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家教孔老师的文章专栏
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发表于:2013-09-13阅读:27次
目录第一章  集合··························l第l节  集合与集合的运算·················1知识点精讲···························1基本题型及思路要点·······················2题型1  集合的基本概念·····················2题型2  集合间的基本关系··················4题型3  集合的运算·······················8题型4 集合的创新型问题··················12题型5 错题型纠正······················· 17第二章  函数··························21第1节  映射与函数的概念··················21知识点精讲···························21基本题型及思路要点·······················21题型1  映射与函数的概念··················21题型2  判断函数的等价性··················24题型3  函数解析式··················25第2节  函数的定义域、值域问题(最值)······························32知识点精讲···························32基本题型及思路要点·······················32题型4  函数定义域的求法··················32题型5  函数值域的求法····················34第3节  函数的性质·······················43知识点精讲···························43基本题型及思路要点·······················43题型6  函数奇偶性··················44题型7  函数单调性··················48题型8  函数周期性··················55题型9  函数性质的综合应用················59第4节  二次函数························62知识点精讲···························62基本题型及思路要点·······················62题型10  三个二次之间的关系······························64题型11  一元二次方程的实根分布及条件······························· 68题型12  二次函数“定轴动区间”与“动轴定区间”问题······················70第5节  反函数·························72知识点精讲···························72基本题型及思路要点·······················73题型13  求反函数························73题型14  互为反函数的两函数的性质·········75题型15  原函数与反函数图象的关系········76第6节  指数与指数函数····················77知识点精讲···························78基本题型及思路要点·······················78题型16  指数运算及指数方程、指数不等式····78题型17  指数函数的图象及性质·············84题型18  指数函数中恒成立的问题···········89第7节  对数与对数函数···················90知识点精讲··························· 91基本题型及思路要点······· ···············92题型19  对数运算及对数方程、对数不等式····92题型20  对数函数的图象及性质············98题型21  对数函数中恒成立的问题··········103第8节  幂函数·························104知识点精讲···························104基本题型及思路要点·····················105题型22  求幂函数的定义域···············105题型23  幂值的大小比较··················106题型24  幂函数性质的综合应用············108题型25  对勾函数······················112题型26  分段函数与抽象函数·············112第9节  函数的图象·······················125知识点精讲···························125基本题型及思路要点··················126题型27  判断函数的图象·················126题型28  函数图象的应用·················128第10节  函数与方程······················132知识点精讲··························· 132基本题型及思路要点······················133题型29  求函数的零点····················133题型30  方程根的个数与函数零点的存在性问题··························137题型31  用二分法求方程的近似解·········138第11节  函数模型及其应用··········139知识点精讲··························· 139基本题型及思路要点···············140题型32  函数在解决实际问题中的应用······140题型33  实际问题中的图形信息题与表格信息问题·····························146第12节  函数的综合··················149题型34  函数中恒成立问题··········152题型35  函数中的信息题··············159第三章  三角函数························190第l节  任意角的概念与弧度制·············190知识点精讲···························190基本题型及思路要点··················190题型1  角的概念的扩充···············190题型2  一个角的半角在第几象限··········192题型3  弧长与扇形面积公式··············194第2节  任意角的三角函数···············195知识点精讲····· ······················196基本题型及思路要点·· ···············197题型4  三角函数线·················199题型5  三角函数值符号的确定·······202第3节  公式·························· 203知识点精讲····· ··········· ·········· 203基本题型及思路要点··················207题型6  诱导公式与化简求值············· 207题型7  倍(半)角、辅助角公式··········210题型8  角、函化一·················216第4节  三角函数的图象与性质 ············218知识点精讲··························· 218基本题型及思路要点············· 220题型9  已知三角函数值求角···········220题型10  求角的范围············222题型11  三角函数的最值···············228题型12  图像的伸缩与平移············ 232题型13  单调性、周期性与对称性···········241第5节  解三角形························253知识点精讲··············· ····· ······253基本题型及思路要点···· ·············253题型14  解三角形 ·······················253题型15  判断三角形形状 ·················262题型16  解三角形··············265题型17  错题型纠正··················268第四章  平面向量·········· ···········276第1节  平面向理的基本概念及线性运算·····276知识点精讲 ·························· 276基本题型及思路要点··········· ···· ···  277题型1  向里的基本概念 ················277题型2  向量的线性运算··· ···············278题型3  