2020高考模拟邯郸二模-答案
河北省邯郸市2020届高三年级第二次模拟考试数学(理科)试卷含答案
邯郸市2020届高三年级第二次模拟考试高三理科数学注意事项：1．考试时间120分钟，总共150分．2．答卷前，考生务必将自己的姓名、班级和考场填写在答题卡上，并把条形码贴在答题卡的指定位置．3．回答选择题时，选出每小题答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑。
如需改动，用橡皮擦干净后，再选涂其他答案标号．回答非选择题时，将答案写在答题卡上，写在本试卷上无效．4．考试结束后，将本试卷和答题卡一并交回．一、选择题：本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．已知集合{}13log >=a a A ，{}93>=a a B ，则)(B C A R =A ．（0，3）B ．（1，3）C ．（0，2]D ．（1，2]2．已知复数ii z 328+-=（i 为虚数单位），下列说法： ①复数z 在复平面内对应的点在第四象限；②5=z ；③z 的虛部为i 2-；④i z 21-=．其中正确的有A ．1个B ．2个C ．3个D ．4个3．中国农历的“二十四节气”是凝结着中华民族的智慧与传统文化的结晶，“二十四节气”歌是以“春、夏、秋、冬”开始的四句诗，2016年11月30日，“二十四节气”正式被联合国教科文组织列入人类非物质文化遗产，也被誉为“中国的第五大发明”．某小学三年级共有学生500名，随机抽查100名学生并提问“二十四节气”歌，只能说出春夏两句的有45人，能说出春夏秋三句及其以上的有32人，据此估计该校三年级的500名学生中，对“二十四节气”歌只能说出第一句“春”或一句也说不出的大约有A ．69人B ．84人C ．108人D ．115人4．已知f （x ）是R 上的奇函数且单调递增，则下列函数是偶函数且在（0，+∞）上单调递增的有 ①)(x f y =；②)(2x x f y +=；③)(x f y =；④)()(x f x f e ey -+=A ．①②③B ．①③④C ．②③④D ．①②④5．设实数x ，y 满足不等式组⎪⎩⎪⎨⎧≥≤+≥+-,0,03,04y y x y x ，若z=ax+y 的最大值为1，则a=A ．41-B ．41 C ．2- D ．2 6．已知函数ϕϕsin 2cos cos 2sin )(x x x f +=图象的一个对称中心为)03(，π-．则ϕ的一个可能值为A ．3π-B ．3πC ．65π-D ．65π 7．设直线0:=++c by ax l 与圆C ：422=+y x 相交于A ，B 两点，且32=AB ，则“222=+b a ”是“2=c ”的A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件，8．已知α为锐角，且42cos tan 22+-==m m m αα，，则)4(sin 2πα+= A ．32 B ．2132+ C ．54 D ．59 9．已知直线)41(0)14(:>=+--a m y a abx l 与双曲线)0,0(12222>>=-b a b y a x 的两条渐近线交于A ，B 两点，O 为坐标原点，若△OAB 为直角三角形，则双曲线的离心率e 的最大值为A ．2B ．3C ．2D ．510．2020年3月31日，某地援鄂医护人员A ，B ，C ，D ，E ，F6人（其中A 是队长）圆满完成抗击新冠肺炎疫情任务返回本地，他们受到当地群众与领导的热烈欢迎．当地媒体为了宣传他们的优秀事迹，让这6名医护人员和接见他们的一位领导共7人站一排进行拍照，则领导和队长站在两端且BC 相邻，而BD 不相邻的排法种数为A ．36种B ．48种C ．56种D ．72种11．在直三棱柱111C B A ABC -中，平面ABC 是下底面．M 是BB 1上的点，AB=3，BC=4，AC=5，CC 1=7，过三点 A 、M 、C 1作截面，当截面周长最小时，截面将三棱柱分成的上、下两部分的体积比为A ．109B ．910C ．1110D ．1011 12．如图，在△ABC 中，tanC=4．CD 是AB 边上的高，若32=⋅-AD BD CD ，则△ABC 的面积为A ．4B ．6C ．8D ．12二、填空题：本大题共4小题，每小题5分，共20分．13．抛物线y=2x 2上的点A （1，2）到焦点F 的距离为 ．14．曲线()n x y f x x e ==在x=1处的切线与坐标轴围成三角形的面积为23e ，则n= ． 15．在△ABC 中，4AB =，8AC AB ⋅=，则AB BC ⋅= ．16．已知三棱锥P —ABC 中，PA=AB=AC=2，PA ⊥平面ABC ，A 到平面PBC ，则三棱锥外接球的表面积为 ． 三、解答题：共70分．解答应写出文字说明、证明过程或演算步票．第17～21题为必考题，第22、23题为选考题，考生根据要求作答．（一）必考题：共60分．17．（本小题满分12分）已知数列{}n a 满足数列{}2log n a 的前n 项和为1(1)2n A n n =+． （1）求数列{}n a 的通项公式及前n 项和n S ；（2）若数列1n a ⎧⎫⎨⎬⎩⎭的前n 项和为n T ，求8n n S T -的最小值．18．（本小题满分12分）2020年初，一场新冠肺炎疫情突如其来，在党中央强有力的领导下，全国各地的医务工作者迅速驰援湖北，以大无畏的精神冲在了抗击疫情的第一线，迅速控制住疫情．但国外疫情严峻，输入性病例逐渐增多，为了巩固我国的抗疫成果，保护国家和人民群众的生命安全，我国三家生物高科技公司各自组成A 、B 、C 三个科研团队进行加急疫苗研究，其研究方向分别是灭活疫苗、核酸疫苗和全病毒疫苗，根据这三家的科技实力和组成的团队成员，专家预测这A 、B 、C 三个团队未来六个月中研究出合格疫苗并用于临床接种的概率分别为34，23，12，且三个团队是否研究出合格疫苗相互独立． （1）求六个月后A ，B 两个团队恰有一个研究出合格疫苗并用于临床接种的概率；（2）设六个月后研究出合格疫苗并用于临床接种的团队个数为X ，求X 的分布列和数学期望．19．（本小题满分12分）在直三棱柱ABC —A 1B 1C 1中，AB ⊥BC ，BB 12BC ，D 是CC 1的中点。
2020届邯郸市第二中学高三英语二模试卷及参考答案
2020届邯郸市第二中学高三英语二模试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ABritain's brilliant bridges have aided trade and brought communities together and are always the most exciting part of the journey. These must-see bridges are now tourist attractions in their own right.Clifton Suspension Bridge, BristolDescribed byits legendary engineer Isambard Kingdom Brunel as “my first love, my darling”, in was originally designed for horse-drawn traffic. Now, more than four million vehicles a year cross the 1,352ft-Jong toll (收费) bridge over the Avon Gorge. The £ l toll for every journey pays for its repair. The history of the bridge, dating back to 1864, is