De thi HSG huyen Toan 8

<span class='text_page_counter'>(1)</span>PHONGGD&DTHIYEN-AN DUONG. KV rHI cHoN HQC sINHGIoI t'6P a Nam hoc 2011'20L2. oEcsiNHTHuc MON:TOAN Bhi 1: (2.0ttidm). 111. t. I. a.ChO-+-t--v'. t. -n. Tinh gi6 tri cuabi6u thuc. xyz. y' x' . x - + / ' Y Z Y 2+ Z z x. 11 =----=-=-. z' z' +ZxY rll. - *nU * ; = t h o a m d n d i d u k i Q + c r 0 a + b v A a , b , c * 0 b.Cho. -. Chtmgminh.anBm. I * ' Uzotl. a+b+c. I *-rb20ll. I C20l. Bdi2: (2.0tliim). Giaiphuongtrinh. (x-2)',(!:] l'-,,(+l =o \;'-t)-". to[-.t,1. tx-I). cuaphuongtrinh Biri 3: (r.0 tli6m).Tim nghiQmnguyOn l+x+x2+*':Y'. = di€mc?nhBC,bi€tAB 5cm' trung ld M co ABC gi6c tam Cho (2.0 dicm). Bii 4: va vudnggoc voi Bc cit duong B qua = thing Duong l3cm. = AM 6cm va Ac voi BC cit duongthangAB o E' goc vuong vd C qua thing thangAM o D. Duong ChtmgminhrangCDf ME' F (AB < AC)' cdrcduongcaoBD virCE'Gqi ABC gi6c tam Cho (2.0 didm). Bhi 5: minhrdng:AB'AE + F D . F E : A F 2 ' ld giaodi6mcuaBC vir DE' Chrmg co c6cc4nhthoam d na < b S c ' Bhi6: (1.0didm).Chotamgi6cABC a. 9bc' Chimgminhrang(a + b + c)" < --------Hdt-----------. Gidm thi so l:...'.. Ho vdtOn:.. r""r"'r"i"'r""'.

<span class='text_page_counter'>(2)</span> A\1. PHONGGD&DTHUYENAN DUONG DAP AN DE THI CHQN HQC SINH GIOI. NNON: TOANL6P S Nnm hoc 2011- 2012 Bdi 1:(2.0didm). a. Tir gi6thi6tta c6: xy * xz + yz: 0. T ac o : x 2+ 2 y z : x 2+ 2 y z - x y - x z - y z = ( x - y ) ( x - z ) -x) (x- vXy-zXz- x) _, _ _ x ' ( z y ) + y ' . ( x z ) . + z ' ( y V' Y 6 vJA " (* vXy z)(z* x) (x yXv z)(z- x) b. Ta c6: 1 1 I I I -I+ - +1- - I <+-+-+ abca+b+cabca+b+cabc(a+b+c) /. ,rc(a+b+c)+ab. ^. /. r\,r. e ( a\ + b ) .' /# = 0 < + ( a + b ) ( c + b ) ( a\+ c ) =/6\ abc(a+b+c) [u*b=0. 0'5d '.sd. +b - U^< + a + b * - - - ; a -----==U r\/. /\. /. 0'25d. [a=-b. olu+c=o<+lb=-c. lt lc+a=0 Khi d6 ta c6: 1l. lc=-a 0.5d. ffi=ry= 111111 J--. a20t3. I. J-=-I-I-. a2013 b2013' c2013 a20t3' (_a)t0,,. =C 2 0 1 3 a20t3. 111. Suyra. 0.25d. -_-I-l--. a 2 0 1 +3 9 2 0 1 3* a 2 0 1 3. a2013 62013 C2013. Bii 2: (2.0didm). DiK: x * +l '). ., r vx -- 1 L , u ^ (l). = " D [' t u x+l' x-l l <+ u:v hoflcl0u:v. T a c 6 : 1 0.u 2+ vt -l l .u v: 0 e (u- v) .( Ou-v;:g. *N6uu:v. -x+2 g1= 0. x+1 x-l "6*-2. [x=3 * N6ulou: v c6I o.*-z =**2 o (x -:)(ex - 6)= s *"1 2 lX=x+l x-1 L3. 0.75al 0.75d 0.5d. Biri3: (1.0ili6m). T a c 6 :* ' +. * l : ('x * l ) t * 1 t o v d i m q ix 4 2' ". 5x2+lIx+7: 5(x+*lt*9to 10' 20. vdi msi x. 0.25d 0.25d.

<span class='text_page_counter'>(3)</span> NOn(1 * x * x2 + r ' ) - ( l + x + x t ) . I * x * x t + x ' < ( 1 + x + x 2 + x3) + (5x2+11x+7) 0.25d t + *' < (x+2)2hay x3 . y' . (x + 2)3 €*'<i+x*x do d6 tr: 1x+1)3 = o, 0.25d : 1 + + x 2+ x 3 e [ * (x+1)3. x. S u yr a. lx--l. N6ux:0thiy:1 N 6 ux : - 1 t h i y : 0 Bhi 4: (2.0tliim) Ggi K li giaodi€m cuaAM vd EC, tr€ndo4nMK l6y di6m I s a oc h oM I : M A : 6 c m Tri gi6cABIC ld hinh binh hinh =)AB = IC = 5cm,AI= 2AM =l}cm,AC = l3cm vu6ng tai I = AI2 + IC2- ACz= AAIC. = fr =900. B. L4icoBm = diM = 900. ABEK co BC, KM la c6cdulng cao (I) + M ld tryc tdm+ EMIBK AMBD= AMCK(c.g.c)+ MD = MK Me MB : MC vi DMC = BMK :+ ADMC = AKMB(c.g.c). (II). +ffi=ffi=DCttBK. " _. 0.5t1 0.5d 0.5d 0.5d. Tt (I) vd (II) suyra EMI DC Bhi 5: (2.0tli6m). Tr€n do4n thing AF laY di€m M. sao cho. D FME=Fil. AADB.,,AAEC-> -49 AE. AC. :t ^ffiE=.ffib AADE..,oAABC ^ ^. Do do FME = ABC = AME = ABF AAME.., AABF AM. AE. AB. AF. ^F ^I. FM = p=+fD.FE = AF.FM FD AF Vfly AB.AE + FD.FE: AF(AI'A+ FM) : AF.AF = AFz Bhi 6: (1,0didm) Tu gidthi6tbaira ta c6: zb>b+ a > c =+4b - c > 0 = (b -c).(ab- c) < 0. l.0iI. AFME.- AFDA :t. (l) = 4b2+ c' < 5bc=+(ZA+c)t < 9bc (2). M d :( a + b + c ) 2< ( 2 b + c ) z Tu (l) va(2)suyra: (arb+ .)) SdA + c)2<9bc.Tac6diAuph6ichungminh. l.0tl. 0,5d 0,5d.

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