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2021考研全国硕士研究生招生考试数学二真题+答案床上床

2021考研全国硕士研究生招生考试数学二真题+答案

2021考研数学考试12月27日上午结束,收到很多同学反馈今年考研数学题目不难相对比较简单,为了方便考研人在考研结束之后核对以及2022考研人了解考情,下面和郑州启航考研一起来看下2021考研数学二真题及答案解析(完整版)。由于数学试题的特殊性,一些计算符号和数学单位无法直接在发布,只能以图片版的形式发表。如果看不清楚的话,大家可以给我留言。我单独给你发题。数学二真题解析:#考研数学#

是信情乎

数学篇|历年考研数学真题及答案解析

无论是第几遍做真题,做错的题目,都要做记号,并找出错因。如果下一次还犯类似错误(尤其是计算失误),一定要好好反思反思。

卢令

2021考研数学二真题及答案解析

2021年考研大部分专业已经结束了,只有一部分考试时间很长的专业课还在进行。下面是顺哥收集到的2021年考研数学二的真题及答案解析。如果有错误的话希望大家留言指正,感谢大家!相关文章推荐:2021年考研政治单选题真题及答案(部分)2021年全国硕士研究生入学统一考试英语(一)试题2021年考研英语二真题及答案解析选择题1-3选择题4-6选择题7-8选择题9-10填空题11-13填空题14-16解答题17-18解答题19-20解答题21解答题22解答题22解析#考研数学#

