PHNG VN TON - HBKHN (Chuyn ton luyn thi C H Thi ln lp 10 a ch: Bc Lm - Ph Lng -H ng - H Ni) -----------------***------------------ www.luyenthi24h.com (THCS THPT LUYN THI C H) (Chnh sa ln th3) H tn: Trng: Lp: . xoyz( , , ) Ma b ca b c LI NI U Vikinhnghim10nmchuynluynthiCaongiHccho nhiuth h hcsinh,ti thyas ccem hcsinhrtcn c mt cuns tay tra cu cng nh tng hp li kin thc mn Ton. Ti liu ny c ti bin son vi mong mun tng hp ton b lng kin mn ton thc t lp 7 n lp 12 dng trong k thi tuyn sinh i Hc ca B Gio Dc v o To. Mc d rt c gng, nhng ti liu cng khng th trnh khi nhng thiust.Tisbsungthngxuynvalnach www.luyenthi24h.com (Trong mc ti liu t bin son). Ti y ti cng a lnrtnhiutiliunthivcccthithcacctrngTHPTkhc, gip cho cc bn hc sinh thun li khi tham kho. Bn c mun tm ni luyn thi tt, lp t hc sinh, c th lin lc vi ti theo a ch di y: Tc gi: Phng Vn Ton - HBKHN a Ch:Bc Lm, Ph Lng, H ng, HN in thoi:0985.62.99.66 Email: luyenthi24h@gmail.com Website: www.luyenthi24h.com Bc Lm, Ngy Thng Nm MC LC STTLPTRANG I S 1Gi tr tuyt i7 2Tnh cht ca hai t s bng nhau7 3Hng ng thc ng thc ng nh8 4Cn bc hai9 5Tam thc bc hai10 6H phng trnh bc nht10 7Phng trnh bt phng trnh10 8Bt ng thc10 9Cp s cng cp s nhn11 10Cng thc lng gic11 11T hp nh thc Niutn11 12Gii hn ca hm s11 13Kho st v v th hm s12 14o hm11 15Nguyn hm12 16M logarith12 17S phc12 HNH HC 1Cng thc trong tam gic 8+9 2Phng php ta trong mt phng 10 3Hnh hc khng gian 11 4Phng php ta trong khng gian 12 CC CNG THC KHC 1Cng thc tnh chu vi, din tch 2Cc tp hp s Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 1 1)GI TR TUYT I 00x khi xxx khi x> = < | | 0, x x R > e22x x =Vi0 a >ta c | |x ax ax a> > < | | x a a x a < < < 2)TNH CHT CA HAI T S BNG NHAU Nua cb d=..., ,a c a c a c ma ncb d b d b d mb nda c a b a bad bcb a c d b b+ + = = = = = + + = = = 3)HNG NG THC NG NH 2 2 2( ) 2 a b a ab b + = + +2 2( )( ) a b a b a b = +2 2 2( ) 2 a b a ab b = + 3 3 2 2 3( ) 3 3 a b a a b ab b + = + + +3 3 2 2( )( ) a b a b a ab b + = + +3 3 2 2 3( ) 3 3 a b a a b ab b = + 3 3 2 2( )( ) a b a b a ab b = + + Cc hng ng thc m rng 4 4 3 2 2 3 4( ) 4 6 4 a b a a b a b ab b + = + + + +4 4 3 2 2 3 4( ) 4 6 4 a b a a b a b ab b + = + + 2 2 2 2( ) 2 2 2 a b c a b c ab bc ca + + = + + + + +1 21 ( 1)( ... 1)n n na a a a a = + + + +1 2 2 1( )( ... )n n n n n na b a b a a b ab b = + + + + 4)CN BC HAI Ac ngha0 A>2A A = 0, A A > Ch quan trng: 2| | A B A B =vi0 B > . AB A B =nu 00AB > >. AB A B = nu 00AB s s A AB B=nu 00AB > > A AB B= nu 00AB s = >Tri du1 20 P x x = = + >= >Hai nghim m 1 21 200. 0S x xP xxA > = + 4)Du ca tam thc bc hai 2( ) ( 0) f x ax bx c a = + + =-Nu0 A , gi hai nghim l 1 2, x x(1 2x x < ) th( ) f xcng du vi h s a 1 2( ; ) ( ; ) x x x e +v( ) f xtri du vi h s a 1 2( ; ) x x x eT suy ra 0( ) 0,0af x x> > A < 0( ) 0,0af x x> > A s 0( ) 0,0af x x< < A < 0( ) 0,0af x x< s A s 5)So snh nghim ca phng trnh bc hai Cho tam thc bc hai 20 ( 0) ax bx c a + + = =v hai s < < > > 1 2( ) 0( ) 0afx xaf < < < < < 1 2( ) 0( ) 0afx xaf < < < < > 1 2( ) 0( ) 0afx xaf > < < < < < 1 20( ) 0( ) 02afx xafS A > >< < < >< < 6)H PHNG TRNH BC NHT Cho h phng trnh bc nht hai n 1 1 12 2 2a x b y ca x b y c+ = + =

