T :Toỏn Tin Trng THPT Khỏnh Lõm CNG ễN TP HC Kè I MễN TON LP 12 NM HC 2010-2011 PHN I: GII TCH A) Lí THUYT: Cỏc kin thc c bn cn nm Chng I: NG DNG O HM KHO ST V V TH CA HM S Hm s, tớnh n iu ca hm s Mi liờn h gia s ng bin, nghch bin ca mt hm s v du o hm cp mt ca nú im cc i, im cc tiu, im cc tr ca hm s Cỏc iu kin cú im cc tr ca hm s Giỏ tr ln nht, giỏ tr nh nht ca hm s trờn mt hp s ng tim cn ng, ng tim cn ngang, ca th Cỏc bc kho sỏt hm s v v th hm s (tỡm xỏc nh, xột chiu bin thiờn, tỡm cc tr, tỡm im un (nu cn), tỡm tim cn, lp bng bin thiờn, v th) Giao im ca hai th Chng II HM S LU THA, HM S M, HM S LễGARIT Lu tha Lu tha vi s m nguyờn, s m hu t, s m thc Cỏc tớnh cht Lụgarit Lụgarit c s a ca mt s dng (a > 0, a 1) Cỏc tớnh cht c bn ca lụgarit Lụgarit thp phõn, s e v lụgarit t nhiờn Hm s lu tha Hm s m Hm s lụgarit (nh ngha, tớnh cht, o hm v th) Phng trỡnh, bt phng trỡnh m v lụgarit B) CC BI TP C BN CN RẩN LUYN: Bi 1: Kho sỏt v v th ca cỏc hm s a) y = x3 - 3x c) y = b) y = x4 - 2x2 + x +1 x2 Bi 2: Kho sỏt v v th ca cỏc hm s a) y = 2x x x b) y = x x c) y = x+2 Bi 3: Bin lun theo m s nghim ca PT: x3 - 3x - m = Bi 4: CMR: th (C) ca hm s y = x luụn ct ng thng (d) : y = m - x vi mi giỏ tr ca m x +1 Bi 5: Tỡm GTLN, GTNN ca hm s a, f(x) = 3x3 - x2 -7x +1 trờn [ ; c, y = x - lnx trờn [ ; e ] ] b, y=x+ d, y = sin x trờn [ ; x ] sin x trờn [ ; ] Bi 6: Vit PTTT ca th hm s y = x3 - 3x2 + ti im A( ; -2) ( Hoc ti im cú honh bng 2; hoc ti im cú tung bng 2; hoc tip tuyn cú h s gúc bng 9; ) Bi 7: Cho HS y = x3 + ( m + )x2 + - m ( m l tham s) cú th l ( C m ) Xỏc nh m HS cú im cc i l x = -1 Bi 8: Tớnh giỏ tr ca biu thc sau: 2log3 2+ 4log815 + ( ) (3 ) 27 A =9 B = 16 C = log 63 + log 56 log 72 D = ln + ln(e e ) + 101lg e , 75 T :Toỏn Tin Trng THPT Khỏnh Lõm log 24 log 72 G= log 18 log 72 E = log log 400 + log 45 3 H= 81log3 + 27log9 36 + 34log9 Bi 9: Rỳt gn biu thc a3( a + a3) (a >0) a (a +a ) Bi 10: a, Chng minh ( ) < ( )3 b, So sỏnh cỏc s log v log Bi 11: V th cỏc hm s : y = 2x , y = 2.3 x , y = log x , Bi 12: Tớnh o hm ca cỏc hm s a, y = 5x2 + lnx - 7.3x b, y = x.ex Bi 13: Gii cỏc PT sau c, y = ln(1-2x), b, log ( x 2) = log 27 x a, x x = x Bi 14 : Gii cỏc PT sau a, 32x+1 - 5.3x + = c, 25x - 7.5x + = d, 4.9x - 12x + 8.16x =0 b, 2x + + 2x + = 5x +1 + 3.5x c, log x + log x = d, log x + log x + log x = e, log ( x + 1) + log ( x + 1) = g, log x + log (4 x) = 2 Bi 15: Gii cỏc BPT sau : a, 9x - 5.3x + < b, log ( x + 2) > log ( x + 2) c, log 32 x log x + > d, log ( x3 ) x +1 Bi lm thờm: Bi 1: Cho hm s y = x + m( x + 1) + cú th l (Cm) 1) Kho sỏt v v th (C) ca hm s