2019高考卷-2019年江苏卷高考试题
绝密★启用前
2019年普通高等学校招生全国统一考试（江苏卷）
数学Ⅰ
注意事项
考生在答题前请认真阅读本注意事项及各题答题要求
1．本试卷共4页，均为非选择题(第1题~第20题，共20题)。本卷满分为160分，考试时间为120分钟。
考试结束后，请将本试卷和答题卡一片交回。
2．答题前，请务必将自己的姓名、准考证号用0.5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位
置。
3．请认真核对监考员从答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符。
4．作答试题，必须用0.5毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效。
5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗。
参考公式：
样本数据12,,,nxxx…的方差2211niisxxn，其中11niixxn．
柱体的体积VSh，其中S是柱体的底面积，h是柱体的高．
锥体的体积13VSh，其中S是锥体的底面积，h是锥体的高．
一、填空题：本大题共14小题，每小题5分，共计70分．请把答案填写在答题卡相应位
．．．．．．
置上．．．
1．已知集合{1,0,1,6}A，{|0,}BxxxR，则AB .
2．已知复数(2i)(1i)a的实部为0，其中i为虚数单位，则实数a的值是 .
3．下图是一个算法流程图，则输出的S的值是 .
1
4．函数276yxx的定义域是 .
5．已知一组数据6，7，8，8，9，10，则该组数据的方差是 .
6．从3名男同学和2名女同学中任选2名同学参加志愿者服务，则选出的2名同学中至少
有1名女同学的概率是 .
7．在平面直角坐标系xOy中，若双曲线2221(0)yxbb经过点（3，4)，则该双曲线的
渐近线方程是 .
8．已知数列*{}()nanN是等差数列，nS是其前n项和.若25890,27aaaS，则8S的
值是 .
9．如图，长方体1111ABCDABCD的体积是120，E为1CC的中点，则三棱锥E-BCD的
体积是 .
10．在平面直角坐标系xOy中，P是曲线4(0)yxxx上的一个动点，则点P到直线
x+y=0的距离的最小值是 .
11．在平面直角坐标系xOy中，点A在曲线y=lnx上，且该曲线在点A处的切线经过点（-e，
-1)(e为自然对数的底数），则点A的坐标是 .
12．如图，在ABC△中，D是BC的中点，E在边AB上，BE=2EA，AD与CE交于点O.
若6ABACAOEC，则ABAC的值是 .
1
13．已知tan2π3tan4，则πsin24的值是 .
14．设(),()fxgx是定义在R上的两个周期函数，()fx的周期为4，()gx的周期为2，且
()fx是奇函数.当2(]0,x
时，2()1(1)fxx，(2),01()1,122kxxgxx，
其中k>0.若在区间(0，9]上，关于x的方程()()fxgx有8个不同的实数根，则k的
取值范围是 .
二、解答题：本大题共6小题，共计90分．请在答题卡指定区域．．．．．．．内作答，解答时应写出文字
说明、证明过程或演算步骤．
15．（本小题满分14分）
在△ABC中，角A，B，C的对边分别为a，b，c．
（1）若a=3c，b=2，cosB=23，求c的值；
（2）若sincos2ABab，求sin()2B的值．
16．（本小题满分14分）
如图，在直三棱柱ABC－A1B1C1中，D，E分别为BC，AC的中点，AB=BC．
求证：（1）A1B1∥平面DEC1；
（2）BE⊥C1E．
17．（本小题满分14分）
1
如图，在平面直角坐标系xOy中，椭圆C:22221(0)xyabab的焦点为F1（–1、0），
F2（1，0）．过F2作x轴的垂线l，在x轴的上方，l与圆F2:222(1)4xya交于
点A，与椭圆C交于点D.连结AF1并延长交圆F2于点B，连结BF2交椭圆C于点E，
连结DF1．
已知DF1=52．
（1）求椭圆C的标准方程；
（2）求点E的坐标．
18．（本小题满分16分）
如图，一个湖的边界是圆心为O的圆，湖的一侧有一条直线型公路l，湖上有桥AB（AB
是圆O的直径）．规划在公路l上选两个点P、Q，并修建两段直线型道路PB、QA．规
划要求：线段PB、QA上的所有点到点O的距离均不小于圆．．．．O的半径．已知点A、B
到直线l的距离分别为AC和BD（C、D为垂足），测得AB=10，AC=6，BD=12（单位：
百米）．
（1）若道路PB与桥AB垂直，求道路PB的长；
（2）在规划要求下，P和Q中能否有一个点选在D处？并说明理由；
（3）在规划要求下，若道路PB和QA的长度均为d（单位：百米）.求当d最小时，P、
Q两点间的距离．
1
19．（本小题满分16分）
设函数()()()(),,,fxxaxbxcabcR、()f'x为f（x）的导函数．
（1）若a=b=c，f（4）=8，求a的值；
（2）若a≠b，b=c，且f（x）和()f'x的零点均在集合{3,1,3}中，求f（x）的极小
值；
（3）若0,01,1abc，且f（x）的极大值为M，求证:M≤427．
20．（本小满分16分）
定义首项为1且公比为正数的等比数列为“M－数列”.
（1）已知等比数列{an}*()nN满足：245324,440aaaaaa，求证：数列{an}
为“M－数列”；
（2）已知数列{bn}*()nN满足：111221,nnnbSbb，其中Sn为数列{bn}的前n项
和．
①求数列{bn}的通项公式；
②设m为正整数，若存在“M－数列”{cn}*()nN，对任意正整数k，当k≤m时，
都有
1kkkcbc
成立，求m的最大值．
1
2019年江苏高考试题(数学_word解析版)
2019年普通高等学校招生全国统一考试（江苏卷）数学（全卷满分160分，考试时间120分钟）参考公式：棱锥的体积13V Sh =，其中S 为底面积，h 为高．一、填空题：本大题共14小题，每小题5分，共计70分．请把答案填写在答题卡相应位置上．．．．．．．．． 1．（2019年江苏省5分）已知集合{124}A =，，，{246}B =，，，则A B = ▲ ．【答案】{}1,2,4,6。
【考点】集合的概念和运算。
【分析】由集合的并集意义得{}1,2,4,6AB =。
2．（2019年江苏省5分）某学校高一、高二、高三年级的学生人数之比为334::，现用分层抽样的方法从该校高中三个年级的学生中抽取容量为50的样本，则应从高二年级抽取 ▲ 名学生． 【答案】15。
【考点】分层抽样。
【解析】分层抽样又称分类抽样或类型抽样。
将总体划分为若干个同质层，再在各层内随机抽样或机械抽样，分层抽样的特点是将科学分组法与抽样法结合在一起，分组减小了各抽样层变异性的影响，抽样保证了所抽取的样本具有足够的代表性。
因此，由350=15334⨯++知应从高二年级抽取15名学生。
3．（2019年江苏省5分）设a b ∈R ，，117ii 12ia b -+=-（i 为虚数单位），则a b +的值为 ▲ ． 【答案】8。
【考点】复数的运算和复数的概念。
【分析】由117ii 12i a b -+=-得()()()()117i 12i 117i 1115i 14i ===53i 12i 12i 12i 14a b -+-+++=+--++，所以=5=3a b ，，=8a b + 。
4．（2019年江苏省5分）下图是一个算法流程图，则输出的k 的值是 ▲ ．【答案】5。
【考点】程序框图。
【分析】根据流程图所示的顺序，程序的运行过程中变量值变化如下表：是否继续循环k 2k 5k 4-+循环前 0 0 第一圈 是 1 0 第二圈 是 2 －2 第三圈 是 3 －2 第四圈 是 4 0 第五圈 是 5 4 第六圈否输出5∴最终输出结果k=5。
2019年高考真题地理江苏卷解析版
2019年普通高等学校招生全国统一考试·江苏高考(2019·江苏高考·T1-2)雾灵山位于北京与承德交界处,海拔2 118米,素有“京东第一峰”的美称,是观赏日出和日落的理想之地。
下表为“雾灵山部分日期的日出和日落时刻表”。
据此回答1、2题。
日期日出时刻日落时刻①7:32 17:08②6:31 18:15③4:45 19:39④7:22 16:491.四个日期中,太阳直射点最靠近赤道的是( )A.①B.②C.③D.④2.一游客于7月某日去雾灵山旅游,当日的太阳视运动轨迹是( )【解析】1选B,2选B。
第1题,当太阳直射赤道时,全球昼夜等分,昼长为12个小时,当太阳直射点最靠近赤道的时候,地球上的昼长应当接近12个小时,因此可以计算四个日期的昼长时间,最接近12个小时的即为太阳直射点最靠近赤道的日期。
①昼长为9小时36分,②昼长为11小时44分,③昼长为14小时54分,④昼长为9小时27分。
第2题,雾灵山位于北半球,7月是北半球夏季,北半球日出东北日落西北,排除C、D。
太阳直射北半球,北半球昼长大于12个小时,因此正确答案选B,本题容易错选A,注意昼长大于12个小时,在该图当中,太阳在正午的时候一定要越过地球的中心点,即位于中心点偏南方向。
(2019·江苏高考·T3-4)下图为某次地质野外考察时拍摄的照片。
照片中界面M之上的“甲”是一水平岩层,界面M之下的“乙”是一向斜,“丙”是地表沟谷,N是岩层层面。
读图完成3、4题。
3.界面M反映的地质含义不同于N的是( )A.沉积物变化B.古气候变化C.古环境变化D.构造运动变化4.该区域( )A.甲抬升前持续接受沉积B.乙形成时代晚于甲岩层C.乙形成后经历长期侵蚀D.丙是背斜受侵蚀的结果【解析】3选D,4选C。
第3题,由材料和图片可知,M上部的岩层是水平的,M下部的岩层是弯曲的,因此M表达的地质意义和N不同就在于弯曲岩层经过地壳的挤压形成了褶皱,而上部的岩层主要以外力作用为主,如沉积作用,因此水平方向的岩层是没有经过挤压作用的;无法看出古气候的变化和古环境的变化,通过岩层的顺序只可以判断地壳运动的变化,而沉积物的变化也无法判断。
2019年江苏高考英语真题(含答案)
2019年普通高等学校招生全国统一考试（江苏卷）英语第一节：单项填空（共15小题；每小题1分，满分15分）请认真阅读下面各题，从题中所给的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。
例：It is generally considered unwise to give a child _______ he or she wants.A. howeverB. whateverC. whicheverD. whenever答案是B。
21. We have entered into an age _______ dreams have the best chance of coming true.D. which A. what C. when D. that22. The musician along with his band members ______ ten performances in the lastthree months.A. gives B has given C. have given D. give23. The doctor shares his phone number with the patients ______ they need medicalassistance.A. if onlyB. as ifC. even thoughD. in case24. More wind power stations will ____________ to meet the demand for clean energy.A. take upB. clear upC. hold upD. spring up25. Scientists have obtained more evidence ______ plastic is finding its way intothe human body.A. whatB. thatC. whichD. where26. Nowadays the ___________ for travelling is shifted from shopping to food andscenery.A. priorityB. potential C proportion D. pension27. Favorable policies are ___________ to encourage employees' professional development.A. in effectB. in commandC. in turnD. in shape28. Unlike traditional gyms, app-backed gyms offer people ___________ options toexercise.A. casualB. regularC. flexibleD.tight29. A few months after he had arrived in China, Mr. Smith ___________ in love withthe people and culture there.A. would fallB. had fallenC. has fallenD. fell30. ______ the convenience of digital payment, many senior citizens started to use smart phones.A. To enjoyB. EnjoyingC. To have enjoyedD. Enjoy31. What a pity! You missed the sightseeing, or we _________a good time together.A. hadB. will haveC. would have hadD. had had32. China's image is improving steadily, with more countries_____ its role ininternational affairs.A. recognizingB. being recognizedC. to be recognizedD. recognized33. They are trying to make sure that 5G terminals_____ by 2022 for the Beijing Winer Olympics.A. will installB. will have been installedC. are installedD. have been installed34.A city is the product of the human hand and mind, _____ man's intelligence andcreativity.A. resemblingB. reflectingC. reviewingD. restoring35.—Let's take a coffee break.— __________ We' ve been working for hours.A. Why bother?B. What for?C. You got me there.D. You said it.第二节：完形填空（共20小题；每小题1分，满分20分）请认真阅读下面短文，从短文后各题所给的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。
