n n n n n n a a a a a a a a − − − = + + + + !"#$%&'( )*+$%, - ./0, x x = + 1 x N ∈ 23 0$ 4!"#%! 5"+6$$&*6!78!9- : -; x x ⇔ = ⇔ = <=, ab + 3 >ab ba ab ba + + M M .?$ 1 3 :2ab a b a b Z a b = + ∈ ≤ ≤ @%A 1 2ab ba a b + = + BCDEF1>29 1 2 > > ab ba a b a b ⇒ + = + ⇒ + M M 1CDEF1>292 G" :a b ≤ ≤ ( ) ( ) ( ) ( ) 1 2 ;H H; :I I:a b ⇒ = <=,;H3H;3I:3:I !"!#$%&!"!'() *"!+,&-&.&/ - JKL M@$ 7 $$$ n nthuaso a = 7 n m m n a a a + = 7 ( ) m n m n a a a m n m n N a − = ≥ ∈ ≠ 1 2 m n m n a a = 7N =&( 3 1 2a a a a = = ≠ 7E& O 1 2 31 I2 I31 2 31 >2 > n n n n x y x y x y x y = = = = 7FPQ M@$RI3 M@$ SQ37FP: M@$R 3 M@$SQ3 0"# - B - .?$ - - - - Q : : = = = - I - - H H 1 2 H = = = = G":T: T Q > I I : H ⇒ < < < <= - T - 1 -Q - - − M $- Q 9I ( ) -> Q - -⇒ = I ( ) > - - > > > H -> - - Q Q Q Q 1Q 2 = = = = - -Q 917-2 -Q 91 -Q 7-Q- - 77-Q- - 7- -Q 2 U -Q 7- - 77- - M <=!K- -Q 91- Q 2 > I- -Q I -Q - - ⇒ − M 0*"!'1#$2!3!45 67!)8!!9:'1 1. ;< 70VWXLYZ6"[B\[$"] 7L^$$$"- 7L^$+$$"I 7L^$$R$"H 7L^$>$"- <4=4'1 2 - - n n a a a a a a − ⇔ M M 2 > > n n b a a a a a − ⇔ M M 2 n n n i i c a a a a a − = ⇔ ∑ M M 2 : n n n i i d a a a a a − = ⇔ ∑ M M - 2 ->3Q ->3Q 2 ->3H ->3H n n n n f a a a a a a g a a a a a a a − − ⇔ ⇔ M M M M ><4=4'1$ D"_9$ > $ Q $ $ - $ $ _ ⇔ `1$ 7$ - 7$ Q 7281$ 7$ 7$ > 72a 9: _91$ 7 - $ - 7 Q $ Q 7271$ 7 $ 7 > $ > 72 DbO6c - 9::7 Q 9::::7de # -4 9+[7f98 98 > 98 de # -47 9+[8G"%A_91+[7$ 7$ - 7$ Q 727 71+[8$ 8$ 8$ > 29+K71$ 7$ - 7$ Q 7281$ 7$ 7$ > 72 F&B=%g 4,B%^%[$"d#P SBd#PR^$%A $" Dh 7 M I D"; ; 7; M :Dh; H 7H M :1Đề thi chn HSG lớp 9 huyn Văn B"n năm hc 2009 - 2010) .?$; ; 7; M :ij; ; 7; 9:4 2 Uj4#; H 7H 89;1; ; 7; 827`H8;1;2a 9;:48: 9:1;42 M : <=; H 7H M : ?D"; ; 7; M Dh; H 7H M 1ig/0.L :Y6&kl/--2 2. @ABCD:E#7 ( ) ( ) - - 2 3 1 2 - 1 2 n n n n n n n n n n a n N a b a b a a b ab b a b Z a b a b n k k N a b a b − − − − ∀ ∈ − = − + + + + ∈ ⇒ − − ⇒ = ∈ − + M M ( ) ( ) - - 2 - n n n n n n b k N n k a b a b a a b ab b − − − − ∀ ∈ = + + = + − + − + ( ) - 3 n n n k a b a b a b ⇒ = + + + ≠ − M D#BLWX Dh6c- 7I 7 M - ?67!)8!!9:F - Dhe =jF =mh 7nKB9 %b 7.