武汉市2013届高中毕业生四月调研测试

武汉市2024届高中毕业生四月调研考试英语试卷武汉市教育科学研究院命制2024.4.25本试题卷共12页，67题。

全卷满分150分。

考试用时120分钟。

★祝考试顺利★注意事项：1.答题前，先将自己的姓名、准考证号填写在试卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

2.选择题的作答：每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑。

写在试卷、草稿纸和答题卡上的非答题区域均无效。

3.非选择题的作答：用黑色签字笔直接答在答题卡上对应的答题区域内。

写在试卷、草稿纸和答题卡上的非答题区域均无效。

4. 考试结束后，请将本试卷和答题卡一并上交。

第一部分听力(共两节，满分30分)做题时，先将答案标在试卷上。

录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

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。

例：How much is the shirt?A.£ 19.15.B.£ 9.18.C.£ 9.15.答案是 C。

1. What is the man busy with?A. A visit.B. A project.C. A video.2. What do the speakers plan to do tomorrow?A. Go camping.B. Do some shopping.C. Find a blanket.3. Where are the speakers going to?A. A station.B. Another country.C. Their hometown.4. What does the woman think of Jimmy?A. Silent.B. Caring.C. Hard-working.5. What are the speakers talking about?A. The new laws.B. A healthy lifestyle.C. Profitable industries.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。

湖北省武汉市部分学校新2013届高三起点调研测试数学（文）试题一、选择题（50分）1．设集合U ＝{1，2，3，4，5，6}，集合A ＝{1，2，5}，U C B ＝{4，5，6}，则A∩B ＝ A ．{1，2} B ．{5} C ．{1，2，3} D ．{3，4，6}2．下列命题中，真例题的是 A ．0x R ∃∈，0xe ＜0 B ．x R ∀∈，22xx >C ．“a ＋b ＝0”的充要条件是“ab＝－1” D ．“a ＞1，b ＞1”是“ab ＞1“的充分条件 3．设x ∈R ，向量a ＝（x ，1），b ＝（1，－2），且a ⊥b ，则｜a ＋b ｜＝A ．5B ．10C ．25D ．104．如图，中心均为原点O 的双曲线与椭圆有公共焦点，M ，N 是双曲线的两顶点，若M ，O ，N 将椭圆长轴四等分，则双曲线与椭圆的离心率的比值是 A ．3 B ．2C ．3D ．25．某程序框图如下图所示，该程序运行后输出的S 的值是A ．－3B ．－12C ．13D ．26．如上图是某几何体的三视图，则该几何体的体积为 A ．16 B ．24 C ．34 D ．487．已知公差不为0的等差数列{n a }的前n 项和为S n ，S 3＝a 4＋6，且1413,,a a a 成等比数列，则a 10＝ A ．19 B ．20 C ．21 D ．228．右图是甲．乙两组各7名同学体重（单位：kg ）数据的茎叶图，设甲．乙两组数据的平均数依次为1x ，2x ，标准差为1x ，2x ，则A ．1x ＞2x ，1x ＞2xB ．1x ＞2x ，1x ＜2xC ．1x ＜2x ，1x ＜2xD ．1x ＜2x ，1x ＞2x9．已知函数y ＝sinax ＋b （a ＞0）的图象如图所示，则函数log ()a y x b =+的图象可能是10．若函数y ＝f （x ）（x ∈R ）满足f （x ＋2）＝f （x ），且x ∈［－1,1］时，f （x ）＝1－x 2，函数g（x ）＝lg (0)1(0)x x x x >⎧⎪⎨-<⎪⎩，则函数h （x ）＝f （x ）－g （x ）在［－5,5］上的零点个数为A ．5B ．7C ．7D ．10二、填空题（35分） 11．设不等式组0202x y ≤≤⎧⎨≤≤⎩表示的平面区域为D ，在区域D 内随机取一个点，则此点到坐标原点的距离大于2的概率是＿＿＿＿ 12．设a ，b ∈R ，a ＋bi ＝11712ii--（i 为虚数单位），则a ＋b ＝＿＿＿＿＿ 13．若sin cos 1sin cos 2αααα+=-，则tan2α＝＿＿＿14．某地区恩格尔系数y （%）与年份x 统计数据如下表：从散点图可以看出y 与x 线性相关，且可得回归方程为$4055.25y bx =+$，则b $＝＿＿＿，据此模型可预测2012年该地区的恩格尔系数（%）为＿＿＿＿15．已知圆柱M 的底面半径与球O 的半径相同，且圆柱M 与球O 的表面积相等，则它们的体积之比＝＿＿＿＿16．已知等差数列{n a }的首项及公差均为正数，令2012n n n b a a -=+（*n N ∈，n ＜2012），当kb 是数列{n b }的最大项时，k ＝＿＿＿＿17．已知△FAB ，点F 的坐标为（1,0），点A ，B 分别在图中抛物线y 2＝4x 及圆（x－1）2＋y 2＝4的实线部分上运动，且AB 总是平行于x 轴，，则△FAB 的周长的取值范围是＿＿＿＿三．解答题（75分） 18．（本小题满分12分） 某研究性学习小组对昼夜温差与某种子发芽数的关系进行研究，他们分别记录了四天中每天昼夜温差与每天100粒种子浸泡后的发芽数，得到如下资料：（I ）求这四天浸泡种子的平均发芽率；（II ）若研究的一个项目在这四天中任选2天的种子发芽数来进行，记发芽的种子数分别为m ，n （m ＜n ），则（m ，n ）的形式列出所有的基本事件，并求“m ，n 满足3040m n >⎧⎨>⎩”的事件A 的概率。