kept alive through a programme of tours, events and exhibitions.Infinity Bridge, Stockton-On-TeesA pedestrian and cycle footbridge across the River Tees, its working title was the North Shore Footbridge, before it was given its grander name when opened in 2009. It is particularly spectacular (壮观) at night. The arches of the bridge are also lit white and, on calm nights, their reflection in the water appears as an infinity symbol, thereby inspiring the name which was chosen by the public.Tower Bridge, LondonAn engineering wonder built from thousands of tons of Cornish granite, Portland stone and steel, it took construction workers eight years to complete. More than 120 years old, it's a popular tourist attraction, as well as a functional bridge. Visitors can take in the views over the capital and experience seeing London life through the Glass Floor.Iron Bridge, ShropshireOpened in 1781, this is the first arch bridge in the world to be made out of cast iron. Recognised as one of the great symbols of the industrial revolution, it transformed the cart of bridge building and was a crucial factor in the development of the iron trade in Shropshire.1.Which bridge has the longest history?A.Clifton Suspension Bridge.B.Infinity Bridge.C.Tower Bridge.D.Iron Bridge.2.What can we know about Infinity Bridge?A.People can just walk on it.B.The public give it two names.C.It's well worth visiting at night.D.It's arch is the biggest on the earth.3.What do Clifton Suspension Bridge and Tower Bridge have in common?A.They are both over 120 years old.B.Visitors should pay for passing them.C.They have the same original design.D.Visitors can have a good view of London on them.BBarred owls(大林鸮猫头鹰) are a large species native to eastern North America, but they began moving west at the start of the 20th century. By 1973,large numbers of barred owls had arrived in the western state ofWashington. Later they moved south intoOregonandCalifornia.In parts of thePacific Northwest, the owls are now believed to be causing a drop in the population of a smaller, less aggressive bird: the northern spotted owl. In many ways, the barred owl is the spotted owl's worst enemy. The barred owl has more babies per year and eats the same animals, like squirrels and wood rats. And their numbers are now larger in many parts of the spotted owl's traditional territory.David Wiens is a biologist with the U.S. Geological Survey, a federal agency that studies the Earth and its natural resources. He and other officials are doing something unusual to protect spotted owls: killing barred owls. It is a controversial, experimental program. More than 2,400 barred owls have already been shot.Wiens is the son of a well-known bird expert and grew up with the fascination for birds. He has mixed feelings about the program. "It's a little distasteful, I think, to go out killing barred owls to save another owl species," he says. But he adds, “We knew that barred owls were out competing spotted owls and their numbers were growing too fast."To catch barred owls, officials put digital bird callers on the ground. Then they step back and wait as several sounds from the devices fill the air. All of this happens in the dark of night. Barred owls dislike other birds in their territory, so they will fly down and chase other owls out. That is when Wiens and his team try to shoot them.4. What's the