Đề thi HSG cấp tỉnh Toán 9 Gia Lai (2006-2007)

5 601 6
Đề thi HSG cấp tỉnh Toán 9 Gia Lai (2006-2007)

Đang tải... (xem toàn văn)

Thông tin tài liệu

SỞ GIÁO DỤC VÀ ĐÀO TẠO KỲ THI CHỌN HỌC SINH GIỎI CẤP TỈNH GIA LAI  TOÁN   !"##$%!&'( ĐỀ BÀI: Bài 1: ")&$( (*+, ( )   n n − -!.  )/012345678 n 9 :(;<345=78!+; x xy y+ + = 9 Bài 2: ")&$( (> !:$3!* A  =  ? ?  @ − 9   @ + 9 :(AB78!+;  C C @ @x x x− + + + − = 9 Bài 3: ")&$( *+,/012!D ) )a b c )!E  ( )    ? a b c+ + +  ≥  ( )  a b c ab bc ca+ + + + + 9 F!*GB4+#H.I Bài 4: ")&$( .%12!D ) ) )a b x y !JK<  ax by+ = )   ax by+ = ) ? ? ax by+ = ) @ @ ax by+ = L%!+M=:$3!* B  =    ax by+ 9 Bài 5: ")&$( +5N!F!&O Oxy .+:.P " (P   y ax=  " (a ≠ )&$  Q @ F a    ÷   /H&7!F " (d   @ y a = − 1.1./0!+R.H9A M PH&$:S!#; !+5+:.P  " (P 9T  MH  /3E/0&7!F  " (d  !T  H 9* +,!P3E MF MH= 9 Bài 6: ")&$( .&7!+U"V(/H6W4XY=&7!+U9O!&7!+U"Z(G  /0&.TXY!T/H!-G !+./0"V(!T97!F[!"V( !T\"\#%(9*+,    9PM PN PA+ ≥ 9 "-!(  Họ tên thí sinh:………………………………Số báo danh:……… ]^!1JS!_) ĐÁP ÁN VÀ HƯỚNG DẪN CHẤM `Vab Bài 1: ( 1,5 điểm ) a) E ( ) ( )    n n n n− = − 9 ( ) n n + 9  ( ) n n− PH!L12345P5!-5 ( ) n n−  M   9  ( ) n n + PH!L12345P5!-5 ( ) n n +  M   9 cd4 ( )   n n −  M  @ eeeeeeeeeeeeeeeeeeeee)& E ( )   n n − =  ( ) ( )  n n n− + 9 n 9 -3 ?n k = )!; ( )   n n −  M  ? 9 -3 ? n k = + )!; n −  M  ? )5 ( )   n n −  M  ? 9 -3 ? n k = + )!; n +  M  ? )5 ( )   n n −  M  ? 9 cd4 ( )   n n −  M  ? eeeeeeeeeeeeeeeeeeeee)& .H+ ? /H @ 345!2f39 cd4 ( )   n n −  M   eeeeeeeeeeeeeeeeeeee999)& b) E x xy y+ + =  ⇔  ( ) ( )   x y+ + = eeeeeeeeeeeee )&   )    )    )    )   x y x y x y x y + = + =   + = − + = −  ⇔  + = + =  + = − + = −   )  ) ? )  ?)  x y x y x y x y = =   = − = −  ⇔  = =  = − = −  eeeeeeeeeeeee)& cd478!+;E%<345PH  ( ) ( ) Q Qx y = ) ( ) ( ) Q Q ?x y = − − ) ( ) ( ) Q Qx y = ) ( ) ( ) Q ?Q x y = − − eeeee9)& Bài 2: ( 1,5 điểm ) a) A = ? ?  @ − 9 ( )   ?  @ + eeeeeeeee999999999999999999999999999& g ( ) ( ) ? ?  @  ?  @ − + g ? ? eeeeeeeeeeee)&  b) '3#< C Cx− ≤ ≤ 9 N! C C t x x= − + + ≥ eeeeeeeeeeeeeeeeee9)& h34+    @  t x − − = 9 cd478!+;E6T   @ t t− − = eeeeeeeeeeee)& AB/HP.T<W)!E< @t = 9 i.&E C C @x x− + + = )4    @ x+ − = )4 x = ± C eee999)& Bài 3: ( 1,5 điểm ) +70-!)!E  ( )     a b a b ab− ≥ ⇒ + ≥ 9F!