2017年北京海淀区高三模拟和期末试题

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2017年北京市海淀区高三二模英语试题及答案

2017年北京市海淀区高三二模英语试题及答案

海淀区高三年级第二学期期末练习英语2017.05本试卷共12页,共150分。

考试时间120分钟。

注意事项:1.考生务必将答案答在答题卡上,在试卷上作答无效。

2.答题前考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写。

3.答题卡上选择题必须用2B铅笔作答,将选中项涂满涂黑,黑度以盖住框内字母为准,修改时用橡皮擦除干净。

非选择题必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答,未在对应的答题区域内作答或超出答题区域作答的均不得分。

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

每段对话后有一道小题,从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话后,你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1. Where are the speakers? A. At a cinema. B. At the railway station. C. At the airport.2. What size of juice does the woman order? A. Small. B. Medium. C. Large.3. What’s the possible relationship between the speakers? A. Classmates. B. Colleagues. C. Father and daughter.4. What are the two speakers mainly talking about? A. Easter plans. B. A new movie. C. Weekend activities.5. How does the woman feel? A. Excited. B. Surprised. C. Worried.第二节(共10小题;每小题1.5分,共15分)听下面4段对话或独白。

2017年海淀区高三第一学期期末试题

2017年海淀区高三第一学期期末试题

海淀区高三年级第一学期期末练习英语2017.01本试卷共12页,共150分。

考试时间120分钟。

注意事项:1.考生务必将答案答在答题卡上,在试卷上作答无效。

2.答题前考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写。

3.答题卡上选择题必须用2B铅笔作答,将选中项涂满涂黑,黑度以盖住框内字母为准,修改时用橡皮擦除干净。

非选择题必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答,未在对应的答题区域内作答或超出答题区域作答的均不得分。

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

每段对话后有一道小题,从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话后,你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1.Which of the following does the woman suggest?A. B. C.2. What kind of novels does the woman like most?A. Fantasies.B. Science fiction.C. Detective stories.3.When do high schools usually start?A. At 8:30AM.B. At 8:15AM.C. At 7:30AM.4. What does the man invite the woman to do?A. Plan a wedding.B. Watch a new movie.C. Go to a concert.5. Where does the conversation most probably take place?A. At a gas station.B. At a car wash.C. At a repair shop.第二节(共10小题;每小题 1.5分,共15分)听下面4段对话或独白。

