SAMPLE 8

　　[数学类]

　　题目序号

　　题型归类

　　第1题

　　段落结构题型

　　第2题

　　审题定位与引申推导题型

　　第3题

　　审题定位与细节推导题型

　　第4题

　　审题定位与关键词语题型

　　第5题

　　指代词题型

　　Computer programmers often remark that computing machines, with aperfect lack of discrimination, will do any foolish thing they are told to do.The reason for this lies, of course, in the narrow fixation of the computingmachines intelligence on the details of its own perceptions itsinability to be guided by any large context. In a psychological description ofthe computer intelligence, three related adjectives come to mind:single-minded, literal-minded, and simple-minded. Recognizing this, we shouldat the same time recognize that this single-mindedness, literal-mindedness, andsimple-mindedness also characterizes theoretical mathematics, though to alesser extent.

　　Since science tries to deal with reality, even the most precisesciences normally work with more or less imperfectly understood approximationstoward which scientists must maintain an appropriate skepticism. Thus, forinstance, it may come as a shock to mathematicians to learn that theSchrodinger equation for the hydrogen atom is not a literally correctdescription of this atom, but only an approximation to a somewhat more correctequation taking account of spin, magnetic dipole, and relativistic effects; andthat this corrected equation is itself only an imperfect approximation to an infiniteset of quantum field-theoretical equations. Physicists, looking at the originalSchrodinger equation, learn to sense in it the presence of many invisible termsin addition to the differential terms visible, and this sense inspires anentirely appropriate disregard for the purely technical features of theequation. This very healthy skepticism is foreign to the mathematical approach.

　　Mathematics must deal with well-defined situations. Thus,mathematicians depend on an intellectual effort outside of mathematics for thecrucial specification of the approximation that mathematics is to takeliterally. Give mathematicians a situation that is the least bit ill-defined,and they will make it well-defined, perhaps appropriately, but perhapsinappropriately. In some cases, the mathematicians literal-mindedness may haveunfortunate consequences. The mathematicians turn the scientists theoreticalassumptions that is, their convenient points of analytical emphasis, intoaxioms, and then take these axioms literally. This brings the danger that theymay also persuade the scientists to take these axioms literally. The question,central to the scientific investigation but intensely disturbing in themathematical context what happens if the axioms are relaxed? is therebyignored.

　　The physicist rightly dreads precise argument, since an argumentthat is convincing only if it is precise loses all its force if the assumptionson which it is based are slightly changed, whereas an argument that isconvincing though imprecise may well be stable under small perturbations of itsunderlying assumptions.

　　1. The author discusses computing machines in the first paragraphprimarily in order to do which of the following?

　　[A] Indicate the dangers inherent in relying to a great extent onmachines.

　　[B] Illustrate his views about the approach of mathematicians toproblem solving.

　　[C] Compare the work of mathematicians with that of computerprogrammers.

　　[D] Provide one definition of intelligence.

　　2. It can be inferred form the text that scientists make which ofthe following assumptions about scientific arguments?

　　[A] The literal truth of the arguments can be made clear only in amathematical context.

　　[B] The arguments necessarily ignore the central question of scientificinvestigation.

　　[C] The arguments probably will be convincing only to otherscientists.

　　[D] The premises on which the arguments are based may change.

　　3. According to the text, mathematicians present a risk to scientistfor which of the following reasons?

　　[A] Mathematicians may provide theories that are incompatible withthose already developed by scientists.

　　[B] Mathematicians may define situations in a way that isincomprehensible to scientists.

　　[C] Mathematicians may convince scientists that theoreticalassumptions are facts.

　　[D] Scientists may come to believe that axiomatic statements areuntrue.

　　4. The author suggests that the approach of physicists to solvingscientific problem is which of the following?

　　[A] Practical for scientific purposes.

　　[B] Detrimental to scientific progress.

　　[C] Unimportant in most situations.

　　[D] Expedient, but of little long-term value.

　　5. The author implies that scientists develop a healthy skepticism becausethey are aware that

　　[A] mathematicians are better able to solve problems than arescientists.

　　[B] changes in axiomatic propositions will inevitably underminescientific arguments.

　　[C] well-defined situations are necessary for the design of reliableexperiments.

　　[D] some factors in most situations must remain unknown.

