考研高等数学一试题

最近有很多小伙伴问我如何利用好数学真题，知道做一遍不够，知道要研究真题，但是不知道如何利用好真题，今天就给大家说道说道。1、了解卷子不管是什么考试都要先知道考试的试题是怎么分布，比如：客观题多少道，占分多少；主观题多少道，占分多少；考试时间是多少分钟，用多少时间做客观题，多少时间做主观题。1.1 先了解卷子分布。知道一张卷子最基本的分布：客观题是多少，主观题是多少，各占分值多少，考试时间是多少，这里强调一点考试时间，一定要按规定的时间减去15分钟。一是涂卡，二是平复心情用。1.2 做题顺序额。考场上考的是谁拿分多，懂了吗？就是先做自己会做的，尤其是自己比较熟悉的一部分，相对简单的部分，比如：线代。2、了解自己知己知彼方能百战百胜，现在既然了解了卷子的基本情况，就要对自己有个全面的了解。2.1 现在复习的状况。先要了解到现在为止，数学复习的怎么样？第一轮基础是否打牢，如果没有打牢，赶快去补习，不要留有任何问题。如果第一轮复习完毕，第二轮该何去何从？利用做真题检验自己现在对知识的掌握情况。2.2 擅长点在哪里？是高等数学好还是线代好，明确自己的擅长的地方，方便在做题的时候一旦时间紧张有所取舍。另一方面就是做题顺序，可以迅速得分。知道哪里掌握的还可以的情况，现在趁着还有时间，赶快补足较弱的地方。不要等到上考场了才临时看两眼，其他科目行，但是数学决定不行。3、查漏补缺这里呢，主要是通过做真题了解自己对哪里的知识点掌握得还不够好，有重点地去学习。3.1 一点思路都没有。当遇见无从下手的题时，那么就要认真研究答案了，从答案中去知道考的知识点是什么，破题点是什么，解题思路是什么，如果让你出题考这个知识点怎么出题。多思考才能找到破题的地方。3.2 有思路，但解题时出现对知识点的遗忘。如果真的出现这样的情况，要分清是对知识点的遗忘还是对知识点的不掌握。遗忘就要赶快去翻书，并且记下来。不掌握就要认真学，保证对知识点的充分理解，掌握。3.3 有思路，但拿不到满分。这种情况下通常是遗漏了某些重要的步骤，导致无法拿到满分。遇到这样的情况一定要对照答案，查看到底是什么地方的知识点还需要在本题的答案中呈现出来。3.4 总结题型。把做过的真题中，自己拿不到分的地方，总结一下。将相关的破题点、方法、解题技巧、遗忘的点都总结在相关的笔记中，反复看，反复记忆。10月份做题时还可以翻阅资料，11月开始做题就不允许翻任何的资料了，严格按照考场的要求。建议留出一两套在11月初真正模拟，然后在查漏补缺。最后祝大家考出理想分数。

十一月已经过半，相信很多研友都在忙着刷真题，但是刷真题只是简单地做一篇、然后再对着答案改一遍就完事了吗？今天小编就来告诉大家，如何更加有效地在最后一个月的时间里利用真题。一、如何复习真题这个其实很关键了，有些同学题目一做，答案抄完，然后就把试卷扔在一边，其实这是非常错误的。这种复习方式简直是在浪费时间。第一，必须严格按照考试时间和纪律做真题。完全按照考试时间来，中途不许上厕所不许玩手机不许聊天。就假设自己正在考研，找一张白纸作为答题纸，书写工整、字迹清晰、步骤明确，不得跳步越项。切忌草草了事，敷衍应付！第二，认真根据答案批改这里要先提醒一点，每年考试难度都不一样，所以不必太在意分数。更不可因为某年的试卷分数过低还怀疑自我，保持心态最重要。批改过程中要做好记录，查漏补缺。一定要按照答案要求严格批改，必须自己对自己负责。哪怕分数低点也没关系。第三，错题集有这个相信很多同学都有。其实在复习的最后阶段，我们只需要复习错题集就足够了。有了错题集、你的目标会更加明确，心态也会更加的踏实自然，可以"有的放矢";而不会明明紧张得要死，却发现"无事可做"。也就是说，错题集存在的根本原因，是为了给你提供一个复习的目的。它会很明确地告诉你，你还有哪些软肋、还有哪些知识点没掌握。会为你后面的复习提供一个目标，不至于让你太过于盲目。下面小编来根据具体学科为大家提供真题复习的范围和推荐书籍。二、高等数学这可以说是考研最大的一个门槛，无数人都挂在那颗名叫“高数”的树上。