2018北京一模选择题

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北京市中考2018海淀数学一模试卷(含答案)

B． 2015 年 12 月至 2017 年 6 月，我国手机在线教育课程用户规模占在线教育用户规模的比例持续上升
C． 2015 年 12 月至 2017 年 6 月，我国手机在线教育课程用户规模的平均值超过
7000 万
D． 2017 年 6 月，我国手机在线教育课程用户规模超过在线教育用户规模的
70%
）
3．若正多边形的一个外角是 120 °，则该正多边形的边数是（
A.6
B. 5
C. 4
4．下列图形中，既是中心对称图形，也是轴对称图形的是（
） D.3
）
2
2
5．如果 a
b
1 ，那么值是（ ab
）
A.2
B. 2
C.1
D. 1
6．实数 a， b， c， d 在数轴上的对应点的位置如图所示 . 若 b d 0 ，则下列结论中正确的是（
8．如图 1，矩形的一条边长为 x ，周长的一半为 y .定义 (x, y) 为这个矩形的坐标 . 如图 2，在平面直角坐标系中，直线 x 1,y 3 将第一象限划分成 4 个区域 . 已知矩形 1 的坐标的对应点 A 落在如图所示的双曲
线上，矩形 2 的坐标的对应点落在区域④中 .
则下面叙述中正确的是（
11789 4987
13764 9798
14426 11990
在线教育用户
手机在线教育课程用户
0 2015年 12月
2016年 6月
2016年 12月
2017年时间 6月
（以上数据摘自《 2017 年中国在线少儿英语教育白皮书》）
根据统计图提供的信息，下列推断一定不合理．．．的是（
）
A ． 2015 年 12 月至 2017 年 6 月，我国在线教育用户规模逐渐上升

北京延庆区2018年初三英语一模附答案

延庆区2018年初三一模英语一、单项填空（共6分，每题0.5分）从以下各题所给的A、B、C、D四个选项中，选择能够填入空白处的最正确选项。

1. My younger sister is one month old. name is Linda.A. HeB. HimC. SheD. Her2. --- Where is your mother?--- She’s working her office.A. inB. toC. onD. for3. --- do you watch TV?--- Twice a week.A. How oftenB. How longC. How manyD. How much4. Get up early, you’ll be late for the train.A. butB. orC. andD. so5. --- What do you often do in your spare time?--- I basketball with my friends.A. playsB. playC. playedD. am playing6. Bill is one of boys in our class.A. tallB. tallerC. tallestD. the tallest7.--- Peter, what did you buy?--- I a souvenir in the Capital Museum.A. buyB. boughtC. will buyD. am buying8. When my father came home, I my homework.A. was doingB. am doingC. didD. have done9.Look! Andy over there.A. dancesB. dancedC. is dancingD. will dance10.Nice to see you again. We each other since 2021.A. won’t seeB. don’t seeC. didn’t seeD. haven’t seen11.A new hospital in our hometown next year.A. were builtB. buildC. will be builtD. will build12.--- Jack, can you tell me ?--- She is in the art room.A. where is AnnB. where Ann isC. where was AnnD. where Ann was二、完形填空（共8分，每题1分）阅读下面的短文，把握其大意，然后从短文后各题所给的A、B、C、D四个选项中，选择最正确选项。

北京市朝阳区2018届九年级5月综合练习(一模)英语试题(WORD版)含答案

市区九年级综合练习（一）英语试卷2018. 5学校班级考号知识运用（共14 分）一、单项填空（共 6 分，每小题 0.5 分）从下列各题所给的A、B、C、 D 四个选项中，选择可以填入空白处的最佳选项。

1. Look! That old man is crossing the roa D. Let’s go and help ______.A. meB. himC. herD. them2. In order to keep cool, many people go swimming _______ summer．A. inB. atC. onD. to3. Hurry up, _______ you’ll be late for school．A. andB. butC. soD. or4. I think skiing is ______ than running.A. excitingB. more excitingC. most excitingD. the most exciting5. Jack ______ a good rest as soon as he finishes the exam.A. hasB. hadC. is havingD. will have6. Every year many foreigners ________ to China to learn Chinese.A. comeB. cameC. have comeD. will come7. —Where’s Bob?— He ______ in the library now.A. readsB. readC. is readingD. will read8．I _______ a picnic with my brother last Sunday. It was great.A. haveB. hadC. will haveD. am having9. I ______ my grandparents since 2016. I miss them very much.A. won’t seeB. don’t seeC. haven’t seenD. didn’t see10. My mother _______ to music when I got home at five o’clock yesterday.A. listensB. listenedC. was listeningD. has listened11. Some new computers ________ to that village school last month.A. giveB. are givenC. gaveD. were given12. —Excuse me, could you tell me ______?—Sorry, sir. I wasn’t there at that time yesterday.A. how the accident happensB. how the accident happenedC. how does the accident happenD. how did the accident happen二、完形填空（共 8 分，每小题 1 分）通读下面的短文，掌握其大意，然后从短文后各题所给的A、B、C、 D 四个选项中，选择最佳选项。

2018北京市西城一模英语试题及答案

西城区高三统一测试英语2018.4本试卷共9页，共120分。

考试时长100分钟。

考生务必将答案答在答题卡上，在试卷上作答无效。

考试结束后，将本试卷和答题卡一并交回。

第一部分：知识运用（共两节，45分）第一节单项填空（共15小题；每小题1分，共15分）从每题所给的A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

例：It’s so nice to hear from her again. _____, we last met more than thirty years ago.A. What’s moreB. That’s to sayC. In other wordsD. Believe it or not答案是D。

1. —Is there a hospital nearby? I hurt my ankle, and cannot move now.—It’s about 3 blocks away. I _____ you there.A. tookB. takeC. will takeD. have taken2. Rosa _____ this washing machine for more than ten years. She is thinking about buying a new one.A. is usingB. usedC. had usedD. has been using3. This course is of great interest to students, _____ to improve their writing skills.A. hopeB. to hopeC. hopingD. hoped4. —Vivien, you look blue. What’s wrong?—There are so many papers _____. I’m really busy recently.A. finishB. to finishC. finishingD. finished5. _____ at the differences between her culture and theirs, Annie wanted to return home.A. ConfusingB. ConfusedC. Having confusedD. To confuse6. The old bank, _____ appearance is not a pretty sight, is extremely beautiful on the inside.A. whoseB. whereC. whenD. which7. The famous player tried again and again after each failure. T hat’s _____ he succeeded at last.A. whatB. whenC. whetherD. why8. Usually Beijing Roast Duck _____ together with special pancakes, green onions and sweet sauce.A. was servedB. will serveC. is servedD. served9. _____ gas prices are rising, people are looking for less expensive ways to get around.A. Now thatB. Even ifC. AlthoughD. Unless10. _____ annoys the teacher most is that all the students are too quiet in class.A. WhatB. ThatC. WhenD. Who11. Passengers _____ talk to the driver while the bus is moving, because it will take his focus offthe road.A. would notB. must notC. may notD. need not12. _____ to manage time wisely, and you can make the most out of each day.A. LearningB. To learnC. LearnedD. Learn13. It rained this morning, _____ actually didn’t bother me because I like walking in the rain.A. whatB. whenC. whereD. which14. Parents need to encourage kids to develop their potential _____ putting too much pressure onthem.A. withoutB. besidesC. byD. for15. —What a shame! We misunderstood each other for such a long time.—Yes, I wish I _____ with you earlier.A. communicateB. had communicatedC. communicatedD. would communicate第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

2018年北京海淀区初三一模英语试卷详解

2018年北京海淀区初三一模英语试卷(详解)乙、卖麻钉掉2. A.of B.in C.at D.on【答案】【解析】Peter plays the piano in the music club Sunday afternoons.D考查介词。

句意为：皮特周日下午在音乐俱乐部弹奏钢琴。

在具体某一天的上午下午或晚上用介词on ，选D 。

3. A.How much B.How old C.How long D.How many【答案】【解析】— do you walk in the park every morning?—About 20 minutes.C考查疑问副词。

句意为：---你们每天早上在公园走多长时间？---大约二十分钟。

How much 多少，对不可数名词提问；How old 多大，对年龄提问；How long 多长，对时间、距离等提问；How many 多少，对可数名词提问。

根据答语，可知选C 。

4. A.for B.or C.but D.so【答案】I had a fever, I went to see a doctor.D1.A.myB.hisC.herD.your【答案】【解析】Mr. Cook plans to give away all money to charity.B 考查形容词性物主代词。

