Đề, đáp án HSG Tỉnh Yên Bái năm học 2004-2005

ĐÊ ̀ THI HO ̣ C SINH GIO ̉ I CÂ ́ P TI ̉ NH – HƯƠ ́ NG DÂ ̃ N GIA ̉ I Năm ho ̣ c: 2004 – 2005 Ba ̀ i 1 (4 điểm).   !"#"$ %&%'!"& () *+&(∈,-.)∈,-/.)/#* 0& () #*() 1( 1 ) #( # #)= ⇔ + + = + +  1( 1 2) 3( 3 4) ⇔ + = ⇔ + = 5)/#&4)/43⇔3(63/43⇒(7 8&374)*594.3:71&;4);3 ,<)71⇒=>? ,<)73749>?: 5@A&BCD>?"43 Ba ̀ i 2 (4 điểm). %!+< E E E E E E E E ) ( (  (  ) ( ( ) - - + = - - % F &G H < I &(JK)* L & 91:⇒9(M E (:9( E M) E :6) E 69( E M) E :M( E 7 ⇔9( E M) E :9(M E (6M1:7 ⇔99( E M) E :N91M E :(M91M:O7 8 H < I (JK)&91M E :(71M Biê ̣ n luâ ̣ n: P, L <JK1⇒ 1 ( 1  = +  G F  1 ( 1  = + " H  I < F !+Q H Q H & 1 )  1 ≠ ± + 6, L <)7Q H !+Q H  L  I & 1 ( 1  = + 6, L <)J& , L < 1 )  1 ≠ ± + ⇔ ) 1  ) ± ≠ − ⇒!+Q H  L  I & 1 ( 1  = +  , L < 1 )  1 = ± + ⇔ ) 1  ) ± = − ⇒!+Q H = I  P, L <71&!+Q H  L == L  I (JK) P, L <7M1&!+Q H = I  Kê ́ t luâ ̣ n: P, L <71&!+Q H  L  I ∀(K) P, L <7M1&!+Q H = I  P, L <JK1 H )7&!+Q H  L  I  1 ( 1  = + P, L <JK1. ) 1  ) ± ≠ −  H )J&!+Q H  L  I & 1 ( 1  = + P, L <J ± 1. ) 1  ) ± = −  H )J&!+Q H = I  Ba ̀ i 3 (4 điểm). R?A+<ASTU!+<UV<A9(.A:W(. A"<A&    =+++ =+−+ 4:19E :EX9 yax ayaax % F & L & E E( E9X E: E  ( 9X E:A   91: E( 9 1:A 4  9E: E( 9 :A 4  + − + = + − + =   ⇔   + + + = + + + =   YZ L A9E:M91:&9 E M364:A6E7⇔9M1:9M4:A6E7⇔ E A 9 1:9 4: = − − − 5Q H A∈[⇔ E 9 1:9 4:− −M ⇒ E  1 E E E  1 E  1− ⇔ − + − ⇔ −M M M \<A+&M1;E⇒M1∈]K1-KE^⇔∈]E--X-M1^ F  L A⇒∈]E--X^ F  _  Ba ̀ i 4 (4 điểm). B∆`aB<=b`.c`Rc+d9e:b!∆R`B*%'8" T(fSag<R.`W8hc+d9e:bi*Bf& :BR"!ZS`Bi* ):RejjiB* :B`a7a. · `Bi 7k  *f`RiB"lmVUmSf`RiB0a. % F &:L&n`a8Z& µ µ 1 E ` `= 91: op I  L & µ µ 1 E ` B= 9< H !< I  L  L a: Y I  L & µ µ E 1 B `= 9< H p L <Ri:  H 91:.9E: H 9X:<A+& µ µ 1 E B B= ⇒BR" H !Z L < F  · `Bi ): L & µ 1 e =  » `R 7 µ · E E*B `Bi= ⇒RejjiB : H : H  · `Bi 7k  ⇒n`a8H<⇒  X `R E = 8 L &Ri7  X `R E = *n`iBL · `Bi 7k  ⇒ ·  B`i X= \<A+&n`Re"HLH<⇒e`7`R⇒`B7E* `R  X= q0FHR%&n`%R"HFLH<& E E `R  X X X X `% R% E 4 4 1k 4 = = ⇒ = − = 5Z I A&8 I Q L < F Q H Z`BiR" H & E 1  X X # X* \  X E E 4 1k   = × + × =  ÷  ÷   Ba ̀ i 5 (4 điểm). B`aB8`ajjB8.B8r`a.cs`Ba8h<b e*B)\ ∆ `ea 7 1 -\ ∆ 8eB 7 E *mVUm`aB8* % F &&\ `B8 7\ aB8  \ `B8 7\ `e8 6\ eB8  1 E 1 E 1 % i 8 e Ra B ` e q 8 B ` a \ aB8 7\ aeB 6\ Be8 ⇒\ `e8 7\ aeB 9X: qtcaq*& `ea 1 \ aq*e` E =  aeB 1 \ aq*eB E = * e`a eaB \ e` \ eB ⇒ = 94: & e`8 eB8 \ e` \ eB = 93: u9X:.94:93:& `ea `e8 `e8 1 E `e8 Be8 \ \ \   \ \ = ⇒ = 5@A& `aB8 1 E 1 E \   E  = + + 7 ( ) E 1 E  + . ĐÊ ̀ THI HO ̣ C SINH GIO ̉ I CÂ ́ P TI ̉ NH – HƯƠ ́ NG DÂ ̃ N GIA ̉ I Năm ho ̣ c: 2004 – 2005 Ba ̀ i 1 (4 điểm). 