人教版高二(上)数学教案(全册)

1、a b ab 0a b ab 0a b ab0(aa (a2)(a4)与 (aa (a2)(a4) (a 2a15)(a 2a 7 022(aa (a2)(a4)x421和 103 21 3 23 2( 3 2) ( 10) 2 6 5 24 25 0221110b 时 =b a 时 时32a3a2aa1 a 1 a 1log ( log ( 当a时32a3a2aalog (a log (a 32aabac bca(ac)bc) ab 0b c ab(b) c(b) a cbac bcab c d且ac bdaa b ac bc ac bdc d bc bdb c d且ac bda a b d

2、c d ac bdcc d(ac)bd) (ab)(cd)abcda b 0 cd 0b c 0且ac bc；a, b c 0且ac bcabc (ab)ca bab 0acc 0时(ab)c 0ac bc 3c 0时(ab)c 0ac bcb 0 c d 0acbd推论1 a且a b,c 0 ac bc ac bdc d,b 0bc bda bab0且0cd c d1 1 0a b c 0dc da b 0c db0,a bnn N n( 且 推论2 anb 0n N n( 且 a abnn b anna b a bnnnba abnna b a bn 4 练习3eeb 0 c d 0 e0

3、a，ac bd11a b 0a c b dee ac bd 0c d 0 ac bde01 1a,bRab, a b1 1 ba0 a b 0a bba 01 1 1 0a b c,cR abc 0，aabc 0abc 0a b c 2ab2acbc 0222a b c2 abacbc02241 1 1 abbcca a b cabc0abacbc0abc1 1 1 0a b c1 1 与 a b |a|b|1 1 baa b 0|a|b| a b即 当a babbaba 0ab00ab1 1aba bb1 b aababa1 0a 0 ba0a baba b 1 0bab aba 0a 0

4、1aa a b c d 0 sinsinacbd0sin 1 log 0b 0,c d 0ac bda11ac bd a,bRa b 2aba b22b 2ab (ab)a222当a b时，(ab) 02 a b 22 2a b时，(ab) 02a,bR 5baab,b aba b a 2( a) ( b) 2 ab 2a b22ababab aba b 时 ab22aRa,b,cRa b c 333abcb c abc (ab) c a b3ab 3abca3333322 (abc)(ab) (ab)cc 3ab(abc)22 (abc)a 2abb acbcc 3ab222 (abc)(a

5、 b c abbcca)2221 (abc)(ab) bc) (ca) 2222a,b,cRa b c 333a,b,cR 0 a b c abca,b,cR abc33abc( a) ( b) ( c) 3 a b c 3333a b cabc3333333abc3 abc3,a ,a R ,n 且nNa 12na a a12n nna a a nn12n6a a aa a an12nn12nnN ,a R i n*iab ab2以abD 过C 则2ABaC bCD ababCD ab2a,b,ca b c 222a b 2b c c a 22222222(a b c ) 2abbc2ca2

6、22a b c 222 ab6ab3ab,ab,xR2x 1 2x x与22x 1 2x x 2 ）4343a b b c c a 2(abc)222222222a b (ab)b c bc) c a (ca)2222222227x2 y2x y若x,yR Q(x,y) (x,y) G(,y) 222H(x,y) Q(x,y) (x,y)G(x,y) H(x,y)1 x y均x yx y2 x y x yx y2222222() 22442x2 y2x yQ(x,y)(x,y)22(x,y)G(x,y)2xy2xyH(x,y) xy G(x,y)G(x,y) H(x,y)x y2 xyQ(x,

7、y) (x,y)G(x,y) H(x,y)11252ab a,bR (a ) b ) 22ab11(a b )211ab(a ) b ) 22ab2ab abb a)2 )22)2 25aba b2222 ,yx yx y2 p px1 yx ys x s24x yx,yR xy2 8x y p px y 2 p当2 yx y(x y) 2 px当xysxmins1xy s4xy 221yxy(xy) s24maxlgxlog 10 2 (x x1 lgx 0 log 10 0 xxlgxlog 10 2 lgxlg 10 2xx0 x10 x 1lgx 0log 10 0 x(lgx)(lo

