广东省佛山一中、珠海一中、金山中学2019-2019学年高一下学期期中考试试题英语Word版含答案
广东省佛山市第一中学、珠海市第一中学、金山中学2018_2019学年高一语文下学期期中试题(含解析)

广东省佛山市第一中学、珠海市第一中学、金山中学2018-2019学年高一语文下学期期中试题(含解析)一、现代文阅读论述类文本阅读阅读下面的文字,完成下列小题。
文字创造的过程,是把对外间世界的体认,通过民族共同的心理基础转换成表意符号的过程。
中国人由事物外形到意义转借的实践证得的思维方式,于《说文解字》的“六书”法表现得非常切实。
因而在中国,语义学问题隐含着世界观和思维方式的成分。
中国式的语义学不仅限于从哲学、逻辑学的角度解释语言符号间的意义关联。
它实质上牵连着和综合着文字学和语源学的诸多要素,而且通过文字训诂和语源梳理来透视字和词的意义生成、确认和变异,从而使语义分析与文化精神史发生深刻的因缘。
比如,当我们谈论叙事结构,在《说文解字》中发现“结,缔也”,也就是把绳子打成纽结;“构,盖也”,也就是把木材交错架设成屋,“结构”一词的动词性也就跃然纸上了。
谈论中国人对叙事结构的把握,是不能忽视这个词语的动词性,以及动词性所包含的生命投入和生命体验的。
因此我们在思考西方论者把结构视为“多重秩序”、视为“分解——编配”之时,就会从中国结构的动词性及其包含的生命体验的角度,进行质疑和体系的重构了。
返回原点不是为了把自己封闭起来,而是为了在一个坚实的文化根本点上,组织新的思路,走向新的具有现代中国特色的理论体系。
在这番返回和走向的曲折路程中,必然要参照世界人类的现代智慧,参照起步较早的西方现代叙事理论的新进展。
因此建立中国叙事学思路的关键的另一步,就是“参照”。
参照应该伴随着我们思维的全过程,但不能代替我们的思维过程。
参照是创造的催化剂,但不是创造本身。
当我们为了参照而去了解西方信息,并且找出其中的关键所在的时候,眼光就应该停留在这个关键点上,在这里以“中国眼光”与“西方眼光”进行相互注视、交流和质询,考察中西异同,反省异同的原因,清理各自的历史线索,把握其间的文化密码。
文化对行原理在这里是运用得非常活跃的,这种“关键点上的眼光对视”,将会使我们在中西对话中拓展学术视野,形成自身的学术体系。
广东省珠海市一中2019-2020学年高一下学期期中数学考试试卷(PDF版,无答案)

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三、解答题:共 70 分.解答题应写出文字说明,证明过程或演算步骤.
2018-2019学年广东省佛山一中、珠海一中、金山中学高一下学期期中考试试题英语(含答案)

广东佛山一中、珠海一中、金山中学2018-2019学年高一下学期期中联考英语试题(珠海一中金山中学佛山一中)2019.5.5命题人:陶小明汤倩审题人:郭书廷第一部分:单项填空(共 20 小题;每小题1.5分,满分 30 分), 从 A、B、C、D 四个选项中,选出可以填入空白处的最佳选项。
1. One of our rules is that every student _______ wear school uniform while at school.A. mightB. couldC. shallD. will2. Our school makes _______ a rule that students______ bring their mobile phones to campus.A. it; needn’tB. it; mustn’tC. that; mustn’tD. that; needn’t3. Something terrible _______ if Li Chang was not coming to eat in his restaurant ______ he always did.A. must have happened; whatB. could have happened; asC. must have happened; asD. could have happened; what4. It is so wet there that the trees are extremely tall, some _________ over 90 meters.A. are measuredB. are measuredC. measuredD. measuring5. The fact is ______ I earned my passage by working as an unpaid hand, which ______ my appearance.A. that; accounts forB. \; accounts forC. how; give an explanation toD. \; give an explanation to6. How happy we are! The holiday we have been looking forward _______ at last.A. to has comeB. having comeC. to having comeD. has come7. It is not always easy for the public to see _______ use a new invention can be of to human life.A. whoseB. whatC. whichD. that8. Evidence has been found through years of study _______ children’s early sleeping problems are likely to continue when they grow up.A. whetherB. howC. thatD. why9. Y ou are saying that everyone should take equal responsibility, and that is _______ I disagree.A. whyB. whereC. whatD. how10. _______ is no doubt _______ Shanghai Book Traders will make greater and greater contributions to the development of Shanghai.A. It; thatB. There; whatC. There; thatD. It; what11. _________ the Silk Road covered a huge distance ________ modern day Xi’an with the Middle East and Europe, today one area in particular is associated with the name of the Silk Road.A. Why; linkingB. Why; linkedC. Although; linkedD. Although; linking12. It ________ long before we ________ the result of the experiment.A. will not be; will knowB. is; will knowC. will not be; knowD. is know13.One can always manage to do more things, no matter ________ full one’s schedule is in life.A. whereB. whenC. whatD. how14. Y ou have to take some necessities such as ropes, a flash, boots, ________ you may get lost in the mountain if going hiking.A. in caseB. in order thatC. now thatD. so that15. Some great people said it was their primary school teachers and their lessons _______ they were fond of ________ influenced their whole lives.A. which; thatB. that; whichC. which; whichD. that; that16. This is the small house less than 15 square meters, under _______ roof lives a large family of three generations.A. whichB. whoseC. asD. that17. Biarni was hoping to join his father _______ was with Eric, but he was blown off course and found himself in an unknown land, ________ he eventually reached Greenland.A. who; from whereB. who; from whichC. what; from whereD. what; from which18. Today, the Xinjiang Autonomous Region remains an international crossroad ________ traders from surrounding countries, and tourists from all over the world regular meet.A. whoseB. whereC. whenD. why19. Paper cuts used for religious purposes ________ as offerings to the dead. People ________ whom the dead person was related would make these offerings on special days.A. are used; toB. using; toC. are used; forD. using; for20. Michael put up a picture of Lionel Messi beside the bed to keep himself _______of his own dreams.A. remindingB. to remindC. remindedD. remind第二部分阅读理解(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和D四个选项中,选出最佳选项。
广东佛山一中、珠海一中、金山中学高一下学期期中考试试题物理Word版含答案

—学年度下学期期中考试高一级物理试题命题人:陈升审题人:黎裔康一、单选题(本大题共8小题,每题4分,共32分。
每个小题给出的四个选项中,只有一个正确。
)1.关于曲线运动,下列说法正确的是( )A. 做曲线运动的物体,加速度可能不变B. 做曲线运动的物体,速度也可以保持不变C. 做曲线运动的物体,它受到的合外力方向可能与速度方向相同D. 只要物体做圆周运动,它所受的合外力一定指向圆心“套圈圈”是许多人喜爱的一种游戏,如图所示,小孩和大人直立在界外同一位置,在同一竖直线上不同高度先后水平抛出小圆环,并恰好套中前方同一物体,假设小圆环的运动可视为平抛运动,则( )A. 小孩抛出的圆环速度大小较小B. 两人抛出的圆环速度大小相等C. 大人抛出的圆环运动时间较短D. 小孩抛出的圆环运动时间较短如图所示,A、B、C分别是自行车的大齿轮、小齿轮和后轮的边缘上的三个点,到各自转动轴的距离分别为3r、r和10r。
支起自行车后轮,在转动踏板的过程中,A、B、C三点( )A. 角速度大小关系是B. 线速度大小关系是C. 加速度之比是D. 转速之比是如图所示,长度为的轻质细杆OA,A端固定一质量为3kg的小球,以O点为圆心,在竖直平面内做圆周运动,若小球通过最高点时的速度为,取,则此时轻杆OA受到小球的作用力为( )A. 6N的拉力B. 6N的压力C. 54N的拉力D. 54N的压力如图所示,套在竖直细杆上的环A由跨过定滑轮且不可伸长的轻绳与B相连,在外力作用下A沿杆以速度匀速上升经过P、Q,经过P点时绳与竖直杆间的角度为,经过Q点时A与定滑轮的连线处于水平方向,则( )A. 经过P点时,B的速度等于B. 经过Q点时,B的速度方向向下C. 当A从P至Q的过程中,B处于超重状态D. 当A从P至Q的过程中,绳的拉力等于B的重力如图所示,A,B,C三颗人造地球卫星绕地球做匀速圆周运动,已知三颗卫星的质量关系为,轨道半径的关系为,则三颗卫星( )A. 线速度大小关系为B. 加速度大小关系为C. 向心力大小关系为D. 周期关系为7.人造卫星绕地球做匀速圆周运动,假如卫星的线速度增大到原来的2倍,卫星仍做匀速圆周运动,则( )A. 卫星的向心加速度增大到原来的4倍B. 卫星的角速度增大到原来的4倍C. 卫星的周期减小到原来的D. 卫星的轨道半径减小到原来的发射地球同步卫星时,先将卫星发射至近地圆轨道1,然后经点火,使其沿椭圆轨道2运行,最后再次点火,将卫星送入同步圆轨道3,轨道1、2相切于Q点,轨道2、3相切于P点,如图所示,则当卫星分别在1、2、3轨道上正常运行时,以下说法正确的( )A. 卫星在轨道3上的速率大于在轨道1上的速率B. 卫星在轨道3上经过P点的速率小于在轨道2上经过P点的速率C. 卫星在轨道2上运动的周期大于它在轨道3上运动的周期D. 卫星在轨道1上经过Q点时的向心加速度等于它在轨道2上经过Q点时的向心加速度二、多选题(本大题共6小题,每题4分,共24分。