1 11 2 2 12 2a bD a b a ba b= = 1 11 2 2 12 2xc bD c b c bc b= = 1 11 2 2 12 2ya cD a c a ca c= = Nu0 D =h c nghim duy nht xDxD= , yDyD=Nu0 D =+ Nu0xD =hoc0yD =th h v nghim + Nu0x yD D = =th h c v s nghim Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 47)PHNG TRNH BT PHNG TRNH 1)Phng trnh cha cn 20 BA BA B> = = 00AA B BA B >

= >= 2)Bt phng trnh cha cn 200AA B BA B> < >< 200AA B BA B> s >s 2000ABA BA BB >

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> 0 BA BA B> > > 3)Phng trnh c du gi tr tuyt i 0 BA BA B> = = A B A B = = 4)Bt phng trnh c du gi tr tuyt i 0 BA BB A B> < < < 0 BA BB A B> s s s 00BBA BA BA B<

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s 2 2A B A B > > 5)Phng trnh cha cn v du gi tr tuyt i 2A B A B = = 6)Bt phng trnh cha cn v du gi tr tuyt i 2A B A B > >2A B A B > >20 AA BA B> < < 20 AA BA B> s s Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 57)Cc bt phng trnh khc 00. 00, 00, 0ABA BA BA B=

=

s >

01 100B AA BA BA B< <

> < th2 x y xy + > . Du = xy rax y =M rng:Cho 1 2, ,..., 0nx x x >th 1 2 1 2... . ...nn nx x x n x x x + + + >Du = xy ra1 2...nx x x = = = 2)Bt ng thc Bunhiacopski Cho 4 s thc 1 2, a av 1 2, bb . Ta c ( ) ( )( )22 2 2 21 1 2 2 1 2 1 2a b a b a a b b + s + +Du = xy ra 1 21 2a ab b=M rng: Cho hai b s thc( )1 2, ,...,na a av( )1 2, ,...,nbb b , mi b gmns ( ) ( )( )22 2 2 2 2 21 1 2 2 1 2 1 2... ... ...n n n na b a b a b a a a b b b + + + s + + + + + +Du = xy ra 1 21 2...nna a ab b b= = = 3)Bt ng thc Trbsep (Chebyshev) Cho hai dy 1 2...na a a > > >v 1 2...nb b b > > >th 1 1 2 2 1 2 1 2( ... ) ( ... )( ... )n n n nn a b a b a b a a a b b b + + + > + + + + + +Du = xy ra 1 21 2......nna a ab b b= = = = = = Nu 1 2...na a a > > >v 1 2...nb b b s s sth bt ng thc i chiu. 4)Bt ng thc cha du gi tr tuyt i | | | | | | | | | | x y x y x y s + s + | | | | | | | | | | x y x y x y s s + Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 69)CP S CNG CP S NHN ( )nul csc, cng sai d ( )nul csn, cng bi q nh ngha1 n nu u d+ = + 1.n nu u q+ =S hng