高二數(shù)學選修1-1、1-2數(shù)學知識點 文科

高二數(shù)學選修1-1、1-2數(shù)學知識點(文科)選修1,1、1-2數(shù)學知識點第一部分簡單邏輯用語1、命題:用語言、符號或式子表達的，可以判斷真假的陳述句.真命題:判斷為真的語句.假命題:判斷為假的語句.2、“若，則”形式的命題中的稱為命題的條件，稱為命題的結(jié)論.pqpqpqqp3、原命題:“若，則”逆命題:“若，則”，p，q，q，p否命題:“若，則”逆否命題:“若，則”4、四種命題的真假性之間的關(guān)系:(1)兩個命題互為逆否命題，它們有相同的真假性;(2)兩個命題為互逆命題或互否命題，它們的真假性沒有關(guān)系(5、若，則是的充分條件，是的必要條件(pq,pqqp若pq,，則是的充要條件(充分必要條件)(pqA,B利用集合間的包含關(guān)系:例如:若，則A是B的充分條件或B是A的必要條件;若A=B，則A是B的充要條件;6、邏輯聯(lián)結(jié)詞:?且(and):命題形式;?或(or):命題形式;pq,pq,?非(not):命題形式.，ppq,pqpq,，p真真真真假真假假真假假真假真真假真假假假,7、?全稱量詞——“所有的”、“任意一個”等，用“”表示;全稱命題p:;全稱命題p的否定p:。，,x,M,p(x)，x,M,，p(x)?存在量詞——“存在一個”、“至少有一個”等，用“”表示;，，特稱命題p:;特稱命題p的否定p:;，x,M,p(x),x,M,，p(x)第二部分圓錐曲線F1、平面內(nèi)與兩個定點，F(xiàn)的距離之和等于常數(shù)(大于)的點的軌跡稱為橢圓(FF1212即:。|MF|，|MF|,2a,(2a,|FF|)1212這兩個定點稱為橢圓的焦點，兩焦點的距離稱為橢圓的焦距(2、橢圓的幾何性質(zhì):y軸上焦點在焦點的位置焦點在軸上x圖形villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,2222xyyx標準方程，,,,10ab，,,,10ab，，，，2222abab,,,axa且,,,byb,,,bxb范圍且,,,aya、、,,a,0,a,0,,0,a,0,a，，，，，，，，1212頂點、、,,0,b,0,b,,b,0,b,0，，，，，，，，1212軸長,2b,2a短軸的長長軸的長、、Fc,,0Fc,0Fc0,,Fc0,焦點，，，，，，，，1212222FFccab,,,2焦距，，12關(guān)于軸、軸、原點對稱yx對稱性2cb離心率ee,,,,,101，，2aa3、平面內(nèi)與兩個定點，的距離之差的絕對值等于常數(shù)(小于)的點的軌跡FFFF1212稱為雙曲線(即:。||MF|,|MF||,2a,(2a,|FF|)1212這兩個定點稱為雙曲線的焦點，兩焦點的距離稱為雙曲線的焦距(4、雙曲線的幾何性質(zhì):焦點在y軸上焦點的位置焦點在軸上x圖形2222xyyx標準方程,,,,10,0ab,,,,10,0ab，，，，2222ababxa,,xa,或，yR,xR,ya,ya,,范圍或，,,a,0,a,0,,0,a,0,a、、，，，，，，，，頂點1212軸長,2b,2a虛軸的長實軸的長Fc,,0Fc,0Fc0,,Fc0,焦點、、，，，，，，，，1212222FFccab,,，2，，焦距12yx關(guān)于軸、軸對稱，關(guān)于原點中心對稱對稱性villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,2cb離心率ee,,，,11，，2aaba漸近線方程yx,,yx,,ab5、實軸和虛軸等長的雙曲線稱為等軸雙曲線(、平面內(nèi)與一個定點和一條定直線的距離相等的點的軌跡稱為拋物線(定點稱為6lFF拋物線的焦點，定直線稱為拋物線的準線(l7、拋物線的幾何性質(zhì):2222ypx,2ypx,,2xpy,2xpy,,2標準方程p,0p,0p,0p,0，，，，，，，，圖形頂點0,0，，軸y對稱軸軸xpppp,,,,,,,,F,0F,,0F0,F0,,焦點,,,,,,,,2222,,,,,,,,ppppx,,x,y,,y,準線方程2222離心率e,1y,0y,0范圍x,0x,0,,,8、過拋物線的焦點作垂直于對稱軸且交拋物線于、兩點的線段，稱為拋物線的“通,,,,2p徑”，即(9、焦半徑公式:p2,,，F(xiàn)xF,xy,ypxp,,20若點在拋物線上，焦點為，則;，，，，0002p2,,，F(xiàn)yF,xy,xpyp,,20若點在拋物線上，焦點為，則;，，，，0002第三部分導數(shù)及其應(yīng)用villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,fxfx,，，，，211、函數(shù)從到的平均變化率:fxxx，，12xx,21fx，,x,fx()()002、導數(shù)定義:在點處的導數(shù)記作;(fxx,,，，y,fx,()lim0x,x00,x,0,xyfx,,xfx,，，，，，，003、函數(shù)在點處的導數(shù)的幾何意義是曲線在點處的切yfx,x，，0線的斜率(4、常見函數(shù)的導數(shù)公式:'n'n,1