《数学与应用数学毕业
论文
政研论文下载论文大学下载论文大学下载关于长拳的论文浙大论文封面下载
-对近几年高考数学压轴
题
快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题
的探究》
曲靖师范学院
论文题目:对近几年高考数学压轴题的探究
作者、学号:
学院、年级:数学与信息科学学院 2006级 学科、专业:数学 数学与应用数学
指 导 教 师:
完 成 日 期:2010年5月26日
曲靖师范学院教务处
Opinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutions and grass-roots party organizations. According to my actual County, the county to carry out the education practice put forward the following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to further implement the central eight regulations and < The opposition party and government austerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force of the county and the ecological culture of the county and county construction.In educational practice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutions directly under the township, street, and community, village, non-public economic organizations, social organizations and other grass-roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses of law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competition of alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration of resources. To further broaden their horizons, effective integration of resources within the group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win-win principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and approval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, to achieve leveraging the development, ensure that the value of state-owned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition, improve management and operation of the market. At the same time, according to the need of industrial development, vigorously the introduction of high-quality management management personnel, and strive to build a high-quality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious research about social support the development of cultural undertakings in the country and the XX policy, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.
曲靖师范学院
本论文(
设计
领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计
)经答辩小组全体成员审查，确认符合曲靖师范学院本科(学士学位)毕业论文(设计)质量要求。
答辩小组签名
主 姓 名 工 作 单 位 职 称 席 副教授 曲靖师范学院数学与信息科学学院
曲靖师范学院数学与信息科学学院 教授
曲靖师范学院数学与信息科学学院 成 副教授
曲靖师范学院数学与信息科学学院 讲 师
曲靖师范学院数学与信息科学学院 员 助 教
答辩日期:2010年5月26日
work style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the2rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmali
原创性声明
本人声明:所呈交的论文(设计)是本人在指导教师指导下进行的研究工作成果。除了文中特别加以标注和致谢的地方外，论文(设计)中不包含其他人已发表或撰写过的研究成果。参与同一工作的其他同志对本研究所作的任何贡献已在论文(设计)中作了明确的说明并表示了谢意。
签名: 日期: 2010年5月26日 。
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财务内部控制制度的内容财务内部控制制度的内容人员招聘与配置的内容项目成本控制的内容消防安全演练内容
。
签名: 指导教师签名: 日期: 2010年5月26日。
ntatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif3y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the whole
对近几年高考数学压轴题的探究
摘 要
高考数学压轴题一般是指高考数学试卷中的最后一道题，是高考数学卷中综合性和探索性最强，难度最大，具有深刻的高等数学(甚至现代数学)背景的题. 高考数学压轴题入口宽，深入难，要想突破它并拿到一定的分数绝不是一件容易的事.每年都有不少学生对高考数学压轴题产生恐惧感，而且得分率都较低甚至多数为零分.要想顺利解答高考数学压轴题，除有扎实的基础知识，灵活应用知识的能力外，还需紧扣“双基”，对压轴题作一定的反思、回味、 总结. 因此，本毕业论文对近几年高考数学压轴题的类型、背景、设问方式、解答策略进行了一定的探究，希望帮助师生做好压轴题的复习，使考生从一个全新的角度去思索高考题，以使尽可能多的学生经阅读、训练后在高考场上解答压轴题时能发挥自如，获得高分.
关键词: 高考数学压轴题; 类型; 背景;设问方式; 解答策略
service to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the4rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doubl
The Exploration of Mathematical Finale Problems of College
Entrance in Recent Years
Abstract:Mathematical finale problems of college entrance examination generally refers to the last one problem on the mathematical paper , which is the most comprehensive, exploratory and difficult one .And the problems have profound advanced mathematics ( even modern mathematics) background.What’s more, the problems cover a lot of knowledge and
are difficult to find the answer to them in deep . Therefore ,It is not easy for the candidates to get a certain score .Every year , many students are afraid of them, and get a low score even zero.If one wants to find the answer to the problems easily, one would master “basic
knowledge and skills ”, and rethink them again and again except for having solid basic knowledge. this thesis is aim at exploring the problems’type, background, way of question
and solution strategy in recent years in hope that this paper can help students and teachers review this kind of problem effectiuely, and can make the candidates think about the problem from a new perspective. In this case, the candidates can easily find the answer to the problems and get a high scores through doing some exercises.
Keywords:mathematical finale problems of college entrance; type; backgrounds; way of question ; solution strategy
nsformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif5y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the impleme
目 录
1 引言 ................................................................. 1 2 文献综述 ............................................................. 1
2.1 国内外研究现状 ....................................................... 1 2.2 国内外研究现状评价 ................................................... 2
2.3 提出问题 ............................................................. 2 3 高考数学压轴题的类型探究............................................. 2 3.1 代数型压轴题 ......................................................... 2
3.2 几何型压轴题 ......................................................... 6 4 高考数学压轴题的背景分析............................................. 8
5 高考数学压轴题的设问方式探究......................................... 9 6 解答高考数学压轴题的策略探究......................................... 10 6.1 过好心理素质关 ....................................................... 11 6.2 牢固掌握数学基础知识 ................................................. 11 6.3 形成系统的数学知识结构 ............................................... 12 6.4 加强能力培养 ......................................................... 12 6.5 加强解题策略指导 ..................................................... 13 6.6 加强学生思维独创性的培养 ............................................. 14 6.7 强化练习 ............................................................. 16 7 高考数学压轴题回顾与展望............................................. 16 8 结论 ................................................................. 17 8.1 主要发现 ............................................................. 17 8.2 启示 ................................................................. 17 8.3 局限性 ............................................................... 18 8.4 努力方向 ............................................................. 18
参考文献 ............................................................. 19
ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the6rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo
1 引言
高考数学压轴题一般是指高考数学试卷中的最后一道题.高考数学压轴题是高考数学卷中综合性和探索性最强，难度最大，具有深刻的高等数学(甚至现代数学)背景的题，其情景新颖，寓创新意识于其中，关注试题由知识型向能力型的转化，具有探索性和创新性.高考数学压轴题是学生考试过程中最后要冲刺的“坡顶”，是试卷命题者为提高试卷区分度而设计的一道题.由于高考数学压轴题难度高，有较好的区分度，有知识和能力考查的综合性，成为命题者和师生高度关注的对象.同时也由于每年都有不少学生对高考数学压轴题产生恐惧感，得分率都较低甚至多数为零分，使其具有珍贵的教学价值.因此，本毕业论文从高考数学压轴题的类型、背景、一般设问方式、解答策略几个方向来探究高考数学压轴题，希望帮助师生做好压轴题的复习，使考生从一个全新的角度去思索高考题，找到更多的解题灵感，解除思维困境，减少时间失分，增强对思维方向的信心.也希望对改进教学方法，提高教学效果，培养学生的独创性思维作一点贡献.