盖被子

2016考研英语二真题及答案解析

2016考研英语二真题及答案解析 Section I Use of EnglishDirections:Read the following text。 Choose the best word(s) for each numbered blank and mark A, B, C or D on the ANSWER SHEET。 (10 points)Happy people work differently。 They’re more proctive, more creative, and willing to take greater risks。 And new research suggests that happiness might influence 1 firms work, too。Companies located in place with happier people invest more, according to a recent research paper。 2 , firms in happy places spend more on R&D(research and development)。That’s because happiness is linked to the kind of longer-term thinking 3 for making investment for the future。The researchers wanted to know if the 4 and inclination for risk-taking that come with happiness would 5 the way companies invested。 So they compared U.S。 cities’ average happiness 6 by Gallup polling with the investment activity of publicly traded firms in those areas。7 enough, firms’ investment and R&D intensity were correlated with the happiness of the area in which they were 8。 But it is really happiness that’s linked to investment, or could something else about happier cities 9 why firms there spend more on R&D? To find out, the researches controlled for various 10 that might make firms more likely to invest like size, instry , and sales-and-and for indicators that a place was 11 to live in, like growth in wages or population。 They link between happiness and investment generally 12 even after accounting for these things。The correlation between happiness and investment was particularly strong for younger firms, which the authors 13 to “less confined decision making process” and the possible presence of younger and less 14 managers who are more likely to be influenced by sentiment。’’ The relationship was 15 stronger in places where happiness was spread more 16。 Firms seem to invest more in places。17 this doesn’t prove that happiness causes firms to invest more or to take a longer-term view, the authors believe it at least 18 at that possibility。 It’s not hard to imagine that local culture and sentiment would help 19 how executives think about the future。 It surely seems plausible that happy people would be more forward –thinking and creative and 20 R&D more than the average,” said one researcher。1。 [A] why [B] where [C] how [D] when2。 [A] In return [B] In particular [C] In contrast [D] In conclusion3。 [A] sufficient [B] famous [C] perfect [D] necessary4。 [A] indivialism [B] modernism [C] optimism [D] realism5。 [A] echo [B] miss [C] spoil [D] change6。 [A] imagined [B] measured [C] invented [D] assumed7。 [A] sure [B] odd [C] unfortunate [D] often8。 [A] advertised [B] divided [C] overtaxed [D] headquartered9。 [A] explain [B] overstate [C] summarize [D] emphasize10。 [A] stages [B] factors [C] levels [D] methods11。 [A] desirable [B] sociable [C] reputable [D] reliable12。 [A] resumed [B] held [C] emerged [D] broke13。 [A] attribute [B] assign [C] transfer [D] compare14。 [A] serious [B] civilized [C] ambitious [D] experienced15。 [A] thus [B] instead [C] also [D] never16。 [A] rapidly [B] regularly [C] directly [D] equally17。 [A] After [B] Until [C] While [D] Since18。 [A] arrives [B] jumps [C] hints [D] strikes19。 [A] shape [B] rediscover [C] simplify [D] share20。 [A] pray for [B] lean towards [C] give away [D] send actSection II Reading ComprehensionPart ADirections:Read the following four texts。 Answer the questions below each text by choosing A, B, C or D。 Mark your answers on the ANSWER SHEET。 (40 points)Text 1It’s true that high-school coding classes aren’t essential for learning computer science in college。 