李永乐考研题

说到网红如今不再是一个新鲜话题，而且网红往往存在于一些热门领域比如美食、搞笑或者直播行业，但其实在教育领域也存在着一些网红，比如此前向大家介绍的北大最美博士学姐杨慧琴，这位长相美丽而且智商情商很高的女生，在各类网站上的粉丝已经超过了500万，人气很高的她甚至还把自己的学习方法分享给了很多网友，有人还跟着杨慧琴的方法进行学习，学习成绩得到了飞速的提升，很多人认为这样的网红才是正能量网红。除了杨慧琴这样的教育类学生博主外，其实在如今网络盛行的时代，也诞生了不少的网红教师，比如大家十分熟悉的复旦思修老师陈果，又如大家十分喜欢的华师大教授戴建业等等，而在中小学教师队伍中其实也出现了一位大名鼎鼎的网红数学物理教师，甚至他时不时的会通过自己的分享向大家传授自己的观点，他就是来自于人民大学附属中学的李永乐老师。李永乐老师如今在各大平台的粉丝量已经突破了数百万，而且这位把数学和物理讲的十分透彻和风趣幽默的中学教师，凭着这样的风格惹来了很多人的喜欢，甚至一些网友还给李永乐起了一个让人听着十分霸气的外号“永乐大帝”。这位人大附中网红教师，其实有着不寻常的求学经历，那就是在高考的时候李永乐以高分考上了北大，在北大就读期间以双学位毕业并且保送到了清华读研，也就是说李永乐有着北大和清华的双重求学经历，而且还是硕士生，按照一般人的轨迹会选择去一些科研机构或者像华为阿里这样的国际性大公司求职，甚至一些人选择出国留学，但对教育一直充满热爱的李永乐在10多年前中学教师队伍中清北毕业生还是稀罕词汇的时代选择进入到了中国人民大学附属中学执教。李永乐在2年前还曾经对考上清华北大难度大还是中500万难度大做出了一个具体的计算，让其一下子在各大平台获得了千万点击量，李永乐甚至还成为了很多人膜拜的对象，但是今天要给大家介绍的这位教师和人大附中李永乐同名，而且是清华的一位老教授，如今已经年过八旬，却依然活跃在考研培训当中，被很多人称之为“线代王”。这位李永乐老师就是很多考研人熟悉的数学名师，甚至很多人还通过看这位老教授的视频在考研当中线性代数获得了满分，李永乐从多年前开始从事考研辅导工作，那个时候与王式安、陈文灯等人成为了考研数学界最老团队成员，虽然这几位考研名师已经都年龄不小了，但是可以看到他们依然活跃在考研辅导的讲台上，让人感慨他们的精力旺盛。考研线代王李永乐，虽然名气不及像张宇、李林等后起之秀，但是因为他在领域中的地位很高，所以每年还是获得了很多人的认可，而李永乐作为清华应用数学系教授，从退休以来就一直从事于考研辅导工作，而几十年的丰富经验更是很多人没有的资本。从其介绍中可以看到，李永乐曾作为研究生考试北京阅卷组组长，同时在考研数学大纲及命题中多次出现，作为一名年过8旬的老人，不单单通过自己的辅导赢了学生的口碑，更通过自己的这种活法让自己思维清晰，就如同很多退休后闲不住的人一样，以这种方式获得了晚年的快乐。对此你是如何看待的呢？

不知道今年考研数学降低线性代数比例后，有没有影响李永乐老师在备考同学们心中的地位。但是在往年，李永乐老师是当之无愧的“救世主”。李永乐老师被称为“线代王”，是无冕之王。李老师在线性代数的地位，就相当于肖秀荣老师在考研政治的地位一样，无可替代。李老师从事考研数学辅导已经十多年，主编的复习全书，相信考数学的考生一定熟知。本人当年也使用过该书，用着非常顺手。李永乐老师是清华大学数学科学系教授，曾任全国硕士研究生入学考试北京地区数学阅卷组组长。并多次参加考研数学大纲修订和全国性数学考试命题工作，经验非常丰富。往年，临近最后，如果考生感觉自己超过国家线的希望不大时，本人都会建议考生去熟悉李永乐老师的线性代数资料，基本超过95%的考生都能凭借线性代数高分过线。线性代数是一门非常奇特学科线性代数并像高等数学一样，计算比较复杂。该科目的特点是，知识非常琐碎，需要大量记忆，并且记忆内容非常抽象、前后联系非常紧密，如果有个别概念、性质掌握不好，甚至会出现崩盘现象。尤其是常考的矩阵知识，它就涉及相似矩阵、合同矩阵、正定矩阵、正交矩阵、伴随矩阵等。而向量这部分，向量组线性相关的性质就10来个。如果考生能够熟悉这些概念，灵活运用这些性质，认真计算，线性代数就可以拿到不错分数。据相关机构统计，线性代数得满分的考生超过半数是李老的门生。就这样一位经验丰富的老教授，针对考前给出的建议，你确定不看一下吗？李永乐老师给出的建议首先，李老师表示考生一定放平稳心态，李老师特意指出，考生备考非常辛苦，但是越到关键时刻越要平稳。其次，李老师对考研数学整体难度进行分析。虽然，2021考研数学试题结构有所调整，但是整体难度不会有太大变化，只是题型出现调整。此外，李老师提别指出，计算准确性。一定保证拿到应该拿的分，会做的题不要丢分，保证计算准确。考生在做模拟题不适应新题型是正常现象，但是需要沉着应对。关键点是，李老师特别强调，考生在最后复习时，是不是仍然以真题为主？最后，李老师建议考生，一定注意保证健康，合理饮食。以上就是李老师给出的建议，赶紧转给身边需要的人吧。保持身体状况，在今年尤为重要千万不要出现感冒，尤其是北方同学。各大省份均发布相关要求，如果出现身体不适，甚至无法进入考场。外出时候一定戴口罩，勤洗手，常通风。相关材料，考生一定记得准备。

在我们之前的文章中和大家说过暑期数学的复习规划，其中说到了暑期数学应该有计划的进行刷题以提高自己做题的准确率和书写规范。那么这次我们还是请到了之前给大家做规划的145学长和大家说一下暑期到底刷哪本习题集，到底怎么刷。1、选取哪些习题集？暑假期间我主要做了四本习题集，分别是《李永乐660题》、《张宇1000题》、《张宇闭关修炼100题》、《汤家凤1800题》。给大家依次讲一下这几本练习册的特点和优劣：《李永乐660题》：全部是选择题和填空题，难度较低题量较少，适合刚开始刷题，对数学题还不够熟悉的同学进行练手。《张宇1000题》：里面有选择填空和简答题，题型覆盖比较广泛。难度分为两类，一类是简单题目，一类是拔高题目。综合来说这本习题集难度、题量、题型都比较全，很适合大家全程使用。《汤家凤1800题》：汤神的书和宇哥1000题很相似，都是覆盖面很广包含内容很全的习题集。不过汤神的这本书题量比较大，较适合基础较好，时间较为充裕的同学使用。《张宇闭关修炼》：这本书放在最后说是因为宇哥今年把这本书进行改版了。以前的闭关修炼只有一百道重点难题，现在的闭关修炼则是从36讲和1000题中挑出的题集合成一本书。比较适合时间不够想要抓住重点复习的同学。学长建议：因为我数学基础比较好，时间也比较充裕，所以去年做题比较多。大家如果时间不是很充足的话，可以选择两本书进行练习即可。其中张宇1000题和汤家凤1800题大家任选其一即可，二者的重复度还是很高的。如果大家有其他的练习册推荐，也可以在下方评论区留言。2、习题集应该怎么刷？大家在进行刷题的过程中应该分出步骤和阶段。第一阶段：不计时间以完全掌握知识点和题型。开始做题的时候能大家会出现做题的第一个难关，就是不适应。难以将所学知识灵活的应用到题目的解答上面。这个时候大家不要着急追赶准确率和做题速度，应当静下心来把每道题的知识点、题型、易错点、解题套路详细整理。我用下面这道题为例给大家演示一下：第二阶段：进行专项题型突破。在大家完成了第一阶段的刷题之后，应该对数学题有一个初步的了解，同时也适应了数学的出题方式。在第一阶段之后，大家会对自己哪部分知识点掌握的还不够充足、做题容易在哪里出错会有一个清晰的认识。因此我们的第二阶段刷题就是要集中突破这些薄弱点，不足我们的短板。这一块的习题在做的过程中要不断的回顾基础知识点，同时熟悉出题思路和常见答题套路，具体步骤和第一阶段类似我就不赘述了。第三阶段：综合训练、计时完成。在弥补自己的薄弱点之后，大家就可以开始进行各种题型的综合训练了。这一阶段的习题大家可以从以往做过的习题中自行选取，也可以利用真题或者模拟题进行训练。在联系的时候要注意控制时间，在做对的基础上提高做题速度。真题每套应该在两个半小时内完成，这样大家在考场上才能游刃有余。3、遇到难题怎么办？大家在进行刷题的过程中会遇到不少的难题，如果感觉自己实在解答不出来，可以直接翻阅答案解答。但是大家要注意，翻阅答案解答对的过程是为了让大家了解难题的解题思路和知识点是如何复合在一起进行考察的，一定不要做完就过去了。难题在类型上主要分为：知识点复合型、思路清奇型、计算困难型。除了第二种在出题思路上难为大家的题目比较难突破外，其余两种都可以通过拆分题目和逻辑的推导进行解答。大家在练习过程中要注意积累这部分习题的解答经验。同时在刷题过程中大家应该准备一本错题本进行记录。（如果不知道怎么整理错题本的同学可以查看我们以往的推文：数学，如何整理错题笔记？140分学长总结的模板，拿去直接用！）数学的练习重在积累，在大家刷题的过程中一定要记住时刻回顾和整理自己的做题套路、知识点等细节。我们是为了更快更准的答卷而刷题而非为了刷题而刷题。今天的干货分享就到这儿啦，希望对大家的暑期数学复习能够有所帮助。

2020年考研初试已经尘埃落定，肖秀荣、汤家凤、李永乐、张宇、何凯文等考研辅导名师又火了一把。就以政治为例，虽然有同学感觉今年肖秀荣老师题目押中率不如往年高，但是立刻有不少同学出来反对：你就考前突击一两月，非得把原题答案喂到你嘴边才叫押中？而更多的考生则是对肖秀荣老师顶礼膜拜：肖大大你太厉害了，全抄的材料。可见认真做了肖四肖八的同学，应该确实从中受到了不少启发，在考试中给了自己莫大的帮助。更有网友认为：考研政治就是肖秀荣老师一个人的考试，其他考生都是抄材料而已。考研名师的“神话”，实则体现了考试本身的含金量在降低以肖秀荣为代表的考研辅导老师被“神化”，学生对他们顶礼膜拜，一方面反映他们在考研的应试上确实有一套独特的方法，掌握了出题的规律，能够按照套路揣摩出出题人的用意；另一方面，也反映出研究生考试的弊端，考察的能力和知识点十分有限，只要按照套路来，就不难破解。只不过，破解这个套路的是考研的辅导团队，考生个人单打独斗还很难做到，这也反过来进一步凸显了考研辅导机构在备考过程中的作用和价值。“神预测”对考生来说是幸事，但对学校和导师来说是难事这对考生来说，确实是一件幸事，有人帮忙归纳概括，总结规律，预测考点甚至考题，能够节省不少复习备考的时间，还可能在短时间内提高分数。但是从另一个角度来说，研究生初试的题目就降低了含金量，对学生的能力考察就非常有限，部分科目拿高分，往往体现的只是背书效果如何，而非知识点掌握是否扎实，分析归纳能力是否适合科研等。名校推免生比例不断增长，是因为推免生的优势更明显这从某个角度也可以解释，为什么绝大部分名校更愿意接受保研的同学，而且保研同学所占比例越来越高。根据中国教育在线的统计数据，2020年，北京大学信号与信息处理、理论物理、高等教育学、统计学、企业管理等专业只招收推免生，推免比例达到100%；暨南大学的西方经济学、新闻学等专业推免生占比高达80%，另外如东南大学、中国科学技术大学、兰州大学等985高校，从2015年到2020年，推免生人数几乎都增长了一倍左右。而之所以出现这样的情况，是因为普遍观点认为，推免生的基础知识更扎实，主动意识更强烈，有较好的学习习惯，学习能力、科研经历、学术研究潜力等也较考研的同学更强。在学校和导师看来，学习科研是一个长期的连续的过程，而不是依靠短时间集中针对部分知识的学习就可以训练出很强的科研能力的，特别是对于进入大学不久就以考研为目标的同学，实际上是把大学上成了高中强化班，在反复的训练中强化应试能力，但是创新思维，动手能力往往是非常欠缺的，所以即便这部分同学能在初试中考高分，但是并不一定会受到导师的欢迎。推免生比例增长引发的教育公平问题但是这可能又会引发教育公平的问题，不止一次看到有人呼吁，让保研的同学与考研的同学一起参考，凭分数录取才是最公平的。特别是对于普通院校的同学来说更是如此：保研比率太低，绝大部分同学只能通过考研的方式才有机会进入更高平台，这让他们没有太多时间精力来做别的事情，只能把注意力都集中在复习备考上。