main problem with spotted owls?A. They are being starved to death.B. They have more babies each year.C. They are invaded by another bird.D. They are hunted by man.5. Why are barred owls being killed?A. They are eating the spotted owls.B. They are killing each other to survive.C. They are putting the spotted owls in danger.D. They are destroying large areas of forests.6. Why did the officials release the bird sounds?A. To kill barred owls.B. To puzzle barred owls.C. To protect barred owls.D. To frighten barred owls.7. What can be the best title for the text?A. Killing One Animal to Save Another.B. Keeping the Balance of Nature.C. Protecting Birds in Danger.D. Preventing Birds from Playing Fair.CAdvertisers tend to think big and perhaps this is why they're always coming in for criticism. Their critics(批评家)seem to hate them because they have so much money to throw around. Why don’t they stop advertising and reduce the price of their goods? After all, it’s the consumer who pays.The poor old consumer! He'd have to pay a great deal more if advertising didn't create mass markets for products. It is precisely because of the heavy advertising that consumer goods are so cheap. But we get the wrong idea if we think the only purpose of advertising is to sell goods. Another equally important function is to inform. A great deal of the knowledge we have about household goods is largely from the advertisements we read. Advertisements introduce us to new products or remind us of the existence of ones we already know about. Supposing you wanted to buy a washing machine, it is more than likely you would obtain details regarding performance, price, etc., from an advertisement.Lots of people pretend that they never read advertisements, but this claim may be seriously doubted. It is hardly possible not to read advertisements these days. And what fun they often are, too! Just think what a railway station or a newspaper would be like without advertisements. Would you enjoy gazing at a blank wall or reading railway byelaws while waiting for a train? A cheerful, witty advertisement makes such a difference to a dull wall or a newspaper full of the incidents and disasters.We must not forget, either, that advertising makes a positive contribution to our pockets. The fact that we pay so little for our daily paper, or can enjoy so many broadcast programmers is due entirely to the money spent by advertisers. Just think what a newspaper would cost if we had to pay its full price!Another thing we mustn't forget is the “small ads.” What a tremendously useful service they perform for the community! Just about anything can be accomplished through these columns. For instance, you can find a job, buy or sell a house, announce a birth, marriage or death in what used to be called the “hatch, match and dispatch” column(栏目) but by far the most fascinating section is the personal or “agony” column. No other item in a newspaper provides such entertaining reading or offers such a deep insight into human nature. It's the best advertisement for advertising there is!8. What is the main idea of this passage?A. Advertisements steal money from our pocketsB. The critics get the wrong idea of advertisements.C. Advertisers perform a useful service to communities.D. Advertisements are everywhere.9. What is the attitude of the author toward advertisements?A. He appreciates the role of advertisements.B. He doubts the effect of advertisements.C. He believes what is said in advertisements.D. He complains too many advertisements in daily life.10. Which of the following is Not True?A. The personal or “agony” column makes us know more about human nature.B. The only purpose of advertising is to sell goods.C. A newspaper will cost us more if there is no advertisement on it.D. Advertisement makes our life color1 ful.11. Whicof the following shows the structure of the passage?