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100 đề thi học sinh giỏi toán lớp 8 có lời giải. Có hướng dẫn giải chi tiết dễ hiểu, rất hay. Bộ đề được sưu tập trong những năm qua.100 đề thi học sinh giỏi toán lớp 8 có lời giải. Có hướng dẫn giải chi tiết dễ hiểu, rất hay. Bộ đề được sưu tập trong những năm qua.
x2 x x4 2008x 2007 x 2008 x 3x x x x x2 x2 x2 x2 x x x 64 x x x x x2 10 x 21 m AB GB BC HD AH HC 2008 S hai c can, m c v k N b M th th nh s th nh ph n bao nhi u k nh ph t c b minh r ph n s k 11 (4 c chia h l H ch gi 1- m v chia tr 1c m k ,b cho AD = BC T b x x2 cho m ng ph n cu l thi nh ph th m 2c k c x4 ni n c s k 11 v tr n c bao nhi u v s d s t nhi n n x8 t m s k S m ng nh sau: th m s k 11 ph n k ch s gi ng kh ng m th n nh ABC c n t A, c g BDC s g ch s th th th hai nh ni n n g im s rn tay ch c l v kh ng can n chia cho m v l Cho tam gi can c dung t xu c nh th thi t s ng v n n3 n chia h cho v x Nh n ng l C ti th m s g ng l 16 v s d l m Ch B ? 6l n 4l ,m s b chia v s chia (4 n em can c dung t 200 T nguy n t c th n chia dung t th gi L -2009 c l nc b l Sau b k v vi n v m A = 200 Tr n AB l l vi n nh i D IL C THI H C SINH GI I L : (5 a) 2015 2014 2015 2014 x (5 y y z b) c) ( a) X4 + 6y2 -7 = 2011x z x 2014 2014 : (x2 8)2 + 36 ng minh : l am ts h ut ng th c sau : 2012 x c2 a2 c : x19 + x5 2013x 2014 x a b Cho tam gi A 2B b c x1995 G i AE Ax c t CD t i F Trung n AI c ng th ng qua E song song v i AB c t AI G a) Ch b) Ch ng minh : AEF ~ = FK.FC c) i 12cm (4 2015 2015 a2 b2 b2 c2 nh nh t c a A = 6x 9x a) Ch ng minh b b) : H Th Song m i bi u th b) c) Cho ba s h u t Th H NGH c 2013-2014) c a c x2 -1 Qua E k tia Ax t CD K t AC = 9cm, BC = - 2014 150 a 4a a a 7a 14a x 1969 1971 x 20 x 11x 30 x 13x 42 1970 ( I c) Tam HA' AA' HB' BB' HC' CC' IM, IN (AB BC CA ) AA' BB' CC' 18 2014) 1) 2) : (3 : (4 x 2010 nh: :( a 5: (7 b) c) 3x x2 27 3x2 : x ) 2) a) x : (2 1) 2) 1) A ) x yz y x 2009 zx x 2008 z xy x 2010 x 1 x y 2x x 27 3x 8x x 2x D = CB.CK t -3 2009 z x 2008 - 2014 b) b) x : x(x + 4)(x + 6)(x + 10) + 128 + x5 + x3 + cho x2 - 4x x2 x 2x : x 1 x2 x2 a ab + a + b1) n2 n + b 2c bc + b + ac + 2c + b2) n5 n + a) C Cho ABC OA' AH OB' BK OC' CI - AB) - 2014) b 5x2 + 8x A = 10x2 c) y x x 7x y x Gi a) (x + x)2 + 4(x2 + x) = 12 b c) x x x x x y 2 y 2007 2006 2005 2004 Ox), AOB = 8a CA DB OC OB ; DB theo a +10x+21 -2014 :( (a2 + 1)(b2 + 1)(c2 A (1 :( 1 1 )(1 )(1 ) (1 ) 2 x ( x 1) ( x 2) ( x 9) ) P( x) 2x2 2x x2 x f(x) = x1994 + x1993 +1 cho g(x) = x2 :( :( n ) x x m x x a b c a b a c b 15n 225 - |x - 3| =14 c a b c u 5: ( CA DB OA2 OB 8a N GV: 1)Cho (6 ): : P 3x x 2y x 2y