2020年新GRE数学模拟考试试题及答案.doc

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。

2020年高考数学全真模拟试卷(4)(2月份)一、填空题（本大题共14小题，共70.0分）1. 已知集合A ={x|1<x <3}，B ={x|2<x <4}，则A ∪B =________．2. 已知a ，b ∈R ，i 是虚数单位．若a +i =2−bi ，则(a +bi)2= ______ ．3. 从总体中抽取一个样本：3、7、4、6、5，则总体标准差的点估计值为______ ．4. 执行如图所示的框图，若输出的结果为12，则输入的实数x 的值是______．5. 平行四边形ABCD 中，AB =5，AD =3，|BA ⃗⃗⃗⃗⃗ +BC ⃗⃗⃗⃗⃗ |=4，则AB ⃗⃗⃗⃗⃗ ⋅BC ⃗⃗⃗⃗⃗ =______．6. 各项均为正数的等比数列{a n }中，若a 2a 3a 4=a 2+a 3+a 4，则a 3的最小值为 ．7. 用数字1，2，3，4，5组成没有重复数字的五位数，其中奇数的个数为_____．8. 已知sinβ=35(π2<β<π)，且sin(α+β)=cosα，则tan(α+β)=______．9. 函数f(x)=2x+1x+1的值域为________．10. 若a =(23)x ，b =x 2，c =log 23x ，则当x >1时，a ，b ，c 的大小关系是________(从小到大)． 11. 正方体ABCD −A 1B 1C 1D 1的棱长为4，点P 是棱BB 1上一点，若异面直线AC 1与PD 所成角的余弦值为√1133，则BP =______．12. 已知的定义域为R ，则实数a 的取值范围是______．13. 已知f(x)是定义在R 上的奇函数，且在[0,+∞)上单调递增，若f(lg x)<0，则x 的取值范围是________． 14. 过双曲线x 2a 2−y 2b 2=1(a >0,b >0)的一个焦点F 作渐近线的垂线l ，垂足为M ，l 交y 轴于点E ，若FM ⃗⃗⃗⃗⃗⃗ =2ME⃗⃗⃗⃗⃗⃗ ，则该双曲线的渐近线方程为______． 二、解答题（本大题共11小题，共124.0分）15. 在△ABC 中，已知cosC +cosAcosB −√3sinAcosB =0(Ⅰ)求角B 的大小；(Ⅱ)若a +c =1，求b 的取值范围．16. 如图，在四棱锥P −ABCD 中，已知底面ABCD 为矩形，且AB =√2，BC =1，E ，F 分别是AB ，PC 的中点，PA ⊥DE ．(1)求证：EF//平面PAD ；(2)求证：平面PAC ⊥平面PDE ．17.已知椭圆C：x2a2+y2b2=1(a>b>0)的一个顶点为(0,−1)，离心率e=√22．(1)求椭圆C的方程；(2)过M(0,m)(−1<m<0)的直线l交椭圆C于A、B两点，试问：在椭圆C上是否存在定点T，使得无论直线l如何转动，以AB为直径的圆恒过定点T？若存在，求出m的值及点T的坐标；若不存在，请说明理由．18.如图，PQ为某公园的一条道路，一半径为20米的圆形观赏鱼塘与PQ相切，记其圆心为O，切点为G.为参观方便，现新修建两条道路CA、CB，分别与圆O相切于D、E两点，同时与PQ 分别交于A、B两点，其中C、O、G三点共线且满足CA=CB，记道路CA、CB长之和为L．(1)①设∠ACO=θ，求出L关于θ的函数关系式L(θ)；②设AB=2x米，求出L关于x的函数关系式L(x)．(2)若新建道路每米造价一定，请选择(1)中的一个函数关系式，研究并确定如何设计使得新建道路造价最少．x3(x∈R)19.已知函数f(x)=4x+ax2−23(1)当a=1时，求函数的单调区间；(2)若函数在区间[1,+∞)上是减函数，求实数a的取值范围．20.数列{a n}中，a1=2，a n+1=a n+cn(c是常数，n=1，2，3，…)，且a1，a2，a3成公比不为1的等比数列．(1)求c的值；(2)求{a n}的通项公式．21.在平面直角坐标系xOy中，设点P(x,5)在矩阵M=[1234]对应的变换下得到点Q(y−2,y)，求M−1[y x]．22.[选修4—4：坐标系与参数方程]在直角坐标系xOy中，直线C1：x+y=4，曲线C2：{x=1+cosθ,y=sinθ(θ为参数)，以坐标原点为极点，x轴正半轴为极轴建立极坐标系．(1)写出直线C1与曲线C2的极坐标方程；(2)若射线l：θ=α(ρ>0)分别交C1与C2于A，B两点，求|OB||OA|的取值范围．23.已知f(x)=x2+a|x|−b．(1)当a =−1，b =2时，解不等式f(x)≥0；(2)若|f(1)|≤1，|f(3)|≤1，求|f(2)|的最大值．24. 已知f(x)=(1+ax)n =a 0+a 1x 1+a 2x 2+⋯+a n x n ，若对于任意n ∈N ∗，都有∑a i n i=0=(23)n ． (1)求实数a 的值；(2)若[f(x)]2=b 0+b 1x +b 2x 2+⋯+b 2n x 2n ，求13b 1+132b 2+133b 3+⋯+132n b 2n 的值．