th n1( 1)nu u dn = + 11.nnu uq =3 s hng lin tip1 12n nnu uu+ +=21 1.n n nu u u+ =Tng n s hng u -Tng ca mt s dy s c quy lut ( 1)1 2 3 ...2n nn++ + + + =2 2 2( 1)(2 1)1 2 ...6n n nn+ ++ + + = 23 3 3( 1)1 2 ...2n nn+(+ + + =( ( 1)( 2)1.2 2.3 ... ( 1)3n n nn n+ ++ + + + = 10)T HP NH THC NIUTN S cc hon v ! 1.2.3...nP n n = =S cc chnh hp!( )!knnAn k= S cc t hp!!( )!kk nnkn ACk n k P= = Tnh cht ca t hp11 1k n k k kn n n nC C C C = = +Nh thc Niutn0( )nn k n k knka b Ca b=+ = 0 1 1 1 1... ...n n k n k k n n n nn n n n nCa C a b Ca b C ab C b = + + + + + + 12)GII HN CA HM S -Cc php ton v gii hn Cho f(x) v g(x) l hai hm s c gii hn khi 0x x . Khi | |0 0 0lim ( ) ( ) lim ( ) lim ( )x x x x x xf x gx f x gx = | |0 0 0lim ( ) ( ) lim ( ). lim ( )x x x x x xf xgx f x gx = 1 211...( )2[2 ( 1) ]2n nnS u u un u un u n d= + + ++=+ =1 21...11n nnS u u uquq= + + +=Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 7( )00 00lim ( )( )lim lim ( ) 0( ) lim ( )x xx x x xx xf xf xgxgx gx = = | |00 0lim ( )( )lim ( ) lim ( )x xg xg xx x x xf x f x (= ( -Mt s gii hn c bn 0sinlim 1xxx=01lim 1xxex=1lim 1xxex| |+ = |\ . -Tnh lin tc ca hm s Cho hm s( ) y f x =xc nh trn khong( ; ) a b . Hm s f c gi l lin tc ti im 0( ; ) x a b enu 0 00lim lim ( )x x x xf x+ = = Hm s f c gi l lin tc trn khong( ; ) a bnu n lin tc ti mi im trn khong . Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 811)CNG THC LNG GIC -Cng thc c bn 2 2sin cos 1 x x + =sintancosxxx=coscotsin xxx= 2211 tancosxx+ =2211 cotsinxx+ = tan .cot 1 x x = -Cng thc nhn i sin2 2sin .cos x x x =22tantan 21 tanxxx= 2cot 1cot 22cotxxx=222 2cos2 1 2sin2cos 1cos sinx xxx x= = =

-Cng thc nhn ba 3sin3 3sin 4sin x x x = 3cos3 4cos 3cos x x x = 323tan tantan3 tan .tan . tan1 3tan 3 3x xx x x xx | | | |= = + ||\ . \ . 323cot cotcot 31 3cotx xxx= sin 2sin( 1) .cos sin( 2) n n n = cos 2cos( 1) .cos cos( 2) n n n = -Cng thc h bc 21 cos2sin2xx=21 cos 2cos2xx+= 33sin sin3sin4x xx=33cos cos3cos4x xx+=4cos4 4cos2 3sin8x xx +=4cos 4 4cos2 3cos8x xx+ +=21 cos 2tan1 cos2xxx=+

