DE THI THU DH NANG CAO

    !"#$%" &'()(*"+,-.,(/01&23 45 Câu I (2 đim)6&$&,-78 9  9 : /; /y x x m x= + + + + <=>?3&@+,: - ; /6 &A$7%3B,BC>?3&@&,-78D&(-E6 6 F-"&G"))(%3H@<I*->J>K'")3&L") /y x= + <M3>?3&@: - ;3N(9>(J-1&O".(P3:Q/;RSR 7*$<&$<%<3(T13UVT"<I*: - ;3N(SB,BU!"))=<BW("&*U6 Câu II (2 đim)6 1. (A(&P1&KX")3HF"& 9 9 9 9 x y y x  + − =   + − =   2. (A(1&KX")3HF"& 97("7("7("  =++ xxx Câu III (2 đim) /6 Y"&3&J3Y<&BZ33&J3H["\$*V7("&H*D&(]U*V&F"&1&L"))(W(&N".^(>K'")3H["3O-:Q;.%" DY"&E/]U*"&3H_<&$,"&6 6 H$")D&!"))(*"<&$&*(>(J-RS<8>@"&R>`a,(>$N"SE*b6\B,SV+,&*("c* >K'")3&L")BU!"))=<BW("&*UB,<d")BU!"))=<BW(S6He"\B,SV+fV&*(>(J-B,7*$ <&$E.:BW(.+,-`378<&$3HKW<B,.b*;6 *; g%<>@"&3O-B,.%"DY"&-h3<iU")$N(3(T13ja(P"S6 .; g%<>@"&B@3HY<I*B,7*$<&$3ja(P"S<=3&J3Y<&+W""&f36 Câu IV (1 đim).F-->J.f31&KX")3HF"&7*U<=")&(P-# 9  / : /; :/ ; /x m x m x+ ≥ + + − + 6 k#Mỗi thí sinh chỉ chọn câu Va hoặc Vb Câu Va (3 đim;6Chương trình cơ bản /6 H$")-h31&L")3l*>`4\VR<&$>(J-:9Q/;B,&*(>K'")3&L")<=1&KX")3HF"&+, / #  / d x y− + = B,  #  9 d x y+ − = 6m(T31&KX")3HF"&>K'")3&L")>(]U*B,3N$BW(&*(>K'") 3&L") /  ,d v d -`33*-)(%<<O"<=>n"&+,)(*$>(J-<I* /  ,d v d 6 6 H$")D&!"))(*"BW(&P3l*>`4\VoR<&$&*(>K'")3&L") / /  / #  / / x y z− + − ∆ = = −  /  9 #  /  x y z+ − − ∆ = = − B,-h3<iU:;#\  pV  po  pq\rVpsoptE6m(T31&KX")3HF"&-h3 1&L")3T1\2<BW(-h3<iU:;>?")3&'(7$")7$")BW( / ∆ B,  ∆ 6 96 F-1&i"3&u<<I*781&j< ( )  / i− Câu Vb. (3 đim).Chương trình nâng cao /6 H$")-h31&L")3l*>`4\VR<&$v+(1 : ;E <=1&KX")3HF"&   / q x y + = B,>(J-:r/Q/; m(T31&KX")3HF"&>K'")3&L")>(]U*>(J-B,<M3 : ;E 3N(&*(>(J-RS7*$<&$+,3HU")>(J-<I* >$N"3&L")S6 6 H$")D&!"))(*"BW(&P3l*>`4\VoR<&$9>(J-:/Q9Qr;RS:QQ/;R:QQ/;6F-3l* >`<I*>(J-7*$<&$  pS  p  >N3)(%3H@"&w"&f36 96 (A(.f31&KX")3HF"&  q Rt  /s +$) q+$) q +$)x x x+ ≤ − xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-; yyz OU { `(aU") (J-   / / g|E ¡ u.(T"3&(e"#V}E9\  ps\p9E9:\p/;    x≥ ∀ ∈¡ ,-78>?").(T"3He" ¡ ,-78D&!")<=<u<3H@ (W(&N"# +(- x y →±∞ = ±∞ SA").