湖北黄冈市2013年高三年级4月份模拟考试数学（理）试题第I 卷（选择题，共50分）一、选择题（本大题共10小题，每小题5分，共50分，在每小题给出的四个选英中，只有一个是符合题目要求的） 1．ο2013sin 的值属于区间A ．)0,21(- B ．)21,1(-- C ．)1,21( D ．1(0,)22．下列命题中，真命题是 A ．00,0x x R e ∃∈≤使得B ．2,2x x R x ∀∈>C ．1,11a b ab >>>是的充分条件D ．22sin 3(,)sin x x k k Z xπ+≥≠∈ 3．由直线222cos (02)2xy y x π==≤≤与函数的图象围成的封闭图形的面积为A ．4πB ．2πC ．πD ．2π4．已知复数32(z i i =-+为虚数单位）是关于x 的方程220(,x px q p q ++=为实数）的一个根，则p q +的值为A ．22B ．36C ．38D ．425．若直线ex e y x y +=-=与曲线3相切，则实数a 的值为A ．—4B ．—2C ．2D ．4 6．设某大学的女生体重y （单位：kg ）与身体x （单位：cm ）具有线性相关关系。

根据一组样本数据（),2,1)(,n i y x ti Λ=，用最小二乘法建立的回归方程是71.8585.0-=x y ，则下列结论中不正确的是A ．y 与x 具有正的线性相关关系B ．回归直线过样本点的中心（y x ,）C ．若该大学某女生身高增加1cm ，则其体重约增加0.85kgD ．若该大学某女生身高为170cm ，则可断定其体重必为58.79kg7．某三棱锥的三视图如所示，该三棱锥的体积为 A ．20B ．340C ．56D ．608．已知直线x=2与双曲线14:22=-y y C 的渐近线交于E 1、E 2两点，记2211,e OE e OE ==，任取双曲线C 上的点P ，若),(21R b a be ae ∈+=，则A ．1022<+<b aB ．21022<+<b a C ．122≥+b aD ．2122≥+b a9．假设你家订了一份早报，送报人可能在早上6：30—7：30之间把报纸送到你家，你父亲离开家去上班的时间在早上7：00—8：00之间，则你父亲在离开家前能得到报纸的概率为A ．31B ．127C ．87D ．8110．已知函数),0()0,()(+∞⋃-∞是定义在x f 上的偶函数，当0>x 时，1)(4)(2),2(21,20,12)(|1|-=⎪⎩⎪⎨⎧>-≤<-=-x f x g x x f x x f x 则函数的零点个数为A ．4B ．6C ．8D ．10二、填空题：本大题共6小题，考生共需作答5小题，每小题5分，共25分。