Students without experience can catch up after a few introctory courses, said Tom Cortina, the assistant dean at Carnegie Mellon’s School of Computer Science。However, Cortina said, early exposure is beneficial。 When younger kids learn computer science, they learn that it’s not just a confusing, endless string of letters and numbers – but a tool to build apps, or create artwork, or test hypotheses。 It’s not as hard for them to transform their thought processes as it is for older students。 Breaking down problems into bite-sized chunks and using code to solve them becomes normal。 Giving more children this training could increase the number of people interested in the field and help fill the jobs gap, Cortina said。Students also benefit from learning something about coding before they get to college, where introctory computer-science classes are packed to the brim, which can drive the less-experienced or-determined students away。The Flatiron School, where people pay to learn programming, started as one of the many coding bootcamps that’s become popular for alts looking for a career change。 The high-schoolers get the same curriculum, but “we try to gear lessons toward things they’re interested in,” said Victoria Friedman, an instructor。 For instance, one of the apps the students are developing suggests movies based on your mood。The students in the Flatiron class probably won’t drop out of high school and build the next Facebook。 Programming languages have a quick turnover, so the “Ruby on Rails” language they learned may not even be relevant by the time they enter the job market。 But the skills they learn – how to think logically through a problem and organize the results – apply to any coding language, said Deborah Seehorn, an ecation consultant for the state of North Carolina。Indeed, the Flatiron students might not go into IT at all。 But creating a future army of coders is not the sole purpose of the classes。 These kids are going to be surrounded by computers-in their pockets ,in their offices, in their homes –for the rest of their lives, The younger they learn how computers think, how to coax the machine into procing what they want –the earlier they learn that they have the power to do that –the better。21.Cortina holds that early exposure to computer science makes it easier to _______A。 complete future job trainingB。 remodel the way of thinkingC。 formulate logical hypothesesD。 perfect artwork proction22.In delivering lessons for high - schoolers , Flatiron has considered their________A。 experienceB。 interestC。 career prospectsD。 academic backgrounds1、[答案]C how[解析]根据空格所在句子可以看出,空格处应该是一个引导宾语从句的从属连词,做influence的宾语。四个选项的意思中,只有C。 how引导后面的内容做influence的宾语,前后意思合理。2、[答案]B In particular[解析]空格的前一句话的内容是:坐落在幸福人群所在地的公司投资更多的钱。空格所在句的内容是:坐落在幸福人群所在地的公司在…方面投入更多的钱。很显然,前后句子是总分关系。选项中,只有B选项可以体现总分关系。3、[答案]D necessary[解析]根据空格处前后的内容,_____ for making investments for the future是做后置定语修饰longer-term thinking和happiness。幸福,这种持久的思维模式对于对未来进行投资_______,四个选项中只有D。 necessary 做后置定语符合前后内容。其他选项与原文内容语义不符。4、[答案]C optimism[解析]空格处的内容与inclination for risk-taking由and连接,构成并列关系,后面that come with happiness定语从句既修饰空格处的内容,也修饰inclination for risk-taking,所以选项中可以由that come with happiness修饰的只有C选项optimism。5、[答案]D change[解析]空格处的内容和the way companies invested构成动宾搭配。选项中A。 echo 回声 B。 miss 思念 C。 spoil 溺爱 D。 change 改变,所以只有D选项可以和the way companies invested构成通顺语义。故D项正确。6、[答案]B measured[解析]原文:So they compared U.S。 cities’ average happiness_______ by Gallup polling with the investment activity of publicly traded firms in those areas。 所以他们比较美国城市的平均幸福,这种幸福是根据盖洛普在上市公司的投资活动地区民意调查来________。 A imagined 想象,D assumed 假定与民意调查的客观性是不符的,故排除,C invented 发明,与文意不符,故选B measured,衡量,测量。7、[答案]A sure[解析]若要判断此空的答案,需要结合文章上下文来判断。这句话和本篇完型的第二段的首句的含义是相同的。