但名校保研比例的升高，对他们来说，确实是上升的通道越来越窄。严格意义上来说，统考的方式看上去确实更公平，但是考试只是一种手段，并不是目的，学校的目的是选拔人才，考高分的同学确实不一定适合科研。导师需要的是学习能力强，学习习惯良好，具备创新思维的研究生，这确实是一个长期积累的过程，而保研的同学经历了大学三年的考研能一直保持在一个较为稳定的水平，某种程度上来说他们不需要去反复练习来应付考试，更多的时间精力是投入在知识拓展和科研实践上。所以从概率上来说，他们更适合从事科研。双非院校考生比例占据绝大多数，更凸显了高考的重要性2020年考研报名人数首次突破300达到341万，这个数字已经比五年前翻了一番还多，近两年更是爆发式增长，每年报考增长人数都在50万以上。但在考研大军中，来自双一流高校考研的同学不足20%，双非高校的考生超过了80%，在名校推免生能满足专业招生需求的情况下，要从如此庞大的考研大军中去筛选适合的考生，并不是一件容易的事情。推免比例的升高，考研难度的增大，进一步凸显了高考的重要性，一考定终身的说法虽然有些夸张，但是却也在很大程度上反映了社会的现实。从这个意义上来说，研究生资格的竞争从高中阶段就已经开始。在竞争如此激烈的情况下，容不得抱有侥幸心理的偷懒，时刻都需要保持奋进的精神状态。高校毕业生的出路需要拓宽，不能都唯学历论当然，也是时候释放一下对学历的迷信，高校毕业生的出路不应该紧紧与学历绑在一起，当每年有将近半数的高校毕业生选择考研的时候，这本身就说明本科教育的意义越来越弱化，很多高校甚至变成了考研的集训基地，这不该是高等教育应有的本质。高校专业设置应该更科学合理，避免过于趋同，不同类型的高校就应该培养不同类型的人才，而不是所有高校都像一个方向发展，然后来拍高矮顺序，这样始终有人领先占有优势，也始终会有人处于劣势，难以翻盘。

2020考研英语一真题及答案【完整版】！【完形】Directions: 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)Even if families don't sit down to eat together as frequently as before, millions of Britons will nonetheless have got a share this weekend of one of that nation's great traditions: the Sunday roast. 1 a cold winter's day, few culinary pleasures can 2 it. Yet as we report now. The food police are determined our health. That this 3 should be rendered yet another quilty pleasure 4 to damage our health.The Food Standards Authority (FSA) has 5 a public worming about the risks of a compound called acrylamide that forms in some foods cooked 6 high temperatures. This means that people should 7 crisping their roast potatoes, reject thin -crust pizzas and only 8 toast their bread. But where is the evidence to support such adarmlist advice? 9 studies have shown that acrylamide can cause neurological damage in mice, there is no 10 evidence that it causes cancer in humans.Scientists say the compound is 11 to cause cancer but have no hard scientific proof 12 the precautionary principle it could be argued that it is 13 to follow the FSA advice. 14 it was rumourded that smoking caused cancer for years before the evidence was found to prove a 15Doubtless a piece of boiled feef can always be 16 up on Sunday alongside some steamed vegetables, without the York shire pudding and no wine. But would life be worth living? 17 ,the FSA says it is not telling people to cut out roast foods 18 , but rece their lifetime intake.However its 19 risks coming a cross as being pushy and overprotective. Constant health scares just 20 with no one listening.1. [A]In [B]Towards [C]on [D]Till2. [A ]match [B]express [C]satisfy [D]influence3.[A]patience [B]enjoyment [C]surprise [D]concem4.[A]intensified [B]privileged [C] compelled [D]guaranteed5. [A]issued [B]received [C]ignored [D]cancelled6. [A] under [B]at [C]for [D]by7. [A]forget [B]regret [C]finish [D] avoid8. [A]partially [B]regularly [C] easily [D]initially9. [A]Unless [B]Since [C]If [D]While10.[A] secondary [B]extermal [C] conclusive [D] negative11.[A]insufficient [B]bound [C]likely [D]slow12.[A]On the basis of [B]At the cost of [C] In addition to [D]In contrast to13.[A]interesting [B]advisable [C]urgent [D]fortunate14.[A]As usual [B]In particular [C]By definition [D]After all15.[A]resemblance [B]combination [C] connection [D]pattern16.[A]made [B]served [C]saved [D]used17.[A]To be fair [B]For instance [C]To be brief [D]In general18.[A]reluctantly [B]entirely [C] graally [D] carefully19.[A] promise [B] experience [C]campaign [D] competition20.[A]follow up [B]pick up [C] open up [D]end up答案（1-20）1. on2. match3. enjoyment4. intensified5. issued6. at7. avoid8. easily9. while10. conclusive11. bound12. on the basis of13. advisable14. after all15. connection16. served17. to be fair18. entirely19. campaign20. end up【阅读】Section III Reading ComprehensionPart A Directions: 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 1A group of labour MPs, among them Yvette Cooper, are bringing in the new year with a call to institute a UK "town of culture" award. The proposal is that it should sit alongside the existing city of culture title, which was held by Hull in 2017 and has been awarded to Coventry for Zozl. Cooper and her colleagues argue that the success of the crown for Hull, where it brought in220m of investment and an avalache of arts, out not to be confined to cities.Britain' town, it is true are not prevented from applying, but they generally lack the resources to put together a bit to beat their bigger competitions. A town of culture award could, it is argued, become an annual event, attracting funding and creating jobs.Some might see the proposal as a boo by prize for the fact that Britain is no longer be able to apply for the much more prestigious title of European capital of culture, a sought-after award bagged by Glasgow in 1990 and Livorpool in 2008. "A cynic might speculate that the UK is on the verge of disappearing into an endless fever of self-celebration in its desperation to reinvent itself for the post-Brexit world: after town of culture, who knows that will follow-village of culture? Suburb of culture? Hamlet of culture?It is also wise to recall that such