2017年北京市海淀区高三第二次模拟考试语文

2017年北京市海淀区高三第二次模拟考试语文

2017年北京市海淀区高三第二次模拟考试语文一、本大题共8小题,共24分。

(一)阅读下面材料,完成问题。

(13分)“三山五园”是对北京西郊皇家园林的总称,这种说法出现于清朝中晚期。

“三山五园”包括香山静宜园、玉泉山静明园、万寿山清漪园(颐和园)、畅春园和圆明园。

静宜园位于地势较高的香山,园中建筑因山就势,参差错落,散点式镶嵌在山体之中。

“园林之胜,重在山水。

”水池作为点缀,或出现在殿前以丰富较窄的院落空间,或处于园中以增加园林趣味。

静宜园占地149公顷,1677年成为康熙的行宫,后来虽有添建,但一直保持着非常好的自然生态,深邃优雅。

静明园的个性与静宜园不同。

静明园所在的玉泉山,湖山尺度非常有限,占地仅65公顷。

玉泉山虽因泉水丰沛而得名,但水面并不大,山体狭长,呈南北走向。

在这种地形上如何建设园林呢?建筑要和湖山尺度配合好,建筑群采用散点布局,高低相映。

山顶上的香岩寺和玉峰塔规模不大,山脚下的建筑多为一层,这样就凸显出玉峰塔的高耸。

乾隆非常喜欢玉泉山的风光,亲自为静明园内十六景命名,正殿名为“廓然大公”,后殿名为“涵万象”,意蕴深远。

畅春园位于今北京大学西墙外畅春园宿舍一带,原是明代武清侯李伟修建的私家园林“清华园”,也叫“李园”,康熙时更名为畅春园。

畅春园以水景为主,水面宽阔,“江淮以北亦当第一也”,清朝改建时仍“因水成景”。

畅春园的叠山艺术也堪称一绝,原来的土山和新添建的假山,岗峰连接;加之遍植各色鲜花树木,绿树成荫,给人天人合一之感,是兼有政治和游乐功能的离宫型园林。

被称为“万园之园”的圆明园,既有金碧辉煌的宫殿,也有玲珑剔透的亭台楼阁,又吸取了欧洲的建筑形式,是世界园林的集大成者。

圆明园也是中国古典园林中平地造园的典范,园内步移景易,景观层出不穷,特色之多,首屈一指。

圆明园占地350公顷,在“三山五园”中规模最大。

有仙境、欧式园林等景观,也有理政、居住、宗教等场所,这些层峦叠嶂的建筑都是雍正至咸丰五朝皇帝改造的结果,也大多体现出其治国理念。

2017海淀期末语文试题及答案

2017海淀期末语文试题及答案

北京市海淀区2017年高三第一学期期末语文试题2017.01一、本大题共7小题,共22分。

阅读下面的材料,完成1—7题。

材料一:太空之家①我国成功发射入轨的天宫二号,是一个长10米、最大直径3米多、重约8吨的人造航天器。

天宫二号在离地球近400公里的近地轨道上运行,开展各种工作和实验;它既是一个真正的太空实验室,也是能供航天员居住的“太空之家”。

②高智能是天宫二号作为“太空之家”的一个突出特点。

天宫二号可以自主进行飞行轨道及姿态调整、运行状态的智能化诊断等工作。

科研人员整合了航天器十多个分系统的数据,把复杂、晦涩的专业数据浓缩成52组画面,为航天员执行任务提供了清晰、直观、舒适的显示界面。

③科幻电影中技术人员像插拔U盘一样快捷更换损坏部件的场景,将在天宫二号内真实上演。

天宫二号在供配电、热控、数据管理等系统方面采用了高集成化模块设计,打造出“插拔式”接口,航天员在几分钟内就能完成一次维修更换。

这是天宫二号作为“太空之家”的一个新亮点。

④两名航天员要在太空驻留..30天,为避免出现“粮草不足”问题,科研人员研制了在轨补给系统。

天宫二号在太空可以边飞行边“加油”,而不必像天宫一号那样,起飞前必须把“油箱”加满,携带一吨多的推进剂。

天宫二号起飞前只加了半箱“油”,节省的重量..产品和航天员的生活物资。

..用来携带更多的载荷⑤科研人员还对天宫二号的居住环境进行了精心设计,使其更宜居。

航天员生活在由神舟十一号和天宫二号组成的组合体中,吃饭、睡觉在神舟飞船内,工作、娱乐和锻炼..在天宫二号内,15立方米的空间被紧凑地隔成多个功能区。

工作区和生活区的噪音控制在50分贝以内:舱内空气温度控制在22—24摄氏度,相对湿度控制在45%—55%,这是人体感觉最舒适的温湿度。

⑥此外,科研人员在天宫一号基础上,对电子邮件传输、天地视频通话等系统进行了改进。

天宫二号增加了邮件下行能力;航天员能与地面视频互动,也能与家人私密通话。

海淀区高三学年级第一学期期末练习语文试题答案2017

海淀区高三学年级第一学期期末练习语文试题答案2017

海淀区高三年级第一学期期末练习语文参考答案及评分标准 2017.1一、(本大题共7小题,共22分)1.(2分)D 2.(2分)C 3.(2分)B4. (5分)参考答案:伴随卫星是一种微小型航天器(1分),在太空中围绕主航天器不同角度地伴随飞行(1分),负责记录主航天器的工作情况(1分),随时对主航天器的表面状态进行监测,实施安全防卫(1分)。

评分标准:每点1分,共4分;语言表达,1分。

5.(2分)A 6.(3分)D7.(6分)参考答案:①在轨补给技术,能持续提供动力补给,可使天宫二号携带更多的生活物资。

②拥有伴随卫星,随时对天宫二号表面状态进行检查,保障航天器安全运行。

③再生生命保障系统,能使排出的体液循环再生,以维持航天员的生命健康。

评分标准:每点2分。

意思对即可。

二、(本大题共6小题,共21分)8. (3分) B 9.(3分)C 10.(3分)D11.(4分)参考答案:于是二年/定公以为司空/乃别五土之性/而物各得其所生之宜/咸得厥所/由司空为鲁大司寇/设法而不用/无奸民评分标准:断对两处得1分,断对四处得2分,断对六处得3分,全部断对得4分。

12.(4分)参考答案:儒者在做王公时,以仁义、礼法修朝施政,使君义达于百姓、通于四海,取得人心归服、天下一家的效果。

评分标准:答对一点得1分,答对两点得3分,答对三点得4分。

意思对即可。

13.(4分)答案示例:孔子制定了让百姓生有所养、死得安葬的制度,可证明荀子所说的“儒者法先王、隆礼义”;孔子做中都宰一年就使西方诸侯国向鲁国学习,证明儒者确为“社稷之臣、国君之宝”;孔子把土地按照性质分类,使各种作物都得到很好的生长,证明了“万物得宜乃君子(儒者)所长”的观点。

评分标准:《孔子家语》中的事例与《儒效》中的观点对应,每句2分,共4分。

三、(本大题共4小题,共17分)14.(3分)C 15.(3分)D16.(5分)答案示例:本诗中,作者以酒为旗鼓,把笔当作刀槊和军队(2分),排兵布阵,纵横驰骋,最终扫尽逆虏、取得胜利(2分)。

2017北京市海淀区高三英语一模试卷及答案(精品资料).doc

2017北京市海淀区高三英语一模试卷及答案(精品资料).doc

【最新整理,下载后即可编辑】海淀区高三年级第二学期期中练习英语2017.04第一部分:听力理解(共三节,30分)第一节(共5小题;每小题1.5分,共7.5分)听下面5段对话。

每段对话后有一道小题,从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话后,你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1. What’s the man’s Chinese animal?A. B. C.2. How does the woman want the beef?A. Rare.B. Medium.C. Well-done.3. What time does the meeting start?A. At 9:30am.B. At 10:00am.C. At 10:15am.4. How does the woman feel about the news?A. Excited.B. Terrified.C. Disappointed.5. Where does the conversation probably take place?A. At a store.B. At a bank.C. In a police station.第二节(共10小题;每小题1.5分,共15分)听下面4段对话或独白。

每段对话或独白后有几道小题,从每题所给的A、B、C三个选项中选出最佳选项。

听每段对话或独白前,你将有5秒钟的时间阅读每小题。

听完后,每小题将给出5秒钟的作答时间。

每段对话或独白你将听两遍。

听第6段材料,回答第6至7题。

6. What class did the man like best?A. Science.B. Biology.C. Public speaking.7. What is the woman probably doing?A. Asking for information.B. Offering help.C. Giving advice.听第7段材料,回答第8至9题。

