少需要60×46+100×94=12160．故选：C．设票价为60元的票数为x张，票价为100元的票数为y张，根据题意可列出，当购买的60元的票越多，花钱就越少，从而可求解．本题考查一元一次不等式组的应用，读懂题意列出不等式关系式，本题关键是要知道当购买的60元的票越多，花钱就越少即可求解．8.【答案】B【解析】解：去分母得：x+m-3m=3x-9，整理得：2x=-2m+9，解得：x=，∵关于x的方程+=3的解为正数，∴-2m+9＞0，解得：m＜，当x=3时，x==3，解得：m=，故m的取值范围是：m＜且m≠．故选：B．直接解分式方程，再利用解为正数列不等式，解不等式得出x的取值范围，进而得出答案．此题主要考查了分式方程的解以及不等式的解法，正确解分式方程是解题关键．9.【答案】D【解析】解：当x≥0时，y1=x，又，∵两直线的交点为（2，2），∴当x＜0时，y1=-x，又，∵两直线的交点为（-1，1），由图象可知：当y1＞y2时x的取值范围为：x＜-1或x＞2．故选：D．首先由已知得出y1=x或y1=-x又相交于（-1，1），（2，2）两点，根据y1＞y2列出不等式求出x的取值范围．此题考查的是两条直线相交问题，关键要由已知列出不等式，注意象限和符号．10.【答案】A【解析】【分析】本题考查了二元一次方程组的应用，以实物图形为题目主干，图形形象直观，直接反映了物体的数量关系，仔细观察图形，可知题中有两个等量关系：单独一个纸杯的高度+3个纸杯叠放在一起高出单独一个纸杯的高度=9，单独一个纸杯的高度+8个纸杯叠放在一起高出单独一个纸杯的高度=14．根据这两个等量关系，可列出方程组，再求解．【解答】解：设每两个纸杯叠放在一起比单独的一个纸杯增高xcm，单独一个纸杯的高度为ycm，则，解得，则99x+y=99×1+7=106cm，即把100个纸杯整齐的叠放在一起时的高度约是106cm．故选A．11.【答案】9.6×106【解析】解：将9600000用科学记数法表示为9.6×106．故答案为9.6×106．科学记数法的表示形式为a×10n的形式，其中1≤|a|＜10，n为整数．确定n的值时，要看把原数变成a时，小数点移动了多少位，n的绝对值与小数点移动的位数相同．当原数绝对值＞1时，n是正数；当原数的绝对值＜1时，n是负数．本题考查科学记数法的表示方法．科学记数法的表示形式为a×10n的形式，其中1≤|a|＜10，n为整数，表示时关键要正确确定a的值以及n的值．12.【答案】2.5【解析】解：∵两条尺长AC和BD相等，OC=OD∴OA=OB∵OC：OA=1：2∴OD：OB=OC：OA=1：2∵∠COD=∠AOB∴△AOB∽△COD∴CD：AB=OC：OA=1：2∵CD=10mm∴AB=20mm∴2x+20=25∴x=2.5mm．要求零件的厚度，由题可知只需求出AB即可．因为CD和AB平行，可得△AOB∽△COD，可以根据相似三角形对应边成比例即可解答．本题只要是把实际问题抽象到相似三角形中，利用相似三角形的相似比，列出方程，通过解方程求出零件的内孔直径AB即可求得x的值．13.【答案】516【解析】解：画树状图如图：∵共有16种等可能结果，两名同学的植树总棵数为19的结果有5种结果，∴这两名同学的植树总棵数为19的概率为，故答案为：．首先根据题意画出树状图，然后由树状图求得所有等可能的结果与两名同学的植树总棵数为19的情况，再利用概率公式即可求得答案．本题考查的是用列表法或画树状图法求概率．列表法或画树状图法可以不重复不遗漏的列出所有可能的结果，列表法适合于两步完成的事件，树状图法适合两步或两步以上完成的事件．注意概率=所求情况数与总情况数之比．14.【答案】（2，4）或（3，4）或（8，4）【解析】【分析】这是一道代数与几何知识综合的开放型题，综合考查了等腰三角形和勾股定理的应用，属于策略和结果的开放，这类问题的解决方法是：数形结合，依理构图解决问题．分PD=OD（P在右边），PD=OD（P在左边），OP=OD三种情况，根据题意画出图形，作PQ垂直于x轴，找出直角三角形，根据勾股定理求出OQ，然后根据图形写出P的坐标即可．【解答】解：当OD=PD（P在右边）时，根据题意画出图形，如图所示：过P作PQ⊥x轴交x轴于Q，在直角三角形DPQ中，PQ=4，PD=OD=OA=5，根据勾股定理得：DQ=3，故OQ=OD+DQ=5+3=8，则P1（8，4）；当PD=OD（P在左边）时，根据题意画出图形，如图所示：过P作PQ⊥x轴交x轴于Q，在直角三角形DPQ中，PQ=4，PD=OD=5，根据勾股定理得：QD=3，故OQ=OD-QD=5-3=2，则P2（2，4）；当PO=OD时，根据题意画出图形，如图所示：过P作PQ⊥x轴交x轴于Q，在直角三角形OPQ中，OP=OD=5，PQ=4，根据勾股定理得：OQ=3，则P3（3，4），综上，满足题意的P坐标为（2，4）或（3，4）或（8，4）．故答案为：（2，4）或（3，4）或（8，4）.15.【答案】4【解析】【分析】本题主要考查菱形的性质及反比例函数的比例系数k的几何意义．反比例函数图象上的点与原点所连的线段、坐标轴、向坐标轴作垂线所围成的直角三角形面积S的关系，即S=|k|．连接AC交OB于D，由菱形的性质可知AC⊥OB．根据反比例函数中k的几何意义，得出△AOD的面积=1，从而求出菱形OABC的面积=△AOD的面积的4倍．【解答】解：连接AC交OB于D．∵四边形OABC是菱形，∴AC⊥OB．∵点A在反比例函数y=的图象上，∴△AOD的面积=×2=1，∴菱形OABC的面积=4×△AOD的面积=4．16.【答案】2π【解析】【分析】本题考查了圆锥的计算：圆锥的侧面展开图为一扇形，这个扇形的弧长等于圆锥底面的周长，扇形的半径等于圆锥的母线长．先利用三角函数计算出BO，再利用勾股定理计算出AB，然后利用圆锥的侧面展开图为一扇形，这个扇形的弧长等于圆锥底面的周长，扇形的半径等于圆锥的母线长和扇形的面积公式计算圆锥的侧面积．【解得】解：如图，∠BAO=30°，AO=，在Rt△ABO中，∵tan∠BAO=，∴BO=tan30°=1，即圆锥的底面圆的半径为1，∴AB==2，即圆锥的母线长为2， ∴圆锥的侧面积=×2π×1×2=2π．故答案为2π．17.【答案】解（1）去括号，得x 2+4x +3=1，移项、合并同类项，得x 2+4x +2=0．∵a =1，b =4，c =2，∴x =−a ±√a 2−4aa2a =-2±√2．∴x 1=-2+√2，x 2=-2-√2．（2）去分母，得x （x +2）-（x -1）（x +2）=3，解得x =1．经检验x =1不是原方程的解．故原方程无解；（3），①×5+②得13x =26，解得x =2，把x =2代入①得4+y =3，解得y =-1．∴方程组的解为{a =−1.a =2,【解析】（1）先把方程化为一般式，然后利用求根公式解方程；（2）先把分式方程化为整式方程，再解整式方程，然后进行检验确定原分式方程的解；（3）利用加减消元法解方程组．本题考查了解一元二次方程-公式法：用求根公式解一元二次方程的方法是公式法．也考查了解分式方程和二元一次方程组． 18.【答案】解：设乙每分钟打x 个字，则甲每分钟打（x +5）个字，根据题意得：1000a +5=900a ，解得：x =45， 经检验，x =45是原方程的解，且符合题意，∴x +5=50．答：甲每分钟打50个字，乙每分钟打45个字．【解析】设乙每分钟打x 个字，则甲每分钟打（x+5）个字，根据工作时间=工作总量÷工作效率结合甲打一篇1000字的文章与乙打一篇900字的文章所用的时间相同，即可得出关于x 的分式方程，解之经检验后即可得出结论．本题考查了分式方程的应用，找准等量关系，正确列出分式方程是解题的关键．19.【答案】解：（1）∵点A （12，2）在反比例函数y =a a （m 为常数）的图象上， ∴m =12×2=1．∴反比例函数y =a a （m 为常数）对应的函数表达式是y =1a ．设直线l 对应的函数表达式为y =kx +b （k ，b 为常数，k ≠0）．∵直线l 经过点A （12，2），D （1，0）， ∴{12a +a =2a +a =0， 解得{a =4a =−4，∴直线l 对应的函数表达式为y =-4x +4．（2）由反比例函数图象的中心对称性可知点C 的坐标为C （-12，-2）．∵CE ∥x 轴交直线l 于点E ，∴y E =y C ．∴点E 的坐标为E （32，-2）．（3）如图，作AF ⊥BN 于点G ，与射线BN 交于点G ，作CH ⊥BN 于点H ，∵点B （3，n ）在反比例函数图象上，∴n =13，∴B （3，13），G （12，13），H （-12，13）．在Rt △ABG 中，tan ∠ABH =aa aa =2−133−12=23， 在Rt △BCH 中，tan ∠CBH =aa aa =13+23+12=23， ∴tan ∠ABN =tan ∠CBN ．【解析】（1）将点A （，2）代入y=求出m 的值，再将A （，2），D （1，0）分别代入y=kx+b ，求出k 、b 的值；（2）由反比例函数图象的中心对称性可知点C 的坐标为C （-，-2），由y E =y C 求出E 点坐标．（3）作AF ⊥BN 于点G ，与射线BN 交于点G ，作CH ⊥BN 于点H ，由于点B （3，n ）在反比例函数图象上，求出n=，在Rt △ABG 中、Rt △BCH 中，求出tan ∠ABH 和tan ∠CBH 的值即可．本题考查了反比例函数综合题，涉及待定系数法求函数解析式、反比例函数的性质、三角函数的定义等知识，值得关注．20.【答案】解：（1）批发购进乌鱼所需总金额y （元）与进货量x （千克）之间的函数关系式y =24x ；（2）设该经销商购进乌鱼x 千克，则购进草鱼（75-x ）千克，所需进货费用为w 元． 由题意得：{89%×(75−a )+95%a ≥93%×75.a >40解得x ≥50．由题意得w =8（75-x ）+24x =16x +600．∵16＞0，∴w 的值随x 的增大而增大．∴当x=50时，75-x=25，W最小=1400（元）．答：该经销商应购进草鱼25千克，乌鱼50千克，才能使进货费用最低，最低费用为1400元．【解析】（1）根据所需总金额y（元）是进货量x与进价的乘积，即可写出函数解析式；（2）根据总零售量不低于进货量的93%这个不等关系即可得到关于进价x的不等式，解不等式即可求得x的范围．费用可以表示成x的函数，根据函数的增减性，即可确定费用的最小值．本题考查了一次函数的性质，利用一次函数的性质确定函数的最值，关键是正确求得x 的取值范围．21.【答案】解：（1）（1-20%-50%）×360°=108°，即“步行”部分所对应的圆心角的度数是108度．（2）20÷50%=40（人），即该班共有40名学生．（3）乘车的人数=40-20-12=8人，如图所示．【解析】（1）根据扇形统计图的定义，各部分占总体的百分比之和为1，先求出“步行”部分所占的百分比，再乘以360°得所对应的圆心角的度数；（2）由扇形统计图得知骑车人数占总人数的50%，又由频率分布直方图得知骑车人数为20，所以该班总人数为20÷50%=40．考查扇形统计图和频率分布直方图．该题将扇形统计图与频率分布直方图有机地结合在一起，能进一步理解二者之间的区别和联系．22.【答案】解：（1）BF=CG；证明：在△ABF和△ACG中∵∠F=∠G=90°，∠FAB=∠GAC，AB=AC∴△ABF≌△ACG（AAS）∴BF=CG；（2）DE+DF=CG；证明：过点D作DH⊥CG于点H（如图2）∵DE⊥BA于点E，∠G=90°，DH⊥CG∴四边形EDHG为矩形∴DE=HG，DH∥BG∴∠GBC=∠HDC∵AB=AC∴∠FCD=∠GBC=∠HDC又∵∠F=∠DHC=90°，CD=DC∴△FDC≌△HCD（AAS）∴DF=CH∴GH +CH =DE +DF =CG ，即DE +DF =CG ；（3）仍然成立．证明：过点D 作DH ⊥CG 于点H （如图3）∵DE ⊥BA 于点E ，∠G =90°，DH ⊥CG∴四边形EDHG 为矩形，∴DE =HG ，DH ∥BG ，∴∠GBC =∠HDC ，∵AB =AC ，∴∠FCD =∠GBC =∠HDC ，又∵∠F =∠DHC =90°，CD =DC ，∴△FDC ≌△HCD （AAS ）∴DF =CH ，∴GH +CH =DE +DF =CG ，即DE +DF =CG ．方法2．（2）如图2，连接AD ，S △ABC =S △ABD +S △ACD =12AB ×DE +12AC ×DF =12AB ×DE +12AB ×DF =12AB （DE +DF ），S △ABC =12AB ×CG ，∴12AB ×CG =12AB （DE +DF ），即：DE +DF =CG ．（3）同（2）的方法得出，DE +DF =CG ．【解析】（1）由于有∠F=∠G=90°，∠FAB=∠GAC ，AB=AC ，故由AAS 证得△ABF ≌△ACG ⇒BF=CG ；（2）过点D 作DH ⊥CG 于点H （如图）．易证得四边形EDHG 为矩形，有DE=HG ，DH ∥BG ⇒∠GBC=∠HDC ．又有AB=AC ⇒∠FCD=∠GBC=∠HDC ．又∠F=∠DHC=90°⇒CD=DC ，可由AAS 证得△FDC ≌△HCD ⇒DF=CH ，有GH+CH=DE+DF=CG ．（3）同（2）的方法即可得出结论．方法2、（2）（3）利用面积法即可得出结论．本题考查了等腰直角三角形的性质及全等三角形的判定和性质求解；作出辅助线是正确解答本题的关键．23.【答案】解：（1）∵抛物线L 3：y =2x 2-8x +4，∴y =2（x -2）2-4，∴顶点为（2，4），对称轴为x =2，设x =0，则y =4，∴C （0，4），∴点C关于该抛物线对称轴对称的对称点D的坐标为：（4，4）；（2）∵以点D（4，4）为顶点的L3的友好抛物线L4还过点（2，-4），∴L4的解析式为y=-2（x-4）2+4，∴L3与L4中y同时随x增大而增大的自变量的取值范围是：2≤x≤4时；（3）a1=-a2，理由如下：∵抛物线L1的顶点A在抛物线L2上，抛物线L2的顶点B也在抛物线L1上，∴可以列出两个方程，①+②得：（a1+a2）（m-h）2=0，∴a1=-a2．【解析】（1）设x=0，求出y的值，即可得到C的坐标，把抛物线L3：y=2x2-8x+4配方即可得到抛物线的对称轴，由此可求出点C关于该抛物线对称轴对称的对称点D的坐标；（2）由（1）可知点D的坐标为（4，4），再由条件以点D为顶点的L3的“友好”抛物线L4的解析式，可求出L4的解析式，进而可求出L3与L4中y同时随x增大而增大的自变量的取值范围；（3）根据：抛物线L1的顶点A在抛物线L2上，抛物线L2的顶点B也在抛物线L1上，可以列出两个方程，相加可得：（a1+a2）（m-h）2=0，可得a1=-a2本题属于二次函数的综合题，涉及了抛物线的对称变换、抛物线与坐标轴的交点坐标以及新定义的问题，解答本题的关键是数形结合，特别是（3）问根据已知条件得出方程组求解，有一定难度．。