2 文献综述
2.1国内外研究现状
从迄今所参阅到的文献资料[1—23]中所了解的信息来看， 高考数学压轴题综合性、灵活性、探索性都很强，考查的知识跨度比较大，涉及的数学思想方法多，对学生的能力要求高，因而许多研究者从不同角度、方向对它进行了一些研究.如在《新课程
,,1背景下高考数学试题研究》一文中刘得柱从高考改革的国家政策，高考试题的研究现状，高考数学试题的变化及新趋势做了详述;在《一道高观点下的数学高考压轴题》一,,2文中李兴无认真分析了一道具有高等数学知识背景的试题并作出两个推广;在《高考
,,3压轴题解法探究》一文中柳
书
关于书的成语关于读书的排比句社区图书漂流公约怎么写关于读书的小报汉书pdf
春结合数列本身的结构特点及近几年的一些高考试题详述了几种数列不等式的证明方法;在《江西高考数学压轴题新解及对证明数列不等式的
,,4启示》一文中曾建强对2006年江西高考理科数学压轴题给出两种新的证明方法及两点证明过程中的启示;在《怎样做才叫“拔高”课本—2005年两道高考压轴题与课本上
,,5一道例题的对比》一文中权宽一通过压轴题与例题的对比阐述了高三数学复习必须以课本为主，同时应对课本上的知识和方法加以“拔高”，使知识在“拔高” 中得到“升
,,6华”，从而使知识融会贯通;在《上通现代数学，下达中学课堂》一文中何龙泉通过对近几年来全国和部分省市高考数学题中一些典型试题进行深入分析并阐述了高考数
wind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif7y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s and
学题特别是所谓的压轴题都有深刻的高等数学(甚至现代数学);在《由一道2007年高
,,7考数学压轴题引发的思考》一文中余锦银通过分析每年高考的数学试题以及2007年的高考试题阐述了多数考生不能将数学试卷做完的原因是多方面的，但其中原因之一是不能自觉根据高考试题的一般设问方式灵活使用“跳步作答”和“借步作答”等技巧;
,,8在《高等数学背景下的高考数学命题探析》一文中懂裕华通过探析高考命题中以高等数学为背景的试题阐述了尽管有些高考试题的设计来源于高等数学，但解决方法最终还是中学所学的内容，而且高考中这部分问题的占分比例也不大，因此，没必要将高等数学的知识引进到高中数学中，等等.
2.2国内外研究现状评价
综上所述，迄今国内外对高考数学压轴题的研究是多种多样的，就所参阅到的多数研究者的研究来看，许多研究者对高考数学压轴题的研究或是对某一年的压轴题进行探析，或是就某一道题进行推广，或是就某一个方面做阐述，同时一些高考压轴题解答过程的给出灵活性、技巧性、创新性太强，普遍性、系统性不足，对指导一般的学生掌握、
突破压轴题并拿到一定的分数是很困难的.
2.3提出问题
针对国内外的研究现状，我们需要找出一些对于大多数学生都能够理解掌握的做数学压轴题的更普遍，更通用，更全面，更有效的技巧、方式方法，使大多数学生或是初学者产生更多灵感，找到解决压轴题的关键点.因此，本毕业论文从相对较普遍的归类，分析背景、设问方式，总结解题策略几个方面对高考数学压轴题进行了一定探究. 3 高考数学压轴题的类型探究
纵观近几年的高考数学题，发现高考的数学压轴题一般分为两大类:代数型压轴题和几何型压轴题.
3.1代数型压轴题
代数型压轴题重点表现为函数形式的综合题和数列形式的综合题，并且它们之间有着密切的联系.
函数思想的实质是用联系、变化的观点提出数学对象，建立函数关系，使问题得到解决. 数、式、方程、不等式、数列及极限、三角函数、导数等都是以函数为中心的.
函数形式的综合题在高考数学压轴题中主要有以下几种形式:
? 、函数内容本身的综合，如函数概念、图像、最值等方面的综合;
e sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the8rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving the
? 、函数与其它数学知识的综合，如方程、不等式、数列、解析几何、极限和导数等内容与函数的综合，这里主要体现函数思想的运用;
? 与实际问题的综合，主要体现在数学模型的构造和函数关系的建立，这类问题一般要经过变形转化，归结为二次函数、均值不等式、数列或导数的问题解决.
例 1(2007年江苏):已知是不全为零的实数，函数a,b,c,d
232,方程有实数根且的实数根，，，，gx,0fx,0，，，，gx,bx，cx，dfx,ax，bx，cx，d,
都是的根;反之的实数根都是的根. ，，，，，，，，，，fgx,0fgx,0gx,0
d(?)求的值.
c(?)若求的取值范围. a,0,
c(?)若求的取值范围. ，，g1,0,a,1,
解: 由于第(?)问、第(?)问容易求解，下面仅对第(?)问进行解答.
d,0b,,c,由题设且由第(?)问知，可得所以 ，，g1,0,
2，，，，gx,bx，cx,,cxx,1.
，，gx,0,cx(x,1),0于是可化为.
322，，，，fx,x,cx，cx,xx,cx，ca,1当得,所以
2 ，，，，，，，，，，,,fgx,gxgx,cgx，c
2432，，，，,,cxx,1cx,2cx，2cx,cx，1,所以
可化为 ，，，，fgx,0
2432，，，，,cxx,1cx,2cx，2cx,cx，1,0 (1).
432cx,2cx，2cx,cx，1,0显然方程的根都是方程的根, ,cx(x,1),0
)的根也应是方由题意知方程(1程的根. ,cx(x,1),0
432cx,2cx，2cx,cx，1,0因此要求方程 (2)无实数根
(x,0或x,1显然不是方程(2)的实数根).
432，，fx,cx,2cx，2cx,cx，1记，
432，，fx,cx,2cx，2cx,cx，1x则方程(2)无实数便等价于函数的图像与轴无交点.