北京市海淀区2017届高三上学期期末考试英语试题

北京市海淀区2017届高三上学期期末考试英语试题

海淀区高三年级第一学期期末练习英语2017.01本试卷共12页,共150分。

考试时间120分钟。

注意事项:1.考生务必将答案答在答题卡上,在试卷上作答无效。

2.答题前考生务必将答题卡上的姓名、准考证号用黑色字迹的签字笔填写。

3.答题卡上选择题必须用2B铅笔作答,将选中项涂满涂黑,黑度以盖住框内字母为准,修改时用橡皮擦除干净。

非选择题必须用黑色字迹的签字笔按照题号顺序在各题目的答题区域内作答,未在对应的答题区域内作答或超出答题区域作答的均不得分。

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

每段对话后有一道小题,从每题所给的A、B、C三个选项中选出最佳选项。

听完每段对话后,你将有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话你将听一遍。

1. Which of the following does the woman suggest?A. B. C.2. What kind of novels does the woman like most?A. Fantasies.B. Science fiction.C. Detective stories.3. When do high schools usually start?A. At 8:30AM.B. At 8:15AM.C. At 7:30AM.4. What does the man invite the woman to do?A. Plan a wedding.B. Watch a new movie.C. Go to a concert.5. Where does the conversation most probably take place?A. At a gas station.B. At a car wash.C. At a repair shop.第二节(共10小题;每小题1.5分,共15分)听下面4段对话或独白。