25. 2018年2月22日，在韩国平昌冬奥会短道速滑男子500米比赛中，中国选手武大靖以连续打破世界纪录的优异表现，为中国代表队夺得了本届冬奥会的首枚金牌，也创造了中国男子冰上竞速项目在冬奥会金牌零的突破.根据短道速滑男子500米的比赛规则，运动员自出发点出发进入滑行阶段后，每滑行一圈都要依次经过4个直道与弯道的交接口A k (k =1,2,3,4).已知某男子速滑运动员顺利通过每个交接口的概率均为34，摔倒的概率均为14.假定运动员只有在摔倒或到达终点时才停止滑行，现在用X表示该运动员滑行最后一圈时在这一圈内已经顺利通过的交接口数．(1)求该运动员停止滑行时恰好已顺利通过3个交接口的概率；(2)求X的分布列及数学期望E(X)．【答案与解析】1.答案：{x|1<x<4}解析：本题主要考查函数的并集及其运算，属于较易题．解：本题考查集合的并集运算．由并集定义可得A∪B={x|1<x<4}．2.答案：3−4i解析：解：由a，b∈R，且a+i=2−bi，得{a=2−b=1，即a=2，b=−1．∴a+bi=2−i．∴(a+bi)2=(2−i)2=3−4i．故答案为：3−4i．由已知等式结合复数相等的条件求得a，b的值，则复数a+bi可求，然后利用复数代数形式的乘法运算得答案．本题考查了复数代数形式的乘法运算，考查了复数相等的条件，是基础题．3.答案：√2解析：解：样本数据：3、7、4、6、5的平均数为：×(3+7+4+6+5)=5，x=15×[(3−5)2+(7−5)2+(4−5)2+(6−5)2+(5−5)2]=2，方差为s2=15所以标准差为s=√2．故答案为：√2．根据平均数与方差、标准差的计算公式，即可求出结论．本题考查了平均数，方差与标准差的计算问题，是基础题目．4.答案：√2解析：解：若执行y =x −1，由x −1=12，即x =32∉(−∞,1],∴不成立，若执行y =log 2x ，由log 2x =12，得x =√2∈(1,+∞)，成立故答案为：√2本题主要考查的是条件函数f(x)={x >1,x ≤1log 2x,x >1，根据函数表达式进行计算即可得到结论． 本题主要考查程序框图的识别和判断，根据条件得到函数f(x)的表达式是解决本题的关键，比较基础． 5.答案：−9解析：解：由题意得，AB =5，AD =3，BD =4∴cos∠ABC =−35∴AB ⃗⃗⃗⃗⃗ ⋅BC ⃗⃗⃗⃗⃗ =5×3×(−3)=−9 故答案为−9．运用数量积的定义和直角三角形的知识可解决．本题考查平面向量的数量积和平行四边形法则．6.答案：√3解析：本题考查了等比数列的概念，等比数列的性质和利用基本不等式求最值．利用等比数列的概念得q >0，再利用等比数列的性质得a 32=1q +q +1，最后利用基本不等式求最值得结论．解：因为数列{a n }是各项均为正数的等比数列，所以公比q >0．由a 2a 3a 4=a 2+a 3+a 4得a 33=a 3q +a 3+a 3q ，即a 32=1q +q +1，所以a32≥3，即a3≥√3．因此a3的最小值为√3．故答案为√3．7.答案：72解析：用1、2、3、4、5组成无重复数字的五位奇数，可以看作是填5个空，要求个位是奇数，其它位置无条件限制，因此先从3个奇数中任选1个填入，其它4个数在4个位置上全排列即可．解：组成无重复数字的五位奇数，则个位只能排1，3，5中的一个数，共有3种排法，然后还剩4个数，剩余的4个数可以在十位到万位4个位置上全排列，共有A44=24种排法．由分步乘法计数原理得，由1、2、3、4、5组成的无重复数字的五位数中奇数有3×24=72个．故答案为72．8.答案：−2解析：解：∵sinβ=35，π2<β<π，∴cosβ=−√1−sin2β=−45，又sin(α+β)=cosα=cos[(α+β)−β]=cos(α+β)cosβ+sin(α+β)sinβ=−45cos(α+β)+35sin(α+β)，∴25sin(α+β)=−45cos(α+β)，∴tan(α+β)=−2．故答案为：−2．依题意，可求得cosβ=−45，由于α=(α+β)−β，巧用两角差的余弦即可求得tan(α+β)的值． 本题考查两角和与差的余弦函数，“凑角”是关键，考查三角函数间的关系式的应用，属于中档题．9.答案：(−∞,2)∪(2,+∞)解析：本题考查函数的值域，属于基础题． 解：∵f(x)=2x+1x+1=2(x+1)−1x+1=2−1x+1，1x+1≠0，∴f(x)≠2，∴函数f(x)的值域为(−∞,2)∪(2,+∞)． 故答案为(−∞,2)∪(2,+∞)．10.答案： c <a <b解析：本题考查指对数函数，幂函数性质的应用，属于中档题． 利用特值及指对数，幂函数的性质求解大小． 解：方法一：由题意x >1，∴当x =2，a =(23)2=49，b =4，c =log 232<0， 则c <a <b ， 故答案为c <a <b ． 方法二：y =(23)x 、y =x 2、三个函数图象如下图，由图象可知，x >1时，c <a <b ． 故答案为c <a <b ．11.