titles are not a cure-all. A badly run "year of culture"washes in and out of a place like the tide, bringing prominence for a spell but leaving no lasting benefits to the community. The really successful holders of such titles are those that do a great deal more than fill hotel bedrooms and bring in high-profile arts events and good press for a year. They transform the aspirations of the people who live there; they nudge the self-image of the city into a bolder and more optimistic light.It is hard to get right, and requires a remarkable degree of vision, as well as cooperation between city authorities, the private sector, community groups and cultural organisations. But it can be done: Glasgow's year as European capital of culture can certainly be seen as one of complex series of factors that have turned the city into the power of art, music and theatre that it remains today.A "town of culture" could be not just about the arts but about honouring a town's peculiarities-helping sustain its high street, supporting local facilities and above all celebrating its people and turn it into action.21. Cooper and her colleagues argue that a "town of culture" award could [A] consolidate the town-city ties in Britain.[B] promote cooperation among Britain's towns.[C] increase the economic strength of Britain's towns.[D] focus Britain's limited resources on cultural events.22. According to Paragraph 2, the proposal might be regarded by some as [A] a sensible compromise.[B] a self-deceiving attempt.[C] an eye-cotching bonus.[D] an inaccessible target.23. The author suggests that a title holder is successful only if it [A] endeavours to maintain its image.[B] meets the aspirations of its people.[C] brings its local arts to prominence.[D] commits to its long-term growth.24. Glasgow is mentioned in Paragraph 3 to present [A] a contrasting case.[B] a supporting example.[C]a background story.[D] a related topic.25. What is the author's attitude towards the proposal?[A] Skeptical[B] Objective[C] Favourable[D] Critical答案（21-25）21.D focus Britain's limited resources on cultural events.22.B a self-deceiving attempt.23.D commits to its long-term growth.24.B a supporting example.25.C Favourable.Text2Scientific publishing has long been a licence to print money, Scientists need journals in which to publish their research, so they will supply the articles without monetary reward. Other scientists perform the specialised work of peer review also for free, because it is a central element in the acquisition of status and the proction of scientific knowledge.With the content of papers secured for free, the publisher needs only find a market for its journal. Until this century, university libraries were not very price sensitive. Scientific publishers routinely report profit margins approaching 40% on their operations, at a time when the rest of the publishing instry is in an existential crisis.The Dutch giant Elsevier, which claims to publish 25% of the scientific papers proced in the world, made profits of more than f 900m last year, while UK universities alone spent more than f 210m in 2016 to enable researchers to access their own publicly funded research;both figures seem to rise unstoppably despite increasingly desperate efforts to change them.The most drastic, and thoroughly illegal, reaction has been the emergence of Sci-Hub, a kind of global photocopier for scientific papers, set up in 2012, which now claims to offer access to every pay walled article published since 2015. The success of Sci-Hub, which relies on researchers passing on copies they have themselves legally accessed, shows the legal ecosystem has lost legitimacy among its users and must be transformed so that it works for all participants.In Britain the move towards open access publishing has been driven by funding bodies.In some ways it has been very successful. More than half of all British scientific research is now published under open access terms; either freely available from the moment of publication,or pay walled for a year or more so that the publishers can make a profit before being placed on general release.Yet the new system has not worked out any cheaper for the universities. Publishers have responded to the demand that they make their proct free to readers by charging their writers fees to cover the costs of preparing an article. These range from around500 to $5,000.A report last year pointed out that the costs both of subscriptions and of these "article preparation costs" had been steadily rising at a rate above inflation.In some ways the scientific publishing model resembles the economy of the social internet:labour is provided free in exchange for the hope of status, while huge profits are made by a few big firms who run the market places. In both cases, we need a rebalancing of power.26. Scientific publishing is seen as "a licence to print money" partly because [A] its funding has enjoyed a steady increase.[B] its marketing strategy has been successful.[C] its payment for peer review is reced.