1'x,，，fx,0于是考虑,令,得. 2
eatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif9y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuang
c,0?当时:
111,,,, ,,,,，,,,,,x 22,,,,2
- 0 + f'(x)
为减函数 极小值 为增函数 f(x)
116,3cx,，，，，fx,fx,所以当时，. 极小值最小值216
432，，fx,cx,2cx，2cx,cx，1x函数的图像与轴无交点 16,3c16,3c,,0,c,0;,0,c,. 1616
c,0时: ?当
111,,,, ,,,,，,,,,,x 22,,,,2
+ 0 - f'(x)
为增函数 极大值 为减函数 f(x)
16,3c1，，，，fx,fx,x,所以当时,. 极大值最大值162
432，，fx,cx,2cx，2cx,cx，1x函数的图像与轴无交点 16,3c16,,0,c,0;,c,,c,0. 163
c显然不存在这样的点.
c,0，，fx,1x? 当时:函数的图像与轴无交点，满足题意.
16，,c0,综上所述知:所求的取值范围是. ,,3，,
评注:此例是一道典型的函数形式综合题，运用导数研究函数的性质(单调性、极
work style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the10rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmali
值、最值)是高考数学压轴题的一种比较常见的形式.利用导数知识对此例进行解答是一种巧妙的方法，但也可应用初等方法进行解答.
数列是高中代数的重点内容之一,也是与大学数学有衔接的内容，由于在测试学生的逻辑推理能力和理性思维水平及考查学生创新意识和创新能力等方面有不可替代的作用，因此,在近几年高考中有着重要的地位.数列形式的综合题不仅考查数列、等差数列和等比数列、数列极限及数学归纳法等基本知识、基本技能，并且常与函数、方程、解析几何、不等式等知识相结合，同时考查学生在数学学习和研究过程中知识的迁移、组合、融会，进而考查学生的数学素养和学习潜能，为学生展现其创新意识和发挥创造能力提供广阔空间.
,,bb,bb,a例2(2009年江西理科第22题):每项都为正数的数列，，，且对n12
b，bb，bfgcd,c，d,f，gc,d,f,g满足 的正数都有. ，，，，，，，，1，b1，b1，b1，bcdfg
14b,a,b(1)当，时，求通项. n25
1,b,rbbn(2)证明:对任意,存在与有关的常数r，使得对于各个正整数，有. nr
b，bb，b1n2n,1,解:(1)由题意，可得, ，，，，，，，，1，b1，b1，b1，b1n2n,1
41，b，bn,1n2b，114n,152b,,b,a,再由，得 整理得, n39b，225n,1，，，，1，b1，bnn,125
nn1,b1,b11,b13,13,1nn,1n,,,bb,,又因为，整理得,从而得到且满足题设nnnnn1，b31，b31，b3，13，1nnn,1
的所有条件.
n3,114b,b,a,所以当，时，所求通项为. nn3，125
b，bcdac，d证明:(2)因为题设中的值仅与有关,所以将其记作.则 c，d，，，，1，b1，bcd
ng and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif11y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fu
b，bb，b1nn,1a,,, n，1，，，，，，，，1，b1，b1，b1，b1nn,1
b，x，，，，gx,x,0而函数在定义域上有 ，，，，1，b1，x
11b，，，，，，gx,fb,，b,1，，，，，，，，，，，，gx,fb,，b,1gx,fb,，0,b,1;;; 因2，，，，1，b1，b
,，，a,fbn,N此对，都恒成立. n，1
2,b1,,n，，，，afb，fb,,0,,,,又因为,得 2n22，，1，b,,n
1,,1,2，，，，1,，1,2，，，，fbfbfbfb，，fb,,,b n，，，，fbfb，，，，1,fb，1,2fb
，，，，1,fb，1,2fb1r,,b,r,即有,即命题(2)得证. 取nr，，fb
评注:数列形式的综合题是高考数学压轴题的热点题型，此例是考查特殊与一般思想、函数与方程思想、等价转化思想方面的一道好题.
3.2 几何型压轴题
几何型压轴题主要是以直线和圆锥曲线的关系来命题的，题目的特点是:
? 、基础知识要非常扎实，并能灵活应用;
?、 综合性较强，在解题中几乎处处涉及函数方程、向量、不等式、直线等内容，同时体现各种能力的综合;
? 、计算量大，要求具有较高的运算能力和较强的逻辑推理能力.
22xy，，G:，,1a,b,0o，，，，E2,2F6,1例3(2009年山东卷):设椭圆过,两点,为22ab
坐标原点.
G(?)求椭圆的方程;
G(?)是否存在圆心在原点的圆，使得该圆的任意一条切线与椭圆恒有两个交点
,,
NMOM,ONMN，，且,若存在，写出该圆的方程，并求的取值范围，若不存在，说明理由.
sm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the12rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to further
b,2简解:由于第(?)问容易求解,并求得,,下面仅对第(?)问进行a,22
解答.
,,
设,,,,,,则 OM,rON,r，，，，Mx,yNx,yx,rcos,y,rsin,1211221111
,, ,. x,rcos，，,，90y,rsin，，,，902222
N因，为椭圆上的两个动点，于是可得 M
2222,,,,cos，90,,sin，90r,，，r，，,cossin，，，，r,r,2211,, ，,1，,184842222cos,sin,1sin,cos,1即 ,. ，,，,228484rr12
22r，r3111112于是可得,即. ,，,，2222884rrrr1212
,,
oMN设坐标原点到直线的距离为,因为OM,ON，所以 r
,,,,
OM,ONOM,ONrr212 r,,,,6,,,22223MNr，r12OM，ON
822x，y,G因此存在圆心在原点的圆使之该圆的任意一条切线与椭圆恒有两个交点3
,,
NMOM,ON，，且,
2222,,,,,,,,1cossinsincos,,,,,，， 又因 22,,,,8484rr,,,,12
512244,sin,cos,，，，sin,，cos, 6432
1122sincos,,,， 6432
1122sin2,,，0,sin2,,1，且,. 12832
119，，,,所以, 22,,32256rr，，12
16,rr,42所以. 123
11S,rr,MN,rrr,MN,r又因为，即,所以 ,MON121222
lang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif13y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tra
162. ,MN,r,MN,6,4233
4因此 . 6,MN,233
4，，故此的取值范围为 . MN6,23,,3，，
评注:此例是一道以椭圆几何性质为素材的解析几何试题，旨在考查学生分析问题的能力.
总之，近几年的高考试题中，以“数列”、“函数”、“圆锥曲线”为主要知识的压轴题是高考数学压轴题的热点题型，主要考查学生等价转化能力、数形结合能力、分析问题和解决问题的能力、推理和运算能力、较强的思辩能力、信息迁移能力、创新意识和创新能力等,同时还具有较强的区分度，有利于高校选拔优秀人才. 4 高考数学压轴题的背景分析
数学教育家李彝先生认为数学教育要“上通数学”.通过对近几年来全国和部分省市数学高考题中若干典型试题的探研发现从表面上看压轴题与其它解答题没什么异同，解题的方法也是初等，但对其深入剖析可知有些试题本身就是一道高等数学题，有些是现代数学家们正在研究的一些前沿问题的一个特例;有些是某个现代数学概念以一种学生能够接受的方式给出的，之后以此作为出发点通过逻辑推理得出一些“好”的结论.也即很多数学高考压轴题有着深刻的高等数学(甚至现代数学)背景，充分体现了中学数学“上通数学”.