答案：1解析：解：设BP =t ，以D 为原点，DA 为x 轴，DC 为y 轴，DD 1为z 轴，建立空间直角坐标系，则A(4,0，0)，C 1(0,4，4)，P(4,4，t)，D(0,0，0)， AC 1⃗⃗⃗⃗⃗⃗⃗ =(−4,4，4)，DP ⃗⃗⃗⃗⃗ =(4,4，t)， ∵异面直线AC 1与PD 所成角的余弦值为√1133，∴|cos <AC 1⃗⃗⃗⃗⃗⃗⃗ ，DP ⃗⃗⃗⃗⃗ >|=|AC 1⃗⃗⃗⃗⃗⃗⃗⃗ ⋅DP ⃗⃗⃗⃗⃗⃗||AC 1⃗⃗⃗⃗⃗⃗⃗⃗ |⋅|DP ⃗⃗⃗⃗⃗⃗ |=4t √48⋅√32+t 2=√1133， 由t >0，解得t =1， ∴BP =1． 故答案为：1．设BP =t ，以D 为原点，DA 为x 轴，DC 为y 轴，DD 1为z 轴，建立空间直角坐标系，利用向量法能求出结果．本题考查异面直线所成角的余弦值的求法，考查空间中线线、线面、面面间的位置关系等基础知识，考查运算求解能力，是中档题．12.答案：[−1,0]解析：本题考查函数的定义域及其求法，考查转化化归思想，是中档题． 把f(x)=√3x 2+2ax−a −1的定义域为R 转化为3x2+2ax−1−1≥0对任意x ∈R 恒成立，即x 2+2ax −a ≥0对任意x ∈R 恒成立，再由判别式小于等于0求解． 解：∵f(x)=√3x 2+2ax−a −1的定义域为R ， ∴3x2+2ax−1−1≥0对任意x ∈R 恒成立， 即3x2+2ax−a≥1=30恒成立，即x 2+2ax −a ≥0对任意x ∈R 恒成立， ∴△=4a 2+4a ≤0，则−1≤a ≤0． 故答案为[−1,0]．13.答案：(0,1)解析：本题主要考察了利用函数性质解不等式的相关问题，熟练掌握相关知识点是解决此类问题的关键． 解：由奇函数y =f(x)在[0,+∞)上递增，且f(0)=0， 得函数y =f(x)在(−∞,0)上递增，， 由f(lgx)<0，则lgx <0，得0<x <1， 即x 的取值范围是(0,1) ， 故答案为(0,1)．14.答案：y =±√2x解析：本题考查双曲线渐近线方程，难度一般，属中档题．由双曲线的标准方程可得右焦点F ，渐近线方程，利用FM ⃗⃗⃗⃗⃗⃗ =2ME ⃗⃗⃗⃗⃗⃗ ，求出M 的坐标，代入渐近线y =ba x ，即可得出结论．熟练掌握双曲线的标准方程及其性质、确定M 的坐标是解题的关键． 解：如图所示．取右焦点F(c,0)，渐近线y =ba x.∵FM ⊥OM ，∴可得直线FM 的方程为y =−ab (x −c)， 令x =0，解得y =acb，∴E(0,acb ). ∵FM ⃗⃗⃗⃗⃗⃗ =2ME ⃗⃗⃗⃗⃗⃗ ， ∴M(c 3,2ac3b)，又M 在渐近线y =ba x 上，∴2ac 3b=b a ×c3，解得√2a =b ．∴该双曲线的渐近线方程为：y =±√2x ． 故答案为：y =±√2x ．15.答案：解：(Ⅰ)由已知得cosAcosB +cosC =√3sinAcosB ，即cosAcosB +cos[π−(A +B)]=√3sinAcosB ． cosAcosB −cos(A +B)=√3sinAcosB ．所以sinAsinB =√3sinAcosB ，两边除以sin A cos B ，得，tanB =√3， ∴B =π3，(Ⅱ)由余弦定理可得b 2=a 2+c 2−2ac ⋅cosB =a 2+c 2−ac =(a +c)2−3ac =1−3ac ． ∵a +c =1≥2√ac ， ∴ac ≤14．∴b 2=1−3ac ≥14，即b ≥12．再由b <a +c =1，可得 12≤b <1，故边b 的取值范围是[12,1)．解析：(Ⅰ)利用两角和的余弦公式，将cosAcosB +cosC =√3sinAcosB ，变形为sinAsinB =√3sinAcosB ，即可求B ．(Ⅱ)由余弦定理可得b 2=1−3ac ，利用基本不等式求出b ≥12，再由b <a +c =1，求出边b 的取值范围．本题考查三角函数公式，余弦定理、基本不等式的综合灵活应用，考查转化变形、计算能力，属于中档题．16.答案：证明：(1)取PD中点G，连AG，FG，因为F，G分别为PC，PD的中点，所以FG//CD，且FG=12CD.又因为E为AB中点，所以AE//CD，且AE=12CD．所以AE//FG，AE=FG.故四边形AEFG为平行四边形．所以EF//AG，又EF⊄平面PAD，AG⊂平面PAD，故EF//平面PAD.(2)设AC∩DE=H，由△AEH∽△CDH及E为AB中点得AHCH =AECD=12，又因为AB=√2，BC=1，所以AC=√3，AH=13AC=√33．所以AHAE =ABAC=√2√3，又∠BAC为公共角，所以△HAE∽△BAC．所以∠AHE=∠ABC=90°，即DE⊥AC.又DE⊥PA，PA∩AC=A，所以DE⊥平面PAC，又DE⊂平面PDE，所以平面PAC⊥平面PDE．解析：本题考查线面平行的判定，考查面面垂直的判定，属于中档题． (1)由题意得到EF//AG ，利用线面垂直的判定即可证明； (2)由题意可得DE ⊥平面PAC ，再利用面面垂直的判定证明即可．17.