　　[答案与考点解析]

　　1. 【答案】B

　　【考点解析】这是一道写作手法题。旨在考察考生的语言基本功和对文章段落结构的认识。这是一道比较难的题目。通过仔细阅读第一段并且把第一段和本文其它段落相联系，可推导出本题的正确选项是B。原文作者借用大家所熟悉的computing machines作为例子来帮助我们更好的了解theoretical mathematics的特点?？忌诮馓馐币欢ㄒ侗鸪鲎髡叩男醋魇址ê鸵馔?。

　　2. 【答案】D

　　【考点解析】这是一道审题定位与引申推导题。通过本题题干中的arguments一词可将本题的答案信息来源迅速确定在尾段。通过仔细阅读理解尾段的内容并且根据尾段的内容进行推导，可得知本题的正确选项应该是突出the premisesmay change的选项D?？忌诮馓馐奔匆弑秆杆偕筇舛ㄎ坏哪芰Γ忠弑咐斫庠纳畈愫宓哪芰?。

　　3. 【答案】C

　　【考点解析】这是一道审题定位与细节推导题。根据本题题干中的risk一词可将本题的答案信息来源确定在原文倒数第二段的倒数第二句，通过仔细阅读倒数第二段的倒数第二句和第三句，尤其是倒数第二句中danger一词后面的同谓语从句，我们可以推断出本题的正确选项是突出theoretical assumptions are facts的选项C?？忌诮馓馐币欢ㄒ朴谏钊肜斫庠牡暮?，千万不能只停留在文字的表面。

　　4. 【答案】A

　　【考点解析】本题是一道审题定位与关键词语题。通过本题题干中的physicists可将本题的答案信息来源迅速确定在第二段的倒数第二句。通过阅读本句以及它的前后句，尤其是它后面的一句话，我们可以推断出本题的正确选项应该是表达healthy含义的选项A，因为该选项中的practical是一个表示肯定的词语?？忌诮馓馐币欢ㄒ朴谏筇舛ㄎ?，更要善于理解句间关系所表达的内容。

　　5. 【答案】D

　　【考点解析】这是一道指代词题型。根据本题题干中的healthy skepticism可将本题的答案信息来源迅速确定在第二段的尾句，该句中的指代词this暗示我们本题的真正答案信息来源在第二段的倒数第二句，通过仔细阅读和理解倒数第二段的第二句话，我们可以得知强调invisible的选项D是本题的正确选项，因为该选项中含有unknown一词。考生在解题时应注意指代词的作用和功能，更要注意对原文细节的理解和把握。

　　[参考译文]

　　计算机程序员经常说计算机器会执行任何愚蠢的命令，因为它们完全缺乏辨别力。当然，其原因在于计算机的智力在其感知细节上的狭窄固定性它不能被冗长的上下文所引导。三个相关的形容词可以用来对计算机进行心理上的描述：单一的思维，刻板的思维，简单的思维。在认识到这一点的同时，我们也应该认识到这种单一的思维，刻板的思维，简单的思维同样可以用来描述理论数学。

　　由于科学总是处理现实的问题，即使最精确的科学也通常在或多或少的不完全理解的近似的基础上探讨现实，对此，科学家必须保持适当的怀疑。例如，当数学家得知关于氢原子的薛定谔方程并不是对这种原子的精确的描述，而只是在考虑了旋转、磁极以及相对论作用的基础上一个稍微正确的近似方程，并且这个所谓的正确方程自身也只是对一个无穷量子理论场的不完美的近似时，他们一定深感震惊。当物理学家看到最初的薛定谔方程时，他们从中感知到在可见的各种关系之外，仍然存在着许多不可见的关联，而这种感知就会激励物理学家合理地忽略方程中纯技术的特色。这种非常有益的怀疑态度对于数学领域而言则是较为陌生的。

　　数学家必须研究精确界定的情况。因此，数学家依赖数学以外的努力来对数学照字面意义理解的近似性加以详细的说明。当给予数学家一个不确定程度较小的情形时，他们会把它转化成一个完全确定的状态。这种转化可能是合适的，也可能是不合适的。在某些情形下，数学家的这种刻板思维可能会产生不幸的后果。数学家把科学家的理论假设，也就是科学家分析重点的权宜之点，转化成公理，然后依据精确字义理解这些公理。他们可能还会说服科学家依据字义理解公理，这就会带来危险?？蒲Ъ业鞑榈闹行奈侍?，在数学领域则成为极其扰乱人心的问题，因而被忽略如果公理不严谨会发生什么情况?