武汉武昌2013届高三期末调研考试数学(理)试题一、选择题：本大题共10小题，每小题5分，共50分．1．复数3132i ⎛⎫+ ⎪ ⎪⎝⎭（i 为虚数单位）的值是（ ）A ．-1B ．1C ．-iD ．i 2．命题“所有奇数的立方都是奇数”的否定是（ ） A ．所有奇数的立方都不是奇数 B ．不存在一个奇数，它的立方是偶数 C ．存在一个奇数，它的立方是偶数 D ．不存在一个奇数，它的立方是奇数 3．某天清晨，小明同学生病了，体温上升，吃过药后感觉好多了，中午时他的体温基本正常，但是下午他的体温又开始上升，直到半夜才感觉身上不那么发烫了．下面大致能反映出小明这一天（0时~ 24时）体温的变化情况的图是 （ ）4．已知数列{a n }是等差数列，a 1+a 3+a 5=105，a 2+a 4+a 6=99，{a n }的前n 项和为S n ，则使得S n 达到最大的n 是 （ ） A ．18 B ．19 C ．20 D ．21 5．某多面体的三视图（单位：cm ）如图所示，则此多面体的体积是 （ ） A ．312cmB ．23cm 3C ．56 cm 3D ．78cm 36．已知a>b ，二次三项式ax 2 +2x +b ≥0对于一切实数x 恒成立．又o x R ∃∈，使220oo ax x b ++=成立，则22a b a b+-的最小值为（ ） A ．1B 2C ．2D ．27．过抛物线y2=4x的焦点F的直线交抛物线于A，B两点，点O是坐标原点，则|AF|·|BF|的最小值是（）A．2 B C．4 D．8．已知变量x ，y 满足约束条件211y x y x y ≤⎧⎪+≥⎨⎪-≤⎩，则z=3|x| +y 的取值范围为（ ）A ．[-1,5]B ．[1, 11]C ．[5, 11]D ．[ -7, 11]9．函数f （x ）=23420122013123420122013x x x x x x ⎛⎫+-+-+-+ ⎪⎝⎭cos2x 在区间[-3，3]上的零点的个数为 （ ） A ．3 B ．4 C ．5 D ．610．O 是锐角三角形ABC 外心，由O 向边BC ，CA ，AB 引垂线，垂足分别是D ，E ，F ，给出下列 命题：①0OA OB OC ++=； ②0OD OE OF ++=；③||OD ：||OE ：||OF =cosA ：cosB ：cosC;④R λ∃∈，使得()||||AB ACAD AB SINB AC SINCλ=+。

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武汉市2024届高中毕业生四月调研考试思想政治试卷武汉市教育科学研究院命制2024.4.26本试题卷共6页，21题。

全卷满分100分。

考试用时75分钟。

★祝考试顺利★注意事项：1.答题前，先将自己的姓名、准考证号、考场号、座位号填写在试卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。

2.选择题的作答：每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑。

写在试卷、草稿纸和答题卡上的非答题区域均无效。

3.非选择题的作答：用黑色签字笔直接答在答题卡上对应的答题区域内。

写在试卷、草稿纸和答题卡上的非答题区城均无效。

4.考试结束后请将本试卷和答题卡一并上交。

一、选择题：本题共16小题，每小题3分，共48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.马克思在《哲学的贫困》中指出：“当文明一开始的时候，生产就开始建立在级别、等级和阶级的对抗上，最后建立在积累的劳动和直接的劳动的对抗上。