北京市海淀区2017届高三上学期期末考试数学理试题含答案

北京市海淀区2017届高三上学期期末考试数学理试题含答案

海淀区高三年级第一学期期末练习数学(理科) 2017.1本试卷共4页,150分。

考试时长120分钟。

考生务必将答案答在答题卡上,在试卷上 作答无效。

考试结束后,将本试卷和答题卡一并交回。

一、选择题共8小题,每小题5分,共40分。

在每小题列出的四个选项中,选出符合题目要求的一项.1.抛物线22y x =的焦点到准线的距离为A .12B .1C .2D .32.在极坐标系中,点π(1,)4与点3π(1,)4的距离为A .1 BCD3.右侧程序框图所示的算法来自于《九章算术》.若输入a 的值为16,b 的值为24,则执行该程序框图输出的结果为A .6B .7C .8D .94.已知向量,a b 满足2+=0a b ,()2+⋅=a b a ,则⋅=a bA .12-B .12C .2-D .25.已知直线l 经过双曲线2214x y -=的一个焦点且与其一条渐近线平行,则直线l 的方程可能是A.12y x =-+B.12y x =C.2y x =D.2y x =-6.设,x y 满足0,20,2,x y x y x -≤⎧⎪+-≥⎨⎪≤⎩则22(1)x y ++的最小值为A .1B .92C .5D .97.在手绘涂色本的某页上画有排成一列的6条未涂色的鱼,小明用红、蓝两种颜色给这些鱼涂色,每条鱼只能涂一种颜色,两条相邻的鱼不.都.涂成红色....,涂色后,既有红色鱼又有蓝色鱼的涂色方法种数为 A .14B .16C .18D .208.如图,已知正方体1111ABCD A B C D -的棱长为1,,E F 分别是棱AD ,B 1C 1上的动点,设1,AE x B F y ==.若棱.1DD 与平面BEF 有公共点,则x y +的取值范围是 A .[0,1] B .13[,]22 C .[1,2]D .3[,2]2二、填空题共6小题,每小题5分,共30分. 9.已知复数z 满足(1i)2z +=,则z =________.10.在261()x x+的展开式中,常数项为________.(用数字作答)11.若一个几何体由正方体挖去一部分得到,其三视图如图所示,则该几何体的体积为________.12.已知圆C :2220x x y -+=,则圆心坐标为_____;若直线l 过点(1,0)-且与圆C 相切,则直线l 的方程为____________.13.已知函数2sin()y x ωϕ=+π(0,||)2ωϕ><.① 若(0)1f =,则ϕ=________;② 若x ∃∈R ,使(2)()4f x f x +-=成立,则ω的最小值是________.14.已知函数||()e cos πx f x x -=+,给出下列命题:①()f x 的最大值为2;②()f x 在(10,10)-内的零点之和为0; ③()f x 的任何一个极大值都大于1. 其中所有正确命题的序号是________.俯视图主视图ABCD1D 1A 1B 1C E F三、解答题共6小题,共80分.解答应写出文字说明、演算步骤或证明过程. 15.(本小题满分13分)在∆ABC 中,2c a =,120B =,且∆ABC(Ⅰ)求b 的值; (Ⅱ)求tan A 的值.16.(本小题满分13分)诚信是立身之本,道德之基.某校学生会创设了“诚信水站”,既便于学生用水,又推进诚信教育,并用“周实际回收水费周投入成本”表示每周“水站诚信度”.为了便于数据分析,以四周为一周期......,下表为该水站连续十二周(共三个周期)的诚信度数据统计: 第一周 第二周 第三周 第四周第一个周期95% 98% 92% 88% 第二个周期94% 94% 83% 80% 第三个周期 85% 92% 95% 96% (Ⅰ)计算表中十二周“水站诚信度”的平均数x ;(Ⅱ)分别从上表每个周期的4个数据中随机抽取1个数据,设随机变量X 表示取出的3个数据中“水站诚信度”超过91%的数据的个数,求随机变量X 的分布列和期望; (Ⅲ)已知学生会分别在第一个周期的第四周末和第二个周期的第四周末各举行了一次“以诚信为本”的主题教育活动.根据已有数据,说明两次主题教育活动的宣传效果,并根据已有数据陈述理由.17.(本小题满分14分)如图1,在梯形ABCD 中,//AB CD ,90ABC ∠=,224AB CD BC ===,O 是边AB 的中点.将三角形AOD 绕边OD 所在直线旋转到1A OD 位置,使得1120AOB ∠=,如图2.设m 为平面1A DC 与平面1A OB 的交线.(Ⅰ)判断直线DC 与直线m 的位置关系并证明; (Ⅱ)若直线m 上的点G 满足1OG A D ⊥,求出1A G 的长; (Ⅲ)求直线1A O 与平面1A BD 所成角的正弦值.AOBCD 1图ODCB2图1A18.(本小题满分13分)已知(0,2),(3,1)A B 是椭圆G :22221(0)x y a b a b+=>>上的两点.(Ⅰ)求椭圆G 的离心率;(Ⅱ)已知直线l 过点B ,且与椭圆G 交于另一点C (不同于点A ),若以BC 为直径的圆经过点A ,求直线l 的方程.19. (本小题满分14分)已知函数()ln 1af x x x=--. (Ⅰ)若曲线()y f x =存在斜率为1-的切线,求实数a 的取值范围;(Ⅱ)求()f x 的单调区间;(Ⅲ)设函数()ln x ag x x+=,求证:当10a -<<时,()g x 在(1,)+∞上存在极小值.20.(本小题满分13分)对于无穷数列{}n a ,{}n b ,若1212max{,,,}min{,,,}(1,2,3,)k k k b a a a a a a k =-=,则称{}n b 是{}n a 的“收缩数列”.其中,12max{,,,}k a a a ,12min{,,,}k a a a 分别表示12,,,ka a a 中的最大数和最小数.已知{}n a 为无穷数列,其前n 项和为n S ,数列{}n b 是{}n a 的“收缩数列”. (Ⅰ)若21n a n =+,求{}n b 的前n 项和; (Ⅱ)证明:{}n b 的“收缩数列”仍是{}n b ; (Ⅲ)若121(1)(1)22n n n n n n S S S a b +-+++=+(1,2,3,)n =,求所有满足该条件的{}n a .海淀区高三年级第一学期期末练习数学(理科)答案及评分标准2017.1一、选择题(共8小题,每小题5分,共40分)1.B2.B3. C4.C5.A6. B7.D8.C 二、填空题(共6小题,每小题5分,共30分,9. 1i -10.15 11.16312.(1,0);1)y x =+和1)y x =+13.π6,π214.①②③三、解答题(共6小题,共80分) 15.