例4(2005年全国高考数学全国卷理22题):
，，，，，，，，，，gx,xlogx，1,xlog1,x0,x,1gx(?)设函数,求的最小值; 22
pp，p，p，？，p,1ppp？(?)设正数，，，，满足，证明: nn12331222
ppppppnlogloglog，，，,,？ nn121222222
对第(?)小题作进一步分析:
ppppppnlogloglog，，，,,？要证,只需证 nn121222222
k2pnppp,n122i, logloglogloglog2ppppn，，，,,,,？n,i21222222,i1
or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the14rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle,
kn21,,pi即 , ，，3p,,,,i2,,,1i
上式的左边为一乘积且不等号是“”，自然会想到均值不等式 ,
22ab , ab,,11ab，，ab
，，a,b3此式的左边为正数的几何平均数，右边是调和平均数，为了弄清它和式的关系，
11122把此式变形为:ab,. 1111，22ab
再将上式推广，得到:
1，，mnmn，,1若且， 则 4. mnR,,abR,,ab,，，mn，ab
a,b4式表示的仍是的几何平均数和调和平均数之间的关系，只是这里的平均数是加权，，
n4平均数，再把式推广到个正数的均值不等式. ，，
，，m，m，？，m,1命题:设，，且 ，则 aaaR,,,？,mmmR,,,？,12n12n12n
1mmmn125aaa？, . ，，12nmmm12n，，，？aaa12n
5由式容易得到 ，，
kn2p111,,npppi122pppp？,,,,,,,. n,i12,,n2pnpp22,,,i1122？，，，pppn122
n所以，，3成立，因而原命题成立.综上所述，可知，此题是一道个正数的加权平均数问
5题，其背景是均值不等式.掌握了这一点，便可更一般地考察这个问题，如原题中对，，
数的底数是2，但可以改为3，因此下面一命题成立.
nn33
pppp,,,,？命题:设正数满足则. p,1ppnlog,,n123,,iii33,,i1i1
从此例可看到，尽管其内容设计来源于高等数学，但解决的方法最终还是中学所学的内容,同时也能考查学生的数学素养和数学潜能，因此这类试题常常会被选作为考题.
n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif15y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member
高考数学压轴题中具有现代数学知识背景的题是时常出现的，若能对这类试题进行深入挖掘、认真思考，对其背景进行细致的探析，这对高考复习将会提供极大的帮助. 5 高考数学压轴题的设问方式探究
高考数学压轴题通常以“分步设问，分散难点，渐次递进”的方式设多个问题，若从几个设问之间的层次关系角度来分类，可分为“递进式”设问方式;“并列式” 设问方式;“类比式” 设问方式.
(1)、“递进式”设问方式.
“递进式”设问方式是指题目中有两个或两个以上的小问题，并且问题的内容是依次深入，其难度逐渐增加，前一问与后一问之间彼此相关联层层递进的一种设问方式.对于采取递进式设问方式设置的问题，因为前一问通常是后一问的铺垫，所以后一问也通常需要应用前一问得出的正确结论进行解答,即借步作答.近几年高考解析压轴题通常采用这种设问方式，特别涉及数列不等式的压轴题一般采用这种设问方式.
(2)、“并列式” 设问方式.
“并列式” 设问方式是指题目中设置的每个小问题的解答彼此独立，相互并列且互不包含，各不影响，前一问做对与否对后一问的正确作答没有任何影响的一种设问方.近几年高考压轴题中，只有是对数学对象进行某方面深挖掘的特难问题，高考命题式
专家才将其分解为几个难度稍低的问题.
(3)、“类比式” 设问方式.
“类比式” 设问方式是指问题中明确了某个数学对象的某一属性，且还需明确同类事物中另一对象是否也具有相同或相似的属性的设问方式(此类问题常常根据两个对象各自之间的属性所可能具有的相同或相似的因果关系来以一事物的正确与否去证明另一事物的正确与否.这类问题的原型一般是考生很熟悉的性质和结论.但经过类比得到新情景则是考生不太熟悉的解答，此类问题关键在于认真读题和分析题目中原情景的关系特征，之后在新情景中进行合理的类比或是关系借鉴，探析出类似的结论再进行验证.而据统计，此类问题在高考数学压轴题中较少见.
总之，数学压轴题一般都要求考生具有能从多个角度，多个方面去探索，去发现，去创新的能力，若知其高考压轴题的设问方式及应答策略，则可以从一个全新的角度去思考高考压轴题，间接地找到更多的解题灵感，解除思维困境，减少时间失分，增强其思维方向的信心.
ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the16rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. 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Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. 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6 解答高考数学压轴题的策略探究
高考数学压轴题每年都有所创新，具有较高的能力要求和良好的区分度.高考数学压轴题本身及解答过程都涉及很多个知识点和多种数学思想方法，同时在突出“三基”考查时，增大了思考量和计算量，能较好的考查考生的思维品质，创新能力和学习潜能，及由感性思维到理性思维的飞跃，使高考与素质教育形成良性互动，怎样才能顺利解答高考数学压轴题呢,以下从几个方面探究顺利解答高考数学压轴题的策略. 6.1过好心理素质关
由于高考数学压轴题具有较强的综合性，创新性，较高的区分度，使得很多平时学习成绩一般的学生在未高考之前就打算将压轴题放弃， 一些平时中上成绩的学生会对其产生恐惧感，在解压轴题时 ，发现自己或教师总结出来的套路都用不上.高考是一种选拔性考试，其压轴题的命题材料、方式都有所不同，但其目的主要是培养学生用数学的方法，思维方式去处理其它问题.
其次，在平常的测试中就有不少学生根本没有时间做这题，即使有时间也会看一眼就害怕，尝试着做一下之后也很少能做出，久而久之，将会在心理产生一种想法，这种题不是出给我做的，是为高智商的人所设置的.由此可见，高考压轴题入口宽，深入难.一般而言第一问不会很难.其实3到5分是很容易得到的，只要能调整好心理状态，沉着冷静地逐步深入，就可能柳暗花明.