2019年高考语文江苏卷含答案
只字。于诗若文无所不比拟，而尤精西京六朝青莲少陵氏。公又以其绪余为传奇，若《紫
箫》、《还魂》诸剧，实驾元人而上。每谱一曲，令小史当歌，而自为之和，声振寥廓。
识者谓神仙中人云。
公与予约游具区灵岩虎丘诸山川，而不能办三月粮，逡巡中辍。然不自言贫，人亦
不尽知公贫。公非自信其心者耶？予虽为之执鞭，所忻慕焉。
（）
A.汤显祖持身端洁，拒绝了时相张居正的利诱，海内士人都以结识他为荣幸。
B.因为上书批评当权者徇私情、塞言路，汤显祖被贬官至广东，做了徐闻尉。 语文试卷 第 3 页（共 16 页）
C.汤显祖辞官回家后，当地官员争相与他交往，而汤显祖不为私事开口求人。 D.汤显祖与邹迪光相约三月份到江南一带游玩，但没准备好粮食，因而作罢。 7.把文中画线的句子翻译成现代汉语。（10 分） （1）见者益复啧啧曰：“此儿汗血，可致千里，非仅仅蹀躞康庄也者。”
丁丑会试，江陵公①属其私人啖以巍甲而不应。曰：“吾不敢从处女子失身也。”公虽 一老孝廉乎，而名益鹊起，海内之人益以得望见汤先生为幸。至癸未举进士，而江陵物 故矣。诸所为附薰炙者，骎且澌没矣。公乃自叹曰：“假令予以依附起，不以依附败乎？”
语文试卷 第 2 页（共 18 页）
而时相蒲州、苏州两公，其子皆中进士，皆公同门友也。意欲要之入幕，酬．以馆选，而
3.下列诗句与“悯农馆”里展示的劳动场景，对应全部正确的一项是（3 分） （ ）
①笑歌声里轻雷动，一夜连枷响到明
效 ②种密移疏绿毯平，行间清浅縠纹生
③分畴翠浪走云阵，刺水绿针抽稻芽
语文试卷 第 1 页（共 16 页）
④阴阴阡陌桑麻暗，轧轧房栊机杼鸣
A.①织布②插秧③车水④打稻
B.①织布②车水③插秧④打稻
绝密★启用前
2019年全国普通高考江苏卷语文试题及答案解析
2019年全国普通高考江苏卷语文试题及答案解析语文 I 试题一、语言文字运用（15分）1．在下面一段话的空缺处依次填入词语，最恰当的一组是（3分）提到桃花源，许多人会联想到瓦尔登湖。
真实的瓦尔登湖，早已成为▲的观光胜地，梭罗的小木屋前也经常聚集着▲的游客，不复有隐居之地的气息。
然而虚构的桃花源一直就在我们的心中，哪怕▲在人潮汹涌的现代城市，也可以获得心灵的宁静。
A．名闻遐迩闻风而至杂居 B．名噪一时闻风而至栖居C．名噪一时纷至沓来杂居 D．名闻遐迩纷至沓来栖居【答案】D【详解】本题考查辨析近义成语和词语的能力。
辨析近义词语的关键就是要仔细分辨它们的细微差别。
首先阅读语境，把握语境含义，然后抓住相异语素，分析其意义差异，同时可联系日常习惯用语，推断词语意义及用法。
“名闻遐迩”，形容名声很大；“名噪一时”，指名声传扬于一个时期。
语境强调的是瓦尔登湖成为观光胜地，应填“名闻遐迩”。
“闻风而至”，一听到消息就来，形容行动迅速；“纷至沓来”，形容接连不断的到来。
语境强调的是人们都纷纷来到瓦尔登湖，应填“纷至沓来”。
“杂居”侧重混杂而处，“栖居”侧重栖息居住，语境强调在“现代都市”居住，所以应填“栖居”。
故选D。
2．在下面一段文字横线处填入语句，衔接最恰当的一项是（3分）在南方，芭蕉栽植容易，几乎四季常青。
▲至于月映蕉影、雪压残叶，那更是诗人画家所向往的了。
①它覆盖面积大，吸收热量大，叶子湿度大。
②古人在走廊或书房边种上芭蕉，称为蕉廊、蕉房，饶有诗意。
③因此蕉阴之下，是最舒适的小坐闲谈之处。
④在旁边配上几竿竹，点上一块石，真像一幅元人的小景。
⑤在夏日是清凉世界，在秋天是分绿上窗。
⑥小雨乍到，点滴醒人；斜阳初过，青翠照眼。
A．①③②④⑥⑤ B．①④②③⑥⑤C．②①④③⑤⑥ D．②③④①⑤⑥【答案】A【详解】本题考查语言表达简明、连贯、得体的能力。
这道题采用的是客观选择题形式，做题时要注意把握基本内容，初步分层归类，先在小范围内排序，然后再考虑层次间的衔接，这其中应先找出关联词、代词以及表时间、地点的词语，然后据此进行句间连缀排列。
(精校版)2019年江苏卷语文高考试题文档版(含答案)
绝密★启用前语文I试题注意事项考生在答题前请认真阅读本注意事项及各题答题要求1．本试卷共8页，包含选择题（第1题~第6题，第12题，第15题~第16题，第18题~第19题，共11题）、非选择题（第7题~第11题，第13题~第14题，第17题，第20题~第21题，共10题）两部分。
本卷满分为160分，考试时间为150分钟。
考试结束后，请将本试卷和答题卡一并交回。
2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置。
3．请认真核对监考员在答题卡上所粘贴的条形码上的名字、准考证号与本人是否相符。
4．作答选择题（第1题~第6题，第12题，第15题~第16题，第18题~第19题），必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案。
作答非选择题，必须用0．5毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效。
一、语言文字运用（12分）1．在下面一段话的空缺处依次填入词语，最恰当的一组是（3分）提到桃花源，许多人会联想到瓦尔登湖。
真实的瓦尔登湖，早已成为▲的观光胜地，梭罗的小木屋前也经常聚集着▲的游客，不复有隐居之地的气息。
然而虚构的桃花源一直就在我们的心中，哪怕▲在人潮汹涌的现代城市，也可以获得心灵的宁静。
A．名闻遐迩闻风而至杂居B．名噪一时闻风而至栖居C．名噪一时纷至沓来杂居D．名闻遐迩纷至沓来栖居2．在下面一段文字横线处填入语句，衔接最恰当的一项是（3分）在南方，芭蕉栽植容易，几乎四季常青。
▲至于月映蕉影、雪压残叶，那更是诗人画家所向往的了。
①它覆盖面积大，吸收热量大，叶子湿度大。
②古人在走廊或书房边种上芭蕉，称为蕉廊、蕉房，饶有诗意。
③因此蕉阴之下，是最舒适的小坐闲谈之处。
④在旁边配上几竿竹，点上一块石，真像一幅元人的小景。
⑤在夏日是清凉世界，在秋天是分绿上窗。
⑥小雨乍到，点滴醒人；斜阳初过，青翠照眼。
2019年江苏卷高考英语阅读题真题解析
2019年江苏卷高考英语阅读题真题解析（正文开始）Part ASection 1: Multiple ChoiceIn this section, you will read several passages. Each passage is followed by several questions. Choose the best answer for each question and mark the corresponding letter (A, B, C or D) on the Answer Sheet.Passage 1Questions 1-3 are based on the following passage.A recent survey conducted in Jiangsu Province gathered data on the daily habits of students in different grades. The results show that a majority of students spend an average of 3 to 4 hours per day on their smartphones. This excessive screen time not only affects their academic performance but also poses health risks.According to the survey, the main reason for excessive smartphone use among students is social media. They spend a significant amount of time browsing through social media platforms, such as WeChat and Weibo, which greatly distracts them from focusing on their studies. As a result, their homework completion rate decreases and their grades suffer.Furthermore, the prolonged use of smartphones has been linked to various health issues. Students who spend more time on their phones are prone to experiencing eye strain, sleep disorders, and poor posture. Thesehealth problems not only affect their physical well-being but also impact their ability to concentrate and learn effectively.In order to address this issue, experts suggest that parents and teachers play a crucial role in guiding students to develop healthy smartphone habits. They should encourage students to limit their screen time, engage in physical activities, and create a balanced daily routine that includes both studying and leisure activities. By doing so, students can improve their academic performance and overall well-being.1. What did the survey in Jiangsu Province focus on?A. Students' academic performance.B. Students' daily smartphone habits.C. Students' social media platforms.D. Students' health risks.2. According to the survey, what is the main reason for excessive smartphone use among students?A. Poor academic performance.B. Lack of physical activities.C. Social media platforms.D. Homework completion rate.3. Which of the following is NOT mentioned as a health issue caused by prolonged smartphone use?A. Eye strain.B. Sleep disorders.C. Poor posture.D. Lack of concentration.Passage 2Questions 4-6 are based on the following passage.Athlete's foot, also known as tinea pedis, is a common fungal infection that primarily affects the skin on the feet. The infection is caused by various types of fungi, which thrive in warm, moist environments such as shoes, socks, and locker room floors.The symptoms of athlete's foot include itching, burning, and redness on the affected areas of the feet. In some cases, blisters and ulcers may also develop. If left untreated, athlete's foot can spread to other parts of the body and result in more severe infections.To prevent athlete's foot, it is important to practice good foot hygiene. This includes keeping your feet clean, dry, and well-ventilated. Avoid walking barefoot in public areas such as locker rooms and showers, and make sure to wear clean socks and shoes that allow your feet to breathe.If you suspect you have athlete's foot, it is recommended to see a healthcare professional for diagnosis and treatment. Anti-fungal creams or powders are commonly prescribed to treat the infection. Additionally, it is important to continue practicing good foot hygiene even after the infection has cleared to prevent future occurrences.4. What is athlete's foot?A. A fungal infection.B. A type of ulcer.C. A foot hygiene practice.D. An infectious disease.5. Where do fungi that cause athlete's foot thrive?A. Feet.B. Shoes.C. Socks.D. Locker room floors.6. What should be done to prevent athlete's foot?A. Wear dirty socks.B. Keep feet moist.C. Walk barefoot in public areas.D. Practice good foot hygiene.Section 2: MatchingIn this section, you will read five short extracts in which people are talking about their jobs or careers. Match each extract with the correct person (A-E). There are two extra people.7. Speaker A8. Speaker