其实考研数学的命题，都是从题库中选取的题目，出题规律很明显，真题利用价值非常高，所以做真题是性价比非常高的复习方式。1、范围考研数学的真题总共有1988-2019总共32年的试卷。其中1988-1996(共5个卷种，卷1、2相当于现在的数学一，卷3相当于现在的数学二，卷4、5相当于现在的数学三)，卷面分值100分；1997-2002(数学一、二、三、四各一套试卷)，卷面分值100分；2003-2008(数学一、二、三、四各一套试卷)，卷面分值150分；2009-2019(数学一、二、三各一套试卷)，卷面分值150分。当然没有必要把这么多试卷全做了，小编这里推荐大家只需要做1997年之后的题目就可以。有些同学可能会疑惑，为什么要做这么二十年前的试卷呢？原因有两个，第一，早年的真题有一些相当经典的题目，试卷的质量也比较高，例如98和99两年的。第二，考研大纲几十年来变化一直不大，不像中学教学大纲，隔几年就改版一次。所以即使二十年前的试卷仍然有一定参考价值。2、书籍推荐这里给大家推荐两本首先是大名鼎鼎的李永乐！这位大神不多解释了，大家都懂得。这本书主要对2005以后的真题进行了详细解析，但是也附赠了1987-2005的试卷和答案。还有一位也是很多研友耳熟能详的老师——张宇！这本书收录了1987年以后所有考研真题详解，也是非常好的真题解析教材。三、英语1、范围英语真题不需要像数学那样做那么多，建议至少做到除去近三年真题外，其他年份的真题的4篇阅读都刷过一遍。得阅读者得天下。2、错题集英语的错题主要在于词汇、语法记忆不全和长难句的分析方面。因为英语归根到底还是一个需要大量记忆及背诵的科目。3、推荐书籍张剑黄皮书，这也是考研圈中非常有名的一位老师了，相必大家都不陌生。他的真题覆盖范围也比较广，解析比较透彻，是本不错的辅导书。四、专业课这是一个非常麻烦、非常需要人脉的事情。因为大多数高校是不会提供专业课的真题的。而且各个高校、尤其是自主命题的高校，对于外校考研的学生其实不是那么友好的。很多同学在考研专业课上走了很多弯路，就是因为没有真题在手，复习的特别盲目，甚至连大概难度都无法预测，最终栽了跟头。1、直接去目标院校购买虽然大部分的高校已经不提供考研历年真题，但是还有一些学校会提供上一年的考研真题。建议你去学校的研招办询问，运气好的话他们会提供一份。在院校附近的一些打印店里，会有老板卖该院校的专业课真题，不过比较贵，大概300块一份。黑心商家啊！2、找研究生学长学姐要这个方法可谓是最靠谱的了，但是非常考研你的人脉。对于那些刚考上研究生的学长学姐们，大部分都有真题、或者有渠道获得真题。而且是考上研究生的，对于真题和复试都有自己的见解，如果此刻结交了，在你进入考研复试的时候也能对你有很大的帮助！这里注意区别真假，有的骗子就是冒充学长学姐骗钱的！每年都有无辜的研友们上当受骗，这里建议线下交易。3、网上搜索现在网络比较发达，很多读研的同学会把考研真题和经验分享到网上，这个时候考生可以根据自己掌握的信息区分。考研真题哪怕是回忆版都比没有强！但是网上信息鱼龙混杂、真假难辨，各位研友要谨慎！4、多渠道购买专业课真题，因为比较难以获得，所以网上有很多电商就是卖真题赚钱的。淘宝上这类店家层出不穷，但也要小心挂羊头卖狗肉。还有一种是考研机构，他们也有自己的内部渠道能搞到真题，这种比较靠谱，因为一般人不会干砸自己招牌的事情。最后有的研友们会问，为什么没有政治的？其实政治这门课时效性很明细，真题的意义并不大，所以就不再推荐了。至于最后的模拟考试，推荐肖秀荣的四套卷和八套卷。还是和其他科目一样，完全按照考研时间和纪律来考试。