转眼，又将一年……回顾这一年又是一年7.11秋实过后又谈冬藏心有乾坤从容淡定春暖花开播种希望养兵千日蓄势待发养兵千日蓄势待发---海淀区高三英语二模试题分析及教学建议2019.05.09各校调研期中期末一模二模摸清起点诊断与调研预测与评估终点冲刺命题功能划分依据高中英语课程标准7级要求、考试说明确定的考试内容和要求，旨在考查学生的英语基础知识和英语应用能力。

诊断激励引导预测保温笔试:100分钟120分题型和高考一致，难度接近高考力图考查英语学科的核心素养指导思想功能定位试卷命制试卷特色关键词：立德树人、核心素养、联系生活、贴近时代主要载体：力求命制这样一份卷子：不仅考知识、考能力、考素养，还能够有文化、有价值、有灵魂！语法填空语篇完形填空语篇阅读理解语篇、书面表达情境试卷结构题型题量分值权重计分语法填空101510%完形填空203020%85分阅读理解204026.6%书面表达第一节11510%35分书面表达第二节12013.3%52120100%120分第一部分知识运用（语法填空和完形）2. 凸显主干语法时态语态复合句非谓语动词形容词副词1. 凸显语篇理解题号考点1非谓语动词---动词ing 形式2介词（大小写）3时态语态---一般现在时4冠词5代词---宾语从句6代词---反身代词7非谓语动词-动词不定式8词形变化---形容词变副词9词形变化---名词复数10形容词最高级3. 合理把握难度语言、词汇、语法3篇，每篇70-90词语法填空高考命题精神传达1个细则：大小写不对扣0.5分2个注重：注重主干知识，注重基础3个度：准确度难度宽度整卷难度；与去年持平完形填空语篇的育人功能：夹叙夹议，引人深思，富有哲理，读故事的过程中启迪心灵讲评时要突出：期中402期末413一模437二模4152018高考402无题目！上下文的重要性，首尾呼应的关注故事线和情感线的脉络梳理，完形典型试题：I was studying chemistry at college because my family thought it was the key to success. One day, my professor took me aside and asked a very simple question, “Why are you in my class when it’s obvious that you have little or no 11 in chemistry?”I came up with an explanation by 12 pressure from my dad, but he knew it was just a /an 13 excuse. He gave me the following advice.11. A. achievement B. doubt C. interest D. belief12. A. blaming B. gathering C. overcoming D. reducing13. A. accurate B. weak C. direct D. innocent“Success can only be measured by oneself,and each of us is14.Your success will not be the same as mine,as your neighbor’s or your parents’.There is no secret formula(公式), no examination you have to15,and no guarantee,but there is a secret ingredient—16.To be successful in life in the broadest sense,you must pursue your passion.17it is fixing cars or exploring the world,you must be passionate about your18and set a path to achieve it.Only then will you find true19.”14.A.different B.perfect C.honest D.creative15.A.design B.pass C.control D.stand16.A.knowledge B.confidence C.passion D.effort17.A.Unless B.Because C.While D.Whether18.A.study B.need C.goal D.gift19.A.fortune B.friendship C.character D.happinessSince I was just nineteen years old, that was pretty profound advice to 20 , but I knew instinctively (本能地) that he was 21 . I made a conscious self-examination of my short life to 22 where my passion was hiding. It was so 23 that even my kid sister could have told me my true passion was music. It was in my genes. I could play the piano by ear, but had 24 considered music as a hobby.20.A.confirm B.absorb C.remember D.seek21.A.sensitive B.generous C.kind D.right22.A.choose B.report C.discover D.follow23.A.likely B.obvious C.popular D.practical24.A.only B.even C.never D.seldomCould I be a successful musician? Or a songwriter? Or a music critic? There was only one way to find out, so I took my professor’s 25 and switched to the university’s music school.I studied harmony and composition, learned how to play a clarinet(单簧管) and 26 the symphony orchestra. I felt as though I was on top of the world, and that 27 has never left me.25.A.message B.lecture C.advice D.view26.A.helped B.started C.hosted D.joined27.A.feeling B.experience C.expression D.appreciationI’m now fifty-four years old,and a very happy and28man. As I look at the walls of my small office,I still get a thrill at seeing the records I29,the photos of the famous musicians I was lucky enough to play with,and the praises from many of the finest instrumentalists in the world who I am honored to call my friends.Life was a long journey,and not a/an30one,but I followed my passion and succeeded.28.A.independent B.patient C.brave D.contented29.A.bought B.made C.received D.copied30.A.easy B.good C.ordinary D.safecontent: happy and excited be content with be content to docontented: happy and excited because your life is good第二部分阅读理解记叙文390w 记叙文380w 应用文356w 说明文343w 科技类说明文369w 记叙文376w 议论文445w 事理性说明文422w 说明文406w 事理性说明文407 议论文418w 议论文457w 说明文294w 说明文358w 说明文423w1879w 1947w 2018w 期末期中一模海淀二模：1974+415=23892018高考：1878+402=2280二模应用文408w 记叙文363w 事理性说明文457w 事理性说明文457w 说明文289w 1974w能力板块名称板块分值1获取信息（细节）142推断隐义43概括主旨64意图观点态度45词义推测26语篇结构10阅读试题讲解建议：体裁，题材，文本价值篇章结构和逻辑，精彩词句，长难句解题技巧，干扰项特点文章标题特点：主旨或引子A篇：应用文31. Which of the Pacsafe bag is a good choice for beach travel?A. The Quiksilver40L Pack.B. The Vibe 25L Backpack.C. The Quiksilver X Collab Bag.D. 25L Anti-theft Backpack.32. If you are interested in fashion, which destination should youchoose?A. Sri Lanka.B. Japan.C. Hong Kong.D. Berlin.33. What can you enjoy in all the three places mentioned?A. Beautiful beaches.B. Amazing food.C. Fascinating art.D. Cool snowboarding.34. The main purpose of the passage is to ________.A. share personal travelling experiencesB. offer practical tips on taking adventureC. present cultures in different countriesD. recommend favorable travel destinationsB篇：The Miracle of Love35. What can we learn about the newborn babies?A. The boy’s heart had stopped beating.B. The boy was 2 minutes older than the girl.C. The twins were born 14 weeks before the due date.D. The twins were expected to live for only 20 minutes.36. When the couple knew they would lose the boy, they ________.A. begged the doctor to save himB. took his shirt off and then put him in bedC. wrapped him with his blanket to keep him warmD. talked to him and made close physical contact with him37. What’s the best title for the passage?A. The Power of Hug.B. The Miracle of Love.C. The Bond Between Twins.D. The Responsibility of Parents.C篇：蒙娜丽莎的微笑D篇：What a Messy Desk Says About You42. The underlined word “immaculate” in paragraph 1 probably means _____.A. messyB. tidyC. terribleD. comfortable43. Which of the following can best explain the broken window theory?A. Chaos begets chaos.B. Misfortune may be an actual blessing.C. Bad news has wings.D. When a door shuts, a window opens.44. Which of the following will Dr. Vohs probably agree with?A. More virtue exists in organized people.B. Creativity results from tidiness and discipline.C. Disorderly surroundings help to create new ideas.D. Workers’ good habits guarantee the success of a project.45. What can we conclude from the study results?A. The naturally neat people tend to be very creative.B. A messy office will cause quite low working efficiency.C. Environments can affect people’s way of thinking and behavior.D. People’s personalities are determined by their working environments.七选五：Exam Anxiety人文关怀！46: 段尾。