B9. Speaker C10. Speaker D11. Speaker EA. I work in a large advertising agency, helping to create and design new marketing campaigns for our clients. It's a fast-paced and creative environment, and I enjoy the challenges that come with it.B. My job involves managing a team of engineers in a manufacturing company. We are responsible for developing new products and improving manufacturing processes. It requires strong leadership and problem-solving skills.C. I am a freelance journalist, specializing in travel writing. I have the opportunity to visit different countries and share my experiences with readers. It's a dream job for someone who loves traveling and writing.D. I am a nurse at a local hospital. My work mainly involves caring for patients, administering medication, and assisting doctors during procedures. It's a rewarding job, as I get to make a positive impact on people's lives.E. I am a computer programmer in a technology startup. My role is to develop software applications and solve technical problems. I enjoy the intellectual challenge and the opportunity to innovate in this field.Answers: 7. B, 8. C, 9. A, 10. D, 11. E（正文结束）。
高考真题-2019年江苏卷数学高考试题文档
绝密★启用前2019年普通高等学校招生全国统一考试（江苏卷）样本数据12,,,n x x x …的方差()2211n i i s x x n ==-∑，其中11n i i x x n ==∑．柱体的体积V Sh =，其中S 是柱体的底面积，h 是柱体的高． 锥体的体积13V Sh =，其中S 是锥体的底面积，h 是锥体的高． 一、填空题：本大题共14小题，每小题5分，共计70分．请把答案填写在答题卡相应位置上．．．．．．．．． 1．已知集合{1,0,1,6}A =-，{|0,}B xx x =>∈R ，则A B =I ▲ .2．已知复数(2i)(1i)a ++的实部为0，其中i 为虚数单位，则实数a 的值是 ▲ . 3．下图是一个算法流程图，则输出的S 的值是 ▲ .4．函数y =的定义域是 ▲ .5．已知一组数据6，7，8，8，9，10，则该组数据的方差是 ▲ .6．从3名男同学和2名女同学中任选2名同学参加志愿者服务，则选出的2名同学中至少有1名女同学的概率是 ▲ .7．在平面直角坐标系xOy 中，若双曲线2221(0)y x b b-=>经过点（3，4)，则该双曲线的渐近线方程是▲ .8．已知数列*{}()n a n ∈N 是等差数列，n S 是其前n 项和.若25890,27a a a S +==，则8S 的值是 ▲ .9．如图，长方体1111ABCD A B C D -的体积是120，E 为1CC 的中点，则三棱锥E -BCD 的体积是 ▲ .10．在平面直角坐标系xOy 中，P 是曲线4(0)y x x x=+>上的一个动点，则点P 到直线x +y =0的距离的最小值是 ▲ .11．在平面直角坐标系xOy 中，点A 在曲线y =ln x 上，且该曲线在点A 处的切线经过点（-e ，-1)(e 为自然对数的底数），则点A 的坐标是 ▲ .12．如图，在ABC △中，D 是BC 的中点，E 在边AB 上，BE =2EA ，AD 与CE 交于点O .若6AB AC AO EC ⋅=⋅u u u r u u u r u u u r u u u r，则ABAC的值是 ▲ .13．已知tan 2π3tan 4αα=-⎛⎫+ ⎪⎝⎭，则πsin 24α⎛⎫+ ⎪⎝⎭的值是 ▲ . 14．设(),()f x g x 是定义在R 上的两个周期函数，()f x 的周期为4，()g x 的周期为2，且()f x 是奇函数.当2(]0,x ∈时，()f x =(2),01()1,122k x x g x x +<≤⎧⎪=⎨-<≤⎪⎩，其中k >0.若在区间(0，9]上，关于x 的方程()()f x g x =有8个不同的实数根，则k 的取值范围是 ▲ .二、解答题：本大题共6小题，共计90分．请在答题卡指定区域．．．．．．．内作答，解答时应写出文字说明、证明过程或演算步骤． 15．（本小题满分14分）在△ABC 中，角A ，B ，C 的对边分别为a ，b ，c ．（1）若a =3c ，b ，cos B =23，求c 的值； （2）若sin cos 2A B a b =，求sin()2B π+的值． 16．（本小题满分14分）如图，在直三棱柱ABC －A 1B 1C 1中，D ，E 分别为BC ，AC 的中点，AB =BC ． 求证：（1）A 1B 1∥平面DEC 1； （2）BE ⊥C 1E ．17．（本小题满分14分）如图，在平面直角坐标系xOy 中，椭圆C :22221(0)x y a b a b+=>>的焦点为F 1（–1、0），F 2（1，0）．过F 2作x 轴的垂线l ，在x 轴的上方，l 与圆F 2:222(1)4x y a -+=交于点A ，与椭圆C 交于点D .连结AF 1并延长交圆F 2于点B ，连结BF 2交椭圆C 于点E ，连结DF 1． 已知DF 1=52． （1）求椭圆C 的标准方程； （2）求点E 的坐标．18．（本小题满分16分）如图，一个湖的边界是圆心为O 的圆，湖的一侧有一条直线型公路l ，湖上有桥AB （AB 是圆O 的直径）．规划在公路l 上选两个点P 、Q ，并修建两段直线型道路PB 、QA ．规划要求：线段PB 、QA 上的所有点到点O 的距离均不小于圆．．．．O 的半径．已知点A 、B 到直线l 的距离分别为AC 和BD （C 、D 为垂足），测得AB =10，AC =6，BD =12（单位：百米）． （1）若道路PB 与桥AB 垂直，求道路PB 的长；（2）在规划要求下，P 和Q 中能否有一个点选在D 处？并说明理由；（3）在规划要求下，若道路PB 和QA 的长度均为d （单位：百米）.求当d 最小时，P 、Q 两点间的距离．19．（本小题满分16分）设函数()()()(),,,f x x a x b x c a b c =---∈R 、()f 'x 为f （x ）的导函数． （1）若a =b =c ，f （4）=8，求a 的值；（2）若a ≠b ，b =c ，且f （x ）和()f 'x 的零点均在集合{3,1,3}-中，求f （x ）的极小值； （3）若0,01,1a b c =<=…，且f （x ）的极大值为M ，求证:M ≤427． 20．（本小满分16分）定义首项为1且公比为正数的等比数列为“M －数列”.（1）已知等比数列{a n }*()n ∈N 满足：245324,440a a a a a a =-+=，求证：数列{a n }为“M －数列”； （2）已知数列{b n }*()n ∈N 满足：111221,n n n b S b b +==-，其中S n 为数列{b n }的前n 项和． ①求数列{b n }的通项公式；②设m 为正整数，若存在“M －数列”{c n }*()n ∈N ，对任意正整数k ，当k ≤m 时，都有1k k k c b c +剟成立，求m 的最大值．2019年普通高等学校招生全国统一考试（江苏卷）数学Ⅰ·参考答案一、填空题：本题考查基础知识、基本运算和基本思想方法.每小题5分，共计70分. 1.【答案】{1,6}.【解析】由题意利用交集的定义求解交集即可. 【详解】由题知，{1,6}A B =I .【点睛】本题主要考查交集的运算，属于基础题. 2.【答案】2【解析】本题根据复数的乘法运算法则先求得z ，然后根据复数的概念，令实部为0即得a 的值.【详解】2(a 2)(1i)222(2)i a ai i i a a i ++=+++=-++Q ，令20a -=得2a =.【点睛】本题主要考查复数的运算法则，虚部的定义等知识，意在考查学生的转化能力和计算求解能力. 3. 【答案】5【解析】结合所给的流程图运行程序确定输出的值即可. 【详解】执行第一次，1,1422x S S x =+==≥不成立，继续循环，12x x =+=； 执行第二次，3,2422x S S x =+==≥不成立，继续循环，13x x =+=； 执行第三次，3,342xS S x =+==≥不成立，继续循环，14x x =+=；执行第四次，5,442xS S x =+==≥成立，输出 5.S =【点睛】识别、运行程序框图和完善程序框图的思路： (1)要明确程序框图的顺序结构、条件结构和循环结构． (2)要识别、运行程序框图，理解框图所解决的实际问题． (3)按照题目的要求完成解答并验证． 4.【答案】[－1,7]【解析】由题意得到关于x 的不等式，解不等式可得函数的定义域. 【详解】由已知得2760x x +-≥, 即2670x x --≤ 解得17x -≤≤，故函数的定义域为[－1,7].【点睛】求函数的定义域，其实质就是以函数解析式有意义为准则，列出不等式或不等式组，然后求出它们的解集即可． 5.【答案】53【解析】由题意首先求得平均数，然后求解方差即可.【详解】由题意，该组数据的平均数为678891086+++++=，所以该组数据的方差是22222215[(68)(78)(88)(88)(98)(108)]63-+-+-+-+-+-=. 【点睛】本题主要考查方差的计算公式，属于基础题. 6.【答案】710【解析】先求事件的总数，再求选出的2名同学中至少有1名女同学的事件数，最后根据古典概型的概率计算公式得出答案.【详解】从3名男同学和2名女同学中任选2名同学参加志愿服务，共有2510C =种情况.若选出的2名学生恰有1名女生，有11326C C =种情况， 若选出的2名学生都是女生，有221C =种情况， 所以所求的概率为6171010+=. 【点睛】计数原理是高考考查的重点内容，考查的形式有两种，一是独立考查，二是与古典概型结合考查，由于古典概型概率的计算比较明确，所以，计算正确基本事件总数是解题的重要一环.在处理问题的过程中，应注意审清题意，明确“分类”“分步”，根据顺序有无，明确“排列”“组合”. 7.【答案】y =【解析】根据条件求b ，再代入双曲线的渐近线方程得出答案.【详解】由已知得222431-=，解得b =b = 因为0b >，所以b =因为1a =，所以双曲线的渐近线方程为y =.【点睛】双曲线的标准方程与几何性质，往往以小题的形式考查，其难度一般较小，是高考必得分题.双曲线渐近线与双曲线标准方程中的,a b 密切相关，事实上，标准方程中化1为0，即得渐近线方程. 8.【答案】16【解析】由题意首先求得首项和公差，然后求解前8项和即可.【详解】由题意可得：()()()25811191470989272a a a a d a d a d S a d ⎧+=++++=⎪⎨⨯=+=⎪⎩， 解得：152a d =-⎧⎨=⎩，则8187840282162S a d ⨯=+=-+⨯=. 【点睛】等差数列、等比数列的基本计算问题，是高考必考内容，解题过程中要注意应用函数方程思想，灵活应用通项公式、求和公式等，构建方程（组），如本题，从已知出发，构建1a d ,的方程组. 9.【答案】10【解析】由题意结合几何体的特征和所给几何体的性质可得三棱锥的体积. 【详解】因为长方体1111ABCD A B C D -的体积为120， 所以1120AB BC CC ⋅⋅=， 因为E 为1CC 的中点，所以112CE CC =， 由长方体的性质知1CC ⊥底面ABCD ，所以CE 是三棱锥E BCD -的底面BCD 上的高，所以三棱锥E BCD -的体积1132V AB BC CE =⨯⋅⋅=111111201032212AB BC CC =⨯⋅⋅=⨯=. 【点睛】本题蕴含“整体和局部”的对立统一规律.在几何体面积或体积的计算问题中，往往需要注意理清整体和局部的关系，灵活利用“割”与“补”的方法解题. 10.【答案】4【解析】将原问题转化为切点与直线之间的距离，然后利用导函数确定切点坐标可得最小距离【详解】当直线22gR r 平移到与曲线4y x x =+相切位置时，切点Q 即为点P 到直线22gR r的距离最小.由2411y'=-=-，得)x =，y =即切点Q ，则切点Q 到直线22gR r4=，故答案为：4．【点睛】本题考查曲线上任意一点到已知直线的最小距离，渗透了直观想象和数学运算素养.采取导数法和公式法，利用数形结合和转化与化归思想解题. 11.【答案】(e,1)【解析】设出切点坐标，得到切线方程，然后求解方程得到横坐标的值可得切点坐标. 【详解】设点()00,A x y ，则00ln y x =.又1y x'=， 当0x x =时，01y x '=， 点A 在曲线ln y x =上切线为0001()y y x x x -=-， 即00ln 1xy x x -=-， 代入点(),1e --，得001ln 1ex x ---=-， 即00ln x x e =，考查函数()ln H x x x =，当()0,1x ∈时，()0H x <，当()1,x ∈+∞时，()0H x >， 且()'ln 1H x x =+，当1x >时，()()'0,H x H x >单调递增， 注意到()H e e =，故00ln x x e =存在唯一的实数根0x e =，此时01y =，故点A 的坐标为(),1A e .【点睛】导数运算及切线的理解应注意的问题：一是利用公式求导时要特别注意除法公式中分子的符号，防止与乘法公式混淆．二是直线与曲线公共点的个数不是切线的本质，直线与曲线只有一个公共点，直线不一定是曲线的切线，同样，直线是曲线的切线，则直线与曲线可能有两个或两个以上的公共点． 12.【解析】由题意将原问题转化为基底的数量积，然后利用几何性质可得比值.【详解】如图，过点D 作DF //CE ，交AB 于点F ，由BE =2EA ，D 为BC 中点，知BF =FE =EA ,AO =OD .