 TRƯNG THPT TRC NINH B ĐỀ KHO ST TRƯC K THI ĐI HỌC NĂM 2010 Môn: Toán !"#$%&' Bài 1(2 điểm): !' ()*+,&+-.&/00123&4'56+7 8 8 9 9 !' :9 9 !'y x x= + − 8' ;&</&<=5*>2?&@2?2ABC2DE5&.$&FG.$HI&2.': Bài 2(3 điểm): !' )I$DJ&<;  8 8 ! 8 8  !' 8' K x y x y xy x y x y  + + =  + +   − − + + − =   Lx y R ∈ ' 8' )$DJ&<;  8 8 + :& 5*+ 5*+8 :8 & 'x x x x x+ = − L0M x R ∈ ' N' ;&-52?$DJ&<;+F5AI&-5&<*2*O P QR 8        8 8 !S 8 !S8 !  !':*  8' R P'* R R # 8 m x m m x − − + − + − = − Bài 3(1 điểm): *&TUIV5A&,5V0FW5H2XVLVYQ5,55O NSA SB SC a= = = LZ#': </5OLV[DE&\G2?L+*5*YVY:]&?&]5B75A$:V &^*: Bài 4(2 điểm): !']&]5$H  ! 8 8 # :! 'x x dx + ∫ 8'<*_&$`&*O2axy 5*2?NQ!':bc$$DJ&<;2D&`UdF05e& 5fFUDJ5,5&<=5&g2axLy&T&-&OhLi+*5*UI&]5&,5hij\&: Bài 5(1 điểm): <*BW0MI&g2akGl5*2D&`U !  ! ! 8 Q ' ! 8 x t y t t R z t = +   = + ∈   = +  L2D&`U 8  *&FG.56_&$`h' 8kmGm!Y#0i' 8knGn8lmPY#:g*2?56 U!0U 8 :o.&$DJ&<;2D&`U N dF8QNQ!'L23&5e&2D&`U ! 0U 8 [ DE&&OV0+*5*&,5V5H2X: Bài 6(1 điểm): *x, y, z #≥ 0 8 8 8 Nx y z+ + = :T N N N 8 8 8 N 8 8 ! ! ! x y z y z x + + ≥ + + + ::::::::::::::::::.&::::::::::::::::::  TRƯNG THPT TRC NINH B KHO ST TRƯC K THI ĐI HỌC NĂM 2010 Môn: Toán !"#$%&' Đáp n vắn tắt: V! !' ! 2? aUF ? pA+7  8 8 9 9 !' :9 9 !'y x x= + − ⇔ GYk R q8k 8 n!' pr sQ  Q  x x y y →−∞ →+∞ = +∞ = +∞ Q N t R R Q t # #Q !y x x y x x= − = ⇔ = = ± pVV  #:8P pg52%B*)2LQ5-5&<4 #:8P po12%2&4 #:8P 8' ! 2? pg #' Ox∈ &@BC2DE52.'&.$&FG.$HI&: pD&`U2dF0MI+7A5B5A$DJ&<; GYBkq' pU&&56'B05XBI$&+F5AI R 8 N 8 !  '  ' R R x x k x a I x x k  − + = −  − =  #:8P pA 8 #  '  ' ! # k I A x =  ⇔  − =  *_5 8 8 R  !'  ' N R ! #!' x x k B x ax  − =   − + =   #:8P p@I'L5X5*&a&&.$&FG.UFG\&U! GY#:ocG2?&@BC2DE5N &.$&FG.$&M'5[026IV'$)5A8I$kQB'0MkB,5 ! ± L &T5$DJ&<;!'$)5A8.$kB,5 ! ±  #:8P (i  N N ! ! 8 8 a a− ≠ < − ≠ >hoÆc #:8P V8  aUF ? !' ! 2? pI 8 8  !'  !' P  !' !'u !'  !'v K x y x y x y  − + − = ⇔  − − − + − =  :_& ! ! u x v y = −   = −  L&F2DE5I 8 8 P  ' K u v uv u v  + =  + =  #:8P p)<2DE5  N : 8 u v u v + =   =  Qp)<2DE5  ! ! ! 8 u x v y = − =   = − =  *_5 ! 8 ! ! u x v y = − =   = − =  #:P# N 8 x y =  ⇒  =  *_5 8 N x y =   =  #:8P 8' ! 2? p( 5*+ #x ≠ :h N N + 5*+ 5*+8 :85*+ + 'x x x x x⇔ + = − #:8P + 5*+ ':5*+ :8+ 5*+ ' #x x x x x⇔ + − = #:8P + 5*+ #Q8+ 5*+ #x x x x⇔ + = − = #:8P ! Q <5& Q L ' R 8 x k x l k l Z π π π ⇔ = − + = + ∈ #:8P N' ! 