ĐỀ THI THỬ ĐH CÓ Đ.A NĂM 2011

  !"" #$% Thời gian làm bài 180 phút &'()*+ Câu I (2 đim),-. / / 0 "1 "y x x m x= + + + + 234567,0 - 1 " 8%9,9:456,-.;-<   =->%?62@-4A4BCD "y x= + 2E4560 - 1F/4A-GHI0!J"1KLK 22%2MGNM2@0 - 1FL9,9#329O Câu II (2 đim) 1. (8IGBP?= / / / / x y y x  + − =   + − =   2. (8GBP?= " 2 0" Q10"  1 Q 2 x x x − − + = − Câu III (2 đim) " RAR29SA?TQN?;UN=GDOFV4BC?TH-0 J 1% ;RW<"U?X2,  ?;#24A-KL2.46K4YZ,4FL<[!Q9,LN7,\ 4BCD9#329O9,2]9#329OL?^Q9,LN7_N4A-9, 2<09O7,-Y.2?BO29,[1 1 `%246H-9,%;R-a2bFMGcZIL 1 `%24696?R2@9,2cZIL23AR27O_ Câu IV (1 đim).=--4A_GBP?=23I-$ / " 0 "1 0" 1 "x m x m x+ ≥ + + − +  &d$Mỗi thí sinh chỉ chọn câu Va hoặc Vb Câu Va (3 đim1Chương trình cơ bản " ?-aGDe4Y)QNK24A-&0/J"19,4BCD23GBP?=7, " $ " !d x y− + = 9, $ / !d x y+ − = fMGBP?=4BCD4U&9,F9O4BC D " ,d v d -Y-%22H234g7,4A-2@ " ,d v d   ?;#9OIe4Y)QNhK24BCD " " " $ " " x y z− + − ∆ = = − " / $ " x y z+ − − ∆ = = − 9,-a2b0+1$Q iN ih ijQk Nilhim<!fMGBP?=-a GDMGQn29O-a2b0+145C9O " ∆ 9, ∆  / =-Gbo22@.Gc2 ( ) !!p " i− Câu Vb. (3 đim).Chương trình nâng cao " ?-aGDe4Y)QNK2NG7 0 1H 23GBP?= " x y a b − = 9,7,4A-_;q Y201(eZ " KZ 7,2%24BCD4U9,9O2%24BCI-2S2@01 c-?r==,FVZ " KZ 9,2%24BCI-2S2@0123ZIR2;# 4s  ?;#9OIe4Y)QNhK2/4A-0"J/Jk 1KL0!J!J"1K0 J!J"1=-e 4Y2@4A-2 iL i 4F%?6t_ / (8_GBP?= j !Km "l 7 j7 j 7x x x+ ≤ − uMu 0%Y2;#8R2=^-1 v&v(w H x YZ A-  " " `y< ¡ +oM^$Nz</Q ilQi/</0Qi"1  ! x ≥ ∀ ∈ ¡ ,-.45M?^ ¡ ,-.;#232o2?6 (OF$ 7- x y →±∞ = ±∞ L8M^ Q −∞ ! +∞ Nz i!i N +∞ −∞ 56 N " k") Q ! m ! / ! m ! m " &BP?=,4Y4A-2@4560 - 19,4BCDN<Qi" Q / i/Q i-Q<! ! / ! x x x m =  ⇔  + + =  BCDN<Qi"2E4560 - 1F/4A-GHI;9,2g;  0 1 / !g x x x m= + + = 23I-GHI;%2!;9,2g;  p ! p j ! j 0!1 ! ! ! m m g m m  ∆ > − > <    ⇔ ⇔    ≠ ≠    ≠  0{1 43,4Y2@L9,t-| /  B C B C x x x x m + = −   =  0"1 23}z0Q1</Q ilQi-i" I.322%2MGNMFL9,7,}z0Q L 1< / l " B B x x m+ + + K}z0Q  1< / l " C C x x m+ + +  %2MGNMFL9,9#32;9,2g;}z0Q L 1}z0Q  1<k" ⇔ 0 / l " B B x x m+ + + 10 / l " C C x x m+ + + 1<k" ⇔ 0 / l B B x x+ 10 / l C C x x+ 1i0-i"10 / l B B x x+ i / l C C x x+ 1i0-i"1 <k" ⇔ p0  1 "~ 0 1 /l /0 "100 1 0 11 B C B C B C B C B C B C B C x x x x x x x x m x x x x x x+ + + + + + − + + i- i -i <! ! m ! m ! m M•G9O0"14B•2 p- €mj-i/l-i/0-i"10p€ -k/1i- i -i <! ⇔ j- €"/-i""<!GBP?