句意为：库克先生计划把他的所有钱捐给慈善机构。

此处指的是库克先生的钱，故用his ，选B 。

【解析】考查连词。

句意为：我发烧了，……我去看了医生。

前后为因果关系，故选D 。

5. A.fast B.faster C.fastest D.the fastest【答案】【解析】Nowadays, new subways run than the old ones.B考查副词比较级。

句意为：现在，地铁比以前快多了。

由than 可知是前后对比，用比较级，选B 。

6. A.Can B.Need C.Must D.Should【答案】【解析】— you come to my birthday party this Friday night?—Sure, I'd love to.A考查情态动词。

2018年北京市海淀区高考一模数学试卷(理科)【解析版】

2018年北京市海淀区高考数学一模试卷（理科）一、选择题共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项．1．（5分）已知集合A＝{0，a}，B＝{x|﹣1＜x＜2}，且A⊆B，则a可以是（）A．﹣1B．0C．l D．22．（5分）已知向量＝（l，2），＝（﹣1，0），则+2＝（）A．（﹣1，2）B．（﹣1，4）C．（1，2）D．（1，4）3．（5分）执行如图所示的程序框图，输出的S值为（）A．2B．6C．8D．104．（5分）如图，网格纸上小正方形的边长为1，若四边形ABCD及其内部的点组成的集合记为M，P（x，y）为M中任意一点，则y﹣x的最大值为（）A．1B．2C．﹣1D．﹣25．（5分）已知a，b为正实数，则“a＞1，b＞1”是“lga+lgb＞0”的（）A．充分而不必要条件B．必要而不充分条件C．充分必要条件D．既不充分也不必要条件6．（5分）如图所示，一个棱长为1的正方体在一个水平放置的转盘上转动，用垂直于竖直墙面的水平光线照射，该正方体在竖直墙面上的投影的面积记作S，则S的值不可能是（）A．1B．C．D．7．（5分）下列函数f（x）中，其图象上任意一点P（x，y）的坐标都满足条件y≤|x|的函数是（）A．f（x）＝x3B．C．f（x）＝e x﹣1D．f（x）＝ln（x+1）8．（5分）已知点M在圆C1：（x﹣1）2+（y﹣1）2＝1上，点N在圆C2：（x+1）2+（y+1）2＝1上，则下列说法错误的是（）A．的取值范围为B．取值范围为C．的取值范围为D．若，则实数λ的取值范围为二、填空题共6小题，每小题5分，共30分．9．（5分）复数＝．10．（5分）已知点（2，0）是双曲线C：的一个顶点，则C的离心率为．11．（5分）直线（t 为参数）与曲线（θ为参数）的公共点个数为．12．（5分）在△ABC中，若c＝2，，，则sin C＝，cos2C＝．13．（5分）一次数学会议中，有五位教师来自A，B，C三所学校，其中A学校有2位，B学校有2位，C学校有1位．现在五位教师排成一排照相，若要求来自同一所学校的教师不相邻，则共有种不同的站队方法．14．（5分）设函数．①若f（x）有两个零点，则实数a的取值范围是；②若a≤﹣2，则满足f（x）+f（x﹣1）＞﹣3的x的取值范围是．三、解答题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程．15．（13分）已知．（I ）求的值；（Ⅱ）求f（x）的单调递增区间．16．（13分）流行性感冒多由病毒引起，据调查，空气月平均相对湿度过大或过小时，都有利J＝﹣些病毒繁殖和传播，科学测定，当空气月平均相对湿度大于65010或小于40%时，有利于病毒繁殖和传播．下表记录了某年甲、乙两个城市12个月的空气月平均相对湿度（I）从上表12个月中，随机取出1个月，求该月甲地空气月平均相对湿度有利于病毒繁殖和传播的概率；（Ⅱ）从上表第一季度和第二季度的6个月中随机取出2个月，记这2个月中甲、乙两地空气月平均相对湿度都有利于病毒繁殖和传播的月份的个数为X，求X的分布列；（Ⅲ）若a+b＝108，设乙地上表12个月的空气月平均相对湿度的中位数为M，求M的最大值和最小值．（只需写出结论）17．（14分）已知三棱锥P﹣ABC（如图1）的平面展开图（如图2）中，四边形ABCD为边长为的正方形，△ABE和△BCF均为正三角形，在三棱锥P﹣ABC中：（I）证明：平面P AC⊥平面ABC；（Ⅱ）求二面角A﹣PC﹣B的余弦值；（Ⅲ）若点M在棱PC上，满足，，点N在棱BP上，且BM⊥AN，求的取值范围．18．（13分）已知函数f（x）＝．（I）当a＝0时，求函数f（x）的单调递增区间；（Ⅱ）当a＞0时，若函数f（x）的最大值为，求a的值．19．（14分）已知椭圆C：（a＞b＞0）的离心率为，且点T（2，1）在椭圆C上，设与OT平行的直线l与椭圆C相交于P，Q两点，直线TP，TQ分别与x轴正半轴交于M，N两点．（I）求椭圆C的标准方程；（Ⅱ）判断|OM|+|ON|的值是否为定值，并证明你的结论．20．（13分）设A＝（a i，j）n×n＝是由1，2，3，…，n2组成的n行n列的数表（每个数恰好出现一次），n≥2且n∈N*．既是第i行中的最大值，也是第j列中的最若存在1≤i≤n，1≤j≤n，使得a i，j小值，则称数表A为一个“N﹣数表”a i为数表A的一个“N﹣值”，，j对任意给定的n，所有“N﹣数表”构成的集合记作Ωn．（1）判断下列数表是否是“N﹣（2）数表”．若是，写出它的一个“N﹣（3）值”；，；（Ⅱ）求证：若数表A是“N﹣数表”，则A的“N﹣值”是唯一的；（Ⅲ）在Ω19中随机选取一个数表A，记A的“N﹣值”为X，求X的数学期望E（X）．2018年北京市海淀区高考数学一模试卷（理科）参考答案与试题解析一、选择题共8小题，每小题5分，共40分．在每小题列出的四个选项中，选出符合题目要求的一项．1．（5分）已知集合A＝{0，a}，B＝{x|﹣1＜x＜2}，且A⊆B，则a可以是（）A．﹣1B．0C．l D．2【解答】解：∵集合A＝{0，a}，B＝{x|﹣1＜x＜2}，且A⊆B，∴﹣1＜a＜2，∴a可以是1．故选：C．2．（5分）已知向量＝（l，2），＝（﹣1，0），则+2＝（）A．（﹣1，2）B．（﹣1，4）C．（1，2）D．（1，4）【解答】解：根据题意，向量＝（l，2），＝（﹣1，0），则2＝（﹣2，0）则+2＝（﹣1，2）；故选：A．3．（5分）执行如图所示的程序框图，输出的S值为（）A．2B．6C．8D．10【解答】解：当k＝0时，满足继续循环的条件，则S＝0，k＝1；当k＝1时，满足继续循环的条件，则S＝2，k＝2；当k＝2时，满足继续循环的条件，则S＝10，k＝3；当k＝3时，不满足继续循环的条件，故输出的S＝10，故选：D．4．（5分）如图，网格纸上小正方形的边长为1，若四边形ABCD及其内部的点组成的集合记为M，P（x，y）为M中任意一点，则y﹣x的最大值为（）A．1B．2C．﹣1D．﹣2【解答】解：根据题意知，A（﹣2，﹣1），B（2，﹣1），C（4，2），D（0，2）；设z＝y﹣x；平移目标函数z＝y﹣x，当目标函数过点D时，y﹣x取得最大值为2﹣0＝2．故选：B．5．（5分）已知a，b为正实数，则“a＞1，b＞1”是“lga+lgb＞0”的（）A．充分而不必要条件B．必要而不充分条件C．充分必要条件D．既不充分也不必要条件【解答】解：由lga+lgb＞0得lgab＞0，即ab＞1，当a＞1，b＞1时，ab＞1成立，当a＝4，b＝，满足ab＞1，但b＞1不成立，则“a＞1，b＞1”是“lga+lgb＞0”的充分不必要条件，故选：A．6．（5分）如图所示，一个棱长为1的正方体在一个水平放置的转盘上转动，用垂直于竖直墙面的水平光线照射，该正方体在竖直墙面上的投影的面积记作S，则S的值不可能是（）A．1B．C．D．【解答】解：由题意知，棱长为1的正方体在竖直墙面上的投影面积S的最小值为正方形，且边长为1，其面积为1；最大值为矩形，且相邻的两边长为1和，其面积为1×＝；∴S的取值范围是[1，]；又＜，∴不可能的是选项D．故选：D．7．（5分）下列函数f（x）中，其图象上任意一点P（x，y）的坐标都满足条件y≤|x|的函数是（）A．f（x）＝x3B．C．f（x）＝e x﹣1D．f（x）＝ln（x+1）【解答】解：函数f（x）图象上任意一点P（x，y）的坐标都满足条件y≤|x|的函数的图象位于下图中的①、②或④的区域，在A中，f（x）＝x3的图象位于③，④的部分区域，故A错误；在B中，f（x）＝的图象位于②③的部分区域，故B错误；在C中，f（x）＝e x﹣1的图象位于①②③④的部分区域，故C错误；在D中，f（x）＝ln（x+1）的图象位于②的区域，故D正确．故选：D．8．（5分）已知点M在圆C1：（x﹣1）2+（y﹣1）2＝1上，点N在圆C2：（x+1）2+（y+1）2＝1上，则下列说法错误的是（）A．的取值范围为B．取值范围为C．的取值范围为D．若，则实数λ的取值范围为【解答】解：∵M在圆C1上，点N在圆C2上，∴∠MON≥90°，∴≤0，又OM≤+1，ON≤+1，∴当OM＝+1，ON＝+1时，取得最小值（+1）2cosπ＝﹣3﹣2，故A正确；设M（1+cosα，1+sinα），N（﹣1+cosβ，﹣1+sinβ），则＝（cosα+cosβ，sinα+sinβ），∴||2＝2cosαcosβ+2sinαsinβ+2＝2cos（α﹣β）+2，∴0≤||≤2，故B错误；∵两圆外离，半径均为1，|C1C2|＝2，∴2﹣2≤|MN|≤2+2，即2﹣2≤||≤2+2，故C正确；∵﹣1≤|OM|≤+1，≤|ON|≤+1，∴当时，≤﹣λ≤，解得﹣3﹣2≤λ≤﹣3+2，故D正确．故选：B．二、填空题共6小题，每小题5分，共30分．9．（5分）复数＝1+i．【解答】解：＝＝i+1．故答案为：1+i．10．（5分）已知点（2，0）是双曲线C：的一个顶点，则C的离心率为．【解答】解：根据题意，点（2，0）是双曲线C：的一个顶点，则a＝2，双曲线的方程为，则b＝1，则c＝＝，则双曲线的离心率e＝＝；故答案为：．11．（5分）直线（t为参数）与曲线（θ为参数）的公共点个数为2．【解答】解：直线（t为参数）消去参数t，得x﹣2y＝0，曲线（θ为参数）消去参数，得（x﹣2）2+y2＝1，联立，得或．∴直线（t为参数）与曲线（θ为参数）的公共点个数为2．故答案为：2．12．（5分）在△ABC中，若c＝2，，，则sin C＝，cos2C＝．【解答】解：△ABC中，若c＝2，，，利用正弦定理：，则：，所以：cos2C＝1﹣2sin2C＝1﹣＝．故答案为：．13．（5分）一次数学会议中，有五位教师来自A，B，C三所学校，其中A学校有2位，B学校有2位，C学校有1位．现在五位教师排成一排照相，若要求来自同一所学校的教师不相邻，则共有48种不同的站队方法．【解答】解：有五位教师来自A，B，C三所学校，其中A学校有2位，B学校有2位，C学校有1位．现在五位教师排成一排照相，要求来自同一所学校的教师不相邻，先安排A学校和C学校的三位老师，有中排法，再把B学校的两位老师插空排到A学校和C学校的三位老师的空位中，并对B学校的两位老师进行排序，有＝24种排法，由乘法原理得不同的排列方法有：＝48种，故答案为：48．