第二段的首句:Companies located in places with happier people invest more,含义为:坐落在幸福人们多的地方的公司会加大研发投入力度。本段首句其实是对于这一中心的重复阐述,因此选A。8、[答案]D headquartered[解析]原文:firms’ investment and R&D intensity were correlated with the happiness of the area in which they were _________。公司的投资与研发强度与公司所_______的地区的幸福度相关。依据第7题的答案,我们可以推断,这句话所填写的单词和located应该是近义, A advertised 广告; B divided 分割; C overtaxed 负担过重;均与本文含义不符,故选D,headquartered设立总部。9、[答案]A explain[解析]原文:…could something else about happier cities ______ why firms there spend more on R&D? 此句也是对于本文中心的再次论证。还有其他的什么可以__________公司在幸福的城市加入研发投入力度吗? 这句话之后就是具体的原因陈述。B overstate 夸张; C summarize总结;D emphasize 强调;均不符合文意,所以以上三项皆排除。故选A express 解释,阐释。10、[答案]B factors[解析]原文: To find out, the researchers controlled for various ________that might make firms more likely to invest — like size, instry, and sales ,为了找到答案,研究人员控制了各种各样的可能会让公司加大投资的_______——比如大小、行业和销量——,联系上下文,我们可以看出,这个空格其实就是下文size, instry, and sales的上义词,可以包含这三个名词的内容。A stages 阶段;C levels 水平,标准; D methods 方法;均不符合文意。故选B factors 原因,因素。11、[答案]A desirable[解析]该句意思为:研究者掌控了各种使公司更愿意投资的因素(比如规模、行业、销售),也掌控了居住起来____的住处的征兆(比如工资或人数的增长)。此处需填入形容词,前后两句为并列关系,感情色彩应保持一致,所填词应和空前more likely to invest更可能投资,以及空后like举例的内容涨工资一致,也是好事,所以答案desirable可取的、令人满意的为正确选项。Sociable善于交际的,reputable有声望的,reliable可靠的虽为正向词汇,但均与上下文衔接不紧密,因此答案为desirable。12、[答案]B held[解析]即使说明这些问题,总体来讲,快乐与投资之间的关系____。Resume继续、重新开始,hold保持不变,维持,emerge出现,break破裂。前后为递进,说明这些问题后,二者关系应仍然保持不变,所以hold为正确答案。13、[答案]A attribute[解析]该句意思为:快乐与投资之间的相互关系对年轻的企业特别强烈,作者把这一点____于“缺少编纂的做决定过程”。此处考搭配,attribute…to把……归咎于,assign…to把……指派给,transfer…to把……传递给,compare…to把……相比较,其中attribute…to符合文意,作者把这一点归因于于“缺少编纂的做决定过程”。14、[答案]D experienced[解析]该题为并列平行关系考查,and前后情感色彩、所属范畴应保持一致,younger并列,应为less experienced缺少经验的,故为正确答案。Serious严肃的,civilized文明的,ambitious有野心的,与年龄无直接关系,故排除。15、[答案]C also[解析]该句话上一句为The correlation between happiness and investment was particularly strong,此句为The relationship was 15 stronger,显然,二者之间为并列关系,因此选择also也。Thus表结果,instead表转折,never从不,不符合此处逻辑。16、[答案]D equally[解析]此题考查副词。四个选项中,A选项rapidly意为“迅速地”, B选项regularly意为“常规地”,C选项意为directly“直接地”,D选项equally“平等地”。此处讨论的是公司投资与快乐之间的关系。空格后指出,相较于在快乐不平等的地方,或者幸福感有巨大鸿沟的地方,公司更愿意在大多数人都较为幸福的领域投资, D选项equally是对inequality的反义复现,因此,D选项是正确选项。17、[答案]C While[解析]此处考察上下文的逻辑关系。上文指出,公司愿意在幸福的领域里投资, 而空格后则提到“这并不能证明幸福引发了公司扩大投资或者采用较长远的眼光看问题”,显然,这二者之间是转折关系,正确选项为C选项While “然而”。A选项 After“在……之后” , B选项Until “直到”,D选项Since“因为”或“自从”,都不符合文意。18、[答案]C hints[解析]空格所在句的前半句质疑了投资与幸福的关系,后半句的作者表现的态度是“believe”, 因此此处要填入一个表积极立场的词,且能与后面的at that possibility构成搭配, 表明“作者”的认可态度。A选项arrive“到达”,B选项jumps“跳跃”,D选项strikes“打击;罢工”,均不能与at that possibility搭配,C选项hints“暗示”符合语意,因此正确答案为C。19、[答案]A shape[解析]结合文意,此处是在正面论述“当地文化和氛围”对公司运营的影响,且二者之间的因果关系一直贯穿全文。四个选项中,A选项shape意为“形成,塑造” B选项rediscover“重新发现”, C选项simplify“简化”,D选项share“分享”, 其中只有A 选项最贴近语意,因此正确答案为A。20、[答案]B lean towards[解析]此处考察固定词组。 A选项pray for意为“为……祈祷”,B选项lean towards意为“向……倾斜”,C选项give away意为“泄露; 失去;赠送”,D选项send out意为“发送,发出”。空格所在句的前后语意为“快乐的人比普通人更加的具有正向思维,更有创造力,并且更加的_____研究和发展。”可知最符合文意的只能是选项B。Section II Reading ComprehensionPart AText 121、[答案][B]remodel the way of thinking[解析]观点题。根据题干Cortina holds回文定位在第二段。第二段指出Cortina认为过早的接触电脑是有益的,紧接着指出当小孩子学习电脑科学,他们就学习了如何去开发手机应用程序,或者创作艺术,或者验证假设。对于他们来说与大孩子相比,改变思维并不难。综上所述,[B]remodel the way of thinking是对原文“transform their thought”的同义置换。22、[答案][B] interest[解析]事实细节题。根据题干关键信息“in delivering lessons for high-schoolers”、“Flatiron has considered”,定位到第三段。整个第三段在叙述Flatiron School。其中,第三行The high-schoolers get the same curriculum, but “we try to gear lessons toward things they’re interested in”(高中生们上同样的课程,但是“我们力图以他们的兴趣来调整课程”),表明了该校开设课程的依据是“学生的兴趣”,故选[B] interest。23、[答案][A] help students learn other computer languages[解析]细节题。根据Deborah Seehorn 定位到文章第五段最后一句。Deborah说他们学习的技能(如何思考问题具有逻辑性并组织结果)可以应用到编码语言中去。选项[A]帮助学生学习另外的电脑语言是对这句话的概括。