(T"3&(e" \ −∞  +∞ V} pp V +∞ −∞ ?3&@ V / r/4 \ t 9 t t  / &KX")3HF"&&$,"&>`)(*$>(J-<I*>?3&@: - ;B,>K'")3&L")VE\p/ \ 9 p9\  p-\E   9  x x x m =  ⇔  + + =  K'")3&L")VE\p/<M3>?3&@: - ;3N(9>(J-1&O".(P3D&(B,<&nD&(   : ; 9 g x x x m= + + = <=&*(")&(P-1&O".(P3D&%<D&(B,<&nD&(   q  q :;    m m g m m  ∆ > − > <    ⇔ ⇔    ≠ ≠    ≠  :~; &(>=&$,"&>`<I*SB,3&w*-•" 9 6 B C B C x x x x m + = −   =  :/; *<=€}:\;E9\  ps\p-p/ P78)=<<%<3(T13UVT"3N(SB,+,€}:\ S ;E  9 s / B B x x m+ + + R€}:\  ;E  9 s / C C x x m+ + + %<3(T13UVT"3N(SB,BU!"))=<D&(B,<&nD&(€}:\ S ;6€}:\  ;Er/ ⇔ :  9 s / B B x x m+ + + ;6:  9 s / C C x x m+ + + ;Er/ ⇔ :  9 s B B x x+ ;:  9 s C C x x+ ;p:-p/;:  9 s B B x x+ p  9 s C C x x+ ;p:-p/;  Er/ ⇔   : 6 ; /0 : ; 9s 9: /;:: ;  9: ;; B C B C B C B C B C B C B C x x x x x x x x m x x x x x x+ + + + + + − + + t t t xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-; p-  p-pE T3&•1BW(:/;3*>K•<  -  ‚tq-p9s-p9: ‚-r ;p-  p-pE ⇔ t-  ‚//-p/E ⇔ // / / m ± = 3&w*-•">(ƒUD(P":~; T3+UZ"#mW( // / / m ± = 3&F3&w*-•"VeU<iU6 t   / / (ƒUD(P"#  9R 9x y≤ ≤ ≤ ≤ *<= 9 9 9 9 x y y x  + − =   + − =   ⇔  :9 ;   :9 ;  x y x y y x y x  − + − =   − + − =   :9 ; :9 ;  :9 ;  :9 ;  x y y x x y y x ⇒ − + − = − =  ⇔  − =  ⇔   9 9 x y x y  =    =    =    =    (J-3H*3*3&fV  9 R  9 x x y y = =     = =   3&w*-•"6 T3+UZ"#P<=&P<=&*(")&(P-  9 R  9 x x y y = =     = =   t t t t  / *<= 97("7("7("  =++ xxx  / $7\ / $7s\ 7("     c c x − − ⇔ + + =    $7 $7s :/ 7("  ;  $7 6 $7q $7   $7 : $7q $7 ;  c x c x x c x c x c x c x c x c x ⇔ + + − = ⇔ + = ⇔ + =  $7 c x⇔ = &$h<<$7q\p<$7\E $7  q  c x x k π π = ⇔ = + R <$7q\p<$7\E $7q $7:  ;c x c x π ⇔ = −  s 9  x k x k π π π π  = +  ⇔   = − +   T3+UZ"#&KX")3HF"&<=.*&l")&(P- q  x k π π = + R , s 9  x k v x k π π π π = + = − +  t t t t   / / K'")3H["3O-:Q/;.