[D] its content acquisition costs nothing.!27. According to Paragraphs 2 and 3, scientific publishers Elsevier have [A] thrived mainly on university libraries.[B] gone through an existential crisis.[C] revived the publishing instry.[D] financed researchers generously.28. How does the author feel about the success of Sci-Hub? [A] Relieved.[B] Puzzled.[C] Concerned.[D] Encouraged.29. It can be learned from Paragraphs 5 and 6 that open access terms [A] allow publishers some room to make money.[B] render publishing much easier for scientists.[C] rece the cost of publication substantially.[D] free universities from financial burdens.30. Which of the following characterises the scientific publishing model?[A] Trial subscription is offered.[B] Labour triumphs over status.[C]Costs are well controlled.[D] The few feed on the many.答案（26-30）26.D its content acquisition costs nothing.27.A thrived mainly on university libraries.28.D Encouraged.29.A allow publishers some room to make money.30.D The few feed on the many.Text 3Progressives often support diversity mandates as a path to equality and a way to level the playing field. But all too often such policies are an insincere form of virtue-signaling that benefits only the most privileged and does little to help average people.A pair of bills sponsored by Massachusetts state Senator Jason Lewis and House Speaker Pro Tempore Patricia Haddad, to ensure "gender parity" on boards and commissions, provide a case in point.Haddad and Lewis are concerned that more than half the state-government board are lessthan40 percent female. In order to ensure that elite women have more such opportunities, they have proposed imposing government quotas. If the bills become law, state boards and commissions will be required to set aside 50 percent of board seats for women by 2022.The bills are similar to a measure recently adopted in Califomia, which last year became the first state to require gender quotas for private companies. In signing the measure, California Governor Jerry Brown admitted that the law, which expressly classifies people on the basis of sex, is probably unconstitutional.The US Supreme Court frowns on sex based classifications unless they are designed to address an "important" policy interest, Because the California law applies to all boards, even where there is no history of prior discrimination, courts are likely to rule that the law violates the constitutional guarantee of "equal protection".But are such government mandates even necessary? Female participation on corporate boards may not currently mirror the percentage of women in the general population, but so what?The number of women on corporate boards has been steadily increasing without government interference. According to a study by Catalyst, between 2010 and 2015 the share of women on the boards of global corporations increased by 54 percent.Requiring companies to make gender the primary qualification for board membership will inevitably lead to less experienced private sector boards. That is exactly what happened when Norway adopted a nationwide corporate gender quota.Writing in The New Republic, Alice Lee notes that increasing the number of opportunities for board membership without increasing the pool of qualified women to serve on such boards has led to a "golden skirt "phenomenon, where the same elite women scoop up multiple seats on a variety of boards.Next time somebody pushes corporate quotas as a way to promote gender equity,remember that such policies are largely self-serving measures that make their sponsors feelgood but do little to help average women.31.The author believes that the bills sponsored by Lewis and Haddad will [A] help little to rece gender bias.[B] pose a threat to the state government.[C] raise women's position in politics.[D] greatly broaden career options.32. Which of the following is true of the Califormia measure?[A] It has irritated private business owners.[B] It is welcomed by the Supreme Court.[C] It may go against the Constitution.[D] It will settle the prior controversies.33. The author mentions the study by Catalyst to illustrate [A] the harm from arbitrary board decision. [B]the importance of constitutional guarantees.[C] the pressure on women in global corporations.[D] the needlessness of government interventions.34. Norway's adoption of a nationwide corporate gender quota has led to [A] the underestimation of elite women's role[B] the objection to female participation on boards.[C]the entry of unqualified candidates into the board.[D] the growing tension between labor and management.35. Which of the following can be inferred from the text?[A] Women's need in employment should be considered.[B] Feasibility, should be a prime concern in policy making.[C] Everyone should try hard to promote social justice.[D] Major social issues should be the focus of legislation.