2020年新GRE数学模拟考试试题及答案
GRE_OG_数学精选
1.y=2x2+7x – 3x y本体答案不确定。
我开始做的时候被题目放了烟雾弹，以为要经过什么特别处理，像配方啥的。
但配着配着就感觉不对劲，x与y只有函数关系，没有绝对的大小关系嘛。
汗2.The figure above shows the graph of a function f, defined by f(x)=|2x|+4for all numbers x. For which of the following functions g defined for allnumbers x does the graph of g intersect the graph of f ?A g(x)=x–2B g(x)=x+3C g(x)=2x – 2D g(x)=2x+3E g(x)=3x – 2这个题就是问两个函数图象相交的问题，根据观察，要与这个折线相交的直线的斜率满足的条件是要么是正斜率比2大，要么是负斜率比-2小，因此只能选E了。
3.Each employee of a certain company is in either Department X orDepartment Y, and there are more than twice as many employees inDepartment X as in Department Y. The average (arithmetic mean) salaryis $25,000 for the employees in Department X and is $35,000 for theemployees in Department Y. Which of the following amounts could bethe average salary for all of the employees in the company?Indicate all such amounts.A $26,000B $28,000C $29,000D $30,000E $31,000F $32,000G $34,000本题我们要注意到题目中的more than twice的字眼，我们当做twice算的时候，结果是（25000*2+35000）/3约等于28333，因为有more than，所以选的答案要么是比前面这个数大，要么小，又由于more的是X部门的，那么肯定会将平均工资给拉低了，因此，选比前面那个数小的答案，AB都可以了。
2020年GRE模拟试题及答案(卷五)
2020年GRE模拟试题及答案（卷五）Investors are grateful that the attorney general has stepped in to pursue inquiries into misfeasance on the financial markets, given that the regulators officially charged with policing the industry have been _____.A：diffidentB：meticulousC：straightforwardD：implacableE：tenacious答案：AA significant element of the Gothic genre, the literary grotesque is sometimes inaccurately discussed as if it were a _____Gothic or, conversely, as if it were something entirely different from Gothic.A：synonym forB：characteristic ofC：counterweight toD：ramification ofE：deviation from答案：AIn his study of Senegambian cleric Shaykh Mass Kah (1827-1936), Bala S. K. Saho notes that it is difficult to fully (i) _____many of the oral accounts on which the study relies. Saho’s work shows, however, thatdespite this absence of (ii)_____ , oral history can provide useful sources from which historians can reconstruct the past.Blank (I)Blank (II)A：comprehend D：partialityB：reproduce E：argumentationC：validate F：corroboration答案：CFThe city’s traffic-planning department has been working hard to (i) _____drivers. Closely spaced stop lights have been added on roads into town, causing delays. Pedestrian underpasses designed to allow traffic to flow freely across major intersections have been (ii)_____ .Blank (I)Blank (II)A：assist D：enhancedB：calm E：stabilizedC：discourage F：removed答案：CFThe (i) _____current-generation solar cells are (ii)_____ : although experimental cells have reached efficiencies greater than 40 percent, most commercially available cells in the early part of the twenty-first century still struggle to get past about 20 percent.Blank (I)Blank (II)A：attractions of D：clearB：limitations of E：unmatchedC：improvements in F：misunderstood答案：BDEven those observers who are the most _____about genetic privacy issues would have to concede that genetic discrimination is rare: there have only been two cases of any notoriety.A：sanguineB：zealousC：candidD：objectiveE：apathetic答案：BShe constantly _____herself for not living up to her own ideals—for not working hard enough or not having motives that were pure enough.A：exaltedB：coddledC：excoriatedD：mollifiedE：deluded答案：CAncient cart ruts found on Malta were created in soft limestone that begins to dissolve when exposed to rainfall. Their forms thus necessarilybecome (i)_____over time and their original features are (ii)_____ .Blank (I)Blank (II)A：solidifed D：refinedB：degraded E：replicatedC：conspicuous F：obscured答案：BFMaking loans and fighting poverty are normally two of the least glamorous pursuits around, but remarkably enough put the two together, and you have an economic innovation that has become not just (i) _____but downright (ii) _____.Blank (I)Blank (II)A：popular D：chicB：pointless E：unfathomableC：dangerous F：sensible答案：ADConvinced of the gravity of her poetry, Voigt must have found the reviews of her most recent collection (i)_____ reading: one amused reviewer thought that it was unrecognizable as poetry but decidedly (ii)_____ .Blank (I)Blank (II)A：tempting D：inspiringB：depressing E：irritatingC：thrilling F：diverting答案：BFCommon and easily accessible resources (prey for predators or hosts for parasites) should be, all other things being equal, used frequently, yet in some environments apparently accessible and suitable resources remain _____.A：vulnerableB：unobtainableC：sustainableD：depletedE：unexploited答案：EEven though the authors repeatedly_____ their own shrewdness, they show a remarkable credulousness toward far-fetched ideas such as carbon-eating trees and cloud-making machinery.A：soft-pedalB：extolC：deprecateD：broadenE：compromise答案：BThe (i)_____ of molecular oxygen on Earth-sized planets aroundother stars in the universe would 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 planetary atmosphere (an abiotic process).Blank (I)Blank (II)A：dearth D：a controversialB：presumption E：an unambiguousC：detection F：a possible答案：CEIn reviewing cases decided by lower courts, Supreme Court justices search for precedents to justify their arguments. Reliance on precedent (i)_____ judicial restraint: the precedent (ii)_____ a judge’s ability to determine the outcome of a case in a way that he or she might choose if there were no precedent.Blank (I)Blank (II)A：promotes D：establishesB：compromises E：constraintsC：promulgates F：prioritizes答案：AEAs he has matured as a scholar, Felmar has come to see the merit of qualification. His conclusions, which early in his career he (i) _____, are now often (ii) _____.Blank (I)Blank (II)A：stated as absolute D：hedgedB：refused to reveal E：simplifiedC：backed up extensively F：reiterated答案：ADThe inconspicuous location and lack of striking vistas that characterize the villa reflect the_____ aspect of its creator’s personality.A：volatileB：grandioseC：gregariousD：self-effacingE：imperious答案：DThe chairman, faced with the need to forge a consensus on a number of proposals,acknowledged that it would be difficult to reconcile the push for a radical overhaul with the stance of those who want _____change.A：deliberateB：indiscriminateC：genuineD：immediateE：wholesale答案：ARecently released statistics on the prevalence of heart disease in the United States, while (i)_____ , nevertheless reflect a decline from heights reached in the 1960s, before health officials began publicly (ii)_____ people to guard against heart disease.Blank (I)Blank (II)A：definite D：entreatingB：sobering E：defyingC：implausible F：absolving答案：BDThe humor in this play derives from its (i)_____ . The new production, however, inexplicably goes in the opposite direction; it is so (ii)_____ that the audience does not even seem to realize that the play is supposed to be a comedy.Blank (I)Blank (II)A：verbal nimbleness D：accessibleB：political allusions E：ploddingC：deadpan dialogue F：implausible答案：AETo say the actors were (i)_____ their director is an understatement: a director who is visibly bored by his cast and their performances is hard to (ii)_____ .Blank (I)Blank (II)A：disappointed in D：lambastB：accepting of E：displeaseC：motivated by F：suffer答案：BFWhen pulsars were first discovered, some of the astrophysicists involved briefly (i)_____ these types of stars might be (ii)______extraterrestrial intelligence. Specifically, the pulsar’s periodic radiation pattern was initially interpreted as (iii)______ rather than—as it turned out to be—the natural product of the spinning of a neutron star.Blank (I)Blank (II)Blank (III)A：ignored whether D：suggestive of G：a deliberate hoaxB：thought that E：unrelated to H：an episodic phenomenonC：disavowed that F：evidence against I：a constructed code答案：BDIThere has been great enthusiasm in the United States for reducing fossil fuel dependence by increasing production of biofuels from crops such as corn and switchgrass, but this (i)_____ about biofuel’s potential should be (ii)_____ by a realistic appraisal of the costs and challenges of biofuel production.Blank (I)Blank (II)A：forbearance D：temperedB：exuberance E：delineatedC：obduracy F：exacerbated答案：BDUntil now,old snapshots and home movies faded and crumbled and were eventually (i)_____.Only a few precious mementos were preserved and passed along. But as photography moves into the digital realm, family albums and home videos seem capable of (ii)_____: our capacity to store them is, for all practical purposes, approaching the infinite. Is such a transformation a good thing? The natural world teaches us that (iii)_____ are vital to ecological health. Does a similar principle apply to communal memory?Blank (I)Blank (II)Blank (III)A：archived D：transmission G：death and decayB：discarded E：immortality H：predator and preyC：reproduced F：revolution I：reproduction and renewal答案：BEGThe threat of litigation makes the art authentication industry _____ realm: connoisseurs refuse to communicate in writing and confidential agreements bind authenticators to silence.A：an opportunisticB：a clandestineC：a moralizingD：a xenophobicE：an anarchistic答案：BRecent research runs counter to the long-cherished notion that a small drop in body temperature during and after surgery is either _____ or actually protects the patient by slowing metabolism and reducing the body’s demand for blood and oxygen.A：beneficialB：immaterialC：inconsequentialD：preventiveE：prophylacticF：redundant答案：BCThe automation of many of the functions performed at the factory, although initially inspiring_____ in many of the company’s employees, has had none of the deleterious effects forecast either within or beyond the organization.A：indifferenceB：optimismC：ambitionD：arroganceE：trepidation答案：EOne thing both authors have in common is a striking amount of _____: they claim to know how massive institutions, some of them richly endowed, all of them central to American society and culture, should be reshaped.A：hubrisB：proprietyC：biasD：prescienceE：indolence答案：AMaking the shift to the 90-nanometer manufacturing process has been (i) _____for semiconductor companies. This process effectively doubles the manufacturing capacity of the industry, but it (ii)_____ enormous technical challenges because some components of the new semiconductor chips are no more than five to seven molecules thick.Blank (I)Blank (II)A：an unanticipated boon D：circumventsB：a routine accomplishment E：entailsC：a significant struggle F：resolves答案：CEThere has been (i) _____elephant’s fabled mental capacities until recently, when these behavioral observations have begun to be (ii) _____by brain science. MRI scans of an elephant’s brain suggest that even relative to its overall size it has a large hippocampus, the component in the mammalian brain linked to memory and an important part of its limbic system, which is involved in processing emotions.Blank (I)Blank (II)A：surprising credence given to D：buttressedB：a widespread dismissal of E：anticipatedC：only anecdotal evidence for F：overwhelmed答案：CDThe description of Green’s scholarship as (i)_____ is grossly misleading: while her research on interstellar particles is not especially novel, the conclusions she draws from her data are (ii)_____ .Blank (I)Blank (II)A：esoteric D：remarkably pioneeringB：tendentious E：dubiously supportedC：derivative F：strangely comforting答案：CDThe brain has become, for many people, _____ the biologicalmachinations of the self, and the self-knowledge promised by neuroscience has ignited a hunger to understand how new findings weigh in on age-old questions.A：tantamount toB：synonymous withC：implicated inD：divorced fromE：detached fromF：subservient to答案：ABIf you follow your intuition, you will more often than not err by misclassifying a random event as (i)_____. We are far too willing to (ii)_____ the belief that much of what we see in life is random.Blank (I)Blank (II)A：uncharacteristic D：countenanceB：systematic E：rejectC：arbitrary F：champion答案：BEWithin the culture as a whole, the natural sciences have been so successful that the word “scientific”is often used in (i)_____ manner: it is often assumed that to call something “scientific”is to imply that its reliability has been (ii)_____ by methods whose results cannotreasonably be (iii)_____.Blank (I)Blank (II)Blank (III)A：an ironic D：maligned G：exaggeratedB：a literal E：challenged H：anticipatedC：an honorific F：established I：disputed答案：CFIThe researcher found that in assessing others, many people hold an unconscious view that competence and warmth are (i)_____: when they perceive a person to be highly capable, they infer that he or she must have a tendency to be (ii)_____.Blank (I)Blank (II)A：equally important D：ambitiousB：mutually reinforcing E：unfeelingC：inversely related F：disingenuous答案：CEThe era’s examples of _____ that are cited by the author can be balanced in part by certain examples of dissent during the same period.A：diversityB：authoritarianismC：forbearanceD：volatilityE：lucidity答案：BThe researcher noted that microbes, although _____, make up far more of the living protoplasm on Earth than all humans, animals and plants combined.A：invisibleB：omnipresentC：diminutiveD：ubiquitousE：minusculeF：ethereal答案：CEAerial viewings of the gigantic stone horse attributed to the Native American Quechuan people fail to _____ the considerable artistry required to create the piece: the horse appears crudely constructed unless carefully examined from the ground.A：revealB：justifyC：manifestD：mitigateE：diminishF：undercut答案：ACHarper Lee’s narration in To Kill a Mockingbird is _____, mixing an adult’s and a child’s perspective according to no logic other than the immediate exigencies of the plot.A：a paradigmB：a hodgepodgeC：a modelD：an innovationE：a patchworkF：an embarrassment答案：BEChanges made to ecosystem in order to achieve a goal, such as food production or flood control, often _____ significant unforeseen trade-offs between other important products and service the ecosystems provide.A：predictB：delayC：foretellD：obscureE：yieldF：engender答案：EFThe (i)_____ of molecular oxygen on Earth-sized planets aroundother stars in the universe would 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 planetary atmosphere (an abiotic process).Blank (I)Blank (II)A：dearth D：a controversialB：presumption E：an unambiguousC：detection F：a possible答案：CEThe painter’s problem, like that of an author whose early literary masterpiece exhausts the themes it embodies, is how to_____his first highly acclaimed efforts with works of comparable significance and presence.A：combineB：illuminateC：realizeD：amendE：follow答案：ESince many African farmers face a soil fertility problem, providing funding for fertilizer seems_____ ; closer examination of the data raises some troubling questions, however.A：imprudentB：expensiveC：unimpeachableD：modernE：worrisome答案：CIn years prior to the Civil War, Philadelphia’s African American press encouraged readers to be vaccinated against the smallpox.This journalistic campain was initially (i)_____,appealing to readers’sense of communal duty, and became even more(ii)_____once the war started, as smallpox outbreaks began to occur on Philadelphia’s city skirts.Blank (I)Blank (II)A：hortatory D：controversialB：ineffective E：urgentC：widespread F：inopportune答案：AEA hallmark of certain nineteenth-century mystery novels was the reform agenda of their authors, who ostensibly sought to expose economic injustice while depicting the seamy underside of urban life. In reality, however,these claims to a radical political agenda were often (i)_____, meant to give lurid thrillers the appearance of (ii)_____.Blank (I)Blank (II)A：authentic D：escapist appealB：complicated E：high-minded purposeC：disingenuous F：gripping suspense答案：CEIt remains a mystery how Theobroma cacao, which scholars believe originated in lowland Amazonia, was introduced to tropical Mesoarnerica. It must have been a (i)_____process: cacao trees do not easily sprout from seed,need years to mature, and grow only in humid lowland forest. Moreover, in a tropical climate, cacao pods spoil quickly,rendering their transport from lowland Amazonia to tropical Mesoamerica in a single journey by foot or canoe (ii)_____.Blank (I)Blank (II)A：clandestine D：unlikelyB：protracted E：redundantC：spontaneous F：expeditious答案：BDUnlike some mammals—cows and sheep, for instance—that are notably _____, lions have a wide range of facial expressions.A：tractableB：impassiveC：solitaryD：socialE：sluggish答案：BThe research on otters’environmental requirements is surprisingly (i)_____. One reason for this has to do with the estimation of how much they use different areas. Doing so may be (ii)_____ in some kinds of terrain, such as Shetland where the Eurasian otters are active in daytime and have clear individual markings. There it is possible to identify the individuals over