没有对抗就没有进步。

这是文明直到今天所遵循的规律。

”对此解读正确的是①“文明一开始的时候”指的是原始社会氏族制度形成时期②“生产建立在阶级的对抗上”表明生产关系状况制约生产发展③“积累的劳动”与“直接的劳动”的对抗意味着阶级的对立④“没有对抗就没有进步”揭示了只有阶级斗争才能推动社会发展A.①②B.①④C.②③D.③④2.在二十届中央纪委三次全会上，习近平总书记明确提出深入推进党的自我革命“九个以”的实践要求，“以自我监督和人民监督相结合为强大动力”是其中一个重要方面。

党坚持自我监督和人民监督相结合①根本目的是传导监督压力，让党员干部习惯在监督环境中工作生活②是我们党将发展人民民主与坚持全面从严治党有机结合的必然要求③有利于推动我们党的特殊利益与中国人民的根本利益保持高度一致④表明我们党勇于坚持真理、修正错误，推进党的自我革命向纵深发展A.①②B.①③C.②④D.③④思想政治试卷第1页(共6页)3.2024年1月，国务院办公厅印发《关于发展银发经济增进老年人福祉的意见》提出，强化财政金融支持，通过地方政府专项债券、普惠养老专项再贷款等支持符合条件的银发经济产业项目，加快银发经济规模化、标准化、集群化、品牌化发展。

2.4风和降水 教学目标：1．了解风是怎样形成的。

2．知道风向、风速的表示方法和度量单位。

3．学会用风向标、风速仪测定风向和风速，了解目测风向、风速的方法。

4．了解风对人类活动和动物行为的影响。

5、理解空气湿度及其与气温之间的关系 6、知道观测湿度的常用仪器，学会测量空气湿度 7、理解空气湿度与天气的关系 8、理解空气中水汽凝结的原因 9、学会测量降水量 重点难点： 1.风的观测 2.风的形成；目测风向、风速 3、相对湿度的观测； 4、凝结与降水的的形成； 5、湿度与降水的关系。

教学课时：1课时 教学过程： 一．风是怎样形成的 实验：一个充气气球产生风的现象 问：为什么有风？（充气气球内的气压〉外界的气压） 通过实验能否得出风的形成与什么有关？ 分析：气压与高度的关系。

同一高度、不同区域的气压一定相同吗？高压区？低压区？ 提问：高压区和低压区之间的空气会如何运动? (气压高处指向气压低处的——股力量，推动空气形成风) 类比：水流动的方向?直接原因是什么?空气流动的方向?直接原因是什么? (气压差是形成风的) 直接原因。