答案（31-35）31.A help little to rece gender bias.32.C It may go against the Constitution.33.D the needlessness of government interventions.34.C the entry of unqualified candidates into the board.35.B Feasibility should be a prime concern in policymaking.Text4 :Last Thursday, the French Senate passed a digital services tax, which would impose an entirely new tax on large multinationals that provide digital services to consumers or users in France. Digital services include everything from providing a platform for selling goods and services online to targeting advertising based on user data, and the tax applies to gross revenue from such services. Many French politicians and media outlets have referred to this as a"GAFA tax," meaning that it is designed to apply primarily to companies such as Google,Apple, Facebook and Amazon-in other words, multinational tech companies based in the United States.The digital services tax now awaits the signature of President Emmanuel Macron, who has expressed support for the measure, and it could go into effect within the next few weeks.But it has already sparked significant controversy, with the Unite Sates trade representative opening an investigation into whether the tax discriminates against American companies,which in turn could lead to trade sanctions against France.The French tax is not just a unilateral move by one country in need of revenue. Instead,the digital services tax is part of a much larger trend, with countries over the past few years proposing or putting in place an alphabet soup of new international tax provisions. These have included Britain's DPT (diverted profits tax).Australia's MAAL (multinational antiavoidance, law), and India's SEP (significant economic presence) test, to name but a few. At the same time, the European Union. Spain,Britain and several other countries have all seriously contemplated digital services taxes.These unilateral developments differ in their specifics, but they are all designed to tax multinationals on income and revenue that countries believe they should have a right to tax,even if international tax rules do not grant them that right. In other words, they all share a view that the international tax system has failed to keep up with the current economy.In response to these many unilateral measures, the Organization for Economic Cooperation and Development (OECD) is currently working with 131 countries to reach aconsensus by the end of 2020 on an international solution. Both France and the United States are involved in the organization's work, but France's digital services tax and the American response raise questions about what the future holds for the international tax system.France's planned tax is a clear warning: Unless a broad consensus can be reached on reforming the international tax system, other nations are likely to follow suit, and American companies will face a cascade of different taxes from dozens of nations that will prove burdensome and costly.36.The French Senate has passed a bill to [A] regulate digital services platforms.[B] protect French companies interests.[C] impose a levy on tech multinationals.[D] curb the influence of advertising.37. It can be learned from Paragraph 2 that the digital services tax [A] may trigger countermeasures against France.[B] is apt to arouse criticism at home and abroad.[C] aims to ease international trade tensions.[D] will prompt the tech giants to quit France.38. The countries adopting the unilateral measures share the opinion that [A] redistribution of tech giants' revenue must be ensured.[B] the current international tax system needs upgrading.[C] tech multinationals' monopoly should be prevented.[D] all countries ought to enjoy equal taxing rights.39. It can be learned from Para 5 that the OECO's current work [A] is being resisted by US companies.[B] needs to be readjusted immediately.[C] is faced with uncertain prospects.[D] needs to in involve more countries.40. Which of the following might be the best title for this text?[A] France Is Confronted with Trade Sanctions[B] France leads the charge on Digital Tax[C] France Says "NO" to Tech Multinationals[D] France Demands a Role in the Digital Economy答案（36-40）36.C impose alevy on tech multinationals.37.A may trigger countermeasures against France.38.B the current international tax system needs upgrading39.C is faced with uncertain prospects.40.B France leads the charge on Digital TaxPart B Directions:In the following text, some sentences have been removed. For Questions 41-45, choose the most suitable one from the fist A-G to fit into each of the numbered blanks. There are two extra choices, which do not fit in any of the gaps. Mark your answers on ANSWER SHEET. (10 points)[A] Eye fix actions are brief[B] Too much eye contact is instinctively felt to be rude[C] Eye contact can be a friendly social signal[D] Personality can affect how a person reacts to eye contact[E] Biological factors behind eye contact are being investigated [F] Most people are not comfortable holding eye contact with strangers[G] Eye contact can also be aggressive.In a social situation, eye contact with