向量的基本定理的应用·············282题型4  共线向量定理的应用···············285题型5  向量与三角形的四心···············285题型6  利用向量法解平面几何问题·········290第2节  向量的坐标运算和数量积···········292知识点精讲···························292基本题型及思路要点 ·········· ·········294题型7  向量的坐标运算···················294题型8  向量共线的坐标表示···············296题型9  平面向量的数量积·················297题型10  向量在物理方面的应用···········299题型11  平面向量与不等式·············300第五章  数列··························327第1节  等差数列与等比数列···············327知识点精讲···························327基本题型及思路要点·········· ··········330题型1  证明数列是等差(等比)数列···················· ·········· 330题型2  等差(等比)数列的通项及五个基本量的关系····················· ····· ·· 325题型3  等差(等比)数列的求和·············338题型4  等差(等比)数列的性质·············343第2节  数列的通项公式与求和·············346知识点精讲···························346基本题型及思路要点·····················346题型5  数列的通项的求解·················346题型6  数列的求和····················361题型7  数列问题中的函数思想············405第六章  不等式·························420第1节  不等式的概念与性质··············420知识点精讲· ························· 420基本题型及思路要点··················420题型1  比较数(式)的大小·················420题型2  不等式性质的应用·················424题型3  取值范围的判定·································425第2节  均值不等式与不等式的证明·········427知识点精讲···························427基本题型及思路要点··················428题型4  利用基本不等式求函数最值·········428题型5  利用基本不等式证明不等式·········433题型6  不等式的证明····················435第3节  不等式的解法·····················444知识点精讲··· ············ ···········444基本题型及思路要点······················446题型7  有理不等式的解法·················446题型8  绝对值不等式的解法···············449题型9  超越不等式的解法·················451策4节  二元一次不等式(组)与简单的线性规划问题···························· 451知识点精讲··························  451基本题型及思路要点·····················452题型10  二元一次不等式表示平面区域······452题型11  简单的线性规划·················453题型12  线性规划的范围问题··············457题型13  简单线性规划问题的实际应用······460基本题型及思路要点······················463题型14  用构造法证不等式··············479题型15 放缩法证明不等式·············489第七章  立体几何·······················511第l节  空间几何体······················511知识点精讲· ······················· 511基本题型及思路要点······················512题型1  空间几何体的三视图·············512题型2  立体几何中的识图技巧············516第2节点、线、面的位置关系·············521知识点精讲··························521基本题型及思路要点······················522题型3  平面的基本性质与推论·············522题型4  空间中的平行关系················523题型5  空间中的垂直关系·· ··············528第3节  空间角及其空间距离的计算·······  540知识点精讲··························555基本题型及思路要点············· ···556题型6  空间角及其空间距离的计算········556题型7  空间向量及其应用················556题型8  点到平面距离的求法·············559题型9  立体几何中的翻折问题············562第八章  直线与圆的方程··················591第l节  直线方程··· ··················· 591知识点精讲··························591基本题型及思路要点······················592题型1  直线的方程· ·········· ··········592题型2  两直线的平行和垂直·································596第2节  圆的方程······················ 605知识点精讲· ···· ··················· 605基本题型及思路要点······ ···············606题型3  待定系数法求圆的方程·············606第3节 直线与圆的位置关系···············610知识点精讲········· ················610基本题型及思路要点····················· 611题型4  直线与圆的位置关系···············611题型5  圆与圆的位置关系·· ··············623第九章  圆锥曲线方程····················627第1节  椭圆························627知识点精讲·························627基本题型及思路要点·····················627题型1  椭圆的标准方程··· ··············628题型2  椭圆的几何性质·················629第2节  双曲线·······················639知识点精讲·························639基本题型及思路要点·····················640题型3  双曲线的标准方程················640题型4  双曲线的几何性质················642第3节  抛物线·······················646知识点精讲·························646基本题型及思路要点·····················647题型5  抛物线的标准方程··············647题型6  抛物线的几何性质················648第4节  轨迹问题············· ········ 650知识点精讲······ ·················· 650思路归纳及思路要点····· ··············· 650题型7  求轨迹方程······ ·········650第5节  直线与圆锥曲线的位置关系········665知识点精讲······· ················ 665基本题型及思路要点·····················665题型8  直线与圆锥曲线位置关系的判定·····665题型9  相交弦长问题····················675题型10  定值、最值、定点、定直线问题···679第十章  常用逻辑用语····················771第l节  命题及其关系、充分条件与必要条件··771知识点精讲·························771基本题型及思路要点·····················771题型1  四种命题及关系···················771题型2  充分条件、必要条件、充要条件的判断······························772第2节  