!"# !$ %&'( Thi gian lm bi: 180 pht không k thi gian giao đê )*!+, /0 y x x= − !"#$%&'()*+',-." )*+!, /0 )",' α /)0 π α π < < 1 2 α = 34 ) A α α + = 5'6/)07 2z i z i− = + 348%'()5' 9 z z= + )*1+ 2$, /0 : !"#$)%7 ( ) ( ) ;" ;" x x− + − = )*"+!, /0 :< !"#$)%7 x x x x x + − + + > − − + )*$+!, /0 344'=)% ( ) ;I x x x dx= − ∫ )*3+!, /0 $',S.ABCD',&ABCD;$%>"'*a?)"'@AB'=*S. #CD"%>"",'ECD"ABCD:F M ;#%"+'()CDG H;$ '%%>"",''()D #@HGI",'"J))CD"SBCABCD."KL 34 +4'M',S.ABCDM"''NHCD"SBC Oa )*4+!, /0 3#"M>"")EPF)-QR&6' S"D"dCD"P', !"#$ 2 7 1 x y z d − + − = = − G ( ) 7 LP x y z+ − + = 3$F)-")+I '() S"D"d CD"P !"#$CD"Q""EP''P -M" ." )*5+!, /0 3#"CD"EPF)-QR&$%>"AIB',+GT:F+U?;V ; W;#%"+'()BABGHTGT;")'()IUA3$F)-''X'Y;* '()$%>"AIB+I',-8 !" )*6+ 2$, /0 Z# S"3[\3[]Z);^,F'_,',1F'+'`,' )'()# S"?_, W''FN-R%"M4'# S""1F'M L?1F'M1F'M34R'%<+_,',CF' M )*! +!, /0''8 !"a, b, c)&a/)0 a b c+ + ≤ 3$"#/ <'()+%5'7 ( ) ( ) ( ) b b b a b c P b c c a a b = + + + − − + − − + − − #################78################ - Họ và tên thí sinh & Số báo danh : - Thí sinh không đưc s dng tài li!u - Cán b$ coi thi không gi%i thích g& thêm. 9:; < !"# !$ %'( = >8?@ABCDEB-ABF/GH- TZ'<8 E=&8);S"!; W''()-'''<"M 'V&%'V%#$&;S"V&(?'?W;"'',+')/L?2 + T34;O''M'Ec"$a'<'V"<'+ !"5"E)"+'() TZ+;a"+'''=%M>";#Y = IJIKL8BMKN, / )*!+, /0 y x x= − !"#$%&'()*+',-." O != ! d3eZ7Bfg L2 d:E*7 ; x y →±∞ = ±∞ ZM>"',P'^ h K L h L y x x x y x = − = = ⇔ = L2 dII3 R −∞ L +∞ &h dLTLd & L +∞ −∞ T1 d[*''**R ' fLG& ' fL [*''+%*R ' fG& ' fT1 L2 d["#''M" ( ) GL−∞ ( ) G+∞ ["'#M" ( ) LG dZ 6 4 2 -2 -4 -6 -10 -5 5 10 L2 = !"#$%&'()*+',-." ! :i+H G o o x y L2 E o o x y= ⇒ = − ( ) h f⇒ = − L2 ^& !"#$%&'()*+HGT; &fTRTT)&&fTRd L2 )*+!, /0 )",' α /)0 π α π < < 1 2 α = 34 ) A α α + = 5'6/)07 2z i z i− = + 348%'()5' 9 z z= + ! )$ π α π < < LG' L α α > < L2 )', j ' 2 c x α α + = ⇒ = ;*', ' 2 x = − $ ' L α < L2 @%&#) 1 2 ) 2 2 ' 1 ' k 2 2 A α α α α α α + − + ÷ + = = = = − ÷ L2 ZC ( ) ?z a bi z a bi a b R= + ⇒ = − ∈ L2 3)',7 ( ) ( ) ( ) ( ) 2 2 2 2 1 z i z i a bi i a bi i a b a b i i a b a a b b − = + ⇔ + − − = + ⇔ − + − + = + − = = ⇔ ⇔ − + = = @%&#) 1z i= + L2 ( ) ( ) 9 1 1 1 b 9 L i i i= + + + = − + ⇒ = L2 )*1+ 2$, /0: !"