'',0?;?;?;?;C(x),nx(sinx),cosx(cosx),,sinx11''x'xx'x(logx)?;?;?;?,(lnx),(a),alna(e),eaxlnax5、導數(shù)運算法則:,,,fxgxfxgx,,,，，，，，，，，，，1，，，，;,,,fxgxfxgxfxgx,,，，，，，，，，，，，，，，，2，，，，;,，，,,fxfxgxfxgx,，，，，，，，，，，,,gx0，，，，,,2gx，，gx，，3，，，，，，，，(,ab,fx,0yfx,6、在某個區(qū)間內(nèi)，若，則函數(shù)在這個區(qū)間內(nèi)單調(diào)遞增;，，，，，，,fx,0yfx,若，則函數(shù)在這個區(qū)間內(nèi)單調(diào)遞減(，，，，,,yfx,fx,0fx,07、求函數(shù)的極值的方法是:解方程(當時:，，，，，，0,,1fx,0fx,0fx如果在x附近的左側(cè)，右側(cè)，那么是極大值;，，，，，，，，00,,2fx,0fx,0fxx如果在附近的左側(cè)，右側(cè)，那么是極小值(，，，，，，，，00yfx,ab,8、求函數(shù)在上的最大值與最小值的步驟是:，，,,1yfx,ab,求函數(shù)在內(nèi)的極值;，，，，，，2yfx,fafb將函數(shù)的各極值與端點處的函數(shù)值，比較，其中最大的一個是最，，，，，，，，大值，最小的一個是最小值(9、導數(shù)在實際問題中的應(yīng)用:最優(yōu)化問題。第四部分復數(shù)villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,1(概念:2,z(1)z=a+bi?Rb=0(a,b?R)z=z?0;,,(2)z=a+bi是虛數(shù)b?0(a,b?R);,2,(3)z=a+bi是純虛數(shù)a=0且b?0(a,b?R)z，,0(z?0)z<0;,,z(4)a+bi=c+dia=c且c=d(a,b,c,d?R);,2(復數(shù)的代數(shù)形式及其運算:設(shè)z=a+bi,z=c+di(a,b,c,dR)，則:?12(1)z?z=(a+b)?(c+d)i;12(2)z.z=(a+bi)?(c+di),(ac-bd)+(ad+bc)i;12(a，bi)(c,di)，,acbdbcad(3)z?z=(z?0);,12，i22222，，cdcd(c，di)(c,di)3(幾個重要的結(jié)論:1，i1,i2(1);?(1,i),,2i,i;,,i;1,i1，i4n4n，14n，24n，34n4n，14，24n，3i(2)性質(zhì):T=4;;i,1,i,i,i,,1,i,,ii，i，i，i,0;1z,1,zz,1,z,(3)。zmmmnmn，mnmnm4(運算律:(1)z,z,z;(2)(z),z;(3)(z,z),zz(m,n,N);1212zz11(),5(共軛的性質(zhì):?;?;?;?。z,z(z,z),z,zzz,z,z12121212zz226(模的性質(zhì):?;?;?||z|,|z||,|z,z|,|z|，|z||zz|,|z||z|1212121212z|z|11nn||,;?;|z|,|z|z|z|22第五部分統(tǒng)計案例1(線性回歸方程?變量之間的兩類關(guān)系:函數(shù)關(guān)系與相關(guān)關(guān)系;?制作散點圖，判斷線性相關(guān)關(guān)系,y,bx，a?線性回歸方程:(最小二乘法)n,xynxy,,ii,i,1,b,,n2(x,y)注意:線性回歸直線經(jīng)過定點。2,xnx,,i,i,1,aybx,,,,villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,n(x,x)(y,y),ii,1i2(相關(guān)系數(shù)(判定兩個變量線性相關(guān)性):r,nn22(x,x)(y,y),,ii,,11ii注:?>0時，變量正相關(guān);<0時，變量負相關(guān);x,yx,yrr??越接近于1，兩個變量的線性相關(guān)性越強;?接近于0時，兩個變量之|r||r|間幾乎不存在線性相關(guān)關(guān)系。3(回歸分析中回歸效果的判定:nn,,,22?總偏差平方和:?殘差:;?殘差平方和:;e,y,y(y,y)(yi,yi)iii,,i,,1i1i,n2(y,y),iinn,22,12i?回歸平方和:,;?相關(guān)指數(shù)。R,1,(y,y)(yi,yi),,in2,,1i1i(y,y),ii,1i2注:?得知越大，說明殘差平方和越小，則模型擬合效果越好;R2?越接近于1，，則回歸效果越好。R4(獨立性檢驗(分類變量關(guān)系):2隨機變量K越大，說明兩個分類變量，關(guān)系越強，反之，越弱。第六部分推理與證明一(推理:?合情推理:歸納推理和類比推理都是根據(jù)已有事實，經(jīng)過觀察、分析、比較、聯(lián)想，在進行歸納、類比，然后提出猜想的推理，我們把它們稱為合情推理。?歸納推理:由某類食物的部分對象具有某些特征，推出該類事物的全部對象都具有這些特征的推理，或者有個別事實概括出一般結(jié)論的推理，稱為歸納推理，簡稱歸納。