%"DY"&E/<=1&KX")3HF"&#:\r;  p:Vr/;  E/ (ƒUD(P"# / 9x ≤ ≤ 6„1&KX")3HF"&>K'")3H["3*<=  / / : ;y x= + − − BW( /y ≥ xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-; m,  / / : ;y x= − − − BW( /y ≤ 6 &J3Y<&BZ33&J<i"3F-  ( ) ( ) 9 9     / / 9  / / / : ; / / : ; q / : ; V x dx x dx x dx π π π = + − − − − − − = − − ∫ ∫ ∫ h3\‚E7("3BW(   x π π − ≤ ≤ 6 \E/ ⇒ 3E  π − \E9 ⇒ 3E  π a\E<$73a3R  / : ;x− − E<$736 mZVmE    q $7c tdt π π π − ∫ E     :/ $7 ; c t dt π π π π − + = ∫ t t t t  / *; l(+,3HU")>(J-<I*6 *<= RBN AB BN AM BN BM⊥ ⊥ ⇒ ⊥ \ a$>=3*-)(%<SBU!")3N(S7UVH*SE  MN R   3KX")3uE  MN 6 mZVESEEE  MN E  b  O--h3<iU")$N(3(T1+,R.%"DY"&E  b S .;h3E\bRSEVb  *-)(%<SBU!")3N(S"e"  ES  pS  V *-)(%<BU!")3N("e"  E  p  UVH*.  E  E  pS  pS  E\  p*  pV   |$>=\  pV  E.  ‚*  D&!")>…(6 ja(P"S<=>%V+,SR>K'")<*$S6 &J3Y<&     / / / *\ : ; : ; s / / V y a x y a b a= ≤ + = − 6 &J3Y<&3ja(P"S+W""&f3D&(ESE    b a− 6 t t t t m / *<= 9  / : /; :/ ; /x m x m x+ ≥ + + − +    : /;: /; : /; : /;x x x m x x x⇔ + − + ≥ − + + + (ƒUD(P" /x ≥ − xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-; &(>=.f31&KX")3HF"&3KX")>KX")BW(   / / / / x x m x x x x + + ≥ + − + − +  ⇔   / / / / x x m x x x x + + − ≥ − + − + :~; h33E  / / x x x + − + R.f31&KX")3HF"&:~;<=aN")#3‚3   m≥ :/; *<=       † R †  / 9 / : /; / x x t t x x x x x x − − + = = ⇔ = − + + − + − + 6 SA").(T"3&(e" \ r/ / 9− +  +∞ 3} p r 3  9  9 9 +    mZV // ‡ 9 Q /9 t   +   ∈     6Sf31&KX")3HF"&>•<&$<=")&(P-D&(B,<&nD&(:/;<= ")&(P- // ‡ 9 Q /9 t   +   ∈     D&(B,<&nD&( // ‡ 9 ˆQ ‰ /9 *\ : ; t M f t m + ∈ ≥ BW(€:3;E3‚3  €}:3;E/‚3 SA").(T"3&(e" 3  /   9  9 9 + €}:3; p r €:3;  / q „.A").(T"3&(e"# // ‡ 9 ˆQ ‰ /9 / / *\ : ; q  t M f t khi x + ∈ = = mZVV<.33KX")>KX")BW( / q m ≤ t t t t m* 9 / / K'")3&L")>(]U*:9Q/;<=aN") # *\ 9 by a b∆ + − − = K'")3&L") ∆ 3N$BW(&*(>K'")3&L") /  ,d v d -`33*-)(%<<O"<=>n"&+,)(*$<I* /  ,d v d D&(B,<&nD&( /  : R ; : R ;d d∆ = ∆  /  $7: Ra ; $7: Ra ;c c⇔ ∆ = ∆ t xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-;        t: ; t: ;   a b a b a b a b a b a b − + ⇔ = + + ⇔ − = +   a b a b⇔ − = + &$h<  a b a b− = − −  9 a b ⇔ − = &$h< 9 a b + = &l"*E9R.E/&$h<*E/R.Er96 mZV<=&*(>K'")3&L")3&w*-•"VeU<iU.,(3$%"9\pV‚/EB,\‚9VE t t t  / mv<3X<&n1&KX")<I* / /  / #  / / x y z− + − ∆ = = − B,  /  9 #  /  x y z+ − − ∆ = = − +i"+K•3+, :Q /Q/;R : Q/Q;u v= − = − r r 6h31&L"):;7$")7$")BW( / ∆ B,  ∆ "&Z"<h1Bv<3X :Q /Q/;R : Q/Q;u v= − = − r r +,-<h1Bv<3X<&n1&KX")6 *<= ( ) / / /   / Q Q 9Q sQ 9:/QQ; /     / n   − − = = − − = −  ÷ − −   r 6h31&L"):;<=aN") :;#\pVp-E6 h3<iU:;<=3O-:rQ/Qr9;B,.