2019年北京海淀区高三二模英语试卷一、语法填空（每题1.5分，共10题，计15分）1.To me, the most beautiful thing is the ocean. It is beautiful because it has a calmingeffect. When 1 （listen） to the sound of the waves, I feel peaceful. 2 the age of 10, I went to the beach for the first time. With my feet in the water, I felt totally relaxed, and the sound of the ocean really 3 （comfort） me. From then on, I often dream of floating in the ocean, feeling carefree.2.Discovering yourself plays 1 important role in inspiring your confidence. Bydoing so, you could know 2 you are weak in. And you may also realize you're quite a great person with great strengths. So when you're in a hard situation, you will believe in 3 （you） and spend the most difficult time with confidence. Otherwise you may give up and then lose everything. Therefore, the ability 4 （trust）yourself will decide your future a lot.th3.The year 2018 marks the 40anniversary of China's reform and opening-up. Thepast four decades has seen China shift its society from a farmers' community to a digital culture 1 （successful）. Under the leadership of CPC, many 2 （achievement） can be seen in every field. The life of the Chinese people has improved, with millions of people being lifted out of poverty. The country now has the world's 3 （large） high-speed rail network. And with around 800 million Internet users, China has become the world's fastest-growing online shopping market.二、完形填空（每题1.5分，共20题，计30分）4.I was studying chemistry at college because my family thought it was the key tosuccess. One day, my professor took me aside and asked a very simple question, "Why are you in my class when it's obvious that you have little or no 1 in chemistry? "I came up with an explanation by 2 pressure from my dad, but he knew it wasjust a /an 3 excuse. He gave me the following advice.1. 2. 3. 4. 5. 6. 7."Success can only be measured by oneself, and each of us is 4 . Your successwill not be the same as mine, as your neighbor's or your parents'. There is no secret formula（公式）, no examination you have to 5 , and no guarantee, but there is a secret ingredient— 6 . To be successful in life in the broadest sense, you must pursue your passion. 7 it is fixing cars or exploring the world, you must be passionate about your 8 and set a path to achieve it. Only then will you find true 9 ."Since I was just nineteen years old, that was pretty profound advice to 10 , but I knew instinctively （本能地）that he was 11 . I made a conscious self-examination of my short life to 12 where my passion was hiding. It was so 13 that even my kid sister could have told me my true passion was music. It was in my genes. I could play the piano by ear, but had 14 considered music as a hobby.Could I be a successful musician? Or asongwriter? Or a music critic? There was only oneway to find out, so I took myprofessor's 15 and switched to theuniversity's music school. I studied harmony andcomposition, learned how to play a clarinet（单簧管） and 16 the symphony orchestra. I felt as though I was on top of the world, and that 17 has never left me.I'm now fifty-four years old, and a very happy and 18 man. As I look at the walls of my small office, I still get a thrill at seeing the records I 19 , the photos of the famous musicians I was lucky enough to play with, and the praises from many of the finest instrumentalists in the world who I am honored to call my friends.Life was a long journey, and not a/an 20 one, but I followed my passion and succeeded.A.achievementB.doubtC.interestD.beliefA.blamingB.gatheringC.overcomingD.reducingA.accurateB.weakC.directD.innocentA.differentB.perfectC.honestD.creativeA.designB.passC.controlD.standA.knowledgeB.confidenceC.passionD.effortA.UnlessB.BecauseC.WhileD.Whether9.10.11.12.13.14.15.16.17.18.19.20.A.fortune B.friendship C.character D.happiness A.confirm B.absorb C.remember D.seekA.sensitiveB.generousC.kindD.rightA.chooseB.reportC.discoverD.followA.likelyB.obviousC.popularD.practical A.only B.even C.never D.seldomA.messageB.lectureC.adviceD.viewA.helpedB.startedC.hostedD.joinedA.feelingB.experienceC.expressionD.appreciation A.independent B.patient C.brave D.contented A.bought B.made C.received D.copiedA.easyB.goodC.ordinaryD.safe三、阅读理解（每题2分，共15题，计30分）5.Everyone at Pacsafe is always eager to get out in the world and enjoy new cultures,food, and experiences. With that in mind we asked a few of our top travel bugs for their best travel destination recommendations for 2019. They also included their favorite Pacsafe bag to take on the trip. Enjoy and hopefully get some ideas for your own globe-trotting adventure.Sri Lanka—Alison Hanko, Global Marketing DirectorI'm going to Sri Lanka this summer holiday and can't wait. It's close to Hong Kong where I live and I've always wanted to go. The food is supposed to be amazing. It seems really relaxing and I really want to do the Kandy to Badulla train ride, which looks just stunning. We've booked a good mix of beaches, some time in a safari tent to hopefully see elephants in the wild.For my bag, I'll most likely take the Quiksilver 40L Pack because it has the built-in wet pack for my bikinis. It's also a great size for a week-long trip in a warm climate.Japan—Ben Barras, Creative DirectorJapan is definitely my best travel destination recommendation. The culture, the streets, the architecture, the inspiration you get from all of that is amazing. The food is also fascinating. It's where I'm most planning to go. Tokyo obviously, but also visiting the mountains. You can go snowboarding, which I haven't done for years.A.The Quiksilver 40L Pack.B.The Vibe 25L Backpack.C.The Quiksilver X Collab Bag.D.25L Anti-theft Backpack.（1）A.Sri Lanka. B.Japan. C.Hong Kong. D.Berlin.（2）A.Beautiful beaches.B.Amazing food.C.Fascinating art.D.Cool snowboarding.（3）A.B.C.D.（4）I have a Vibe 25L Backpack which you can pack a lot in. The thing I like most about it is that it's compact, but still fits plenty in. I'll pair that up with a larger travel bag for the rest of my things and use the backpack to get around day to day.Berlin—Phil Hayes, Executive VP of Global DesignFor me, it's definitely Berlin. I'm particularly excited about the fashion, which I hear is pretty full on. Also the art galleries and history. Food, nightlife. Everything I've heard about Berlin is pretty cool, so I'm going to suck as much as I can out of it. World's Global Style Network had the Berlin shopping list that came out recently, so I'm going to follow that through as well.Bag wise, it will be the Quiksilver X Collab Bag. It's the 25L Anti-theft Backpack. It's normally my go-to bag for city trips because it's super easy to lock on the plane and in bars, and it's just the right amount of space.Which of the Pacsafe bag is a good choice for beach travel?If you are interested in fashion, which destination should you choose?What can you enjoy in all the three places mentioned?The main purpose of the passage is to .share personal travelling experiencesoffer practical tips on taking adventurepresent cultures in different countriesrecommend favorable travel destinations6.On March 25, 2010, Kate and David heard the words every parent dreads: Theirnewborn wasn't going to make it. Their twins—a girl and a boy—were born two minutes apart and 14 weeks premature, weighing just over two pounds each. Doctors had tried to save the boy for 20 minutes but saw no improvement. His heartbeat was nearly gone,and he'd stopped breathing. The baby had just moments to live."I saw him gasp （喘息）, but the doctor said it was no use, " Kate told the Daily Mail five years later. "I know it sounds stupid, but if he was still gasping, that was a signA.B.C.D.（1）A.B.C.D.（2）A.The Power of Hug.B.The Miracle of Love.C.The Bond Between Twins.D.The Responsibility of Parents.（3）Still, the couple knew this was likely a goodbye. In an effort to cherish her last minutes with the tiny boy, Kate asked to hold him."I wanted to meet him, and for him to know us, " Kate told Today . "We'd resigned ourselves to the fact that we were going to lose him, and we were just trying to make the most of those last, precious moments."Kate unwrapped the boy, whom the couple had already named J amie, from his hospital blanket and asked David to take his shirt off and join them in bed. The first-time parents wanted their son to be as warm as possible and hoped the skin-to-skin contact would improve his condition. They also talked to him."We were trying to persuade him to stay, " Kate told the Daily Mail . "We explained his name and that he had a twin that he had to look out for and how hard we had tried to have him."Then something miraculous happened. Jamie gasped again—and then he started breathing. Finally, he reached for his father's finger.The couple's lost boy had made it."We're the luckiest people in the world, " David told Today .Eight years later, Jamie and his sister, Emily, are happy and healthy. The couple only recently told the kids the story of their birth. "Emily burst into tears, " Kate said. "She was really upset, and she kept hugging Jamie. This whole experience makes you cherish them more."What can we learn about the newborn babies?The boy's heart had stopped beating.The boy was 2 minutes older than the girl.The twins were born 14 weeks before the due date.The twins were expected to live for only 20 minutes.When the couple knew they would lose the boy, they .begged the doctor to save himtook his shirt off and then put him in bedwrapped him with his blanket to keep him warmtalked to him and made close physical contact with himWhat's the best title for the passage?7.It's common knowledge that the woman in Leonardo daVinci's most famous painting seems to look back at observers,following them with her eyes no matter where they stand in the room. But this common knowledge turns out wrong.A new study finds that the woman in the painting is actually looking out at an anglethat's 15.4 degrees off to the observer's right—well outside of the range that people normally believe when they think someone is looking right at them. In other words, said the study author, Horstmann, "She's not looking at you." This is somewhat ironic, because the entire phenomenon of a person's gaze （凝视）in a photograph or painting seeming to follow the viewer is called the "Mona Lisa effect" . That effect is absolutely real, Horstmann said. If a person is illustrated or photographed looking straight ahead, even people viewing the portrait from an angle will feel they are being looked at. As long as the angle of the person's gaze is no more than about 5 degrees off to either side, the Mona Lisa effect occurs.This is important for human interaction with on-screen characters. If you want someone off to the right side of a room to feel that a person on-screen is looking at him or her, you don't cut the gaze of the character to that side—surprisingly, doing so would make an observer feel like the character isn't looking at anyone in the room at all.Instead, you keep the gaze straight ahead.Horstmann and his co-author were studying this effect for its application in the creation of artificial-intelligence avatars（虚拟头像） when Horstmann took a long look at the "Mona Lisa" and realized she wasn't looking at him.To make sure it wasn't just him, the researchers asked 24 people to view images of the "Mona Lisa" on a computer screen. They set a ruler between the viewer and the screen and asked the participants to note which number on the ruler intersected Mona Lisa's gaze. To calculate the angle of Mona Lisa's gaze as she looked at the viewer, they moved the ruler farther from or closer to the screen during the study. Consistently, the researchers found, participants judged that the woman in the "Mona Lisa" portrait was not looking straight at them, but slightly off to their right.So why do people repeat the belief that her eyes seem to follow the viewer?Horstmann isn't sure. It's possible, he said, that people have the desire to be looked at, so they think the woman is looking straight at them. Or maybe the people who first coined the term "Mona Lisa effect" just thought it was a cool name.A.B.C.D.A. B.C. D.（2）A.B.C.D.（3）A.B.C.D.（4）attracts the viewers to look backseems mysterious because of her eyesfixes her eyes on the back of the viewerslooks at the viewers wherever they standWhat gaze range in a painting will cause the Mona Lisa effect?The experiment involving 24 people was conducted to .confirm Horstmann's beliefcreate artificial-intelligence avatarscalculate the angle of Mona Lisa's gazeexplain how the Mona Lisa effect can be appliedWhat can we learn from the passage?Horstmann thinks it's cool to coin the term "Mona Lisa effect" .The Mona Lisa effect contributes to the creation of artificial intelligence.Feeling being gazed at by Mona Lisa may be caused by the desire for attention.The position of the ruler in the experiment will influence the viewers'judgement.8.What a Messy Desk Says About YouFor some time, psychologists have been studying how personality traits affect health and health-related choices. Not surprisingly, they have found that people blessed with innate conscientiousness, meaning that they are organized and predictable,typically eat better and live longer than people who are disorderly. They also tend to have immaculate offices.A.messyB.tidyC.terriblefortable（1）（2）What has been less clear is whether neat environments can produce good habits even in those who aren't necessarily innately conscientious. To find out, researchers at the University of Minnesota conducted a series of experiments. In the first experiment,they randomly assigned a group of college-age students to spend time in two office spaces, one of which was very neat, the other wildly cluttered （乱堆） with papers and other work-related stuff. The students spent their time filling out questionnaires unrelated to the study. After 10 minutes, they were told they could leave with an apple or a chocolate bar. Those students who sat in the orderly office were twice as likely to choose the apple as those who sat among the mess.A second experiment, however, found that working in chaos has its advantages, too.In this one, college students were placed in a messy or a neat office and asked to dream up new uses for Ping-Pong balls. Those in messy spaces generated ideas that were significantly more creative, according to two independent judges, than those in offices where stacks of papers and other objects were neatly arranged.The results were something of a surprise, says Dr. Vohs, the leader of the study. Few previous studies found much virtue in disorder. The broken window theory, proposed decades ago, holds that even slight disorder and neglect can encourage indifference and poor discipline.But in the study by Dr. Vohs, disordered offices encouraged originality and a search for novelty. In the final portion of the study, adults were given the choice of adding a health "boost" to their lunchtime smoothie that was labeled either "new" or "classic".The volunteers in the messy space were far more likely to choose the new one; those in the tidy office generally chose the classic version."Disorderly environments seem to inspire breaking free of tradition, " Dr. Vohs and her co-authors conclude in the study, "which can produce fresh insights."The implications of these findings are also practical. "My advice would be, if you need to think outside the box for a future project" , Dr. Vohs says, "Then let the clutter rise and free your imagination. But if your primary goal is to eat well or to go to the gym, pick up around your office first. By doing this, the naturally messy can acquire some of the discipline of the conscientious."The underlined word "immaculate" in paragraph 1 probably means .Which of the following can best explain the broken window theory?B.C.D.A.B.C.D.（3）A.B.C.D.（4）Misfortune may be an actual blessing.Bad news has wings.When a door shuts, a window opens.Which of the following will Dr. Vohs probably agree with?More virtue exists in organized people.Creativity results from tidiness and discipline.Disorderly surroundings help to create new ideas.Workers' good habits guarantee the success of a project.What can we conclude from the study results?The naturally neat people tend to be very creative.A messy office will cause quite low working efficiency.Environments can affect people's way of thinking and behavior.People's personalities are determined by their working environments.四、七选五（每题2分，共5题，计10分）9.Exam AnxietyHas this ever happened to you? You've been studying hard for your midterm, but when you walk into your exam, your mind goes blank, your heart races fast, you get sweaty palms and find it hard to breathe. 1Everyone feels stressed during exams. Usually, it results from a fear of failure, lack of adequate preparation time and bad experiences taking tests in the past. This is normal and often helps you work harder, think faster and generally improve your performance. 2 You may also feel that other people are managing the exam better than you. This can cause you to feel that your mind has "gone blank" on information you know you have revised.3 Some choose to ignore the problem, while others don't review because they think they will do badly anyway and even miss exams due to the anxiety. It can also be really easy to think that if you don't try and then you fail, you won't feel as bad as if you fail after trying really hard.So what can you do to fight against the negative mindset and stay calm before and during your test? 4 Yes, this seems obvious, but it's worth repeating. If you feel confident that you've prepared thoroughly, you'll feel more confident walking into the test. The second tip is simple: just start. The blank page can maximize yourA.B.C.D.E.F.G.anxiety. 5 You can always go back and change things later if needed, but a few quick answers can get the ball rolling. Besides, allocating（分配） your time is equally important. Look through the whole test before getting started. Mentally allocate how much time you'll spend on each section. If there's time to recheck, even better.The first thing you should do is to be prepared.People often deal with exam stress in many unhelpful ways.If these classic signs of exam anxiety sound familiar, you're not alone!Therefore, people need an appropriate amount of pressure to help deal with exams.Realizing time is almost up and that there's still a lot of blank space will make you desperate.However, if you are overly anxious about the result, you may be unable to focus on your work.After you get the paper, dive right in by getting some questions done to build up your confidence.五、书面表达（共两题，35分）10.假设你是红星中学高三学生李华，得知2020年第18届世界中学生运动会（World MiddleSchool Games） 将在中国福建晋江举行，组委会正面向全国招募志愿者。