21 cos 2cot1 cos2xxx+= -Biu dinsin , cos , tan , cot x x x xtheo 2tanxt 22sin1txt=+ 221cos1txt=+ 22tan1txt= 21cot2txt=Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 9 -Cng thc cng sin( ) sin .cos cos .sin x y x y x y + = + cos( ) cos .cos sin .sin x y x y x y + = sin( ) sin .cos cos .sin x y x y x y = cos( ) cos .cos sin .sin x y x y x y = +tan tantan( )1 tan .tanx yx yx y++ = cot .cot 1cot( )cot cotx yx yy x+ =+ tan tantan( )1 tan .tanx yx yx y =+ cot .cot 1cot( )cot cotx yx yy x+ = -Cng thc bin i tch thnh tng 1sin .sin [cos( ) cos( )]2x y x y x y = +1cos .cos [cos( ) cos( )]2x y x y x y = + +1sin .cos [sin( ) sin( )]2x y x y x y = + + | |1cos .sin sin( ) sin( )2x y x y x y = + +tan tantan . tancot cotx yx yx y+=+ -Cng thc bin i tng thnh tch sin sin 2sin cos2 2x y x yx y+ + = cos cos 2cos cos2 2x y x yx y+ + =sin sin 2cos sin2 2x y x yx y+ = cos cos 2sin sin2 2x y x yx y+ = sin( )tan tancos .cosx yx yx y++ =sin( )cot cotsin .sinx yx yx y++ = sin( )tan tancos .cosx yx yx y =sin( )cot cotsin .siny xx yx y = -Cng thc c bit khc sin cos 2sin 2 cos4 4x x x x | | | |+ = + = ||\ . \ . sin cos 2sin 2 cos4 4x x x x | | | | = = + ||\ . \ . 21 sin 2cos4 2xx | |+ = |\ . 21 sin 2sin4 2xx | | = |\ . 21 sin2 (sin cos ) x x x = Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 10-Cc cung lin kt: i B Ph - Hn km ; 2 sin( ) sin x x = cos( ) cos x x =sin cos2x x | | = |\ .cos sin2x x | | = |\ . sin cos2x x | |+ = |\ .cos sin2x x | |+ = |\ . sin( ) sin x x = cos( ) cos x x = sin( ) sin x x + = cos( ) cos x x + = -Cng thc nghim 2sin sin2x kxx k = + = = +tan tan x x k = = +cos cos 2 x x k = = + cot cot x x k = = + c bit sin 0 x x k = = cos 02x x k = = +sin 1 22x x k = = + cos 1 2 x x k = =sin 1 22x x k = = + cos 1 2 x x k = = + -Gi tr lng gic Cng thc chuyn i n v t 0sang x radian v ngc li 00180x =0 0180x= 0 0300450600900120013501500180Gc Rad0 6 4 3 2 23 34 56Sin0 12 22 32 1 32 22 120 Cos1 32 22 120-12 -22-32 -1 Tan0 13 1 3 - 3 -1 -13 0 Cot3 1 13 0 -13 -1- 3 Bin son: Phng Vn Ton 0985.62.99.66 www.luyenthi24h.com 1112)KHO ST V V TH HM S 1)ng bin, nghch bin -nh ngha Cho hm s( ) y f x =xc nh trn khong( ; ) a bNu 1 21 2( ) ( )x xf x f x< < 1 2, ( ; ) x x a b eth( ) f xng bin trn( ; ) a bNu 1 21 2( ) ( )x xf x f x< > 1 2, ( ; ) x x a b eth( ) f xnghch bin trn( ; ) a b -nh l Cho hm s( ) y f x =c o hm trn (a;b) Nu'( ) 0 f x > ( ; ) x a b eth( ) f xng bin trn( ; ) a bNu'( ) 0 f x < ( ; ) x a b eth( ) f xnghch bin trn( ; ) a b 2)Cc tr Cho hm s( ) y f x =c o hm cp I v cp II ti 0x x = Hm s t cc tr ti x0

00'( ) 0'( )f xf xdoi dau khi xdi qua x= (1) Hm s t cc i ti x0

00'( ) 0''( ) 0f xf x =