　　物理学家惧怕精确的论断是对的，因为一个仅仅因其精确性而使人信服的论断，当它所基于的假设略微改变时，其说服力就会丧失殆尽，而一个尽管不精确却具有说服力的论断，却会在它的基础假设受到小干扰时，依旧岿然不动。

　　SAMPLE 8

　　[数学类]

　　题目序号

　　题型归类

　　第1题

　　段落结构题型

　　第2题

　　审题定位与引申推导题型

　　第3题

　　审题定位与细节推导题型

　　第4题

　　审题定位与关键词语题型

　　第5题

　　指代词题型

　　Computer programmers often remark that computing machines, with aperfect lack of discrimination, will do any foolish thing they are told to do.The reason for this lies, of course, in the narrow fixation of the computingmachines intelligence on the details of its own perceptions itsinability to be guided by any large context. In a psychological description ofthe computer intelligence, three related adjectives come to mind:single-minded, literal-minded, and simple-minded. Recognizing this, we shouldat the same time recognize that this single-mindedness, literal-mindedness, andsimple-mindedness also characterizes theoretical mathematics, though to alesser extent.

　　Since science tries to deal with reality, even the most precisesciences normally work with more or less imperfectly understood approximationstoward which scientists must maintain an appropriate skepticism. Thus, forinstance, it may come as a shock to mathematicians to learn that theSchrodinger equation for the hydrogen atom is not a literally correctdescription of this atom, but only an approximation to a somewhat more correctequation taking account of spin, magnetic dipole, and relativistic effects; andthat this corrected equation is itself only an imperfect approximation to an infiniteset of quantum field-theoretical equations. Physicists, looking at the originalSchrodinger equation, learn to sense in it the presence of many invisible termsin addition to the differential terms visible, and this sense inspires anentirely appropriate disregard for the purely technical features of theequation. This very healthy skepticism is foreign to the mathematical approach.

　　Mathematics must deal with well-defined situations. Thus,mathematicians depend on an intellectual effort outside of mathematics for thecrucial specification of the approximation that mathematics is to takeliterally. Give mathematicians a situation that is the least bit ill-defined,and they will make it well-defined, perhaps appropriately, but perhapsinappropriately. In some cases, the mathematicians literal-mindedness may haveunfortunate consequences. The mathematicians turn the scientists theoreticalassumptions that is, their convenient points of analytical emphasis, intoaxioms, and then take these axioms literally. This brings the danger that theymay also persuade the scientists to take these axioms literally. The question,central to the scientific investigation but intensely disturbing in themathematical context what happens if the axioms are relaxed? is therebyignored.

　　The physicist rightly dreads precise argument, since an argumentthat is convincing only if it is precise loses all its force if the assumptionson which it is based are slightly changed, whereas an argument that isconvincing though imprecise may well be stable under small perturbations of itsunderlying assumptions.

　　1. The author discusses computing machines in the first paragraphprimarily in order to do which of the following?

　　[A] Indicate the dangers inherent in relying to a great extent onmachines.

　　[B] Illustrate his views about the approach of mathematicians toproblem solving.

　　[C] Compare the work of mathematicians with that of computerprogrammers.

　　[D] Provide one definition of intelligence.

　　2. It can be inferred form the text that scientists make which ofthe following assumptions about scientific arguments?

　　[A] The literal truth of the arguments can be made clear only in amathematical context.

　　[B] The arguments necessarily ignore the central question of scientificinvestigation.

　　[C] The arguments probably will be convincing only to otherscientists.

　　[D] The premises on which the arguments are based may change.

　　3. According to the text, mathematicians present a risk to scientistfor which of the following reasons?

　　[A] Mathematicians may provide theories that are incompatible withthose already developed by scientists.

　　[B] Mathematicians may define situations in a way that isincomprehensible to scientists.

　　[C] Mathematicians may convince scientists that theoreticalassumptions are facts.

　　[D] Scientists may come to believe that axiomatic statements areuntrue.

　　4. The author suggests that the approach of physicists to solvingscientific problem is which of the following?

　　[A] Practical for scientific purposes.

　　[B] Detrimental to scientific progress.

　　[C] Unimportant in most situations.

　　[D] Expedient, but of little long-term value.

　　5. The author implies that scientists develop a healthy skepticism becausethey are aware that

　　[A] mathematicians are better able to solve problems than arescientists.

　　[B] changes in axiomatic propositions will inevitably underminescientific arguments.

　　[C] well-defined situations are necessary for the design of reliableexperiments.

　　[D] some factors in most situations must remain unknown.