答案：解：(1)由题意，b =1，c a =√22，∴a =√2，b =1，c =1， ∴椭圆C 的方程为x 22+y 2=1；(2)①当直线l 的斜率不存在时，以AB 为直径的圆的方程为：x 2+y 2=1， 此时与椭圆交点为(0,1)，(0,−1)；②当直线l 的斜率为0时，直线l 的方程为y =m ，此时以AB 为直径的圆的方程为：x 2+(y −m)2=2(1−m 2)， 当定点为(0,1)时，解得m =−13，当定点为(0,−1)时，解得m =13∉(−1,0)，∴m =−13，在椭圆上可能存在定点T(0,1)满足条件；③斜率存在时，设直线l 的方程为：y =kx −13，A(x 1,y 1)，B(x 2,y 2)， 与椭圆方程联立，可得(1+2k 2)x 2−43kx −169=0，∴x 1+x 2=4k3(1+2k 2)，x 1x 2=−169(1+2k 2)，TA ⃗⃗⃗⃗⃗ ⋅TB⃗⃗⃗⃗⃗ =(k 2+1)x 1x 2−43k(x 1+x 2)+169=(k 2+1)(−169(1+2k 2))−43k ⋅4k 3(1+2k 2)+169=0，∴过M(0,−13)的直线l 斜率存在时，以AB 为直径的圆过定点T(0,1)，综上所述，m =−13时，过M(0,−13)的直线无论如何转动，以AB 为直径的圆过定点T(0,1)．解析：(1)由题意，b =1，ca =√22，求出a ，b ，即可求椭圆C 的方程；(2)讨论直线l 的斜率不存在，设出直线l 的方程，求得圆的方程，求得定点T ，讨论直线l 的斜率存在，设出直线方程，联立椭圆方程，运用韦达定理和圆的性质，结合向量垂直的条件，即可得到存在定点T ．本题考查椭圆的方程和性质，主要考查椭圆方程的运用，联立直线方程和椭圆方程，运用韦达定理，同时考查直线和圆的位置关系，考查运算能力，属于中档题．18.答案：解：(1)①在RTΔCDO中，∠ACO=θ，所以，所以，在RTΔAGC中，所以，其中，②设AC=y，则在RTΔAGC中CG=√y2−x2，由RTΔCDO与RTΔAGC相似得，COAC =ODAG，即√y2−x2−20y=20x，即x√y2−x2−20x=20y，即x√y2−x2=20(x+y)，即x√y−x=20√x+y即x2(y−x)=400(x+y)，化简得CA=y=x3+400xx2−400，L(x)=2CA=2x3+800xx2−400其中x∈(20,+∞);(2)选择(1)中的第一个函数关系式，研究．，令L′(θ)=0，得令，当θ∈(0,θ0)时，L′(θ)<0，所以L(θ)递减；当时，L′(θ)>0，所以L(θ)递增，所以当时，L(θ)取得最小值，新建道路何时造价也最少．解析：本题主要考查函数模型的应用和导数的实际应用，考查实际应用能力和计算能力，属于中档题．(1)根据题意求函数的解析式即可；(2)利用导数求函数的最值即可．19.答案：解：(1)a=1时，f(x)=4x+x2−23x3，f′(x)=4+2x−2x2，令f′(x)>0，解得：−1<x<2，令f′(x)<0，解得：x>2或x<−1，故f(x)在(−∞,−1)，(2,+∞)上单调递减，在(−1,2)上单调递增；(2)f′(x)=4+2ax−2x2，若f(x)在[1,+∞)递减，则2ax≤2x2−4即a≤x−2x在[1,+∞)恒成立，令g(x)=x−2x，x∈[1,+∞)，则g′(x)=1+2x2>0，则g(x)在[1,+∞)递增，g(x)≥g(1)=−1，故a≤−1．即a的取值范围是(−∞,−1].解析：本题考查了函数的单调性、最值问题，考查导数的应用以及转化思想，是一道中档题．(1)求出函数的导数，解关于导函数的不等式，求出函数的单调区间即可；(2)求出函数的导数，问题转化为a≤x−2x 在[1,+∞)恒成立令g(x)=x−2x，x∈[1,+∞)，根据函数的单调性求出a的范围即可．20.答案：解：(1)a1=2，a2=2+c，a3=2+3c，因为a1，a2，a3成等比数列，所以(2+c)2=2(2+3c)，解得c=0或c=2．当c=0时，a1=a2=a3，不符合题意舍去，故c=2．(2)当n≥2时，由于a2−a1=c，a3−a2=2c，a n−a n−1=(n−1)c，所以a n−a1=[1+2++(n−1)]c=n(n−1)2c．又a1=2，c=2，故a n=2+n(n−1)=n2−n+2(n=2,3，···).当n=1时，上式也成立，所以a n=n2−n+2(n=1,2，···)解析：本题考查数列的性质和应用，解题时要注意计算能力的培养．(1)由题意知(2+c)2=2(2+3c)，解得c =0或c =2.再由当c =0时，a 1=a 2=a 3，不符合题意舍去，知c =2．(2)由题意知a n −a n−1=(n −1)c ，所以a n −a 1=n(n−1)2c.由此可知a n ．21.答案：解：∵点P(x,5)在矩阵M =[1234]对应的变换下得到点Q(y −2,y)， ∴依题意，[1234][5x]=[y y−2]，即{x +10=y −23x +20=y 解得{x =−4y =8 由逆矩阵公式知，矩阵M =[1234]的逆矩阵M −1=[−2132−12]， ∴M −1[y x]=[−2132−12][8−4]=[−1016]．