14．（5分）设函数．①若f（x）有两个零点，则实数a的取值范围是（﹣，]；②若a≤﹣2，则满足f（x）+f（x﹣1）＞﹣3的x的取值范围是（﹣1，+∞）．【解答】解：①若a＝0，则f（x）＝，由f（x）＝0，可得x＝0，x＝﹣，符合题意；若a＜0，x＝0符合题意；若x＝﹣符合题意，则a＞﹣，即为﹣＜a＜0；若a＞0，则x＝0和x＝﹣符合题意，可得a≤，综上可得，a的范围是（﹣，]；②若x＜a≤﹣2，则x﹣1＜a﹣1≤﹣3，f（x）的导数为3x2﹣3＞0，可得f（x）＜f（﹣2）＝﹣2，f（x﹣1）＜﹣27+9＝﹣18，即有f（x）+f（x﹣1）＜﹣30，不符题意；则x≥a，若x﹣1≥a，f（x）+f（x﹣1）＞﹣3，即为x+x﹣1＞﹣3，解得x＞﹣1；若a﹣1≤x﹣1＜a，f（x）+f（x﹣1）＞﹣3，即为x+（x﹣1）3﹣3（x﹣1）＞﹣3，化为x3﹣3x2+x+5＞0，由于a≤﹣2，且a≤x＜a+1，可得g（x）＝x3﹣3x2+x+5的导数g′（x）＝3x2﹣6x+1＞0，即g（x）在[a，a+1）递增，g（a）取得最小值，且为a3﹣3a2+a+5，且a3﹣3a2+a+5，而在a≤﹣2时，a3﹣3a2+a+5递增，且为负值，不符题意．综上可得a的范围是（﹣1，+∞）．故答案为：（﹣，]，（﹣1，+∞）．三、解答题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程．15．（13分）已知．（I ）求的值；（Ⅱ）求f（x）的单调递增区间．【解答】解：（Ⅰ）直接将x ＝带入，可得：＝＝2．（Ⅱ）由＝因为函数y＝sin x 的单调递增区间为（k∈Z），令（k∈Z），解得（k∈Z），故f（x ）的单调递增区间为（k∈Z）．16．（13分）流行性感冒多由病毒引起，据调查，空气月平均相对湿度过大或过小时，都有利J＝﹣些病毒繁殖和传播，科学测定，当空气月平均相对湿度大于65010或小于40%时，有利于病毒繁殖和传播．下表记录了某年甲、乙两个城市12个月的空气月平均相对湿度（I ）从上表12个月中，随机取出1个月，求该月甲地空气月平均相对湿度有利于病毒繁殖和传播的概率；（Ⅱ）从上表第一季度和第二季度的6个月中随机取出2个月，记这2个月中甲、乙两地空气月平均相对湿度都有利于病毒繁殖和传播的月份的个数为X ，求X 的分布列；（Ⅲ）若a +b ＝108，设乙地上表12个月的空气月平均相对湿度的中位数为M ，求M 的最大值和最小值．（只需写出结论）【解答】（本题满分13分）解：（Ⅰ）设事件A ：从上表12个月中，随机取出1个月，该月甲地空气月平均相对湿度有利于病毒繁殖和传播．用A i 表示事件抽取的月份为第i 月，则Ω＝{A 1，A 2，A 3，A 4，A 5，A 6，A 7，A 8，A 9，A 10，A 11，A 12}共12个基本事件， A ＝{A 2，A 6，A 8，A 9，A 10，A 11}共6个基本事件，所以，该月甲地空气月平均相对湿度有利于病毒繁殖和传播的概率．（4分）（Ⅱ）在第一季度和第二季度的6个月中，甲、乙两地空气月平均相对湿度都有利于病毒繁殖和传播的月份只有2月和6月，故X 所有可能的取值为0，1，2．，，随机变量X的分布列为：（Ⅲ）a+b＝108，设乙地上表12个月的空气月平均相对湿度的中位数为M，则M的最大值为58%，最小值为54%．（13分）17．（14分）已知三棱锥P﹣ABC（如图1）的平面展开图（如图2）中，四边形ABCD为边长为的正方形，△ABE和△BCF均为正三角形，在三棱锥P﹣ABC中：（I）证明：平面P AC⊥平面ABC；（Ⅱ）求二面角A﹣PC﹣B的余弦值；（Ⅲ）若点M在棱PC上，满足，，点N在棱BP上，且BM⊥AN，求的取值范围．【解答】（本题满分14分）证明：（Ⅰ）证法一：设AC的中点为O，连接BO，PO．由题意，PO＝1，AO＝BO＝CO＝1因为在△P AC中，P A＝PC，O为AC的中点所以PO⊥AC，因为在△POB中，PO＝1，OB＝1，所以PO⊥OB因为AC∩OB＝O，AC，OB⊂平面ABC所以PO⊥平面ABC因为PO⊂平面P AC（4分）所以平面P AC⊥平面ABC证法二：设AC的中点为O，连接BO，PO．因为在△P AC中，P A＝PC，O为AC的中点，所以PO⊥AC，因为P A＝PB＝PC，PO＝PO＝PO，AO＝BO＝CO所以△POA≌△POB≌△POC所以∠POA＝∠POB＝∠POC＝90°所以PO⊥OB因为AC∩OB＝O，AC，OB⊂平面ABC所以PO⊥平面ABC因为PO⊂平面P AC（4分）所以平面P AC⊥平面ABC证法三：设AC的中点为O，连接PO，因为在△P AC中，P A＝PC，所以PO⊥AC设AB的中点Q，连接PQ，OQ及OB．因为在△OAB中，OA＝OB，Q为AB的中点所以OQ⊥AB．因为在△P AB中，P A＝PB，Q为AB的中点所以PQ⊥AB．因为PQ∩OQ＝Q，PQ，OQ⊂平面OPQ所以AB⊥平面OPQ因为OP⊂平面OPQ所以OP⊥AB因为AB∩AC＝A，AB，AC⊂平面ABC所以PO⊥平面ABC因为PO⊂平面P AC（4分）所以平面P AC⊥平面ABC解：（Ⅱ）由PO⊥平面ABC，OB⊥AC，如图建立空间直角坐标系，则O（0，0，0），C（1，0，0），B（0，1，0），A（﹣1，0，0），P（0，0，1）由OB⊥平面APC，故平面APC的法向量为由，设平面PBC的法向量为，则由得：令x＝1，得y＝1，z＝1，即由二面角A﹣PC﹣B是锐二面角，所以二面角A﹣PC﹣B的余弦值为（9分）（Ⅲ）设，0≤μ≤1，，，令得（1﹣λ）•1+（﹣1）•（1﹣μ）+λ•μ＝0即，μ是关于λ的单调递增函数，当时，，所以．（14分）18．（13分）已知函数f（x）＝．（I）当a＝0时，求函数f（x）的单调递增区间；（Ⅱ）当a＞0时，若函数f（x）的最大值为，求a的值．【解答】解：（Ⅰ）当a＝0时，，故，令f'（x）＞0，得0＜x＜e；故f（x）的单调递增区间为（0，e）（4分）（Ⅱ）方法1：令则由，故存在，g（x0）＝0故当x∈（0，x0）时，g（x）＞0；当x∈（x0，+∞）时，g（x）＜0故故，解得（13分）故a的值为e2．（Ⅱ）方法2：f（x）的最大值为的充要条件为：对任意的x∈（0，+∞），且存在x0∈（0，+∞），使得，等价于对任意的x∈（0，+∞），a≥e2lnx﹣x且存在x0∈（0，+∞），使得a≥e2lnx0﹣x0，等价于g（x）＝e2lnx﹣x的最大值为a．∵，令g'（x）＝0，得x＝e2．x，g′（x），g（x）的变化如下：故g（x）的最大值为g（e2）＝e2lne2﹣e2＝e2，即a＝e2．（13分）19．（14分）已知椭圆C：（a＞b＞0）的离心率为，且点T（2，1）在椭圆C上，设与OT平行的直线l与椭圆C相交于P，Q两点，直线TP，TQ分别与x轴正半轴交于M，N两点．（I）求椭圆C的标准方程；（Ⅱ）判断|OM|+|ON|的值是否为定值，并证明你的结论．【解答】解：（Ⅰ）由题意，解得：，，故椭圆C的标准方程为；（Ⅱ）根据题意，假设直线TP或TQ的斜率不存在，则P点或Q点的坐标为（2，﹣1），直线l的方程为，即．联立方程，得x2﹣4x+4＝0，此时，直线l与椭圆C相切，不合题意．故直线TP和TQ的斜率存在．设P（x1，y1），Q（x2，y2），则直线，直线故，由直线，设直线（t≠0）联立方程，当△＞0时，x1+x2＝﹣2t，，|OM|+|ON|＝＝＝＝＝4．20．（13分）设A＝（a i，j）n×n＝是由1，2，3，…，n2组成的n行n列的数表（每个数恰好出现一次），n≥2且n∈N*．若存在1≤i≤n，1≤j≤n，使得a i，j既是第i行中的最大值，也是第j列中的最小值，则称数表A为一个“N﹣数表”a i，j为数表A的一个“N﹣值”，对任意给定的n，所有“N﹣数表”构成的集合记作Ωn．（1）判断下列数表是否是“N﹣（2）数表”．若是，写出它的一个“N﹣（3）值”；，；（Ⅱ）求证：若数表A是“N﹣数表”，则A的“N﹣值”是唯一的；（Ⅲ）在Ω19中随机选取一个数表A，记A的“N﹣值”为X，求X的数学期望E（X）．【解答】（本题满分13分）解：（Ⅰ）A是“N﹣数表”，其“N﹣值”为3，B不是“N﹣数表”．（3分）证明：（Ⅱ）假设a i，j 和a i'，j'均是数表A的“N﹣值”，①若i＝i'，则a i，j＝max{a i，1，a i，2，…，a i，n}＝max{a i'，1，a i'，2，…，a i'，n}＝a i'，j'；②若j＝j'，则a i，j＝min{a1，j，a2，j，…，a n，j}＝min{a1，j'，a2，j'，…，a n，j'}＝a i'，j'；③若i≠i'，j≠j'，则一方面a i，j＝max{a i，1，a i，2，…，a i，n}＞a i，j'＞min{a1，j'，a2，j'，…，a n，j'}＝a i'，j'，另一方面a i'，j'＝max{a i'，1，a i'，2，…，a i'，n}＞a i'，j＞min{a1，j，a2，j，…，a n，j}＝a i，j；矛盾．即若数表A是“N﹣数表”，则其“N﹣值”是唯一的．（8分）解：（Ⅲ）解法1：对任意的由1，2，3，…，361组成的19行19列的数表A＝（a i，j ）19×19．定义数表B＝（b j，i ）19×19如下，将数表A的第i行，第j列的元素写在数表B的第j行，第i列，即b j，i ＝a i，j（其中1≤i≤19，1≤j≤19）由题意，得：①数表B是由1，2，3，…，361组成的19行19列的数表②数表B的第j行的元素，即为数表A的第j列的元素③数表B的第i列的元素，即为数表A的第i行的元素④若数表A中，a i，j是第i行中的最大值，也是第j列中的最小值则数表B中，b j，i是第i列中的最大值，也是第j行中的最小值．定义数表C＝（c j，i ）19×19如下，其与数表B对应位置的元素的和为362，即c j，i ＝362﹣b j，i（其中1≤i≤19，1≤j≤19）由题意得：①数表C是由1，2，3，…，361组成的19行19列的数表②若数表B中，b j，i是第i列中的最大值，也是第j列中的最小值则数表C中，c j，i是第i列中的最小值，也是第j列中的最大值特别地，对由1，2，3，…，361组成的19行19列的数表A＝（a i，j ）19×19①数表C是由1，2，3，…，361组成的19行19列的数表②若数表A中，a i，j是第i行中的最大值，也是第j列中的最小值则数表C中，c j，i是第i列中的最小值，也是第j列中的最大值即对任意的A∈Ω19，其“N﹣值”为a i，j（其中1≤i≤19，1≤j≤19），则C∈Ω19，且其“N﹣值”为c j，i ＝362﹣b j，i＝362﹣a i，j．记C＝T（A），则T（C）＝A，即数表A与数表C＝T（A）的“N﹣值”之和为362，故可按照上述方式对Ω19中的数表两两配对，使得每对数表的“N﹣值”之和为362，故X的数学期望E（X）＝181．（13分）解法2：X所有可能的取值为19，20，21，…，341，342，343．记Ω19中使得X＝k的数表A的个数记作n k，k＝19，20，21，…，341，342，343，则．则，则，故，E（X）＝181．（13分）。

