【1】微臣教育GRE数学---B班(强化练习班)__第一、二章

Bo Wang (UVA)
GRE Math
Aug 2015
9 / 106
Example
x 3=1 Quantity A x Solution: x = 4 §±quantity Aåß¿A Quantity B 3
Bo Wang (UVA)
GRE Math
Aug 2015
10 / 106
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Bo Wang (UVA)
GRE Math
Aug 2015
16 / 106
Integers)Í
Integers)ÍßPositive Integers')ÍßNegative IntegersK)Í ÿ% ":µ '+' ='ß '*'='ßK +K=KßK *K='
Example 1
a,b,c are all integers, suppose a3 b 4 c 5 is negative then which of the following CANNOT be true? A a+b >0 B b+c >0 C a+c >0 D ac > 0 E abc > 0
Example 6
M If N 2 and 5 are both integers, which of the following expression must also be an integer? M A N+ 7 NM B 7
C D E
2 N +M 10 NM 10
N +M 2 5
Bo Wang (UVA)
GRE Quantitative Reasoning (Step 2)

gre sub科目GRE数学（GRE Math）GRE数学是GRE考试中的一个重要科目。

在GRE数学中，主要涵盖了代数、几何、概率与统计等数学领域的知识。

下面将从几个方面介绍GRE数学的一些重要内容。

一、代数（Algebra）代数是GRE数学中的一个重要部分。

代数涉及了方程、不等式、函数、多项式等内容。

在代数的学习中，需要掌握解方程、求根、因式分解、多项式运算等基本技巧。

此外，还需要熟悉各类函数的性质，如线性函数、二次函数、指数函数、对数函数等。

二、几何（Geometry）几何也是GRE数学中的一个重要内容。

几何主要包括平面几何和立体几何两个部分。

在平面几何中，需要掌握平行线、垂直线、三角形、四边形、圆等基本图形的性质和计算方法。

在立体几何中，需要了解立体图形的表面积和体积计算方法，如长方体、正方体、圆柱体、圆锥体等。

三、概率与统计（Probability and Statistics）概率与统计是GRE数学中的另一个重要内容。

概率涉及了事件发生的可能性，需要掌握概率的计算方法和性质。

统计则关注数据的收集、整理和分析，需要了解统计学中的基本概念和统计量的计算方法。

四、数论与离散数学（Number Theory and Discrete Mathematics）数论与离散数学是GRE数学中的一些较为高级的内容。

数论涉及了整数的性质和性质的证明，需要理解素数、最大公约数、最小公倍数等概念。

离散数学则关注离散对象的性质和计算方法，如集合论、图论、逻辑等。

五、数据分析（Data Analysis）数据分析是GRE数学中的一个重要考点。

数据分析主要包括数据的收集、整理、分析和解释等内容。

在数据分析中，需要掌握数据的描述统计方法，如平均数、中位数、众数、标准差等，以及数据的图表表示和解读。

GRE数学是GRE考试中不可忽视的一部分。

在备考过程中，需要对代数、几何、概率与统计、数论与离散数学以及数据分析等内容进行系统的学习和掌握。

2022年GRE考试数学几何部分总结范文2022人教版一年级数学下册总结范文新东方金牌名师直冲高分！2022年GRE考试全程课程火热开售中>>GRE数学考试对大陆考生来说难度不太大，并不算是一块难啃的骨头。

GRE考试拿高分的主要难度集中在对专业术语及题意理解上，不过，为了稳妥起见，大家还需要认真复习GRE数学题所涉及到的概念，公式，并对GRE数学常考题有一定的了解。

1.两条直线比斜率:一条某轴intercede3,y轴intercede4,和一条某轴intercede4,一个y轴intercede3.解：lope1=(4-0)/(0-3)=-4/3lop2=(3-0)/(0-4)=-3/4注意由于两条直线的斜率是负数,后者斜率大一些.2.直线y+某=4,与某^2+y=4交点的距离解：meykey:根号2。

4-某=4-某23.有一个题目觉得很有意思，就是问y=某某某+1和y=某-1的图是下列哪一个比较简单。

选的是D。

(veryure)4.一直线在某轴截距为a，Y轴上截距为b，问斜率是多少。

(-b/a)解：两点式：列出两点(a,0)(0,b),k=(b-0)/(0-a)=-b/a5.圆里头最长的线段是哪条就是直径6.图中一三角形,某,,Z分别为两个角的外角,Y为第三个内角,问某+Z 与180+Y的大小解：Y+(180-某)+(180-Z)=180(内角和为180)可退出Y+180=某+Z所以相等7.钝角三角形，两短边为6，8，问其面积与24的大小。