*GB4+"j>( ⇔  a b = 9 78!D   b c bc+ ≥ 9j> ⇔  b c= 9    c a ca+ ≥ 9j> ⇔  c a= 9 i.&E    a b c ab bc ca+ + ≥ + + ) ) )a b c R∀ ∈ 9j> ⇔ a b c= = "(e99)& PTE ( )   a − ≥  ⇒    a a+ ≥ "(9j> ⇔  a = 9 78!D   b b+ ≥ "?(9j> ⇔  b = 9    c c+ ≥ "@(9j> ⇔  c = 9 k."()!E ( ) ( )     a b c ab bc ca+ + ≥ + + "(eeeeeeee)& O"()"?()"@()"(!k./-)!&7l  ( )    ? a b c+ + +  ≥  ( )  a b c ab bc ca+ + + + + eeeee999)& j> ⇔ a b c= = = eeeeeeeeeeeeeeeeeee9)& Bài 4: ( 1,5 điểm ) jm!< ax by+ = "(    ax by+ = "(  ? ? ax by+ = "?(  @ @ ax by+ = "@( W"(/0 x y + )!E ( ) ( ) ? ? ax by xy ax by x y+ + + = + 9 4"(/H"?(/H.&F!*!+5)!E  ( )  xy x y+ = + "( W"?(/0 x y + )!E ( ) ( ) @ @   ax by xy ax by x y+ + + = + 4"(/H"@(/H.&F!*!+5)!E  ( )   xy x y+ = + "(  cd4 )x y !JK<  ( ) ( )      xy x y xy x y + = +   + = +   9 AB<H4)!&7l    x y xy + =   = −   ⇔  )  )  x y x y = − =   = = −  eeeeeeeeeee)& c0 ) x y= − = )<&K.E6T    @  C    a b a b a b a b − + =   + =   − + =   + =   ⇒  a b = = 9 +7l ) x y= = − )!78!D!n!3&7l a b= = eeee99)& cd4       B ax by x y= + = + = − eeeeeeeeeee99)& Bài 5: ( 1,5 điểm ) ( Giám kh#o t$ v& h'nh ) jm! a > "/0 a < )!78!D(9 AB1o ( ) QM x y " (P∈ 9-!;  y ax= 9 E  Q @ H x a   −  ÷   eeeeeeeeeeeeeeeeeeee99)& i.&E      @ MF x y a   = + −  ÷        @ x ax a   = + −  ÷       @     x a x a = + + "(eeeeeeeeeeee99)& cH    @ MH y a   = +  ÷       @ ax a   = +  ÷      @     x a x a = + + "( p"(/H"(134+&'3B*eeeeeeeeeee99)& Bài 6: ( 2 điểm )  E ) )O I N !FH9h34+ · · MNI PNO= 9 .H+)%!% MIN /H PON PqP7l!W!T I /H O 9 i.&E · · NMI NPO= 9 h34+ MI rr PO 4 PO AB⊥ 9 cd4 P PH&$Ls=3 AB "#* N (eeeee9)& h34+ · · PAB PNA= 4 · · PAM PNA= 9 i.&E!% ANP /H MAP &t6Teeeeeeeeee999)& h34+  9PA PM PN= eeeeeeeeeeeeeeeeeee99)&     PM PN+ ≤ "&(eeeeeeeeeeeeeee)&   . Qx y = ) ( ) ( ) Q ?Q x y = − − eeeee9)& Bài 2: ( 1,5 điểm ) a) A = ? ?  @ − 9 ( )   ?  @ + eeeeeeeee 999 999 999 999 999 999 999 999 999 & g ( ) ( ) ? ?  @  ? . AB⊥ 9 cd4 P PH&$Ls=3 AB "#* N (eeeee9)& h34+ · · PAB PNA= 4 · · PAM PNA= 9 i.&E!% ANP /H MAP &t6Teeeeeeeeee 999 )& h34+  9PA PM PN= eeeeeeeeeeeeeeeeeee 99 )&  . b = 9 78!D   b c bc+ ≥ 9 j> ⇔  b c= 9    c a ca+ ≥ 9 j> ⇔  c a= 9 i.&E    a b c ab bc ca+ + ≥ + + ) ) )a b c R∀ ∈ 9 j> ⇔ a

Ngày đăng: 02/07/2014, 23:00

Từ khóa liên quan

Tài liệu cùng người dùng

  • Đang cập nhật ...

Tài liệu liên quan