注:歸納推理是由部分到整體，由個別到一般的推理。?類比推理:由兩類對象具有類似和其中一類對象的某些已知特征，推出另一類對象也具有這些特征的推理，稱為類比推理，簡稱類比。注:類比推理是特殊到特殊的推理。?演繹推理:從一般的原理出發(fā)，推出某個特殊情況下的結(jié)論，這種推理叫演繹推理。注:演繹推理是由一般到特殊的推理?！叭握摗笔茄堇[推理的一般模式，包括:?大前提---------已知的一般結(jié)論;?小前提---------所研究的特殊情況;?結(jié)論---------根據(jù)一般原理，對特殊情況得出的判斷。二(證明?直接證明?綜合法一般地，利用已知條件和某些數(shù)學定義、定理、公理等，經(jīng)過一系列的推理論證，最后推導villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChiefofthefirstsectionmarkedmydraftstatement.Workedafterafewmonths,I'vebeenburiedintheofficialprogram,veryrigidmonotonyofclericalcareer,flavourless.1939of7Augustbetween,County,andSecretarytoIwithtoOfficemeeting,forGovernmentestablishedoneyearstoworkreported,fortimerush,priornotforfullprepared,hadtoinwaybyrankAnnMrdescribedoneyearstoaboutpeople,andfiscal,andbuilt,andtaught,andinsurancefiveaspectsimportantmatters,Iaccordinglydetailednarrativefinishingwritten,completedWujiangGovernmentestablishedoneyearstoofworkreport.TurnbackandforthmonthShanRoad,apartfromtheSecretary,Mrrankfootdiseaseimmobility,bamboocarinsteadofwalkingoutside,squarefoot(exceptformyselfand4guards),thewuxing,peace,SIan,Guangde,doorwayswing,ZhangZhutothedestination--wearingBu.Atdiweitotheimportanttownsoftroopsisdifficulttoaccess,wehavetochangeangles,Shanruggedtrails,Sunandrainontheway,hardshipexceptions,ifthepatrioticandpassionsofthewar,thanthesuccessfulcompletionoftasks.Anoldfrail,rank,long-distanceLawtonregrets,admirable!InNovember1939,IwasadmittedtotheFacultyoflaw,CollegeoflawandpoliticsinShanghai,butresignedfromthepostoffice,bidfarewelltothisshortandmemorablelife.(J)thesiazhenboatburiedJapanesemorningofOctober18,1937,siazhensicktoshunTangQiao-cutters,1fromNanxuntownjiaxingtoJapaneseboats,caughtdraggingbehind3smallboats,loadedwithmilitarygoods.Siazhentoolatetoescape,jumpedashoreJapancatchupwiththeboat,forcinghimtorowaboat.MeanwhilecaughtthemigrantsvillageZhangShun.Siazhenwassickforalongtime,出所要證明的結(jié)論成立，這種證明方法叫做綜合法。綜合法又叫順推法或由因?qū)Чā?分析法一般地，從要證明的結(jié)論出發(fā)，逐步尋求使它成立的充分條件，直至最后，把要證明的結(jié)論歸結(jié)為判定一個明顯成立的條件(已知條件、定義、定理、公理等)，這種證明的方法叫分析法。分析法又叫逆推證法或執(zhí)果索因法。2(間接證明------反證法一般地，假設(shè)原命題不成立，經(jīng)過正確的推理，最后得出矛盾，因此說明假設(shè)錯誤，從而證明原命題成立，這種證明方法叫反證法。villagetemplesCentralOfficeeveryday,carryouttheirduties.CorrespondencerelatingtoeducationbytheChie