广东省佛山一中、珠海一中、金山中学2018_2019学年高一化学下学期期中试题

广东省佛山一中、珠海一中、金山中学学年高一化学下学期期中试题(含解析)可能会用到的相对原子质量:、、、、、。
第一部分选择题(共分)一、单项选择题(本大题共小题,每小题分,共分。
在每小题给出的四个选项中,只有一个选项符合题目要求,选对的得分,选错或不答的得分。
).关于有机物说法正确是的. 有机物可分烃和烃的衍生物. 含有碳、氢元素的化合物叫烃. 有机物都不溶于水,但易溶于有机溶剂. 有机物都能燃烧【答案】【解析】【详解】项、根据分子组成中是否含有碳、氢以外的元素,有机物可分为烃和烃的衍生物,故正确;项、仅含有碳、氢元素的化合物叫烃,含有碳、氢元素的化合物不一定是烃,如乙醇、乙酸属于烃的含氧衍生物,故错误;项、大多数有机物不溶于水,而低级的醇、醛和羧酸等可溶于水,故错误;项、大多数有机物可发生燃烧,如烃、烃的含氧衍生物等,而四氯化碳不能燃烧,故错误。
故选。
【点睛】本题考查有机物的结构与性质,侧重分析与应用能力的考查,把握有机物的组成、性质、有机反应为解答的关键。
.下列说法正确的是. 只要含有金属元素的化合物一定是离子化合物. 全部元素都由非金属元素构成的化合物一定是共价化合物. 离子化合物一定是电解质. 共价化合物一定是非电解质【答案】【解析】试题分析:.含有金属元素的化合物不一定是离子化合物,例如氯化铝是共价化合物,错误;.全部元素都由非金属元素构成的化合物不一定是共价化合物,例如氯化铵等铵盐是离子化合物,错误;.离子化合物一定是电解质,正确;.共价化合物不一定是非电解质,例如等,错误,答案选。
考点:考查化学键与化合物关系判断.下列各组物质中,化学键类型完全相同的是. 和. 和. 和. 和【答案】【解析】【分析】一般来说,活泼金属元素与活泼非金属元素间形成离子键,非金属元素之间形成共价键,相同元素的原子间形成非极性键,不同元素的原子间形成极性键;离子化合物中存在离子键(可能含共价键),共价化合物中只存在共价键。
广东省佛山市第一中学最新高一下学期期中考试语文试卷 Word版含答案

本试卷共22小题,满分150分.考试用时150分钟.注意事项: 1.选择题每小题(包括1-10题)选出把答题卡上对应的答案信息点涂黑;如需改动,用橡皮擦干净后,再选涂其它答案,答案不能答在试卷上。
2.非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答题卡各题目指定区域内相应位置上;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液,不按以上要求作答的答案无效。
一、基础知识(每小题3分,共9分)1.下列各句中,加横线的成语使用正确的一项是( )A.为化解部分旅客的不满情绪,他们设立了“旅客投诉中心”,此举说明他们不光有良好的服务意识,还有闻过则喜的雅量.B.奚羽先生指导弟子写论文时强调,学术论文要有的放矢,论证严密,语言准确而简洁,不能模棱两可,也不能有那些繁文缛节。
C.我攀过陡峭的崖壁,历尽艰辛,登上绝顶,放眼望去,天无涯际,顿觉自己渺小,登高自卑之感油然而生。
D.近两三年来,某市大型商场新增营业面积相当于过去十年所增营业面积的三倍,但前往购物的消费者却寥寥无几,出现了僧多粥少的局面. 2.下列句子中,没有语病的一项是( )A。
“千金易得,一将难求”,我们既要重视对引进人才的使用,也要切实提高原有科技骨干的待遇,充分调动他们钻研业务的积极性。
B.做任何事情都应该上心,不然很难取得应有的成绩,比如说学习,你成绩的好坏在很大程度上取决于你自觉刻苦的程度。
C.今年下半年,教育部将发布高考改革实施意见,这一改革措施旨在从根本上解决一考定终身,搭建人才成长的“立交桥".D.作为一个全新的、相对成熟的行业,不仅电子商务在一定程度上改变了人类的生活方式,也冲击了历史悠久的传统商业模式。
3.依次填入下面一段文字横线处的语句,衔接最恰当的一组是( )中国“美术片”造型主要取材和借鉴中国古代壁画、民间年画、舞台戏曲、庙宇泥塑等的人物形象、道具设计。
角色造型或富丽堂皇,追求形式感很强的“装饰风格", , 。
广东省珠海市第一中学2019-2020学年高一下学期期中考试英语试题含答案 PDF版

高一年级第二学期(英语)期中试题(用时:120分钟满分:150分)I. 听力(共20小题;每小题1分,满分20分)第1节(共5小题;每小题1分,满分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。
每段对话读两遍。
1. What time is it now?A. 9:10.B. 9:50.C. 10:00.2. What does the woman think of the weather?A. It’s nice.B. It’s warm.C. It’s cold.3. What will the man do?A. Attend a meeting.B. Give a lecture.C. Leave his office.4. What is the woman’s opinion about the course?A. Too hard.B. Worth taking.C. Too long.5. What does the woman want the man to do?A. Speak louder.B. Apologize to her.C. Turn off the radio.第2节(共15小题;每小题1分,满分15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。
每段对话或独白读两遍。
听第6段材料,回答第6、7题。
6. How long did Michael stay in China?A. Five days.B. One week.C. Two weeks.7. Where did Michael go last year?A. Russia.B. Norway.C. India.听第7段材料,回答第8、9题。
8. What food does Sally like?A. Chicken.B. Fish.C. Eggs.9. What are the speakers going to do?A. Cook dinner.B. Go shopping.C. Order dishes.听第8段材料,回答第10~12题。
广东省佛山一中、珠海一中、金山中学2018-2019学年高一下学期期中考试生物试题 Word版含解析

佛山市第一中学2018-2019学年度下学期期中考试高一生物一、单项选择题1.下列关于细胞分裂的叙述中,正确的是( )A. 一定有DNA 的复制B. 一定有细胞周期C. 一定有同源染色体的配对D. 一定有纺锤体的出现【答案】A【解析】【分析】1、真核细胞的分裂方式有三种:有丝分裂、无丝分裂和减数分裂;原核细胞的分裂为二分裂。
2、有丝分裂和减数分裂的比较:比较项目有丝分裂 减数分裂 染色体复制 间期减I 前的间期 同源染色体的行为联会与四分体 无同源染色体联会现象、不形成四分体,非姐妹染色单体之间没有交叉互换现象 出现同源染色体联会现象、形成四分体,同源染色体的非姐妹染色单体之间常常有交叉互换现象 分离与组合也不出现同源染色体分离,非同源染色体自由组合 出现同源染色体分离,非同源染色体自由组合 着丝点的行为中期位置 赤道板 减Ⅰ在赤道板两侧,减Ⅱ在赤道板 断裂 后期 减Ⅱ后期 【详解】不论的细胞的有丝分裂、无丝分裂、减数分裂还是细菌的二分裂,都有DNA 复制过程,因此在细胞分裂过程中一定有DNA 的复制,A 正确;只有进行有丝分裂的细胞,在连续分裂过程中有细胞周期,B 错误;真核细胞减数分裂时一定有同源染色体的配对,而有丝分裂、无丝分裂和原核细胞的二分裂均没有同源染色体的配对,C 错误;真核细胞有丝分裂和减数分裂时一定有纺锤丝的出现,而无丝分裂和原核细胞的二分裂均没有纺锤丝的出现,D 错误;故选A 。
【点睛】本题考查细胞分裂的知识,考生识记细胞的分裂方式、明确各种细胞分裂过程和特点是解题的关键。
2.如图为细胞周期中细胞核的部分变化示意图,图示时期()A. 既可能是分裂期的前期,也可能是末期B. 染色体数目和DNA分子数已加倍C. 细胞中正在形成纺锤体D. 是观察染色体形态和数目的最佳时期【答案】C【解析】【分析】有丝分裂不同时期的特点:(1)间期:进行DNA的复制和有关蛋白质的合成,即染色体的复制,DNA数目加倍,但染色体数目不变;(2)前期:核膜、核仁逐渐解体消失,出现纺锤体和染色体;(3)中期:染色体形态固定、数目清晰,是观察染色体形态和数目的最佳时期;(4)后期:着丝点分裂,姐妹染色单体分开成为染色体,染色体数目加倍;(5)末期:核膜、核仁重建、纺锤体和染色体消失.由此可见,图示细胞处于有丝分裂前期,据此答题。
广东省佛山市第一中学2019-2020学年高一下学期期中考试语文及答案

佛山一中2019-2020学年下学期高一期中考试题语文2020年4月本试卷共8页,21小题,满分150分,考试时间150分钟。
注意事项:1.答题前,考生务必用黑色笔迹的钢笔或签字笔将自己的姓名、考号填写在答题卷上。
2.每小题选出答案后,用2B铅笔把答题卷上对应题目的选项的答案信息点涂黑;如需改动,用橡皮擦干净后,再选涂其他答案,答案不能答在试卷上。
非选择题必须用黑色字迹的钢笔或签字笔作答,答案必须写在答题卷各题目指定区域内相应位置上;如需改动,先划掉原来的答案,然后再写上新的答案;不准使用铅笔和涂改液。
不按以上要求作答的答案无效。
3.作答选做题时,请先用2B铅笔填涂选做题的题组号对应的信息点,再作答。
漏涂、错涂、多涂的,答案无效。
一.实用类文本阅读(本题共3小题,12分)阅读下面的文字,完成1-3小题。
材料一:科学必须严谨,科普无须严肃。
2017年,科技类综艺节目迎来“小爆发”,化高冷科技为电视语言让科学知识变得有声有色、逐渐培养、形成了固定的收视群。
然而,新鲜感和第一波热度过后,人们发现,“叫好又叫座”之难使不少科技类综艺节目陷入尴尬境地。
但科技确实是综艺创作的“富矿”。
如何让“不食人间烟火”的科技类综艺节目飞入寻常百姓家?复杂的原理、专业的实验、陌生的装置……当这些出现在眼前时,你是否想立马换台?科技元素的可看性不强,基因解码、柔性电子技术等生僻词汇也会令观众听而却步。
因此要想吸引观众、持续调动观众积极性,必须要给“科学”加些料。
开拓科技类综艺节目这一蓝海,不仅要展示科技这一“面子”,更要提升温度这一“里子”,将科学与情怀、梦想,与人们的生活相结合,让科技有“人气儿”、有“人味儿”因此,一档科技类节目不仅需要充实的内容将节目装扮得更有意义,更需要接地气的讲述和呈现,让节目真正走进百姓的内心。
(摘编自《光明日报》)材料二:材料三:曾经有学者将科技类节目比喻为“砸石头”节目,与已经受到市场认可的节目类型不同,内核较硬的科技类节目不但“难啃”,并长期处在“投石问路”的状态。
广东省佛山一中、珠海一中、金山中学2018-2019学年高一英语下学期期中试题(1)

广东省佛山一中、珠海一中、金山中学2018-2019学年高一英语下学期期中试题第一部分:单项填空(共 20 小题;每小题1.5分,满分 30 分), 从 A、B、C、D 四个选项中,选出可以填入空白处的最佳选项。