中国科学院大学硕士研究生入学考试高等数学（甲）考试大纲一、 考 试 性 质中国科学院大学硕士研究生入学高等数学（甲）考试是为招收理学非数学专业硕士研究生而设置的选拔考试。它的主要目的是测试考生的数学素质，包括对高等数学各项内容的掌握程度和应用相关知识解决问题的能力。考试对象为参加全国硕士研究生入学考试、并报考理论物理、原子与分子物理、粒子物理与原子核物理、等离子体物理、凝聚态物理、天体物理、天体测量与天体力学、空间物理学、光学、物理电子学、微电子与固体电子学、电磁场与微波技术、物理海洋学、海洋地质、气候学等专业的考生。二、 考试的基本要求要求考生系统地理解高等数学的基本概念和基本理论，掌握高等数学的基本方法。要求考生具有抽象思维能力、逻辑推理能力、空间想象能力、数学运算能力和综合运用所学的知识分析问题和解决问题的能力。三、 考试方法和考试时间高等数学（甲）考试采用闭卷笔试形式，试卷满分为150分，考试时间为180分钟。四、考试内容和考试要求（一）函数、极限、连续考试内容函数的概念及表示法 函数的有界性、单调性、周期性和奇偶性 复合函数、反函数、分段函数和隐函数 基本初等函数的性质及其图形数列极限与函数极限的概念 无穷小和无穷大的概念及其关系 无穷小的性质及无穷小的比较 极限的四则运算 极限存在的单调有界准则和夹逼准则 两个重要极限：， 函数连续的概念 函数间断点的类型 初等函数的连续性 闭区间上连续函数的性质 函数的一致连续性概念考试要求1. 理解函数的概念，掌握函数的表示法，并会建立简单应用问题中的函数关系式。2. 理解函数的有界性、单调性、周期性和奇偶性。掌握判断函数这些性质的方法。3. 理解复合函数的概念，了解反函数及隐函数的概念。会求给定函数的复合函数和反函数。4. 掌握基本初等函数的性质及其图形。5. 理解极限的概念，理解函数左极限与右极限的概念，以及函数极限存在与左、右极限之间的关系。6. 掌握极限的性质及四则运算法则，会运用它们进行一些基本的判断和计算。7. 掌握极限存在的两个准则，并会利用它们求极限。掌握利用两个重要极限求极限的方法。8. 理解无穷小、无穷大的概念，掌握无穷小的比较方法，会用等价无穷小求极限。9. 理解函数连续性的概念（含左连续与右连续），会判别函数间断点的类型。10. 掌握连续函数的运算性质和初等函数的连续性，熟悉闭区间上连续函数的性质（有界性、最大值和最小值定理、介值定理等），并会应用这些性质。11．理解函数一致连续性的概念。（二）一元函数微分学考试内容导数的概念 导数的几何意义和物理意义 函数的可导性与连续性之间的关系 平面曲线的切线和法线 基本初等函数的导数 导数的四则运算 复合函数、反函数、隐函数的导数的求法 参数方程所确定的函数的求导方法 高阶导数的概念 高阶导数的求法 微分的概念和微分的几何意义 函数可微与可导的关系 微分的运算法则及函数微分的求法 一阶微分形式的不变性 微分在近似计算中的应用 微分中值定理 洛必达（L’Hospital）法则 泰勒(Taylor)公式 函数的极值 函数最大值和最小值 函数单调性 函数图形的凹凸性、拐点及渐近线 函数图形的描绘 弧微分及曲率的计算考试要求1. 理解导数和微分的概念，理解导数与微分的关系，理解导数的几何意义，会求平面曲线的切线方程和法线方程，了解导数的物理意义，会用导数描述一些物理量，掌握函数的可导性与连续性之间的关系。2. 掌握导数的四则运算法则和复合函数的求导法则，掌握基本初等函数的求导公式。了解微分的四则运算法则和一阶微分形式的不变性，会求函数的微分。3. 了解高阶导数的概念，会求简单函数的n阶导数。4. 会求分段函数的一阶、二阶导数。5. 会求隐函数和由参数方程所确定的函数的一阶、二阶导数6. 会求反函数的导数。7. 理解并会用罗尔定理、拉格朗日中值定理、柯西中值定理和泰勒定理。8. 理解函数的极值概念，掌握用导数判断函数的单调性和求函数极值的方法，掌握函数最大值和最小值的求法及其简单应用。9. 会用导数判断函数图形的凹凸性，会求函数图形的拐点以及水平、铅直和斜渐近线，会描绘函数的图形。10. 掌握用洛必达法则求未定式极限的方法。11.了解曲率和曲率半径的概念，会计算曲率和曲率半径。