another person can show that you are paying attention in a friendly way, But it can also be antagonistic such as when a political candidate turns toward their competitor ring a debate and makes eye contact that signals hostility.Here's what hard science reveals about eye contact: We know that a typical infant will instinctively gaze into its mother's eyes, and she will look back. This mutual gaze is a major part of the attachment between mother and child. In althood, looking someone else in a pleasant way can be a complimentary sign of paying attention. It can catch someone's attention in a crowded room, "Eye contact and smile" can signal availability and confidence, a common-sense notion supported in studies by psychologist Monica Moore.42. Neuroscientist Bonnie Augeung found that the hormone oxytocin increased the amount of eye contact from men toward the interviewer ring a brief interview when the direction of their gaze was recorded. This was also found in high- functioning men with some autistic spectrum symptoms, who may tend to avoid eye contact. Specific brain regions that respond ring direct gaze are being explored by other researches, using advanced methods of brain scanning.43. With the use of eye-tracking technology, Julia Minson of the Harvard Kennedy School of Government concluded that eye contact can signal very different kinds of messages,depending on the situation. While eye contact may be a sign of connection or trust in friendly situations, it's more likely to be associated with dominance or intimidation in adversarial situations. "Whether you' re a politician or a parent, it might be helpful to keep in mind that trying to maintain eye contact may backfire if you' re trying to convince someone who has a different set of beliefs than you," said Minson.44. When we look at a face or a picture, our eyes pause on one spot at a time, often on the eyes or mouth. These pauses typically occur at about three per second, and the eyes then jump to another spot, until several important points in the image. are registered like a series of snapshots. How the whole image is then assembled and perceived is still a mystery although it is the subject of current research.45. In people who score high in a test of neuroticism, a personality dimension associated with self-consciousness and anxiety, eye contact triggered more activity associated with avoidance,according to the Finnish researcher Jari Hietanen and colleagues "Our findings indicate that people do not only feel different when they are the centre of attention but that their brain reactions also differ." A more direct finding is that people who scored high for negative emotions like anxiety looked at others for shorter periods of time and reported more comfortable feelings when others did not look directly at them.答案（41-45）41. C Eye contact can be a friendly social signal42.E Biological factors behind eye contact are being investigated43.G Eye contact can also be aggressive44.A Eye fixactions are brief45.D Personality can affect how a person reacts to eye contactPart CDirections: Read the following text carefully and then translate the underlined segments into Chinese. Your translation should be written neatly on the ANSWER SHEET. (10points)Following the explosion of creativity in Florence ring the 14h century known as the Renaissance, the modern world saw a departure from what it had once known. It turned from God and the authority of the Roman Catholic Church and instead favoured a more humanistic approach to being. Renaissance ideas had spread throughout Europe well into the 17h century,with the arts and sciences flourishing extraordinarily among those with a more logical disposition. (46) with the Church's teachings and ways of thinking eclipsed by the Renaissance,the gap between the Medieval and modern periods had been bridged leading to new and unexplored itellectual territories.During the Renaissance, the great minds of Nicolaus Copernicus, Johannes Kepler and Galileo Galilei demonstrated the power of scientific study and discovery. (47) Before each of their revelations many thinkers at the time had sustained more ancient ways of thinking.including the geo-centric view that the Earth was a the centre of our universe. Copernicus theorized in 1543 that all of the planets that we knew of revolved not around the Earth, but the Sun, a system that was later upheld by Galileo at his own expense. Offering up such a theory ring a time of high tension between scientific and religious minds was branded as heresy and any such heretics that continued to spread these lies were to be punished by imprisonment or even death.