8、g 10) 2xlgxlog 10 2x1ab1 则ab 41a,bR0 ab 414,bab0ab 若a 0则 x x)(0 xyy2 x x )(0 x 2 x230 x1 1x 01x x 即时2x x 1x2 2x x424y 4 x) 4()3即x 时y 2 23273max 270 x 101x2 191 x x ) 2x x x )y222222221 2x x )x )4222 () 323342 392x 1x ,x y 22时y23max27max1 1xxx x11x 1 x1 0 0 x1111x=x11 2 ( 1 211xx1x1x111x1x 0 (x即 时) 1

9、x1x1 min x13时13 x(23x)x y max y114xx y 2 y54xmin36 0 x 时y 12xx ,y 1 62x3 2x ,(x 0)y2x31 11 2 2x 2x 3 2x 3 4 yy22233xx xx x 3 43 1033323 2x 2 2x 2 6x 2 y22当 x2即x时xxx1223y 2 6min 2 3 12 2 3243 61 22x2 x x x；2 6x3333 39 3 2x 2x 3 2x 33y2223x2x 2x2x 2x2 236332x y 时3632即x2x22minx22x22x24x1x22x2 1 (x21 1

10、x 111 (x 2x22x12x12(x14 x 1(x 00(x111(x 2 (x 1(x2(xx22x22x2() 1即y2xR 且x 1x 1 2y 221 y2 0 x 1 y 2 x ( )x222 21 yy1 322又x2( ) (x ) 22 222 21 3 3 21 y 2( ) x22 24 113 24(x 1 y ) 即2a b 1x ya,b,x,yR且x ya b y ( )1( ) ab xx yx yx yxyay xb ab2x y( a b)2 x即ab(x y) ( a b)时2xyy2将一块边长为axa x(a2x) ,(0 x )则其容积为V22

11、1V 4x(a2x)(a2x)41 4x(a2x)(a2x) 2a3 343a4x a2x x 即6a 2a36练习4 74 2x ,(xR ) y2xa2a3 x(a2x) ,(0 x )( y2)26 0y 3x692y 3x4)3x2xx2 121x ,27yloglog (3x)设x92733( ,x 2 3)4若0 x 1,求y x x )42 31 1x y若x,yR且2x y 1(32 2)1b0a3ab(ab) m3 (R2,h4m)x +3x233334x + x= x222223x( ) ( ) 3(x ) 0222x +3x2am a,ma0, b a0mba)bbm)a

12、m a0bm baaab+ab55233 2a +b ) ab+ab)=(a ab)+b ab)55233253252 3 13=a a b ) b a b)=a b )a b)3223222233=a+a )(a +ab+b)222,ba+,a +ab+b 022a a ) 0 a+a )(a +ab+b)02222a +b ab+ab3 25523mnmn行m ，t,t，12SS2SS(mn)2mnt mt n S,tt , t 11222m 2nmn2122SS(mn) S4(mn) S(mn)22t t n22(mn)2mn(mn)12m,nm t t 0 t b0时，2b2baaba

13、 ab0 ( ) 12当ba0时，b2bab (ab)2a b1 ab 14 22,)24 3 在 yxx2yy24 311 2 2(x1)(1x24)1 2xx, 则1x 24x x 24x221122x224x232yy 2 1x x x +x 40 1021122y 2x242,) 在y y y x3112,cb +c)+c +a)+a +b)abc222222b +c bc, a0, b +c)abc2222c +a)abc, a +b)abc2222b +c)+c +a)+a +b)abc222222b,cb +c)+c +a)+a +b)abc222222设,c ，2b (ab)

14、a222b b c c a 2(abc) a22222211 b 2若a+b= a22a2b2aba2b2ab ab| () 0222222 152b (ab) a22222c bc)， c a (ca) b222222b b c c a 2(abc) a22222211(a )b )1211(ab2222( a b )1222211 b 2 a221 1 1(abc)( )9a b ca, 1119(abc)()ab bc ca2abc3bc ca ab 21 1 11abc3abc, 33a b c, abc abc abcb a c a c b3( )( )( )a b a c b ca