（三）一元函数积分学考试内容原函数和不定积分的概念 不定积分的基本性质 基本积分公式 定积分的概念和基本性质 定积分中值定理 变上限定积分定义的函数及其导数 牛顿－莱布尼茨（Newton－Leibniz）公式 不定积分和定积分的换元积分法与分部积分法 有理函数、三角函数的有理式和简单无理函数的积分 广义积分（无穷限积分、瑕积分） 定积分的应用考试要求1. 理解原函数的概念，理解不定积分和定积分的概念。2. 熟练掌握不定积分的基本公式，熟练掌握不定积分和定积分的性质及定积分中值定理。掌握牛顿－莱布尼茨公式。熟练掌握不定积分和定积分的换元积分法与分部积分法。3. 会求有理函数、三角函数有理式和简单无理函数的积分。4. 理解变上限定积分定义的函数，会求它的导数。5. 理解广义积分（无穷限积分、瑕积分）的概念，掌握无穷限积分、瑕积分的收敛性判别法，会计算一些简单的广义积分。6. 掌握用定积分表达和计算一些几何量与物理量（平面图形的面积、平面曲线的弧长、旋转体的体积及侧面积、截面面积为已知的立体体积、功、引力、压力）及函数的平均值。（四）向量代数和空间解析几何考试内容向量的概念 向量的线性运算 向量的数量积、向量积和混合积 两向量垂直、平行的条件 两向量的夹角 向量的坐标表达式及其运算 单位向量 方向数与方向余弦 曲面方程和空间曲线方程的概念 平面方程、直线方程 平面与平面、平面与直线、直线与直线的夹角以及平行、垂直的条件 点到平面和点到直线的距离 球面 母线平行于坐标轴的柱面 旋转轴为坐标轴的旋转曲面的方程 常用的二次曲面方程及其图形 空间曲线的参数方程和一般方程 空间曲线在坐标面上的投影曲线方程考试要求1. 熟悉空间直角坐标系，理解向量及其模的概念。2. 熟练掌握向量的运算(线性运算、数量积、向量积)，掌握两向量垂直、平行的条件。3. 理解向量在轴上的投影，了解投影定理及投影的运算。理解方向数与方向余弦、向量的坐标表达式，会用坐标表达式进行向量的运算。4. 熟悉平面方程和空间直线方程的各种形式，熟练掌握平面方程和空间直线方程的求法。5. 会求平面与平面、平面与直线、直线与直线之间的夹角，并会利用平面、直线的相互关系（平行、垂直、相交等）解决有关问题。6. 会求空间两点间的距离、点到直线的距离以及点到平面的距离。7. 了解空间曲线方程和曲面方程的概念。8. 了解空间曲线的参数方程和一般方程。了解空间曲线在坐标平面上的投影，并会求其方程。9. 了解常用二次曲面的方程、图形及其截痕，会求以坐标轴为旋转轴的旋转曲面及母线平行于坐标轴的柱面方程。（五）多元函数微分学考试内容多元函数的概念 二元函数的几何意义 二元函数的极限和连续 有界闭区域上多元连续函数的性质 多元函数偏导数和全微分的概念及求法 全微分存在的必要条件和充分条件 多元复合函数、隐函数的求导法 高阶偏导数的求法 空间曲线的切线和法平面 曲面的切平面和法线 方向导数和梯度 二元函数的泰勒公式 多元函数的极值和条件极值 拉格朗日乘数法 多元函数的最大值、最小值及其简单应用 全微分在近似计算中的应用考试要求1. 理解多元函数的概念、理解二元函数的几何意义。2. 理解二元函数的极限与连续性的概念及基本运算性质，了解二元函数累次极限和极限的关系 会判断二元函数在已知点处极限的存在性和连续性 了解有界闭区域上连续函数的性质。3. 理解多元函数偏导数和全微分的概念 了解二元函数可微、偏导数存在及连续的关系，会求偏导数和全微分，了解二元函数两个混合偏导数相等的条件 了解全微分存在的必要条件和充分条件，了解全微分形式的不变性。4. 熟练掌握多元复合函数偏导数的求法。5. 熟练掌握隐函数的求导法则。6. 理解方向导数与梯度的概念并掌握其计算方法。7. 理解曲线的切线和法平面及曲面的切平面和法线的概念，会求它们的方程。8. 了解二元函数的二阶泰勒公式。9. 理解多元函数极值和条件极值的概念，掌握多元函数极值存在的必要条件，了解二元函数极值存在的充分条件，会求二元函数的极值，会用拉格朗日乘数法求条件极值，会求简单多元函数的最大值、最小值，并会解决一些简单的应用问题。10. 