(本小题满分13分)解:(Ⅰ)由∆ABC 面积公式及题设得1sin 2S ac B ==122a a ⨯=,解得1,2,a c ==由余弦定理及题设可得2222cos b a c ac B =+-114212()72=+-⨯⨯⨯-=,又0,b b >∴. (不写b>0不扣分)(Ⅱ)在∆ABC 中,由正弦定理sin sin a bA B =得:sin sin a A B b ==, 又120B =,所以A 是锐角(或:因为12,a c =<=)所以cos A ==所以sin tan cos A A A === 16. (本小题满分13分)解:(Ⅰ)十二周“水站诚信度”的平均数为x =95+98+92+88+94+94+83+80+85+92+95+96=91%12100⨯(Ⅱ)随机变量X 的可能取值为0,1,2,3三个周期“水站诚信度”超过91%分别有3次,2次,3次1212(0)44464P X ==⨯⨯=32112112314(1)44444444464P X ==⨯⨯+⨯⨯+⨯⨯=32132132330(2)44444444464P X==⨯⨯+⨯⨯+⨯⨯=32318(3)44464P X==⨯⨯=随机变量X的分布列为X0 1 2 3P1327321532932 171590123232323232EX=⨯+⨯+⨯+⨯=.(Ⅲ)本题为开放问题,答案不唯一,在此给出评价标准,并给出可能出现的答案情况,阅卷时按照标准酌情给分.给出明确结论,1分,结合已有数据,能够运用以下三个标准中的任何一个陈述得出该结论的理由,2分.标准1:会用主题活动前后的百分比变化进行阐述标准2:会用三个周期的诚信度平均数变化进行阐述标准3:会用主题活动前后诚信度变化趋势进行阐述可能出现的作答情况举例,及对应评分标准如下:情况一:结论:两次主题活动效果均好.(1分)理由:活动举办后,“水站诚信度”由88%→94%和80%→85%看出,后继一周都有提升.(2分)情况二:结论:两次主题活动效果都不好.(1分)理由:三个周期的“水站诚信度”平均数分别为93.25%,87.75%,92%(平均数的计算近似即可),活动进行后,后继计算周期的“水站诚信度”平均数和第一周期比较均有下降.(2分)情况三:结论:第一次主题活动效果好于第二次主题活动.(1分)理由:第一次主题活动举办的后继一周“水站诚信度”提升百分点(94%-88%=6%)高于第二次主题活动举办的后继一周“水站诚信度”提升百分点(85%-80%=5%).(2分)情况四:结论:第二次主题活动效果好于第一次主题活动.(1分)理由:第一次活动后“水站诚信度”虽有上升,但两周后又有下滑,第二次活动后,“水站诚信度”数据连续四周呈上升趋势. (2分)(答出变化)情况五:结论:两次主题活动累加效果好.(1分)理由:两次主题活动“水站诚信度”均有提高,且第二次主题活动后数据提升状态持续周期好.(2分)情况六:以“‘两次主题活动无法比较’作答,只有给出如下理由才给3分:“12个数据的标准差较大,尽管平均数差别不大,但比较仍无意义”.给出其他理由,则结论和理由均不得分(0分).说明:①情况一和情况二用极差或者方差作为得出结论的理由,只给结论分1分,不给理由分2分.②以下情况不得分. 情况七: 结论及理由“只涉及一次主题活动,理由中无法辩析是否为两次活动后数据比较之结果”的. 例:结论:第二次主题活动效果好.理由:第二次主题活动后诚信度有提高.③其他答案情况,比照以上情况酌情给分,赋分原则是:遵循三个标准,能使用表中数据解释所得结论.17. (本小题满分14分)解:(Ⅰ)直线DC //m .证明:由题设可得//,CD OB 1CD AOB ⊄平面,1OB AOB ⊂平面, 所以//CD 平面1A OB .又因为CD ⊂平面1A DC ,平面1ADC 平面1A OB m =所以//CD m .法1:(Ⅱ)由已知224AB CD BC ===,O 是边AB 的中点,//AB CD ,所以//CD OB ,因为90ABC ∠=,所以四边形CDOB 是正方形, 所以在图1中DO AB ⊥,所以结合题设可得,在图2中有1DO OA ⊥,DO OB ⊥, 又因为1OA OB O =,所以1DO AOB ⊥平面. 在平面AOB 内作OM 垂直OB 于M ,则DO OM ⊥. 如图,建立空间直角坐标系O xyz -,则11,0),(0,2,0),(0,0,2)A B D -,所以1(,2)A D =.设,0)G m ,则由1OG A D ⊥可得10A D OG ⋅=,即(,2),0)30m m ⋅=-+=解得3m =.所以14AG =. (Ⅲ)设平面1A BD 的法向量(,,)x y z =n ,则110,0,A D A B ⎧⋅=⎪⎨⋅=⎪⎩nn即20,30,y z y ⎧++=⎪⎨+=⎪⎩令1y =,则1x z =,所以=n ,设直线1A O 与平面1A BD 所成角为θ,则sin θ=1115cos ,A O n A O n A O n⋅<>==⋅法2:(Ⅱ)由已知224AB CD BC ===,O 是边AB 的中点,//AB CD ,所以//CD OB ,因为90ABC ∠=,所以四边形CDOB 是正方形, 所以在图1中DO AB ⊥,所以结合题设可得,在图2中有1DO OA ⊥,DO OB ⊥, 又因为1OA OB O =,所以1DO AOB ⊥平面. 又因为1OG AOB ⊂平面,所以DO OG ⊥. 若在直线m 上的点G 满足1OG A D ⊥,又1OD A D D =,所以1OG AOD ⊥平面, 所以1OG OA ⊥,因为11120,//AOB OB AG ∠=,所以160OAG ∠=, 因为12OA =,所以14A G =.(注:答案中标灰部分,实际上在前面表达的符号中已经显现出该条件,故没写不扣分) (Ⅲ)由(II )可知1OD OA OG 、、两两垂直,如图,建立空间直角坐标系Oxyz -,则10,0,0),(2,0,0),((0,0,2)O A B D -(, 所以11(2,0,2),(A D A B =-=- 设平面1A BD 的法向量(,,)n x y z=,则110,0,n A D n A B ⎧⋅=⎪⎨⋅=⎪⎩即220,30,x z x -+=⎧⎪⎨-+=⎪⎩令1x =,则1y z =,所以(1,3,1)n =,设直线1A O 与平面1A BD 所成角为θ,则 sin θ=1115cos ,AO n AO n AO n ⋅<>==⋅18. (本小题满分13分) 解:(Ⅰ)由已知2,b =由点(3,1)B 在椭圆G 上可得29114a +=,解得212,a a ==.所以2228,c a b c =-==所以椭圆G 的离心率是c e a == (Ⅱ)法1:因为以BC 为直径的圆经过点A ,所以AB AC ⊥,由斜率公式和(0,2),(3,1)A B 可得13AB k =-,所以3Ac k =,设直线AC 的方程为32y x =+. 由2232,1124y x x y =+⎧⎪⎨+=⎪⎩得2790x x +=,由题设条件可得90,7A C x x ==-,所以913()77C -,-,所以直线BC 的方程为213y x =-. 法2:因为以BC 为直径的圆经过点A ,所以AB AC ⊥,由斜率公式和(0,2),(3,1)A B 可得13AB k =-,所以3Ac k =,设C C C x y (,) ,则23C Ac Cy k x -==,即32C C y x =+① 由点C 在椭圆上可得221124C C x y +=② 将①代入②得2790C C x x +=,因为点C 不同于点A ,所以97C x =-,所以913()77C -,-,所以直线BC 的方程为213y x =-. 法3:当直线l 过点B 且斜率不存在时,可得点(3,1)C -,不满足条件.