解：(小)8.三角形三边为8,5,6,问5,6夹角于90谁大mykey:前者大.9.三角形三条边6，8，10.5，问6和8所对的两个角相加与90度比解：小于。

(因为由勾股定律知其一定是钝角三角形)10.45度的直角三角形，面积是16，问斜边。

解：答案是8(简单)11.一个圆，a度的扇形的其他剩余面积的比是多少解：答案是a/(360-a)12.圆里面有个三角形，其中一条边是直径。

GWC填空讲义2017年8月微臣GRE冲刺班使用说明本讲义属于GWC（微臣GRE）练习的填空部分，供微臣2017年GRE冲刺班使用，共5个Section，每个Section 10道题目，合计50道题目。

这些题目出自2014年—2015年GRE考试中的珍题，我们将其中在最近3年考试中反复出现的高频题目进行挑选，组成这本GWC填空讲义。

在课程开始之前，在拿到讲义之后，在课前应当进行讲义的预习，不计时间，完成讲义上所有题目的练习。

在课程进行之中，应当每天跟随老师讲解的节奏，认真细致地弄明白每一道题目的方程等号、强词、对应关系、答案与选项单词以及3s版本。

同时每天下课后，要进行当日笔记的整理与总结。

在课程结束之后，用空白版本的讲义，掐时间，对每道题目进行计时训练。

其中第一部分15分钟完成，第二部分30分钟完成，第三部分30分钟完成，第四部分20分钟完成。

在对答案之后，要能自己标出每道题目的方程等号和强词，弄懂每个选项单词的含义，写出本题的3s 版本。

每道题目至少要训练3遍。

上考场前，GWC的所有题目务必烂熟于心，同时，记住了这些题目的答案并不意味着真的会了这些题目，大家掌握的应该不仅仅是这50个填空题目，弄懂关系才是王道。

掌握微臣的填空程序，才是这些题目背后更大的价值。

最后，祝各位考试顺利，早日杀G成功。

Section 11.Though the volume of radioactive waste produced by nuclear power plants is _______, theproblem of how to dispose of that waste is not: rather, it is of major importance.A.unmanageableB.troublingC.significantD.smallE.deceptive2.Carmen’s affection for her sister, though not _______, was plainly too great to permit apainless departure.A.unsteadyB.ambivalentC.carelessD.unboundedE.noticeable3.Readers may initially be irked by the book’s apparent (i)_______ but, once immersed in the4.The national bank has been uncommonly powerful in comparison to its counterparts in othernations. It retains this potency partly because its control of the nation’s banking system is5.Although movie critic Pauline Kael had a distaste for sycophancy, she also had a need for(i)_________, as a consequence of these competing feeling, she sent very (ii)________ signals6.Biologists have little (i)______ drawing the link between the success of humanity and human(ii)______. Indeed, many biologists claim that this attribute, the ability to (iii)______, or, to put it more sharply, to make individuals subordinate their self-interest to the needs of the group,7.Coagulation factors are useful proteins whose simple names — many are known only byRoman numerals —______ their importance and the specificity of their roles in the thinning and clotting of blood.A.nullifyB.obviateC.mitigateD.belieE.maskF.accentuate8.For all the ______ the new CEO has received from the press recently, her staff have adecidedly less rosy view of her.A.encomiumsB.tributesC.evaluationsD.critiquesE.attentionF.publicity9.When studying the ancient Greek astronomers, Copernicus realized that despite the intrinsicbeauty of many of their arguments, the ancients often made claims that ______ logic.A.refutedB.questionedC.influencedD.swayedE.defiedF.disregarded10.It is hardly ______ the committee calls for: rudimentary competence would be an improvementon the current chaos.A.accountabilityB.disarrayC.unrulinessD.faultlessnessE.loyaltyF.perfectionSection 21.History teaches us that science is not _________ enterprise, indeed, it is quite the opposite, amotley assortment of tools designed to safeguard researchers against their own biases.A.an opportunisticB.an anomalousC. a haphazardD. a collectiveE. a monolithic2.The museum’s compelling new architectural exhibition looks at eleven projects around theworld that have had major (i)__________ impacts despite modest budgets. It is part of (ii)_________ in the museum’s architecture and design department, which in the past has3.Recent scholarship has questioned the (i)________ of tropical forests around the world.Archaeologists have shown, for example, that the largest contiguous tract of what was thought to be virgin rain forest in the southern Amazon had been transformed into a cultural parkland before European contact, and many of the forest islands in West Africa’s savanna forest4.The slow pace of job creation was without precedent for the period of recovery from arecession, but the conditions that conspired to cause the recession were also (i)_______. The stock market declined sharply, and rampant business investment slumped. Then an ensuing spate of scandals (ii)__________ public trust in the way companies were run. And yet, despite5.Those who took Clark’s old-mannered compliance for obsequiousness (i)______ him: hisapparent (ii)______ veiled a fervent (iii)______ of the authority that others exercised over him,6.The (i)______ quality of much contemporary drawing may be attributable to the use ofphotography as a drawing shortcut. Photography (ii)______ modern arts, but when it is used asa tracing tool in order to (iii)______ the difficulties of achieving correct proportion, the7.The laboratory maze has grown ever less_______ since it was first invented instead of hopingto lose a rodent in a