目錄第一章  集合··························l第l節  集合與集合的運算·················1知識點精講···························1基本題型及思路要點·······················2題型1  集合的基本概念·····················2題型2  集合間的基本關系··················4題型3  集合的運算·······················8題型4 集合的創新型問題··················12題型5 錯題型糾正······················· 17第二章  函數··························21第1節  映射與函數的概念··················21知識點精講···························21基本題型及思路要點·······················21題型1  映射與函數的概念··················21題型2  判斷函數的等價性··················24題型3  函數解析式··················25第2節  函數的定義域、值域問題（最值）······························32知識點精講···························32基本題型及思路要點·······················32題型4  函數定義域的求法··················32題型5  函數值域的求法····················34第3節  函數的性質·······················43知識點精講···························43基本題型及思路要點·······················43題型6  函數奇偶性··················44題型7  函數單調性··················48題型8  函數周期性··················55題型9  函數性質的綜合應用················59第4節  二次函數························62知識點精講···························62基本題型及思路要點·······················62題型10  三個二次之間的關系······························64題型11  一元二次方程的實根分布及條件······························· 68題型12  二次函數“定軸動區間”與“動軸定區間”問題······················70第5節  反函數·························72知識點精講···························72基本題型及思路要點·······················73題型13  求反函數························73題型14  互為反函數的兩函數的性質·········75題型15  原函數與反函數圖象的關系········76第6節  指數與指數函數····················77知識點精講···························78基本題型及思路要點·······················78題型16  指數運算及指數方程、指數不等式····78題型17  指數函數的圖象及性質·············84題型18  指數函數中恒成立的問題···········89第7節  對數與對數函數···················90知識點精講··························· 91基本題型及思路要點······· ···············92題型19  對數運算及對數方程、對數不等式····92題型20  對數函數的圖象及性質············98題型21  對數函數中恒成立的問題··········103第8節  冪函數·························104知識點精講···························104基本題型及思路要點·····················105題型22  求冪函數的定義域···············105題型23  冪值的大小比較··················106題型24  冪函數性質的綜合應用············108題型25  對勾函數······················112題型26  分段函數與抽象函數·············112第9節  函數的圖象·······················125知識點精講···························125基本題型及思路要點··················126題型27  判斷函數的圖象·················126題型28  函數圖象的應用·················128第10節  函數與方程······················132知識點精講··························· 132基本題型及思路要點······················133題型29  求函數的零點····················133題型30  方程根的個數與函數零點的存在性問題··························137題型31  用二分法求方程的近似解·········138第11節  函數模型及其應用··········139知識點精講··························· 139基本題型及思路要點···············140題型32  函數在解決實際問題中的應用······140題型33  實際問題中的圖形信息題與表格信息問題·····························146第12節  函數的綜合··················149題型34  函數中恒成立問題··········152題型35  函數中的信息題··············159第三章  三角函數························190第l節  任意角的概念與弧度制·············190知識點精講···························190基本題型及思路要點··················190題型1  角的概念的擴充···············190題型2  一個角的半角在第幾象限··········192題型3  弧長與扇形面積公式··············194第2節  任意角的三角函數···············195知識點精講····· ······················196基本題型及思路要點·· ···············197題型4  三角函數線·················199題型5  三角函數值符號的確定·······202第3節  公式·························· 203知識點精講····· ··········· ·········· 203基本題型及思路要點··················207題型6  誘導公式與化簡求值············· 207題型7  倍(半)角、輔助角公式··········210題型8  角、函化一·················216第4節  三角函數的圖象與性質 ············218知識點精講··························· 218基本題型及思路要點············· 220題型9  已知三角函數值求角···········220題型10  求角的范圍············222題型11  三角函數的最值···············228題型12  圖像的伸縮與平移············ 232題型13  單調性、周期性與對稱性···········241第5節  解三角形························253知識點精講··············· ····· ······253基本題型及思路要點···· ·············253題型14  解三角形 ·······················253題型15  判斷三角形形狀 ·················262題型16  解三角形··············265題型17  錯題型糾正··················268第四章  平面向量·········· ···········276第1節  平面向理的基本概念及線性運算·····276知識點精講 ·························· 276基本題型及思路要點··········· ···· ···  277題型1  向里的基本概念 ················277題型2  向量的線性運算··· ···············278題型3  向量的基本定理的應用·············282題型4  共線向量定理的應用···············285題型5  向量與三角形的四心···············285題型6  