15、bc3+2+2+2=9ab bc ca 3(abbc)(ca)3222211113ab bc ca(abbc)(ca)11192(abc)()ab bc cacab9111abbcca 2abc3bc ca ab 2 16a21b21112( ) ( ) a b1已知,且a 222bayxy设,xsin2cos2abab333已知,R() 3+22(ab)20a b ,+22b (ab)(a abb ) ab(ab)a33223(a b ) ab(ab)334(a b ) a ab(ab)b (ab)33333abab33() 3221125(a ) b ) 4设a+b=22ab2ab 114

16、1ab 4 ab22ab111 122a b 1 11aba b2 (a ) b ) 222ab2 ab 21 211142 222 2 3 7 2 5 173 7 0, 2 5 0( 3 7) (2 5)222 2 552 2 ( 3 7) (2 5)y2232(x y ) (x y )22333 2 y 3x y (x y ) x y 2x yx66222266333x y (x y ) 2x y2222332 y xyx2232 y 2xy xyx2231133(x y ) (x y )2232(x y ) x y 3x y (x y ) x y 6x y2236622226633 x

17、y 2x y (x y )663333 2113(x y ) (x y )xy22332a+b+c=ab+bc+ca0a+b+c=0 a+b+) =02a2b2c2 2ab+bc+ca0ab+bc+ca0 a+b+c=0ab+bc+caa+b+2b c 0a222 1812(ab) bc) (ca) 0222a+b+c=0 c=a+bab+bc+ca=ab+a+c=ab a+) =a b ab222bb2(a ) 0=224l l 2l ，22 l l 2l 44 l 2 l 2 24 l l22424 1 1 4l2 l 2 l 2 24 及 1已知0 2sin2cot21cos4sinco

18、s 0sin4sin 12)cos1 + 0)cos14 4cos1 02(2cos20 192已知aba2secbtan a b2(asecbtan) a b222tan b sec 2abtansec (atanbsec) 02 a2222a b 4ab 4 3S3设,cc2222abcosC 4ab 2 3absinC2cosC 2 3sinC3sinC cosC 2sin(C )16112 x 1x 22 )212x2x2| x 1x | x| 1x x x ) 2222212112| x 1x x 1x 2221x1x= , 11x cossin sin2则x221121sin1 x

19、 1x 221 1 32 2x0,yx+y=x y1 1 (2 ) 321 1 32 2x yx y 32 2y xx yx y1x sin , y cos x0,yx+y=222 201 1 x y21 ) )则22 22 3(2cot tan ) 32 222 y 1| x 2xy y 2x2x222r, yr, (0r，| x 2xy y |r cos 2r cossinr sin |则2222222 r |cos2sin2 2r 2 2r 222241 (xyxy sec , y sec , (0, )x222cos()1则1 (xy 1 1 11 b 0 a 1ab0,a b=ab

20、aa sec ,b tan , (0 )a1,b0,a b=1 2221 a 1 b a1 b111sectan则sec sectana21 22 211 1 100 a b 2, a2a2a11x a , y a , (a x y 2)2aa22112 2 y a a 则x222aa211x y a a 2 2 （当a=1）2aa2x2 y22x y 2 2x y2 2即y 2x2b 1 asinxbcosx 12 1若a2|ab a b ) 1|b0,a b=0 1 x x 1ab |a 1b b 1a 122 22abcd,R+1 2abd bca cd b d acabcdm=abd

21、bca cd b d ac,+abcdm1abcd abca cd ab d abcabcdm 2ab ab cd d c m2log (nlog (n1nnlog (n log (n 0n2nn (n (n ( n222 (n (n nnn22nn2n21n2log (nlog (n 1n2时,nn1 111 2 1 23n22221111n2n(n n1 n1 1111 1 111111 22 1 23n22 2 3n1 nn2220,c , c , a ,4441ab a64a)a 2 1,cab+bc+caabc,c0a bc 则b+c=a0ab+bc+ca=b+)+bc0 a0b c