x 2y 3x (4 b) ): : x 2005 x 8038 18 x : x 2y x c )2 = a2 + b2 + c2 + 2ab 2ac 2bc + y2 ( x y ) b) Cho a) 2013-2014 x x : 3x x 2 x 4004 3x 6022 24 20 5x x 2013 a) b) BC = 3BM; AC = 3AN c BPQ? C (2 2) = IN.IC ): - 2014) : (3 x4 b/ Cho ) 30x2 + 31x 30 (a - b)2012 + (b - c)2013 + (c - a)2014 (4 ) n A = n + 4n - 20n - 48 36 A = n + 4n + 6n + 4n5 + n4 (5 ) x m x : M x2 x x 2x 2014 x2 x 0 FED 5: (5,5 a/ b/ CH.CD = CB.CK c/ AB.AH + AD.AK = AC2 ? 16 n Bi = i y y4 x4 y = x x y4 y x (y3 1)(x 1) (x y) ( x + y = y - 1= - - 1= - y 1)(x x 1) x y x y x y2 (x y) = xy(x y2 y2 x y2 yx xy y x x 1) = = xy(y2 x x = 5; - 2; ; 1;1; 7;7 x y (x y 1) xy(x y) x y xy x y = x x y (x x y xy x y (x y) 2 y x( y) y( x) xy(x y 3) y) = x y x(x 1) y(y 1) xy(x y2 3) 2(x y) x y2 = xy = x y ( 2xy) xy(x y 3) u c n ch ng minh (x2 + x )2 + 4(x2 t y = x2 + x 2 y + 4y - 12 = y + 6y - 2y -12 = (y + 6)(y - 2) = y = - 6; y = 2 *x +x =+x+6>0v im ix * x2 + x = x2 + x - = x2 + 2x - x - = x(x + 2) (x + 2) = (x + 2)(x - 1) = x = - 2; x = V y nghi m c - ; x =1 x x x x x x 2008 2007 2006 2005 2004 2003 x x x x x x ( 1) ( 1) ( 1) ( 1) ( 1) ( 1) 2008 2007 2006 2005 2004 2003 x 2009 2008 x 2009 2007 (x 2009)( 2008 x 2009 2006 x 2009 2005 x 2009 2004 x 2009 2003 x 2009 x 2009 x 2009 x 2009 x 2009 x 2009 2008 2007 2006 2005 2004 2003 2008 2007 2007 m) ADE = E1 E 0 2005 2004 ) 2003 2004 CDF (c.g.c) F1 = 90 EDF = 90 V y 2006 2005 2008 2003 E B Ch ng minh M 2006 ADE = F2 CDF (c.g.c) E2 F1 = 90 Ch ng minh O, C, I th ng E1 iD F2 ; 2005 2007 1 ; 2004 2006 y x + 2009 = I C O A D 2003 x = -2009 F DI = BI = EF EF DI = BI I thu ng trung tr c c a DB Hay O, C, I th i 4: B I thu ng th ng CO D m) nh t = 2(x )2 + nh t ADE (AD2 = 2ax + a2 = 2(x2 DE2 nh nh t BD = AE = T A i; AE = BD = x (0 < x < a) i x)2 + x2 = 2x2 DE2 = AD2 + AE2 = (a = c BD ax) a2 (0 x= m AB, AC AD.AE = AD + V y SBDEC = SABC BDEC nh t AD.BD = )+ AD(AB = AD)= (AD A x )2 + SADE i = AB2 D, E l m AB, AC S x 16 x2 5x 2x 2x (AD2 20 E C x x x(4 x 16 x 2x x[(2 x) x 2x 5x 5( x 1) 2 x x x( x 1) x 5 2x x 2x x x( x 2) x(2 x 4)(2 x 4) x( x 2) x.2( x 2).2( x 2) x( x 2) 4( x 2) 4x x x(x 2) - (x - 2) x( x 2) AB 20.05 12 25 15.15 25 2 x( x 2) AC 625 15 20 AB AC BC 15 hay HB HA BA HB BC 2 BH 25 3,5(cm) 20 HA 25 15 (3 a) x2 m) 4x + = 25 c) 4x 12.2x + 32 = b) x 17 1990 S t: x 21 x 1986 1004 m) c a bi u th c: A m) tc o ch cm ts , ta v m) 21 s xz y 2xz 1 y z xy z 2xy m ch s bi t r ng s s s HC' CC' b) G i AI C; IM, IN th t ng minh r ng: AN.BI.CM = BN.IC.AM (AB BC CA) c) Ch ng minh r ng: AA'2 BB'2 CC'2 tr ng HA' AA' yz x yz x HB' BB' THI CH N H C SINH GI I m): m) -3 m) c) 4x 12.2x +32 = 2x.2x 