设直线BC 的方程为1(3)y k x -=-,点C C C x y (,)由2213,1124y kx k x y =+-⎧⎪⎨+=⎪⎩可得222(31)6(13)3(13)120k x k k x k ++-+--=,显然0∆>,此方程两个根是点B C 和点的横坐标,所以223(13)12331C k x k --=+,即22(13)4,31C k x k --=+所以22361,31C k k y k --+=+ 因为以BC 为直径的圆经过点A , 所以AB AC ⊥,即0AB AC ⋅=. (此处用1AB AC k k ⋅=-亦可)2222963961(3,1)(,)3131k k k k AB AC k k -----⋅=-⋅=++2236128031k k k --=+,即(32)(31)0k k -+=,1221,,33k k ==-当213k =-时,即直线AB ,与已知点C 不同于点A 矛盾,所以12,3BC k k ==所以直线BC 的方程为213y x =-. 19. (本小题满分14分) 解:(Ⅰ)由()ln 1af x x x =--得221'()(0)a x af x x x x x+=+=>.由已知曲线()y f x =存在斜率为1-的切线, 所以'()1f x =-存在大于零的实数根, 即20x x a ++=存在大于零的实数根,因为2y x x a =++在0x >时单调递增, 所以实数a 的取值范围0∞(-,).(Ⅱ)由2'()x af x x+=,0x >,a ∈R 可得 当0a ≥时,'()0f x >,所以函数()f x 的增区间为(0,)+∞; 当0a <时,若(,)x a ∈-+∞,'()0f x >,若(0,)x a ∈-,'()0f x <, 所以此时函数()f x 的增区间为(,)a -+∞,减区间为(0,)a -.(Ⅲ)由()ln x a g x x+=及题设得22ln 1('()(ln )(ln )a x f x x g x x x --==), 由10a -<<可得01a <-<,由(Ⅱ)可知函数()f x 在(,)a -+∞上递增, 所以(1)10f a =--<,取e x =,显然e 1>,(e)lne 10e a af e=--=->, 所以存在0(1,e)x ∈满足0()0f x =,即 存在0(1,e)x ∈满足0'()0g x =,所以(),'()g x g x 在区间(1,)+∞上的情况如下:x0(1,)x0x0(,)x +∞'()g x- 0 +()g x极小所以当10a -<<时,()g x 在(1,)+∞上存在极小值. (本题所取的特殊值不唯一,注意到0(1)ax x->>),因此只需要0ln 1x ≥即可)20. (本小题满分13分)解:(Ⅰ)由21n a n =+可得{}n a 为递增数列, 所以12121max{,,,}min{,,,}21322n n n n b a a a a a a a a n n =-=-=+-=-,故{}n b 的前n 项和为22(1)2n n n n -⨯=-.- (Ⅱ)因为12121max{,,,}max{,,,}(1,2,3,)n n a a a a a a n +≤=,12121min{,,,}min{,,,}(1,2,3,)n n a a a a a a n +≥=,所以1211211212max{,,,}min{,,,}max{,,,}min{,,,}n n n n a a a a a a a a a a a a ++-≥-所以1(1,2,3,)n n b b n +≥=. 又因为1110b a a =-=, 所以12121max{,,,}min{,,,}n n n n b b b b b b b b b -=-=,所以{}n b 的“收缩数列”仍是{}n b .(Ⅲ)由121(1)(1)22n n n n n n S S S a b +-+++=+(1,2,3,)n =可得 当1n =时,11a a =;当2n =时,121223a a a b +=+,即221b a a =-,所以21a a ≥;当3n =时,123133263a a a a b ++=+,即3213132()()b a a a a =-+-(*), 若132a a a ≤<,则321b a a =-,所以由(*)可得32a a =,与32a a <矛盾;若312a a a <≤,则323b a a =-,所以由(*)可得32133()a a a a -=-, 所以3213a a a a --与同号,这与312a a a <≤矛盾; 若32a a ≥,则331b a a =-,由(*)可得32a a =. 猜想:满足121(1)(1)22n n n n n n S S S a b +-+++=+(1,2,3,)n =的数列{}n a 是: 1212,1,,1,n a n a a a a n =⎧=≥⎨>⎩.经验证,左式=121212(1)[12(1)]2n n n S S S na n a na a -+++=++++-=+, 右式=112112(1)(1)(1)(1)(1)()22222n n n n n n n n n n n a b a a a na a +-+--+=+-=+. 下面证明其它数列都不满足(Ⅲ)的题设条件.法1:由上述3n ≤时的情况可知,3n ≤时,1212,1,,1,n a n a a a a n =⎧=≥⎨>⎩是成立的.假设k a 是首次不符合1212,1,,1,n a n a a a a n =⎧=≥⎨>⎩的项,则1231k k a a a a a -≤===≠,由题设条件可得2212(1)(1)222k k k k k k k k a a a b ----+=+(*), 若12k a a a ≤<,则由(*)式化简可得2k a a =与2k a a <矛盾;若12k a a a <≤,则2k k b a a =-,所以由(*)可得21(1)()2k k k k a a a a --=- 所以21k k a a a a --与同号,这与12k a a a <≤矛盾; 所以2k a a ≥,则1k k b a a =-,所以由(*)化简可得2k a a =.这与假设2k a a ≠矛盾.所以不存在数列不满足1212,1,,1,n a n a a a a n =⎧=≥⎨>⎩的{}n a 符合题设条件.法2:当i n ≤时,11212max{,,,}min{,,,}i i i i a a a a a a a a b -≤-=,所以1121()ki k i a a b b b =-≤+++∑,(1,2,3,,)k n =即112()k k S ka b b b ≤++++,(1,2,3,,)k n =由1(1,2,3,)n n b b n +≥=可得(1,2,3,,)k n b b k n ≤=又10b =,所以可得1(1)k n S ka k b ≤+-(1,2,3,)k =, 所以12111(2)[02(1)]n n n n n S S S a a na b b b n b +++≤++++⨯++++-,即121(1)(1)22n n n n n nS S S a b +-+++≤+ 所以121(1)(1)22n n n n n n S S S a b +-+++≤+等号成立的条件是1(1,2,3,,)i i n a a b b i n -===,所以,所有满足该条件的数列{}n a 为1212,1,,1,n a n a a a a n =⎧=≥⎨>⎩.(说明:各题的其他做法,可对着参考答案的评分标准相应给分)。