1. One of our rules is that every student _______ wear school uniform while at school.A. mightB. couldC. shallD. will2. Our school makes _______ a rule that students______ bring their mobile phonesto campus.A. it; needn’tB. it; mustn’tC. that; mustn’tD. that; needn’t3. Something terrible _______ if Li Chang was not coming to eat in his restaurant______ he always did.A. must have happened; whatB. could have happened; asC. must have happened; asD. could have happened; what4. It is so wet there that the trees are extremely tall, some _________ over 90 meters.A. are measuredB. are measuredC. measuredD. measuring5. The fact is ______ I earned my passage by working as an unpaid hand, which ______ my appearance.A. that; accounts forB. \; accounts forC. how; give an explanation toD. \; give an explanation to6. How happy we are! The holiday we have been looking forward _______ at last.A. to has comeB. having comeC. to having comeD. has come7. It is not always easy for the public to see _______ use a new invention can beof to human life.A. whoseB. whatC. whichD. that8. Eviden ce has been found through years of study _______ children’s early sleeping problems are likely to continue when they grow up.A. whetherB. howC. thatD. why9. You are saying that everyone should take equal responsibility, and that is _______I disagree.A. whyB. whereC. whatD. how10. _______ is no doubt _______ Shanghai Book Traders will make greater and greater contributions to the development of Shanghai.A. It; thatB. There; whatC. There; thatD. It; what11. _________ the Silk Road covered a huge distance ________ modern day Xi’an with the Middle East and Europe, today one area in particular is associated with the nameof the Silk Road.A. Why; linkingB. Why; linkedC. Although; linkedD. Although; linking12. It ________ long before we ________ the result of the experiment.A. will not be; will knowB. is; will knowC. will not be; knowD. is know13.One can always manage to do more things, no matter ________ full one’s schedule is in life.A. whereB. whenC. whatD. how14. You have to take some necessities such as ropes, a flash, boots, ________ you may get lost in the mountain if going hiking.A. in caseB. in order thatC. now thatD. so that15. Some great people said it was their primary school teachers and their lessons _______ they were fond of ________ influenced their whole lives.A. which; thatB. that; whichC. which; whichD. that; that16. This is the small house less than 15 square meters, under _______ roof livesa large family of three generations.A. whichB. whoseC. asD. that17. Biarni was hoping to join his father _______ was with Eric, but he was blown off course and found himself in an unknown land, ________ he eventually reached Greenland.A. who; from whereB. who; from whichC. what; from whereD. what; from which18. Today, the Xinjiang Autonomous Region remains an international crossroad ________ traders from surrounding countries, and tourists from all over the world regular meet.A. whoseB. whereC. whenD. why19. Paper cuts used for religious purposes ________ as offerings to the dead. People ________ whom the dead person was related would make these offerings on special days.A. are used; toB. using; toC. are used; forD. using; for20. Michael put up a picture of Lionel Messi beside the bed to keep himself _______of his own dreams.A. remindingB. to remindC. remindedD. remind第二部分阅读理解(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和D四个选项中,选出最佳选项。
2018-2019学年广东省佛山一中、珠海一中、金山中学高一下学期期中数学试题(解析版)

广东省佛山一中、珠海一中、金山中学 高一下学期期中数学试题一、单选题1.设集合{}1,2,4A =,{}240B x x x m =-+=.若{}1A B ⋂=,则B =( ) A .{}1,3- B .{}1,0C .{}1,3D .{}1,5【答案】C【解析】∵ 集合{}124A ,,=,{}2|40B x x x m =-+=,{}1A B ⋂= ∴1x =是方程240x x m -+=的解,即140m -+= ∴3m =∴{}{}{}22|40|43013B x x x m x x x =-+==-+==,,故选C2.若sin 0α<,且tan 0α>,则α是( ) A .第一象限角 B .第二象限角C .第三象限角D .第四象限角【答案】C【解析】sin 0α<,则α的终边在三、四象限;tan 0α>则α的终边在三、一象限,sin 0α<,tan 0α>,同时满足,则α的终边在三象限.3.函数()xf x 23x 7=+-的零点所在的一个区间是( )A .10,2⎛⎫ ⎪⎝⎭B .1,12⎛⎫⎪⎝⎭C .31,2⎛⎫⎪⎝⎭D .3,22⎛⎫⎪⎝⎭【答案】C【解析】利用零点存在定理可判断零点所在的区间. 【详解】()f x 为R 上的增函数,又()35120, 2.8 2.50.3022f f ⎛⎫=-=-=> ⎪⎝⎭,故零点所在对的区间为 31,2⎛⎫⎪⎝⎭,选C . 【点睛】不可解方程的零点所在区间应该通过零点存在定理来寻找,一般地要先考虑函数的单调性,再选择合适的区间(),a b ,使得()()0f a f b <,其中,a b 要依据解析式的形式来选取(()(),f a f b 要容易计算).4.已知432a =,254b =,1325c =,则( ) A .b a c << B .a b c << C .b c a << D .c a b <<【答案】A【解析】先将b a 和转换为同为2为底的指数,422335244a b ==>=,a 和c 可以转换为指数相同1223332554c a ==>=.所以b a c <<. 【详解】因为422335244a b ==>=,1223332554c a ==>=,所以b a c <<,故选A . 【点睛】1.比较幂值大小时,要注意区分底数相同还是指数相同.是用指数函数的单调性,还是用幂函数的单调性或指数函数的图象解决.要注意图象的应用,还应注意中间量0、1等的运用.2.指数函数的图象在第一象限内底大图高(逆时针方向底数依次变大).当幂的底数不确定时,要注意讨论底数的不同取值情况.3.根据指数函数图象判断底数大小的问题,可以通过直线x =1与图象的交点进行判断.如图是指数函数(1)y =a x ,(2)y =b x ,(3)y =c x ,(4)y =d x 的图象,底数a ,b ,c ,d 与1之间的大小关系为c >d >1>a >b.规律:在y 轴右(左)侧图象越高(低),其底数越大.属于较易题目.5.函数()f x 在(,)-∞+∞单调递减,且为奇函数.若(1)1f =-,则满足1(2)1f x -≤-≤的x 取值范围是( ) A .[2,2]- B .[1,1]-C .[0,4]D .[1,3]【答案】D【解析】根据奇函数的性质由(1)1f =-,可以求出(1)f -的值,再利用函数的单调性结合已知1(2)1f x -≤-≤,可以求出x 取值范围. 【详解】()f x Q 为奇函数,()()f x f x ∴-=-. (1)1f =-Q ,(1)(1)1f f ∴-=-=.故由1(2)1f x -≤-≤,得(1)(2)(1)f f x f ≤-≤-. 又()f x 在(,)-∞+∞单调递减,121x ∴-≤-≤,13x ∴≤≤.故选:D 【点睛】本题考查了利用奇函数的单调性求解不等式问题,考查了数学运算能力. 6.已知1sin23α=,则2cos 4πα⎛⎫-= ⎪⎝⎭( )A .16 B .13C .23D .56【答案】C【解析】运用两角差的余弦公式展开后再计算平方的结果,结合已知条件得到答案 【详解】222211cos cos sin 42222cos cos sin πααααααα⎛⎫⎛⎫-=+=++ ⎪ ⎪ ⎪⎝⎭⎝⎭ 11222sin α=+, 123sin α=Q ,21124263cos πα⎛⎫∴-=+= ⎪⎝⎭,故选C 【点睛】本题主要考查了两角差的余弦公式以及二倍角公式,熟练运用公式来解题是关键,较为基础7.等差数列{a n }的首项为1,公差不为0.若a 2,a 3,a 6成等比数列,则{a n }前6项的和为( ) A .-24 B .-3 C .3D .8【答案】A【解析】根据等比中项的性质列方程,转化为1,a d 的形式,由此解得d 的值,进而求得数列{}n a 的前6项和. 【详解】设等差数列{a n }的公差为d ,依题意得2326a a a =⋅,即(1+2d )2=(1+d )(1+5d ),解得d=-2或d =0(舍去),又a 1=1,∴S 6=6×1+652⨯×(-2)=-24. 故选: A 【点睛】本小题主要考查等比中项的性质,考查等差数列通项公式的基本量计算,属于基础题. 8.圆2228130x y x y +--+=的圆心到直线10ax y +-=的距离为1,则a =( ) A .43-B .34-C .3D .2【答案】A【解析】试题分析:由2228130x y x y +--+=配方得22(1)(4)4x y -+-=,所以圆心为(1,4),因为圆2228130x y x y +--+=的圆心到直线10ax y +-=的距离为1,所以224111a a +-=+,解得43a =-,故选A.【考点】 圆的方程,点到直线的距离公式【名师点睛】直线与圆的位置关系有三种情况:相交、相切和相离. 已知直线与圆的位置关系时,常用几何法将位置关系转化为圆心到直线的距离d 与半径r 的大小关系,以此来确定参数的值或取值范围.9.已知等差数列{}n a 的公差为d ,关于x 的不等式2120dx a x +≥的解集为[0,9],则使数列{}n a 的前n 项和n S 取得最大值的正整数n 的值为( ) A .4 B .5 C .6 D .7【答案】B【解析】试题分析:∵关于x 的不等式2120dx a x +≥的解集为[]0,9,∴,分别是一元二次方程的两个实数根,且.∴,可得:,∴.∴,可得:,.∴使数列{}n a 的前项和n S 最大的正整数的值是.故选B .【考点】等差数列的前项和.10.