24、[答案][C] become better prepared for the digitalized world[解析]推理题。根据题干关键词“the last paragraph”和“Flatiron students”回文定位在最后一段。最后一段第一句指出Flatiron的学生不会全都进入IT界。紧接着第二句说明培养编码人员不是唯一目的,第三句进一步指出这些学生将会一生“被电脑包围”(生活在电脑时代),对比四个所给选项,[C] become better prepared for the digitalized world与原文意思一致,故正确。25、[答案][A] persuade[解析]词义题。根据题干关键信息“coax”(Line 4, Para.6),定位到最后一段第四行how to coax the machine into procing what they want(如何…电脑生产他们想要的),且该部分是与how computers think(电脑是如何思维的)并列的,都是学生学习的具体内容。正是因为两者并列,因此根据单词think可知coax同样含有一定比喻色彩,且coax指的是“让电脑生产他们想要的”一种手段或方式。将四个选项分别带入原文:[A] persuade“劝说,劝诱”,即“劝诱电脑生产他们想要的”,语意恰当,是正确选项;[B] frighten“吓唬,使惊吓”,即“吓唬电脑去生产他们想要的”,该方式带有贬义色彩,故排除;[C] misguide“误导”,与[B]同理,故排除;[D] challenge“挑战”,即“挑战电脑去生产他们想要的”,语义不通顺,故排除。因此,本题正确答案为[A] persuade。Text 226、[答案][A] its drastically decreased population[解析]本题属于细节题,考查了考生对文章首段中关于草原鸡数量的变化的理解。根据对首段首句当中生物学家预测的数量是2百万,而在首段末句出现but转折以及末句当中关于草原鸡现在真实的剩余数量只有2万2千只,都可以说明草原鸡的数量急剧的下降;另外,这道题还有一种做法是通过第二段首句的主语的作用,某些情况下,文章中间段落的首句主语起到承上启下的作用,那么中间段落首句主语就会有概括上一段的作用,本文第二段的首句:The crash was a main reason USFWS decided to formally list the bird as threatened。 就是对第26题题干和正确选项的同义替换,根据第二段第一句的主语:the crash (这种暴跌),对应正确选项A。27、[答案][D] went against conservation policies[解析]本题属于推理题,根据题干信息:the “Threatened” tag 令许多环境学家感到失望,定位到第二段的第三句,因此,原因应该出自第三句之后,而第四句和第五句中间有很明显的转折词but,因此答案定位在第五句,很多同学可能会问,这里并没有表示原因的词去与题干当中的in that进行对应,但是在我们的钻石卡的课程中提到,原文当中给出原因的并不一定是直接给出表示原因的连词或者介词,在本文第三句的but Ashe and others argued that the “threatened” tag gave the federal government flexibility to try out new, potentially less confrontational conservation approaches。 当中的gave这个词是“使得”的意思,A使得B如何如何,也就是A是B的原因,因此这道题的答案是D (违反了保护措施)。28、[答案][B] volunteer to set up an equally big habitat[解析]本题属于推理题,根据题干当中给出的位置信息(第三段)以及表示条件与结果的逻辑关系的if这个信息,可以迅速定位到第三段的第一句,其中题干当中的if与文章当中的as long as 进行对应,而题干当中的表示结果的部分与as long as 之前进行对应,因此,正确选项应该出自as long as 之后,也就是原文当中的:they had signed a range-wide management plan to restore prairie chicken habitat。 “签订一系列管理计划去恢复草原鸡的栖息地”,对应到的正确选项是B (volunteer to set up an equally big habitat 帮助搭建同样大小的栖息地)29、[答案][D] the states[解析]本题属于细节题。答案定位在文章第三段最后一句,从Ashe所说的话中“states remain in the driver’s seat for managing the species”可以得出,选项D the states在管理物种方面起着领导作用。30、[答案][B] the win-win rhetoric[解析]本题属于推断题。答案定位在文章最后一段,从Jay Lininger所说的话中,可以得知他认为政府应该为导致鸟类濒临灭绝的产业负责任,因此可以得出,他最可能支持本段开头所提出的双赢的说法。Text 331、[答案][D] what deep reading requires cannot be guaranteed[解析]细节题。根据题干回文定位到第二段第一句“what makes…management techniques don‘t seem sufficient”,,但是这句并没有提及原因。真正的原因是第二段最后一句“Deep reading requires not just time, but a special kind of time which can’t be obtained merely by becoming more efficient”。(深度阅读需要的不仅仅是时间,而且仅仅通过高效率所获得的那种时间也不够),因此选项D what deep reading requires cannot be guaranteed为正确答案。32、[答案][B] make passing time fulfilling[解析]细节题。根据题干回文定位到第三段第五句:we feel a pressure to fill these different-sized bottles(days, hours, minutes) as they pass。故正确答案应该与to fill…相一致。这句话中将时间单位天,小时和分钟比喻成了不同大小的瓶子。而压力来自于我们填充这些大小不一的瓶子时,即把自己的时间充实起来时。故正确答案为选项B,其中passing time是原文as they pass的同义替换,making … fulfilling是to fill的同义替换。33、[答案][D] achieve immersive reading[解析]细节题。根据题干定位到第四段第二句:…such ritualistic behavior helps us “step outside time’s flow” into “soul time。 (这种仪式化行为指代有助于我们从拜托时间流进入灵魂阅读),soul time 即选项D 中immersive reading (沉浸式阅读),故正确答案为选项D。题干“scheling regular times for reading helps”是题干中的“such ritualistic behavior helps”的同义改写,“soul time”是“immersive reading”的同义替换。34、[答案][A] reading becomes your primary business of the day[解析]细节题。根据题干中的carry a book with you at all times can work if, 可以定位到第四段倒数第二句 “providing you dip in often enough, so that reading becomes the default state”(假定你经常沉浸在阅读中,以至于阅读成为一种默认设置),因此可以确定选项A reading becomes your primary business of the day(阅读成为你一天中的主要事情)为正确答案。35、[答案][B] How to Find Time to Read[解析]主旨题。