(48) Despite attempts by the Church to suppress. this new generation of logicians and rationalists, more explanations for how the universe functioned were being made at a rate that the people could no longer ignore.It was with these great revelations that a new kind of philosophy founded in reason was born.The Church's long- standing dogma was losing the great battle for truth to rationalists and scientists. This very fact embodied the new ways of thinking that swept through Europe ring most of 17h century. (49) As many took on the ty of trying to integrate reasoning and scientific philosophies into the world, the Renaissance was over and it was time for a new era-the Age of Reason.The 17h and I8h centuries were times of radical change and curiosity, Scientific method,rectionism and the questioning of Church ideals was to be encouraged, as were ideas of liberty, tolerance and progress. (50) Such actions to seek knowledge and to understand what information we already knew were captured by the Latin phrase' sapere aude' or dare to know',after Immanuel Kant used it in his essay" An Answer to the Question: What is Enlightenment?".It was the purpose and responsibility of great minds to go forth and seek out the truth, which they believed to be founded in knowledge.答案（46-50）46.随着教会的教义和思维方式在文艺复兴时期黯然失色，中世纪与现代之间的鸿沟得以弥合，从而出现了新的及尚未开发的知识领域。47.在每个真理揭示之前，当时的许多思想家都采用了更古老的思维方式，仍旧沿用以前的思维模式，其中包括认为地球是宇宙中心的地球中心说。48.尽管教会试图镇压这-代逻辑学家和理性主义者，但人们对宇宙如何运转的解释却越来越多，并且以-种不容忽视的速度在增加。49.当许多人承担起将理性科学的哲学融入世界的责任时，文艺复兴时代已经结束，并且开启了一个新的时代。50.此类寻求知识和了解已知信息的行为被拉丁语概括为：“sapere aude"即"敢于求知”作文Section ll WritingPart A51. Directions:The students union of your university has assigned you to inform the international students about an upcoming singing contest. White a notice in about 100 words.Write your answer on the ANSWER SHEET.Do not use your own name in the notice. (10 points)小作文：通知留学生唱歌比赛 【参考范文】NoticeDec.21, 2019In order to enrich the campus life and provide the colorful life for you, the Students' Union is preparing the upcoming singing contest, which will be held in the auditorium in our university on the evening of December 31, 2019. Now, the Union is recruiting contestants for this competition.Anyone who are fond of signing or interested in the competition, please send his or her application to students’union@sohu.com before next Wednesday. Besides, there are generous awards in gratitude for this activity. Please do not hesitate to contact us if you have any queries concerning the singing contest. Meanwhile, volunteers for this activity are badly needed to assist us in organizing the relevant affairs.We are looking forward to your participation.The Students' UnionPart B52. Directions:Write an essay of 160-200 words based on the pictures below, In your essay, you should1) Describe the picture briefly,2) Interpret the implied meaning, and3) Give your comments.Write your answer on the ANSWER SHEET. (20 points)大作文：习惯良好的时间管理习惯 【参考范文】Portrayed distinctively by the two cartoons above is an impressive scene: a girl in the left picture is doing homework and saying that early completion is better. Nevertheless, the boy in the right picture is sitting in front of the desk and saying that he will not finish the homework until the last minute.Undoubtedly, the symbolic implication of the pictures is to show us that importance should be attached to the formation of good habits, especially the good habit of time management. On the one hand, efficient time management is critical to personal development. As the old saying goes,“Time is money," and in the fast-paced modern life, it seems that we always have a lot of things to do and we are very busy. In the face of such a situation, we have to realize that efficiency holdsthe key to saving time and time management skills hold the key to personal success. On the other hand, good time management habits play a vital role in the development of the whole society. There is no doubt that, to a large extent, social progress is closely related to the efforts of each indivial. If we can develop the good habit of time management, we are much more likely to improve efficiency and have a better performance in the learning and working process, which is anintegral part of social advances and prosperity.From what has been mentioned above, we can come to the conclusion that the sense of efficient time management skills is of equal importance in personal and social progress.Therefore,we ought to take advantage of the phenomenon to enlighten the public and the press is expected to take a lead in advertising the value of developing good time management habits. Only in this way can we have a bright future.以上便是整理的2020年全国硕士研究生入学统一考试英语一试题及答案，2021考研的小伙伴可以参考真题，准备明年12月的考研初试。下面分享一份公共课书单，希望对大家有用：【英语书单】单词：闪过英语《考研词汇闪过》按重要程度划分了频考词、基础词、偶考词、超纲词，划重点，后期冲刺只背高频词和基础词，省时间。真题：《考研真相》（英语二：考研圣经）：一词一句讲解真题，重点词汇和每个句子都有详细讲解，不怕你看不懂，还有排除干扰项的方法，帮助提高答对率，适合基础弱的人。作文：英语一《写作160篇》/英语二《写作宝中宝》：通过词句段篇先教你学会写作文，再用三步作文法帮你拔高，专门针对基础薄弱的。【数学书单】《张宇真题大全解》：从94年到现在的真题都包括了，讲解很好，帮助研究数学题型。李永乐王式安660题：用这本书练习做题，都是经典题型！同济六版/七版《高等数学》上、下同济五版/六版《线性代数》课本：《线性代数》、《概率论》、《数理统计》【政治书单】官方红宝书（政治大纲解析）；风中劲草（三本书）、肖秀荣系列：精讲精练、1000题、讲真题、形势与政策、冲刺八套卷、最后四套卷；蒋中挺冲刺5套卷；启航20天20题