若平面α截三棱锥所得截面为平行四边形,则该三棱锥中与平面α平行的棱有( ) A .0条 B .1条C .2条D .0条或2条【答案】C【解析】考虑特殊情况,作正四面体进行考虑,明显可见,三棱锥中与平面α平行的棱有2条 【详解】因为平行于三棱锥的两条相对棱的平面截三棱锥所得的截面是平行四边形,所以该三棱锥中与平面α平行的棱有2条,故选C. 【点睛】本题考查线面平行的关系,属于简单题11.正方形ABCD 边长为2,点E 为BC 边的中点,F 为CD 边上一点,若5AF AE ⋅=u u u r u u u r,则AF =u u u r( )A .5B 17C 210D .52【答案】D【解析】设DF kDC =u u u r u u u r,把,AE AF u u u r u u u r 都用,AB AD u u u r u u u r 表示并运算,由已知求出k ,然后可求得AF u u u r .【详解】设DF kDC =u u u r u u u r ,则AF AD DF AD kDC AD k AB =+=+=+u u u r u u u r u u u r u u u r u u u r u u u r u u u r,1122AE AB BE AB BC AB AD =+=+=+u u u r u u u r u u u r u u u r u u u r u u u r u u u r ,所以1()()2AE AF AB AD k AB AD ⋅=+⋅+u u u r u u u r u u u r u u u r u u u r u u u r 2211(1)4222k AB AD k AB AD k =+++⋅=+u u u r u u u r u u ur u u u r ,所以425k +=,34k =,所以33242DF =⨯=u u u r ,52AF ===u u u r.故选:D . 【点睛】本题考查求向量的模,解题关键是选取基底,把向量用基底表示出来. 12.已知ABC ∆中,角,,A B C 所对的边分别是,,a b c ,且cos cos C A =,点M 在边AC上,且cos 7AMB ∠=-,BM =AB =( ) A .4 B .2CD【答案】A【解析】根据正弦定理可通过边角关系式求得sin A ;再利用同角三角函数关系求得sin AMB ∠;再次利用正弦定理求得AB .【详解】由正弦定理可知:cos cos C A =cos 2sin cos sin A C B A A C =()2sin cos A C B A ⇒+=2sin cos B B A =cos A ⇒=1sin 2A ⇒=cos AMB ∠=sin AMB ⇒∠= 在AMB ∆中,sin sin BM AB A AMB=∠2=解得:4AB =本题正确选项:A 【点睛】本题主要考察正弦定理解三角形和边角关系式的化简,关键是将边角关系式中的边化成角的关系,从而能够得到所需的三角函数值.13.将偶函数())cos(2)(0)f x x x ϕϕϕπ=+-+<<的图像向右平移π6个单位,得到()y g x =的图像,则()g x 的一个单调递减区间( ) A .,36ππ⎛⎫-⎪⎝⎭ B .2,63ππ⎛⎫⎪⎝⎭C .7,1212ππ⎛⎫ ⎪⎝⎭D .5,36ππ⎛⎫ ⎪⎝⎭【答案】B【解析】首先化简函数()f x 的解析式,然后结合平移变换的结论得到()g x 的解析式,最后确定其单调区间即可. 【详解】由函数的解析式可得:())cos(2)2sin 26f x x x x πϕϕϕ⎛⎫=+-+=+- ⎪⎝⎭, 函数为偶函数,则0x =时,262x k ππϕπ+-=+,即()23k k Z πϕπ=+∈, 令0k =可得()20,3πϕπ=∈, 故2()2sin 22sin 22cos 2362f x x x x πππ⎛⎫⎛⎫=+-=+= ⎪ ⎪⎝⎭⎝⎭, 图像向右平移π6个单位,可得()2cos 22cos 2636g x x f x x πππ⎡⎤⎛⎫⎛⎫-=- ⎛⎫=-= ⎪ ⎪⎢⎥⎝⎭⎝⎭⎣⎝⎦⎪⎭,函数的单调递减区间满足:2223k x k ππππ≤-≤+,解得:()263k x k k Z ππππ+≤≤+∈, 当0k =时,单调递减区间为2,63ππ⎛⎫⎪⎝⎭,故选项B 正确, 其余选项无法找到整数k 满足所给的区间. 故选:B .【点睛】本题主要考查三角函数的奇偶性,三角函数的平移方法,三角函数的单调区间等知识,意在考查学生的转化能力和计算求解能力.14.已知定义在R 上的奇函数()f x 满足(2)()f x f x +=-,当1[]0,x ∈时,()f x =12()()g x f x x =--在区间[]4,8-上所有零点之和为( ) A .8B .6C .4D .2【答案】A【解析】根据的奇偶性和对称性,推出函数的周期性,根据函数与方程之间的关系,转化为两个函数交点问题,利用对称性进行求解即可. 【详解】解:∵奇函数()f x 满足()()2f x f x +=-,∴()()()42f x f x f x +=-+=,即()f x 是周期为4的周期函数, 同时函数()f x 关于1x =对称, ∵若10x -≤≤,则01x ≤-≤,∴()()f x f x -==-即()f x =10x -≤≤,若12x ≤≤,则120x -≤-≤,021x ≤-≤此时()()2f x f x =-=,12x ≤≤, 若23x ≤≤,则021x ≤-≤,120x -≤-≤此时()()2f x f x =-=23x ≤≤,由()()102g x f x x =-=-得()12f x x =-, 作出函数()f x 与12y x =-,在[]3,6-上的图象,由图象知两个函数图象有4个交点, 且四个交点,两两关于点()2,0对称, 设彼此对称的交点横坐标为a ,b ,c ,d , 则22a b +=,22c d+=,得4a b +=,4c d +=, 即448a b c d +++=+=,函数()()12g x f x x =--在区间[]4,8-上所有零点之和为8, 故选A .【点睛】本题主要考查函数与方程的应用,根据条件求出函数的周期,利用数形结合转化为两个函数的交点问题是解决本题的关键.二、填空题15.已知向量()1,3a =r ,()2,1b =--r ,()1,2c r =,若向量a kb +r r 与向量c r 共线,则实数k 的值为______. 【答案】13-【解析】先由()1,3a =v ,()2,1b =--v 得出向量a kb +v v 的坐标表示,再由向量a kb +v v 与向量c v共线,即可求出结果. 【详解】因为向量()1,3a =v ,()2,1b =--v ,所以()123a kb k k +=--v v ,;又()2,4c =v,向量a kb+v v 与向量c v 共线,所以()()412230k k ---=,解得13k =-. 故答案为13-【点睛】本题主要考查向量的坐标运算,熟记共线向量定理即可,属于基础题型. 16.已知0x >,0y >2是2x 与4y 的等比中项,则12x y+最小值为_________. 【答案】9【解析】根据等比中项定义得出,x y 的关系,然后用“1”的代换转化为可用基本不等式求最小值. 【详解】由题意22242(2)x y x y +⋅==,所以21x y +=,所以121222()(2)5y x x y x y x y x y +=++=++22529y x x y≥+⋅=,当且仅当22y x x y =,即13x y ==时等号成立. 所以12x y+最小值为9. 故答案为:9. 【点睛】本题考查等比中项的定义,考查用基本不等式求最值.解题关键是用“1”的代换找到定值,从而可用基本不等式求最值.17.α、β是两个平面,m 、n 是两条直线,有下列四个命题:(1)如果m ⊥n ,m ⊥α,n ∥β,那么α⊥β.(2)如果m ⊥α,n ∥α,那么m ⊥n . (3)如果α∥β,m ⊂α,那么m ∥β. (4)如果m ∥n ,α∥β,那么m 与α所成的角和n 与β所成的角相等.其中正确的命题有________.(填写所有正确命题的编号) 【答案】②③④【解析】试题分析::①如果m ⊥n ,m ⊥α,n ∥β,不能得出α⊥β,故错误; ②如果n ∥α,则存在直线l ⊂α,使n ∥l ,由m ⊥α,可得m ⊥l ,那么m ⊥n .故正确; ③如果α∥β,m ⊂α,那么m 与β无公共点,则m ∥β.故正确④如果m ∥n ,α∥β,那么m ,n 与α所成的角和m ,n 与β所成的角均相等.故正确 【考点】命题的真假判断与应用;空间中直线与直线之间的位置关系;空间中直线与平面之间的位置关系18.意大利著名数学家斐波那契在研究兔子的繁殖问题时,发现有这样的一列数:1,1,2,3,5,8……该数列的特点是:前两个数均为1,从第三个数起,每一个数都等于它前面两个数的和,人们把这样的一列数所组成的数列称为“斐波那契数列”,则______.【答案】0【解析】利用斐波那契数列的通项公式分析可得:,,,…根据归纳推理可得结果.【详解】 根据题意,,, ,… … 则,故答案为0. 【点睛】本题主要考查数列的求和以及归纳推理的应用,涉及斐波那契数列的性质.归纳推理的一般步骤: 一、通过观察个别情况发现某些相同的性质. 二、从已知的相同性质中推出一个明确表述的一般性命题(猜想).19.已知A 是直角坐标平面内一定点,点(0,0)O ,若圆22()(–12)3x y -+=上任意一点M 到定点A 与点(0,0)O 的距离之比是一个定值λ,则这个定值λ的大小是________. 15【解析】设(,)A m n ,(,)M x y ,按距离之比为定值求出M 点的轨迹方程,它就是方程22()(–12)3x y -+=,比较后可得λ. 【详解】设(,)A m n ,(,)M x y ,则2222()()MA x m y n MOx yλ-+-==+,整理得:222222(1)(1)220x y mx ny m n λλ-+---++=,易知210λ-≠,方程化为2222222220111m n m n x y x y λλλ++--+=---,已知圆22()(–12)3x y -+=的一般式方程为222420x y x y +--+=,所以2222222124121mnm n λλλ⎧=⎪-⎪⎪=⎨-⎪⎪+=⎪-⎩,解得2545m n λ⎧=⎪⎪⎪=⎨⎪⎪=⎪⎩.故答案为:5. 【点睛】本题考查平面轨迹方程,解题时由M 点到,A O 两点距离之比为常数λ,求出M 的轨迹方程,它就是已知圆,比较系数可得结论.20.已知2()log (41)xf x x =+-,则使得2(21)1log 5f x -+<成立的x 的取值范围是______. 【答案】(0,1)【解析】先化简函数()f x ,求出函数()f x 的奇偶性和单调性,然后化简要求的结果()2211log 5f x -+<,最后运用单调性得到不等式,继而求出结果【详解】()()()22222411log 41log 41log 2log log 222x xxxx x xf x x +⎛⎫=+-=+-==+ ⎪⎝⎭, ()()()2log 22x x f x f x --=+=,故()f x 为偶函数 令()20xt t =>,()21log g t t t ⎛⎫∴=+ ⎪⎝⎭,当01t <<时,()g t 为减函数 当1t ≥时,()g t 为增函数 则当0x <时,()f x 为减函数 当0x ≥时,()f x 为增函数()2211log 5f x -+<Q ,()221log 51f x -<-,()()2521log 12f x f -<=, 211x ∴-<,1211x -<-<, 1211x -<-<, 022x <<,故01x <<则x 的取值范围是()0,1 【点睛】本题主要考查了函数的单调性和奇偶性,对于题目中的已知条件和问题进行化简是本题的关键,将其转化为运用函数的单调性解不等式,渗透了转化思想.三、解答题21.在ABC ∆中,60A ∠=o ,3.7c a =()1求sin C 的值;()2若7a =,求ABC ∆的面积.【答案】(1(2)【解析】()1由37c a =,根据正弦定理可得3sin sin 7C A =,从而可求出答案;()2根据同角的三角函数的关系求出cos C ,再根据诱导公式以及两角和正弦公式求出sin B ,利用三角形面积公式计算即可. 【详解】(1)60A ∠=o ,37c a =,由正弦定理可得33sin sin 77C A ===(2)若7a =,则3c =,C A ∴<,22sin cos 1C C +=Q ,又由()1可得13cos 14C =,()131sin sin sin cos cos sin 2142147B AC A C A C ∴=+=+=+⨯=,11sin 7322ABC S ac B ∆∴==⨯⨯= 【点睛】本题考查了正弦定理、两角和的正弦公式以及三角形的面积公式,属于基础题. 正弦定理是解三角形的有力工具,其常见用法有以下三种:(1)知道两边和一边的对角,求另一边的对角(一定要注意讨论钝角与锐角);(2)知道两角与一个角的对边,求另一个角的对边;(3)证明化简过程中边角互化;(4)求三角形外接圆半径. 22.在数列{}n a 中,首项112a =前n 项和为n S ,且1)21(n n S a n N *+=-∈ (1)求数列{}n a 的通项;(2)若31()2nn n b n a =+⨯⋅,求数列{}n b 的前n 项和n T .【答案】(1)132n n n a -=;(2)1(21)334n n n T ++⋅-=.