( ①=" Paragraph" 1, ②=" paragraph" 2, ③=" paragraph" 3, ④=" paragraph" 4 ⑤=" paragraph" 5) A B.C. D.DA 10-year-old swimmer with sky-high dreams and a name to match them has broken a record previously held by Olympian Michael Phelps.Clark Kent Apuada, whose friends call him“Superman", swam the 100-meter butterfly in 1:09.38 at the Far Western Long Course Championships in his home state of California this Sunday. That's a second faster than the record Phelps set at the same event in 1995 with a time of 1: 10. 48 in the same category of boys under 10.Clark, a rising fifth-grader who is Filipino-American, told HuffPost he's been dreaming about breaking Phelps' record ever since he started swimming competitively at age 7."I was so motivated,"Clarksaid about his win."I was so happy that I was able to beat that record.”Phelps competed in his first Olympics at age 15. He went on to become the mostdecoratedOlympian in history, with 28 medals overall. “Everyone in the crowd was excited when they realized what a special swim they had just seen when we announced the long-standing record had been broken,"Cindy Rowland,Pacific Swimming's director, wrote in an email.Clarkwon first place for all the swimming events he competed in at this year's Far Western Championships. Pacific Swimming or PacSwim, a regional association that is part of USA Swimming, organizes the Far Western Long Course Championships. Cynthia Apuada,Clark' s mother,said that her child seems to be “living by his name at this point”。
2020届河北省邯郸市高三第二次模拟考试英语试题
邯郸市2020届高三年级第二次模拟考试高三英语第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1 What is the man’s attitude towards the plan?A. Positive.B. Ambiguous.C. Disapproving.2. Where does this conversation most probably take place?A. At a train station.B. At a bus stop.C. At the museum.3. What will the woman talk about next?A. Her school.B. Her marks.C. Study tips.4. What is the man doing now?A. Complaining about a film.B. Taking a walk outside.C. Reading film reviews.5. What does the woman mean?A. She won’t hold a birthday party.B. She is planning a birthday party.C. She hopes to have a different birthday.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料，回答第6、7题。
河北省邯郸市2020届高三第二次模拟数学(文)试题(带答案解析)
9．已知双曲线C： 的右焦点为F，点N在C的渐近线上（异于原点），若M点满足 ，且 ，则|MN|＝（）
A．2aB． C．4aD．
10．已知曲线 绕原点顺时针旋转 后与 轴相切，若 ，则 （）
A． B．1C． D．2
11．在长方体ABCD﹣A1B1C1D1中，AA1＝2AB＝2AD＝4，过AA1作平面α使BD⊥α，且平面α∩平面A1B1C1D1＝l，M∈l.下面给出了四个命题：这四个命题中，真命题的个数为（）
A． B． C． D．
5．记Sn为等差数列{an}的前n项和，若a1+3a5＝12，则S7＝（）
A．18B．21C．24D．27
6．已知向量 （5，5）， 2 （﹣3，11），则向量 在向量 方向上的投影为（）
A．1B． C． D．﹣1
7．已知函数f（x）＝sin2xcosφ+cos2xsinφ图象的一个对称中心为 ，则φ的一个可能值为（）
河北省邯郸市2020届高三第二次模拟
数学（文)试题
1．已知集合 ， ，若 ，则 ＝（）
A．0B．1C．2D．3
2．已知 为虚数单位，复数 满足 ，则复数 在复平面内对应的点在（）
A．第一象限B．第二象限C．第三象限D．第四象限
3．已知 ，则（）
A． B． C． D．
4．如图所示，在边长为4的正三角形中有一封闭曲线围成的阴影区域.在正三角形中随机撒一粒豆子，它落在阴影区域内的概率为 ，则阴影区域的面积为（）
①l∥AC；
②BM⊥AC；
③l和AD1所成的角为60°；
④线段BM长度的最小值为 .