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2017年北京海淀区高三模拟和期末试题2017海淀一模A Commitment to LifeThe snow was falling and the roads had become dangerous. The schools were dismissedearly, but much to my surprise, my 36 wasn’t canceled. So I went, feeling especiallyheroic. As far as I could see, I was risking my life to keep my 37 . Snow or no snow, Iwould be on time for my scheduled donation at the local 38 center.When I got there, I discovered I wasn’t 39 . Four more “hero-types” were alreadylying back in donor chairs with lines 40 to their veins, and machines quietly pumpingaway to 41 their lifesaving gifts.Seeing my fellow donors honoring their own commitments, I realized why I was there. I lay back in my donor chair, ready to make a difference in the life of someone I would never 42 .To be honest, I’d never really thought about why I donate. I just do it. But a few months ago, during one of my 43 donations I learned that my blood was specifically for a cancer patient and for a newborn baby—b oth patients needed what I would give in order to live. I’ve viewed my visits to the blood center 44 ever since.My wife Karen is a 45 , too. And more importantly, she has been on the bone marrow (骨髓) list for fifteen years, ever since she signed up to provide bone marrow to a kindergartner with leukemia(白血病). That little girl died before Karen’s bone marrow could help her, 46 Karen was called again recently. Her test results were still on file, and it turned out she was a potential 47 for someone else. The caller asked Karen if she would still be willing to become a bone marrow donor. “Yes,” she said and then immediately began answering questions on the pages of paperwork for further testing. It was a race48 time.I wish I could say that this 49 was won. It wasn’t. The caller later thanked Karen for her participation and asked a few more questions—including whethe r or not she’d 50 on the donor list. “Of course, “Karen answered.Last week Karen gave blood and next week I’ll make my usual donation. I’ll 51 an afternoon from my schedule and make an appointment. I don’t know whose life my donation may 52 . Most likely it will be a 53 , but on any day the person needing a blood product could be you or me or maybe a loved one. It is worthwhile to 54 our time to donate.I really do feel 55 every time I donate. And I like the feeling.36. A. appointment B. class C. meeting D. flight37. A. secret B. balance C. shape D. word38. A. service B. shopping C. blood D. care39. A. alone B. welcome C. late D. lucky40. A. exposed B. attached C. applied D. added41. A. examine B. produce C. collect D. clean42. A. meet B. forget C. miss D. recognize43. A. regular B. unexpected C. special D. pleasant44. A. wisely B. differently C. hesitantly D. carefully45. A. receiver B. doctor C. patient D. donor46. A. or B. but C. and D. for47. A. risk B. customer C. match D. partner48. A. beyond B. with C. against D. of49. A. honor B. test C. prize D. race50. A. rank B. sign C. appear D. remain51. A. clear B. separate C. lose D. remove52. A. touch B. affect C. create D. enrich53. A. child B. stranger C. hero D. friend54. A. waste B. save C. kill D. take55. A. empty B. grateful C. proud D. Nervous【答案】36-40 ADCAB 41-45 CAABD46-50 BCCDD 51-55 ABBDC 2017海淀二模The Sweetest ThingWhen I was ten, I was crazy about candy. Whenever in our small-town __36__ with my mom, I would run my fingers through my favorite candy on the shelf.Once there, thinking about all things sweet, I noticed a man a few feet away pushing buttons on the ATM machine. Dressed in a suit, he seemed to be late for something, __37__ waiting for his cash to appear. The machine made a noise, and he immediately __38__ a pile of bills and headed out. Curiously, I walked over to the ATM, where I started pressing the buttons as if knowing the __39__. Then I looked into the bottom of the machine. There I saw it: a beautiful, crisp $20 bill! __40__ I wanted to believe my magic made the cash appear, I knew the man in the suit must have left it behind.I held the money in my hand, staring at the number “20” and feeling __41__ than I ever had. I thought about slipping the money into my pocket. No one would know, but it didn’t feel __42__. I knew it didn’t belong to me. I had to find its owner and give it back! So I told my mom what had happened. “We’ll look for him.” she said kindly. We rushed out and found him stepping into his car in the parking lot! We __43__ him and asked whether he had left money at the cash machine.“Let me __44__,” he said, pulling out his wallet and bills. “Twenty, forty, eighty…Oh! You’re right,” he said with surprise, “I’m __45__ a $20 bill.”“Here you go,” I said, smiling with pride, as if I was a(n) __46__ who had solved a mystery. “Thank you so much,” he said, bending down and shaking my hand. My heart __47__. Before saying goodbye, he asked my mom for my name and __48__. “I want to send your daughter a thank-you card,” he said.On my way home, my __49__ was racing. Twenty dollars. What could I have done with it? I bet I could have bought a puppy or every single candy bar in town! But now __50__ of that would happen. Yet I knew I had done the right thing.A few weeks later, I got a box with a note. I ripped it open to find packages of candy.“Dear Felice, Thank you very much for __51__ my $20. You are a great girl, and I appreciate your __52__.I hope you enjoy this candy. Best Wishes, Tom.”Tom included his business card. It turned out he was vice-president for the candy company. The candy tasted sweet, each __53__ reminding me that what I had done mattered. Although my honesty wouldn’t always be __54__ with candy, it would make a difference to someone. And that was the __55__ part of all.36. A. school B. church C. store D. bank37. A. angrily B. excitedly C. hopefully D. anxiously38. A. covered B. seized C. handed D. posted39. A. machine B. assistant C. man D. password40. A. Though B. Since C. Once D. Until41. A. smarter B. stronger C. prettier D. richer42. A. right B. good C. fair D. easy43. A. caught B. approached C. guided D. searched44. A. try B. think C. check D. guess45. A. sparing B. seeking C. missing D. changing46. A. engineer B. detective C. manager D. designer47. A. hurt B. sank C. swelled D. jumped48. A. address B. age C. habit D. birthday49. A. car B. memory C. time D. mind50. A. both B. none C. some D. either51. A. returning B. remembering C. keeping D. lending52. A. loyalty B. devotion C. honesty D. bravery53. A. dollar B. bite C. product D. choice54. A. marked B. replaced C. shared D. rewarded55. A. sweetest B. hardest C. freshest D. heaviest【答案】36-40: CDBDA 