2018高三英语朝阳一模试题(版,含答案)

北京市朝阳区高三年级第一次综合练习英语学科测试2018.3（考试时间100分钟满分120分)本试卷共10页。

考生务必将答案答在答题卡上，在试卷上作答无效。

第一部分：知识运用（共两节，45分）第一节单项填空（共15小题；每小题1分, 共15分）从每题所给的A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

例：It’s so nice to hear from her again. _____,we last met more than thirty years ago.A. What’s moreB. That’s to sayC. In other wordsD. Believe it ornot答案是D。

1.Peter has previous experience, ______I think he’s the right person for the job.A. orB. butC. forD. so2. ––What did the doctor say about your injury?––She said I should avoid doing too much exercise ______ it feels better.A. untilB. sinceC. ifD. while3. The meal itself was not so good—______ was boringly brown including vegetables.A. nothingB. everythingC. anythingD. something4. Don’t worry. A number of efforts are being made ______ the whole system operating normally.A. being keptB. keptC. keepingD. to keep5. Hawking believes the earth is unlikely to be the only planet _____ life has developed gradually.A. thatB. whyC. whereD. whose6. ––Cathy is not coming to your birthday party tonight.––But she ______!A. promisedB. promisesC.will promiseD. had promised7.Don’t forget to send ______ attended the conference a follow-up email.A. howeverB. whateverC. whoeverD. wherever8.Your red coat looks so good. It stood out clearly ______ the snow.A. acrossB. againstC. throughD. over9. Look! Here’s a photo ______ in my classroom at primary school. Can you recognize me in it?A. takenB. takingC. to takeD. being taken10. ––Are the repairs finished yet?––Yes, they ______ when I came back home.A.would be completedB. would completeC. had completedD. had been completed11. Sometimes it seems to bother the teacher ______ all the students are being too quiet.A. howB. whatC. thatD. where12. ______ such a problem before, we handled the situation very well this time.A. Deal withB. Dealing withC. To deal withD. Having dealt with13. It seems late to say anything. We probably ______ it if we had made an offer sooner.A. would have gotB. would getC. had gotD. got14. I think Ana ______ her packing since she started getting things ready early this morning.A. finishesB. has finishedC. had finishedD. would finish15. What I love most about reading novels is ______ the authors vividly describethe characters.A. whatB. whyC. howD. whom第二节完形填空（共20小题；每小题1.5分，共30分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。

2018年北京市门头沟区中考一模英语试卷及答案

2018年北京市门头沟区中考一模英语试卷知识运用（共14 分）一、单项填空（共6 分，每小题0.5 分）从下面各题所给的A、B、C、D 四个选项中，选择可以填入空白处的最佳选项。

1. Tom is my best friend. ______ is very nice.A. HeB. SheC. HimD. Her2. I often go to the museums ______Sundays.A. atB. inC. onD. to3. —______ did da Vinci write his diary in code?—Because he wanted to keep his ideas secret, I think.A. WhatB. WhereC. WhoD. Why4. I think listening is ______ than reading in English learning.A. difficultB. more difficultC. most difficultD. the most difficult5. —Can you speak Chinese, Jim?—Yes, I ______, but just a little.A. canB. mustC. mayD. need6. Jack ______ something helpful in the community every week.A. doB. doesC. has doneD. was doing. Last Monday my mother ______ a big meal for my birthday.A. cookB. cooksC. is cookingD. cooked8. My teacher ______when I came into the office.A. workB. worksC. is workingD. was working 9. Tina is my friend. We ______ each other for 12 years.A. knowB. knewC. have knownD. will know10. My family ______ a picnic next Sunday.A. haveB. will haveC. was havingD. has had11. Many new buildings ______ in Mentougou last year.A. buildB. are builtC. builtD. were built12. —Tim, could you tell me ______ to the U.S.A.?—Oh, yes. I went there last year.A. when did you goB. when will you goC. when you wentD. when you will go二、完形填空（共8 分，每小题1 分）阅读下面的短文，掌握其大意，然后从短文后各题所给的A、B、C、D 四个选项中，选择最佳选项。

2018北京中考海淀一模英语试题

海淀区九年级第二学期期中练习英语2018.5知识运用(共14分)一单项填空(共6分,每小题0.5分)从下面各题所给的A,BC,D四个选项中,选择可以填入空白处的最佳选项。

1.Mr.Cook plans to give away all _ money to charity.A. myB. hisC.herD.your2.Peter plays the piano in the musie club__Sunday afternoons.A.ofB.inC.atD.on3.-__ do you walk in the park every momning?-About 20 minutes.A.How muchB.How oldC.How longD.How many4.I had a fever,__ _I went to see a doctor.A.forB.orC.butD.so5.Nowadayw,new subways run__ than the old ones.A.fastB.fasterC.fastestD.the fastest6.-__you come to my birthday party this Friday night?-Sure,I'd love to.A.CanB.NeedC.MustD.Should7.I think I__my new project tomorrow.A.startB.startedC.will startD.was starting8.They _ their holidays in Paris last summer.A.spendB.spentC.will spendD.are spending9.-Hello!May I speak to Mary,please?-Sorry.She_ __a shower now.A.hasB.hadC.will haveD.is having10.Linda_ __a lot since I saw her last time.A.has changedB.will changeC.is changingD.changedlions of emails_ __all over the world every day.A.sendB.sentC.are sentD.were sent12.-What beautiful photos!Can you tell me__一I took them in the Summer Palace.A.where you took themB.where you will take themC.where did you take themD.where will you take them二完形填空(共8分,每小题1分)阅读下面的短文,掌握其大意,然后从短文后各陋所给的A,B、C、D四个选项中,选择最佳选项。

2018年北京西城历史一模试题及答案

北京市西城区2018年九年级统一测试历史试卷 2018.4第一部分选择题一、选择题(本大题30小题，每小题1．5分，共45分。

在每小题列出的四个选项中，只有一项最符合题目要求，请将该选项前的字母代号填涂在答题卡上。

) 1．观察右图，导致两地房屋建筑样式不同的主要原因是A ．生活习惯B ．劳动技术C ．自然条件D ．生产工具2．春秋战国时期，提出“仁者爱人”“为政以德，譬如北辰，居其所而众星共之”的思想家是A ．老子B ．孔子C ．墨子D ．韩非 3．右图是古代某一著名水利工程的示意图，它是世界上唯一留存并仍在使用的无坝引水水利工程。

其修建者是 A ．郭守敬 B ．商鞅 C ．李冰 D ．李春4．据右侧“笔记卡片”判断，这页笔记记录的主题是 A ．秦始皇建立中央集权制度 B ．汉武帝巩固大一统 C ．唐玄宗开创开元盛世 D ．宋太祖强化中央集权5．魏晋南北朝时期，我国一位数学家将圆周率精确到小数点后第7位数字，领先世界近一千年。

这位数学家是 A ．祖冲之B ．贾思勰C ．刘徽D ．宋应星6．右图是一位同学设计的“中国朝代更迭示意图”的片段。

其中“？”处应为 A ．西晋 B ．隋朝 C ．宋朝 D ．元朝7．“唐朝的社会风气显示出开放、进取、兼容并蓄的精神风貌。

”下列文物能支撑该观点的是A．①③ B．②③ C．①④ D．③④8．据统计：武则天时期，有67人为宰相，其中科举出身者20人，比例占3O％；唐玄宗时期有26人为相，其中科举出身者12人，比例近5O％；安史之乱后，有185人为相，其中科举出身者116人，比例近7O％，进士为相者107人，约占宰相总人数的6O％。

这说明①武则天时期，开始实行科举选官制度②唐朝统治者比较重视科举制③武则天以后，科举出身的宰相逐渐增多④唐朝科举制逐步走向衰落A．①② B．①③ C．③④ D．②③9．观察右图，图中“？”政权的建立者是A．杨坚B．赵构C．赵匡胤D．朱元璋10．世界上最早的纸币是我国宋代的A．会子 B．交子 C．飞钱 D．宝钞11．下列语句中，能够反映长江流域已成为我国古代经济重心的是A．南朝四百八十寺，多少楼台烟雨中 B．忆昔开元全盛日，小邑犹藏万家室C．苏湖熟，天下足D．买不尽松江布，收不尽魏塘纱12．下列图示反映了中国古代王朝行政机构设置的主要情况，按其设置的时间先后排序，正确的是A．图1、图2、图3 B．图2、图3、图1C．图3、图2、图1 D．图2、图1、图313．下列名言中，表达了民族英雄戚继光抗敌决心的是A．开辟荆榛逐荷夷，十年始克复先基B．封侯非我意，但愿海波平C．我自横刀向天笑，去留肝胆两昆仑 D．生当作人杰，死亦为鬼雄14．某历史兴趣小组进行研究性学习，收集到一些图片资料。

北京市朝阳区2018年初中英语一模试题(Word版含答案)2018.4

北京市朝阳区2018 年初中毕业考试知识运用(共40 分)一、单项填空(共24 分,每小题2 分)从下列各题所给的A、B、C、D 四个选项中,选择可以填入空白处的最佳选项。

1. My father is a teacher. works in No. 5 Middle School.A. IB. HeC. SheD. You2. We usually have the first class 8:00 in the morning.A. atB. inC. onD. for3. —Excuse me, is the bank, please?—It's next to the supermarket.A. whichB. whenC. whereD. what4. Laura is than you, I think.A. tallB. taller C tallest D. the tallest5. Li Lei is very kind. He often me with my English.A. helpsB. is helpingC. helpedD. will help6. —Where is Jim now?—He football on the playground.A. playB. playedC. is playingD. has played7. My mother to music when I got home yesterday.A. listensB. will listenC. has listenedD. was listening8. —What did Mr Brown do bofore he came to China?—He in a car factory.A. worksB. worked C is working D. will work9. Mr. Green, a fumous writer, our school next week.A. visitedB. visitsC. was visitingD. will visit10.They will go to the park if it next Sunday.A. doesn’t rainB. won’t rianC. didn’t rainD. isn’t raining11.The trees here two years ago .A. plantB. plantedC. are plantedD. were planted12. —Do you know ?—Tomorrow morning .A. when will they come to visit usB. when did they come to visit usC. when they will come to visit usD. when they came to visit us二、完形填空(共16 分,每小题2 分)通读下面的短文,掌握其大意,然后从短文后各题所给的A、B、C、D 四个选项中,选择最佳选项。