利用向量法解平面幾何問題·········290第2節  向量的坐標運算和數量積···········292知識點精講···························292基本題型及思路要點 ·········· ·········294題型7  向量的坐標運算···················294題型8  向量共線的坐標表示···············296題型9  平面向量的數量積·················297題型10  向量在物理方面的應用···········299題型11  平面向量與不等式·············300第五章  數列··························327第1節  等差數列與等比數列···············327知識點精講···························327基本題型及思路要點·········· ··········330題型1  證明數列是等差（等比）數列···················· ·········· 330題型2  等差（等比）數列的通項及五個基本量的關系····················· ····· ·· 325題型3  等差(等比）數列的求和·············338題型4  等差(等比）數列的性質·············343第2節  數列的通項公式與求和·············346知識點精講···························346基本題型及思路要點·····················346題型5  數列的通項的求解·················346題型6  數列的求和····················361題型7  數列問題中的函數思想············405第六章  不等式·························420第1節  不等式的概念與性質··············420知識點精講· ························· 420基本題型及思路要點··················420題型1  比較數(式)的大小·················420題型2  不等式性質的應用·················424題型3  取值范圍的判定·································425第2節  均值不等式與不等式的證明·········427知識點精講···························427基本題型及思路要點··················428題型4  利用基本不等式求函數最值·········428題型5  利用基本不等式證明不等式·········433題型6  不等式的證明····················435第3節  不等式的解法·····················444知識點精講··· ············ ···········444基本題型及思路要點······················446題型7  有理不等式的解法·················446題型8  絕對值不等式的解法···············449題型9  超越不等式的解法·················451策4節  二元一次不等式(組）與簡單的線性規劃問題···························· 451知識點精講··························  451基本題型及思路要點·····················452題型10  二元一次不等式表示平面區域······452題型11  簡單的線性規劃·················453題型12  線性規劃的范圍問題··············457題型13  簡單線性規劃問題的實際應用······460基本題型及思路要點······················463題型14  用構造法證不等式··············479題型15　放縮法證明不等式·············489第七章  立體幾何·······················511第l節  空間幾何體······················511知識點精講· ······················· 511基本題型及思路要點······················512題型1  空間幾何體的三視圖·············512題型2  立體幾何中的識圖技巧············516第2節點、線、面的位置關系·············521知識點精講··························521基本題型及思路要點······················522題型3  平面的基本性質與推論·············522題型4  空間中的平行關系················523題型5  空間中的垂直關系·· ··············528第3節  空間角及其空間距離的計算·······  540知識點精講··························555基本題型及思路要點············· ···556題型6  空間角及其空間距離的計算········556題型7  空間向量及其應用················556題型8  點到平面距離的求法·············559題型9  立體幾何中的翻折問題············562第八章  直線與圓的方程··················591第l節  直線方程··· ··················· 591知識點精講··························591基本題型及思路要點······················592題型1  直線的方程· ·········· ··········592題型2  兩直線的平行和垂直·································596第2節  圓的方程······················ 605知識點精講· ···· ··················· 605基本題型及思路要點······ ···············606題型3  待定系數法求圓的方程·············606第3節 直線與圓的位置關系···············610知識點精講········· ················610基本題型及思路要點····················· 611題型4  直線與圓的位置關系···············611題型5  圓與圓的位置關系·· ··············623第九章  圓錐曲線方程····················627第1節  橢圓························627知識點精講·························627基本題型及思路要點·····················627題型1  橢圓的標準方程··· ··············628題型2  橢圓的幾何性質·················629第2節  雙曲線·······················639知識點精講·························639基本題型及思路要點·····················640題型3  雙曲線的標準方程················640題型4  雙曲線的幾何性質················642第3節  拋物線·······················646知識點精講·························646基本題型及思路要點·····················647題型5  拋物線的標準方程··············647題型6  拋物線的幾何性質················648第4節  軌跡問題············· ········ 650知識點精講······ ·················· 650思路歸納及思路要點····· ··············· 650題型7  求軌跡方程······ ·········650第5節  直線與圓錐曲線的位置關系········665知識點精講······· ················ 665基本題型及思路要點·····················665題型8  直線與圓錐曲線位置關系的判定·····665題型9  相交弦長問題····················675題型10  定值、最值、定點、定直線問題···679第十章  常用邏輯用語····················771第l節  命題及其關系、充分條件與必要條件··771知識點精講·························771基本題型及思路要點·····················771題型1  四種命題及關系···················771題型2  充分條件、必要條件、充要條件的判斷······························772第2節  