stretches of coast of a few kilometers and to see what kinds of coast they use. However, the field conditions are (iii)_____.Blank (I)Blank (II)Blank (III)A：straightforward D：quite problematic G：routineB：controversial E：relatively simple H：deceptiveC：difficult F：largely unnecessary I：exceptional答案：CEIEarly practitioners of the natural sciences developed methods to remove distortions caused by either the research environment or the researcher. Such methods, especially with respect to the researcher, were considered to (i)_____ those (ii)_____ subjectivity whose unbridled expression was thought to (iii)_____ research.Blank (I)Blank (II)Blank (III)A：restrain D：incursions of G：corruptB：reveal E：restrictions on H：justificationC：disguise F：acknowledgements of I：expedite答案：ADGAlthough one can adduce myriad of examples of ecosystem disruption by nonindigenous species, nevertheless most introduced species that survive in fact appear to have quite _____ effects on the ecosystem they have invaded.A：minimalB：triflingC：markedD：conspicuousE：intriguingF：deleterious答案：ABAt Cerro Portezuelo, the task of separating grinding tools from the larger collection of excavated stone objects was (i)_____ the ancient practice of recycling grinding tool fragments for building materials, hammer stones, and other purposes that (ii)_____ their original use.Blank (I)Blank (II)A：complicated by D：complementedB：important to E：obscuredC：independent from F：underscored答案：AEThe researcher noted that microbes, although _____, make up far more of the living protoplasm on Earth than all humans, animals and plants combined.A：invisibleB：omnipresentC：diminutiveD：ubiquitousE：minusculeF：ethereal答案：CEAerial viewings of the gigantic stone horse attributed to the Native American Quechuan people fail to _____ the considerable artistry required to create the piece: the horse appears crudely constructed unless carefully examined from the ground.A：revealB：justifyC：manifestD：mitigateE：diminishF：undercut答案：ACHarper Lee’s narration in To Kill a Mockingbird is _____, mixing anadult’s and a child’s perspective according to no logic other than the immediate exigencies of the plot.A：a paradigmB：a hodgepodgeC：a modelD：an innovationE：a patchworkF：an embarrassment答案：BEChanges made to ecosystem in order to achieve a goal, such as food production or flood control, often _____ significant unforeseen trade-offs between other important products and service the ecosystems provide.A：predictB：delayC：foretellD：obscureE：yieldF：engender答案：EFThe (i)_____ of molecular oxygen on Earth-sized planets around other stars in the universe would not be (ii)_____ sign of life: molecularoxygen can be a signature of photosynthesis (a biotic process) or merely of the rapid escape of water from the upper reaches of a planetary atmosphere (an abiotic process).Blank (I)Blank (II)A：dearth D：a controversialB：presumption E：an unambiguousC：detection F：a possible答案：CEOne of the peculiarities of humans is that we irrationally gravitate to the predictable and avoid risk, whatever the reasons for this _____, it is hardly a sound basis for dealing with complex, long-term problems A：eccentricityB：predilectionC：vacillationD：proclivityE：waveringF：cowardice答案：BDIn protoscientific (for example, in ancient Greece), claims about the physical world were often accepted as true if they were reasonable; experimental verification, if thought necessary at all, was _____.A：utilitarianB：perfunctoryC：egregiousD：empiricalE：inductive答案：BAlthough scientific progress leads to constant revision of ideas, one observation that has remained _____ over the years is that there are a lot of insects in the world: some 950,000 species have been identified.A：robustB：significantC：strongD：perplexingE：confoundingF：obscure答案：ACIn the discussions on international patent law, many (i)_____ issues will probably be pushed far into the future. This cautious approach makes diplomatic sense, since attempts over the past 15 years to reach international agreements on patents have (ii)_____ just such sensitive issuesBlank (I)Blank (II)A：contentious D：approachedB：stimulating E：articulatedC：subjective F：foundered on答案：AFIn the northeastern United States, beaver populations had been critically reduced or even _____ in large areas at the end of nineteenth century; as a result, several states instituted prohibitions on beaver trapping.A：diminishedB：extirpatedC：eliminatedD：devaluedE：weakenedF：underrated答案：BCViewing people as ‘’social atoms’’that obey rather simple rule (which are not unlike the laws of physics), one may discover certain (i)_____. Take, for example, the way channels emerge when people move in crowds. In the midst of initially (ii)_____ movements, one person begins to follow another—in an effort to avoid collisions—and streams of movement emerge. As more people join in, there is greater pull on others to join the flow, and the particular channels become (iii)_____.Blank (I)Blank (II)Blank (III)A：apparent contradictions D：inflexible G：self-defeatingB：unproductive tendencies E：straightforward H：self-aggrandizing C：lawlike regularities F：chaotic I：self-perpetuating答案：CFIGiven children’s active fantasy lives, one might think of truthfulness as (i)_____ virtue in young children, but it turns out that lying is the more (ii)_____ skill. A child who is going to lie must recognize the truth, intellectually conceive of an alternate reality, and be able to convincingly sell that new reality to someone else. Therefore, lying (iii)_____ cognitive development and social skills in a way that honesty simply does not.Blank (I)Blank (II)Blank (III)A：an instinctive D：advanced G：underminesB：an acquired E：practical H：forgoesC：a conscious F：mundane I：demands答案：BDIAfter rising continuously over the summer, commodity prices fell, leaving analyst wondering whether the downward trend is a turning point or merely a _____ before demand picks up in the winter months.A：spikeB：upsurgeC：harbingerD：portentE：lullF：respite答案：EFThe juxtaposition of fertile alluvial soils originating in the Andes with the infertile inland soils of central Amazon Basin is one example of _____ of the soil conditions that can be found in the tropics.A：intractabilityB：heterogeneityC：incompatibilityD：disparatenessE：instabilityF：fragility答案：BDHis new role gives the normally clownish actor achance to impress audiences with his (i)_____. He is among the most uninhibited comic performers around, but here he buttons his lip and stares straight ahead.Perhaps without quite knowing it, the audience waits for a wink, a hint that some of the (ii)_____ spirit that animated his previous movies might be lurking inside the (iii)_____ manner he presents in this film.Blank (I)Blank (II)Blank (III)A：raillery D：madcap G：facetiousB：effusiveness E：lugubrious H：reserved C：forbearance F：edifying I：beguiling答案：CDH。
GRE考试数学历年真题全景解析2024
GRE考试数学历年真题全景解析2024GRE考试是许多申请研究生学位的学生必须参加的考试之一。
数学部分是其中一个重要的组成部分。
为了帮助考生更好地掌握GRE数学考试的内容和解题技巧，本文将对2024年的GRE数学历年真题进行全景解析。
一、整数与基本运算整数是数学的基础，GRE数学考试经常涉及整数的概念和运算。
在2024年的数学部分真题中，有一道题目如下：1. 若a和b都是整数，且a>b>0，则a^2 - b^2等于多少？解析：首先，我们可以利用差平方公式将a^2 - b^2进行分解。
根据差平方公式，我们有a^2 - b^2 = (a+b)(a-b)。
根据题目中的条件a>b>0，我们可以确定a+b>a-b>0。
因此，答案是a^2 - b^2 = (a+b)(a-b)。
二、代数与方程代数和方程是GRE数学考试中的另一个重要主题。
在2024年的数学部分真题中，有一道关于代数与方程的题目如下：2. 对于方程2x + 3y = 12，下列哪个点是其解？(A) (1, 5)(B) (3, 4)(C) (6, 0)(D) (-2, 6)(E) (0, 4)解析：我们可以将选项依次代入方程2x + 3y = 12中，看哪个选项满足等式。
对于选项(A)，代入x=1，y=5后，我们得到2(1) + 3(5) = 2+ 15 = 17，不满足等式。
同样地，对于选项(B)、(C)、(D)、(E)，都不能满足等式。
所以，这个方程没有整数解。
三、概率与统计概率与统计是GRE数学考试中的另一个考点。
在2024年的数学部分真题中，有一道关于概率与统计的题目如下：3. 一组学生的平均年龄是20岁，如果其中5名学生的年龄为22岁，另外3名学生的年龄为18岁，其他学生的年龄保持不变，则平均年龄变为多少岁？解析：首先，我们可以计算这组学生的总年龄。
根据题目，我们可以知道总年龄为20 * (5+3+n)，其中n代表其他学生的数量。
GRE数学强化 答案版
1. Which of followings is f(-x) = -f(x)? A) Key: A
2
x3 x 2 +1
B) x 4 x 2
C) x ( x x )
2
D) x ( x x)
3 2
2. If x + y ≤ 11, what is the greatest value of x*y? (x and y are positive integers) __30___. 3. In a rectangle of which width and height is 10 and 12 each, a circle is located. If the diameter of the circle is 8, what is the area of the rectangle except the circle? __120-16pi___. 4. x and y are positive integers greater than 1. If 4x + 12y = 100 and x < y, what is the value of x? Key: 4 5. 一个数把它的小数点(radix point)向右移 6 次，得到的数是原来这个数的倒数(reciprocal) 的 9 倍，求这个数。___0.003 & -0.003___. 6. 三角型三边长 5，6，8，问 5，6 边夹的那个角(intersection angle)和 90 度比较。前者大 7. 投资本金$96,000 (principal)，simple interest，第一个月拿了$960 利息，问 simple annual interest rate 多少。Key: 12% 8. 是一个正五边形(regular pentagon)，它的边长是另一个正五边形边长的两倍，问小的那个 正五边形是大的正五边形面积的几分之几。__1/4___. 9. 给一组四个数，为82, 84, 85, 87，另外一组是这四个数都减去一个x，问两组的standard deviation大小。一样大 10.数列题， An
GRE(QUANTITATIVE)综合模拟试卷20(题后含答案及解析)
GRE（QUANTITATIVE）综合模拟试卷20(题后含答案及解析) 题型有：1. 计算题1．When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?正确答案：112．Ellen has received the following scores on 3 exams: 82, 74, and 90. What score will Ellen need to receive on the next exam so that the average(arithmetic mean)score for the 4 exams will be 85?正确答案：94解析：Let x represent the score on Ellens next exam. This initial step of assigning a variable to the quantity that is sought is an important beginning to solving the problem. Then in terms of x, the average of the 4 exams iswhich is supposed to equal 85. Now simplify the expression and set it equal to 85:Solving the resulting linear equation for x, you get246 + x = 340 x = 94Therefore, Ellen will need to attain a score of 94 on the next exam.3．A mixture of 12 ounces of vinegar and oil is 40 percent vinegar, where all of the measurements are by weight. How many ounces of oil must be added to the mixture to produce a new mixture that is only 25 percent vinegar?正确答案：7.2解析：Let x represent the number of ounces of oil to be added. Then the total number of ounces of the new mixture will be 12 + x, and the total number of ounces of vinegar in the new mixture will be(0.40)(12). Since the new mixture must be 25 percent vinegar,Therefore,(0.40)(12)=(12+ x)(0.25)4.8 = 3 + 0.25x 1.8 = 0.25x7.2 = xThus, 7.2 ounces of oil must be added to produce a new mixture that is 25 percent vinegar.4．In a driving competition, Jeff and Dennis drove the same course at average speeds of 51 miles per hour and 54 miles per hour, respectively. If it took Jeff 40 minutes to drive the course, how long did it take Dennis?正确答案：37.8 minutes解析：Let x be the time, in minutes, that it took Dennis to drive the course. The distance d, in miles, is equal to the product of the rate r, in miles per hour, and the time t, in hours; that is,d=rtNote that since the rates are given in miles per hour, it is necessary to express the times in hours; for example, 40 minutes equalsof an hour.Thus, the distance traveled by Jeff is the product of his speed and his time,(51)()miles, and the distance traveled by Dennis is similarly represented by(54)()miles. Since the distances are equal, Thus, it took Dennis approximately 37.8 minutes to drive the course.5．Working alone at its constant rate, machine A takes 3 hours to produce a batch of identical computer parts. Working alone at its constant rate, machine B takes 2 hours to produce an identical batch of parts. How long will it take the two machines, working simultaneously at their respective constant rates, to produce an identical batch of parts?