\$VB94%b 7o%dhB947%b @%A%&'%g ?h 0G2!H2 9:#I - - - 2 - ;1 2 2 - ;1 2 n n n n a n N b n N + + − ∀ ∈ + ∀ ∈ M M 2 H : n n + − M - 2 - ; n n a − M 7<93p%b 7.\$V94%bh - - ; k k − M ij - - ; k k q − = 7nKB947$ -1 2 - :1 - 2 :- -- ;1: - 2 ; k k k k k k k q + + + − = − + − = + M <=947%b q - - ; n n − M +2E&* 2 H -; n n + − M 7<9p%bB 7H89 M -; 7.\$V94%bh H -; k k + − M ij H -; k k q + − = 7nKB947$ 3 [ ] H1 2 1 H 2 H H 1H 2 k k k k k k + + + − = + − + + − − − ( ) -; -; I -;1 I 2 -;q k q k = + − = − + M <=947%b q H -; n n + − M JG2!H2<4=4'1 P!=% ; I > ;>x y M P!=% Q Q>xyM 0G?D"09- 7- - 7- 77- $rDh0$" +rDh0$"> r0P"s KL $r09- 7- - 7- 77- 91- 7- - 271- 7- Q 2771- :: 7- 2 9-17-27- 17-27t7- :: 17-2 91-7- 7t7- :: 2 <=0 +rFQu[^$0$%&'09>1-7- > 7- : 7t7- -; 2 > r0 >B0R0 0G2!M+Đề thi HSG Toán 9 năm 2010 -2011/DUv 1 2 1 -2 QQ - n A n n n = − − − M NJG2!F@ $2 +2 0VWXK$W& 2 0VWX =mG565 W2 0VWX%wW&h 45 45O3! 0G2!CP4'A145 F"#4hBg = =$ CDEF oDFF$[LYBg$ 2F [L$" =wu[@$^$L $" e ?F $ $" =$$" -2F L$+$"6"%+B$ =$ $$" B=L6$5" = 9$ 4 $ - 4- $ 4 12 <$+$"$+h$Y?#@$ =$$-$B f(*"j+cf^$#@$ =%6"12F&+B 4 =$ +4xh$@$ ="6"#@$ $ $ - $ G"%$h$Y?#@$$ $ - $ h$$" 2F $$"B$$"oDFF^$B B=$$"B$+[ ^$B"%$ "oDFF12 e ?F $$"$ =$ B$$ "L %QH $""H7$"; .?D#H7 ; ⇔ Q7Q7 ; ⇔ Q7 ; ⇔ Q78; ; ⇔ Q8Q ; ⇔ Q182 ; $u1Q;298 ; <=9;4714 ∈ F2 D#- H7 ; ⇔ H78- ; ⇔ HH ; ⇔ H182 ; $u1H;298 ; <=9;4714 ∈ F2 %2."<+(#+[^$;6"$#?6c%%[ +p h$";y%^$+c D"+$7Q+$"1$+ ∈ F2Dh6c$7+ $" !ij$7Q+9!3$7+9=$+! ,h= Cách 1:!K+p h !8=91$7Q+281$7+29$7Q+8$8+9:+ F&B=!8= G"! Q= 0 =6$= Cách 2: nKop h Q=8!9Q1$7+281$7Q+29Q$7Q+8_8Q+9:$ F&B=Q=8! G"! Q= $u1Q29= Cách 3 :nK+p h !7=91$7Q+271$7+29$7-+7$7+9$7+ 5 F&B=!7= G"! ! 0 =6$= Cách 4: nK+p h !7:=9$7Q+7:1$7+29$7Q+7:$7:+9:$7+ F&B=!7:= G"! := $u1:28= "#$%6"##?6$%A%&$6$#+p h$ 46b/ [u+[^$4%uh$1 2f+[^$ ^$$y!Q^$$y=!K+p h!8=c4V$1h "^$+c2!K+p h!7=cu"6$^$$+c ^$+y!Q^$+y=!K+p hQ=8!c4V +!K+p h!7:=cu"6$^$++c ?Dh6c =(*182172$ "-Q ! $182172 129 182172 12 =(*S8B7$R 6"$R[+K^$QL^$b$ "H1-2 @12B1-2 =6$182172$"$ =$ BH <=182172 -Q ;R:JB'J1'HG)#$'!"