labyrinth, today’s scientists design mazes to elicit a few simple, easily measured behaviors.A.intricateB.extensiveC.effectiveD.convolutedefulF.prevalent8.Jackie Wullschlager’s biography of Hans Christian Andersen ______ the insipid sweetnesswith which Andersen coated his life and reveals a vulnerable gingerbread man with a bitter almond where his heart should be.A.conjures upB.imaginesC.strips awayD.overlooksE.removesF.ignores9.Far from _________ innovations, as the patent system was designed to do, the patenting ofconcepts such as gene sequences gives individuals and corporations a legal chokehold over ideas that should be useful to all.A.spurringB.recognizingC.codifyingD.acknowledgingE.fosteringF.cataloging10.Doris Kearns Goodwin’s elegant, incisive study of Lincoln ________ those whose knowledgeof Lincoln is an amalgam of high school history and popular mythology as well as those who are experts.A.gratifyB.enticeC.inspireD.confuseE.perplexF.pleaseSection 31.The province has long claimed to be just another developing region, even as its economy________ those of other regions and threatens to eclipse the rest of the country combined.A.parallelsB.bolstersC.corroboratesD.outstripsE.engages2.Many readers today consider the moral sentiments expressed in the ancient writers’ work to bequite vapid, and in the seventeenth century they were similarly regarded as ______.A.jejuneB.didacticC.dogmaticD.tendentiousE.arcane3.So, perhaps the lesson is that rather than wanting their monarchy to (i) ______ its modernized4.The (i)________ of molecular oxygen on Earth-sized planets around other stars in the universewould not be (ii)_______ sign of life: molecular oxygen can be a signature of photosynthesis (a biotic process) or merely of the rapid escape of water from the upper reaches of a planetary5.There are two opposing theories about mountain formation and climate over the past 40million years: either the surge of mountain building (i)________ the global cooling, or vice versa. The first of these two theories asserts that widespread mountain building cooled the earth as result of (ii)________mountains and climate. For example, mountain glaciers tend to be (iii)________: once established, they increase the reflectivity of the surface, thus lowering6.Gravitational waves----ripples in the geometry of space-time----are analogous toelectromagnetic waves. The challenge in trying to observe these waves directly is that they are extremely weak. To make waves large enough to be (i)________, the most (ii)________ events in the universe are required: supernova explosions, the formation of black holes, or the collision of stars. Even so, the effects are (iii)________. The geometry changes so little that a7.Any notion of justice in the fortunes of artists is _________: works of equal value and qualityproduce quite different returns or no returns at all.A.baselessB.clichéC.untenableD.insultingE.condescendingF.idealistic8.Although legislators on both sides of the issues have repeatedly________ a desire to find amiddle ground, until now no acceptable compromise has been achieved.A.discussedB.proclaimedC.professedD.rejectedE.disownedF.betrayed9.Tompkinson’s prior donations to the university, while very generous, failed to _________ themagnitude of her latest gift.pensate forB.portendC.clarifyD.predictE.offsetF.undermine10.Space is often referred to as the final frontier, as the only realm of which humankind has still togain substantial understanding, yet the ocean is also another vast area about which our knowledge is ________.A.erroneousB.confusingC.frustratingD.rudimentaryE.delusiveF.sketchySection 41.In protoscientific times (for example, in ancient Greece), claims about the physical world wereoften accepted as true if they were reasonable; experimental verification, if thought necessary at all, was ______.A.utilitarianB.perfunctoryC.egregiousD.empiricalE.inductive2.Barring the discovery of new letters, hidden diaries, or the like, fresh information abouteminent people is hard to find because their lives have been so intensely _________.A.ridiculedB.scrutinizedC.admiredD.embellishedE.underrated3.The material covered in this article has been (i)______in previous publications, and since4.The author paints a rather dark picture of book publishing as a hidebound industry, one that isfacing a profound change in its mode of production but is so (i) _______ its past as to be5.Proponents of international regulation of environmental issues have always struggled againstscientific uncertainty and economic hostility. The two obstacles, from a political standpoint, often have been closely