根据文章首段转折之后出主旨。But one specific complaint is made especially mournfully: There’s never any time to read。(但是其中一个特别悲哀的抱怨是:没有时间阅读)。第二、三、四段都在论证深度阅读才是解决之道。因此选项Dhow to find time to read为正确答案。Text 436、[答案][B] having a family with children[解析]根据题干给出的mark, successful life等词可以定位到第二段的第一句话,successful life可以找到原词,而mark对应milestone,including后面的内容就是这种生活的特征,包含“结婚,有孩子,有家,60岁退休”,和选项对比,只有B项符合原文给出的特征,属于同意替换。A项这里未提,略有干扰的是后面but句中的different paths,但这和题干不符,C项的退休后工作和原文刚好相反,D项未提到。37、[答案][C] attach importance to pre-martial finance[解析]根据题干给出的段落序号可以定位到第三段,另又提到young people,故可以定位到第三段开头第一句话。题干问的是年轻人倾向于……,题干中的tend在这句话中可以找到同意置换词more likely,句子中后面有5个to do表示年轻人倾向于做什么,所以答案就在这些动词不定式中。和选项对比,只有C项符合原文的含义“婚前或者有孩子之前要有经济保障”,属于同意替换。A项这里未提,也不符合当下年轻人的生活习惯,B项和原文刚好相反,原文说的是经常换工作来提升职业,而选项说的是长时间做一份工作,D项只是有childcare outside the home和原文一样,但是原文说的是父母都工作对孩子好,选项则是说年轻人更注重照顾孩子,两者含义并不相符。38、[答案][D] reach almost all aspects of American life[解析]根据题干给出的the priorities and expectations等词可以定位到第四段的第一句话的中间,that后面的内容是对这两个名词的修饰,故答案应该在这个从句中。和选项对比,只有D项符合原文,ripple through和选项中的reach属于同意替换。A项和B项这里均未提,C项只是politics和preferences这两个词有在文中出现,但是语义并不相符。39、[答案][D] getting established is harder for the young[解析]根据题干给出的young and old等词可以定位到第五段开头,这句话有冒号,解释key point,所以答案应该在冒号之后,题目问的是他们同意什么,也就是观点,所以可以再缩小范围为believe后面的内容为正确选项的含义。和选项对比,只有D项符合原文,属于同意替换。A项和C项这里均未具体提及,B项相对干扰性强,但是文中只是提到说在实现这些重要成就时,晚辈会比长辈遇到更艰难的挑战,并不是说老辈比晚辈创造了更多的成就,故排除。40、[答案][C] His parents’ good life has little to do with a college degree[解析]根据题干给出的Schenider可以定位到最后一段开头。这段话开头就说这个人认为今天的生活更艰难,后面的内容都在介绍他的生活。因为题干除了这个人名之外并没有给出其他更细定位的信息,可以选择从选项定位入手反推正确答案。A项“他毕业后找到一个理想工作”,文章只在最后一段第二句后面说到这个问题,但并没有说这个工作是dream work,故排除。B项的work steady在第三局也有提到,但并没有说是父母认为的,故排除。C项说到父母的好生活在第四、五句有提到,尤其引号中的内容和选项相符,故为正确答案。D项认为工作很有挑战性,这并没有提到,属于无中生有。Part B41、[答案]D (Express your emotions)[解析]emotions一词在本段中原词复现了两次,而且出现了其下义词,比如sad, angry,本段最后一句提到对待情绪的方式是:acknowledge and express what we feel appropriately。选项D与此完全对应。因此确定正确答案为D选项。42、[答案]F (Be easily pleased)[解析]该段通过举例来说明段落主题,提到it cost less than a fiver but she was overjoyed,本句话的含义是“虽然礼物不值钱,但是让她特别开心”。并且核心词overjoyed与小标题F中pleased属于近义词。该段第二句话在转折后提到the reality is these things have little lasting impact on our happiness levels,即“这些东西对我们的幸福水平影响很小。”接着最后一句总结到“感激生活中的小事情是提升我们幸福感的一个好方式”,因此本段重点在于强调要感激生活中的小事情,所以正确答案是F选项。43、[答案]A (Be silly)[解析]该段开头提及一个问题,那么问题的答案正是本段的中心句。第二句正是对问题的解答,根据本句话的前半部分:if we alts could inlge in a bit of silliness and giggling, 核心词silliness与选项A中的silly为同源词,因此确定选项A为正确答案。44、[答案]B (Have fun)[解析]首先明确本段中第二句为转折句,在找段落中心时,是必读部分。本句话含义是“成年人有能力按照自己的想法去享受时光(enjoy the things)”,紧接着下句举例说明享受的这些快乐的事情分别有哪些。因此本段重点在于说明成年人可以按照自己的意愿享受快乐时光。故选择 Have fun 。45、[答案]E (Don’t overthink it)[解析]该段主题句是段落首句it’s important to add that we shouldn’t try too hard to be happy,强调“我们不应该着急要快乐”。第二句借科学家的话提到这样做的不良影响,下文更是引用哲学家庄子的话来证明这一论点,最后一句再次突出,我们应以孩子为榜样,对于孩子来说,快乐不是一个目标,而是他们生活方式的自然副产品。可见,该段整体上是总分的结构,先提出论点再论证。此外too hard与选项E中的overthink属于近义表达,natural与overthink是反义复现。因此,答案选E。Section III Translation46、[解析]句1:The supermarket is designed to lure customers into spending as much time as possible within its doors。[题目考点]被动语态,不定式短语作目的状语[句子结构]简单句。句子的主干是“The supermarket is designed to……”,被动语态翻译的时候变为主动,不定式短语做目的状语,可以翻译为“旨在……”。“lure……into”表示引诱……做……,在这里可以意译为“意在……”。“as much time as possible”表示“尽可能长的时间……”[重点词汇] design:设计;lure:吸引,引诱。[参考译文]超市旨在吸引顾客在店里停留尽量长的时间。句2:The reason for this is simple: The longer you stay in the store, the more stuff you’ll see, and the more stuff you see, the more you’ll buy。[题目考点]并列结构,比较结构[句子结构]复合句。本句用连词and连接两个比较句。本句包含一个常用的比较结构“the+形容词+……,the+形容词+……”表示“越……,越……”。[重点词汇] the more……, the more……:越…,越…。[参考译文]原因非常简单:顾客在店里停留的时间越长,看到的商品越多;看到的商品越多,买的越多。句3:And supermarkets contain a lot of stuff。[题目考点]词的翻译[句子结构]简单句。本句是简单的主语+谓语+宾语结构。“contain”原本表示“包含,包括”,在本句中可以意译为“陈列”。