!' )Y4$">W&$";W&> !./$">W&$";W&> Cách 1<4c$">Wu>476146 ∈ F6T>26" %6$>W&$;W&> 0)*>$";W&>>-:-I6"%\-I$" >W&B=69-I 0)oYWu>47-I-I Cách 2$8 > ⇒ 87 > ⇒ 7:12$8> ; ⇒ 8>7Q ; ⇒ 7: ;1-2@12B1-2 =6$7: > )oYLoY69-I Cách 39>!79;=7> ⇒ >!9>=7-=7Q ⇒ -1=7-2 > ⇒ =7- > .#6z)oY^$=+c#6z)Y^$+c;7>9-I +[P$""$"W&-$ "-W&:H 6 !Cách 1:$!7-9-=7:H ⇒ !9=7=8Q ⇒ =8Q ⇒ =947Q14 ∈ F2 ⇒ 9-147Q27:H9-47:QI G"+[P499:QI Cách 2:@!9=7=8Q =6$ 1!8=29=8QF !{==8Q ≥ ⇒ = ≥ Q> ⇒ g *+[P <=!9=W"%=9Q9:QI Cách 3$9!7- -9-!7Q;HQ 12 Uj4#9-=7:H 9-=7-HH 1-2 @12B1-2 =6$-89-1!8=27:QI ⇒ 9-1!8=27:QI <+[P9:QI SK%O0%% &'()*+,-./012345"6)7. $+6cd^$b+cHQCDEF^$b +cI .?./$?$B+1$ ≤ +2 $1$+29I$9I$|3+9I+|6"%1$|+|291$+$|+3 ∈ F2 G"$7+9HQI1$|7+]29HQ =6$$|7+|9Q D/j$|+| =$ d+cQ1$| ≤ +|2$%&' $| > G"% $ I H +| : + ;H II >Q $L+cCDEF+c> !./$?$B+1$ ≤ +2 $1$+29>$9>$|+9>+|6"%1$|+|29 G"$+9->$|+|9 =6$$|+|9-9Q D/j$|+| =$ L+c-1$| ≤ +|2$%&' $| G"% $ > > +| - Q + I - 481-8+9.:)4""6)8*+;(345"6)7. ? $+6cCDEF^$b+coDFF^$ b+c: !./#?$B+?V$ ≤ + 7 $1$+29$9$|+9+|1$|+|293$| ≤ +G"%$+9$|+|12 Uj4#$+9`$+a1$+29:9: 1-2 @12B1-2 =6$$|+|9:$#6&k' $| - > : G"% $ - > : +| : Q> H + : Q> H '(345"6))*+1<.#-8= MD"$$B+1${+2 $2Dh6c $$"+1$+29+ +2Dh6c $4x$"+CDEF^$$+cCDEF ^$)BW&6"K$(") 2G#!K6%CDEF1;->I2 !> $2U/&( ^$$B+p&(^$+i?"uW"$$ "++&( ^$$B+<=1$+29+ +2./6W&6"K$$"+1${+2$$9+47614 ∈ F2 ,h6c1$+291+62 B= $B+$"W6$"WW"%&(b^$ $B+f&( ^$+B612 i?"u +B6$"W$$"WW"%&( ^$+ B6f&( ^$$B+1-2 @12B1-2 =6$'#&( ^$$B+B'# ^$+ B6+c$ G"%$(Y6"$'%f+c$ h 1$+291+62 2;-$>IW&I:;->I291>II2 >I$IW&H1>II291IH23 I$"H1IH29H<=1;->I29H F!K.?V$4x$"+B$$"+W&6 +$" 6 W&6 - 6 $"6 - W&6 6 8- $"6 W&6 | 6 $"6 W&1WA=+ 6 6 - 6 WA=?W,K$P uW"%e #6 6?4bB[W&+c25"hyBLWX6$ 1$+291+6 2916 6 - 29916 | 6 296 1B6 $"6 2 F&B=CDEF1$+2$ 6"WA=#K$$ "+3+"6 36 "6 - 36"%6 6 - W&6"#K$5"h 6 6"&$%jL&$ ;- >I >I I 8 I H - <[WA=K$&6%&'/ "#}8 6&k'CDEF^$+$$CDEF^$$6wCDEF^$4 e ?Bh+$ M/'45T'4 $ =$ $CDEF+cF#4#b\ &( W =Y Dh6c $2$14#2$ =$ +2$S$ =$ 2-7B71 ∈ F2$ =$ !