=9#I- fSN;#23%?62@-t-|N^2b ! m  " " •;I$ ! /K! /x y≤ ≤ ≤ ≤ 23 / / / / x y y x  + − =   + − =   ⇔ 0/ 1 ! 0/ 1 ! x y x y y x y x  − + − =   − + − =   0/ 1 0/ 1 ! 0/ 1 ! 0/ 1 ! x y y x x y y x ⇒ − + − = − =  ⇔  − =  ⇔ ! ! / / x y x y  =    =    =    =    A-?_N ! / K ! / x x y y = =     = =   t-| M7S$I23I23I- ! / K ! / x x y y = =     = =   ! m ! m ! m ! m " ;$ Q 2 2 ! x x ≠   ≠   &BP?=BP4BP9O 0" Q1 " 2 0" Q1 " 2  Q 2 "  Q 2 " 2 0Q 2 1 0" Q10" 2 1 " Q Q 2 Q 2 Q2 " ! 0Q "102 "1 ! Q " 2 " x x c x x x x x x x x x x x x − − − − = ⇔ = − − − − ⇔ = ⇔ − = + − + − ⇔ − + − = ⇔ − + = =  ⇔  = −  i1Q<";#t-|;9=;432Q<! i12Q<k" Kx k k π π ⇔ = + ∈¢ t-| M7S$&BP?=23eI- Kx k k π π = + ∈¢  ! m ! m ! m ! m  " " BC?TH-0 J"1%;RW<"23GBP?=$0Qk 1 i0Nk 1 <" •;I$ " /x≤ ≤ ‚GBP?=4BC?T23 " 0 1y x= + − − 9O y ≥ f, " 0 1y x= − − − 9O y <  AR29SA2b=- ! m  ( ) ( ) / / " " / " " 0 1 " 0 1 ~ " 0 1 V x dx x dx x dx π π π = + − − − − − − = − − ∫ ∫ ∫ aQ€ <9O x π π − ≤ ≤  Q<" ⇒ < π − Q</ ⇒ < π ZQ<2ZK " 0 1x− − <2 fSNf< ~ c tdt π π π − ∫ < j 0"  1 jc t dt π π π π − + = ∫ ! m ! m ! m " 1 (e7,?4A-2@ 23 KBN AB BN AM BN BM⊥ ⊥ ⇒ ⊥ Q Z43-%2L9#FLN?L< MN K   BPo< MN  fSN<L<<< MN < b  H--a2bFMG7,K%;RW< b L 1a<Q[!KL<N[!  -%2L9#FL^ <L iL N -%29#F^ < i +N? < < iL iL <Q i iN  y43Q iN < € ;#4s cZIL234%N7,LK4BC2L AR2 " " " Q 0 1 0 1 l " " V y a x y a b a= ≤ + = −  AR2cZIL7O_;<L< b a−  ! m ! m ! m ! m f " 23 / " 0 "1 0" 1 "x m x m x+ ≥ + + − +  0 "10 "1 0 "1 0 "1x x x m x x x⇔ + − + ≥ − + + + •;I "x ≥ − 43_GBP?=BP4BP9O " " " " x x m x x x x + + ≥ + − + − +  ⇔ " " " " x x m x x x x + + − ≥ − + − + 0{1 a< " " x x x + − + K_GBP?=0{123ZF$€  m≥ 0"1 23 ƒ K ƒ ! " / " 0 "1 " x x t t x x x x x x − − + = = ⇔ = − + + − + − +  L8M^ Q k" " /− +  +∞ z i! k   / / / +  ! ! fSN "" „ / !J "/ t   +   ∈     L_GBP?=4|223I-;9,2g;0"123I- "" „ / !J "/ t   +   ∈     ;9,2g; "" „ / …!J † "/ Q 0 1 t M f t m + ∈ ≥ 9O}01<€ }z01<"€  L8M^  ! "  / / / + }z01 i !k }01  " j ‚8M^$ "" „ / …!J † "/ " " Q 0 1 j t M f t khi x + ∈ = = fSNN2BP4BP9O " j m ≤ ! m ! m ! m ! m f / " " BCD4U&0/J"123ZF $ Q / !by a b∆ + − − = BCD ∆ F9O4BCD " ,d v d -Y-%22H234g7,2@ " ,d v d ;9,2g; " 0 K 1 0 K 1d d∆ = ∆  " 0 KZ 1 0 KZ 1c c⇔ ∆ = ∆  m0 1 m0 1 a b a b a b a b a b a b − + ⇔ = + + ⇔ − = +  a b a b⇔ − = + a2 a b a b− = − − ! m ! m  / !a b⇔ − = a2 / !a b+ = e</K<"a2<"K<k/ fSN234BCDt-|N^2b,%/QiN€"!