THI TUYỂN SINH lớp 10 THPT CHUYÊN QUỐC học HUẾ năm học 2012 2013 môn TOÁN

  !"#$%&'())*)+ ), )) /012345%6(78 Thời gian làm bài : 150 phút (không kể thời gian giao đề) 9:6(2,0 điểm)  ( ) ( )       x y x y x x y y  + = + +   − − =   9:6)(2,0 điểm) u, v ( ) ( )        u u v v v + + − + − + = !"    u v uv + + = 9:6+(2,0 điểm) #$%&'()&'*(+,-.)/#-0''1+ #$0./ 2$0 3 456)7#$%&'(-8456)7 #$%&'1(-9):;.#4#$03<7: ;/#4#$03 2$0=,.)7#$03+ #$%&'(>"#?"@)+#$%&'*(>"#?"A B@+A9 - 2$0@A+/)9/<C<D-E) (!"!/9F4#D#$% G(!""E<"H  9:6,(2,0 điểm) (B",>I<Jx, y, zK"L#M$#N,:, xOyOz)     x y z + + = G(!"PM-Q,>I  8  8  8RR8 Q    O  O  ORRO Q )    Q Q            + + + + + = 9:6;((2,0 điểm) (!"PISTU!#VP"W> "F#$%G:SX<,YKWGPX  G(5)<I#Z5[\ B"]K^T       5 x y T y x y + = − ______E4_______ Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm. E`)>SRRRRRRRRRRRRaGIRRRRRRRRRRRRR U:bT"]RRRRRRRRRR U:bT"]RRRRRRRR  <  !" 24/6/2012 /01 234(78 =>?2 Bài 1 (2đ) 6@6%AB%CD4E5FG4%( ( ) ( )       x y x y x x y y  + = + +   − − =   E#L#)7 ( ) ( )     & ( & (   x x y y x x y y  − + − =   − − =    Q8cQ 2W,\5  _58)\  _ d     d u v u v uv u v  =    = + =    ⇔   = =     =    Q8cQ e7,\df)\     d    x x x x y y y y  = −    =  − =   ⇔   = − − =       =   B$Dg"&_f_(8&_f(8&f_(8&f( Q8cQ e7,\f)\d       d  x x x x y y y y  = −    =  − =   ⇔   = − − =       =   B$Dg"&_f_(8&_f(8&f_(8&f( E#L"&_f_(8&_f(8&f_(8&f(8&_f_(8&_f(8&f_(8&f( Q8cQ Bài 2 (2đ) %H'I'JK5%L'MNOJPH'%H( ( ) ( )        u u v v v+ + − + − + = %Q4E$64%(    u v uv + + = B;4 ( ) ( )       & (    & (  u u v v u u v v + + − + − + = ⇒ + + = − + − + Q8cQ ( ) ( )       & (    & (  u u v v u u v v + + − + − + = ⇒ + − = − + + − Q8cQ a,       & ( 8   & ( u v u v u v u v + − = + − − + + − = − + + − + Q8cQ 9#,[)\ a,     & ( & (  u v uv u v u v uv uv + + = + − + + = Q8cQ Bài 3 Câu a (1 đ) %Q4E$64%9R:5QE6I'4S656TBUCV'5FH4EUCW4E5FX4Y Q8c `h<#?"T./)9 B ∠ /h\ ∠ @.&9.@/F4#$%&'(( i ∠ @.\ ∠ 9&99jj@A(> ∠ /h\ ∠ 9 Q8c B ∠ 9/h\ ∠ 9 Q8c B;# ∠ /9[ ∠ 9\ ∠ /h[ ∠ 9/h[ ∠ 9 \ ∠ 9[ ∠ 9[ ∠ 9\Q   9#/9<!F4#D"F#$% Q8c Bài 3 Câu b (1đ) %Q4E$64%FZ4E5P$E6I'R:5P$E6I''[4Y B ∠ 9\ ∠ @.\ ∠ .9 B ∠ 9\ ∠ .9 9#39\3.9 a,\.89\9. #?"89P"> ,. B;#9 ⊥ .  Q8c 9Ejj9>k. ⊥ E&( Q8c 9 ∠ .h\ ∠ /h>3.hl3/h a,h  \h. h/ Bh9  \h. h/ 9#h\h9 Q8c 99jjE> h .E \ /h /. \ h9 . ih\h9>.E\. &( B;&()&(,"EH- Q8c Bài 4 Câu a (1 đ) G$'I'JK4EM\]4^CD4ER_`N\Na5%bP$c4Ud4E5%W6'I'U6eMf6A4JPM( `g\gaO:     x y z + + = B  x O   O  x >mn5n 95<J>5\oW5\c Q8c p4,5\o  y [  z \ g   qgr\&[r(q&g_(&gr_(\  o  9<J8oOOr>oOg_Ogr_ p4,gs\m:Y,> B$D:Y8rKG Q8c p4,5\c  y [  z \  c qr\c&[r(q&_c(&r_c(\  c  9<J8cOOr>_cV?<8c8m etV$D5\c8\m8r\gcK>,C,TG Q8cQ Bài 4 Câu b (1đ) %Q4E$64%FZ4E5d45h6)+JK4EM\]4^CD4EP  NP ) NP + NiiNP )+ JPH'%H( P  gP ) gP + giigP )+ O:    Q Q            + + + + + = B\   [   [  d Q8c u-  c [  m [  gc \   q  n \  cn [  mn [  gcn )7"`,>I Q8c 9#\   [    c m gc   + +  ÷   [ d  \   [ c  [ d  [ m  [ gc   gc  \ c   \ c c  [ c m  [ c gc  f\   [ c  [ d  [ m  [ oc  [ c  [ ( )   c Q8c B=,>>"QQ<C8IL,>I  8  8  8 8 Q  K"L>,C,TG Q8c Bài 5 Câu a (1đ) %Q4E$64%FZ4E^6A45j'%'kP4%l4E5QE6I''m'I'Un4%4Z$5FH4E%Ho' 5F]4$S5UCW4E5FX4pI4fj4%qRM344%b%D4%Ho'pZ4E)q ) Y `./9<!P"%&'8X( '.vX8'/vX8'vX8'9vX p4,'P"&W>(!./9a ./9 \a './ [a '/ [a '9 [a '9. p4,'P"!./9a ./9 Oa './ [a '/ [a '9 [a '9. 9#<,Ya ./9 va './ [a '/ [a '9 [a '9. Q8c Ba './ \   '. /Ev   '. '/v   X  &/E<N,T3'./( Q8c Ba '/ v   X  8a '9 v   X  8a '9. v   X  Q8c e)ta ./9 v   X  [   X  [   X  [   X  \X  Q8c Bài 5 Câu b (1đ) %H`O:\R:'I'JK5%L'^CD4E5%P\Ur6JPH'%H`s\t)Y G$E6I5Fu4%b4%v5'kP       5 x y T y x y + = − Y B     5 & ( x y T xy + = −   Q  & ( Q  x y xy xy xy xy + ≤ = ⇒ < ≤ ⇒ − > Q8c       & ( g  & ( & ( & ( xy y x y x y xy T xy xy xy xy xy xy + + + ≥ ⇒ ≥ = = − − − Q8c  & & (( Q & (  g g xy xy xy xy T + − < − ≤ = ⇒ ≥ Q8c 9^,#0!5:)V:5\\ w\E6I5Fu4%b4%v5'kPR:, Q8c . G(5)<I#Z5[ B"]K^T       5 x y T y x y + = − ______E4_______ Thí sinh không được sử dụng tài liệu. Giám thị không giải thích gì thêm. 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