2018年北京东城高三一模数学试题及答案word版

数学（文科）学校 _____________ 班级 _______________ 姓名 ______________ 考号 ___________本试卷共 5 页， 150 分。

考试时长120 分钟。

考生务势必答案答在答题卡上，在试卷上作答无效。

考试结束后，将本试卷和答题卡一并交回。

第一部分（选择题共40分）一、选择题共8 小题，每题 5 分，共 40 分。

在每题列出的四个选项中，选出吻合题目要求的一项。

（ 1）若会集A{ x |3x1}，B{ x | x1或 x2} ，则AI B（ A）{ x | 3 x1}（ B）{ x | 3 x 2}（ C）{ x | 1 x 1}（ D）{ x |1 x 2}i在复平面内对应的点位于（ 2）复数z1i（ A）第一象限（B）第二象限（ C）第三象限（D）第四象限x y20,（ 3）若x, y满足2x y20, 则y x 的最大值为y0,（A）2（B）1（C）2（D）4（ 4）执行以以下图的程序框图，假如输出的S值为 30，那么空白的判断框中应填入的条件是（ A）n2开始（ B）n3（ C）n4n0, S0（ D）n5否是n n1输出 SS S2n结束（ 5）某三棱锥的三视图以以下图，则该三棱锥最长棱的棱长为（ A ） 2（ B ）2 2（ C ）2 3（ D ） 4（ 6）函数 f ( x)4 2x 的零点所在区间是x（A ） (0, 1 )（B ） (2（ C ） (1, 3)（D ） (2（ 7）已知平面向量 a,b, c 均为非零向量，则“1,1)23, 2)2(a b)c(b c)a ”是“向量 a,c 同向”的（ A ）充足而不用要条件（ B ）必需而不充足条件（ C ）充足必需条件（ D ）既不充足也不用要条件（ 8）为弘扬中华传统文化，某校组织高一年级学生到古都西安游学．在某景区，因为时间关系，每个班只好在甲、乙、丙三个景点中选择一个旅游． 127名同学决定投票来选定旅游的景点，高一班的商定每人只好选择一个景点，得票数高于其他景点的当选．据认识，在甲、乙两个景点中有 18 人会选择甲，在乙、丙两个景点中有18 人会选择乙．那么关于这轮投票结果，以下说法正确的选项是 ①该班选择去甲景点旅游；②乙景点的得票数可能会超出9 ；③丙景点的得票数不会比甲景点高；④三个景点的得票数可能会相等.（ A ）①② （B ）①③（ C ）②④（D ）③④第二部分（非选择题共 110 分）二、填空题共 6 小题，每题5 分，共 30 分。

2018年北京西城区初三一模英语试卷详解

2018年北京⻄城区初三⼀模英语试卷(详解)⼀、单项选择2. A.in B.on C.at D.with【答案】【解析】—What's the weather like in Australia July?—It is winter there, so it's a little cold.A考查时间介词。

句意为：在七⽉，澳⼤利亚的天⽓如何？表示在七⽉，⽤介词in ，选A 。

3. A.bright B.brighter C.brightest D.the brightest【答案】【解析】The North Star is one of stars in the night sky.D考查形容词最⾼级。

句意为：北极星是夜晚天空中最亮的星星之⼀。

One ofthe+adj.最⾼级+n.复数表示最……的……之⼀。

选D 。

4. A.so B.or C.but D.and【答案】I'd love to go to the theatre tonight, I am too busy.C1.A.theyB.themC.theirD.themselves【答案】【解析】—Jack, thank you for the flowers.—It's all right. I hope you like .B 考查代词的宾格形式。

句意为：杰克，感谢你送我的花。

—没关系，我希望你喜欢。

Like 为动词，其后接代词宾格，选B 。

【解析】考查连词。

句意为：今天晚上我想去电影院，……我很忙。

前后为转折关系，故选C 。

5. A.visit B.visited C.have visited D.are visiting【答案】【解析】We a few museums while we were in London.B考查时态。

句意为：我们在伦敦的时候参观了⼏家博物馆。

根据were 可知是过去做的事情，⽤⼀般过去时，选B 。

2018北京高考一模单选汇编

一、【海淀一模】1. The course is designed to help students learn to show respect for .A. othersB. bothC. thoseD. either2. He will never make progress in math he really wants to learn it.A. ifB. as long asC. unlessD. in case3. A report on food safety in Beijing on January 15th, 2018 and it has received positive reviews.A. publishedB. was publishedC. has publishedD. has been published4. good air quality, the government is replacing coal fuel with natural gas.A. GuaranteedB. GuaranteeingC. To guaranteeD. Guarantee5. leaves the classroom last should turn off the lights.A. WhichB. WhoC. Whichever D .Whoever6.This problem again? We it many times!A. are discussingB. discussedC. had discussedD. have discussed7. On Sunday morning, Nancy plans for the trip when her mother walked in.A. is reviewing B_ will review C. was reviewing D . reviewed8.——I went to the concert last night. It was fantastic!—You were so lucky! How I wish I the ticket too.A.had gotB. would getC. gotD. get9.Once by the soccer team, yourself need to train three times a week.A. acceptingB. acceptedC. to acceptD. accept10.— Have you heard that Space X sent a Tesla car into space?—Yes. they have achieved is amazing.A. WhereB. HowC. ThatD. What11. It is through decades of hard work China has progressed to a new stage.A. thatB. whereC. whichD. what12.The mayor made a statement his concern for the misuse of shared bicycles.A. voicedB. voiceC. voicingD. having voiced13. Michael was happy that he had a roof _ his head when it rained.A. onB. overC. upD. around14. You something great, otherwise you wouldn’t have got the promotion.A. should doB. must doC. should have doneD. must have done15.Across the street is the research center Stephen Hawking made his ground-breaking discoveries in physics.A. whereB. thatC. whenD. which二、【西城一模】1. —Is there a hospital nearby? I hurt my ankle, and cannot move now.—It’s about 3 blocks away. I _____ you there.A. tookB. takeC. will takeD. have taken2. Rosa _____ this washing machine for more than ten years. She is thinking about buying a newone.A. is usingB. usedC. had usedD. has been using3. This course is of great interest to students, _____ to improve their writing skills.A. hopeB. to hopeC. hopingD. hoped4. —Vivien, you look blue. What’s wrong?—There are so many papers _____. I’m really busy recently.A. finishB. to finishC. finishingD. finished5. _____ at the differences between her culture and theirs, Annie wanted to return home.A. ConfusingB. ConfusedC. Having confusedD. To confuse6. The old bank, _____ appearance is not a pretty sight, is extremely beautiful on the inside.A. whoseB. whereC. whenD. which7. The famous player tried again and again after each failure. T hat’s _____ he succeeded at last.A. whatB. whenC. whetherD. why8. Usually Beijing Roast Duck _____ together with special pancakes, green onions and sweet sauce.A. was servedB. will serveC. is servedD. served9. _____ gas prices are rising, people are looking for less expensive ways to get around.A. Now thatB. Even ifC. AlthoughD. Unless10. _____ annoys the teacher most is that all the students are too quiet in class.A. WhatB. ThatC. WhenD. Who11. Passengers _____ talk to the driver while the bus is moving, because it will take his focus off the road.A. would notB. must notC. may notD. need not12. _____ to manage time wisely, and you can make the most out of each day.A. LearningB. To learnC. LearnedD. Learn13. It rained this morning, _____ actually didn’t bother me because I like walking in the rain.A. whatB. whenC. whereD. which14. Parents need to encourage kids to develop their potential _____ putting too much pressure on them.A. withoutB. besidesC. byD. for15. —What a shame! We misunderstood each other for such a long time.—Yes, I wish I _____ with you earlier.A. communicateB. had communicatedC. communicatedD. would communicate三、【朝阳一模】21. You can smoke here _____ you leave a window open to let the smoke out.A. even thoughB. so thatC. in caseD. as long as22. —Can we play on the football field now?—No, the grass _____.A. will be cutB. is being cutC. was cutD. has been cut23. It hasn’t been announced _____ the plane is to take off.A. whereB. whenC. howD. why24. The problem is _____ his ability and I don’t think he can solve it.A. beyondB. toC. againstD. within25. _____ around the school, the retired teachers were impressed by its new look.A. ShowingB. To be shownC. Having shownD. Shown26. Travelling abroad is a great way to find out _____ life is like in another part of the world.A. whatB. howC. whereD. that27. —You seem to be familiar with the school.—I _____ here for three years. It’s great to be back.A. studiedB. have studiedC. had studiedD. study28. The goals _____ he had fought all his life no longer seemed important to him.A. after whichB. with whichC. for whichD. at which29. The agreement _____ between the two companies last week will come into effect soon.A. to signB. to be signedC. signedD. signing30. —What kind of food do you prefer?—_____ but Japanese.A. SomethingB. AnythingC. EverythingD. Nothing31. Sir Denis has made it known that he _____ much of his collection to the nation after his death.A. has leftB. leftC. would leaveD. will leave32. —What’s the matter with Coco?—She has a headache because she _____ too long; she ought to stop working now.A. has been readingB. was readingC. readsD. had read33. I saw them whispering to each other; obviously they did not want _____ by others.A. to hearB. to be heardC. hearingD. being heard34. —Mom, I’m going to Diana’s birthday party tomorrow.—OK, but you _____ stay there too late. Be sure to get home before 10 pm.A. couldn’tB. wouldn’tC. mustn’tD. might not35. If Nina _____ that her husband would go to the bus stop to meet her, she wouldn’t have walked back home.A. knowsB. knewC. has knownD. had known四、【丰台一模】1. Teenagers get less and less sleep, them at a higher risk of physical and mental health problems.A. puttingB. putC. to putD. being put2. —Isn’t that Ann’s brother over there?—No. It be him. He never wears glasses.A. won’tB. must notC. can’tD. may not3. A splendid eight-minute show on Beijing at the closing ceremony of the 2018 Winter Olympics.A. stagedB. will be stagedC. had stagedD. was staged4. Jack is determined to get a seat for the concert it means standing in a queue all night.A. so thatB. in caseC. even thoughD. as if5. —Winter is over at last. Time to put away my gloves and boots.— Great! I for this for months.A. will waitB. have been waitingC. was waitingD. waited6. —A bookbar is being built near our school.—Yes. It is said that the bar soon.A. has openedB. will openC. would openD. opened7. Beijing plans to build its first bicycle lane connects a residential area with a business center.A. whichB. whoC. whatD. where8. Travel Frog by a Japanese game studio has become a hit in China.A. to be createdB. createdC. being createdD. creating9. In a meeting, Xi Jinping shared a story on his parents passed down important moral values to him.A. whatB. whichC. howD. when10. students to exercise, a university in Wuhan recently launched a fitness app.A. To encourageB. Having encouragedC. EncouragedD. Encouraging11. —Our country is developing at an amazing speed!—Yes. This is makes me feel so proud.A. whichB. whyC. whereD. what12. —Thank you for reminding me of the time，otherwise I late yesterday.—Don’t mention it.A. had beenB. would have beenC. should beD. would be13. Information technology is taught in most schools, we have entered the information society.A. soB. whileC. andD. for14. In the UK the clocks forward 1 hour at 1am on the last Sunday in March, and back 1 hour at 2am on the lastSunday in October.A. wentB. are goingC. goD. have gone15. It’s important for a girl to know what colors look good her skin．A. atB. onC. aboveD. against五、【石景山一模】1. — How can I wake up so early?—Set the alarm at 5:00 am., you will make it.A. andB. butC. orD. so2. After class, the teacher couldn’t leave,by the students.A. surroundedB. to surroundC. was surroundedD. surrounding3. I keep the picture where I can see it every day, reminds me of the days in my hometown.A. thatB. whichC. whoD. when4. Self confidence is a kind of quality and that is it takes to do everything well.A. whyB. thatC. whatD. which5. ~Why do you drink so much coffee?~Well, it doesn’t keep me awake in the night, I see no harm in it.A. whenB. as long asC. as thoughD. while6. As is known, only hard leads to happiness.A. workB. worksC. workedD. working7. After college, he was employed in a middle school and there ever since.A. would workedB. had workedC. workedD. has worked8. It is reported the housing prices in some big cities fall in different degrees.A. whichB. whatC. thatD. where9. ~Where was I?~You you didn’t like your job.A. had saidB. saidC. were sayingD. has said10. students English well, the teacher tries to speak English in class very often.A. TeachingB. TaughtC. To teachD. Teach11. If the traffic so heavy, I could have been back by 6 o’clock.A. hadn’t beenB. wasn’tC. couldn’t beD. hasn’t been12. We are living in an age most of things are done on cell phones.A. whichB. thatC. whoseD. when13. She was such a proud person that she would die she would admit she was wrong.A. sinceB. whenC. unlessD. before14. The accident have been caused by a dog running across the road, but we don’t know for sure.A. mightB. shouldC. willD. must15. Star skater Wu Dajing won China’s first gold medal at the 2018 PyeongChang Olympic Winter Games breaking world record in short track men’s 500m.A. toB. byC. withD. in六、【东城一模】1. Scientists are building a powerful instrument, which ______ them see deep into space.A. has helpedB. will helpC. helpedD. would helped2. Large groups that want to visit the museum have to get permission ______ they visit.A. unlessB. whereC. asD. before3. Since 18th January, 2018, some airlines in China ______ mobile phone use on their aircrafts.A. allowB. allowedC. have allowedD. had allowed4. The dictionary has 100 new words _________ into its latest edition.A. addB. addingC. addedD. being added5. Moving abroad means entering a culture ______ the customs and the language are different.A. whereB. whenC. whichD. whose6. —Could you tell me ______ the train from New York will be arriving on time?—Yes, sir. It should be arriving in 10 minutes.A. whenB. howC. whyD. if7. The snowstorm ______ several days before it hit the northern areas.A. would predictB. had predictedC. would be predictedD. had been predicted8. I ______ not have her new telephone number; let me check.A. mayB. mustC. shallD. need9. Once Jason becomes interested in some topic, he can’t help thinking about it ______ he goes.A. howeverB. whereverC. wheneverD. whomever10. The book ______ next year is supposed to be a best-seller.A. publishingB. being publishedC. to be publishedD. to have published11. The trouble is ______ we can reach the conference center within twenty minutes in the rush hour.A. whatB. howC. whenD. why12. Mike hasn’t appeared for two weeks, ______ his friends are wondering what has happened to him.A. soB. butC. orD. for13. Electric cars produce about 80 percent less pollution than cars ______ gas-powered motors.A. fromB. byC. forD. with14. ______ that he had fallen behind, Peter started to quicken his pace.A. RealizedB. To realizeC. Having realizedD. Having been realized15. Can you imagine what the modern world ______ like without smartphones?A. wereB. would beC. had beenD. would have been一、海淀一模1-5ACBCD 6-10DCABD 11-15 ACBDA二、西城一模1-5CDCBB 6-10 ADCAA 11-15BDDAB三、朝阳一模21—25 DBBAD 26—30 AACCB 31—35 DABCD四、丰台一模1-5ACDCB 6-10BABCA 11-15 DBDCD五、石景山一模1--5AABCB 6--10 DDCBC 11-15 ADAAB六、东城一模: 1-5BDCCA 6-10 DDABC 11-15 BADCB。