的()()()3632AO EC AD AC AE AB AC AC AE =-=+-u u u r u u u r u u u r u u u r u u u r u u ur u u u r u u u r u u u r g g g()223131123233AB AC AC AB AB AC AB AC AB AC ⎛⎫⎛⎫=+-=-+- ⎪ ⎪⎝⎭⎝⎭u u ur 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 u u u r u u u r g g g 22223211323322AB AC AB AC AB AC AB AC AB AC ⎛⎫=-+=-+= ⎪⎝⎭u u ur 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 u u u r u u u r g g g ， 得2213,22AB AC =u u ur u u u r即,AB =u u u r u u r故AB AC=【点睛】本题考查在三角形中平面向量的数量积运算，渗透了直观想象、逻辑推理和数学运算素养.采取几何法，利用数形结合和方程思想解题. 13.【解析】由题意首先求得tan α的值，然后利用两角和差正余弦公式和二倍角公式将原问题转化为齐次式求值的问题，最后切化弦求得三角函数式的值即可.【详解】由()tan 1tan tan tan 2tan 1tan 13tan 1tan 4αααααπααα-===-++⎛⎫+ ⎪-⎝⎭， 得23tan 5tan 20αα--=，解得tan 2α=，或1tan 3α=-.sin 2sin 2cos cos 2sin 444πππααα⎛⎫+=+ ⎪⎝⎭)22222sin cos cos sin sin 2cos 2sin cos αααααααα⎫+-=+⎪+⎝⎭222tan 1tan =2tan 1ααα⎫+-⎪+⎝⎭， 当tan 2α=时，上式222212==22110⎫⨯+-⎪+⎝⎭ 当1tan 3α=-时，上式=22112133=210113⎛⎫⎛⎫⎛⎫⨯-+--⎪ ⎪ ⎪⎝⎭⎝⎭⎪ ⎪⎛⎫-+ ⎪ ⎪⎝⎭⎝⎭综上，sin 24πα⎛⎫+= ⎪⎝⎭ 【点睛】本题考查三角函数的化简求值，渗透了逻辑推理和数学运算素养.采取转化法，利用分类讨论和转化与化归思想解题.14.【答案】13⎡⎢⎣⎭【解析】分别考查函数()f x 和函数()g x 图像的性质，考查临界条件确定k 的取值范围即可. 【详解】当(]0,2x ∈时，()f x =即()2211,0.x y y -+=≥又()f x 为奇函数，其图象关于原点对称，其周期为4，如图，函数()f x 与()g x 的图象，要使()()f x g x =在(0,9]上有8个实根，只需二者图象有8个交点即可.当1g()2x =-时，函数()f x 与()g x 的图象有2个交点； 当g()(2)x k x =+时，()g x 的图象为恒过点（-2，0）的直线，只需函数()f x 与()g x 的图象有6个交点.当()f x 与()g x 图象相切时，圆心（1，0）到直线20kx y k -+=的距离为1，1=，得k =函数()f x 与()g x 的图象有3个交点；当g()(2)x k x =+过点（1,1）时，函数()f x 与()x 的图象有6个交点，此时13k =，得13k =.综上可知，满足()()f x g x =在(0,9]上有8个实根的k 的取值范围为134⎡⎫⎪⎢⎪⎣⎭，. 【点睛】本题考点为参数的取值范围，侧重函数方程的多个实根，难度较大.不能正确画出函数图象的交点而致误，根据函数的周期性平移图象，找出两个函数图象相切或相交的临界交点个数，从而确定参数的取值范围. 二、解答题 15.【答案】（1）c =（2. 【解析】(1)由题意结合余弦定理得到关于c 的方程，解方程可得边长c 的值；(2)由题意结合正弦定理和同角三角函数基本关系首先求得cos B 的值，然后由诱导公式可得sin()2B π+的值.【详解】（1）因为23,3a cb B ===， 由余弦定理222cos 2a c b B ac +-=，得2222(3)323c c c c+-=⨯⨯，即213c =.所以3c =. （2）因为sin cos 2A Ba b =， 由正弦定理sin sin a b A B =，得cos sin 2B Bb b=，所以cos 2sin B B =.从而22cos (2sin )B B =，即()22cos 41cos B B =-，故24cos 5B =.因为sin 0B >，所以cos 2sin 0B B =>，从而cos 5B =.因此πsin cos 2B B ⎛⎫+== ⎪⎝⎭【点睛】本题主要考查正弦定理、余弦定理、同角三角函数关系、诱导公式等基础知识，考查运算求解能力.16.【答案】（1）见解析；（2）见解析.【解析】(1)由题意结合几何体的空间结构特征和线面平行的判定定理即可证得题中的结论； (2)由题意首先证得线面垂直，然后结合线面垂直证明线线垂直即可. 【详解】（1）因为D ，E 分别为BC ，AC 的中点，所以ED ∥AB .在直三棱柱ABC-A 1B 1C 1中，AB ∥A 1B 1， 所以A 1B 1∥ED .又因为ED ⊂平面DEC 1，A 1B 1⊄平面DEC 1， 所以A 1B 1∥平面DEC 1.（2）因为AB =BC ，E 为AC 的中点，所以BE ⊥AC .因为三棱柱ABC-A 1B 1C 1是直棱柱，所以CC 1⊥平面ABC . 又因为BE ⊂平面ABC ，所以CC 1⊥BE .因为C 1C ⊂平面A 1ACC 1，AC ⊂平面A 1ACC 1，C 1C ∩AC =C ， 所以BE ⊥平面A 1ACC 1.因为C 1E ⊂平面A 1ACC 1，所以BE ⊥C 1E .【点睛】本题主要考查直线与直线、直线与平面、平面与平面的位置关系等基础知识，考查空间想象能力和推理论证能力.17.【答案】（1）22143x y +=；（2）3(1,)2E --. 【解析】(1)由题意分别求得a ,b 的值即可确定椭圆方程；(2)解法一：由题意首先确定直线1AF 的方程，联立直线方程与圆的方程，确定点B 的坐标，联立直线BF 2与椭圆的方程即可确定点E 的坐标；解法二：由题意利用几何关系确定点E 的纵坐标，然后代入椭圆方程可得点E 的坐标. 【详解】（1）设椭圆C 的焦距为2c .因为F 1(－1，0)，F 2(1，0)，所以F 1F 2=2，c =1.又因为DF 1=52，AF 2⊥x 轴，所以DF 232==， 因此2a =DF 1+DF 2=4，从而a =2由b 2=a 2-c 2，得b 2=3.因此，椭圆C 的标准方程为22143x y +=.（2）解法一：由（1）知，椭圆C ：22143x y +=，a =2，因为AF 2⊥x 轴，所以点A 的横坐标为1.将x =1代入圆F 2的方程(x -1) 2+y 2=16，解得y =±4.因为点A 在x 轴上方，所以A (1，4).又F 1(-1，0)，所以直线AF 1：y =2x +2.由()2222116y x x y =+⎧⎪⎨-+=⎪⎩，得256110x x +-=， 解得1x =或115x =-.将115x =-代入22y x =+，得125y =-，因此1112(,)55B --.又F 2(1，0)，所以直线BF 2：3(1)4y x =-.由223(1)4143y x x y ⎧=-⎪⎪⎨⎪+=⎪⎩，得276130x x --=，解得1x =-或137x =. 又因为E 是线段BF 2与椭圆的交点，所以1x =-.将1x =-代入3(1)4y x =-，得32y =-.因此3(1,)2E --.解法二：由（1）知，椭圆C ：22143x y +=.如图，连结EF 1.因为BF 2=2a ，EF 1+EF 2=2a ，所以EF 1=EB ，从而∠BF 1E =∠B .因为F 2A =F 2B ，所以∠A =∠B ， 所以∠A =∠BF 1E ，从而EF 1∥F 2A.因为AF 2⊥x 轴，所以EF 1⊥x 轴.因为F 1(-1，0)，由221143x x y =-⎧⎪⎨+=⎪⎩，得32y =±.又因为E 是线段BF 2与椭圆的交点，所以32y =-. 因此3(1,)2E --.【点睛】本题主要考查直线方程、圆的方程、椭圆方程、椭圆的几何性质、直线与圆及椭圆的位置关系等基础知识，考查推理论证能力、分析问题能力和运算求解能力. 18.【答案】（1）15（百米）；（2）见解析；（3）17+. 【解析】解：解法一：（1）过A 作AE BD ⊥，垂足为E .利用几何关系即可求得道路PB 的长； （2）分类讨论P 和Q 中能否有一个点选在D 处即可.（3）先讨论点P 的位置，然后再讨论点Q 的位置即可确定当d 最小时，P 、Q 两点间的距离． 解法二：（1）建立空间直角坐标系，分别确定点P 和点B 的坐标，然后利用两点之间距离公式可得道路PB 的长；（2）分类讨论P 和Q 中能否有一个点选在D 处即可.（3）先讨论点P 的位置，然后再讨论点Q 的位置即可确定当d 最小时，P 、Q 两点间的距离． 【详解】解法一：（1）过A 作AE BD ⊥，垂足为E . 由已知条件得，四边形ACDE 为矩形， 6, 8DE BE AC AE CD =====. 因为PB ⊥AB ，所以84cos sin 105PBD ABE ∠=∠==. 所以12154cos 5BD PB PBD ===∠. 因此道路PB 的长为15（百米）.（2）①若P 在D 处，由（1）可得E 在圆上，则线段BE 上的点（除B ，E ）到点O 的距离均小于圆O 的半径，所以P 选在D 处不满足规划要求.②若Q 在D 处，连结AD ，由（1）知10AD ==，从而2227cos 0225AD AB BD BAD AD AB +-∠==>⋅，所以∠BAD 为锐角.所以线段AD 上存在点到点O 的距离小于圆O 的半径.因此，Q 选在D 处也不满足规划要求. 综上，P 和Q 均不能选在D 处. （3）先讨论点P 的位置. 当∠OBP <90°时，线段PB 上存在点到点O 的距离小于圆O 的半径，点P 不符合规划要求；当∠OBP ≥90°时，对线段PB 上任意一点F ，OF ≥OB ，即线段PB 上所有点到点O 的距离均不小于圆O 的半径，点P 符合规划要求.设P 1为l 上一点，且1PB AB ⊥，由（1）知，115P B =，此时11113sin cos 1595PD PB PBD PB EBA =∠=∠=⨯=； 当∠OBP >90°时，在1PPB △中，115PB PB >=. 由上可知，d ≥15. 再讨论点Q 的位置.由（2）知，要使得QA ≥15，点Q 只有位于点C 的右侧，才能符合规划要求.当QA =15时，CQ ==此时，线段QA 上所有点到点O 的距离均不小于圆O 的半径.综上，当PB ⊥AB ，点Q 位于点C 右侧，且CQ =d 最小，此时P ，Q 两点间的距离PQ =PD +CD +CQ =17+因此，d 最小时，P ，Q 两点间的距离为17+. 解法二：（1）如图，过O 作OH ⊥l ，垂足为H.以O 为坐标原点，直线OH 为y 轴，建立平面直角坐标系.因为BD =12，AC =6，所以OH =9，直线l 的方程为y =9，点A ，B 的纵坐标分别为3，−3. 因为AB 为圆O 的直径，AB =10，所以圆O 的方程为x 2+y 2=25. 从而A （4，3），B （−4，−3），直线AB 的斜率为34. 因为PB ⊥AB ，所以直线PB 的斜率为43-， 直线PB 的方程为42533y x =--.所以P （−13，9），15PB ==.因此道路PB 的长为15（百米）.（2）①若P 在D 处，取线段BD 上一点E （−4，0），则EO =4<5，所以P 选在D 处不满足规划要求. ②若Q 在D 处，连结AD ，由（1）知D （−4，9），又A （4，3）， 所以线段AD ：36(44)4y x x =-+-≤≤.在线段AD 上取点M （3，154），因为5OM =<=，所以线段AD 上存在点到点O 的距离小于圆O 的半径.因此Q 选在D 处也不满足规划要求. 综上，P 和Q 均不能选在D 处. （3）先讨论点P 的位置. 当∠OBP <90°时，线段PB 上存在点到点O 的距离小于圆O 的半径，点P 不符合规划要求；当∠OBP ≥90°时，对线段PB 上任意一点F ，OF ≥OB ，即线段PB 上所有点到点O 的距离均不小于圆O 的半径，点P 符合规划要求.设P 1为l 上一点，且1PB AB ⊥，由（1）知，115P B =，此时()113,9P -； 当∠OBP >90°时，在1PPB △中，115PB PB >=.由上可知，d ≥15. 再讨论点Q 的位置.由（2）知，要使得QA≥15，点Q 只有位于点C 的右侧，才能符合规划要求.当QA =15时，设Q （a ，9），由15(4)AQ a ==>，得a =4+Q （4+9），此时，线段QA 上所有点到点O 的距离均不小于圆O 的半径.综上，当P （−13，9），Q （4+9）时，d 最小，此时P ，Q 两点间的距离4(13)17PQ =+-=+因此，d 最小时，P ，Q 两点间的距离为17+.【点睛】本题主要考查三角函数的应用、解方程、直线与圆等基础知识，考查直观想象和数学建模及运用数学知识分析和解决实际问题的能力. 19.【答案】（1）2a =；（2）见解析；（3）见解析. 【解析】（1）由题意得到关于a 的方程，解方程即可确定a 的值；（2）由题意首先确定a ,b ,c 的值从而确定函数的解析式，然后求解其导函数，由导函数即可确定函数的极小值.（3）由题意首先确定函数的极大值M 的表达式，然后可用如下方法证明题中的不等式： 解法一：由函数的解析式结合不等式的性质进行放缩即可证得题中的不等式； 解法二：由题意构造函数，求得函数在定义域内的最大值， 因为01b <≤，所以1(0,1)x ∈．当(0,1)x ∈时，2()()(1)(1)f x x x b x x x =--≤-．令2()(1),(0,1)g x x x x =-∈，则1()3(1)3g'x x x ⎛⎫=-- ⎪⎝⎭．令()0g'x =，得1x =．列表如下：所以当13x =时，()g x 取得极大值，且是最大值，故max 14()327g x g ⎛⎫== ⎪⎝⎭．所以当(0,1)x ∈时，4()()27f x g x ≤≤，因此427M ≤．【详解】（1）因为a b c ==，所以3()()()()()f x x a x b x c x a =---=-．因为(4)8f =，所以3(4)8a -=，解得2a =． （2）因为b c =，所以2322()()()(2)(2)f x x a x b x a b x b a b x ab =--=-+++-，从而2()3()3a b f 'x x b x +⎛⎫=-- ⎪⎝⎭．令()0f 'x =，得x =b 或23a b x +=． 因为2,,3a ba b +，都在集合{3,1,3}-中，且a b ≠，所以21,3,33a ba b +===-．此时2()(3)(3)f x x x =-+，()3(3)(1)f 'x x x =+-． ()0f 'x =所以()f x 的极小值为2(1)(13)(13)32f =-+=-．（3）因为0,1a c ==，所以32()()(1)(1)f x x x b x x b x bx =--=-++，2()32(1)f 'x x b x b =-++．因为01b <≤，所以224(1)12(21)30b b b ∆=+-=-+>， 则有2个不同的零点，设为()1212,x x x x <．由()0f 'x =，得121133b b x x ++==．所以()f x 的极大值()1M f x =． 解法一：()321111(1)M f x x b x bx ==-++()()221111211(1)32(1)3999b b x b b b x b x b x -+++⎛⎫=-++--+ ⎪⎝⎭ ()2321(1)(1)227927b b b b b --+++=++23(1)2(1)(1)2272727b b b b +-+=-+(1)24272727b b +≤+≤．因此427M ≤．