　　[答案与考点解析]

　　1. 【答案】B

　　【考点解析】这是一道写作手法题。旨在考察考生的语言基本功和对文章段落结构的认识。这是一道比较难的题目。通过仔细阅读第一段并且把第一段和本文其它段落相联系，可推导出本题的正确选项是B。原文作者借用大家所熟悉的computing machines作为例子来帮助我们更好的了解theoretical mathematics的特点。考生在解题时一定要识别出作者的写作手法和意图。

　　2. 【答案】D

　　【考点解析】这是一道审题定位与引申推导题。通过本题题干中的arguments一词可将本题的答案信息来源迅速确定在尾段。通过仔细阅读理解尾段的内容并且根据尾段的内容进行推导，可得知本题的正确选项应该是突出the premisesmay change的选项D。考生在解题时即要具备迅速审题定位的能力，又要具备理解原文深层含义的能力。

　　3. 【答案】C

　　【考点解析】这是一道审题定位与细节推导题。根据本题题干中的risk一词可将本题的答案信息来源确定在原文倒数第二段的倒数第二句，通过仔细阅读倒数第二段的倒数第二句和第三句，尤其是倒数第二句中danger一词后面的同谓语从句，我们可以推断出本题的正确选项是突出theoretical assumptions are facts的选项C?？忌诮馓馐币欢ㄒ朴谏钊肜斫庠牡暮?，千万不能只停留在文字的表面。

　　4. 【答案】A

　　【考点解析】本题是一道审题定位与关键词语题。通过本题题干中的physicists可将本题的答案信息来源迅速确定在第二段的倒数第二句。通过阅读本句以及它的前后句，尤其是它后面的一句话，我们可以推断出本题的正确选项应该是表达healthy含义的选项A，因为该选项中的practical是一个表示肯定的词语?？忌诮馓馐币欢ㄒ朴谏筇舛ㄎ?，更要善于理解句间关系所表达的内容。

　　5. 【答案】D

　　【考点解析】这是一道指代词题型。根据本题题干中的healthy skepticism可将本题的答案信息来源迅速确定在第二段的尾句，该句中的指代词this暗示我们本题的真正答案信息来源在第二段的倒数第二句，通过仔细阅读和理解倒数第二段的第二句话，我们可以得知强调invisible的选项D是本题的正确选项，因为该选项中含有unknown一词?？忌诮馓馐庇ψ⒁庵复实淖饔煤凸δ?，更要注意对原文细节的理解和把握。

　　[参考译文]

　　计算机程序员经常说计算机器会执行任何愚蠢的命令，因为它们完全缺乏辨别力。当然，其原因在于计算机的智力在其感知细节上的狭窄固定性它不能被冗长的上下文所引导。三个相关的形容词可以用来对计算机进行心理上的描述：单一的思维，刻板的思维，简单的思维。在认识到这一点的同时，我们也应该认识到这种单一的思维，刻板的思维，简单的思维同样可以用来描述理论数学。

　　由于科学总是处理现实的问题，即使最精确的科学也通常在或多或少的不完全理解的近似的基础上探讨现实，对此，科学家必须保持适当的怀疑。例如，当数学家得知关于氢原子的薛定谔方程并不是对这种原子的精确的描述，而只是在考虑了旋转、磁极以及相对论作用的基础上一个稍微正确的近似方程，并且这个所谓的正确方程自身也只是对一个无穷量子理论场的不完美的近似时，他们一定深感震惊。当物理学家看到最初的薛定谔方程时，他们从中感知到在可见的各种关系之外，仍然存在着许多不可见的关联，而这种感知就会激励物理学家合理地忽略方程中纯技术的特色。这种非常有益的怀疑态度对于数学领域而言则是较为陌生的。

　　数学家必须研究精确界定的情况。因此，数学家依赖数学以外的努力来对数学照字面意义理解的近似性加以详细的说明。当给予数学家一个不确定程度较小的情形时，他们会把它转化成一个完全确定的状态。这种转化可能是合适的，也可能是不合适的。在某些情形下，数学家的这种刻板思维可能会产生不幸的后果。数学家把科学家的理论假设，也就是科学家分析重点的权宜之点，转化成公理，然后依据精确字义理解这些公理。他们可能还会说服科学家依据字义理解公理，这就会带来危险。科学家调查的中心问题，在数学领域则成为极其扰乱人心的问题，因而被忽略如果公理不严谨会发生什么情况?

　　物理学家惧怕精确的论断是对的，因为一个仅仅因其精确性而使人信服的论断，当它所基于的假设略微改变时，其说服力就会丧失殆尽，而一个尽管不精确却具有说服力的论断，却会在它的基础假设受到小干扰时，依旧岿然不动。