[重点词汇]contain:包含,包括。[参考译文]超市陈列了大量的商品。句4:The average supermarket, according to the Food Market Institute, carries some 44,000 different items, and many carry tens of thousands more。[题目考点]并列结构[句子结构]复合句。And连接了两个简单句。第一个简单句句子的主干是“The average supermarket carries items……”;第二个简单句句子的主干是“many carry……”。“ according to……”表示“根据……”做方式状语。[重点词汇]Food Market Institute: 食品营销研究院, tens of thousands:成千上万。[参考译文]根据食品营销研究院的调查,一般超市里有约44000种不同的商品;大多数超市都有上万种。句5:The sheer volume of available choice is enough to send shoppers into a state of information overload。[题目考点]词的翻译,不定式短语做目的状语[句子结构]简单句。句子的主干是“The sheer volume of available choice is enough”,不定式“to ……”做目的状语,表示“足够去干……”。[重点词汇]sheer:绝对的,纯粹的; available:可利用的,可供选择的;overload:符合过多。[参考译文]如此众多的选择足以使顾客面对的信息过于繁杂。句6:According to brain-scan experiments, the demands of so much decision-making quickly become too much for us。[题目考点]词的翻译[句子结构]简单句。句子的主干是“the demands……become……”,表示“需求……变得……”。短语“:According to……”做方式状语,表示“根据……”。[重点词汇]brain-scan:脑部扫描 ,decision-making:作出决定,决策。[参考译文]根据脑部扫描实验,需要做这么多的决定很快就会使我们难以承受。句7:After about 40 minutes of shopping, most people stop struggling to be rationally selective, and instead began shopping emotionally—which is the point at which we accumulate the 50 percent of stuff in our cart that we never intended buying。[题目考点]并列结构,定语从句[句子结构]复合句。句子主干为most people stop struggling to be rationally selective and instead began shopping emotionally,其中instead和rationally,emotionally含转折和对比的意味。after about 40 minutes of shopping为介词短语做时间状语。which is the point是which引导的非限制性定语从句,修饰前面的整个句子。at which引导限制性定语从句,修饰point,相当于when,这个定语从句中主干成分为we accumulate the 50 percent of stuff,in our cart做地点状语。句中的最后一个that引导定语从句,修饰前面的先行词the 50 percent of stuff,整个句子中呈现从句套从句的句式。[重点词汇]rationally:理性地;emotionally:情感地,情绪冲动地;accumulate:累积;cart:购物车。[参考译文]大约购物40分钟以后,大部分顾客就无法试图做出理性的选择,而会冲动购物——此时,在购物车里,我们已经装了一半根本没想买的东西。[全文翻译]超市旨在吸引顾客在自己店内停留尽量长的时间。原因很简单:顾客在店里停留的时间越长,看到的商品就会越多;而看到的商品越多,你就会买的越多。超市有大量商品。根据食品营销研究院所说,普通超市大概有44000种不同的商品;很多超市更是会比普通超市多上万种商品。众多选择足以让顾客面临各种信息,不堪重负。根据脑部扫描实验,需要做这么多的决定很快就会使我们难以承受。大约购物40分钟以后,大部分顾客就无法试图做出理性的选择,而会冲动购物——此时,在购物车里,我们已经装了一半根本没想买的东西。Section IV Writing47、 [参考范文]Dear Jack,Your letter of congratulations was received。 Thank you for your nice words on my winning the contest。 In the letter, you asked me about the skills to do translation, so the following are my advice for you。Firstly, you should analyze the sentence structure, thus catching the meaning of the sentence。 Secondly, find the proper words to translate the meaning of the source language into the target language。 Thirdly, revise your translation at least three times to check if there are any mistranslations or missed meanings。I hope my advice helpful。 Wish to see you soon。Yours sincerely,Li Ming48、 [参考范文]Portrayed in the above pie chart is a survey of college students’ purposes of traveling。 The number of students who take traveling as a chance to see beautiful scenes accounts for 37%, while students who would like to travel to relieve pressure from study take up 35 %。There are several reasons behind the trend revealed in the above chart。 To begin with, as the present society is filled with fierce competition, most college students nowadays are under great pressure to stand out among others or to lunch a decent job after graation。 Therefore, they tend to choose traveling as an outlet to relieve their stress。 Secondly, with the fast advancement of the living standards of Chinese families, traveling is increasingly affordable to most college students。 For this reason, students prefer to travel to see different views to enjoy themselves or to make some friends。From my perspective, no matter what reason it is for, traveling is of great benefit for students to