正确答案：6/5 hours, or 1 hour 12 minutes解析：Since machine A takes 3 hours to produce a batch, machine A can produce 1/3 of the batch in 1 hour. Similarly, machine B can produce - of the batch in 1 hour. If we let x represent the number of hours it takes both machines, working simultaneously, to produce the batch, then the two machines will produce - of the job in 1 hour. When the two machines work together, adding their individual production rates, 1/3 and 1/2, gives their combined production rate 1/x. Therefore,Thus, working together, the machines will take 6/5 hours, or 1 hour 12 minutes, to produce a batch of parts.6．At a fruit stand, apples can be purchased for $0.15 each and pears for $0.20 each. At these rates, a bag of apples and pears was purchased for $3.80. If the bag contained 21 pieces of fruit, how many of the pieces were pears?正确答案：13解析：If a represents the number of apples purchased and p represents the number of pears purchased, the information can be translated into the following system of equations.0.15a+ 0.20p = 3.80(total cost)a+p = 21(total number of fruit)From the second equation, a = 21-p. Substituting 21-p into the first equation fora gives0.15(21-p)+ 0.20p = 3.80(0.15)(21)- 0.15p + 0.20p = 3.803.15-0.15p + 0.20p =3.800.05p = 0.65p=13Thus, of the 21 pieces of fruit, 13 were pears.7．To produce a particular radio model, it costs a manufacturer $30 per radio, and it is assumed that if 500 radios are produced, all of them will be sold. What must be the selling price per radio to ensure that the profit(revenue from the sales minus the total production cost)on the 500 radios is greater than $8,200?正确答案：$46.40解析：If y represents the selling price per radio, then the profit is 500(y - 30). Therefore, we set500(y-30)> 8,200Solving the inequality, we get500y- 15,000 > 8,200 500y> 23,200y > 46.4Thus, the selling price must be greater than $46.40 to ensure that the profit is greater than $8,200.Some applications involve computing interest earned on an investment during a specified time period. The interest can be computedas simple interest or compound interest.Simple interest is based only on the initial deposit, which serves as the amount on which interest is computed, called the principal, for the entire time period. If the amount P is invested at a simple annual interest rate of r percent, then the value V of the investment at the end of t years is given by the formulaV = P(1+)where P and V are in dollars.In the case of compound interest, interest is added to the principal at regular time intervals, such as annually, quarterly, and monthly. Each time interest is added to the principal, the interest is said to be compounded. After each compounding, interest is earned on the new principal, which is the sum of the preceding principal and the interest just added. If the amount P is invested at an annual interest rate of r percent, compounded annually, then the value V of the investment at the end of t years is given by the formulaV =If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formulaV =8．If $10,000 is invested at a simple annual interest rate of 6 percent, what is the value of the investment after half a year?正确答案：$10,300解析：According to the formula for simple interest, the value of the investment after 1/2 year is=$10,000(1.03)= $10,3009．If an amount P is to be invested at an annual interest rate of 3.5 percent, compounded annually, what should be the value of P so that the value of the investment is $1,000 at the end of 3 years?正确答案：$901.94解析：According to the formula for 3.5 percent annual interest, compounded annually, the value of the investment after 3 years isP(1 + 0.035)3and we set it to be equal to $1,000P(l + 0.035)3 = $1,000To find the value of P, we divide both sides of the equation by(1 + 0.035)3.P =≈$901.94 Thus, an amount of approximately $901.94 should be invested.10．A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?正确答案：4.91 percent解析：According to the formula for r percent annual interest, compounded quarterly, the value of the investment after 1 year isBy setting this value greater than or equal to $21,000 and solving for r, we getWe can use the fact that taking the positive fourth root of each side of an inequality preserves the direction of the inequality. This is also true for the positive square root or any other positive root.To compute the fourth root, we can use the fact thatfor x ≥0; that is, we can compute afourth root by taking a square root twice:So the least annual interest rate is approximately 4.91 percent.11．Find an algebraic expression to represent each of the following.(a)The square of y is subtracted from 5, and the result is multiplied by 37.(b)Three times x is squared, and the result is divided by 7.(c)The product of(x + 4)and y is added to 18.正确答案：(a)37(5-y2), or 185-37y2(b)(c)18 +(x + 4)(y), or 18 + xy + 4y12．Simplify each of the following algebraic expressions.(a)3x2-6 + x + 11-x2 +5x(b)3(5x-1)-x + 4(c), where x≠4(d)(2x + 5)(3x-l)正确答案：(a)2x2 + 6x + 5(b)14x+l(c)x + 4(d)6x2+13x-513．(a)What is the value of f(x)= 3x2 -7x + 23 when x = - 2 ?(b)What is the value of h(x)= x3-2x2 + x-2 when x = 2?(c)What is the value of k(x)=x-7 when x = 0?正确答案：(a)49(b)0(c)-714．If the function g is defined for all nonzero numbers y by g(y)=, find the value of each of the following. (a)g(2)(b)g(-2)(c)g(2)- g(-2)正确答案：(a)1(b)-1(c)215．Use the rules of exponents to simplify the following.(a)(n5)(n-3)(b)(s7)(t7)(e)(w5)-3(f)(50)(d3)正确答案：(a)n2(b)(sf)7(c)r8(d)(e)(f)d3(g)(h)9x2y316．Solve each of the following equations for x.