北京市海淀区2019年九年级统一测试历史试卷答案及评分参考2019.6第一部分选择题(共45分)第二部分非选择题（4小题，共45分）31.（10分）（1）（3分）为人类的幸福而献身（为人类解放而不懈奋斗）(1分)与恩格斯联合发表了《共产党宣言》，创立了科学社会主义理论（或创立了马克思主义，推动了国际工人运动的发展）；出版了《资本论》，为无产阶级革命斗争提供了强有力的理论武器等；指导并领导了国际工人运动。

（2分，三点中任意一点即可）（2）（4分）A：③ B：① C：② D：②④（3）（2分) 世界联系加强，出现了政治多极化和经济全球化；科技革命与产业革命不断发展；人类生存面临很多严重问题，需要共同面对;和平发展是时代主题。

（四点中任意两点即可）（4）（1分）将马克思主义普遍真理与各国国情相结合；理论联系实际；事实求是；与时俱进。

32.（9分）(1)（4分）①经济交流（经贸、商业交流）之路②印度或南亚③印刷术④民族迁移（族群、人口迁移）（2）（2分）欧洲人占据了世界体系中心地位；全球贸易为资本主义世界生产体系服务；商贸伴随着殖民掠夺与扩张；东方发展从属于西方。

（四点中有2点即可）(3) (1分)A②B①【评分标准】（2分）史实准确，说明准确完整。

（1分）史实准确，说明不完整或有部分失误。

（0分）史实不准确，说明错误或无说明。

33.（本题13分）（1）(4分)①√②③√④×（1）（2分）西式生活方式在节日开始流行；增加新的纪念节日，活动内容丰富；节日活动充分吸收科技成果；革命成为节日的主题；节日礼仪趋向简化；（2分，任意2点即可） （3）（2分）法国1789年7月14日，巴黎群众攻克了象征封建统治的巴士底狱，从而揭开法国大革命序幕。