2? ph 8 !S 8 !S 8  !':*  8'  P'*  8' ! #m x m x m ⇔ − − − − − + − =  p_& [ ] !S 8 P *  8'L QR !Q! 8 t x x t   = − ∈ ⇒ ∈ −     #:8P F2DE5$&  8 8 P !  ' ! t t m f t t t − + = = − + Q 8 8 8 R R t ' Q t ' # !  !' t f t f t t t t − = = ⇔ = ± − + #:8P pbc$VV56w&'&</2*O [ ] !Q!− L&\Gw&'/&=50V&</2*O [ ] !Q!− L/ x NQ N m   ∈ −     &jy2f: #:P# VN  ! 2? pH2D5*56&TUIO&@2X&<F2?565O #:8P p]2DE5 N : NR !8 S ABC a V = #:8P p2DE5 : : 8 : z S MNC S ABC V V=  #:8P N :V : x x NR : z !#" S ABC a V V⇒ = = #:8P VR  !' ! 2? p] ! 8 8 # :! 'I x x dx = + ∫ p_& 8 8 8 N 8 ! ' ! ! N x du dx u x x dv x dx v x  =   = +   + ⇒   =    =   ! ! R N 8 8 # # ! 8 :! ' N N ! x I x x dx x ⇒ = + − + ∫ #:8P p] ! ! R 8 8 8 # # ! 8 u ! v ::: ! ! N R x J dx x dx x x π = = − + = = − − + + ∫ ∫  #:P# pocG ! R : 8 N z K I π = + + #:8P !' ! 2? p@&&5A  Q#'Q #Q 'L #L #:P a Q b a b> > pU5A$&  ! x y a b + = : #:8P UdFNQ!'/ N ! N ! ! 8: 8: Nab a b ab + = ⇒ ≥ ⇒ ≥ :\F{k)G<B05X B K N ! 8 a b a b =  = ⇒  =  #:8P pA ! : : N 8 OPQ S a b ∆ = ≥ :/ OPQ S ∆ j\& N= 'B05XB K 8 a b =   =  #:8P pocGU5A$&  ! K 8 x y + = #:8P VP  !' ! 2? pU 8 5A$&  ! ! ! ! ! 8 Q ' N 8 x t y t t R z t =   = − + ∈   = −  p;2DE5!Q!Q!' #:8P 5AV!n&Q!n8&Q!n8&'L& ! Qq!n8& ! QNq8& ! 'L 2B VB,5LB,5 ! #L !t t⇒ ≠ ≠ ' p,5V5H2X !' u L v # 8' IB IC AB AC =    =   uuur uuuur ur : #:8P ! ! ::: 8 t t =  ⇔ ⇔  =  : #:8P p@2A5A$&U N   8 N Q ' ! 8 x y t R z t =   = ∈   = +  #:8P Bài 6: !' ! 2? 5A onNY N N N 8 8 8 8 8 8  '  '  ' ! ! ! x y z y z x y z x + + + + + + + + #:8P N N 8 8 8 K !  ' R 8 R 8 8 ! 8 ! x x y VT y y + ⇔ + = + + + +  N N 8 8 8 !  ' R 8 8 ! 8 ! y y z z z + + + + + +  N N 8 8 8 !  ' R 8 8 ! 8 ! z z x x x + + + + + + #:8P K K K N N N K N N N R 8 !K 8 !K 8 !K 8 x y z VT + ≥ + + #:8P 8 8 8 K N N N z  ' 8 8 8 " 8 8 8 VT x y z⇒ + ≥ + + = K N z N z N N 8 8 8 8 8 8 8 8 8 VT VP⇒ ≥ − = − = = 2$5' \F{k)G<B05XBkYGYlY!' #:8P .  TRƯNG THPT TRC NINH B ĐỀ KHO ST TRƯC K THI ĐI HỌC NĂM 2010 Môn: Toán !"#$%&' Bài 1(2 điểm): !' ()*+,&+-.&/00123&4'56+7 8. + ::::::::::::::::::.&::::::::::::::::::  TRƯNG THPT TRC NINH B KHO ST TRƯC K THI ĐI HỌC NĂM 2010 Môn: Toán !"#$%&' Đáp n vắn tắt: V! !' ! 2? aUF