A．1B．2C．3D．4
12．已知 若函数 恰有5个零点，则实数 的取值范围是（）
河北省邯郸市2020届高三下学期第二次模拟考试理科综合物理试题_word版含参考答案(加精)
河北省邯郸市高三下学期第二次模拟考试理科综合物 理 试 题二．选择题：14、参考消息网2月10日引用美国媒体报道，中国在研制第二艘航母方面取得极大进展，该航母可能于2019年开始在中国南海海域巡逻；航空母舰的动力多来自核反应堆，其中主要核反应方程式是235114489192056360()U n Ba Kr x n +→++ ，该反应方程式中的x 为A.1B.2C.3D.415.如图所示，系统处于静止状态，不计一切摩擦，细绳、滑轮的质量可忽略，则甲乙两物块的质量之比是A.2B.3C.3D.1 16.在光滑绝缘水平面上，有一个正三角形abc ，顶点abc 处分别固定有一个电荷量相等的正点电荷，如图所示， D 点为正三角形外接圆的圆心，E 、G 、H 点分别为ab 、ac 、bc 的中点，F 点为E 关于c 电荷的对称点，取无穷远处的电势为零，则下列说法中正确的是（ ）A ．D 点的电场强度和电势均为零B ．E 、F 两点的电场强度等大反向、电势相等C．E、G、H三点的电场强度和电势均相同D．若释放c处的正点电荷，则其电势能将逐渐减小17、等效是指不同的物理现象、模型、过程等在物理意义、作用效果或物理规律方面是相同的，它们之间可以相互替代，而保持结论不变；在物理学上，等效方法是一种重要的思维方法，它能化难为易，使复杂问题得到有效的解决；如图所示，理想变压器的初级线圈接交流电源，次级线圈接一个电阻箱（接入电路的电阻为R）,理想变压器的原副线圈的匝数比分别为n1、n2，线路电阻不计，若虚线框中的电路中用一个阻值为R0的电阻等效代替，则下列关系式正确的是A.21nR Rn= B. 12nR Rn= C. 212()nR Rn= D. 221()nR Rn=19、如图所示，内壁光滑的圆形轨道固定在竖直平面内，轨道内甲乙两小球分别固定在轻杆的两端，甲球的质量小于乙球的质量，开始时乙球位于轨道的最低点；现由静止释放轻杆，下列说法正确的是A.甲球下滑的过程中，轻杆对其做正功B.甲球滑回时，一定能回到初始位置C.甲球不可能沿轨道下滑到最低点D.在甲球滑回的过程中，杆对甲球做的功大于杆对乙球的功20、2019年，中国航天最大的看点应属嫦娥五号，根据计划，我国将在今年11月底前后发射嫦娥五号探测器，实现月球软着陆及采样返回；若嫦娥五号的质量为m，在月球表面上受到的重力为P，月球的半径为R，则嫦娥五号在距月球表面高度为h的圆轨道上做匀速圆周运动时A.线速度的大小为()PRm R h + B.周期为2()m R h R Pπ+ C.动能为22()PR R h + D.所受月球的引力大小22()PR R h +21、如图所示，足够长的“U ”形光滑固定金属导轨所在平面与水平面的夹角为θ=300，其中导轨MN 与导轨PQ 平行且间距为L ，导轨平面与磁感应强度为B 的匀强磁场垂直；现使导体棒ab 由静止开始沿导轨下滑并开始计时（t=0）, 下滑过程中ab 与两导轨始终保持垂直且良好接触，t 时刻ab 的速度大小为v,通过的电流为I ；已知ab 棒接入电路的电阻为R ，导轨电阻不计，重力加速度为g ，则：A. 在时间t 内，ab 可能做匀加速直线运动B.t 时刻ab 的加速度大小为2212B L vg mR-C.在时间t 内，通过ab 某一横截面的电荷量为ItD.若在时间t 内ab 下滑的距离为s,则此过程中该电路产生的焦耳热为21122mgs mv -三、非选择题： （一）必考题：22.某同学用图甲所示的装置测量物块与斜面之间的动摩擦因数；已知打点 所用交流电压的频率为50Hz ，物块下滑过程中所得到的纸带的一部分如图乙所示，图中标出了5个连续点之间的距离.（1）物块下滑的加速度为m/s2；打点计时器打C点时，物块的速度大小为m/s（结果保留三位有效数字）（2）测出斜面的倾角为300，已知重力加速度为g=9.8m/s2，可得物块与斜面间的动摩擦因数为（结果保留两位有效数字）23、某实验小组欲测定一个未知电阻Rx的阻值，他们先用多用电表在正确的操作的情况下粗侧电阻Rx的阻值，多用电表的档位选择机器示数如图甲所示；然后该小组利用伏安法测量Rx 的阻值，实验室可提供的器材有：A．电压表V1，量程3V，内阻约3kΩB．电压表V2，量程15V，内阻约15KΩC．电流表A1，量程30mA，内阻约8ΩD．电流表A2，量程0.6A，内阻约0.1ΩE．滑动变阻器R1，最大阻值10Ω，最大电流2AF．滑动变阻器R2，最大阻值3kΩ，最大电流0.5AG．电池组,电动势约3V，内阻很小H．导线、电键若干（1）用多用电表测得该位置电阻Rx的阻值为Ω；（2）用伏安法测量Rx，电流表应选用；电流表应选用，滑动变阻器应选用。