%"DY"&E96 h31&L"):;3(T1\2<BW(:;D&(B,<&nD&(      : R: ;; 9 9 t /   m d I P R m − + + = ⇔ = ⇔ = ± + + mZV<=&*(-h31&L")3&w*-•"VeU<iU+,\pVp 9 t EB,\pV‚ 9 t E6 t t t t 9 / *<= ( ) ( ) ( ) /q   /q /q /q /q / / :/ ; :  ; :/ ;  :/ ;   i i i i i i i − = − − = − − = − = −  mZV1&i"3&u<<I*781&j<3He"+, /q  t t t t m. 9 / / K'")3&L") ∆ >(]U*:r/Q/;<=aN") / / x at y bt = − +   = +  :   a b+ ≠ ; RS / / / / A A x at y bt = − +  ∈∆ ⇒  = +  B,   / / B B x at y bt = − +   = +  6 +,3HU")>(J-<I*SD&(B,<&nD&(   A B M A B M x x x y y y + =   + =  /    /  /  : ;   :/; : ; : ;  a t t t t do a b b t t + =  ⇔ ⇔ + = + ≠  + =  RS : ;E∈ 7UVH*3 / R3  +,&*(")&(P-<I*1&KX")3HF"&q:r/p*3;  p :/p.3;  E9s  q   :q ; :0 /0 ; 9 a b t a b t⇔ + − − − = 6 3 / p3  E 0 /0  q a b a b ⇒ − = ⇔ − = 6&l"*E R.Eq mZV>K'")3&L")<i"3F-<=1&KX")3HF"& / / q x t y t = − +   = +  t t t t xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-;  / l*>`3Hl")3O-3*-)(%<S+,:/Q/Q; *<=  ( ) ( ) ( )                   S  9 : ; 9 MG GA MG GB MG GC MG GA GB GC MG GA GB GC MG GA GB GC GA GB GC + + = + + + + + = + + + + + + = + + + ≥ + + uuuur uuur uuuur uuur uuuur uuur uuuur uuur uuur uuur mZV  pS  p   ≥    GA GB GC+ + afU.Š")\AVH*D&(B,<&nD&( M G≡ t t t t 9 / *<=  ( ) q /s  q  Rt  /s Rt    q Rt  /s           q +$)  +$) q+$) q +$) +$) q+$)  +$) q+$) q +$) q +$)  +$) +$)  +$) +$) /s 0+$) +$)  x x x x x x x x x x x x x x x x x  − ≥   + ≤ − ⇔ + ≥   + ≤ −   − ≥   + ≥  ⇔  + ≤ − +   >     0  +$) t +$)   sq / t /  q x x x x x   ≤ ≤     ⇔  ≤ −     >   ≤ ≤  ⇔   < ≤   Z1")&(P-<I*.f31&KX")3HF"&+,E sq / ˆ/Q ‰ :Q ‰ t q ∪ t t t t   xT3x :%".`<$(3&(D&!"))(A(3&Y<&)F3&e-; . F-1&i"3&u<<I*781&j< ( )  / i− Câu Vb. (3 đim).Chương trình nâng cao /6 H$")-h31&L")3l*>`4VR<&$v+(1 : ;E <=1&KX")3HF"& 