最后，有些教师的不正确舆论导向，过高的评价高考数学压轴题的难度，有时甚至告诉学生高考时放弃压轴题的解答，至此也使很多学生产生不良的心理反应.良好的心理状态能增强解决问题的自信心，会有一种积极主动的探索思想，至之过程.然而若总是受情感的支配，不试一试，做一做，遇到难题就退缩，长久以后，将难以克服由于某种干扰作用的心向而引起的负迁移作用.
因此，解答高考数学压轴题时一定要心平气和，不要急于求成，考场上要学会调整自己的心理平衡，增强自我的思维自信心，充满自信的审视压轴题，激发灵感，寻找问题的突破口.
6.2 牢固掌握数学基础知识
高考数学压轴题以数学知识为根本，从问题入手，把握数学学科的整体意义.用统一的观点组织材料，主要体现对知识的理解和综合知识的灵活应用，据此来考查考生把知识迁移到不同情境中的能力，进一步考查考生理性思维的广度和深度及后续的学习潜
n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif17y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member
能，然而能力是建立在扎实的基础知识之上的，高考说明指出，高中数学的基础知识包括数学概念、法则、定理、定律、公式及其隐含的数学思想方法.由此可知，只有牢固地掌握数学基础知识，才有可能顺利解答高考数学压轴题.
2例5(2008山东，理卷第22题):设抛物线方程为，为直线Fy,,2p，，x,2pyp,0
上任意一点，过引抛物线的切线，切点分别为. Fa,b
(?)求证:三点的横坐标成等差数列. a,b,F
(?)已知:当点的坐标为时，，求此时抛物线的方程. Fab,410，，2,,2p
2cabd(?)是否存在点F，使得点关于直线的对称点在抛物线上，，，x,2pyp,0
,,,co其中，点满足(为坐标原点)，若存在，求出所有适合题意的点F的坐oc,oa，ob
标，若不存在，请说明理由.
此题是解析几何与数列、向量的综合，主要考查考生的分析问题以及解析几何的运算能力，抽象逻辑思维能力，该题的关键是点设法及弦长公式等数学常识和迁移相关知识的能力.主要涉及到抛物线方程及其导数、切线、向量、轴对称、等差数列等基础知识和数形结合、整体处理问题的思想及解决探索性问题的常用方法.该题的背景知识较丰富，解答时需具备较强的运算求解能力，分析问题、语言转换的能力，挖掘问题内部所隐含的知识等能力，由此可知若没有扎实的基础知识，将会寸步难行. 6.3 形成系统的数学知识结构
高考数学压轴题是高中数学知识的交汇点，以及多方面的数学知识或分支和多种思想方法融合各类知识形成一个有机的整体. 高考数学压轴题的解题方法比较复杂或呈交叉状，解题途径呈连环状,同时，考试说明也指出要从学科的整体高度和思维价值的高度思考问题，在知识网络交汇处设计试题，使对数学基础知识的考查达到一定的深度，考查时从学科整体意义和思想价值立意.因此，解答高考数学压轴题须具有良好的数学知识结构.数学知识结构是学生个体头脑里的数学知识按照个人的理解层次、水平结合自己的感知觉，思维记忆、联想类比迁移、推广等组成具有内部规律的整体结构.学生头脑里获得的数学知识结构其实就是数学认知结构，它是数学知识结构与学生心理结构相互作用的产物，体现了学生在头脑里对知识内容的接收、编码、储存、提取等一系列活动的组织方式.
6.4 加强能力培养
高考数学压轴题强调以“能力立意”，其能力指运算求解能力、数据处理能力、推
opinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the18rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, s
理论证能力、想象能力、抽象概括能力及应用和创新能力，而应用和创新能力却是理性思维的高层次体现.在数学的学习和研究过程中对知识的组合、融合、迁移程度越高，体现能力的范围就越广，其创新意识也越强.高考数学压轴题就是考查学生数学能力，数学素养，多种能力协调共进，相互为用的一个好平台.
xpxp,,12例6(2008年江苏，理卷第20题):已知函数，，，，，，gx,3gx,2,312
.函数定义为:对每个给定的实数,若则，，，，，，，，x,R,p,p为常数gxxgx,gx1212
;若则. ，，，，，，，，，，，，gx,gxgx,gxgx,gx1122
(1)求对所有实数成立的充分必要条件(用表示); ，，，，gx,gxxp,p112
a,b(2)设是两个实数，满足,且，若,求证:函数，，，，，，，，p,p,a,bga,gbgxa,b12
b,a在区间 上的单调增区间的长度之和为(在闭区间的长度定义为). ,,,,a,bm,nn,m2
本题情景独特,寓创新意识，富有时代气息.主要考查了充要条件的探求，含绝对值函数，指数函数，不等式的综合应用，充分展现了在知识交汇处设置试题的命题特点.同时涉及到函数和方程的数学思想，分类讨论、数形结合、化归等数学思想充分突现出数学阅读理解能力，函数、不等式简易逻辑综合应用的逻辑推理能力等. 6.5 加强解题策略训练
解题需讲究一定的策略，因为它可以增强效果，提高效率，同时也是一种做题机智，其具体操作如下:在读题解答思索中，应抓住“三性”，“三化”，“三转”，“三思”.
“三性”即(1)目的性:明确解题的最终目标和每一步所要求的目标.(2)准确性:增强概念，运算的准确性.(3)隐含性:认真审题挖掘出题目中所隐含的相关知识，进一步找到解题灵感及合理的解题方向.
“三化”即(1)问题具体化:把题中所涉及的各种概念，数学知识之间的关系更具体明了.有必要时数形结合画出表格或图形，这样便于将一般原理，一般规律应用到具体的解题过程中去.(2)问题简单化:任何一道数学难题剖析开来都是由基础题再加深一层组成的，所以将综合问题分解为与各相关知识相联的简单问题，更易得出解题的“路标”.(3)问题和谐化:注意转换问题的条件或结论，使其表现形式符合数或形内部固有的和谐统一的特点.
“三转”即(1)概念转换能力:高考数学压轴题的转译通常都需要很强的数学概念的转化能力.(2)语言转换能力:压轴题一般都是由通用的文字语言，符号语言、图
erity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif19y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatio
形语言所构成.解答压轴题需具有较强的语言转换能力，有时也需将普通语言转换成数学语言.(3)数形转换能力:其解题中的数形结合是指即分析题目的条件和结论的代数含义又分析其几何意义，试图在代数与几何的结合中能找出解题思路.但若应用数形结合时不注意其特殊性，则容易漏解.