美国1776年7月4日大陆会议在费城正式通过《独立宣言》，标志着美国脱离英国殖民统治独立。

（一个国家2分，不重复计分。

事件和历史意义两方面各1分） （4）（4分）第二栏【评分标准】（3分）主题具体建议与所选资料序号逻辑关系清晰、准确。

B海淀区九年级第二学期期末练习数 学2019.06学校 姓名 准考证号一、选择题（本题共16分，每小题2分）第1-8题均有四个选项，符合题意的选项只有一个．．． 1．27-的立方根是A ．3-B ．3C ．3±D2．如图，直线AB ，CD 交于点O ，射线OM 平分∠AOC ，若∠BOD =80°， 则∠BOM 等于 A ．140°B ．120°C ．100°D ．80°3．科学家在海底下约4.8公里深处的沙岩中，发现了一种世界上最小的神 秘生物，它们的最小身长只有0.000 000 02米，甚至比已知的最小细菌 还要小．将0.000 000 02用科学记数法表示为A ．-7210⨯B ．-8210⨯C ．-9210⨯D ．-10210⨯ 4．实数a，b 在数轴上的对应点的位置如图所示，若a c b -<<，则实数c 的值可能是A ．12-B ．0C ．1D ．725．图1是矗立千年而不倒的应县木塔一角，它使用了六十多种形态各异的斗栱（dǒu gǒng ）．斗栱是中国古代匠师们为减少立柱与横梁交接处的剪力而创造的一种独特的结构，位于柱与梁之间，斗栱是由斗、升、栱、翘、昂组成，图2是其中一个组成部件的三视图，则这个部件是A ．B ．C ．D ．6．已知a b >，则下列不等式一定成立的是A ．55a b ->-B ．55ac bc >C ．55a b -<+D ．55a b +>-7．下面的统计图反映了2013-2018年中国城镇居民人均可支配收入与人均消费支出的情况．（数据来源：国家统计局）根据统计图提供的信息，下列推断不合理．．．的是 A ．2013-2018年，我国城镇居民人均可支配收入和人均消费支出均逐年增加 B ．2013-2018年，我国城镇居民人均可支配收入平均每年增长超过2400元 C ．从2015年起，我国城镇居民人均消费支出超过20000元D ．2018年我国城镇居民人均消费支出占人均可支配收入的百分比超过70%图1 图28．如图，小宇计划在甲、乙、丙、丁四个小区中挑选一个小区租住，附近有东西向的交通主干道a 和南北向的交通主干道b ，若他希望租住的小区到主干道a 和主干道b 的直线距离之和最小，则下图中符合他要求的小区是 A ．甲 B ．乙 C ．丙 D ．丁二、 填空题（本题共16分，每小题2分） 9．当_______x =时，代数式2x x-的值为0． 10．如图，在△ABC 中，∠BAC =90°，D 为BC 中点，若AD =52，AC =3，则AB 的长为 ．11．如图，在⊙O 中，弦BC 与半径OA 相交于点D ，连接AB ，OC ．若∠A =60°，∠ABC =20°，则∠C 的度数为 . 12．如果4m n =+，那么代数式2+m n mnn m m n ⎛⎫-⋅⎪⎝⎭的值是___________． 13．如图，在△ABC 中，P ，Q 分别为AB ，AC 的中点．若1APQ S =△，则PBCQS 四边形=______．（第11题图）（第13题）Q P CBADCBA14．某学习小组做抛掷一枚纪念币的实验，整理同学们获得的实验数据，如下表．抛掷次数 50 100 200 500 1000 2000 3000 4000 5000 “正面向上”的次数193868168349707106914001747“正面向上”的频率0.3800 0.3800 0.3400 0.3360 0.3490 0.3535 0.3563 0.3500 0.3494 下面有三个推断：①在用频率估计概率时，用实验5000次时的频率0.3494一定比用实验4000次时的频率0.3500更准确；②如果再次做此实验，仍按上表抛掷的次数统计数据，那么在数据表中，“正面向上”的频率有更大的可能仍会在0.35附近摆动；③通过上述实验的结果，可以推断这枚纪念币有很大的可能性不是质地均匀的． 其中正确的是___________．15．按《航空障碍灯（MH/T6012-1999）》的要求，为保障飞机夜间飞行的安全，在高度为45米至105米的建筑上必须安装中光强航空障碍灯(Aviation Obstruction light)．中光强航空障碍灯是以规律性的固定模式闪光．在下图中你可以看到某一种中光强航空障碍灯的闪光模式，灯的亮暗呈规律性交替变化，那么在一个连续的10秒内，该航空障碍灯处于亮的状态的时间总和最长可达___________秒．16．右图是在浦东陆家嘴明代陆深古墓中发掘出来的宝玉——明白玉幻方．其背面有方框四行十六格，为四阶幻方（从1到16，一共十六个数目，它们的纵列、横行与两条对角线上4个数相加之和均为34）．小明探究后发现，这个四阶幻方中的数满足下面规律：在四阶幻方中，当数a ，b ，c ，d 有如图1的位置关系时，均有a +b =c +d =17．如图2，已知此幻方中的一些数，则x 的值为___________．三、解答题（本题共68分，第17-22题，每小题5分；第23-26题，每小题6分；第27-28题，每小题7分）解答应写出文字说明、演算步骤或证明过程．17．计算： 04cos45(1)822︒+-+-－． 状态/秒暗亮图1 图218．解不等式组：()48211032x x x x -<-⎧⎪⎨+>⎪⎩，．19．下面是小宇设计的“作已知直角三角形的中位线”的尺规作图过程．已知：在△ABC 中，∠C =90°．求作：△ABC 的中位线DE ，使点D 在AB 上，点E 在AC 上． 作法：如图，① 分别以A ，C 为圆心，大于12AC 长为半径画弧，两弧交于P ，Q ② 作直线PQ ，与AB 交于点D ，与AC 交于点E ． 所以线段DE 就是所求作的中位线． 根据小宇设计的尺规作图过程，（1）使用直尺和圆规，补全图形；（保留作图痕迹） （2）完成下面的证明．证明：连接P A ，PC ，QA ，QC ， DC ，∵ P A =PC ，QA =_________，∴ PQ 是AC 的垂直平分线（________）（填推理的依据）． ∴ E 为AC 中点，AD =DC ． ∴ ∠DAC =∠DCA ，又在Rt △ABC 中，有∠BAC +∠ABC =90°，∠DCA +∠DCB =90°． ∴ ∠ABC =∠DCB （________）（填推理的依据）． ∴ DB =DC ． ∴ AD =BD =DC ． ∴ D 为AB 中点．∴ DE 是△ABC 的中位线．20．关于x 的一元二次方程22(21)10x k x k --+-=，其中0k <． （1）求证：方程有两个不相等的实数根； （2）当1k =-时，求该方程的根．21．如图，在□ABCD 中，∠BAD 的角平分线交BC 于点E ，交DC 的延长线于点F ，连接DE ．（1）求证：DA =DF ；（2）若∠ADE =∠CDE =30°，DE = 求□ABCD 的面积．22．如图，AB 是⊙O 的直径，P A ，PC 与⊙O 分别相切于点A ，C ，连接AC ，BC ，OP ，AC与OP 相交于点D ．（1）求证：90B CPO ∠+∠=︒； （2）连结BP ，若AC ＝125，sin ∠CPO ＝35，求BP 的长．23．如图，在平面直角坐标系xOy 中，直线y x b =+与x 轴、y 轴分别交于点A ，B ，与双曲线2y x=的交点为M ，N ． （1）当点M 的横坐标为1时，求b 的值；（2）若3MN AB ≤，结合函数图象，直接写出b 的取值范围．24．有这样一个问题：探究函数2118y x x=-的图象与性质．小宇从课本上研究函数的活动中获得启发，对函数2118y x x=-的图象与性质进行了探究．下面是小宇的探究过程，请补充完整：（1）函数2118y x x=-的自变量x 的取值范围是 ；（2）如图，在平面直角坐标系xOy 中，完成以下作图步骤：①画出函数214y x =和2y x=-的图象；②在x 轴上取一点P ，过点P 作x 轴的垂线l ，分别交函数214y x =和2y x=-的图象于点M ，N ，记线段MN 的中点为G ；③在x 轴正半轴上多次改变点P 的位置，用②的方法得到相应的点G ，把这些点用平滑的曲线连接起来，得到函数2118y x x=-在y 轴右侧的图象．继续在x轴负半轴上多次改变点P 的位置，重复上述操作得到该函数在y 轴左侧的图象．（3）结合函数2118y x x=-的图象， 发现：①该函数图象在第二象限内存在最低点，该点的横坐标约为 （保留小数点后一位）；②该函数还具有的性质为：_________________（一条即可）．25．某学校共有六个年级，每个年级10个班，每个班约40名同学．该校食堂共有10个窗口，中午所有同学都在食堂用餐．经了解，该校同学年龄分布在12岁（含12岁）到18岁（含18岁）之间，平均年龄约为15岁．小天、小东和小云三位同学，为了解全校同学对食堂各窗口餐食的喜爱情况，各自进行了抽样调查，并记录了相应同学的年龄，每人调查了60名同学，将收集到的数据进行了整理．小天从初一年级每个班随机抽取6名同学进行调查，绘制统计图表如下：小东从全校每个班随机抽取1名同学进行调查，绘制统计图表如下：小云在食堂门口，对用餐后的同学采取每隔10人抽取1人进行调查，绘制统计图表如下：根据以上材料回答问题：（1）写出图2中m的值，并补全图2；（2）小天、小东和小云三人中，哪个同学抽样调查的数据能较好地反映出该校同学对各窗口餐食的喜爱情况，并简要说明其余同学调查的不足之处；（3）为使每个同学在中午尽量吃到自己喜爱的餐食，学校餐食管理部门应为______窗口尽量多的分配工作人员，理由为_________________________________ __．26．在平面直角坐标系xOy 中，抛物线C ：223y ax ax =-+与直线l ：y kx b =+交于A ，B 两点，且点A 在y 轴上，点B 在x 轴的正半轴上． （1）求点A 的坐标；（2）若1a =-，求直线l 的解析式； （3）若31k -<<-，求a 的取值范围．27．已知C 为线段AB 中点，ACM α∠=．Q 为线段BC 上一动点（不与点B 重合），点P在射线CM 上，连接P A ，PQ ，记BQ kCP =． （1）若60α=︒，1k =，①如图1，当Q 为BC 中点时， 求PAC ∠的度数； ②直接写出P A 、PQ 的数量关系；（2）如图2，当45α=︒时．探究是否存在常数k ，使得②中的结论仍成立？若存在，写出k 的值并证明；若不存在，请说明理由．图1 图228．对于平面直角坐标系xOy 中的两个图形M 和N ，给出如下定义：若在图形M 上存在一点A ，图形N 上存在两点B ，C ，使得△ABC 是以BC 为斜边且BC =2的等腰直角三角形，则称图形M 与图形N 具有关系()M N ，φ．（1）若图形X 为一个点，图形Y 为直线y x =，图形X 与图形Y 具有关系()X Y ，φ，则点1(0P ，2(11)P ，，3(22)P -，中可以是图形X 的是_____； （2）已知点()20P ，，点()02Q ，，记线段PQ 为图形X ． ①当图形Y 为直线y x =时，判断图形X 与图形Y 是否既具有关系()X Y ，φ又具有关系()Y X ，φ，如果是，请分别求出图形X 与图形Y 中所有点A 的坐标；如果不是，请说明理由；②当图形Y 为以(0)T t ，为半径的⊙T 时，若图形X 与图形X 具有关系()X Y ，φ，求t 的取值范围．海淀区九年级第二学期期末练习参考答案数 学 2019．06一、选择题（本题共16分，每小题2分）二、填空题（本题共16分，每小题2分）9．2 10．4 11．40 12．813．3 14．②③ 15．7 16．1三、解答题（本题共68分，第17-22题，每小题5分；第23-26题，每小题6分；第27-28题，每小题7分） 17．（本小题满分5分） 解：原式=412?-（ =3-18．（本小题满分5分）解：原不等式组为482(1)1032x x x x ì-<-ïí+>ïî，．①②解不等式①，得3x <． 解不等式②，得2x <． ∴原不等式组的解集为2x <．19．（本小题满分5分）（1）补全的图形如图所示：（作等弧交于两点P ,Q 点1分，直线PQ 1分）（2）QC到线段两端点距离相等的点在线段的垂直平分线上 等角的余角相等20．（本小题满分5分）解：（1）依题意可知，22(21)4(1)54k k k ∆=---=-, ∵0k <,∴0D>．∴方程有两个不相等的实数根. （2）当1k =-时，方程为230x x +=． 解得123,0x x =-=．21．（本小题满分5分）（1）证明：∵ 四边形ABCD 为平行四边形，∴ AB ∥CD ． ∴ ∠BAF =∠F ． ∵AF 平分∠BAD ， ∴ ∠BAF =∠DAF ． ∴ ∠F =∠DAF ． ∴ AD =FD ．（2）解： ∵∠ADE =∠CDE =30°，AD =FD ，∴ DE ⊥AF ．∵tan ∠ADE＝AE DE =，DE = ∴2AE =．∴2ABCD ADE S S AE DE ==⋅=Y V ．22．（本小题满分5分） （1）证明：连接OC ，如图.∵ P A ，PC 与⊙O 分别相切于点A ，C ，∴ OC ⊥PC ，OA ⊥P A ，∠APC =2∠CPO ．∴ ∠OCP =∠OAP =90°．∵ ∠AOC +∠APC +∠OCP +∠OAP =360°， ∴ ∠AOC +∠APC =180°． ∵ ∠AOC =2∠B ， ∴ 90B CPO ∠+∠=︒．（2）解： 连接BP ，如图． ∵ AB 是⊙O 的直径， ∴∠ACB =90°．∴∠ABC+∠BAC =90°． ∵90ABC CPO ∠+∠=︒，∴ ∠BAC =∠CPO =∠APO .∵AC ＝125，sin ∠BAC ＝35,∴ 3AB =,32OA =． ∵32OA =，sin ∠APO ＝35,∴ 2AP =.∴PB =23．（本小题满分6分） 解：（1）∵点M 是双曲线2y x=上的点，且点M 的横坐标为1， ∴点M 的坐标为（1，2）．∵点M 是直线y x b =+上的点，∴1b =．（2）当1b =?时，满足3MN AB =，结合函数图像可得，b 的取值范围是1b ≤-或1b ≥．24．（本小题满分6分） （1）0x ≠； （2）（3）① 1.6-；(在 1.9 1.3至--之间即可)②该函数的其它性质：当0x >时，y 随x 的增大而增大. （写出一条即可）25．（本小题满分6分）解：（1）15.0（2）小东． 理由：小天调查的不足之处：仅对初一年级抽样，不能代表该学校学生总体的情况； 小云调查的不足之处：抽样学生的平均年龄为16岁，远高于全校学生的平均年龄，不能代表该学校学生总体情况.（3）6号和8号（或者只有8；或者5，6，8）．理由：从小东的调查结果看，这几个窗口受到更多的同学的喜爱，应该适当增加这几个窗口的工作人员.注意：（2）（3）的答案不唯一 26．（本小题满分6分）（1）∵ 抛物线C ：223y ax ax =-+与y 轴交于点A ，∴ 点A 的坐标为（0，3）. （2）当1a =-时，抛物线C 为223y x x =-++.∵ 抛物线C 与x 轴交于点B ，且点B 在x 轴的正半轴上，∴ 点B 的坐标为（3，0）. ∵ 直线l ：y kx b =+过A ，B 两点，∴ 330.b k b =⎧⎨+=⎩，解得1,3.k b =-⎧⎨=⎩ ∴ 直线l 的解析式为3y x =-+.（3）如图，当0a >时，当3a =时，抛物线C 过点B （1，0），此时3k =-. 结合函数图象可得3a >. 当0a <时，当1a =-时，抛物线C 过点B （3，0），此时1k =-. 结合函数图象可得1a <-.综上所述，a 的取值范围是1a <-或3a >.27．（本小题满分7分）（1）①解：在CM 上取点D ，使得CD =CA ，连接AD .∵ 60ACM ∠=︒， ∴△ADC 为等边三角形． ∴60DAC ∠=︒.∵C 为AB 的中点，Q 为BC 的中点， ∴AC =BC=2BQ . ∵BQ =CP ,∴AC =BC=CD =2CP . ∴AP 平分∠DAC . ∴∠P AC =∠P AD =30°. ② P A =PQ .（2）存在k =.证明：过点P 作PC 的垂线交AC 于点D . ∵45ACM ∠=︒，∴ ∠PDC =∠PCD=45°.∴PC =PD ，∠PDA =∠PCQ =135°.∵CD =，BQ =，∴CD = BQ . ∵AC =BC ，∴AD = CQ . ∴△P AD ≌△PQC. ∴P A =PQ .28．（本小题满分7分） （1）1P ； （2）① 是， 图1如图1，在直线y x =上取点B ，C ，且BC =2，则满足△ABC 是以BC 为斜边的等腰直角三角形的点A ，在到直线y x =距离为1的两条平行直线上. 这两条平行直线与PQ分别交于1A ，2A 两点. 故图形X 与图形Y 满足(),X Y ϕ.直线y x =与线段PQ 交于点M （1，1），过点M 作MH ⊥y 轴于H ，与1A B 交于点N ，则11MA =，2MN =，可得1A （12-，12+）. 同理可求得2A （12+，12-）. 如图2，在线段PQ 上取点B ，C ，且BC =2，则满足△ABC 是以BC 为斜边的等腰直角三角形的点A 在图中的两条线段上，这两条线段与直线y x =交于3A ，4A 两点. 故图形X 与图形Y 满足(),Y X ϕ.同上可求得3A （12-，12-），4A （12+，12+）.② 1t ≤≤-或25t ≤≤.。

2019年北京市海淀区高三二模英语试卷+内容评析海淀区高三年级第二学期期末练习英语2019.05本试卷共10页，共120分。

考试时长100分钟。

考生务必将答案答在答题纸上，在试卷上作答无效。

考试结束后，将答题纸交回。

1、试卷整体分析此次高三英语二模练习，简单概括为：一“旧”，两“新”。

一“旧”：即指试题难度总体与往年持平，没有太大差异，符合最近几年高考命题难度的总趋势。

两“新”：第一“新”，即指试题题型有所变化，删掉了原来的单项选择，增加了“语法填空”这一新题型，这也是此次二模练习与往年最大的不同；第二“新”是指，本次练习试题更富有时代气息，尤其是阅读理解、书面表达，紧紧围绕高考考试说明的命题方向。