了解全微分在近似计算中的应用（六）多元函数积分学考试内容二重积分、三重积分的概念及性质 二重积分与三重积分的计算和应用 两类曲线积分的概念、性质及计算 两类曲线积分之间的关系 格林（Green）公式 平面曲线积分与路径无关的条件 已知全微分求原函数 两类曲面积分的概念、性质及计算 两类曲面积分之间的关系 高斯（Gauss）公式 斯托克斯（Stokes）公式 散度、旋度的概念及计算 曲线积分和曲面积分的应用考试要求1. 理解二重积分、三重积分的概念，掌握重积分的性质。2. 熟练掌握二重积分的计算方法（直角坐标、极坐标），会计算三重积分（直角坐标、柱面坐标、球面坐标），掌握二重积分的换元法。3. 理解两类曲线积分的概念，了解两类曲线积分的性质及两类曲线积分的关系。熟练掌握计算两类曲线积分的方法。4. 熟练掌握格林公式，会利用它求曲线积分。掌握平面曲线积分与路径无关的条件。会求全微分的原函数。5. 理解两类曲面积分的概念，了解两类曲面积分的性质及两类曲面积分的关系。熟练掌握计算两类曲面积分的方法。6. 掌握高斯公式和斯托克斯公式，会利用它们计算曲面积分和曲线积分。7. 了解散度、旋度的概念，并会计算。8. 了解含参变量的积分和莱布尼茨公式。9. 会用重积分、曲线积分及曲面积分求一些几何量与物理量（平面图形的面积、曲面的面积、物体的体积、曲线的弧长、物体的质量、重心、转动惯量、引力、功及流量等）。（七）无穷级数考试内容常数项级数及其收敛与发散的概念 收敛级数的和的概念 级数的基本性质与收敛的必要条件 几何级数与p级数及其收敛性 正项级数收敛性的判别法 交错级数与莱布尼茨定理 任意项级数的绝对收敛与条件收敛 函数项级数的收敛域、和函数的概念 幂级数及其收敛半径、收敛区间（指开区间）和收敛域 幂级数在其收敛区间内的基本性质 简单幂级数的和函数的求法 泰勒级数 初等函数的幂级数展开式 函数的幂级数展开式在近似计算中的应用 函数的傅里叶（Fourier）系数与傅里叶级数 狄利克雷（Dirichlet）定理 函数在[-l，l]上的傅里叶级数 函数在[0，l]上的正弦级数和余弦级数。函数项级数的一致收敛性。考试要求1. 理解常数项级数的收敛、发散以及收敛级数的和的概念，掌握级数的基本性质及收敛的必要条件2. 掌握几何级数与p级数的收敛与发散情况。3. 熟练掌握正项级数收敛性的各种判别法。4. 熟练掌握交错级数的莱布尼茨判别法。5. 理解任意项级数的绝对收敛与条件收敛的概念，以及绝对收敛与条件收敛的关系。6. 了解函数项级数的收敛域及和函数的概念。7. 理解幂级数的收敛域、收敛半径的概念，并掌握幂级数的收敛半径及收敛域的求法。8. 了解幂级数在其收敛区间内的一些基本性质（和函数的连续性、逐项微分和逐项积分），会求一些幂级数在收敛区间内的和函数，并会由此求出某些数项级数的和。9. 了解函数展开为泰勒级数的充分必要条件。10. 掌握一些常见函数如ex、sin x、cos x、ln(1+x)和(1+x)α等的麦克劳林展开式，会用它们将一些简单函数间接展开成幂级数。11. 会利用函数的幂级数展开式进行近似计算。12.了解傅里叶级数的概念和狄利克雷定理，会将定义在[-l，l]上的函数展开为傅里叶级数，会将定义在[0，l]上的函数展开为正弦级数与余弦级数，会将周期为2l的函数展开为傅里叶级数。13. 了解函数项级数的一致收敛性及一致收敛的函数项级数的性质，会判断函数项级数的一致收敛性。（八）常微分方程考试内容常微分方程的基本概念 变量可分离的微分方程 齐次微分方程 一阶线性微分方程 伯努利（Bernoulli）方程 全微分方程 可用简单的变量代换求解的某些微分方程 可降价的高阶微分方程 线性微分方程解的性质及解的结构定理 二阶常系数齐次线性微分方程 二阶常系数非齐次线性微分方程 高于二阶的某些常系数齐次线性微分方程 欧拉（Euler）方程 微分方程的幂级数解法 简单的常系数线性微分方程组的解法 微分方程的简单应用考试要求1. 掌握微分方程及其阶、解、通解、初始条件和特解等概念。2. 