Truong THPT Nguyen Hue ·Ta toan *** DE KIEM TRA HQC KI I Kh3i IOAB Thai gian: 60 phut Bilt I: (3 di~m) II Giai phuong trinh: ~2X2 - 3x + 1 = x-I 2/G o" • bie 1 A x+m lal va len uan: = 111 ° ° x-I , Bai 2: (3 di~m) { ) , I /G "oh A h • h x-+y+3xy=11 rai y p irong trtn : x+y-xy=1 ~ 21 Tim m d~ h~ phuong trinh sau co vo s6 nghiern: { mx+ y = m+1 x+my = 2 Bili 3: (2 di~m) Trong m?~ phang toa dQ qxy ~ho cac di~m A( -3; I), B(2;4)o 1/ Tim diem C tren true Ox de tam giac ABC vuong tai C. 21 Khi C( I;0) hay tinh dien tich .0.ABC va ban kinh duong trim ngoai ti~~ .0.ABC. Bili 4: (1 di~m) Cho tam giac ABC co AB = .fi,AC = 2,A = 45". Tinh dQ dai canh Be va dien tich tam giac ABC. Bili 5: (Idi~m) Cho a, b,c la cac s6 dirong. Chung minh r~ng: a be., a+1 b+1 e+1 -+-+-+-' ~ + + be ae ab a b e Dang thirc xay ra khi nao? H~t nAp AN MON ToAN KHOI lOAB ~ csu: Bai 1 N(>i dung { X -I> 0 I I .J2X2 - 3x + I = x - I¢:::>, ,. ()2 2x - - 3x + I = x - I { X ~ I x>1 ¢:::>{ 2- ¢:::> [X = 0 ¢:::> X = I x -x=O x= I (co th~ trinh bay each khac) Diem 21 x + m = m (I) x-I (I) ~ X +117 = mx -/11 ¢:::> (I-m)x = -2111 (2) . - 2Jn Khi m -:I: I: (2) ¢:::> x = I-m - 2m I' hi , (I) khi - 2m I I x = a ng I~m cua 11 -:I: ¢:::> m = - \ I-m I-m Khi m = I: (2) ¢:::>O.x = -2 vo nghiern ~ (I) vo nghiern K ~ 1 ' P 'h" - 2m et uan: m -:I: ±I: t co ng rem x = . . I-m m= 1vm=-I: Pt vo nghiern (khong co tru'o'ng hop m = -1 thl cho 1 di~m) £)K: x-:l:l 0,5d Id (3d) 0,25d Bai 2: (3d) { s=x+ y J {S2+P=11 [S=-4,P=-5 II £)at (S- ~ 4P) He ¢:::> ¢:::> . P = xy . S - P = I S = 3, P = 2 " {S = 3 {x + y = 3 [x = 2, y = I VOl P = 2 => xy = 2 ¢:::> ¢:::> x = I; y = 2 " {S = -4 {x + y = -4 [x = + I, y =-S VOl P = -5 ~ xy = -5 ¢:::> ¢:::> x =-5;y = t-I V~y h~ co 4 nghiern: . 0,25d 0,5d 0,5d O,Sd Id { mx+ y = m+ I 21 x+my = 2 D = m' -I; D =m2+m-2' r ' O,Sd 0,5d 0,5d i. Bai 3: (2d) D =m-I { m2 -I = 0 H~ co vo 56 nghiern ¢:::>D = D, =D} =0 ¢:::> m' + 111- 2 = 0 m-I =0 , 0,2Sd 0,5d 0,25d ¢:::> ' ¢:::> 111 = I a/ A(-3;1), B(2;4). C EOX ~ CCa,O) AC = (a + 3;-1); Be = (a - 2;-4) [a=1 .!'lASC vuong tai C ¢:::> AC'.BC = 0¢:::>(a+3)(a-2)+4=0¢:::> a =-2 V~y CC I ;0) hoac CC -2;0) bl TLf cau a ta thay .!'lASC vuong t~i C AS=.JS 2 +3 2 =J34,AC=~42+(-1)2 =J17,BC=J(-1)2+(-4)2 =J17 0,5d D ·• i , h S I AC BC 17 lel1tlc: =- . =- . . 2 2 B ' 'k' h a . .~ R AB J34 an In t ngoai uep: = - ~ . 2 2 (chi tinh durrc AB, AC thl cho O,25d) 0,5a Bai 4: 10 , . 2 J J 1\ r;:::12 ApdungDI COSIn: BC = AB- + AC- - 2AB.AC cos A =2+4-2.,,2.2'2=2 BC=12 D '" . 1 S ) AB C· ) r;:::? 2 12 1 I~n tic 1 tam glac: = - .A .sII1A=-" L - = i 2 2 2 0,50 0,50 Bili 5: 10 ~+~+~+3~a+l+b+l+e+1 be ac ab a b e a be) ) I ~-+-+-~-+-+- be ac ab a b e Ap dung b<1t o~ng thirc Cosi: (1 blab) bel e a ) be + (1e ~ 2fb-;:'-;;;; = 2 ;:; ae + ab ~ 2 ;;; ab + be ~ 2' b Cong v~ theo v~ ~ Dpcrn Dang thirc xay ra ~ a = b = c 0,750 0.250 <;, ' 'r I'" . \ . Truong THPT Nguyen Hue ·Ta toan *** DE KIEM TRA HQC KI I Kh3i IOAB Thai gian: 60 phut Bilt I: (3 di~m) II Giai phuong trinh: ~2X2 - 3x + 1 = x-I 2/G o" • bie 1 A x+m lal va len uan: = 111 ° ° x-I ,. tam giac ABC co AB = .fi,AC = 2,A = 45". Tinh dQ dai canh Be va dien tich tam giac ABC. Bili 5: (Idi~m) Cho a, b,c la cac s6 dirong. Chung minh r~ng: a be., a+1 b+1 e+1 -+-+-+-' ~ + + be ae ab a b e Dang thirc xay ra khi nao? H~t nAp AN. (2 di~m) Trong m?~ phang toa dQ qxy ~ho cac di~m A( -3; I), B(2;4)o 1/ Tim diem C tren true Ox de tam giac ABC vuong tai C. 21 Khi C( I;0) hay tinh dien tich .0.ABC va ban kinh duong trim ngoai ti~~