“三思”即(1)思路:因为压轴题一般都是综合多种知识，多种解题方法，以解答一种方法行不通就赶快尝试另外的解题思路.(2)思想:因高考压轴题的命置一般会充分体现考查其数学思想方法，所以解答时应着重注意使用数学思想方法.(3)思辩:即解题应注意思路、方法的选择.
6.6加强学生思维独创性的培养
平时注意培养学生思维的独创性可间接的提高高考数学压轴题的得分率.其独创性是指独树一帜从一般人都想不到的角度去思索问题，能大胆质疑创新，善于深思、反思问题，经过应用题教学一题多问，一题多解，一题多变，再经过合理的练习进一步培养学生解压轴题的能力.其“一题多问”即培养学生对同一问题从不同的方面提出问题让学生自己思考解答.其“一题多解”即培养学生对同一问题从不同的方向进行思索，分析提出多种异样解法.通过这种训练可以拓宽学生的解题思路,锻炼思维的灵活性，融会贯通知识间的内在联系.其“一题多变”即培养学生对同一道应用题，用多种不同方法叙述，但其本质不变，所反映的深浅程度也不同，如可隐蔽一些条件或条件结论互换，使学生能够在练习中发现问题，在实践中创造性地解决问题.
下面来看一个“一题多解”的例子.
,,例7(2007年高考重庆卷):已知各项均为正数的数列b的前项和S满足,nS,1nn1
,且， ，，，，6S,b，1b，2,n,Nnnn
,,b(?)求通项公式. n
an,,,,aFa(?)设数列，，满足并记为的前n项和，求证:b2,1,1nnnn
,，，. 3F，1,logb，3,n,Nn2n
此题的第(?)问可如下证明.
证法1:利用函数性质证明.
,,13nan,,a,log1，,log，，b2,1,1由题设中可得, 于是有 n22n,,b3n,1n,,
or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the20rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle,
n363,,, Faaaa,，，，？，,log,,？,,,n123n2n253,1,,
3363n2,,又, 3F，1,logb，3,log,,,,，，？,,nn22253n,13n，2,,
3363n2,,令.则有 gn,,,？,,，，,,253n,13n，2,,
33，，，，gn，13n，23n，33n，3,,. ,,,,,2，，gn3n，53n，2，，，，3n，53n，2,,
32又因为. ，，，，，，，，，，3n，3,3n，53n，2,9n，7,0,所以gn，1,gn
27，，，，又因为gn,g1,,1，于是. ，，，，3F，1,logb，3,loggn,0n2n220
即，亦即命题得证. ，，3F，1,logb，3n2n
评注:应用函数性质证明数列不等式一般都要先结合结论构造函数，再利用其单调性、奇偶性、周期性等性质来证明.其中函数的单调性应用较多还常常用到导数法，比较法等来判断其单调性.
证法2:利用放缩法证明.
3c,0由二项式定理知，当时，不等式成立， ，，1，c,1，3c
333111,,,,,,故 3F，1,log21，1，1，？,,,,,,n2253n,1,,,,,,
333,,,,,, ？,log21，1，1，,,,,,,2n253,1,,,,,,
583n，2,log2,,,？, 2253n,1
，，,log3n，2 2
，，,logb，3 2n
证毕.
评注:放缩法是证明不等式中一种常用的很重要的方法，而且若在证明过程中适当放缩可事半功倍.但必须要牢牢抓注放缩的结论，并充分用数列通项本身的条件，经不断尝试便可得解.
证法3: 用数学归纳法证明.
t, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif21y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promo
27n,1? 当时, 31log,，于是显然成F，,，，，，logb，3,log53F，1,logb，3122121214
立.
,? 假设当时结论成立,有 ，，3F，1,logb，3n,k,，，k,Nk2k
n,k，1下证当时,
，，3F，1,logb，3k，12k，1
，，,3F，1，3a,logb，3kk，12k，1
，，，，,logb，3,logb，3，3a2k2k，1k，1
33k，3，，, ,log22，，，，3k，53k，2
32而 ，，，，，，3k，3,3k，53k，2,9k，7,0.
33k，3，，所以,于是 . ，，3F，1,logb，3log,0k，12k，122，，，，3k，53k，2
,n,k，1即当n,N时，结论成立.所以对于一切结论都成立.
评注:利用数学归纳法证明与自然数密切相关的数列问题是一种基本方法，但需注意在证明过程中要充分利用假设，因为构造和利用假设一般是关键.
6.7强化练习
平时应系统地有针对性地去研究最近几年的本省的高考题，同时结合考试说明及每年的试卷评析，进而搞清命题趋势、意图.其次再选择做一些著名中学的模拟试卷，但一定要定量、定期、定时的做，做完之后自己认真批改，并深入思考、总结、反思写心得体会及从解题中找到的规律，经过大量练习、反思总结，高考中解答压轴题时才可能得心应手.
总之，如果学生在平时的学习过程中能有意识地进行上述七个方面的训练，将更有助于高考数学压轴题的解答.
7 高考数学压轴题回顾与展望
纵观近几年的高考数学压轴题，有的题目出得独具匠心，构思巧妙，令人赏心悦目,但其综合性、探索性、难度、区分度都很强.为了帮助学生在做压轴题时能更上一层台阶，下面对2009年高考数学压轴题作一个简要的回顾，对2010年高考数学压轴题作以预测.
ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work step method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the22rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo
(1)、考题统计.
据对2009年高考数学的19套理科试卷中压轴题的统计不难得出:压轴题的平均分值为13分.代数型压轴题共26题，其中涉及函数知识的共有10题，涉及数列知识的共有11题，涉及不等式知识的共有2题，涉及导数知识的有1题，涉及高等数学知识的选答题有2题，几何型压轴题共12题主要是以直线和圆锥曲线来命题.从压轴题设问的数量上看，设计2问的共有25题，设计3问的共有13题.从压轴题设问的方式上看，设问为递进方式的共有19题，设问为并列方式的共有12题，设问为类比方式的共有5题，其它设问方式的共有2题.
(2)、考题预测.
分析2009年高考数学压轴题的命题方向及高考大纲，看出2010年高考数学压轴题的一般命题趋势.由于数学学科的主干知识能突现其整体高度和思维价值，而且综合性较强，其次一些重要的数学思想是对是数学知识在更高层次上的抽象和概括,同时也是反映考生对数学思想方法的掌握程度.因此主干知识、数学思想方法仍是考查的重点，探索性，灵活性，新颖别致仍是考查点，近年来压轴题多以综合问题等出现,因为它能较好地考查考生的思维品质，创新能力和学习潜能.
(3)、一点建议.