2018北京城区高三英语一模七选五 (学生版)汇总

2018城区一模七选五锦集：2018海淀一模：Radar is an electronic device that detects planes, ships, coastlines, landmarks, and even storm clouds. The name radar comes from the first letters of the words radio direction and ranging. As the human eye uses light waves to see, radar “sees” with radio waves. Without radar, planes could not land safely in bad weather and ships could not move safely in thick fog. 51In the 1800s it was discovered that radio waves could be reflected from objects. But scientists did not make great advances in radar research until the 1930s, when the world was threatened by war. 52 It has been used widely in almost every conflict since then.Echoes make it possible for radar to work. When a beam of radio waves is sent out, it strikes on an object and returns an echo. This echo is picked up by radar and recorded on a screen similar to television screen. On the screen an observer sees a flash, or a blip, that shows the direction and distance of the object. 53 Airport control towers use radar to guide planes in for safe landings. Almost all large ships depend on radar to prevent collisions with icebergs or other ships. 54 Weather forecasters “see” the size, direction, and speed of storms on radar screens. Astronomers can even use radar to measure accurately the distance to the moon. Thus, the device has generated major advancements.55 Huge radar antennas have been installed all over the United States. They guard us against possible enemy attacks. We have ballistic—missiles (战略导弹)warning systems that can alert us to attacks when missiles are more than 1,000 miles away. Other radar systems warn us against enemy aircraft and even spying space satellites.A. Police track speeders in radar-equipped cars.B. These measurements are now highly accurate.C. The device can be used in a wide range of fields.D. It is therefore especially valuable to shippers and travelers.E. During World War II many countries used radar effectively.F. Today radar is used by commercial airliners and weather forecasters.G. Strengtheni ng national defense is one of radar’s most important functions.2018西城一模：The Art of Slow ReadingIf you are reading this article in print, chances are that you will only get through half of what I have written. And if you are reading this online, you may not even finish a fifth. 51 They suggest that many of us no longer have the concentration to read articles through to their conclusion.So are we getting stupider? Actually, our online habits are damaging the mental power we need to process and understand textual information. Round-the-clock news makes us read from one article to the next without necessarily engaging fully with any of the content. Our reading is frequently interrupted by the noise of the latest email and we are now absorbing short bursts of words on Twitter and Facebook more regularly than longer texts. 52 But we are gradually forgetting how to sit back, think carefully, and relate all the facts to each other.53 A desperate bunch of academics want us to take our time while reading, and re-reading. They ask us to switch off our computers every so often and rediscover both the joy of personal engagement with printed texts, and the ability to process them fully. What’s to be done then? Most slow readers realize that total rejection of the web is extremely unrealistic. They feel that getaway from technology for a while is the answer.54Personally, I’m not sure whether I could ever go offline for long. Even while writing this article, I am switching constantly between sites, skimming too often, absorbing too little. Internet reading has become too rooted in my daily life for me to change. I read essays and articles not in hard copy but as PDFs. I suspect that many readers are in a similar position. 55 You can download a computer application called Freedom, which allows you to read in peace by cutting off your Internet connection. Or if you want to avoid being disturbed by the Internet, you could always download offline reader Instapaper for your iPhone. If you’re still reading my article, that is slow reading.A. The Internet is probably part of the problem.B. Now some campaigns are advocating slow reading.C. These are the two findings from the recent research projects.D. But if you just occasionally want to read more slowly, help is at hand.E. Some of them have suggested turning their computers off for one day a week.F. Slow reading can help connect a reader to neighborhood and become popular.G. Because of the Internet, we have become very good at collecting information.2018东城一模：Where did your family eat dinner last night? In the car on the way to sport? At McDonald’s? Or at the dinner table? A survey taken a few years ago found that 28% families ate dinner together at home seven nights a week. Another quarter said they ate together three or fewer nights a week.Once upon a time the situation was different. 51 Plates, forks and spoons would be laid out. As dinner time approached, an increasing number of hungry mouths would begin to appear with the question, “What’s for dinner”?52 The data seems to point to two main issues: overworked parents and overscheduled children. When mum or dad do get home in the evening, they are soon in the car again to send the children to soccer, music, tutoring, and a host of other events.This nightly ceremony around the dinner table is both vital and fruitful; it is what keeps a family together. Sure, the conversation is not always significant and children argue. And sometimes the deepest and most meaningful times in a family are not at the table at all. 53 The dinner table is the place where a family builds an identity. Stories are passed down, jokes are exchanged and the wider world is examined through the lens（镜头）of a family’s values. Children pick up vocabulary and a sense of how conversation is structured.54 Dinner time is “family time”. Coming back daily to the same place helps gain familiarity.The significance of dinner time is more than above. Studies show that the more families eat together, the less likely the children are to smoke, drink, get depressed, and develop eating disorders, and the more likely they are to do well in school and learn how to socialize. One professor at Rutgers University in New Jersey stated, “A meal is about civilizing children. 55 ”So start by planning some stay at home family dinners together. Just family talk.A. It’s a time to teach them to be a member of their culture.B. Each night the dining table would be set with a simple cloth.C. Why not cut back on a few activities and have dinner with your family?D. What accounts for this decline in families eating together today though?E. They also learn good table manners, something that will benefit them for life.F. It was important for children and parents to sit down together and get to know each other.G. However, there is still something unique about the time a family spends around the dinner table.2018朝阳一模：CharismaAre leaders born or made? Many leaders throughout history—such as Gandhi, Churchill, Napoleon, and MartinLuther K ing—seem t o h ave a s pecial q uality t hat m ade t hem p owerful a nd p ersuasive. W e c an i dentify that quality as charisma, but can we explain it?Charisma means a natural ability to attract other people and make them admire you. It is a complex mixture o f s ocial a nd e motional (情感的) s kills. 51 Richard W iseman, a f amous p sychologist, p oints out that there are three key qualities of a charismatic person: They feel their own emotions strongly; they inspire strong emotions in other people; and they are unaffected by the influences of other charismatic people.You needn’t worry if you don’t have these qualities. 52 Wiseman says that when you come upon someone who is charismatic, you can copy his or her body language and facial expressions without realizing it. This is called mirroring, and it works partly because people’s behavior influences their emotions.53 He proves his point by giving the example of smiling back at someone who s miled at you. Yoursmiling back suggests that you accept the goodwill from the other person and hope to give it back to him.54 For example, if you stand up straight and raise your chest, you are more likely to feelconfident and inspire others to feel confidence in you. Another expert says that the most charismatic people are usually good listeners. They give others the impression of being focused and modest.Charisma plays a large part in success because it is linked to self-confidence. 55____One successful leadership c oach points o ut that you n eed t o c ome by your s kills and techniques naturally, she warns—if the personality you project is not real, you may come across as insincere.A.This type of physical presence can be used to great effect.B.Today there is growing evidence that charisma can be learned.C.Charismatic persons should be active and sensitive to their surroundings.D.It needs to be recognized that charisma is more than just being optimistic.E.It helps to make strong personal connections and communicate effectively with others.F.But it is worth noting that charisma can’t be a pretended ability although it can be learned.G.He adds you’re unaware of picking up others’ gestures, but you know it makes you feel good.2018石景山一模：A peer is a person who is about the same age as you. Peers affect your life, whether you know i t ornot, just by spending time with you.51 Maybe another student in your science class taught you an easy way to remember the p lanetsin solar system. Maybe you got others excited about your new favorite book and now everyone’s reading it. However, sometimes peers affect one another in another way. 52 Maybe a kid in the n eighborhood wanted you to steal with him.Some kids give in to peer pressure because they want to be liked, to fit in, or because they worry that other kids may make fun of them if they don’t go along with the group. 53 The idea that “everyone’s doing it” may influence some kids to leave their better judgments or their common senses behind.Peer pressure can be extremely strong and hard to get rid of. Experiments have shown how peer pressurecan influence someone to change her/his mind from what she/he knows for sure is a correct answer to the incorrect answer-just because everyone else gives the incorrect answer! 5455 Paying attention to your own feelings and beliefs about what is right and wrong can help youknow the right thing to do. Inner strength and self-confidence can help you stand firm, walk away and resist doing something when you know better.A.Peers can have a good effect on one another.B.Peer pressure is the direct influence on people by peers.C.Good peers may give you a hand when you are in trouble.D.That holds true for people of any age in peer pressure situations.E.Maybe one kid in school tried to get another to cut class with him.F.It can be hard to walk away from peer pressure, but it can be done.G.Others may go along because they are curious to try something new that others are doing.2018 丰台一模：第二节（共5小题；每小题2分，共10分）根据短文内容，从短文后的七个选项中选出能填入空白处的最佳选项。