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丝丝入扣

2021年考研数学二真题、解析

2021年考研数学二真题、解析2021 年全国硕士研究生入学招生考试数二试题一、选择题 :1-10小题,每小题5分,共50分,下列每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号里.

礼也

考研数学|真题一题多解系列,精选001

考研数学的复习离不开一题多解和多题一解的练习。通过多题一解的练习,能培养大家学会对某些方法或步骤的概括、归纳和总结。而通过一题多解的练习,可以让同学们思路更加开阔,发散思维得到训练,学会多角度分析和解决问题。从今天开始,老梁考研数学会陆续推出“考研真题一题多解系列”,精选真题并精妙解析。帮助大家学会多角度分析问题,提高大家综合分析和解决问题的能力。今天带来的是2020年数学三的一道真题,这是一道选择题。通过不同解法,体会不同的思维方法。【例001】(2020数三)【分析一】由于所求极限式中有函数差: 因此,提示我们可用拉格朗日中值定理。【分析二】由于是客观题,解法一求解会用去大量时间,因此可采用排除法,即选用不同的特殊的函数排除错误选项。本例当中,条件是个极限式,故函数在点x=a处不一定有定义,也不一定连续。【分析三】排除错误选项还可以使用“加强条件法”。所谓加强条件法就是:适当的加强题目中某一个条件,使之能用更方便的工具解决问题。【分析四】条件中,除了抽象函数f(x)之外,还有参数a,故可对a采取特殊值以区分选项。【总结】解法一是求解主观题的思路,对客观题来说不做推荐。解法二和解法四都是求解客观题常用的方法,只要有抽象函数和参数,都可以对函数或参数取特殊值。如果解法二和解法四不容易寻找特殊值时,也可采用解法三:加强条件法。特殊值法也可以看作是加强条件法的特例。对于本题,同学们还有什么新解法?欢迎在评论区留言!老梁考研数学永远是你的良师益友!

意境

考研数学|真题分类解析系列,精选004|反用等价无穷小

大家好,我是老梁考研数学!今天老梁继续给大家推送《考研数学真题分类解析系列》第四期,精选了一道比较复杂的无穷小的阶数比较的问题,解题过程中采用了“反用等价无穷小”的技巧使计算得到了简化。这是2013年考研数学二和数学三考卷共有的一道题。真题解析【例004】(2013年数二、三)【解法一】泰勒公式法。所以【解法二】拆凑法,将原式拆成若干项之和,每一项都等价与某个无穷小。【解法三】等价无穷小的反用。处理题中无穷小的乘积是个难点,根据对数能把“乘积转化成加和”的特性和无穷小等价公式,将问题化简。总结(1)本题解法二的(*)式和解法三的(**)式都用到了下面结论:等价无穷小之和的等价性,同学们可以自证一下。(2)此题也可以利用洛必达法则求解,但计算量显然比这三种方法要大,同学们可以试一试!(3)无穷小阶数比较问题是考研数学的高频考点,可以使用多种方法求解。在众多方法中,如何选用最有效的方法是同学们应该考虑的问题。而多做一题多解的题,可以训练同学们的发散思维,从不同的角度去分析解决问题,其效果远比做多道只有单一解答的问题要好得多!方法总结 归纳题型奇思妙解 就找老梁往期回顾考研数学|真题一题多解系列,精选001考研数学|真题一题多解系列,精选002|最后那种方法你肯定想不到考研数学|真题一题多解,精选003|∞-∞型未定式移位变形小技巧考研数学,一文搞懂无穷小可以等价替换的5个情形考研数学|变限积分函数无穷小的等价性