熟练掌握变量可分离的微分方程的解法，熟练掌握解一阶线性微分方程的常数变易法。3. 会解齐次微分方程、伯努利方程和全微分方程，会用简单的变量代换求解某些微分方程。4. 会用降阶法解下列方程：y(n) =f(x)，y″ =f(x，y′ )和y″ =f(y，y′ )5. 理解线性微分方程解的性质及解的结构定理。了解解二阶非齐次线性微分方程的常数变易法。6. 掌握二阶常系数齐次线性微分方程的解法，并会解某些高于二阶的常系数齐次线性微分方程。7. 会解自由项为多项式、指数函数、正弦函数、余弦函数、以及它们的和与积的二阶常系数非齐次线性微分方程。8. 会解欧拉方程。9. 了解微分方程的幂级数解法。10.了解简单的常系数线性微分方程组的解法。11 会用微分方程解决一些简单的应用问题。五、主要参考文献《高等数学》（上、下册），同济大学数学教研室主编，高等教育出版社，1996年第四版，以及其后的任何一个版本均可。

大家好！我是向上好青年！众所周知，考研数学满分是150分，考试时间为180分钟。考研数学试卷从题型结构分为单选题、填空题、解答题。考研数学试卷从内容上包括高等数学、线性代数、概率论与数理统计。其中，高等数学在整个考研数学中具有举足轻重的作用。可以说高等数学是后期线代和概率学习的一个知识积淀。因此，同学们要十分重视高等数学的复习！注重基础基本概念、基本方法、基本性质一直是考研数学的重点，从多年的考研阅卷经验看，考生对数学基本概念掌握不够牢固，理解不够透彻。有些同学在考场上，不知道怎样下手，不知道该用哪个公式。所以，建议考生在数学复习中一定要重视基础知识，要复习所有的公式、定理、定义，多做一些基础题来帮助巩固基本知识。 高等数学中基本概念和性质较多，他们之间的联系也比较多。考生特别要根据高数考试的内容，找出所涉及到的概念与方法之间的联系与区别。注重真题考研历年真题是考研复习必不可少的重要资料，甚至可以毫不夸张地说真题是关系考研成败的关键要素，尤其到了9月份以后，数学复习主要以真题为主。首先考研真题是大家了解考研形势的重要途径。其次考研真题集结了出题老师的精华总结，包含了许多考试信息和讯号，在做真题的过程中，可以掌握出题人的思路以及答题的方式方法。最后真题也是检查考生复习情况的最佳衡量标准。注重归纳总结高等数学涉及的知识点比较多，有些知识点同学们理解起来也比较困难，如果只是一味的做题，容易导致思维混乱，不可能得高分。所以同学们在平时复习时，一定注重归纳总结。高数重点知识点比较多，要逐一击破！数学的复习需要稳扎稳打，掌握住每一个重难点。我是向上好青年，愿你在考研路上勇往直前！考研相关的问题可以私信、评论！

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

【摘要】从大三开始，考生便开始关注与考研政策、择校择专业有关的信息以及考研大纲的消息。了解考研大纲的内容，对初步了解考研很有必要。百优整理了考研数学大纲解析，供考生参考。2019新大纲尚未发布，不过没关系。根据以往经验，大纲的大部分内容是不做大的改动的，所以目前情况下，我们可以参考一下以往的大纲内容，为2019考研备考复习助力!本文通过近年大纲数据进行分析，为考生复习指点迷津。下面根据往年同学备考情况提出一些复习上的建议。2018年考研数学大纲与往年考研大纲保持稳定，根据考研大纲及真题，高等数学是数一、数二、数三中地位最高的，比重最大的科目。从2005年后高数在数一、数三中占比稳定在56%，在数二中占比稳定在78%，因此考研数学的重头戏在高数。下面将基于近年考研大纲及历年真题帮助考生找到高等数学高效的学习方法：1.高数中比较难的有微分中值定理和不等式的证明题，这一部分题目技巧性比较强，难度比较大。2.数一曲线积分和曲面积分在考试中得分率不高，而数二和数三在多元函数微积分里的要求虽然比数一低很多，但得分率也不高。导致这个现象出现的根本原因在于大多数考生对这一部分重视程度不够，基本的积分计算不过关。3.不按照常理出牌。