(a)5x-7 = 28(b)12-5x = x + 30(c)5(x + 2)= l-3x(d)(x + 6)(2x-l)= 0(e)x2+5x-14 = 0(f)x2-x-l = 0正确答案：(a)7(b)-3(c)(d)-6, 1/2(e)-7, 2(f)17．Solve each of the following systems of equations for x and y.(a)x + y = 24x-y = 18(b)3x-y = -5 x + 2y = 3(c)15x-18-2y = -3x + 7 10x + 7y + 20 = 4x + 2 正确答案：(a)x=21y=3(b)x=-1 y=2(c)x=1/2 y=-318．Solve each of the following inequalities for x.(a)-3x>7 + x(b)25x + 16≥10-x(c)16 + x>8x-12正确答案：(c)x<419．For a given two-digit positive integer, the tens digit is 5 more than the units digit. The sum of the digits is 11. Find the integer.正确答案：8320．If the ratio of 2x to 5y is 3 to 4, what is the ratio of x to y?正确答案：15 to 821．Kathleens weekly salary was increased by 8 percent to $237.60. What was her weekly salary before the increase?正确答案：22022．A theater sells children’s tickets for half the adult ticket price. If 5 adult tickets and 8 children’s tickets cost a total of $27, what is the cost of an adult ticket?正确答案：323．Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10 percent simple annual interest, and the remainder of the money was invested in a fund that paid 8 percent simple annual interest. If the interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10 percent and how much at 8 percent?正确答案：$800 at 10% and $2,200 at 8%24．Two cars started from the same point and traveled on a straight course in opposite directions for exactly 2 hours, at which time they were 208 miles apart. If one car traveled, on average, 8 miles per hour faster than the other car, what was the average speed of each car for the 2-hour trip?正确答案：48 mph and 56 mph25．A group can charter a particular aircraft at a fixed total cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12.(a)What is the fixed total cost to charter the aircraft?(b)What is the cost per person if 40 people charter the aircraft?正确答案：(a)$4,320(b)$108。
gre数学考试关于几何的重点试题
gre数学考试关于⼏何的重点试题gre数学考试关于⼏何的重点试题1. If the areas of three of the faces of a rectangular solid are 6,10 and 15, what is the volume of the solid?A.30B.90C.150D.300E.450答案：A2.△RST lies in the XY-plane and points R and T have (x, y) coordinates (0,0) and (6,0), respectively. The area of △RST is 12.The x-coordinate of RThe y-coordinate of S答案：D3.What is the maximum number of nonover-lapping regions into which 3 lines can divide the interior of a circle?A.4B.6C.7D.8E.9答案:C4.The rectangular rug shown in the figure above has a floral border 1 foo t wide on all sides. What is the area, in square feet, of that portion of the rug that excludes the border?A.28B.40C.45D.48E.53答案：A5. The diagram represents a rectangular garden. The shaded regions are planted in flowers, and the unshaded region is a walk 2 feet wide. All angles are right angles.The sum of the areas of the shaded regions2,800 square feet答案：D6.What are the coordinates of point B in the xy-plane above?A.(6,12)B.(6,28)C.(8,20)D.(12,20)E.(14,28)答案：B7.If 9 trees are originally planted in a circular pattern as shown above, what is the least number of trees that must be transplanted so that the 9 trees will be in 2 straight rows?A.4B.5C.6D.7E.8答案：B8.If the sum of the measures of two angles is 180o,each angle is a supplement of the other, whereas, if the sum oftheir measures is 90o, each is a complement of the other.The measure of an angle with a supplement that measures 130o The measure of an angle with a supplement that measures 40o 答案：C9.If a solid pyramid has 4 vertices and 4 faces, how many edges does the pyramid have?A.2B.3C.4D.6E.8答案：D10.A rectangular floor with an area of 12 square meters is drawn to scale with 2 centimeters representing 1 meter.The area of the scale drawing of the floor24 square centimeters答案：A11.In the rectangular coordinate system, line k passes through the point (0,0) and (4,8); line m passes through the points (0,1) and (4,9).The slope of line kThe slope of line m答案：C12.In the stop sign shown in the figure above, all sides have equal length and all angles have equal measure. If the figure could be rotated 225 degrees in a clockwise direction, point G would be in the position of point.A.IB.JC.KD.LE.M答案：B13.What is the ratio of the perimeter of a pentagon with each side of length 6 to the perimeter of an octagon with each side of length 6?A.5/6B.4/5C.3/4D.2/3E.5/8答案：E14.A circular flower bed is inscribed in a flat, square garden plot that measures x meters on each side.The fraction of the garden plot area that is not part of the flower bed if x=50 metersThe fraction of the garden plot area that is not part of the flower bed if x=45 meters答案：C15.The dimensions, in centimeters, of rectangular box R are 6 by 8 by 10. Which of the following cannot be the total surface area, in square centimeters, of two faces of R?A.96B.120C.128D.160E.180答案：E16.The figure above shows a large square formed by fitting three L- shaped tiles and one small square tile together. If a rectangular floor 10 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?A.810B.405C.270D.135E.45答案：A17.A certain rectangle has perimeter 54. If the ratio of the length of the rectangle to the width is 5 to 4, what is the length of the rectangle?A.30B.27C.24D.18E.15答案：E18.In the rectangular coordinate system above, the coordinates of points A and B are shown. If the dotted lines representa second pair of coordinate axes with origin at A, and if the scale is the same on both pairs of axes, what are the coordinat es of point B with respect to the second pair of axes?A.(-33,88)B.(33,48)C.(33,-48)D.