22、0 x yxyb 1设xya,ab1 x y1 x 1 yx yxyxy1 x y 1 x y 1 x y 1 x 1 yb, 则ab bc ca211124 2 2 ab bc(abbc)(ab)bc)ac11111 (nR n , n n1 n2n21 111 1 n n21 n nnnnn22221111 12 n1 n22n11n 中式n12nn1,c且a +b =ca +b c c 24 anbn1 c c0,cx+y2xy1 y1 x ,yx+y 与x+yxy1152 x x1xxx11(x) x (x 0)x 2，设f则xx11 1 1 ()() f) ) () 由f 1 0 0

23、5 )在2,)上单调递增，左边 f(2)2x210 10 y3x292 1t x2 9(t ( ) 则f t ytt )t121 t21 t t t t t ) ft ) 0tt 则f2121 21212ttt t121 2x2103 1 103 f y33x29 25,a+b+c=0和abc=,c,cabc a2则即2,c 2x ax 0bc aa8 a2 0a1 23 ( ,kZ)3 22 2yy +y+ +y =02 2当y=1当y 1 y+ y =y y 221 y 330a ba b (a b a b (a b 2 222222222OO到,AB,，CDAO|+BO|+|+AC|+B

24、D|1b| AO a b2 ，2Oa| BO (a b22b|CO (a b22BA1a| DO a b2| AC | BD 22a b (a b a b (a b 2 2222222221 x x1233 x x12x x12令yy x +y+x+y =02x x12 26xa x a x 1yx+y=xy4x y11x y 2 1令t=xy0t 2 y x24111 17ft) t(0, ft) f( ) 在t444110 a (k kN )2b 若令* ab f) f)|a |CDABCD, F在CD|=,DF|=,|=| AF|222222AOB=BOC=COA=,|=,OB|=,OC

25、|=z|log x)|和|log x)|0 x0aaa| )| | )| ) ) ) )22aaaaaa1x1 xlog x )log2aa1 x1 x1x1 x 1 x 2201log x )log0aa 27|log x)|log x)|aalog x)111x log x) log x) log logalog x)1xxxxxx2a1 x )2x x ) 0 1 x 22x1 x ) 1|log )|log )|xx2xaa x 1 x 11+xlog x) log x) 0aalog x)log x) log x ) 右=2aaa x ) 0 1 x 且0a0且a x =a +by

26、=c +dac+bd222222,yac+bd)ac+)22a +bc +dac+bd+abcd2222222 2ac+bd+ad+bcac+bd+abcd22222222222 2ad +bcabcd222 2xyac+bdb c d a c b c a d b dxy= a2222222222222abcd b d (acbd) acbd a2c2222x =a +ba=, b=222y =c +d2c= , d=22ac+bd= + =xy xy1 x 1 x22x x 2 1x,x121222121 x 1 x 2 1 x 1 x2x x2222x x 2211212121244 28

27、 x x ) 1 x x22121 2 x x ) 12x x x x2222121212x x 2x x22121 21 x 1 x222 1121222x x 2x x22121 2DCABCD，使AB=CD=BP=x,PC=x12BAPB=DPCAP+PDAPMx x取BCAMB=DMC,BM=MC=122AP+PDAM+MD221 x 1 x 1 122121222121 x 1 xx x222 1121222版 第6课x2 7x2(x 1(x 2)32x 1102x113x（x2 1x1）5x3 4x1x 1 x2 5x 6(2 x 294x4 0(xR,x 2) x x222x3

28、0 ( 8 x ) xa(xab)b(xab)(ab)xab(ab)ab(ab)bx aabba bx a bxR时当 a当 a 时ab(ab)abb x xa(a 0 x x2解：原不等式可以化为：(xaxa)01a (a即a a x 1a或若则 x2111 (a a 即(x ) 0 x ,xR若 a若 a则则22122 (a a 即x a x 1a或21c 0 x| x x x xax2bxc022b52c 0 1a 且，aabcc 0 x x 022aa51 x1 0 x 2 x222(axa1 0 x R xax2求 a 30a 0a 0(a 4a(a 0a 2a 1022a 013