“十年寒窗苦读，只为一朝中举”，这是许多科举人士的梦想。现在，科举制度虽然取消了，但是高考与之情况很相似。在很多眼里，清华大学、北京大学是两个非常神圣的地方，无数学子都在为之努力。不过，曾经却有那么一个人，他本科毕业于北大，研究生毕业于清华。可是，在找工作的时候屡屡碰壁，最后，在人大附中当了一名老师，如今，又成为了一名千万级网红。这个人就是李永乐，纵览他的前半生，称得上是一部“江湖传奇小说”。“学霸”李永乐1983年，李永乐出生在东北吉林市。从小他就比较聪明，在别人眼里学习很难，而他却感觉非常的容易。后来，李永乐以优异的成绩考入了当地的重点中学，高中时期，他又在数学和物理方面展现出了超高的天赋。高三那年，李永乐参加了“全国物理竞赛”，在这次比赛中，他的成绩名列前茅。当时，因为考试成绩很好，他获得了北京大学物理系的保送资格，在北大期间攻读物理和经济学。从这些经历上来看，李永乐称得上是一个“学霸级”人物。不过，在进入北大前期，他的表现却有点让人失望。对于很多高考学子而言，上了大学就等于获得了自由，李永乐也有过这样的想法。进入北京大学后，李永乐一度沉迷“社团”和“游戏”，忘记了自己来北京大学的目的。严重的时候，他甚至还选择逃课，直至醒悟的时候，他已经浪费了很多的时间。针对自己的状况，又想了想未来的就业，李永乐决定考研。当时，他选择的是清华大学的电子工程专业。为了弥补自己浪费的时间，李永乐夜以继日地复习功课，经过了一番努力与奋斗，他最终考入了清华大学，攻读电子工程专业硕士研究生。2009年，李永乐从清华大学毕业。一般而言，与“电子工程专业”对口的工作很多，而且李永乐还有着“北大”与“清华”这两个高光标签，想要找一份好工作不难。可是，因为他的性格比较耿直，结果在找工作的时候充满波折、屡屡碰壁。找不到工作碰壁曾经，李永乐向雷曼兄弟和日企索尼投过简历，对方在看到他的履历之后，也很快邀请他来公司面试。结果，在面试之后，两家公司对他大失所望。雷曼兄弟是从事金融行业的，当时，他向李永乐提问：“你平时选择股票都有什么依据”。李永乐毫不犹豫地回答道：“基本都是凭感觉”。对于一家全球知名的金融公司而言，这样的回答显然不能满足他们的要求，李永乐面试失败。当他去索尼面试的时候，原本双方交流得还很顺利，可是当面试官问李永乐：“在工作上你有什么要求吗？”李永乐回答：“不加班”。“加班”是每一个职场人都讨厌的事情，然而，李永乐在面试的时候说出来，无疑会给面试官留下很不好的印象。况且，索尼公司还是一家跨国性电子企业集团，加班是常有的事情。因此，面试结果不言而喻，李永乐失败了。经历过多次失败后，李永乐对自己进行了一次分析，他感觉自己比较的单纯，适合那种“环境单纯、生活规律”的工作。本着这一份心态，他又重新他踏上了求职之路。进入人大附中当时，他比较看好人大附中“物理老师”这一个岗位，为了能够顺利通过面试，李永乐做了充分的准备。因为没有教学经验，所以他先找了一家教育机构锻炼自己的能力，那时的主要工作就是“网上授课”。在此期间，李永乐录制了大量的数学、物理视频，教学水平直线提升。一切准备就绪后，李永乐便向人大附中“发起进攻”。因为北大、清华高材生的名头，再加上在面试中出色的发挥，李永乐顺利进入了这一个学校。进入人大附中之后，李永乐给自己制定了一个“九年规划”，而这个九年规划又被分为“三个过程”。第一个过程，他几乎没有自己的时间，基本都是在备课，一堂40分钟的课程，他需要准备4个多小时。到了第二个过程，他备课已经很熟练，可是，学校又给他安排了各种竞赛课，最忙的时候，李永乐一天只能睡3个小时。如今，李永乐早已经过了第三个过程，他在教学上也越来越得心应手了，教学水平也有了很大的提升。值得一提的是，人大附中的学生经常会在各种知识竞赛中获奖，而这些人大部分都是李永乐的学生。当然，他的成功也不仅仅局限于此。2017年的一天，李永乐正在家中睡觉，他早年在网上讲课的一段视频被发布到了网上，这段视频讲述的是“闰年是怎么回事”。当李永乐得知这件事情后，该视频的点击量已经很高了，一时间，李永乐也成为了网络红人。这件意外之喜，也给李永乐带来了很大的启发：“为何不将自己现在的教学内容发布到网上呢？”于是，李永乐媒体平台上注册了“李永乐老师”的账号，开始定期更新教学视频。一年后，自媒体短视频领域迎来了“爆炸性”发展，借助这股东风，李永乐也成为了一名千万级网红。视频中，他会用严谨的推导让人清楚定理的思路与证明，用通俗的说法让人理解高深的学问，用工整的字迹给学习的人正确的过程。总的来说，课题虽然很深奥，但是他总能另辟蹊径，让诸多的网友听懂。同时，他的授课视频一般都是直入主题，没有一句废话，也不会浪费一点时间。“采得百花成蜜后，为谁辛苦为谁甜，”因为李永乐的视频都是免费的，所以他也备受许多学生家长的称赞！“一个人活着的意义，就在于心中有梦想，并为实现梦想而努力着、奋斗着，”李永乐正在为自己喜欢的事业奋斗着，而且还取得了很大的成绩。

爱心提示：本文只适合对数学非常不敏感人群。不知各位读者可还记得陪伴了我们很多年的各种全解，对于王后雄我们爱恨交加。不知各位读者可还记得人手一科一本的五三，以及有一个文艺的名字的曲一线。考研了之后，在数学界，我们又有了一个新的“男神”——李永乐。我们可以跟着张宇上课，可以跟着汤家凤上课，但一般人都绕不开复习全书，面对这一本熟悉的复习全书，我们究竟应该怎么用？全书一定要仔细看，认真做如果你是那个没有精力去把课本看一遍，把课本后面的系统做一遍，那就从复习全书开始。我一个好朋友数学主要就是做了复习全书，985高校研究生录取。虽然只是个例，但还是说明了一些问题的那要怎么仔细看，认真做呢？通常，我们要把这本书过三遍，那是比较熟的了。第一遍，主要在看，配合一些讲课的基础视频进行学习，很多例题可能还是不会做，问题也不大，看答案就可以，把不会做的弄懂，同时找个本子把自己认为重要的例题记下来，同时友情提示不要把书本画得很乱哦，影响后面两遍做题。第二遍，主要在做例题，这时候可以搭配提高班的视频学习了，视频网上有很多，大家找自己喜欢的老师就可以。在这一遍，尽量不要去看答案，而是找个本子一题一题演算。这个时候要错题集十分重要，错题集不是让大家抄题目哦，记下题号就可以了，这样做的前提是全书要保存好。第三遍，很多同学没有时间和耐心看第三遍就要进入真题的节奏了，这时候第一遍第二遍留下的错题就很重要了。这差不多就是全书的规划了，如果考研的宝宝尤其是在职考研的宝宝们没有时间规划可以私信我做具体时间规划哦！PS:我弟弟让我去做个学习规划师，他高三的学习规划都是我做的，恭喜他提前批面试过了，哪个学校就不透露了。作者：DD姐，毕业两年，多重身份。待字闺中（恨嫁中），移动互联网广告行业摸打滚爬者，周日日托班老师，曾经的资深在职考研者。

本文由木哥原创，欢迎转载分享，转载须注明来自“木哥说教”！今日话题：考研数学该如何选择资料更合适呢？考研数学是很多考研学子不愿意去面对的一门课，因为数学本身就是有一定难度的，尤其是高数里面的一些问题是很多人怎么也想不通的，还有线代和概率需要的是一种全新的思维方式，蛮干是永远都不行的，所以对于基础一般的人来说，选择一本让自己更容易接受的资料也是比较重要的，比如有些老师的东西难度比较大，那么对于基础差的，一上来就被搞蒙了，那后面是没有办法进行的，信心就会越来越小，以至于每年有很多人因为数学而中途放弃这个被自己寄予厚望的目标，所以今天木哥来给大家写一篇这方面的分析，希望能帮到一部分人。那么今天木哥就针对考研学子中大家最为熟悉的三位优秀老师的资料给大家分析一下。第一位：考研数学张宇老师张宇老师算是考研界里面非常有名的一位老师，他的36讲也被历届学生广泛运用，用过张宇老师资料的人应该都知道，他的资料难度稍微有点大，所以对于一些天天号称自己零基础的学生来说作为第一轮复习估计有点困难，但是如果基础还不错的学生，用张宇老师的资料那是非常好的，基本上只要把他的资料反复做，反复温习，吃透，最后发现考研的题型都是那么熟悉，记住一定是要动手去做每一个题目，这个比任何东西都重要，数学切记眼高手低。第二位：考研数学李永乐老师说起李永乐老师，木哥是最熟悉的，因为我当年数学逆袭就是全部靠的他的资料，我没有看任何视频，就是看资料做题目，然后总结，查漏补缺。李永乐老师的资料整体难度上相对于张宇老师来说要简单一点，但是他的资料更注重基础，所以如果你真的如你所说，基础非常烂甚至可以忽略不计，那么李永乐老师的资料或许比较适合你。尤其是他的线代和概率论的辅导讲义，这两本书非常好，木哥当年零基础，完全就是把这两本资料反复吃透，最后这两门的分数应该是接近满分，不懂的一定要去问同学，有时候自己研究几天不如同学的一个提醒，一定不要觉得不好意思，然后就是反复去做就好了。第三位：考研数学汤家凤老师对于汤家凤老师，木哥觉得大家都可以用的，尤其是他的视频讲解的非常好，另外提醒大家一点，千万不要觉得考研数学一定要最新的视频就是最好的，那是误区，其实数学内容每年每月什么变化，所以以前的视频都可以用，木哥觉得汤家凤来说2003和2005年的视频是最经典的，如果明年考研的学生，可以去找来帮助你复习，现在很多视频汤家凤老师都不亲自讲了。当然还有其它有名的老师，木哥就不一一说了，我只找这三个比较典型的说一说，也许你有自己更中意的老师，那都没有关系，重要的是选择了一个老师的资料，就要反复去看，去做，去温习，把厚书变成薄书，这样才能变成自己的，资料不是越多越好，一本足以，一本做十遍，比十本做一遍，效果强百倍。总结：考研数学一定要注重基础，那就是动手能力，任何一个题目拿到手，都要动手一步一步计算出来，计算能力非常重要，现在考研数学的计算量非常大，如果平时不去做，考场上发现自己都会，但是结果都错，所以从现在开始，就要锻炼自己的计算能力。

21考验初期，大家都比较迷茫，下面介绍一下21考研数学资料怎么用，以及这些名师们怎么选择和一些备考干货。张宇学历：博士，启航考研数学老师，从事高等数学教学和考研辅导多年，在全国核心期刊发表论文多篇，一篇入选“2007年全球可持续发展大会”。代表作品：《考研数学高等数学18讲》、《张宇线性代数9讲》、《考研数学概率论与数理统计9讲》、《考研数学题源探析经典1000题》、《张宇考研数学真题大全解》、《张宇考研数学闭关修炼一百八十题》、《考研数学命题人终极预测8套卷》、《张宇考研数学最后4套卷》打开百度APP，查看更多高清图片建议：数学一的高数可以跟着张宇，数学一难度比数二、数三难度要大很多，高数占的分量也更大，张宇的1000题中大多是难题，更适合数学基础比较好的，或者希望数学考到高分的同学使用。授课风格：幽默风趣，讲得很生动，深入浅出张宇授课逻辑思维能力比较强，讲的做题技巧比较多，尤其是在高数方面更为突出，建议数学基础好的可以跟张宇，基础差的直接跟张宇的话容易听不太懂。汤家凤南京大学数学系博士，南京工业大学副教授。文都考研数学老师，曾连续20年从事考研数学教学和命题研究工作，连续十多年担任研究生入学数学考试阅卷组成员。代表作品：《考研数学接力题典1800》、《考研数学绝对考场最后八套题》授课风格：生动形象，风格独树一帜，思路清晰明彻。对考研数学有独创的方法和见解，化抽象为通俗易懂，使枯燥的公式变得容易记忆，对考试的重点及难点把握精准，每年都能准确预测重要考点和方法。建议：汤家凤授课更注重基础，适合基础不好的前期跟着一步一个脚印，21年考研数学考试按以往的出题风格，难度小于20年考研数学，所以21考研应该着重从基础上拓展。数三的高数建议跟着汤老师，不过汤老师口音比较重，听课的时候建议大家认真点。李永乐全国著名考研数学线性代数辅导专家，清华大学应用数学系，现清华大学数学科学系教授，北京高教学会数学研究会副理事长。代表作品：《考研数学复习全书》、《线性代数辅导讲义》、《数学全真模拟400题》、《数学基础过关660题》被广大考研网友誉为“线代王”，曾任全国硕士研究生入学考试北京地区数学阅卷组组长。多次参加考研数学大纲修订和全国性数学考试命题工作。建议：大家线代只跟李永乐一个人，资深辅导专家，李永乐讲线代深入浅出，通俗易懂，对于线代全期只需要一本他的线性代数辅导讲义结合着他的课就可以了。概率论建议大家跟着李永乐团队的王式安，曾连续在考研命题组担任数学的研究工作，对于概率论有自己的方式和见解，同样的，概率论全程只跟着王式安老师就可以了。了解更多考研咨询，可参考下面：21届考研英语备考你必须要了解的，各题型名师及书目推荐这些考研常识很重要，早知道可以避免入坑，直线备考，事半功倍只需要十天，教你系统背会考研英语单词，清北学霸竭力推荐