related, as economic hostile toward environmental regulation for economic reasons have (i)________the considerable scientific uncertainty underlying mostws protecting intellectual property are intended to stimulate creativity, yet some forms ofcreative work have never enjoyed legal protection—a situation that ought to be of great interest. If we see certain forms of creative endeavor (i)________ as a result of uncontrolled copying, we might decide to (ii)________ intellectual property law. Conversely, if unprotected creative work (iii) ________ in the absence of legal rules against copying, we would do well to7.There are many insights in the essays collected in Observations on Modernity, but they areembedded in a dense English translation of a dense German original that may make many of them________ to most readers.A.vapidB.inaccessibleC.sagaciousD.banalE.distressingF.opaque8.Natural causes nerves to die off and muscles to weaken, but regular exercise muscle enlargesfibers and can________ the decline by increasing the strengthen muscle you have left.A.speed upB.stave offC.forestallD.facilitateE.assistF.exploit9.When the atmosphere over the city is at its best, it is peculiarly ______, and this clarity seemsto distill the very special beauty of the place.A.limpidB.acuteC.calmD.sharpE.pellucidF.tranquil10.An apparent paradox led the scientists to pursue their present line of research. They werestruck by the fact that a single mathematic formula can be used to describe physical phenomena that appear to be so ______.A.rudimentaryB.interdependentC.interrelatedplexE.heterogeneousF.dissimilarSection 51.Paintings created in India during the Mughal dynasty were________ in ambition butornamental in presentation: in one direction, they have an affinity with newspaper photographs, while in the other they have the intricacy of jewels.A.metaphoricalB.documentaryC.aestheticD.sectarianE.baroque2.Recent scholarship has questioned the (i)________ of tropical forests around the world.Archaeologists have shown, for example, that the largest contiguous tract of what was thought to be virgin rain forest in the southern Amazon had been transformed into a cultural parkland before European contact, and many of the forest islands in West Africa’s savanna forest3.Scientific papers often (i)______ what actually happened in the course of the investigationsthey describe. Misunderstandings, blind alleys, and mistakes of various sorts will fail to appear in the final written accounts because (ii)______ is a desirable attribute when transmitting4.Even the reader acquainted with the outlines of Pushkin’s biography will be (i)______the(ii)______ so vividly conveyed in Binyon’s biography. Not only was Pushkin’s personal correspondence intercepted and his movements (iii)______, but Tsar Nicholas I’s decision to5. A transformative scientific idea that emerged in the eighteenth century was the realization thatslow, inexorable geological processes follow the basic laws of physics and chemistry. This seems (i)________ conclusion in hindsight, but its implication----that geological processes in the distant past must have (ii)________ these very same laws----was (iii)________ geologists6.Unlike most other serious journals, which drain money from their owners, the Review has longbeen (i)_________. But the formula is not without its imperfections, which have grown more pronounced in recent years. The publication has always been erudite and (i)_________ but not always lively and readable. (iii)_________, accompanied by a certain aversion to risk taking,7.Noise suppression in phones can play an important role in making cellphone networks moreefficient, since when sounds that are________ to the meaningful signal are transmitted, precious network bandwidth is wasted.A.unsuitableB.detrimentalC.irrelevantD.confinedE.limitedF.extraneous8.Although Wynne claims to recognize that________ data are available to make definitivestatement, she offers them nonetheless, arriving at some sweeping generalizations.A.concreteB.finiteC.insufficientD.indirectE.conclusiveF.meager9.His premiership, seemingly cast-iron a year ago, is now so vulnerable that even a good day atthe office does no more than buy him a few weeks of ________ from rebels within his own party.A.controversyB.reproachC.respiteD.reliefE.blameF.deference10.There is frequently a protracted time interval between the introduction of an innovative musicalcomposition and its public acceptance: the concert-going public often spurns the ______ in favor of the familiar for a prolonged period.prehensiveB.intricateC.novelD.originalE.intelligibleplex。