气压差异越大，风就越大，如果两地的气压相等，风就平息了) 小结：风是怎样形成的?——空气的水平运动。

二、风向和风速 1、风向 A、定义：风吹来的方向。

B、方位：8种风向 C、符号：短线段表示 如东风表示为： o-- D、测量仪器：风向标-----箭头的方向即风向。

风向箭头指在哪个方向，就表示当时刮什么方向的风。

讨论:生活中还有哪些方法判定风向 (旗的飘向,烟的飘向,树叶的摇摆方向) 2.风速:用风级表示 A、定义：单位时问内空气流动的距离。

B、单位：米/秒、千米／时。

C、测量仪器：风速仪。

风速仪是靠测量上面风杯的转速来测定的。

D、了解目测风级的方法及不同风级对人类和自然的影响 E、应用：用目测的方法测当地当时的风速。

3、延伸：风是一种自然能源，我们应该如何利用风为人类造福? 思考题:1.风也是一种资源。

湖北省武汉市部分学校2013届九年级四月调研测试英语试卷第二部分笔试部分二、选择填空(本题共15分，每小题1分)将代表最佳答案的字母在答题卡上相应的位置涂黑。

26. Jim isn’t from a poor family, yet he often comes to school wearing the same clothes every day________the week.A. ofB. forC. atD. from27. -- What does Jack’s father do?--He is a teacher. He_____maths at a school.A. taughtB. has taughtC. teaehesD. will teach28. -- It’s a nic e cinema.-- Yes, my uncle______for my last birthday.A. buyB. have boughtC. will buyD. bought29. --Is Mary in the classroom?-- No. She______ to the library.A. goesB. had goneC. has goneD. would go30.--How is everything going in the school, my boy?--_______.A. I am all right, thanksB. Not too bad, I guess.C. Very well, thank you.D. Not at all.31. -- I had a really nice weekend on the beach.-- __________.A. Oh, that's very nice of you.B. CongratulationsC. It's a pleasure.D. I' m glad to hear that.32. The headmaster turned a deaf ear to the _____ of thy parents.A. wordsB. soundsC. voice.D. noise33. --Does Jenny live here?--But I don't know_______.A. Which room does she live inB. in which room lives sheC. which room she lives inD. in which room does she live34. --May I do the rest of the work tomorrow?--Yes, of course. You _____ finish it today.A. mustn'tB. needn'tC. can'tD. shouldn't35. --Do you recognize the music?--Let me_______....Yes, now I do.A. thinkB. considerC. seeD. wonder36. At first he was a little shy in class, but now he seems_______.A. nervousB. kind-heartedC. naturalD. different37. -- Which of those electronic dictionaries do you like most?-- _______ at all. They are both expensive and of little use.A. NoneB. NeitherC.AllD. Both38. My cousin is old enough_______himself.A. to wearB.to put onC. to dressD. to have on39. --I'm sorry. I forgot to post the letter for you.--_______. I'll post it myself, then.A. It doesn’t matterB. You'd better notC. Take it easyD. It's too bad40. --Your teacher look angry.--She _____when she saw all the boy fighting.A. blew upB. jumped upC. looked upD. cheered up三、完形填空（本题共15分，每小题1分）I hurried into the store to get Christmas gifts.Suddenly, I saw a little boy holding a lovely dol l. He kept (41) her hair. I watched him turn to a woman and say. “Are you (42) I don't have enough money?” She said yes and told the boy not to go anywhere before she (43). Then she left.The boy continued to hold the doll. I asked the boy who the do ll was for. He said, “It's the doll that my sister wanted so badly for Christmas. She just knew that Santa would (44) it.” I told him that Santa was going to do that. He said, “No, Santa can't go where my sister is. I have to give the (45) to my mom to take it to her.”l asked him where his sister was. He looked at me (46) and said, “She's gone to heaven. My daddy said that Mom was going to be there with her.” My heart nearly stopped beating. Thenthe boy said, “I told my daddy to tell her not to go there until I got back.” He took out some pictures of him and said, “I want my mom to take these with her so she'll never (47) me. I love my mom so much and I wish she didn't have to leave me, but Daddy said that she (48) to be with my sister.”The boy lowed his head. While he was not looking, I (49) into my purse and asked him, “Shall we count that money again?” He grew (50) and said, “Yes, I just know it has to be enough.” So I put my money with his and we began to (51) it. He said, “Thank you for giving me enough money.” He (52), “I just asked God to give me enough money to buy this doll, and he (53) my prayer.”Soon the woman came back and I left. I remembered a story I had read in the newspaper several days earlier about a (54) driver who hit a car. A little girl was killed and her mother was in serious (55). Two days later, I read the news that the mother had died.41. A. cleaning B. washing C. touching D. cutting42. A. afraid B. surprised C. embarrassed D. sure43. A. returned B. paid C. passed D. apologized44. A. take B. bring C. own D. made45. A. money B. pictures C. chance D. doll46. A. seriously B. sadly C. kindly D. finally47. A. lose B. remained C. forget D. hate48. A. agreed B. needed C. hoped D. preferred49. A. put B. hurried C. drew D. reached50. A. worried B. disappointed C. excited D. confused51. A. collected B. spend C. save D. counted52. A. replied B. continued C. complained D. repeated53. A. appreciated B. remembered C. heard D. copied54. A. lost B. drunk C. frightened D. mistaken55. A. condition B. trouble C. action D. health四、阅读理解（本题共30分，每小题2分）AA. a poster about kittenB. a piece of news about GRUMPY’SC. an advertisement on GRUMPY’SD. a cartoon story about pets57. GRUMPY ' S services are provided _________.A. just in the shop itselfB. for six days a weekC. for freeD. by phone.58. If you need pet sitting service, you _______.A. have to go to CRUMPY'S .B. can ask Richard or Julie about itC. need to visit LondonD. must pay first for it59. Which of the following is not mentioned in the above?A. telephone numberB. e-mail addressC. charge of deliveries.D. addresses of the pet shop60. We learn that GRUMPY’S lies ________.A. in Washington DCB. in ScotlandC. in