(97,88)19. If the perimeter of the rectangle above is 36, then l=A.9B.14C.16D.28E.32答案：B20.If the perimeter of a triangle is 18, then the length of one of the sides cannot beA.1B.3C.6D.8E.9答案：E21.In the figure above, if ABCD is a parallelogram with A at the origin, what are the coordinates of C?A.(6,5)B.(6,6)C.(7,4)D.(8,5)E.(8,6)答案：A22.What fraction of a cubic meter is the volume of a cubic block of stone with edge of length 10 centimeters?(1 meter=100centimeters)A.3/10D.1/100E.1/1000答案：E23.In the rectangular coordinate system above, for how many of the points that lie inside or on the boundary of the shaded region are both coordinates integers?A.sixB.sevenC.eightD.nineE.ten答案：E24. A rectangular tabletop consists of a piece of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop if x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is3 feet wide, what is its approximate length, in feet?A.12B.10C.9D.8E.6答案：E25.In the coordinate plane, points A and B are endpoints of a diameter of a circle with center (-2,1). If the coordinates of A are (-5,5), what are the coordinates of B?A.(0,0)B.(3,-2)C.(3,-1)D.(2,-2)E.(1,-3)答案：E26.Three solid cubes of lead, each with edges 10 centimeters long, are melted together in a level, r ectangular shaped pan. The base of the pan has inside dimensions of 20 centimeters by 30 centimeters, and the pan is 15 centimeters deep. If the volume of the solid lead is approximately the same as the volume of the melted lead, approximately how many cen timeters deep is the melted lead in the pan?A.2.5B.3C.5D.7.5E.9答案：C27.In the figure above, if x, y, and z are integers such that xA.59 and 91B.59 and 135C.91 and 178D.120 and 135E.120 and 178答案：C28.In the rectangular coordinate system above, if P, not shown, is a point AB and if the x-coordinate of P is 1, what is the y-coordinate of P?A.4/3B.3/2C.7/3D.5/2E.8/3答案：A29.There are six marked points on the circle above. How many different lines can be drawn that contain two of the marked points?A.5B.6C.12D.15E.30答案：D30.In the figure above, ABCD is a square. What are the coordinates of point B?A.(-4,2)B.(-2,4)C.(-2,6)D.(4,-6)E.(6,-2) 答案：C。
gre考试题库及答案
gre考试题库及答案GRE考试题库及答案1. 填空题：在下列句子中填入合适的词汇。
- The professor's lecture was so _______ that it left the audience in a state of awe.- The _______ of the new policy was met with mixedreactions from the public.- Despite the _______ of the evidence, the jury remained unconvinced.答案：1. 1) captivating 2) implementation 3) overwhelming2. 阅读理解：阅读以下段落，并回答问题。
"In the realm of environmental science, the concept of sustainability has become increasingly important. It refersto the ability to meet the needs of the present without compromising the ability of future generations to meet their own needs. This involves a delicate balance between economic growth, social development, and environmental protection."问题：根据上文，可持续发展的定义是什么？答案：可持续发展是指在不损害后代满足自身需求的能力的前提下，满足当前需求的能力。
这涉及到经济增长、社会发展和环境保护之间的微妙平衡。
3. 数学问题：解决以下方程。
2024 GRE考试必备数学历年真题练习
2024 GRE考试必备数学历年真题练习在GRE数学部分的备考过程中，历年真题的练习是非常重要的一环。
通过针对性的练习，考生可以熟悉考试题型，了解考点，提升解题速度和准确性。
本文将为大家提供2024年GRE考试的数学历年真题练习，帮助考生更好地备考。
1. 整数1.1 题目选择下列哪个数是正偶数？(A) -12(B) -5(C) 0(D) 9(E) 271.2 解析正偶数是指能够被2整除的正整数。
从选项中排除负数，在0和正数中，只有0能够被2整除，因此答案选(C)。
2. 几何2.1 题目下图中，正方形ABCD的边长为3。
点E是线段BC的中点，点F是线段BD上的一点，且AF的长度为3。
求射线AF与线段CE的交点P到点E的距离。
[图片描述：一个正方形ABCD，边长为3，线段BC的中点为E，线段BD上的一点为F，AF的长度为3]2.2 解析首先，可以得出正方形ABCD的对角线AC的长度为3的开平方乘以2，即AC=3乘以根号2。
由于AE与CF平行且等长，射线AF可以看作与线段BE平行且等长。
因此，三角形BEP是等腰直角三角形，所以BP = EP = EC的一半。
又因为BC=3，所以EC=3/2。
因此，点P到点E的距离为1.5个单位。
3. 概率与统计3.1 题目某次测试的成绩服从正态分布，平均成绩为80分，标准差为5分。
已知一个学生的成绩在85分以上的概率为0.841，求这个学生的成绩。
3.2 解析根据正态分布的性质，均值加上标准差得到的分数对应的概率是大约0.841。
因此，这个学生的成绩应该在平均成绩80分加上标准差5分的位置，即85分。
通过以上三个部分的例题，希望能够帮助到考生更好地了解2024年GRE考试数学部分的题型和解题思路。
在备考过程中，考生还需深入学习数学知识，掌握解题技巧，并进行大量真题练习，提升解题能力。
祝愿各位考生在考试中取得好成绩！。
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2020年新GRE数学模拟考试试题及答案
1. A,B,C,D,E,F排在1,2,3,4,5,6六个位置上,问A不在1, B不在2, C不在3的情况下,共有多少种排法?
(A) 720
(B) 450
(C) 180
(D) 216
(E) 320
2. 一直线L过点A(5,0), B(0,2), 坐标原点为O, 点P(X,Y)为三角形OAB中一点, 问：Y
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
3. In an insurance company, each policy has a paper record and an electric record. For those policies having incorrect paper record, 60% also having incorrect electric record; For policies having incorrect electric record, 75% also having incorrect paper record. 3% of all policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy,what’s the probability that the one having both correct paper and correct electric records?
(A) 0.80
(B) 0.94
(C) 0.75
(D) 0.88
(E) 0.92
4. If Bob can do a job in 20 days and Jane can do the job in 30 days, they work together to do this job and in this period, Bob stop work for 2.5 days and Jane stop work for x days, and the job be finished for 14 days, what is x?
(A) 1.6
(B) 3.2
(C) 1.5
(D) 1.25
(E) 1.15
5. The probability of A is 60% and the probability of B is 50%, what is the most possible probability that neither A nor B would happen?
(A) 0.80
(B) 0.40
(C) 0.75
(D) 0.55
(E) 0.68
6. There are 1200 respondents to a poll, each favoring
their preference for candidates A,B, and C. 54% favored A, 48% favored B, and 42% favored C, and there is 30% favored both A and B. what’s the largest possible number of respondents favoring C, but not C&B, nor C&A?
(A) 25%
(B) 30%
(C) 28%
(D) 38%
(E) 40%
参考答案：
1.解：首先考虑总的可能性为，再考虑A在1，B在2，C在3的
可能性分别为，中重复计算了三者交集，分别为AB在1，2，AC在1，3，BC在2，3，所需将三种情况加回，即，但考虑这三种加回的交集
又重复计算了ABC在1，2，3的情况，所以应减去P33
2.解：在平面直角坐标系中，T
3.解：设总数为x，设incorrect paper record有y, incorrect electric record有z，则：
x·y·60%=3%·x y=5%
x·z·75%=3%·x z=4%
则，两者至少有一个错误的百分比为5%+4%-3%=6%，所准确答案为94%
4.解：1/20(14-2.5)+1/30(14-x)=1，得出x=1.25
5.解：划出图表来能够一目了然：A， B均不发生的概率为40%，最小概率为0.
6.解：A和B的并集为：54%+48%-30%=72%，所C为28%.。