解析：由题意得到{x +10=y −23x +20=y ，从而求出x ，y ，再由逆矩阵公式求出矩阵M 的逆矩阵，由此能求出M −1[y x]．本题考查矩阵变换的应用，是中档题，解题时要认真审题，注意逆矩阵公式的合理运用．22.答案：解：(1)由C 1：x +y =4，得直线C 1的极坐标方程为ρcosθ+ρsinθ=4，由C 2：{x =1+cosθy =sinθ，得(x −1)2+y 2=1，即x 2+y 2=2x ，∴曲线C 2的极坐标方程为ρ=2cosθ； (2)设A(ρ1,α)，B(ρ2,α)，−π4<α<π2， 则ρ1=4cosα+sinα，ρ2=2cosα，|OB||OA|=ρ2ρ1=14⋅2cosα(cosα+sinα)=14(cos2α+sin2α+1)=14[√2cos(2α−π4)+1]，∵−π4<α<π2，∴−√22<cos(2α−π4)≤1，∴0<14[√2cos(2α−π4)+1]≤14(√2+1)， ∴|OB||OA|的取值范围是(0,14(√2+1)].解析：本题考查简单曲线的极坐标方程，考查三角函数最值的求法，是中档题．(1)直接化C 1的普通方程为极坐标方程，化C 2的参数方程为普通方程，进一步化为极坐标方程； (2)设A(ρ1,α)，B(ρ2,α)，−π4<α<π2，则ρ1=4cosα+sinα，ρ2=2cosα，代入|OB||OA|，整理后利用三角函数的最值得答案．23.答案：解：(1)f(x)=|x|2−|x|−2≥0⇒(|x|−2)(|x|+1)≥0，所以|x|≥2，解得x ∈(−∞,−2]∪[2,+∞)．(2)由题意得|a −b +1|≤1，|3a −b +9|≤1，故|f(2)|=|2a −b +4|=12|(a −b +1)+(3a −b +9)−2|≤12(|f(1)|+|f(3)|+2)≤2， 取等条件为{a −b +1=−1,3a −b +9=−1⇒a =−4,b =−2．故|f(2)|的最大值为2．解析：本题考查绝对值不等式． (1)利用分解因式，得|x|≥2求解即可;(2)由已知得a −b +1|≤1，|3a −b +9|≤1，然后将f(2)用f(1)和f(2)表示绝对值不等式的三角不等式求解即可．24.答案：解：(1)由f(1)=(1+a)n =a 0+a 1+a 2+⋯+a n =∑a i n i=0=(23)n ．得a =−13；(2)[f(x)]2=b 0+b 1x 2+b 2x +⋯+b 2n x 2n =[(1−13x)n ]2=(1−13x)2n ，∴b k =C 2n k (−13)k ，令b k 3k =C 2n k (−1)k ，k =1，2，3…，2n ，首先考虑1C 2n+1k+1C 2n+1k+1=k!(2n+1−k)!(2n+1)!+(k+1)!(2n−k)!(2n+1)!=k!(2n −k)!(2n +1−k +k +1)(2n +1)!=k!(2n−k)!(2n+2)(2n+1)!=2n+2(2n+1)C 2nk ，则1C 2nk =2n+12n+2(1C 2n+1k+1C 2n+1k+1)，因此1C 2nk −1C 2nk+1=2n+12n+2(1C 2n+1k−1C 2n+1k+2).故13b 1+132b 2+133b 3+⋯+132n b 2n =−C 2n 1+C 2n 2−C 2n 3+⋯+(−1)k C 2n k +⋯+C 2n 2n=−2n +12n +2(1C 2n+11−1C 2n+13+1C 2n+13−1C 2n+15+⋯+1C 2n+12n−1−1C 2n+12n+1) =−2n +12n +2(1C 2n+11−1C 2n+12n+1)=2n +12n +2(12n +1−1) =n n+1．解析：(1)在已知等式中取x =1，结合∑a i n i=0=(23)n 即可求得a 值；(2)由已知结合(1)可得b k =C 2n k (−13)k ，令b k 3k =C 2n k (−1)k ，k =1，2，3…，2n ，得到1C 2n k =2n+12n+2(1C 2n+1k +1C 2n+1k+1)，因此1C 2n k −1C 2n k+1=2n+12n+2(1C 2n+1k −1C 2n+1k+2)，代入得答案． 本题考查二项式定理的应用，考查组合数公式的性质，考查计算能力，是中档题． 25.答案：解：(1)由题意可知：P =(34)3×14=27256;(2)X 的所有可能值为0，1，2，3，4.则P(A k )=34(k =1,2,3,4)，且A 1，A 2，A 3，A 4相互独立．故P(X =0)=P(A 1)=14，P(X =1)=P(A 1·A 2)=34×14=316，P(X =2)=P(A 1A 2A 3)=(34)2×14=964， P(X =3)=P(A 1A 2A 3A 4)=(34)3×14=27256， P(X =4)=P(A 1A 2A 3A 4)=(34)4=81256，从而X 的分布列为所以E(X)=0×14+1×316+2×964+3×27256+4×81256=525256．解析：(1)由相互独立事件的概率计算公式计算即可；(2)先得出X的可能取值，求出对应概率，列出分布列求出数学期望即可．。