ParisD. in CambridgeBI ran into a stranger as he passed by. “Oh, excuse me, please” was my reply. He said, “Please, excuse me, too; I wasn’t even watching for you.”We were very polite, this stranger and I. We went on our way and we said good-bye.But at home a different story is told-how we treat our loved ones, young and old.Later that day, cooking the evening meal, my daughter stood beside me very still.When I turned, I nearly knocked her down. “Move out of the way,” I shouted at her.My daughter walked away, her little heart broken. I didn’t realize how cruelly (冷酷地) I had spoken.While I lay awake in bed, God’s small voice came to me and said, “When dealing with a stranger, common courtesy(礼貌) you use，but the children you love , you seem to abuse. Look on the kitchen floor, and you will find some flowers there by the door. Those are the flowers your daughter brought for you. She picked them herself, pink, yellow and blue. Your daughter stood quietly not to spoil the surprise, and you never saw the tears in her eyes.” By this time, I felt very small, and now my tears began to fall.I quietly went and knelt by her bed: “Wake up, little girl, wake up,” I said. “Are these the flowers you picked for me?” My daughter smiled, “I found them, out by the tree. I picked them because they are pretty like you. I knew you would like them, especially the blue.”I said, “Daughter, l am sorry for the way l acted today; I should not have shouted at you that way.” My daughter said, “Oh, Mom, that's okay. I love you anyway.”I said, “Daughter, I love you too, and I do like the flowers, especially the blue.”61 . Mother seemed to be acting ______ between a stranger and her daughter.A .in a strange way B. in a friendly wayC. quite differentlyD. almost the same62. The little girl stood beside her mother still in order to ______.A. get something to eatB. pick some flowersC. give her a surpriseD. play a hiding game.63. The underlined word ‘abuse’ in the reading means _______.A. deal with a child in a cruel wayB. treat someone not kindly enoughC. look down on someoneD. refuse to be strict with someone64. Mother didn't realize she was small untilA. she came in and knelt by her daughter's bedC. her daughter walked away and criedB. she found the beautiful flowersD. she 'heard' God' s small voice65. The best title of the passage should be______.A. Don't Shout at AnyoneB. Don't Break Kid's HeartC. Mother and DaughterD. Mother and StrangerCBilly Mills, a Native American, was born and raised on a reservation in the United States. Childhood was not easy for Billy. His family was not well off; he lost his mother when he was seven, and his father passed away five years later. After his father's death, Billy was sent to a boarding school. At school Billy started running to help him forget his problems. To his amazement, he found that he had a talent for running and broke a number of high school records. As a result of his running, he was given an athletic scholarship (奖学金) to the University of Kansas.At the University of Kansas, Billy continued to win many competitions. After graduation he joined the United States Marine corps (海军陆战队). At first he focused (投入) on military (军事) life , but he soon returned to running. He did well enough to race in the 1964 Tokyo Olympics in the 10,000 meters and marathon events.Although he was on the US team, many people did not expect anything from Billy. In the 10,000 meters Billy was almost a minute slower than the favorite, Ron Clarke of Australia. The other favorite to win the Olympic gold was Mohammad Gammoudi of Tunisia. The rest of the runners included Olympic gold and world record holders. All eyes were focused on the front runners, not on Billy.When the race started, everyone was surprised to see Billy Mill at the front with Ron Clarke. For much of the race, the two ran together with Gammoudi just behind them. Everyone else was out of the race, and the crowd expected Mills to tire and slow down.Near the end of the race, Gammoudi ran between Clark and Mills and pushed them aside. The two of them almost fell over and Mills dropped behind into third place. However, Mills was determined not to lose. He raced ahead to win the gold, and set an Olympic l0, 000-meter record. He was the first Native American to win the Olympic l0, 000-meter race.66. It's clear that Billy _______.A. did not have a happy childhoodB. was good at running when he was tenC. he had to study harder to forget his problemsD. his was in a rich family before his parents died67. He was given an athletic scholarship because he ______.A. studied harder than other studentsB. had no parents to support himC. broke many high school recordsD. could win Olympic medals68. The sentence "Everyone else was out of the race," means ______.A. the other runners had already finished the raceB. the other runners were far behindC. the other runners had given upD. the other runners stopped to watch Bill running69. We learn from the reading that _______.A. no one believed Bill could win a medalB. people were not surprised when Bill won the goldC. other Americans had won the Olympic 10,000 meters beforeD. Bill won the gold but failed to set a new record70. What made Bill successful in the Olympics most probably is ________.A. his military lifeC. other runners' supportB. his talent and hard trainingD. the scholarship of the University五、词与短语选择填空（本题共10分，每小题2分）仔细阅读下面五个句子，然后用下面方框中所给的单词或短语填空，使每个句子在结构、句义和逻辑上正确。