每年的高考数学压轴题虽然都会有创新，但是都有一定的来源，建议多关注学术性论文研究成果.据了解，曾有高考题来自于论文研究成果，但同时也要熟悉高等数学背景，其次是应重视归纳课本上的思想方法的基础上“拔高“课本使课本上的思想方法得到”升华“,最后教师要注意每位学生综合能力的考察是否具备认知问题的公平性,这样可避免一些学生考试时一些不必要的心理问题.
8结论
8.1主要发现
高考数学压轴题是富有时代气息的试题，使高考与素质教育形成良性互动，解答高考数学压轴题不仅需要扎实的基础知识，灵活应用知识的能力，熟练掌握解题的通性通法和基本的数学思想方法，还需具有创新性以及去探究、总结往年命题者设置的高考数学压轴题的一般规律，进而预测下一年命题者的命题动向和趋势.因此要想顺利解答高考数学压轴题，必须要紧扣“双基”，对其通性通法和基本的数学思想方法及相关的策略、技巧在做题中要加以灵活应用，从而熟练掌握，其次在学中领悟、探索，在领悟中
cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif23y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image
反思、回味、归纳，进而掌握并会灵活应用，最终在考场中发挥自如. 8.2启示
近几年“高等数学”与“初等数学”的联系越来越紧密，更多高等数学的基本思想、基本方法和基本问题渗入到高考数学压轴题中，要想真正破解压轴题还需熟悉相关的高等数学知识.
8.3局限性
限本人的能力水平有限，本毕业论文仅对与高考数学压轴题相关的几个方面作了简单浅析，不能提供更深入、更透彻的破解压轴题的相关知识，这是本毕业论文的不足. 8.4努力方向
相信除了文中的几点较浅薄的知识外，还有很多更深更广博更有价值的好知识，好的思想方法.在以后的学习、研究中将继续深入探究，探索出更多解答高考数学压轴题的思想和内在规律，为学习者提供一定的帮助，以弥补本毕业论文之不足.
tep method, in accordance with the "" look in the mirror, dress up, wash bath, cure treatment, the general requirements of "fts, sopinions and advice > < < >, < party implementing the guiding ideology of opinions to determine the objectives and requiremen the spirit of general secretary Xi Jinping book series of important speech, earnestly implement the Central Committee really,ment f eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as the guidance, conscientiously implethe following implementation opinions.First, the overall requirementsCounty county education practice to the eighteen Party o roots party organizations. According to my actual County, the county to carry out the education practice put forward-ions and grassctice activities from 20** in January to 99 months, carried out at all levels of departments and directly affiliated institutl pramass line educational practice activity in the city's implementation opinions, the spirit of the party's mass line educationacentral and provincial, municipal unified deployment, according to municipal Party committee "about carrying out the party's Opinions and suggestions on the party's mass line educational practiceAccording to the24rprise and industry group mission to promote leapfrog development., entetrial development, financial investment policy, financial policy and tax policy, and actively seek policy, projects and fundsbout social support the development of cultural undertakings in the country and the XX policy, especially the policy of indusarch ahance core competitiveness, adapt to the need of market competition.(six) seriously study the policy for policy. Serious resed work, and promote the entire workforce knowledge structure, age structure, structure optimization and upgrading ability, enquality professional management team, har-quality management management personnel, and strive to build a high-introduction of high ove management and operation of the market. At the same time, according to the need of industrial development, vigorously theimpr e sense of crisis to adapt to market competition, the sense of urgency, improve the ability to respond to market competition,education and training of cadres and workers of the existing business, firmly establish the concept of the market, enhance th owned assets.(five) to strengthen the construction management personnel. Strengthen the management of-sure that the value of stateeconomic activities, attract injection the social investment to the industry group, to achieve leveraging the development, en , examination and approval procedures, strict regulation ofwin principle, in the framework of national policies and regulations, strict inspection and argumentation, legal consultation-tries and regional resources, mutual trust, mutual benefit, seeking winindusresources. To further broaden their horizons, effective integration of resources within the group, the city resources, other f alienation and characteristics, the pursuit of stability and development of the market.(four) to promote the integration oftion oof the brand, the implementation of key breakthroughs, to enhance the competitive strength, walking business road the competiength. Concentrated manpower, careful planning, packaging and publicity of a number of unique, market influence and coverage ve stro establish brand awareness, awareness of the use of brand, brand value, brand acquisition performance, enhance the competitiitions to develop the correct road, the maximum to avoid investment risk, gain profit.(three) vigorously promote the brand. Tn condo, not the problem of law. The township, street The collar of leading bodies and leading cadres to solve key does nottheir owsolve the door hard, ugly face, something difficult, and arbitrary charges, fines, levies, and breach of privilege, chinakayaainly ervice is not active. The dynamic problem of law enforcement and supervision departments and window units, service industry mcounty. The units directly under the heavy focus on solving Yung lazy drag, buck passing skin, work is not implemented, the ssures roject", "political project", a leadership guide, a set of ideas, orders and prohibitions, and a policy, there are countermeahe county leadership and leading cadres of key performance concept is not correct, do not dare to play, to engage in "image pnts, teal let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesThe central and provincial requireme, without any discount to solve, to improve the style of real implementation of the requirements of real to the grassroots, rctiveespecially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privileges and other issues, timely and effe rd the interests of the masses, pay attention to solve practical problems, solve the people around the unwholesome tendenciesafeguahavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respond to the concerns of the masses, sing problems asked County, township leadership and leading cadres of the four winds, the disadvantages of the style, scale betstandf the taskThe main task of the county's education practice is to seize against "four wind" this focus on centralized solve ouon practice, ensure education practice is not empty is not empty is not partial, not as a mere formality.Two, the key point oervisiidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requirements on injection, really suphe problem, pay more attention to open the door, the participation of the masses, pay more attention to the classification guolve tragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, more focus on the four winds, sseriously as a basic attitude, adhere to positive education, to carry out criticism and self criticism group, adhere to the pspeak e majority of Party members, cadres and the mass line line Marx doctrine view of the masses and the party's education.Always reets and villages, community education activities and the masses of grassroots groups in close contact to strengthen, and thns, stof law supervision departments and window units, service industry, educational practice, pay attention to grasp the heavy towcounty leadership, leadership and leading cadres to focus on outstanding catch to directly contact the service of the masses with step by step.To adhere to the roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-public economic organizations, social organizations and other grass-nd community, village, nonet, anly: the county and below county departments under the organs, enterprises and institutions directly under the township, strecounty and the ecological culture of the county and county construction.In educational practice activities of the unit is mai f thefurther reinforce the basic level. Style of the building of the new results to promote the construction of a powerful force o e the style of the wind, the masses to close, honest and pragmatic people honest image to further establish the foundation tochang es of people strong, the Ministry of Party members and cadres to further improve their thinking and understanding, to furthersm, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party members and cadres of the style and the massrmaliwork style of close ties with the masses law, highlight style building, carry out the whole wind spirit, resolutely oppose fo ion "provincial regulations, municipal provisions of the" twelve "plan and the implementation measures for < on improving thee sectrther implement the central eight regulations and < The opposition party and government austerity waste regulations "," doublservice to the masses of the people, the foundation of consolidating grassroots, promote transformation across efforts, to futyle, or the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuanglang Zhuang, improve their work s