解法二：因为01b <≤，所以1(0,1)x ∈．当(0,1)x ∈时，2()()(1)(1)f x x x b x x x =--≤-．令2()(1),(0,1)g x x x x =-∈，则1()3(1)3g'x x x ⎛⎫=-- ⎪⎝⎭．令()0g'x =，得13x =．列表如下：所以当13x =时，()g x 取得极大值，且是最大值，故max 14()327g x g ⎛⎫== ⎪⎝⎭． 所以当(0,1)x ∈时，4()()27f x g x ≤≤，因此427M ≤．【点睛】本题主要考查利用导数研究函数的性质，考查综合运用数学思想方法分析与解决问题以及逻辑推理能力．20.【答案】（1）见解析；（2）①b n =n ()*n ∈N ；②5.【解析】（1）由题意分别求得数列的首项和公比即可证得题中的结论；（2）①由题意利用递推关系式讨论可得数列{b n }是等差数列，据此即可确定其通项公式；②由①确定k b 的值，将原问题进行等价转化，构造函数，结合导函数研究函数的性质即可求得m 的最大值． 【详解】（1）设等比数列{a n }的公比为q ，所以a 1≠0，q ≠0.由245321440a a a a a a =⎧⎨-+=⎩，得244112111440a q a q a q a q a ⎧=⎨-+=⎩，解得112a q =⎧⎨=⎩．因此数列{}n a 为“M —数列”.（2）①因为1122n n n S b b +=-，所以0n b ≠． 由1111,b S b ==得212211b =-，则22b =.由1122n n n S b b +=-，得112()n n n n n b b S b b ++=-， 当2n ≥时，由1n n n b S S -=-，得()()111122n n n nnn n n n b b b b b b b b b +-+-=---， 整理得112n n n b b b +-+=．所以数列{b n }是首项和公差均为1的等差数列. 因此，数列{b n }的通项公式为b n =n ()*n N∈.②由①知，b k =k ，*k N ∈.因为数列{c n }为“M –数列”，设公比为q ，所以c 1=1，q >0.因为c k ≤b k ≤c k +1，所以1k kq k q -≤≤，其中k =1，2，3，…，m . 当k =1时，有q ≥1；当k =2，3，…，m 时，有ln ln ln 1k kq k k ≤≤-． 设f （x ）=ln (1)x x x >，则21ln ()xf 'x x -=． ()0f 'x =x =e .因为ln 2ln8ln 9ln 32663=<=，所以max ln 3()(3)3f k f ==．取q =k =1，2，3，4，5时，ln ln kq k≤，即k k q ≤， 经检验知1k q k -≤也成立．因此所求m 的最大值不小于5．若m ≥6，分别取k =3，6，得3≤q 3，且q 5≤6，从而q 15≥243，且q 15≤216， 所以q 不存在.因此所求m 的最大值小于6. 综上，所求m 的最大值为5．【点睛】本题主要考查等差和等比数列的定义、通项公式、性质等基础知识，考查代数推理、转化与化归及综合运用数学知识探究与解决问题的能力．数学Ⅱ(附加题)21.【答案】（1）115106⎡⎤⎢⎥⎣⎦；（2）121,4λλ==. 【解析】(1)利用矩阵的乘法运算法则计算2A 的值即可；(2)首先求得矩阵的特征多项式，然后利用特征多项式求解特征值即可.【详解】（1）因为3122⎡⎤=⎢⎥⎣⎦A ，所以231312222⎡⎤⎡⎤=⎢⎥⎢⎥⎣⎦⎣⎦A =3312311223222122⨯+⨯⨯+⨯⎡⎤⎢⎥⨯+⨯⨯+⨯⎣⎦=115106⎡⎤⎢⎥⎣⎦． （2）矩阵A 的特征多项式为231()5422f λλλλλ--==-+--.令()0f λ=，解得A 的特征值121,4λλ==.【点睛】本题主要考查矩阵的运算、特征值等基础知识，考查运算求解能力．22.【答案】（1（2）2.【解析】(1)由题意，在OAB △中，利用余弦定理求解AB 的长度即可； (2)首先确定直线的倾斜角和直线所过的点的极坐标，然后结合点B 的坐标结合几何性质可得点B 到直线l 的距离.【详解】（1）设极点为O .在△OAB 中，A （3，4π），B ，2π），由余弦定理，得AB =（2）因为直线l 的方程为sin()34ρθπ+=，则直线l 过点)2π，倾斜角为34π．又)2B π，所以点B 到直线l 的距离为3sin()242ππ⨯-=.【点睛】本题主要考查曲线的极坐标方程等基础知识，考查运算求解能力． 23.【答案】1{|1}3x x x <->或.【解析】由题意结合不等式的性质零点分段即可求得不等式的解集. 【详解】当x <0时，原不等式可化为122x x -+->，解得x <–13： 当0≤x ≤12时，原不等式可化为x +1–2x >2，即x <–1，无解； 当x >12时，原不等式可化为x +2x –1>2，解得x >1. 综上，原不等式的解集为1{|1}3x x x <->或.【点睛】本题主要考查解不等式等基础知识，考查运算求解和推理论证能力．【必做题】24.【答案】（1）5n =；（2）-32.【解析】(1)首先由二项式展开式的通项公式确定234,,a a a 的值，然后求解关于n 的方程可得n 的值； (2)解法一：利用(1)中求得的n 的值确定有理项和无理项从而可得a ,b 的值，然后计算223a b -的值即可；解法二：利用(1)中求得的n 的值，由题意得到(51-的展开式，最后结合平方差公式即可确定223ab -的值.【详解】（1）因为0122(1)C C C C 4n n n n n n n x x x x n +=++++≥L ，，所以2323(1)(1)(2)C ,C 26n nn n n n n a a ---====， 44(1)(2)(3)C 24nn n n n a ---==． 因为23242a a a =，所以2(1)(2)(1)(1)(2)(3)[]26224n n n n n n n n n ------=⨯⨯，解得5n =．（2）由（1）知，5n =．5(1(1n =+02233445555555C C C C C C =++++a =+解法一：因为*,a b ∈N ，所以024135555555C 3C 9C 76,C 3C 9C 44a b =++==++=，从而222237634432a b -=-⨯=-． 解法二：50122334455555555(1C C (C (C (C (C (=+++++02233445555555C C C C C C =--+-．因为*,a b ∈N ，所以5(1a =-．因此225553((1(1(2)32a b a a -=+-=+⨯=-=-．【点睛】本题主要考查二项式定理、组合数等基础知识，考查分析问题能力与运算求解能力.25.【答案】（1）见解析；（2）见解析.【解析】(1)由题意首先确定X 可能的取值，然后利用古典概型计算公式求得相应的概率值即可确定分布列； (2)将原问题转化为对立事件的问题求解()P X n >的值，据此分类讨论①.b d =，②.0,1b d ==，③.0,2b d ==，④.1,2b d ==四种情况确定X 满足X n >的所有可能的取值，然后求解相应的概率值即可确定()P X n ≤的值.【详解】（1）当1n =时，X的所有可能取值是12X的概率分布为22667744(1),(C 15C 15P X P X ======，22662222(2),(C 15C 15P X P X ======．（2）设()A a b ，和()B c d ，是从n M 中取出的两个点． 因为()1()P X n P X n ≤=->，所以仅需考虑X n >的情况．①若b d =，则AB n ≤，不存在X n >的取法；②若01b d ==，，则AB =≤所以X n >当且仅当AB =此时0 a c n ==，或 0a n c ==，，有2种取法； ③若02b d ==，，则AB =≤3n ≥n ≤，所以X n >当且仅当AB =0 a c n ==，或 0a n c ==，，有2种取法； ④若12b d ==，，则AB =≤所以X n >当且仅当AB =此时0 a c n ==，或 0a n c ==，，有2种取法． 综上，当X n >时，X22242442(,(C C n n P X P X ++====．因此，2246()1((1C n P X n P X P X +≤=-=-==-．【点睛】本题主要考查计数原理、古典概型、随机变量及其概率分布等基础知识，考查逻辑思维能力和推理论证能力．。
江苏2019年高考英语试题卷(含答案和解析)
2019年普通高等学校招生全国统一考试(江苏卷)英语(满分:120分钟，考试时间:120分)第二部分:英语知识运用(共两节，满分35分)第一节:单项填空(共15小题；每小题1分，满分15分)请认真阅读下面各题，从题中所给的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。
例:It is generally considered unwise to give a child _______ he or she wants.A. howeverB. whateverC. whicheverD. whenever答案是B。
21.We have entered into an age _______ dreams have the best chance of coming true.A. whichB. whatC. whenD. that【答案】C【解析】【详解】考查定语从句。
句意：我们已经进入到了一个时代，在这个时代梦想实现的机会最大。
句中先行词为an age（一个时代），且先行词在从句中做时间状语，所以关系词用when。
故选C。
22.The musician along with his band members ___________ ten performances in the last three months.A. givesB. has givenC. have givenD. give【答案】B【解析】【详解】考查现在完成时与主谓一致。
句意：在过去的三个月里，这名音乐家与他的乐队成员已经完成了十场演出。
由“in the last three months”可知，这句话的时态为现在完成时，故排除AD选项。
本句主语为the musician，为第三人称单数形式，句中的“along with his band members”是附加成分，故谓语动词要用第三人称单数形式。
故选B。
2019年江苏省高考英语试卷(附答案解析)
2019年江苏省高考英语试卷第二部分：英语知识运用（共两节，满分 35 分）第一节：单项填空（共15小题；每小题1分，满分15分）请认真阅读下面各题，从题中所给的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．例：It is generally consideredunwise to give a child_______he or she wants.A.however B.whatever C.whicheverD.whenever 答案是B．1. We have entered into an age_______dreams have the best chance of coming true．（）A.whichB.whatC.whenD.that2. The musician along with his band members_______ten performances in the last three months．（）A.givesB.has givenC.have givenD.give3. The doctor shares his phone number with the patients_______they need medical assistance．（）A.if onlyB.as ifC.even thoughD.in case4. More wind power stations will_______to meet the demand for clean energy．（）A.take upB.clear upC.hold upD.spring up5. Scientists have obtained more evidence_______plastic is finding its way into the human body．（）A.whatB.thatC.whichD.where6. Nowadays the_______for travelling is shifted from shopping to food and scenery．（）A.priorityB.potentialC.proportionD.pension7. Favorable policies are _______to encourage employees' professional development．（）A.in effectB.in commandC.in turnD.in shape8. Unlike traditional gyms，app﹣backed gyms offer people_______options to exercise．（）A.casualB.regularC.flexibleD.tight9. A few months after he had arrived in China，Mr．Smith_______in love with the people and culture there．（）A.would fallB.had fallenC.has fallenD.fell10. _______the convenience of digital payment，many senior citizens started to use smart phones．（）A.To enjoyB.EnjoyingC.To have enjoyedD.Enjoy11. What a pity! You missed the sightseeing or we_______a good time together．（）A.hadB.will haveC.would have hadD.had had12. China's image is improving steadily， with more countries_______its role in international affairs．（）A.recognizingB.being recognizedC.to be recognizedD.recognized13. They are trying to make sure that 5G terminals_______by 2022 for the Beijing Winter Olympics．（）A.will installB.will have been installedC.are installedD.have been installed14. A city is the product of the human hand and mind，_______man's intelligence and creativity．（）A.resemblingB.reflectingC.reviewingD.restoring15. ﹣Let's take a coffee break．