武汉市2023届高中毕业生四月调研考试数学试卷参考答案及评分标准填空题：13. 48−14. 5615. 42,3−− 16.解答题：17.（10分）解：（1）由题意，(1)n n S na n n =+−，11(1)(1)n n S n a n n ++=+++. 两式相减得：11(1)2n n n a n a na n ++=+−+. 整理得：12n n a a +−=−，所以{}n a 是等差数列.…………5分（2）由题意：70a >，80a <.由{}n a 公差为2−，故16(2)0a +⋅−>且 17(2)0a +⋅−<.解得：11214a <<.…………10分18.（12分）解：（1sin sin cos sin B C B B A++=.sin sin cos sin sin()A B A B B A B +=++，sin sin cos sin sin cos cos sin A B A B B A B A B +=++sin sin cos sin A B B A B =+.又sin 0B ≠cos 1A A −=，即1sin()62A π−=.由0A π<<，得：3A π=. …………6分（2）ABC ∆面积11sin 22S a bc A ==，代入3A π=，整理得：22a bc =.故2sin 2sin sin A B C =，得：3sin sin 8B C =.又1cos()cos 2B C A +=−=−，即1cos cos sin sin 2B C B C −=−.所以1cos cos 8B C =−. …………12分19.（12分）解：（1）取1A B 中点Q ，连接,PQ EQ ，PQ //=12BC 且FE //=12BC ，有PQ //=FE . 故四边形EFPQ 是平行四边形，所以FP ∥EQ . 又FP ⊄平面1A BE ，EQ ⊂平面1A BE ，所以FP ∥平面1A BE . …………6分 （2）取EF 中点O ，BC 中点G ，由平面1A EF ⊥平面EFCB ，且交线为EF ，故1AO ⊥平面EFCB . 此时，1,,OA OE OG 两两垂直，以O 为原点，1,,OE OG OA 所在直线分别为x 轴、y 轴、z 轴，建立如图所示的空间直角坐标系.有B，1A ，(1,0,0)F −，(C −，1AC中点(P −.(0,FP=， (3,FB =.设平面BFP 的法向量(,,)n x y z =，由00n FP n FB ⎧⋅=⎪⎨⋅=⎪⎩，得030y z x =⎨⎪=⎩，取(1,3,n =−.又1(1,0,A F =−，故所求角的正弦值为11|||17||||7n A F n A F ⋅−==⋅. 所以直线1A F 与平面BFP 所成角的正弦值为7. …………12分20.（12分）解：（1）甲乙正面朝上次数相等的概率为：021222323333333311115()()()()162222C C C C +++=. 由对称性，甲正面朝上次数大于乙和小于乙的概率相等. 故甲正面朝上次数大于乙的概率为1511(1)21632⋅−=.…………6分（2）设甲正面朝上次数大于乙为事件A .方法一：设甲乙均抛掷n 次时，两人正面朝上次数相等的概率为p .若此时甲正面朝上次数小于乙，则事件A 不会发生；若此时甲正面朝上次数等于乙，则甲第(1)n +次抛掷结果为正面朝上才会有事件A 发生；若此时甲正面朝上次数大于乙，则无论甲第(1)n +次抛掷结果如何，都有事件A 发生，由对称性此时甲正面朝上次数大于乙和小于乙的概率相等，均为1(1)2p −. 所以111()(1)1222P A p p =⋅+−⋅=.…………12分方法二：设甲正面朝上次数为X ，乙正面朝上次数为Y .因为""A X Y =>，所以A 表示甲正面朝上次数不大于乙. 有"""1""1"A X Y X Y n X n Y =≤=−<=+−>−.此时A 也表示甲反面朝上次数大于乙.根据对称性，甲正面朝上次数大于乙的概率和甲反面朝上次数大于乙的概率相等.