简单的逻辑联结永词、全称量词与存在量词···························776知识点精讲·························776基本题型及思路要点·····················776题型3  判断命题的真假········· ······776题型4  含有一个量词的命题的否定·········778题型5  结合命题真假求参数的范围·········779第十一章  算法初步····················· 781知识点精讲························· 781基本题型及思路要点····················· 783题型1  已知流程图,计算程序结果的问题····783题型2  已知伪代码,计算程序结果·········792题型3  根据条件,填充不完整的流程图······793题型4  算法和其他问题的综合·············796第十二章  计数原理(文) ···············799题型1 分类加法计数原理················799题型2 分类乘法计数原理·················801第十二章  排列组合与二项式定理(理)······806第1节  基本原理与简单排列组合问题······806知识点精讲·························806基本题型及思路要点·····················808题型1  推导、化简和计算··················808题型2  基本原理和简单排列组合问题的结合·· ····························810第2节  排列题型一不可重复排列···········819知识点精讲 ··················· ·····819基本题型及思路要点·····················819题型3  特元特位问题·············819题型4  捆绑问题················824题型5  插空问题····················825题型6  定序问题····················827第3节  组合题型······················830知识点精讲 ········· ···············830基本题型及思路要点·····················830题型7  分选问题和选排问题·············830题型8  分组问题·················832题型9  分配问题······················ 834第4节  二项式定理·····················836知识点精讲·························836思路归纳及思路要点·····················837题型10  二项式定理中的系数与x幂指数的确定····································837题型11  项和与系数和··················· 840题型12  二项式展开式的二项式系数与系数的最值································ 844第十三章  概率与统计(文)···············848题型1 古典概型·······················848题型2 几何概型·······················850题型3 抽样方法·······················855题型4 频率分布直方图····················859题型5 直线回归方程·····················861题型6 独立性检验······················876第十三章  概率与统计(理)···············881第l节  概率························881知识点精讲·························881基本题型及思路要点·····················882题型1  等可能事件概率的计算一除法·······882题型2  互斥事件的概率一加法和减法·······886题型3  相互独立事件同时发生的概率一乘法······························889第2节  概率分布······················892知识点精讲·························892基本题型及思路要点·····················893题型4  作离散型随机变量的分布列,求E(X),D(X) ·························· 893题型5  正态分布·················· ··· 907第3节  统计························909知识点精讲························909基本题型及思路要点·····················911题型6  随机抽样类型···················911题型7  用样本估计总体···················912题型8  两个随机变量的线性相关··········914题型9  独立性检验·····················916第十四章  导数与定积分·············920第l节导数的概念与运算···················920知识点精讲··· ····················· 920基本题型及思路要点·····················921题型1  导数的定义·····················921题型2  求函数的导数····················923题型3  求曲线的切线方程···············924第2节  导数的应用·····················928知识点精讲·························928基本题型及思路要点·····················930题型4  利用原函数与导函数的关系判断图像······························930题型5  利用导数判断函数的单调性·········934题型6  函数的极值与最值的求解···········937题型7  利用导数解决不等式恒成立问题·····948题型8  利用导数证明不等式·············962题型9  利用导数探讨函数图像的交点······970第3节  定积分与微积分基本定理··········984知识点精讲·························984基本题型及思路要点·····················985题型10  用定积分求曲边梯形的面积········985题型11  求定积分······················989题型12 定积分的换元积分法与分部积分法·························· 990题型13  导数题错题型纠正···············991第十五章  推理与证明····················994第1节  合情推理与演绎推理············994知识点精讲···························· 994基本题型及思路畏示·····················994题型1  归纳推理······················ 994题型2  类比推理······················ 996题型3  演绎推理······················ 999第2节  直接证明、间接证明与数学归纳法···1000知识点精讲·························1000基本题型及思路要点····················1001题型4  不等式的证明·······························1001第十六章  数系的扩充与复数的引入·····1011知识点精讲·························1011基本题型及思路要点·····················1011题型1  复数的运算····················· 1011题型2  复数的几何意义的应用··········1014第十七章  坐标系与参数方程···········1018题型1 极坐标与直角坐标的互化··········1018题型2 利用极坐标求轨?!ぁぁぁぁぁぁぁぁぁぁぁぁ?020题型3 利用极坐标计算求值···············1021题型4 直线的参数方程···············1023题型5 圆和椭圆的参数方程··············1025题型6 参数方程求解曲线弦长············1028题型7 参数方程求最值问题···············1032题型8 极坐标方程与参数方程混合·········1034第十八章  几何证明选讲··············1039题型1 相似三角形的判定和性质定理·······1040题型2 直角三角形的射影定理·············1048题型3 圆的切线的判定和性质定理·········1050题型4 圆周角定理、弦切角定理···········1053题型5 相交弦定理、割线定理、切割线定理···1056题型6 圆内接四边形的判定与性质定理·····1058

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