m = -3 2) Vit phng trỡnh tip tuyờn vi (C) ti im M(x0;y0) thuc (C) , bit f(x0)=0 Chng minh tip tuyn vi (C) ti M cú h s gúc nh nht 2x Bi 2: Kho sỏt v v th (C) ca hm s : y = x +1 1) ng thng (d) i qua I(1; -2) cú h s gúc k Bin lun theo k s giao im ca (d) v (C) 2) Vit phng trỡnh tip tuyn vi (C), bit tip tuyn ú vuụng gúc vi ng thng x+y+2009=0 3) Da vo th (C) hóy bin lun s nghim ca phng trỡnh mx+2x-m-1=0 Bi 3: 1) Cho hm s y = x + (m + 1) x + m (1) a) nh giỏ tr tham s m hm s cú im cc tr b) Khi m = 0, hóy tỡm giỏ tr ln nht ca hm s trờn on ;1 2) Kho sỏt v v thi (C) ca hm s (1) m = 3) Da vo th (C), hóy bin lun s nghim ca phng trỡnh : x x + 2m = 4) Vit phng trỡnh tip tuyn vi (C) ti im M(x0 ; y0) (C), bit f (x0) = T :Toỏn Tin Trng THPT Khỏnh Lõm Bi 4: 1) Kho sỏt v v th (C) ca hm s : y = x + x 2) Da vo th (C), hóy bin lun s nghim ca phng trỡnh : x 3x + m = 3) Vit phng trỡnh tip tuyờn vi (C), bit tip tuyn song song vi ng thng 9x + y + = 4) ng thng (d) i qua im M(0;-2) v cú h s gúc k nh giỏ tr tham s k (d) ct (C) ti im phõn bit 5) Chng minh tip tuyn vi (C) ti im M(0;-2) cú h s gúc ln nht x+2 Bi 5: Cho hm s y = cú th (C) x +1 1) Kho sỏt s bin thiờn v v th (C) 2) Tỡm tt c cỏc giỏ tr ca tham s m ng thng (d) : y = mx + ct th ca hm s ó cho ti hai im phõn bit 3) Vit phng trỡnh tip tuyờn vi (C) mi trng hp sau: a) Ti giao im ca (C) vi trc tung b) Tip tuyn song song vi ng phõn giỏc th hai c) Tip tuyn vuụng gúc vi dng thng (D): 4x-y+2009=0 4) Tớnh tớch cỏc khong cỏch t mt im bt k trờn th (C) n hai ng tim cõn ca (C) 5*)Tỡm nhng im trờn (C) tng cỏc khong cỏch t nú n hai tim cn l nh nht Bi 6: Cho hm s y = x 2x cú th (C) 1) Kho sỏt s bin thiờn v v (C) 2) Da vo th (C), hóy xỏc nh m phng trỡnh x x + 2m m = cú nghim phõn bit Bi 7: Tỡm GTLN v GTNN ca cỏc hm s sau: 1) y = x x 12 x + trờn on [ 2;2] 2) y = x + x + trờn on 2; ln x 3) y = x + x 4) y = , x ; e x 5) y = x + x 6) y = sin x + sin x Bi 8: 1) Gii cỏc phng trỡnh sau: a) 8.3 x + 3.2 x = 24 + x ; b) 12.3 x + 3.15 x x + = 20 [ c) 9.2 x = 32 x + 2) Gii cỏc phng trỡnh sau: x x a) + + = 14 ( c) ) ( ) ; x+5 x + 17 d) 32 x = 0,25.128 x ; b) 21 + + 21 2 2 x + 9.2 x + x + 2 x + = e) x +1 + x + = x + + 16 i) x + 16 = 10.2 x ( ) x ( ) ] ( ) x ( ) x = x +3 ; d) 3.8 x + 4.12 x 18 x 2.27 x = ; g) 25 x + 10 x = 2 x +1 k) 2 x x 22 + x x = x l) + + = Baứi 9: Gii cỏc bt phng trỡnh sau: 1/ 9x 5.3x + < 8/ log ( x 1) > log ( x ) + ; T :Toỏn Tin x 2/ 2 x 3/ + 1-x >6 4/ 12 + 6x > 4.3x + 3.2x 5/ 2.(0,4) x 5.(0,4) x > 6/ 9x 5.3x + < 7/ 25.2x 10x + 5x > 25 Trng THPT Khỏnh Lõm 9/ log1 4x + x 10/ log x + log x 11/ log 0, x log 0, x < 2x