2020届邯郸市高三年级第二次模拟考试试题（精校解析版）
2020届邯郸市高三年级第二次模拟考试试题（精校解析版）2020届邯郸市高三年级第二次模拟考试试题(精校解析版)第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What is the man’s attitude towards the plan?A. Positive.B. Ambiguous.C. Disapproving.2. Where does this conversation most probably take place?A. At a train station.B. At a bus stop.C. At the museum.3. What will the woman talk about next?A. Her school.B. Her marks.C. Study tips.4. What is the man doing now?A. Complaining about a film.B. Taking a walk outside.C. Reading film reviews.5. What does the woman mean?A. She won’t hold a birthday party.B. She is planning a birthday party.C. She hopes to have a different birthday.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
2020届邯郸市高三年级第二次模拟考试试题(精校解析版)
2020届邯郸市高三年级第二次模拟考试试题(精校解析版)第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What is the man’s attitude towards the plan?A. Positive.B. Ambiguous.C. Disapproving.2. Where does this conversation most probably take place?A. At a train station.B. At a bus stop.C. At the museum.3. What will the woman talk about next?A. Her school.B. Her marks.C. Study tips.4. What is the man doing now?A. Complaining about a film.B. Taking a walk outside.C. Reading film reviews.5. What does the woman mean?A. She won’t hold a birthday party.B. She is planning a birthday party.C. She hopes to have a different birthday.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项。
听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
2020年河北省邯郸市高考数学二模试卷(文科)
2020年河北省邯郸市高考数学二模试卷（文科）一、选择题：本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．1．（5分）已知集合{0A =，1，2，3)，{1B =-，0，}a ，若{0A B =I ，2)，则(a =)A ．0B ．1C ．2D ．32．（5分）设i 是虚数单位，若复数z 满足(1)z i i -=，则复数z 对应的点在( ) A ．第一象限B ．第二象限C ．第三象限D ．第四象限3．（5分）已知13213112,log ,log 32a b c ===，则( )A ．b c a <<B ．b a c <<C ．a b c <<D ．c b a <<4．（5分）如图所示，在边长为4的正三角形中有一封闭曲线围成的阴影区域．在正三角形中随机撒一粒豆子，它落在阴影区域内的概率为34，则阴影区域的面积为( )A 3B ．23C ．33D ．435．（5分）记n S 为等差数列{}n a 的前n 项和，若15312a a +=，则7(S = ) A ．18B ．21C ．24D ．276．（5分）已知向量(5,5)a =r ，2(3,11)a b +=-r r ，则向量a r 在向量b r 方向上的投影为( )A ．1B 2C ．2D ．1-7．