故()()P A P A =，由()()1P A P A +=，得1()2P A =.…………12分21.（12分）解：（1）根据双曲线的对称性，双曲线E 过点(2)±和(4,±.所以222284116121a b a b⎧−=⎪⎨⎪−=⎩，解得：2244a b ⎧=⎪⎨=⎪⎩.故双曲线E 的标准方程为22144y x −=. …………4分（2）当直线l 的斜率存在时，设直线l 的方程为(4)2y k x =−+，与双曲线方程联立，得2222(1)(84)161680k x k k x k k −−−+−+=.设1122(,),(,)M x y N x y ，有2122841k k x x k −+=−，2122161681k k x x k −+=−. 设(,1)P t t +.1212121212(1)(1)(41)(41)()()()()y t y t kx k t kx k t k k x t x t x t x t −−−−−−+−−+==−−−− 22222221212222221212(41)()(41)(16168)(41)(84)(41)(1)()16168(84)(1)k x x k k t x x k t k k k k k t k k k t k x x t x x t k k t k k t k −+−+++−−+−+−−++−−==−++−+−−+− 222222(211)8(1)(1)(4)4(4)(8)t t k t k t t k t k t +−−−−−=−+−−−. 当4t =时，不满足12k k 为定值.当4t ≠时，若12k k 为定值，则22228(1)(1)2114(4)(4)(8)t t t t t t t −−−−+−==−−−−，解得3t =，此时124k k =.经检验，当直线l 斜率不存在时，对(3,4)P ，也满足124k k =. 所以点P 坐标为(3,4). …………12分22.（12分）解：（1）令()0f x =，得2ln k x x =. 由0k >得：1x >. 又函数2ln y x x =是(1,)+∞上的增函数，且值域为(0,)+∞. 故对任意0k >，在(1,)+∞上恒存在唯一0x ，使得200ln k x x =.所以函数()f x 恒有唯一零点.…………4分（2）当2e k =时，0x =，故02e k <<时，01x <<.由题意，要求存在0(0,)t x ∈，使得00()()0f x t f x t ++−=.令000()()() (0)F t f x t f x t t x =++−<<，下面证明()F t 在0(0,)t x ∈有零点：00'()'()'()F t f x t f x t =+−−， 记()'()G t F t =，()'()g x f x =.00()()()G t g x t g x t =+−−，00'()'()'()G t g x t g x t =++−.2'()1ln k f x x x =++，233122'()k x k g x x x x−=−=.当0x <<'()0g x <；当x >时，'()0g x >.由02e k <<时，01x <<，222200000022ln (12ln )0x k x x x x x −=−=−>.故0x >00t x <<−时，00x t x t +>−>.有0'()0g x t +>，0'()0g x t −>.此时'()0G t >，有'()F t 在0(0,x 单调递增， 故00t x <<时，00'()'(0)'()'()0F t F f x f x >=−=.故()F t 在0(0, x 单调递增，00((0)2()0F x F f x >==. 又0x →时，()f x →−∞，故0t x →时，()F t →−∞.故()F t 在00()t x x ∈有零点，即()F t 在0(0,)t x ∈有零点，问题得证.…………12分。