如数三的差分方程，以往出现的频率极低，2003年至2016年没出过，但2017年出了一道小题，4分虽小，但三道小题就是一道大题。又如数一的傅里叶级数，以往出现的频率很低，大概四五年才会出一道小题，但是在2008年，考了一道傅里叶级数的大题，11分，这是任何人事先都没有想到的。又比如说多元积分考查，数一的大题大多出在第二类曲线积分或是第二类曲面积分上，因为这里有一些很重要的公式和定理(格林公式和高斯定理)，题目比较好出。但2010年，数一却是一道第一类曲面积分的题目; 2011年也只考了一道二重积分的题目，这在以往的考研中都是很少见的，但是这些题的知识点又是在大纲范围之内的，不能说它超纲。通过以上的分析，考生们要清醒的知道考试大纲只是指明了考试出题的范围，告诉了我们考试的具体内容以及每一部分内容的考试要求，并没有规定哪一部分内容考的高哪部分考的低。基于此，建议广大考生在复习的时候尽可能地全面，不要因为某一个知识点在真题中出现得比较少就不重视。也不要去相信什么押题，数学考的是基本功，不是靠一两套模拟试卷就能抓得起来的。基本功靠什么?靠做题。现在，同学们脑中一定存在两个疑问，怎么做题?题量究竟多大?就这两个问题，根据往年学员备考情况，给出如下一些建议。众所周知，考研题目的一个特点是综合性较强，在基础扎实的前提下，提高解决综合题目的能力。这个阶段考生可以练习一些综合性较强的题目，可以在市面上选取合适的参考书。辅导材料千千万，适合自己才是真。这里要特别提醒一点真题很重要!很重要!很重要!比如如下两题：大家是否有似曾相识之感。考研数学的题量究竟多大为宜?王国维在《人间词话》说——古今之成大事业、大学问者，必经过三种之境界："昨夜西风凋碧树。独上高楼，望尽天涯路。"此第一境也。"衣带渐宽终不悔，为伊消得人憔悴。"此第二境也。"众里寻他千百度，蓦然回首，那人却在灯火阑珊处。"此第三境也。由于考研数学不同于数学竞赛，考研数学考察基本运算能力。考研数学题量是可以大致估计的。正如王国维做学问有三境界，考研数学做题也有三境界：第一境界，借助辅导材料(如李永乐复习全书)梳理考点脉络，题目以单一考点题目为主，题源来自教材或基础阶复习材料，题量约1000题。第二境界，在第一境界基础上，根据强化阶材料总结的真题题型及方法，训练解决综合题型的能力，题源首选2003至2017年十五年真题(数一、二、三相关题)，题量约1000题。第三境界，在第二境界基础上，注意一些数学概念细节，合理处理考试细节，对做过的题进行总结分析，查缺补漏，题源为以前做过仍有问题的题及1987至2002的真题，题量约1000题。首先，一定要用手“做”题而不是用眼“看”题，正所谓“眼过千遍不如手过一遍”;其次，最好规范做题，“误以题小而不做，误以题简而不为”;最后，要养成刻苦钻研、独立思考、独立做题的习惯，“眼高手低”要不得。百优 希望同学们 既然走上了这条考研路，就勇往直前，相信明年的这个时候，你会感谢今年的自己！PS：（有的童鞋问百优，公众号的免费资料还更新吗？ 答：更，会持续更的，只是前一段时间各个官网给百优投诉了，555...，所以后面文章都不让加人家机构的东西，所以没有发文章 ，但是资料是都更新了的，同学们还在汇总的那个连接里保存即可）本公众号除了“百优拼课”下面的拼课版块外，其他的都是免费下载的，我们为大家整理了2019年考研复习资料汇总页面，具体详情关注微信公众号（百优学习网）在干货菜单中找到。