北京市初三物理一模考试试卷西城区含答案

一、单项选择题（下列各小题四个选项中只有一个选项符合题意。

共30分，每小题2分）1．下列四位物理学家中，以其名字命名压强单位的是A．牛顿B．帕斯卡C．瓦特 D．焦耳2．在图1所示的四种现象中，由于光的折射形成的是3．关于声现象，下列说法正确的是A．声音可以在真空中传播 B．吉他是靠琴弦的振动发声C．音乐一定不会成为噪声D．振幅大小决定音调的高低4．在图2所示的四个物态变化的实例中，属于凝华的是5．下列说法中正确的是A．电子的直径大于分子的直径 B．核能和化石能源都属于可再生能源C．超导材料处于超导态时电阻为零 D．水能和太阳能都属于不可再生能源6．图3所示的四个实例中，目的是为了减小摩擦的是7．在图4所示的四种用具中，正常使用时属于费力杠杆的是8．下列说法中正确的是A．液体在凝固过程中放出热量B．液体的沸点随压强的增大而降低C．久放的樟脑球变小是汽化现象 D．蔬菜包上保鲜膜有利于水分蒸发图4A B C D瓶盖起子核桃夹子裁纸刀食品夹图3A B C D陆地冰球鞋上安装滚轮汽车轮胎上安装防滑链运动员在手上涂抹镁粉浴室地砖表面有凹凸花纹图2A B C D深秋，红叶落霜寒冬，滴水成冰初春，冰河消融仲夏，绿叶挂珠图1景物在汽车观后镜中成像C D透过放大镜观察植物BA荷花在水中形成“倒影”景物逆光形成“剪影”9．下列说法中正确的是A ．篮球受到力的作用，运动状态一定改变B ．汽车加速运动时，一定受到非平衡力的作用C ．受非平衡力作用的足球，一定沿着直线运动D ．受到平衡力作用的弹簧，一定不会发生形变10．将两个定值电阻接在同一电路中，如果它们两端的电压相等，则下列判断正确的是A ．这两个电阻的阻值一定相等B ．通过这两个电阻的电流一定相等C ．若两个电阻并联，相同时间电流通过它们做功一定相等D ．若两个电阻串联，相同时间电流通过它们做功一定相等11．图5所示是一种环保型手电筒，筒内有一个能滑动的圆柱形永磁铁，外圈套着一个线圈。

2018年海淀区高三一模试题及答案

2018海淀区高三语文一模试卷语文2018. 4一、本大题共8小题，共24分。

阅读下面的材料，完成1——8题。

材料一北京是世界文化名都，它众多的文化古迹，一直吸引着世人的目光。

其实，北京的自然遗产，特别是植物多样性，也是世界其它名都难以相比的。

《北京植物志》(1992年第3版)，共收入维管植物169科，898属，2088种。

北京作为都城有两千佘年的历史，由于人口聚集，周围环境受到了严重破坏，现有的植物区系和植物群落，与两千年前相比已有很大的不同。

目前，距离城区较远的山区破坏程度较轻，植物种类保存较多，如房山上方山，门头沟东灵山和百花山，延庆松山，怀柔喇叭沟门和云蒙山，密云雾灵山，对这些地区应加以特别的保护。

