ĐỀ THI OLYMPIC 30-4 NĂM 2007

KY ̀ THI OLYMPIC TRUYÊ ̀ N THÔ ́ NG 30/4 L ̀ N THƯ ́ XIII TA ̣ I THA ̀ NH PHÔ ́ HUÊ ́ ĐÊ ̀ THI MÔN TOÁN LỚP 10        Chu ́ y ́ :           !  "  Câu 1#$%&'( )*+,-      −=+ = + ++ yxyx yx xy yx . /  Câu 2#$%&'( 0123a, b, x, y*4%56+ 7 =− byax (-189:;& < aybxyxbaF +++++= ( Câu 3#$%&'( 01ABC=1=A, B9%56+ . . . 7  . 7  BABA − =+ ( 0<1ABC>1%5( Câu 4#$%&'( 0<1?ABCD.@AM>%&B!C()DP, Q, R, S>1%& MPMDMCMB $ =++ E MQMAMDMC $ =++ E MRMBMAMD $ =++ E MSMCMBMA $ =++ ( -F8G;%&MPA = QB = RC = SD. Câu 5#$%&'( HID%JJK1?=1%L>M%&=D%J ! (0<N H OK1=G:J%&=D%J ! ( PPPPPPPPPPPPPPPPPPPQRPPPPPPPPPPPPPPPPPPPPP Ghi chúCán bộ coi thi không giải thích gì thêm S111 TUVWXT) SVY Câu 1: )*+,-      −=+ = + ++ '.#!Z!Z '#/ !Z Z! !Z . [S56+Z\!] ^_ [#' ⇔#Z . \! . '#Z\!'\Z!`/#Z\!' ⇔a#Z\!' . b.Z!c#Z\!'b/#Z\!'\Z!` ⇔#Z\!' 7 b/#Z\!'b.Z!#Z\!'\Z!` ⇔#Z\!'a#Z\!' . b/cb.Z!#Z\!b$'` ⇔#Z\!b$'a#Z\!'#Z\!\$'b.Z!c`  ⇔ . . Z ! $  #7' Z ! $#Z !'  #$' + − =   + + + =  ^_ d#7'⇒Z\!`$^eF>#.'%,f Z . \Zb$`.⇔Z . \Zb/`⇔ Z 7 ! g Z . ! . = − ⇒ =   = ⇒ =  (  #$'F+F-Z . \! . hF>Z\!]( ^_ ij!+=+>#b7Eg'E#.E.' ^_ TUVWXT) SVY Câu 4: 0<1?ABCD.@AM>%&B!C()DP, Q, R, S>1 %& MPMDMCMB $ =++ E MQMAMDMC $ =++ MRMBMAMD $ =++ E MSMCMBMA $ =++ -F8G;%&MPA = QB = RC = SD. )*k=%&M9>1()DG>%& MDMCMBMAMG +++= _ ( ^_ d MPMDMCMB $ =++ ^= GAPA _$ = ( ,3 GBQB _$ = ^ GCRC _$ = ^ GDSD _$ = (  W%=PA = QB = RC = SD ⇔ GA = GB = GC = GD.  TeABCD><1Je%,f%,lmO-G B O F> M >  %&  n!  :  Z1  %8  o ( ) ODOCOBOAOM +++−= (p&O:!9PA = QB = RC = SD(  TeABCD6*><1Je%,f%,lm- 6?O%&M( ^_ S111 TUVWXT) SVY Câu 2: 01 23 a ^ b ^ x ^ y 94%56+ 7 =− byax ( -189:;&< aybxyxbaF +++++= ( ieO ( ) $ 7 ba a y b xF ++       ++       += ( ^_ SH ( ) y;xM = ^       −−= a ; b A ^ ( ) 7 =−∆ byax: (= .       ++       += a y b xMA (> ( ) ∆∈ M   ( ) [ ] . . 7 ba ;AdMA + =∆≥ ( SI<Z*!6 M >-e; A   ( ) ∆ ( ^_ q! ( ) ( ) 7 $ 77 . $ 77 =+ + ≥++ + ≥ ba. ba ba ba F (  ij!  7 = Fmin  %O %,f  I  O  6 ( )         −= . . . / . ;;;y;x;b;a (  S111 TUVWXT) SVY Câu 3: 01ABC=1=A^B9%56+        . 7A \       . 7B `.       − . BA ( 0<1ABC>1%5( =# . 7A '\# . 7B '`.