GRE考试数学部分真题汇编在GRE考试的数学部分，你将会面对各种各样的数学问题和真题。

这些题目旨在考察你对基本数学概念和解题方法的理解和应用能力。

为了帮助你更好地准备数学部分，下面是一些GRE数学部分的真题汇编，供你练习和参考。

1. 问题描述：在一个矩形房间中，地板被铺上了方形瓷砖，每块瓷砖的边长为1英尺。

如果房间的长度是15英尺，宽度是10英尺，那么需要多少块砖来铺满整个房间？解题思路：矩形房间的面积等于瓷砖的总面积。

通过计算可知，房间的面积为15英尺乘以10英尺，等于150平方英尺。

而每块瓷砖的面积为1平方英尺，所以需要150块瓷砖来铺满整个房间。

2. 问题描述：某家电商在一次促销活动中，将一台原价200美元的电脑打折出售，折扣幅度为20%。

这台电脑的促销价是多少美元？解题思路：首先，计算折扣金额，即200美元乘以20%。

将200乘以0.2，得到40美元。

然后，将原价200美元减去折扣金额40美元，得到促销价为160美元。

3. 问题描述：一名体育运动员在一次跳高比赛中，首次跳高1.5米未能成功。

随后，他每次都比前一次跳高的高度多0.2米。

他第5次成功跳高后，跳高的高度是多少米？解题思路：根据题意，运动员每次跳高的高度为1.5米加上前一次跳高的高度增加值。

所以，第2次跳高高度为1.5米加上0.2米，第3次跳高高度为1.7米加上0.2米，以此类推。

根据题意，可以得知第5次跳高高度是1.5米加上4个0.2米的和，等于1.5米加上0.2米乘以4，等于1.5米加上0.8米，结果为2.3米。

4. 问题描述：某公司的年度销售额为1000万美元，其中70%来自国内市场，30%来自国际市场。

如果公司在国际市场上的年度销售额是多少美元？解题思路：根据题意，国际市场销售额占年度销售额的30%。

将1000万美元乘以30%，得到国际市场的年度销售额为300万美元。

以上是一些GRE数学部分的真题汇编，通过解答这些真题，你可以提高自己的数学解题能力和思维灵活性。

2019年普通高等学校招生全国统一考试模拟卷（3）文科数学本试题卷共5页，23题（含选考题）。

全卷满分150分。

考试用时120分钟。

第Ⅰ卷一、选择题：本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一项是符合题目要求的。

1．已知全集，集合，，则（）A．B．C．D．【答案】C【解析】由题意得，，∴，∴．选C．2．欧拉公式（为虚数单位）是由瑞士著名数学家欧拉发现的，它将指数函数的定义域扩大到复数集，建立了三角函数和指数函数的关系，它在复变函数论里占有非常重要的地位．特别是当时，被认为是数学上最优美的公式，数学家们评价它是“上帝创造的公式”．根据欧拉公式可知，表示的复数在复平面中位于（）A．第一象限B．第二象限C．第三象限D．第四象限【答案】C【解析】由已知有，因为，所以在第三象限，所以，，故表示的复数在复平面中位于第三象限，选C．3．如图，“赵爽弦图”是由四个全等的直角三角形（阴影部分）围成一个大正方形，中间空出一个小正方形组成的图形，若在大正方形内随机取一点，该点落在小正方形的概率为，则途中直角三角形中较大锐角的正弦值为（）A．B．C．D．【答案】B【解析】设小正方形的边长为，直角三角形的直角边分别为，，，由几何概型可得，解得，（舍），所以直角三角形边长分别为，，，直角三角形中较大锐角的正弦值为，选B．4．下列命题中：①“”是“”的充分不必要条件②定义在上的偶函数最小值为5；③命题“，都有”的否定是“，使得”④已知函数的定义域为，则函数的定义域为．正确命题的个数为（）A．1个B．2个C．3个D．4个【答案】C【解析】①或，所以“”是“”的充分不必要条件；②因为为偶函数，所以，因为定义区间为，所以，因此最小值为5；③命题“，都有”的否定是“，使得”；④由条件得，，；因此正确命题的个数为①②④，选C．5．《九章算术》中的玉石问题：“今有玉方一寸，重七两；石方一寸，重六两．今有石方三寸，中有玉，并重十一斤（即176两），问玉、石重各几何？”其意思为：“宝玉1立方寸重7两，石料1立方寸重6两，现有宝玉和石料混合在一起的一个正方体，棱长是3寸，质量是11斤（即176两），问这个正方体中的宝玉和石料各多少两？”如图所示的程序框图给出了对此题的一个求解算法，运行该程序框图，则输出的，分别为（）A．90，86B．94，82C．98，78D．102，74【答案】C【解析】执行程序：，，；，，；，，；，，，故输出的，分别为，．故选：C．6．某几何体的三视图如图所示，则该几何体的体积是（）A．B．C．D．【答案】D【解析】由三视图可知：该几何体由两部分构成，一部分侧放的四棱锥，一部分为四分之一球体，∴该几何体的体积是，故选：D．7．已知实数，满足：，则的最大值（）A．8B．7C．6D．5【答案】D【解析】根据不等式组画出可行域是封闭的四边形区域，对目标函数进行分类，当时，令，，这时可行域为直线下方的部分，当目标函数过点时有最大值．当时，令，，这时可行域为直线上方的部分，这时当目标函数过点时有最大值，代入得到最大值为．故答案为：D．8．设，函数的图象向右平移个单位后与原图象重合，则的最小值是（）A．B．C．D．【答案】A【解析】将的图象向右平移个单位后对应的函数为，∵函数的图象向右平移个单位后与原图象重合，所以有，即，又，，故，故选A．9．已知函数与其导函数的图象如图，则满足的的取值范围为（）A．B．C．D．【答案】D【解析】根据导函数与原函数的关系可知，当时，函数单调递增，当时，函数单调递减，由图象可知：当时，函数的图象在图象的下方，满足；当时，函数的图象在图象的下方，满足；22222正视图侧视图俯视图所以满足的解集为或，故选D ．10．若正项递增等比数列满足，则的最小值为（）A ．B ．C ．2D ．4【答案】D 【解析】因为，所以，当且仅当时取等号，即的最小值为，选D ．11．设正三棱锥的高为，且此棱锥的内切球的半径，则（）A ．B ．C ．D ．【答案】D 【解析】取线段中点，设在底面的射影为，连接，，设，则，设，则正三棱锥的表面积，由体积得，，，，，，，选D ．12．已知，若函数恰有三个零点，则下列结论正确的是（）A ．B ．C ．D ．【答案】D 【解析】，可知函数在区间单调递增，在单调递减，在单调递增，如下图，，，，令，则，因为要有三个零点，∴有解，设为，，由，根据图象可得：当时，，，符合题意，此时，当时，可求得，不符合题意．综上所述，，故选D ．第Ⅱ卷二、填空题：本大题共4小题，每小题5分．13．向量，满足，，与的夹角为，则________．