（5分）已知函数()sin 2cos cos2sin f x x x ϕϕ=+图象的一个对称中心为(,0)3π-，则ϕ的一个可能值为( ) A ．3π-B ．3πC ．56π-D ．56π 8．（5分）数学家也有许多美丽的错误，如法国数学家费马于1640年提出了221(0,1,2,)nn F n =+=⋯是质数的猜想，直到1732年才被善于计算的大数学家欧拉算出5641*6700417F =，不是质数．现设4log (1)(1n n a F n =-=，2，)⋯，n S 表示数列{}n a 的前n项和．若3263n n S a =，则(n = ) A ．5B ．6C ．7D ．89．（5分）已知双曲线2222:1(0)4x y C a a a-=>的右焦点为F ，点N 在C 的渐近线上（异于原点），若M 点满足OF FM =u u u r u u u u r ，且0ON MN =u u u r u u u u rg ，则||(MN = ) A ．2aBC ．4aD．10．（5分）已知曲线1x y ae -=绕原点顺时针旋转θ后与x 轴相切，若tan 2θ=，则(a =)A ．12B ．1C ．32D ．211．（5分）在长方体1111ABCD A B C D -中，1224AA AB AD ===，过1AA 作平面α使BD α⊥，且平面α⋂平面1111A B C D l =，M l ∈．下面给出了四个命题：这四个命题中，真命题的个数为( ) ①//l AC ； ②BM AC ⊥；③l 和1AD 所成的角为60︒； ④线段BMA ．1B ．2C ．3D ．412．（5分）已知|2|222,41,()log (1),14,x x f x x x +⎧---⎪=⎨+-<⎪⎩剟…若函数2()()()1g x f x mf x =--恰有5个零点，则实数m 的取值范围是( ) A ．3(0,)2B ．3(0,]2C ．(0,2)D ．(0，2]二、填空题：本大题共4小题，每小题5分，共20分．13．（5分）若实数x ，y 满足01,01,x y x y -⎧⎨+⎩剟剟则2z x y =+的最大值为 ．14．（5分）已知α是锐角，且1sin()63πα-=．则sin()3πα+= ．15．（5分）我国古代数学名著《九章算术g 商攻》中，阐述：“斜解立方，得两堑堵．斜解堑堵．其一为阳马，一为鳖臑”．如图，在一个为“阳马”的四棱锥P ABCD -中，底面ABCD 为矩形，2AB =．3AD =，PA ⊥平面ABCD ，若直线PD 与平面ABCD 所成的角为60︒，则PA = ，该“阳马”外接球体积为 ．16．（5分）已知直线20x my --=与抛物线21:2C y x =交于A ，B 两点．P 是线段AB 的中点，过P 作x 轴的平行线交C 于点Q ，若以AB 为直径的圆经过Q ，则m = ． 三、解答题：共70分．解答应写出文字说明、证明过程或演算步骤．第17～21题为必考题，第22、23题为选考题，考生根据要求作答．（一）必考题：共60分．17．（12分）受突如其来的新冠疫情的影响，全国各地学校都推迟2020年的春季开学．某学校“停课不停学”，利用云课平台提供免费线上课程．该学校为了解学生对线上课程的满意程度，随机抽取了500名学生对该线上课程评分．其频率分布直方图如下：若根据频率分布直方图得到的评分低于80分的概率估计值为0.45． （1）()i 求直方图中的a ，b 值；()ii 若评分的平均值和众数均不低于80分视为满意，判断该校学生对线上课程是否满意？并说明理由（同一组中的数据用该组区间的中点值为代表）；（2）若采用分层抽样的方法，从样本评分在[60，70)和[90，100]内的学生中共抽取5人进行测试来检验他们的网课学习效果，再从中选取2人进行跟踪分析，求这2人中至少一人评分在[60，70)内的概率．18．（12分）已知ABC ∆的内角A ，B ，C 的对边分别为a ，b ，c ，且tan (2)tan b A c b B =-． （1）求A ；（2）若ABC ∆是锐角三角形，且3a =．求cos Cb的取值范围． 19．（12分）如图，在直三棱柱111ABC A B C -中，124CC AC ==，3AB =，90CAB ∠=︒．M 是1CC 的中点．（1）证明：平面11A B M ⊥平面ABM ； （2）求四棱锥11M ABB A -的侧面积．20．（12分）已知长轴长为22222:1(0)x y C a b a b +=>>的左、右焦点分别为1F 、2F ，且以1F 、2F 为直径的圆与C 恰有两个公共点． （1）求椭圆C 的方程；（2）若经过点2F 的直线l 与C 交于M ，N 两点，且M ，N 关于原点O 的对称点分别为P ，Q ，求四边形MNPQ 面积的最大值．21．（12分）已知函数21()3cos ,()2f x x ax f x '=--为()f x 的导函数．。