题型分析：语法填空：共有三个文段，每个文段含3-4个空格，共10个空格，考查动词时态、语态，非谓语动词，定语从句，名词从句，名词，形容词，介词等语法。

作为新题型，本次练习延续了“新题型不难”这一定律，甚至可以说非常简单。

第一部分：知识运用（共两节，45分）第一节语法填空（共10小题；每小题1.5分, 共15分）阅读下列短文，根据短文内容填空。

在未给提示词的空白处仅填写1个适当的单词，在给出提示词的空白处用括号内所给词的正确形式填空。

ATo me, the most beautiful thing is the ocean. It is beautiful because it has a calming effect.When 1 (listen) to the sound of the waves, I feel peaceful. 2 the age of 10, I went to the beach for the first time. With my feet in the water, I felt totally relaxed, and the sound of the ocean really 3 (comfort)me. From then on, I often dream of floating in the ocean, feeling care free.BDiscovering yourselfplays 4 important role in inspiring your confidence. By doing so, you couldknow 5 you are weak in. And you may also realize you’re quite a great person with great strengths. So when you’re in a hard situation, you will believe in 6 (you) and spend the most difficult time with confidence. Otherwise you may give up and then lose everything. Therefore, theability 7 (trust) yourself will decide your future a lot.CThe year 2018 marks the 40th anniversary of China’s reform and opening-up. The past four decades has seen China shift its society from a farmers’ community to a digital culture 8 (successful). Under the leadership of CPC,many 9 (achievement) can be seen in every field. The life of the Chinese people has improved, with millions of people being lifted out of poverty. Thecountry now has theworld’s10 (large) high-speed rail network. And with around 800 million Internet users, China has become the world’s fastest-growing online shopping market.参考答案：第一部分：知识运用（共两节，45分）第一节语法填空（共1小题；每小题1.5分，共15分1.listening2.At3. comforted4.an5. what6.yourself7. to trust 8.successfully9. achievements 10. largest注意：第2小题首字母小写得1分；第6小题yourselves也得1.5分。

2019年北京海淀区初三二模英语试卷一、单项选择（共12小题，每小题0.5分，共6分）1. A.His B.Her C.My D.YourThis is my little sister. name is Tina.2. A.for B.to C.of D.on—Excuse me, sir. Where is the cinema?—It's the fourth floor.3. A.When B.Where C.How D.Why一 do you usually go to school, Kate?—On foot.4. A.or B.so C.and D.but—Hurry up, you will miss the first train of Beiing S2!—OK. I can't wait to see the Great Wall.5. A.must B.might C.can D.couldI'm sorry I go now. My piano lesson will start in ten minutes.6. A.wonderfulB.more wonderfulC.most wonderfulD.the most wonderfulHong Kong-Zhuhai-Macao Bridge is bridge I have ever seen.7. A.buys B.bought C.has bought D.will buy—What a nice silk scarf!一Thanks. My aunt it for me when she travelled in Hangzhou.8.Please turn the TV down. Tony for the math test now.A.studiesB.studiedC.is studyingD.was studying9. A.tells B.tell C.has told D.is tellingEvery morning, Nick's mother him to drink more water at school.10.A.lived B.was living C.has lived D.will liveHenry in London for a long time. He knows a lot about the city.pletesB.was completedC.will completeD.will be completedA large forest park near the lake next year.12.A.how often do you exerciseB.how often yon exerciseC.how often did you exerciseD.how often you exercised—Can you tell me ?—I usually exercise three times a week.二、完形填空（共8小题，每小题1分，共8分）13.Have you ever blown dandelion seeds to make a wish? Me too. Have you evereaten a dandelion（蒲公英）? Me neither."Time to go, Athena, " Mama said from the sidewalk.She 1 open the car door waiting for me. I stepped in the carwith my book. "She knew I didn't eat dandelions. Why did I have topick them with my family every spring? " I thought.My father and grandmother smiled from the front seats of the car, turned and 2 to Brigid, the girl who had just moved in. She stood across the street and watched. I was glad she didn't ask where we were going.We rode into the 3 , not too far from our house just outside Chicago. I set down my book feeling the warm breeze. I told the wind, "I hope we are not there yet."Ⅰhad never seen anyone in the field with us, but I was always 4 that someone would notice us picking dandelions. People in America pulled dandelions from their yards. What would the new neighbors think if they found out our family ate weeds（杂草）?1. 2. 3. 4. 5. 6. 7. 8.We drove west until the houses stopped. Then we stopped. We walked through alarge field. Hundreds of yellow flowers 5 over the soft earth. I looked for a place to hide."What's the matter with you, Athena? " Granny asked. "Nothing, " I said. "But whydo we eat dandelions? No one else does.""The best 6 in the world." Grannyanswered.It seemed to take hours to fill the bags. By the time we were ready to leave, we had enough dandelions. On the way home, Mama and Granny talked about hosting a dinner party for the new neighbors.The night of the party, Brigid arrived with her parents. Mama served octopus with onions, peppers stuffed with lamb and rice, and horta made of dandelions. Our guests ate everything. Brigid tasted the octopus and the lamb. Then she put her fork on the horta. "Wait!" I said. Too late. "You ate the dandelions!" I told her 7 "Not had, "she said and ate another bite. We both laughed.After dinner, Brigid and I went to the backyard. The stars reminded me of dandelions in the soft field. I closed my eyes and made a 8 : to be as open-minded as my family and my new friends.A.pushedB.brokeC.heldD.knockedA.wavedB.ranC.talkedD.droveA.cityB.countryC.factorypanyA.gladB.curiousC.excitedD.afraidA.walkedB.fellC.spreadD.climbedA.woodB.foodC.cottonD.cornA.patientlyB.differentlyC.relaxedlyD.embarrassedlyA.wishB.wordC.dealD.list三、阅读理解（共13小题，每小题2分，共26分）14.Should More Cities Make It Illegal （不合法）to Text While Crossing the Street? Hawaii, the U.S., recently passed a law making it illegal to text or look down at mobile phones while crossing the street. It is the first major U.S. city with a law like this.Do you think more places should pass such a law? Here are some ideas.Sally, Seoul, South KoreaA.SeoulB.SydneyC.HawaiiD.Paris（1）mon. B.Dangerous. C.Strange. D.Unhealthy.（2）A.B.C.D.（3） We should make it illegal in more cities because texting whilewalking can be dangerous. If you are looking at your phone whilewalking, you might not see a car come or the traffic light turn red.Andrew, Sydney, Australia Ⅰdisagree because we have the right to make our owndecisions. The government needs to stop telling us what to do. Afterall, this is a free country. And police need a lot of time to catch realcriminals（犯人）.Madeline, Paris, France This law is a good idea. If this law goes into effect in more cities,people will be upset. But is there really a way to please everyone?This would not be for fun. It would be for the benefit and safety of allthe people.Anjali, Tokyo, Japan People do many things that cause injury（伤害）to themselvesbut are not illegal. People might get hurt from texting while walkingif they're not paying attention. But I still think they should have achoice.recently passed a law making it illegal to text while crossing the street.What does Sally think of texting while walking?According to Madeline, .people might not see a car come while textingthe law would be for the benefit of all the peoplepeople have the right to make their own decisionspeople do many things that cause injury to themselves15."All right, everyone. listen up" said Rey. "I have something important to say."Rey had always had something important to say since the first day of primary school. "This is really a big project." said Rey. "Trust me. As long as I'm in charge, we'll have the most wonderful project ever！""It seems like Rey is always in charge." murmured（小声说）Jake.A.B.C.（1）It was true. Rey always seemed to be in charge ofeverything. He wanted everything to be as perfect as possible,and he just believed that he was the only person who couldmake that happen.This time, Rey decided to do a play about the Wright brothers and the first airplane flight. He announced that he would be the director, and he had also decided on the role that everyone would play. He would play the part of Orville Wright. He even had made the costumes, which Hannah would like to do.The next day, Rey announced he was going to play Wilbur Wright."How can you play both of the Wright brothers？"asked Hannah."I'll just put on different hats for each one." said Rey.The next afternoon, no one showed up at the rehearsal（排练）except Rey. An hour had passed, and he still hadn't heard from others.Finally, Rey called Stephen. "I quit the play." said Stephen. "In fact, we all quit. We're going to do something else."Rey spent the rest of the afternoon working on the play. Moving the set himself took too long, and running around to change costumes left him out of breath. Worst of all, half the airplane dragged on the ground as Rey pulled it across the stage. Rey felt upset and confused.He knew now that he couldn't do the play alone. He needed his friends' help if it was going to work at all.The next day at school. Rey had a talk with his friends. "I'm going to change. I promise I will listen to you. What do you want to do？"Hannah thought the play should be shorter and Jake wanted to make a new airplane that would be easier to handle. Stephen thought everyone should get a chance to play a real part like Wilbur Wright. Fern wanted to be able to act her part the way she wanted."You are probably right." Rey said. "Let's try it your way."Everyone smiled.What did Rey decide to do for the project?To change the classroom setting.To make an airplane for the children.To do a play about the Wright brothers.A.Proud.B.Angry.C.Upset.D.Cheerful.（2）A.they finished their projectB.everyone could play a partC.Rey always had great ideasD.they won the first prize（3）How did Rey feel when he did the play alone?Everyone smiled in the end because .16.Оn July 20, 1969, Neil Armstrong became the firstperson to walk on the moon. The space suit Armstrongwore on his lunar mission has come to symbolize courageand human achievement. In 1971, the Smithsonian'sNational Air and Space Museum （NASM ）, inWashington, D.C., acquired （获得） Armstrong's suit. It stood proudly on display for visitors to admire, until there were changes in the suit's appearance. "Over time, the suit started to show signs of deterioration ." Lisa Young said. Young is an objects conservator （文物修复员） at NASM. It is her job to preserve （维护） historical and cultural objects."Plastics are tricky to conserve, " Young says. They tend to degrade （降解） over time. Neoprene is one type of plastic in Armstrong's suit. The material can turn brittle and break into tiny pieces. This would ruin the space suit. NASM, seeking ways to preserve this historical treasure, removed it from display in 2006.What cause plastic to degrade in the first place? "Many things." Odile Madden says.Madden is a scientist in California. She explains that sunlight, water, humidity and dust can cause plastics to degrade. "Some plastics will break down no matter what we do."Madden says.Yet history can still be saved. Scientists have found that storing plastics in cooler temperatures, with lower humidity levels, can slow degradation. Young says Armstrong's suit is currently in storage at a temperature of 63 °F and a lower relative humidity 30%.These conditions will be maintained when Armstrong's suit returns to a museum display case in time for the 50anniversary of the moon landing.Plastic degradation affects art, too. Artist Claes Oldenburg created False Food Selection in 1966. It consists of plastic food displayed in a wonder box. The plastic food used to look real. Now, some of it has flattened and yellowed. Georgina Rayner is a conservation scientist at Harvard Art Museums, in Cambridge. She says the artwork's thA.B. C.D.（1）A.becoming worseB.losing attentionC.getting strongerD.being valuable（2）A.B.C.D.（3）degradation process. But Rayner is motivated to conserve this artwork and others like it."Plastics are a part of our history." she says. "It's important to preserve them so that future generations can understand the journey we've taken."Neil Armstrong's space suit .is in storage at a higher relative humidityis considered as a symbol of plastic artwas protected at Harvard Art Maseumswas removed from display in 2006The word "deterioration " in Paragraph 1 probably means " ".What can we infer from the passage?Plastic artworks help future generations learn more about history.We can do nothing to prevent plastic objects from breaking down.The acidir gas is a necessity in the preservation of plastic objects.People are advised to use fewer plastic objects in their daily life.17.During this age of technology, life moves fast and people onlyfocus on what comes next, rather than living in the present. Oftentheir daydreaming is centered on the "next" rather than the "now."Technology is all about what's next—the next innovation（创新）, the next platform or the next device. This is most obviouswith the iPhone. The iPhone X has just released, but businessmen and customers are already thinking about the next, newest iPhone. I am already counting the days until l can upgrade my iPhone.Throughout my adolescence（青春期）, almost every single one of my peers have been too wrapped up with the next "great" thing and put too much stress on themselves while losing sense of what is going on now or what they have achieved; it drives me totally crazy. Upon entering high school, I was excited to spend the next four years with my closest friends. Sadly, once I hit my sophomore year（高二）, I began to worry about getting into a good college and what I needed to do for that to happen. By concentrating on what's next, I seem to be missing what's great about high school.A.B.C.D.（1）A.B.C.D.（2）A.B.C.D.（3）（4）Most students in high school look at education as a means to an end; something that will set them up for the next step. Due to this, they pay close attention to the teacher in class, not to enrich their knowledge, but to score high on the test, making them stronger candidates （候选人）for college. What is even more annoying is that universities are now forcing high school students to have a clear idea of what they want to do in life. Most colleges have specialized schools, such as business, nursing and education; in most cases, it is very difficult to switch out of or into one of the specialized schools. Therefore, high schoolers do actually have to focus on what's next.When I go to college. all I am thinking about is still what comes next; that is, how to land a great job out of. college. Everyone around seems to he like me. Actually, I truly hope that people who are in this very similar situation can figure out a way to make the "now" as important, if not more important, than the "next" in life. Taking all of this into consideration, the concept of what comes next is far too ingrained（根深蒂固的）into important things of life, such as technology and education.If people keep racing from one thing to the next, life will pass them by and in a hurry; no one will be able to look back on what they have experienced or achieved, because life will have become a blur（模糊）.The writer mentions the iPhone in Paragraph 2 to show that .the newest iPhone is always the bestyoung customers like new technologythe iPhone X attracts the most attentiontechnology is all about what comes nextWhat can we learn from the passage?High schoolers are forced to have clear ideas about their future jobs.Few students pay close attention to the teacher to score high on tests.Thinking too much about the present gives students too much pressure.Different activities make the students stronger candidates for the college.The writer probably agrees that .students now care too much about unimportant things in lifefuture achievements depend on your plan in your high schoolcollege education usually makes a great difference to most of the peoplepeople should live in the "now" rather than only look ahead to the "next"Which of the following would he the best title for the passage?C.Past, Now and FutureD.Technology, a Key to Future四、任务型阅读（共5小题，每小题2分，共10分）18.（1）（2）（3）（4）Todd Bol is the founder of the non-profit Little FreeLibraries. Bol built the first little library in 2009 to honor hismom, who was a book lover and teacher. Bol wanted toshare his mother's love for reading with others. He decidedto build a wood box and fill it with books. He made it looklike a tiny red schoolhouse. He placed the box of books on apost in his front yard with a sign that read "Free Books". This was the beginning of the Little Free Library.Soon Bol's neighbors noticed this tiny model of a schoolhouse. They began taking the books and replacing them with books of their own. The tiny library was always open.A library card was not needed. The books could be read and returned whenever. It offered people an easy way to read. This library didn't just provide books. It also helped build friendships among community members. As more and more people visited Bol's little library, they began talking with one another. Everyone loved the little library. They shared thoughts, ideas and stories. They got to know one another. After all, as Bol said."It's a magic box with books."Bol's friends and neighbors wanted little libraries of their own. Bol built several and gave them away. One of his friends, Rick Brooks, noticed that the libraries encouraged people to read. He believed that Bol's little libraries could benefit more than just local friends and neighbors. With this in mind, Bol and Brookes came up with a plan to build more than 2, 500 Little Free Libraries around the world. To achieve this goal, they created a website. People can get information about the Little Free Libraries and how they can set up little libraries of their own.Thanks to Bol and Brooks. the Little Free Libraries are encouraging people to read more and to be friendlier. Today there are more than 75, 000 Little Free libraries around the world, and they can be found on almost every continent.When did Bol build the first library?Where did Bol put the box of books?What is the second paragraph mainly about?How did Bol and Brookes achieve their goal?（5）What are the Little Free Libraries encouraging people to do?五、书面表达（二选一）（共10分）19.假如你是李华，加拿大某校学生代表团将要来你校参观。