#$)%7 ( ) ( ) ;" ;" x x− + − = Z]%MPRl L2 3)', ( ) ( ) ;" ;" LPT x x⇔ − + − − = ( ) ( ) 2 ;" 2 ;" b x x x x = − = ⇔ ⇔ = − = − 3/)0]%MP L2 ^& !"#$',"P;Rf2Rf 2 b )*"+!, /0:< !"#$)%7 x x x x x + − + + > − − + Z]%MP7 L L L L x x x x x x ≥ + + ≥ ⇔ ≥ − − + ≠ L2 3)', L 1 x x x x − + = − + ≥ > ∀ ≥ ÷ %&#) Lx x− − + < L2 BPT x x x x x⇔ + − + < + + x x x x ⇔ + + − < + + $RfLM>"/)0< !"#$ L2 ZC x t t x + = ⇒ ≥ $ Lx > 3)', 1 t t t t+ − < + ⇔ − < ⇔ < @%&#) 1 1 t x x ≤ < ⇒ ≤ + < ( ) L L2 L2 b b 1 1 L 1 x x x x x x x x + ≥ − ≥ − + ⇔ ⇔ ⇔ < < − + < + < L2 )*$+!, /0344'=)% ( ) ;I x x x dx= − ∫ 3)', ( ) ; ;I x x x dx x dx x xdx= − = − ∫ ∫ ∫ L2 34 1 x I x dx= = = ∫ L2 34 ;I x xdx= ∫ ZC ; dx du u x x dv xdx x v = = ⇒ = = ; ; ; 1 1 x x x x I dx= − = − = − ∫ L2 1 K2 ; ; 1 I I I⇒ = − = − + = − L2 )*3+!, /0$',S.ABCD',&ABCD;$%>"'*a?) "'@AB'=*S.#CD"%>"",'ECD"ABCD:F M ;#%"+'()CDGH;$'%%>"",''()D #@HGI",'"J) )CD"SBCABCD."KL 34+4'M', S.ABCD M"''N[CD"SBC Oa J M I C A B D S H :FI, J;V; W;#%"+'()ADBC $SAD ⊥ ABCDSI ⊥ ABCD )',IJ ⊥ BCSI ⊥ BC%&#)",'"J)SBCABCD; ¶ KL o SJI = IJf) L2 3#")"'%>"SIJ )',SI f IJ)KL f a SJ SI IJ a= + = L2 BP4'&;@ ABCD f) 3+4'M',S.ABCD; @AIB f ABCD a SI S a a= = 5"CD ⊥ SAD3#")"'%>"SDM',7 1 SH SD SM SM = = L2 3)', 1 SHBC SMBC V SH V SM = = 1 Kb SMBC BCM SHBC a a a V SI S V ∆ = = ⇒ = = m*', SBC S BC SJ a a a ∆ = = = ( ) Kb ? 2K SHBC SBC a V a d H SBC S a ∆ ⇒ = = = )*4+!, /03#"M>"")EPF)-QR&6' S"D"dC D"P', !"#$ 2 7 1 x y z d − + − = = − G ( ) 7 LP x y z+ − + = 3$ F)-")+ I '() S"D" d CD"P !"