29、a a a 0(x) kx 6kx(k2 k的 f 而k 0 0k 136k 4k(k 22k | x 5x51 例 2解集为：x|1x3x 1xx2x312x 2022kka 1211220的解集为x| x , b ()23b 2ax24xa3xRax| x x2 Bx|4xp Ay2,且, 求 p2a 1 时 ya1(1a )2 31xx223x22x30 3 2 0 或 2x2xxx 1x 或2x 32x301x3x2 3 20 1x 2x2x或 x 2x30 x 或x 321x 或2x 3(xx2)(xx0 -2-1 01234 3x 2x6 x32(xx 2)(x 2)0 或 3x

30、2 x(x 4x5)(x x2) 0 22x20 x24x50 x2x(x2) (x (xx2)0 23(xxx2)0且x x 1x|1x 或 2x x (x2) (x (xx2)023 32 (xx2)(xx4)(x x20)(x x2)80 022(x x) 22(x x)120 0222(x x12)(x x10)0221 1 (xxxx)0221 1 4x 或x 32216x1 x1(xxx103xx52x 2k21 k4x 6x322x (62k)xk)204x 6x32而4x2 6x302x (62k)x(3k) 02(62k) 42(3k) 0得 由2 3x 62k06xx2x1

31、(k 6)(x2) (x34(3x2) (x2) (x x2)322 332(x| x 或x且x31111x4 x5 x6 x39x(,( )(4,2(x2x101的xxaxb12x1 a,b x2x1 x x12(a b ( )0f x 定义域 f(x) g(x型 ( )0g xf(x) g(x)3x4 x3 0 3x40 x3x303x4 x3 123x4x3x1x| xx| x x| x2f(x)0(x)0(x)0f f(x)g(x型 或gg(x)0f(x) g(x)2x2 3x2 43x 3443x0 3 20 xx2x 3x20 243x0 x 3x2(43x)2243x64341x

32、2 xx2 5363x526x| x5f(x)0(x) 0(x) g(x型 fgf(x)g(x)22x 6x4 x2 22 6 40 x2x20 x2x 6x4(x2)22 或x1x x2 x|2x或0 x0 x102x1 x11 122x1012x x解 x102x11 x1( 2x1 ( x1) 2 2x1 (x 1x22即12 即 x9x 6xx 3 229 03x3x2 0 x36xx 0 x0 62 35在 3内 9x2 6xx2 9x2 6xx29x 96xx 6 6xx2 即6xx2 x226xx x2 2 2 x x1 1 3 11 x2 x3(x2) x1 4(x (xx2)

33、(x0 x|1x或x 52x3 3x5 5x6x( 2)3x3 x3 3x x3x( 5 4 1 x 2 xx 1(2(x x x2 0 x( 或 2x1 52x x11(1 x )2 3612 2( ) x2 3x3( x22 22 x 2x3x3( 2x3xx x6022x3 183 1xx33 293 02xx23(3 9)(33 2) 03 93 或xxxx223或或xlogx log333log (x 2 x3 10 x10 x310 x31 x或x1(x21(x2xlog (43xx )log (2x log 2,(a 0,a x2aaalog (43xx ) log 2(2x2a

34、a12x 2x10143xx 0 1x 4 x 2当 2243xx 2(2x3x 2212x 2x1043xx 0 1x 4 2x 4当 243xx 2(2xx 或x 221x 2 ；2当 2x4 375log x 1log x x aa1log x 05log x 0a5log xlog x)2或 alog x10aaa5log x 0a1log x 1alog x 1alog x 1a当 a当 a, , 4x x xlogax2aa当 9(log x) log x222aa12(log x4)(2log x 0log x 4aa x a 4aa9(log x) log x2当22aa(log x4)(2log x 0aa12log x 或log x 或0 4x axaaax|a x a,0 a x| x a 或0 x a,a 4或4 s 2 ,( 且 a2ax4aaxx1时x(, (4,) 当 1时当=1时2x22(2 02x2122 1log m x 0当 2或2= 时 4 (x 3x2 0当( , 24 2 3x x1的xx( 0的x2ax aB若B 求a若B 求a若Ba当1时 当2时 B当1时 当 2时 B当