﹣_______We've been working for hours．（）A.Why bother？B.What for？C.You got me there．D.You said it．第二节：完形填空（满分20分）请认真阅读下面短文，从短文后各题所给的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．16. Wildlife has been greatly threatened in the modern age．There are species（物种）that are （1）_______ every day．The white﹣naped crane is a typical example．So scientists are trying their best to（2）_______the species from going out of existence．Chris and Tim work at a zoo, helping endangered cranes with their （3）_______．Emma, a female crane, has been in their （4）_______since she arrived in 2004． Born at an international crane foundation, Emma was（5）_______by humancaretakers．This led to an unexpected（6）_______, though she had a wonderful time there．Emma had （7）_______taken herself as a crane and become deeply attached to humans．She（8）_______to live with male cranes, and even had a（9）_______for killing some of them, which made it （10）_______for her to become a mother．（11）_______, the two zookeepers didn't want to see the extinction （灭绝） of this precious species．With their patience and efforts, they successfully developed a （12）_______ of artificial breeding（人工繁殖） and natural reproduction．This（13）_______Emma to give birth to five baby cranes．The two keepers are proud of their productive work． But before they can be（14）_______, more efforts must be made, because the population of the crane in the wild is on the（15）_______, and many other species appear headed toward extinction．（16）_______, not everyone has realized that wildlife has thoughts, feelings, and most importantly, equal rights to survive．How can we （17）_______the ever﹣widening gap that separates us from other animals? Chris and Tim offered us the（18）_______: human beings took it for grantedthat their（19）_______held all the solutions, but maybe their hearts can be a better（20）_______．（1）A.growingB.migratingpetingD.disappearing（2）A.banB.saveC.splitD.remove（3）A.abortionB.recreationC.reproductionD.administration（4）A.careB.eyeC.mindD.story（5）A.foundB.chosenC.raisedD.seized（6）A.bonusB.consequenceC.victoryD.sacrifice（7）A.neverB.alwaysC.unluckilyD.cheerfully（8）A.likedB.refusedC.decidedD.hesitated（9）A.giftB.skillC.concernD.reputation（10）A.illegalB.inspiringC.importantD.impossible（11）A.ThereforeB.MoreoverC.HoweverD.Instead（12）binationB.collectionC.strategyD.system（13）A.forcedB.forbadeC.taughtD.enabled（14）A.defeatedB.gratefulC.assuredD.tolerant（15）A.listB.riseC.agendaD.decline（16）A.In contrastB.After allC.By the wayD.On the contrary（17）A.leaveB.bridgeC.openD.identify（18）A.courseB.excuseC.answerD.reward（19）A.brainsB.behaviorsC.servicesD.projects（20）A.guideB.treatC.examplepanion第三部分：阅读理解（满分30分）请认真阅读下列短文，从短文后各题所给的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．17.Whatever your age or interests, Buxton has something to see or do to makeyour visit truly memorable．________If you desire physical activities, you can choose activities from swimming to horse riding． Explore the heights with Go Ape, the high wire forest adventure course, or journey beneath the earth at Poole's Cavern． And don't forget: weare surrounded by a natural playground just perfect forwalking, caving, climbing and cycling．________Buxton is justifiably proud of its cultural life and you'll find much to suit all tastes with art, music, opera and the performing arts at Buxton Opera House & Pavilion Arts Centre and Green Man Gallery． There are plenty of opportunities for the creative person to become involved, including workshops and events．________Children love the small train and playgrounds in the Pavilion Gardens andthere's plenty more to explore at the Buxton Museum． There's a new indoor play centre, plus the special events and workshops, and others during school holiday periods．（1）If you want to take an underground journey，which place is the best choice？________A.Poole's Cavern．B.Pavilion Gardens．C.Buxton Museum．D.Green Man Gallery．．（2）Buxton Opera House & Pavilion Arts Centre is special because it offers________．A.rides in small trainsB.courses in modern artsC.artistic and cultural activitiesD.basic courses in horse riding．18. In the 1960s, while studying the volcanic history of Yellowstone National Park, Bob Christiansen became puzzled about something that, oddly, had not troubled anyone before: he couldn't find the park's volcano．It had been known for a long time that Yellowstone was volcanic in nature﹣that's what accounted for all its hot springs and other steamy features．But Christiansen couldn't find the Yellowstone volcano anywhere．Most of us, when we talk about volcanoes, think of the classic cone（圆锥体） shapes of a Fuji or Kilimanjaro, which are created when erupting magma （岩浆） piles up．These can form remarkably quickly．In 1943, a Mexican farmer was surprised to see smoke rising from a small part of his land．In one week he was the confused owner of a cone five hundred feet high．Within two years it had topped out at almost fourteen hundred feet and was more than half a mile across．Altogether there are some ten thousand of these volcanoes on Earth, all but a few hundred of them extinct．There is, however, a second less known type of volcano that doesn't involve mountain building．These are volcanoes so explosive that they burst open in a single big crack, leaving behind a vast hole, the caldera．Yellowstone obviously was of this second type, but Christiansen couldn't find thecaldera anywhere．Just at this time NASA decided to test some new high﹣altitude cameras by taking photographs of Yellowstone．A thoughtful official passed on some of the copies to the park authorities on the assumption that they might make a nice ________ for one of the visitors' centers．As soon as Christiansen saw the photos, he realized why he had failed to spot the caldera: almost the whole park﹣22 million acres﹣was caldera．The explosion had left a hole more than forty miles across﹣much too huge to be seen from anywhere at ground level．At some time in the past Yellowstone must have blown up with a violence far beyond the scale of anything known to humans．（1）What puzzled Christiansen when he was studying Yellowstone？________A.Its complicated geographical features．B.Its ever﹣lasting influence on tourism．C.The mysterious history of the park．D.The exact location of the volcano．．（2）What does the second paragraph mainly talk about？________A.The shapes of volcanoes．B.The impacts of volcanoes．C.The activities of volcanoes．D.The heights of volcanoes．．（3）What does the underlined word "blow﹣up" in the last paragraph most probably mean？________A.Hot﹣air balloon．B.Digital camera．C.Big photograph．D.Bird's view．