De thi Hoc sinh gioi Toan 9 va Dap an (1)

 a b c d+ + + PHÒNG GD-ĐT HUYỆN LONG ĐIỀN KỲ THI CHỌN HỌC SINH GIỎI CẤP HUYỆN NĂM HỌC 2009-2010 MÔN THI : TOÁN Thời gian : 150 phút ( Không kể thời gian giao đề) Ngày thi: 16/01/2010 Bi 1    a c b d =  !"#$%&'()*+,)%) Bi 2 -.+/"01' 2234 %'+ - - - - a b a b + ≥ −  -5'617+8 abc 9:;  ( ) - -  - abc n cba n  = −   = −   <+)!8<- Bi 3 -=>>?  @4 AAAAB -: −+−−− <+ A ≥ -C+1+D"5  E:AA:-FA : - =++++ Bi 4:-GH9D"5  -  : Ex m m y m+ + − = −  3IJK',GH+L)+,'=MN  I%'+"0O+'!+5GH)P)P+L)'Q+,' K Bi 5-  ∆ R.S)+,'@0'" ∆ R.R@ - 4.@ - T@ - 9.@U Bi 6 3 ?G"VGO.4-W>'XKY+,'R+Q"Z?G "VC[+5+/)*+,'R8.C[+\]^_5+/)*8R R. %'+R..].TR. ]4R. -  JKK"+,'R%+R]\9+Z<6U+Z< 69`W  - - - -  I :I F: :aa P = + + + + ĐỀ CHÍNH THỨC a d b c a d b c + − − = + − − MMMMbMMMM ĐP N Bi 1('c++-+,'  - - - -  I :I F: :aa P = + + + + - - - -  :I IB Ba a- = + + + +          : I I B B a a - = − + − + − + + −   : - = − - B =  3I+,' 3I+,' 3I+,'   - - a c do ad bc ad bc b d   = ⇒ = ⇒ =  ÷   3I +,' Bi 2: -+,' de548 ( ) ( ) ( ) - - - - - - - a b ab a b a b a b a b a b a b a b − + − + + = = = − + − − − −  d\2238D#.YPf+- 9 ( ) ( ) - - -a b a b a b a b − + ≥ − × − − eg! - - - - a b a b + ≥ −   -+,' e+/_ - - 33 3  33 3   abc a b c n cba c b a n n  = + + = −   = + + = − +   h-9aai4iI42iI M aa:3BI @jO33 - -  aaa 3 333  :n n n≤ − ≤ ⇔ ≤ ≤ ⇔ ≤ ≤ - 3I+,' 3BI+,' 3I+,' 3-I+,'             a d b c a d b c a d b c + − + =     + + + + − +         a d b c = + + + -  -  a d b c a d ad b c bc + − − = + + − + + - - a d b c a d ad b c bc + − − = + + − − −  a b c d + + + :a  I an⇔ ≤ − ≤ 3BI h:42iI4aa424-F eg!^5' FBIabc = 3I Bi 3(  -+,' @4 AAAAB -: −+−−− <+ A ≥ AABA −+−−= 3-I   -I   AAA −+−−−−−= 3I         −       −−−−=  -I -  AA - 3I ( )( ) -A:AA +−−−−−= 3I ( )( ) -AA:A +−−−−= 3-I -C+1+D"5 E:AA:-FA : - =++++  g6!A4+Z'*= 3BI e<+ A3 <≤ 5 E::-F:AA:-FA : - : - =++++<++++ k8=P+Z'<+ A3 <≤ 3I e<+A25 E::-F:AA:-FA : - : - =++++>++++ k8=P+Z'<+A2 3I eg!=9+Z')!6A4 3-I Bi 4:-+,' e5GH+L)=MN8  -   : E I E :m m m m m+ − + − = − ⇔ − = − ⇒ = 3I+,' C[+ ( ) 3 3 Nx y [Q+,'K'+L) 9 3 3  -  : Em x m y m m+ + − = − ∀ 3I ( ) 3 3 3 3 3 3 3 3 3 3   - : E 3   3  - : E 3 - x y m x y m x y x x y y ⇔ + − + − + = ∀ + − = = −   ⇒ ⇔   − + = =   eg!+,'K'+L)MN- Bi 5 el'+S)@k  +,'  ' - - - AM BM CM= + - - - BN BM MN⇔ = + BMN⇔ ∆ )Pm+@ : BCN ACM BN AM ⇒ ∆ = ∆ ⇒ = · · · 3 3 3 a3 F3 I3BMC BMN NMC⇒ = + = + = +,' Bi 6:3 %'+R..].TR. ]4R. -  %'+%+R\]5;g3 R..].4. -  R. ]4RR\4R - 42Y=@+,' f R\] 4R\R] ≤  - - - - - - - AD AE DE AH+ = = 3BI ⇒ f R\]  ≤ - - - - - - AH AO R ≤ = 3BI eg!@Af R\] 4 - - R n+R\4R] !R+,'+;*)R.3I  O B C A H D E . + PHÒNG GD-ĐT HUYỆN LONG ĐIỀN KỲ THI CHỌN HỌC SINH GIỎI CẤP HUYỆN NĂM HỌC 20 09- 2010 MÔN THI : TOÁN Thời gian : 150 phút ( Không kể thời gian giao đề) Ngày thi: 16/01/2010 Bi 1    a. ]4R. -  JKK"+,'R%+R] 9 +Z<6U+Z< 6 9 `W  - - - -  I :I F: :aa P = + + + + ĐỀ CHÍNH THỨC a d b. @4 AAAAB -: −+−−− <+ A ≥ -C+1+D"5  E:AA:-FA : - =++++ Bi 4:-GH 9 D"5  -  : Ex m m y m+ + − = −  3IJK',GH+L)+,'=MN 