高中所有數(shù)學(xué)公式總結(jié)(免費(fèi)下載版)

1、1高中數(shù)學(xué)常用公式及常用結(jié)論高中數(shù)學(xué)常用公式及常用結(jié)論1.元素與集合的關(guān)系.UxAxCA???UxCAxA???2.德摩根公式.()()UUUUUUCABCACBCABCACB??????3.包含關(guān)系A(chǔ)BAABB?????UUABCBCA????UACB????UCABR???4.容斥原理()()cardABcardAcardBcardAB?????()()cardABCcardAcardBcardCcardAB???????.()()

2、()()cardABcardBCcardCAcardABC?????????5集合的子集個(gè)數(shù)共有個(gè)；真子集有–1個(gè)；非空子集有–1個(gè)；非空的真子集有12naaa?2n2n2n–2個(gè).2n6.二次函數(shù)的解析式的三種形式(1)一般式2()(0)fxaxbxca????(2)頂點(diǎn)式2()()(0)fxaxhka????(3)零點(diǎn)式.12()()()(0)fxaxxxxa????7.解連不等式常有以下轉(zhuǎn)化形式()NfxM??()NfxM???[

3、()][()]0fxMfxN????|()|22MNMNfx?????()0()fxNMfx???.?11()fxNMN???8.方程在上有且只有一個(gè)實(shí)根與不等價(jià)前者是后者的一個(gè)必要而不是充0)(?xf)(21kk0)()(21?kfkf分條件.特別地方程有且只有一個(gè)實(shí)根在內(nèi)等價(jià)于或)0(02????acbxax)(21kk0)()(21?kfkf且或且.0)(1?kf22211kkabk????0)(2?kf22122kabkk???

4、?9.閉區(qū)間上的二次函數(shù)的最值二次函數(shù)在閉區(qū)間上的最值只能在處及區(qū)間的兩端點(diǎn)處取得，具體)0()(2????acbxaxxf??qpabx2??如下：(1)當(dāng)a0時(shí)，若，則；??qpabx2?????minmaxmax()()()()()2bfxffxfpfqa???，，.??qpabx2?????maxmax()()()fxfpfq???minmin()()()fxfpfq?(2)當(dāng)a0時(shí)，若，則，若，則??qpabx2?????mi

5、n()min()()fxfpfq???qpabx2???，.??max()max()()fxfpfq???min()min()()fxfpfq?10.一元二次方程的實(shí)根分布依據(jù)：若，則方程在區(qū)間內(nèi)至少有一個(gè)實(shí)根.()()0fmfn?0)(?xf()mn3互為為互否否逆逆否否否命題逆否命題若非ｐ則非ｑ互逆若非ｑ則非ｐ15.充要條件（1）充分條件：若，則是充分條件.pq?pq（2）必要條件：若，則是必要條件.qp?pq（3）充要條件：若，且

6、，則是充要條件.pq?qp?pq注：如果甲是乙的充分條件，則乙是甲的必要條件；反之亦然.16.函數(shù)的單調(diào)性(1)設(shè)那么??2121xxbaxx???上是增函數(shù)；??1212()()()0xxfxfx??????baxfxxxfxf)(0)()(2121在????上是減函數(shù).??1212()()()0xxfxfx??????baxfxxxfxf)(0)()(2121在????(2)設(shè)函數(shù)在某個(gè)區(qū)間內(nèi)可導(dǎo)，如果，則為增函數(shù)；如果，則為減)(

7、xfy?0)(??xf)(xf0)(??xf)(xf函數(shù).17.如果函數(shù)和都是減函數(shù)則在公共定義域內(nèi)和函數(shù)也是減函數(shù)如果函數(shù))(xf)(xg)()(xgxf?和在其對(duì)應(yīng)的定義域上都是減函數(shù)則復(fù)合函數(shù)是增函數(shù).)(ufy?)(xgu?)]([xgfy?18奇偶函數(shù)的圖象特征奇函數(shù)的圖象關(guān)于原點(diǎn)對(duì)稱，偶函數(shù)的圖象關(guān)于y軸對(duì)稱反過(guò)來(lái)，如果一個(gè)函數(shù)的圖象關(guān)于原點(diǎn)對(duì)稱，那么這個(gè)函數(shù)是奇函數(shù)；如果一個(gè)函數(shù)的圖象關(guān)于y軸對(duì)稱，那么這個(gè)函數(shù)是偶函數(shù)19

8、.若函數(shù)是偶函數(shù)，則；若函數(shù)是偶函數(shù)，則)(xfy?)()(axfaxf????)(axfy??.)()(axfaxf????20.對(duì)于函數(shù)()恒成立則函數(shù)的對(duì)稱軸是函數(shù)兩個(gè)函)(xfy?Rx?)()(xbfaxf???)(xf2bax??數(shù)與的圖象關(guān)于直線對(duì)稱.)(axfy??)(xbfy??2bax??21.若則函數(shù)的圖象關(guān)于點(diǎn)對(duì)稱若則函數(shù))()(axfxf????)(xfy?)02(a)()(axfxf???為周期為的周期函數(shù).)

9、(xfy?a222多項(xiàng)式函數(shù)的奇偶性110()nnnnPxaxaxa???????多項(xiàng)式函數(shù)是奇函數(shù)的偶次項(xiàng)(即奇數(shù)項(xiàng))的系數(shù)全為零.()Px?()Px多項(xiàng)式函數(shù)是偶函數(shù)的奇次項(xiàng)(即偶數(shù)項(xiàng))的系數(shù)全為零.()Px?()Px23.函數(shù)的圖象的對(duì)稱性()yfx?(1)函數(shù)的圖象關(guān)于直線對(duì)稱()yfx?xa?()()faxfax????.(2)()faxfx???(2)函數(shù)的圖象關(guān)于直線對(duì)稱()yfx?2abx??()()famxfbmx??