19. Who cares if people think wrongly that the internet has had more important influences than the washing machine? Why does it matter that people are more impressed by the most recent changes?It would not matter if these misjudgments were just a matter of people'sopinions． However, they have real impacts, as they result in misguided use of scarce resources．The fascination with the ICT （Information and Communication Technology）revolution, represented by the internet, has made some rich counties wrongly conclude that making things is so "yesterday" that they should try to live on ideas． This belief in "post﹣industrial society" has led those countries to neglect their manufacturing sector （制造业）, with negative consequences for their economies．Even more worryingly, the fascination with the internet by people in rich countries has moved the international community to worry about the "digital divide" between the richcountries and the poor countries． This has led companies and individuals to donate money to developing countries to buy computer equipment and internet facilities． The question, however, is whether this is what the developing countries need themost． Perhaps giving money for those less fashionable things such as diggingwells, extending electricity networks and making more affordable washing machines would have improved people's lives more than giving every child a laptop computer or setting up internet centres in rural villages． I am not saying that those things are necessarily more important, but many donators have rushed into fancy programmes without carefully assessing the relative long﹣term costs and benefits of alternative uses of their money．In yet another example, a fascination with the new has led people to believe that the recent changes in the technologies of communications and transportation are so revolutionary that now we live in a"borderless world"． As a result, in the last twenty years or so, many people have come to believe that whatever change is happening today is the result of great technological progress, going against which will be like trying to turn the clock back． Believing in such a world, many governments have put an end to some of the very necessary regulations on cross﹣border flows of capital, labour and goods, with poor results．Understanding technological trends in very important for correctly designing economic policies, both at the national and the international levels, and for making the right career choices at the individual level． However, our fascination with the latest, and our under﹣valuation of what has already become common, can, and has, led us in all sorts of wrong directions．（1）Misjudgments on the influences of new technology can lead to________．A.a lack of confidence in technologyB.a slow progress in technologyC.a conflict of public opinionsD.a waste of limited resources．（2）The example in Paragraph 4 suggests that donators should________．A.take people's essential needs into accountB.make their programmes attractive to peopleC.ensure that each child gets financial supportD.provide more affordable internet facilities．（3）What has led many governments to remove necessary regulations？________A.Neglecting the impacts of technological advances．B.Believing that the world has become borderless．C.Ignoring the power of economic development．D.Over﹣emphasizing the role of international communication．．（4）What can we learn from the passage？________A.People should be encouraged to make more donations．B.Traditional technology still has a place nowadays．C.Making right career choices is crucial to personal success．D.Economic policies should follow technological trends．20. The 65﹣year﹣old Steve Goodwin was found suffering from early Alzheimer's（阿尔兹海默症）, He was losing his memory．A software engineer by profession, Steve was a keen lover of the piano, and the only musician in his family． Music was his true passion, though he had never performed outside the family．Melissa, his daughter, felt it more than worthwhile to save his music, to which she fell asleep each night when she was young． She thought about hiring a professional pianist to work with her father．Naomi, Melissa's best friend and a talented pianist, got to know about this and showed willingness to help．"Why do this? "Steve wondered．"Because she cares．"Melissa said．Steve nodded, tear in eye．Naomi drove to the Goodwin home she told Steve she'd love to hear him play． Steve moved to the piano and sat at the bench, hands trembling as he gently placed his fingers on the keys．Naomi put a small recorder near the piano． Starts and stops and mistakes． Long pauses, heart sinking． But Steve pressed on, playing for the first time in his life for a stranger．"It was beautiful, "Naomi said after listening to the recording．"The music was worth saving．"Her responsibility, her privilege, would be to rescue it． The music was still in Steve Goodwin． It was hidden in rooms with doors about to be locked．Naomi and Steve met every other week and spent hours together． He'd move his fingers clumsily on the piano, and then she'd take his place． He struggled to explain what he heard in his head． He stood by the piano, eyes closed, listening for the first time to his own work being played by someone else．Steve and Naomi spoke in musical code: lines, beats, intervals, moving from the root to end a song in a new key． Steve heard it． All of it． He just couldn't play it．Working with Naomi did wonders for Steve． It had excited within him the belief he could write one last song． One day, Naomi received an email．Attached was a recording, a recording of loss and love, of the fight．Steve called it"Melancholy Flower．"Naomi heard multiple stops and starts, Steve struggling, searching while his wife Joni called him"honey"and encouraged him． The task was so hard, and Steve, angry and upset, said he was quitting． Joni praised him, telling her husband this could be his signature piece．Naomi managed to figure out 16 of Steve's favorite, and most personal, songs．With Naomi's help, the Goodwin family found a sound engineer to record Naomi playing Steve's songs． Joni thought that would be the end． But it wasn't．In the months leading up to the 2016 Oregon Repertory Singers Christmas concert, Naomi told the director she had a special one in mind: "Melancholy Flower．"She told the director about her project with Steve． The director agreed to add it to the playing list． But Naomi would have to ask Steve's permission． He considered it an honor． After the concert, Naomi told the family that Steve's music was beautiful and professional． It needed to be shared in public．The family rented a former church in downtown Portland and scheduled a concert． Bythe day of the show, more than 300 people had said they would attend．