#$C D"Q""EP''P -M"." :FI(1+2t; -2-3t; 5+4t) ∈ d I P. $I ∈ P)', ( ) ( ) ( ) 2 1 L t t t t+ + − − − + + = ⇔ = − ( ) GGI⇒ − L2 $QnnP"FQ',8*" Lx y z m+ − + = L2 ( ) ( ) ( ) ( ) ( ) G G 1 1 d P Q d I Q m m m m = ⇔ = = − + − + ⇔ = ⇔ − = ⇔ = − + + ^&',CD"Q'V$; Lx y z+ − + = Lx y z+ − − = L2 )*5+!, /03#"M>"")EPF)-QR&$%>"AIB', GT:F+U?;V; W;#%"+'()BABGHTGT;")'() IUA3$F)-''X'Y;*'()$%>"AIB+I', -8 !" N J M K I C D A B :Fo;#%"+'()AIM,Ao;$$ ⇒ Anno :Fo ∩ IHfp ⇒ p;#%"+'()IH L2 5" W'A ⊥ IUN,%&#))"'IH;)"''=* 3)', ( ) G LMC MC− ⇒ = uuuur uuuur ⇒ HfIHfAIf L 3#")"'%>"AIH', 2 AB BM BI BM AB AI BM AB BM= = + = ⇒ = ⇒ I;")'()) S"#YG L HG 3F)-+I/) 07 ( ) ( ) ( ) ( ) L b x y x y − + + = + + + = ⇒ IG L2 \ !"#$ S"D"AI',8*"7RT&dfL \ !"#$ S"D"AH',8*"7Rd&dfL ⇒ ATGL L2 3)', ( ) G BA CD D= ⇒ − − uuur uuur L2 )*6+ 2$, /0Z# S"3[\3[]Z);^,F'_ ,',1F'+'`,')'()# S"?_, W''FN -R%"M4'# S""1F'ML?1F'M?1F' M34R'%<+_,',CF'M :F Ω ;M>"")q%7rF,F'_,',1F' W' ;<&NF'#"-R%"M4'Z# S"r ( ) 1 1 1 b 1 n C C C⇒ Ω = L2 :FA;'7r_,',CF'Mr ( ) ( ) ( ) ( ) 1 b 2 n A C C C C C C⇒ = L2 ( ) ( ) ( ) ( ) ( ) ( ) 1 b 2 1 1 1 b 1 C C C C C C n A P A n C C C ⇒ = = Ω )*! +!, /0''8 !"a, b, c)&a/)0 a b c + + ≤ 3$ "#/<'()+%5'7 ( ) ( ) ( ) b b b a b c P b c c a a b = + + + − − + − − + − − 3)', ( ) ( ) ( ) ( ) b b b a b c P a b c a b c + + ≥ + + + + + − − − − − − 3)', ( ) ( ) ( ) b 1 K a a a a a a+ = + − + ≤ − + ( ) ( ) ( ) b 1 K b b b b b b+ = + − + ≤ − + ( ) ( ) ( ) b 1 K c c c c c c+ = + − + ≤ − + ( ) ( ) ( ) ( ) ( ) K K j K a b c P a b c a b c a b c a b c a b c + + ⇒ ≥ + + + + − + + + + ≥ − + + + + + + ZC ( ) t a b c= + + E ( ] LGt ∈ 3)', ( ) K j K t f t t t = − + + ( ) ( ) ( ) ( ) 21 b L h h L b j K t t t f t f t t t t + = ⇒ = ⇒ = ⇔ = − − + + II3 L sh T s L ^& P ≥ )&H P = 8<%."R&#)M a b c= = = . k 2 2 A α α α α α α + − + ÷ + = = = = − ÷ L 2 ZC ( ) ?z a bi z a bi a b R= + ⇒ = − ∈ L 2 3)',7 ( ) ( ) ( ) ( ) 2 2 2 2 1 z. L α α > < L 2 )', j ' 2 c x α α + = ⇒ = ;*', ' 2 x = − $ ' L α < L 2 @%&#) 1 2 ) 2 2 ' 1 . = ( ) ( ) 2 ;" 2 ;" b x x x x = − = ⇔ ⇔ = − = − 3/)0]%MP L 2 ^& !"#$',"P;Rf 2 Rf 2 b )*"+!,