【解析】(1)由1(2)n n n a S S n -=-≥,得数列从第2项开始的递推关系,同时验证3212a a a a =,可得数列{}n a 的通项公式; (2)用错位相减法求n T . 【详解】(1)因为121n n S a +=-,当2n ≥时,121n n S a -=-,所以1122n n n n n a S S a a -+=-=-,即123n n a a +=,132n n a a +=, 又11221a S a ==-,234a =,2132a a =, 所以{}n a 是等比数列,公比为32q =,所以1111133()222n n n n n a a q ---==⨯=.所以132n n n a -=.(2)由(1)133(1)2(1)32n nn n n b n n -=+⨯⨯=+⋅,23233343(1)3n n T n =⨯+⨯+⨯+++⨯L ,①所以23413233343(1)3n n T n +=⨯+⨯+⨯+++⨯L ,②①-②得23126333(1)3n n n T n +-=++++-+⨯L 13(13)3(1)313n n n +-=+-+⨯-131()322n n +=-+⨯, 所以1(21)334n n n T ++⋅-=.【点睛】本题考查由n S 和n a 的关系求数列的通项公式,考查错位相减法求数列的和.在由1n n n a S S -=-求解时要注意2n ≥,也就关系式中一般不包含1a ,所以1a 与2a 的关系要特意去验证,否则可能出错.23.已知在三棱柱111ABC A B C -中,1AA ⊥平面ABC ,AB AC =,E ,F 分别是1AA ,11B C 的中点,(1)求证:BC ⊥平面AEF ﹔(2)判断直线EF 与平面1AB C 的位置关系,并说明理由. 【答案】(1)证明见解析;(2)平行,证明见解析.【解析】(1)连接1A F 后可证11,A F BC AA BC ⊥⊥,从而可得线面垂直;(2)考虑到平面AA 1F 与平面AB 1C 的交线,E ,F 都是中点,因此取B 1C 中点M ,作辅助线后,可证EFMA 是平行四边形,从而得EF 与MA 平行,即可证得线面平行. 【详解】(1)证明:连接1A F ,因为AB AC =,所以1111A B AC =,F 是11B C 中点,所以111A F B C ⊥,而11//B C BC ,所以1A F BC ⊥,1AA ⊥平面ABC ,BC ⊂平面ABC ,所以1AA BC ⊥,又111AA A F A =I ,所以BC ⊥平面1AFA ,即BC ⊥平面AEF ;(2)直线EF 与平面1AB C 平行.证明如下:如图,取1B C 中点M ,连接,MF MA ,由于F 是11B C 中点,所以111//,2MF CC MF CC =,又E 是1AA 中点,所以111//,2AE CC AE CC =, 所以//,AE MF AE MF =,所以AMFE 是平行四边形,所以//EF AM ,EF ⊄平面1AB C ,AM ⊂平面1AB C ,所以//EF 平面1AB C .【点睛】本题考查线面垂直的证明和线面平行的证明,掌握线面平行与垂直的判定定理是解题关键.24.已知平面向量()sin x x =a ,()2sin ,sin x x =b ,函数()1f x =⋅+a b . (1)求()f x 的单调区间;(2)在锐角ABC △中,a ,b ,c 分别是内角A ,B ,C 所对的边,若()4f A =,2a =,求ABC △周长的取值范围.【答案】(1)单调递增区间是,63k k ππππ⎡⎤-+⎢⎥⎣⎦,k Z ∈,单调递减区间是5,36k k ππππ⎡⎤++⎢⎥⎣⎦,k Z ∈.(2)(2+ 【解析】(1)先求得()f x 的表达式,利用正弦函数的单调区间,求得()f x 的单调区间.(2)根据正弦定理求得,b c 边的表达式,由此求得b c +的取值范围,进而求得a b c ++的取值范围.【详解】解:(1)依题意,()22sin cos 1f x x x x =++cos222sin 226x x x π⎛⎫=-+=-+ ⎪⎝⎭.令222262k x k πππππ-≤-≤+,k Z ∈,解得()f x 的单调递增区间是,63k k ππππ⎡⎤-+⎢⎥⎣⎦,k Z ∈, 令3222262k x k πππππ+≤-≤+,k Z ∈. 解得()f x 的单调递减区间是5,36k k ππππ⎡⎤++⎢⎥⎣⎦,k Z ∈. (2)由()4f A =得3A π=.设三角形ABC 的外接圆半径为R ,根据正弦定理得2sin a R A ==. 于是()2sin sin b c R B C +=+2sin sin 33B B π⎡⎤⎛⎫=+- ⎪⎢⎥⎝⎭⎣⎦3sin 2B B ⎫=+⎪⎪⎝⎭4sin 6B π⎛⎫=+ ⎪⎝⎭.因为ABC ∆是锐角三角形且3A π=,所以由2C π<,得232B ππ-<,因此B 的取值范围是,62ππ⎛⎫⎪⎝⎭.而由2,633B πππ⎛⎫⎛⎫+∈ ⎪ ⎪⎝⎭⎝⎭sin 16B π⎛⎫<+≤ ⎪⎝⎭,所以()(b c ⎤+∈⎦,所以()(2a b c ⎤++∈+⎦,即ABC ∆周长的取值范围是(2⎤+⎦. 【点睛】本小题主要考查平面向量数量积的坐标运算,考查三角函数单调区间的求法,考查正弦定理解三角形,知识综合较多,属于中档题.25.为弘扬中华传统文化,学校课外阅读兴趣小组进行每日一小时的“经典名著”和“古诗词”的阅读活动. 根据调查,小明同学阅读两类读物的阅读量统计如下:小明阅读“经典名著”的阅读量()f t (单位:字)与时间t (单位:分钟)满足二次函数关系,部分数据如下表所示;阅读“古诗词”的阅读量()g t (单位:字)与时间t (单位:分钟)满足如图1所示的关系.(1)请分别写出函数()f t 和()g t 的解析式;(2)在每天的一小时课外阅读活动中,小明如何分配“经典名著”和“古诗词”的阅读时间,使每天的阅读量最大,最大值是多少? 【答案】(1)见解析;(2)见解析【解析】(1)设f (t )=2a ?t bt +,代入(10,2700)与(30,7500),解得a 与b. 令()g t =kt ,(040)t ≤<,代入(40,8000),解得k,再令()g t =mt +b ,()4060t ≤≤,代入(40,8000),(60,11000),解得m ,b 的值.即可得到()f t 和()g t 的解析式;(2)由题意知每天的阅读量为()()()h t f t g t =+=28012000t t -++,分020t ≤≤和2060t <≤两种情况,分别求得最大值,比较可得结论.【详解】(1)因为f (0)=0,所以可设f (t )=2a ?t bt +,代入(10,2700)与(30,7500),解得a=-1,b=280.所以()2280f t t t =-+ ,又令()g t =kt ,(040)t ≤<,代入(40,8000),解得k=200,令()g t =mt +b ,()4060t ≤≤,代入(40,8000),(60,11000),解得m=150,b=2000,所以 ()()200(040)150********t t g t t t ≤<⎧=⎨+≤≤⎩.(2)设小明对“经典名著”的阅读时间为()060t t ≤≤,则对“古诗词”的阅读时间为60t -,① 当06040t ≤-<,即2060t <≤时,()()()()228020060h t f t g t t t t =+=-++-=28012000t t -++ =()24013600t --+,所以当40t =时,()h t 有最大值13600. 当406060t ≤-≤,即020t ≤≤时,h ()()()()2280150602000t f t g t t t t =+=-++-+=213011000t t -++,因为()h t 的对称轴方程为65t =, 所以 当020t ≤≤时,()h t 是增函数, 所以 当20t =时,()h t 有最大值为13200. 因为 13600>13200,所以阅读总字数()h t 的最大值为13600,此时对“经典名著”的阅读时间为40分钟,对“古诗词”的阅读时间为20分钟. 【点睛】本题考查了分段函数解析式的求法及应用,二次函数的图象和性质,难度中档.26.已知数列{}n α满足12a =,且2122()n n n a a n N +*+=+∈,2nn na b =(1)求证数列{}n b 是等差数列,并求数列{}n α的通项公式; (2)记23341121111n n n T b b b b b b b b +=++⋅+⋅⋅⋅⋅L L ,求n T ; (3)是否存在实数k,使得12222(1)(1)(1)5nb b b +++≥L 对任意()n *∈N 都成立?若存在,求实数k 的取值范围;若不存在,请说明理由.【答案】(1)证明见解析,(21)2nn a n =-⋅;(2)n T =21n n +;(3)存在且k ≤.【解析】(1)用等差数列的定义证明{}n b 是等差数列,由n b 可得n a ; (2)用裂项相消法求n T ; (3)假设存在实数k ,使得12222(1)(1)(1)5nb b b +++≥L 对任意()n *∈N 都成立,不等式变形为(2k n ≤+,只要求得()(2f n n =+即可,可先证()f n 是递增的,然后可得最小值.【详解】(1)因为2122()n n n a a n N +*+=+∈,所以11222n n n n a a ++=+,即11222n nn n a a ++-=,所以12n n b b +-=,所以{}n b 是等差数列,公差为2,1112a b == , 12(1)21n b n n =+-=-,所以2(21)2n n n n a b n ==-⋅.(2)由(1)111111()(21)(21)22121n n b b n n n n +==--+-+, 所以11111111[(1)()()(1)2335212122121n n T n n n n =-+-++-=-=-+++L . (3)假设存在实数k ,使得12222(1)(1)(1)5nb b b +++≥L 对任意()n *∈N 都成立, 因为2221112121n n b n n ++=+=--, 所以12222(1)(1)(1)n b b b +++=L 3521211321n n n +⨯⨯⨯=+-L ,不等式12222(1)(1)(1)5n b b b +++≥L化为215n +≥,(2k n ≤+,设()(2(2f n n n =+=+ 设1n m ≤<,则02626n m <+<+,1114141n m >>--,110114141n m <-<---<,所以()()f n f m <,所以()f n 是递增数列,min ()(1)83f n f ===,所以3k ≤. 所以存在实数k,使得12222(1)(1)(1)5nb b b +++≥L 对任意()n *∈N 都成立,且3k ≤. 【点睛】本题考查用定义证明等差数列,考查裂项相消法求和,考查与不等式恒成立有关的数列问题.数列不等式恒成立与函数不等式恒成立处理方法是一致的,都可用分离变量法转化为求函数(数列)的最值.27.已知圆O :222x y +=,直线l :2y kx =-. (1)若直线l 与圆O 相切,求k 的值;(2)若直线l 与圆O 交于不同的两点A ,B ,当AOB ∠为锐角时,求k 的取值范围; (3)若12k =,P 是直线l 上的动点,过P 作圆O 的两条切线PC ,PD ,切点为C ,D ,探究:直线CD 是否过定点,若过定点,则求出该定点. 【答案】(1)±1;(2)1k <<-或1k <<(3)直线CD 过定点112-(,). 【解析】(1)由圆心到切线距离等于半径求参数值; (2)只要圆心到直线的距离大于弦长的一半即可.(3)利用P 点坐标,求出直线CD 的方程,由方程确定是否过定点. 【详解】(1)原点O 到直线l的距离为d ==,=解得1k =±;(2)因为OA OB =,AOB ∠为锐角时等价于r d >>即22222r d r >>,∴244221k >⨯>+,解得1k <<-或1k <<; (3)P 在直线1:22l y x =-上,设00(,)P x y ,则以OP 为直径的圆方程为00()()0x x x y y y -+-=,即22000x y x x y y +--=,同22220020x y x y x x y y ⎧+=⎨+--=⎩,相减得002x x y y +=,这就是直线CD 的方程. 又00122y x =-, ∴001(2)22x x x y +-=,01()2202x y x y +--=,由102220x y y ⎧+=⎪⎨⎪--=⎩得121x y ⎧=⎪⎨⎪=-⎩,∴直线CD 过定点112-(,). 【点睛】本题考查直线与圆的位置关系,考查圆中定点问题.直线与圆的位置关系一般用几何方法求解,即求出圆心到直线的距离d ,由d 与半径r 的关系确定直线与圆位置关系,而求直线与圆相交弦长就利用垂径定理得垂直后由勾股定理计算.直线过定点问题,采取基本方法,设动点P 的坐标为参数,由这个参数求出直线CD 方程,分析方程,得定点. 28.已知函数()21g x x ax =-+.(1)求()0g x <的解集; (2)已知函数1()ln f x x a x x=-+,当2a >时,1x 、2x 是()y g x =的两个零点,证明:1212()()2f x f x a x x -<--.