> $2./W ∈ CD1-7-72 ⇒ 1-7281-72 W ⇒ - W ⇒ W ∈ ~3-• F&W≠-BW&(^$S<=W9 2./W ∈ CD1-772 ⇒ 1-728-172 W ⇒ W ⇒ W9 %#:7-QB7Q# = $ !.?V:7-QB7Q$" =W :7-Q817Q2 W ⇒ - W ⇒ W ∈ ~-3• ig 4%g1:7-Q7Q29W≠-BW≠pW≠B7Q 4x$"U W≠-?LY[6"$:7-QB7 Q4x$"-$Y= :7-QS ⇔ :S ⇔ S 7QS ⇔ S ⇔ S <=%g 4%1:7-Q7Q29S ?'(345"6)81@A*+ CDEF^$-B:7Q1 ∈ F2 ./W ∈ CD1-8:7Q2 ⇒ -1:7Q2:1-82 W ⇒ ; W ⇒ W ∈ ~3;• $-8 ; ⇔ -8H ; ⇔ -18:2 ; ⇔ 8: ; ⇔ ⇔ 9;47:14 ∈ F2 F 9;47:-8 ;B :7Q9:1;47:27Q9;:47H> ;W"%1-8:7Q29; F ≠;47:-8 4x$";W"%1-8:7Q29 CDEF^$ - 21 +nn B-n 71∈F€2 !>./W∈CD + + - - 21 n nn n1n72 WB-n7 W 0 =6$n1-n728n1n72 Whn - W @n1n72 WBn - W =6$n W$u-n7 WW"% WW9 9 <=CDEF^$ - 21 +nn B-n7+c C)3)UV':7+W/ F WuL6$@$ =^$[_9$ ! + = • &'#&(^$_+c1!721=721•72 B=&(^$_Wu6"% !7#/1$$ - $ ! 2 =7#/1++ - + = 2 •7#/1 - • 2 G"%&'#&(^$_+c1!721=721•72 )Y-&( !JL?6$5" = F9$ ! + = • $1!721=721•729- 1! ≥ = ≥ • ≥ ≥ 2 0-+[#B[L^$[$=g 5"(* -9-9I-9Q9-- nK#6&k'$ $2h$[5" =q%!79-!9D/5" =)Y-$)Y6"6&k'=- +2h$$@$ = q%1!721=729I-"j1!721=729QW"%!9>=9"j!9 =9-ip)Y$/h$ =)hB($ 9- > 9:I"j9- - 9;-0)Y6"6&k'=;- 2h$+$@$ = q%1!721=721•729--!9-=9•90)Y- - >9I 0"#+$- ;-I6"+$6&k'$Y=)Y-&(I ;XY>Z[\][K]^; >_57 nK#WA=$ $2GA=- +2GA=S>;2GA=#$"W&Q; 6"#WA=6‚u4@uh$%g (* u%hg6&([%*Bz%*Bz=yWA=$23-yWA= +23yWA=2$/#WA=6WA=[ nKWA=[Q;I: P$$^$WA=0 uhI^$WA==:+cQ71I823uh^$WA== Q71829 10 [...]... đó: C(2; 1) y =1 + Giải hệ tìm được + Để 3 đường thẳng trên đồng quy tại điểm C, ta có hệ thức: 2a – b = 5b => a = 3b Vậy ba đường thẳng trên đồng quy khi: a = 3b Bài tập 2(Đề thi HSG Toán 9 năm học 2010 - 2011): Cho ba đường thẳng: (d): y = (m - 1)x + 3m - 5 (d1): y = 4mx - m - 5 (d2): y = (m2 + 4)x + 2m - 4 a) Với giá trị nào của m thì hai đường thẳng (d) và (d1) vuông góc . Q>xyM 0G?D"09- 7- - 7- 77- $rDh0$" +rDh0$"> r0P"s KL $r09- 7- - 7- 77- 91- 7- - 271- 7- Q 2771- :: 7- 2 9-17-27- 17-27t7- :: 17-2 91-7- 7t7- :: 2 <=0 +rFQu[^$0$%&'09>1-7- > 7- : 7t7- -; 2 > r0 >B0R0 0G2!M+Đề thi HSG Toán 9 năm 2010 -2011/DUv 1 2 1 -2 QQ - n A n n n = − − − M NJG2!F@ $2