参考文献
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n measures for < on improving the work style of close ties with the masses law, highlight style building, carry out the wholentatioerity waste regulations "," double section "provincial regulations, municipal provisions of the" twelve "plan and the implemensformation across efforts, to further implement the central eight regulations and < The opposition party and government austte tralang Zhuang, improve their work style, service to the masses of the people, the foundation of consolidating grassroots, promot, the general requirements of "for the people pragmatic honest people as the theme, in carrying forward the spirit of Zhuangeatmenmine the objectives and requirements, step method, in accordance with the "" look in the mirror, dress up, wash bath, cure trent the Central Committee really, opinions and advice > < < >, < party implementing the guiding ideology of opinions to deterimplemhe guidance, conscientiously implement the spirit of general secretary Xi Jinping book series of important speech, earnestly n practice to the eighteen Party of eight, the spirit of the the third Plenary Session of the 18th CPC Central Committee as towing implementation opinions.First, the overall requirementsCounty county educatioroots party organizations. According to my actual County, the county to carry out the education practice put forward the foll-and directly affiliated institutions and grass tmentsf the party's mass line educational practice activities from 20** in January to 99 months, carried out at all levels of depare "about carrying out the party's mass line educational practice activity in the city's implementation opinions, the spirit oied deployment, according to municipal Party committeOpinions and suggestions on the party's mass line educational practiceAccording to the central and provincial, municipal unif25y seek policy, projects and funds, enterprise and industry group mission to promote leapfrog development.y, especially the policy of industrial development, financial investment policy, financial policy and tax policy, and activelpolic e policy for policy. Serious research about social support the development of cultural undertakings in the country and the XXization and upgrading ability, enhance core competitiveness, adapt to the need of market competition.(six) seriously study thre optimquality professional management team, hard work, and promote the entire workforce knowledge structure, age structure, structu-quality management management personnel, and strive to build a high-trial development, vigorously the introduction of highindusto respond to market competition, improve management and operation of the market. At the same time, according to the need of concept of the market, enhance the sense of crisis to adapt to market competition, the sense of urgency, improve the ability of cadres and workers of the existing business, firmly establish theowned assets.(five) to strengthen the construction management personnel. Strengthen the management of education and training -eve leveraging the development, ensure that the value of stateo achiproval procedures, strict regulation of economic activities, attract injection the social investment to the industry group, te framework of national policies and regulations, strict inspection and argumentation, legal consultation, examination and apwin principle, in th-group, the city resources, other industries and regional resources, mutual trust, mutual benefit, seeking win ur) to promote the integration of resources. To further broaden their horizons, effective integration of resources within theet.(fowalking business road the competition of alienation and characteristics, the pursuit of stability and development of the marke, market influence and coverage of the brand, the implementation of key breakthroughs, to enhance the competitive strength, uniqu erformance, enhance the competitive strength. Concentrated manpower, careful planning, packaging and publicity of a number of) vigorously promote the brand. To establish brand awareness, awareness of the use of brand, brand value, brand acquisition p(threeres to solve key does nottheir own conditions to develop the correct road, the maximum to avoid investment risk, gain profit.nd breach of privilege, chinakayao, not the problem of law. The township, street The collar of leading bodies and leading cades, awindow units, service industry mainly solve the door hard, ugly face, something difficult, and arbitrary charges, fines, levi n, work is not implemented, the service is not active. The dynamic problem of law enforcement and supervision departments andng skind a policy, there are countermeasures county. The units directly under the heavy focus on solving Yung lazy drag, buck passire to play, to engage in "image project", "political project", a leadership guide, a set of ideas, orders and prohibitions, aot dacentral and provincial requirements, the county leadership and leading cadres of key performance concept is not correct, do n ents of real to the grassroots, real let group Benefit the public.(a) focus on solving the "four winds" outstanding issuesTheuiremand other issues, timely and effective, without any discount to solve, to improve the style of real implementation of the req around the unwholesome tendencies especially on eat, take the card, Yong lazy luxury, extravagance and waste fees, privilegesople to the concerns of the masses, safeguard the interests of the masses, pay attention to solve practical problems, solve the pe advantages of the style, scale behavior to a large scale investigation, overhaul, cleaning greatly. At the same time, respondhe dishis focus on centralized solve outstanding problems asked County, township leadership and leading cadres of the four winds, tre formality.Two, the key point of the taskThe main task of the county's education practice is to seize against "four wind" ts a meirements on injection, really supervision practice, ensure education practice is not empty is not empty is not partial, not attention to the classification guidance. Orderly, pay more attention to the cooperation and cohesion driven, more strict requre amore focus on the four winds, solve the problem, pay more attention to open the door, the participation of the masses, pay mo criticism group, adhere to the pragmatic, more emphasis on leadership, pay more attention to the layers of the demonstration, d selfand the party's education.Always speak seriously as a basic attitude, adhere to positive education, to carry out criticism anose contact to strengthen, and the majority of Party members, cadres and the mass line line Marx doctrine view of the masses in clattention to grasp the heavy towns, streets and villages, community education activities and the masses of grassroots groups ontact the service of the masses of law supervision departments and window units, service industry, educational practice, payc with step by step.To adhere to the county leadership, leadership and leading cadres to focus on outstanding catch to directly roots organizations. Agencies and branches, each single unit, follow the rules on internal institutions. Educational practice-sspublic economic organizations, social organizations and other gra-directly under the township, street, and community, village, non tice activities of the unit is mainly: the county and below county departments under the organs, enterprises and institutionsl pracconstruction of a powerful force of the county and the ecological culture of the county and county construction.In educationarther establish the foundation to further reinforce the basic level. Style of the building of the new results to promote the to fung and understanding, to further change the style of the wind, the masses to close, honest and pragmatic people honest image cadres of the style and the masses of people strong, the Ministry of Party members and cadres to further improve their thinki s andwind spirit, resolutely oppose formalism, bureaucracy, hedonism and wasteful extravagance to solve the problems, Party member
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