<!9,Q€/N<! ! m ! m " f2P2gGBP2@ " " " $ " " x y z− + − ∆ = = − 9, " / $ " x y z+ − − ∆ = = − 7b7B•7, 0 J "J"1K 0 J"J 1u v= − = − r r aGD0&19O " ∆ 9, ∆ S2aG92P 0 J "J"1K 0 J"J 1u v= − = − r r 7,-2aG92P2gGBP 23 ( ) " " " " J J /J lJ! /0"J J!1 " " n   − − = = − − = −  ÷ − −   r aGD0&123ZF 0&1$Qi Ni-<! a2b0+123H-0k J"Jk/19,%;RW</ aGD0&1MGQn29O0+1;9,2g; 0 K0 11 / / m " ! m d I P R m − + + = ⇔ = ⇔ = ± + + fSN23-aGDt-|N^2b7,Qi Ni / m <!9,Qi N€ / m <! ! m ! m ! m ! m / " 23 ( ) ( ) ( ) "!!j !!p "!!j "!!j "!!j "!!j " " 0" 1 0 1 0" 1 0" 1 i i i i i i i − = − − = − − = − = −  fSNGbo22@.Gc2?^7, "!!j ! m ! m ! m ! m f / " " %24BCI-2S2@0123ZF b y x a = ± (e0Q ! JN ! 1 ! ! 0 1 " x y H a b ∈ ⇒ − = 0"1 %24BCDZ " JZ 23GBP?=7, ! ! ! ! , b b b b y x y x v y x y x a a a a = + − = − + +  %24A-2@Z " JZ  9O2%24BCI-2S0 ! ! ! ! J x y a b y x b a + + 1KL0 ! ! ! ! J x y a b y x b a − − 1 yIR2==,+< + )L <))L AOB ∠ <  0  1OA OB OAOB− uuur uuur uuur uuur 23 OA OB uuur uuur < ! ! ! ! ! ! ! ! 00 1 0 1 100 1 0 1 1 x y x y a b a b y x y x b a b a + + + − + − < ! ! 0 1 j x y a b a b   + −  ÷   < j a b   +  ÷   00"11 0  1OA OB uuur uuur < ! ! ! ! ! ! ! ! 00 10 1 0 10 11 x x y y a a b b y y x x b b a a + − + + − < ! ! 0 1 j x y a b a b   − −  ÷   < j a b   −  ÷   00"11 ! m ! m ! m y43 ab S = ;#4s ! m " e4Y?eH--%2L7,(0"J"J!1 23  ( ) ( ) ( )  L  / 0 1 / 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 fSN iL i  ≥ GA GB GC+ + Z_rQ8N?;9,2g; M G≡ ! m ! m ! m ! m / " 23  ( ) j "l j !Km "l !Km j !Km "l j 7 ! 7 j7 j 7 7 j7 ! 7 j7 j 7 j 7 ! 7 7 ! 7 7 "l ~7 7 ! x x x x x x x x x x x x x x x x x  − ≥   + ≤ − ⇔ + ≥   + ≤ −   − ≥   + ≥  ⇔  + ≤ − +   >   ~ m ~ ! 7 m 7 ! " " ! j x x x x x   ≤ ≤     ⇔  ≤ −     >   ≤ ≤  ⇔  < ≤   SGI-2@_GBP?=7,+< ~ m " …"J † 0!J † j ∪ ! m ! m ! m ! m   . 1 a b a b a b a b a b a b − + ⇔ = + + ⇔ − = +  a b a b⇔ − = +  a2  a b a b− = − − ! m ! m  / !a b⇔ − =  a2  /. 0  1OA OB OAOB− uuur uuur uuur uuur 23 OA OB uuur uuur < ! ! ! ! ! ! ! ! 00 1 0 1 100 1 0 1 1 x y x y a b a b y x y x b a b a + + + − + − < ! ! 0 1 j x y a b a b .  < j a b   +  ÷   00"11 0  1OA OB uuur uuur < ! ! ! ! ! ! ! ! 00 10 1 0 10 11 x x y y a a b b y y x x b b a a + − + + − < ! ! 0 1 j x y a b a b   − − 