2019年北京市海淀区高考地理二模试卷一、本部分共5小题，每小题12分，共44分．在每小题列出的四个选项中，选出最符合题目要求的一项。

某游轮于世界时6月28日17时从甲地出发，经过6天的航行到达乙地。

下图为该游轮航线示意图。

读图，完成下面小题。

1. 该游轮出发时，当地时间为（）A. 27日下午B. 28日上午C. 29日上午D. 29日下午2. 该航程中（）A. 游轮始终顺风顺水航行B. 游客观察到日出时间越来越晚C. 地球公转速度逐渐加快D. 日出时船上桅杆影子指向西北3. 图中（ )A. ①地因板块张裂形成深海沟B. ②地位于太平洋板块内部C. 因暖流影响，③地水温高于④地D. 受盛行风影响，④地海水自西向东流动【答案】1. B 2. B 3. D【解析】本题以游轮行驶的航线为背景，主要考查了学生对洋流、昼夜长短变化规律、日出方向和地球公转知识点的理解。

【1题详解】题干中提到了世界时 6月28日17时从甲地出发，甲地的时区是西经150度，代表西十区。

和世界时(零时区)差十个小时，所以该游轮出发时当地的时间为6月28 日17时-10个小时=6月28日7时，为28日上午。

故答案选择B。

【2题详解】图中显示的区域是北太平洋区域,游轮从甲地到乙地的过程中会受到北太平洋暖流和盛行西风的影响，北太平洋暖流的流向和盛行西风的风向是自西向东，而甲地到乙地的过程是自东向西，所以是逆风逆水行驶，故A错误；因为游轮的出发时间为6月28日，经过6天到达乙地，游轮行驶的时间是在 6月22日到12月22日之间，因为游客的位置在北半球,北半球 6月22日至12月22日期间白昼时间越来越短,故日出时间越来越晚，B正确；因为地球公转太阳的远日点在7月初，地球的公转速度会越来越慢，C错误；因为游轮行驶期间太阳直射点在北半球，北半球的日出方向是从东北日出，故影子指向西南，D错误。