(可能用到的参考结论:函数12ln y x x x=+-在区间(0,)+∞上单调递减)【答案】(1)当22a -≤≤时,解集为∅,当2a <-或2a >时,解集为.(2)见解析. 【解析】(1)按0∆≤和>0∆分类讨论;(2)首先有12x x a +=,121=x x ,,然后化简不等式1212()()2f x f x a x x -<--为1212ln1x x x x <-,为了进一步化简,不妨设12x x >,则有121x x >>,利用211x x =可化二元不等式为一元不等式11112ln 0x x x -+<,然后利用函数的单调性得证. 【详解】(1)24a ∆=-,当0∆≤,即22a -≤≤时,不等式()0<g x 解集为∅;当>0∆,即2a <-或2a >时,210x ax -+=的根为12a x =,22a x =,不等式的解集为(22a a -.综上,当22a -≤≤时,解集为∅,当2a <-或2a >时,解集为(22a a +.(2)由(1)12x x a +=,121=x x ,1212()()f x f x x x --1122121211ln ln x a x x a x x x x x -+-+-=-=2112112212ln x x x x x a x x x x x -+-+-1212ln2x a x x x =-+-2a <-⇔1212ln 1x x x x <-(∵2a >),不妨设12x x >,则1210x x >>>,211x x =, 1212ln1x x x x <-⇔1122ln x x x x <-,即21111ln x x x <-,11112ln 0x x x -+<,设1()2ln h x x x x=+-,则22211()1(1)0h x x x x '=--=--≤,∴函数1()2ln h x x x x=+-在区间(0,)+∞上单调递减, ∴11x >时,11111()2ln (1)0h x x x h x =-+<=. ∴原不等式成立. 【点睛】本题考查解一元二次不等式,考查不等式的证明.对含参数的不等式一般要分类讨论,分类标准一是最高次项系数,二是判别式∆,三是两根的大小(如果有两根).解题时要注意.不等式的证明要注意问题的转化与化归.象本题与零点有关的不等式,要利用零点的性质对不等式变形,两个零点(或极值点),在对称的情况下,不妨赋予大小关系(如设12x x >),便于不等式的化简变形.变量较多时要注意消元,减少变量个数,最后应用一元函数的单调性完成问题的解决.。
广东省佛山市第一中学2019-2020学年高一下学期期中考试 英语 Word版含答案

佛山一中2019-2020学年下学期高一级期中考试题英语2020年5月本试卷共10页, 91小题, 满分150分, 考试时间120分钟。
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第一部分:听力(共两节, 满分15分)第一节听力理解(共6小题;每小题1分, 满分6分)材料及问题播放两遍。
每段后有两个小题, 各段播放前有5秒钟的阅题时间。
请根据各段播放内容及其相关小题的问题, 在5秒钟内从题中所给的A、B、C项中, 选出最佳选项, 并在答题卡上将该项涂黑。
听第一段材料, 回答第1-2题。
1. A. He occupied a parking lot long. B. He forgot his car in the train station.C. He didn’t obey the traffic rules.2. A. Stop driving. B. Refuse to pay the fine.C. Cut down on spending.听第二段材料, 回答第3-4题。
3. A. He will go to a barbecue party. B. He wears a fashionable shirt.C. He needs fashion lessons.4. A. The girl in holey jeans. B. The girl in a white blouse.C. The guy in a Hawaiian shirt.听第三段材料, 回答第5-6题。
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班级:_______________姓名:_______________试室号:_______________座位号:___________ O ••••••••••••••••••••••密••••••••••••••••••••••O••••••••••••••••••••••封••••••••••••••••••••••O••••••••••••••••••••••线2018级高一(下)高一英语期中三校联考 (珠海一中 金山中学 佛山一中)2019.5.5 命题人:陶小明 汤倩 审题人: 郭书廷 第一部分:单项填空(共 20 小题;每小题1.5分,满分 30 分), 从 A 、B 、C 、D 四个选项中,选出可以填入空白处的最佳选项。
1. One of our rules is that every student _______ wear school uniform while at school. A. might B. could C. shall D. will 2. Our school makes _______ a rule that students______ bring their mobile phones to campus. A. it; needn’t B. it; mustn’t C. that; mustn’t D . that; needn’t 3. Something terrible _______ if Li Chang was not coming to eat in his restaurant ______ he always did. A. must have happened; what B. could have happened; as C. must have happened; as D. could have happened; what 4. It is so wet there that the trees are extremely tall, some _________ over 90 meters. A. are measured B. are measured C. measured D. measuring 5. The fact is ______ I earned my passage by working as an unpaid hand, which ______ my appearance. A. that; accounts for B. \; accounts for C. how; give an explanation to D. \; give an explanation to 6. How happy we are! The holiday we have been looking forward _______ at last. A. to has come B. having come C. to having come D. has come 7. It is not always easy for the public to see _______ use a new invention can be of to human life. A. whose B. what C. which D. that 8. Evidence has been found through years of study _______ children’s early sleeping problems are likely to continue when they grow up. A. whether B. how C. that D. why 9. You are saying that everyone should take equal responsibility, and that is _______ I disagree. A. why B. where C. what D. how 10. _______ is no doubt _______ Shanghai Book Traders will make greater and greater contributions to the development of Shanghai. A. It; that B. There; what C. There; that D. It; what 11. _________ the Silk Road covered a huge distance ________ modern day Xi’an with the Middle East and Europe, today one area in particular is associated with the name of the Silk Road. A. Why; linking B. Why; linked C. Although; linked D. Although; linking 12. It ________ long before we ________ the result of the experiment.A. will not be; will knowB. is; will knowC. will not be; knowD. is know13.One can always manage to do more things, no matter ________ full one’s schedule is in life.A. whereB. whenC. whatD. how14. You have to take some necessities such as ropes, a flash, boots, ________ you may get lost in the mountain if going hiking.A. in caseB. in order thatC. now thatD. so that15. Some great people said it was their primary school teachers and their lessons _______ they were fond of ________ influenced their whole lives.A. which; thatB. that; whichC. which; whichD. that; that16. This is the small house less than 15 square meters, under _______ roof lives a large family of three generations.A. whichB. whoseC. asD. that17. Biarni was hoping to join his father _______ was with Eric, but he was blown off course and found himself in an unknown land, ________ he eventually reached Greenland.A. who; from whereB. who; from whichC. what; from whereD. what; from which18. Today, the Xinjiang Autonomous Region remains an international crossroad ________ traders from surrounding countries, and tourists from all over the world regular meet.A. whoseB. whereC. whenD. why19. Paper cuts used for religious purposes ________ as offerings to the dead. People ________ whom the dead person was related would make these offerings on special days.A. are used; toB. using; toC. are used; forD. using; for20. Michael put up a picture of Lionel Messi beside the bed to keep himself _______of his own dreams.A. remindingB. to remindC. remindedD. remind第二部分阅读理解(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和D四个选项中,选出最佳选项。