问一名大学生，大学当中什么科目比较难？大家给出的答案五花八门。学姐罗列了一下数学相关的科目，发现高数是令很多大学生头疼的科目。每次期末考试中，都有很多学生的高数挂科。大学期末考试当中会考到高数，有的专业考研也会考到高数。有的学生就有疑问了：期末考试高数挂科了，考研高数还有希望吗？其实，学姐想说：期末考试成绩跟考研成绩是没有可比性的，因为两者有很大的不同。首先期末考试学生的备考时间不足；然后，考研数学不仅只考高数，还有线性代数、概率论与数理统计等；最后，两者的考试范围、难易程度等也不同。虽然期末考试高数挂科了，但只要积极备考，好好准备，考研数学照样能拿高分。那么，考研数学如何拿高分？1. 重视双基高中学习重视“双基”，大学学习也一样。“双基”包括基础知识跟基本技能。基础知识就是教材上的基本概念、公式、定理。基本技能就是考研所需要具备的各项能力。很多学生基础知识不扎实，概念不清楚、公式记不牢、定理不会用，这样是很难在考试当中拿到高分的。尤其在高数当中有很多的基本概念跟性质，考生备考的时候更要注意理解，学会应用。2. 多做题、勤练习考研数学想要拿高分，多做题、勤练习是必不可少的。只有多做题，我们才会找到题感，遇到相同或者类似的题时，思路如泉涌。当然我们要学会从海量的题库中淘金。不是所有的题都需要做，况且题库中的题是做不完的。我们要学会选择性做题，做题的时候避免做怪题、偏题，选择适合自己能力水平的题来做，还有就是哪里不会补哪里。3. 常反思、多复习只做题不反思，可能就会形成一种错误的思维定式，导致同样的题目反复错。只反思不复习，我们明知有坑，可做题的时候还是止不住往坑里跳。所以，我们不仅要做题，还要常反思、多复习。反思题目的考点、解题思路、易错点、误区等。复习学过的知识点、做错的题目、记不牢的公式等。4. 重视真题的价值考研真题是含金量最高的题，不管哪科的复习，最后少不了的就是研究真题，考研数学也一样。为什么真题的研究价值高呢？因为真题是出题老师间接透露的考试信息，它蕴含了出题老师的出题思路，蕴含了考点、答题规律跟技巧，是考研数学的风向标，也是衡量学生数学成绩的标准。5. 考前掌握应试技巧考研是一次综合性考试，不仅考察学生的知识储备量，还考察学生的临场应变能力。所以考前掌握必要的应试技巧是非常重要的。在考试之前，考生可以通过研究真题的方式，合理分配答题时间，制定准确的答题策略。这样等真正考试的时候，就不至于那么慌乱，也不至于出现突发情况时，没有应对措施。学姐说：大学当中的高数难是公认的，但是难并不意味着它就不能攻克。只要我们想攻克，并且为攻克高数做了全面充足的准备，就一定可以攻克。所以，首先我们不能对它存抵触心理；其次，要迎难而上；再次打牢基础，弥补不足；最后多练习、勤反思、常复习。相信通过我们的持之以恒的努力，定可以取得好成绩。考研数学大家是如何攻克的，欢迎评论区留言，我们共同讨论。

鉴于有些平台无法显示一些特殊的数学符号，笔者就把整理好的资料以图片形式呈现出来。

就总体难度而言，2019年考研数学一试题与2018年相比，难度相差无几。这与近年来的考研趋势是非常契合的，随着考研人数的增加，试题的难度也在增加，这也体现了考研是选拔性考试的特点，不过从2013年开始试题的难度整体是比较平稳的。另外，2019年的考研数学一高数部分试题体现了考研数学的一贯特点：重基础，综合性强，计算量大。首先，考题重在考查学生对基本概念的理解和运用数学的基本方法来解决基本问题的能力。其实从1990年到2019年以来，重基础这个出题的侧重点从未改变过。与此同时，近几年试题中不断凸显的综合性和灵活性增加了考试的难度，要求考生注重对方法的总结和能力的培养，从而做到活学活用。最后，计算量大的特点要求考生要多做题，只有量的积累才能把计算能力提升上来，在考场上不仅做到会，而且要快，这样才能考取理想的分数。考研是一场持久战，要把握好复习的节奏，尤其是对考研数学的复习，制定好复习计划，进而保证高数复习的效率。因此，中公考研制定了比较科学的梯度学习法，把考研数学全年的复习计划划分为四个阶段，即基础阶段(6月份之前)、强化阶段(7-9月份)、提高阶段(10-11月份)以及冲刺模考阶段(12月份)。以上四个阶段循序渐进，每个阶段都有对应的学习任务和目标，一步一个脚印，稳扎稳打。考生在复习中，最重要也是最容易忽视的就是基础阶段，只有打好基础，具备扎实的基本功，这是最关键的一个环节，这与考查目标—重基础是非常契合的。在此基础上，通过适量的练习做到灵活运用，最后才能够转化为考场上的得分能力。最后，中公考研祝各位考生取得优异的成绩，考取理想的学校!