【答案】【解析】由可得，即，代入可得，整理可得，解得，故答案为．14．抛物线的焦点为，点，为抛物线上一点，且不在直线上，则周长的最小值为____________．【答案】【解析】由抛物线定义，抛物线上的点到焦点的距离等于这点到准线的距离，即．所以周长，填．15．在中，内角，，所对的边分别为，，，已知，且，则面积的最大值为________．【答案】【解析】由已知有，，(1)q g x 2t 1210t t 12t t 124e t 222e44et 22214e+e4kt t 12240,et t 12241et t由于，，又，则，，当且仅当时等号成立．故面积的最大值为．16．过双曲线的焦点与双曲线实轴垂直的直线被双曲线截得的线段的长称为双曲线的通径，其长等于(、分别为双曲线的实半轴长与虚半轴长)．已知双曲线（）的左、右焦点分别为、，若点是双曲线上位于第四象限的任意一点，直线是双曲线的经过第二、四象限的渐近线，于点，且的最小值为，则双曲线的通径为__________．【答案】【解析】如图所示：连接，由双曲线的定义知，，当且仅当，，三点共线时取得最小值，此时，由到直线的距离，，由定义知通径等于，故答案为．三、解答题：解答应写出文字说明、证明过程或演算步骤．第17~21题为必考题，每个试题考生都必须作答．第22、23为选考题，考生根据要求作答．（一）必考题：60分，每个试题12分．17．设是数列的前项和，已知，．（1）求数列的通项公式；（2）设，求数列的前项和．【答案】（1）；（2）．【解析】（1）∵，，∴当时，，得；····1分当时，，∴当时，，即，····3分又，····4分∴是以为首项，为公比的等比数列．····5分∴数列的通项公式为．····6分（2）由（1）知，，····7分，····8分当为偶数时，；····10分当为奇数时，，∴．····12分18．2018年为我国改革开放40周年，某事业单位共有职工600人，其年龄与人数分布表如下：年龄段人数（单位：人）180********约定：此单位45岁~59岁为中年人，其余为青年人，现按照分层抽样抽取30人作为全市庆祝晚会的观众．（1）抽出的青年观众与中年观众分别为多少人？（2）若所抽取出的青年观众与中年观众中分别有12人和5人不热衷关心民生大事，其余人热衷关心民生大事．完成下列列联表，并回答能否有的把握认为年龄层与热衷关心民生大事有关？热衷关心民生大事不热衷关心民生大事总计青年12中年5总计30（3）若从热衷关心民生大事的青年观众（其中1人擅长歌舞，3人擅长乐器）中，随机抽取2人上台表演节目，则抽出的2人能胜任才艺表演的概率是多少？0.1000.0500.0250.0100.0012.7063.841 5.024 6.63510.828．【答案】（1），；（2）列联表见解析，没有的把握认为年龄层与热衷关心民生大事有关；（3）．【解析】（1）抽出的青年观众为18人，中年观众12人····2分（2）列联表如下：热衷关心民生大事不热衷关心民生大事总计青年61218中年7512总计131730····4分，····6分∴没有的把握认为年龄层与热衷关心民生大事有关．····7分（3）热衷关心民生大事的青年观众有6人，记能胜任才艺表演的四人为，，，，其余两人记为，，则从中选两人，一共有如下15种情况：，，，，，，，，，，，，，，，····10分抽出的2人都能胜任才艺表演的有6种情况，····11分所以．····12分19．如图，在四棱锥中，四边形是菱形，，平面平面，，，在棱上运动．（1）当在何处时，平面；（2）已知为的中点，与交于点，当平面时，求三棱锥的体积．【答案】（1）当为中点时，平面；（2）．【解析】（1）如图，设与相交于点，当为的中点时，平面，····2分证明∵四边形是菱形，可得：，又∵为的中点，可得：，∴为的中位线，····3分可得，····4分又∵平面，平面，∴平面．····6分（2）为的中点，，则，又，，且，又，．．．····9分又，点为的中点，到平面的距离为．····11分．····12分20．在平面直角坐标系中，点，圆，点是圆上一动点，线段的中垂线与线段交于点．（1）求动点的轨迹的方程；（2）若直线（斜率存在）与曲线相交于，两点，且存在点（其中，，不共线），使得被轴平分，证明：直线过定点．B【答案】（1）；（2）．【解析】（1）由已知，，圆的半径为，依题意有：，····1分····3分故点的轨迹是以，为焦点，长轴长为4的椭圆，即，，．故点的轨迹的方程为．····5分（2）令，，因，，不共线，故的斜率不为0，可令的方程为：，则由，得则，①····7分被轴平分，，即，亦即②····8分而代入②得：③····9分①代入③得：····10分∵直线的斜率存在，∴，∴，此时的方程为：，过定点，综上所述，直线恒过定点．····12分21．设函数．（1）讨论的单调性；（2）设，当时，，求的取值范围．【答案】（1）见解析；（2）．【解析】（1）由题意得，．····1分当时，当，；当时，；∴在单调递减，在单调递增····2分当时，令得，，①当时，，；当时，；当时，；所以f(x)在，单调递增，在单调递减····3分②当时，，所以在单调递增····4分③当时，，；当时，；当时，；∴在，单调递增，在单调递减．····5分（2）令，有．····6分令，有，当时，，单调递增．∴，即．····7分①当，即时，，在单调递增，，不等式恒成立····9分②当，时，有一个解，设为根．∴有，，单调递减；当时，；单调递增，有．∴当时，不恒成立；····11分综上所述，的取值范围是．····12分l（二）选考题（共10分．请考生在第22、23题中任选一题作答．如果多做，则按所做第一题计分）22．【选修4-4：坐标系与参数方程】在平面直角坐标系中，曲线的参数方程为：（为参数，），将曲线经过伸缩变换：得到曲线．（1）以原点为极点，轴的正半轴为极轴建立坐标系，求的极坐标方程；（2）若直线（为参数）与，相交于，两点，且，求的值．【答案】（1）；（2）或．【解析】（1）的普通方程为，把，代入上述方程得，，∴的方程为，令，，所以的极坐标方程为；····5分（2）在（1）中建立的极坐标系中，直线的极坐标方程为，由，得，由，得，所以，∴，而，∴或．····10分23．选修4-5：不等式选讲已知函数，．（1）当时，若的最小值为，求实数的值；（2）当时，若不等式的解集包含，求实数的取值范围．【答案】（1）或；（2）．【解析】（1）当时，，因为的最小值为3，所以，解得或．····5分（2）当时，即，当时，，即，因为不等式的解集包含，所以且，即，故实数的取值范围是．····10分。