ATOUR DETAILSWindsor CastleTime-honored in history, Windsor Castle is proudly located on a wooded hill overlooking the Thames River. Dating back to Norman times, it is famous for sweeping landscaped gardens, which is easy to see why it’s the Queen’s favorite week place. Famous for its architecture and Royal palace, the Castle was built in the 11thcentury after the Norman invasion. It’s home to priceless artworks and you can visit Queen Mary’s Dolls’ House. Remember don’t miss the ceremony—Changing of the Guards.StonehengeStonehenge is located in the county of Wiltshire. This is your chance to see a side of the world-famous stones that most people don’t get a chance to see! You will never forget your first glimpse of grand Stonehenge with its rocks rising up against the skyline on Salisbury Plain. There are many unsolved mysteries about the rocks. Was Stonehenge intended as a religious temple? A clock for astronomy? A burial ground? Make up your own mind as you explore this unique site that has confused the world for 5, 000 years.BathBeautiful Bath was the first city in England to be added to the UNESCO World Heritage List. No tour of Bath would be complete with a visit to the famous Roman Baths that gave the city its name. This beautifully preserved bathing site still has flowing water from Brain’s only hot spring. You will be amazed by the impressive torch-lighting ceremony as dusk falls. You can also have a taste of Bath’s water in Pump Room, where hot waters are drawn for drinking.21. If your family (2 adults and 2 children) want to visit Winsor, Bath and Stonehenge, it will cost you at least ________.A.£188B.£356C.£168D.£34622. Where can visitors see Changing of the Guards?A. In WinsorCastle.B. In Bath.C. In Stonehenge.D. In Pump Room.23. Where is the passage probably taken from?A. a science fiction novelB. a travelling brochureC. a news reportD. a sports magazineBWhen I graduated from high school, I wanted to major in comparative literature. But, once I found out my friends were going into “real” majors, like marketing, nursing, and engineering, I figured I needed to do the same to ensure a good career. So I changed my mind and chose Business Management as my major. I forced myself to believe that I would enjoy it and succeed in the future, but eventually I exhausted myself understanding the economy and trying new marketing techniques. Coming out of this experience, I realize it is ok to be different from others and to study things like art history and other majors offered in the College of Humanities(人文学科)!The worries most people have about a Humanities degree and finding a career afterwards are that the majors are too abstract, and one will not obtain any applicable skills. Actually ideas discussed in Humanities classes, which are occasionally different from what people commonly believe, offer a broad perspective(视角). How could one effectively be an unbiased(无偏见的)writer with only a knowledge of thepopular opinion of society? How could one speak persuasively with closed minds? Only seeing the world through a single perspective leads to missed learning, missed friendships, and missed growth! With a broader perspective, we’ll be freer, more open-minded, and less limited in what we can become!STEM (science, technology, engineering, and mathematics) graduates learn actual skills in their studies, while humanities majors learn “soft skills” like communicating effectively through writing critically and speaking persuasively, synthesizing(综合)ideas through gathering and interpreting information, and developing cultural awareness. Do those soft skills sound useless and inapplicable to you? Think of it. How often do you communicate with others? Produce ideas? Encounter people from other cultures? Every day. Every SECOND of every day. So why not master these skills?If you choose a major in the College of Humanities, you will be needed. The job market is quietly creating thousands of openings a week for people who can bring a humanist’s grace t o our rapidly evolving high-tech future. Your skills will be valuable to any workplace you hope to be in. Chase after your dream major with all your energy, no matter what other people think.24. Why did the author choose Business Management as his major at first?A. He was tired of learning comparative literature.B. He came to enjoy learning marketing techniques.C. He wanted to go to the same university as his friends.D. He believed Business Management was more practical.25. According to the author, what is a possible way to gain a broad perspective?A. Making more friends and learning from them.B. Exchanging ideas in a philosophy class.C. Opening your mind to future possibilities.D. Getting to know the popular opinion of society.26. In which of the following situations do soft skills play the most important role?A. Writing a software program.B. Performing a heart operation.C. Playing a musical instrument.D. Negotiating with a business partner.27. What could be the best title for the passage?A. Stick to Your Desired majorB. Broaden Your PerspectiveC. How to Acquire Soft SkillsD. Humanities vs. STEMCA small school in rural India is gaining attention over the fact that all 300 students are ambidextrous(左右手都灵巧的). Data shows that only one percent of the global population is ambidextrous, but the ambitious founder of Veena Vandini School, in Madhya Pradesh, is aiming to change that, starting at a local level.A former soldier and Veena Vandini School founder VP Sharma stated that he was inspired to focus on ambidexterity training by India’s first president Rajendra Prasad who was in office from 1950 to 1962. Unexpectedly, the president was ambidextrous."I read in a magazine that Dr. Rajendra