By then, Steve was having a hard time remembering the names of some of his friends． He knew the path his life was now taking． He told his family he was at peace．Steve arrived and sat in the front row, surrounded by his family． The house lights faded． Naomi took the stage． Her fingers． His heart．（1）Why did Melissa want to save her father's music？________A.His music could stop his disease from worsening．B.She wanted to please her dying old father．C.His music deserved to be preserved in the family．D.She wanted to make her father a professional．．（2）After hearing Steve's playing，Naomi________．A.refused to make a comment on itB.was deeply impressed by his musicC.decided to free Steve from sufferingD.regretted offering help to her friend．（3）How can the process of Steve's recording be described？________A.It was slow but productive．B.It was beneficial to his health．C.It was tiresome for Naomi．D.It was vital for Naomi's career．．（4）Before Steve finished "Melancholy Flower，"his wife Joni________．A.thought the music talent of Steve was exhaustedB.didn't expect the damage the disease brought aboutC.didn't fully realize the value of her husband's musicD.brought her husband's music career to perfection．（5）How did Steve feel at the concert held in downtown Portland？________A.He felt concerned about his illness．B.He sensed a responsibility for music．C.He regained his faith in music．D.He got into a state of quiet．．（6）What can be a suitable title for the passage？________A.The Kindness of FriendsB.The Power of MusicC.The Making of a MusicianD.The Value of Determination．第四部分：任务型阅读（满分10分）请认真阅读下面短文，并根据所读内容在文章后表格中的空格里填入一个最恰当的单词．请将答案写在答题卡上相应题号的横线上．每个空格只填一个单词．21.The Cost of ThinkingDespite their many differences，all human beings share several defining characteristics，such as large brains and the ability to walk upright on two legs．The first unique human characteristic is that humans have extraordinarily large brains compared with other animals．It seems obvious that evolution should select for larger brains． Mammals（哺乳动物）weighing sixty kilograms have an average brain size of 200 cm3． Modern man has a brain averaging 1200﹣1400 cm3．We are so fond of our high intelligence that we assume that when it comes to brain power，more must be better． Unfortunately， that is not the case．The fact is that a huge brain is a huge drain﹣consumption of energy﹣on the body． It's not easy to carry around，especially when boxed inside a massive skull（颅骨）． It's even harder to provide energy． In modern man，the brain accounts for about 2﹣3% of total body weight， but it consumes 25% of the body's energy when the body is at rest． By comparison，the brains of apes （类人猿） require only 8% of rest﹣time energy． Early humans paid for their large brains in two ways． Firstly， they spent more time in search of food． Secondly，their muscles grew smaller and weaker． It's hardly an obvious conclusion that this is a good way to survive． A chimpanzee（黑猩猩）can't win an argument with a modern man，but it can tear the man apart like a rag doll．Another unique human characteristic is that we walk upright．Standing up，it's easier to find food or enemies． In addition，their arms that are unnecessary for moving around are freed for other purposes，like throwing stones or signaling．As a result，humans can perform very complex tasks with their hands．Yet walking upright has its disadvantage． The bone structure of our ancestors developed for millions of years to support a creature that walked on all fours and had a relatively small head． Adjusting to an upright position was quite a challenge，especially when the bones had to support an extra﹣large skull． Humankind paid for its broad vision and skillful hands with backaches and painful necks．We assume that a large brain makes huge advantages．It seems obvious that these have made humankind the most powerful animal on earth． But humans enjoyed all of these advantages for a full 2 million years during which they remained weak and marginal creatures． Thus humans who lived a million years ago， despite their big brains and sharpstone tools， lived in constant fear of meat﹣eating animals．22. 请阅读下面文字，并按照要求用英语写一篇150词左右的文章．Li Jiang： Have you heard this？ A group of exchange students from the UK are visiting our school next month．Su Hua： Yes， I have． Some are already recommending the traditional Chinese dress for the welcome ceremony．Li Jiang：But it seems people have different opinions．Su Hua： What do you think？Li Jiang： I think it's a good idea． It's an opportunity to make the Chinese culture better known to international students．Su Hua： I agree． But we don't have to dress that way． That's not our dailystyle． Besides， it's not very convenient．Li Jiang： You see， it's the Chinese culture that the British friends are coming for． Just the right occasion．Su Hua： I prefer the school uniform． It's nice． It's also a better display of our school culture．【写作内容】1．用约30个词概括上述信息的主要内容；2．在上述场合，你是否倾向于穿中国传统服装？请说明理由（不少于两点）．【写作要求】1．写作过程中不能直接引用原文语句；2．作文中不能出现真实姓名和学校名称；3．不必写标题．内容完整，语言规范，语篇连贯，词数适当．参考答案与试题解析2019年江苏省高考英语试卷第二部分：英语知识运用（共两节，满分 35 分）第一节：单项填空（共15小题；每小题1分，满分15分）请认真阅读下面各题，从题中所给的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．例：It is generally considered unwise to give a child_______he or she wants.A.however B.whatever C.whicheverD.whenever 答案是B．1.【答案】C2.【答案】B3.【答案】D4.【答案】D5.【答案】B6.【答案】A7.【答案】A8.【答案】C9.【答案】D10.【答案】A11.【答案】C12.【答案】A13.【答案】B14.【答案】B15.【答案】D第二节：完形填空（满分20分）请认真阅读下面短文，从短文后各题所给的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．16.【答案】DBCACBABDDCADCDBBCAA第三部分：阅读理解（满分30分）请认真阅读下列短文，从短文后各题所给的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．17.【答案】AC18.【答案】DAC19.【答案】DABB20.【答案】CBACDB第四部分：任务型阅读（满分10分）请认真阅读下面短文，并根据所读内容在文章后表格中的空格里填入一个最恰当的单词．请将答案写在答题卡上相应题号的横线上．每个空格只填一个单词．21.【答案】characteristics,disadvantages,energy,impact（s）,guard,other,limits,physical,beat,fearful/afraid第五部分书面表达（满分25分）22.【答案】The main question presented in the dialogue is whether the students should wear traditional costumes during a ceremony for foreign students．【高分句型一】The students had each given their own stand and reasons．（概述）I am more inclined to agree with Li Jiang， taking into consideration of the following perspectives．First，traditional costumes are one of the most suitable items when it comes to presenting our culture． They are highly representative of our traditions， and will undoubtedly leave a deep impression on the foreign students who are coming for a 'cultural' exchange．【高分句型二】 Second，attending the event in traditional Chinese dress may open up several opportunities for interaction． The organizer can come up with several activities based on the attire itself， such as inviting the foreign students to try our traditional costumes．To conclude，my advice is that the students should wear traditional Chinese dress for this occasion．（结论）。