41-45: DABCC46-50: BCADB 51-55: ACBDA2017海淀期末I was the fool at school, regarded as a special needs student. I was termed as such. Obviously, because I was not interested in school and did not care for my __36__.Over time, I started to believe in my stupidity. I __37__ the fact that I was in special needs classes and poured it out as anger and depression. But one activity __38__ this view of myself: chess.I started to play chess with my father after school simply because I wanted to __39__ him at something. My father was a __40__ man, fond of physics, writing, religion, …, almost every __41__. He was called a walking dictionary. So, winning in chess against my father would be a __42__ that I had intellectual power. On the small chessboard, I had a chance to __43__ my so-called inability.Game after game, I wanted to beat my father even more. I started to study chess books and play againsta chess computer to __44__ my skills. One weekend, I finally checkmated(将杀) my father on a ferry ride, which made me feel __45__ .Two years later, I became the second board on my school chess team, with our top board being the best high school player in the state. But before the tournament season, our top player __46__ to come. There came my chance to play as top board against the best players in other states.I was determined to show who I had become: a(n) __47__ person able to win with calculation, logic and will. My most __48__ game came in the final round. Our team was facing a high school which only excellent students attended. It was __49__ a match between a special needs student and a smart soul. My opponent(对手) was playing well and kept __50__ while I kept defending to keep my king safe. He spent long trying to break down my defenses, but could not find the final push. I __51__ with more defensive moves, trying to make it as difficult for him as possible. With little__52__ left, he started to make rapid moves. __53__ he could make the final decision, he ran out of time. Honestly, as his clock flag fell, I jumped up out of my seat and kissed the floor out of excitement. Of course it was not the most sportsmen-like __54__, but I could not control my emotions.While holding my winner’s cup, I knew I was not __55__. The inferiority complex(自卑感) had melted away, and I realized that underneath our thoughts, each person is a genius.36. A. habits B. grades C. plans D. benefits37. A. noticed B. explained C. accepted D. ignored38. A. changed B. supported C. questioned D. showed39. A. please B. comfort C. beat D. disturb40. A. smart B. strict C. quiet D. strong41. A. method B. topic C. event D. field42. A. dream B. lesson C. theory D. sign43. A. prove B. expose C. overcome D. promote44. A. teach B. sharpen C. choose D. invent45. A. overjoyed B. disappointed C. puzzled D. interested46. A. promised B. managed C. happened D. failed47. A. brave B. lucky C. active D. intelligent48. A. terrible B. memorable C. dangerous D. popular49. A. normally B. possibly C. actually D. partly50. A. attacking B. smiling C. pausing D. escaping51. A. returned B. quit C. won D. exchanged52. A. patience B. time C. energy D. wisdom53. A. Once B. Until C. Before D. Unless54. A. spirit B. thought C. comment D. behavior55. A. proud B. stupid C. bright D. lazy【答案】36. BCACA 41-45DDCBA46. DDBCA 51-55ABCDB2017海淀期中Back to SchoolI had always longed to get a degree, but raising a family had come first. Now with my last __36__ in middle school, I thought, why not try to __37__ something while I still had the opportunity. When I told my husband Bob my idea, a broad smile lit up his face. “If that’s what you __38__, we’ll make it work.”When we asked the kids for advice, they had mixed __39__. Our daughter, already in college, thought it a great idea while John, in high school, was __40__ that we might be in college at the same time. James, our youngest, wanted to know who would take him to football practice. I __41__ that things would be a little different, __42__ if everyone contributed, it wouldn’t be difficult.The next day we drove to the community college and after a careful research, I chose to __43__ in occupational therapy(康复理疗).Days passed in excitement, enrolling(register)in classes, shopping for __44__ and attending orientation(入学指导). I felt like a kid again, but as the first day of classes drew near, I became __45__. I was simply too old. People would laugh at me. Finally, with encouragement from my family and friends, I stuck with my __46__.As I entered my classroom that first morning, I chose a seat in the back, hoping to __47__ attention. For the rest of that day, I did what I saw the other students do, and gradually, my self-consciousness (embarrassment deriving from the feeling that others are critically aware of you)faded. I found the classes and assignments __48__, and I left that day feeling I might survive. By the end of the first week, I had made a few friends.Studying and keeping up with my duties at home was __49__. No sooner would I begin to study than it was time to drive the kids to their activities. Math and science were __50__ my strong subjects, so I devoted more time to those. When the first semester __51__, I had a 4.0 GPA and was placed on the Honor Roll.By the second year, Bob and the kids were all doing their __52__, and I had learned how to comfortably __53__ my school and home life. My hard work paid off. I was awarded a scholarship and got the bachelor’s degree.As I drove away on the last day of school, I thought about what a difference returning to __54__ had made in my life. I looked much younger and I had more __55__and enthusiasm for life. I even became a therapist. It’s never too late to try again.36. A.classmate B.child C.student D.friend37. A. Remember B.create C.achieve D.improve38. A.Accept B.take C.offer D.want39. A.reactions B.impressions C.requests D.choices40. A.happy B.horrified C.grateful D.relieved41. plained B.noticed C.explained D.Declared42. A.but B.so C.or D.For43. A.fill B.join C.lead D.Major44. A.supplies B.clothes C.instruments D.Souvenirs45. A.determined B.confident C.anxious D.Confused46. A.opinion B.decision C.project D.Promise47. A.avoid B.draw C.receive D.Pay48. A.annoying B.depressing C.demanding D.Interesting49. A. different B. challenging C. rewarding D. Simple50. A.always B.still C.ever D.Never51. A.changed B.started C.ended D.Returned52. A.dishes B.deeds C.homework D.Share53. A.balance B.save C.continue D.Value54. A.family B.society C.school D.Hospital55. A.time B.energy C.money D.Chance【答案】36-40:BCDAB 41-45:CADAC 46-50:BADBD 51-55:CDACB。

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