簡單的邏輯聯結永詞、全稱量詞與存在量詞···························776知識點精講·························776基本題型及思路要點·····················776題型3  判斷命題的真假········· ······776題型4  含有一個量詞的命題的否定·········778題型5  結合命題真假求參數的范圍·········779第十一章  算法初步····················· 781知識點精講························· 781基本題型及思路要點····················· 783題型1  已知流程圖,計算程序結果的問題····783題型2  已知偽代碼,計算程序結果·········792題型3  根據條件,填充不完整的流程圖······793題型4  算法和其他問題的綜合·············796第十二章  計數原理(文) ···············799題型1 分類加法計數原理················799題型2 分類乘法計數原理·················801第十二章  排列組合與二項式定理(理)······806第1節  基本原理與簡單排列組合問題······806知識點精講·························806基本題型及思路要點·····················808題型1  推導、化簡和計算··················808題型2  基本原理和簡單排列組合問題的結合·· ····························810第2節  排列題型一不可重復排列···········819知識點精講 ··················· ·····819基本題型及思路要點·····················819題型3  特元特位問題·············819題型4  捆綁問題················824題型5  插空問題····················825題型6  定序問題····················827第3節  組合題型······················830知識點精講 ········· ···············830基本題型及思路要點·····················830題型7  分選問題和選排問題·············830題型8  分組問題·················832題型9  分配問題······················ 834第4節  二項式定理·····················836知識點精講·························836思路歸納及思路要點·····················837題型10  二項式定理中的系數與x冪指數的確定····································837題型11  項和與系數和··················· 840題型12  二項式展開式的二項式系數與系數的最值································ 844第十三章  概率與統計(文)···············848題型1 古典概型·······················848題型2 幾何概型·······················850題型3 抽樣方法·······················855題型4 頻率分布直方圖····················859題型5 直線回歸方程·····················861題型6 獨立性檢驗······················876第十三章  概率與統計(理)···············881第l節  概率························881知識點精講·························881基本題型及思路要點·····················882題型1  等可能事件概率的計算一除法·······882題型2  互斥事件的概率一加法和減法·······886題型3  相互獨立事件同時發生的概率一乘法······························889第2節  概率分布······················892知識點精講·························892基本題型及思路要點·····················893題型4  作離散型隨機變量的分布列，求E(X）,D(X) ·························· 893題型5  正態分布·················· ··· 907第3節  統計························909知識點精講························909基本題型及思路要點·····················911題型6  隨機抽樣類型···················911題型7  用樣本估計總體···················912題型8  兩個隨機變量的線性相關··········914題型9  獨立性檢驗·····················916第十四章  導數與定積分·············920第l節導數的概念與運算···················920知識點精講··· ····················· 920基本題型及思路要點·····················921題型1  導數的定義·····················921題型2  求函數的導數····················923題型3  求曲線的切線方程···············924第2節  導數的應用·····················928知識點精講·························928基本題型及思路要點·····················930題型4  利用原函數與導函數的關系判斷圖像······························930題型5  利用導數判斷函數的單調性·········934題型6  函數的極值與最值的求解···········937題型7  利用導數解決不等式恒成立問題·····948題型8  利用導數證明不等式·············962題型9  利用導數探討函數圖像的交點······970第3節  定積分與微積分基本定理··········984知識點精講·························984基本題型及思路要點·····················985題型10  用定積分求曲邊梯形的面積········985題型11  求定積分······················989題型12 定積分的換元積分法與分部積分法·························· 990題型13  導數題錯題型糾正···············991第十五章  推理與證明····················994第1節  合情推理與演繹推理············994知識點精講···························· 994基本題型及思路畏示·····················994題型1  歸納推理······················ 994題型2  類比推理······················ 996題型3  演繹推理······················ 999第2節  直接證明、間接證明與數學歸納法···1000知識點精講·························1000基本題型及思路要點····················1001題型4  不等式的證明·······························1001第十六章  數系的擴充與復數的引入·····1011知識點精講·························1011基本題型及思路要點·····················1011題型1  復數的運算····················· 1011題型2  復數的幾何意義的應用··········1014第十七章  坐標系與參數方程···········1018題型1 極坐標與直角坐標的互化··········1018題型2 利用極坐標求軌跡·············1020題型3 利用極坐標計算求值···············1021題型4 直線的參數方程···············1023題型5 圓和橢圓的參數方程··············1025題型6 參數方程求解曲線弦長············1028題型7 參數方程求最值問題···············1032題型8 極坐標方程與參數方程混合·········1034第十八章  幾何證明選講··············1039題型1 相似三角形的判定和性質定理·······1040題型2 直角三角形的射影定理·············1048題型3 圓的切線的判定和性質定理·········1050題型4 圓周角定理、弦切角定理···········1053題型5 相交弦定理、割線定理、切割線定理···1056題型6 圓內接四邊形的判定與性質定理·····1058