北京在气候上处于暖温带向中温带的过渡，在自然地理上处于黄土高原向海河平原的过渡。

这里既是许多暖温带植物以及具热带亲缘的喜温暖的植物分布的北界，也是中温带东北南部许多植物分布的南界。

目前在低山平原地区仍可找到大量具热带、亚热带亲缘成分的植物。

多种落叶阔叶灌丛成片地出现是目前北京山地植物多样性的特色。

不同海拔，不同坡向，无论溪边或半坡，都出现了多种落叶阔叶林丛，这在其它地方很少见到。

而京西和京北山区的突出特点是，在海拔1600米以上的山顶或近顶的“夷平面”上，分布着以多种杂类草为主的亚高山草甸。

亚高山草甸野生草木花卉繁多，不同的时序，不同植物开着不同颜色的花，花色交映，五彩缤纷。

如东灵山和百花山，都有大量可供观赏的花卉，仅百花山中观赏植物就有300余种。

古籍记载：“无名花草，遍山取妍，三时不绝，故为百花山。

”其中国家二级保护植物金莲花尤其引人注意。

北京植物区系中有一定数量的种类已被列入国家重点保护名录。

北京是我国政治、文化等中心，生产和生活给环境带来了较大压力，而交流频繁也给外来植物的入侵带来了便利。

这不仅对农业生产造成损害，还直接导致生物多样性减少。

人类文化的多样性很大程度上起源于生物及其环境的多样性，因此北京在保护好文化遗产之外，保护好独特的自然遗产，意义重大。

2018北京市朝阳区高三(一模)数学(理)含答案

2018北京市朝阳区高三（一模）数学（理） 2018．3（考试时间120分钟满分150分）本试卷分为选择题（共40分）和非选择题（共110分）两部分第一部分（选择题共40分）一、选择题：本大题共8小题，每小题5分，共40分．在每小题给出的四个选项中，选出符合题目要求的一项． 1．已知全集为实数集R ，集合2{30}A x x x =-<，{21}x B x =>，则RA B ()=A ．(0][3,)，-∞+∞B ．(0,1]C ．[)3+∞，D ．[1)，+∞ 2．复数z 满足(1+i)i z =，则在复平面内复数z 所对应的点位于A ．第一象限B ．第二象限C ．第三象限D ．第四象限 3．直线l 的参数方程为=3,1+3x t yt-（t 为参数），则l 的倾斜角大小为A ．6π B ． 3π C ． 32π D ．65π4．已知a b ,为非零向量，则“0a b >⋅”是“a 与b 夹角为锐角”的A ．充分而不必要条件B ．必要而不充分条件C ．充分必要条件D ．既不充分也不必要条件5．某单位安排甲、乙、丙、丁4名工作人员从周一到周五值班，每天有且只有1人值班，每人至少安排一天且甲连续两天值班，则不同的安排方法种数为A ．18B ．24C ．48D ．96 6．某四棱锥的三视图如图所示，则该四棱锥的体积等于A ．34B ．23C ．12D ．137．庙会是我国古老的传统民俗文化活动，又称“庙市”或“节场”．庙会大多在春节、元宵节等节日举行．庙会上有丰富多彩的文化娱乐活动，如“砸金蛋”（游玩者每次砸碎一颗金蛋，如果有奖品，则“中奖”）．今年春节期间，某校甲、乙、丙、丁四位同学相约来到某庙会，每人均获得砸一颗金蛋的机会．游戏开始前，甲、乙、丙、丁四位同学对游戏中奖结果进行了预测，预测结果如下：俯视图正视图侧视图1甲说：“我或乙能中奖”；乙说：“丁能中奖”；丙说：“我或乙能中奖”；丁说：“甲不能中奖”．游戏结束后，这四位同学中只有一位同学中奖，且只有一位同学的预测结果是正确的，则中奖的同学是A ．甲B ．乙C ．丙D ．丁8．在平面直角坐标系xOy 中，已知点(3,0)A ,(1,2)B ，动点P 满足OP OA OB λμ=+,其中,[0,1],[1,2]λμλμ∈+∈，则所有点P 构成的图形面积为A ． 1B ． 2C ． 3D ． 23第二部分（非选择题共110分）二、填空题：本大题共6小题，每小题5分，共30分．把答案填在答题卡上． 9．执行如图所示的程序框图，若输入5m =，则输出k 的值为________．10．若三个点(2,1),(2,3),(2,1)---中恰有两个点在双曲线222:1(0)x C y a a-=>上，则双曲线C 的渐近线方程为_____________．11．函数()sin()f x A x ωϕ=+（0,0,2A ωϕπ>><）的部分图象如图所示，则=ω ；函数()f x 在区间[,3ππ]上的零点为．12．已知点(2,0),(0,2)A B -，若点M 是圆22220x y x y +-+=上的动点，则ABM ∆面积的最小值为． 13．等比数列{}n a 满足如下条件：①10a >；②数列{}n a 的前n 项和1n S <．试写出满足上述所有条件的一个数列的通项公式．14．已知R a ∈，函数211(+1)0π()sin 2,0.22x x x a x x f x x --+⎧+<⎪⎪=⎨⎪>⎪⎩+，，当0x >时，函数()f x 的最大值是；若函数()f x 的图m >50输出k 结束开始输入m k =0m =2m -1 是k =k +1否象上有且只有两对点关于y 轴对称，则a 的取值范围是．三、解答题：本大题共6小题，共80分．解答应写出文字说明，演算步骤或证明过程． 15． (本小题满分13分)在ABC ∆中，已知sin A =，2cos b a A =．（Ⅰ）若5ac =，求ABC ∆的面积；（Ⅱ）若B 为锐角，求sin C 的值． 16．(本小题满分14分)如图1，在矩形ABCD 中，2AB =，4BC =，E 为AD 的中点，O 为BE 中点．将ABE ∆沿BE 折起到A BE '，使得平面A BE '⊥平面BCDE （如图2）．（Ⅰ）求证：A O CD '⊥；（Ⅱ）求直线A C '与平面A DE '所成角的正弦值；（Ⅲ）在线段A C '上是否存在点P ，使得//OP 平面A DE '? 若存在，求出A PA C''的值；若不存在，请说明理由．17．(本小题满分13分)某地区高考实行新方案，规定：语文、数学和英语是考生的必考科目，考生还须从物理、化学、生物、历史、地理和政治六个科目中选取三个科目作为选考科目．若一个学生从六个科目中选出了三个科目作为选考科目，则称该学生的选考方案确定；否则，称该学生选考方案待确定．例如，学生甲选择“物理、化学和生物”三个选考科目，则学生甲的选考方案确定，“物理、化学和生物”为其选考方案．某学校为了解高一年级420名学生选考科目的意向，随机选取30名学生进行了一次调查，统计选考科目人数如下表：（Ⅰ）估计该学校高一年级选考方案确定的学生中选考生物的学生有多少人？（Ⅱ）假设男生、女生选择选考科目是相互独立的．从选考方案确定的8位男生中随机选出1人，从选考方案图1EABCDOA '图2CBDEO确定的10位女生中随机选出1人，试求该男生和该女生的选考方案中都含有历史学科的概率；（Ⅲ）从选考方案确定的8名男生中随机选出2名，设随机变量221,2,ξ⎧=⎨⎩名男生选考方案相同名男生选考方案不同，，求ξ的分布列及数学期望E ξ．18． (本小题满分13分)已知函数ln 1()x f x ax x-=-．（Ⅰ）当2a =时，（ⅰ）求曲线()y f x =在点(1,(1))f 处的切线方程；（ⅱ）求函数)(x f 的单调区间；（Ⅱ）若12a <<，求证：)(x f 1<-． 19． (本小题满分14分)已知椭圆2222:1(0)x y C a b a b+=>>的离心率为2，且过点(1,2．（Ⅰ）求椭圆C 的方程；（Ⅱ）过椭圆C 的左焦点的直线1l 与椭圆C 交于,A B 两点，直线2l 过坐标原点且与直线1l 的斜率互为相反数．若直线2l 与椭圆交于,E F 两点且均不与点,A B 重合，设直线AE 与x 轴所成的锐角为1θ，直线BF 与x 轴所成的锐角为2θ，判断1θ与2θ大小关系并加以证明． 20． (本小题满分13分)已知集合128{,,,}X x x x =是集合{2001,2002,2003,,2016,2017}S =的一个含有8个元素的子集．（Ⅰ）当{2001,2002,2005,2007,2011,2013,2016,2017}X =时，设,(1,8)i j x x X i j ∈≤≤，（i ）写出方程2i j x x -=的解(,)i j x x ；（ii ）若方程(0)i j x x k k -=>至少有三组不同的解，写出k 的所有可能取值；（Ⅱ）证明：对任意一个X ，存在正整数k ，使得方程(1,8)i j x x k i j -=≤≤至少有三组不同的解．2018北京市朝阳区高三（一模）数学（理）参考答案二、填空题：（本题满分30分）三、解答题：（本题满分80分） 15． (本小题满分13分)解：（Ⅰ）由2cos b a A =，得cos 0A >，因为sin A =，所以cos 5A =.因为2cos b a A =，所以4sin 2sin cos 25B A A ===．故ABC ∆的面积1sin 22S ac B ==． ………………….7分（Ⅱ）因为4sin 5B =，且B 为锐角，所以3cos 5B =.所以sin sin()sin cos cos sin 25C A B A B A B =+=+=．………….13分16．(本小题满分14分)证明：（Ⅰ）由已知2AB AE ==，因为O为BE 中点，所以A O BE '⊥．因为平面A BE '⊥平面BCDE ，且平面A BE'平面BCDE BE =，A O '⊂平面A BE '，所以A O '⊥平面BCDE ．又因为CD ⊂平面BCDE ，所以A O CD '⊥． ………….5分（Ⅱ）设F 为线段BC 上靠近B 点的四等分点，G 为CD 中点．由已知易得OF OG ⊥．由（Ⅰ）可知，A O '⊥平面BCDE ，所以A O OF '⊥，A O OG '⊥.以O 为原点，,,OF OG OA '所在直线分别为,,x y z 轴建立空间直角坐标系（如图）．因为2A B '=，4BC =，所以(00(110),(130),(130),(110)A B C D E ,，，，，，，，'---．设平面A DE '的一个法向量为111(,,)x y z =m ，因为(132),(020)A D DE ，，，，'=--=-，所以 0, 0,A D DE ⎧'⋅=⎪⎨⋅=⎪⎩m m 即111130,20. x y y ⎧-+=⎪⎨-=⎪⎩取11z =-，得1)=-m ．而A C '=(1,3,.所以直线A C '与平面A DE '所成角的正弦值sin 3θ== ……….10分（Ⅲ）在线段A C '上存在点P ，使得//OP 平面A DE '. 设000(,,)P x y z ，且(01)A PA Cλλ'=≤≤'，则A P AC λ''=，[0,1]λ∈．因为(00(130)A C ，，'，所以000(,,(,3,)x y z λλ=，所以000,3,x y z λλ==，所以(,3)P λλ，(,3)OP λλ=．若//OP 平面A DE '，则OP ⊥m.即0OP ⋅=m .由（Ⅱ）可知，平面A DE '的一个法向量1)=-m，0-=，解得1[0,1]2λ=∈，所以当12A P A C '='时，//OP 平面A DE '． ……….14分17．(本小题满分13分)解：（Ⅰ）由题可知，选考方案确定的男生中确定选考生物的学生有4人，选考方案确定的女生中确定选考生物的学生有6人，该学校高一年级选考方案确定的学生中选考生物的学生有1018420=1401830⨯⨯人． ……….3分（Ⅱ）由数据可知，选考方案确定的8位男生中选出1人选考方案中含有历史学科的概率为21=84；选考方案确定的10位女生中选出1人选考方案中含有历史学科的概率为310．所以该男生和该女生的选考方案中都含有历史学科的概率为13341040⨯=．…….8分（Ⅲ）由数据可知，选考方案确定的男生中有4人选择物理、化学和生物；有2人选择物理、化学和历史；有1人选择物理、化学和地理；有1人选择物理、化学和政治．由已知得ξ的取值为1,2．2242281(1)4C C P C ξ+===， 1111422228()213(2)4C C C C P C ξ++⨯+===，或3(2)1(1)4P P ξξ==-==. 所以ξ的分布列为所以13712444E ξ=⨯+⨯=． …….13分 18． (本小题满分13分)（Ⅰ）当2a =时，ln 1()2x f x x x-=-.2222ln 22ln ()2x x xf x x x ---'=-=. （ⅰ）可得(1)0f '=，又(1)3f =-，所以()f x 在点（1,3-）处的切线方程为3y =-. ….3分（ⅱ）在区间（0,1）上2220x ->，且ln 0x ->，则()0f x '>. 在区间（1,+∞）上2220x -<，且ln 0x -<，则()0f x '<.所以()f x 的单调递增区间为（0,1），单调递减区间为（1,+∞）. ….8分（Ⅱ）由0x >，()1f x <-，等价于ln 11x ax x--<-，等价于21ln 0ax x x -+->. 设2()1ln h x ax x x =-+-，只须证()0h x >成立.因为2121()21ax x h x ax x x--'=--=，12a <<，由()0h x '=，得2210ax x --=有异号两根.令其正根为0x ，则200210ax x --=. 在0(0,)x 上()0h x '<，在0(,)x +∞上()0h x '>.则()h x 的最小值为20000()1ln h x ax x x =-+-0011ln 2x x x +=-+- 003ln 2x x -=-.又(1)220h a '=->，13()2()30222a h a '=-=-<，所以0112x <<.则0030,ln 02x x ->->.因此003ln 02x x -->，即0()0h x >.所以()0h x >所以()1f x <-. ….….13分19． (本小题满分14分)解：（Ⅰ）由题意得22222,111.2c a a b c ab ⎧=⎪⎪⎪=+⎨⎪⎪+=⎪⎩解得a =1b =，1c =．故椭圆C 的方程为2212x y +=． ….….5分（Ⅱ）12=θθ．证明如下：由题意可设直线1l 的方程为(1)y k x =+，直线2l 的方程为y kx =-，设点11(,)A x y ，22(,)B x y ，33(,)E x y ，33(,)F x y --．要证12=θθ，即证直线AE 与直线BF 的斜率之和为零，即0AE BF k k += ．因为13231323AE BF y y y y k k x x x x -++=+-+ 13231323(1)(1)k x kx k x kx x x x x +++-=+-+ 2121231323[2()2]()()k x x x x x x x x x +++=-+．由22(1),1,2y k x x y =+⎧⎪⎨+=⎪⎩ 得2222(12)4220k x k x k +++-=，所以2122412k x x k -+=+，21222212k x x k -=+．由22,1,2y kx x y =-⎧⎪⎨+=⎪⎩得22(12)2k x +=，所以232212x k =+．所以2221212322244442()20121212k k x x x x x k k k --+++=++=+++．2121231323[2()2]0()()AE BFk x x x x x k k x x x x ++++==-+．所以12=θθ． ….….14分20． (本小题满分13分)解：（Ⅰ）（ⅰ）方程2i j x x -=的解有：(,)(2007,2005),(2013,2011)i j x x =．……2分（ii ）以下规定两数的差均为正，则：列出集合X 的从小到大8个数中相邻两数的差：1，3，2，4，2，3，1；中间隔一数的两数差（即上一列差数中相邻两数和）：4，5，6，6，5，4；中间相隔二数的两数差：6，9，8，9，6；中间相隔三数的两数差：10，11，11，10；中间相隔四数的两数差：12，14，12；中间相隔五数的两数差：15，15；中间相隔六数的两数差：16这28个差数中，只有4出现3次、6出现4次，其余都不超过2次，所以k 的可能取值有4，6．…………………………………………………………6分（Ⅱ）证明：不妨设12820012017x x x ≤<<<≤，记1(1,2,,7)i i i a x x i +=-=，2(1,2,,6)i i i b x x i +=-=，共13个差数．假设不存在满足条件的k ，则这13个数中至多两个1、两个2、两个3、两个4、两个5、两个6，从而 127126()()2(126)749a a a b b b +++++++≥++++=. …………①又127126818721()()()()a a a b b b x x x x x x +++++++=-++--81722()()2161446x x x x =-+-≤⨯+=，这与①矛盾！所以结论成立．……………………………………………………………………13分。