Prasad, India’s first president, used to writ e with both hands. This inspired me to give it a try, “Mr. Sharma said.”Later when I launched my school at my native village, I tried training the students. ""We begin training students from standard Ⅰ and by the time they reach standard Ⅲ, they are comfortable writing with both the hands,” Sharma added. "Students of up to standard Ⅶ can write with speed and accuracy. Further, they can write two scripts at the same time, one with each hand. Students also know several languages, including Urdu. "Every 45-minute class at Veena Vandini includes 15 minutes devoted to handwriting practice, ensuring that every student develops the ability to write with both hands. VP Sharma also believes that the skill better enables students to learn multiple languages, and has them practice writing the same words in different languages at the same time. Although it is widely believed to help increase concentration, more recent studies have found that this is false and studying to become ambidextrous can, in fact, harm cognitive development.A Scientific American study revealed that ambidextrous children performed worse than left- or right-handers on a range of skills, especially in math, memory, and logical reasoning. A study in northern Finland indicated that children who are ambidextrous are much likelier to develop mental health issues, including ADHD, language problems, and academic problems.28.What is special about Veena Vandini School?A.It only accepts 300 students yearly.B.It was set up by India’s first president.C.It mainly teaches how to write with both hands.D.It requires students to learn practical living skills29.In which standard can students write quickly and accurately?A. Standard Ⅲ.B. Standard Ⅳ.C. Standard Ⅵ.D. Standard Ⅶ.30.What might most people think of the skill promoted by VP Sharma?A.It helps students fix their attention.B.It does harm to students’ creativity.C.It increases students’ academic stress.D.It inspires students to learn more languages.31.What do the two studies suggest in the last paragraph?A.Kids are reluctant to write with both hands.B.Kids shouldn’t learn to write with both hands.C.Kids who are ambidextrous always fail in the math test.D.Kids who are ambidextrous often have serious mental illnessDEssentially, everyone has two ages: a chronological(按时间计算的)age, how old the calendar says you are, and a biological age, basically the age at which your body functions as it compares to average fitness or health levels.“Chronological age isn’t how old we really are. It’s merely a number,” said Professor David Sinclair at Harvard University. “It is biological age that determines our health and ultimately our lifespan. We all age biologically at different rates according to our genes, what we eat, how much we exercise, and what environment we live in. Biological age is the number of candles we really should be blowing out. In the future, with advances in our ability to control biological age, we may have even fewer candles on our birthday cake than the previous one.”To calculate biological age, Professor Levine at Yale University identified nine biomarker(生物标志)that seemed to be the most influential on lifespan by a simple blood test. The numbers of those markers, such as blood sugar and immune(免疫的)measures, can be put into the computer, and the algorithm(算式;算法)does the rest.Perhaps what’s most important here is that these measures can be changed. Doctors can take this information and help patients make changes to lifestyle, and hopefully take steps to improve their biological co nditions. “I think the most exciting thing about this research is that these things aren’t set in stone,” Levine said. “People can be given the information earlier and take steps to improve their health before it’s too late.”Levine even entered her own numbers into the algorithm. She was surprised by the results. “I always considered myself a very healthy person. I’m physically active;I eat what I consider a fairly healthy diet. But I did not find my results to be as good as I had hoped they would be. It was a wake-up call,” she said.Levine is working with a group to provide access to the algorithm online so that anyone can calculate their biological age, identify potential risks and take steps to improve their own health in the long run. “No one wants to live an extremely long life with a lot of chronic(慢性的)diseases,” Levine said. “By delaying the development of mental and physical functioning problems, people can still be engaged in society in their senior years. That is the ideal we should be pursuing.”32. Biological age depends on _______.A. whether we can adapt ourselves to the environmentB. how well our body works compared with our peers’C. when we start to take outdoor exerciseD. what the calendar says about our age33. By saying “we may have even fewer candles on our birthday cake than the previous one” in Para. 2, the author means _______.A. we don’t have to celebrate our birthday every yearB. we are chronologically older than last yearC. we might be less happy than the previous yearD. we may be biologically younger than the year before34. What does the author want to tell us by Levine’s example in Para. 5?A. It is necessary to change our diet regularly.B. The test results may give us wrong information.C. Waking up early in the morning is good for our fitness.D. The algorithm can reveal our potential health problems.35. The eventual goal of Levine’s research is to ______.A. free people from chronic diseasesB. work out a solution to genetic problemsC. keep people socially active even in old ageD. provide people with access to scientific theory第二节 (共5小题:每小题2分,满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。