4.2x 8.2x + 4.8 = m) 2x(2x 4) 8(2x 4) = (2x 8)(2x 4) = m) (2x 23)(2x 22) = 2x 23 = ho c 2x 22 = m) ( ( ( ( 2x = 23 ho c 2x = 22 m) x y z m): xy yz xz xyz x = 3; x = xy yz xz ( yz = m) x +2yz = x2+yz xy xz = x(x y) z(x y) = (x y)(x z) m) xy xz ( ( : y2+2xz = (y x)(y z) ; z2+2xy = (z x)(z y) m) A m) xz ( y x )( y z) xy (z x )(z y) abcd m) ( 0,5 m): ph abcd k v (a 1)(b 3)(c 5)(d 3) m N, i k, m N, 31 k abcd k abcd 1353 m 2 m) ( A=1 m) G i (x yz y)(x z) ( m2 k2 = 1353 (m+k)(m k) = 123.11= 41 33 ( k+m < 200 ) m) m+k = 123 m+k = 41 ho c m k = 11 m k = 33 m = 67 m = 37 ho c k = 56 m) abcd K t lu n m) a, b, c, d m 100 (0,2 k = = ,a m) 3136 m): V a) m) SHBC SABC m) S HAB : S ABC m) HA' HB' AA' BB' m) BI IC HA'.BC AA'.BC HC' CC' A HA' ; AA' HC' SHAC ; CC' SABC SHBC SABC SHAB SABC C N HB' BB' I B SHAC SABC H A x B M C D ABI, AIC: AB AN AI CM IC ; ; AC NB BI MA AI m) BI AN CM AB AI IC AB IC IC NB MA AC BI AI AC BI BI AN.CM BN.IC.AM c)V Cx i x ng c a A qua Cx m) -Ch ng m) BC + CD m) +AD2 = BD2 AB2 + AD2 (BC+CD)2 m) 2 AB (BC+AC)2 (BC+AC)2 AB2 (AB+AC)2 BC2 (AB+BC)2 AC2 m) 2 -Ch ) (AB+BC+AC)2 (0, (0, m) m) (AB BC CA) AA'2 BB'2 CC'2 m) ng th c x y BC = AC, AC = AB, AB = BC u) S n4 3n 2n 6n n2 a b ab a bc b a2 b2 x 214 86 AB 22 b2 c2 c2 a2 x 132 84 CD EF c b c ac c b a x 54 82 a c AB = AC =BC n n2 ac abc ac c a2 b2 b2 c2 2 a b c ab a bc b ac c abc c abc abc ac ac c ac abc c abc ac 1 ac c c ac ac c abc ac a b a b c c c b b a c a c2 a2 b2 c2 a2 b2 c2 a2 a2 b2 a b2 c2 a 2( ) ( b c2 a c 2 b c a c b 2 c a c b a c b a c b a b ) a c b 86 ± ;x 1 , 84 82 x 214 x 132 86 84 x 214 x 132 ( 1) ( 86 84 x 300 x 300 x 86 84 x 54 82 x 54 2) ( 3) 82 300 82 300 A E D EO AO DC AC AB AO AB AO DC OC AB BC AO OC EF AB AB DC 2 DC AB DC AB.DC EF B K I N O 0,5 0,5 F M C 0,5 1,0 0,5 AB AO AB BC AC 1 DC AB EF EO DC AB AB DC 1,0 1,0 A (0,8.7 0.82 ).(1,25.7 B (11,81 8,19).0,02 : 11,25 1,25) 31,64 A 101998 f ( x) ax bx c f ( 2) f (3) 13a b 2c A 18 A 195 19 29 x N 102n 102n 1 20 x0 y04 A 3y x x 10 y 3 x x 3x 6y 2 y 1 3y x 2 : x2 27 3x x ... b x 3x 22 32 44 1002 a a a a a 8a a 8a 15 a 8a 22 a 8a a 8a 11 15 15 120 a 8a 12 a 8a 10 a a a 8a 10 x a x 10 x2 x m x n ;(m, n Z ) a 10 x 10a x m n a 10 m.n 10 a mn 10m 10n 100 m(n 10) 10n 10)... 8a 15 10 n 18n Khi ta A= a a/ 2a 3a 4a 3x x x x 3x x x S A0 B S ABCD 20 082 : AB CD MN SC D 2009 -2014) 2.5 1 5 .8 (3n 1)(3n 2) + 6n2 -19n x2 A= (x+1)(x+3)(x+5)(x+7) +20 28 cho x + 8x +12 4,5 a/... _ 180 _ _ QUANG TRUNG : (4 x2 x x4 2014 x 2013x 2014 : (4 x 3x 2 x x : (4 (a+b+c)( a b x x ) c x2 x x2 x x x x x x x : (8 AH (H m x 10 x 21 20 08 AB GB BC HD AH HC -2014 a4 8a 14a 8a 15