高中数学新课标测试模拟试卷（一）一、填空题（本大题共 10 道小题，每小题 3 分，共 30 分）1、数学是研究（）的科学，是刻画自然规律和社会规律的 科学语言和有效工具。

2、数学教育要使学生掌握数学的基本知识、（）、基本思想。

3、高中数学课程应具有多样性和（），使不同的学生在数学上得到不同的发展。

）能力。

4、高中数学课程应注重提高学生的数学（5、高中数学选修 2-2 的内容包括：导数及其应用、（复数的引入。

）、数系的扩充与 6、高中数学课程要求把数学探究、（块和专题内容之中。

）的思想以不同的形式渗透在各个模 7、选修课程系列 1 是为希望在（ ）等方面发展的学生设置的， 系列 2 是为希望在理工、经济等方面发展的学生设置的。

8、新课程标准的目标要求包括三个方面：知识与技能，过程与方法，（9、向量是近代数学中重要和基本的数学概念之一，它是沟通代数、几何与（ 的一种工具。

）。

）10、数学探究即数学（学习的过程。

）学习，是指学生围绕某个数学问题，自主探究、 二、判断题（本大题共 5 道小题，每小题 2 分，共 10 分）1、高中数学课程每个模块 1 学分，每个专题 2 学分。

（） 2、函数关系和相关关系都是确定性关系。

（ 3、统计是研究如何合理收集、整理、分析数据的学科，它可以为人们制定决策提供依 据。

（ 4、数学是人类文化的重要组成部分，为此，高中数学课程提倡体现数学的文化价值。

） ）（ ）5、教师应成为学生进行数学探究的领导者。

（）三、简答题（本大题共4道小题，每小题7分，共28分）1、高中数学课程的总目标是什么？2、高中数学新课程设置的原则是什么？3、评价学生在数学建模中的表现时，评价内容应关注哪几个方面？4、请简述《必修三》中《算法初步》一章的内容与要求。

四、论述题（本大题共2道小题，第一小题12分，第二小题20分）1、请完成《等差数列前n项和》第一课时的教学设计。

2、请您结合自己的教学经验，从理论和实践两个方面谈谈如何改善课堂教学中的教与学的方式，能使学生更主动地学习？答案一、填空题1、空间形式和数量关系2、基本技能3、选择性4、思维5、推理与证明6、数学建模7、人文、社会科学8、情感、态度、价值观9、三角函数10、探究性课题二、判断题1、错，改：高中数学课程每个模块2 学分，每个专题1 学分。

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&gt;7 + x(b)25x + 16≥10-x(c)16 + x&gt;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。

最新gre数学考试数据解释题型方面的典型题目及答案新gre改革后，无论是题型还是难度都发生了一些变化，如果觉得复习gre数学考试比拟难不妨从这些题目练习开始，每篇都是按照分类给大家列举了一些典型题目，本篇主要是针对gre数学考试数据解释题型方面的`典型题目及答案。

希望对大家的复习有所帮助。

The graph above shows how a sample of 10 different voters voted for 5 different candidates . Each voter voted for either one or two of the five candidates.The two candidates receiving the most votes were the winners. The sample constituted 5 percent of those in the district who voted, and the number of votes in the district for each candidate was in the same proportion as the number of votes in the sample for each candidate.7.What fraction of the total number of votes cast did the two winners receive?A.11/18B.11/22C.1/2D.1/3E.3/10答案：A8.What percent of the sample voted for at least one of the two winners?A.11%B.20%C.55%D.61%E.90%答案：E9.How many votes were cast in district X ?A.18B.90C.200D.360新gre改革后，无论是题型还是难度都发生了一些变化，如果觉得复习gre数学考试比拟难不妨从这些题目练习开始，每篇都是按照分类给大家列举了一些典型题目，本篇主要是针对gre数学考试数据解释题型方面的典型题目及答案。