故答案选择B。

【3题详解】从图中看，①地处于亚欧板块和太平洋板块交界处，深海沟是因板块挤压而形成，A错误。

2020/5/9教研云资源页2019年北京海淀区初三⼆模数学试卷(详解)⼀、选择题（本⼤共8⼩题，每⼩题2分，共16分，）1.A.B.C.D.【答案】【解析】的⽴⽅根是（ ）．A ，故选．2. A.B. C. D.【答案】【解析】如图，两条直线，交于点，射线平分，若=，则等于（）．C ，则．（对顶⻆相等）由题意．（互补）．．3. A.B.C.D.【答案】【解析】科学家在海底下约公⾥深处的沙岩中，发现了⼀种世界上最⼩的神秘⽣物，它们的最⼩身⻓只有⽶，甚⾄⽐已知的最⼩细菌还要⼩．将⽤科学记数法表示为（ ）．B ．2020/5/9教研云资源页故选．4. A.B. C. D.【答案】【解析】实数，在数轴上的对应点的位置如图所示，若，则实数的值可能是（ ）．D ∵，，∴，∵．故选．5. A.拱B.翘C.斗D.升【答案】【解析】图是矗⽴千年⽽不倒的应县⽊塔⼀⻆，它使⽤了六⼗多种形态各异的⽃栱（dǒu gǒng ）．⽃栱是中国古代匠师们为减少⽴柱与横梁交接处的剪⼒⽽创造的⼀种独特的结构，位于柱与梁之间，⽃栱是由⽃、升、栱、翘、昂组成，图是其中⼀个组成部件的三视图，则这个部件是（ ）．图图C由三视图定义知，正确．故选．6. A.B.C.D.已知，则下列不等式⼀定成⽴的是（ ）．2020/5/9教研云资源页【答案】A 选项：B 选项：C 选项：D 选项：【解析】D ，则，错．，当时，；当时，，当时，，故不⼀定成⽴．，则不⼀定成⽴，错．，则，⼀定成⽴．故选 D .7. A.B.C.D.【答案】【解析】下⾯的统计图反映了年中国城镇居⺠⼈均可⽀配收⼊与⼈均消费⽀出的情况．根据统计图提供的信息，下列推断的是（ ）．年我国城镇居⺠⼈均可⽀配收⼊与⼈均消费⽀出统计图城镇居民人均可支配收入城镇居民人均消费支出年份金额元数据来源：国家统计局年，我国城镇居⺠⼈均可⽀配收⼊和⼈均消费⽀出均逐年增加年，我国城镇居⺠⼈均可⽀配收⼊平均每年增⻓超过元从年起，我国城镇居⺠⼈均消费⽀出超过元年我国城镇居⺠⼈均消费⽀出占⼈均可⽀配收⼊的百分⽐超过D 城镇居⺠⼈均消费⽀出占⼈均可⽀配收⼊百分⽐为，故不合理．故选．不.合.理.8.2020/5/9教研云资源页A.甲B.⼄C.丙D.丁【答案】【解析】如图，⼩宇计划在甲、⼄、丙、丁四个⼩区中挑选⼀个⼩区租住，附近有东⻄向的交通主⼲道和南北向的交通主⼲道，若他希望租住的⼩区到主⼲道和主⼲道的直线距离之和最⼩，则下图中符合他要求的⼩区是（ ）．C分别以主⼲道、主⼲道所在直线为轴、轴建⽴平⾯直⻆坐标系，设⼩区坐标，则⼩区到主⼲道、主⼲道距离和，∴，平移直线，依次经过甲、⼄、丙、丁四个⼩区，最⼩即与轴交点纵坐标最⼩．故选．⼆、填空题（本⼤共8⼩题，每⼩题2分，共16分，）9.【答案】【解析】当时，代数式的值为．由题意知且，得．故答案为：．10.【答案】如图，在中，，为中点，若，，则的⻓为 ．2020/5/9教研云资源页【解析】延⻓⾄，使，连，∵为中点，∴，在和中，，∴≌，∴，，∵，，∴，，∵，∴，∵，∴，在中，．故答案为：．11.【答案】【解析】如图，在⊙中，弦与半径相交于点，连接，．若，，则的度数为 .连接．2020/5/9教研云资源页∵，，∴为等边三⻆形．∴，∵，∴，∴，∵，∴．12.【答案】【解析】如果，那么代数式的值是 ．，∵，∴，∴原式，故答案为：．13.【答案】【解析】如图，在中，，分别为，的中点．若，则．∵、分别为、中点，边形2020/5/9教研云资源页∴，，∴，∴，∴，∵，∴．边形边形14.【答案】【解析】某学习⼩组做抛掷⼀枚纪念币的实验，整理同学们获得的实验数据，如下表：抛掷次数“正⾯向上”的次数“正⾯向上”的频率下⾯有三个推断：①在⽤频率估计概率时，⽤实验次时的频率⼀定⽐⽤实验次时的频率更准确．②如果再次做此实验，仍按上表抛掷的次数统计数据，那么在数据表中，“正⾯向上”的频率有更⼤的可能仍会在附近摆动．③通过上述实验的结果，可以推断这枚纪念币有很⼤的可能性不是质地均匀的．其中正确的是 ．②③由频率估概率知，⼤量重复试验时，随试验次数增加，纪念币正⾯向上频率在附近摆动，呈稳定趋势，故②正确；纪念币正⾯向上概率约为，并⾮，故纪念币质地不均匀，③正确；每次试验频率随机，故①错误．15.按《航空障碍灯》的要求，为保障⻜机夜间⻜⾏的安全，在⾼度为⽶⾄⽶的建筑上必须安装中光强航空障碍灯．中光强航空障碍灯是以规律性的固定模式闪光．在下图中你可以看到某⼀种中光强航空障碍灯的闪光模式，灯的亮暗呈2020/5/9教研云资源页状态亮暗时间秒【答案】【解析】规律性交替变化．那么在⼀个连续的秒内，该航空障碍灯处于亮的状态的时间总和最⻓可达 秒．从秒秒，每秒，航空障碍灯亮秒，暗秒，周期性变化．则连续秒内，最多亮秒．16.【答案】【解析】右图是在浦东陆家嘴明代陆深古墓中发掘出来的宝⽟——明⽩⽟幻⽅．其背⾯有⽅框四⾏⼗六格，为四阶幻⽅（从到，⼀共⼗六个数⽬，它们的纵列、横⾏与两条对⻆线上个数相加之和均为）．⼩明探究后发现，这个四阶幻⽅中的数满⾜下⾯规律：在四阶幻⽅中，当数，，，有如图的位置关系时，均有．如图，已知此幻⽅中的⼀些数，则的值为 ．图图由，知，①，2020/5/9教研云资源页由知，⼜，则，得②，由①②知．三、解答题（共68分）17.【答案】【解析】计算：．．．18.【答案】【解析】解不等式组：．．原不等式组为，解不等式①，得，解不等式②，得，∴原不等式组的解集为．①②19.下⾯是⼩宇设计的“作已知直⻆三⻆形的中位线”的尺规作图过程．已知：在中，．求作：的中位线，使点在上，点在上．作法：如图，①分别以，为圆⼼，⼤于⻓为半径画弧，两弧交于，两点；2020/5/9教研云资源页（1）（2）（1）（2）【答案】（1）（2）【解析】②作直线，与交于点，与交于点．所以线段就是所求作的中位线．根据⼩宇设计的尺规作图过程，使⽤直尺和圆规，补全图形．（保留作图痕迹）完成下⾯的证明．证明：连接，，，，，∵， ，∴是的垂直平分线（ ）（填推理的依据）．∴为中点，．∴，⼜在中，有，．∴（ ）（填推理的依据）．∴．∴．∴为中点．∴是的中位线．画图⻅解析．；到线段两端点距离相等的点在线段的垂直平分线上；等⻆的余⻆相等．补全的图形如图所示：；到线段两端点距离相等的点在线段的垂直平分线上；等⻆的余⻆相等．20.（1）（2）（1）（2）【答案】关于的⼀元⼆次⽅程，其中．求证：⽅程有两个不相等的实数根．当时，求该⽅程的根．证明⻅解析．，．2020/5/9教研云资源页（1）（2）【解析】依题意可知，，∵，∴，∴⽅程有两个不相等的实数根．当时，⽅程为，解得，．故⽅程的根为，．21.（1）（2）（1）（2）【答案】（1）（2）【解析】如图，在平⾏四边形中，的⻆平分线交于点，交的延⻓线于点，连接．求证：．若，，求平⾏四边形的⾯积．证明⻅解析．．∵四边形为平⾏四边形，∴．∴．∵平分，∴．∴．∴．∵，，∴．∵，，∴．平行 边形22.（1）（2）（1）（2）【答案】（1）（2）【解析】如图，是⊙的直径，，与⊙分别相切于点，，连接，，，与相交于点．求证：．连结，若，，求的⻓．证明⻅解析．．连接，如图，∵，与⊙分别相切于点，，∴，，，∴，∵，∴，∵，∴．连接，如图，∵是⊙的直径，∴，∴，∴，∵，，∴，，∵，，∴，∴．23.（1）（2）（1）（2）【答案】（1）（2）【解析】如图，在平⾯直⻆坐标系中，直线与轴、轴分别交于点，，与双曲线的交点为，．当点的横坐标为时，求的值．若，结合函数图象，直接写出的取值范围．．或．∵点是双曲线上的点，且点的横坐标为，∴点的坐标为．∵点是直线上的点，∴．当时，满⾜，结合函数图象可得，的取值范围是或．2020/5/9教研云资源页24.（1）（2）12（3）（1）（2）1（3）【答案】有这样⼀个问题：探究函数的图象与性质．⼩宇从课本上研究函数的活动中获得启发，对函数的图象与性质进⾏了探究．下⾯是⼩宇的探究过程，请补充完整：函数的⾃变量的取值范围是 ．如图，在平⾯直⻆坐标系中，完成以下作图步骤：①画出函数和的图象．②在轴上取⼀点，过点作轴的垂线，分别交函数和的图象于点，，记线段的中点为．③在轴正半轴上多次改变点的位置，⽤②的⽅法得到相应的点，把这些点⽤平滑的曲线连接起来，得到函数在轴右侧的图象．继续在轴负半轴上多次改变点的位置，重复上述操作得到该函数在轴左侧的图象．结合函数的图象，发现：该函数图象在第⼆象限内存在最低点，该点的横坐标约为 （保留⼩数点后⼀位）．该函数还具有的性质为： （⼀条即可）．画图⻅解析．（在⾄之间即可）2020/5/9教研云资源页2（1）（2）12（3）【解析】当时，随的增⼤⽽增⼤函数的⾃变量的取值范围是．观察图象可得，第⼆象限内最低点的横坐标为（在⾄之间即可）．答案不唯⼀，如：当时，随的增⼤⽽增⼤．25.某学校共有六个年级，每个年级个班，每个班约名同学．该校⻝堂共有个窗⼝，中午所有同学都在⻝堂⽤餐．经了解，该校同学年龄分布在岁（含岁）到岁（含岁）之间，平均年龄约为岁．⼩天、⼩东和⼩云三位同学，为了解全校同学对⻝堂各窗⼝餐⻝的喜爱情况，各⾃进⾏了抽样调查，并记录了相应同学的年龄，每⼈调查了名同学，将收集到的数据进⾏了整理．⼩天从初⼀年级每个班随机抽取名同学进⾏调查，绘制统计图表如下：表：窗⼝⼈数窗⼝⼈数⼩东从全校每个班随机抽取名同学进⾏调查，绘制统计图表如下：表：2020/5/9教研云资源页（1）（2）（3）（1）（2）（3）【答案】窗⼝⼈数窗⼝⼈数⼩云在⻝堂⻔⼝，对⽤餐后的同学采取每隔⼈抽取⼈进⾏调查，绘制统计图表如下：表：窗⼝⼈数窗⼝⼈数根据以上材料回答问题：写出图中的值，并补全图．⼩天、⼩东和⼩云三⼈中，哪个同学抽样调查的数据能较好地反映出该校同学对各窗⼝餐⻝的喜爱情况，并简要说明其余同学调查的不⾜之处．为使每个同学在中午尽量吃到⾃⼰喜爱的餐⻝，学校餐⻝管理部⻔应为 窗⼝尽量多的分配⼯作⼈员，理由为 ．岁，画图⻅解析．⼩东（答案不唯⼀）．号和号（或者只有；或者，，）（答案不唯⼀） ; 从⼩东的调查结果看，这⼏个窗⼝受到更多的同学的喜爱，应该适当增加这⼏个窗⼝的⼯作⼈员2020/5/9教研云资源页（1）（2）（3）【解析】⼩天调查的不⾜之处：仅对初⼀年级抽样，不能代表该学校学⽣总体的情况；⼩云调查的不⾜之处：抽样学⽣的平均年龄为岁，远⾼于全校学⽣的平均年龄，不能代表该学校学⽣总体情况．从⼩东的调查结果看，这⼏个窗⼝受到更多的同学的喜爱，应该适当增加这⼏个窗⼝的⼯作⼈员．26.（1）（2）（3）（1）（2）（3）【答案】（1）（2）【解析】在平⾯直⻆坐标系中，抛物线与直线交于，两点，且点在轴上，点在轴的正半轴上．求点的坐标．若，求直线的解析式．若，求的取值范围．．．或．∵抛物线与轴交于点，∴点的坐标为．时，抛物线为，∵抛物线与轴交于点，且点在轴的正半轴上，∴点的坐标为，∵直线过，两点，2020/5/9教研云资源页（3）∴，解得，∴直线的解析式为．如图当时，当时，抛物线过点，此时，结合函数图象可得，当时，抛物线过点，此时，结合函数图象可得，综上所述，的取值范围是或．27.12（1）（2）1（1）【答案】已知为线段中点，．为线段上⼀动点（不与点重合），点在射线上，连接，，记．若，．如图，当为中点时，求的度数．图直接写出、的数量关系．如图，当时．探究是否存在常数，使得②中的结论仍成⽴？若存在，写出的值并证明；若不存在，请说明理由．图．2020/5/9教研云资源页2（2）12（1）（2）【解析】．存在，使得②中的结论成⽴，证明⻅解析．在上取点，使得，连接．∵，∴为等边三⻆形．∴．∵为的中点，为的中点，∴．∵，∴．∴平分．∴．．过点作的垂线交于点．∵，∴．∴，．∵，，∴．∵，∴，∴≌．∴．28.2020/5/9教研云资源页（1）12（2）（1）12（2）【答案】（1）1（2）【解析】对于平⾯直⻆坐标系中的两个图形和，给出如下定义：若在图形上存在⼀点，图形上存在两点，，使得是以为斜边且的等腰直⻆三⻆形，则称图形与图形具有关系．若图形为⼀个点，图形为直线，图形与图形具有关系，则点，，中可以是图形的是 ．已知点，点，记线段为图形．当图形为直线时，判断图形与图形是否既具有关系⼜具有关系，如果是，请分别求出图形与图形中所有点的坐标；如果不是，请说明理由．当图形为以为圆⼼，为半径的⊙时，若图形与图形具有关系，求的取值范围．是，，，，．或．有题意，得：当坐标为，坐标为时，是以为斜边且的等腰直⻆三⻆形，∴可以是图象，经验证，，不满⾜题意，故答案为．是，如图，在直线上取点，，图且，则满⾜是以为斜边的等腰直⻆三⻆形的点，在到直线距离为的两条平⾏直线上，这两条平⾏直线与分别交于，两点．2020/5/9教研云资源页https:///#/print?id=09d1319b977a4d5bb3be2a55f99b362d&type=analyze21/222故图形与图形满⾜，直线与线段交于点，过点作轴于，与交于点，则，，可得，同理可求得：，如图，在线段上取点，，且，图则满⾜是以为斜边的等腰直⻆三⻆形的点在图中的两条线段上，这两条线段与直线交于，两点．故图形与图形满⾜．同上可求得，．如图所示，，，，和均为等腰直⻆三⻆形，∴，，∴，，∴若在⊙上，则点在以为圆⼼，或为半径的圆上，∵圆形与图具有关系，∴线段上存在点到的距离为或．如图，2020/5/9教研云资源页图当在右侧，时，，当⊙与线段相切时，，，，∴，∴，此时，．如图，图当在⊙上时，，∴，当在⊙上时，，，∴，∴，此时．综上，的取值范围是或．22/22。

北京海淀区2019届高三二模英语模拟试题第一部分：知识运用（共两节，45分）第一节单项填空（共10小题；每小题1.5分，共15分）ASpring is coming. Everything is waking from its winter sleep. The fields___1___(dress) in a fresh robe of green. The wild flowers begin to peep forth(隐隐露出). Birds sing among the trees, and begin to get their nests ready ___2___ summer. Men are now sowing seeds in the fields. The days are ___3___(warm), for brighter sunshine has come again. Everything is full of life and joy.【答案】1. are dressed2. for3. warmer【解析】这是一篇记叙文。

文章记叙了春天来到，万物复苏的景象。

【1题详解】考查时态，语态。

田野上穿着一件新鲜的绿色长袍。

dress意为“给……穿衣服”。

表示“穿着……”，应用be dressed结构。

根据前两句可知，该空应用一般现在时态。

且主语是复数名词fields，故填are dressed。

【2题详解】考查介词。

ready常和介词for搭配，表示“为……做好准备”，故填介词for。

【3题详解】考查形容词比较级。

根据后面的brighter sunshine可知，该句表达：因为更明亮的阳光又来了，所以天更暖和了。

且该空作表语，故填形容词的比较级warmer。

BAstronauts are people who go out into space. Being an astronaut is an exciting job. While in space, astronauts can look down and see ___4___（cloud）, land, and water. They can even see the moon up close. Astronauts get the chance ___5___(see) more stars than you or I have ever seen. Being an astronaut may be exciting, ___6___it is not an easy job. A person who ___7___(want) to be an astronaut has to study for years. There are many things an astronaut must learn to do before going into space. 【答案】4. clouds5. to see6. but7. wants【解析】这是一篇记叙文。