# $ '#7 BA + '# $ '#7 BA − '(  ≥ # $ '#7 BA + ']E# . BA − ']  ≤ . BA −  ≤ $ 7 BA − r π  ⇒ # . BA − ' ≥ # $ 7 BA − '  ⇒ # . BA − ' ≥ # $ 7 )BA( − '  d# . 7A '\# . 7B '`.# . BA − 'F># . BA − '] q!.# $ '#7 BA + '# $ '#7 BA − '] Q!# $ 7 )BA( − '](  pefFo# $ '#7 BA + ' ≤ ^=# $ '#7 BA + '# $ '#7 BA − ' ≤ # $ '#7 BA − ' W%=.# $ '#7 BA + '# $ '#7 BA − ' ≤ .# $ '#7 BA − ' ≤ .# . BA − '  i-Fj!e# . 7A '\# . 7B '`.# . BA − '-*=        = + − = − ' $ '#7 # $ 7 . BA BABA  ⇔ A`B` 7 π ( ij!1ABC>1%5(  S111 TUVWXT) SVY Câu 4: 0<1?ABCD.@AM>%&B!C()DP, Q, R, S>1 %& MPMDMCMB $ =++ E MQMAMDMC $ =++ MRMBMAMD $ =++ E MSMCMBMA $ =++ -F8G;%&MPA = QB = RC = SD. )*k=%&M9>1()DG>%& MDMCMBMAMG +++= _ ( ^_ d MPMDMCMB $ =++ ^= GAPA _$ = ( ,3 GBQB _$ = ^ GCRC _$ = ^ GDSD _$ = (  W%=PA = QB = RC = SD ⇔ GA = GB = GC = GD.  TeABCD><1Je%,f%,lmO-G B O F> M >  %&  n!  :  Z1  %8  o ( ) ODOCOBOAOM +++−= (p&O:!9PA = QB = RC = SD(  TeABCD6*><1Je%,f%,lm- 6?O%&M( ^_ S111 TUVWXT) SVY Câu 5: HID%JJK1?=1%L>M %&=D%J! ( 0<N H OK1=G:J %&=D%J! ( 0%Ls  #Z  E!  '^`^.^7^$^_( #Z  E!  '=&F>M,lf #.6E.6t'^#.6E.6t\'^#.6\E.6t\'^#.6\E.6t'Fo6^6t∈u ^_ W%1=_%L v! GS ^=G:.%L =D%JJJ26& ( ^_ p%=%&;%O2.%L:!w=D%J! ( WK1>? %&>!x5H O; K1%=(  Kiểm tra 45 phút (lấy điểm 15 phút) lần 1 Lớp 10A Câu 1#.%&'WBG!e+%5%&<j%8> yD1%5Nz Câu 2#$%&'0j { } { . 7A x x= ∈ + <¡ F> { } { 7 $B x x= ∈ − ≥¡ qkn||2%&- ^ ^A B A B C A∪ ∩ ¡ Câu 3#$%&'( )*+,-      −=+ = + ++ yxyx yx xy yx . /  Kiểm tra 45 phút (lấy điểm 15 phút) lần 1 Lớp 10A Câu 1#.%&'WBG!e+%5%&<j%8> yD-<1=%,lAN%5Nz Câu 2#$%&'0j { } { $ _A x x= ∈ + <¡ F> { } { 7 $B x x= ∈ − ≥¡ qkn||2%&- ^ ^A B A B C A∪ ∩ ¡ Câu 3#$%&'( )*+,-      −=+ = + ++ yxyx yx xy yx . /  Kiểm tra 45 phút (lấy điểm 15 phút) lần 1 Lớp 10A Câu 1#.%&'WBG!e+%5%&<j%8> yD1%5=%,l!eNz Câu 2#$%&'0j { } { 7 $A x x= ∈ + <¡ F> { } { 7 .B x x= ∈ − ≥¡ qkn||2%&- ^ ^A B A B C A∪ ∩ ¡ Câu 3#$%&'( )*+,-      −=+ = + ++ yxyx yx xy yx . /  . KY ̀ THI OLYMPIC TRUYÊ ̀ N THÔ ́ NG 30/4 L ̀ N THƯ ́ XIII TA ̣ I THA ̀ NH PHÔ ́ HUÊ ́ ĐÊ ̀ THI MÔN TOÁN LỚP 10   . OK1=G:J%&=D%J ! ( PPPPPPPPPPPPPPPPPPPQRPPPPPPPPPPPPPPPPPPPPP Ghi chúCán bộ coi thi không giải thích gì thêm S111 TUVWXT)